Thomas Criton

Debora Vilona

Guy Jacob

Maurice Médebielle

Elise Dumont

Lionel Joucla

Emmanuel Lacôte

Synthesis and Properties of Higher Nuclearity Polyazanes

Keywords: Nitrogen, Oxidation, Molecular Modeling, Azo Compounds, Radical-Cations

Polyazanes (that is, higher nuclearity homologues of hydrazines) with increasing numbers of bound nitrogen atoms (from 3 to 5) were prepared via additions of lower order polyazanes to diazo reagents, including the first pentazane ever described. A structure was obtained. It was shown that the polynitrogen chains adopt a helical conformation. DFT modeling shows that the arrangement subsists in solution. While the polyazanes are all reducing agents, they become less so with the increasing number of nitrogens.

Many heavier p-block elements lead to electronically precise homoatomic all  linear chains. [START_REF] Rheingold | Homoatomic Rings, Chains and Macromolecules of Main-Group Elements[END_REF] For example, Silicon atoms can form homonuclear polysilanes, which are widely used for ceramics, as solar cells elements, etc. [START_REF] Kumar | [END_REF] Sulfur forms over 30 allotropes, in particular rings, but other cyclic structures with catenated sulfur atoms (with or without additional Carbons in the rings) also exist, [3] with important properties for biology or batteries. [4][5][6] On the other hand, in the second period, and with the obvious exception of Carbon, -type single-element chains atoms are generally unstable. This is the case for oxygen, whose polyatomic chains can easily decompose to release dioxygen and oxidized compounds. That is a key for ozonolysis, where 3 contiguous oxygen atoms are initially part of a cycle. [7][8] Similarly, a linear 4-oxygens chain has been suggested as a key intermediate in radical hydroxylations. [START_REF] Khursan | Organic tetroxides and mechanism of peroxy radical recombination[END_REF] Hydrazines are well-known, reactivity-rich, 2-N molecules, where the two nitrogen atoms are single-bonded. [START_REF] Schmidt | Hydrazine and Its Derivatives : Preparation, Properties, Applications[END_REF] The scenario quickly changes with higher nuclearities. Triazanes have been first synthesized decades ago, [START_REF] Linke | [END_REF][12][13] but little attention has been given to their properties. [14] While tetrazenes, which feature both single and double-bonded nitrogen atoms, are stable moieties, only a handful of all  tetrazanes exist, [15][16][17][18] and no higher order polyazane has ever been reported. We approached this field when we noticed the dearth of data regarding the reactivity of even the smallest polyazanes, triazanes. We wanted to understand how chemical properties were affected by the addition of additional nitrogen atoms in the chain, and also to extend the chemical space of higher-order polyazanes to longer chains. We report herein our initial results. In order to get comparison points we targeted an assay of 6 polyazanes: two triazanes (2a-b), two tetrazanes (3a-b) and two pentazanes (4a-b). We assumed that because of all the consecutive lone pairs on the nitrogen atoms, the chains would be very electron-rich, and that the all  chains could be stabilized by the attachment of electron-withdrawing groups. Therefore, all the target polyazanes are built similarly. They feature a terminal amine (Figure 1, top nitrogens) substituted by two alkyl groups; all other nitrogens are substituted by carbamate groups; their -end can be substituted either by a proton or a methyl. Triazanes 2a and 2b were prepared using the Dreiding/Mayr methodology. [12,13] Dimethylamine was added to di-tert-Butyl azodicarboxylate (DABD) in acetonitrile at rt, yielding 98% of 2a. Triazane 2b was obtained in 86% yield upon methylation of the potassium salt of 2a in THF/DMF (1:1) at 0°C. While there are methods to access the unsaturated 4Ntetrazenes, e.g. by reaction of a nitrene derived from a hydrazine with a diazo reagent, [19][20] or by oxidative coupling of hydrazines, [21][22][23] , there was only one method to access the saturated fully -bonded tetrazanes, i.e. the dimerization of captodative radicals (which can only deliver symmetric molecules). [15][16][17][18]24] One report in the literature mentioned that an -sulfonyl anion serendipitously added sequentially to two equivalents of an azodicarboxylate. [25] This suggested to us that hydrazinyl anions may be good reactive intermediates toward the formation of dissymmetric tetrazanes. We thus decided to prepare 3a and 3b by a nucleophilic addition 2N + 2N route. Boc-protected 1,1-dimethyl hydrazine 1a was deprotonated by Potassium bis(trimethylsilyl)amide (KHMDS) in a 1:1 THF/DMF mixture at -80°C, reacted with di-isopropyl azodicarboxylate (DIAD), and quenched with acetic acid at low temperature.

Tetrazane 3a was obtained in a very poor 10% yield. It decomposed quickly at room temperature. We suspected that the decomposition was due to the presence of a proton on the chain. The methylation of the terminal NH position was achieved by trapping the intermediate anion at low temperature with MeI. Gratifyingly, 3b was thus obtained in 70% yield, and proved more stable. For the unknown pentazanes, a similar retrosynthetic strategy required the addition of a triazane anion to an azodicarboxylate. Triazane 2a was first deprotonated with NaH in THF at -40°C, and the resulting anion was reacted with DIAD (Table 1, Entry 1). Unfortunately, no evolution was observed. When the solvent mix was made more polar by adding DMF, 65% of the desired pentazane 4a was isolated after quenching the reaction at low temperature with acetic acid (entries 2-3). Switching to KHMDS as the base further increased the yield by nearly 10% (entry 4). Furthermore, the reaction was complete after only 15 minutes (entry 5). A temperature increase to -20°C led to a loss in yield (to 59%, entry 6), while a lower temperature (-80°C) resulted in a slower reaction (only 38% isolated yield after 15 minutes, entry 7). Therefore, the optimal conditions appear to be these of entry 5, likely because of the better reactivity of the potassium anion of 2a. When the quenching agent was exchanged to methyl iodide, pentazane 4b was isolated (76%, entry 8). The pentazanes proved stable over silica. They were identified by HRMS and the structure of 4a was confirmed by X-ray diffraction (see below). They are the first examples of molecules containing 5 contiguous nitrogen atoms bounds by single  bonds. In contrast, the 1 H NMR spectrum of 4a was extremely complicated due to the presence of rotamers. We heated the samples at 80°C to get coalescence of the signals, but this resulted in a rapid decomposition. HRMS analysis of the decomposition products suggested that the pentazane had been cleaved in a mixture of hydrazines and triazanes. We presumed that the proton at the  position enabled this decomposition. Indeed, the methylation of said position in 4b delivered a much more thermally stable pentazane. Its 1 H-NMR analysis at 373 K led to a clean spectrum in which coalescence was achieved for almost all the signals.

With the array of polyazanes in hands, we could start the study of their properties, as well as how the latter change with the introduction of additional nitrogen atoms.

