Smaher E Butt

Mirdyul Das

Jean-Marc Sotiropoulos

Wesley J Moran
email: w.j.moran@hud.ac.uk

Computationally Assisted Mechanistic Investigation into Hypervalent Iodine Catalysis: Cyclization of N-Allylbenzamide

Previous experimental work identified 2-iodoanisole as the best precatalyst for the oxidative cyclization of N-alkenylamides into 2-oxazolines. Herein, we describe our investigation into the effect on reaction rate based on the structure of the iodoarene precatalyst. We also reveal the mechanism of the cyclisation based on DFT modelling and obtain a clear correlation between observed reaction rates and computationally derived activation energies for different iodoarenes.

In addition, the rate-limiting step is shown to be the cyclization of the substrate which is zero order in the concentration of the iodoarene precatalyst. The rate of the cyclization is found to correlate with the ease of oxidation of the iodoarene, however the most easily oxidized iodoarenes generate iodine(III) species that decompose readily. Finally, loss of iodoarene from the cyclized intermediate can proceed by either ligand-coupling or SN2 displacement (reductive elimination), and this is shown to be substrate dependent.

INTRODUCTION

Hypervalent iodine chemistry has continued to receive considerable attention from synthetic practitioners over the past decades with a wide variety of useful reactivities revealed. [START_REF] Grelier | Hypervalent organoiodine compounds: from reagents to valuable building blocks in synthesis[END_REF] Hypervalent iodine compounds can possess reactivity profiles comparable to some heavy metal and transition metal complexes but may not suffer from disadvantages such as toxicity, cost or scarcity. In particular, the ability to access reactive  3 -iodanes in-situ from iodoarenes and an oxidant has permitted the discovery of a range of reactions that are catalytic in iodoarene. [START_REF] Yusubov | Iodine catalysis: A green alternative to transition metals in organic chemistry and technology[END_REF] This is especially important as the preparation and isolation of  3 -iodanes is problematic in many cases and often requires considerable experimental investigation to identify suitable conditions. [START_REF] Antien | Synthesis of [7]Helicene Enantiomers and Exploratory Study of Their Conversion into Helically Chiral Iodoarenes and Iodanes[END_REF] As such, the insitu generation and reaction of  3 -iodanes can be advantageous as isolation is avoided and, of course, allows catalytic applications.

Fuchigami reported in 1994 that 4-iodoanisole can be used in as little as 5 mol% to catalyze the gem-difluorination of dithioketals in an electrochemical cell. 4 However, the first examples of iodoarene catalysis are often ascribed to the two groups of Ochiai and Kita who simultaneously published their studies in 2005. Ochiai described the iodobenzene-catalyzed -acetoxylation of ketones employing m-chloroperbenzoic acid as the stoichiometric oxidant. 5 Four other iodoarene precatalysts were investigated in this study but these were all found to give similar or inferior yields of product (67% with p-methoxy-, 84% with p-methyl-, 81% with p-chloro-, and 58% with p-nitroiodobenzene); however, there is no mention of the effect on the rate of the reaction. Kita and co-workers reported the spirocyclization of phenols using as little as 1 mol% of hypervalent iodine reagent with m-chloroperbenzoic acid as the re-oxidant. 6 Later, Li and co-workers investigated the syn-diacetoxylation of alkenes catalyzed by six different iodoarenes and discovered that iodomesitylene provided the highest yields and diastereoselectivities (Scheme 1a). [START_REF] Zhong | Metal-Free, Organocatalytic Syn Diacetoxylation of Alkenes[END_REF] Similarly, Zhdankin demonstrated that 5-iodo-m-xylene was superior to four other iodoarenes in the conversion of oximes into nitrile oxides. [START_REF] Yoshimura | Hypervalent Iodine Catalyzed Generation of Nitrile Oxides from Oximes and their Cycloaddition with Alkenes or Alkynes[END_REF] Murphy described an iodoarene-catalyzed intramolecular alkene arylation strategy to access polycyclic aromatic hydrocarbons which was superior with 4-iodotoluene rather than iodobenzene, 4-iodoanisole or 1-iodo-4-nitrobenzene (Scheme 1b). [START_REF] Zhao | Iodoarene-Catalyzed Intramolecular Alkene Arylation for the Synthesis of Polycyclic Aromatic Hydrocarbons[END_REF]

Scheme 1. Effect of iodoarene substitution on reaction outcomes

In this regard, we reported that 2-iodoanisole is a superior precatalyst for the oxidative cyclization of N-alkenylamides such as 1 into 2-oxazolines 2 compared to several other iodoarenes (Scheme 1c). [START_REF] Alhalib | Iodoarene-Catalyzed Cyclizations of Unsaturated Amides[END_REF] We also discovered that the cyclization of N-propargyl amides and -amidoketones performed better with 2-iodoanisole as the precatalyst compared to iodobenzene. [START_REF] Kamouka | Iodoarene-catalyzed cyclizations of N-propargylamides and amidoketones: synthesis of 2-oxazolines[END_REF] We were interested in investigating the mechanism of our cyclization of N-alkenylamides using kinetic and computational techniques, especially as relatively few such studies of hypervalent iodine reactions have been reported to date. [START_REF] Sreenithya | Hypercoordinate Iodine(III) Promoted Reaction and Catalysis: An Update on Current Mechanistic Understanding[END_REF][START_REF] Ganji | A. DFT Mechanistic Investigation Into Phenol Dearomatization Mediated by an Iodine(III) Reagent[END_REF] Of crucial importance to our study, was the determination of the reasons behind the different reaction outcomes with iodoarene precatalyst variation.

Houk, Xue and co-workers recently published a computational study on the mechanism and origins of chemo-and stereoselectivities in the chiral iodoarene-catalyzed difluorination of styrenes. 14 This report is a tour de force in rationalizing the reasons for enantioselectivies in the difluorination reaction but does not consider the initial iodoarene oxidation. Indeed, the authors state that "the overall activation free energy of 18.9 kcal/mol is not consistent with the 60 h reaction times required experimentally." Studying the early part of the reaction mechanism is critical for our study as we are interested in understanding the generation and catalytic properties of the hypervalent iodine species involved.

RESULTS AND DISCUSSION

Model Reaction, Initial Rate Data and Proposed Catalytic Cycle. We initiated our study by investigating the rate of cyclization of N-allylbenzamide 1 using different iodoarene precatalysts under our standard reaction conditions of 1.5 equivalents of Selectfluor as oxidant, 1.5 equivalents of trifluoroacetic acid (TFA) in acetonitrile at room temperature, ~20 o C (Scheme 2).

We saw a clear and substantial difference in initial rates between different precatalysts as well as marked variation in final yields of products. With iodobenzene 4 as precatalyst, the initial rate was just 5.16 x 10 -6 s -1 meaning that 50% conversion of starting material took 52 hours. Employing 2-iodotoluene 5 led to a somewhat faster reaction; however, the presence of the electron-withdrawing p-nitro group in 6 dramatically reduced the rate. The electron-donating omethoxy and p-methoxy groups in 2-iodoanisole 7 and 4-iodoanisole 8 respectively led to significantly increased rates. The presence of the second o-methoxy substituents in 9 had a detrimental effect on the rate of cyclization compared to 7, which was somewhat countered by the ester in the para-position of iodoarene 10. Most important from a synthetic standpoint is that the use of 2-iodoanisole led to the highest yield of oxazoline 2 after purification, in accord with our previous observations. Scheme 2. Initial rates for conversion of N-allylbenzamide 1 into oxazoline 3 with iodoarene precatalysts 4-10, determined by [START_REF] Grelier | Hypervalent organoiodine compounds: from reagents to valuable building blocks in synthesis[END_REF]

H NMR analysis

In order to determine the order of the reaction with respect to the iodoarene concentration, we carried out the Variable Time Normalization Analysis (VTNA), which involved changing the initial quantity of 2-iodoanisole 7 and monitoring the rate of reaction by NMR analysis. [START_REF] Burés | A Simple Graphical Method to Determine the Order in Catalyst[END_REF] The profiles of reactions performed with different catalyst loadings are plotted on a normalized time scale, t[cat]T n , against the concentration of the substrate 1. The best fit of the data led to the conclusion that the reaction is zero order in 2-iodoanisole 7 (Scheme 3). This unusual finding is in accord with our previous experimental findings during reaction optimization but it does not help to rationalize the relatively high catalyst loadings required for acceptable yields of products.

A reaction which is zero order in catalyst is one where the catalyst is fully saturated in substrate(s) and this is more common in photochemical reactions, [START_REF] Toby | Does a Photochemical Reaction Have a Kinetic Order[END_REF] or heterogeneous catalysis. [START_REF] Lin | Asymmetric cycloetherification based on a chiral auxiliary for 4-acyloxy-1-butene substrates during oxidation with iodosylbenzene via a 1,3-dioxan-2-yl cation[END_REF] In our case, this finding can be rationalized by consideration of the NMR spectra obtained during the kinetic experiments, as only the iodoarenes were observed in their initial concentrations. That is, no  3 -iodanes were observed by NMR analysis during the course of the reactions. This suggested that the concentration of  3 -iodane in the reaction mixture was very low and upon formation by oxidation of an iodoarene, the  3 -iodane initiated the reaction sequence. In addition,  3 -iodanes tend to have low solubility (especially compared to the precursor iodoarenes), therefore the reaction could be occurring in a heterogeneous fashion; indeed, precipitation occurs during the course of these reactions.

Scheme 3. Determination of reaction order with respect to concentration of 2-iodoanisole 7

The mechanism proposed in the original study involved oxidation of the iodoarene precatalyst to the iodine(III) species, which coordinated to the alkene of N-allylbenzamide 1 and activated it to intramolecular attack by the amide oxygen forming intermediate 11 (Scheme 4). Loss of a proton and displacement of the iodonium by trifluoroacetate formed the final product 3. It was found that some of the trifluoroacetate esters 3 were unstable to chromatographic purification, therefore saponification to the alcohol 2 was performed during workup. It was anticipated that trifluoroacetate would be bound to the iodine(III) center during the course of the reaction, but fluoride was also present in solution. Similar reaction mechanisms have been proposed for other cyclizations of alkene substrates with hypervalent iodine compounds. 18 Scheme 4. Proposed mechanism for the iodoarene-catalyzed cyclization of N-allylbenzamides 1

At this point we decided to study the reaction mechanism computationally to help rationalize the differences in rates observed with different iodoarenes precatalysts with the intention to use the knowledge gained to identify superior precatalysts.

