Mendret Alice Schmitt

Michel Roustan

Stephan Brosillon

Julie Mendret
email: julie.mendret@umontpellier.fr

Ozonation using hollow fiber contactor technology and its perspectives for micropollutants removal in water: A review

Keywords: Membrane contactor, Ozonation, Micropollutants, Mass transfer, Modeling

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

To protect the ecosystem and drinking water resources, requirements on water treatment will become increasingly stricter. It is only a matter of time before treatment plants will be required to incorporate treatment steps to ensure that micropollutants (i.e. harmful substances, detectable in the environment at very low concentrations (ng/L up to µg/L)) are eliminated and do not enter the water bodies. For instance, in Switzerland, a new Swiss water protection act entered into force in 2016 aiming to reduce the discharge of micropollutants from wastewater treatment plants (WWTPs) (Office fédéral de l'environnement, 2014). As a consequence, selected WWTPs must be upgraded by an advanced treatment for micropollutants abatement with suitable and economic options such as ozonation. Ozone treatment is easy to automate and clean to handle. It provides a chemical-free means of removing 90 percent of emerging contaminants [START_REF] Prieto-Rodríguez | Application of solar AOPs and ozonation for elimination of micropollutants in municipal wastewater treatment plant effluents[END_REF][START_REF] Snyder | Ozone oxidation of endocrine disruptors and pharmaceuticals in surface water and wastewater[END_REF]. It can be quite simply incorporated into existing and new applications and is a reliable and control-supported process. Another advantage of ozonation is the direct oxidation, breaking the molecule which is destroyed and not only absorbed. Ozonation is thus an interesting technology for water reuse since it can both disinfect and oxidize, or be used with other technologies in a multiple-barrier concept.

The conventional reactors used during the ozonation processes are presented in Table 1. A schematic drawing of each reactor is exposed in Figure 1. Depending on the application (i.e.

the objectives of the ozonation), the reactor is chosen according to its contact time (especially for slow reactions), its hydrodynamics (especially for fast and moderately fast reaction, where a plug flow is preferable), and its ozone transfer (especially for very fast reaction, where a high interfacial area is preferable). Generally, ozone in water treatment is injected in the form of bubbles, with disadvantages such as operational costs, stripping of volatile organic compounds, high footprint of the reactor, mass transfer limitations (leading to high energetic costs) and foam generation. Moreover, in some cases, these processes do not ensure a controlled dosage, and can lead to the production of by-products sometimes more dangerous than the original products [START_REF] Gao | Theoretical investigation on the kinetics and mechanisms of hydroxyl radical-induced transformation of parabens and its consequences for toxicity: Influence of alkyl-chain length[END_REF][START_REF] Gogoi | Occurrence and fate of emerging contaminants in water environment: A review[END_REF][START_REF] Schlüter-Vorberg | Toxification by transformation in conventional and advanced wastewater treatment: the antiviral drug acyclovir[END_REF]. Venturi injector Gas 0.06-0.21 [START_REF] Roustan | Transferts gaz-liquide dans les procédés de traitement des eaux et des effluents gazeux[END_REF] 1-10 (Roustan,

2003)

N.A.

High mass transfer [START_REF] Cachon | Gases in Agro-food Processes[END_REF][START_REF] Ozkan | Experimental investigations of air and liquid injection by venturi tubes[END_REF] High gas-liquid interfacial area

High energy efficiency

Applicable to short contact time [START_REF] Briens | Ozonation and advanced oxidation of wastewater: Effect of O3 dose, pH, DOM and HO.-scavengers on ozone decomposition and HO . generation[END_REF] No additional equipment needed (i.e. located directly in the process stream) [START_REF] Bauer | Mass transfer characteristics of a venturi liquid-gas contactor[END_REF] Minimal maintenance [START_REF] Cachon | Gases in Agro-food Processes[END_REF] Power from a recirculating pump required, or pressurized water supply [START_REF] Cachon | Gases in Agro-food Processes[END_REF] Petroleum refining, Hydrogenation, Fermentation, Waste-water treatment [START_REF] Briens | Ozonation and advanced oxidation of wastewater: Effect of O3 dose, pH, DOM and HO.-scavengers on ozone decomposition and HO . generation[END_REF] Water (in) Water (out)

The use of membrane contactors for ozone diffusion in water treatment recently emerged as a very interesting option. Indeed, by using a bubbleless operation, membrane contactors can overcome these challenges. Indeed, membrane contactors have been pointed out as a good alternative for the transfer of gas to the liquid phase (Alves dos [START_REF] Alves Dos Santos | Polymeric Materials for Membrane Contactor Devices Applied to Water Treatment by Ozonation[END_REF][START_REF] Berry | Modelling of Ozone Mass-Transfer through Non-Porous Membranes for Water Treatment[END_REF][START_REF] Pabby | State-of-the-art review on hollow fibre contactor technology and membrane-based extraction processes[END_REF][START_REF] Stylianou | Ozone Mass Transfer Studies in a Hydrophobized Ceramic Membrane Contactor: Experiments and Analysis[END_REF], and to control the dosage of ozone during ozonation processes [START_REF] Atchariyawut | Application of ozonation membrane contacting system for dye wastewater treatment[END_REF][START_REF] Bamperng | Ozonation of dye wastewater by membrane contactor using PVDF and PTFE membranes[END_REF][START_REF] Berry | Modelling of Ozone Mass-Transfer through Non-Porous Membranes for Water Treatment[END_REF][START_REF] Janknecht | Ozone-water contacting by ceramic membranes[END_REF][START_REF] Jansen | Hollow fiber membrane contactors-A means to study the reaction kinetics of humic substance ozonation[END_REF][START_REF] Leiknes | Ozone transfer and design concepts for NOM decolourization in tubular membrane contactor[END_REF][START_REF] Merle | MEMBRO 3 X, a Novel Combination of a Membrane Contactor with Advanced Oxidation (O 3 /H 2 O 2 ) for Simultaneous Micropollutant Abatement and Bromate Minimization[END_REF][START_REF] Picard | Ceramic membranes for ozonation in wastewater treatment[END_REF][START_REF] Pines | Investigation of an Ozone Membrane Contactor System[END_REF][START_REF] Shanbhag | Membrane-Based Ozonation of Organic Compounds[END_REF][START_REF] Shanbhag | Single-phase membrane ozonation of hazardous organic compounds in aqueous streams[END_REF][START_REF] Stylianou | Application of a ceramic membrane contacting process for ozone and peroxone treatment of micropollutant contaminated surface water[END_REF][START_REF] Stylianou | Ozone Mass Transfer Studies in a Hydrophobized Ceramic Membrane Contactor: Experiments and Analysis[END_REF][START_REF] Wenten | Ozonation through ceramic membrane contactor for iodide oxidation during iodine recovery from brine water[END_REF][START_REF] Zoumpouli | A Single Tube Contactor for Testing Membrane Ozonation[END_REF]. The following list describes the major advantages of a membrane contactor technology:

• This process has a smaller foot print than conventional reactor, thanks to its large interfacial area. Since treatment of wastewater are targeted, very fast reaction will occur and thus the transfer will be accelerated by the reaction, as a consequence it is interesting to develop high interfacial area in the reactors. According to Reed et al., membrane contactors have an interfacial area between 1640 and 6562 m 2 /m 3 .

According to Chabanon et al., membrane contactors have a surface area/volume ratio around 1,000-10,000 m²/m3, whereas this ratio is between 50 and 600 m²/m3 for a bubble column and between 10 and 500 m²/m3 for a packed column. [START_REF] Chabanon | 3.9 Membranes Contactors for Intensified Gas-Liquid Absorption Processes[END_REF]. In contrast, conventional contactors have an interfacial area between 3 and 492 m 2 /m 3 . [START_REF] Reed | Chapter 10 Membrane contactors[END_REF]. [START_REF] Pines | Investigation of an Ozone Membrane Contactor System[END_REF] have carried out calculations, an hypothetical case of 167 m 3 /h flow rate and 2 mg/L transferred ozone dose was used in order to compare the volume required for hollow fiber membrane contactors (PVDF) configurations compared to a fine-bubble diffuser contactor. The assumptions were a gas O3 concentration of about 6%, no chemical reaction and a system mass transfer limited. [START_REF] Stylianou | Ozone Mass Transfer Studies in a Hydrophobized Ceramic Membrane Contactor: Experiments and Analysis[END_REF] have carried out the same calculations based on their experimental results obtained with ceramic tubular membrane. The volume of each reactor was 12 m 3 , 1.9 m 3 and 0.15 m 3 respectively for bubble column; ceramic tubular membrane contactor and PVDF hollow fiber membrane. This first approach demonstrates the real interest of membrane contactor to increase the compactness of the unit operation.

• The mass transfer (i.e. the KLa) obtained with a membrane contactor is significantly higher than with other conventional reactors. For a membrane contactor, the mass transfer is estimated between 0.05 and 0.50 s-1, whereas it is between 0.005 and 0.12 s-1 for a bubble column and between 0.0004 and 0.07 s-1 for a packed column. The difference is mainly due to a surface area/volume ratio particularly interesting with the membranes.

• The compound of interest (i.e. here the ozone molecule) has a uniform distribution, thanks to the large exchange surface (i.e. interfacial area) offered by the hollow fiber membranes.

• The risk of flooding and of entrainment of the dispersed phase is avoided thanks to a bubbleless process.

• Increasing the production capacity of a membrane contactor is easy by adding more membrane modules (i.e. this process is especially modular).

• The exchange surface is independent of the flow rates. The process can work efficiently at different gas/liquid ratios, and therefore has a wide range of capacities for the same number of modules.

• Operations are performed under low pressures because transfer is driven by the concentration gradient and not by the pressure gradient. Therefore, energy requirement by this process is lower.

• A gas stream recycling can be implemented, and thus energy and reagent savings can be made.

• Thanks to the independent flow adjustment for gas and liquid phases, an optimization of applied reagent dosage (i.e. here ozone) also allows to save reagent.

• All the ozone diffused through the membrane is transferred into the liquid phase (reacting or not in this phase), due to the bubbleless process. The rest (in the gas phase) can be recycled to the ozone generator thanks to a lower moisture content than in conventional processes [START_REF] Phattaranawik | Mass transfer studies in flat-sheet membrane contactor with ozonation[END_REF][START_REF] Stylianou | Ozone Mass Transfer Studies in a Hydrophobized Ceramic Membrane Contactor: Experiments and Analysis[END_REF]. In comparison to bubble column where 25% of ozone is not transferred in the liquid phase, fewer reagents are needed for the same oxidation.

• Less by-products (e.g. bromates) could be produced than in conventional ozonation processes thanks to the minimization of the dissolved ozone concentration ( [START_REF] Heeb | Oxidative treatment of bromide-containing waters: Formation of bromine and its reactions with inorganic and organic compounds -A critical review[END_REF][START_REF] Merle | MEMBRO 3 X, a Novel Combination of a Membrane Contactor with Advanced Oxidation (O 3 /H 2 O 2 ) for Simultaneous Micropollutant Abatement and Bromate Minimization[END_REF].

On the contrary, according to several studies, the main disadvantages of the membrane contactor process are the following [START_REF] Gabelman | Hollow fiber membrane contactors[END_REF][START_REF] Mulder | Basic principles of membrane technology[END_REF].

• The risk of wetting is important and depends on the transmembrane pressure. Its consequence is a lower ozone transfer.

• A risk of bubbling is common and also depends on the transmembrane pressure.

Ozone which is diffused by bubbles through the membrane may not be completely transferred into the liquid phase, and thus stays in gaseous form.

• The liquid can cause the fouling of the fibers. Fouling is one of the main problems in the application of porous membrane for water treatment [START_REF] Van Geluwe | Ozone oxidation for the alleviation of membrane fouling by natural organic matter: A review[END_REF].