Crystal structure and conformation in solution. Crystals suitable for X-ray diffraction were obtained by slow evaporation of saturated solutions in diethyl ether at 0°C. The X-ray structure of 2a shows the three N atoms linked by  bonds. Starting from the Me2N end, the bond lengths are 1.408 Å, and 1.383 Å. They are shorter than the bond length found in hydrazine (1.446 Å), but close to the one reported on carboxylate-protected 1,2-dimethyl hydrazine-1,2-dicarboxyl-ate (1.386 Å). [26] The dimethylamino nitrogen displays a sp 3 hybridization, and the remaining two nitrogen atoms are sp 2 hybridized, albeit the sum of bond angles of the central atom is closer to 360° than that of the terminal sp 2 one (357.8° vs. 352.4°). This difference reflects the influence of the carboxylate groups. The dihedral angle along the N chain is 105° (Fig. 2). The two carboxylate groups generate a dihedral angle of 56.9°. The minimization of the steric hindrance between the CO2R groups explains the helical structure observed. The X-ray structure of 4a follows the same trends. Starting from the Me2N end, the bond lengths are 1.400 Å, 1.393 Å, 1.398 Å, and 1.386 Å. Apart from the dimethylamino nitrogen, which displays a sp 3 hybridization (average bond angle of 111.9°), all the nitrogen atoms exhibit a sp 2 hybridization. The dihedral angles along the N chain (starting from the Me2N) are 98.2° and 86.2° respectively for the all-N dihedra, resulting in a helical arrangement of the polyazane chain, which tends to minimize the repulsion between the CO2R groups (Fig. 2). We optimized the polyazane structures through DFT calculations (see SI, Fig. S1). Interestingly, the computed solution structures overlap quite tightly with those in the crystal (except for the freely-rotating t-butyl groups). The calculated conformation for 3a, for which no structure could be obtained is similar to that of 4a with a helical arrangement. From this, we propose that the conclusions drawn for pentazanes are also valid for the tetrazanes. There is therefore a fair degree of periodicity in the polyazane family.

Redox properties. Hydrazines being well-known reducing agents, we examined how the redox properties are affected when additional nitrogens are linearly installed on a polyazane chain. We therefore measured the oxidation potentials of the polyazanes by cyclic voltammetry. The parent Boc-protected UDMH derivatives 1a (featuring an N-H bond) and 1b (where the NBoc nitrogen is also methylated) were chosen as comparison points. The values obtained are reported in the third column of Table 2. Boc-UDMH 1a exhibits an oxidation potential of 0.82 V (vs. SHE, entry 1). Methylation of the nitrogen increases the potential to 0.96 V (entry 2). An additional nitrogen in the chain resulted in an increased anodic peak potential (1.22 V, entry 3), which did not change by methylation of the terminal nitrogen (1.19 for 2b, entry 4). The trend is maintained as additions of nitrogen atoms further increases the potential required for oxidation. Tetrazane 3b, requires 1.32 V (entry 5), pentazane 4a requires 1.43 V (entry 6) and pentazane 4b requires 1.49 V (entry 7) to be oxidized, respectively. Tetrazane 3a was not stable enough at room temperature to lead to significant results.

The oxidations are all irreversible, likely due to the short lifetime of the radical-cations generated. DFT calculations were therefore performed to locate the most oxidizable site in the polyazanes. The redox potential of all the molecules was estimated first through a Born-Haber thermodynamic cycle (see SI for details). [27] Indeed, redox potentials are related to the Gibbs free energy difference between the molecules in the oxidized state (radical cation species) and the solvated molecule in the ground state (neutral molecule). Geometry optimizations were then performed for both the neutral and radical cationic species at the DFT-M06-2X/6-31+G(d,p) level of theory, both in gas phase and solvated media with acetonitrile being treated implicitly.

The calculated [28] redox potentials are in excellent agreement with the experimental ones (second column in Table 2, in brackets). The oxidation trend is well respected since Triazane 2a was found easier to oxidize than Tetrazane 3b and Pentazane 4a (Figure 3). For the three systems, the spin density is mostly distributed between the nitrogens N1 and N2 (Figure 4). However, DFT inspection reveals interesting differences in the populations of the radical center. For triazane 2a and pentazane 4a, the values identify N1 as the predominant radical center (0.57 and 0.65 respectively), whereas the unpaired electron is more delocalized for 3b with the first nitrogen bearing a spin density of ~ 0.31. For the three systems, the inter-nitrogen distances most affected by the oxidation are that of the N1-N2 bonds, which are shortened by 0.07 Å upon one-electron oxidation. Conversely, the natural population analysis indicates that the nitrogen atoms sustain most of the cationic charge generated upon oxidation, with a total charge ranging between +0.5 and +0.7 a.u. (see ESI). For compounds 2a and 4a, the first nitrogen is the most affected, with an increase of the atomic charged by +0.37 a.u., whereas the charge of the radical cation derived from 4b is distributed more equally over the two nitrogens, with a larger distribution of the remaining spin density contributions on the two others nitrogens and the carbonyl oxygens notably. The calculations indicate that the most oxidizable site is the nitrogen directly connected to the dimethyl substituents, since the electron is easily removed from it, but that there seems to be a difference between the odd-numbered polyazane (2a, 4a) and the even-numbered one (3b). Perhaps this reflects the lower stability of the tetrazanes compared to both the tri-and pentazanes, as it develops a larger positive charge density next to a withdrawing group.

To conclude, polyazanes are a new class of nitrogen-containing molecules that until now had not been considered as a family with similar properties. We showed that this is indeed the case, as similarly substituted polyazanes with growing numbers of linked nitrogen atoms gradually fold to form helices and become increasingly less oxidizable. Further work will focus on enlarging the chemical space accessible (e. g. to longer, or branched chains) and unearthing new properties of these new main group oligomers.

Entry for the

Figure 1 .

 1 Figure 1. Target Polyazanes for this work.

  Reaction was quenched with AcOH; [b] No reaction was observed; [c] Reaction was quenched with MeI.

Figure 2 .

 2 Figure 2. Structures of triazane 2a (left) and pentazane 4a (right). There is a slight disorder around the t-butyl groups, which can freely rotate; Z = CO2iPr.

Figure 3 .

 3 Figure 3. Evolution of the measured (black diamonds) and calculated (red squares) first redox potential of the polyazanes.

Figure 3 .

 3 Figure 3. Cartoon representation of the structures of Triazane 2a, Tetrazane 3a and Pentazane 4a in the radical cation form, optimized at the M06-2X/6-31+G(d,p) level of theory and spin density representation (isovalue 0.10).

Table 1 .

 1 Optimization of the reaction conditions for the synthesis of Pentazanes 4a and 4b (Concentration was 0.2 M)

	Entry	Solvent	Base	t (min)	T (°C)	Product, Yield (%)
	1 [a]	THF	NaH	90	-40	-

[b]

Table 2 .

 2 Electrochemical data for several polyazanes.

	Entry	Compounds	(V) [a]	(V) [b]
	1	Hydrazine 1a	0.82; 1.53; 1.75	0.82 (=)
	2	Hydrazine 1b	0.96	0.92 (-0.04)
	3	Triazane 2a	1.22; 1.91	1.31 (+0.09)
	4	Triazane 2b	1.19	1.23 (+0.04)
	5	Tetrazane 3b	1.32	1.43 (+0.11)
	6	Pentazane 4a	1.43	1.53 (+0.10)
	7	Pentazane 4b	1.49	1.51 (+0.02)

[a] Anodic peak potential with a glassy carbon working electrode (3 mm) with 0.1 M n-Bu4NPF6 as supporting electrolyte in MeCN; all potentials are given vs. SHE;

[b]

Computed absolute Redox Potential obtained through Born-Haber thermodynamic cycle at the M06-2X/6-31+G(d,p) level of theory, given vs. SHE (see ESI). Values in parenthesis correspond to the difference between the calculated and measured values of the first oxidation potential.

Table 3 .