Mechanism of Iodoarene-Catalyzed Cyclization of N-allylbenzamide 1.

We began our modelling of the reaction mechanism by ignoring the initial oxidation of the iodoarene, like other published studies, and started with bis(trifluoroacetoxy)iodobenzene 12, which should be formed under the reaction conditions (Figure 1). Loss of a trifluoroacetate ligand from 12 to form 13 followed by formation of activated alkene complex 14, i.e. a dissociative mechanism, was found to be possible but of high energy. In contrast, an associative mechanism whereby a trifluoroacetate ligand formed a hydrogen-bond with the incoming amide and underwent a concerted rotation-coordination process was of lower energy, i.e. formation of intermediate 15a via TS[14-15a]. However, the barrier was further reduced to 21.3 kcal mol -1 when an extra molecule of trifluoroacetic acid was involved in the alkene activation i.e., TS[14-15b], leading to the intermediate 15b. Cyclization of 15b (and 15a) proceeded through TS[15-16], which was higher in energy by 4.7 kcal mol -1 , to form iodonium 16. Loss of a proton formed oxazoline 17 which was then converted to the final product 3 with loss of iodobenzene 4. Two possible mechanisms were envisaged here: ligand coupling and SN2 displacement, the latter of which can also be termed reductive elimination. Modelling revealed that the SN2 process would proceed through TS[17-3]S which is 5 kcal mol -1 lower in energy than the corresponding ligand coupling transition state TS[17-3]LC. Attempts to model the reaction mechanism with  3 -iodanes bearing fluoride ligands were unsuccessful. [START_REF]cyclization reaction occurred with pre-formed bis(trifluoroacetoxy)iodoarene without any fluorine sources present in the reaction mixture[END_REF] Attempts to find mechanistic pathways involving cisaddition to the alkene were also not fruitful. The optimized geometries of all structures in the calculated mechanism conformed to our expectations with all bond lengths and angles being as anticipated (Figure 2). Importantly, the whole mechanistic pathway has been connected by IRC (intrinsic reaction coordinate) calculations (see SI for details). The modelling of the TS[15-16] transition state for each iodoarene proceeded as expected, however the presence of a substituent in the 2-position led to two diastereomeric transition states.

For example, with 2-iodoanisole the two diastereomeric transition states 18a and 18b had an energy difference of 1.3 kcal mol -1 (Figure 3). Comparing the experimentally determined initial rates with the computationally derived free energy values for the rate-limiting step showed a good match for all of the iodoarenes studied (Table 1). The data suggested that installing an electron-withdrawing group para to the iodine led to a raising of the activation energy and a lowering of the rate (entry 3) whereas an electrondonating group in the ortho or para position lowered the activation energy and increased the rate (entries 4 and 5). Interestingly, having two ortho-methoxy groups did not lead to an additive effect and the activation energy was similar to having a single methoxy group in the ortho or para position (entry 6 versus entries 4 and 5). The only outlier was iodoarene 10 which performed worse than anticipated from its calculated value (entry 7). transition state energies than 2-iodoanisole. The oxidation of the iodoarene to the  3 -iodane had been ignored up to this point in our computations as it was presumed to be complex with several discrete mechanistic steps. However, our hypothesis was that more easily oxidized iodoarenes correlated with lower transition state energies and faster reaction rates. Accordingly, the oxidation potential was computed for our studied iodoarenes using the method described by Nicewicz and coworkers. 20 These values were compared with the experimental rate values and a clear correlation was observed, confirming our hypothesis (Figure 4). In addition, the experimental rate values were shown to be proportional to the corresponding calculated HOMO energies of the iodoarenes. With this correlation confirmed, the identities of iodoarenes with lower oxidation potentials were sought as these were envisaged to lead to superior catalysts. 1-Iodo-2,4-dimethoxybenzene 19 and 2-iodo-1,3,5-trimethoxybenzene 20 were quickly identified as being more easily oxidized and their oxidation potentials were calculated to be 1.40 V and 1.34 V respectively. Unfortunately, kinetic experiments with these precatalysts in our cyclization reaction indicated that the reactions were somewhat slower than when using 2-iodoanisole 7 as the precatalyst and, crucially, the yields of product were only 20-30%. Furthermore, the iodoarenes 19 and 20 disappeared during the course of the reactions.

In order to probe the oxidation of the iodoarenes, the rate of oxidation by Selectfluor was monitored by 1 H NMR analysis (Scheme 5). Iodobenzene 4, 2-iodotoluene 5 and ester 10 required about 24 hours to reach full conversion to the  3 -iodane (entries 1, 2 and 3). 2-Iodoanisole 7 was fully oxidized in about 14 hours (entry 4) and 4-iodoanisole 8 was slightly quicker (entry 5).

However, 1-iodo-2,4-dimethoxybenzene 19 and 2-iodo-1,3,5-trimethoxybenzene 20 were completely consumed by the oxidant but no products were evident by NMR analysis (entries 6 and 7). It is known that 1,3,5-trimethoxybenzene decomposes under electrolysis in aqueous sulfuric acid to generate carboxylic acids, carbon dioxide and water. [START_REF] Hamza | Electrochemical oxidation of 1,3,5-trimethoxybenzene in aqueous solutions at gold oxide and lead dioxide electrodes[END_REF] It appears that iodoarenes 19 and 20 undergo a similar decomposition process under our reaction conditions on a slightly faster time scale to the desired cyclization which accounts for the low chemical yields of 2-oxazoline obtained.

Fujita and co-workers discovered that 2-iodo-1,3-dimethoxybenzene 9 can combine with its oxidized form, i.e. 2-(diacetoxyiodo)-1,3-dimethoxybenzene, under acidic conditions to generate a diaryliodonium salt; this side-reaction was proposed to be the cause of the relatively low yield of product using 9 as a pre-catalyst in an oxylactonization reaction. [START_REF] Shimogaki | Enantioselective Oxidation of Alkenylbenzoates Catalyzed by Chiral Hypervalent Iodine(III) To Yield 4-Hydroxyisochroman-1-ones[END_REF] Scheme 5. Monitoring of the oxidation of iodoarenes by 1 H NMR Minor modifications to 2-iodoanisole 7 (still our optimal precatalyst) could be investigated to identify a slightly more efficient catalytic system, however these analogs would probably not be commercially available and, so, would be of little impact. 1-Iodo-2,4-dimethoxybenzene 19 could be a highly efficient precatalyst in other hypervalent iodine mediated processes that occur on a faster timescale than its decomposition; however, not being able to recover the iodoarene is a disadvantage.

Interestingly, the experimentally derived initial rate of cyclization catalyzed by iodoarene 10 matches well with the calculated oxidation potential and HOMO energy but not with the calculated activation energy value (vide supra). This suggests that there was a change in the rate determining step with this iodoarene from the cyclization event to the iodoarene oxidation. Indeed, the rate of oxidation of 10 was comparable with that of iodobenzene 4.

Displacement of Iodoarene by Ligand Coupling or SN2 Displacement. In our original report, cyclization of cis-alkene 21 was reported to lead to formation of product 2 as only one diastereomer; with the relative stereochemistry being assigned by NMR analysis. [START_REF] Zhao | Iodoarene-Catalyzed Intramolecular Alkene Arylation for the Synthesis of Polycyclic Aromatic Hydrocarbons[END_REF] Applying the calculated mechanism for N-allylamide 1 to the cyclization of 21 suggested that the all-syn diastereomer 23 would be formed rather than 22. It was suspected that a change in mechanism was responsible for the observed stereochemistry of 22 due to ligand coupling being favored over SN2 displacement. This SN2 process was more difficult in this case because of the increased sterics at the secondary carbon atom bonded to the iodane compared to the primary carbon in 17.

In order to confirm this hypothesis, the cyclization of 24 was calculated using 2-iodoanisole 7 as the pre-catalyst (Scheme 6). To reduce the computational resource required, the methyl amide 24 was modelled rather than the 4-methoxyphenyl amide 21 as this was not envisaged to impact on the stereochemistry determining step.

The free energies of the cyclized structures 26 and 27 resulting from trans-addition to the alkene compare favorably with the energies of the corresponding structures 16 and 17 for the cyclization of N-allylamide 1. As previously observed, reaction pathways proceeding through cis-additions could not be found. Conversion of iodane 27 to the final product could be achieved through either SN2 displacement or ligand coupling, but, in contrast to N-allylamide, the latter pathway was favored by 3.9 kcal mol -1 resulting in a highly diastereoselective reaction. This result corroborated our stereochemical assignment of the product 22 and confirmed our hypothesis. Note that the allsyn diastereomer 29 is thermodynamically more stable than 28 but the reaction is under kinetic control. The optimized geometries are shown in Figure 5.

CONCLUSION

An in-depth analysis of the iodoarene-catalyzed cyclization of N-allylbenzamide 1 has been conducted using a combination of computational and kinetic experiments. A mechanism has been delineated which accounts for the experimental differences in rate observed with different iodoarene precatalysts and, importantly, the calculated free energy values correlate with our experimental results. The cyclization event has been shown to be rate-limiting and more electronrich iodoarenes lead to lower G ǂ values for this step. The reaction has been found to be zero order in the precatalyst 2-iodoanisole 7 but the reaction model breaks down with more electron-rich iodoarenes due to competitive decomposition. The optimal choice of precatalyst for related processes is likely to be affected by the rate of the desired reaction; i.e. if the rate of reaction is faster than decomposition then a more electron-rich precatalyst such as 1-iodo-2,4dimethoxybenzene 19 could be the best option.

