Evaluation of nanofiltration for the extraction of Volatile Fatty Acids from fermentation broth Evaluation de la nanofiltration pour l'extraction d'acides gras volatils produits par fermentation

Keywords: Nanofiltration, biomass valorisation, separation, organic acids Nanofiltration, valorisation de la biomasse, separation, acides organiques

Nanofiltration (NF) is a pressure-driven membrane process used for liquid-phase separation, which is promising for biomass separation and purification. In this work, two NF membranes (NF-45 and XLE) are used for the separation and valorization of volatile fatty acids (VFAs), one kind of useful chemical building blocks, from fermentation broth produced using municipal solid waste.

The objective of this work is to investigate NF process for the separation and purification of VFAs from fermentation broth.

Experiments are carried out with synthetic solutions with increasing complexities, from single, binary and ternary solutions of VFAs, i.e., acetic (Ac), propionic (Pr), and butyric acid (Bu), to mixed solutions containing VFAs and inorganic salts at different compositions. The influence of ionic composition as well as of the solution pH on the transfer of the solutes are discussed. Then, a real fermentation broth containing three VFAs, inorganic ions and organic matters is also investigated.

For synthetic solutions containing dissociated VFAs (pH 8), it is observed that for a given VFAs proportion in the feed, regardless of the total concentration, the proportion of VFAs in the permeate remains constant when the filtration flux is higher than a specific value. From the perspective of mass transfer, this observation means that in a mixed solution, the individual charged solute transfer is controlled by the total amount of charge transferred through the membrane. Indeed, it is found that the individual VFA flux increases linearly with the total solute flux and does not depend on the total concentration but only on the VFAs proportions in the feed.

More complex solutions containing VFAs with the addition of three inorganic salts (Na2SO4, NaCl, and CaCl2) are further investigated. Again, constant permeate proportions for organic and inorganic solutes (anions as well as cations) are observed for a given feed proportion, when the filtration flux is higher than a certain value. Then, it is concluded that, for any couple of VFAs (Ac/Pr, Pr/Bu, or Ac/Bu), the plateau value of the relative proportion of the individual VFA in the Abstract 2 permeate is nearly fixed by its proportion in the feed, for all the conditions investigated. This conclusion can be extended to couples of VFAs/inorganic anions and couples of cations.

Solution pH significantly changes the retention of VFAs and the permeate proportion of VFAs.

A model to describe the VFAs retention versus pH is presented. It is shown that the model can describe the retention of VFAs versus solution pH by considering an increase of the VFAs pKa values by about 1.2 units or a membrane effective pKa value of about 5.4 to 5.8.

Finally experiments are carried out with a real fermentation broth. It is observed that whatever charged or uncharged solutes, even for unknown organic matters in the real fermentation broth, a constant proportion in permeate is observed when the filtration flux is higher than a certain value.

This observation indicate that the plateau value could be related to the nature of solutes and membranes, and this method could be used to compare the separation performances of different membranes.

Separation factor is used to characterize the separation performance of the two membranes on the real fermentation broth. The separation factors between VFAs in the real fermentation broth are higher than those obtained with synthetic solutions, indicate that there are additional parameters that could influence the separation performance of the nanofiltration process. The NF-45 membrane can more efficiently change the VFAs proportion in the permeate, Ac and Pr are greatly enriched in the permeate, while Bu is enriched in the retentate. The XLE membrane has a very high VFAs retention (>95%), it can change the proportion of VFAs and other organic matters (OM) in the permeate, and can be used to concentrate the VFAs fermentation broth and remove the hindering organics such as ethanol.

Chapter I Introduction

Global change leads to restrictions on carbon emissions, in order to develop a low-carbon economy, biomass resources are becoming a subject of increasing concern. On the other hand, with the increasing of the human population and the improvement of living standards, the per capita waste production is also growing rapidly, especially in developing countries. Convert waste into resources will constitute a virtuous circle, not only reducing carbon emissions but also produce valuable renewable resources at the same time, which will be a beneficial attempt.

Fermentation is a very economical process in transfer biomass into useful carbon resources.

Fermentation has already been widely used in food processes, energy processes, and waste/wastewater treatment. With the help of fermentation, waste biomass can be transfer into useful chemical products. However, the produced streams contain not only the target solutes but also other impurities, a down-stream process for the further separation and valorization is thus required.

Membrane processes are low energy requirements, low cost, and high product yield separation processes, which are normally considered as environmentally friendly. As a stilldeveloping technology, membrane processes have a bright future for the separation of molecules with different sizes and charges. Membrane process, especially nanofiltration (NF), has gained more and more attention in the field of biorefinery, and are highly recommended for the separation of renewable resources from fermentation broth.

The current project is aimed to produce Volatile fatty acids (VFAs), a promising chemical building blocks from municipal solid waste. This project will concern the production of VFAscontaining streams by anaerobic fermentation, and the possible recovery and separation of VFAs using nanofiltration.

The following sections will firstly introduce the production of VFAs via fermentation, the composition of the fermentation broth, and the operating conditions that influence the production.

Then give an introduction to membrane processes, especially nanofiltration, and the previous results on VFAs valorization by nanofiltration process. The parameters influence nanofiltration performance, and nanofiltration on the application of VFAs is discussed.

I.1 Properties, production, and applications of Volatile Fatty Acids

Valorization of waste biomass into valuable chemicals is an interesting attempt; research in this area is accelerating [START_REF] Tuck | Valorization of Biomass: Deriving More Value from Waste[END_REF]. As a group of organic carbon sources that could be produced from organic waste, VFAs are attracting more and more researchers' attention [START_REF] Atasoy | Bio-based volatile fatty acid production and recovery from waste streams : Current status and future challenges[END_REF]3].

Volatile Fatty Acids (VFAs), also referred to as Short-Chain Fatty Acids (SCFAs), are fatty acids having up to six carbon atoms which can be volatilized at atmospheric pressure [START_REF] Lee | A review of the production and applications of waste-derived volatile fatty acids[END_REF]. VFAs are a critical substrate for the production of biodegradable plastics and bioenergy, and have the potential to become chemical building blocks. As indicated in Table I-1, propionic acid is selected as one of the top 30 value-added chemicals from biomass by the U.S. Department of Energy [START_REF] Werpy | Top Value Added Chemicals from Biomass: Volume I --Results of Screening for Potential Candidates from Sugars and Synthesis Gas[END_REF].

Table I-1

List of top 30 potential building blocks, adapted from ref. [START_REF] Werpy | Top Value Added Chemicals from Biomass: Volume I --Results of Screening for Potential Candidates from Sugars and Synthesis Gas[END_REF] Separation and extraction techniques rely on the difference between the physic-chemical properties of individual compounds. The properties of VFAs are introduced with possible treatments.

Acetic, propionic, and butyric acids have 2, 3, and 4 carbon atoms, respectively, and their size enlarged continuously. The increase of their size leads to the decreasing diffusion coefficient values, indicate that the sequence of diffusion coefficient of the three VFAs is acetic acid>propionic acid>butyric acid. Therefore, a separation process based on molecule size, e.g. nanofiltration at low pH, can retain more butyric acid than acetic and propionic acids [START_REF] Xiong | Integrated acidogenic digestion and carboxylic acid separation by nanofiltration membranes for the lignocellulosic carboxylate platform[END_REF]. Viscosity (mPa.s, 30 °C) 0.982 [START_REF] Rahul | Thermodynamic properties of binary liquid systems of ethanoic acid, propanoic acid, and butanoic acid with 3-chloroaniline as a function of various temperatures[END_REF] 0.962 [START_REF] Rahul | Thermodynamic properties of binary liquid systems of ethanoic acid, propanoic acid, and butanoic acid with 3-chloroaniline as a function of various temperatures[END_REF] 1.3852 [START_REF] Rahul | Thermodynamic properties of binary liquid systems of ethanoic acid, propanoic acid, and butanoic acid with 3-chloroaniline as a function of various temperatures[END_REF] Diffusion coefficient (D, ×10 5 cm 2 .s -1 ) (25 °C, 0.03~0.06 mol.L -1 )

1.212 [START_REF] Dunn | The diffusion of monocarboxylic acids in aqueous solution at 25°[END_REF] 1.057 [START_REF] Dunn | The diffusion of monocarboxylic acids in aqueous solution at 25°[END_REF] 1.021 [START_REF] Albery | Diffusion coefficients of carboxylic acids[END_REF] 0.946 [START_REF] Dunn | The diffusion of monocarboxylic acids in aqueous solution at 25°[END_REF] 0.824 [START_REF] Albery | Diffusion coefficients of carboxylic acids[END_REF] Furthermore, the boiling point values of VFAs also increase with their molecular weights, indicate that acetic acid is easier to be distilled from the mixture, shown that a traditional distillation process can separate the three VFAs [START_REF] Lin | Modeling of esterification of acetic acid with n -butanol in the presence of Zr ( SO 4 ) 2 • 4H 2 O coupled pervaporation[END_REF][START_REF] Reyhanitash | Recovery of Volatile Fatty Acids from Fermented Wastewater by Adsorption[END_REF].

VFAs have similar pKa values. When deprotonated, the VFAs molecules are monovalent anions. Therefore, VFAs can be extracted from the fermentation broth by an electro-chemical driven process, e.g. electrodialysis [START_REF] Tao | Recovery and concentration of thermally hydrolysed waste activated sludge derived volatile fatty acids and nutrients by microfiltration, electrodialysis and struvite precipitation for polyhydroxyalkanoates production[END_REF].

In addition, due to the charge of VFAs, they can be absorbed and recovered from the broth using ion exchange resin; however, separation of individual VFA by adsorption was not achieved [START_REF] Reyhanitash | Recovery of Volatile Fatty Acids from Fermented Wastewater by Adsorption[END_REF].

I.1.2 Production of VFAs by fermentation

VFAs production can be carried out via both synthetic methods from petrochemical derivatives, and biological methods such as fermentation. Nowadays, most (about 90%) of VFAs are produced through petro-based methods due to the lower cost. However, in the food and beverage industries, the VFAs used are required as natural produced, therefore bio-based VFAs must be used. The demands for bio-based VFAs are growing due to both increasing desire for natural products and increasing costs of crude oil [START_REF] Hatti-Kaul | Industrial biotechnology for the production of bio-based chemicals -a cradle-to-grave perspective[END_REF]. Recently, the increasing demands for the valorization of biomass boost the demands of VFAs [START_REF] Atasoy | Bio-based volatile fatty acid production and recovery from waste streams : Current status and future challenges[END_REF].

The bio-based VFAs production can be classified into two categories according to the purposes. The first category is to produce VFAs used for food or beverage industries, which requires high purity and high yield. Those VFAs are usually produced from sugar or grain using commercial bacteria. For instance, Acetobacter, Gluconacetobacter, and Gluconobacter are the most used bacteria families for acetic acid production [START_REF] Raspor | Biotechnological applications of acetic acid bacteria[END_REF]. The second category is to produce VFAs used for bio-based chemicals with the purpose to replace the petro-based chemicals and form cradle to cradle cycle. Nowadays, bio-based VFAs, especially waste-derived VFAs have been paid more and more attention [START_REF] Atasoy | Bio-based volatile fatty acid production and recovery from waste streams : Current status and future challenges[END_REF].

In general, VFAs production from fermentation is an anaerobic process that includes hydrolysis and acidogenesis (which was also widely known as acidogenic fermentation [START_REF] Bengtsson | Acidogenic fermentation of industrial wastewaters: Effects of chemostat retention time and pH on volatile fatty acids production[END_REF] or dark fermentation [START_REF] Su | Improving hydrogen production from cassava starch by combination of dark and photo fermentation[END_REF]). This process is presented in Figure I-1. During the hydrolysis, complex organic polymers in waste are degraded and broken into smaller and simpler organic monomers by the enzymes produced by microorganisms. Then the organic monomers can be absorbed into the microorganism cell, at anaerobic condition, those monomers will transfer to organic acids such as acetic, propionic, and butyric acids, this step is so-called acidification.

I.1.2.1 Microorganisms for VFAs fermentation

The industrial acetic acid (vinegar) production is normally carried out using Acetobacter, Gluconacetobacter, and Gluconobacter strains [START_REF] Raspor | Biotechnological applications of acetic acid bacteria[END_REF][START_REF] Prust | Complete genome sequence of the acetic acid bacterium Gluconobacter oxydans[END_REF]. Acetobacter pasteurianus is observed as the most common bacteria for vinegar production from rice [START_REF] Nanda | Characterization of acetic acid bacteria in traditional acetic acid fermentation of rice vinegar (komesu) and unpolished rice vinegar (kurosu) produced in Japan[END_REF], then, Acetobacter aceti and Acetobacter xylinum are used for higher fermentation temperature [START_REF] Ohmori | Isolation and Identification of Acetic Acid Bacteria for Submerged Acetic Acid Fermentation at High Temperature[END_REF]. An overview of the different genera and species of acetic acid bacteria strains from 1898 to 2008 is given in ref. [START_REF] Yamada | Genera and species in acetic acid bacteria[END_REF].

Propionic acid is produced using Clostridum (Clostridum propionicum) [START_REF] Stinson | EFFECT OF PH ON ORGANIC-ACID PRODUCTION BY CLOSTRIDIUM-PROPIONICUM IN TEST TUBE AND FERMENTER CULTURES[END_REF][START_REF] Janssen | ISOLATION OF CLOSTRIDIUM-PROPIONICUM STRAIN-19ACRY3 AND FURTHER CHARACTERISTICS OF THE SPECIES[END_REF] and Propionibacterium (Propionibacterium acidipropionici) [START_REF] Quesada-Chanto | Microbial production of propionic acid and vitamin B12 using molasses or sugar[END_REF] strains. During the production of propionic acid using propionic bacteria, acetic acid is a common by-product. Modification of the operating conditions can increase the production of propionic acid. It is reported that decrease the fermentation pH from 7.0 to 6.0 increases the ratio of propionic: acetic from 0.45:1 to 1.8:1 [START_REF] Stinson | Effect of pH on organic acid production by Clostridium propionicum in test tube and fermentor cultures[END_REF].

Butyric acid can be produced using many strains such as Clostridium, Butyrivibrio, Butyribacterium, Sarcina, Eubacterium, Fusobacterium, and Megasphera strains. Among those strains, Clostridium is the bacteria strain most used for butyric acid production [START_REF] Zigová | Advances in biotechnological production of butyric acid[END_REF]. During the production of butyric acid, acetic and propionic acid can be produced as by-products. The metabolic pathways for Clostridium acetobutylicum to produce acetic and butyric acid from glucose are known [START_REF] Girbal | Regulation of metabolic shifts in Clostridium acetobutylicum ATCC 824[END_REF].

The above mentioned VFAs production bacteria stains can efficiently transfer specific carbon sources (e.g., glucose) into VFAs. However, during the production of waste-derived VFAs, the raw material often contains a variety of bacteria (e.g., food waste [START_REF] Dahiya | Acidogenic fermentation of food waste for volatile fatty acid production with co-generation of biohydrogen[END_REF]), or even the raw material is bacteria cell itself (e.g., waste activated sludge [START_REF] Liu | Acidogenic fermentation of proteinaceous sewage sludge: Effect of pH[END_REF]). Therefore, the competition between VFAs production bacteria and other bacteria reduces the productivity of VFAs and generates many byproducts (i.e., methanol and ethanol [START_REF] Tamis | Enrichment of Plasticicumulans acidivorans at pilot-scale for PHA production on industrial wastewater[END_REF][START_REF] Marang | Impact of non-storing biomass on PHA production: An enrichment culture on acetate and methanol[END_REF]), which determined that the composition of the wastederived fermentation broth are complex.

The fermentation broth contains not only acetic (Ac), propionic (Pr), butyric (Bu), valeric (Va) acids, but also remaining unfermented feed materials, for instance, glucose, peptone, glycerol, and inorganic salts such as NaCl, CaCl2, NH4Cl, etc. [START_REF] Murali | Fermentation of wet-exploded corn stover for the production of volatile fatty acids[END_REF][START_REF] Yin | Enhancement of acidogenic fermentation for volatile fatty acid production from food waste: Effect of redox potential and inoculum[END_REF][START_REF] Yuan | Improved bioproduction of shortchain fatty acids (SCFAs) from excess sludge under alkaline conditions[END_REF][START_REF] Bouchoux | Investigation of nanofiltration as a purification step for lactic acid production processes based on conventional and bipolar electrodialysis operations[END_REF]. The pathways of production of VFAs have been given by some researchers. According to Fitz equation [START_REF] Boyaval | Production of propionic acid[END_REF], the fermentation of propionate can be theoretically described as Eq. (I.1) (glucose as raw material) and Eq. (I.2) (lactic acid as raw material). For glucose and glycerol as the raw materials, two experimental equations (Eq. (I.3), Eq. (I.4))

are provided by ref. [START_REF] Yin | Acidogenic fermentation of the main substrates of food waste to produce volatile fatty acids[END_REF].

C 6 H 12 O 6 + H 2 O ⟶ 0.086Ac + 0.103Pr + 0.096Bu (I.3)

C 3 H 8 O 3 + H 2 O ⟶ 0.084Ac + 0.138Pr + 0.043Bu (I.4)
However, the description of the production from complex raw materials such as waste activated sludge can be more difficult. Liu et al. [START_REF] Liu | Acidogenic fermentation of proteinaceous sewage sludge: Effect of pH[END_REF] provided a theoretical equation (Eq. (I.5))

for acidogenic fermentation of proteinaceous sewage sludge by a stoechiometric coefficient method, showing that acetic acid is the main product of the fermentation of protein, which agrees with other results [START_REF] Mengmeng | Optimal production of polyhydroxyalkanoates (PHA) in activated sludge fed by volatile fatty acids (VFAs) generated from alkaline excess sludge fermentation[END_REF].

CN 0.29 H 2.05 O 0.74 + H 2 O ⟶ 0.235Ac + 0.009Pr + 0.013iso_Bu + 0.025Bu + 0.004iso_Va + 0.008Va (I.5)

Control the fermentation condition such as adjust to an alkaline pH can change the bacteria genus level of distribution in the fermentation broth [START_REF] Zheng | Pyrosequencing Reveals the Key Microorganisms Involved in Sludge Alkaline Fermentation for Efficient Short-Chain Fatty Acids Production[END_REF], but it is difficult to control the distribution of bacteria genus precisely. Due to the practical problems faced in waste-derived VFAs production, most publications use activated sludge as fermentation strain. Activated sludge usually contains a large genus of bacteria; meanwhile, waste activated sludge is also a good raw material for VFAs fermentation [START_REF] Yuan | Improved bioproduction of shortchain fatty acids (SCFAs) from excess sludge under alkaline conditions[END_REF][START_REF] Zhang | Understanding Short-Chain Fatty Acids Accumulation Enhanced in Waste Activated Sludge Alkaline Fermentation: Kinetics and Microbiology[END_REF][START_REF] Yu | Toward understanding the mechanism of improving the production of volatile fatty acids from activated sludge at pH 10.0[END_REF].

I.1.2.2 Biomass for fermentation produces VFAs

There is a great interest in producing VFAs by fermentation of various biomass like household solid waste [START_REF] Lin | A nutrient formulation for fermentative hydrogen production using anaerobic sewage sludge microflora[END_REF] or waste streams such as wastewater [START_REF] Yarimtepe | Volatile fatty acid production dynamics during the acidification of pretreated olive mill wastewater[END_REF] or waste activated sludge [START_REF] Liu | Full-scale production of VFAs from sewage sludge by anaerobic alkaline fermentation to improve biological nutrients removal in domestic wastewater[END_REF], with a double purpose of waste treatment and valorization. On the one hand, municipal solid waste (MSW) generated today is continuously increasing. The total urban waste generated each day almost doubled within 20 years [START_REF] Hoornweg | What a Waste: A Global Review of Solid Waste Management[END_REF], and an increasing trend can be expected up to 2050 [START_REF] Kaza | What a waste 2.0 A global snapshot of solid waste management to 2050[END_REF].

Many biomass is produced while the utilization of them is few. Thus enormous cost has paid for the disposal of those solid wastes. On the other hand, unlike other biological processes, for the production of VFAs, fermentation process does not require the sterilization to cultivate a particular microorganism [3]. Therefore, VFAs fermentation is regarded as an energy-saving and economical process [3], and the organic-rich waste like MSW can be considered as the raw material.

The most commonly used wastes are excess sludge from wastewater treatment plants, food waste and organic fraction of municipal solid waste (OFMSW), wastewaters generated from agricultural, dairy, pulp and paper industries are used to produce VFAs too [START_REF] Lee | A review of the production and applications of waste-derived volatile fatty acids[END_REF].

Primary sludge (PS, suspended solids and organics withhold or settled by the primary treatment processes like grilling or sedimentation) and waste activated sludge (WAS, the bacteria cells and adhesion suspended solids produced by aeration tank) are generated in 240 million wet tons in Europe, USA and China combined from municipal wastewater treatment plants [START_REF] Wang | Technologies for reducing sludge production in wastewater treatment plants: State of the art[END_REF].

Usually, one ton of dairy wastewater with chemical oxidation demand (COD) of 300 mg/L can produce 9 kilograms of excess sludge (contain 80% of water), and usually the cost to dispose or reuse those sludge can contribute more than 50% of the total cost of the wastewater treatment [START_REF] Nowak | Optimizing the Use of Sludge Treatment Facilities at Municipal WWTPs[END_REF].

On the other hand, both primary sludge and waste activated sludge are highly organic-rich.

Primary sludge and waste activated sludge can have a total COD ranging from 14,800 mg/L to 23,000 mg/L [START_REF] Lee | A review of the production and applications of waste-derived volatile fatty acids[END_REF], and usually have good carbon: nitrogen: phosphorus ratio, making them an appropriate source for VFAs production.

Food waste or kitchen waste is another organic-rich solid waste commonly used for VFAs production, mainly because it has a high total COD ranging from 91,900 to 166,180 mg/kg [START_REF] Lee | A review of the production and applications of waste-derived volatile fatty acids[END_REF]. It is also the dominant component (22%-54%) in huge volumes of municipal solid waste (MSW).

The challenge to utilize the food waste for VFAs production is to effectively separate it from MSW to avoid interference of other undesired components such as glass, plastics, aluminum cans, and ferrous metals [START_REF] Lee | A review of the production and applications of waste-derived volatile fatty acids[END_REF]. Utilization of organic fraction of municipal solid waste (OFMSW) can face the same problem too, although it contains a total COD as high as 150,600 to 347,000 mg/kg [START_REF] Cavinato | Influence of temperature and hydraulic retention on the production of volatile fatty acids during anaerobic fermentation of cow manure and maize silage[END_REF].

High concentration organic wastewaters are commonly used for VFAs production. Food, agricultural, pulp, and paper industries wastewaters have a high concentration of COD. For instance, palm oil mill effluents, having a COD about 88,000mg/L, can be fermented into VFAs with a concentration as high as 15,300 mg/L [START_REF] Hong | Semi-Continuous and Continuous Anaerobic Treatment of Palm Oil Mill Effluent for the Production of Organic Acids and Polyhydroxyalkanoates[END_REF]. The sugar industry also generates effluents with a total suspended solid of 5,000mg/L and soluble COD of 2,300-8,000mg/L, suitable for anaerobic digestion [START_REF] Kim | Effects of Various Pretreatments for Enhanced Anaerobic Digestion with Waste Activated Sludge[END_REF].

I.1.2.3 Fermentation process and the influence of fermentation conditions

As aforementioned, there are two steps (hydrolysis and acidogenesis) in the production of VFAs, hydrolysis is commonly considered as the rate-limiting step [START_REF] Fdez | The use of thermochemical and biological pretreatments to enhance organic matter hydrolysis and solubilization from organic fraction of municipal solid waste (OFMSW)[END_REF]. For instance, cell wall and extracellular polymeric substances (EPS) in excess activated sludge play as physical and chemical barriers protecting its intracellular from hydrolysis [START_REF] Tang | Energy efficiency of pre-treating excess sewage sludge with microwave irradiation[END_REF]. Moreover, the biodegradability of food waste, as well as OFMSW, can be lower if they contain a high percentage of lignocellulosic materials, fats or proteins.

Considering the hindrance of the cell wall, EPS, as well as macromolecules in the raw material for VFAs production, a physicochemical pre-treatment is usually applied before fermentation.

Chemical and physical pre-treatment using ozone [START_REF] Cesaro | Sonolysis and ozonation as pretreatment for anaerobic digestion of solid organic waste[END_REF], hydrogen peroxide [START_REF] Eskicioglu | Synergetic pretreatment of sewage sludge by microwave irradiation in presence of H2O2 for enhanced anaerobic digestion[END_REF], ultrasound [START_REF] Cesaro | Sonolysis and ozonation as pretreatment for anaerobic digestion of solid organic waste[END_REF],

microwave [START_REF] Marin | Effect of microwave irradiation on anaerobic degradability of model kitchen waste[END_REF] or thermal [START_REF] Fdez | The use of thermochemical and biological pretreatments to enhance organic matter hydrolysis and solubilization from organic fraction of municipal solid waste (OFMSW)[END_REF] can break the macromolecules into smaller ones and increase the soluble COD. In order to improve the yield and productivity, recently, hybrid pre-treatment such as ozone + ultrasound [START_REF] Xu | Combination treatment of ultrasound and ozone for improving solubilization and anaerobic biodegradability of waste activated sludge[END_REF], hydrogen peroxide + microwave [START_REF] Eskicioglu | Synergetic pretreatment of sewage sludge by microwave irradiation in presence of H2O2 for enhanced anaerobic digestion[END_REF] and ultrasound + thermal [START_REF] Shahriari | Anaerobic digestion of organic fraction of municipal solid waste combining two pretreatment modalities, high temperature microwave and hydrogen peroxide[END_REF] are also applied. The combined processes all involve the mechanism of accelerating the generation of OH• radicals, and then better oxidation performance is observed [START_REF] Eskicioglu | Synergetic pretreatment of sewage sludge by microwave irradiation in presence of H2O2 for enhanced anaerobic digestion[END_REF]. Single and combined pre-treatment can improve VFAs production. However, there is still a need for a comprehensive comparison of the techno-economic of those pre-treatments, a further improvement of cost-benefit improvement is required [START_REF] Lee | A review of the production and applications of waste-derived volatile fatty acids[END_REF].

Besides the operating mode, the reactor can be classified into two types according to the existing forms of microorganism. For the first type of bioreactor, the microorganism is suspended in the reactor (such as a fluidized bed reactor and continuous stirred tank reactor). In the second type of reactor, with immobilized biomass, the microorganisms are attached to a packing material with a high specific surface (porous or not), which avoid the loss of microorganism.

Besides the composition of the raw material (feed composition), production of VFAs is also influenced by many parameters, such as solution pH, temperature, hydraulic retention time (HRT), solids/sludge retention time (SRT), organic loading rate (OLR), C/N/P rate, and microelements. pH is considered as the most important condition in VFAs fermentation. It can change the bacteria genus level of distribution in the fermentation broth, and low pH is beneficial for the acidification of soluble organic substrates [START_REF] Zheng | Pyrosequencing Reveals the Key Microorganisms Involved in Sludge Alkaline Fermentation for Efficient Short-Chain Fatty Acids Production[END_REF]. The objective of VFAs production can be either focus on the total amount of VFAs produced from the substrate or higher yield of more favorable component, i.e., butyric acid. It is reported that alkaline pH is more suitable for acetic and propionic production, while acidic and neutral conditions can produce more butyric acid [START_REF] Horiuchi | Selective production of organic acids in anaerobic acid reactor by pH control[END_REF]. The pH value to obtain the maximum yield of VFAs is reported as pH 8 [START_REF] Horiuchi | Selective production of organic acids in anaerobic acid reactor by pH control[END_REF], pH 9 [START_REF] Khiewwijit | Production of volatile fatty acids from sewage organic matter by combined bioflocculation and alkaline fermentation[END_REF], pH 10 [27] and pH 11 [START_REF] Zhao | Effect of initial pH on short chain fatty acid production during the anaerobic fermentation of membrane bioreactor sludge enhanced by alkyl polyglcoside[END_REF]. Even though those reports have some difference in the optimum pH values, an alkaline pH, i.e., between 9 and 11 is more favorable for the production of VFAs from waste activated sludge [START_REF] Zhang | Understanding Short-Chain Fatty Acids Accumulation Enhanced in Waste Activated Sludge Alkaline Fermentation: Kinetics and Microbiology[END_REF][START_REF] Pham | Volatile fatty acids production from marine macroalgae by anaerobic fermentation[END_REF][START_REF] Infantes | Influence of pH, temperature and volatile fatty acids on hydrogen production by acidogenic fermentation[END_REF]. However, if the production of butyric acid is the main propose, acidic pH can have better yield for butyric acid. It is shown that low pH values (4-6) are more favorable for butyric acid production [START_REF] Dahiya | Acidogenic fermentation of food waste for volatile fatty acid production with co-generation of biohydrogen[END_REF][START_REF] Horiuchi | Selective production of organic acids in anaerobic acid reactor by pH control[END_REF][START_REF] Fang | Phototrophic hydrogen production from glucose by pure and cocultures of Clostridium butyricum and Rhodobacter sphaeroides[END_REF][START_REF] Fang | Effect of pH on hydrogen production from glucose by a mixed culture[END_REF]. Then, depends on the objectives, more total VFAs yield or more specific VFA production, the optimum fermentation pH can be alkaline or acidic.

Temperature is another important factor, depending on the microorganism used, the optimum temperature can be different. Hasan et al. investigated temperature range from 4 ℃ to 75℃, the yield of VFAs increase as temperature increased from 4 to 30℃ and peaked at 30℃, then slightly decrease from 35℃ to 75℃. They suggest the optimized temperature is 30℃ [START_REF] Mahmud Hasan | Volatile fatty acids production from anaerobic treatment of cassava waste water: effect of temperature and alkalinity[END_REF]. Yang et al. use thermophilic micro-aerobic fermentation (temperature form 55 to 75℃) to produce VFAs from waste activated sludge, suggested that the optimized temperature is 60 ℃, which has a yield of 2.9g COD/L [START_REF] Yang | Effects of temperature on hydrolysis performance and short-chain fatty acids production during thermophilic micro-aerobic fermentation of waste activated sludge[END_REF].

The composition of VFAs in the real fermentation broth used in the current work are within the range of the previous results. To be better understand the influence of composition on separation performance, higher concentrations are used for the synthetic broths.

I.1.3 Applications of VFAs

The VFAs produced by acidogenic fermentation of waste can be used as variable renewable carbon resources such as produce biodegradable plastics, generate bioenergy and added to wastewater treatment plant as carbon sources for nitrogen and phosphorus removal (shown in

I.1.3.1 Biological nutrient removal

The accumulation of nitrogen (N) and phosphorus (P) in a water body can lead to severe environmental problems, such as eutrophication [START_REF] Chislock | Eutrophication : Causes, Consequences, and Controls in Aquatic Ecosystems[END_REF]. Therefore, strict wastewater emission standards on nitrogen and phosphorus were established by many countries [START_REF] Directive | Directive 2010/75/EU of the European Parliament and of the Council[END_REF]. It is generally recommended that the wastewater treated by conventional activated sludge wastewater treatment plant should have a nutrient composition of C:N:P=100:5:1 in order to have efficient nitrogen and phosphorus removal. However, the composition of N and P in wastewater usually exceeds the recommended ratio, and then additional carbon resources need to add to improve the nitrogen and phosphorus removal. VFAs can be used as an alternative to commercial carbon resources, e.g., methanol and glucose.

Many lab-scaled applications shown that waste-derived VFAs perform even better than the commercial carbon resources for the denitrification [START_REF] Kim | Continuous fermentation of food waste leachate for the production of volatile fatty acids and potential as a denitrification carbon source[END_REF][START_REF] Lim | Volatile fatty acids production from food wastes and its application to biological nutrient removal[END_REF]. Then, it is further noticed that VFAs with shorter carbon chains (C≤3, formic, acetic, and propionic acid) are more efficient in transferring nitrate into nitrite than longer-chained VFAs [START_REF] Li | Comparison on kinetics and microbial community among denitrification process fed by different kinds of volatile fatty acids[END_REF].

The use of VFAs for phosphorus removal is also investigated. The addition of VFAs can increase the uptake of phosphorus by activated sludge at the aerobic stage, and also increase the release of phosphorus at the anaerobic stage, then improved the phosphorus removal. Unlike the denitrification, it is shown that longer chained and branched VFAs (e.g., iso-butyric, iso-valeric acids) is more efficient for phosphorus removal [START_REF] Abu-Ghararah | The effect of organic compounds on biological phosphorus removal[END_REF]. In practice, during a long period of operation (5.5 years), it is shown that the addition of VFAs can optimize the enhanced biological phosphorus removal process [START_REF] Randall | The effect of volatile fatty acids on enhanced biological phosphorus removal and population structure in anaerobic/aerobic sequencing batch reactors[END_REF].

Recently, a full-scale application of waste-derived VFAs used for nutrient removal in the domestic wastewater treatment plant is reported, the removal rates of nitrogen and phosphorus are 72.39% and 89.65% respectively, shown that it is technically and economically feasible to produce waste-derived VFAs for nutrient removal [START_REF] Liu | Full-scale production of VFAs from sewage sludge by anaerobic alkaline fermentation to improve biological nutrients removal in domestic wastewater[END_REF].

I.1.3.2 Bioenergy and biofuel

Traditional energies are facing a crisis; for instance, the limitation of carbon emission restrict the use of fossil fuel, nuclear power can be expensive and risk environmental pollution, hydroenergy may damage the ecosystem. Consequently, alternative energy should be given more attention. In the European Union, biomass can take more than half of the proportion amongst all the renewable resources [START_REF] Bentsen | Biomass for energy in the European Union -a review of bioenergy resource assessments[END_REF]. Waste-derived VFAs were believed to be an inexpensive energy source that can generate different forms of energy. Direct generation of electricity can be achieved through microbial fuel cells, and valuable fuels can be produced by VFAs such as biodiesel, biogas or hydrogen.

Microbial fuel cell (MFC) is a bio-electrochemical system that is capable of converting chemical energy directly from organic substrates to electricity [START_REF] Oliot | Ion transport in microbial fuel cells: Key roles, theory and critical review[END_REF], regarded as a promising technology for wastewater treatment as well as energy recovery. In most MFC processes, fermentation broth contains rich VFAs can be directly used for electricity generation, make these processes economically attractive. Previous works indicated that energy recovery efficiency depends on the electron donors. For VFAs, acetic and propionic acids were considered preferred substrates in the operation of MFC, while longer chain fatty acids such as butyric and valeric acids will reduce the degradation rate [START_REF] Choi | Performance of microbial fuel cell with volatile fatty acids from food wastes[END_REF].

Biodiesel is esters of fatty acids. Biodiesel is normally produced from vegetable oil, plant oil, or animal fat. Production of biodiesel from microbial lipids is considered as promising [START_REF] Subramaniam | Microbial lipids from renewable resources: Production and characterization[END_REF]. Due to shorter metabolic pathways and higher theoretical efficiency to convert VFAs into lipids than sugar-based carbon sources (e.g., glucose and glycerol). Waste-derived VFAs are suggested as better candidates for biodiesel production [START_REF] Liu | Efficient bioconversion of high-content volatile fatty acids into microbial lipids by Cryptococcus curvatus ATCC 20509[END_REF].

The production of microbial lipids is more favor shorter chain VFAs, i.e., acetic acid, due to that acetic acid is utilized prior to longer chained ones [START_REF] Liu | Bioconversion of volatile fatty acids derived from waste activated sludge into lipids by Cryptococcus curvatus[END_REF][START_REF] Huang | Improved volatile fatty acid production during waste activated sludge anaerobic fermentation by different bio-surfactants[END_REF]. The use of mixed VFAs as the substrate with more acetic acid proportion (acetic: propionic: butyric = 6:2:1) is reported to have a high lipid yield [START_REF] Liu | Efficient bioconversion of high-content volatile fatty acids into microbial lipids by Cryptococcus curvatus ATCC 20509[END_REF].

Biogas is a valuable resource generated by anaerobic fermentation, and it is commonly used for heat and power generation as it contains 65-70% (v/v) of methane. Up-flow Anaerobic Sludge Blanket (UASB) is one of the most efficient biogas generators. Anaerobic digestion in a UASB reactor involves a series of biochemical reactions, which can be classified into hydrolysis, acidogenesis, and methanogensis. VFAs are the most important intermediate substrates during the three steps. According to Van Lier et al., 75% of methane production in UASB is derived from acetate [START_REF] Van Lier | Effects of acetate, propionate, and butyrate on the thermophilic anaerobic degradation of propionate by methanogenic sludge and defined cultures[END_REF]. Wong et al. use VFAs as the raw material, at the composition of acetate/propionate/butyrate at 6:3.7:4.4 g/L, organic loading rate (OLR) of 10.4g COD/L/day, the production of biogas can reach 322L/kg COD and the methane can hold 81% of the volume in biogas [START_REF] Wong | Effect of volatile fatty acid composition on upflow anaerobic sludge blanket (UASB) performance[END_REF].

In general, one can observe that the applications of VFAs for energies and biofuel are more favor shorter chain VFAs than others.

I.1.3.3 Biodegradable plastics (Polyhydroxyalkanoates)

Among the potential utilization, the production of biodegradable plastics (i.e., polyhydroxyalkanoates) is one of the most promising applications of VFAs [START_REF] Bengtsson | A process for polyhydroxyalkanoate (PHA) production from municipal wastewater treatment with biological carbon and nitrogen removal demonstrated at pilot-scale[END_REF].

Polyhydroxyalkanoates (PHA) were recognized as a fully biodegradable and biocompatible polymer. Due to the similar characteristics, PHA is a promising alternative resource to petrochemical derivate plastic. Many publications on synthesizing of PHA from VFAs are reported previously, shown that VFAs are suitable for the production of PHA. The yield of PHA production from excess sludge fermented VFAs is reported to reach 56.5% of dry cell weight [START_REF] Mengmeng | Optimal production of polyhydroxyalkanoates (PHA) in activated sludge fed by volatile fatty acids (VFAs) generated from alkaline excess sludge fermentation[END_REF].

Another report showed a lower PHA yield (39%) from grass digested VFAs [START_REF] Cerrone | Medium chain length polyhydroxyalkanoate (mcl-PHA) production from volatile fatty acids derived from the anaerobic digestion of grass[END_REF].

The production of PHA can be produced by mixed microorganisms, and the composition of PHA is more depends on the feed composition [START_REF] Duque | Response of a three-stage process for PHA production by mixed microbial cultures to feedstock shift: Impact on polymer composition[END_REF]. It is reported that a higher proportion of butyric acid is more favorable for the production of PHA [START_REF] Yang | Optimization of growth media components for polyhydroxyalkanoate ( PHA ) production from organic acids by Ralstonia eutropha[END_REF]. For a common VFAs composition directly obtain from fermentation, the productivities are similar. PHA productivity is reported at 0.048 g.L -1 .h -1 for VFAs obtained from palm oil mill effluent fermentation [START_REF] Setiadi | Production of polyhydroxyalkanoate (PHA) by Ralstonia eutropha JMP 134 with volatile fatty acids from palm oil mill effluent as precursors[END_REF], similar productivity (0.06 g.L -1 .h -1 ) is reported for VFAs generated from olive oil mill wastewater [START_REF] Campanari | Development of a micro-cogeneration laboratory and testing of a natural gas CHP unit based on PEM fuel cells[END_REF].

However, the co-existence of organic impurities, i.e., methanol and ethanol, in the fermentation broth hindered the productivity of PHA due to the increase of unfavorable population of bacteria [START_REF] Tamis | Enrichment of Plasticicumulans acidivorans at pilot-scale for PHA production on industrial wastewater[END_REF][START_REF] Marang | Impact of non-storing biomass on PHA production: An enrichment culture on acetate and methanol[END_REF]. In addition, even though PHAs are promising alternative plastic for the future and can be produced from organic waste, the large scare utilization of PHA still facing a much higher cost (5-10 times than petroleum-based polymers) and the difficulty to extract [START_REF] Serafim | Optimization of polyhydroxybutyrate production by mixed cultures submitted to aerobic dynamic feeding conditions[END_REF].