 3 Computed nitrogen-nitrogen distances for Triazane 2a, Tetrazane 3b and Pentazane 4a

	Polyazane	2a			3b			4a
	Bond	N1-N2	N2-N3	N1-N2	N2-N3	N3-N4	N1-N2	N2-N3	N3-N4	N4-N5
	Radical	1.33	1.37	1.33	1.36	1.37	1.34	1.37	1.37	1.37
	Cation
	Neutral	1.39	1.38	1.40	1.36	1.37	1.40	1.37	1.37	1.37
	molecule

-Page No. Synthesis and Properties of Higher Nuclearity Polyazanes

  Table of Contents (Please choose one layout)

	Layout 1:
	COMMUNICATION
	Polyazanes up to 5 -bonded nitrogen	Thomas Criton, Debora Vilona, Guy
	atoms were prepared via sequential	Jacob, Maurice Médebielle,* Elise
	additions to diazo reagents. Structural	Dumont,* Lionel Joucla,* Emmanuel
	analyses showed that the polynitrogen	Lacôte*
	chains adopt a helical conformation
	maintained by the carboxyl substituents. The conformations subsist in solution. Polyazanes are increasingly less reducing the more N atoms are in the chain.	O Page No. O N O N N O N O N O O O

Acknowledgements

We thank CNES, ArianeGroup, CNRS, CPE Lyon, Université Claude Bernard Lyon 1, ENS Lyon, the SYSPROD project, the AXELERA Pôle de Compétitivité (PSMN Data Center), Institut de Chimie de Lyon, and DGA & Agence de l'innovation de défense for funding of this work. T. C. thanks DGA and CNRS for a Ph. D. stipend. D. V. thanks CNES for a postdoctoral grant.


PhD Ali Gharaviri

Simone Pezzuto

PhD Mark Potse

PhD Sander Verheule

MD, PhD Giulio Conte

PhD Rolf Krause

MD, PhD Ulrich Schotten
email: schotten@maastrichtuniversity.nl

MD, PhD Angelo Auricchio

Flutter

Left atrial appendage electrical isolation reduces atrial fibrillation recurrences: a simulation study Gharaviri: Atrial fibrillation recurrences after catheter ablation

Keywords: Arrhythmia, Atrial fibrillation, Catheter ablation Fibrosis, Pulmonary vein isolation, Atrial Fibrillation recurrence, Left atrial appendage electrical isolation, in-silico study

Pulmonary vein (PV) isolation (PVI) improves freedom from atrial tachyarrhythmia recurrences in patients with paroxysmal and persistent atrial fibrillation (AF). [START_REF] Verma | Approaches to catheter ablation for persistent atrial fibrillation[END_REF] However, PVI has a limited success rate in persistent AF patients (persAF) and ablation techniques adjunctive to PVI isolating non-PV triggers remains an area of debate in these patients. [START_REF] Verma | Approaches to catheter ablation for persistent atrial fibrillation[END_REF] Recently, there has been a growing interest in the electrical and anatomical role of the left atrial appendage (LAA) in triggering and sustaining AF, particularly in persAF or after repeated AF ablation procedures. [START_REF] Biase | Left Atrial Appendage Isolation in Patients With Longstanding Persistent AF Undergoing Catheter Ablation: BELIEF Trial[END_REF] Whether isolation of triggers originating from the LAA or substrate modification caused by LAA isolation (LAAI) is the underlying mechanism for AF recurrence prevention is still unknown.

We investigated the effect of LAAI in a structurally detailed model of the human atria, extensively described previously 3 (supplemental material). The model entails wall thickness heterogeneities, endocardial trabeculated network, and a subepicardial layer with realistic fiber orientations. The material properties for the atria were set to produce an approximately normal P-wave during sinus rhythm (Table S1).

In total, 20 different pacing locations were selected in both atria based on reported possible sources of extra-PV ectopic focal activity in AF patients 4 (Figure).

In each simulation, AF was initiated by applying incremental pacing with the duration of 2 seconds at a selected pacing site. The pacing cycle length started with 280ms and gradually reduced to 124ms. AF initiation likelihood was compared between control (no ablation) and catheter ablation (CA) simulations with different degrees of fibrosis. CA simulations included four groups: PV isolation (PVI), PVI plus linear lesions encircling the left atrial posterior wall (BOX), PVI plus LAA circumferential isolation (PVI + LAAI), and BOX + LAAI. Virtual ablation lesions consisted of tissue volumes modeled by non-conductive elements. The outcome of the stimulation protocol was analyzed in terms of the type of selfsustained rhythm after 2 seconds of stimulations. If no activity was observed, the initiation was considered unsuccessful. Otherwise, a distinction between AF and atrial flutter (AFL) was made (supplemental material), with the latter being considered unsuccessful.

The spatial distribution of fibrosis was uneven, with patches or islands presenting higher degree of fibrosis (Figure S1). [START_REF] Gharaviri | Epicardial Fibrosis Explains Increased Endo-Epicardial Dissociation and Epicardial Breakthroughs in Human Atrial Fibrillation[END_REF] Simulations were performed without fibrosis, with moderate fibrosis, and severe fibrosis, in which 0%, 50%, and 70% of elements were fibrotic. [START_REF] Gharaviri | Epicardial Fibrosis Explains Increased Endo-Epicardial Dissociation and Epicardial Breakthroughs in Human Atrial Fibrillation[END_REF] In total, 300 simulations were performed. Each simulation group entails 60 simulations (20 simulations for each fibrosis degree).

In control simulations, an increase in the fibrosis degree led to a significant increase in AF In our control group, the averaged AF cycle length (AFCL) was 149ms, value previously reported in AF patients. In simulations without fibrosis or with moderate fibrosis, CAs caused a significant AFCL prolongation (Table S2). In severe fibrosis simulations only the presence of LAAI concomitant with CAs could significantly increase AFCL.

The simulations were performed on a single atrial geometry and inter-subject variability could have effects on simulations results. However, the in-depth study of the atrial anatomy effect on AF initiation is beyond the scope of this study.

We modelled LAAI and investigated its effect on AF recurrences in the presence of different degrees of fibrosis. As presented, adding LAAI to either PVI or BOX significantly lowered AF recurrence rate in severe fibrosis simulations, which is consistent with clinical studies mentioning the significant effect of LAAI in lowering AF recurrence rates in persAF. [START_REF] Biase | Left Atrial Appendage Isolation in Patients With Longstanding Persistent AF Undergoing Catheter Ablation: BELIEF Trial[END_REF] Finally, we could demonstrate that the mechanisms underlying AF initiation prevention in the presence of LAAI is not due to isolating triggers in LAA, but rather related to the reduction of AF conduction pattern complexity as a result of substrate modification due to LAAI.

  = persistent atrial fibrillation patients LAA = left atrial appendage LAAI = left atrial appendage isolation CA = catheter ablation

  initiation likelihood. In simulations without fibrosis or with moderate fibrosis (which may represent paroxysmal AF patients), PVI and BOX caused a significant reduction in AF initiation likelihood, either by preventing initiation of fibrillation or by converting AF into AFL (Figure). In contrast, in PVI and BOX simulations with severe fibrosis (which may represent persAF) we observed no significant reduction in AF initiation likelihood. In simulations with LAAI on top of PVI or BOX, we observed a comparable reduction in AF initiation likelihood as in PVI only or BOX simulations in the absence of fibrosis or in the presence of moderate fibrosis. In severe fibrosis, adding LAAI to PVI or BOX further reduced AF initiation likelihood by at least one third. An increase in fibrosis degree in control simulations led to a significant increase fibrillation wave generation rate and therefore a significant increase in AF conduction pattern complexity, quantified as number of waves per cycle (Figure). In simulations without fibrosis or with moderate fibrosis, CAs caused a significant reduction in fibrillation wave generation rate and AF conduction pattern complexity. In contrast, in severe fibrosis simulations, a significant reduction in wave generation rate and AF pattern complexity was only observed in simulations with LAAI plus PVI or BOX.

Figure 1 .

 1 Figure 1. A) Catheter ablation patterns and pacing points (pacing locations located outside of

Figure .