Loss of iodoarene from the reaction intermediate can occur by either SN2 displacement by a nucleophile (reductive elimination) or by ligand coupling at the iodine(III) center. Both pathways are possible but SN2 displacement is favored at primary carbons whereas ligand coupling is preferred with secondary carbons.

EXPERIMENTAL SECTION

General. [START_REF] Grelier | Hypervalent organoiodine compounds: from reagents to valuable building blocks in synthesis[END_REF] H NMR spectra were recorded in ppm from tetramethylsilane with the solvent resonance as the internal standard. All purchased reagents were used as received without further purification. Compounds 1, 23 10 24 and 20 [START_REF] Heng | Designing Inhibitors Against Fructose 1,6bisphosphatase: Exploring Natural Products for Novel Inhibitor Scaffolds[END_REF] were prepared by the literature procedures and the characterization data matched the reported values.

General Procedures for Kinetic Experiments

Rate Data: Amide 1 (1 equiv) was added to a borosilicate NMR tube along with the iodoarene precatalyst (0.2 equiv), Selectfluor (1.5 equiv), TFA (1.5 equiv) and CD3CN (1 mL) to generate a 0.3 M solution of 1. The reaction mixture was monitored and the conversion of amide 1 was recorded by 1 H NMR spectroscopy (400 MHz, 298 K) for up to 24 hours at 25 ˚C. Assuming the reaction is first order in 1, the rate constant was determined by linearization of the decay curve followed by linear fitting for only the initial part of the reaction. Results are summarized in the supporting information table S1.

Effect of Catalyst Loading:

The order of the cyclization reaction with respect to 2-iodoanisole was determined by the Variable Time Normalization Analysis (VTNA) as described by Burés (Scheme 3). 14 Amide 1 (1 equiv) was added to a borosilicate NMR tube along with 2-iodoanisole (10 & 30 mol%), Selectfluor (1.5 equiv), TFA (1.5 equiv) and CD3CN (1 mL). The reaction mixture was monitored by 1 H NMR spectroscopy (400 MHz, 298 K) to study the effect of different catalyst loadings. The concentration of 1 was recorded for a period of 40 hours and plotted against a normalized time scale t[cat]T n ; calculated by multiplying each time point by the total concentration of catalyst used in each experiment raised to an arbitrary power. The power value was adjusted to be zero as that produced the overlay of the curves (Scheme 3). The numerical data, along with the concentration of 1 at specific times, are listed in the supporting information.

Computational Methods: Quantum chemical calculations were performed using Gaussian 09, 26 and GaussView was used for molecular modelling. 27 The geometry optimizations were performed in the gas phase under standard conditions using density functional theory (DFT) [START_REF] Becke | A new mixing of Hartree-Fock and Local Density Functional Theories[END_REF][START_REF] Becke | Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior[END_REF]30 in combination with the 6-31+G(d,p) [START_REF] Hariharan | The Influence of Polarization Functions on Molecular Orbital Hydrogenation Energies[END_REF] basis set for all atoms except iodine, for which the SDD [START_REF] Igel-Mann | Pseudopotentials For Main Group Elements (IIIa through VIIa)[END_REF] (Stuttgart/Dresden) effective core potential was used. All the bond lengths are given in Angstroms. Vibrational frequency calculations were performed in order to determine the imaginary frequencies for the respective molecules. The imaginary frequencies verified whether the stationary points are minima, having no imaginary frequencies, or transition states, possessing one imaginary frequency. The connectivity of the transition states was confirmed by computing IRC (intrinsic reaction coordinate) from the transition-state geometry towards both the reactant and product. [START_REF] Gonzalez | An Improved Algorithm for Reaction Path Following[END_REF][START_REF] Gonzalez | Reaction path following in mass-weighted internal coordinates[END_REF] Solvent effects were taken into account using the conductor-like polarizable continuum model (CPCM). [START_REF] Cossi | Structures, and Electronic Properties of Molecules in Solution with the C-PCM solvation Model[END_REF] Single-point calculations on the gas-phase optimized geometries were performed to estimate the change in energy in the presence of the solvent, acetonitrile. The triple-zeta quality 6-311++G(d,p) basis set along with SDD for I was used to account for the solvent effects. The Gibbs free energy values provided in the text are Gibbs energy in solution, Gsoln, calculated by using the equation Gsol = Esolv + Gnes + ΔGcorr_gas. [START_REF] Ho | Comment on the Correct Use of Continuum Solvent Models[END_REF] The sums of the electronic and thermal free energies (G) for reactants and transition states were obtained by the standard procedure in the framework of the harmonic approximation. [START_REF] Mcquarrie | Molecular Thermodynamics[END_REF] The ΔG ǂ of the reactions were calculated from the differences in the G values of the transition states and the reactants.

ASSOCIATED CONTENT

Figure 1 . 1 .

 11 Figure 1. Calculated potential energy profile for the PhI(O2CCF3)2 12-mediated cyclization of Nallylbenzamide 1. Free energies are reported in kcal mol -1 .

Figure 2 .

 2 Figure 2. Calculated geometries of intermediates and transition structures of the PhI(O2CCF3)2-

Figure 3 .

 3 Figure 3. Calculated geometries of two diastereomeric transition states 18a and 18b and the

Figure 4 .

 4 Figure 4. Correlation between calculated oxidation potentials of iodoarenes and experimental rate data derived free energies of TS[15-16]

Figure 5 .

 5 Figure 5. Optimized geometries of intermediate 27 and the ligand coupling and SN2 transition states.

Table 1 .

 1 Comparison of experimental rate data with calculated free energies of rate-limiting step Oxidation

	with different iodoarenes
	entry ArI	k / s -1	G ǂ calc /
				kcal mol -1
	1	iodobenzene 4	5.16 x 10 -6 25.1
	2	2-iodotoluene 5	7.73 x 10 -6 25.9
	3	2-iodo-5-	1.01 x 10 -6 26.0
		nitrotoluene 6
	4	2-iodoanisole 7	5.78 x 10 -5 23.4
	5	4-iodoanisole 8	7.00 x 10 -5 23.2
	6	2-iodo-1,3-	5.66 x 10 -5 23.5
		dimethoxybenzene
		9
	7	methyl 4-iodo-3,5-	5.87 x 10 -5 21.9
		dimethoxybenzoate
		10

of Iodoarenes. Computing transition state energies is computationally demanding, therefore we sought a simple, fast method to predict iodoarene structures with lower TS

[15-16]

Ochiai, M.; Takeuchi, Y.; Katayama, T.; Sueda, T.; Miyamoto, K. Iodobenzene-catalyzed αacetoxylation of ketones. In situ generation of hypervalent (diacyloxyiodo)benzenes using mchloroperbenzoic acid. J. Am. Chem. Soc. 2005, 127, 12244-

12245.6 Dohi, T.; Maruyama, A.; Yoshimura, M.; Morimoto, K.; Tohma, H.; Kita, Y. Versatile

Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B: Condens. Matter 1988, 37, 785.

ACKNOWLEDGMENT

We thank the University of Huddersfield for a postgraduate scholarship (SEB) and the Université de Pau et des Pays de l'Adour for access to their computer cluster. We appreciate useful discussions with Professor Andy Laws (University of Huddersfield).

Supporting Information

The following files are available free of charge. Kinetic data and computational details, including Cartesian coordinates and energies (pdf).

AUTHOR INFORMATION

Corresponding Author

*E-mail: w.j.moran@hud.ac.uk ORCID Wesley J. Moran: 0000-0002-5768-3629 Smaher Butt: 0000-0001-9861-5924

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Notes

The authors declare no competing financial interests.


I Ben Ali

M Turki

J Belhadj
email: jamel.belhadj@esstt.rnu.tn

X Roboam

Systemic Design and Energy Management of a Standalone Battery-less PV/Wind driven Brackish Water Reverse Osmosis Desalination System

Keywords: systemic design, electrochemical and water storage, quasi-static modeling, water/power management, renewable energy

This work investigates a small-scale reverse osmosis desalination system dedicated for off-grid communities lacking freshwater. This system, constituted of motor-pumps, desalination process and hydraulic network (pipes and valves), is powered by hybrid photovoltaic-wind turbine source. It exploits hydraulic storage in water tanks filled when renewable energy is available instead of electrochemical storage. Such specificity makes the power/freshwater supply a challenging issue for these communities. To maximize freshwater production of this autonomous system, a "systemic design approach" integrating couplings between architecture, sizing, and energy management is proposed. According to the specific system architecture and its component sizing, a specific quasi-static model-based energy management strategy (EMS) is developed. In this regard, the influence of the main component sizing on the system energy efficiency and the EMS performance is analyzed. This study proved the strongly coupling between power/water management and pump sizing. According to the iterative process of the systemic design approach, simulation results showed that the EMS objective is reached by increasing the brackish water storage tank capacity and improving the system energy efficiency. The latter is achieved by choosing the pumps-combination composed of three pumps having the lowest rated powers (0.37kW/0.37kW/1.5kW), but offering higher energy efficiency over other analyzed pumps-combinations.

Introduction

Reverse osmosis (RO) desalination applications have been becoming the primary choice to produce freshwater from brackish or sea water for many water-stressed regions [START_REF] Greenlee | Reverse osmosis desalination: water sources, technology, and today's challenges[END_REF][START_REF] Ghaffour | Technical review and evaluation of the economics of water desalination: Current and future challenges for better water supply sustainability[END_REF] not only for drinking, but also for agriculture [START_REF] Burn | Desalination techniques -A review of the opportunities for desalination in agriculture[END_REF].