Therefore, increase the proportion of the more favorable VFA, butyrate, remove the hindering organic impurities in the fermentation broth, can improve productivity. Besides, the extraction and processing of PHA still need more research [START_REF] Suriyamongkol | Biotechnological approaches for the production of polyhydroxyalkanoates in microorganisms and plants -A review[END_REF].

I.2 Nanofiltration process and its applications for VFAs valorization

The bottleneck restricting the production of renewable resources from waste is the high recovery and separation costs. Many endeavors are made for the recovery of VFAs [START_REF] Scoma | Recovery of VFAs from anaerobic digestion of dephenolized Olive Mill Wastewaters by Electrodialysis[END_REF][START_REF] Jones | Removal and recovery of inhibitory volatile fatty acids from mixed acid fermentations by conventional electrodialysis[END_REF][START_REF] Tugtas | Recovery of volatile fatty acids via membrane contactor using flat membranes: Experimental and theoretical analysis[END_REF][START_REF] Zacharof | Recovery of volatile fatty acids (VFA) from complex waste effluents using membranes[END_REF],

and it is further pointed out that the separation of individual VFAs components can greatly revalue the waste-derived VFAs [START_REF] Atasoy | Bio-based volatile fatty acid production and recovery from waste streams : Current status and future challenges[END_REF]. Therefore, Atasoy et al. suggest that any method attempts to separate VFAs is welcome [START_REF] Atasoy | Bio-based volatile fatty acid production and recovery from waste streams : Current status and future challenges[END_REF].

A comparison of several traditional methods and membrane processes in the separation and recovery of VFAs from waste fermentation is given [START_REF] Yesil | Anaerobic fermentation of organic solid wastes: volatile fatty acid production and separation[END_REF], showing that membrane processes have some advantages above traditional treatments (Table I-4). Membrane processes include concentration-driven processes such as pervaporation (PV) and membrane extraction, pressure-driven processes, e.g., nanofiltration (NF), as well as electrochemical driven membrane processes, for instance, electrodialysis (ED). Nanofiltration is recommended as one of the most promising membrane processes for VFAs separation [START_REF] Atasoy | Bio-based volatile fatty acid production and recovery from waste streams : Current status and future challenges[END_REF]. The following sections are mainly focused on the nanofiltration process.

I.2.1 Introduction of the nanofiltration process

Nanofiltration (NF) is a pressure-driven membrane process used for liquid-phase separation.

Pressure-driven membrane processes include Microfiltration (MF), Ultrafiltration (UF), Nanofiltration (NF) and Reverse Osmosis (RO), which were classified by their pore size, charge and pressure (see Table I -5). Their structures are the same; at one side of the membrane, the pressure exerted on the solution as a driving force, the solution was separated as permeate and retentate. The pressure difference between the feed and permeate side (i.e., transmembrane pressure, TMP) can force the solvent to pass through while the particles and some dissolved components will be retained based on their properties such as size, shape, and charge.

MF has the largest pore (0.1um to 10 um) and the highest permeability, a high flux can be observed at low pressure. MF generally to be used to separate suspended particles and microorganisms from the liquid. UF has smaller pores (2nm to 100nm), the permeability is much lower than MF, and higher operating pressure is required. UF can be used for the removal of suspended solids and high molecular weight solutes such as proteins. The pore size of NF is smaller than UF, and the surface of the NF membrane is charged, which is usually used to remove multivalent ions and dissolved organic matters with a molecular weight above 150g.mol -1 . RO membrane is often considered as dense membrane without predefined pores, permeation of solutes are because of the solution-diffusion effect. RO is the most widely used process in seawater desalination, RO can also be used as a concentration step. and sucrose (MW 342) [START_REF] Cadotte | Nanofiltration membranes broaden the use of membrane separation technology[END_REF]. The retention mechanism in NF is a combination of different contributions, mainly due to the size (steric effect) and to the charge of the solutes and the membrane. NF is efficient for the recovery and selective removal of different kinds of products from complex solutions. Then more and more researchers reported the potential of NF in the field of organic separation and purification [START_REF] Bowen | Characterization and prediction of separation performance of nanofiltration membranes[END_REF][START_REF] Levenstein | Utilization of the Donnan effect for improving electrolyte separation with nanofiltration membranes[END_REF][START_REF] Bouchoux | Nanofiltration of glucose and sodium lactate solutions: Variations of retention between single-and mixed-solute solutions[END_REF].

After three decades of development and advance, nanofiltration becomes a mature process in many domains for instance water softening [START_REF] Watson | Low-energy membrane nanofiltration for removal of color, organics and hardness from drinking-water supplies[END_REF], brackish water desalination [START_REF] Lhassani | Selective demineralization of water by nanofiltration application to the defluorination of brackish water[END_REF], wastewater treatment [START_REF] Chen | Treatment of textile desizing wastewater by pilot scale nanofiltration membrane separation[END_REF], whey demineralization [START_REF] Cuartas-Uribe | A study of the separation of lactose from whey ultrafiltration permeate using nanofiltration[END_REF][START_REF] Cuartas-Uribe | Comparison of the behavior of two nanofiltration membranes for sweet whey demineralization[END_REF], organic acid production [START_REF] Bouchoux | Investigation of nanofiltration as a purification step for lactic acid production processes based on conventional and bipolar electrodialysis operations[END_REF] or drinking water production [START_REF] Jacangelo | Role of membrane technology in drinking water treatment in the United States[END_REF].

Recently, many new membranes were invented to improve the NF performances, such as surface modified membrane [START_REF] Kochkodan | A comprehensive review on surface modified polymer membranes for biofouling mitigation[END_REF], nanoparticles enhanced membrane [START_REF] Balta | A new outlook on membrane enhancement with nanoparticles: The alternative of ZnO[END_REF], 2D materials fabricated membrane [START_REF] Han | Ultrathin Graphene Nanofiltration Membrane for Water Purification[END_REF][START_REF] Mi | Graphene Oxide Membranes for Ionic and Molecular Sieving[END_REF]. Those newly emerged membranes could be promising to solve some remaining problems that slow down the application of NF in industries, such as fouling control and improving the separation between solutes [START_REF] Van Der Bruggen | Drawbacks of applying nanofiltration and how to avoid them: A review[END_REF]. Then, additional prospects are pointed out, for instance, the predictive modeling of NF processes for more complex solutions (i.e., with solutions have more than 2, 3, or 4 ions), and also new applications for a wider range of cases (e.g., renewable resources) [START_REF] Mohammad | Nanofiltration membranes review: Recent advances and future prospects[END_REF].

I.2.2 Parameters to describe NF performance

It is essential to measure the performance of NF processes. A good way to compare the performances of different membranes is to compare their characteristic parameters. There are many parameters that can be used to measure the efficiency of NF processes, for instance, permeate flux, retention, separation factor, purity, and yield (product recovery) of a target product.

I.2.2.1 Permeate flux

The pressure is the driving force to push water and solutes toward the permeate side of the NF membrane. The pressure between the concentrate side and permeate side is called transmembrane pressure (TMP). The permeate flux can be defined as the volumetric flux rate of permeate per unit area of the membrane, usually denoted as Jv,

𝐽𝐽 𝑉𝑉 = 1 𝐴𝐴 • 𝑑𝑑𝑉𝑉 𝑑𝑑𝑑𝑑 (I.8)
V, total volume permeated through the membrane within time t, A, effective area of the membrane, t, time of duration of filtration.

The unit of permeate flux is m 3 .m -2 .s -1 , permeate flux is calculated by measurement of the volume of permeate during a certain time, then divide the effective filtration area. Generally, permeate flux increases with the transmembrane pressure.

The flux obtained with pure water (Jw) varies linearly with the transmembrane pressure (∆𝑃𝑃).

Then, the membrane permeability (𝐿𝐿 𝑝𝑝𝑝𝑝 ) can be determined using the following equation:

𝐿𝐿 𝑝𝑝𝑝𝑝 = 𝐽𝐽 𝑤𝑤 ∆𝑃𝑃 (I.9)
The unit of pure water permeability is m 3 .m -2 .s -1 .Pa -1 .

I.2.2.2 Retention

Retention is also used to characterize the ability of the membrane to retain a given solute.

𝑅𝑅(%) = �1 - 𝐶𝐶 𝑝𝑝 𝐶𝐶 𝑓𝑓 � • 100 (I.10)
𝐶𝐶 𝑓𝑓 The concentration of the solute in the feed (mol.L -1 ),

𝐶𝐶 𝑝𝑝 The concentration of the solute in the permeate. (mol.L -1 ).

I.2.2.3 Separation factor

Separation factor (Sf) can be used to define the separation efficiency considering the separation of two solutes, a and b. It is calculated according to the following relationship

𝑆𝑆𝑆𝑆 = (𝐶𝐶 𝑎𝑎 /𝐶𝐶 𝑏𝑏 ) 𝑝𝑝 (𝐶𝐶 𝑎𝑎 /𝐶𝐶 𝑏𝑏 ) 𝑓𝑓 = 1-𝑅𝑅 𝑎𝑎 1-𝑅𝑅 𝑏𝑏 (I.11)
Depends on the retention sequence of solutes a and b, the separation factor observed can be between 0 and 1 or from 1 to ∞. SF values higher than 1, mean that the NF retentate is a solution enriched in solute b compared to the feed. The increase in value of the separation factor means better separation efficiency of the NF process on the two solutes.

I.2.2.4 Yield and Purity

Yield also can be used to characterize the separation performance of NF. If the purified fraction of the target solute is in the permeate, the yield is defined according to the following equation:

𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌(%) = � 𝑉𝑉 𝑝𝑝 𝐶𝐶 𝑝𝑝 𝑉𝑉 𝑓𝑓 𝐶𝐶 𝑓𝑓 � • 100 (I.12)
Otherwise, if the purified fraction is the retentate, the yield is defined according to the following equation:

𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌(%) = � 𝑉𝑉 𝑟𝑟 𝐶𝐶 𝑟𝑟 𝑉𝑉 𝑓𝑓 𝐶𝐶 𝑓𝑓 � • 100 (I.

I.2.3 Retention mechanisms

The retention of solutes is due to three mechanisms, so-called steric exclusion, Donnan exclusion, and Dielectric exclusion.

I.2.3.1 Steric exclusion (size effect)

For neutral and non-polarized solutes, which could be considered as spherical particles, the steric effect considers that the retention of a solute is fixed according to the ratio between its size and that of the membrane pores.

The resulting retention can be written as:

𝑅𝑅 = {1 -�1 -� 𝑅𝑅 𝑠𝑠 𝑅𝑅 𝑝𝑝 � 2 �} 2 (I.15)
𝑅𝑅 𝑠𝑠 Radius of the solute;

𝑅𝑅 𝑝𝑝 Radius of membrane pore.

The size effect has been wildly reported [START_REF] Palmeri | Theory of pressure-driven transport of neutral solutes and ions in porous ceramic nanofiltration membranes[END_REF][START_REF] Bouguen | Enhanced retention of neutral solute and charged solute with NF inorganic membrane by chemical grafting and physico-chemical treatment[END_REF][START_REF] Kimura | Rejection of neutral endocrine disrupting compounds (EDCs) and pharmaceutical active compounds (PhACs) by RO membranes[END_REF][START_REF] Garcia-Martin | Pore size analysis from retention of neutral solutes through nanofiltration membranes. The contribution of concentration-polarization[END_REF].

However, it was also reported that the retention of a neutral solute does not depend only on its molecular weight, but that its shape can have an influence too. Laufenberg et al. found that branched isomers of propanol and butanol can have significantly higher retention than their straight-chain isomers, which means that the structure or the shape of a molecule can be an important factor during RO process as well as NF [START_REF] Laufenberg | The influence of intermolecular interactions on the selectivity of several organic acids in aqueous multicomponent systems during reverse osmosis[END_REF].

The water shell surrounding the solutes can also enlarge the solute size compared to Stokes radius and lead to an increase of the steric effect. Once the number of water molecules form the solute water shell is reduced (i.e., dehydration), the retention of solute decreases. It is reported that the retention of glucose is reduced in the presence of salt ions, especially of those show low retention [START_REF] Bargeman | Nanofiltration of multicomponent feeds. Interactions between neutral and charged components and their effect on retention[END_REF]. Further investigation showed that the decrease of saccharides retention can be due to the dehydration of saccharides in the presence of electrolytes [START_REF] Boy | Relationship between volumetric properties and mass transfer through NF membrane for saccharide/electrolyte systems[END_REF][START_REF] Boy | How do ions enhance the transfer during nanofiltration of saccharides? Experimental assessment of the dehydration assumption[END_REF].

I.2.3.2 Charge effect

When considering the transfer of charged solutes, for instance, acetate ion, propionate ion, sulfate ion, and chloride ion, etc., the charge effect (Donnan effect) should be taken into account.

Nanofiltration membranes are usually charged as a characteristic of the membrane material.

The polymer membranes are commonly negatively charged while some ceramic nanofiltration membranes can be positively charged [START_REF] Peeters | Retention measurements of nanofiltration membranes with electrolyte solutions[END_REF]. The exclusion mechanism is the fact that charged membrane materials will repulse co-ions and attract counter-ions. If we consider the nanofiltration membrane surface as a solid plane surface, the negative charge on the membrane surface and the counter-ion attracted to it will form an electrical double layer. The charge properties of NF membrane can be characterized by some methods like streaming potential and streaming current (to measure the membrane surface zeta potential), electro-osmosis (determine zeta potential through membrane pore, i.e., perpendicular to the membrane surface) or charged solute retention.

Donnan exclusion is severely affected by ionic strength and solution pH. As the concentration of charged solutes increases, the thickness of the slipping region boundary layer decreases, and the zeta potential decreases. The decrease of membrane charge due to increase in ionic strength makes the electrostatic repulsion weaker, and then lower ions retention at high concentration compared to that in low concentration is observed. This phenomenon is called "screening effect".

For a negatively charged membrane, as the solution pH decreases, H + will combine to the weak acid group (generally carboxylic acid group). When the pH reaches a certain degree, the membrane charge will be totally neutralized. This pH value is called the isoelectric point (IEP) of the membrane. IEP is one of the characteristics of the membrane and mainly depends on the membrane material. Most polyamide membranes have an IEP between pH 3 to pH 5 [START_REF] Bowen | Modelling the performance of membrane nanofiltration-critical assessment and model development[END_REF]. pH affects the exclusion by decreasing the membrane charge, which also narrows the electrical double layer.

At neutral pH, when the concentration of solutes is low, and the solute size is significantly smaller than the membrane pore size, the charge effect is the primary mechanism in electrolytes retention. Schaep et al. used two negative charged NF membranes and one positively charged NF membrane, obtained the retentions of NaCl, MgCl2, NaSO4, MgSO4 at different concentrations. It is suggested that, for loose membrane (NTR 7450), charge effect is the major exclusion mechanism. On the other hand, for the denser membrane, since the pore size is close to the radius of the solute, the steric effect can play a role in solutes retention [START_REF] Schaep | Retention mechanisms in nanofiltration[END_REF]. The same phenomenon also exists in organic electrolytes. Khunnonkwao et al. reported that the retention of succinic acid by nanofiltration membrane (NF-45) at 0.1 mol.L -1 at pH 7 is higher than 90%. When the concentration increases to 0.7 mol.L -1 , the retention dramatically decreases to less than 20% [START_REF] Khunnonkwao | A two steps membrane process for the recovery of succinic acid from fermentation broth[END_REF].

Bouchoux et al. also reported that when the concentration of sodium lactate increases from 0.1M to 1M, the retention of sodium lactate decreases from 80% to 25% [START_REF] Bouchoux | Investigation of nanofiltration as a purification step for lactic acid production processes based on conventional and bipolar electrodialysis operations[END_REF].

For the retention of weak acids, dissociation needs to be taken into consideration. The percentage of the dissociated form of a weak acid is fixed according to its pKa and pH of the solution. Dissociation of a weak acid 𝐻𝐻𝐻𝐻 is shown in Eq. (I. [START_REF] Su | Improving hydrogen production from cassava starch by combination of dark and photo fermentation[END_REF])

𝐻𝐻𝐻𝐻 ⇌ 𝐻𝐻 + + 𝐻𝐻 - (I.16)
The dissociation constant 𝐾𝐾 𝑎𝑎 is the equilibrium constant of dissociated and undissociated compound, given by Eq. (I.17), then, the pKa of weak acid 𝐻𝐻𝐻𝐻 is defined in Eq. (I. [START_REF] Nanda | Characterization of acetic acid bacteria in traditional acetic acid fermentation of rice vinegar (komesu) and unpolished rice vinegar (kurosu) produced in Japan[END_REF].

𝐾𝐾 𝑎𝑎 = [𝐻𝐻 + ][𝐴𝐴 -] [𝐻𝐻𝐴𝐴]
(I.17)

𝑝𝑝𝐾𝐾 𝑎𝑎 = 𝑌𝑌𝑙𝑙𝑙𝑙 10 (𝐾𝐾 𝑎𝑎 ) = 𝑌𝑌𝑙𝑙𝑙𝑙 10 [𝐻𝐻 + ][𝐴𝐴 -]
[𝐻𝐻𝐴𝐴]

(I.18) there should be more acetate than acetic acid. At neutral pH (pH=7), more than 99% of acetic acid exists as Ac -, the charge effect can significantly affect the retention of acetate in diluted solution.

For polyprotic acids, multiple pKa values are observed, the composition of their aqueous solution in a certain pH can be more complicated.

pH can dramatically affect the retention of a weak acid in a dilute solution. In neutral form (at pH 2.2), retention of succinic acid is about 25%, while in the ionized form (pH 7.6), the retention can be close to 100% [START_REF] Khunnonkwao | Integration of Nanofiltration in the Production of Succinic Acid[END_REF].

I.2.3.3 Dielectric exclusion

The dielectric effect was considered another charge effect since the beginning of the 21 st century [START_REF] Yaroshchuk | Dielectric exclusion of ions from membranes[END_REF]. This is because a model only considering the steric effect and Donnan equilibrium cannot successfully predict the retention of divalent ions. For instance, the retention of CaCl2 experimental value [START_REF] Vezzani | Donnan equilibrium and dielectric exclusion for characterization of nanofiltration membranes[END_REF][START_REF] Schaep | Modelling the retention of ionic components for different nanofiltration membranes[END_REF]. The mechanisms of dielectric exclusion still need investigatiom.

Two kinds of mechanisms are proposed, that are image forces [START_REF] Yaroshcuk | Rejection mechanisms of NF membranes[END_REF] and ion solvation [START_REF] Oatley | Review of the dielectric properties of nanofiltration membranes and verification of the single oriented layer approximation[END_REF].

Generally, it is believed that the dielectric constant values in the bulk solution and in the polymeric matrix are different. The dielectric constant of an aqueous solution is usually much higher than the value in the polymeric matrix. As an example, Sanjob et al. reported that the dielectric constant of water could be decreased as much as 50% in a nanocavity compared to the value in bulk water [START_REF] Senapati | Dielectric constant of water confined in a nanocavity[END_REF].

I.2.3.4 Co-ions competition

In a bulk solution, the total amount of anions and cations are equal and the solution maintain neutral, this condition is called electroneutrality.

As aforementioned, nanofiltration membrane has lower retention for monovalent anions, for instance, Cl -and Ac -, than divalent ones such as SO4 2-and succinate because of the weaker charge effect as well as smaller size (possibly due to less hydration number). When a mixture of monovalent and divalent ions such as NaCl and Na2SO4 was filtrated by a nanofiltration membrane, negative retention of Cl -sometimes appeared (Figure I-5). Indeed, divalent anion SO4 2-has a bigger size as well as stronger electric repulsion, can be almost totally retained by the membrane, while monovalent cations Na + having a smaller size, can easily pass through it. Due to the electroneutrality across the membrane, the transfer of Na + has to be equilibrated by monovalent anions, Cl -. Then, for some feed composition, the concentration of Cl -in the permeate can be much higher than that in the feed, meaning a negative value of the Cl -retention. For other permeating ions and non-permeate ions, this phenomenon also exists, i.e. Nielsen and Jonsson reported a lower than -200% retention of NaNO3 in the mixture of NaNO3 : Na2SO4 = 1 : 10 [START_REF] Nielsen | Bulk-phase criteria for negative ion rejection in nanofiltration of multicomponent salt solutions[END_REF].

Negative retention is a particular case of co-ions competition. In general, during the filtration, once two or more than two co-ions exist in the solution, co-ions competition should occur. Negative retention due to co-ions competition was used to improve the selectivity of nanofiltration, to achieve negative retention of one solute, while maintaining positive retention as high as possible for the other. Polyelectrolytes were commonly used as an additive substance to improve the separation [START_REF] Postel | On negative retentions in organic solvent nanofiltration[END_REF]. Divalent salts like Na2SO4 also were reported to be beneficial for the improvement of separation [START_REF] Umpuch | Nanofiltration as a purification step in production process of organic acids: Selectivity improvement by addition of an inorganic salt[END_REF]. For instance, by adding 0.25 mole of Na2SO4 into the binary solution of glucose and lactate, the maximum separation factor between glucose and lactate increases from 1.1 to 1.9, meanwhile, the flux to obtain the highest separation factor increases from 0.05×10 -5 m 3 .m -2 . s -1 to 0.2×10 -5 m 3 .m -2 . s -1 [START_REF] Bouchoux | Investigation of nanofiltration as a purification step for lactic acid production processes based on conventional and bipolar electrodialysis operations[END_REF].

I.2.4 Parameters influencing the nanofiltration performances I.2.4.1 Feed composition

Retention of ions contained in single electrolyte solutions was widely reported. The influence of ions size and charge was discussed [START_REF] Schaep | Influence of ion size and charge in nanofiltration[END_REF], and a qualitative prediction of the retention sequence of ions with different valence and size was given [START_REF] Wang | Separation performance of a nanofiltration membrane influenced by species and concentration of ions[END_REF]. It was observed that the retention of symmetric electrolytes (i.e. NaCl, KCl, and MgSO4) in diluted solution is governed by the membrane co-ions due to electrostatic repulsion, and that the retention of asymmetric electrolytes (i.e., Na2SO4, CaCl2, and MgCl2) is dominated by the ions with the highest valence [START_REF] Luo | Effects of pH and salt on nanofiltration-a critical review[END_REF]. Many models based on irreversible thermodynamics are built and can successfully describe the retention of single electrolyte solutions [START_REF] Peeters | Retention measurements of nanofiltration membranes with electrolyte solutions[END_REF][START_REF] Schaep | Modelling the retention of ionic components for different nanofiltration membranes[END_REF][START_REF] Timmer | Transport of lactic acid through reverse-osmosis and nanofiltration membranes[END_REF].

However, when more complex solutions are concerned, like multi-electrolytes systems, there are interactions between the different ions. Then, the retention of ions in mixed solutions cannot be predicted from the ones obtained with single solutions. An attempt to use an irreversible thermodynamic model to predict the individual ions retentions in a Cd 2+ /Ni 2+ binary solution showed that the experimental retention of the less retained ion, Cd 2+ , is 10% lower than that predicted by the model [START_REF] Murthy | Separation of binary heavy metals from aqueous solutions by nanofiltration and characterization of the membrane using Spiegler-Kedem model[END_REF]. With binary systems containing two co-ions and only one counterion, it was reported that when one of the co-ions is totally retained by the membrane, the retention of the other decreases significantly. It was attributed to the co-ions competition. For instance, during NF of a mixture containing NaCl and an organic acid sodium salt, with a molecular weight (MW) of 700 g.mol -1 and retention higher than 99%, negative retention of Cl -was observed [START_REF] Perry | Intermediate Reverse Osmosis Ultrafiltration ( RO UF ) Membranes for Concentration and Desalting of Low Molecular Weight Organic Solutes[END_REF].

The same results, i.e., negative retention of the less retained ion, were also reported with ions of smaller molecular weight (lesser than 200 g.mol -1 ), especially with solutions containing multivalent and monovalent ions. As an example, negative retention of Cl -was observed in the presence of SO4 2- [START_REF] Szoke | Characteristics of thin-film nanofiltration membranes at various pH-values[END_REF], as well as for Na + in the presence of Ca 2+ [START_REF] Vonk | Positive and Negative Ion Retention Curves of Mixed Electrolytes in Reverse Osmosis with a Cellulose Acetate Membrane . An Analysis on the Basis of the Generalized Nernst-Planck Equation[END_REF].

Such interactions of charged solutes in mixed solutions not only depend on operating conditions such as filtration flux but also on the feed composition, i.e., concentration and proportions of ions. It was reported that for a mixed solution containing NaCl and an organic acid sodium salt, the retention of Cl -decreases to more negative values when the proportion of organic acid salt in the feed increases [START_REF] Raspor | Biotechnological applications of acetic acid bacteria[END_REF]. This was also observed with solutions containing Na2SO4 and NaNO3, for which negative values are obtained for the retention of NO3 -when the concentration ratio of SO4 It was found that the retention of the less retained solutes, lactate, acetate, and formate, decreases in the presence of a more retained solute, succinate, and that this decrease is more important for increasing proportion of succinate [START_REF] Kang | Removal of organic acid salts from simulated fermentation broth containing succinate by nanofiltration[END_REF]. An overview of the negative retention phenomenon is provided, the possible mechanisms behind are discussed. The author concluded that current experimental results are not sufficient to predict the negative retention phenomenon, and further investigations are required [START_REF] Yaroshchuk | Negative rejection of ions in pressure-driven membrane processes[END_REF].

Besides the ions, co-existing neutral and charged solutes could also influence the performance of nanofiltration

Many authors reported the decrease of uncharged solutes retentions in the presence of inorganic salts. For instance, the retention of glucose decreased in the presence of KCl [START_REF] Nilsson | The influence of pH, salt and temperature on nanofiltration performance[END_REF] and NaCl [START_REF] Bouchoux | Nanofiltration of glucose and sodium lactate solutions: Variations of retention between single-and mixed-solute solutions[END_REF]. On the other hand, the retentions of charged solutes also decrease in the presence of inorganic salts, like retention of sodium lactate in the presence of NaCl and Na2SO4 [START_REF] Umpuch | Nanofiltration as a purification step in production process of organic acids: Selectivity improvement by addition of an inorganic salt[END_REF].

The mechanisms of the solutes retentions decrease in the presence of inorganic salts are not the same for neutral and charged solutes. The decrease of the retention of uncharged solutes in the presence of inorganic salts can be due to their dehydration, leading to a smaller hydration size [START_REF] Boy | How do ions enhance the transfer during nanofiltration of saccharides? Experimental assessment of the dehydration assumption[END_REF][START_REF] Teychené | Why Are Saccharides Dehydrated in the Presence of Electrolytes? Insights from Molecular Modeling and Thermodynamic Measurements[END_REF]. Another possibility could be due to the swelling of the membrane due to the adsorption of salts [START_REF] Nilsson | The influence of pH, salt and temperature on nanofiltration performance[END_REF]. On the other hand, the influence of inorganic salts on the retention of charged solutes could occur due to the screening effect and co-ions competition as previously mentioned. The addition of inorganic salts increases the ionic concentration of the solution, then the electrostatic interaction between membrane and charged solutes is weakened, and lower retention is observed [START_REF] Khunnonkwao | A two steps membrane process for the recovery of succinic acid from fermentation broth[END_REF]. In addition, the existence of more retained co-ions (i.e., SO4 2-), could compete with the less retained co-ions (i.e., lactic acid), which leads to a decrease in retention of less retained co-ions [START_REF] Umpuch | Nanofiltration as a purification step in production process of organic acids: Selectivity improvement by addition of an inorganic salt[END_REF].

For organic impurities, the influence on the retention of organic acid is also reported. The influence of uncharged organic solute such as glucose is negligible on the retention of other solutes, both for the charged solute, i.e., NaCl [START_REF] Wang | The possibility of separating saccharides from a NaCl solution by using nanofiltration in diafiltration mode[END_REF], and uncharged solute, i.e., xylose [START_REF] Sjoman | Separation of xylose from glucose by nanofiltration from concentrated monosaccharide solutions[END_REF]. The charged organic solutes act as the inorganic salts, which could influence solutes retentions by both increasing the ionic concentration [START_REF] Khunnonkwao | A two steps membrane process for the recovery of succinic acid from fermentation broth[END_REF], and compete with the less/more retained co-ions [START_REF] Kang | Removal of organic acid salts from simulated fermentation broth containing succinate by nanofiltration[END_REF].

However, most of the results are obtained in synthetic solutions. For more complex solutions, especially with real fermentation broth, some unexpected results were reported. For instance, it is reported that the retention of butyric acid in a real digestion liquor maintained at nearly 100%, for all the conditions (pH and transmembrane pressure) investigated [START_REF] Xiong | Integrated acidogenic digestion and carboxylic acid separation by nanofiltration membranes for the lignocellulosic carboxylate platform[END_REF]. Meanwhile, the retentions of other VFAs (acetic and propionic acids) decrease when the solution pH decreases [START_REF] Xiong | Integrated acidogenic digestion and carboxylic acid separation by nanofiltration membranes for the lignocellulosic carboxylate platform[END_REF]. Another publication shows that the retention sequence of acetate and butyrate is Ac<Bu in synthetic solutions by DL membrane, changed to Bu<Ac when filtrate a real fermentation broth with the same type of membrane.

The aforementioned results indicate that there could be more complicated solutes interactions in the real fermentation broth than in synthetic solutions.

I.2.4.2 Solution pH

A thin-film composite membrane (TFCM), like NF-45 membrane, is composed of a thin nanoporous active layer made of polyamide, then supported by a macroporous layer made of polysulfone [START_REF] Gohil | A review on semi-aromatic polyamide TFC membranes prepared by interfacial polymerization: Potential for water treatment and desalination[END_REF]. The membrane charge can come from the dissociation of functional groups, adsorption of ions from solution, and the adsorption of polyelectrolytes, ionic surfactants, and charged macromolecules [START_REF] Schaep | Evaluating the charge of nanofiltration membranes[END_REF]. Among those sources, dissociation of functional groups is commonly considered as the main contribution of the pH-dependent membrane charge [START_REF] Coronell | Quantification of Functional Groups and Modeling of Their Ionization Behavior in the Active Layer of FT30 Reverse Osmosis Membrane[END_REF][START_REF] Tiraferri | Direct quantification of negatively charged functional groups on membrane surfaces[END_REF].

For TFCMs, the solutes separation only involves the polyamide active layer, and the functional groups (carboxylic and amino groups) on the active layer determine the membrane surface charge [START_REF] Coronell | Quantification of Functional Groups and Modeling of Their Ionization Behavior in the Active Layer of FT30 Reverse Osmosis Membrane[END_REF][START_REF] Coronell | Ionization Behavior , Stoichiometry of Association , and Accessibility of Functional Groups in the Active Layers of Reverse Osmosis and Nanofiltration Membranes[END_REF]. It is commonly observed that when the solution pH is higher than the isoelectric point (IEP) of the membrane, the membrane surface charge increases with pH. This theory can be proved by the measurement of the zeta potential of the membrane [START_REF] Hoang | The effect of feed pH on the performance of a reverse osmosis membrane[END_REF][START_REF] Mänttäri | Effect of pH on hydrophilicity and charge and their effect on the filtration efficiency of NF membranes at different pH[END_REF]. However, the zeta potential measurement is solute-dependent and cannot provide a quantitative measurement of the membrane charge. Recently, heavy-ion probes were used as a new method to determine the membrane charge, and dissociation of carboxylic functional groups on the active layer is referred to as the primary source of membrane charge [START_REF] Coronell | Quantification of Functional Groups and Modeling of Their Ionization Behavior in the Active Layer of FT30 Reverse Osmosis Membrane[END_REF][START_REF] Tiraferri | Direct quantification of negatively charged functional groups on membrane surfaces[END_REF].

For the nanofiltration of strong electrolytes, the charge of solutes is nearly unchanged, the influence of solution pH on solutes retention can be attributed to the dissociation of membrane functional groups leading to the variation of the membrane surface charge. For small symmetric salts, i.e., NaCl and KCl, various reports have shown that when the solution pH becomes higher than the IEP of the membrane, the retentions of salts increase with pH due to the increase of membrane charge [START_REF] Nilsson | The influence of pH, salt and temperature on nanofiltration performance[END_REF][START_REF] Hoang | The effect of feed pH on the performance of a reverse osmosis membrane[END_REF][START_REF] Childress | Relating nanofiltration membrane performance to membrane charge (electrokinetic) characteristics[END_REF][START_REF] Kim | Effect of pH on the rejection of inorganic salts and organic compound using nanofiltration membrane[END_REF]. However, for weak electrolytes such as organic acids, the retention mechanism is more sophisticated, as both the charge of membrane and solutes vary with solution pH [START_REF] Luo | Effects of pH and salt on nanofiltration-a critical review[END_REF]. Besides, the size of organic acids can be much larger than the size of inorganic electrolytes. Thus, the molecular weight (MW) of organic acids needs to be first discussed. When the MW of an organic acid is higher than the molecular weight cut off (MWCO) of the membrane, regardless of the solute and membrane charge, high retention is observed. Therefore, the retentions of organic acids that have MW higher than MWCO of the membrane are independent of solution pH [START_REF] Wang | Nanofiltration of L-phenylalanine and L-aspartic acid aqueous solutions[END_REF].

For the nanofiltration of small monovalent organic acids, i.e., acetic acid, low retention is expected for its neutral form, since its MW (60 g.mol -1 ) is much lower than the MWCO of nanofiltration membranes (200-500 g.mol -1 ). When the solution pH increases, the proportion of dissociated acetic acid increases; meanwhile, the membrane surface charge also increases, then stronger electrostatic interactions between membrane and solutes are expected, and then higher retention in diluted solution should be observed. It is reported that the retention of acetic acid increased from nearly 0% at pH 2.9 to more than 90% when the solution pH increased to 9.1 at acetic acid concentration of 5g/L (about 83 mM) [START_REF] Weng | Separation of acetic acid from xylose by nanofiltration[END_REF]. Similar results are reported by other authors [START_REF] Choi | A study on the removal of organic acids from wastewaters using nanofiltration membranes[END_REF][START_REF] Han | Nanofiltration of model acetate solutions[END_REF]. Those observations suggested that in diluted solutions, the retention of small monovalent organic acids with MW lower than MWCO of the membrane is mainly fixed by charge effect.

Retention observed for a weak electrolyte solution can be considered as the combination of the retentions of undissociated and dissociated form, and the proportion of those two forms are determined by dissociation constant and solution pH. Then, if the retentions of those two forms as a function of solution pH are acquired individually, the retention of the solute can be estimated by their proportion at different solution pH according to the dissociation constant (Ka). It is reported that the mass transfer parameter of undissociated lactic acid is independent of solution pH, while the mass transfer parameter of dissociated lactic acid linearly increases with pH. The retention of lactic acid at different pH can be simulated from those two parameters [START_REF] Timmer | Transport of lactic acid through reverse-osmosis and nanofiltration membranes[END_REF]. However, the authors only investigated a short range of pH values (2.88 to 4.93), and the influence of ionic concentration is not discussed.

Besides the weak electrolyte in the solution, the functional groups at the membrane surface can be dissociated when pH changes. It is suggested that an effective dissociation constant (Keff) can be used to describe the dissociation of membrane functional groups [START_REF] Wamser | Detection of Surface Functional Group Asymmetry in Interfacially-Polymerized Films by Contact Angle Titrations[END_REF]. The pKeff values for various polyamide films are reported as 5 to 9 [START_REF] Wamser | Detection of Surface Functional Group Asymmetry in Interfacially-Polymerized Films by Contact Angle Titrations[END_REF]. Thereafter, the concentration of membrane functional groups at the membrane surface is reported to be determined by heavy ions probes, and the dissociation constant of membrane is simulated [START_REF] Coronell | Quantification of Functional Groups and Modeling of Their Ionization Behavior in the Active Layer of FT30 Reverse Osmosis Membrane[END_REF][START_REF] Tiraferri | Direct quantification of negatively charged functional groups on membrane surfaces[END_REF].

As previously introduced, the retention of small weak acids in dilute solution depends on the dissociation of solute as well as the dissociation of membrane. Thus, it is expected to observe an increase of the retentions of weak acids with solution pH following an S-shaped dissociation curve.

This S-shaped retention curve was observed in the retention of sulfamethoxazole and ibuprofen by a loose NF membrane [START_REF] Nghiem | Role of electrostatic interactions in the retention of pharmaceutically active contaminants by a loose nanofiltration membrane[END_REF], as well as nanofiltration of succinic acid [START_REF] Khunnonkwao | A two steps membrane process for the recovery of succinic acid from fermentation broth[END_REF] and sulfuric acid [START_REF] Szoke | Characteristics of thin-film nanofiltration membranes at various pH-values[END_REF][START_REF] Schaep | Salt retention of Zirfon (R) membranes[END_REF][START_REF] López | Experimental and theoretical study of nanofiltration of weak electrolytes: SO4 2-/HSO4 -/H+ system[END_REF].

The retentions of weak electrolytes in diluted solutions are strongly influenced by pH, and the variation of the retention versus pH could be linked to the dissociation constant of solute as well as the effective dissociation constant of membrane.

I.2.5 Recovery of VFAs using nanofiltration

Aliphatic acids, such as formic and acetic acids are considered as toxic components during many fermentation processes [START_REF] Nguyen | Assessing nanofiltration and reverse osmosis for the detoxification of lignocellulosic hydrolysates[END_REF][START_REF] Maiti | Modeling of the separation of inhibitory components from pretreated rice straw hydrolysate by nanofiltration membranes[END_REF]. The attempt to use NF for the removal of acetic acid from fermentation broth is reported in an industrial scale application in 1996 [START_REF] Han | Downstream processing of acetate fermentation broths by nanofiltration[END_REF]. High retention (99%) of glucose while low retention (60%) of acetic acid was achieved as 30 ℃, pH 5.6 and acetate concentration of 20g/L [START_REF] Han | Downstream processing of acetate fermentation broths by nanofiltration[END_REF]. Then many other reports also showed that NF can remove acetic acid from fermentation broth and keep sugars in the retentate at the same time [START_REF] Nguyen | Assessing nanofiltration and reverse osmosis for the detoxification of lignocellulosic hydrolysates[END_REF][START_REF] Maiti | Modeling of the separation of inhibitory components from pretreated rice straw hydrolysate by nanofiltration membranes[END_REF]. Based on the knowledge that VFAs can inhibit many fermentation processes, the continuous removal of VFAs from fermentation broth can be beneficial for the fermentation. An attempt is reported that the regular extraction of VFAs from the fermentation broth by NF can significantly decrease the total acid concentration in the fermentation broth, even though the improvement of VFAs yield is not significant from the control (without extraction) [START_REF] Xiong | Integrated acidogenic digestion and carboxylic acid separation by nanofiltration membranes for the lignocellulosic carboxylate platform[END_REF].

The demands for the separation between VFAs are raises since recently. Separation of volatile fatty acids is a difficult task for membrane processes since they have similar molecular weight, similar pKa, same structure, and same charge. So far, several articles were published recently using nanofiltration to separate acetic acid from propionic and butyric acids [START_REF] Xiong | Integrated acidogenic digestion and carboxylic acid separation by nanofiltration membranes for the lignocellulosic carboxylate platform[END_REF][START_REF] Zacharof | Recovery of volatile fatty acids (VFA) from complex waste effluents using membranes[END_REF][START_REF] Choi | A study on the removal of organic acids from wastewaters using nanofiltration membranes[END_REF][START_REF] Zacharof | Nanofiltration of treated digested agricultural wastewater for recovery of carboxylic acids[END_REF][START_REF] Ragaini | Separation of some light monocarboxylic acids from water inbinary solutions in a reverse osmosis pilot plant[END_REF].

The main results are presented in Table I-6.

According to those publications, Different kinds of Nanofiltration membranes either self-made or commercial produced have been tested, synthetic solutions and real fermentation broth have been used, the concentration of single VFA differ from 1mM to 100mM, the mixture of VFAs have a wide ratio and contain several kinds of salts concentrated from 0 to 120mM. Broad operation conditions have also been applied, as pH from 3 to 11 and pressure form 1.3 to 24 bar.