 . Figure 1

Funding: This work was supported by the Swiss National Supercomputing Centre (CSCS project ID s778), by grants to US from the Netherlands Heart Foundation (CVON2014-09, RACE V), and the EU (ERACoSysMED H2020 ERA-NET). Dr Conte is supported by the Swiss National Foundation (SNF) (Ambizione grant no PZ00P3_180055 / 1).


Mohamed Ayman Kammoun

Sana Gassara

John Palmeri

Raja Ben Amar

André Deratani

Nanofiltration performance prediction for brackish water desalination: case study of Tunisian groundwater

Keywords: Membrane desalination, Groundwater, Nanofiltration, Performance prediction, Software validation

published or not. The documents may come

Introduction

The Southern Mediterranean countries have been identified as undergoing one of the most important water crises in the world. This is the case for Tunisia, one of these countries, which has been suffering for several years from a water shortage that makes problematic the drinking water supply in some areas and at particular times of the year. Several studies predict that rising living standards and the development of the agriculture, industry and tourism sectors, will exacerbate the water scarcity in such a way that supply disruption could be extended to the whole of the country [START_REF] Elloumi | La gouvernance des eaux souterraines en Tunisie[END_REF]. Indeed, according to the Tunisian national water supply agency (SONEDE), the consumption of drinking water, which attained 381 Mm 3 in 2010, is expected to increase to 450 and 500 Mm 3 in 2020 and 2030, respectively [START_REF] Ites | Etude stratégique : Système hydraulique de la Tunisie à l'horizon 2030[END_REF].

Considering the growing water scarcity and the increasing demand for drinking water, Tunisia is moving more and more towards the exploitation of unconventional resources including brackish groundwater reserves and, more recently, seawater. Tunisian groundwaters can be roughly classified into two predominant types of brackish waters: (i) those coming from deep aquifers with a salinity between 1.5 and 3 g.L -1 comprising a high proportion of sulfate, calcium and magnesium divalent ions (type 1) and (ii) those coming from sedimentary coastal aquifers with a salinity between 3 and 5 g.L -1 (type 2), [START_REF] Hamdane | La gestion des ressources en eau souterraines (nappes et aquifères) comme biens communs : Cas de la Tunisie, Synthèse régionale sur l'approche économique de la gestion de la demande en eau en Méditerranée[END_REF]. In recent years, the salinization of the latter has resulted from intrusion of marine water caused by the over-exploitation of these resources. In this case, the main contaminants are the chloride and sodium ions [START_REF] Ben Hammouda | Egenkamps: Geochimical and isotopic investigation to study the origin of mineralization of the coastal aquifer of Sousse, Tunisia[END_REF].

Desalination becomes then essential to avoid soil sterilization in agricultural watering and to make water suitable for human consumption and everyday household needs [START_REF] Gnaneswar | Desalination of deep groundwater aquifers for freshwater supplies -Challenges and strategies[END_REF]. Reverse osmosis (RO) is the most common membrane technology used for performing this task [START_REF] Shenvi | A review on RO membrane technology: Developments and challenges[END_REF]. This process, based on dense membranes operating at high pressure, produces overqualified permeate in most of the cases [START_REF] Karabelas | New insights into organic gel fouling of reverse osmosis desalination membranes[END_REF]. Therefore, RO suffers from the following three key limitations: high energy consumption, low water recovery, and excessive membrane fouling [START_REF] She | Membrane fouling in osmotically driven membrane processes: a review[END_REF][START_REF] Badruzzaman | Impacts of silica on the sustainable productivity of reverse osmosis membranes treating low salinity brackish groundwater[END_REF][START_REF] Mohammad | Nanofiltration membranes review: Recent advances and future prospects[END_REF]. Nowadays, for obvious economic reasons one the most important issues is the energetic impact of the RO desalination process. One way of overcoming this challenge is the integration of technologies less demanding in terms of energy consumption, such as nanofiltration (NF). NF shows clear advantages over RO, including higher permeate fluxes and lower operating pressure, resulting in lower investment costs. Moreover, although ion rejection is lower than for RO technology, requirement specifications can often be met using NF, thereby providing a better cost-effective option in many cases [START_REF] Talaeipour | An investigation of desalination by nanofiltration, reverse osmosis and integrated (hybrid NF/RO) membranes employed in brackish water treatment[END_REF][START_REF] Yousefi | Application of nanofilter in removal of phosphate, fluoride and nitrite from groundwater[END_REF][START_REF] A H Mahvi | Nitrate removal from aqueous solutions by nanofiltration[END_REF][START_REF] Van Der Bruggen | Nanofiltration in Encyclopedia of membrane science and technology[END_REF].

In contrast to RO, NF membranes are considered as porous and exhibit nominal cutoffs between 200 and 1000 Da [START_REF] Talaeipour | An investigation of desalination by nanofiltration, reverse osmosis and integrated (hybrid NF/RO) membranes employed in brackish water treatment[END_REF]16]. Only the membranes with the tightest pores are used for desalination treatment. Two groups can be distinguished in the literature regarding the rejection of monovalent ions (NaCl), as non-exhaustively presented in Table 1. [17]

[21] [START_REF] Song | Analysis of nanofiltration membrane performance during softening process of simulated brackish groundwater[END_REF] The first group, including for example the NF270 (Dow Filmtec), NFX (Snyder), DK (GE osmonics) NF membranes, is characterized by a high selectivity between monovalent and divalent ions for single solutions with typical rejections of less than 60% (NaCl) and higher than 90% (MgSO 4 ), respectively. On the other hand, these membranes offer higher permeate flow rates than the second group (Table 1), which have rejection properties closer to RO membranes.

The 1 st membrane group is generally suggested for cutting down the total hardness of surface, sea and ground waters due to their high mono/divalent ion selectivity [START_REF] Su | Effect of feed water characteristics on nanofiltration separating performance for brackish water treatment in the Huanghuai region of China[END_REF][START_REF] Song | Performance of UF-NF integrated membrane process for seawater softening[END_REF][START_REF] Nguyen | A Deratani Desalination and removal of pesticides from surface water in Mekong Delta by coupling electrodialysis and nanofiltration[END_REF] while the 2 nd group is preferred for removing the total salinity and pollutants [START_REF] Chmiel | Computer Simulation of Nanofiltration, Membranes and Processes[END_REF]. However, it was also reported that the NaCl concentration has a strong impact on salinity removal performance.

Therefore, the data in Table 1 are only indicative as the ion composition of real solutions and the precise plant configuration and operating conditions all have a dramatic effect on the performances of NF membranes. The electrostatic interactions between the ionic species in a multi-component feed and between the ions and the membrane charge are highly non-linear and cannot, in general, be predicted straightforwardly using as sole input single salt rejections performances. There are furthermore currently ill-understood non-electrostatic interactions (steric, dielectric, hydration, …) that complicate quantitative modeling [START_REF] Altaee | A Computational Model to Estimate the Performance of 8 inches RO Membranes in Pressure Vessel[END_REF]. It is therefore usually impossible to predict the NF performance of a given membrane and therefore judge its suitability for a given application from the limited performance characteristics communicated by the membrane manufacturers.