Typically, these applications, especially small-scale units for off-grid communities, are powered by renewable energies [START_REF] Bourouni | Design and optimization of desalination reverse osmosis plants driven by renewable energies using genetic algorithms[END_REF][START_REF] Ali | Membrane technology in renewable-energy-driven desalination[END_REF][START_REF] Abdelkareem | Recent progress in the use of renewable energy sources to power water desalination plants[END_REF]. The most commonly used renewable energies to power such desalination units are the solar energy [START_REF] Ahmed | Solar powered desalination -Technology, energy and future outlook[END_REF][START_REF] Ghafoor | Techno-economic feasibility of solar based desalination through reverse osmosis[END_REF] and the wind energy [START_REF] Loutatidou | Wind-powered desalination for strategic water storage: Technoeconomic assessment of concept[END_REF][START_REF] Khan | A hybrid renewable energy system as a potential energy source for water desalination using reverse osmosis: A review[END_REF]. For example, according to the comprehensive review and the techno-economic feasibility carried out, respectively, in [START_REF] Ghaffour | Renewable energy-driven desalination technologies: A comprehensive review on challenges and potential applications of integrated systems[END_REF] and [START_REF] Ghafoor | Techno-economic feasibility of solar based desalination through reverse osmosis[END_REF], photovoltaic PV-RO desalination systems are considered better than other desalination combinations due to their availability in the market and economic feasibility; this has encouraged poor farmers in rural regions to use these systems to produce freshwater. Another technoeconomic analysis of several wind-driven variable flow RO systems in United Arab Emirates was conducted [START_REF] Loutatidou | Wind-powered desalination for strategic water storage: Technoeconomic assessment of concept[END_REF]. This analysis concluded that Wind-RO combination is an economic alternative to produce freshwater. However, although wind and solar energies are the most widespread and environmentally friendly Renewable Energy Sources (RESs) worldwide, both are of variable and intermittent nature due to unpredictable and rough changes in weather conditions (e.g. simultaneous cloudy sky or wind speed slowing down). For that, using single RES cannot always meet the electrical demand of the RO plant during the day [START_REF] Jurasza | A review on the complementarity of renewable energy sources: Concept, metrics, application and future research directions[END_REF].

Hybrid power generation systems, such as solar PV panels combined with wind turbine [START_REF] Khan | A hybrid renewable energy system as a potential energy source for water desalination using reverse osmosis: A review[END_REF], are becoming more suitable with the advantage that one RES could be available when the other is not [START_REF] Abdelkareem | Recent progress in the use of renewable energy sources to power water desalination plants[END_REF]. Such a temporal complementarity will increase the reliability and improve the environmental aspect of the desalination system [START_REF] Jurasza | A review on the complementarity of renewable energy sources: Concept, metrics, application and future research directions[END_REF]. On the other hand, standalone RO systems can be powered by different combinations of renewable energy sources (e.g. PV-RO, Wind-RO and PV/Wind-RO) with one or more energy storage device, such as batteries [START_REF] Khan | A hybrid renewable energy system as a potential energy source for water desalination using reverse osmosis: A review[END_REF],

super capacitors [START_REF] Soric | Eausmose project desalination by reverse osmosis and batteryless solar energy: Design for a 1 m 3 per day delivery[END_REF], fuel cell [START_REF] Clarke | Multi-objective optimization of renewable hybrid energy systems with desalination[END_REF][START_REF] Maleki | Design of a cost-effective wind/photovoltaic/hydrogen energy system for supplying a desalination unit by a heuristic approach[END_REF], and diesel generator backup [START_REF] Khalifa | Evaluation of different hybrid power scenarios to Reverse Osmosis (RO) desalination units in isolated areas in Iraq[END_REF]. A summary of different studied standalone small-scale RES-brackish water RO units in different sites around the world is reported in Table1. a major concern [START_REF] Al-Nory | An energy management approach for renewable energy integration with power generation and water desalination[END_REF], especially for remote and poverty areas. Therefore, minimizing or even suppressing the energy storage device such as electrochemical storage means is a challenging issue facing such standalone desalination systems, especially in the light of continuous freshwater supply.

In case of RES-RO desalination system without batteries, freshwater will be produced by a variable and discontinuously operated desalination system. That is, RO membrane will operate under variable feed pressure. It has been demonstrated that the operation of the RO membrane under variable power supply remains unaffected [START_REF] Richards | Renewable energy powered membrane technology: Impact of solar irradiance fluctuations on performance of a brackish water reverse osmosis system[END_REF][START_REF] Freire-Gormaly | Experimental quantification of the effect of intermittent operation on membrane performance of solar-powered reverse osmosis desalination systems[END_REF]. Moreover, several studies at the laboratory scale have demonstrated the possibility of operating RES-RO desalination units without battery storage device [START_REF] Mohamed | A direct coupled photovoltaic seawater reverse osmosis desalination system toward battery based systems -a technical and economical experimental comparative study[END_REF][START_REF] Riffel | Small-scale photovoltaic-powered reverse osmosis plant without batteries: design and simulation[END_REF][START_REF] Thomson | Laboratory demonstration of a photovoltaic-powered seawater reverse osmosis system without batteries[END_REF]. Another study concluded that it is possible to completely eliminate batteries in PV-RO systems; it needs to automatically adjust the operating point of the RO-pump with fluctuating solar energy [START_REF] Bilton | Photovoltaic reverse osmosis -Feasibility and a pathway to develop technology[END_REF]. An economic analysis was also conducted in [START_REF] Bilal | The Economic Analysis of Portable PhotoVoltaic Reverse Osmosis (PVRO) System[END_REF] for PV-RO system with and without battery, where results demonstrated that battery-less PV-RO system is more economically suitable than that using battery storage. A comprehensive review of desalination technologies powered by solar energy including solar PV-RO desalination systems without batteries was conducted in [START_REF] Sharon | A review of solar energy driven desalination technologies[END_REF]. It is concluded that coupling RO and PV systems is relatively straightforward, especially for small-scale units.

Another option to reduce the capital cost is to store water in a storage tank such as the example of using buffer tank for freshwater storage [30] [45]. Such an alternative enables to minimize the needed number of batteries and overcome the challenge of longer-term renewable energy variation. In ref. [START_REF] Kumarasamy | Optimal operation of battery-less solar powered reverse osmosis plant for desalination[END_REF], authors showed that the system productivity increased up to 36% by storing produced freshwater. It was demonstrated that a buffer tank can be considered as a surrogate energy storage device. The concept is that the generated renewable energy during sunny and/or windy days is a stored energy in the form of water. This can be considered very cost-effective and environmentally friendly alternative compared with RES-RO units using battery banks or diesel generator backup.

In this context, a focus on a standalone small-scale Brackish Water Reverse Osmosis (BWRO) desalination system in rural area is put forward in this paper. This system is powered by hybrid PV/Wind turbine source without electrochemical storage device, but exploiting hydraulic storage (brackish water and freshwater) in storage tanks. The idea is: i) to take advantage of storing the well brackish water and the produced freshwater in tanks when renewable energy is available, and ii) to exploit motor-pumps modularity (i.e. several pumping subsystems that can be switched on/off and tuned) versus the given generated power. For this sake, an experimental BWRO desalination unit at the laboratory scale (freshwater production of 300 liters/h) using an elevated brackish water storage tank was designed and mounted to investigate the feasibility and reliability of PV/Wind-BWRO desalination system in rural areas. A second storage tank is also used in this unit to store the produced freshwater, for later use when renewable energy is unavailable.

To overcome the variable and discontinuously operated PV/Wind-BWRO unit, a specific energy (power and water flows) management is then required in order to manage simultaneously power and water flows into the desalination system while fulfilling technological (power and pressure ranges) and functional (tank filling state) constraints of the system. The energy management strategy to be developed must take into consideration the strongly coupled system design: "water/power management and device sizing". In particular, the generated power from RESs is strongly coupled with the water process system efficiency. In addition to that, the coupling between sizing and management performance is of a paramount importance in this study. Therefore, it is mandatory to study the sizing of pumps and the different pump-combinations in the desalination system to get an optimal system design enabling to maximize as much as possible the freshwater production according to the available generated power. All of these aspects put forward the necessity of a "systemic design approach" integrating the strong coupling between architecture (modularity), sizing and flow (power, water) management. In this regard, authors in ref. [START_REF] Roboam | Optimal system management of a water pumping and desalination process supplied with intermittent renewable sources[END_REF] have investigated a global optimization approach taking account of the couplings between the system architecture, sizing and energy management. They proposed an optimization dispatching algorithm for sharing the variable input power between the three installed motor-pumps: the choice of the objective function for the optimization algorithm to evaluate the operating efficiency has been justified. The influence of the pump sizing on the system efficiency has been also analyzed.

This paper proposes a first design approach based on specific modeling and management strategy. It primarily aims to maximize as much as possible the water production of the system according to the renewable energy generation. First, a quasi-static modeling stemming from dynamic modeling of the experimental BWRO desalination test bench is developed for simulations. In order to validate the developed model, the latter is compared with the experimental model obtained from experimental characterizations of the BWRO test bench.

Then, an energy management strategy is developed using Deterministic Rule-based power sharing algorithm.

Such algorithm should conveniently dispatch the instantaneous generated power between the different water process subsystems into the studied system while taking into consideration: i) the aforementioned system constraints, and ii) the objective of maximizing freshwater production. For the sake of optimality, the sizing influence of both pump combinations and brackish water storage tank capacity on the energy management performance is then analyzed. As regards the capacity sizing of the freshwater storage tank, it is not studied during simulations and analysis, since it is viewed as an infinite storage tank (in simulations) aiming to store a maximum amount of produced freshwater.

This paper is organized as follows: the architecture and specifications of the BWRO desalination system are described in Section 2. The adopted systemic design approach is defined in Section 3. The analytical modeling of the studied system is detailed in Section 4. The EMS is described in Section 5. Section 6 is dedicated to analyze the simulation results. In this Section the influence of pumps and tank capacity sizing on the energy management performance are investigated and analyzed. Finally, main conclusions and prospects are summarized in Section 7.

Nomenclature

Acronyms

Description of the BWRO desalination system

System architecture overview

The studied system, depicted in Fig. 1, consists of small-scale standalone brackish water pumping and desalination unit. It is mainly composed of two hydro-mechanical subsystems:

1) "Water Pumping Process" that uses well Pump(s) (WP) to pump brackish water from the well to an elevated storage tank T1. This process is dedicated for gravitational brackish water storage.