From the results shown in Table I-6, it can be concluded that the retention of VFAs differs amongst different membranes. However, operating conditions can have a much more significant influence on the retention of VFAs than the influence of different NF membranes. As shown in the table, when pH and operating pressure change, the retention of VFAs can differ from close to 0% (at pH close to 3 and low pressure) to higher than 90% (at pH higher than 7 and high pressure).

The composition and salts concentration can also have an influence on VFAs retention. However, based on the results reported, it is not possible to predict the NF performances on VFAs for different conditions. Therefore, further investigations are needed.

As previously mentioned, applications of VFAs can either require shorter chain VFAs (i.e., acetic acid) for nutrient removal, energy, and biofuel or need longer chain VFAs (i.e., butyric acid)

for bio-plastics. Then, the separation of acetic and butyric acids can be beneficial for both applications. According to the retentions of acetic and butyric acids reported in mixed solutions, the separation factor (as previously defined, 𝑆𝑆 𝑓𝑓 = 1-𝑅𝑅 𝑎𝑎 1-𝑅𝑅 𝑏𝑏 , 𝑅𝑅 𝑎𝑎 < 𝑅𝑅 𝑏𝑏 , the separation factor is always higher than one) calculated for different conditions are given in Table I-7. It is shown that except for ref. [START_REF] Xiong | Integrated acidogenic digestion and carboxylic acid separation by nanofiltration membranes for the lignocellulosic carboxylate platform[END_REF], the separation coefficient values between acetic acid and butyric acid are lower than 1.72. Therefore, the selectivity of NF for VFAs separation still needs to be improved.

I.3 Aims and outlines of the thesis

The thesis project is part of the RECOWER project. The RECOWER project, which is the abbreviation of pRocEss COupling fermentation and separation for solid WastE valoRization, is one of the five projects funded by 3BCAR Carnot Institute in 2017 with a duration of 36 months. As previously mentioned, the composition of the feed, solution pH, as well as the inorganic and organic impurities present in the broth are of great importance for the performance of nanofiltration. The subsequent investigation should consider those factors. The main objective of this thesis is to investigate the influence of those factors on the performance of nanofiltration process, estimate the separation performance, and propose the possible applications of fermentation broth using nanofiltration. The following chapters will discuss the aforementioned factors separately, and then the real fermentation broth which could be influenced by all those factors will be addressed.

The material and methods used are presented in Chapter II.

In The influence of the co-existing inorganic anions and cations on the separation performance of NF on VFAs at pH 8 is discussed in Chapter IV. The co-ions competition between anions (VFAs -, Cl -, and SO4 2-) and between cations (Na + and Ca 2+ ) is carefully discussed at different compositions. Then, the influence of divalent cations on VFAs retention is also studied. This chapter extended the objectives in Chapter III to the more complex solutions, the influence of the feed composition on electrolytes retentions is deeply discussed.

Chapter V studies the impact of the pH on the retention of VFAs, both in single solutions and mixed solutions. Synthetic solutions at in single, binary, and ternary solutions with different concentrations at pH range from 3 to 8 are investigated, the dissociation of VFAs as well as membrane functional groups are discussed. Then a model is proposed to describe the retention of VFAs in synthetic solutions versus pH at different total concentrations.

The application of the nanofiltration process for the synthetic and real fermentation broths is reported in Chapter VI. Two NF membranes are used for the treatment of synthetic and real fermentation broths; the pH of the real fermentation both is adjusted in order to improve the selectivity of the NF process. This Chapter will discuss the possible influence of unknown organic impurities for the retention mechanism of VFAs, then can give experimental references for the feasibility of the NF process for the application of VFAs containing streams.

This chapter listed all the chemicals and instruments used in this project. The properties of the membranes used are also given. Then, the methods used to characterize the membrane properties and collect the experimental data are provided. The compositions of the solutions used for several investigations are listed separately. Finally, the treatment of those experimental data is also provided in detail.

II.1 Chemicals

The chemicals used for the experimental investigation including three VFAs (acetic, propionic, and butyric acids) and VFAs sodium salts (sodium acetate, sodium propionate, sodium butyrate), as well as three inorganic salts (Na2SO4, NaCl, and CaCl2). The VFAs and VFAs sodium salts were provided by Acros organics, with more than 99% of purity. The characteristics of the VFAs, VFAs sodium salts, and inorganic salts were listed in Table II The concentrations of salts were measured by ion chromatography (IEC, Dionex, France). The characteristics of the ion chromatography system are listed in Table II-5. Samples were diluted to a maximum of 1000 folds by ultra-pure water before analysis (all samples with high concentrations were diluted to the concentration range from 0.5 mM to 5 mM). For the real fermentation broth, the concentration of total organic carbon (TOC) was measured by TOC Shimadzu 5050A. The details of the TOC analyzer were listed in Table II-6. (TC: Total carbon; IC: inorganic carbon; TOC: the difference of TC and IC.) The samples were diluted to a maximum of 25 folds before analysis (all samples with a high concentration of TOC were diluted to the concentration range from 50 mg.L -1 to 200mg.L -1 ). The pure water permeability and the retention of 100mM of glucose solution of NF-45 and XLE membranes are given in Figure II-1. The experimental points were fitted using a model proposed by Timmer et al. [START_REF] Timmer | Transport of lactic acid through reverse-osmosis and nanofiltration membranes[END_REF] as follows.

𝑅𝑅 𝑖𝑖 = 𝑅𝑅 𝑠𝑠𝑖𝑖 ×𝐽𝐽 𝐽𝐽+𝐵𝐵 𝑠𝑠𝑖𝑖 (II.1)
In this equation, 𝐵𝐵 𝑠𝑠𝑖𝑖 is the mass transfer parameter of solute i and 𝑅𝑅 𝑠𝑠𝑖𝑖 is the rejection parameter of solute i. 𝐽𝐽 is the filtration flux. 𝐵𝐵 𝑠𝑠𝑖𝑖 and 𝑅𝑅 𝑠𝑠𝑖𝑖 were experimentally obtained by fitting.

In the following chapters, individual solute retention and global retention are also fitted using the same model.

Besides, Eq. (II.1) also gives the variation of solute retention versus filtration flux. Then, the retention of solute at a specific filtration flux can be calculated from the fitted function.

It is shown that the pure water permeability of XLE membrane (1.5×10 -6 m•s -1 •bar -1 ) is lower than NF-45 membrane (2.0×10 -6 m•s -1 •bar -1 ). Then the glucose retention of XLE membrane is nearly 99.9% at high filtration flux, much higher than that of NF-45 (92%). This observation indicates that XLE membrane is much tight than NF-45 membrane, and a much higher VFAs retention is expected.

The current project was aimed to reveal the solutes transfer mechanism, larger retention variation is beneficial for the comparison of different operating conditions. Therefore, most of the experiments were done by NF-45 membrane, while XLE membrane was used for verification and comparison between two types of membranes. The total volume of the cell was 400mL, the dead volume (volume of porous disc and tube) of this system is about 4 cm 3 . The stirring speed was set at 108 rpm. A piece of NF-45 or XLE membrane was placed at the bottom of the cell, supported by a 316L stainless steel porous disc.

The active membrane surface was 30 cm 2 . Pressurized air was used to pressurize the cell. The pressure was controlled manually by a valve. Filtration was operated at room temperature (between 20 and 27℃). For each experiment, 400 mL of solution was initially fed into the cell. Then, the pressure was increased step by step (4, 8, 12, 16, 20 bar). In order to thoroughly rinse the entire system, a volume of 20 cm 3 feed was required to pass through the membrane (collected in the beaker) at the initial transmembrane pressure, then 1-2 cm 3 of permeate was collected by a disposable polyethylene bottle as a sample.

Increase transmembrane pressure to the next pressure value, a volume of 8 cm 3 permeate was needed to rinse the membrane and tube before taking a sample for this pressure.

For each transmembrane pressure, 3 cm 3 of permeate was collected in the beaker to stabilized the filtration flux, then, from 3 cm 3 to 8 cm 3 , the permeate was timed and measured three times by a timer and an electronic balance, the filtration flux obtained was the average of the three filtration flux calculated from the time and weight records of the permeate.

For each experiment, approximatively 60mL of permeate was collected in total. It means that in the worst case, the concentration factor would be equal to 1. In addition to pure water permeability, retention of glucose (molecular weight: 180g.mol -1 )

was used as a reference to detect any membrane modification during the experiments. In this work, once an abnormally pure water permeability was detected (more than 20% difference between two consecutive permeability measurements) or one piece of membrane was used over one month, rejection of Glucose will be tested, to have a reference for membrane damage as well as fouling.

Once a membrane sample presents visible mechanical damage or a significant increase or decrease of Glucose rejection (more than 5%), it was being replaced by a new one.

Four pieces of NF-45 membrane and two pieces of XLE membrane are used in this thesis project. No fouling was observed for all the pieces of membranes used, all the membrane changes were due to mechanical damage, contamination, or exposed in the air and completely dried.

For NF-45 membrane, the pure water permeability was between 1.6×10 -6 m•s -1 •bar -1 and 2.0×10 -6 m•s -1 •bar -1 for all the four pieces of membrane. The glucose retentions for the four pieces of membranes were within 90% to 93% at a transmembrane pressure of 20 bar. For XLE membrane, the pure water permeability was between 1.5×10 -6 m•s -1 •bar -1 and 1.9×10 -6 m•s -1 •bar - 1 , and the glucose retentions were higher than 99.5% at a transmembrane pressure of 20 bar.

II.4 Experimental procedures

The experimental investigation was aimed to reveal the mass transfer mechanism and separation performance of NF process on complex solutions such as fermentation broth contain

VFAs. The synthetic solutions from s1 to s12 were filtrated by NF-45 membrane. Then, to verify that if the results obtained with NF-45 membrane were repeatable for another membrane, nanofiltration of solution s9 was also carried out using XLE membrane. The experimental results obtained with these solutions were discussed in Chapter III.

II.4.2 Nanofiltration of synthetic solutions of VFAs: influence of inorganic ions

Synthetic solutions with VFAs sodium salts and three inorganic salts were used to investigate the influence of additionally charged solutes on the mass transfer of VFAs.

Since SO4 2-and Ca 2+ are divalent ions, the equivalent concentration was used during the investigation of VFAs solutions with inorganic salts. Nanofiltration of single solutions of the three inorganic salts at three ionic concentrations (100mEq.L -1 , 200mEq.L -1 , and 500mEq.L -1 ) and mixed solutions containing VFAs and three inorganic salts at two ionic concentrations (200mEq.L -1 and 500mEq.L -1 ) and six proportions (Ac/Bu binary VFAs solutions and Ac/Pr/Bu ternary VFAs solutions with the three salts at ratio of VFAs:salts at 1:1, 2:3, and 1:4 respectively) Acetate (%) [START_REF] Yuan | Improved bioproduction of shortchain fatty acids (SCFAs) from excess sludge under alkaline conditions[END_REF][START_REF] Yuan | Improved bioproduction of shortchain fatty acids (SCFAs) from excess sludge under alkaline conditions[END_REF][START_REF] Yuan | Improved bioproduction of shortchain fatty acids (SCFAs) from excess sludge under alkaline conditions[END_REF] were investigated by NF-45 membrane. The compositions of synthetic solutions are summarized in Table II-9.

The results obtained will be discussed and compared in Chapter IV. Then, to confirm the results obtained from NF-45 membrane can be extended to another membrane, the filtration of synthetic solutions of s40 was carried out using XLE membrane. The experimental results obtained with these solutions will be discussed in Chapter V. The real fermentation broth contain many organic matter/impurities (e.g., ethanol and butanol, as shown in Table II -12), could hinder the following processes. It is impossible and also not necessary to identify the compositions of those organic matter/impurities (OM), the compositions is obtained as the difference of TOC and the theoretical TOC values of the three VFAs obtained from HPLC (i.e., TOCOM=TOC-TOCVFAs). Experiments were also carried out with synthetic fermentation broths with the similar compositions and pH as the real fermentation previously mentioned, and the real fermentation broth, to investigate if the results previously obtained with synthetic solutions can be extended to a more complex system.

In order to identify the influence of each main component (Cl -, Na + , Ca 2+ , and Ethanol), synthetic fermentation broths were prepared with only VFAs, with the addition of NaCl, and with the addition of CaCl2 respectively according to the compositions of the real fermentation broth.

Table II-13 summarizes the compositions of the synthetic fermentation broths used for the experimental investigation. Synthetic broths Syn1, Syn2, and Syn3 at pH 5.7 and pH 8 were filtrated by XLE membrane, while Syn4, Syn5, and Syn6 at pH 5.7 were filtrated by NF-45 membrane.

Then, the experiments were carried out with the real fermentation broth. Nanofiltration using XLE membrane at the initial pH was firstly carried out. The real fermentation both at the initial pH (pH 5.7) used for NF-45 membrane was recycled from the retentate and permeate of the previous filtration using XLE membrane. Then, after the filtration using NF-45 membrane, the permeate and retentate were recycled again. The recycled real fermentation broth was adjusted to pH 6.6 using NaOH solution, and filtration is carried out using the pH adjusted real fermentation broth. Finally, the recycled real fermentation broth was adjusted to pH 8.2 and the last filtration is applied using NF-45 membrane.

The experiments with real fermentation broth using the two membranes are listed in Table II-14. The results obtained from synthetic and real fermentation broths by the two membranes will be compered and discussed in Chapter VI.

II.5 Data treatment

The experimental results discussed in this manuscript including filtration flux, solute retention, solute proportion, as well as separation factor, those data were acquired using the following equations.

The filtration flux was calculated via Eq. (II.2).

𝐽𝐽 = 1 𝐴𝐴 • 𝛥𝛥𝑉𝑉 𝛥𝛥𝑑𝑑 (II.2)
𝛥𝛥𝑉𝑉, total volume of water and solute permeated through the membrane within time 𝛥𝛥𝛥𝛥, (m 3 , measured by the weight of the permeate, assuming the density of the permeate equal to 1×10 6 g.m -

3 )

𝐻𝐻, effective area of the membrane (m 2 )

𝛥𝛥𝛥𝛥, duration of filtration (s), measured by a timer.

The individual solute retention was calculated from Eq. (II.3).

𝑅𝑅(%) = �1 - 𝑐𝑐 𝑖𝑖 𝑝𝑝 𝑐𝑐 𝑖𝑖 𝑓𝑓 � • 100% (II.3)
The proportion of individual solute i in the feed and permeate were calculated from Eqs. (II.4) and (II.5) respectively.

𝑃𝑃 𝑖𝑖 𝑓𝑓 = 𝑐𝑐 𝑖𝑖 𝑓𝑓 𝑐𝑐 𝑡𝑡𝑡𝑡𝑡𝑡𝑎𝑎𝑙𝑙 𝑓𝑓 = 𝑐𝑐 𝑖𝑖 𝑓𝑓 ∑ 𝑐𝑐 𝑖𝑖 𝑓𝑓 𝑛𝑛 𝑖𝑖=1 (II.4) 𝑃𝑃 𝑖𝑖 𝑝𝑝 = 𝑐𝑐 𝑖𝑖 𝑝𝑝 𝑐𝑐 𝑡𝑡𝑡𝑡𝑡𝑡𝑎𝑎𝑙𝑙 𝑝𝑝 = 𝑐𝑐 𝑖𝑖 𝑝𝑝 ∑ 𝑐𝑐 𝑖𝑖 𝑝𝑝 𝑛𝑛 𝑖𝑖=1 (II.5)
In a mixed solution contain more than three solutes, the relative proportions of solute i and j, for the couple of two solutes i and j, in the feed and permeate are given in Eqs. (II.6), (II.7), (II.8), and (II.9) respectively. Then, the ratio between the proportion of solute i in the permeate and feed was obtained from Eq. (II.10).

𝑃𝑃 𝑖𝑖_𝑖𝑖

𝑟𝑟𝑟𝑟 𝑖𝑖 = 𝑃𝑃 𝑖𝑖 𝑝𝑝 𝑃𝑃 𝑖𝑖 𝑓𝑓 (II.10) When 𝑟𝑟𝑟𝑟 𝑖𝑖 > 1, it means that solute i is enriched in the permeate. If 𝑟𝑟𝑟𝑟 𝑖𝑖 < 1, it means that solute i is impoverished in the permeate.
The separation factor (𝑆𝑆𝑆𝑆 𝑖𝑖,𝑗𝑗 ) defines the separation efficiency between two solutes, i and j, which was calculated according to Eq.(II.11).

𝑆𝑆𝑆𝑆 𝑖𝑖,𝑗𝑗 = 𝑐𝑐 𝑖𝑖 𝑝𝑝 /𝑐𝑐 𝑗𝑗 𝑝𝑝 𝑐𝑐 𝑖𝑖 𝑓𝑓 /𝑐𝑐 𝑗𝑗 𝑓𝑓 = 𝑝𝑝 𝑖𝑖 𝑝𝑝 /𝑝𝑝 𝑖𝑖 𝑓𝑓 𝑝𝑝 𝑗𝑗 𝑝𝑝 /𝑝𝑝 𝑗𝑗 𝑓𝑓 = 𝑟𝑟𝑟𝑟 𝑖𝑖 𝑟𝑟𝑟𝑟 𝑗𝑗 (II.11)
Depends on the values of 𝑟𝑟𝑟𝑟 𝑖𝑖 and 𝑟𝑟𝑟𝑟 𝑗𝑗 , the separation factor could be in between 0 to 1 (when 𝑟𝑟𝑟𝑟 𝑖𝑖 < 𝑟𝑟𝑟𝑟 𝑗𝑗 ) or from 1 to ∞ (when 𝑟𝑟𝑟𝑟 𝑖𝑖 > 𝑟𝑟𝑟𝑟 𝑗𝑗 ). In this manuscript, to keep the calculated separation factor between two solutes always higher than 1, the separation factor was calculated using the ratio between proportion in the permeate and feed of the solute which is enriched in the permeate divided by that of the one impoverished in the permeate (i.e., 𝑟𝑟𝑟𝑟 𝑖𝑖 > 𝑟𝑟𝑟𝑟 𝑗𝑗 ).

𝑟𝑟𝑟𝑟 𝑖𝑖 and 𝑆𝑆𝑆𝑆 𝑖𝑖,𝑗𝑗 calculated from proportion and relative proportions are the same.

𝑟𝑟𝑟𝑟 𝑖𝑖 ratio between the proportion of solute i in the permeate and feed 𝑟𝑟𝑟𝑟 𝑗𝑗 ratio between the proportion of solute j in the permeate and feed

Chapter III

Nanofiltration of synthetic solutions of VFAs

This chapter aims to investigate the influence of VFAs composition on the performance of nanofiltration, size and charge effects are discussed for single and mixed solutions.

As previously mentioned (Chapter I), at a neutral solution pH, the NF membrane is negatively charged. Besides the size effect, there are two charge effects on the mass transfer mechanism of charged solutes, i.e., ionic concentration induced screening effect and co-ions competition due to the interactions of more than two ions with the same sign of charge.

For a single solution, there is only the influence of ionic concentration; the solutes and membrane charge are screened when the ionic concentration increases, and then the retention decreases. However, in a mixed solution, besides the screening effect, the individual solutes retentions are also affected by co-ions competition. This phenomenon leads to the retention of the more retained solute increase while the retention of the less retained one decreases [START_REF] Kang | Removal of organic acid salts from simulated fermentation broth containing succinate by nanofiltration[END_REF]. Then,

the

III.1 Retentions of VFAs in single and mixed solutions

III.1.1 Solutes retentions in single solutions

Retentions of VFAs in single solutions (s1-s3, see Chapter II, Table II- The same tendencies are obtained for propionate (72%, 68%, and 45%) and butyrate (88%, 73%, and 55%).

At pH 8, the VFAs are in their dissociated form and negatively charged (see pKa values in Chapter II, Table 2.1). It is known that the retention of charged solutes depends on the combination of steric effects and electrostatic interactions between the charged solutes and the charged membrane. The higher retentions observed at low concentrations are mainly due to electrostatic repulsions since both VFAs and membrane are negatively charged at pH 8. Then, increasing VFAs concentrations result in lower retentions due to the screening effect [START_REF] Umpuch | Nanofiltration as a purification step in production process of organic acids: Selectivity improvement by addition of an inorganic salt[END_REF][START_REF] Nilsson | The influence of pH, salt and temperature on nanofiltration performance[END_REF].

On the other hand, one can observe that the retentions of VFAs follow a sequence of acetate<propionate<butyrate, in agreement with their molecular weights (acetate, 59 g.mol -1 , propionate, 73 g.mol -1 and butyrate, 87 g.mol -1 ). Comparable result was previously reported with other carboxylic acid salts at the same concentration (100 mM) with the following sequence for the solutes retentions: formate (45 g.mol -1 ) < acetate (59 g.mol -1 ) < lactate (89 g.mol -1 ) [START_REF] Kang | Removal of organic acid salts from simulated fermentation broth containing succinate by nanofiltration[END_REF]. Retentions of acetate and propionate decrease from 74% and 82%, for a total concentration of 100 mM, to 51% and 68%, at 200 mM, and to 30% and 50% respectively for a total concentration of 500 mM. As previously mentioned for single solutions, the influence of the total concentration on individual solutes retentions is due to the screening effect. Then, one can notice that the retention of propionate is higher than that of acetate, following the molecular weight, for any total concentration and that the retention difference between acetate and propionate increases with the total concentration.

The same trends are observed with binary solutions of acetate and butyrate (acetate: Since the retention mechanism of nanofiltration is a combination of size and charge, it is expected that the retention of solutes with the same charge decreases for increasing molecular weight. Indeed, this was previously observed during NF of single solutions of formate (46.03 g.mol -1 ), acetate (60.05 g.mol -1 ), and lactate (90.08 g.mol -1 ) at a given concentration, with various membranes, NF1, NF2 and NF270 [START_REF] Zaman | New polymeric membrane nanofiltration for succinate recovery: a comparative study[END_REF]. However, contradictory results have also been reported

for different membranes and more complex solutions. For instance, for given operating conditions (dead-end nanofiltration, transmembrane pressure 15 bar, total concentration 50mM and pH 8.25), it was observed that with HL and NF270 membranes the retention of acetate is lower than that of butyrate, whereas the reverse is obtained with DK, DL, and LF10 membranes [START_REF] Zacharof | Nanofiltration of treated digested agricultural wastewater for recovery of carboxylic acids[END_REF]. The retentions of carboxylic acids contained in a real digestion liquor, a more complexed solution, during cross-flow nanofiltration using DL and DK membranes were also reported. They were compared with the retentions obtained with single or mixed synthetic solutions. It was observed that the retention of butyric acid during NF of the digestion liquor was much higher (close to 100%) than that observed with synthetic solutions. On the other hand, on the contrary to the molecular weight sequence, higher retention of acetate was obtained compared to that of propionate (at pH 7). However, the explanation was not identified [START_REF] Xiong | Integrated acidogenic digestion and carboxylic acid separation by nanofiltration membranes for the lignocellulosic carboxylate platform[END_REF]. Firstly, one can observe that the retention differences between individual VFAs in mixed and single solutions decrease when the filtration flux increases. The retentions in mixtures (binary and ternary solutions) are different from those obtained with single solutions. Indeed, for most of the cases, it seems that the retention of the less retained solute (Ac) in the mixture decreases compared to that in a single solution, while the retention of the more retained solute (Bu) increases compared to that in a single solution. Furthermore, the increase and decrease are more significant at high concentrations and low filtration flux. For Pr, the VFA has retention in-between of Ac and Bu, its retention can be either higher or lower compared to single solution. No clear trend at different compositions can be drawn.

These results are in agreement with previous ones concerning the retention of monovalent and divalent organic acid salts of various molecular weight in single solutions and mixtures (formate, acetate, lactate, and succinate). Indeed, it was also reported that the retention of the most retained solute, succinate, was higher in the binary mixtures than in the single solutions. Meanwhile, the retentions of the less retained acid salts, formate, acetate, and lactate, decreased significantly in the presence of succinate and even reached negative values under certain conditions. The extent of decline of monovalent acid salt retentions followed the sequence: formate>acetate>lactate [START_REF] Kang | Removal of organic acid salts from simulated fermentation broth containing succinate by nanofiltration[END_REF]. This trend, i.e., increase of the retention of the more retained solute and decrease of the less retained solute, was mentioned as "distribution effect" [START_REF] Kang | Removal of organic acid salts from simulated fermentation broth containing succinate by nanofiltration[END_REF] or "co-ions competition" [START_REF] Luo | Effects of pH and salt on nanofiltration-a critical review[END_REF][START_REF] Li | Separation Of (L)-glutamine from fermentation broth by nanofiltration[END_REF]. For binary solutions of Ac/Pr and Ac/Bu, one can observe that when the proportion of the less retained solute (acetate) decreases from 50% to 20%, the retentions of both VFAs tend to decrease.

This decrease is more pronounced for the binary solution of Ac/Pr than for that of Ac/Bu (Figure

III-11a).

Different authors suggested that the concentration ratio between the co-ions is one of the major factors influencing the retention decrease of the less retained solute [START_REF] Khunnonkwao | A two steps membrane process for the recovery of succinic acid from fermentation broth[END_REF][START_REF] Nilsson | The influence of pH, salt and temperature on nanofiltration performance[END_REF]. For instance, during nanofiltration of a mixed solution of Na2SO4 and NaNO3, a decrease of the NO3 -retention was observed for an increasing concentration ratio of SO4 2-/NO3 -in the feed [START_REF] Nielsen | Bulk-phase criteria for negative ion rejection in nanofiltration of multicomponent salt solutions[END_REF]. Similar results were observed for the retention of acetate in a succinate/acetate binary solution, i.e. a decrease of acetate retention for increasing succinate/acetate ratio [START_REF] Khunnonkwao | A two steps membrane process for the recovery of succinic acid from fermentation broth[END_REF].

As previously explained, this phenomenon, called "co-ions competition" [START_REF] Luo | Effects of pH and salt on nanofiltration-a critical review[END_REF] or "distribution effect" [START_REF] Kang | Removal of organic acid salts from simulated fermentation broth containing succinate by nanofiltration[END_REF], is due to the "competition" or "distribution" of the co-ions.

Current observation at high concentration and low filtration flux is in agreement with previous research, showing that for binary mixtures increase the proportion of more retained solute (or decrease the proportion of less retained one) makes the retention of the less retained solute decrease [START_REF] Khunnonkwao | A two steps membrane process for the recovery of succinic acid from fermentation broth[END_REF][START_REF] Nielsen | Bulk-phase criteria for negative ion rejection in nanofiltration of multicomponent salt solutions[END_REF][START_REF] Umpuch | Nanofiltration as a purification step in production process of organic acids: Selectivity improvement by addition of an inorganic salt[END_REF][START_REF] Kang | Removal of organic acid salts from simulated fermentation broth containing succinate by nanofiltration[END_REF][START_REF] Su | Rejection of ions by NF membranes for binary electrolyte solutions of NaCl, NaNO3, CaCl2 and Ca(NO3)2[END_REF].

III.2 Solute transfer in mixed solutions

III.2.1 Proportions of VFAs in the permeate

The aim of NF process on VFAs separation is to change the VFAs proportion between the feed and permeate. Therefore, the comparison of VFAs proportion in the permeate at different compositions and operating conditions can give guidance for further separation. For all the concentrations investigated, one can observe that the proportion of the less retained solute in the permeate increases when the filtration flux increases, and reaches a plateau (namely Pi * ) when the filtration flux is higher than a certain value. This is the case for Ac in Ac/Pr, Ac/Bu, and Ac/Pr/Bu mixtures and for Pr in Pr/Bu mixture. At the same time, the proportion of the more retained solute decreases as the filtration flux increases, then remains nearly constant at high filtration flux. This is the case for Pr in Ac/Pr mixture and Bu in Ac/Bu, Pr/Bu, and Ac/Pr/Bu mixtures. For the ternary mixture Ac/Pr/Bu, the proportion of Pr, which has a retention between the ones of acetate and butyrate, decreases slightly compared to that in the feed (from 33% to 31%).

Then, comparing the results obtained with binary and ternary solutions, the proportion of Ac increases 9%, 16%, and 15% in Ac/Pr, Ac/Bu and Ac/Pr/Bu solutions respectively, the proportion of Bu decreases 16%, 8%, and 12% in Ac/Bu, Pr/Bu and Ac/Pr/Bu solutions respectively. This observation indicate that the existence of other co-ions has a significant influence on the ionic proportions in the permeate. Thus, the higher the difference between solutes' retentions in single solutions, the higher the difference between solutes proportions in the permeates of mixtures.

For mixed solutions with different proportions (Ac: Pr = 20% :80%, Ac: Bu = 20% :80%, Ac:

Pr: Bu = 20%: 20% :60%, Ac: Pr: Bu = 20%: 60% :20%, and Ac: Pr: Bu = 60%: 20% :20%), the same tendencies can be also observed (shown in Figure .

Those results indicate that, for a given proportion in the feed, regardless of the concentration, one fixed solute proportion (𝑃𝑃 𝑖𝑖 𝑝𝑝 * ) is found in the permeate when the filtration flux is higher than a certain value. The previous results show that the proportion of VFA in the permeate at low filtration flux is not the same as that obtained at high filtration flux.

As an example, the proportion differences of Ac and Bu to the constant values (𝑃𝑃 𝑖𝑖 𝑝𝑝 * -𝑃𝑃 𝑖𝑖 𝑝𝑝 ) for ternary solutions (Ac:Pr:Bu=33%:33:33%) at a total concentration of 100, 200, and 500 mM is given in Figure III-14. Results for Pr are not shown due to that the difference is too small (from 33% in the feed to 31% in the permeate at the plateau value).

Figure III-14

The proportion difference to the constant values (proportion difference = 𝑃𝑃 𝑌𝑌 𝑝𝑝 * -𝑃𝑃 𝑌𝑌 𝑝𝑝 ) for ternary solutions (Ac:Pr:Bu=33%:33:33%) at total concentration of 100, 300, and 500 mM, using NF-45 membrane, at pH 8.

It is shown that the total concentration has an influence on the proportion of VFAs in the permeate at low filtration flux. One can also observe that the higher the concentration, the higher The proportions in the feed and the proportion in the permeate obtained for high filtration flux (the plateau values, 𝑃𝑃 𝑖𝑖 𝑝𝑝 * ) are given to compare the separation performance. The ratio between proportion in the permeate and feed is calculated for each VFA, then the separation factors between every two VFAs are determined (as defined in Chapter II). In fact, the separation factor between two VFAs is the ratio of the two VFAs in the permeate divided by the ratio of the two VFAs in the feed. The results for all the feed proportions are listed in Table III-1. The comparison of the results in Table III-1 with three solutes is complicated. Ternary figures are drawn to visualize the results and see if a general trend can be drawn. For Ac, it is observed that the contour lines representing the Ac proportion in the feed (grey dashed lines parallel to the axis of Bu) are always lower than the contour lines representing the Ac proportion in the permeate (solid black lines). This indicates that the proportion of Ac in the permeate is always higher than the proportion of Ac in the feed. Moreover, the contour lines representing the Ac proportions in the feed and permeate are not parallel, the more difference being obtained at the Ac axis, while the less difference is obtained at the Pr axis. This means that for a given Ac feed proportion, the presence of Bu makes the proportion of Ac in the permeate decrease more than the presence of Pr.

For Bu, the contour lines representing the Bu proportion in the feed (grey dashed lines parallel to the axis of Pr) are always higher than the contour lines representing the Bu proportion in the permeate (solid black lines). This indicates that the proportion of Bu in the permeate is always lower than that in the feed. Again, the contour lines represent the proportions in the feed and permeate are not parallel, the two types of contour lines show more difference at the Ac axis, while show less difference between each other at the Bu axis. This means that for a given Bu feed proportion, the presence of Ac make the proportion of Bu in the permeate increase more than the presence of Pr.

However, for Pr, the contour lines representing the Pr proportion in the feed (grey dashed lines parallel to the axis of Ac) crossover the contour lines representing the Pr proportion in the permeate (solid black lines). This indicates that the proportion of Pr in the permeate is lower than that in the feed on the right side of the triangle, while it is higher than that in the feed on the left side of the triangle. The conditions for which observe the permeate proportions equals to the feed proportions are shown on the purple dashed line. One can observe that the highest values of the separation factors for Ac/Pr, Pr/Bu, and Ac/Bu occur for the ternary solution with identical proportions in the feed (Ac:Pr:Bu=33%:33%:33%).

It decreases the more as the proportions are different. For binary solutions (Ac/Pr and Ac/Bu), the same trend is observed, the higher separation factors are observed for the solutions with identical proportions (Ac:Pr=50%:50% and Ac:Bu=50%:50%). This result indicates that when the proportion differ from equal proportion condition, the separation performance decreases.

III.2.2 Solute transfer in mixed solutions

The proportion of solute i in the permeate is defined as Eq. (III.1).

𝑃𝑃 𝑖𝑖 = 𝑐𝑐 𝑖𝑖 𝑝𝑝 𝑐𝑐 𝑠𝑠 𝑝𝑝 = 𝑐𝑐 𝑖𝑖 𝑝𝑝 ∑(𝑐𝑐 𝑖𝑖 𝑝𝑝 ) (III.1)
The individual solute flux is defined as Eq. (III.2).

𝐽𝐽 𝑖𝑖 = 𝐽𝐽 𝑤𝑤 𝑐𝑐 𝑖𝑖 𝑝𝑝 (III.2)
The total solute flux is the sum of all the solute flux in the mixture, shown in Eq. (III.3).

𝐽𝐽 𝑠𝑠 = 𝐽𝐽 𝑤𝑤 𝑐𝑐 𝑠𝑠 𝑝𝑝 = ∑ 𝐽𝐽 𝑖𝑖 = ∑(𝐽𝐽 𝑤𝑤 𝑐𝑐 𝑖𝑖 𝑝𝑝 ) (III.3)
Then, Eq. (III.1) can be rewritten as Eq. (III.4).

𝑃𝑃 𝑖𝑖 = 𝑐𝑐 𝑖𝑖 𝑝𝑝 𝑐𝑐 𝑠𝑠 𝑝𝑝 = 𝑐𝑐 𝑖𝑖 𝑝𝑝 ∑(𝑐𝑐 𝑖𝑖 𝑝𝑝 ) = 𝐽𝐽 𝑤𝑤 𝑐𝑐 𝑖𝑖 𝑝𝑝 ∑(𝐽𝐽 𝑤𝑤 𝑐𝑐 𝑖𝑖 𝑝𝑝 ) = 𝐽𝐽 𝑖𝑖 𝐽𝐽 𝑠𝑠 (III.4)
Therefore, the proportion of solute i in the permeate also represents the contribution of solute i to the total solute transfer.

For electrolyte solutions, 𝐽𝐽 𝑠𝑠 represents the total amount of charge transferred through the membrane, 𝑃𝑃 𝑖𝑖 represents the contribution of ion i to the charge transfer. It is shown that whatever the conditions, the individual solute flux increases with the total solute flux and that this variation is linear, the coefficient of determination (R 2 ) of the linear approach is higher than 0.997. The individual solute flux versus total solute flux for mixtures at different concentrations and proportions are given in Figure III-18. For all the conditions investigated, the coefficient of determination (R 2 ) of a linear approach is higher than 0.996.

According to Eq. (III.4), the slope of each linear fitting represents the contribution of one given solute to the total solute transfer, that is the proportion of the given solute in the permeate.

For binary solutions with identical proportion in the feed, on the one hand, Ac contributes 59%

to the total solute transfer in the presence of Pr, increases to 66% when coupled with Bu. On the other hand, Bu contributes only 34% to the total solute transfer when Ac is present, this contribution increases to 43% when coupled with Pr. The contribution of Pr to the total solutes transfer increases from 41% in the presence of Ac to 57% in the presence of Bu.

For binary solutions with different proportions, for instance, Ac/Pr binary solutions with Ac:Pr at 50%:50% and 20%:80%, increasing the feed proportion of Pr from 50% to 80%, the contribution of Ac to the total solutes transfer decreases from 59% to 26%. The same tendency can be found for Ac/Bu binary solutions with Ac:Bu at 50%:50% and 20%:80%. Increasing the feed proportion of Bu from 50% to 80% leads to the decrease of Ac contribution to the total solute transfer from 66% to 31%.

For ternary solutions, the contribution of Ac to the total solute transfer increases from 26% for Ac:Pr:Bu=20%:60%:20%, 31% for Ac:Pr:Bu=20%:20%:60%, 45% for Ac:Pr:Bu=33%:33%:33%, to 72% for Ac:Pr:Bu=60%:20%:20%.

In general, for binary solutions, one can observe that the contribution of Ac to the total solute flux (i.e., the proportion in the permeate) is higher than its proportion in the feed, and that the contribution of Bu for the transfer of the total solutes is lower than its proportion in the feed. The contribution of Pr for the mass transfer is depended on the existence of the other VFAs. When coupled with Ac, the least retained VFA, the contribution of Pr decreases, and in the presence of Bu, the most retained VFA, the contribution of Pr increases, compared to its proportion in the feed.

In the ternary solution, when both Ac and Bu are present, the contribution of Pr for the transfer of the total solutes shows a slight decrease compared to its proportion in the feed except for Ac:Pr:Bu=20%:20%:60%.

The individual contributions of VFAs to the total solutes transfer through the membrane at different feed proportions show the mechanism of co-ions competition. Indeed, in a binary solution with two co-ions, for a given charge flux, the less retained co-ion contributes more to the charge flux, while the more retained one contributes less to the charge flux. The contribution of each co-ions, which represents its proportion in the permeate, depends on their proportions in the feed. When the feed proportion of the more retained co-ion increases, the contribution of the less retained one needs to decrease in order to maintain the same total amount of charge transfer, and vice versa.

III.2.3 Solute transfer with XLE membrane

It was previously observed that despite the change in concentration, the proportion of VFAs in the permeate remains the same for a given feed proportion when the filtration flux is higher than a specific value. This finding could be unique for the NF-45 membrane or universal for different NF membranes. Then, an additional membrane, XLE membrane is tested to verify the finding previously mentioned.

III.2.3.1 Individual solutes retentions in ternary solutions

The retentions of VFAs ternary solutions (Ac:Pr:Bu=33%:33%:33%) at three total concentrations (100, 200, and 250mM) by XLE membrane are given in Figure III-19. The result at 500mM is not obtained due to a too low filtration flux, then, instead of 500mM, the total concentration of 250mM is used.

It is observed that the retentions of VFAs at different total concentrations observed similar retention at the same filtration flux. when the filtration flux is higher than 0.25 ×10 -5 m.s -1 , the retentions of all the VFAs are higher than 97%. Even though the differences of VFAs retentions are very small, one can observe that the retention sequence is Ac<Pr<Bu, following their MWs.

This observation is in agreement with the result observed using NF-45 membrane. .s -1

) total solute flux (×10 -6 mol.m -2 .s -1 )

Despite that the solute concentration in the permeate of XLE membrane is very low, one can still observe that, when the filtration flux increases, the proportion of Ac in the permeate increases while the proportion of Bu decreases, reach a plateau at 43% and 27% respectively when the filtration flux is higher than a certain value. The permeate proportion of Pr slightly decreases from 33% to 30%.

Furthermore, it is shown that this filtration flux required for the permeate proportion to reach constant value (lower than 0.1 × 10 -5 m.s -1 ) is much lower than that observed for NF-45 membrane (about 0.5×10 -5 m.s -1 ). It seems that concentration does not have a significant influence on the filtration flux required to reach the constant proportion for XLE membrane. One can observe that the individual solutes flux increase linearly when the total solute flux increases, the coefficient of determination (R 2 ) of the linear approach is higher than 0.997.

In general, the experimental results observed for XLE membrane are in agreement with that are obtained using NF-45 membrane. It is also noticed that, even for a tight membrane that has a

VFAs retention much higher NF-45 membrane, for the same feed proportion (Ac:Pr:Bu=33%:33%:33%), the permeate observed similar proportions (Ac:Pr:Bu at 48%:31%:22% and 43%:30%:27% using NF-45 and XLE membrane respectively), as showed in Figure III-21.

This finding deserved further investigation.

III.3 Conclusion

The understanding of the mass transfer mechanism of complex solutions (i.e., solutions having more than 2 co-ions) was pointed out as one of the most important prospects for the application of NF process [START_REF] Mohammad | Nanofiltration membranes review: Recent advances and future prospects[END_REF]. The co-ions competition phenomenon is frequently observed during the nanofiltration of mixed electrolyte solutions. Some trends were reported, showing that the solution concentration, as well as solutes proportions, can influence the individual solute retention.