The question that arises from the previous discussion is how to decide which kind of membrane technology (NF or RO) and membrane should be used for desalting the different types of Tunisian groundwaters. This requires having an efficient modeling tool to save time by limiting the number of experimental validations. In the case of RO, most of the manufacturers provide prediction software such as for example ROSA (Dow Filmtech) [START_REF] Wang | Transport of organic electrolytes with electrostatic and steric-hindrance effects through nanofiltration membranes[END_REF]. For the reasons mentioned above, it is more difficult to have the equivalent for NF. It should be noted that the ROSA software, which is well-recognized as a suitable tool for estimating RO membrane performance in relation to the plant operating conditions, also has an NF database. In this paper, comparison of performance prediction with the Nanoflux ® software, which is well adapted for NF transport mechanism, was carried out in the case of the NF270 and NF90 membranes, each being associated with a different group (Table 1). To do so, we confronted the model predictions with the results of filtration experiments carried out using the two simulated major types of Tunisian groundwaters. The obtained data were discussed in terms of water quality and productivity efficiency in order to optimize the membrane and process choice vs. the ground water ionic composition.

Materials and methods

Theory

The structure of NF membranes was assumed to be a bundle of straight cylindrical capillaries characterized by their pore radius r p and effective length l eff (Fig. 1) and the external solutions to be ideal and perfectly stirred so that concentration polarization could be neglected in the present study. The system was considered isothermal with a temperature T of 298 K. The composition of the feed was fixed by the concentration of the N ions making up the mixture, each denoted by a concentration C (i=1..N). In the same way, and i c denote their concentration in the permeate and inside the membrane, respectively. z the ion valance, R the gas constant, T the temperature, F the Faraday constant, φ the electric potential in the membrane, ,

i c K the v i c i i d i i i i i d i i J c K dx d F RT D K c z dx c d D K j , , , + - - = φ 6
convective ion hindrance factor ( v J is the volume flux density based on the membrane area). Eq.

(1) has to be coupled with an explicit expression of the local electroneutrality inside pores:

1 0 N i i m i z c X = + = ∑ (2)
where

p m Fr X σ 2 =
is the effective membrane charge (moles/m 3 of pore volume) for cylindrical pores and related to the surface charge density σ. The normalized membrane charge is defined as:

= (3)
with is the total salt concentration. Furthermore, in NF, the electric current density across the membrane vanishes,

1 0 N c i i i J F z J = = = ∑ (4)
which allows one to obtain a relation between the electric potential gradient and the ionic concentrations. The volume averaged Stokes equation is given:

0 1 v p dP d J L dx dx φ ρ = - - (5)
where is the pure water permeability and In NF the HET equations must be solved using the filtration condition boundary. First, the ionic molar fluxes i J are related to solution volume flux J v as follows :

p i i v J C J = (6)
Second, the distribution of ions at the membrane/solution interfaces is described by the following modified Donnan equations,

(0 |0 ) (0 ) exp / ( ) f i i i i D c C z F RT φ -+ +   = Φ - ∆   ( 7
) ( | ) ( ) exp / ( ) eff eff p i eff i i i D l l c l C z F RT φ + - -   = Φ - ∆   (8)
where

0 -| 0 + and - eff l | + eff l
denote the membrane/solution interfaces at the feed side and the permeate side, respectively. i Φ is the steric partitioning coefficient of ion i defined as the ratio between the available section (i.e. taking into account the finite size of the ion) and the pore cross section and D φ ∆ is the dimensionless Donnan potential arising at each nanopore/external solution interface.

Finally, at the one membrane element level theoretical ion rejection predictions for multielectrolyte solutions can be obtained from:

1 p i i f i C R C = - (9)
NanoFlux ® is a commercial nanofiltration simulation program (CNRS) that can solve numerically the HET model for up to eleven ionic species and composite membrane systems with up to three distinct layers. Given the composition of the feed solution, the characteristics of the membrane, and the configuration of the NF installations, NanoFlux ® uses an internal single salt database to predict the NF performance for arbitrary ionic mixtures in terms of ionic rejection and volume flux density [START_REF] Lefebvre | Nanofiltration modeling: a comparative study of the salt filtration performance of a charged ceramic membrane and an organic nanofilter using the computer simulation program nanoflux[END_REF][START_REF] Palmeri | Process modeling of brackish and seawater nanofiltration[END_REF][START_REF] Lefebvre | Nanofiltration Theory: Good co-ion exclusion approximation for single salts[END_REF][START_REF] Bukšek | Zeta potential determination of polymeric materials using two differently designed measuring cells of an electrokinetic analyzer[END_REF].

Experimental part

Materials

Two commercial NF membranes (NF90 and NF270) and one RO membrane (BW30) from Dow Filmtec were used in this work. The solutions used to characterize the charge and the performance properties of the membranes were prepared by dissolving salts of analytical grade salts without further purification in deionized water (18 MΩ/cm, Millipore Milli-Q): NaCl, CaCl 2 , Na 2 SO (Carlo Erba) and MgSO 4 (Merck Eurolab). All the solutions were filtered (0.45 µm) prior to use to remove the residual insoluble impurities.

Nanofiltration pilot

Tangential filtration experiments were carried out using a nanofiltration pilot (Figure 2) consisting of a feed tank (1) equipped with a temperature control loop (2), a positive displacement pump (3), a 2.5" stainless steel pressure vessel accommodating 2540 filtration element (4), a pressure regulating valve (5) and a sampling loop [START_REF] Gnaneswar | Desalination of deep groundwater aquifers for freshwater supplies -Challenges and strategies[END_REF]. A programmable logic controller ( 7) is used to control the equipment and to retrieve the data from the sensors (feed and permeate flow, feed pressure and retentate, feed tank level). Sampling loop sensors allow pH, temperature and conductivity measurements of the retentate and permeate. The flow rate of the feed was set at 7.9 L.min -1 . The membranes were first immersed at least overnight in water

Permeability measurement

Membrane permeability was determined from the volume flux (J v ) by circulating water through the membrane system. J v (L.m -2 .h -1 ) was calculated using Eq (10):

= (∆ . ) (10)
where V p (L) is the volume of permeate, ∆t (h) is the permeation time and A (m 2 ) is the active membrane surface area. Membrane permeability (L.m -2 .h -1 .bar) was determined from the slope of the linear variation of J v as a function of applied pressure P (bar).

Ionic composition of simulated brackish waters from South Tunisia

The major ion composition is reported in Table 2 for groundwater found in three locations of South Tunisia that were selected as a function of their sulfate/chloride ratio and salinity. Sfax well 1 is representative of type 1 brackish waters (sulfate/chloride ratio > 1 and salinity < 3 g/L) and Sfax well 2 and Gabés of type 2 ones (sulfate/chloride ratio < 1 and salinity > 3 g/L). Synthetic waters were prepared from the compositions reported in Table 2 and denoted Feed 1, Feed 2 and Feed 3, respectively. Each of these parameters is compared with the corresponding value of Tunisian standards for drinking water. The ion composition did not show the presence of HCO -3 at least not to a large extent. Feed 3 contains about 188 mg/L accounting for the higher pH value of 8. This concentration is, however, low compared to the other ones and was therefore not considered a relevant parameter even if it was taken into account in the preparation of the simulated feed.

Salt rejection measurement

The salt concentrations in permeate and feed solutions were determined by ion chromatography (DIONEX ICS-1000) analysis. The salt rejection was calculated using Eq [START_REF] She | Membrane fouling in osmotically driven membrane processes: a review[END_REF].

Zeta potential

The zeta potential is the electric potential in the interfacial double layer at the location of the slip plane relative to a point in the bulk fluid away from the interface. It characterizes the membrane surface charge and can be used for the quantification of its magnitude. The membrane surface zeta potential was determined with a SurPASS electro-kinetic analyzer (Anton Paar, GmbH) based on the streaming potential method. An adjustable gap cell in which the membrane samples were mounted was used with a height of about 100 µm [START_REF] Gassara | Deratani Pore size tailoring of poly(ether imide) membrane from UF to NF range by chemical post-treatment using aminated oligomers[END_REF][START_REF] Pontié | Novel approach combining physicochemical characterizations and mass transfer modelling of nanofiltration and low pressure reverse osmosis membranes for brackish water desalination intensification[END_REF]. The KCl electrolyte solution at different concentrations was circulated in the cell between two pieces of membrane that were immersed in the electrolyte overnight before the measurement. The pH of the electrolyte was controlled by HCl 10 -1 M and NaOH 10 -1 M solutions. The zeta potential was calculated using the Helmholtz-Smoluchowski equation from the measured streaming voltage as a function of pH (from pH 4 to pH 10).