2) "Reverse Osmosis (RO) Desalination Process" enabling to produce freshwater using a RO membrane(s) fed by a High Pressure Pump (HPP). The HPP exploits the stored amount of brackish water in the tank T1

to feed the RO membranes under high pressure. The produced freshwater is stored in the tank T2.

This unit would be powered via a Direct Current (DC) bus with a variable generated power Pdc offered along wind speed and solar irradiation conditions (PV/Wind turbine) without battery storage.

The hydraulic architecture of the desalination system depicted in Fig. 2 is defined so that the desalination system includes two independent hydraulic subsystems decoupled through the elevated water storage tank T1. The latter presents the first key element of the chosen architecture. In other words, pumped brackish water from the well can be stored into the elevated tank T1, when renewable energy is available, for later or simultaneous use by the RO desalination process to produce freshwater. The latter in turn is stored in high capacity tank T2, for later use when the renewable energy is unavailable. This constitutes the second key element of the system architecture.

Therefore, the electrochemical storage device can be replaced by hydraulic storage (brackish water and freshwater) in water tanks.

Experimental test bench

An experimental test bench, shown in Fig. 3, was designed and mounted in our research laboratory (L.S.E in ENIT-UTM, Tunis, Tunisia). The synoptic scheme of the experimental test bench is depicted in Fig. 4. The specifications of the presented test bench are reported in Table 2. This experimental unit is used for the experimental characterizations of the hydro-mechanical processes in order to validate the system model. Indeed, the two hydro-mechanical processes have been experimentally characterized and dynamically modeled in previous studies [START_REF] Khiari | Experimental prototype of reverse osmosis desalination system powered by intermittent renewable source without electrochemical storage: Design and characterization for energy-water management[END_REF][START_REF] Ali | Systemic design of a reverse osmosis desalination process powered by hybrid energy system: Bond graph modeling approach & experimental validation[END_REF][START_REF] Ali | Energy management of reverse osmosis desalination process powered by a hybrid renewable energy source[END_REF][START_REF] Khiari | Robust DC-bus voltage control for batteryless brackish water reverse osmosis desalination prototype operating with variable wind and solar irradiation[END_REF].

Based on the dynamic modeling of hydro-mechanical processes of the presented RO unit, a quasi-static modeling is developed for energy management which is described in Section 4. Inferior minimum limit level Lmin Inf : 0.2 m Superior minimum limit level Lmin Sup : 0.25 m Inferior maximum limit level Lmax Inf : 1.9 m Superior maximum limit level Lmax Sup : 2 m

Well motor

Characteristic specificity of the chosen architecture

Due to the hydraulic processes decoupling, the system has more degrees of freedom than conventional used architecture where motor-pumps are usually coupled in series (without brackish water storage tank). In fact, the system can independently operate as: i) "pumping system" by operating solely the water pumping process in case of low level of generated power, or ii) "RO desalination system" by operating solely the RO desalination process in case of high level of generated power, or also iii) "pumping and RO desalination system" in case of very high level of generated power. In the latter operating mode, the two hydraulic processes operate simultaneously to pump brackish water from the well to fill the storage tank and, in the same time, produce freshwater using the pumped brackish water from T1. Indeed, this configuration offers a great flexibility for the experimental characterization of each hydro-mechanical process.

Within this hydraulic configuration, the "gravitational water storage" involves an advantage of great importance in terms of energy efficiency improvement; this fact enables to take benefit of an additional free hydraulic energy boosting the RO desalination energy efficiency. As a result, freshwater productivity can be improved. This point has been highlighted in previous work [START_REF] Ali | Optimized Fuzzy Rule-based Energy Management for a Battery-less PV/Wind-BWRO Desalination System[END_REF]. Moreover, besides the advantage of being environmentally friendly, another advantage of using hydraulic storage over electrochemical storage device is the simplicity of such a configuration (no need to control laws), as well as it offers lower cost alternative (no need to additional power converters for control and no maintenance requirements).

On the other hand, the studied system is classified among complex energy systems. Its complexity is characterized by the combination of components of different natures and functionalities, all interacted within the system under study. Such heterogeneity leads to several physical phenomena coexistence, and several system constraints of different domains. These constraints can be listed as: i) functioning under variable energy supply (i.e. variable feeding power and pressures), ii) technological constraints of pumping devices (power ranges) and RO membrane (flow-pressure range), and iii) functioning constraints (i.e. filling state of the storage tank). This makes the modeling and the flow (power, water) management of the system a difficult task.

Given the diversification of the system constraints, it becomes necessary to move towards a new approach permitting to connect all system components by integrating "intra"-and "inter-disciplinary" coupling. This methodology is based on the "systemic design approach" [START_REF] Roboam | Systemic design methodologies for electrical energy systems: analysis, synthesis and management[END_REF] described in the following section.

Definition of the systemic design approach

The adopted systemic design approach is described in Fig. 5. It relies on the choice of: i) architecture and components, ii) sizing, and iii) development of control/management process. The design has to meet requirements defined by the bill of specifications. This consititutes a fundamental and preliminary step for the designer. Therefore, satisfying the bill of specifications needs a "synthesis" (i.e. structure determination) and "sizing" (i.e. parameters determination) that meet: i) these requirements while anticipating by "simulation" and "analysis" (Fig. 5) of the system being designed, ii) system performance, and iii) system constraints.

The systemic design approach is an iterative process based on three main phases:

-Phase 1: the choice of the system architecture (as defined in the previous section). This allows performing the modeling and simulation of these components.

-Phase 2: the optimal pre-sizing of the system components. Such a phase allows characterizing of these elements and specifying the instantaneous energy transfers during an idealized operating cycle. This leads to understand the energy behavior of the system.

-Phase 3: the optimization of the energy flows into the system with the objective of determining the optimal energy management of the system.

Therefore, following the energy optimization and the simulation of the system behavior it may happen that the components previously chosen are oversized or undersized. For that reason, the "system sizingenergy optimization" cycle is repeated several times off-line in order to refine the system specifications. The objective here is to design a system that should be well adapted to the energy management strategy which, in turn, will be implemented on-line. For this sake, several iterations are performed in this work as part of the systemic design by testing several combinations of different sized pumps and even different storage tank capacities. At each iteration, the architecture is defined, then, the system components are characterized and modeled based on the experimental set-up. This provides deep understanding of the system energy behavior. At the end of the cycle, the proposed energy management strategy is applied to the chosen architecture, and obtained results are analyzed.  Development of a system optimal sizing tool  Exploiting this tool for techno-economic analysis of the system Objectives Fig. 5. Optimization process of a complex energy system by the systemic approach

Systemic approach

System modeling

This study focuses on the steady-state functioning of the system in order to simplify the energy management task.

The quasi-static model constitutes a "power flow model" derived from dynamic energy behavior throughout the desalination chain. Therefore, in order to develop the quasi-static model of the hydro-mechanical system, several physical fields have to be considered. As depicted in Fig. 6, it consists of the following subsystems from right to left: hydraulic load, centrifugal pump, and three phase induction motor fed and controlled by a voltage source inverter. The subsystems are linked each other by power flow variables: electrical voltage and current (Vdc, Ip), motor-pump torque and speed (Tp, Ω), and pump flow rate and pressure (Qp, Pp=ρgHMT). The HMT describes the total dynamic head (in meter) which depends on hydraulic load and pressure losses in pipelines ∆Ppipe, ρ is the water density and g is the gravity acceleration.

Hydraulic subsystems modeling

As depicted in Fig. 1 and Fig. 2, we have two different hydro-mechanical subsystems decoupled through a storage tank T1. The modeling task here depends on the hydraulic load type of each subsystem:

1) In case of typical load as for the "first water subsystem", where the water is moved from one level (the well) to another (i.e. an elevated tank) as shown in Fig. 2, a pressure drop in pipelines ΔPpipe occurs. The latter is caused by the height difference Hgeo (geodetic head that the pump must overcome), and the hydraulic losses depending on the pump water flow Qp=QWP [START_REF] Gülich | Centrifugal Pumps[END_REF][START_REF]Grundfos research and technology[END_REF]. Thus, the hydraulic load model of the first process (e.g. case of one well pump) is expressed by:

2 pipe geo WP P gH kQ     (1)
where, k is a constant.

2) The "second subsystem" is related to the water RO desalination process; it involves a complex and nonlinear hydraulic load (RO membrane + Control Valve (CV)) coupled to the HPP. The latter offers high water pressure to feed the RO membrane to produce freshwater. Based on the dynamic model of the RO membrane previously developed and detailed [START_REF] Ali | Systemic design of a reverse osmosis desalination process powered by hybrid energy system: Bond graph modeling approach & experimental validation[END_REF] and [START_REF] Turki | Bond Graph modeling and analysis of an autonomous reverse osmosis desalination process fed by a hybrid system (photovoltaic-wind)[END_REF], the static model of the RO membrane expressed by ( 3), ( 4) and ( 5) is deduced by neglecting the dynamic elements effect, with some approximations:

  2 feed mod ule valve reject P R R Q  (2) feed fresh membrane P Q R  (3) feed fresh reject Q Q Q  (4)
Where, Qfeed and Pfeed denote respectively the feed flow rate and pressure of the RO membrane, Qfresh the produced freshwater flow rate, Qreject the rejected water flow rate (very salted water), and (Rmodule, Rvalve, Rmembrane) are the RO membrane parameters whose experimental values are reported in Table 3. Indeed, hydraulic losses into the RO process via the control valve CV (Fig. 2), the RO module and the RO membrane are modeled as resistances such as Rmodule, Rvalve, Rmembrane. It should be noted that a RO module can include one or several RO membranes coupled in series. In the studied case, each module contains one RO membrane.

Based on (2), ( 3) and ( 4), the static model of the hydraulic load (i.e. RO module) of the second process is deduced and expressed by [START_REF] Ali | Membrane technology in renewable-energy-driven desalination[END_REF] with respect to Qfeed.