However, the mechanism was not clear.

In this Chapter, it was observed that the retention of the more retained solute increases compared to that in single solution, while that of the less retained one decreases. This is in agreement with previous reported results.

A general trend was observed regarding the variation of the VFAs proportions in the permeate versus filtration flux. When the filtration flux is higher than a specific value, the proportion of solutes in the permeate remains constant, regardless the change in total concentration. However, the filtration flux required to reach this plateau value depends on the total concentration. Moreover, it was found that in the mixed solutions, the individual solute transfer is controlled by the total amount of charge transferred through the membrane. Indeed, it was pointed out that the individual solute flux increases linearly with the total solute flux and does not depend on the total concentration but only on the VFAs proportions in the feed. The general trend obtained using NF-45 membrane is further checked with a second membrane (XLE membrane), and the conclusions are the same.

Furthermore, it is found that the proportion in the feed influences the separation factor between solutes. For binary solutions, the higher separation factors between Ac/Pr and Ac/Bu are observed for solutions with identical proportions (Ac:Pr=50%:50%, and Ac:Bu=50%:50% respectively).

For ternary solutions, the highest separation factors between Ac/Pr, Pr/Bu, and Ac/Bu are also obtained for solutions with identical proportions (Ac:Pr:Bu=33%:33%:33%). Moreover, the results observed for ternary solutions with identical VFAs proportion are also the highest among all the conditions (Binary and ternary solutions) investigated. This observation indicates that for mixed solutions with identical proportions, the more solutes in the solutions, the higher the separation factor between each couple of solutes.

.

Chapter IV

Nanofiltration of synthetic solutions of VFAs: influence of inorganic ions

This chapter aims to extend the investigation of solutes composition from VFAs solutions to solutions with VFAs and inorganic salts.

In the previous discussion (Chapter III), a general trend is observed for individual VFAs proportions in the permeate of mixed solutions at different concentrations and proportions. That is, the proportion of the least retained solute (Ac) in the permeate is higher than that in the feed, while the proportion of the most retained solute (Bu) in the permeate is lower than the proportion of Bu in the feed. The permeate proportion of the VFA, which has the retention in-between the two (i.e. Pr), can be either higher (with more Ac in the solution) or lower (with more Bu in the mixture) depends on the proportion.

In the current chapter, more complex solutions, containing VFAs sodium salts (acetate, propionate, and butyrate) and inorganic salts (Na2SO4, NaCl, and CaCl2) are investigated.

Synthetic solutions from single solutions of each solute at different concentrations to mixed solutions of two (Ac/Bu) or three (Ac/Pr/Bu) VFAs with inorganic salts at the ratio of VFAs: salts = 1:1, 2:3, to 1:4 at a different total concentrations are investigated. The general trend obtained in Chapter III is verified with the more complex solutions, and the influence of additional inorganic salts on the mass transfer of VFAs is explored.

In this chapter, the retentions of individual solutes in single and mixed solutions are firstly discussed. Then, the mass transfer of anions and cations is investigated, the influence of co-ions (SO4 2-, Cl -) and counter-ions (Na + , Ca 2+ ) on individual solute transfer is investigated. Furthermore, the separation of VFAs at different compositions with different inorganic salts is also discussed.

All the results discussed in the current chapter are obtained using NF-45 membrane at pH 8.

IV.1 Individual solutes retention in single solutions

Retentions of VFAs sodium salts and three inorganic salts, namely Na2SO4, NaCl, and CaCl2, decrease when the concentration increases. However, one can observe that the influence of concentration is more pronounced for NaCl, and less significant for Na2SO4, the influence of concentration on the retentions of VFAs and CaCl2 is in-between of NaCl and Na2SO4. As already observed in Chapter III, the retention sequence of VFAs is Ac<Pr<Bu. Then, it is observed that the retention sequence for the three inorganic salts is NaCl<CaCl2<Na2SO4. Put the six solutes together, the retention of Na2SO4 is higher than the retentions of VFAs, especially at high concentrations; the retentions of CaCl2 and NaCl are lower than the retentions of VFAs. Thus, for the five anions with sodium as counter-ions, the retention sequence is Cl -<Ac -<Pr -<Bu -<SO4 2-.

at
As discussed in Chapter I, the retention mechanism of NF is a combination of size and charge effects. On the one hand, the retention sequence of solutes with the same charge and counter-ions is expected to follow their sizes (which are related to their MWs and hydration). As already mentioned in Chapter III, the retention sequence of organic salts followed their MWs, for instance, it is reported that the retention sequence of three carboxylic acid sodium salts (formate (45 g.mol - 1 ), acetate (59 g.mol -1 ), and lactate (89 g.mol -1 )) follows their molecular weights (MWs) [START_REF] Kang | Removal of organic acid salts from simulated fermentation broth containing succinate by nanofiltration[END_REF].

On the other hand, charge repulsion can also play a role in the retention of ions. Retention of symmetric salts like NaCl is governed by ions with the same sign of charge as the membrane (namely, co-ions), while the retention of asymmetric salts (i.e., CaCl2 and Na2SO4) is dominated by the ions having higher valence [START_REF] Luo | Effects of pH and salt on nanofiltration-a critical review[END_REF]. In addition, the charge effect is influenced by ionic concentration. The increase of ionic concentration screens the electrostatic interactions between membrane and ions, then the charge repulsion is weakened, and the retention of ions decreases.

This phenomenon is reported as screening effect [START_REF] Khunnonkwao | A two steps membrane process for the recovery of succinic acid from fermentation broth[END_REF][START_REF] Umpuch | Nanofiltration as a purification step in production process of organic acids: Selectivity improvement by addition of an inorganic salt[END_REF].

The retention sequence found for VFAs follows their MWs. However, the retention sequence of inorganic salts with different counter-ions is more complicated. Indeed, different sequences were reported with NaCl, CaCl2, and Na2SO4 for various NF membranes [START_REF] Peeters | Retention measurements of nanofiltration membranes with electrolyte solutions[END_REF]. Except for positively charged membranes, retention of Na2SO4 is always the highest among the three. Then, for negatively charged membranes, the retention sequences of NaCl and CaCl2 are different for different membranes [START_REF] Peeters | Retention measurements of nanofiltration membranes with electrolyte solutions[END_REF]. Thereafter, further investigation showed that the retention sequence of these three salts is concentration-dependent. It is reported that the retention sequence of the two salts at 10mM is CaCl2<NaCl, then changed to NaCl<CaCl2 when concentration increases to 100mM for an ESNA 1 (Nitto Denko, Japan) membrane [START_REF] Wang | Separation performance of a nanofiltration membrane influenced by species and concentration of ions[END_REF]. Similar observations are reported for other polymeric membranes. For instance, retention sequence is CaCl2< NaCl for TFCS membrane [START_REF] Hafiane | Removal of hexavalent chromium by nanofiltration[END_REF], NF-45 membrane [START_REF] Peeters | Retention measurements of nanofiltration membranes with electrolyte solutions[END_REF], DF 10 membrane [START_REF] Wang | Role of coexistence of negative and positive membrane surface charges in electrostatic e ff ect for salt rejection by nano fi[END_REF], and NF270 membrane [START_REF] Boo | High Performance Nanofiltration Membrane for Effective Removal of Perfluoroalkyl Substances at High Water Recovery[END_REF] when concentration is within the range of 1~10 mM. The retention sequence changes as NaCl<CaCl2 for Desal DK-5 membrane [START_REF] Ren | Separation and Purification Technology Influence of inorganic salt on retention of ibuprofen by nanofiltration[END_REF][START_REF] Straatsma | Can nanofiltration be fully predicted by a model?[END_REF], and retention sequence of NaCl<MgCl2 is found for NF-45 and SU 200 membranes [START_REF] Wang | Experimental investigation on separation performance of nanofiltration membranes for inorganic electrolyte solutions[END_REF], at concentration of 100mM. In those investigations, retention of Na2SO4 remains the highest among the three salts.

The present results are obtained at an ionic concentration higher than 100mM, then the result agrees with the trend previously mentioned (NaCl<CaCl2<Na2SO4).

Based on the previously reported results, there could two possible explanations for the alteration of the retention sequence of NaCl and CaCl2 (i.e., CaCl2<NaCl at concentration lower than 10 mM and NaCl< CaCl2 at concentration higher than 100 mM). On the one hand, the membrane polymers could capture/adsorb the counter-ions, especially for alkaline-earth metal ions at the second group, for instance, Mg 2+ and Ca 2+ , reducing the negative membrane charge that could even become positive [START_REF] Wang | Role of coexistence of negative and positive membrane surface charges in electrostatic e ff ect for salt rejection by nano fi[END_REF][START_REF] Teixeira | The role of membrane charge on nanofiltration performance[END_REF][START_REF] Bruni | The role of the electrolyte on the mechanism of charge formation in polyamide nanofiltration membranes[END_REF]. Then when there are only trace amounts of ions in the solution, the charge interactions between Cl -in CaCl2 and membrane could be weaker than the charge interactions between Cl -in NaCl and membrane, due to weaker membrane charge in the presence of Ca 2+ . Therefore, lower retention of CaCl2 compared to the retention of NaCl is observed. On the other hand, Ca 2+ has much higher hydration free energy (-1650 kJ.mol -1 ) than Na + (-365 kJ.mol -1 ) and Cl -(-340 kJ.mol -1 ), the hydration radius of Ca 2+ (0.412-0.420 nm) is bigger than that of Na + (0.276-0.360 nm) and Cl -(0.324-0.332 nm) [START_REF] Tansel | Significance of thermodynamic and physical characteristics on permeation of ions during membrane separation: Hydrated radius, hydration free energy and viscous effects[END_REF]. Then, at high concentration, when the charge effect is weakened,, the retention of CaCl2 could be higher than the retention of NaCl due to a bigger size [START_REF] Tansel | Significance of thermodynamic and physical characteristics on permeation of ions during membrane separation: Hydrated radius, hydration free energy and viscous effects[END_REF].

In addition, the size of SO4 2-is bigger than that of Cl -own to both higher MW and larger hydration shell [START_REF] Ren | Influence of inorganic salt on retention of ibuprofen by nanofiltration[END_REF], then higher retention of Na2SO4 at high concentration than retention of NaCl is observed. Thus, when the concentration increases, the decrease of Na2SO4 retention is less significant than the decrease of NaCl retention. Similar results are also reported by other authors [START_REF] Ren | Influence of inorganic salt on retention of ibuprofen by nanofiltration[END_REF][START_REF] Tanninen | Effect of electrolyte strength on acid separation with NF membranes[END_REF].

In conclusion, for ions having the same valence, the retention is fixed by the co-ions whereas for ions of different valences, the retention is fixed by the ion having the highest retention [START_REF] Luo | Effects of pH and salt on nanofiltration-a critical review[END_REF]. It is noticed that the retentions of SO4 2-in mixed solutions are nearly equal to that in single solutions. The retention curves of individual VFA show different behaviors at different compositions: the least retained VFA, Ac, decreases the most with the presence of Na2SO4, followed by Pr, which is intermediately retained, and then the retention of the most retained VFA, Bu, slightly decreases compared to that in single solutions. Furthermore, with the addition of SO4 2-, it seems that the retention of Ac in Ac/Pr/Bu ternary solutions decreases more than in Ac/Bu binary solutions for VFAs : salts at 1:1 and 1:4. However, at conditions that VFAs : salts=2 : 3, this result is not observed.

In addition, negative retentions of Ac -are obtained with VFAs : Na2SO4 = 2 : 3 at an ionic concentration of 500 mEq.L -1 , both in binary and ternary solutions. When the ratio of VFAs :

Na2SO4 decreases to 1 : 4, the retention of Ac -decreases more and the retention of Pr -is also negative at low filtration flux. This result indicates that the retention difference between VFAs and SO4 2-increases when decreasing the concentration ratio between VFAs (the less retained solutes) and SO4 2-(the more retained solute).

As discussed in Chapter III, the retentions of ions in mixed solutions differ from those in single solutions. In the mixed solution containing two ions with the same sign of charge, the retention of the more retained ion tends to increase while that of the less retained one decreases. A decrease of the retention of the less retained solute is observed when the concentration ratio between the less and more retained solutes decreases. This phenomenon is called "distribution effect" [START_REF] Kang | Removal of organic acid salts from simulated fermentation broth containing succinate by nanofiltration[END_REF] or "co-ions competition" [START_REF] Luo | Effects of pH and salt on nanofiltration-a critical review[END_REF][START_REF] Li | Separation Of (L)-glutamine from fermentation broth by nanofiltration[END_REF]. In current work, SO4 2-is the most retained ion. The retentions of VFAs are lower than that of SO4 2-and follow their MWs (Ac<Pr<Bu). Then, retentions of VFAs decrease in the mixture compared to their retentions in single solutions, and the trend of decline is Bu -< Pr -<Ac -, which is the reverse of their MWs sequence. However, the retention of SO4 2-does not increase in the mixed solutions. One can observe that the retention sequence in the mixed solutions is Cl -< Ac -< Pr -< Bu -, the same as that in single solutions, for all the compositions investigated. Then, it is observed that the retentions of Cl -, the least retained solute, decrease in the mixtures compared to those in single solutions and even reach negative values for some conditions. For the retentions of VFAs, it is observed that their retentions in the mixtures at the conditions that VFAs: salts = 1:1 are similar to those in single solutions. When the total concentration increases to 500 mEq.L -1 , despite the fact that the retentions of individual VFAs in single and mixed solutions are not obtained at the same filtration flux, it seems that one single curve can represent the results obtained in single and mixed solutions.

Moreover, the decreasing trend of Cl -retention is related to the ratio between VFAs and NaCl. Indeed, when the ratio between VFAs and NaCl decreases from 1:1, 2:3, to 1:4, the decrease of Cl -retention becomes less and less pronounced. On the other hand, it seems that the increase of Pr -retentions in the mixed solutions compared to those in single solutions for VFAs: salt = 2:3 are more significant than at VFAs: salts = 1:1.

In Ac -/Pr -/Bu -/Cl -system, Cl -is the least retained anion and Bu -is the most retained one. Then, as previously reported, retentions of Cl -in mixed solutions are expected to be lower than those in single solutions, while retentions of Bu -in the mixtures are expected to increase compared to single solutions. However, while the decrease of Cl -retention compared to that in single solutions is observed, the increase of Bu -retention compared to that in single solutions is not clear. This observation is the same as that previously reported for VFAs+Na2SO4 systems. The co-ions competition phenomenon is generally observed as the decrease of the retention of the less retained co-ions [START_REF] Khunnonkwao | A two steps membrane process for the recovery of succinic acid from fermentation broth[END_REF][START_REF] Nielsen | Bulk-phase criteria for negative ion rejection in nanofiltration of multicomponent salt solutions[END_REF][START_REF] Umpuch | Nanofiltration as a purification step in production process of organic acids: Selectivity improvement by addition of an inorganic salt[END_REF][START_REF] Kang | Removal of organic acid salts from simulated fermentation broth containing succinate by nanofiltration[END_REF][START_REF] Su | Rejection of ions by NF membranes for binary electrolyte solutions of NaCl, NaNO3, CaCl2 and Ca(NO3)2[END_REF]. The increase of the more retained co-ions in the mixed solution compared to that in single solution is only reported by a few works [START_REF] Szoke | Characteristics of thin-film nanofiltration membranes at various pH-values[END_REF][START_REF] Kang | Removal of organic acid salts from simulated fermentation broth containing succinate by nanofiltration[END_REF]. In the conditions we investigated, the decrease of the less retained co-ions is observed for VFAs+Na2SO4 and VFAs+NaCl systems. However, no significant increase of the more retained co-ions is observed. This observation is probably due to the definition of retention. Indeed, by definition, the retention of any ions is lower than 100%; when the retention of one solute approaches 100%, any increase is no more significant. However, retention of the less retained solute can reach negative value with no limit reported yet. Therefore, the increase in retention of more retained solute is less significant and harder to observe, while the decrease in retention of less retained solute is more significant and easier to observe.

IV.2.2 Influence of VFA counter-ions (Na + and Ca 2+ ) on individual solutes retentions In these two systems, VFAs sodium salts were combined with NaCl and CaCl2. Therefore, the only difference between the two systems is that one part of the counter-ions, Na + , is replaced by the same amount of Ca 2+ .

As for the VFAs+NaCl system, the retention sequence of anions is Cl -< Ac -< Pr -< Bu -, in single and mixed solutions for all the compositions investigated. One can observe that the retentions of VFAs in NaVFAs+ CaCl2 system seem slightly lower than in VFAs+NaCl system, especially for ternary Ac/Pr/Bu solutions. On the other hand, the retentions of Cl -in the NaVFAs+ CaCl2 system are significantly higher than the retention of Cl -with NaCl. When the concentration ratio of VFAs: salts decreases from 1:1, 2:3 to 1:4, the differences between the Cl -retentions in the two systems gradually enlarged.

Current results indicate that the counter-ions can significantly influence the retention of ions in mixed solutions. When one part of the counter-ions was changed from Na + to Ca 2+ , the retention difference between VFAs and Cl -decreased, showing that the co-ions competition between VFAs and Cl -decreases in the presence of Ca 2+ . Moreover, when the proportion of Ca 2+ increases, the co-ions competition decreases. It was shown that the retention difference between SO4 2-and Cl -in a NaCl/Na2SO4 binary system decreases dramatically when the solution pH decreases from 8 to 3 [START_REF] Szoke | Characteristics of thin-film nanofiltration membranes at various pH-values[END_REF]. A further interpretation by Luo et al. compared the retentions of SO4 2-and Cl -reported in ref. [START_REF] Szoke | Characteristics of thin-film nanofiltration membranes at various pH-values[END_REF], shown that the retention of SO4 2-maintain nearly equal to that in single solutions, while the retention of Cl -in mixed solution decreases compared to that in single solution [START_REF] Luo | Effects of pH and salt on nanofiltration-a critical review[END_REF]. Furthermore, the authors suggested that the difference between retention of Cl -in single and mixed solutions is due to coions competition, and the co-ions competition phenomenon is influenced by solution pH [START_REF] Luo | Effects of pH and salt on nanofiltration-a critical review[END_REF].

The maximum retention difference between Cl -in single and mixed solutions are observed at neutral pH [START_REF] Luo | Effects of pH and salt on nanofiltration-a critical review[END_REF]. In ref. [START_REF] Luo | Effects of pH and salt on nanofiltration-a critical review[END_REF], Luo et al. also suggested that the influence of solution pH on the retention of strong electrolyte is mainly due to the variation of membrane charge [START_REF] Luo | Effects of pH and salt on nanofiltration-a critical review[END_REF]. Therefore, we suggested that the observation in ref. [START_REF] Szoke | Characteristics of thin-film nanofiltration membranes at various pH-values[END_REF] probably indicate that the membrane charge can influence the co-ions competition.

As discussed previously, many scientists suggest that the membrane charge can be controlled by the competitive adsorption of co-ions and counter-ions. When the concentration of Ca 2+ in the solution increases, the negative membrane charge decreases [START_REF] Schaep | Modelling the retention of ionic components for different nanofiltration membranes[END_REF][START_REF] Bruni | The role of the electrolyte on the mechanism of charge formation in polyamide nanofiltration membranes[END_REF][START_REF] Mazzoni | Nanofiltration: Role of the electrolyte and pH on desal DK performances[END_REF].

Based on those reports, we suggest that the reduction of the retention difference between VFAs and Cl -in the presence of Ca 2+ could be related to the reduction of membrane charge. Indeed, the NF membrane is an ion-exchange membrane. For the two cations investigated in this work, the cation exchange sequence is Ca 2+ >Na + . Therefore, when changing one part of Na + into Ca 2+ , the cation equilibrating the membrane changed from only Na + to the combination of Na + and Ca 2+ .

Then, the thickness of electrical double layer (EDL) decreases and the negative membrane charge decreases. One can observe that the retentions of Ca 2+ are higher than the retentions of Na + , both in single and mixed solutions. The retentions of cations are similar in VFAs binary and ternary solutions, indicate that the presence of Pr does not significantly influence the retentions of cations, and the retentions of cations are determined by their concentration ratio. Then, retentions of Ca 2+ in mixed solutions are always higher than those in CaCl2 single solutions, and the retentions of Na + in mixtures are always lower than those in NaCl single solutions. Thus the retention differences between Na + and Ca 2+ increases in the mixed solutions, and the differences are even higher at high concentration (500 mEq/L). For the concentration of 500 mEq/L, when the ratio of Na + : Ca 2+ decreases from 2:3 to 1:4, the retention of Na + decreases and negative values are even observed at low filtration flux for the ratio of 1:4, both in VFAs binary and ternary solutions.

In the NaVFAs+CaCl2 system, Na + is the less retained cation, and Ca 2+ is the more retained one. The retention of Na + decreases compared to that in NaCl single solutions, while the retention of Ca 2+ increases compared to that in CaCl2 single solutions. When the ratio of Na + : Ca 2+ decreases, the retentions of both Na + and Ca 2+ decrease. A similar observation is reported for the filtration of Na + and Ca 2+ binary solution by a KP 90 CA reverse osmosis membrane, the retentions of Na + in the mixed solutions are much lower than in the single solution, and negative values are reached at low filtration flux. In addition, when the concentration ratio of Ca 2+ and Na + decreases from 76.2mM : 20.8mM to 120mM : 20.5mM, the retention of Na + slightly decreased [START_REF] Vonk | Positive and Negative Ion Retention Curves of Mixed Electrolytes in Reverse Osmosis with a Cellulose Acetate Membrane . An Analysis on the Basis of the Generalized Nernst-Planck Equation[END_REF]. Our results are in agreement with the previous reported ones, and one can conclude that the co-ions competition between the cations show the same behavior as that between anions. Current results are in agreement with the results observed in Chapter III. Indeed, for a given proportion in the feed, regardless of the concentration, one fixed solute proportion (𝑃𝑃 𝑖𝑖 𝑃𝑃 * ) is found in the permeate when the filtration flux is higher than a certain value. The data in Table IV- One can observe that, for all the conditions investigated, the proportion of solute in the permeate increases when its proportion in the feed increases. Then, the proportion of SO4 2-in the permeate is always lower than its proportion in the feed, meanwhile, the proportion of Cl -in the permeate is always higher than that in the feed, whatever the cation composition, Na + only or mixed Na + and Ca 2+ . However, with the same Cl -proportion in the feed, when there are both Na + and Ca 2+ in the mixed solution, the proportion of Cl -in the permeate is slightly lower than that with only Na + as counter-ion (Figure IV-10a). This observation is the same as that reported for individual solutes retentions, i.e. the co-ions competition between VFAs and Cl -seems to be reduced in the presence of Ca 2+ . The proportion of individual VFAs in the permeate show different behaviors with the addition of SO4 2-or Cl -. With the presence of SO4 2-, VFAs proportion in the permeate is higher than that in the feed. Ac proportion increases the most, followed by Pr, and Bu proportion increases the least. With the presence of Cl -, VFAs proportion in the permeate is lower than that in the feed. Ac proportion decreases the least, followed by Pr, and Bu proportion decreases the most. It seems that, with the addition of a more retained co-ion (i.e., SO4 2-), the proportion of VFAs in the permeate increases, the least retained VFA increases the most, while the most retained VFA increases the least. On the contrary, with the addition of a less retained co-ion (i.e., Cl -), the As can be expected from the co-ions competition phenomenon previously discussed for anions, the proportions of both Na + and Ca 2+ in the permeate increase as their proportion in the feed increase.

IV.3 Solute transfer in

Furthermore, one can observe that for different ratio of VFAs : salts as well as VFAs compositions (100 mEq.L -1 , 200 mEq.L -1 , for binary and ternary solutions), one single continuous curve can fit all the conditions. This observation indicate that the influence of anions composition in the feed on the permeate proportion of cations is not significant.

IV.3.1.3 Relative proportions of VFAs in the permeate

In a more complex solution, the relative proportion of two solutes (defined in Chapter II, Eqs. The relative proportions of VFAs in the feed solutions with the addition of inorganic salts are nearly the same for the three couples (i.e., about 50% for all the VFAs in the three couples). One can observe that the relative proportions of VFAs in the permeate for the conditions with the addition of inorganic salts are nearly the same too. The relative proportions of Ac in the couples of Ac/Pr and Ac/Bu are 59%±2% and 67%±3% respectively; the relative proportions of Pr in the couples of Ac/Pr and Pr/Bu are 41%±2% and 59%±2% respectively; the relative proportions of Bu in the couples of Pr/Bu and Ac/Bu are 41%±2% and 33%±3% respectively. This observation indicates that the addition of salts does not significantly influence the permeate proportion of

VFAs. Furthermore, one can observe that for all the VFAs at all the conditions investigated (VFAs without and with the addition of inorganic salts at different compositions), one single polynomial curve can fit the relative proportions in the permeate versus relative proportions in the feed. The formulas of the polynomial curves are given for Ac, Pr and Bu in the couples of Ac/Pr, Pr/Bu, and Ac/Bu. y is the proportion in the permeate, x is the proportion in the feed.

The relative proportion of one solute in the permeate versus that in the feed (namely, enrichment factor) can be simulated by a binomial formulas. Amongst those formulas, the x is the feed proportion and the y represents the enrichment factor of a given solute in the permeate compared to that in the feed. Using the relative proportion of Ac in the feed and permeate for the couple of Ac/Pr as an example. The fitting formula is y=1.361x-0.361x 2 , when 𝑥𝑥 = 0, 𝑦𝑦 = 1.361, indicate that when the relative proportion of Ac in the feed is near to 0%, the relative proportion of Ac in the permeate is 1.361 times higher than that in the feed. When 𝑥𝑥 = 1, 𝑦𝑦 = 1, shown that when the relative proportion of Ac in the feed is near to 100%, the relative proportion of Ac in the permeate is near to 1. Then, the enrichment factor of Ac for the couple of Ac/Pr decreases when the relative proportion of Ac in the feed increases. On the contrary, the enrichment factor for Pr for the couple of Ac/Pr increases when the feed proportion of Pr increases. It increases from 0.64 when the proportion of Pr in the feed is near to 0%, to about 1 when the proportion of Pr in the feed is near to 100%. The same findings are observed for the couples of Pr/Bu and Ac/Bu.

Present results show that for any couple of solutes, their relative proportions in the permeate are fixed by their relative proportion in the feed and do not depend on the presence of co-ions.

For cations, the same conclusion is also observed (shown in

IV.3.3 Influence of the composition on the separation factors between VFAs

The aim of the investigation on solutes proportions in the feed and permeate is to investigate the separation performance of NF on VFAs at different compositions. In current Chapter, four types of mixed solution systems (VFAs without salt, VFAs+Na2SO4, VFAs+NaCl, and VFAs+CaCl2) are investigated. It is concluded that the concentration of the solution does not influence the separation, therefore, the comparison of separation is applied for different feed proportions. In order to compare the influence of the addition of salts, the conditions with identical proportions of VFAs (i.e., Ac:Bu=1:1 and Ac:Pr:Bu=1 For binary solutions of VFAs (Ac:Bu=1:1), it seems that the addition of 100 mEq.L -1 of salts (VFAs:salts=1:1), increases the separation factor between Ac and Bu for all the conditions. Then, when the proportions of VFAs:salts decrease to 2:3 and 1:4 (meanwhile, the ionic concentration of the mixed solutions increases to 500 mEq.L -1 ), the separation factor decreases for the systems of VFAs+Na2SO4 and VFAs+CaCl2, but, remains nearly constant for VFAs+NaCl system (Figure

IV-20a).

For ternary solutions (Ac:Pr:Bu=1:1:1), with the addition of 100 mEq.L -1 of salts In Chapter III, it is concluded that the separation factor between Ac/Bu obtained in binary solutions at identical proportion (Ac:Bu=50%:50%) is higher than with other proportion (Ac : Bu=20%:80%). Then, the highest separation factors between VFAs are observed for ternary solution with identical proportion (Ac: Pr: Bu=33%:33%:33%).

Current observation is in agreement with the previous results. Indeed, for binary VFAs solutions, the addition of a third co-ion makes the VFAs+salts systems become ternary electrolyte solutions. As observed in Chapter III, the presence of an additional co-ion (Pr -) increases the separation factor between Ac and Bu. In the current systems, the presence of the additional coions (SO4 2-and Cl -) also increases the separation factor between Ac and Bu.

As observed in Chapter III, decreasing the ratio of Ac:Bu and Ac:Pr:Bu from 50%:50% and 33%:33%:33% to 20%:80% and 20%:20%:60% respectively, the separation factor between Ac and Bu decreases. In current systems, when the ratio of VFAs : salts decreases from 1:1, 2:3 to 1:4, the proportions of these mixed electrolyte solutions are farther from identical proportion, the decrease of separation factor between Ac and Bu is also observed, except for VFAs+NaCl.

However, the influence of ionic composition on the separation of complex electrolytes solutions still needs further investigation.

For ternary VFAs solutions, the addition of a fourth co-ion (SO4 2-or Cl -) decreases the separation factors between VFAs except for VFAs+NaCl system at 1:1. It should be noticed that the proportions of co-ions in the quaternary electrolyte solutions are not at identical even when the ratio of VFAs : salts=1:1 (when VFAs : salts=1:1, the proportion of individual solute is Ac :

Pr : Bu : salts=17%: 17%:17%: 49%). As reported in Chapter III, the best separation is observed for the condition with identical proportion, thus the separation factor in the quaternary electrolyte solutions could be lower than that in ternary VFAs solutions with identical proportion.

Nevertheless, when the proportion is farther form the identical proportion (i.e., VFAs : salts decreases form 1:1, 2:3 to 1:4), the separation factors between VFAs all decreases. However, for the system of VFAs+NaCl, the separation factors between VFAs decrease less compared to that for the other two systems (VFAs+CaCl2 and VFAs+Na2SO4).

In addition, both for binary and ternary VFAs solutions, the separation factors between VFAs are lower in VFAs+CaCl2 system compared to those in VFAs+NaCl system. Then, when one part of counter-ions is changed from Na + to Ca 2+ , the separation performance of NF on VFAs decreases. with NaCl, and with CaCl 2 , respectively, using NF-45 membrane. It was reported that the addition of inorganic salts can increase the selectivity between charged and uncharged solutes. The addition of NaCl can gradually increase the maximum separation factor between sodium lactate and glucose, from about 1.1 (without NaCl) to 1.5 (with 1000mEq.L -1 of NaCl). Then, the addition of Na2SO4 can also increase the separation factor between the two solutes, maximum separation factor can reach 1.9 with 1000mEq.L -1 of Na2SO4 [START_REF] Umpuch | Nanofiltration as a purification step in production process of organic acids: Selectivity improvement by addition of an inorganic salt[END_REF].

Indeed, the mechanism for the influence of inorganic salts on the separation of sodium lactate and glucose is not the same as the mechanism for the influence of inorganic salts for the separation of VFAs. From the experimental data reported in ref. [START_REF] Umpuch | Nanofiltration as a purification step in production process of organic acids: Selectivity improvement by addition of an inorganic salt[END_REF], it was observed that the addition of salts can decrease both the retention of lactate and glucose, due to the screening effect and dehydration respectively, the decrease of glucose retention (10% with 1000mEq.L -1 of NaCl) is less than the decrease of lactate retention (30%, at J=0.2×10 -5 m.s -1 , with 1000mEq.L -1 of NaCl).

Therefore, the retention difference between glucose and lactate increases, and then higher separation factor is observed. With the addition of Na2SO4, the same phenomenon was observed, the decrease of glucose retention due to the addition of Na2SO4 is less than 4% (with 1000mEq.L - 1 of Na2SO4), meanwhile, the retention of lactate decreases 50%, at J=0.2×10 -5 m.s -1 , with 1000mEq.L -1 of Na2SO4, then, an even better separation factor was achieved.

Beside the screening effect, the co-ions competition can also play a role. The decrease of lactate retention due to the influence of inorganic salts is a combination of screening effect (total ionic concentration increase) and co-ions competition (between Lac -/Cl -and Lac -/SO4 2-).

Lac -is the more retained co-ion while Cl -is the less retained co-ion for the mixed solution of glucose/lactate/NaCl. Then, in the presence of Cl -, the retention of lactate should increase.

However, the experiments were done at different ionic concentration (from 100mEq.L -1 (only 100mM of glucose and 100mEq.L -1 of lactate) to 1100mEq.L -1 (100mM of glucose, 100mEq.L -1 of lactate with 1000mEq.L -1 of salts)), there is the influence of screening effect and the observed lactate retention decrease is the result of co-ions competition (tends to increase the retention of lactate) and screening effect (tends to decrease the lactate retention).

SO4 2-is the more retained co-ions and Lac -is the less retained co-ions for the mixed solution of glucose/lactate/Na2SO4. In the presence of SO4 2-, the co-ions competition between Lac -and SO4 2-tends to decrease the lactate retention, the same as the trend of screening effect. Therefore, retention of lactate decreases less (30%, at J=0.2*10 -5 m.s -1 ) in the presence of NaCl, while lactate retention decreases more (50%, at J=0.2*10 -5 m.s -1 ) and even reached negative value at low filtration flux when lactate is coupled with Na2SO4 [START_REF] Umpuch | Nanofiltration as a purification step in production process of organic acids: Selectivity improvement by addition of an inorganic salt[END_REF].

The current chapter shows the co-ions competition phenomenon between six co-ions in mixed solutions. It is shown that the ionic compositions do not significantly influence the co-ion competition between co-ions. This demonstrates that the behaviors of neutral and charged solutes in the mixed solution are different.

IV.4 Conclusions

It was pointed out in in Chapter III that for a given VFAs proportion in the feed, a fixed proportion in the permeate is obtained. That is due to the transfer of individual VFAs are controlled by the total VFAs transfer. Then the individual VFAs transfer is the result of co-ions competition, and the contribution of each VFA for the total solute transfer depends on its proportion in the feed.

In the current Chapter, we investigated the influence of the addition of salts (Na2SO4, NaCl, and CaCl2) on the performance of nanofiltration on VFAs solutions. The co-ions competition phenomenon observed in Chapter III is investigated in the more complex systems (with five anions and two cations).

In the single solutions, the retention sequences of the five anions and two cations are Cl -<Ac - <Pr -<Bu -<SO4 2-and Na + <Ca 2+ respectively. Then, in the mixed solutions, it is observed that the permeate proportions of the more retained co-ions (anions or cations, i.e., SO4 2-among VFAs -/ SO4 2-, VFAs -among Cl -/VFAs -, and Ca 2+ among Na + /Ca 2+ ) decrease while the permeate proportions of less retained co-ions (anions or cations, i.e., VFAs -among VFAs -/SO4 2-, Cl -among Cl -/VFAs -, and Na + among Na + /Ca 2+ ) increase compared to their proportions in the feed. This observation extended the general trend of co-ions competition observed for VFAs mixed solutions.

For all the systems investigated (VFAs+Na2SO4, VFAs+NaCl, and NaVFAs+CaCl2), for a given proportion in the feed, a fixed proportion in the permeate is observed, when the filtration flux is higher than a certain value. This observation applies to both anions and cations.

The proportion of each ion in the feed strongly influences its proportion in the permeate. The proportion of one given ion in the permeate increases when its proportion in the feed increases, for all the ions investigated.

With the presence of Ca 2+ , the proportion of Cl -in the permeate is slightly lower than the proportion of Cl -in the permeate with Na+ as only counter-ion, indicating that the presence of Ca 2+ slightly reduced the co-ions competition between VFAs -and Cl -. This observation needs further investigation.

It is observed that the relative proportions of any couples of solutes in the permeate are nearly only depended on their relative proportions in the feed. The mass transfer investigation suggests that a complex mixed solution can be separated into various couples of solutes, the individual solute transfer is controlled by the combined solutes transfer, and does not influenced by the transfer of other co-ions.

The separation factors between Ac/Pr, Pr/Bu, and Ac/Bu for VFAs, VFAs+Na2SO4, VFAs+NaCl, and NaVFAs+CaCl2 are given. On the contrary to what observed with mixed solution with uncharged and charged solutes, the addition of both co-ions (anions) and counterions (cations) does not have a significant influence on the separation factors between VFAs.

Chapter V

Influence of the pH on the retention of VFAs

This chapter investigated the retention of VFAs with different compositions at different pH, aim to figure out the variation of charge interaction between VFA and membrane.

Chapters III and IV give the influence of solution composition on the retentions of VFAs at pH 8, when the solutes and membrane are both negatively charged. From the knowledge in Chapter I, it is known that the pH of the solution can significantly influence the retention of VFAs, due to the change in the membrane charge and solutes dissociation.

On the one hand, the fraction of dissociated VFAs in the solution is depending on the pKa values of each solute and the solution pH. The retention of undissociated VFAs is mainly due to size effect, and the retention of dissociated VFAs could be due to both size and charge effect when the membrane is also charged. The influence of solution pH changes the fraction of dissociated VFAs and then changes the VFAs retention.

On the other hand, the membrane charge is mainly fixed by the dissociation of functional groups on the membrane surface, and the fraction of dissociated functional groups on the membrane determines the membrane charge density. Solution pH can also change the fraction of dissociated functional groups on the membrane.

Therefore, the retention of VFAs versus solution pH is related to the dissociation of both solutes and membrane functional groups.

In this chapter, the influence of solution pH on the retention of individual and global retention (i.e. the weighted average of all the individual solutes retentions in the mixture) of VFAs in single and mixed solutions is investigated. Retentions and global retentions of VFAs in single and mixed solutions respectively with different total concentrations are measured and calculated respectively.

The influence of solution pH on solutes dissociation and membrane charge is discussed based on the assumption that the dissociated and undissociated VFAs transfer through the membrane separately. The impact of ionic concentration is taken into account, and the influence of solution pH on solute charge as well as membrane charge is explored.

All the results discussed in this chapter are obtained using NF-45 membrane.

Equations used in the investigation:

The total concentration of VFAs in the feed and permeate are given in Eq. (V.1) and Eq. (V.2).

𝐶𝐶 𝑓𝑓 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 = ∑ 𝐶𝐶 𝑖𝑖 𝑓𝑓 𝑛𝑛 𝑖𝑖=1 (V.1) 𝐶𝐶 𝑝𝑝 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 = ∑ 𝐶𝐶 𝑖𝑖 𝑝𝑝 𝑛𝑛 𝑖𝑖=1 (V.2)

𝐶𝐶 𝑖𝑖

𝑓𝑓 and 𝐶𝐶 𝑖𝑖 𝑝𝑝 represent the concentration of individual VFA i in the feed and permeate solution respectively.

Then the global retention of VFAs, is defined in Eq. (V.3).

𝑅𝑅 𝑠𝑠𝑡𝑡𝑝𝑝 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 = 1 - 𝐶𝐶 𝑉𝑉𝑉𝑉𝑉𝑉𝑠𝑠 𝑝𝑝 𝐶𝐶 𝑉𝑉𝑉𝑉𝑉𝑉𝑠𝑠 𝑓𝑓 = 1 - ∑ 𝐶𝐶 𝑖𝑖 𝑝𝑝 𝑛𝑛 𝑖𝑖=1 ∑ 𝐶𝐶 𝑖𝑖 𝑓𝑓 𝑛𝑛 𝑖𝑖=1 (V.
∑ 𝑃𝑃 𝑖𝑖 𝑓𝑓 𝑛𝑛 𝑖𝑖=1 = 1 (V.5)
The fraction of dissociated VFAs in the single solution is given in Eq. (V.6).

𝑃𝑃 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 - 𝑠𝑠𝑠𝑠𝑡𝑡 = 10 𝑝𝑝𝑝𝑝-𝑝𝑝𝑝𝑝 𝑎𝑎𝑖𝑖 1+10 𝑝𝑝𝑝𝑝-𝑝𝑝𝑝𝑝 𝑎𝑎𝑖𝑖 (V.6)
With 𝑝𝑝𝐾𝐾 𝑎𝑎𝑖𝑖 represent the pKa value of individual VFA i. i represent Ac, Pr, or Bu.