Gas/liquid contactors are less sensitive to fouling than filtration membranes) because no flow circulates through the membrane pores [START_REF] Van Geluwe | Ozone oxidation for the alleviation of membrane fouling by natural organic matter: A review[END_REF][START_REF] Yu | CO2 capture using a superhydrophobic ceramic membrane contactor[END_REF]. However, membrane contactors have generally a small diameter, and therefore suspended particles in the gas phase or in the liquid phase can cause plugging [START_REF] Van Geluwe | Ozone oxidation for the alleviation of membrane fouling by natural organic matter: A review[END_REF]. When the gas circulates in the lumen and the liquid in the shell side, this phenomenon is limited. There is little available literature on ozone transfer into water with membranes, and to date no literature concerning the fouling during such a process. Most studies focus on ozone as a pretreatment (i.e. as a supplementary agent) within hybrid treatment processes, leading to the reduction of fouling or the increase of the biodegradation of contaminants in membrane bioreactor, and therefore to better membrane performances [START_REF] Kim | Effect of ozone dosage and hydrodynamic conditions on the permeate flux in a hybrid ozonation-ceramic ultrafiltration system treating natural waters[END_REF][START_REF] Laera | Removal of organics and degradation products from industrial wastewater by a membrane bioreactor integrated with ozone or UV/H 2O 2 treatment[END_REF][START_REF] Van Geluwe | Ozone oxidation for the alleviation of membrane fouling by natural organic matter: A review[END_REF][START_REF] Zoumpouli | A Single Tube Contactor for Testing Membrane Ozonation[END_REF].

• The overall resistance to transfer is increased due to the addition of a new phase (i.e.

the membrane).

• A bypass may be created into the shell side. If the liquid is in the shell side, a part of the water could not be treated. If the gas is in the shell side, a part of the oxidizing compound could not be transferred in the other phase.

In recent years, very interesting reviews on advanced oxidation processes for water treatment were generated, but none concerning the ozonation with membrane contactors [START_REF] Von Gunten | Oxidation Processes in Water Treatment: Are We on Track?[END_REF]. In this context, this review focuses on the ozonation of water using membrane contactors, that had not yet been previously reviewed in detail. Hollow fibers and tubular technologies for the elimination of micropollutants in water are described more specifically.

The significance of the membrane material is highlighted, as well as the importance of the modeling in order to optimize the transfer. Conversely, processes like ozonation on catalytic membranes, or ozonation for cleaning, are not covered. Several mechanisms occur simultaneously and by chain reactions during degradation of an organic substance M. In the first case, molecular ozone can directly oxidize the polluting substance. In the second case, ozone can decompose into hydroxyl radicals. This way leads to a succession of radical reactions, initiated by the interaction between hydroxyl radicals and ozone [START_REF] Gordon | The chemistry and reactions of ozone in our environment[END_REF][START_REF] Westerhoff | Applications of ozone decomposition models[END_REF]. Hydroxyl radicals are non-selective and have strong oxidation properties [START_REF] Kanakaraju | Advanced oxidation process-mediated removal of pharmaceuticals from water: A review[END_REF].

General principles of ozonation

Ozonation reaction

These mechanisms coexist and the kinetic expression of the reaction can be described by equation 1:

= + ° = + 1
Where:

• rM: reaction rate (mol.L -1 .s -1 )

• [HO°]: concentration of hydroxyl radicals (mol.L -1 )

• [O3]: concentration of molecular ozone (mol.L -1 )

• kO3 , kHO°: second-order rate constant for the reaction of micropollutant (M) with O3

and HO° (L. mol -1 s -1 )

• R=[HO°]/[O3]: ratio between the concentration of hydroxyl radicals and the concentration of molecular ozone, varying between 10 -9 and 10 -7 and depending on the water type (according to [START_REF] Elovitz | Hydroxyl Radical/Ozone Ratios During Ozonation Processes. II. The Effect of Temperature, pH, Alkalinity, and DOM Properties[END_REF] The mechanism favoring the oxidation efficiency depends on the kO3 value, which is a second order rate constant. When kO3 < 100 mol.L -1 .s -1 , the main way of degradation is the radical mechanisms. When kO3 is between 100 and 10,000 mol.L -1 .s -1 , both radical and molecular mechanisms occur simultaneously with the same order of magnitude. When kO3 > 10,000 mol.L -1 .s -1 , molecular mechanisms are promoted. [START_REF] Bourgin | Effect of operational and water quality parameters on conventional ozonation and the advanced oxidation process O3/H2O2: Kinetics of micropollutant abatement, transformation product and bromate formation in a surface water[END_REF] 2.1. Ozonation efficiency for the elimination of micropollutants in water Advanced treatment technologies remove MP more efficiently than primary and secondary treatments [START_REF] Luo | A review on the occurrence of micropollutants in the aquatic environment and their fate and removal during wastewater treatment[END_REF]. Several studies about the application of ozonation for MP elimination have been carried out [START_REF] Behera | Occurrence and removal of antibiotics, hormones and several other pharmaceuticals in wastewater treatment plants of the largest industrial city of Korea[END_REF][START_REF] Huber | Oxidation of Pharmaceuticals during Ozonation and Advanced Oxidation Processes[END_REF][START_REF] Lishman | Occurrence and reductions of pharmaceuticals and personal care products and estrogens by municipal wastewater treatment plants in Ontario, Canada[END_REF][START_REF] Paxéus | Removal of selected non-steroidal anti-inflammatory drugs (NSAIDs), gemfibrozil, carbamazepine, b-blockers, trimethoprim and triclosan in conventional wastewater treatment plants in five EU countries and their discharge to the aquatic environment[END_REF][START_REF] Santos | Occurrence and risk assessment of pharmaceutically active compounds in wastewater treatment plants. A case study: Seville city (Spain)[END_REF]. Ozone eliminates a wide range of MP in WWTP, with a dose of dissolved ozone around 3-8 mgO3/L [START_REF] Gomes | Application of ozonation for pharmaceuticals and personal care products removal from water[END_REF][START_REF] Hollender | Elimination of organic micropollutants in a municipal wastewater treatment plant upgraded with a full-scale post-ozonation followed by sand filtration[END_REF][START_REF] Margot | Treatment of micropollutants in municipal wastewater: Ozone or powdered activated carbon?[END_REF][START_REF] Nakada | Removal of selected pharmaceuticals and personal care products (PPCPs) and endocrinedisrupting chemicals (EDCs) during sand filtration and ozonation at a municipal sewage treatment plant[END_REF][START_REF] Reungoat | Ozonation and biological activated carbon filtration of wastewater treatment plant effluents[END_REF][START_REF] Reungoat | Removal of micropollutants and reduction of biological activity in a full scale reclamation plant using ozonation and activated carbon filtration[END_REF][START_REF] Rosal | Occurrence of emerging pollutants in urban wastewater and their removal through biological treatment followed by ozonation[END_REF]. This process is also efficient on several pharmaceuticals often detected in surface waters [START_REF] Suez ; Tootchi | Transformation products of pharmaceutically active compounds during drinking water ozonation[END_REF]. The degradation efficiency of MP depends on several parameters (see 2.3. Influential parameters), in particular their reaction rates with O3 and HO°, which involve different mechanisms of MP removal (see 2.3.2. Influence of the reaction rate of the compound with O3 and HO°).

From equation 1, a chemical kinetic model can be deducted for the prediction of micropollutants abatement by ozonation [START_REF] Elovitz | Hydroxyl Radical/Ozone Ratios During Ozonation Processes. I. The Rct Concept[END_REF][START_REF] Guo | Prediction of micropollutant abatement during homogeneous catalytic ozonation by a chemical kinetic model[END_REF][START_REF] Lee | Prediction of micropollutant elimination during ozonation of a hospital wastewater effluent[END_REF][START_REF] Lee | Prediction of micropollutant elimination during ozonation of municipal wastewater effluents: use of kinetic and water specific information[END_REF][START_REF] Lee | Advances in predicting organic contaminant abatement during ozonation of municipal wastewater effluent: reaction kinetics, transformation products, and changes of biological effects[END_REF][START_REF] Wang | Comparison of pharmaceutical abatement in various water matrices by conventional ozonation, peroxone (O3/H2O2), and an electro-peroxone process[END_REF] :

- = + ° ° 2
Where:

• kO3 , kHO° : second-order rate constant for the reaction of micropollutant (M) with O3 and HO°

• ∫[O3]dt and ∫[HO°]dt : O3 and HO° exposures, which are defined as the time-integrated concentration of O3 and HO° over a given reaction period

Other species than molecular ozone and hydroxyl radicals play an important role in the mechanisms of ozone consumption [START_REF] Westerhoff | Applications of ozone decomposition models[END_REF]. As shown in Figure 2, a part of hydroxyl radicals does not react with micropollutants but with scavengers. The presence of scavengers depends on the matrix to treat (e.g. natural water, drinking water, and wastewater) [START_REF] Briens | Ozonation and advanced oxidation of wastewater: Effect of O3 dose, pH, DOM and HO.-scavengers on ozone decomposition and HO . generation[END_REF]. It corresponds to some background water constituents, for instance carbonates [START_REF] Yao | Pilot-scale evaluation of micropollutant abatements by conventional ozonation, UV/O3, and an electro-peroxone process[END_REF]. By scavenging hydroxyl radicals, some compounds can inhibit the ozone decomposition without producing hydrogen peroxide or superoxide radical ions.

Other compounds can promote ozone decomposition by forming superoxide radical ions.

Water with natural organic matter will be consequently complex to model because of its heterogeneity [START_REF] Westerhoff | Applications of ozone decomposition models[END_REF] The efficiency of ozonation process depends on the matrix to treat. For instance, water is a complex mixture with a lot of different compounds, both organic and inorganic. They react simultaneously, with molecular and free-radical mechanisms. Therefore, it is possible to formulate the overall ozone consumption of water using two criteria. The first one is the Immediate Ozone Demand (IOD), which represents the amount of ozone to apply before detecting a measurable residue of ozone. It reflects very fast reactions of the natural organic matter of the water with ozone. The higher the pH and the temperature of the water are, the faster the ozone self-destructs. The second criterion is the slow consumption velocity. This is defined by kd, which is in this case a first order rate constant. In order to determine these two characteristics, a graph (see Figure 3) can be drawn, representing the residual ozone in function of the transferred ozone dose. The intercept of the straight line with the horizontal axis gives the IOD, and the slope allows calculating k d τ, which is the Damköhler number [START_REF] Roustan | Development of a Method for the Determination of Ozone Demand of a Water[END_REF] .

Figure 3: Determination of Immediate Ozone demand (mg/L) and kd (min -1 ), in a G/L contactor operating continuously for the 2 phases, adapted from [START_REF] Roustan | Transferts gaz-liquide dans les procédés de traitement des eaux et des effluents gazeux[END_REF] For instance, for a surface water at 18°C, the IOD is about 0.4 gO3/m 3 and the kd about 0.18 min -1 [START_REF] Roustan | Transferts gaz-liquide dans les procédés de traitement des eaux et des effluents gazeux[END_REF]. Another example is provided by the works of Cruz-Alcalde et al., 2019. The authors measured an average IOD of 16 mgO3/L at the outlet of the biological treatment of 5 different WWTP.

Antoniou et al. predicted the ozone dose to be transferred to remove 42 pharmaceuticals. They found that the sensitivity of pharmaceuticals to degradation with ozone differs, depending on the target compound, but mostly on the matrix (i.e. the type of water) [START_REF] Antoniou | Required ozone doses for removing pharmaceuticals from wastewater effluents[END_REF].