Results and discussion

Three simulated solutions with ionic compositions representative of brackish groundwaters found in South Tunisia (Table 2) were filtered using two NF membranes (NF90 and NF270) and one RO membrane (BW30) for comparison. The salinity spans the range of 2222-5394 mg/L with sulfate/chloride ratio varying from 2 to about 0.5. Two different NF modeling tools (Rosa and Nanoflux ® available from Dow Filmtec and CNRS, respectively) were used to predict the permeate flow rate and the salt rejection as a function of the applied pressure in the range of 2 -14 bar. The obtained simulation results were compared with the experimental ion rejection data.

Desalination performances of NF and RO membranes

Feed 1 is characterized by the lowest salinity with a value that exceeds the standard of Tunisian regulation for drinking water ( respectively. Considering these data, it was expected that NF could lead to permeate with composition meeting the Tunisian regulation for drinking water. Figure 3 shows the NF90 and NF270 performances in terms of filtration flux (J v ) and permeate salinity as a function of the applied pressure for Feed 1 and Feed 2. The membrane permeability values obtained from the linear variation of J v as a function of the applied pressure are seen to be decreasing with increasing feed salinity (from Feed 1 to Feed 2, see Table 3). The intensity of this effect, however, is strongly dependent on the rejection rate, as it is more than four times higher in the case of the NF90 membrane (group 2). This observation can be accounted for by an apparent viscosity enhancement in nano-scale pores (electroviscous effect) related to electrostatic interactions between the membrane charges, the ions in solution and water : the flow induced streaming potential acts back on the ions in solution to reduce the flow driving force produced by the transmembrane pressure gradient, leading to a decrease in slope that can be interpreted as an enhanced apparent viscous (on the other hand at the relatively low salt concentrations studied osmotic pressure effects are weak) [START_REF] Palmeri | Modeling of multi-electrolyte transport in charged ceramic and organic nanofilters using the computer simulation program NanoFlux[END_REF][START_REF] Palmeri | Process modeling of brackish and seawater nanofiltration[END_REF].

As expected from the diffusion / convection transfer mechanism, the passage of ions across the membrane decreases with an increase of applied pressure (Figure 3). At low pressure and permeate flow rate, the weak concentration difference between both sides of the membrane induced by the convective transport is counterbalanced by diffusive transport from the concentrated solution to the diluted one which enables a high passage of ions. The permeate flux increases with the trans-membrane pressure reducing the diffusion contribution with respect to convection leading to the observed decrease of ion passage until a high-pressure plateau is reached.

Feed 2 mainly differs from Feed 1 by its chloride content, which is about three times higher (Table 2). The lower rejection of monovalent ions by membranes of group 1 could then primarily be responsible for the strong decrease of ion rejection from Feed 1 to Feed 2 observed in the case of the NF270 membrane (Table 3). Another important factor is related to how an increase of salinity in the feed solution causes the screening of membrane charges, thereby inducing a reduction of Donnan exclusion and resulting in an alteration of both NF membrane performances. It should be noted that the water quality produced in all cases is in accordance with the Tunisian standards in term of salinity (<2000 mg/L). However, treatment of Feed 1 by NF90 leads to permeate with a too low-level salinity requiring a remineralization operation. The ion composition of permeates obtained using NF270 and NF90 membranes at respective transmembrane pressure of 6 and 10 bar (recovery about 15 %) is given in Table 4. The value of 10 bar and 6 bar were chosen since it appears to be a good compromise between salinity removal and applied pressure. In that case, most permeates fully comply with the Tunisian standards for drinking water as defined in Table 2 except in the case of treatment of Feed 2 by NF270 where the sodium and chloride contents in the permeate exceeded the required values. These results confirm that membranes of group 1 are not appropriate for treating waters with too high content in monovalent ions due to their high divalent/monovalent selectivity. To continue the comparison, NF270 is more productive and less energy consuming in terms of filtration flux than NF90 whereas its permeate salinity is much higher. NF270 (and group 1 NF membranes) can be considered as the right choice to treat Tunisian groundwaters with a low NaCl content without any need to remineralize permeate. On the other hand, NF90 (and group 2 NF membranes) are particularly well-suited to treat waters similar to Feed 2.

To highlight in greater detail the behavior of the two studied membranes, representative of the two groups defined in introduction (Table 1), the rejection performance for each ion is reported in Figure 4. The difference in separation performance between the two membranes is related to their porous structure, as NF270 is known to have a larger pore size than that of NF90 [START_REF] Azaïs | Nanofiltration for wastewater reuse: Counteractive effects of fouling and matrice on the rejection of pharmaceutical active compounds[END_REF][START_REF] Wilf | The Guidebook to Membrane Desalination Technology, Reverse Osmosis, Nanofiltration and Hybrid Systems Process, Design, Application and Economics[END_REF].

Moreover, they both have a negatively charged surface at neutral pH as determined by their zeta potential [START_REF] Wilf | The Guidebook to Membrane Desalination Technology, Reverse Osmosis, Nanofiltration and Hybrid Systems Process, Design, Application and Economics[END_REF]. Owing to its restricted pore size, which impedes the convective and diffusive mobility of ions, NF90 can retain more than 98 % of the divalent ions and about 90 % of the monovalent ones for the two types of feed solutions. The quasi-quantitative rejection of sulfate ions by the two membranes originates from strong electrostatic interactions between the -2 ion charge and the membrane surface. In contrast to NF90, NF270 rejects more selectively divalent anion than divalent cations. Actually, cations act as membrane counter-ions and their passage depends on the rejection of the other ions to ensure the electroneutrality of concentrate and permeate according to the Donnan equilibrium effects. In the case of feed 1, the sulfate feed concentration is higher than that of chloride. The divalent Mg 2+ and Ca 2+ cations are therefore highly retained to ensure electroneutrality in the concentrate. By contrast, in the case of feed 2, the chloride feed concentration is higher than that of sulfates. The passage of chloride through the membrane because of its lower valance, smaller size and its high mobility causes the passage of a certain number of divalent counter ions (besides the monovalent ones) to ensure electroneutrality in both permeate and concentrate sides. Consequently, the rejection of divalent cations is greater in the case of feed 1 than in feed 2 [START_REF] Azaïs | Nanofiltration for wastewater reuse: Counteractive effects of fouling and matrice on the rejection of pharmaceutical active compounds[END_REF]. In all cases, chloride can be seen in Figure 4 as the less retained ion and appears to be a discriminating and limiting parameter. Then, monitoring the concentration of chlorides in permeate is essential to verify the compliance of nanofiltered water with the standards.