For a mixed solution, the total proportion of dissociated VFAs, 𝑃𝑃 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 - 𝑚𝑚𝑖𝑖𝑚𝑚 , is the weighted average of individual proportions of dissociated VFAs, shown in Eq. (V.7).

𝑃𝑃 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 - 𝑚𝑚𝑖𝑖𝑚𝑚 = ∑ (𝑃𝑃 𝑖𝑖 𝑓𝑓 × 10 𝑝𝑝𝑝𝑝-𝑝𝑝𝑝𝑝 𝑎𝑎𝑖𝑖 1+10 𝑝𝑝𝑝𝑝-𝑝𝑝𝑝𝑝 𝑎𝑎𝑖𝑖 ) 𝑛𝑛 𝑖𝑖=1 (V.7)
𝑃𝑃 𝑖𝑖 𝑓𝑓 represent the proportion of individual VFA i with 𝑝𝑝𝐾𝐾 𝑎𝑎𝑖𝑖 in the feed solution. i represent Ac, Pr, or Bu.

For mixed solutions, one average pKa value, 𝑝𝑝𝐾𝐾 𝑎𝑎_𝑎𝑎𝑎𝑎 , can be determined using the following equation, Eq. (V.8). Retention (%)

𝑃𝑃 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠

Filtration flux (m/s)

J 1 J 2 J 3 J 4 100mM
Retention (%)

Filtration flux (m/s)

J 1 J 2 J 3 J 4 Retention (%) Filtration flux (m/s) J 1 a b Figure V-2
Retentions of Bu in single solutions, versus filtration flux at different solution pH and varying total concentration, using NF-45 membrane. Retentions at J 1 =0.2×10 -5 m.s -1 , J 2 =0.5×10 -5 m.s -1 , J 3 =1×10 -5 m.s -1 , and J 4 =1.5×10 -5 m.s -1 are compared, for 500mM, only J 1 is in the experimental range. The retention mechanism of VFAs by NF membrane is a combination of size and charge effect.

At pH 3, VFAs are uncharged, and the retention is mainly due to size effect. Since VFAs have much lower MWs than the MWCO of the membrane, low retention is expected. In addition, it is known that the influence of concentration on the retention of a neutral solute is negligible, as reported for glucose solutions for instance both in single [START_REF] Bouchoux | Nanofiltration of glucose and sodium lactate solutions: Variations of retention between single-and mixed-solute solutions[END_REF][START_REF] Umpuch | Nanofiltration as a purification step in production process of organic acids: Selectivity improvement by addition of an inorganic salt[END_REF] and mixed (glucose/xylose) solutions [START_REF] Sjoman | Separation of xylose from glucose by nanofiltration from concentrated monosaccharide solutions[END_REF]. Then the concentration is expected to have a negligible influence on the retention of VFAs at pH 3, as observed. On the contrary, at pH 8, both the VFAs and the membrane are charged, and the charge effect plays an important role in VFAs retention. Indeed, much higher retentions than those obtained at pH 3 are observed, and the retentions increase with solution pH from 3 to 8. Similar results were also reported in previous works investigating the retention of weak acids [START_REF] Khunnonkwao | A two steps membrane process for the recovery of succinic acid from fermentation broth[END_REF][START_REF] Szoke | Characteristics of thin-film nanofiltration membranes at various pH-values[END_REF][START_REF] Weng | Separation of acetic acid from xylose by nanofiltration[END_REF][START_REF] Schaep | Salt retention of Zirfon (R) membranes[END_REF]. Furthermore, when the concentration of VFAs increases, the ionic strength of the solution increases, and then the charge interactions between membrane and VFAs are weakened. This is reported as a screening effect [START_REF] Khunnonkwao | A two steps membrane process for the recovery of succinic acid from fermentation broth[END_REF][START_REF] Umpuch | Nanofiltration as a purification step in production process of organic acids: Selectivity improvement by addition of an inorganic salt[END_REF], according to which the retention is expected to decrease with the concentration, as observed. Moreover, the retention follows the dissociation curve.

These results are in agreement with previous ones obtained with other weak acid, e.g. succinic acid, for which it was reported that, for different filtration flux, the retention increases with the solution pH following the fraction of the divalent form (Suc 2-) [START_REF] Khunnonkwao | A two steps membrane process for the recovery of succinic acid from fermentation broth[END_REF]. for three concentrations, using NF-45 membrane. J 1 =0.2×10 -5 m.s -1 , J 2 =0.5×10 -5 m.s -1 , J 3 =1×10 -5 m.s -1 , J 4 =1.5×10 -5 m.s -1 , for 500mM, only J 1 is in the experimental range. The dissociation curves of Ac and Pr are given as references and the pK a of each VFA is marked in the figure. Retentions of Bu in single solutions, at given filtration flux versus solution pH for three concentrations, using NF-45 membrane. J 1 =0.2×10 -5 m.s -1 , J 2 =0.5×10 -5 m.s -1 , J 3 =1×10 -5 m.s -1 , J 4 =1.5×10 -5 m.s -1 , for 500mM, only J 1 is in the experimental range. The dissociation curve of Bu is given as reference and the pK a of Bu is marked in the figure. For all the pH investigated, it seems that the proportion of Ac in the permeate increases when the filtration flux increases, reaches a plateau when the filtration flux is higher than a certain value.

On the contrary, the proportion of Bu in the permeate decreases and reaches a plateau value when the filtration flux is higher than a certain value. Furthermore, the filtration flux required to reach the plateau value for different pH is not the same, the lower the solution pH, the higher the filtration flux required to reach the plateau value. As observed in Chapter III, the permeate proportion of given solute at given solution pH does not change with the total concentration. and 52% to 60% and 68%, respectively. Meanwhile, the proportions of Bu for the couples of Pr/Bu and Ac/Bu decrease from about 48% at pH 3 to 40% and 32% respectively at pH 8. For Pr, its proportion decreases in the presence of Ac while increases in the presence of Bu. Besides, one can observe that the variation of the relative proportions of all VFAs in the permeate with solution pH follows a sigmoid curve, the higher the solution pH, the more significant the difference between the relative proportions of VFAs. Ac/Bu, in the permeate versus solution pH in the binary (Ac:Pr=50%:50%, Pr:Bu=50%:50%, Ac:Bu=50%:50%) and ternary (Ac:Pr:Bu =33%:33%:33%) solutions, using NF-45 membrane. Global retentions at J 1 =0.2×10 -5 m.s -1 , J 2 =0.5×10 -5 m.s -1 , J 3 =1×10 -5 m.s -1 , and J 4 =1.5×10 -5 m.s -1 are compared, for 500mM, only J 1 is in the experimental range. Global retentions at J 1 =0.2×10 -5 m.s -1 , J 2 =0.5×10 -5 m.s -1 , J 3 =1×10 -5 m.s -1 , and J 4 =1.5×10 -5 m.s -1 are compared, for 500mM, only J 1 is in the experimental range. Ac/Bu (Ac: Bu =50%:50%) at given filtration flux versus solution pH for three total concentrations, using NF-45 membrane. The filtration flux J 1 =0.2×10 -5 m.s -1 , J 2 =0.5×10 -5 m.s -1 , J 3 =1×10 -5 m.s -1 , J 4 =1.5×10 -5 m.s -1 , for 500mM, only J 1 is in the experimental range. The fitting curves are obtained from sigmoid curve fitting. The percentage of the dissociation VFAs at each pH values are given as references. at given filtration flux versus solution pH for three total concentrations, using NF-45 membrane. The filtration flux J 1 =0.2×10 -5 m.s -1 , J 2 =0.5×10 -5 m.s -1 , J 3 =1×10 -5 m.s -1 , J 4 =1.5×10 -5 m.s -1 , for 500mM, only J 1 is in the experimental range. The fitting curves are obtained from sigmoid curve fitting. The percentage of the dissociation VFAs at each pH values are given as references. It is known that the retentions of charged solutes decrease when the ionic concentration increases at neutral or alkaline conditions. This phenomenon is reported by many authors, and it is due to the screening effect [START_REF] Khunnonkwao | A two steps membrane process for the recovery of succinic acid from fermentation broth[END_REF][START_REF] Umpuch | Nanofiltration as a purification step in production process of organic acids: Selectivity improvement by addition of an inorganic salt[END_REF]. When the solution pH decreases, the influence of concentration is less significant at low pH than at high pH. This phenomenon could be due to two factors.

On the one hand, for a lower pH value, only part of those weak acids are dissociated, then the ionic concentration is lower than the ionic concentration at high pH, and the influence is weaker.

The concentration of dissociated VFAs in the solution, 𝑐𝑐 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 -, which represent the ionic concentration of the solution, is given by Eq. (V.9).

𝑐𝑐 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 -= 𝑐𝑐 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 × 𝑃𝑃 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 - (V.9)
𝑐𝑐 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 is the concentration of dissociated and undissociated VFAs in the solution, 𝑃𝑃 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 -is the proportion of dissociated VFAs in the solution, which is obtained from Eqs. (V.6). It is shown that 𝑐𝑐 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 -is pH-dependent, approximately equal to 0 at pH 3 while equivalent to 𝑐𝑐 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 at pH 8.

Therefore, the influence of ionic concentration is nearly negligible at pH 3, increase when pH increase, and reaches the maximum at pH 8.

On the other hand, the membrane charge is also pH-dependent. It is generally believed that the negative membrane charge is lowest at IEP of the membrane (4.0 for NF-45 membrane). When the pH increases, the membrane is more negatively charged and the zeta potential which represent membrane charge reaches a plateau when pH higher than about 7 [START_REF] Chen | Physicochemical characterization of tight nanofiltration membranes for dairy wastewater treatment[END_REF]. The weakened membrane charge could reduce the screening effect, and then the screening effect is more pronounced at high pH values. This phenomenon is proved by the nanofiltration of strong electrolyte solution, for which the dissociation of solute is negligible. In a report investigating the retention of KCl at different concentrations and solution pH, it was observed that the retention of KCl decreases with the increasing KCl concentration at pH 9 and 7, then the influence of KCl concentration become nearly negligible when solution pH dropped to 5 [START_REF] Nilsson | The influence of pH, salt and temperature on nanofiltration performance[END_REF].

For simplification, the latter discussions use VFAs retention to represent retention/global retention of VFAs in single and mixed solutions.

V.2 Description of the VFAs retention versus pH

The observed retention of a weak acid, like VFA, is a combination of the retentions of the dissociated and undissociated forms of the acid, the proportions of which are provided by Eq. (V.6), according to the pKa of the acid and the pH of the solution .

From previous work, it is suggested that the interactions between undissociated and dissociated forms of weak acids are not significant [START_REF] Timmer | Transport of lactic acid through reverse-osmosis and nanofiltration membranes[END_REF]. The mass transfer parameters of dissociated and undissociated lactic acid were determined from an experimental investigation concluding that the two forms transfer through the membrane separately [START_REF] Timmer | Transport of lactic acid through reverse-osmosis and nanofiltration membranes[END_REF]. Therefore, this is what will be assumed in the following.

Then, the retention of VFAs can be calculated as the weighted average of undissociated and dissociated VFAs retentions using the following equation.

𝑅𝑅 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 𝑐𝑐𝑎𝑎𝑡𝑡 = 𝑅𝑅 𝐻𝐻𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 × (1 -𝑃𝑃 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 -) + 𝑅𝑅 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 -(𝑐𝑐 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 -) × 𝑃𝑃 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 - (V.10)
𝑃𝑃 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 -is the proportion of dissociated VFAs in the solution obtained from Eq. (V.6). 𝑅𝑅 𝐻𝐻𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 is the retention of undissociated VFAs, 𝑅𝑅 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 -(𝑐𝑐 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 -) is the retention of dissociated VFAs.

Eq. (V.10) is used with the following assumptions:

(1) Dissociated and undissociated VFAs transfer through the membrane independently;

(2) Retention of HVFAs, 𝑅𝑅 𝐻𝐻𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 , is that obtained at pH 3 and does not depend on the concentration;

(3) Retention of VFAs -, 𝑅𝑅 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 -(𝑐𝑐 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 -), is that obtained at pH 8 at the corresponding ionic concentration.

The calculation of the second term in Eq. (V.10) requires to know the values of and pH 8, using NF-45 membrane. Points are experimental values and the curves are those from equations in table 4.

𝑅𝑅 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 -(𝑐𝑐 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 -) for different ionic concentrations.

Table V-1

VFAs retention as a function of ionic concentration at a filtration flux of 0.2×10 -5 m.s -1 and pH 8, using NF-45 membrane. for the 3 total concentrations investigated. As previously mentioned, the variation of individual

Equation 𝑅𝑅 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 -(𝑐𝑐 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 -) = 𝑎𝑎 + 𝑏𝑏 × 𝑐𝑐 𝑐𝑐
VFAs retentions in single and mixed solutions with solution pH are not the same, the global retention is considered for mixed solutions. One can observe that both experimental and calculated VFAs retentions increase with solution pH following a sigmoid curve. However, the calculated retentions are always higher than the experimental ones, for single, binary, and ternary solutions.

The highest differences between calculated and experimental VFAs retentions are observed at the concentration of 100mM, for all the solutions investigated. Since size effect is almost not influenced by the pH, this overestimation of retention can be attributed to an overestimation of the charge effect on the VFA retention. This is confirmed by the greater overestimation observed at low concentration.

As previously explained, charge effect is due to both the solute and membrane charge, which vary with the solution pH according to their respective pKa values.

Previous calculation was made considering the theoretical pKa values of the VFAs. Then, Equation (V.10) was further used to determine the pKa values to fit experimental and calculated variations of the VFAs retention versus pH (namely fitted pKa, pKa-f). The values of 𝑃𝑃 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 -were obtained from Eqs. (V.6) and (V.8), for single and mixed solutions respectively. The fitted pKa-f values are obtained from Eq. (V.10) using the Origin software.

The results are reported in Table V-2, that gives the fitted pKa-f values and the fitting coefficient of determination (R 2 ). For comparison, the theoretical pKa values for single solutions and global pKa values (from Eq. (V.8)) for mixed solutions are also reported as well as the differences between pKa-f and pKa (pKa-f-pKa), for all the compositions investigated.

One can observe that for each condition, the fitting is in excellent agreement with the experimental values (R 2 > 0.982). Then the fitted pKa-f values obtained at different concentrations and proportions are similar, no clear trend is observed. The average pKa-f value for all the compositions is about 1.24±0.09 units higher than the theoretical pKa values of the solutions.

Table V-2 Theoretical pK a , fitted pK a , pK a-f , and the differences between pK a and pK a-f obtained from the fitting of the retention curves for single, binary, and ternary solutions at three concentrations for the filtration flux of J 1 (0.2×10 -5 m.s -1 ) , using NF-45 membrane. Further calculations on higher filtration flux (i.e., J2, J3, and J4) are carried out, and the results are given in Table V-4. It is shown that when the filtration flux increase, the fitted pKa_f values decrease. The detailed calculation is not shown.

Solutions

Table V-3

Theoretical pK a , fitted pK a , pK a-f , and the differences between pK a and pK a-f obtained from the fitting of the retention curves for single, binary, and ternary solutions at two concentrations and filtration flux of J 2 (0.5×10 -5 m.s -1 ), J 3 (1×10 -5 m.s -1 ), and J 4 (1.5×10 -5 m.s -1 ) , using NF-45 membrane. The difference between the fitted pKa_f and solution pKa (pKa-f-pKa) for various compositions The retention of sulfuric acid is reported to increase with solution pH, from nearly 0% at pH 1, to close to 100% when the pH higher than 5, for various NF membranes investigated [START_REF] López | Experimental and theoretical study of nanofiltration of weak electrolytes: SO4 2-/HSO4 -/H+ system[END_REF][START_REF] Tanninen | Effect of electrolyte strength on acid separation with NF membranes[END_REF].

Solutions

Then, in the two publications, it was observed that the retention of sulfuric acid begins to increase with solution pH once the pH reaches a value that is about 1 pH unit higher than its pKa2 (1.99) [START_REF] López | Experimental and theoretical study of nanofiltration of weak electrolytes: SO4 2-/HSO4 -/H+ system[END_REF][START_REF] Tanninen | Effect of electrolyte strength on acid separation with NF membranes[END_REF]. This observation indicate if the pKa value of sulfuric acid increases by 1 unit (i.e., pKa + 1), then the retention could be in accordance with the dissociation curve of sulfuric acid.

The theoretical pKa values considered are the ones in water, at 25 °C and infinite dilution.

However, it is known that the properties of the bulk solution can significantly influence the pKa values of weak acids. For instance, it was reported that the pKa of acetic acid increases from 4.76 to 9.72 when the dielectric constant of the solvent decreases from ε=78.3 (water, 25 °C) to ε = 32.64 (methanol, 25 °C) and that pKa values of propionic and butyric acids also follow the same trend [START_REF] Marshall | The potentiometric measurement of acid dissociation constants and pH in the system methanol-water. pKa values for carboxylic acids and anilinium ions[END_REF]. Moreover, it is known that in a confined space, the dielectric constant can be lower than in the bulk [START_REF] Aguilella-Arzo | Dielectric saturation of water in a membrane protein channel[END_REF]. Then one can expect a higher solute pKa for confined solution due to the decrease of dielectric constant. This could be an explanation the higher pKa values necessary to fit the results.

On the other hand, previous calculations were made considering that the membrane charge remains constant. Indeed, it was assumed that the retention of the charged VFA was identical to that obtained at pH 8 at the corresponding ionic concentration. However, not only the proportion of charged solute but also the membrane charge can vary with the pH.

In order to consider the change of the membrane charge with the pH, and its impact on the retention of dissociated VFAs, a correction parameter, α, is introduced in the model. The modified model is shown in Eq. (V.11). The pKeff values obtained from the fitting are correlated to the pKa values of the membrane functional groups. The pKeff values (from 5.44 to 5.80) obtained from the fitting are within the range of the membrane pKa values previously reported. Indeed, for carboxylic functional groups on polyamide films, pKa values from 5 to 9 were obtained by contact angle titration [START_REF] Wamser | Detection of Surface Functional Group Asymmetry in Interfacially-Polymerized Films by Contact Angle Titrations[END_REF].

𝑅𝑅 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 𝑐𝑐𝑎𝑎𝑡𝑡 = 𝑅𝑅 𝐻𝐻𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 × (1 -𝑃𝑃 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 -, 𝑝𝑝𝑝𝑝 𝑎𝑎 ) + α × 𝑅𝑅 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 -(𝑐𝑐 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 -, 𝑝𝑝𝑝𝑝 𝑎𝑎 ) × 𝑃𝑃 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 -, 𝑝𝑝𝑝𝑝 𝑎𝑎 (V.
Furthermore, the first pKa values reported for five different NF/RO membranes with polyamide active layer using heavy ions probes were between 5.23 and 5.72 [START_REF] Coronell | Quantification of Functional Groups and Modeling of Their Ionization Behavior in the Active Layer of FT30 Reverse Osmosis Membrane[END_REF][START_REF] Coronell | Ionization Behavior , Stoichiometry of Association , and Accessibility of Functional Groups in the Active Layers of Reverse Osmosis and Nanofiltration Membranes[END_REF]. Current results indicate that the retention of charged solute could be directly related to the dissociation of membrane functional groups that determines the membrane charge.

It was also reported in previous work that the experimental dissociation curves were broadened compared with simulated ones [START_REF] Wamser | Detection of Surface Functional Group Asymmetry in Interfacially-Polymerized Films by Contact Angle Titrations[END_REF]. Current results also show the broadening of the correction parameters versus solution pH compared with simulated dissociation curves (see Figure V-23b).

This could be due to that carboxylic functional groups on the NF membrane have different pKa values, as suggested in ref. [START_REF] Coronell | Quantification of Functional Groups and Modeling of Their Ionization Behavior in the Active Layer of FT30 Reverse Osmosis Membrane[END_REF] and [START_REF] Wamser | Detection of Surface Functional Group Asymmetry in Interfacially-Polymerized Films by Contact Angle Titrations[END_REF]. The different pKa values observed for the carboxylic functional groups on the membrane could occur due to the site-site interactions between functional groups on the polymer chains, which may be related to the low dielectric constant within the aliphatic chain and/or inside the confined membrane pores [START_REF] Coronell | Quantification of Functional Groups and Modeling of Their Ionization Behavior in the Active Layer of FT30 Reverse Osmosis Membrane[END_REF][START_REF] Koper | Proton binding by linear , branched , and hyperbranched polyelectrolytes[END_REF][START_REF] Sadeghpour | Influence of alkali metal counterions on the charging behavior of poly ( acrylic acid )[END_REF].

In addition, the three different pKeff values (5.4 for 500mM and 5.75 for 100mM, and 5.80 for 200mM) obtained for three total concentrations seem indicate that the membrane/solute charge interaction is concentration-dependent. This could be due to the ionization of functional groups.

Indeed, as previously mentioned concerning VFAs, the ionization constant of weak acid decreases with ionic concentration according to Debye-Hückel law [START_REF] Borkovec | Ionization Processes and Proton Binding in Polyprotic Systems : Small Molecules , Proteins , Interfaces and Polyelectrolytes[END_REF] so that a lower pKa value can be observed at higher ionic concentration. Current result is in agreement with this trend.

V.3 Conclusion

Solution pH as well as ionic concentration have significant influence for the nanofiltration of On the one hand, increasing the pKa values of the VFAs by 1.24 units, the calculated retention curves can fit the experimental ones. Based on the knowledge that the dielectric constant in a confined space can decrease, and that the pKa of VFAs increases when the dielectric constant in the solution decreases, this explanation could be partially realistic. Further calculation also showed that when the filtration flux increase, the experimental retention curves are more close to the theoretical ones, i.e. the fitted pKa becomes close to the theoretical value.

On the other hand, considering a correction parameter related to the membrane charge, the calculated retention curves can also be in agreement with the experimental ones. The correction Therefore, this explanation could also be realistic.

The current work discussed the VFAs retention through a simple model which can be applied to single and mixed VFAs solutions, the different possible mechanisms for the influence of solution pH on VFAs retention were discussed. However, since the influence of pH involves the dissociation of VFAs as well as of the membrane, the influence of each cannot be distinguished.

Further work is still required to reveal the different mechanisms and to which extent can those mechanisms influence the retention of electrolytes.

This chapter investigated the retention and separation performance of nanofiltration process on a real fermentation broth at different pH, aim to explore the possible treatment.

The possible applications of VFAs are introduced in Chapter I, it is reported that higher proportion of butyric acid is more favorable for PHA (polyhydroxyalkanoates) production [START_REF] Yang | Optimization of growth media components for polyhydroxyalkanoate ( PHA ) production from organic acids by Ralstonia eutropha[END_REF].

On the contrary, butyric acid is considered as unfavorable for energies and biofuel applications, as it can reduce the degradation rate for MFC (microbial fuel cell) process [START_REF] Choi | Performance of microbial fuel cell with volatile fatty acids from food wastes[END_REF], and reduce the production of microbial lipids [START_REF] Liu | Bioconversion of volatile fatty acids derived from waste activated sludge into lipids by Cryptococcus curvatus[END_REF][START_REF] Huang | Improved volatile fatty acid production during waste activated sludge anaerobic fermentation by different bio-surfactants[END_REF]. Furthermore, it is observed that, in the fermentation broth, organic impurities such as ethanol and methanol can hinder the following applications such as PHA fermentation [START_REF] Tamis | Enrichment of Plasticicumulans acidivorans at pilot-scale for PHA production on industrial wastewater[END_REF][START_REF] Marang | Impact of non-storing biomass on PHA production: An enrichment culture on acetate and methanol[END_REF].

Then, there are three main objectives for the NF process for the treatment of fermentation broth containing VFAs. Firstly, inorganic ions like Cl -are generally unfavorable components for VFAs valorization, the removal of Cl -by NF is considered. Then, it is more favorable to change the proportions of acetic, propionic, and butyric acids according to the requirement of the following applications. Finally, it is necessary to extract VFAs and remove hindering organics (i.e., ethanol and methanol).

VI.1 Individual solutes retentions in synthetic and real fermentation broths

VI.1.1 Individual solutes retentions in synthetic broths

The experimental investigation is firstly carried out with synthetic broths with similar compositions as the real fermentation broth. The composition of the VFAs real fermentation broth is shown in Table VI-1. It mainly contains Ac, Pr, Bu, and Cl -, the cations compositions are mainly Na + and Ca 2+ , with trace amount of NH4 + and K + .

As already mentioned in Chapter II, the TOC of VFAs is calculated from the concentration of VFAs in the real fermentation broth obtained using HPLC, then the TOC of organic matters/impurities (OM) is the TOC other than the TOC of VFAs (TOC-TOC_VFAs). From the composition obtained from HPLC analysis, ethanol is the main contributor of the TOC of OM (244 mg.L -1 of TOC_ethanol out of 334mg.L -1 TOC_OM, 73%). One can observe that the retentions of VFAs at acidic condition are lower than the retentions at alkaline condition. Indeed, retentions of Ac, Pr, and Bu at pH 5.7 without the addition of salts (Syn1) for the filtration flux of 1*10 -5 m.s -1 are 91%, 93%, and 96% respectively, while the retentions of VFAs at pH 8 for the same filtration flux are all above 98%. On the other hand, the retention of Cl -at pH 5.7 is lower than that at pH 8, especially at low filtration flux.

Then, it is shown that the differences between individual VFAs retentions without and with the addition of inorganic salts at pH 5.7 are lower than 5%, especially at high filtration flux.

Similar phenomenon is found for VFAs retentions at pH 8. Current observation shows that the addition of NaCl and CaCl2 can only influence the retention of VFAs to a limited extent. This result is in agreement with that observed for NF-45 membrane in Chapter IV. Furthermore, it is observed that the retention sequence of the four solutes is Cl -<Ac<Pr<Bu at pH 8, the same as that observed in Chapter IV using NF-45. However, at pH 5.7, the retention sequence of the four anions changed to Ac<Pr<Bu≈Cl -, reverse sequence is observed between the retentions of VFAs and Cl -.

It is discussed in Chapter V that the solution pH has a significant influence for the retention of VFAs. At diluted solutions, the retention of dissociated VFAs is much higher than the retention of the undissociated ones, due to the charge effect. Then, the retention of VFAs observed at pH 5.7 is a combination of the retentions of undissociated and dissociated VFAs. The increase of solution pH increases VFAs retention, due to a higher proportion of dissociated VFAs as well as higher membrane charge.

In order to figure out the retentions of dissociated and undissociated VFAs, a calculation based on VFAs dissociation and electroneutrality both in the feed and permeate is carried.

Firstly, the dissociation of the three VFAs all depend on the dissociation constant of each VFA and 𝐻𝐻 + concentration in the solution, both in the feed and permeate. In the mixed solution, 𝐻𝐻 + concentration is the same for the three VFAs. The dissociation of the three VFAs at given 𝐻𝐻 + concentration in the feed or permeate can be given in Eq. (VI.1).

[𝐻𝐻 + ] = 𝑝𝑝 𝑎𝑎 𝑉𝑉𝐴𝐴 ×{[𝐴𝐴𝑐𝑐]-[𝐴𝐴𝑐𝑐 -]} [𝐴𝐴𝑐𝑐 -] = 𝑝𝑝 𝑎𝑎 𝑃𝑃𝑟𝑟 ×{[𝑃𝑃𝑟𝑟]-[𝑃𝑃𝑟𝑟 -]} [𝑃𝑃𝑟𝑟 -] = 𝑝𝑝 𝑎𝑎 𝐵𝐵𝐵𝐵 ×{[𝐵𝐵𝐵𝐵]-[𝐵𝐵𝐵𝐵 -]} [𝐵𝐵𝐵𝐵 -] (VI.1)
Then, the concentration of anions and cations in the solution are equal. The concentration of 𝐻𝐻 + and 𝑂𝑂𝐻𝐻 -is negligible (concentration of 𝐻𝐻 + is lower than 10 -2 mM at pH 5.7, and concentration of 𝑂𝑂𝐻𝐻 -is about 10 -3 mM at pH 8, more than two magnitudes lower than the concentration of solute). Then, the electroneutrality in the feed and permeate is given in Eq. (VI.2).

[𝑁𝑁𝑎𝑎 + ] + [𝐶𝐶𝑎𝑎 2+ ] = [𝐻𝐻𝑐𝑐 -] + [𝑃𝑃𝑟𝑟 -] + [𝐵𝐵𝐵𝐵 -] (VI.2)
[𝐻𝐻 + ] concentration of 𝐻𝐻 + in the feed or permeate 𝐾𝐾 𝑎𝑎 𝑉𝑉𝐴𝐴 , 𝐾𝐾 𝑎𝑎 𝑃𝑃𝑟𝑟 , 𝐾𝐾 𝑎𝑎 𝐵𝐵𝐵𝐵 the dissociation constant of Ac, Pr, and Bu respectively, in the feed or permeate.

[𝐻𝐻𝑐𝑐] , [𝑃𝑃𝑟𝑟] , [𝐵𝐵𝐵𝐵] the concentrations of both dissociated and undissociated Ac, Pr, Bu, respectively, in the feed or permeate. One can observe that the retention sequence of dissociated VFAs in the system is Ac -<Pr -<Bu -, and for the undissociated VFAs, the retention sequence is Ac<Pr<Bu, both following their MWs.

Then, it is found that the retention of Cl -is lower than the retention of dissociated VFAs but higher than the retentions of undissociated VFAs.

Therefore, considering the retention sequence of the dissociated forms, the sequence of anions is Cl -<Ac -<Pr -<Bu -at pH 5.7 using XLE membrane, following their MWs. This sequence is the same as that obtained at pH 8 by XLE membrane and NF-45 membrane (reported in Chapter IV). The retentions of all the cations in the synthetic broths at acidic (pH 5.7) and alkaline (pH 8) conditions are given in Figure VI-4. Similar to the retention of VFAs, the retention of Na + and Ca 2+ at pH 5.7 is lower than that at pH 8, especially at low filtration flux. For the synthetic broth with the addition of CaCl2, the retention sequence is Na + <Ca 2+ , the same as that reported in

Chapter IV with NF-45 membrane.

Then, one can observe that, as the total concentration increases from 117mM (Syn1, VFAs without salts) to 141mM (Syn2, VFAs+NaCl), the retention of Na + slightly decreases, showing the influence of screening effect. Then, in the presence of Ca 2+ (Syn3, VFAs+CaCl2, ionic concentration 165mEq.L -1 ), the retention of Na + decreases more compared to other compositions, this observation could be due to the influence of both screening effect and co-ions competition. One can observe that the retention sequence for VFAs and Cl -is Cl -<Ac<Pr<Bu. This retention sequence is the same as that observed for mixed solutions (i.e., VFAs+NaCl and VFAs+CaCl2) at pH 8 reported in Chapter IV. The sequence observed at pH 5.7 is not differed from that observed at pH 8 as that reported previously using XLE membrane. This could be due to that the retention of Cl -using NF-45 membrane (15% at filtration flux = 1×10 -5 m/s, pH 5.7) is much lower than that using XLE membrane (95% at filtration flux = 1×10 -5 m/s, pH 5.7), a lower pH value is required to obtain the reverse trend. Then, it is observed that the retentions of VFAs in synthetic broths without salts (Syn4) and with addition of NaCl (Syn5) are similar. However, with the addition of CaCl2 (Syn6), the retentions of VFAs slightly increased. Nevertheless, the differences between the retentions of VFAs for the three synthetic broths are below 10%, except for the conditions at the lowest filtration flux. This indicates that the influence of inorganic salts on VFAs retentions is not significant, as already concluded in Chapter IV.

For the retentions of cations, one can observe that as the concentration of synthetic broths increases from 116mM (Syn4, VFAs without salts), 140mM (Syn5, VFAs+NaCl), to 164mEq.L - 1 (Syn6, VFAs+CaCl2), the retention of Na + decreases gradually.

Indeed, in synthetic broths Syn4 and Syn5, Na + is the only cation in the solution, while in the synthetic broth Syn6, both Na + and Ca 2+ are presented. The decrease of Na + retention in synthetic broth Syn5 compared to Syn4 could be due to the screening effect, since the total concentration increases from 116mM to 140mM. Then, the decrease of Na + retention in synthetic broth Syn6 could be due to the combination of screening effect and co-ions competition between Na + and Ca 2+ . Current observation is in agreement with the result obtained using XLE membrane. Similar observations are reported in Chapter IV and ref. [START_REF] Vonk | Positive and Negative Ion Retention Curves of Mixed Electrolytes in Reverse Osmosis with a Cellulose Acetate Membrane . An Analysis on the Basis of the Generalized Nernst-Planck Equation[END_REF]. The previous investigation has shown that the XLE membrane has higher retention of VFAs than the NF-45 membrane at both pH 5.7 and pH 8. When operated at pH 8, retentions of all the VFAs are higher than 98% and nearly no retention difference between VFAs is observed.

Therefore, it is difficult to compare the individual solutes retentions at pH 8. In the following section, the investigation of XLE membrane with the real fermentation broth is only made at the initial pH (pH 5.7).

The retentions of all the anions and cations in the real fermentation broth at the initial pH (pH 5.7) are given in Figure VI-7. The concentration of K + in the permeate is below the detection limit of the analytical method, thus the retention of K + is not shown. The retentions of Ac, Pr, and Bu in the real fermentation broth are 95%, 96%, and 99% respectively, at a filtration flux of 1×10 -5 m.s -1 , slightly higher than those in synthetic broths (about 90%, 93%, and 96% for Ac, Pr, and Bu respectively, filtration flux=1×10 -5 m.s -1 ). The retention sequence of VFAs and Cl -is Ac<Pr<Cl -<Bu, the same as that observed in synthetic broths.

For the cations, the retention of the divalent ion, Ca 2+ , observed the highest among all the cations, followed by Na + and NH4 + . The retention sequence of all the cations is NH4 + <Na + <Ca 2+ . The retentions of all the anions and cations are similar to those in the synthetic broths, indicating that the presence of other impurities (e.g. ethanol and butanol) has no significant influence on the retentions of the main components.

VI.1.2.2 Nanofiltration using NF-45 membrane

In Chapter V, it is shown that the retentions of VFAs using NF-45 membrane are significantly influenced by solution pH, high pH is beneficial for VFAs retention as well as separation.

Therefore, the following investigations on the real fermentation broth using NF-45 membrane are operated at increasing solution pH (i.e., 5.7, 6.6, and 8.2).

As mentioned in Chapter II, the same batch of VFAs real fermentation broth is used for the experiments using both XLE and NF-45 membranes. The volume of the VFAs real fermentation broth (about 800 mL) is not enough for all the experiments and the retentate and permeate has to be recycled after each experiment.

The real fermentation both at the initial pH (pH 5.7) used for NF-45 membrane was recycled from the retentate and permeate of the previous filtration using XLE membrane. Then, after the filtration using NF-45 membrane, the permeate and retentate were recycled again. The recycled real fermentation broth was adjusted to pH 6.6 using NaOH solution, and filtration is carried out using the pH adjusted real fermentation broth. Finally, the recycled real fermentation broth was adjusted to pH 8.2 and the last filtration is applied using NF-45 membrane.

Due to the recycle and reuse, the compositions of the real fermentation broth slightly modified between different experiments. However, the modification of the compositions between all the four experiments is below 2%.

The retentions of all the anions and cations in the real fermentation broth at pH 5.7, 6.6, and For the retentions of anions, it is observed that the retention sequence in the real fermentation broth is Cl -<Pr<Ac<Bu, for the three pH values investigated. The retention sequence of Ac and Pr is altered compared to that in ternary solutions and synthetic solutions (Ac< Pr<Bu).

According to the composition of the real fermentation broth, ethanol is the major component beside VFAs. Experiments for VFAs ternary solutions with the addition of 10mM and 50mM of ethanol were carried out at pH 5.7, in order to test if the presence of ethanol can influence the retention sequence between Ac and Pr. However, the experimental results show that no reverse sequence between the retentions of Ac and Pr is observed.

The alteration of retention sequence of Ac and Pr in a real fermentation broth was also reported by Xiong et al., using Desal DK and DL membrane to filtrate digested liquor at a solution pH of 7 [START_REF] Xiong | Integrated acidogenic digestion and carboxylic acid separation by nanofiltration membranes for the lignocellulosic carboxylate platform[END_REF]. The mechanism of the alteration in retention sequence is unknown and deserves further investigation.

Then, the retentions of VFAs gradually increase when the solution pH increase from 5.7, 6.6, to 8.2. Meanwhile, the retention of Cl -continuously decreased when pH increase, a negative value of Cl -retention is observed at low filtration flux at pH 8.2.

The increase of VFAs retentions and decrease of Cl -retention when solution pH increases shows the enhancement of co-ions competition between VFAs -and Cl -. As discussed in Chapter The retentions of the TOC of the real fermentation broth (TOC), the TOC of the three VFAs (TOCVFAs), and the TOC of the organic matters/impurities (TOCOM) are given in Figure VI-13.

It is observed that the retention sequence of the TOC of the real fermentation broth, the TOC of the three VFAs, and the TOC of the organic matters/impurities is TOCOM<TOC< TOCVFAs. At the filtration flux of 1 ×10 -5 m/s, the retention of TOCOM, TOC, and TOCVFAs are 57%, 94%, and 97% respectively. The retentions of the TOC of the real fermentation broth and the TOC of VFAs are much higher than the retention of TOCOM. This result indicate that it is possible to reject VFAs while remove OM in the retentate.

Figure VI-10

The retentions of the TOC of real fermentation broth (TOC all ), the TOC of the three VFAs (TOC VFAs ), and the TOC of the organic matters/impurities (TOC VFAs ) using XLE membrane at pH 5.7.

VI.2 Proportions of individual solutes in the permeate of synthetic and real fermentation broths

Following the results of the previous chapters, it is concluded that for a given solute proportion in the feed, there is a fixed solute proportion in the permeate when the filtration flux is higher than a certain value, both for NF-45 membrane and XLE membrane at different pH values investigated.

In this section, this finding will be checked with synthetic and real fermentation broths.

VI.2.1 Synthetic fermentation broths

The permeate proportions of all the anions in the six synthetic broths versus filtration flux One can observe that, for a given solute proportion in the feed, it seems that a given solute proportion in the permeate is obtained, except for low filtration flux, both for VFAs and Cl -.

In the permeate of XLE membrane, the proportion of Ac increases compared to that in the feed, while the proportion of Bu and Cl -decrease compared to their proportions in the feed; the proportion of Pr in the permeate only slightly increases compared to that in the feed (Figure VI-11a). In the permeate of NF-45 membrane, the proportions of Ac, Pr, and Bu increase and decrease following the same trend as that in the permeate of XLE membrane. However, the proportion of Cl -increases compared to that in the feed.

Ac Bu

The relative proportions of VFAs is considered to compare the performance of the two membranes on the separation of VFAs. The relative proportion is defined in Chapter II using Eqs.

(II.6), (II.7), (II.8), and (II.9). Then, the relative proportions of Ac, Pr, and Bu in the permeate versus filtration flux for the couples of Ac/Pr, Pr/Bu, and Ac/Bu using XLE and NF-45 membranes are given in Figure Considering the couple of Ac/Pr, one can observe that the relative proportion of Ac increases in the permeate compared to that in the feed, while the relative proportion of Pr decreases in the permeate compared to that in the feed, when filtration flux increase. The relative proportions of Ac and Pr in the permeate both reaches a plateau when the filtration flux is higher than a certain value. This observation is found in the permeate of both XLE and NF-45 membranes for the synthetic broths without and with salts. And the same results are observed for the couples of Pr/Bu and Ac/Bu too. Current observation indicates that relative proportions of solutes in the permeate mainly depends on the relative feed proportions, and the addition of inorganic salts does not influence the relative proportion in the permeate. This result is in agreement with that observed in Chapter IV using NF-45 membrane at pH 8, Then, one can observe that the relative proportion of Ac for the couple of Ac/Pr increases from 50% in the feed to 58% in the permeate (at the plateau value) using XLE membrane. However, for NF-45 membrane, the relative proportion only slightly increased from 60% in the feed to 62% in the permeate (at the plateau value). Similar observations can be found for the couples of Pr/Bu and Ac/Bu. These results indicate that at pH 5.7, XLE membrane can be more efficient to modify the VFAs proportion in the permeate compared to NF-45 membrane.