Specifically, most of the difference is explained by the Dissolved Organic Carbon (DOC) of the water to be treated [START_REF] Antoniou | Required ozone doses for removing pharmaceuticals from wastewater effluents[END_REF][START_REF] Hansen | Ozonation for source treatment of pharmaceuticals in hospital wastewater -Ozone lifetime and required ozone dose[END_REF]. Antoniou et al. correlated the specific dose of ozone required to achieve reduction by one decade of each investigated pharmaceutical with the DOC of the effluent, which consumes a part of the dissolved ozone available by reacting with it.

Influence of the reaction rate of the compound with O3 and HO°

As seen previously, the rate constant kO3 is a significant parameter for the ozonation efficiency. This parameter depends on the compound. A high second order reaction rate with O3 leads to a good elimination of the pollutant. Yue et al. showed that compounds with a high kO3 were effectively removed with a rate superior to 95% with an ozone dose transferred varying between 0.3 and 1.5 mg/L, and a contact time of 8.6 min during pilot-scale experiments using a conventional ozonator [START_REF] Yue | Evaluation of pilot-scale oxidation of several PPCPs/EDCs (pharmaceuticals and personal care products/endocrine disrupting compounds) during drinking water ozonation treatment[END_REF]. Bourgin et al. came to the same conclusions during conventional ozonation of surface water (i.e. Lake Zürich water, Switzerland). For instance, diclofenac and carbamazepine, with a kO3 superior to 10 4 M -1 .s -1 , were removed at more than 90% even for the lowest ozone dose transferred of 0.5 mg.L -1 [START_REF] Bourgin | Effect of operational and water quality parameters on conventional ozonation and the advanced oxidation process O3/H2O2: Kinetics of micropollutant abatement, transformation product and bromate formation in a surface water[END_REF]. Zimmermann et al. showed the same results within a gas bubble column. For substances reacting fast with ozone (e.g. diclofenac and carbamazepine, kO3=10 4

M -1 .s -1 ), they observed a good elimination for an ozone dosage transferred between 0.21 to 1.24 gO3.gDissolved Organic Carbon -1 , except for the lowest dose [START_REF] Zimmermann | Kinetic assessment and modeling of an ozonation step for full-scale municipal wastewater treatment: Micropollutant oxidation, by-product formation and disinfection[END_REF].

For compounds with a low to moderate reaction rate with O3 (i.e. ozone resistant compounds with kO3 up to 10 1 M -1 .s -1 , and moderately ozone-resistant compounds with kO3 between 10 2 and 10 3 M -1 .s -1 ), generally, oxidation increases with increasing ozone exposure and is influenced by the quality of the water matrix [START_REF] Bourgin | Effect of operational and water quality parameters on conventional ozonation and the advanced oxidation process O3/H2O2: Kinetics of micropollutant abatement, transformation product and bromate formation in a surface water[END_REF][START_REF] Yue | Evaluation of pilot-scale oxidation of several PPCPs/EDCs (pharmaceuticals and personal care products/endocrine disrupting compounds) during drinking water ozonation treatment[END_REF][START_REF] Zimmermann | Kinetic assessment and modeling of an ozonation step for full-scale municipal wastewater treatment: Micropollutant oxidation, by-product formation and disinfection[END_REF]. Yue et al. showed variable results. For instance, ibuprofen and clorfibric acid were removed between 3 and 62%. The same phenomena was observed for bezafibrate, which was removed between 28 and 99% under the same ozone exposure [START_REF] Yue | Evaluation of pilot-scale oxidation of several PPCPs/EDCs (pharmaceuticals and personal care products/endocrine disrupting compounds) during drinking water ozonation treatment[END_REF]. Bourgin et al. found that sucralose (i.e. compound which only react with HO° and have a low reaction rate with O3) was removed between 19 and 90%. The author also found that during conventional ozonation of resistant compounds, the abatement was moderate, even with a high ozone dose transferred of 3 mg03.L -1 [START_REF] Bourgin | Effect of operational and water quality parameters on conventional ozonation and the advanced oxidation process O3/H2O2: Kinetics of micropollutant abatement, transformation product and bromate formation in a surface water[END_REF]. In their work about transformation by-products of pharmaceutically compounds during drinking water ozonation, Tootchi et al. selected carbamazepine as pharmaceutical with a fast reaction rate with ozone and bezafibrate as pharmaceutical with a slow to moderate reaction rate with ozone (i.e.

respectively over and under 10 4 M -1 .s -1 ). The authors found that the major oxidation pathway for carbamazepine was the direct route (i.e. reaction with molecular ozone), while for bezafibrate it was both radical and molecular reactions [START_REF] Suez ; Tootchi | Transformation products of pharmaceutically active compounds during drinking water ozonation[END_REF].

Influence of operating parameters

Other parameters have an influence on the ozonation efficiency. For example, a higher pH promotes free radical mechanisms and causes a faster ozone decomposition because of the presence of hydroxide anions [START_REF] Briens | Ozonation and advanced oxidation of wastewater: Effect of O3 dose, pH, DOM and HO.-scavengers on ozone decomposition and HO . generation[END_REF][START_REF] Mecha | Impact of ozonation in removing organic micro-pollutants in primary and secondary municipal wastewater: Effect of process parameters[END_REF]. A higher temperature leads to a better mobility of the water molecules and thus to a lower water viscosity and a higher water diffusivity. A higher ionic strength decreases the solubility of ozone and thus makes ozonation processes more difficult. The influence of these parameters is discussed later with more details in the specific case of membrane contactors (section 5).

Ozonation by-products

During the ozonation reaction, a low mineralization can occur (i.e. the oxidation could be incomplete). It conducts to the accumulation of intermediates, which are degradation byproducts. These by-products in some cases, but not systematically, could be potentially more toxic than the initial contaminants [START_REF] Gao | Theoretical investigation on the kinetics and mechanisms of hydroxyl radical-induced transformation of parabens and its consequences for toxicity: Influence of alkyl-chain length[END_REF][START_REF] Gomes | Application of ozonation for pharmaceuticals and personal care products removal from water[END_REF][START_REF] Luo | A review on the occurrence of micropollutants in the aquatic environment and their fate and removal during wastewater treatment[END_REF][START_REF] Margot | Treatment of micropollutants in municipal wastewater: Ozone or powdered activated carbon?[END_REF][START_REF] Petala | Influence of ozonation on the in vitro mutagenic and toxic potential of secondary effluents[END_REF][START_REF] Petala | Wastewater reclamation by advanced treatment of secondary effluents[END_REF]Stalter et al., 2010aStalter et al., , 2010b;;von Gunten, 2003a).

Several by-products can be cited as examples, like the NDMA (i.e. N-Nitrosodimethylamine), or the formaldehydes, which are produced by the reaction between ozone and natural organic matter [START_REF] Hollender | Elimination of organic micropollutants in a municipal wastewater treatment plant upgraded with a full-scale post-ozonation followed by sand filtration[END_REF][START_REF] Richardson | Disinfection by-products and other emerging contaminants in drinking water[END_REF][START_REF] Samadi | The formation of aldehydes and ketones ozonation by-products and their variation through general water treatment plant in hamadan, Iran[END_REF][START_REF] Wert | Formation of oxidation byproducts from ozonation of wastewater[END_REF].

According to Gao et al., the products of parabens after reaction with hydroxyl radicals have a higher toxicity to green algae than the original paraben. They showed that when the alkylchain length of the parabens increases, the ecotoxicity of the degradation products also increases [START_REF] Gao | Theoretical investigation on the kinetics and mechanisms of hydroxyl radical-induced transformation of parabens and its consequences for toxicity: Influence of alkyl-chain length[END_REF].

Bromates are other degradation by-products. They are formed during the ozonation of bromide-containing waters, such as river waters [START_REF] Nobukawa | The genotoxity of by-products by chlorination and ozonation of the river water in the presence of bromide ions[END_REF]von Gunten, 2003a). Bromates are potentially carcinogenic and are not removed in biological filtration processes. Moreover, it is the only ozonation by-product regulated in drinking water [START_REF] Merle | MEMBRO 3 X, a Novel Combination of a Membrane Contactor with Advanced Oxidation (O 3 /H 2 O 2 ) for Simultaneous Micropollutant Abatement and Bromate Minimization[END_REF]von Gunten, 2003a). Therefore, a lot of studies about water ozonation focus on this compound. A limit was established by the European Union at 10 µg/L in drinking water, but with the recommendation for the member states of having a lower value if possible (AIDA, 1998). The bromate-forming mechanism is described in the Figure 4. In order to minimize bromates' formation, several solutions can be considered. The first one is an ammonia (NH3) addition. NH3 does not alter the ozone stability, and therefore does not interfere with oxidation processes. NH3 reacts with HOBr, which is an important intermediate of the bromates' formation. Adding NH3 leads to a lower bromates' formation up to a certain concentration of ammonia (except during the initial phase of ozonation in which it has no influence). No improvement is noticed beyond this limit. A balance between HOBr and NH3 is established, which always leaves a fraction of HOBr, transformed then into BrO3 -(i.e. bromates). This method is therefore not efficient with waters that already have a medium or high level of ammonia (von Gunten, 2003b) .

A second solution to minimize bromates' formation is a pH depression. This method influences bromates' formation by shifting the balance between HOBr and OBr -toward HOBr. When the pH decreases, hydroxyl radicals' exposure decreases as well, leading to a smaller overall oxidant exposure (i.e. ozone and hydroxyl radicals' exposure) and a lower bromates' formation. In the same way as the solution of ammonia addition, this solution does not reduce the initial fast bromates' formation, which is almost independent of the pH (von Gunten, 2003b).

Generalities on membrane contactors with hollow fibers

Principle of a G/L membrane contactor with hollow fibers

In gas/liquid membrane contactors, the membrane acts as an interface between two phases. In contrast with membranes used for filtration, membrane contactors are non-selective (i.e. they don't offer any preference between compounds). The phases could be liquid/liquid or gas/liquid. The phases are keeping separated. The operation is bubbleless, thus the transfer takes place mainly by diffusion and not by dispersion of one phase into another. The driving force of the transfer is the concentration gradient. However, the pressure gradient have to be taken carefully to keep the interface at the entrance of the pores [START_REF] Gabelman | Hollow fiber membrane contactors[END_REF] and thus avoid some problems with the membrane.

Depending on the membrane material, the fluids, and the operational conditions, the interface could be on one side or the other of the membrane, and sometimes inside. For a gas/liquid system and a hydrophobic membrane, the phase that fills the pores is the gas one. For a hydrophilic membrane, the liquid phase fills the pores. The best configuration for the diffusion of ozone is described in a next part.

Membranes could be made with organic (polymers) or inorganic (ceramic) materials. The selection of the material is made according to the future use of the membrane contactor, the fluids to keep in contact, the desired fluxes, etc.

According to several sources about gas absorption membrane contactor [START_REF] Al-Saffar | Removal of carbon dioxide from gas streams using a gas/liquid hollow fibre module[END_REF][START_REF] Demontigny | Using polypropylene and polytetrafluoroethylene membranes in a membrane contactor for CO2 absorption[END_REF][START_REF] Dindore | Modelling of cross-flow membrane contactors: Physical mass transfer processes[END_REF][START_REF] Li | Oxygen transfer characteristics of hydrophilic treated polypropylene hollow fiber membranes for bubbleless aeration[END_REF], counter-current mode performs better than co-current mode. According to [START_REF] Demontigny | Using polypropylene and polytetrafluoroethylene membranes in a membrane contactor for CO2 absorption[END_REF], counter-current mode can be up to 20% more efficient than co-current mode.

Mass transfer using membrane contactors

As described by Bamperng et al. (see Figure 5), the absorption of a gas into the liquid phase is broken down into several parts [START_REF] Bamperng | Ozonation of dye wastewater by membrane contactor using PVDF and PTFE membranes[END_REF]. The first is a transport of the interested gas from the bulk of gas to the interface, between gas phase and a membrane. The second is the transport of gas through the membrane pores. The last part is the dissolution of a gas component into a liquid, eventually with a chemical reaction in addition which accelerates the transfer.