To conclude this part, it is really interesting to compare the performance of brackish water reverse osmosis (BWRO) membranes with that of the group 2 NF ones. Figure 5 shows the variation of permeate flow rate and salinity as a function of applied pressure for filtration using NF90 and BW30 in the case of the groundwater Feed 3 having a higher salinity than Feed 1 and Feed 2 with a large content of both chloride and sulfate anions. The salinity of permeate meets the requirement of Tunisian standards for optimum applied pressures of about 10 and 6 bar in the case of NF90 and BW30, respectively. Beyond these values, the permeate needs to be remineralized. It should be noted that all the ion parameters are fully in compliance with the requirement of the Tunisian regulation for drinking water. In Figure 5, it can be seen that the Table 5 shows the parameters of permeates obtained with the two membranes at applied pressures of 10 and 14 bar. These data are given only for comparison as the recovery rates are too low for an efficient BW30 operation. Again, NF appears to be the better solution for the production of drinking water from this type of groundwater both in terms of productivity and desalination performance. At this point, it is obviously essential to have a prediction tool to decide what kind of membranes (NF group 1 and 2 membranes or BWRO) could the best suited in terms of desalination performance and specific energy consumption estimated by the produced volume of desalinated water at a given pressure depending on the feed groundwater salinity and ionic composition (sulfate and chloride anion content). This is the objective of the following section in which two available softwares (ROSA and Nanoflux ® ) were tested and their simulation data confronted with the previous experimental results.

Nanofiltration performance prediction : software validation

ROSA prediction

As above mentioned, ROSA is popular software and well-established prediction tool used successfully for the performance assessment and design of RO systems [START_REF] Wang | Transport of organic electrolytes with electrostatic and steric-hindrance effects through nanofiltration membranes[END_REF]. This is illustrated by the modeling of ion rejections obtained in the case of Feed 3 treated with the BWRO membrane BW30. Although comparison with the experimental data in Figure 6 shows only fairly good overall agreement for all the ions studied, in the domain close to the rejection plateau (applied pressure beyond 10 bar) the agreement is excellent with deviations of less than 1 %. The ROSA database contains also NF membranes produced by Dow Filmtec including the NF270 and NF90. The performance of this prediction tool was then checked for the NF treatment of the studied Tunisian groundwaters. It was demonstrated previously that NF270 and NF90 should be the best choice for desalting Feed 1 and Feed 2, respectively. Figure 7 presents the modeling of ion rejections as a function of the permeate flow rate in these two cases.

It can be seen in Figure 7 that ROSA simulation gives the right order for ion rejection experimentally found SO 4 2-≥ Mg 2+ ≥ Ca 2+ > Na + > Cl -. However, the ROSA predictions systematically overestimate the rejection performance of the membrane representative of group 1 (NF270). This is especially seen in the case of the monovalent ions with a minimum deviation of about 40% and 25 % for chloride and sodium on the high flux plateau (applied pressure 10 bar and higher). On the other hand, the simulation of divalent ion rejection appears to be much better with a difference of less than 10 % in the same conditions. For purposes of comparison, the same modeling was performed with NF90 (group 2). Closer agreement between the experimental monovalent ion rejection data and the ROSA simulation curves (about 10 % at plateau) were obtained in this case. Actually, group 2 NF membranes exhibit performance similar to those of BWRO membranes. Consequently, although it is thought that the transport mechanism is different between these two kinds of membranes (tight NF and RO), the ROSA software can lead to a good estimation of the NF90 performance. In contrast, this is not the case for group 1 NF membranes. With a higher selectivity between monovalent and divalent ions (a signature of NF membranes) the difference in transport mechanism is brought to the forefront and experimental data for monovalent ion rejection could not be properly predicted by the ROSA software.

Another point to mention is the discrepancy between the permeate flux simulation and experimental data. As seen in Figure 7, the maximum flux at 15 bar is about 50 % and 25%

lower than the values obtained with NF270 and NF90, respectively. The increase in ionic strength leads also to a decline of the experimental permeate flow rate particularly noticeable in the concentration range between 10 -2 and 10 -1 M. This observation is due to the rise in osmotic pressure (Figure 8, left). Although this qualitative effect on membrane performance is well taken into account by the ROSA modeling, the predicted amplitude of the flow rate drop is much greater than the experimentally observed one. Apart the large overestimation of ion rejection seen in Figure 8 (left) in the case of 10 -1 M NaCl feed, the pure water permeability data input in the ROSA database (about 11 L/h.m 2 .bar) that is one and half times lower than the experimental one (16.3 ± 1.0 L/h.m 2 .bar) could likely be responsible of the observed discrepancy for the 10 -3 and 10 -2 M NaCl feeds. The membrane surface charge originates from the ionization of functional groups and/or the adsorption of charged species, especially in the case of polyvalent ions [START_REF] Ortiz-Albo | Phenomenological prediction of desalination brines nanofiltration through the indirect determination of zeta potential[END_REF]. As seen in Interestingly, ROSA can predict more or less the rejection at pH values corresponding to the plateau (pH = 10) but fails at lower pH when the membrane surface charge shows a large variation. We do not know how the ROSA software is designed for predicting the rejection performance of NF membranes, but it appears clearly that the electrical interactions between the charged solutes and the membrane are not considered in their full complexity and totality. To further investigate this issue, the following section is devoted to the validation of a prediction tool, Nanoflux ® , specifically designed to address the particularities of NF membrane transport.

Nanoflux ® validation

The Nanoflux ® prediction tool is based on an internal database containing the specific membrane parameters (pore radius % , normalized membrane charge and effective pore length 6 gives the different membrane parameters used by Nanoflux ® for establishing the simulation curves presented below. From these data, it can be seen clearly that the feed composition impacts the normalized membrane charge and thereby the electrical interactions with the solutes. As indicated before, the membrane charge density decreases with the increase of the feed ionic strength by charge screening. This accounts for the reduction of from Feed 1 to Feed 2. However, an increase of this parameter is observed for Feed 3 in spite of a further increase of the salt content. As can be noted from the composition of Feed 3 in Table 2, the pH of this solution is 8 compared to about 6

for the previous ones, explaining the increase membrane charge. Thus, by taking into account the electrical interactions more specifically, prediction of NF membrane performance can be more accurate.

Conclusion

It was demonstrated in this study that the two predominant brackish water types found in South Tunisia can be treated by NF technology. Two groups of NF membranes were considered depending on their divalent/monovalent selectivity. The advantage of this approach is that a better productivity of permeates complying with the Tunisian requirements for drinking water can be obtained. The conclusion of this study can be summarized in the following way:

-The sulfate/chloride ratio appeared to be the key factor for choosing the more appropriate membrane to treat specified low salinity groundwaters. Thus, it was found that Tunisian groundwaters can be roughly divided into two families separated by the sulfate/chloride ratio of about 1. The experimental results showed that the group 1 NF membranes as exemplified by NF270, are suitable for treatment of low salinity feeds having a large proportion of sulfate ions over chloride ions. By contrast, the group 2 NF membranes with ion rejections close to those of RO (like NF90) provided an optimal compromise for groundwaters from the sedimentary coastal aquifers containing a high proportion of chloride ions.

-Validation of available software was undertaken to have a decision-making tool for selecting the right membrane as a function of the feed to be treated and the water quality to be produced. It was shown that Nanoflux ® , a prediction tool specifically designed for taking into account the complexity of NF membrane transport, can be a useful tool for this technology. On the other hand, the ROSA software designed for RO was not found to be generally useful for the prediction of NF membrane performance because it does not appear to account for the electric interactions between membrane and solutes.

Table 1 :

 1 Some commercial nanofiltration membranes classified with respect to their mono-

Figure 1 .D

 1 Figure 1. Schematic diagram of a membrane pore used in the modeling with r p the pore radius and l eff the effective pore length. The positions 0 -and l + eff denote the axial coordinates just outside the pore, 0 + and l - eff denote the axial coordinates just inside the pore.

=

  ∑ the local ion charge density.

  before being used in any experimental work and each membrane was conditioned by filtering pure water at 17 bar during 1 hour to avoid any compression effects and to establish leak tightness. All filtration experiments were carried out with an applied pressure range of 2-15 bar at room temperature (25°C).