The proportions of cations (Na + and Ca 2+ ) in the permeate of synthetic broths Syn3 and Syn6 As observed for anions, the proportion of Na + in the permeate increases while the proportion of Ca 2+ decreases with filtration flux, reached a plateau when the filtration flux is higher than a certain value. In addition, one can observe that with the feed proportions of Na + and Ca 2+ similar in Syn3 and Syn6 (67%:33% and 69%:31% respectively), the same proportion in the permeate (Na + :Ca 2+ =91%:9%) is observed using both XLE and NF-45 membranes. This shows that the two membranes have similar capabilities to the modification of Na + and Ca 2+ proportions, when the filtration flux is higher than a certain value. It is observed that the proportions of Ac increase, Bu and Cl -decrease, while Pr remain nearly constant when the filtration flux increases. The proportions of all the anions reach constant values when the filtration flux is higher than a certain level, as observed for synthetic broths.

For the cations, it is shown that the proportion of Na + decreases when the filtration flux increases, reached a constant proportion of 40% when the filtration flux is higher than a certain value. This result is in agreement with that observed for synthetic broths. in the permeate is much lower than that in the feed, while the proportion of NH4 + in the permeate is much higher than that in the feed. When the filtration flux increases, the permeate proportion of Ca 2+ increases, meanwhile the permeate proportion of NH4 + decreases before reach a constant proportion when the filtration flux is higher than a certain value. This behavior is also observed for the proportions of cations in the permeate of synthetic broth (Syn 3, shown in Figure .

For NF-45 membrane, it is always observed that the differences between the individual solutes proportions in the permeate continuously increase when the filtration flux increase, and reached a constant value when the filtration flux is higher than a certain value. The same observation is found for anions using XLE membrane. However, when the proportion of cations in the permeate is considered using XLE membrane, it seems that different behavior is observed. The differences between individual cations proportions in the permeate firstly reach the highest value at the lowest filtration flux investigated, then decrease when the filtration flux increase, before reaching a constant value when the filtration flux is higher than a given level. This abnormal behavior requires further investigation.

The anions and cations proportions in the permeate of the real fermentation broth using NF- As for synthetic broths, one can observe that the proportions of individual anions in the permeate change with filtration flux, the proportion of Cl -and Pr increase while the proportions of Ac and Bu decrease, reach a plateau when the filtration flux is higher than a certain value for the three pH investigated.

For the cations, the proportions of monovalent cations, Na + , NH4 + , and K + in the permeate all increase, while the proportion of Ca 2+ decreases, for the three pH investigated. It is noticed that except for the proportions of Na + and Ca 2+ in the permeate at pH 5.7, a constant proportion is observed for each cation when the filtration flux is higher than a given value.

In addition, one can observe that when the solution pH increases, the filtration flux required to obtain the constant permeate proportion significantly decreases from more than 1.25 ×10 -5 m.s - 1 at pH 5.7, to about 0.5 ×10 -5 m.s -1 at pH 8.2. This is in agreement with what was observed for VFAs ternary solutions in Chapter V. For the permeate of NF-45 membrane, one can observe that when the pH increases from 5.7, 6.6, to 8.2, the differences between the relative proportions of VFAs in the permeate enlarged. For the same VFAs feed proportions, the higher the difference between VFAs proportions in the permeate, the better the separation. Therefore, this observation indicates that best separation between VFAs is observed at the highest pH for NF-45 membrane.

For a given feed composition, the previous investigation has shown that the best separation is obtained when the permeate proportion reaches the plateau value. Therefore, the following discussion and comparison use the relative proportions at the plateau value.

To The relative proportions of two solutes in the feed and permeate represent the separation performance of NF on the two solutes. Indeed, as defined, the separation factor between the two solutes can be calculated from their proportions in the feed and permeate use Eq.(II.11). Therefore, for a given feed proportion, the separation factor is the quotient of the relative proportions of the two solutes in the permeate, the more difference between the proportions of the two solutes in the permeate, the higher the separation performance.

For the results using XLE membrane at pH 5.7, one can observe that the relative proportions of Ac and Pr in the feed and permeate of synthetic and real fermentation broths for the couple of Ac/Pr can be fitted with one single curve. Then, when the relative proportions of Bu in the feed are about 50%, the proportions of Bu in the permeate obtained for the real fermentation broth are about 10% and 6% lower than that observed for synthetic broths, for the couples of Pr/Bu and Ac/Bu respectively.

For the results using NF-45 membrane at various pH values, firstly, it is observed that the relative proportions of Ac and Pr in the feed and permeate in the real fermentation is the reverse compared to that in the synthetic broths for the couple of Ac/Pr.

At pH 5.7 and pH 8, one can observe that the relative proportions of Pr and Ac in the permeate of the real fermentation broth are always higher than those observed in the synthetic solutions/broths. The improvement for the couple Pr/Bu is much significant compared to that of the couple of Ac/Bu. Indeed, for the couple of Ac/Bu, the relative proportions of Ac and Bu in the feed and permeate for synthetic solutions/broths and the real fermentation broth are similar both for pH 5.7 and 8.

Current results show that the performance of XLE membrane on the separation of VFAs is similar for synthetic and real fermentation broths. The presence of organic and inorganic components in the real fermentation broth does not influence the separation performance of XLE membrane on VFAs. For NF-45 membrane, the separation performance between Ac and Bu is nearly the same for synthetic and real fermentation broths at pH 5.7 and 8, showing the negligible influence of organic and inorganic components in the real fermentation broth. However, the mass transfer of Pr is greatly improved in the real fermentation broth, meaning that there is an additional mechanism improving the membrane separation performance (i.e., the enhancement of the transfer of Pr in real fermentation broth compared to that in synthetic solutions).

The comparison between the relative proportions of VFAs in the feed and permeate for the synthetic and real fermentation broth using XLE and NF-45 membranes at pH 5.7 is given in VFAs and OM reach a plateau once the filtration flux is higher than a certain value. This observation confirms that, for a mixed solution as complex as a real fermentation broth, when the feed proportion is fixed, one given permeate proportion can be observed when the filtration flux is higher than a certain value. One can also observe that the TOC corresponding to VFAs in the permeate are dramatically decreases from 92% in the feed to 45% in the permeate at the plateau value, while the proportion of TOC corresponding to OM increases from 8% in the feed to 55% in the permeate at the plateau value. Then, regarding TOC, NF with XLE membrane provides a retentate significantly enriched in VFAs.

VI.3 Performances of NF for the treatment of VFAs fermentation broth

The applications of NF for the treatment of real fermentation broth containing VFAs can have many possibilities. Three kinds of applications are discussed, which are (1) inorganic salts removal, (2) VFAs composition modification (Individual VFAs separation), and (3) organic matter (OM) removal.

VI.3.1 Case 1: Inorganic salts removal

Inorganic salts are usually unfavorable and even considered as an impediment for biological applications. To remove the inorganic salts, the separation between VFAs (as a total) and Cl -as well as Ca 2+ and Na + is discussed. One can observe that the proportion of Cl -decreases in the permeate of XLE membrane (from 20% to 16%), while increases in the permeate of NF-45 membrane, for the three pH values investigated. It is shown that the separation factor between VFAs and Cl -is 1.3 at initial pH (5.7) using XLE membrane, while increased to 2.0 using NF-45 at the same pH. Then, when the solution pH increases to 6.6 and 8.2, the separation factor between VFAs and Cl -increases to 3.4 and 4.0 respectively. Current results show that NF-45 has much better separation performance on VFAs and Cl -compared to XLE membrane.

The proportion of Ca 2+ and Na + in the feed and permeate (at the constant values) as well as the separation factor between Na + /Ca 2+ are given in Table VI-5. It is observed that the proportion of Na + in the permeate increases with the two membranes for all the pH investigated. Then, the separation factor between Ca 2+ and Na + is 2.3 using XLE membrane, while increases to 3.2 using NF-45 membrane at the initial pH (5.7).

Then, despite the separation factor between Ca 2+ and Na + using NF-45 membrane can vary when the solution pH increases from 5.7, 6.6 to 8.2, it is observed that the proportion if Ca 2+ and Na + in the permeate are 63%±2% and 19%±2% respectively. This shows that the pH seems does not influence the separation between Ca 2+ and Na + . Then, considering the separation between monovalent (i.e., Na + , NH4 + , and K + ) and divalent (i.e., Ca 2+ ) cations, the proportions of monovalent and divalent cations in the feed and permeate for the two membranes at different pH are listed in Table VI-6.

For monovalent cations, one can observe that the proportion in the feed is 55% ±2%, then a proportion of 81%±2% in the permeate is observed for the two membranes at different pH values.

The current observation is in agreement with the result observed for synthetic broths (i.e., Syn3 and Syn6) using XLE and NF-45 membranes. It seems that the two membranes have similar performance for the separation of monovalent and divalent cations. At the initial pH (5.7), one can observe that the separation factor between Ac/Pr obtained using NF-45 membrane is higher than that obtained using XLE membrane, while the separation factors between Pr/Bu and Ac/Bu shown the reverse. Then, when increasing the solution pH, the separation factors between VFAs observed using NF-45 all increase, the highest values are all observed at pH 8.2. The separation factors between Ac/Pr and Pr/Bu in the real fermentation broth are much higher than that observed in synthetic solutions. However, the separation factor between Ac/Bu is similar (slightly higher) to that observed in synthetic solutions. One can observe that the proportion of Ac+Pr is enriched in the permeate, while the proportion of Bu is enriched in the retentate. At initial pH (5.7), the separation factor between Ac+Pr and Bu is better using XLE membrane; then, at pH 8.2, higher separation factor is observed using NF-45 membrane. At the best condition (NF-45 membrane at pH 8.2), the highest separation factor obtained for Ac+Pr and Bu is 3.8.

VI.3.3 Case 3: Organic matters removal

Ethanol and methanol are common by-products during anaerobic fermentation, and they are considered as unfavorable organic matters (OM) for PHA production.

In the previous section, it is shown that the retention of OM (mainly ethanol) is much lower than the retention of VFAs using XLE membrane, then, the OM (other than the TOC of VFAs) is enriched in the permeate and it is possible to remove the OM from the fermentation broth.

Table VI-9 shows the proportions of VFAs and OM (in terms of TOC) in the feed and permeate and the separation factor between VFAs/OM using XLE membrane. The separation factor between VFAs/OM is as high as 14.8, indicating that a good separation between VFAs and OM can be achieved.

VI.4 Conclusions

Current Chapter investigated the nanofiltration of synthetic broths containing only VFAs, VFAs with two salts (NaCl and CaCl2), as well as a real fermentation broth containing anions (Ac, Pr, Bu, and Cl -) and cations (Ca 2+ , Na + , NH4 + , and K + ) using two NF membranes (XLE and NF-45 membranes). The experiments were operated at various total concentrations and pH values.

The results showed that, the modification of individual VFAs retention due to the influence of the addition of inorganic salts is less than 10%, especially at high filtration flux, for the two membranes investigated. Then, the retentions of individual solutes in the real fermentation broth are slightly higher than that in the synthetic broths, for both membranes.

It was observed that the retention sequence of anions in synthetic broths is Cl -<Ac<Pr<Bu, following their molecular weights, for NF-45 membrane at pH 5.7 and 8, as well as for XLE membrane at pH 8. However, compared to other conditions, the retention sequence of VFAs and Cl -altered (i.e., Bu≈Cl ->Ac>Pr) for synthetic broths at pH 5.7 using XLE membrane. Further investigation showed that the observed retention of VFAs is a combination of the retentions of dissociated and undissociated VFAs, if only consider the dissociated forms, the retention sequence is Cl -< Ac -< Pr -< Bu -, as observed for pH 8.

Then, for XLE membrane, the retention sequence of anions and cations in the real fermentation broths are the same as that in the synthetic broths (i.e., Bu>Cl ->Pr>Ac and Ca 2+ >Na + ). However, for NF-45 membrane, the retention sequence of Ac and Pr was modified (i.e., Bu>Ac>Pr>Cl -) in the real fermentation broth compared to that in synthetic broths (i.e., Bu>Pr>Ac>Cl -). Similar results were already observed previously. Some experiments (not shown) were carried out to understand the mechanism explaining this modification but no clear explanation was drawn.

With the two types of NF membranes for all the synthetic and real fermentation broths at all the compositions and solution pH values investigated, it was observed that when the filtration flux is higher than a certain value, the individual solutes proportions in the permeate are constant for a given feed proportion.

Considering the relative proportion of VFAs, the performances of the two membranes for the separation of VFAs in synthetic and real fermentation broths were compared and discussed.

For the XLE membrane, it was observed that the relative proportions of VFAs in the feed and permeate obtained in synthetic and real fermentation broth are similar. For NF-45 membrane, the relative proportions of Ac and Bu for the couple of Ac/Bu are similar for the synthetic and real fermentation broths at pH 5.7 and 8.2. However, the relative proportions of Ac and Pr for the couple of Ac/Pr are the reverse in the real fermentation broth compared to that obtained in synthetic solutions/broths. This is due to the decrease in Pr retention (i.e. increase in Pr transfer)

previously reported, and further investigation is required to reveal the mechanism behind.

According to the separation factors between VFAs obtained at the plateau values of VFAs proportions in the permeate, XLE membrane is the better candidate for the separation of VFAs at pH 5.7. In contrast, at pH 8.2, NF-45 membrane has better separation performance compared to XLE membrane.

Besides, it was also noticed that the performance of the two membranes on the separation of monovalent and divalent cation are quite similar, both for synthetic and real fermentation broths.

This also deserves further investigation.

Finally, the possible applications of NF for the treatment of real fermentation were discussed.

It was observed that NF-45 is the better candidate for inorganic salts removal as well as modification of VFAs composition. At pH 8.2, the separation factor between VFAs and Cl -is 4.0, and the separation factor between shorter chained VFAs (i.e., Ac and Pr) and longer chained VFAs (i.e., Bu) is 3.8, using NF-45 membrane.

XLE membrane can be used to remove organic matters (OM) from VFAs, a separation factor of 14.8 between OM and VFAs is observed at the best condition.

General conclusions and perspectives

Global change leads to serious environmental problems, which has become an increasing concern for the last decades. Adopt renewable resources such as biomass to replace fossil resources could reduce the carbon emission and it is considered as one of the most beneficial way to slow down the global change.

Volatile Fatty Acids (VFAs) are promising biochemicals that can be used for biodegradable plastics and bioenergy production, and they also have the potential to become chemical building blocks. However, despite VFAs have many perspectives, the recovery and purification of VFAs from raw materials such as a fermentation broth are still challenging and hinder further applications.

Membrane processes are regarded as promising processes for the valorization of VFAs as well as other biomass. The VFAs are monovalent weak electrolytes with increasing molecular weights, and NF is considered as good option to separate individual VFAs. Nevertheless, some bottlenecks regarding the separation performance and mass transfer through the membrane may limit the application of NF for VFAs valorization. The retention of NF membrane on organic solutes depends on filtration flux, ionic concentration, solutes proportions, solution pH, as well as the presence of additional inorganic salts. The interactions between charged solutes as well as that between charged and uncharged solutes need further investigation. Thus, it was difficult to predict and improve the separation performance of NF process on organic solutes.

The objective of the thesis was to investigate the separation and valorization of aqueous solutions containing VFAs using nanofiltration. Synthetic solutions with increasing complexities from single, binary, and ternary solutions of VFAs (i.e., Ac, Pr, and Bu), to mixed solutions containing VFAs and inorganic salts at different compositions were firstly tested, the influence of solution pH on the retention of VFAs was also discussed in order to reveal the mass transfer mechanisms. Then, a real fermentation broth contain VFAs, inorganic salts, as well as organic matters, which was obtained by fermentation of municipal solid waste (MSW), was investigated.

Two NF membranes (NF-45 and XLE) were used for the investigation, and the performances of the two membranes on the separation and valorization of VFAs were discussed.

In the first part, synthetic solutions containing dissociated VFAs (pH 8) with various compositions were studied.

It was observed that in mixed solutions, the retention of the more retained solute increases compared to the one in single solution, while that of the less retained one decreases. This is in agreement with previous reported results. The retention sequence of the three VFAs is 𝑅𝑅 𝐴𝐴𝑐𝑐 -< 𝑅𝑅 𝑃𝑃𝑟𝑟 -< 𝑅𝑅 𝐵𝐵𝐵𝐵 -, following their MWs, observed for the two membranes investigated.

Then, it was found that for a given VFAs proportion in the feed, regardless of the total concentration, the proportion of VFAs in the permeate remains constant when the filtration flux is higher than a specific value. The filtration flux required to reach this constant plateau value increases with the increase of total concentration. From the perspective of mass transfer, this observation means that in a mixed solution, the individual charged solute transfer is controlled by the total amount of charge transferred through the membrane (i.e. total solute flux). Indeed, it was found that the individual VFA flux increases linearly with the total solute flux and does not depend on the total concentration but only on the VFAs proportions in the feed. This was observed for the two membranes used. Moreover, for a given feed proportions, it was observed that the permeate proportions are similar for the two membranes, despite their retention on VFAs are different.

Furthermore, the proportion in the feed influences the separation factors between VFAs. For identical proportion of each VFAs in the feed (i.e., Ac:Pr=50%:50% and Ac:Bu=50%:50% in binary solutions and Ac:Pr:Bu=33%:33%:33% in ternary solutions), the highest separation factors between VFAs were obtained. Moreover, for identical feed proportion, the separation factors between VFAs obtained in ternary solutions are always higher than that obtained in binary solutions.

In the second part, more complex solutions containing VFAs with the addition of three inorganic salts (Na2SO4, NaCl, and CaCl2) were further investigated.

The same retention sequence was observed for all the anions (𝑅𝑅 𝐶𝐶𝑡𝑡 -< 𝑅𝑅 𝐴𝐴𝑐𝑐 -< 𝑅𝑅 𝑃𝑃𝑟𝑟 -< 𝑅𝑅 𝐵𝐵𝐵𝐵 -< 𝑅𝑅 𝑆𝑆𝑆𝑆 4 2-), and cations (𝑅𝑅 𝑁𝑁𝑎𝑎 + < 𝑅𝑅 𝐶𝐶𝑎𝑎 2+ ), for single and mixed solutions, following their valence and MWs. In the mixed solutions, the retention of the more retained co-ion increases compared to the one in single solution, while that of the less retained one decreases, for all the anions and cations investigated. This results are in agreement with those observed in the first part.

In any condition, it was found that constant permeate proportions for organic and inorganic solutes (anions as well as cations) are obtained for a given feed proportion, when the filtration flux is higher than a certain value. Furthermore, it was concluded that, for any couple of co-ions (Ac/Pr, Pr/Bu, Ac/Bu, VFAs -/ SO4 2-or VFAs -/Cl -) in any mixed solution (binary, ternary, and with the addition of salts), the plateau value of the relative proportion of the individual co-ions in the permeate is fixed by its proportion in the feed. This conclusion was also extended to couples of cations (e.g., Na + /Ca 2+ ).

The separation factors between Ac/Pr, Pr/Bu, and Ac/Bu for the systems of VFAs, VFAs+Na2SO4, VFAs+NaCl, and NaVFAs+CaCl2 were determined. On the contrary to what was reported in previous studies with mixed solution containing uncharged and charged solutes, it was observed that the addition of both co-ions (anions) and counter-ions (cations) does not have a significant influence on the separation factors between VFAs.

In the third part, single and mixed VFAs solutions at various total concentrations and solution pH were investigated. The influence of solution pH on the retention of VFAs as well as the relative proportions of VFAs was discussed.

It was shown that the solution pH significantly changes the retention of VFAs as well as the permeate proportion of VFAs. However, for any pH value, a constant permeate proportion is observed for a given proportion in the feed when the filtration flux is higher than a specific value.

The filtration flux required to reach the plateau value increases when the solution pH decreases. At last, the separation performance of nanofiltration was evaluated. Synthetic broths with the three VFAs and inorganic salts, as well as a real fermentation broth produced from municipal solid waste were investigated.

The retention sequences of the charged solutes in synthetic solutions are 𝑅𝑅 𝐶𝐶𝑡𝑡 -< 𝑅𝑅 𝐴𝐴𝑐𝑐 -< 𝑅𝑅 𝑃𝑃𝑟𝑟 -< 𝑅𝑅 𝐵𝐵𝐵𝐵 -for anions and 𝑅𝑅 𝑁𝑁𝑎𝑎 + < 𝑅𝑅 𝐶𝐶𝑎𝑎 2+ for cations, observed using the two membranes. The same retention sequences were observed for the real fermentation broth, except for the reversed retention sequence between Ac and Pr for NF-45 membrane.

Then, it was found that whatever charged or uncharged solutes, even for unknown organic matters in the real fermentation broth, a constant proportion in permeate is observed when the filtration flux is higher than a certain value. This shows that the plateau value could be related to the nature of solutes and membranes, and this method could be used to compare the separation performances of different membranes.

Separation factor was used to characterize the separation performance of the two membranes with the real fermentation broth. It was observed that the separation factors between VFAs in the real fermentation broth are higher than those obtained with synthetic solutions. So, there are additional parameters that could influence the separation performance of the nanofiltration process.

It was observed that the NF-45 membrane can more efficiently separate Cl -from VFAs as well as modify the VFAs proportion in the permeate than XLE membrane. Ac and Pr are enriched in the permeate, while Bu is enriched in the retentate. The XLE membrane has a very high VFAs retention (>95% for all the VFAs). It can modify the proportion of VFAs and other organic matters (OM) in the permeate. Therefore, XLE membrane can be used to concentrate the VFAs fermentation broth and remove the hindering organics such as ethanol.

Besides, for the synthetic and real fermentation broths, it was observed that the proportions of divalent and monovalent cations proportion in the feed and permeate are similar. This indicates that the two membranes have similar abilities for the separation of mono/divalent cations.

This work also points out some interesting perspectives.

In current work, it was found that the solutes proportions in the permeate reached a plateau for VFAs in dissociated and undissociated form. It could be interesting to check if this observation is universal for all the solutes, as well as for different membranes. If it is universal, then this parameter could be used to compare the separation performances of different membranes on specific solutes. Furthermore, nanofiltration of solutions with non-aqueous solvents (e.g., organic solvent nanofiltration) need to be checked.

During the investigation on VFAs retention versus pH, the calculation can be carried out to mixed VFAs solutions by considering VFAs as one single solute. It needs to be checked if this simplification can also apply to other solutes (with more difference in pKa values).

Besides, investigation of the unexpected Pr transfer in the real fermentation broth when using NF-45 membrane could reveal the additional interactions.

Figure I- 1

 1 Figure I-1 Production of volatile fatty acids from waste, adapted from ref. [4].

  Those factors affecting the fermentation process are shown in Figure I-2.

Figure I- 2

 2 Figure I-2Production of waste-derived volatile fatty acids and their applications, adapted from ref.[START_REF] Lee | A review of the production and applications of waste-derived volatile fatty acids[END_REF]

Figure

  Figure I-2).

Figure I- 3

 3 Figure I-3 Schematic diagram of a typical two-chamber microbial fuel cell, adapted from ref.[START_REF] Du | A state of the art review on microbial fuel cells: A promising technology for wastewater treatment and bioenergy[END_REF]

Figure I- 4

 4 Figure I-4 Relationship between pH of solution and dissociation status of acetic acid

Figure I- 5

 5 Figure I-5 Schematic diagram of negative retention of NaCl in a mixture of NaCl and Na 2 SO 4 , adapted from [137].

  It aims to couple fermentation and separation processes to valorize solid urban wastes for the production of platform molecules. The schematic diagram of the RECOWER project is shown in Figure I-6. This project is cooperated between two research units, TBI and LGC. The fermentation broth contains VFAs is generated from bio-waste using a leaching bed reactor (LBR) by TBI, then, the VFAs-riched fermentation broth is treated via membrane processes such as NF and ED by LGC. The aim of the current thesis project is to investigate the nanofiltration of VFAs-containing streams, explore the possibility of nanofiltration for the separation and purification of waste-derived VFAs.

Figure I- 6

 6 Figure I-6 Schematic diagram of the RECOWER project: production and valorization of VFAs from solid waste

Figure II- 1

 1 Figure II-1 (a) Pure water permeability and (b) glucose retention of XLE and NF-45 membranes. T= 25 °C.

Figure II- 2

 2 Figure II-2 Schematic diagram of the filtration system

Figure II- 3

 3 Figure II-3 Composition of the synthetic VFAs solutions

  individual solutes retentions in the mixed solutions at different concentrations are influenced by the combination of screening effect and co-ions competition. This chapter gives an experimental study, dealing with the influence of the feed composition on nanofiltration of VFAs salts at pH 8, for which VFAs are totally dissociated. The retentions of solutes are measured, proportions of individual VFAs in the permeate of mixed solutions are calculated to discuss the influence of composition on the mass transfer mechanism of single and mixed VFAs solutions. Solution complexity is increased from single VFAs (acetate, propionate, and butyrate) at different concentrations to mixtures of VFAs (binary and ternary solutions) of different compositions. The experiments are carried out using NF-45 membrane for all the conditions, then, a XLE membrane is also used, the results obtained with the two membrane is compared and discussed.

  8) as a function of filtration flux are represented in Figure III-1a for the different concentrations. One can observe that for any solute, the retention increases with the filtration flux. Moreover, for a given filtration flux, the retention of the individual VFAs continuously decreases for increasing concentrations. The retentions of individual VFAs at various concentrations are compared at a given filtration flux of 2×10 -6 m•s -1 in Figure III-1b. The retention of acetate decreases from 65 % to 38 % as its concentration increases from 100mM to 500 mM with an intermediate value of 59 % at 200mM.

Figure III- 1 III. 1 . 2

 112 Figure III-1 Retention of VFAs in single solutions for different concentrations (a) retention versus filtration flux (b) retention versus concentration at a filtration flux of 2×10 -6 m.s -1 , using NF-45 membrane, at pH 8.

  butyrate=50%: 50%) (Figure and ternary solutions (acetate: propionate: butyrate=33%: 33%: 33%) (FigureIII-4). For the given filtration flux aforementioned, retentions of acetate and butyrate in binary mixture decrease from 72% and 86% at 100mM, to 58% and 80% at 200mM, then decline to 24% and 60% respectively for the total concentration of 500mM (Figure III-3b). For ternary solutions, the retentions of acetate, propionate and butyrate are 68%, 79% and 86% at 100mM, 49%, 68% and 77% at 200mM, and go down to 24%, 43%, and 58% at 500mM (FigureIII-4b). From these results, a general trend can be drawn. Indeed, for any composition and filtration flux, the same retention sequence is observed, i.e., acetate<propionate<butyrate. This sequence, already observed with single solutions, follows the VFAs molecular weights. For mixed solutions with different concentrations and proportions, i.e., Ac: Pr = 20% :80% (Figure III-5), Ac: Bu = 20% :80% (Figure III-6), Ac: Pr: Bu = 60%: 20% :20% (Figure III-7), Ac: Pr: Bu = 20%: 60% :20% (Figure III-8), and Ac: Pr: Bu = 20%: 20% :60% (Figure III-9), the same tendencies (i.e., Ac<Pr<Bu) can be also observed.

Figure III- 2 Figure III- 3 Figure III- 4 Figure III- 5 Figure III- 6 Figure III- 7 Figure III- 8 Figure III- 9

 23456789 Figure III-2 Individual VFAs retention in binary (acetate: propionate=50%:50%) solutions (a) retention versus filtration flux at different concentrations (b) retention versus concentration at a filtration flux of 2×10 -6 m.s -1 , using NF-45 membrane, at pH 8.

Figure III- 10 Filtration

 10 Figure III-10 Comparison of Individual VFAs retentions between mixtures and single solutions (Retention difference=𝑅𝑅 𝑚𝑚𝑖𝑖𝑚𝑚𝑉𝑉𝑉𝑉𝐴𝐴 -𝑅𝑅 𝑠𝑠𝑠𝑠𝑡𝑡 𝑉𝑉𝑉𝑉𝐴𝐴 ) for all the conditions investigated using NF-45 membrane, at pH 8.

Figure III- 11 Figure

 11 Figure III-11 Comparison of individual VFAs retentions in single and mixed solutions with different proportions at a filtration flux of 2×10 -6 m.s -1 and the total concentration of 500mM (a) Binary solutions (b) Ternary solutions using NF-45 membrane, at pH 8.

However, for ternary

  mixtures, no clear trend is observed for the retentions of individual VFAs obtained with mixtures of different proportions (Figure III-11b).

Figure III- 12 Figure

 12 Figure III-12 Individual VFAs proportions in the permeate for Binary (Ac/Pr, Ac/Bu, Pr/Bu) and ternary (Ac/Pr/Bu) solutions at different concentrations with equal VFAs proportion (50% or 33%) in the feed, using NF-45 membrane, at pH 8.

  Proportion in the permeate (%) Filtration flux (m/s) Ac:Pr:Bu = 20%:80%:0% 25% Proportion in the permeate (%) Filtration flux (m/s) 75% Ac Pr Proportion in the permeate (%) Filtration flux (m/s) 100 200 500 mM Proportion in the permeate (%) Filtration flux (m/s) 100 200 500 mM 32% Proportion in the permeate (%) Filtration flux (m/s) Ac:Pr:Bu = 20%: 0%:80% 68% Proportion in the permeate (%) Filtration flux (m/s) Ac Bu Proportion in the permeate (%) Filtration flux (m/s) Proportion in the permeate (%) Filtration flux (m/s) Proportion in the permeate (%) Filtration flux (m/s) Ac:Pr:Bu = 20%:20%:60% 100 200 500 mM 21% 31% Proportion in the permeate (%) Filtration flux (m/s) 48% Ac Pr Bu Proportion in the permeate (%) Filtration flux (m/s) Proportion in the permeate (%) Filtration flux (m/s) Proportion in the permeate (%) Filtration flux (m/s) Ac:Pr:Bu = 20%:60%:20% 100 200 500 mM 14% 27% Proportion in the permeate (%) Filtration flux (m/s) 59% Ac Pr Bu Proportion in the permeate (%) Filtration flux (m/s) Proportion in the permeate (%) Filtration flux (m/s) Proportion in the permeate (%) Filtration flux (m/s) Ac:Pr:Bu = 60%:20%:20% 100 200 500 mM 11% 16% Proportion in the permeate (%) Filtration flux (m/s) 72% Ac Pr Bu Proportion in the permeate (%) Filtration flux (m/s) Proportion in the permeate (%) Filtration flux (m/s)

Figure III- 15

 15 Figure III-15 The proportion difference to the constant values (proportion difference = 𝑃𝑃 𝑌𝑌 𝑝𝑝 * -𝑃𝑃 𝑌𝑌 𝑝𝑝 ) for binary solutions of Ac/Pr, Pr/Bu and Ac/Bu with identical proportions at total concentration of 100, 200, and 500 mM, using NF-45 membrane, at pH 8.

Figure

  Figure III-16a shows the ternary contour graphs of the VFAs proportions in the permeates of single and mixed solutions for all the proportions investigated. Those plots use the proportion of Ac, Pr, and Bu in the feed as three coordinates, and color from dark blue to deep red to represent the proportion of corresponding VFA in the permeate from 0 to 1 (with contour lines at 0.20, 0.40, 0.60, and 0.80 indicated). The red points correspond to the proportion of the solutions used for the experimental study, and the color and contour lines filling the space between those points represent the proportion of VFAs in the permeate at corresponding feed proportion obtained by linear interpolation of the experimental values. For each axis, the scale represents the proportion of one VFA in the feed from 0% to 100%; three vertices correspond to single solutions of VFAs, points

Figure

  Figure shows the separation factors between Ac/Pr, Pr/Bu, and Ac/Bu in binary and ternary solutions. The color from dark blue to deep red represents the separation factors from the minimum to the maximum, 1.37 to 1.51 for Ac/Pr, 1.32 to 1.44 for Pr/Bu, and 1.89 to 2.17 for Ac/Bu.

Figure III- 16

 16 Figure III-16 (a) VFAs proportions in the permeate, and (b) separation factors between VFAs, at all the compositions in the feed investigated, using NF-45 membrane, at pH 8.

Figure III- 17

 17 Figure III-17 Individual solute flux as a function of total solute flux, for binary (Ac/Pr, Ac/Bu, Pr/Bu) and ternary (Ac/Pr/Bu) solutions at different concentrations with the equal VFAs proportion (50% or 33%), NF-45 membrane, at pH 8.

Figure III- 17

 17 Figure III-17 shows the individual solute flux versus total solute flux, for binary and ternary solutions (Ac/Pr, Ac/Bu, Pr/Bu, and Ac/Pr/Bu) at different concentrations with identical proportion of VFAs.

  The co-ions competition phenomenon in a ternary solution is more complicated. The least retained co-ion always contributes more to the charge flux, while the most retained co-ion always contributes less to the charge flux, compared to their contributions to the feed (i.e., feed proportions). The co-ion having an intermediate retention behaves differently according to the contributions of the least and most retained co-ions in the feed, as shown with Pr in Figure III-16a.

Figure III- 20

 20 Figure III-20 (a) Solutes proportions in the permeate versus filtration flux and (b) individual solute flux versus total solute flux for VFAs ternary solutions (Ac:Pr:Bu=33%:33%:33%) at various concentrations using XLE membrane, at pH 8. The error bar represent the error of the analysis.

  The individual solutes flux versus total solute flux for VFAs ternary solutions at three concentrations are shown in Figure III-20b.

Figure III- 21

 21 Figure III-21 Comparison of the solute proportions in the permeate versus filtration flux for VFAs ternary solutions (Ac:Pr:Bu=33%:33%:33%) at various concentrations using XLE and NF-45 membranes, at pH 8. The error bar represent the error of the analysis.

  three concentrations are given in Figure IV-1. The fitting curves are plotted and the solutes retentions at a given filtration flux are calculated based on the model proposed by Timmer et al. [143], as introduced in Chapter II. Figure IV-2 shows the retentions of the three VFAs and three inorganic salts at a filtration flux of 2×10 -6 m.s -1 versus concentrations. Then we can compare the retentions of the six solutes at given filtration flux.

Figure IV- 1

 1 Figure IV-1 and Figure IV-2 show that the retentions of all the solutes in single solutions

Figure IV- 1 Figure IV- 2 IV. 2 . 1

 1221 Figure IV-1 Retentions of (a) VFAs (acetate, propionate, and butyrate) and (b) salts (Na 2 SO 4 , NaCl and CaCl 2 ) in single solutions at different concentration, using NF-45 membrane.

Figure IV- 3

 3 Figure IV-3 Retention of individual anions at different compositions: (a) Ac/Bu binary solution with Na 2 SO 4 , (b) Ac/Pr/Bu ternary solution with Na 2 SO 4 , using NF-45 membrane.

Figure IV- 4

 4 Figure IV-4 shows the anions retentions in binary solutions of Ac/Bu and ternary solutions of Ac/Pr/Bu with the addition of NaCl. The concentration ratio between VFAs and NaCl in the feed is controlled as the same as that in the VFAs+Na2SO4 systems. The retentions of Ac, Pr, Bu, and NaCl in single solutions as well as the fitted retention curves at the corresponding total ionic concentration as the mixture are given as references.

Figure IV- 4

 4 Figure IV-4 Retention of individual anions at different compositions: (a) Ac/Bu binary solution with NaCl, (b) Ac/Pr/Bu ternary solution with NaCl, using NF-45 membrane.

Figure IV- 5

 5 Figure IV-5 shows the anions retentions in binary solutions of Ac/Bu and ternary solutions of Ac/Pr/Bu with the addition of CaCl2. The ratio between VFAs and CaCl2 in the feed is controlled as the same as that in VFAs+Na2SO4 and VFAs+NaCl systems. The retentions of VFAs as well as Cl -in VFAs+NaCl system at corresponding concentrations and proportions are given as references.

Figure IV- 5

 5 Figure IV-5 Retention of individual anions at different compositions: (a) Ac/Bu binary solution with CaCl 2 , (b) Ac/Pr/Bu ternary solution with CaCl 2 , using NF-45 membrane.

Figure IV- 6

 6 Figure IV-6 Retention of individual cations at different compositions: (a) Ac/Bu binary solution with CaCl 2 , (b) Ac/Pr/Bu ternary solution with CaCl 2 , using NF-45 membrane.

mixed solutions IV. 3 . 1

 31 Proportions of solutes in the permeate IV.3.1.1 Proportions of anions in the permeate The proportions of individual solutes versus filtration flux for VFAs+Na2SO4 binary and ternary solutions are given in Figure IV-7. One can observe that the proportion of SO4 2-in the permeate decreases while the proportions of VFAs in the permeate increases when the filtration flux increases, reach a plateau (namely 𝑃𝑃 𝑖𝑖 𝑃𝑃 * ) when the filtration flux is higher than a given value. Then, for the proportions of VFAs in the permeate, it is observed that the permeate proportion of the least retained VFA, Ac, increases the most, followed by Pr, the intermediately retained VFA, and the most retained VFA, Bu, increases the least. The permeate proportions of all the anions in VFAs+ NaCl and VFAs+ CaCl2 systems are given in Figure IV-8 and Figure IV-9 respectively. It is shown that the proportion of Cl -in the permeate increases when the filtration flux increases, meanwhile, the proportions of VFAs decrease when the filtration flux increases, all those anions permeate proportions reach a plateau (𝑃𝑃 𝑖𝑖 𝑃𝑃 * ) when the filtration flux is higher than a given value. For VFAs, on the contrary of to what observed in VFAs+ Na2SO4 system, the permeate proportion of the least retained VFA, Ac, decreases the least, followed by Pr, the intermediately retained VFA, and the most retained VFA, Bu, decreases the most.

Figure IV- 7 Figure IV- 8

 78 Figure IV-7 Proportions of all the solutes in the permeate versus filtration flux, for (a) Ac/Bu binary solution with Na 2 SO 4 , (b) Ac/Pr/Bu ternary solution with Na 2 SO 4 , using NF-45 membrane.

  1 can be visualized in Figure IV-10, that gives the proportions of individual inorganic salts and VFAs in the permeate versus their proportions in the feed.

Figure IV- 10

 10 Figure IV-10 Variation of the permeate proportions versus the feed proportions for (a) inorganic salts (b) individual VFAs, using NF-45 membrane, at pH 8.

  in the permeate decrease, the proportion of the least retained VFA decreases the least, while the proportion of the most retained one decreases the most.IV.3.1.2 Proportions of cations in the permeateThe permeate proportions of all the cations in VFAs+CaCl2 system are plotted in Figure IV-11 versus filtration flux. One can observe that the permeate proportion of Na + increases while permeate proportion of Ca 2+ decreases when the filtration flux increases, reach a plateau at a given filtration flux. This observation is the same as that for anions.

Figure IV- 11 Figure IV- 12

 1112 Figure IV-11 Proportions of all the cations in the permeate versus filtration flux, for (a) Ac/Bu binary solution with CaCl 2 , (b) Ac/Pr/Bu ternary solution with CaCl 2 , using NF-45 membrane, at pH 8.

Figure IV- 13

 13 Figure IV-13 Variation of the permeate proportions versus the feed proportions for VFAs mixed solutions with the addition of CaCl 2 , using NF-45 membrane at pH 8.

Figure IV- 14

 14 Figure IV-14 Relative proportions of VFAs in the couples of (a) Ac/Pr, (b) Pr/Bu, and (c) Ac/Bu, for all the compositions investigated, using NF-45 membrane at pH 8.

  Figure IV-15 shows the individual solute flux versus the total solute flux in binary solutions of Ac/Bu (Ac : Bu = 50% : 50%), and ternary solutions of Ac/Pr/Bu (Ac : Pr : Bu = 33% : 33% : 33%) at different concentrations with addition of Na2SO4. The individual solutes flux versus total solute flux obtained with VFAs+NaCl (Figure IV-16) and VFAs+CaCl2 (Figure IV-17) systems are also given.

Figure IV- 18

 18 Figure IV-18 gives the individual VFAs flux versus the combined solute flux for the couples of Ac/Pr, Pr/Bu, and Ac/Bu in mixed solutions without and with the addition of Na2SO4, NaCl, and CaCl2 respectively. The relative proportion of Ac, Pr, and Bu in the feed for three couples are all equal to 50%.