Henry's law

At the interface between the 2 phases, the Henry's law is applicable if the following assumptions are respected. The solute (i.e. here the ozone) has to be slightly soluble in the solvent (xO3 < 0.05) and the gas phase is assumed to be perfect (moderate pressure and a temperature far from the condensation temperature) [START_REF] Roustan | Transferts gaz-liquide dans les procédés de traitement des eaux et des effluents gazeux[END_REF]).

=

.

[3]

According to this law, dissolved gases concentrations (Ci in mol/L) are proportional to the partial pressure of the gas in the air (pi in hPa), depending on the dissolution constant of the gas (KHI in mol.kg -1 .hPa -1 or mol.L -1 .hPa -1 ). Henry's law constant depends on the compound and can be expressed in several ways, and thus in several units.

The membrane mass transfer coefficient

The membrane mass transfer coefficient km is defined by the following relation, using the membrane structure properties: (Mavroudi et al., 2006) [4] Where:

= ! " ×$ % ×
km : Mass transfer coefficient in the membrane (m.s -1 ).

-Dg : Diffusion coefficient in the gas phase (m 2 .s -1 )

εm: Membrane porosity (dimensionless)

τm : Membrane tortuosity (dimensionless)

lm : Membrane thickness (m)

Molar flux

The molar flux of the compound of interest (i.e. here the ozone) at the gas side can be expressed by: & = " × ' ,")* -,")*, + ,)-+ . [START_REF] Berry | Modelling of Ozone Mass-Transfer through Non-Porous Membranes for Water Treatment[END_REF] [5]

Where:

-Ji : Molar flux of the compound of interest across the membrane (mol.m -2 .s -1 )

kg: Mass transfer coefficient in the gas (m.s -1 ).

-/ 0,123,045678296 : Concentration of the compound of interest at the interface on the gas side (mol.m -3 ) -/ 0,123 : Concentration of the compound of interest in the gas bulk (mol.m -3 )

The molar flux across the membrane can be described by: & = × ' ,")*, + : ) + -,")*, + ,)-+ . (Berry et al., 2017) [6] Where:

-Ci,gas,membrane: Concentration at the gas-membrane interface (mol.m -3 ), which can described by Ci,gas,membrane =C,i,gas,interface/S, where S is the solubility of the gas in the membrane.

Some studies assumed that Ci,gas,membrane=Ci,gas (i.e. the concentration at the gas-membrane interface) is continuous [START_REF] Pines | Investigation of an Ozone Membrane Contactor System[END_REF][START_REF] Shen | A novel approach to ozonewater mass transfer using hollowfiber reactors[END_REF].

-Ci,gas,interface : Concentration at the membrane-liquid interface on the membrane side (mol.m -3 ), which can described by Ci,gas,interface=Ci,liquid,interface x He, where He is the Henry's law constant (dimensionless, as described in [7]) and Ci,liquid,interface is the concentration at the membrane-liquid interface on the liquid side.

The molar flux at the liquid phase side is described in the following equation.

& = ; × ' , <= , + ,)-+ -, <= . (Berry et al., 2017) [8] Where:

-kL: Mass transfer coefficient in the liquid (m.s -1 ) -/ 0,>0?@0A,045678296 : Concentration of the compound of interest at the interface on the liquid side (mol.m -3 ) -/ 0,>0?@0A : Concentration of the compound of interest in the liquid bulk (mol.m -3 ) Therefore, thanks to the previous equations, the following formula can be used to express the molar flux from the overall mass transfer coefficient [START_REF] Berry | Modelling of Ozone Mass-Transfer through Non-Porous Membranes for Water Treatment[END_REF].

& = ; × ,")* B -+ × , <= [9]
Where KL is the overall mass transfer coefficient (m.s -1 ) described in the following section (see 3.2.4).

The mass balance on the liquid phase for steady state conditions can be described by: Where:

-KL : Overall mass transfer coefficient (m.s -1 ) -km, kg, kL: Mass transfer coefficient, respectively in the membrane, in the gas, and in the liquid (m.s -1 ). When a chemical reaction occurs in the liquid, kL can be replaced with

W X = Y Z [ \ ., such as E = ] ^_ `abc defgbahi ] ^_ `abchjb defgbahi
. E is called the enhancement factor and takes into account the effect of the reaction, which increases the concentration gradient and therefore the transfer speed at the interface (see Figure 5) [START_REF] Nguyen | Contacteurs à membranes denses pour les procédés d ' absorption gazliquide intensifiés : application à la capture du CO 2 en post combustion Phuc Tien[END_REF]. E can also be described in terms of Hatta number and instantaneous enhancement factor.

-Aouter, Am, Ainner: Respectively the outer, logarithmic mean, and inner surface of the membrane (m 2 ) -S: Solubility (e.g. of ozone) in the membrane material (dimensionless) 27 -He: Solubility (e.g. of ozone) in water (dimensionless). He can be described by the following equation.

+ = D k = l ,m ,;
n +< (Roustan, 2003) [13] This equation is one form of the Henry's law. For the dissolution of ozone in water at 295K, the Henry's constant is 3.823 (mg/L)/(mg/L) [START_REF] Atchariyawut | Application of ozonation membrane contacting system for dye wastewater treatment[END_REF]. At 293K, this same constant is reduced to 2.907 [START_REF] Roustan | Transferts gaz-liquide dans les procédés de traitement des eaux et des effluents gazeux[END_REF].

For hollow fibers membranes where the gas flows inside the fibers and the liquid outside, the previous equation becomes

D ; = V B× " × + V × + + ;
, where di, dln, do are respectively the inner, logarithmic mean, and outer diameters of the fibers (m).

Membrane materials

G M L G M L G M L G M L a d c b
The material of the membrane affects its performance and has to be chosen according to its application. Properties of the membrane, especially the pore size and the surface porosity, influence the transfer rate. Membranes can be classified in 3 categories: dense, porous, or composite (see Figure 6). According to Bakeri et al., the higher the pore size is, the higher the membrane mass transfer coefficient is (i.e. resistance within membrane is higher in dense membrane than in microporous) [START_REF] Bakeri | A novel surface modified polyetherimide hollow fiber membrane for gas-liquid contacting processes[END_REF]). Yet, higher pores increase the risk of wetting, which reduces the transfer quickly [START_REF] Bakeri | A novel surface modified polyetherimide hollow fiber membrane for gas-liquid contacting processes[END_REF]. Therefore, the operating pressure can be higher with dense membrane than with microporous because no bubbles are formed (i.e. no risk of bubbling). However, during their experiments, Pines et al. found a global mass transfer coefficient comparable between a Teflon nonporous membrane (i.e. a dense membrane) and different porous membranes (see Figure 7). The porous membranes used in this work were made with Teflon, PVDF, or PTFE. The pore volume was from 45 up to 55%. The pore size was from 0.5 up to 5 µm, and membrane thickness from 0.102 to 0.254 mm. [START_REF] Pines | Investigation of an Ozone Membrane Contactor System[END_REF] Figure 7: Global mass transfer coefficient at liquid side Reynolds number of 2000 for different materials, adapted from [START_REF] Pines | Investigation of an Ozone Membrane Contactor System[END_REF] According to Nguyen et al., a dense material can compete with classical porous membrane contactors materials, depending on the dense skin thickness (i.e. it can have the same mass transfer coefficient in the membrane) (see Figure 8). In their work, the authors highlighted the interest of composite fibers for the CO2 absorption. The fibers were fabricated from porous polymers as supports and coated with dense permeable (here to CO2) materials. The use of a dense or a composite membrane seems therefore to be a possible solution to avoid bubbling and wetting problems (i.e. transmembrane pressure limitations), without minimizing the global mass transfer. [START_REF] Chabanon | 3.9 Membranes Contactors for Intensified Gas-Liquid Absorption Processes[END_REF][START_REF] Nguyen | A dense membrane contactor for intensified CO2 gas/liquid absorption in postcombustion capture[END_REF] [START_REF] Mulder | Basic principles of membrane technology[END_REF]. Membranes can also be hybrid (i.e. composed with both organic and inorganic materials).

Ceramic membranes could be a good alternative for membrane contactors in comparison to organic membranes because of their chemical, thermal, and mechanical stabilities. They seem therefore to be an appropriate material for the use of ozone, which is a strong oxidant.

However, those membranes have hydrophilic properties due to the presence of hydroxyl groups on their surface, and thus water is able to penetrate in their pores resulting in a higher mass transfer resistance [START_REF] Bamperng | Ozonation of dye wastewater by membrane contactor using PVDF and PTFE membranes[END_REF][START_REF] Stylianou | Ozone Mass Transfer Studies in a Hydrophobized Ceramic Membrane Contactor: Experiments and Analysis[END_REF]. Consequently, ceramic membranes have a lower mass transfer coefficient compared to hydrophobic organic membranes. The surface of ceramic membranes can be modified by grafting hydrophobic compounds in order to solve this problem. The ozone mass transfer of such membranes may be 5 times higher than non-grafted ceramic membranes [START_REF] Picard | Ceramic membranes for ozonation in wastewater treatment[END_REF]. In the experiments of Kukuzaki et al., the authors used shirasu porous glass (i.e. as membrane), coated with nonafluorohexyltrichlorosilane (i.e. a highly hydrophobic compound). The ozone mass transfer coefficient of these membranes was higher than the one of non-coated membranes (i.e. the overall mass transfer coefficient was about 10 -6 m/s for the hydrophilic non-coated membranes and about 10 -5 m/s for the hydrophobic coated membranes) [START_REF] Kukuzaki | Ozone mass transfer in an ozone-water contacting process with Shirasu porous glass (SPG) membranes-A comparative study of hydrophilic and hydrophobic membranes[END_REF].

Other disadvantages of ceramic membranes have to be considered. Ceramic membranes have a higher cost than polymeric counterparts (i.e. ≥ $1,000 /m² versus $100/m², respectively for the ceramic versus the polymeric membrane material), due to higher production costs and expensive starting materials [START_REF] Amin | An overview of production and development of ceramic membranes[END_REF][START_REF] Ciora | Ceramic membranes for environmental related applications[END_REF]. However, the membrane performance stability can be assured because of a higher cleaning efficiency with harsh chemical if necessary (thanks to better chemical and thermal resistances). Therefore, ceramic membranes have less fouling propensity, and thus a longer operational life, making the cost of ceramic membranes more competitive [START_REF] Ciora | Ceramic membranes for environmental related applications[END_REF][START_REF] Guerra | Development of a Techno-Economic Model to Compare Ceramic and Polymeric Membranes[END_REF].

Moreover, another drawback is the higher inner diameter of the ceramic in comparison to polymeric membranes, leading to a lower surface area per unit volume. Tubular membranes (i.e. internal diameter between 5 mm and 15 mm) and capillary membranes (i.e. internal diameter between 0.5 mm and 5 mm) can be produced with ceramic materials, but hollow fibers (i.e. internal diameter < 0.5 mm) are tougher to obtain, unlike with polymeric materials [START_REF] Amin | An overview of production and development of ceramic membranes[END_REF].

Hydrophobic/hydrophilic membrane

As explained before, pores are filled with liquid in hydrophilic membranes while they are filled with gas using a hydrophobic membrane. Ozone and oxygen diffusion are higher in gas than in water, thus the membrane resistance is lower with a hydrophobic membrane.

However, wetting and condensation problems may occur, unlike with hydrophilic membrane (see 5.1 Transmembrane operating pressure (TMP) using membrane as gas/liquid contactor).

Sustainability

The sustainability of membrane material under highly reactive character of ozone is one of the main challenges of using a membrane contactor for ozonation.