 

RR P R Q RR RR          (5)
According to the hydraulic structure of the desalination process depicted in Fig. 2

        (6)
Where, PHPP denotes the proper pressure given by the HPP which is expressed in the next subsection by [START_REF] Ghafoor | Techno-economic feasibility of solar based desalination through reverse osmosis[END_REF], Ptank is the resulting pressure from the stored amount of brackish water in the tank T1, Hasp and Pasp denote respectively the brackish water aspiration height and pressure of the HPP.

Storage tank modeling

A storage tank is characterized by the stored water level L. The first tank T1 is modeled by ( 7) describing a timevarying model.

) tt WP HPP t L t t L t Q t Q t dt S        1 1 ( ) ( ) ( ( ) ( )
where, S1 being the surface area of T1, and (QWP and QHPP) denote respectively the well pump and the HP pump flow rates (i.e. input and output flow rates of the tank).

Hydro-Mechanical subsystem modeling

The static model of a centrifugal pump is obtained by neglecting the dynamic elements effect from its dynamic model performed in previous work [START_REF] Ali | Systemic design of a reverse osmosis desalination process powered by hybrid energy system: Bond graph modeling approach & experimental validation[END_REF]. Thus, the static part of a centrifugal pump is modeled as follows:

    2 p p p p P ,Q a bQ cQ       (8)     p p p p p T ,Q a bQ Q f       (9)
Where, Pp being the water pump pressure, Qp the pump flow rate, Tp the pump torque, Ω the motor-pump angular speed, and fp is the coefficient of the hydraulic friction in the pump. The pump parameters (a, b, c, fp) have been experimentally identified and are reported in Table 3.

Quasi-static model of a hydro mechanical process

With regard to the three-phase Induction Motor (IM) driving the centrifugal pump, the Power Field Oriented Control (PFOC) method has been applied through the associated inverter as depicted in Fig. 7. In such a case, the inverter is used to regulate the magnetic flux and control the torque being cascaded with the DC-link voltage control loop [START_REF] Turki | Control strategy of an autonomous desalination unit fed by PV-wind hybrid system without batter storage[END_REF][START_REF] Khiari | Power control strategy for PV/Wind reverse osmosis desalination without battery[END_REF]. In the Park's d-q reference frame linked to rotating field, the rotor flux is controlled through the d-axis (φrd = φr, φrq = 0). By neglecting power losses via the inverter (denoted ∆PIM in Fig. 6), the power balance is given by: dc p sq sq sd sd

V I V I V I  (10)
As a result, based on the above equation and the original equations of the stator and rotor voltages in the d-q reference frame, while neglecting the dynamic elements (i.e. fast transients), the electrical power PIM feeding the motor-pump can be expressed versus the angular speed and the electromagnetic torque (Ω, Tm). The latter variables are in turn expressed versus pump flow rate Qp and are given by ( 11) and ( 12).

( , ) ( , )

m p p p m T Q T Q f      (11) 22 ( ) 4 ( ( )
Q Q a       (12)
Where, Phyd-load denotes the hydraulic load pressure describing the analytical model of the hydraulic load of each hydro-mechanical process. It should be pointed out that the full expression of the motor-pump angular speed Ω(Qp) can be derived from ( 1) and ( 8) in case of "pumping process", and from ( 5), ( 6) and ( 8) in case of "desalination process", by choosing the positive root of the 2 nd order equation.

As a result, PIM can be expressed with respect to the pump flow rate Qp by (13).

Q R R T Q Q T Q L L L             P ( 13
)
where,

2 m sr s r r L R R R L     (14)
The obtained equation ( 13) presents a nonlinear and multivariable expression of the feeding electrical power of the motor-pump with its corresponding hydraulic load. In order to determine the pump flow rate with respect to its feeding electrical power, ( 13) can be reversed by using the "fsolve" function under Matlab  software. The inverse expression (i.e. Qp=f(PIM)) describes the quasi-static model of a whole hydro-mechanical process in the desalination system.

Practical validation of the quasi-static model

In order to validate the developed models of the two hydro-mechanical processes, model-based simulation results are compared to the models extracted from experimental characterizations (in steady-state) of each hydromechanical process of the desalination experimental set-up (for more details on the experimental characterizations see sub-section 3.2) in ref. [START_REF] Ali | Optimized Fuzzy Rule-based Energy Management for a Battery-less PV/Wind-BWRO Desalination System[END_REF]). This comparison is illustrated by Fig. 8 that presents the water flow rate variation curves Qp=f(PIM) for the three used motor-pumps (WP1, WP2 and HPP) with respect to the drawn electrical power by each motor-pump. According to this, an energetic coherence between the dynamic and quasi-static models of each hydro-mechanical process has been proved. These results put forward the great worth of the quasistatic modeling to be used in order to set and optimize the energy management strategy which is defined and discussed in the next section.

Energy management strategy

This section is divided into two parts. The first one is devoted for setting the energy management problem. The second part is dedicated to describe the energy management strategy (EMS) that is based on deterministic rules.

Setting the water/power management problem

As electrochemical storage is substituted by hydraulic storage in water tanks, the desalination system includes two decoupled and independent hydro-mechanical subsystems. The energy requirements of these subsystems are not the same depending on their operating points. The latter depend on both the hydraulic characteristic curve of the pump (imposed following the rotational angular speed of the motor-pump) and the hydraulic load characteristic curve of each pump. This needs to develop a specific EMS permitting to manage simultaneously the power and water flows into the system while fulfilling the technological (power and pressure ranges) and functional (tank filling state) constraints. The principle of the proposed EMS is defined such as the input variable generated power from RESs can be dispatched between the different pumping devices according to a power sharing factor (αi) defined as:

i p i dc   PP (15)
With:

1 1 n i i      (16)
min max

i i i p p p  P P P  (17)
Inf Sup min max

L L L   (18)
Where Ppi and i denote respectively the electrical power that should be addressed to the i th motor-pump of the system, and its corresponding power sharing factor, Pdc denotes the input DC-link power to be dispatched, and n is the total number of pumping devices.

The objective of the EMS described by equations ( 15), ( 16), ( 17) and ( 18) is to maximize the freshwater production of the system according to the available renewable energy generation while respecting the system constraints. Maximizing freshwater production following the available renewable energy is beneficial in terms of freshwater storage that presents a new form of energy storage. The idea is to maximize and store freshwater, for later use when renewable energy is unavailable.

The power value Ppi for the i th switched-On pump is considered as reference value that should be given by the EMS based on [START_REF] Maleki | Design of a cost-effective wind/photovoltaic/hydrogen energy system for supplying a desalination unit by a heuristic approach[END_REF]. The choice of the Ppi value is constrained by both the power range of the i th motor-pump and the tank filling state confines as defined in ( 17) and [START_REF] Aybar | Solar powered RO desalination: investigations on pilot project of PV powered RO desalination system[END_REF], respectively. This principle is applied for all pumping devices. Thus, according to both input generated power and the T1 filling state, the i value is computed and subsequently the Ppi value of each pump is determined. Then, according to the power value Ppi and to the operation time of each pump the brackish water level in the tank T1 (defined by ( 7)) will be varied (i.e. increased or decreased). For example, in case of low value of 1 = (PWP1/ Pdc), the well pump (WP1) operates in the region of low efficiency due to the very low input power. For this reason, no remarkable increase in the water level can be noticed, but on the other side the high pressure pump (HPP) operates with high input power and good efficiency (i.e. PHPP = 2Pdc = (1-1) Pdc, in case of n = 2). This, advantageously leads to increase the freshwater production. On the opposite case with higher 1 values, WP efficiency can be improved and the brackish water level in the tank increases accordingly. This enables to increase the storage amount of brackish water in the tank for later use by the RO process when the renewable energy is available. It is also possible to simultaneously store brackish water in the tank and produce freshwater when the renewable energy is abundant (i.e. very high generated power supply). Therefore, the generated power from renewable sources is strongly coupled with the water process system efficiency: in particular, the importance of respecting pumping power limits as defined in [START_REF] Khayet | Optimization of solar-powered reverse osmosis desalination pilot plant using response surface methodology[END_REF] is put forward to prevent problematic operations that degrade efficiency and could also reduce the lifetime of pumps. The latter issue emphasizes the first coupling between "power and subsystems efficiency".

On the other hand, EMS performance is affected when modifying the sizing of motor-pumps. It depends on the choice of the motor-pump rated power: here respectively (0.75kW and 2.2kW) as initial combination in the desalination system, then (0.37kW and 2.2kW) as a second combination. Indeed, by choosing another motorpump with lower rated power, but with relatively high flow rate, energy efficiency of the motor-pump can be relatively improved with a lower power consumption Ppi. Consequently, EMS performance will be influenced.

This issue emphasizes the second coupling between "sizing and management performance".

A third coupling between "tank level and power management" has to be managed. Indeed, after a certain operation time of the WP(s), the maximum filling level of the tank T1 can be attained and subsequently WPs must be shut down. On the other hand, operating the HPP is only possible if the tank T1 is not empty.

Based on this strongly coupled system design (water management and pump sizing), a Deterministic Rule-based EMS is developed. It consists of deterministic energy dispatch that evaluates the system states of the desalination system based on set rules, then computes the respective energy dispatches.

It should be noted that the experimental desalination test bench installed in our research laboratory (L.S.E in ENIT-UTM, Tunis, Tunisia) presents a prototype including two pumping devices: one WP and one HPP. Indeed, the experimental test bench is exploited for two sizing steps: the first sizing is 0.75kW for well pumping and 2.2kW for the RO process, and the second sizing is respectively 0.37kW and 2.2kW whose characteristics are reported in Table 2. It is a simplified case study, but the methodology may be extrapolated to any number of subsystems. In this work, it can be extrapolated to three pumping devices: two parallel WPs functioning through exploiting pumps modularity versus the input power, and one HPP. So, in the next subsection the influence of both "pump sizing" and "modularity" on management performance are investigated and analyzed.