Figure 2 .

 2 Figure 2. Presentation of the nanofiltration pilot used in this study: (1) feed tank; (2) temperature control loop; (3) pressure pump; (4) 2.5" stainless steel pressure vessel; (5) pressure regulating valve; (6) sampling loop; (7) programmable logic controller.

Figure 3 .

 3 Figure 3. Effect of pressure on permeate flux and salinity for filtration of Feed 1(left) and Feed 2 (right) using the NF90 and NF270 membranes.

Figure 4 .

 4 Figure 4. Rejection of monovalent and bivalent ions by NF270 and NF90 membranes at a fixed trans-membrane pressure of 10 bar for Feed 1 and Feed 2.

Figure 5 .

 5 Figure 5. Effect of pressure on permeate flux and salinity for filtration of Feed 3 using the NF90 and BW30 membranes. The dashedline represents the lower limit of Tunisian salinity norm.

Figure 6 .

 6 Figure 6. Ion rejections as a function of permeate flux for Feed 3 treated with BW30. Solid curves are simulation results obtained with ROSA and symbols the experimental results.

Figure 7 .

 7 Figure 7. Ion rejections as a function of permeate flux for Feed 1/NF270 (left) and Feed 2/NF90 (right). Solid curves are simulation obtained with ROSA and symbols the experimental results.

FeedFigure 8 .

 8 Figure 8. Comparison between simulated and experimental ion rejections as a function of permeate flux for different NaCl feed concentration at pH 6 (left) and the corresponding permeate flux as a function of NaCl feed concentration (right). Solid curves are simulation results obtained with ROSA and symbols the experimental results.

Figure 9 .

 9 Figure 9. Ion rejections as a function of permeate flux for 10 -2 M NaCl feed at various pH (left). Solid curves are simulation obtained with ROSA and dots the experimental results. Zeta potential of the NF270 membrane surface as a function of pH and KCl concentration (right).

Figure 9 (

 9 Figure 9 (right), membrane surface charge is strongly affected by pH of the contacting solution (isoelectric point between 3 and 4) [44]. NF270 becomes more negatively charged as the pH increases before reaching a plateau at neutral pH. Next, a second experiment was designed to examine if this effect is taken into account by ROSA. Figure 9 (left) displays the NF270 ion rejection for a 10 -2 M NaCl feed at three different pH values(3, 6 and 10). This concentration was chosen to discriminate the effect of pH change from that of ionic strength. It appears from the experimental data that the rejection at 15 bar decreases from about 90 % to 50 % when decreasing the pH from 10 to 3. This result is consistent with the membrane charge inferred from the zeta potential values shown in Figure9(right). A higher membrane charge is expected to lead to a higher ion rejection in the case of a single salt due to the Donnan exclusion.

&

  '(( ) required to solve the set of equations describing the HET model. This database is built from the rejection data of neutral solutes (% ) and of representative single salts including NaCl, Na 2 SO 4 , MgSO 4 , CaCl 2 in different conditions of pH and concentration. By decomposing the feed solution in a combination of single salts, the software defines a new set of membrane parameters by mathematical interpolation according to the feed composition and pH. Calculation using the HET model then enables Nanoflux ® to predict membrane performance in terms of flux and ion rejection. For instance, Table

For

  example, Figures 10 and 11 present the comparison between the simulation curves given by Nanoflux ® for the ion rejection in the case of Feed 1 using NF270 and NF90 and those for Feed 3 using NF90, respectively. As can be seen, the experimental rejections of the five ions (Na + , Cl -, SO 4 2-, Ca 2+ and Mg 2+ ) are well fitted by the modeling enabling a reliable assessment of membrane performance in all cases studied.

Figure 10 .

 10 Figure 10. Ion rejections as a function of permeate flux for Feed 1 nanofiltered by NF270 (left) and by NF90 (right). Solid curves are simulation results obtained with Nanoflux ® and symbols the experimental results.

Figure 11 .

 11 Figure 11. Ion rejections as a function of permeate flux for Feed 3 nanofiltered by NF90. Solid curves are simulation results obtained with Nanoflux ® and symbols the experimental results.

Table 2 :

 2 Physicochemical parameters of 3 brackish groundwaters found in the south of Tunisia compared with the Tunisian standards for drinking water.

	Parameters	Sfax well 1	Sfax well 2	Gabés	Tunisian standards
				(Feed 1)	(Feed 2)	(Feed 3)	NT 09.14 (2013) [6]
		pH	6.2	6	8	6.5 -8.5
	Na + (mg/L)	571	837	1430	200
	Cl -(mg/L)	500	1400	1900	500
	Mg 2+ (mg/L)	77	99	106	100
	Ca 2+ (mg/L)	74	208	320	200
	SO 4	2-(mg/L)	1000	793	1450	500
	HCO 3	-(mg/L)	-	-	188	-
	Salinity of
	simulated solutions	2222	3337	5394	]200 -2000[
	(mg/L)

Table 2

 2

) by only 10 %. However, it contains high concentrations of sodium and sulfate ions with values that exceed the norms by 65 and 50 %, respectively. Feed 2 has intermediate salinity (3337 mg/L) with high concentrations of sodium, chloride and sulfate exceeding the standards by approximately 76 %, 64 % and 37 %

Table 3 :

 3 Membrane

	Membrane	Feed 1		Feed 2		Feed 1/Feed 2
		Permeability	! # $	Permeability	! # $	Permeability	Rejection
						decrease	decrease
		(L.m -2 .h -1 .bar)	%	(L.m -2 .h -1 .bar)	%	%	%
	NF270	14.3	75.7	13.7	55.3	4	29
	NF90	7.4	97.1	6.2	93.8	17	4

permeability and salinity rejection at 10 bar for filtration of Feed 1and Feed 2 using the NF90 and NF270 membranes.

Table 4 :

 4 Ion composition of permeates and productivity at 6 bar (NF270) and 10 bar (NF90). Not complying with the Tunisian standards for drinking water.

			SO 4	2-	Cl -	Mg 2+	Ca 2+	Na +	Salinity	Permeate	Recovery
			mg/L	mg/L	mg/L	mg/L	mg/L	mg/L	flow rate	(%)
										L/h.m -2
	NF270	Feed 1 55.4 Feed 2 24.8 1207 * 15.2 46.8 433 * 384 9 11.2 245.7	705.3 1727	85.6 83.2	18 17.5
	NF90	Feed 1	5.7	37	0.58 0.67	21	65 *	71	15.6
		Feed 2	2.9	137	0.52	2.4	59	201	56	13.1

*

Table 5 :

 5 Parameters of permeates and productivity for treatment of Feed 3 at 10 and 14 bar.

		Applied	Cl -	Na +	Salinity	Permeate	Recovery
		Pressure	mg/L	mg/L	mg/L	flow rate	(%)
						L/h.m -2
	NF90	10	104	64	200	48	10.1
		14	58.6	41.7	135	72.2	15.2
	BW30	10	57	34	99*	21	4.4
		14	43.7	37	77.2*	32.8	6.9

* Not complying with the Tunisian standards for drinking water.

Table 6 :

 6 Parameters determined by Nanoflux ® for the modeling performance of the studied NF membranes as a function of the used feed solutions.

			NF270			NF90
		%		& '((	%		& '((
		(nm)		(µm)	(nm)		(µm)
	Feed 1	0.525	-1.245	3.167	0.42	-46.63	8.92
	Feed 2	0.525	-0.748	13.84	0.42	-22.45	21.0
	Feed 3	-	-	-	0.42	-30.00	35.0

List of symbols:

A Membrane area, (m 2 )