Bamperng et al. compared a membrane contactor with PVDF material to a membrane contactor with PTFE material, for the ozonation of dye wastewater. They found that PTFE has a better sustainability because its performance was barely reduced, while PVDF lost 30% of its initial performance within a few hours [START_REF] Bamperng | Ozonation of dye wastewater by membrane contactor using PVDF and PTFE membranes[END_REF]. Dos Santos et al.

investigated the resistance to ozone oxidation of organic (i.e. polymeric) membranes in order to select the best material to use in ozonation process for water treatment. The authors showed that materials with electrophilic atoms attached to the carbon in the polymer backbone (e.g.

PVDF and PTFE) have a good resistance to ozone. They observed that membranes with single C-C or Si-C bonds (e.g. PP and PDMS) also have a good resistance to ozone but showed structural modifications after a long period of use. Lastly, materials with carbon-carbon double bonds (e.g. PEI and PES) were highly degraded (Alves dos [START_REF] Alves Dos Santos | Polymeric Materials for Membrane Contactor Devices Applied to Water Treatment by Ozonation[END_REF].

Ozonation using membrane contactors

In this review, experiments using oxygen as gas (instead of ozone) have also been taken into account as oxygen and ozone are oxidizing gas, and have a relatively similar behavior.

Transmembrane operating pressure (TMP) using membrane as gas/liquid contactor

If the pressure of the liquid is too high, membrane could be wetted (i.e. the liquid phase penetrates into the membrane pores and the membrane loses its hydrophobicity), creating a stagnant film which interferes with the transfer. The transfer is therefore better when the gas/liquid interface is kept at the membrane surface. Moreover, ozone diffusivity is better inside the gas than inside the liquid, and thus ozone transfer is promoted when the interface is located on the liquid side of the membrane. It highlights the importance of the material used, especially its hydrophobicity [START_REF] Goh | Modification of membrane hydrophobicity in membrane contactors for environmental remediation[END_REF][START_REF] Picard | Ceramic membranes for ozonation in wastewater treatment[END_REF][START_REF] Xu | A review on polymer-based membranes for gasliquid membrane contacting processes: Current challenges and future direction[END_REF].

Picard et al. quantified the influence of the membrane's humidity. The authors studied the drying time of wet membranes before an experiment, and made a correlation with the transfer rates obtained. They concluded that water inside the membrane pores is a major limiting factor to the transfer [START_REF] Picard | Ceramic membranes for ozonation in wastewater treatment[END_REF]. The maximum pressure to avoid this phenomenon is called the breakthrough transmembrane pressure, or the liquid entry pressure of water (LEPw), or the wetting pressure [START_REF] Choi | Preparation and characterization of polyvinylidene fluoride by irradiating electron beam[END_REF][START_REF] Smolders | Terminology for Membrane Distillation[END_REF]. It is defined by Laplace equation such as z{| = -}~Z A •

, with dp the diameter of the largest pore, B the form factor of the pore, and € X the superficial tension of the liquid [START_REF] Xu | A review on polymer-based membranes for gasliquid membrane contacting processes: Current challenges and future direction[END_REF]. In order to determine the LEPw of a membrane, the method described by Smolder and Franken can be used [START_REF] Smolders | Terminology for Membrane Distillation[END_REF]) [START_REF] Choi | Preparation and characterization of polyvinylidene fluoride by irradiating electron beam[END_REF]. This consists of applying a slight pressure in the liquid phase of about 0.3 x 10 5 Pa, during at least 10min. Then, the pressure is increased by step of 0.68 x 10 3 Pa. The LEPw is reached when a continuous flow is observed in the permeate side (i.e. in the gas phase).

The liquid pressure has to be higher than the gas pressure, in order to avoid bubbling (i.e. cross of bubbles in the liquid side), but lower than the breakthrough transmembrane pressure.

This TMP depends on the membrane pore size: small pores allow higher pressure. For instance, microporous membranes have a breakthrough transmembrane pressure of about 20 kPa. [START_REF] Fang | Condensation studies in gas permeable membranes[END_REF] 5 inside the fibers). Ozone flux was calculated from a mass balance in the gas phase or in the liquid phase. Concentration gradient is the driving force for the ozone transfer into the membrane. When the liquid flow velocity increased, the resistance to ozone transfer at the interface between the gas and liquid phases decreased (i.e. the liquid mass transfer coefficient kL increases). The concentration difference was maintained high and thus higher ozone flux could be transferred. This trend was demonstrated for both porous and non-porous membranes. According to Zoumpouli et al., liquid flow velocity is the dominant parameter for ozone transfer, followed by membrane thickness and ozone gas concentration [START_REF] Zoumpouli | A Single Tube Contactor for Testing Membrane Ozonation[END_REF]. However, it must be noticed that in these experiments, the impact of other parameters (e.g. the pH) was not investigated.

For practical applications, it seems interesting to keep a high liquid velocity to have a high mass transfer and to keep important shear forces at the surface of the membrane that could decrease a possible fouling. However, higher liquid velocity implies lower residence time. For many applications, it is important to reach a given value of dissolved ozone concentration in order to get sufficient kinetic reaction or good disinfection level. As a consequence, a compromise between high liquid velocity (i.e. high transfer) and high dissolved ozone concentration should be found.

Effect of gas

5.2.2.1. Gas velocity Ozone flux is not influenced by gas velocity. The work of Bamperng et al (see Figure 9)

showed that when gas velocity increases, ozone flux is not impacted [START_REF] Bamperng | Ozonation of dye wastewater by membrane contactor using PVDF and PTFE membranes[END_REF].

These experiments were made using water, direct red 23, and acid blue 113 (i.e. two dyes)

and with a hollow fiber polyvinylidenefluoride (PVDF) membrane module. The ozone was produced with ozone generator by pure oxygen. The gas velocity varied between 0.12 and 0.22 m/s, and the ozone concentration was 40 mg/L. The liquid phase velocity was set at 0.46 m/s and the initial dye concentration was set as 100 mg/L. The ozone fluxes for pure water were determined by mass balance in the liquid phase, and the ozone fluxes for dye solution by mass balance in the gas phase. Results showed that for both water and dye solution (i.e. the liquid phase), the ozone flux did not evolve with an increasing gas velocity.

As seen previously (5.2.1), ozone flux is influenced by liquid velocity, therefore the mass transfer resistance is in the liquid phase, and not in the gas phase [START_REF] Atchariyawut | Application of ozonation membrane contacting system for dye wastewater treatment[END_REF][START_REF] Atchariyawut | Separation of CO2 from CH4 by using gas-liquid membrane contacting process[END_REF][START_REF] Bamperng | Ozonation of dye wastewater by membrane contactor using PVDF and PTFE membranes[END_REF][START_REF] Berry | Modelling of Ozone Mass-Transfer through Non-Porous Membranes for Water Treatment[END_REF][START_REF] Khaisri | Comparing membrane resistance and absorption performance of three different membranes in a gas absorption membrane contactor[END_REF]. In addition, Pines et al.

found that the resistance is higher in the liquid film than in the membrane [START_REF] Pines | Investigation of an Ozone Membrane Contactor System[END_REF].

Nature of the gas

According to Berry et al., unlike ozone, the mass transfer resistance of oxygen is located in the membrane [START_REF] Schwarzenbach | The Challenge of Micropollutants in Aquatic Systems[END_REF]. Côté et al. showed that oxygen mass transfer coefficient was better with pure oxygen than with air [START_REF] Côté | Bubble-free aeration using membranes: mass transfer analysis[END_REF]. According to the authors, this difference in transfer comes from the formation of nitrogen bubbles (i.e. with air), which strip the oxygen. The bubbles are formed against the fibers, and then escape to the liquid side and its outside in the form of gas, since the water is initially saturated with nitrogen at atmospheric pressure. Thus, the mass transfer in a membrane contactor depends on the nature of the gas. These results were obtained with gas inside the fibers and liquid in the shell.

Concentration in the gas

When the concentration of ozone in the gas increases, the dissolved ozone concentration measured at the outlet of the contactor in the liquid phase also increases. Stylaniou et al.

obtained the results represented in the Figure 10, at a liquid temperature of 20°C, with a hydrophobically modified α-Al2O3 ceramic membrane [START_REF] Stylianou | Ozone Mass Transfer Studies in a Hydrophobized Ceramic Membrane Contactor: Experiments and Analysis[END_REF]. It is important to note that the membrane used was tubular, which implies a larger diameter than with hollow 5.2.2.4. Operating gas pressure and oxidant partial pressure

In the experiments of Côté et al. with dense hollow fiber membranes, the global mass coefficient K is independent of oxygen partial pressure up to 3 bars (K=28.3 x 10 -6 m.s -1 ) [START_REF] Côté | Bubble-free aeration using membranes: mass transfer analysis[END_REF]. However, at higher pressure, K dropped to 23.3 x 10 -6 m.s -1 . Côté explained this drop with the apparition of micro-bubbles on the surface of the fibers. This phenomenon could be avoided with a higher water velocity, preventing the partial pressure from exceeding the saturation point. In contrast, Ahmed et al. showed in their studies that the mass transfer coefficient K increases with increasing operating pressure (Ahmed et al., 2004).

The same result was obtained in previous studies (Ahmed andSemmens, 1992a, 1992b;[START_REF] Li | Oxygen transfer characteristics of hydrophilic treated polypropylene hollow fiber membranes for bubbleless aeration[END_REF]. Li et al. found that, for hydrophilic treated polypropylene hollow fiber membranes, when the operating pressures increases from 20 to 100 kPa, the membrane resistance decreased almost linearly from 8.8 x 10 -4 to 4.6 x 10 -4 s.m -1 (i.d 1/K), giving a higher oxygen flux due to the higher partial pressure of oxygen [START_REF] Li | Oxygen transfer characteristics of hydrophilic treated polypropylene hollow fiber membranes for bubbleless aeration[END_REF]. These results go against Côté's conclusions. However, the same ultimate pressure beyond which bubbles appear was mentioned. It represents one of the limits of this process.

Effect of temperature

The experiments of Stylaniou et al. showed that temperature has a very little impact on the dissolved ozone concentration, compared to the influence of liquid velocity, pH, and ozone concentration values in the gas phase [START_REF] Stylianou | Ozone Mass Transfer Studies in a Hydrophobized Ceramic Membrane Contactor: Experiments and Analysis[END_REF]. However, temperature affects ozone diffusivity, decomposition rate constant, and ozone solubility in the water. At the interface, Henry's law is applicable (see 3.2.1), which depends on the temperature [START_REF] Sotelo | Henry's law constant for the ozone-water system[END_REF]. When the temperature increases, water molecules have a greater mobility, and thus the viscosity of water decreases and its diffusivity increases (by around 1.2 times every 5°C according to Stylaniou et al.). As a consequence, the mass transfer coefficient in the liquid phase raises. In the same way, when the temperature increases, lower energy is required for the reaction between ozone and hydroxyl ions, and thus the ozone decomposition rate increases (by around 1.5 times every 5°C). Conversely, ozone equilibrium concentration decreases (by around 1.15 times) due to the decrease of gas solubility. Therefore, it seems important to take this factor into account.