In this work, the suitable power range [Pmin -Pmax] of each pumping device has been experimentally identified (for more details see ref. [START_REF] Ali | Optimized Fuzzy Rule-based Energy Management for a Battery-less PV/Wind-BWRO Desalination System[END_REF]) while functioning with a given hydraulic load.

Rule-based EMS

According to the given power Pdc, and given the hydraulic loads characteristics, a modular approach (i.e. several motor-pumps that can be switched on/off and tuned) for energy management is applied to the studied system. This management approach is based on different operating modes that can be switched during the system operation.

Indeed, from the power ranges of motor-pumps, three main operating modes are considered and explained in Table 4. The operating mode preference essentially depends on: i) the given power supply Pdc, ii) the stored water level L in the tank T1 that must vary on its specified confines (Lmin Inf ≤ L ≤ Lmax Sup ), and iii) the operating power range of each pumping device [Pmin -Pmax].

Table 4 The possible operating modes of the BWRO desalination system

Operating mode Description Mode P Pumping mode: at least one WP is switched On, the HPP is shut down. During this mode, pumped brackish water (to be traited) is stored in the tank T1.

Mode D Deslination mode: all WPs are shut down and the HPP is switched On. During this mode, the stored brackish water in the tank is exploited to produce freshwater.

Mode P&D 'Pumping and Desalination' mode: the HPP and at least one WP are switched On. This mode is recommended when the genrated power is abundant.

Mode OFF

The system is shut down.

Regarding the storage tank T1, four limit levels (Lmin Inf , Lmin Sup , Lmax Inf , Lmax Sup ) are defined in this study. The idea of choosing such boundaries is to maintain the tank filling state within an acceptable range [Lmin Sup -Lmax Inf ].

Moreover, each limit interval ([Lmin Inf -Lmin Sup ], [Lmax Inf -Lmax Sup ]) permits to avoid respectively the tank emptying and overflow. These intervals make a "safety margin" against the successive occurrence of motorpumps-switched On/Off. For example, within the [Lmin Inf -Lmin Sup ] margin the HPP must be shut down in order to avoid emptying the tank and only the WP should operate to increase the water level if the renewable power is available. This may avoid the successive HPP-switched On/Off. The opposite case is considered for the [Lmax Inf -

Lmax Sup ] margin.

In order to study the influence of pump sizing and modularity on management performance, four pump combinations are proposed that are summarized in Table 5 and corresponding operating ranges are illustrated in Fig. 9. For example, for Comb.3 where the WP1, WP2 and HPP are used, three different power ranges have to be considered in the energy management that are respectively as follows: [120W-1020W], [120W-370W] and [620W-1800W]. Three additional limits are also added which are as follows: (2170W = 370W+1800W), (2820W = 1020W+1800W), and (3190W = 370W+1020W+1800W). As a result, nine power intervals are obtained to be tested on the input generated power Pdc in the rule-based power sharing algorithm. So, the decision making for power sharing depends on the Pdc value and the filling state of the storage tank as depicted in Fig. 9.

For example, if (Pdc = 700W ϵ [620W-1020W]) and (Lmin Sup < L < Lintermed) then (α1 = 1, α2 = 0 and α3 = 0). That means that the WP1 is set On (i.e. PWP1 = Pdc), and the {WP2 and HPP} are shut down (i.e. PWP2 = PHPP = 0). In this case, the system takes benefit of the total generated power to operate only in pumping mode in order to increase the brackish water storage amount in the tank. When the generated power increases (e.g. Pdc = 1000W)

and the brackish water level exceeds the intermediate level (i.e. L > Lintermed), then (α1 = 0, α2 = 0 and α3 = 1). In this case, the system operates only in desalination mode (i.e. PHPP = Pdc) to produce freshwater and the well pumps are both shut down (i.e. PWP1 = PWP2 = 0).

According to the different pump-combinations four different Deterministic Rule-based algorithms are developed and tested for energy management. One example of the developed rule-based algorithms is described through the flowchart depicted in Fig. 10 giving an idea on the mode preference according to the input power and the current water level in the tank. Indeed, the presented algorithm offers several degrees of freedom permitting to optimize the different pumps operation, namely: for the input electrical power by defining thresholds (PWP min , PWP max , PHPP min , PHPP max , Pmax=PWP max +PHPP max ), and for the storage tank by defining thresholds (Lmin Inf , Lmin Sup , Lintermed, Lmax Inf , Lmax Sup ). The intermediate level defined by ( 19) is a supplementary threshold limit defining the power dispatching strategy. So, as illustrated in Fig. 9 under this level (L ≤ Lintermed), the priority is addressed to the well pumping (brackish water storage) over the desalination process so that WP(s) can function as much as possible to fill the storage tank. In addition, when the renewable energy is abundant, it is possible to operate simultaneously the two processes while ensuring that: QWP ≥ QHPP in order to prevent emptying the tank. In this case, the system operates in pumping mode with "desalination mode in a moderate way". On the opposite, when L > Lintermed there is enough stored brackish water. This enables to switch the priority to the desalination process over well pumping leading to maximize the freshwater production. In addition to that, when the renewable energy is abundant both processes can operate simultaneously while ensuring that: QWP ≤ QHPP in order to prevent tank overflow. In this case, the system operates in desalination mode with "pumping mode in a moderate way". This strategy is implemented and described through the flowchart of one developed EMS that is illustrated in Fig. 10. Note that the flow rate Qpi of the i th pump is computed by inverting the expression (13) and using the reference feed power value of the i th pump calculated by [START_REF] Maleki | Design of a cost-effective wind/photovoltaic/hydrogen energy system for supplying a desalination unit by a heuristic approach[END_REF]. The task here is to compute the instantaneous values of the i factor enabling to reach the sought objective of EMS. Simulation results are analyzed in the next section.

Inf Sup min max intermed 2 HPP WP LLQ L Q      (19)

Simulation results analysis

This section is dedicated to analyze the EMS performance through simulations where different components sizing and different pump-combinations are considered.

The simulations have been accomplished using real data of hybrid PV/Wind power generation recorded every hour from January to December, 2007 of a region in Southeast Tunisia: Djerba-Midoun. The PV source is composed of 8 monocrystalline modules (from elysun) of 250Wp each, where the total generated power is of 2kWp. As for the wind turbine source, the Aeolos-H 2kW wind turbine is used with rated power of 2kW.

The different dispatch algorithms have been coded under Matlab © software using the simulation parameters reported in Table 6 where the considered sampling period is 2.5 minutes (i.e. the sampling period is Ts = 2.5 x 60 = 150s). Indeed, an interpolation has been performed on the recorded hourly power profile in order to modify the sampling period (Ts = 1h) which represents a long time interval for the proposed EMS. A daily and weekly power profiles, depicted in Fig. 11, were considered for tests and analysis. It should be noted that during simulations two RO membranes have been considered. Results of the developed EMS for each pump combination are reported in Table 7. These results are assessed in terms of freshwater production qfresh (in m 3 ) for the two presented power profiles. As it is previously explained, the main objective of the EMS is to maximize as much as possible the freshwater production while taking benefit of the available renewable energy. This permits to increase as much as possible the freshwater amount storage that will be used later when renewable energy is unavailable. In such a way, electrochemical storage device can be avoided. According to this criterion, best results (i.e. the higher produced freshwater amount) are indicated in bold type in Table 7. It can be deduced from this table that the most appropriate combination in terms of freshwater production is Comb.4 where two parallel identical well pumps with a rated power of 0.37kW each are used for the welling process. The pump modularity approach is applied here; according to the generated input power level the well pumping process can operate either a single pump (0.37kW), or simultaneously the two parallel pumps where the input power is shared between them. This approach has the advantage of operating only one pump WP2 with lower rated power (0.37kW), but with higher energy efficiency when the given input power is very low compared with the single pump WP1 (0.75kW). Then, when the input power level rises, the modularity approach offers the possibility to operate simultaneously more than one pump operating each with good energy efficiency.

Moreover, the influence of HPP sizing on the system efficiency is also analyzed: so the previously used HPP (EBARA EVM2 22F/2.2) is substituted now by a new HPP (rated power of 1.5kW instead of 2.2kW) and used for all previous pump combinations. The new HPP, where characteristics are reported in Table 8, was selected from the Grundfos manufacturer's catalog. Its electrical and hydraulic characteristic curves were taken from the Grundfos Product Center, an online tool proposed by Grundfos for the research and design of pumps. Simulation results for the different pump combinations with the new HPP are reported in Table 9. For the sake of visibility, the obtained results are illustrated in Fig. 12 and Fig. 13 where changes on the freshwater amounts are more visualized. It is noticed that the freshwater production is improved when using the new HPP whose rated power is lower than the first one, but with higher energy yield. On the other hand, besides to the influence of pump sizing, the influence of the brackish water storage tank sizing (capacities C1 and C2) on the management performance is also investigated by doubling the tank capacity (C2=4.36m 3 ). As it can be seen in Table 7, Table 9, Fig. 12 and Fig. 13 when doubling the hydraulic storage capacity, the freshwater production is improved for all combinations. This means that increasing the hydraulic storage capacity enables to improve the system productivity and the renewable energy use. The later in turn could play an important role in the energy optimization. In addition to that, Comb.4 is always still the most appropriate combination in terms of freshwater production, especially when using the new HPP (1.5kW -CRE 1-21).

All of the above mentioned findings highlight the great importance of:

-The strongly coupling between "the power and subsystems efficiency", and coupling between "the pump sizing and the energy management performance".

-The strongly coupling between "water management and pump sizing". It should be pointed out that designing the desalination system based on the modularity approach is advantageous for non-expert small communities enabling them to easily configure such a desalination unit. In such a case the system becomes flexible and is assembled from modular components such as motor-pumps, RO membranes and even the solar PV modules. So, non-experts have the possibility to reduce or extend in a second step the number of these modular components according to the community demand. This can reduce the capital cost, and makes its maintenance and repair tasks simpler and easier than conventional design approaches.