Figure IV- 15

 15 Figure IV-15 Individual solute flux versus total solute flux, for (a) Ac/Bu binary solution with Na 2 SO 4 , (b) Ac/Pr/Bu ternary solution with Na 2 SO 4 , using NF-45 membrane.

)Figure IV- 16 Figure IV- 17 Figure IV- 18

 161718 Figure IV-16 Individual solute flux versus total solute flux, for (a) Ac/Bu binary solution with NaCl, (b) Ac/Pr/Bu ternary solution with NaCl, using NF-45 membrane.

IV. 3 . 2 . 1

 321 Cations transferThe individual cations flux versus the total cations flux in the NaVFAs+ CaCl2 system are given in Figure IV-19. One can notice that the linear relationship between individual cations flux and total cations flux is observed. Then, for cations, it is also observed that for a given feed proportion, the individual solute flux is fixed by the total solute flux (i.e., total charge transfer).

Figure IV- 19

 19 Figure IV-19 Individual solute flux versus total solute flux, for (a) Ac/Bu binary solution with CaCl 2 , (b) Ac/Pr/Bu ternary solution with CaCl 2 , using NF-45 membrane.

: 1 : 1 )

 11 are chosen and visualized in Figure IV-20. In Figure IV-20a, the separation factor between Ac/Bu obtained for binary VFAs solutions (Ac:Bu=1:1) without, with Na2SO4, with NaCl, and with CaCl2 for VFAs:salts at 1:1, 2:3 and 1:4 are compared. In Figure IV-20b, the separation factors of Ac/Pr, Pr/Bu, and Ac/Bu for ternary VFAs solutions (Ac:Pr:Bu=1:1:1) at different VFAs:salts proportions are compared.

(

  VFAs:salts=1:1), it seems that the separation factors of Ac/Pr, Pr/Bu, and Ac/Bu slightly increases with the addition of NaCl, and slightly decreases with the addition of Na2SO4 and CaCl2 compared to the condition without the addition of salts. When the ratio of VFAs:salts=1:1 decreases to 2:3 and 1:4 (the ionic concentration increases to 500 mEq.L -1 ), those separation factors all decrease compared to those without the addition of salts. With the addition of NaCl, the separation factors between VFAs decrease slightly, while decreases more with the addition of Na2SO4 and CaCl2 (Figure IV-20b).

Figure IV- 20

 20 Figure IV-20 Separation factors between Ac/Pr, Pr/Bu, and Ac/Bu in (a) VFAs Binary solutions (Ac:Bu=1:1), and (b) VFAs Ternary solutions (Ac:Pr:Bu=1:1:1) without addition of salt, with Na 2 SO 4 ,with NaCl, and with CaCl 2 , respectively, using NF-45 membrane.

3 )

 3 Eq. (V.3) can be rewritten as the weighted average of individual VFAs retentions, considering the proportion of individual solute in the mixed solution,𝑅𝑅 𝑠𝑠𝑡𝑡𝑝𝑝 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 = ∑ 𝑃𝑃 𝑖𝑖 𝑓𝑓 𝑅𝑅 𝑖𝑖 𝑚𝑚𝑖𝑖𝑚𝑚 𝑛𝑛 𝑖𝑖=1 (V.4)In Eq. (V.4), 𝑅𝑅 𝑖𝑖 𝑚𝑚𝑖𝑖𝑚𝑚 is the retention of individual VFA i in the mixed solution, 𝑃𝑃 𝑖𝑖 𝑓𝑓 is the proportion of individual VFA i in the feed solution, and the sum of the proportions of individual VFA i in the feed is 1.

V. 1

 1 Figure V-1 and Figure V-2. The curves are fitted according to the model proposed by J. M. K.Timmer et al.[START_REF] Timmer | Transport of lactic acid through reverse-osmosis and nanofiltration membranes[END_REF], and the solute retention at a given filtration flux is calculated from the fitted equation as explained in Chapter II. Retentions at J1=0.2×10 -5 m.s -1 , J2=0.5×10 -5 m.s -1 , J3=1×10-5 m.s -1 , and J4=1.5×10 -5 m.s -1 are obtained from the fitting curves for different concentrations. For 500mM, only J1 is shown since the other filtration flux are not in the experimental range.

Figure V- 1

 1 Figure V-1Retentions of (a) Ac, and (b) Pr in single solutions, versus filtration flux at different solution pH and varying total concentration, using NF-45 membrane. Retentions at J 1 =0.2×10 -5 m.s -1 , J 2 =0.5×10-5 m.s -1 , J 3 =1×10 -5 m.s -1 , and J 4 =1.5×10 -5 m.s -1 are compared, for 500mM, only J 1 is in the experimental range.

  The retentions of Ac, Pr, and Bu at given filtration flux (J1, J2, J3, and J4) versus solution pH for the three concentrations are plotted in Figure V-3 and Figure V-4. The fitting curves of solutes retentions versus pH are obtained from sigmoid curve fitting by Origin software. The dissociation curves of Ac, Pr, and Bu (obtained from Eq. 5.6) are also plotted as references. For the concentration of 500mM, the filtration flux is much lower than that at lower concentrations, then only the retentions at J1 are shown. One can observe that the increase of the individual VFA retentions versus the solution pH follows a sigmoid curve, for the four filtration flux investigated. The different curves are obtained according to the filtration flux, for a given pH, the retention increases for increasing filtration flux.

Figure V- 3

 3 Figure V-3 Retentions of (a) Ac and (b) Pr in single solutions, at given filtration flux versus solution pHfor three concentrations, using NF-45 membrane. J 1 =0.2×10 -5 m.s -1 , J 2 =0.5×10 -5 m.s -1 , J 3 =1×10 -5 m.s -1 , J 4 =1.5×10 -5 m.s -1 , for 500mM, only J 1 is in the experimental range. The dissociation curves of Ac and Pr are given as references and the pK a of each VFA is marked in the figure.

Figure V- 4

 4 Figure V-4Retentions of Bu in single solutions, at given filtration flux versus solution pH for three concentrations, using NF-45 membrane. J 1 =0.2×10 -5 m.s -1 , J 2 =0.5×10 -5 m.s -1 , J 3 =1×10 -5 m.s -1 , J 4 =1.5×10 -5 m.s -1 , for 500mM, only J 1 is in the experimental range. The dissociation curve of Bu is given as reference and the pK a of Bu is marked in the figure.

2

 2 Individual VFAs retentions in mixed solutionsThe retentions of individual Ac, Pr, and Bu in ternary solutions (s6, Ac: Pr: Bu = 33%: 33%: 33%) at given filtration flux (J1, 0.2×10 -5 m.s -1 ) and three total concentrations are plotted versus solution pH in Figure V-5. The retentions of VFAs in single solutions at the same concentration and filtration flux are also given as references. The individual VFAs retentions obtained at different pH values versus filtration flux, and individual VFAs retentions versus pH obtained for the other three filtration flux values (J2, J3, and J4) show similar behavior at that observed at J1, those results are not shown.As observed for single solutions, the individual VFAs retentions in mixed solutions increase with pH following an S-shape curve. An exception is observed for the retention of Ac at the highest concentration (500 mM), that firstly increases with the pH, reaches a maximum at pH 6.6, and decreases when the pH increases to 8. At low pH values, the individual VFAs retentions in the mixed solutions are similar to those in single solutions at the same concentration. But, at high pH value (pH 8), the individual VFAs retentions in single and mixed solutions are different. In the mixed solution, the retention of the most retained VFA, Bu, is similar to that in the single solution while the retention of the least retained VFA, Ac, is lower than in the single solution and that of the intermediately retained VFA, Pr, nearly unchanged between single and mixed solutions.Then the retention differences between VFAs in the mixed solutions are larger compared to those in single solutions, especially at high concentration. Furthermore, one can observe that the retentions of individual VFAs follow the same sequence (Ac<Pr<Bu) for the three total concentrations and whatever the solution pH between 3 and 8.Retention of VFAs at low pH are mainly fixed by size effect, then the co-existence of other VFAs does not influence the individual VFAs retentions in the mixed solutions. Then, similar retentions are expected for single and mixed solutions, as observed. When the pH increases, the contribution of charge effect gradually increases due to both the increase of the percentage of dissociated VFAs in the solution and the increase of membrane charge. At high pH values, VFAs are dissociated, and the retention of VFAs are dominated by charge effect. Then, higher retention at high pH values compared to low pH values is observed.

Figure V- 5

 5 Figure V-5 Individual VFAs retentions in Ac/Pr/Bu ternary mixture with three concentrations versus solution pH at a filtration flux of J 1 =0.2×10 -5 m.s -1 , using NF-45 membrane.

  individual VFAs in the permeate versus filtration flux for ternary solutions (Ac:Pr:Bu=33%:33%:33%) at three concentrations (100, 200, 500mM) and various solution pH values are given in Figure V-6.

Figure V- 6 8 (

 68 Figure V-6 Individual solutes proportions in the permeate versus filtration flux for ternary solutions (Ac:Pr:Bu=33%:33%:33%) at all the concentrations and various solution pH, using NF-45 membrane. (a) Proportion of Ac, (b) Proportion of Pr, (c) Proportion of Bu, (d) Proportions of the three VFAs.

Figure V- 7 Figure V- 8 Figure V- 9

 789 Figure V-7Relative proportions of Ac and Pr for the couple of Ac/Pr in ternary solutions (Ac:Pr:Bu=33%:33%:33%) at all the concentrations and various solution pH from 3 to 8, using NF-45 membrane.

Figure V- 10 7 Figure V- 11 28 Figure V- 12

 107112812 Figure V-10 Individual solutes proportions in the permeate versus filtration flux for Ac/Pr binary solutions (Ac:Pr =33%:33%:33%) at all the concentrations and various solution pH, using NF-45 membrane.

Figure V- 13

 13 Figure V-13 compares the relative proportions (at the plateau value) of Ac, Pr, and Bu in the permeate for binary and ternary solutions at different solution pH. It is shown that the relative proportions of VFAs in binary and ternary solutions are nearly the same. Then, as the solution pH increase, the relative proportions of Ac for the couples of Ac/Pr and Ac/Bu increase from 51%

7 Figure V- 13

 713 Figure V-13 Relative proportions of Ac, Pr, and Bu for the couples of (a) Ac/Pr, (b) Pr/Bu and (c)Ac/Bu, in the permeate versus solution pH in the binary (Ac:Pr=50%:50%, Pr:Bu=50%:50%, Ac:Bu=50%:50%) and ternary (Ac:Pr:Bu =33%:33%:33%) solutions, using NF-45 membrane.

  shown that the solution pH can significantly change the proportion of individual VFAs in the permeate. When the pH increases, the charge of membrane and VFAs both increases, leading to stronger co-ions competition, and then the differences between relative proportions of VFAs in the permeate increases. The individual VFAs retentions in the mixed solutions are influenced by the presence of other VFAs, especially at high pH values. Thus, the variation of individual VFAs retentions versus solution pH in the mixed solutions are influenced by both solution pH and co-ions competition between VFAs. Therefore, the variation of individual solutes retentions in single and mixed solutions with solution pH are not the same. V.1.3 Global retentions in mixed solutions The previous discussion has shown that, due to the co-ions competition phenomenon, the variation of individual VFAs retentions in single and mixed solutions with solution pH are different. Global retention, which is defined as the weighted average of individual VFAs retentions in the mixed solution, is introduced into the discussion. Global retention of the mixed solution instead of individual ones at different solution pH is investigated. The global retentions of VFAs in binary (s4, Ac: Pr = 50%:50%; s5, Ac: Bu = 50%:50%) and ternary (s6, Ac: Pr: Bu = 33%:33%:33%) solutions at different solution pH and total concentrations versus filtration flux are given in Figure V-4 and Figure V-15. The curves are fitted and the global retention at given filtration flux is calculated as that for single solutions (explained in Chapter II). Global retention of VFAs at J1=0.2×10 -5 m.s -1 , J2=0.5×10 -5 m.s -1 , J3=1×10 -5 m.s -1 , and J4=1.5×10 -5 m.s -1 are obtained from the fitting curves for different total concentrations. As for single solutions, for 500mM, only the results at J1, are shown. For all the mixed solutions, one can observe that the global retentions of VFAs increase with filtration flux. At a given filtration flux, the global retentions of VFAs in all the mixed solutions increases gradually when the solution pH increases.

Figure V- 14

 14 Figure V-14Global retentions of VFAs in binary solutions (a) Ac/Pr and (b) Ac/Bu of varying total concentration versus filtration flux, using NF-45 membrane. Global retentions at J 1 =0.2×10 -5 m.s -1 , J 2 =0.5×10 -5 m.s -1 , J 3 =1×10 -5 m.s -1 , and J 4 =1.5×10 -5 m.s -1 are compared, for 500mM, only J 1 is in the experimental range.

Figure V- 15

 15 Figure V-15Global retentions of VFAs in ternary solutions (Ac/Pr/Bu) of varying total concentration versus filtration flux, using NF-45 membrane. Global retentions at J 1 =0.2×10 -5 m.s -1 , J 2 =0.5×10 -5 m.s -1 , J 3 =1×10 -5 m.s -1 , and J 4 =1.5×10 -5 m.s -1 are compared, for 500mM, only J 1 is in the experimental range.

1

 1 figure as references.

Figure V- 16

 16 Figure V-16 Total VFAs retentions of VFAs in binary solutions (a) Ac/Pr (Ac: Pr =50%:50%) and (b)Ac/Bu (Ac: Bu =50%:50%) at given filtration flux versus solution pH for three total concentrations, using NF-45 membrane. The filtration flux J 1 =0.2×10 -5 m.s -1 , J 2 =0.5×10 -5 m.s -1 , J 3 =1×10 -5 m.s -1 , J 4 =1.5×10 -5 m.s -1 , for 500mM, only J 1 is in the experimental range. The fitting curves are obtained from sigmoid curve fitting. The percentage of the dissociation VFAs at each pH values are given as references.

Figure V- 17

 17 Figure V-17Total VFAs retentions of VFAs in ternary solutions Ac/Pr/Bu (Ac: Pr: Bu=33%:33%:33%) at given filtration flux versus solution pH for three total concentrations, using NF-45 membrane. The filtration flux J 1 =0.2×10 -5 m.s -1 , J 2 =0.5×10 -5 m.s -1 , J 3 =1×10 -5 m.s -1 , J 4 =1.5×10 -5 m.s -1 , for 500mM, only J 1 is in the experimental range. The fitting curves are obtained from sigmoid curve fitting. The percentage of the dissociation VFAs at each pH values are given as references.

V. 1 . 4

 14 Figure V-18 shows the retentions of VFAs in single solutions (Ac, Pr, and Bu) and the global retentions of VFAs in mixed solutions (Ac/Pr, Ac/Bu, and Ac/Pr/Bu) at a filtration flux of 0.2×10 - 5 m.s -1 and different solution pH as the function of VFAs concentration/total concentration. Same trends are obtained for individual retentions in single solutions and global retentions in mixed ones. One can observe that for the lowest pH values, the retention remains almost constant when the concentration increases. On the contrary, for the highest pH values, the retention decreases with the concentration.

Figure V- 18

 18 Figure V-18Retentions/global retentions of VFAs at a filtration flux of 0.2×10 -5 m.s -1 in single (Ac, Pr, Bu) binary (Ac/Pr, Ac/Bu) and ternary (Ac/Pr/Bu) solutions as a function of total concentration for various solution pH, using NF-45 membrane.

Figure V- 19

 19 Figure V-19 gives the retentions of VFAs in single solutions and the global retentions of VFAs in binary and ternary mixtures at a filtration flux of 0.2×10 -5 m.s -1 and pH 8 versus the concentration. These variations are fitted using Origin software with an exponential function. The functions, as well as the parameters obtained from the fitting for the different solutions, are listed in Table V-1.

Figure V- 19

 19 Figure V-19 Retentions of acetate, propionate, butyrate (a) and the global retentions of Ac/Pr, Ac/Bu binary and Ac/Pr/Bu ternary mixed solutions (b) versus concentration at a filtration flux of 0.2×10 -5 m.s -1and pH 8, using NF-45 membrane. Points are experimental values and the curves are those from equations in table 4.

Figure V- 20

 20 Figure V-20 gives the variations of the calculated (using Eq. (V.10)) and experimental VFAs retentions in single and mixed solutions versus the pH at a given filtration flux J1 (0.2×10 -5 m.s -1 )

Figure V- 20

 20 Figure V-20 Calculated and experimental VFAs retention in single (left side), binary, and ternary (right side) solutions versus the solution pH for various total concentrations, using NF-45 membrane. The experimental and calculated VFAs retentions are obtained at filtration flux=0.2×10 -5 m.s -1 .

Figure V- 21

 21 Figure V-21 gives the variations of calculated and experimental VFAs retentions versus pH at different concentrations for filtration flux J1 (0.2×10 -5 m.s -1). Calculated values are those obtained from Eq. (V.10) considering the individual pKa_f values for each solutions (pKa-f=pKa +1.24). It is shown that it is possible to describe the influence of the pH on the VFAs retention using the previous model on the condition to consider a modified value of the solutes pKa that is 1.24 pH units higher than the theoretical values.

Figure V- 21

 21 Figure V-21 Calculated VFAs retentions with pK a-f =pK a +1.24 compared with experimental VFAs retentions in single, binary, and ternary solutions at different solution pH and varying total concentrations, using NF-45 membrane. The experimental and calculated VFAs retentions are obtained at filtration flux=0.2×10 -5 m.s -1 .

(

  single, binary, and ternary solutions at a total concentration of 100mM, 200mM, and 500mM) versus filtration flux is given in Figure V-22. One can observe that the difference between pKa-f and pKa (pKa-f-pKa) decreased from about 1.24±0.09 at J1, 1.04±0.09 at J2, 0.86±0.09 at J3, to 0.76±0.10 at J4 following an exponential curve. This observation indicates that when the filtration flux increases, the fitted pKa (pKa-f) approaches the theoretical value. Nevertheless, an increase of about 1 unit (1.00±0.24) of the solutes pKa values is needed to describe the variation of VFAs retention versus pH.

Figure V- 22

 22 Figure V-22 Average difference between the fitted pK a_f and solution pK a (pK a-f -pK a ) for various compositions (single, binary, and ternary solutions at concentration of 100mM, 200mM, and 500mM) versus filtration flux. Results obtained using NF-45 membrane.

11 )

 11 Figure V-23b gives the fitting curves for the ternary solutions at three concentrations as an example. One can notice that the experimental curves are slightly broaden compared to the fitted curves. At pH lower than 5.6, 𝛼𝛼 is higher than the simulation curve.

Figure V- 23

 23 Figure V-23 Correction parameter α (obtained from Eq. (V.11)) as a function of solution pH, (a) for all the compositions investigated, (b) for the ternary solutions (Ac/Pr/Bu) and fitting using Eq. (V.12) with pK eff values in Table V-4. Results obtained using NF-45 membrane. The values are obtained at filtration flux=0.2×10 -5 m.s -1 .

Figure V- 24

 24 Figure V-24 shows the comparison of calculated VFAs retentions at given filtration flux (0.2×10 -5 m.s -1 ) in single and mixed solutions at three concentrations using Eq. (V.11) and the experimental ones versus solution pH. The values of correction parameter α used in the calculation are obtained from Eq. (V.12), considering pKeff values equal to 5.75, 5.80, and 5.44 for the concentration of 100mM, 200mM, and 500mM respectively. One can observe that the calculated retentions fit well with the experimental ones.

Figure V- 24

 24 Figure V-24 Calculated global retentions take the dissociation of the membrane into consideration (pK aeff of the membrane are 5.80, 5.75, and 5.44 respectively for 100mM, 200mM, and 500mM) compared with experimental obtained global retention of VFAs single, binary, and ternary solutions at different solution pH and varying total concentration, filtration flux=0.2×10 -5 m.s -1 . Results obtained using NF-45 membrane.

  weak acids. Solution pH can change the ratio of dissociated/undissociated weak acids, as well as modify the membrane charge. Ionic concentration can screen the charge interactions between charged membrane and dissociated weak acids. Current work investigated the influence of both pH and concentration on the retention of VFAs in single and mixed solutions.It was observed that VFAs retentions increase with either filtration flux or solution pH.Retentions of VFAs increase with solution pH follows the dissociation curves of VFAs. Then, retentions of VFAs decrease when the concentration increases, showing the influence of screening effect. This influence is nearly negligible at pH 3, then becomes stronger when the solution pH increases. Besides, the permeate proportion of Ac increases while the permeate proportion of Bu decreases when the solution pH increases, due to the co-ions competition. However, the proportion of Pr in the permeate is nearly unchanged whatever the solution pH. Furthermore, based on the assumption that the dissociated and undissociated VFAs transfer through the membrane independently, calculation of VFAs retentions at different solution pH and concentrations for a given filtration flux was carried out. By only considering the dissociation of VFAs, the calculated retention curves were higher and parallelled to the experimental ones, indicate there is an additional influence of solution pH.

  parameters can be fitted by a constant value (namely pKeff ) for each concentration. The obtained pKeff values are 5.75, 5.80, and 5.44 for VFAs solutions at the total concentration of 100mM, 200mM, and 500 mM respectively. Those values(5.44-5.80) observed are within the range of the pKa values[START_REF] Werpy | Top Value Added Chemicals from Biomass: Volume I --Results of Screening for Potential Candidates from Sugars and Synthesis Gas[END_REF][START_REF] Xiong | Integrated acidogenic digestion and carboxylic acid separation by nanofiltration membranes for the lignocellulosic carboxylate platform[END_REF][START_REF] Rahul | Thermodynamic properties of binary liquid systems of ethanoic acid, propanoic acid, and butanoic acid with 3-chloroaniline as a function of various temperatures[END_REF][START_REF] Dunn | The diffusion of monocarboxylic acids in aqueous solution at 25°[END_REF][START_REF] Albery | Diffusion coefficients of carboxylic acids[END_REF] for carboxylic functional groups on polyamide films reported previously.

  In the current Chapter, two NF membranes, namely XLE and NF-45, are used. As introduced in Chapter II, XLE membrane is much tight than NF-45 membrane, thus XLE membrane could be beneficial for the extraction of VFAs and remove the impurities (e.g., ethanol), while NF-45 could be used for the modification of VFAs composition.The experimental investigation is firstly applied to synthetic broths with composition and pH close to the real fermentation broth. Then, a real fermentation broth contains VFAs is filtrated.The results obtained in previous Chapters are also used for comparison. The retentions of individual solutes in mixed solutions, synthetic broths and real fermentation broth by the two membranes are discussed. The proportions of individual solutes in the permeate are investigated as well. Then, the performances of the two membranes on the modification of feed and permeate proportions for the synthetic and real broths are further compared, and the possible applications of NF on the treatment of VFAs fermentation broth are given.

Figure VI- 1

 1 Figure VI-1 and Figure VI-2 show the retentions versus filtration flux for all the anions in the synthetic broths at acidic (pH 5.7) and alkaline (pH 8) conditions by XLE membrane.

Figure VI- 1 8 RetentionFigure VI- 2

 182 Figure VI-1 The retentions of all anions in the synthetic solutions versus filtration flux (a) pH 5.7, (b) pH 8. Membrane used: XLE membrane, VFAs feed proportions: Ac:Pr:Bu=1:1:1.

[

  𝐻𝐻𝑐𝑐 -], [𝐻𝐻𝑐𝑐 -], [𝐻𝐻𝑐𝑐 -] the concentration of dissociated Ac, Pr, Bu, respectively, in the feed or permeate. [𝑁𝑁𝑎𝑎 + ], [𝐶𝐶𝑎𝑎 2+ ] the concentration of 𝑁𝑁𝑎𝑎 + and 𝐶𝐶𝑎𝑎 2+ , in the feed or permeate. In Eqs. (VI.1) and (VI.2), the three variables are [𝐻𝐻𝑐𝑐 -] , [𝑃𝑃𝑟𝑟 -] , and [𝐵𝐵𝐵𝐵 -] , the input parameters ([𝐻𝐻𝑐𝑐], [𝑃𝑃𝑟𝑟], [𝐵𝐵𝐵𝐵], [𝑁𝑁𝑎𝑎 + ], and [𝐶𝐶𝑎𝑎 2+ ]) can be experimentally obtained by HPLC analysis. By solving Eqs. (VI.1) and (VI.2) using Matlab, the concentrations of dissociated VFAs, i.e., [𝐻𝐻𝑐𝑐 -], [𝑃𝑃𝑟𝑟 -], and [𝐵𝐵𝐵𝐵 -], in the feed and permeate are obtained. Then, the concentration of undissociated VFAs in the feed and permeate are obtained by mass balance. Then, from the concentrations of individual dissociated and undissociated VFAs in the feed and permeate, the retentions of individual dissociated and undissociated VFAs can be calculated using Eq. (II.2).

Figure VI- 3 Figure

 3 Figure VI-3 Retentions of (a) dissociated VFAs, (b) undissociated VFAs in the synthetic solutions without and with salts. Retention of Cl -is also given as reference. Using XLE membrane for synthetic solutions Syn1, Syn2, and Syn3 at solution pH 5.7. VFAs feed proportions: Ac:Pr:Bu=1:1:1.

Figure VI- 4

 4 Figure VI-4 The retentions of all cations versus filtration flux in the synthetic solutions using XLE membrane at (a) pH 5.7 (b) pH 8. VFAs feed proportions: Ac:Pr:Bu=1:1:1.

b

  This phenomenon is in agreement with the results previously observed using NF-45 membrane in Chapter IV. VI.1.1.2 Nanofiltration using NF-45 membrane The synthetic broths are prepared according to the composition of VFAs in the real fermentation broth (Ac:Pr:Bu=45:31:40 mM), then NaCl and CaCl2 are added respectively to simulate the influence of Cl -and Ca 2+ (namely, Syn4, Syn5, and Syn6), at the same pH as the real broth (pH 5.7).

Figure VI- 5

 5 Figure VI-5 and Figure VI-6 give the retentions of all the anions and cations versus filtration flux with the synthetic broths at pH 5.7.

Figure VI- 5 7 RetentionFigure VI- 6

 576 Figure VI-5 The retentions of all anions (a) and all cations (b) in the synthetic broths with and without salts, using NF-45 membrane at pH 5.7. VFAs feed proportions: Ac:Pr:Bu=45:31:40.

Figure VI- 7

 7 Figure VI-7 Retentions of all the anions (a) and cations (b) in the real fermentation broth using XLE membrane at pH 5.7. The compositions of the real fermentation broth are Ac:Pr:Bu:Cl = 45:31:40:29 mM, and Na + :NH 4 + :K + :Ca 2+ = 46:11:4:24 mM for anions and cations respectively.

8. 2

 2 are given in Figure VI-8, and the comparison of individual ions retentions at the three pH values are given in Figure VI-9.

Figure VI- 8 Figure VI- 9

 89 Figure VI-8 Retentions of all the anions (a) and cations (b) in the real fermentation broth at pH 5.7, 6.6, and 8.2 using NF-45 membrane. The compositions of the real fermentation broth are Ac:Pr:Bu:Cl = 45:31:43:27 mM, and Na + :NH 4 + :K + :Ca 2+ = 51:11:4:25 mM at pH 5.7, Ac:Pr:Bu:Cl = 43:33:40:26 mM, and Na + :NH 4 + :K + :Ca 2+ = 56:11:4:27 mM at pH 6.6, and Ac:Pr:Bu:Cl = 44:30:41:25 mM, and Na + :NH 4 + :K + :Ca 2+ = 57:11:4:27 mM at pH 8.2, for anions and cations respectively.

  using XLE and NF-45 membranes at pH 5.7 are given in Figure VI-11. For the six synthetic broths, the VFAs feed proportions are Ac:Pr:Bu=1:1:1 for Syn1, Syn2, and Syn3 filtrated by XLE membrane, and Ac:Pr:Bu=45:31:40 for Syn4, Syn5, and Syn6 filtrated by NF-45 membrane. The addition of NaCl and CaCl2 changes the feed composition but does not change the VFAs proportion.

Figure VI- 11

 11 Figure VI-11 Individual solutes proportions in the permeate for the six synthetic broths (Syn1 and Syn4, NaVFAs, Syn2 and Syn5, NaVFAs+NaCl, Syn3 and Syn6, NaVFAs+CaCl 2 ) at pH 5.7, using (a) XLE membrane (b) NF-45 membrane. Proportions of Ac:Pr:Bu are 1:1:1 for Syn1, Syn2, and Syn3, and 45:31:40 for Syn4, Syn5, and Syn6. 24 mM NaCl is added in Syn2 and Syn4, then 24 mM of CaCl 2 is added in Syn3 and Syn6.

  using XLE and NF-45 membranes versus filtration flux are given in Figure VI-13.

Figure VI- 13 1 Figure VI- 14

 13114 Figure VI-13 Proportion of cations in the permeate for synthetic broths (Syn3 and Syn6, NaVFAs+CaCl 2 ), using (a) XLE membrane, (b) NF-45 membrane. The proportion of cations in the feed are given for each condition.

45 membrane at pH 5 . 7 , 6 . 6 ,

 5766 and 8.2 are given in Figure VI-15.

Figure VI- 15

 15 Figure VI-15 Solutes proportions in the permeate of NF-45 membrane for the real fermentation broth at three pH values, (a) anions (b) cations. The compositions of the real fermentation broth are Ac:Pr:Bu:Cl = 45:31:43:27 mM, and Na + :NH 4 + :K + :Ca 2+ = 51:11:4:25 mM at pH 5.7, Ac:Pr:Bu:Cl = 43:33:40:26 mM, and Na + :NH 4 + :K + :Ca 2+ = 56:11:4:27 mM at pH 6.6, and Ac:Pr:Bu:Cl = 44:30:41:25 mM, and Na + :NH 4 + :K + :Ca 2+ = 57:11:4:27 mM at pH 8.2, for anions and cations respectively.

  The relative proportion of VFAs in the permeate of XLE and NF-45 membranes for the real fermentation broth are given in Figure For the permeate of XLE membrane, one can observe that the proportion of Ac increases, while the proportion of Pr decreases when the filtration flux increases for the couple of Ac/Pr. However, the reverse trend is observed for the couple of Ac/Pr in the permeate of NF-45 membrane, the proportion of Pr increases while the proportion of Ac decreases when the filtration flux increases. For the couples of Pr/Bu and Ac/Bu, the proportion of Bu decreases in the permeate while the proportions of Pr and Ac increase in the permeate when the filtration flux increases, for the permeates of both XLE and NF-45 membranes.

  compare the performances of the two membranes for VFAs separation in the synthetic solutions/broths and real fermentation broth, the relative proportions of individual VFA in the permeate (at the plateau value) versus that in the feed are given in Figure VI-17. For XLE membrane, synthetic and real fermentation broths at pH 5.7 are compared. For NF-45 membrane, synthetic broths at pH 5.7, as well as the real fermentation broth at pH 5.7, 6.6, and 8.2 are compared. The results for synthetic solutions with and without the addition of salts at pH 8 using NF-45 membrane shown in Chapter IV are also given for comparison.

Figure VI- 17 .

 17 Figure One can observe that, for synthetic broths, the differences between the relative proportions of the two VFAs out of three are higher for XLE membrane for all the three couples compared to NF-45 membrane. Then, for the real fermentation broth, the differences between the relative proportions of the two VFAs out of three are similar for the couples of Ac/Pr and Pr/Bu, for the couple of Ac/Bu, the difference between the permeate proportions of Ac and Bu for XLE membrane is much larger than that of NF-45.

Figure VI- 19

 19 Figure VI-19 TOC of VFAs, and TOC of organic matters (OM) proportions in the permeate of XLE membrane for the real fermentation broth.

  The proportions of VFAs and Cl -in the feed and permeate (at the constant values), as well as the separation factor between VFAs/Cl -are given in Table VI-4. The separation factor between VFAs and Cl -is calculated using Eq.(II.11). For the results with XLE membrane, VFAs are enriched in the permeate. Therefore, the calculation uses the ratio of VFAs and Cl -in the permeate divided by the ratio of VFAs and Cl -in the feed (shown in Eq. (VI.3)). When the feed proportion is the same, the separation factor is the quotient of the proportion of the permeate proportions of VFAs and Cl -.𝑆𝑆𝑆𝑆 (𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠/𝐶𝐶𝑡𝑡 -_XLE) = (𝑝𝑝 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 𝑝𝑝 /𝑝𝑝 𝐶𝐶𝑡𝑡 - 𝑝𝑝 )/(𝑝𝑝 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 𝑓𝑓 /𝑝𝑝 𝐶𝐶𝑡𝑡 - 𝑓𝑓 ) (VI.3)For the results using NF-45 membrane, the separation factor is obtained using the ratio of VFAs and Cl -in the feed divided by the ratio of VFAs and Cl -in the permeate (shown in Eq.(VI.4)).𝑆𝑆𝑆𝑆 (𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠/𝐶𝐶𝑡𝑡-_NF-45) = (𝑝𝑝 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 𝑓𝑓 /𝑝𝑝 𝐶𝐶𝑡𝑡 - 𝑓𝑓 )/(𝑝𝑝 𝑉𝑉𝑉𝑉𝐴𝐴𝑠𝑠 𝑝𝑝 /𝑝𝑝 𝐶𝐶𝑡𝑡 - 𝑝𝑝 ) (VI.4)

Figure VI- 20

 20 Figure gives the separation factors between Ac/Pr, Pr/Bu, and Ac/Bu in synthetic solutions (Ac:Pr:Bu=33%:33%:33%) and real fermentation broths versus solution pH using XLE and NF-45 membranes. For XLE membrane, one can observe that the separation factors decrease when solution pH increases. The separation factors between VFAs observed with real fermentation broth are higher than those observed with synthetic solutions, except for Ac/Pr. For NF-45 membrane, it is shown that the separation factors increase when the solution pH increases.

Figure VI- 20

 20 Figure VI-20 Separation factors between Ac/Pr, Pr/Bu, and Ac/Bu in synthetic solutions (Ac:Pr:Bu=33%:33%:33%) and real fermentation broths versus solution pH, (a) XLE membrane, (b) NF-45 membrane. The results obtained using NF-45 membrane for synthetic solutions are zoomed in to identify the individual points.

Then, a model

  to describe the VFAs retention versus pH was proposed based on the following assumptions: (1) The undissociated and dissociated VFAs transfer through the membrane independently; (2) Retention of HVFAs is that obtained at pH 3 and does not depend on the concentration; (3) Retention of VFAs -is that obtained at pH 8 at the corresponding ionic concentration. It was shown that the model can describe the retention of VFAs versus solution pH by considering an increase of the VFAs pKa values by about 1.2 units or a membrane effective pKa value of about 5.4 to 5.8.

Figure I

 I Figure I Chromatogram of the three VFAs with HPLC (Jasco)

Table I -

 I 2 Properties of VFAs

	Name	Acetic acid	Propionic acid	Butyric acid	Valeric acid	Caproic acid
	Structure
	Molecular weight (g.mol -1 )	60.05	74.08	88.11	102.13	116.16
	pKa (25℃)	4.76	4.88	4.82	4.84	4.88
	Boiling point (℃)	117.9	141.15	163.75	185.8	205.8

Table I -

 I 3 Composition of VFAs in fermentation broths

	Hydraulic retention time, HRT (h)	pH	Raw material	Acetic (mg/L)	Propionic (mg/L)	Butyric (mg/L)	Valeric (mg/L)	Caproic (mg/L)	Reference
	-	-	Olive Mill Wastewater	6641	433	2252	495	922	[58]
		5		750	1373	1865	19
		6		1885	1000	1692	34
		7		1481	1253	1365	29
	36	8	Composite food waste	2250	896	682	20		[27]
		9		3154	1095	903	22
		10		4192	1293	788	27
		11		884	1468	1182	19
		3		806	1028
		5		1838	988	1894	1180
	245	7 9	Sludge	4563 8523	3594 3819	4441 3772	4764 3912		[28]
		11		8164	3412	3412	3585
		12		2184	1402	2428	994
	7.2-14.4	5		666-980	20-100	2890-3036
	3-12.5 3-9.1	6 7	Sludge	713-1005 1000-1259	165-390 40-145	2597-3130 2630-2900			[59]
	4-12.8	8		2480-2940 1420-1780	190-520
		5.2	Sugar beet	555-665	26-29	983-1664	5-6
	14.2-15	5.2	Sugar beet	519	5	1104	11		[60]
		5.2	Sucrose	490-780		2350
	24-48 72-192	4.9-5.5 4.9-5.5	OFMSW	382-479 620-1080	55-81 193-611	211-408 2781-2744			[61]
	60	5.25-6.55	Sucrose	2708	1648	7172			[41]
	54-95 134	5.5 5.5	Food waste	95-103 137	8-12 0	593-793 898			[62]
	40	4		952	0	2181
	12 11	5 6	Food waste	1326 1529	134 142	2151 1828			[63]
	18	7		1780	286	1555
		4		5336	50	1810
	6	5 6	Glucose	845 1035	37 118	1730 1423			[64]
		7		1165	635	1333
									Real
	5.5	-	Municipal solid waste	2701	2277	3507			fermentation broth used
									in this work

Table I - 4

 I4 Comparison of several processes in separation and purification of VFAs, adapted from ref.

		Higher product yields	The feed needs to be acidified for
	Solvent	Suitable for carboxylate salt	efficient extraction
	Extraction	production	Extractants needs to be regenerated
		Lower costs	by additional processes
		Developing technology
		High product yields
	Membrane Separation	Suitable for a wide range of applications Low energy	Membrane fouling and clogging Largely untried in complex waste systems
		Economic
		Easy to scale up
		[99]
	Methods	Advantages	Disadvantages
		Well established
	Precipitation	Higher product yields Low capital costs	Generating solid wastes
		Products of high purities
	Distillation	Well established Highly pure products Byproducts can be used as fertilizer	High energy High capital costs
			High resin costs
	Adsorption	Well established Easily operable	High energy demand due to resin regeneration
			Separation is not highly selective

Table I - 5

 I5 Overview of pressure-driven membrane processes and their characteristics, adapted from ref.

			[100]
		Microfiltration	Ultrafiltration	Nanofiltration	Reverse
		(MF)	(UF)	(NF)	Osmosis (RO)
	Permeability (L/h.m 2 .bar)	>1000	10-1000	1.5-30	0.05-1.5
	Pressure (bar)	0.1-2	0.1-5	3-20	5-120
	Pore size (nm)	100-10000	2-100	0.5-2	<0.5
	Rejection
	• monovalent ions	-	-	-	+
	• multivalent ions	-	-/+	+	+
	• small organic compounds	-	-	-/+	+
	• macromolecules	-	+	+	+
	• particles	+	+	+	+
	Separation mechanism	Sieving	Sieving	Sieving/charge effects	Solution -diffusion
	Applications	Clarification, pretreatment, removal of bacteria	Removal of bacteria, viruses macromolecules,	Removal of small organics and relatively multivalent ions	Ultrapure water,

desalination Nanofiltration was first developed in the middle of the 1980s, due to the need for low energy consumption, low operation pressure, and high flux reverse osmosis (RO) membrane for water softening.