Effect of transfer direction

The majority of the studies about ozonation using a membrane contactor use the gas in the shell side and the liquid inside the fibers. The main advantage of this configuration is a good distribution of the dissolved ozone in the liquid, thus allowing a good treatment of the pollutants. However, this configuration is more favorable to clogging. The circulation of the liquid in the shell side greatly reduces this risk. Nevertheless, a risk of short circuit in the shell appears, and therefore this configuration promotes the formation of areas without dissolved ozone, in which the pollutants are not treated (i.e. there is a risk of mal-distribution of the dissolved ozone and of channeling of the water in the carter [START_REF] Dindore | Modelling of cross-flow membrane contactors: Physical mass transfer processes[END_REF]. According to Wenten et al., the best configuration for iodide ozonation with a membrane contactor is the one illustrated in the Figure 11 where the gas (ozone) passes through the tube side (i.e. inside the fibers) and the liquid (acidic iodide) solution passes through the shell side [START_REF] Wenten | Ozonation through ceramic membrane contactor for iodide oxidation during iodine recovery from brine water[END_REF]. It corresponds to the configuration where the higher iodine concentration is obtained at the outside of the system (i.e. the objective was to oxidize iodide into iodine). In their study and for this configuration, the highest iodine concentration reached 300 mg/L, after a contact time of 720s. For the other configuration, where the ozone was flowing in the shell side, the highest concentration reached 35 mg/L, after a contact time of 1800s. According to the authors, the difference between the two results can be explained by the reaction of the ozone with the membrane material when the gas was running in the shell side. It causes the transformation of the ozone into oxygen, which reacts very slowly with iodide. KLa is 6 times higher with fast reaction time in the liquid than without (i.e. 0.240 s -1 for 0.040 s -1 without) [START_REF] Roustan | Transferts gaz-liquide dans les procédés de traitement des eaux et des effluents gazeux[END_REF]. Therefore, the oxygen mass transfer is also 6 times higher with fast reaction than without. This is reflected in the mass transfer model with the several dimensionless numbers. The first one is the Hatta's number. It gives information on the competition between reaction and diffusion speed, inside the liquid film. It also indicates where the chemical reaction takes place. For a second order reaction (see 2.1, this number is defined by

) = … L M,NMOPMQ ! ,;
;

, where † ‡ˆ,X is the diffusivity of ozone in liquid phase (m².s -1 ), / 0,>0?@0A is the concentration of the targeted compound in the liquid phase (mol.m -3 ), kL is the transfer coefficient in liquid phase (m.s -1 ), and kO3 is the 2 nd order reaction rate constant of ozone with the compound of interest (m 3 . mol -1 s -1 ). If Ha is small (i.e. Ha<0.3), the reaction is slow compared to the diffusion. If Ha is high (i.e. Ha>3), the reaction is fast compared to the diffusion.

The enhancement factor (‰

= Š =C ) ‹+ + ,)-+ OE ‹ -‹+ -) +)-V Š =C ) ‹+ + ,)-+ OE ‹V= -‹+ -) +)-V
) describes the importance of the chemical reaction on the mass transfer at the interface between the gas and liquid phase. If E=1, the reaction does not accelerate the transfer. If E>1, the reaction accelerates the transfer.

Another number is helpful to characterize the transfer, and to determine the material which reacted in the liquid film: the M criterion, such as: =

•>@Ž •65•664 >0?@0A 80>' 24A •@>Y '8 >0?@0A

•>@Ž 25 5"6 045678296 •65•664 123 24A >0?@0A

. When M=1, all the compound quantity transferred from the gas phase to the liquid phase is also transferred to the bulk of liquid. Therefore, the chemical reaction only takes place in the bulk of liquid and the reaction does not accelerate the mass transfer (i.e. E=1 and Ha<0.3).

The concentration profile of the compound in the liquid film is linear. When M<1, the reaction takes place in both liquid film and bulk of liquid, and thus reaction accelerates the transfer (i.e. E>1 and Ha between 0.3 and 3). When M=0, all the compound in the liquid phase reacts in the film. No molecule reaches the bulk of liquid. The reaction accelerates the transfer (i.e. E>1 and Ha>3).

Effect of pH

According to Wenten et al., pH of the liquid phase does not have a significant impact on the ozonation of iodide into iodine [START_REF] Wenten | Ozonation through ceramic membrane contactor for iodide oxidation during iodine recovery from brine water[END_REF]. However, several studies revealed the opposite [START_REF] Bamperng | Ozonation of dye wastewater by membrane contactor using PVDF and PTFE membranes[END_REF][START_REF] Stylianou | Ozone Mass Transfer Studies in a Hydrophobized Ceramic Membrane Contactor: Experiments and Analysis[END_REF]. Free radicals mechanisms are promoted with increasing pH and ozone decomposition is faster due to the presence of hydroxide anions. Therefore, ozone resistant compounds may react by indirect reaction thanks to the formation of hydroxyl radicals, which are non-selective oxidants. Simultaneously, ozone decomposition at higher pH keeps the ozone concentration gradient higher, and thus promotes the flux through the membrane.In their experiments on dye solutions, Bamperng et al. showed that the higher the pH solution was, the higher the ozone flux was [START_REF] Bamperng | Ozonation of dye wastewater by membrane contactor using PVDF and PTFE membranes[END_REF]. In the study of Stylaniou et al., the reaction rate constant increased with the pH increase (see Table 3) [START_REF] Stylianou | Ozone Mass Transfer Studies in a Hydrophobized Ceramic Membrane Contactor: Experiments and Analysis[END_REF]. [START_REF] Stylianou | Ozone Mass Transfer Studies in a Hydrophobized Ceramic Membrane Contactor: Experiments and Analysis[END_REF].

Ionic strength was adjusted by the addition of NaCl solution. The authors made the same experiments for different temperatures (i.e. 15, 25, 30 and 30°C), with different concentrations (i.e. 0, 0.2 and 0.4 M). All the plots present the same trend as in the Figure 10, where the dissolved ozone concentration at the outlet of the contactor decreases when the liquid velocity increases. Zero ionic strength corresponds to the use of deionized water without the addition of NaCl.

An increase of ionic strength decreases the solubility of ozone and thus also decreases the equilibrium concentration of ozone at the interface between gas and liquid, as described by Henry's law (see 3.2.1). The ionic strength has also an impact on the surface tension, and thus on the allowable transmembrane pressure (see 5.1. Indeed, dissolved salts increase the surface tension, and in the same way the breakthrough pressure.

Effect of surfactant

Côté et al. studied the impact of surfactant in liquid phase on the oxygen flux [START_REF] Côté | Bubble-free aeration using membranes: mass transfer analysis[END_REF]. For these experiments, commercial soap containing 3.2% by weight of anionic surfactant was added to the initial deoxygenated water. It appeared that the addition of soap increased the mass transfer coefficient (i.e. 7% for a liquid velocity of 2.28 cm/s and 20% for a velocity of 7.71 cm/s). According to the authors, it is a significant parameter because the amount added (i.e. 190.5 mg/L) is equivalent to approximately 6 mg/L of surfactant (i.e. lauryl sulphate), which is a concentration often observed in wastewater [START_REF] Boon | Measurement of aerator performance[END_REF].Surfactants have an impact on the surface tension, and thus on the allowable transmembrane pressure (see 5.1. Indeed, surfactants decrease the surface tension, and in the same way the breakthrough pressure. Therefore, the risk of wetting is higher.

Effect of membrane material

The membrane material has a significant role in the mass transfer efficiency. As mentioned above (see 3.1), membranes have to be porous in order to facilitate the transfer, and hydrophobic to avoid the wetting phenomenon, which leads to the formation of a stagnant film inside the membrane and thus to a reduced mass transfer. Ozone is a very strong oxidant, and thus can attack the membrane material if this one is not sufficiently resistant. For an application of ozonation with a membrane contactor, two materials stand out: the PVDF and the PTFE which are the only organic membranes that can be used with ozone. According to Bamperng et al., PTFE leads to a more stable and higher flux than PVDF for a long operation period (i.e. few hours of use) [START_REF] Bamperng | Ozonation of dye wastewater by membrane contactor using PVDF and PTFE membranes[END_REF].

Summary table of the effect of parameters on mass transfer

First results on micropollutants

During their experiments, Stylaniou et al. showed the technical feasibility of a membrane contactor for the removal of various micropollutants in surface waters with diffusion of ozone and peroxone [START_REF] Stylianou | Application of a ceramic membrane contacting process for ozone and peroxone treatment of micropollutant contaminated surface water[END_REF]. They studied the transformation of carbamazepine (CBZ), benzotriazole (BZT), p-chlorobenzoic acid (pCBA), atrazine (ATZ), and the formation of bromates in a ceramic tubular membrane contactor, where the gas was in the shell side. The CBZ was removed at more than 90%, with a diminution of its concentration below 0.1 µM at 0.4mgO3/mgDOC. BTZ, pCBA, and ATZ was removed respectively at 70, 57, and 49%. The removal efficiency followed the reactivity order of the compounds with O3.

The addition of peroxone reduced the elimination of CBZ by 8%, but increased the elimination of ozone-resistant compounds (i.e. pCBA and ATZ) by about 5-10%.

In order to make a comparison between the different contacting ozonation processes, batch experiments (i.e. conventional, prepared by continuously bubbling ozone and therefore O3 saturated) and continuous experiments with ceramic tubular membranes having different inner surface per volume were performed. The results for the CBZ (i.e. the ozone reactive compound) were similar whatever the process. However, the hydroxyl radical exposure was slightly higher in the conventional experiments for ozone and peroxone processes, which leads to a better abatement of ozone-resistant compounds in the conventional process. Thus, the authors suggest that using a membrane with a high inner surface per volume, like for instance the hollow fibers, leads to a better efficiency of ozonation processes thanks to a more uniform distribution of oxidants (i.e. ozone and peroxone) in the water to be treated.

Concerning the bromate formation, Stylaniou and al. showed that ozone concentration lower than 20 mg/L are required to be under the regulated concentration limit of bromate (i.e. they did not achieve this limit even at a concentration of 0.020 mg/L, which was the lowest concentration used during their experiments). Indeed, European Commission and US EPA defined this limit at 10 µg/L in drinking water (EC directive 98/83; USEPA,1998). The ozone concentration is a very important parameter to minimize the formation of these compounds. In their experiments, Stylaniou et al. found a high bromate concentration of 49 µg/L at 0.8 mgO3/mgDOC with the ozone process. In these experiments, comparing with conventional process, membrane processes led to a higher bromates' formation. To conclude, the authors suggest that the use of membrane contactor with both a low ozone gas concentration and the highest possible inner surface per volume are required to improve the micropollutants abatement and to reduce the bromates' formation.

Merle et al. worked on a combination of a membrane contactor with advanced oxidation process for the abatement of micropollutants and the minimization of the bromates' formation [START_REF] Merle | MEMBRO 3 X, a Novel Combination of a Membrane Contactor with Advanced Oxidation (O 3 /H 2 O 2 ) for Simultaneous Micropollutant Abatement and Bromate Minimization[END_REF]. The authors used PTFE hollow fiber membrane. The water flowed inside the fibers, and the gas inside the shell. They focused especially on bromates' production, and studied the abatement of pCBA because of its high reactivity with hydroxyl radicals and low reactivity with molecular ozone (i.e. ozone-resistant compound). Compared to the conventional peroxone process (i.e. with bubbles), this process showed a better abatement of micropollutants and less bromates formation, for groundwater and surface water treatment.

For instance, for a groundwater containing 180 µg.L -1 of bromides and 0.48 mgDCO.L -1 , with a hydrogen peroxide concentration of 5.67 mgH2O2.L -1 , and an ozone concentration in the gas phase of 0.5 g.Nm -3 , an abatement of p-CBA of 95% was achieved after 300 s of residence time, and less than 0.5 µg/L of bromates were produced. In the conventional process, 8 µg.L -1 was formed under the same conditions. It can be noted that with a higher ozone concentration in the gas phase (i.e. 1g/Nm 3 , 2.5 g/Nm 3 and 10 g/Nm 3 in these experiments), the p-CBA abatement was better and faster, but more bromates were produced.

Modeling of ozone and oxygen mass transfer through membrane contactors for the elimination of micropollutants

Several studies have investigated the modeling of ozone and oxygen transport through membrane contactors during ozonation processes, from the gas phase to the liquid phase.