The adopted concept of storing the generated renewable energy during sunny and/or windy days in the form of water offers a simple, very cost-effective and environmentally friendly alternative, especially for small-scale desalination units. Nonetheless, this solution does not deal with the impact of frequent system shutdown or successive On/Off cycling of motor-pumps that may occur. Generally, this may increase the potential wear on motor-pumps and reduce their lifetime. For this purpose, the systemic design approach is applied in this work to investigate the suitable pump combination and sizing according to both the chosen architecture and the available renewable energy, in one-side. Indeed, this approach puts forward the strong coupling between the renewable generated power and the water process system efficiency, and coupling between device sizing (especially motorpumps) and energy management performance. Such a design approach can help to reduce the non-recommended successive On/Off cycling of motor-pumps and the frequent system shutdown. In the other-side, the proposed power sharing algorithm is developed so that successive On/Off of motor-pumps is minimized following the available PV/Wind generated power. This is achieved by including supplementary level limits (Lintermed, Lmin Inf , Lmin Sup , Lmax Inf , Lmax Sup ) on the brackish water storage tank T1. The idea is to operate the pump in a moderate way rather than setting it Off in some level intervals, and favoring single-pump operation rather than multi-pump operation in other level intervals making a safety margin against the successive occurrence of pumps-switched On/Off. Besides to the deterministic rules, fuzzy logic is also a useful tool that can be used in the energy management for this sake. For example, a genetic algorithm optimized fuzzy logic-based energy management strategy was previously developed by authors (ref. [START_REF] Ali | Optimized Fuzzy Rule-based Energy Management for a Battery-less PV/Wind-BWRO Desalination System[END_REF]) and applied to the first pump combination Comb.1 of the desalination unit with a storage tank capacity of 2.18 m 3 . This helps to reduce the number of successive On/Off of motor-pumps.

Conclusion

This work is within the context of complex energy system design. The principle of the adopted systemic design approach is to start from component system characterization, going through the modeling phase, to achieve an efficient energy management in real-time. In this regard, the system architecture was defined so that continuously freshwater productivity and supply are insured while taking into account the environmental and capital cost issues. This is achieved by means of integrating hydraulic storage (brackish water and freshwater) in water tanks when renewable energy is available instead of electrochemical storage device; the available renewable energy can be stored in the form of water. This is very advantageous and cost-effective in terms of energy storage. An experimental BWRO desalination test bench at the laboratory scale has been installed by authors according to the defined system architecture. It is considered as a prototype in order to investigate the feasibility and reliability of such autonomous desalination system in rural and poverty region for drinking and/or agriculture. The different hydraulic processes were previously experimentally characterized. Based on both previous experimental study and dynamic modelling, a quasi-static model of the whole desalination system was carried out and presented in this work for simulations and performance analysis. Then, a deterministic rule-based energy management strategy (EMS) was defined enabling to manage simultaneously the water and power flows into the system. The EMS was developed so that freshwater production is maximized according to the available generated power while fulfilling the technical and functional constraints of the system. Maximizing the system productivity and storing freshwater is beneficial from a continuous water supply perspective, especially when renewable energy is not available. For the sake of system design optimality, the influence of the component sizing (pumps and tank capacity) on the system efficiency and the energy management performance were investigated and analyzed in this work. Several pumps sizing and combinations for two different capacities of the brackish water storage tank are proposed. It was demonstrated that there is a strong coupling between "power and system efficiency", a coupling between "sizing and management performance", and also a third coupling between "tank level and power management". All of these couplings and their interrelationships are defined within the so-called systemic design approach.

Simulation results showed that by applying the modularity approach, the most convenient components sizing corresponds to the motor-pumps of lower rated powers, but offering higher energy efficiencies compared to those of higher rated powers. The same observation was noticed when increasing the capacity of the brackish water storage tank. These findings demonstrated that the available renewable energy use can be optimized and the freshwater production can be maximized by choosing the convenient system architecture and the optimized components sizing, highly correlated with the energy management strategy.

Another issue was highlighted in this work related to the influence of the successive switching On/Off of motorpumps on their lifetime. The adopted systemic design approach with the defined system architecture and the developed EMS enabled to initially reduce the number of pumps-switching On/Off events. However, this issue has to be addressed with the greatest accuracy. For instance, renewable energy forecast can be a viable solution to predict renewable power generation for the next time intervals. This enables to significantly improve the energy management performance while taking into consideration the constraint of motor-pumps lifetime by reducing the number of pumps-switching On/Off events.

All of these findings justify a deep and more sophisticated study to investigate global optimization approaches taking account of the couplings between the system architecture, sizing and energy management, while respecting the different system constraints.

Fig. 1 .Fig. 2 .

 12 Fig.1. Synoptic of the autonomous BWRO desalination system

Fig. 4 .

 4 Fig.3. Experimental BWRO desalination test bench



  Sizing of the complex energy system  Development of an optimal energy management of the system  Experimental validation of the energy management, …etc.

Fig. 6 .

 6 Fig. 6. Synoptic of the quasi-static modeling of a single-pump hydro-mechanical process: a power flow model This section is divided into five parts: the first one is devoted for the modeling of the hydraulic subsystems (i.e. hydraulic loads). The second part presents the storage tank analytical model. The third part describes the hydromechanical subsystems modeling. Then, the analytical quasi-static model of a hydro mechanical process is presented in the fourth part. The last one is dedicated to the practical validation of the quasi-static model for each hydro-mechanical process.

Fig. 7 .

 7 Fig.7. Block diagram of the control strategy of a single-pump hydro-mechanical process

Fig. 8 .

 8 Fig.8. Comparison of the developed and experimental models for the different hydro-mechanical subsystems of (a) well pump WP1 (b) well pump WP2 and (c) high pressure pump HPP.

Fig. 9 .Fig. 10 .

 910 Fig.9. Power ranges for different pump combinations with operating mode preference according the stored water level

Fig. 11 .

 11 Fig.11. Daily (a) and weekly (b) PV-Wind generated electrical power profiles

Fig. 13 .

 13 Fig.[START_REF] Soric | Eausmose project desalination by reverse osmosis and batteryless solar energy: Design for a 1 m 3 per day delivery[END_REF]. Produced freshwater quantity (in m 3 ) for the different pump-combinations for a weekly power profile.

Table 1

 1 Summarry of the reported standalone small-scale RES-BWRO units (≤ 10m 3 /d) in the last decade

	Ref. Year Country	PV (kW)	Wind (kW)	Battery	Diesel	Hydrogen Freshwater	Energy
					(kW)	(m3/d)	Recovery (%)

Table 2

 2 Specifications of the experimental desalination test bench

	Components	Characteristics	Component constraints
	High Pressure Pump (HPP)

Model: EBARA EVM2 22F/2.2 Type: centrifugal 3-ph motor pump Power output: 2.2 kW Rated Pressure: 8.17-18.6 bar Rated flow rate: 20-60 l/min Minimum absorbed electric power: 620 W Maximum absorbed electric power: 1800 W Well Pump 1 (WP1) Model: PEDROLLO CP158 Type: centrifugal 3-ph motor pump Power output: 0.75 kW Rated Pressure: 2.5-3.4 bar Rated flow rate: 10-90 l/min Minimum absorbed electric power: 120 W Maximum absorbed electric power: 1020 W Well Pump 2 (WP2) Model: LOWARA CEA70/3 Type: centrifugal 3-ph motor pump Power output: 0.37 kW Minimum absorbed electric power: 120 W Maximum absorbed electric power: 370 W

  , the feed pressure Pfeed of the RO module results from the sum of different pressures as follows:

	feed P	HPP P	tank P	asp P
		HPP P	Inf min () g L L	gH	asp

Table 3

 3 Hydraulic parameters of different components of the experimental desalination test bench

	Component	Parameter	Value	Unit
	HPP	a	0.0002317	Ns²/m²
		b	-0.0005198	Ns²/m²
		c	-0.002427	Ns²/m²
		fp	0.0038	Nms
	WP1	a	4e-5	Ns²/m²
		b	-1.767e-5	Ns²/m²
		c	0.0002	Ns²/m²
		fp	0.0019	Nms
	WP2	a	2.446e-5	Ns²/m²
		b	-6.507e-5	Ns²/m²

Table 5

 5 Different pump combinations

		Comb.1	Comb.2	Comb.3	Comb.4
	Pump combination	WP1/HPP	WP2/HPP	WP1/WP2/HPP	WP2/WP2/HPP
		(0.75/2.2 KW)	(0.37/2.2 KW)	(0.75/0.37/2.2 KW)	(0.37/0.37/2.2 KW)

Table 6

 6

	Simulation parameters
	Symbol	Description	Value	Unit
	k1	Number of samples in a day	553	samples
	k2	Number of samples in a week	4009	samples
	k3	Number of samples in a year	210217	samples
	Ts	Sampling period	150	s
	Tt	Total time for one day	82950	s
	FSmax	Maximum Filling State of the tank	100	%
	FSmin	Minimum Filling State of the tank	10	%
	FS0	Initial Filling State of the tank	60	%

Table 7

 7 Produced freshwater quantity (in m 3 ) according to component sizing

	Comb.1	Comb. 2	Comb.3	Comb.4

Table 9

 9 Produced freshwater quantity (in m 3 ) according to component sizing using the new HPP 1.5kW -CRE 1-21 Produced freshwater quantity (in m 3 ) for the different pump-combinations for a daily power profile.

		Comb.1	Comb.2	Comb.3	Comb.4
	Storage tank T1 capacity C1: 2.18 m 3
	Daily power profile	12.05	11.97	12.07	12.1
	Weekly power profile	79.5	79.82	79.95	80.24
	Storage tank T1 capacity C2: 4.36 m 3
	Daily power profile	12.31	12.28	12.35	12.34
	Weekly power profile	81.74	81.56	82.04	82.12

Acknowledgment

This work was supported by the Tunisian Ministry of Higher Education and Research under Grant LSE-ENIT-LR 11ES15 and the European project "ERANETMED -EDGWISE" ID 044".