It was then realized that this kind of membrane has a special ability to separate low molecular weight organics such as glycine (with MW of 62) and glycerin (MW 92) from glucose

(MW 180)

Table I -6

 I Retention of VFAs by different NF membranes at various conditions

	Membrane and producer	pH	Temperature (℃)	Pressure (bar)	Acetic	Retention (%) Propionic	Butyric	(10	Flux	Resource	Impurity	Concentrati on	salt concentration (mM)	reference

-3 L.m -3 .m -2 .h) (mM)

	CPA2-2540	-	21-43	17.2	35.7-73.0	-	-	17.69-38.46	single solution		1.25-9.6	-	[175]
	(Hydranaut ics)	-	21	17.2	-	65.1-80.1	-		single solution		1.38-8.06	-	[175]
	NF-1 (PA) (self-made)	natural solution pH	-	-	89	-	-	-	single solution		-	-	[179]
	NF-2 (PA) (self-made) NFX (self-made) Sempas Membrante Desal-5 DK (GE) chnik GmbH (Jäger Umwelt-Technik) PA 100 (self-made)	-natural solution pH -natural solution pH 2.9-9.1 3-7 3.14-10.72 natural solution pH 3-7 3-9	--------	---8-10 4.9-24.5 -8-24 15 --8-24 -	38 10-99.5 --15.2 0-94.2 46.9 0.08-59.6 19.9-87.5 --0-62.5 28.0-19.2	------22.3-52.5 -65.7 -28.5-46.4 -	--31 ---100 31.14-79.95 -81.99 100 -	-------2.09-28.8 ----	fermentation broth single solution fermentation broth single solution mixed solution digestion liquor mixed solution and sludge digestion liquor single solution digestion liquor mixed solution	sugars alcohol long-chained acid sugars alcohol long-chained acid xylose 50g/L Hexanoic acid 25g/L, sugars 20mg/L about 2.5g/L other OM Hexanoic acid 25g/L, sugars Sugars, furfural acids	28.1 -9.18 8.33-66.67 83.26 17.5 50-100 10 17.5 25	---------50mM-100mM NaCl CaCl2 Na2CO3 NaHCO3 --	[176] [179] [176] [178] [177] [6] [180] [98,174] [6] [172]
	Desal-5 DL (GE) PA150 (self-made)	3.14-10.72 3-9	--	15 -	17.3-84.6 3.06-28.9	--	-14.86-83.73 -	5.06-39.6 -	mixed solution and sludge digestion liquor mixed solution	20mg/L about 2.5g/L other OM Sugars, furfural acids	50-100 25	NaHCO3 50mM-100mM NaCl CaCl2 Na2CO3 -	[98,174] [172]
	ES10 ( Nitto PA400 (self-made)	3.3-8.4 3-9	-	1.3-2.8 -	14.1-99.6 5.15-25.74	--	--	--	single solution and binary solution mixed solution	Sugars, furfural acids	0.83-8.33 25	0-4mM NaCl and 2mM MgSO4 -	[165] [172]
	Denko) HL (GE) PES 150 (self-made) MPF-34 Systems) (Koch Membrane	3.62-8.52 3.14-10.72 3-9 3.45-8.39 -	--25	1.3-2.8 15 -1.3-2.8 -	-1.1-74.5 0.4-49.5 --	26.6-97.9 -3.4-84.9 -	--0.67-72.19 --77	-11.42-52.8 ---	single solution mixed solution and sludge digestion liquor mixed solution single solution fermentation broth	Sugars, furfural acids about 2.5g/L other OM Sugars, alcohol, long-chained acid	0.67-6.75 25 50-100 0.67-6.75 8.64	0.4-4mM NaCl+2mM MgSO4 50mM-100mM NaCl -CaCl2 Na2CO3 NaHCO3 0.4-4mM NaCl+2mM MgSO4 -	[165] [172] [98,174] [165] [176]
	LF10 (Nitto Denko)	3.14-10.72	-	15	24.8-91.3	-	17.18-90.71	3.6-21.1	mixed solution and sludge digestion liquor	about 2.5g/L other OM	50-100	50mM-100mM NaCl NaHCO3 CaCl2 Na2CO3	[98,174]
	NF270 (Dow	3.33-8.25		1.3-2.8	2.9-84.1	-	-	-	single solution solution and binary			50-500mg/L0-4mM MgSO4 NaCl and 2mM	[165]
	Filmtec)	8.25	-	15	-	-	69.74	15.4	sludge digestion liquor		15.81	about 2.5g/L other OM	[98,174]
	NF200 (Dow Filmtec)	2.8-3.6 3.14-10.72	--	8-10 15	1.9-13.4 32.1-86.1	--	-21.87-83.16	-3.04-37.5	single solution and mixed solution mixed solution and sludge digestion liquor	Organic acid 9.5g/L, ethanol 10%v/v about 2.5g/L other OM	8.33-66.67 50-100	-50mM-100mM NaCl NaHCO3 CaCl2 Na2CO3	[178] [98,174]

Table I -7 Separation of acetic and butyric acids by previous research Membrane pH Pressure (bar) Solution Acetic retention Butyric retention Separation coefficient Ref.

 I

		3	8		0.01	1	∞
	Desal-5 DL	5	8		0.24	1	∞
		7 3	8 8	acidogenic digestion liquor	0.62 0.00	1 1	∞ ∞	[6]
	Desal-5 DK	5	8		0.11	1	∞
		7	8		0.60	1	∞
	ES 10 NF270	7.3 7.3	2.8 2.8	Synthetic wastewater	0.95 0.75	0.97 0.81	1.72 1.31	[165]
	Desal-5 DK 8.25	15	liquor of digested	0.57	0.45	1.28
	Desal-5 DL 8.25	15	agricultural sludge	0.46	0.34	1.22
	Desal-5 HL 8.25	15	(HAc, HPr	0.24	0.40	1.27	[98]
	NF270	8.25	15	concentration 21.10	0.53	0.70	1.57
	LF10	8.25	15	and 15.81mM)	0.72	0.62	1.36
	Desal-5 DK	-	15		0.29	0.37	1.13
	Desal-5 DL	-	15	mix solution of acetic	0.17	0.29	1.17
	Desal-5 HL	-	15	and butyric acids	0.27	0.30	1.04	[174]
	NF270	-	15	(50mM)	0.32	0.22	1.15
	LF10	-	15		0.29	0.30	1.01

Table II -1 Characteristics of VFAs Name Acetic acid Propionic acid Butyric acid Structure Molecular weight

 II

	(g.mol -1 )	60.05	74.08	88.11
	pK a (25℃)	4.76	4.88	4.82

Table II -2 Characteristics of VFAs sodium salts VFAs sodium salts Sodium acetate Sodium propionate Sodium butyrate

 II

	The concentrations of Ac, Pr, and Bu in single solutions were measured by a refractometer
	(ATAGO AX500, USA). VFAs concentrations in mixed solutions were obtained by High-
	Performance Liquid Chromatography (HPLC) (Jasco LC Net II / ADC, Japan) equipped with a
	Shodex SH1011 (Showa Denko, Japan) column and a UV detector (wavelength was set at 280nm).
	The details of the HPLC conditions are depicted in Table II-4. All the samples with high VFAs
	concentration were diluted to be in the concentration range from 5mM to 50mM.
	Chemical formula	CH 3 COONa	C 2 H 5 COONa	C 3 H 7 COONa
	Molecular weight (g.mol -1 )	82.03	96.07	110.88
		Table II-3 Characteristics of the inorganic salts
		Inorganic salts	Molecular weight (g.mol -1 )
		Na 2 SO 4	142.04
		NaCl	58.44
		CaCl 2	110.98
	II.2 Analytical methods
	In the NF experiments, solution pH, and temperature in the feed, permeate, and retentate were
	measured before and after the filtration at once. Solutes (VFAs and inorganic salts, both anions
	and cations) concentrations in the feed, permeate, and retentate were taken samples and measured.

Table II -5 Characteristics of the ion chromatography analysis

 II

		Dionex ICS 3000
	Ion type	Anion, cation
	Column	IonPac TM AS11, IonPac TM CS12
	Temperature	30ºC
	Mobile phase	NaOH: 5 mM (95%)+100mM (5%); MSA (Methanesulfonic acid): 20mM (100%)
	Flow rate	1 mL.min -1
	Pump	GP40
	Auto sampler	AS50
	Injection volume	25μL
	Suppresser	ASRS_4mm (137mA) CSRS_4mm (59mA)
	Conductivity detector	CD20

II.3 Membranes and nanofiltration (process) set-up

	Table II-6 Characteristics of the total organic carbon (TOC) analysis
		TOC Shimadzu 5050A
	Analyte	TC, IC, TOC (TC-IC)
	TC method	Catalytically aided combustion oxidation
	IC method	Pre-acidification
	Acidification	H 3 PO 4 (25% v/v)
	Flow rate	150 mL.min -1 (carrier gas)
	Detection range	50 ppb -4000 ppm
	II.3.1 NF membranes
	Two types of flat sheet composite membranes, NF 45 and XLE (Filmtec, Dow), were used in
	this thesis project, the main characteristics of which are provided in Table II-7.

Table II -7 Characteristics of NF-45 and XLE, Dow Filmtec membranes MWCO (g.mol -1 ) Material of active layer Maximum Temperature (℃) Max. pressure (bar) pH range Membrane isoelectric point Pure water permeability

 II

								(m•s -1 •bar -1 ,
								25℃)
	NF-45	150-300 Polyamide	45℃	41[181]	2-12 3-10) (recommended	4.0[182]	1.57×10 -6 [183]
	XLE	100	Polyamide	45℃	41	2-11	4 [184]	2.16×10 -6 [185]

  [START_REF] Bengtsson | Acidogenic fermentation of industrial wastewaters: Effects of chemostat retention time and pH on volatile fatty acids production[END_REF]. The feed volume, 𝑉𝑉 𝑓𝑓 , permeate volume, 𝑉𝑉 𝑝𝑝 , and retentate volume, 𝑉𝑉 𝑟𝑟 , were determined, as well as the concentrations of the feed, C 𝑓𝑓 , permeate, 𝐶𝐶 𝑝𝑝 , and retentate, 𝐶𝐶 𝑟𝑟 , using the previously detailed analytical methods. The mass balance, 𝑉𝑉 𝑓𝑓 C 𝑓𝑓 = 𝑉𝑉 𝑝𝑝 𝐶𝐶 𝑝𝑝 + 𝑉𝑉 𝑟𝑟 𝐶𝐶 𝑟𝑟 , was checked, and it was observed that the maximum

	difference does not exceed 5%.
	Membrane conditioning and cleaning procedures are crucial to obtain accurate data. The
	membrane was first immersed in ultra-pure water for 24 hours. It was then compacted by filtering
	ultra-pure water at a pressure of 20 bar until the filtration flux, 𝐽𝐽 reaches a constant value, three
	filtrations and a minimum of 1.5 h are required. The linearity of 𝐽𝐽 versus ∆𝑃𝑃 was checked and the
	mean hydraulic permeability 𝐿𝐿 𝑝𝑝0 was calculated by the slope of 𝐽𝐽/∆𝑃𝑃. After each NF experiment,
	the membrane was washed twice by filtering 200 mL of ultra-pure water and pure water
	permeability was measured to check any membrane fouling or aging.

salts Proportion in the feed (%) Ac Pr Bu Na 2 SO 4 NaCl CaCl 2

	Solutions s34 to s40 were filtrated by NF-45 membrane. The pH values of each solution are
	listed in Table II-11.
	Table II-9 Composition of the synthetic solutions for three total concentrations, 100mM, 200mM and
			500mM
	Solution number VFAs:s13 Concentration (mEq.L -1 ) 100, 200, 500 -				100
	s14	100, 200, 500	-				100
	s15	100, 200, 500	-				100
	s16	200	1:1	25		25	50
	s17	200	1:1	17 17 17	50
	s18	500	2:3	20		20	60
	s19	500	2:3	13 13 13	60
	s20	500	1:4	10		10	80
	s21	500	1:4	7	7	7	80
	s22	200	1:1	25		25	50
	s23	200	1:1	17 17 17	50
	s24	500	2:3	20		20	60
	s25	500	2:3	13 13 13	60
	s26	500	1:4	10		10	80
	s27	500	1:4	7	7	7	80
	s28	200	1:1	25		25	50
	s29	200	1:1	17 17 17	50
	s30	500	2:3	20		20	60
	s31	500	2:3	13 13 13	60
	s32	500	1:4	10		10	80
	s33	500	1:4	7	7	7	80
	II.4.3 Influence of the pH on the retention of VFAs
	Solution pH influences the dissociation of VFAs as well as the surface charge of the membrane.
	Synthetic solutions with neutral forms of VFAs (i.e., acetic acid, propionic acid, and butyric acid,
	pH≈3) were used to investigate the influence of solution pH on the retentions of VFAs. The feed
	compositions of single, binary, and ternary solutions are summarized in Table II-8. Three total
	concentrations were investigated (100mM, 200mM and 500mM). Each solution was adjusted to
	different pH values between 3 and 8 using NaOH.

Table II -

 II [START_REF] Tao | Recovery and concentration of thermally hydrolysed waste activated sludge derived volatile fatty acids and nutrients by microfiltration, electrodialysis and struvite precipitation for polyhydroxyalkanoates production[END_REF] Composition of the real fermentation broth

	Organics	Inorganics
	Components	Concentration(mM)	Components	Concentration (mM)
	Ac	44.41	Cl -	28.96
	Pr	30.76	SO 4 2-	0.32
	Bu	39.96	Na +	46.34
	Ethanol	10.17	NH 4 +	10.96
	Butanol	1.72	K +	3.98
			Ca 2+	24.09
	Total VFAs Concentration (mM)	115.13	Total cations concentration (mEq.L -1 )	109.46
	TOC (mg.L -1 )	4425.17
	TOC VFAs (mg.L -1 )	4091.38
	TOC OM (mg.L -1 )	333.79

Table II -

 II [START_REF] Hatti-Kaul | Industrial biotechnology for the production of bio-based chemicals -a cradle-to-grave perspective[END_REF] Compositions and pH values of the synthetic fermentation broths

	Components	pH 5.7 and 8 (XLE)	pH 5.7 (NF-45)
		Syn 1 Syn 2 Syn 3	Syn 4 Syn 5 Syn 6
	Ac (mM)	39	39	39	45	45	45
	Pr (mM)	39	39	39	31	31	31
	Bu (mM)	39	39	39	40	40	40
	NaCl (mM)		24			24
	CaCl 2 (mM)			24			24
	Total VFAs concentration (mM)	117	117	117	116	116	116

Table II -

 II [START_REF] Raspor | Biotechnological applications of acetic acid bacteria[END_REF] Filtrations on the pH-adjusted real fermentation broths

	Membranes	Real fermentation broth
		pH 5.7 (initial) pH 6.6 pH 8.2
	XLE	√
	NF-45	√	√	√

Table III - 1

 III1 VFAs proportions in the feed and permeate and corresponding separation factor for all the conditions investigated, using NF-45 membrane, at pH 8.

	Feed proportion	Permeate proportion (𝑃𝑃 𝑌𝑌 𝑝𝑝 * )	Permeate/Feed	Separation factor
	Ac	Pr	Bu	Ac	Pr	Bu	Ac	Pr	Bu	Ac/Pr Pr/Bu Ac/Bu
	1.00			1.00			1.00
		1.00			1.00			1.00
			1.00			1.00			1.00
	0.50 0.50		0.59	0.41		1.18 0.82		1.45
	0.20 0.80		0.25	0.75		1.27 0.93		1.37
	0.50		0.50	0.66		0.34	1.32		0.68		1.95
	0.20		0.80	0.32		0.68	1.60		0.85		1.89
	0.00 0.50 0.50		0.58	0.42		1.15 0.85		1.37
	0.20 0.20 0.60	0.31	0.21	0.48	1.56 1.05 0.80	1.48	1.32	1.95
	0.20 0.60 0.20	0.27	0.59	0.14	1.37 0.98 0.69	1.39	1.42	1.98
	0.33 0.33 0.33	0.47	0.31	0.22	1.41 0.94 0.65	1.51	1.44	2.17
	0.60 0.20 0.20	0.72	0.16	0.11	1.21 0.81 0.57	1.49	1.43	2.13

  Proportions of all the solutes in the permeate versus filtration flux, for (a) Ac/Bu binary solution with CaCl 2 , (b) Ac/Pr/Bu ternary solution with CaCl 2 , using NF-45 membrane.

		100 100	a a				100 100	b b
	Proportion in the permeate (%) Proportion in the permeate (%)	20 60 80 20 60 80	Ac:Bu:Cl=25%:25%:49% 200 mEq.L -1 Ac Bu Cl Ac:Bu:Cl=25%:25%:49% 88% 8% 200 mEq.L -1 Ac Bu Cl 7% 79% 14%			Proportion in the permeate (%) Proportion in the permeate (%)	10 20 50 60 70 80 90 20 60 80	Ac:Pr:Bu:Cl=16%:16%:16%:52% 200 mEq.L -1 2% 3% Ac Pr Bu Cl Ac:Pr:Bu:Cl=17%:17%:17%:49% 89% 5% 200 mEq.L -1 5% 78% 7% Ac Pr Bu Cl 10%
		0 0	4%				0 0
	0.0E+00 0.0E+00 0 20 60 80 100 0.0E+00 0 10 80 90 100 0.0E+00 0 20 60 80 100 0.0E+00 100 Figure IV-9 0.0E+00 Ac:Bu:Cl=20%:20%:61% 5.0E-06 1.0E-05 5.0E-06 1.0E-05 5.0E-06 1.0E-05 Filtration flux (m/s) 1.5E-05 1.5E-05 1.5E-05 500 mEq.L -1 Ac Bu Cl Proportion in the permeate (%) Filtration flux (m/s) 9% 4% 87% Ac:Bu:Cl=9%:9%:81% 500 mEq.L -1 Ac Bu Cl Proportion in the permeate (%) Filtration flux (m/s) 95% 2% 3% 5.0E-06 1.0E-05 1.5E-05 5.0E-06 1.0E-05 1.5E-05 5.0E-06 1.0E-05 1.5E-05 Filtration flux (m/s) Ac:Bu:Cl=22%:22%:56% 500 mEq.L -1 Ac Bu Cl Proportion in the permeate (%) Filtration flux (m/s) 83% 11% 6% Filtration flux (m/s) 0 20 80 Ac:Bu:Cl=12%:12%:77% 500 mEq.L -1 Ac Bu Cl Proportion in the permeate (%) 90% 6% 3%	2.0E-05 2.0E-05 2.0E-05 2.0E-05 2.0E-05 2.0E-05	0.0 0.0 0.8	Proportion in the permeate (%) Proportion in the permeate (%) Proportion in the permeate (%) Proportion in the permeate (%)	0.0E+00 0.0E+00 0 10 60 70 80 90 100 0.0E+00 0 10 80 90 100 0.0E+00 0.0E+00 0 10 20 70 80 90 100 0.0E+00 100 0 10 80 90	5.0E-06 5.0E-06 5.0E-06 Filtration flux (m/s) 1.0E-05 1.5E-05 1.0E-05 1.5E-05 1.0E-05 1.5E-05 Ac:Pr:Bu:Cl=13%:13%:14%:60% 500 mEq.L -1 Ac Pr Bu Cl Filtration flux (m/s) 90% 5% 3% 2% Ac Pr Bu Cl Filtration flux (m/s) 1.2% 1.8% 2.0E-05 2.0E-05 2.0E-05 0.8% 96.2% Ac:Pr:Bu:Cl=7%:7%:7%:80% 500 mEq.L -1 5.0E-06 1.0E-05 1.5E-05 2.0E-05 5.0E-06 1.0E-05 1.5E-05 2.0E-05 5.0E-06 1.0E-05 1.5E-05 2.0E-05 Filtration flux (m/s) Ac:Pr:Bu:Cl=11%:11%:11%:67% 500 mEq.L -1 Ac Pr Bu Cl Filtration flux (m/s) 86% 6% 4% 3% Filtration flux (m/s) Ac:Pr:Bu:Cl=5%:5%:5%:84% 500 mEq.L -1 Ac Pr Bu Cl 3% 2% 1% 94%

Table IV -

 IV 1 summarizes the proportions of all the anions in the feed and permeate for all the conditions investigated. The proportions in the permeate are obtained from the individual solutes proportions at the plateau values.

Table IV - 1

 IV1 Comparison of the solute proportion in the feed and permeate, using NF-45 membrane, at pH 8

			Proportion in the feed			Proportion in the permeate
	Ac	Pr	Bu	VFAs SO4 2-Cl -(Na) Cl -(Ca)	Ac	Pr	Bu	VFAs SO4 2-Cl -(Na) Cl -(Ca)
	0.24		0.24	0.48	0.52	0.51		0.24	0.76	0.24
	0.16 0.16 0.16	0.48	0.52	0.36 0.23 0.18	0.77	0.23
	0.19		0.19	0.38	0.62	0.38		0.22	0.60	0.40
	0.13 0.13 0.13	0.39	0.61	0.27 0.20 0.15	0.62	0.38
	0.09		0.09	0.18	0.82	0.26		0.14	0.40	0.60
	0.06 0.06 0.06	0.19	0.81	0.18 0.13 0.10	0.40	0.60
	0.25		0.26	0.51	0.49	0.14		0.07	0.21	0.79
	0.16 0.16 0.16	0.48	0.52	0.10 0.06 0.04	0.20	0.80
	0.20		0.20	0.40	0.60	0.09		0.05	0.14	0.86
	0.12 0.12 0.12	0.36	0.64	0.06 0.04 0.03	0.12	0.88
	0.09		0.09	0.19	0.81	0.04		0.02	0.05	0.95
	0.06 0.06 0.06	0.19	0.81	0.02 0.01 0.01	0.05	0.95
	0.25		0.25	0.51	0.49	0.14		0.07	0.21	0.79
	0.17 0.17 0.17	0.51	0.49	0.10 0.07 0.05	0.22	0.78
	0.22		0.22	0.44	0.56	0.12		0.06	0.18	0.82
	0.11 0.11 0.11	0.33	0.67	0.06 0.05 0.04	0.15	0.85
	0.12		0.12	0.24	0.76	0.07		0.04	0.11	0.89
	0.05 0.05 0.05	0.16	0.84	0.03 0.02 0.02	0.07	0.93

  2.5, 2.6, 2.7, and 2.8) can give information for the separation of the two solutes. The relative proportions of Ac, Pr, and Bu in feed and permeate for the couples of Ac/Pr, Pr/Bu, and Ac/Bu at binary and ternary solutions without and with inorganic salts are listed in TableIV-2.

	Table IV-2 can be visualized in Figure IV-14. The relative permeate proportions of Ac, Pr,
	and Bu in the couples of Ac/Pr, Pr/Bu, and Ac/Bu are plotted versus their relative feed proportions
	in the feed.

Table IV - 2

 IV2 Relative proportions of VFAs in the feed and permeate, for single and mixed solutions at different proportions without and with salts, using NF-45 membrane at pH 8.

	s28	0.25		0.25	0.51	0.49	1.00	0.50			0.50	1.00	1.00	0.67			0.33	1.00
	s29	0.17 0.17 0.17	0.51	0.49	0.50	0.50	0.50	0.49	0.50	0.51	0.59	0.66	0.41	0.58	0.34	0.42
	Solution s30 s31 No. s32	0.22 0.11 0.11 0.11 0.22 Proportion in the feed 0.44 0.33 Ac Pr Bu VFAs Na2SO4 NaCl CaCl2 0.56 0.67 0.12 0.12 0.24 0.76	Relative proportion in the feed 0.50 0.50 Pr 0.50 0.49 0.50 0.50 Ac/Pr Ac/Bu 1.00 Ac 0.51 Ac/Pr Pr/Bu Ac/Bu Pr/Bu 1.00 Bu 0.50 1.00 0.50 0.50 1.00	1.00 0.57 Ac/Pr Ac/Bu 0.65 Relative proportion in the permeate 0.35 Ac Pr 0.65 0.43 0.58 0.35 Ac/Pr Pr/Bu Ac/Bu Pr/Bu 1.00 0.42 Bu 1.00 0.64 0.36 1.00
	s1 s33	1 0.05 0.05 0.05	0.16	0.84	1.00 0.50	1.00 0.50	0.50	0.50	0.50	0.50	1.00 0.57	1.00 0.64	0.43	0.57	0.36	0.43
	s2		1						1.00	1.00					1.00	1.00
	s3			1							1.00	1.00					1.00	1.00
	s4	0.5	0.5				0.50		0.50				0.59		0.41
	s5	0.2	0.8				0.20		0.80				0.25		0.75
	s6	0.5		0.5				0.50			0.50			0.66			0.34
	s7	0.2		0.8				0.20			0.80			0.32			0.68
	s8		0.5	0.5						0.50		0.50				0.58	0.42
	s9	0.2	0.2	0.6			0.50	0.25	0.50	0.25	0.75	0.75	0.60	0.39	0.40	0.30	0.61	0.70
	s10	0.2	0.6	0.2			0.25	0.50	0.75	0.75	0.50	0.25	0.31	0.66	0.69	0.81	0.34	0.19
	s11	0.33 0.33 0.33			0.50	0.50	0.50	0.50	0.50	0.50	0.60	0.68	0.40	0.58	0.32	0.42
	s12	0.6	0.2	0.2			0.75	0.75	0.25	0.50	0.25	0.50	0.82	0.87	0.18	0.59	0.13	0.41
	s16	0.24		0.24	0.48	0.52	1.00	0.50			0.50	1.00	1.00	0.68			0.32	1.00
	s17	0.16 0.16 0.16	0.48	0.52	0.50	0.50	0.50	0.50	0.50	0.50	0.60	0.67	0.40	0.57	0.33	0.43
	s18	0.19		0.19	0.38	0.62	1.00	0.50			0.50	1.00	1.00	0.64			0.36	1.00
	s19	0.13 0.13 0.13	0.39	0.61	0.50	0.50	0.50	0.50	0.50	0.50	0.57	0.64	0.43	0.57	0.36	0.43
	s20	0.09		0.09	0.18	0.82	1.00	0.49			0.51	1.00	1.00	0.65			0.35	1.00
	s21	0.05 0.05 0.06	0.17	0.83	0.49	0.50	0.51	0.50	0.50	0.50	0.60	0.70	0.40	0.61	0.30	0.39
	s22	0.25		0.26	0.51	0.49	1.00	0.50			0.50	1.00	1.00	0.68			0.32	1.00
	s23	0.16 0.16 0.16	0.48	0.52	0.50	0.50	0.50	0.49	0.50	0.51	0.61	0.69	0.39	0.59	0.31	0.41
	s24	0.20		0.20	0.40	0.60	1.00	0.50			0.50	1.00	1.00	0.68			0.32	1.00
	s25	0.12 0.12 0.12	0.36	0.64	0.50	0.50	0.50	0.50	0.50	0.50	0.60	0.68	0.40	0.58	0.32	0.42
	s26	0.09		0.09	0.19	0.81	1.00	0.50			0.50	1.00	1.00	0.68			0.32	1.00
	s27	0.06 0.06 0.06	0.17	0.83	0.50	0.50	0.50	0.50	0.50	0.50	0.61	0.69	0.39	0.59	0.31	0.41

Table IV - 3

 IV3 Separation factor between Ac/Pr, Pr/Bu, and Ac/Bu at corresponding proportion in the feed for all the solutions investigated, using NF-45 membrane.

	Solution number	Ac	Pr	Proportion in the feed Bu Na 2 SO 4 NaCl CaCl 2	Separation factor Ac/Pr Pr/Bu Ac/Bu
	s4	0.5 0.5			1.45
	s5	0.2 0.8			1.37
	s6	0.5		0.5			1.95
	s7	0.2		0.8			1.89
	s8		0.5 0.5			1.37
	s9	0.2 0.2 0.6		1.48	1.32	1.95
	s10	0.2 0.6 0.2		1.39	1.42	1.98
	s11	0.33 0.33 0.33		1.51	1.44	2.17
	s12	0.6 0.2 0.2		1.49	1.43	2.13
	s16	0.24		0.24	0.52		2.07
	s17	0.16 0.16 0.16	0.52	1.50	1.35	2.03
	s18	0.19		0.19	0.62		1.83
	s19	0.13 0.13 0.13	0.61	1.38	1.33	1.83
	s20	0.09		0.09	0.82		1.86
	s21	0.06 0.06 0.06	0.81	1.41	1.29	1.82
	s22	0.25		0.26	0.49		2.11
	s23	0.16 0.16 0.16	0.52	1.52	1.48	2.24
	s24	0.20		0.20	0.60		2.08
	s25	0.12 0.12 0.12	0.64	1.52	1.39	2.10
	s26	0.09		0.09	0.81		2.14
	s27	0.06 0.06 0.06	0.81	1.52	1.42	2.15
	s28	0.25		0.25	0.49		2.06
	s29	0.17 0.17 0.17	0.49	1.39	1.40	1.95
	s30	0.22		0.22	0.56		1.89
	s31	0.11 0.11 0.11	0.67	1.30	1.38	1.79
	s32	0.12		0.12	0.76		1.84
	s33	0.05 0.05 0.05	0.84	1.33	1.34	1.78

Table IV -

 IV 3 summarizes the separation factors (as defined in Chapter II) between Ac/Pr, Pr/Bu, and Ac/Bu at corresponding proportions in the feed for all the conditions investigated. The proportions of VFAs in the permeate used to calculate the separation factors are the plateau values previously observed. Despite the variety of compositions, one can observe that the separation factors between Ac/Pr and Pr/Bu are within the range of 1.29 to 1.52, separation factors between Pr/Bu are systematically slightly lower than that of Ac/Pr, except for the conditions with addition of CaCl2. Separation factors between Ac/Bu are in-between 1.78 to 2.24.

Table V -

 V 4 pK eff values (obtained from Eq. (V.12)) and the coefficient of determination for the fitting at different compositions, filtration flux=0.2×10 -5 m.s -1 . Results obtained using NF-45 membrane.

	Solution	100mM pK eff R 2	200mM pK eff R 2	500mM pK eff R 2
	Ac	5.79 0.822	5.80 0.984	5.52 0.944
	Pr	5.74 0.877	5.84 0.990	5.42 0.970
	Bu	5.78 0.924	5.69 0.829	5.46 0.892
	Ac/Pr	5.64 0.987	5.80 0.966	5.36 0.951
	Ac/Bu	5.64 0.989	5.71 0.970	5.46 0.946
	Ac/Pr/Bu	5.91 0.971	5.95 0.978	5.39 0.970
	It is shown that the pKeff values obtained for different solutions at low concentrations (100mM
	and 200mM) are comparable (5.75 ±0.09, and 5.80±0.08 respectively), while the pKeff values
	obtained at the highest concentration (500mM) is about 0.33 unit lower (5.44±0.05).

Table VI -

 VI 1 Composition of the real fermentation broth NaCl and 24mM of CaCl2 are added respectively in order to simulate the influence of inorganic salts. The chosen VFAs proportion (1:1:1) for the synthetic broths can be compared with the ternary solutions with identical VFAs proportion. The proportion of Ac:Pr:Bu for synthetic broths (i.e., Syn 4, Syn 5, and Syn 6) that filtrated by NF-45 membrane is 45:31:40, the same as that for the real fermentation broth, in order to compare the permeate proportions between synthetic and real fermentation broths.

	Organics	Inorganics
	Components	Concentration(mM)	Components	Concentration (mM)
	Ac	44.41	Cl -	28.96
	Pr	30.76	SO 4 2-	0.32
	Bu	39.96	Na +	46.34
	Ethanol	10.17	NH 4 +	10.96
	Butanol	1.72	K +	3.98
			Ca 2+	24.09
	Total VFAs Concentration (mM)	115.13	Total cations concentration (mEq.L -1 )	109.46
	TOC (mg.L -1 )	4425.17
	TOC VFAs (mg.L -1 )	4091.38
	TOC OM (mg.L -1 )	333.79
	The compositions of the 6 synthetic broths are given in Table VI-2. Two membranes, i.e., XLE
	and NF-45 membranes, are used in the experimental investigation. The proportion of Ac:Pr:Bu
	for synthetic broths (i.e., Syn 1, Syn 2, and Syn 3) filtrated by XLE membrane is 1:1:1, the total
	VFAs concentration (117 mM) is similar to that of the real fermentation broth (115 mM). Then
	24mM of

Table VI - 2

 VI2 Compositions and pH values of the synthetic fermentation broths

	Components	pH 5.7 and 8 (XLE)	pH 5.7 (NF-45)
		Syn 1 Syn 2 Syn 3	Syn 4 Syn 5 Syn 6
	Ac (mM)	39	39	39	45	45	45
	Pr (mM)	39	39	39	31	31	31
	Bu (mM)	39	39	39	40	40	40
	NaCl (mM)		24			24
	CaCl 2 (mM)			24			24
	Total VFAs concentration (mM)	117	117	117	116	116	116
	VI.1.1.1 Nanofiltration using XLE membrane

Table VI - 3

 VI3 Total organic carbon (TOC) in the feed, permeate, and retentate of real fermentation broth using XLE membrane.

	Samples	TOC (mg/L) TOC TOC -VFAs TOC -OM
	Feed		4425±0 4091±0	334±0
		8 bar 543±0	358±2	185±2
	Permeate	12 bar 371±0 16 bar 298±0	199±4 142±6	172±4 156±6
		20 bar 258±0	117±7	141±7
	Retentate	5054±0 4767±0	287±0

  However, the proportions of Ca 2+ and NH4 + show different behaviors. The proportion of Ca 2+

		100	a
			Ac:Pr:Bu:Cl=31%:21%:28%:20%
	Proportion in the permeate (%)	20 40 60 80	144 mM Ac Pr Bu Cl		pH=5.7	11% 16% 25% 48%
		0
		0.0E+00	5.0E-06	1.0E-05	1.5E-05	2.0E-05
		100	Na:Ca:NH4=44%:47%:9% Filtration flux (m/s) b
	Proportion in the permeate (%)	20 40 60 80	Na Ca NH4 118 mEq.L -1	pH 5.7	40% 20% 40%
		0
		0.0E+00	5.0E-06	1.0E-05	1.5E-05	2.0E-05
				Filtration flux (m/s)

Table VI - 4

 VI4 Proportions of VFAs and Cl -in the feed and permeate as well as the separation factor between VFAs/Cl -for the real fermentation broth

			XLE membrane			NF-45 membrane
	pH	Feed	permeate	Separation	Feed	permeate	Separation
		VFAs Cl -	VFAs Cl -	factor	VFAs Cl -	VFAs Cl -	factor
	5.7 0.80 0.20	0.84 0.16	1.3	0.82 0.18	0.69 0.31	2.0
	6.6				0.81 0.19	0.56 0.44	3.4
	8.2				0.82 0.18	0.53 0.47	4.0

Table VI - 5

 VI5 Proportions of Na + and Ca 2+ in the feed and permeate as well as the separation factor between Na + /Ca 2+ for the real fermentation broth

			XLE membrane			NF-45 membrane
	pH	Feed	permeate Separation	Feed	permeate Separation
		Na + Ca 2+	Na + Ca 2+	factor	Na + Ca 2+	Na + Ca 2+	factor
	5.7 0.44 0.47	0.40 0.19	2.3	0.44 0.43	0.61 0.19	3.2
	6.6				0.45 0.43	0.65 0.17	3.7
	8.2				0.45 0.43	0.62 0.21	2.8

Table VI - 6

 VI6 Proportions of monovalent (i.e., Na + NH 4 + , and K + ) and divalent (i.e., Ca 2+ ) cations in the feed and permeate as well as the separation factor between monovalent/divalent cations for the real fermentation broth

			XLE membrane			NF-45 membrane
	pH	Feed	permeate	Separation	Feed	permeate	Separation
		mono di	mono di	factor	mono di	mono di	factor
	5.7 0.53 0.47	0.81 0.19	3.8	0.57 0.43	0.81 0.19	3.2
	6.6				0.57 0.43	0.83 0.17	3.7
	8.2				0.57 0.43	0.79 0.21	2.8

Table VI - 7

 VI7 Proportions of VFAs in the feed and permeate as well as the separation factor between VFAs for the couples of Ac/Pr, Pr/Bu, and Ac/Bu for the real fermentation broth

					XLE membrane			NF-45 membrane
	Couples pH	Feed	permeate Separation	Feed		permeate Separation
			Ac	Pr	Ac	Pr	factor	Ac	Pr	Ac	Pr	factor
		5.7 0.31 0.21	0.56 0.3	1.3	0.31	0.21	0.37 0.38	1.5
	Ac/Pr	6.6						0.31	0.21	0.35 0.5	2.2
		8.2						0.31	0.21	0.33 0.54	2.4
		5.7 0.21 0.28	0.3 0.14	2.8	0.21	0.3	0.38 0.25	2.1
	Pr/Bu	6.6						0.21	0.29	0.5 0.15	4.7
		8.2						0.21	0.29	0.54 0.13	5.8
		5.7 0.31 0.28	0.56 0.14	3.6	0.31	0.3	0.37 0.25	1.4
	Ac/Bu	6.6						0.31	0.29	0.35 0.15	2.2
		8.2						0.31	0.29	0.33 0.13	2.4

Table VI - 8

 VI8 Proportions of Ac+Pr and Bu in the feed and permeate as well as the separation factor between Ac+Pr and Bu for the real fermentation broth

			XLE membrane			NF-45 membrane
	pH	Feed	permeate	Separation	Feed	permeate	Separation
		Ac+Pr Bu	Ac+Pr Bu	factor	Ac+Pr Bu	Ac+Pr Bu	factor
	5.7 0.65 0.35	0.86 0.14	3.3	0.64 0.36	0.75 0.25	1.7
	6.6				0.64 0.36	0.85 0.15	3.2
	8.2				0.64 0.36	0.87 0.13	3.8

Table VI - 9

 VI9 Proportions of VFAs and OM in the feed and permeate as well as the separation factor between VFAs/OM using XLE membrane for the real fermentation broth

			XLE membrane
	pH	Feed	permeate	Separation
		VFAs OM	VFAs OM	factor
	5.7 0.92 0.08	0.45 0.55	14.8

s40 √ √ √ √ √ √

Nomenclature

Chapter II

Materials and methods

Chapter VI NF of VFAs fermentation broths

IV, this is due to the dissociation of VFAs as well as to the increase of the pH-induced membrane surface charge. A similar observation was reported in ref. [START_REF] Szoke | Characteristics of thin-film nanofiltration membranes at various pH-values[END_REF] too.

For the cations, the retention sequence in the real fermentation broth is NH4 + <Na + ≈K + <Ca 2+ , at the three pH values investigated (Figure . The divalent cation, Ca 2+ has much higher retention than monovalent cations (Na + , K + , and NH4 + ). When the solution pH increases, the retentions of the monovalent cations gradually increase. Meanwhile, the retention of Ca 2+ increases with pH from 5.7 to 6.6, then remains nearly constant when solution pH increases to 8.2.

The retention sequence of Ca 2+ and Na + is the same as that observed in single and mixed solutions in Chapter IV (i.e., Na + <Ca 2+ ).

VI.1.3 Removal of organic impurities from the real fermentation broth

The real fermentation broth contains many organic matter/impurities (e.g., ethanol and butanol, as shown in Table VI-1), which could hinder the downstream processes such as PHA production.

The TOC of the real fermentation broth can be experimentally obtained (namely TOC), the compositions of VFAs can be also obtained by HPLC analysis. Therefore, the TOC due to the organic matter/impurities (OM) can be obtained as the difference of TOC and the theoretical TOC values of the three VFAs obtained from HPLC (i.e., TOCOM= TOC-TOCVFAs).

The concentrations of total organic carbon (TOC) in the feed, permeate, and retentate of the real fermentation broth using XLE membrane are measured, and the concentrations are given in Table VI-3. The TOC analysis for the feed, permeate, and retentate of real fermentation broth using NF-45 membrane is not obtained due to that the samples were improperly stored.

One can observe that VFAs holds more than 90% of the TOC in the real fermentation broth.

Then the contribution of VFAs on the TOC in the permeate decrease rapidly as the transmembrane pressure increase. At the transmembrane pressure of 20bar, the contribution of VFAs on the TOC in the permeate is only about 45%. It is concluded that better separation factors between Cl -/VFAs and Na + /Ca 2+ are observed using NF-45 membrane compared to that observed using XLE membrane. Furthermore, increasing the solution pH from 5.7 to 8.2 can double the separation factor between Cl -/VFAs, while much less influence of solution pH is observed on the separation factor between Na + /Ca 2+ .

In general, by using NF-45 membrane, Na + and Cl -in the real fermentation broth is enriched in the permeate, while Ca 2+ and VFAs -is enriched in the retentate.

VI.3.2 Case 2: VFAs composition modification

As introduced in Chapter I, VFAs composition is critical for the following applications like PHA (polyhydroxyalkanoates) and bioenergy productions. Higher proportions of Ac and Pr are more favorable for bioenergy production, while higher Bu proportion is beneficial for the production of PHA. In order to compare the ability of the two membranes on the modification of VFAs compositions, the proportions and separation factors between Ac/Pr, Pr/Bu, and Ac/Bu are considered separately.

The separation factor between the two solutes in a couple can be directly calculated from the relative proportions in the feed and permeate, as previously discussed.

The proportions of Ac, Pr, and Bu in the feed and permeate, as well as the separation factors between Ac/Pr, Pr/Bu, and Ac/Bu using the two membranes at different pH values are listed in