Most of these works focused on applications such as CO2 absorption, acid gas capture (i.e.

gas-liquid absorption), or liquid-liquid extraction [START_REF] Faiz | Separation of olefin/paraffin gas mixtures using ceramic hollow fiber membrane contactors[END_REF][START_REF] Zhang | Hollow fiber membrane contactor absorption of CO2 from the flue gas: review and perspective[END_REF].

The modeling of such processes is useful for a better understanding of the physical and chemical phenomena occurring. It enables the evaluation of parameters' influence, and therefore can lead to an optimization of the modeled process. Before modeling, membrane ozonation was described through global mass transfer coefficients, and therefore could not be scaled-up to different devices or experimental conditions. [START_REF] Kukuzaki | Ozone mass transfer in an ozone-water contacting process with Shirasu porous glass (SPG) membranes-A comparative study of hydrophilic and hydrophobic membranes[END_REF][START_REF] Stylianou | Ozone Mass Transfer Studies in a Hydrophobized Ceramic Membrane Contactor: Experiments and Analysis[END_REF]. In addition, modelling can be used in design and optimization of cross-flow membrane modules for multi-components membrane gas absorption processes.

Several types of computational approaches can be seen for ozone transport simulation in membrane contactor processes. Three methods will be presented here. In the first one, dimensionless numbers are used (in particular the Sherwood number) and hypotheses are assumed in order to simplify the equations and to avoid a numerical resolution. In the second approach presented here, ozone concentrations are obtained from the partial pressures. In the last method, software like Comsol Multiphysics for example is used in order to solve the transfer equations and directly determine concentration profiles, by simulating the ozone mass transfer through a membrane into a liquid. A synthesis of several studies on this subject is available in Table 5. [START_REF] Stylianou | Ozone Mass Transfer Studies in a Hydrophobized Ceramic Membrane Contactor: Experiments and Analysis[END_REF]. The gas was a mixture of ozone and oxygen, and flowed in the shell of the contactor. The liquid was in the tube. Based on experiments, the authors developed a mathematical model, representing the occurring phenomena and extracting the most important parameters. A first step was to model only the mass transfer, without taking into account the enhancement factor due to ozone decomposition. The transfer was considered as a multiphase system with three steps: diffusion in gas phase, transfer through the membrane pores, and diffusion to water. This is therefore a convection-diffusion mechanism. Generally, the steady state partial differential conservation equation is solved in order to obtain the ozone mass transfer. However, the authors used the Leveque solution and the corresponding Sherwood number, since all the experimental conditions matched (e.g. laminar flow). The dissolved ozone concentration at the outlet of the contactor was then obtained thanks to a mass balance and the Sherwood number.

/ 8 = / 6? + '/ " -/ 6? .• K -X-•_,Z ˜" @ Z,™šƒ› A M oe • 14]
With:

-/ 8 : Solute concentration at the tube outlet (mol.m -3 ) -/ 6? : Solubility of ozone in the liquid (/ 6? = ž{ 8 , where H is a variant of the Henry's law constant in mol.m -3 .hPa -1 and { 8 the partial ozone pressure in hPa) (mol.m -3 ) -/ " : Feed ozone concentration (mol.m -3 ) -Ÿ : Total tube length (m) - † ‡ˆ,X : Diffusivity of ozone in the liquid phase (i.e. water) (m².s -1 )

-Sh : Sherwood number of the liquid phase (Sh can be described by a global form such as By using the Euler explicit numerical discretization scheme with a fine mesh, for example with a discretization at N points with step such as δ=L/N, a set of differential equations results can be found easily.

ℎ = ¢ Z X £ - = ¤ × ¥• } × ¦ L ,
For Reynolds numbers of the liquid side up to 100 (i.e. laminar regime), dissolved ozone concentration at the outlet of the membrane contactor calculated with the developed model fit well with the experimental results (deviation around 5%). Moreover, ozone properties (e.g. diffusivity, ozone equilibrium concentration, ozone self-decomposition order and rate) calculated from the model fit the experimental and theoretical data. The extrapolation of data for the study of different devices and experimental conditions is possible, by changing the value of major physical parameters (e.g. diffusivity, solubility). The authors also studied the influence of several parameters such as the liquid velocity, the pH, the gas concentration, the membrane length, and the temperature. They came to the conclusion that the pH and the ozone concentration have the greatest impact on the dissolved ozone concentration at the outlet of the contactor. Moreover, they noted that the ozone flux increased with the liquid velocity (i.e. with the Reynolds number). to Sherwood number and can be deducted from this correlation. It can also be calculated from the Wilson plot method, a method which is also valid for the determination of the membrane mass transfer coefficient. With this method, the liquid mass transfer and the membrane mass transfer coefficients can be separated from the overall mass transfer coefficient. The authors focused on liquid mass transfer coefficient. They deduced this coefficient for the ozone from the oxygen coefficient, using in particular the surface renewal theory (see Equation 15). [START_REF] Cussler | Diffusion : mass transfer in fluid systems[END_REF] [15]

W X, ‡ˆ= l -•_,Z -•oe,Z n ".® × W X, ‡¯= 0.789 × W X, ‡¯
To model ozone mass transfer with a chemical reaction, an enhancement factor was added to the individual transfer coefficient of the liquid film. The global transfer coefficient is described by the equation [12] (see 3.2.4. The overall mass transfer coefficient).

The authors described the procedure followed for calculating ozone fluxes without chemical reaction (i.e. with pure water), and with chemical reaction (i.e. with sodium nitrite solutions).

The procedure with pure water can be summarized in several main steps. First, the ozone flux is assumed and the effluent ozone concentrations in both gas and liquid streams are calculated by mass balance. The average ozone concentrations are then determined. The concentrations at both membrane surfaces, and the ozone partial pressures at the membrane surfaces are calculated, and the flux are deducted from these pressures. Finally, the new calculated flux is compared with the flux previously assumed. When the difference between the assumed and the calculated flux is smaller than 0.01%, the procedure is finished. If not, the calculated flux is the new assumed flux, and the procedure begins again (i.e. the loop begins again). With a chemical reactions, the procedure is more complex than without, due to the presence of oxidation. Phattaranawik at al. concluded that both procedures can be used to design the ozonation membrane contactor in pilot scale. However, the mathematical model should be refined with residual ozone concentration because of the authors' assumption of zero effluent ozone concentrations in the liquid stream.

6.3. Determination of concentration profiles with software for the resolution of transfer equations Another approach is the numerical modeling thanks to Computational Fluid Dynamics (CFD) software [START_REF] Berry | Modelling of Ozone Mass-Transfer through Non-Porous Membranes for Water Treatment[END_REF][START_REF] Zoumpouli | A Single Tube Contactor for Testing Membrane Ozonation[END_REF]. The steps of the CFD simulation set-up are described by Tu et al. [START_REF] Tu | Computational fluid dynamics: A practical approach, Computational Fluid Dynamics: A Practical Approach[END_REF]. The first step is to define a domain (2-D or 3-D) and a geometry based on the studied membrane dimensions. For a gas/liquid membrane contactor, 3 domains can be defined: the gas phase, the membrane, the liquid phase. Then, the optimal mesh has to be chosen in order to obtain the best compromise between accuracy and computing time. The model can be scaled if necessary, and the convergence criteria have to be set, representing the acceptable residual after all the iterations. The next step is the specification of the governing equations (i.e. species and momentum equations), and of the boundary conditions. The CFD software takes care to couple and solve these equations, and therefore concentration profiles are obtained [START_REF] Berry | Modelling of Ozone Mass-Transfer through Non-Porous Membranes for Water Treatment[END_REF] .

During their works, Berry et al. used Comsol Multiphysics ® in order to obtain concentration profiles. The simulation was made with the gas flowing inside the tube and the liquid outside, in a non-porous capillary membrane made with PDMS. The gas was pure oxygen or a mixture of ozone and oxygen. Variations from 3.5 to 2210 of the liquid side Reynolds number were performed, corresponding to a laminar flow. The regime was also laminar on the gas side. The equations solved by the software, and their application conditions, are synthetized in Table 6.

Table 6: Governing equations of the mass transport used by Berry et al. liquid flowing inside the tube and the gas in the shell, in a non-porous tubular membrane made with PDMS. The gas studied was a mixture of ozone and oxygen. The effect of added peroxone (i.e. H2O2) in the liquid phase was also investigated. The liquid side Reynolds number was varied up to 290. For Reynolds numbers less than 100, the simulation results

were moderately overpredicted, in comparison to experimental measures. This may be a result of a non-uniform dispersion of O3 for low flowrates. For Reynolds numbers over 100, results obtained during the experiments fitted well with the simulation results, with an absolute difference lower than 0,5 mg/L. Their main conclusion is the importance of the liquid velocity as a major parameter for the determination of the ozone global transfer, followed, in that order, by the membrane length and the gas concentration.

Conclusion

Membrane contactors for ozone diffusion is a recent unit operation for water treatment by ozonation. Using a hollow fiber membrane contactor, ozone is added uniformly to the water to be treated, through many dosing points and with a great mass transfer surface area. It leads to a better transformation rate of micropollutants than with conventional ozonation processes, and potentially to a lower bromates' formation thanks to a lower residual ozone concentration.

In addition, membrane contactors offer other advantages, like its modularity, its small foot print, and the independent flow adjustment for gas and liquid phases. Gas can also be recycled, leading to energy and reagents savings.

Many parameters influence the mass transfer during ozonation using membrane contactors.

When carefully chosen, the efficiency of the process can then be greatly enhanced. For instance, the choice of the fiber material used is a crucial parameter. It has to provide a good ozone transfer through the membrane, but resist to ozone even for a long use. PTFE and PVDF membranes seem to be good choices for an ozonation application. The pressures to apply to the different phases also depend on the material chosen. The transmembrane pressure seems to be the major difficulty of membrane contactor technology. It has to be set carefully, in order to avoid bubbling and wetting problems.

The modeling of membrane processes for ozonation is useful to optimize reactor design and operating conditions and to study the influence of membrane properties. This optimization enables to achieve the best pollutant removal, for the minimum by-products' production and the minimum ozone consumption.

. An important challenge to overcome will be the development of more efficient membrane material. Hydrophobic membranes have to be manufactured with coating or grafting techniques, which could lead to complicated modification routes and excessive use of chemicals. Moreover, studies about long term stability of the membranes used will be essential to apply the process on an industrial scale. Finally, a key point concerns the manufacture of affordable module with an optimized hydrodynamic and a high mass transfer coefficient.

Bibliography

Ahmed, T., Semmens, M.J., 1992a. The use of independently sealed microporous hollow fiber membranes for oxygenation of water: model development.

Figure 2 :

 2 Figure 2: Ozonation reaction in water during oxidation of a pollutant M

Figure 4 :

 4 Figure 4: Bromate formation -chemical pathway, adapted from von Gunten, 2003b

Figure 5 :

 5 Figure 5 : Mass transfer regions and resistance-in-series in non-wetted membrane contactor, adapted from Atchariyawut et al., 2007

(

  Surface area of membrane per volume of liquid (m 2 .m -3 ) -x : Direction of the flow (m) -uL,mean : Mean liquid velocity (m.s -1 ) Integrating the previous equation leads to the following relation, allowing the calculation of the theoretical KLa. The boundary conditions are such that the concentration of the compound of interest (i.e. the ozone) at the liquid inlet (i.e. x=0) is zero, and is equal to Ci,liquid,out at the liquid outlet (i.e. x=L, representing the membrane length): 4. The overall mass transfer coefficientThe total resistance can be described by the resistance in series model, by analogy to Ohm'Berry et al., 2017) [12]

  Figure 6: Membrane configurations (a. non-wetted porous membrane, b. wetted porous membrane, c. dense membrane, d. composite membrane), adapted from Nguyen et al., 2011

Figure 8 :

 8 Figure 8: Effective mass transfer coefficient of a dense skin layer versus the layer thickness for a polymer permeability of 500 Barrer, adapted from Nguyen et al., 2011

Figure 9 :

 9 Figure 9: Ozone molar transfer flux as function of gas flow velocities with PVDF membrane at T=28°C, liquid phase velocity = 0,46 m/s, and initial dye concentration = 100 mg/L, adapted from Bamperng et al., 2010

Figure 11 :

 11 Figure 11: Configuration of membrane contactor with internal/external ozone transfer

  where A, B, C are empirical constants, Sc is the Schmidt number, Re is the Reynolds number, Lc is the hydraulic diameter of the liquid phase, D is the diffusivity, and KL is the overall mass transfer) -uL,mean : Mean liquid velocity (m.s -1 ) -di : Internal diameter of the tube (m) Then, the mass transfer model was completed with the ozone decomposition (i.e. a mass transfer and reaction model were defined). Generally, conservation equations (i.e. diffusion and convection terms), and reaction terms, are solved numerically. Transfer and reaction are assumed to occur simultaneously. Transfer, as mentioned before, is assumed to follow Leveque relation, and reaction rate is assumed to depend on the cross-sectional averaged solute concentration. The governing equation for the perimeter averaged ozone concentration is described by the following equation: u X,'624 §/ §¨= 4 † ℎ § 2 '/ •ª -/. -« ¬ 15

6. 2 .

 2 Development of a mass transfer model by using transfer coefficient and partial pressuresThe mass transport in a membrane contactor (i.e. across concentration boundary layer of gas phase, through porous membrane, and liquid boundary layer) can be described with global and individual mass transfer coefficients. In order to determine these coefficients, the resistance-in-series model can be used. Phattaranawik, Leiknes, and Pronks studied ozone mass transfer in porous flat-sheet membrane contactor, made with PVDF(Phattaranawik et al., 2005). The liquid side Reynolds numbers ranged from 454 to 1469 for the experiments with O2, and to 1136 for the experiments with O3, both corresponding to a laminar flow. To model mass transfer without reaction, the authors determined ozone mass transfer coefficients indirectly from oxygen transfer measurements to remove ozone decomposition and potential reactions in the liquid. The oxygen mass transfer coefficient in the liquid phase is correlated

  Gas section (0 ≤ r ≤Ri)Membrane section (0 ≤ r ≤ Ri+Lm) Liquid section (Ri+Lm≤ r ≤ the r-directions at all the boundaries are almost zero (ur,g=0) Inlet: Averaged velocity specified at the inlet (uz,L=uL,mean whenz=0)

Table 1 :

 1 Conventional reactors used for ozonation, adapted from Suez, 2007

Table 2

 2 summarizes the advantages and disadvantages of various organic materials which can be used for membrane contactor.

	501

Table 2 :

 2 Synthesis of the different organic materials used in membrane contactors (* Material resistant towards ozone) 502 4.2. Membrane materials used for ozonation with membrane contactors 4.2.1. Organic/inorganic membrane Organic membranes are made with polymers. They are often used because of the possibility to modulate their intrinsic properties (e.g. mechanical, thermal, selectivity, etc). These membranes can be prepared by sintering, stretching, track-etching, phase inversion, or other ways. A material often used with ozone is for instance the PVDF (i.e. polyvinylidene fluoride)[START_REF] Atchariyawut | Separation of CO2 from CH4 by using gas-liquid membrane contacting process[END_REF][START_REF] Bamperng | Ozonation of dye wastewater by membrane contactor using PVDF and PTFE membranes[END_REF][START_REF] Jansen | Hollow fiber membrane contactors-A means to study the reaction kinetics of humic substance ozonation[END_REF][START_REF] Khaisri | Comparing membrane resistance and absorption performance of three different membranes in a gas absorption membrane contactor[END_REF][START_REF] Leiknes | Ozone transfer and design concepts for NOM decolourization in tubular membrane contactor[END_REF][START_REF] Pines | Investigation of an Ozone Membrane Contactor System[END_REF].

Inorganic membranes are made with ceramic, metals, glass, or zeolite. They can be porous (e.g. ceramic) or dense (e.g. made with metals or glass). Ceramics are the major class of inorganic membranes. These membranes are prepared by mixing a metal (e.g. aluminium, titanium, silicium, zirconium) with a non-metal (i.e. nitride, oxide, or carbide). They are prepared by sintering or sol-gel processes, and have a great thermal, chemical, and mechanical stability

  [START_REF] Pines | Investigation of an Ozone Membrane Contactor System[END_REF][START_REF] Stylianou | Ozone Mass Transfer Studies in a Hydrophobized Ceramic Membrane Contactor: Experiments and Analysis[END_REF][START_REF] Zoumpouli | A Single Tube Contactor for Testing Membrane Ozonation[END_REF]. In the experiments of Atchariyawut et al.,Bamperng et al., Pines et al., Stylianou et al., and Zoumpouli et al., ozone flowed through the shell side and the liquid through the tube side (i.e.

	.2. Effect of several parameters on mass transfer
	5.2.1. Effect of liquid velocity
	Ozone flux increases with increasing liquid velocity (Atchariyawut et al., 2009; Bamperng et
	al., 2010;

Table 3 :

 3 Influence of pH on reaction order and rate constant of ozone decomposition at 20°C, adapted from Stylianou et al., 2016 Stylaniou et al. investigated the effect of ionic strength on ozone flux

			Rate constant of
	pH	Reaction order n	ozone decomposition K′ (1/s•(L/mg)(n-1))
			(±5%)
	4	2	0,0017
	6	2	0,0049
	9	1	0,624

Table 4 :

 4 Effect of parameters on mass transfer

Parameters Range in litterature Influence on the ozone transfer when the parameter increases Sources Liquid velocity 0.002 -0.9 m/s + (Atchariyawut et al., 2009; Bamperng et al., 2010; Pines et al., 2005; Stylianou et al., 2016; Zoumpouli et al., 2018)

				Li et al., 2010)
	Temperature	15 -50°C	+	(Stylianou et al., 2016)
	pH	4 -9	+	(Bamperng et al., 2010; Stylianou et al., 2016)
	Ionic strength	0 -0.4 mol/L	-	(Stylianou et al., 2016)
	Surfactant	0 -6 mg/L	+	(Côté et al., 1989)
	Chemical reaction	With or Without (pure water)	+ (With)	(Stylianou et al., 2016)
	Transfer direction	In/Out or Out/In	+ (In/Out)	(Wenten et al., 2012)
				(Atchariyawut et al., 2009,
	Gas velocity	0.003 -0.22 m/s	=	2007; Bamperng et al., 2010; Berry et al., 2017; Khaisri et
				al., 2009)
	Concentration of O3 in the gas	20 -60 mg/L	+	(Stylianou et al., 2016)
	Operating gas pressure	6.9 -413.7 kPa	+	(Ahmed et al., 2004; Ahmed and Semmens, 1992a, 1992b;

Table 5 :

 5 Synthesis of the studies about modelling of ozone diffusion with membrane

	contactors
	Publication	Modeling and determination of	Type of membrane	Investigated parameters
				Liquid velocity
	Ozone Mass Transfer Studies in a			Liquid pH
	Hydrophobized Ceramic Membrane Contactor: Experiments and Analysis.	Concentration of dissolved ozone at the module output	Tubular membrane Porous (Ceramic -Al2O3)	Gas concentration Membrane length Temperature
	(Stylianou et al., 2016)			Order of the ozone decomposition
				reaction
		Ozone transfer coefficient
	Mass transfer studies in flat-sheet membrane contactor with ozonation (Phattaranawik et al., 2005)	(developed indirectly from the oxygen transport) Ozone flux Ozone concentration at	Plane membrane Porous (PVDF)	Flow rates Temperature Matrix for ozone flux determination (pure water/solution of sodium nitrite)
		membrane/liquid interface
		Concentration profiles		Liquid velocity
	A single tube contactor for testing	Transfer resistance	Tubular membrane	Matrix (pure water/surface water/waste
	membrane ozonation	Transfer coefficients	Non porous	water/solution with humic acid)
	(Zoumpouli et al., 2018)	Ozone flux	(PDMS)	Membrane diameter
		Residual ozone concentration		Gas concentration
				Membrane length,
	Modeling of ozone mass transfer	Concentration profiles	Non porous	Thickness membrane
	through non-porous membranes for	Transfer resistance	capillary membrane	Liquid velocity
	water treatment (Berry et al., 2017)	Overall transfer coefficient	(PDMS)	Gas diffusivity in the membrane
				Gas solubility in the membrane
	6.1. Development of a mass transfer model based on dimensionless numbers
	Stylianou, Kostoglou, and Zouboulis studied the ozone mass transfer in a hydrophobized
	ceramic membrane contactor

  J. Memb. Sci. 69, 11-20. Ahmed, T., Semmens, M.J., 1992b. Use of sealed end hollow fibers for bubbleless membrane aeration: experimental studies. J. Memb. Sci. 69, 1-10. Ahmed, T., Semmens, M.J., Voss, M.A., 2004. Oxygen transfer characteristics of hollowfiber, composite membranes. Adv. Environ. Res. 8, 637-646. AIDA, 1998. Directive n° 98/83/CE du 03/11/98 relative à la qualité des eaux destinées à la

fibers (see 4.2.1). The ozone concentration was measured with potassium iodide method. The authors made the same experiments for different temperatures (i.e. 15, 25, 30 and 30°C), with different concentrations (i.e. 20, 40 and 60 mg/L). All the plots present the same trend as seen in the Figure 10.

The concentration of a compound (e.g. ozone or oxygen) at the interface between gas and liquid is linked to its partial pressure by Henry's law (see 3.2.1) with respect to its concentration in the gas phase (i.e., / 045678296 = L •_,'ƒ" 3 where s is the dimensionless partition coefficient for ozone [START_REF] Stylianou | Ozone Mass Transfer Studies in a Hydrophobized Ceramic Membrane Contactor: Experiments and Analysis[END_REF]). Therefore, when the concentration in the inlet gas increases, partial pressure also increases. According to the results of Stylaniou presented previously, the increase of partial pressure should raise the same way. The model established by the authors resulted in the determination of the concentration profiles. It can be used as a base for the prediction of the ozone and oxygen transfer for various designs, materials, and hydraulic conditions. Sherwood numbers obtained with this model fit with those found in the literature [START_REF] Berry | Modelling of Ozone Mass-Transfer through Non-Porous Membranes for Water Treatment[END_REF] . The main conclusions are as follow. First, the gas solubility is a parameter which cannot be neglected, in particular for the oxygen. The main resistance of the ozone transfer is on the liquid side, and the main resistance of the oxygen transfer is in the membrane.

Zoumpouli et al. had a similar approach than Berry et al. [START_REF] Zoumpouli | A Single Tube Contactor for Testing Membrane Ozonation[END_REF]. However, the configuration of the membrane contactor was different. The simulation was made with the No mutual interaction between the gases of the mixture (O2/O3) [START_REF] Dhingra | Mixed gas transport study through polymeric membranes[END_REF] Isotropic mass diffusivity of i

Boundary conditions

Axial symmetry: no material flow across the boundary (ꝺug,j/ꝺr=0 when r=0)

Gas-membrane interface: interfacial transport defined by the solubility laws (Cm1,j=Cg,j,i/Sj when r=Ri)

Concentrations of O2 and O3 nulle: CL,j,0=0

Tube inlet: Cg,j=Cg,j,0 Membrane inlet: insulated boundary (ꝺCm,j/ꝺz=0 when z=0)

Membrane-liquid interface: interfacial transport defined by the solubility laws (Cm1,j=HjCL,j,i when r=Ri+Lm) Tube outlet: the gas flux is predominantly by convection (ꝺug,j/ꝺz=0 when z=L)