Photovoltaic electrodialysis system for brackish water desalination: Modeling of global process

Journal of Membrane Science 274 (2006) 138–149

Photovoltaic electrodialysis system for brackish water desalination: Modeling of global process J.M. Ortiz, E. Exp´osito, F. Gallud, V. Garc´ıa-Garc´ıa, V. Montiel ∗ , A. Aldaz Grupo de Electroqu´ımica Aplicada y Electrocat´alisis, Departamento de Qu´ımica F´ısica and Instituto Universitario de Electroqu´ımica, Universidad de Alicante, Ap. 99, 03080 Alicante, Spain Received 16 May 2005; received in revised form 1 July 2005; accepted 8 August 2005 Available online 14 November 2005

Abstract The shortage of drinking water is a major problem in the South East of Spain. In these areas, it is essential to make use of water from underground reservoirs, most of which are over exploited and suffer from saline contamination given their proximity to the sea. The desalination of brackish water is a means of obtaining low cost drinking water. The method of desalination designed in this paper uses an electrodialysis system fed by photovoltaic modules that is simple, reliable, and low cost because it does not include battery storage or a battery regulator. These systems are of particular interest for isolated zones with access to wells of brackish water where connection to the electric grid is not possible. In this paper, the feasibility of the desalination of brackish water using an electrodialysis system powered by photovoltaic energy and the influence of experimental parameters has been studied. Likewise, a mathematical simulation model that allows predicting and simulating the functioning of a system of these characteristics under different meteorological conditions has been developed. The model has been applied with satisfactory results to the desalination of a NaCl solution in different experimental conditions. Data given by the mathematical simulation model was contrasted with experimental results in order to compare the reliability of the model, and good agreement was obtained. The application of this model allows the design of an electrodialysis system powered by photovoltaic energy (electrodialyzer size and the number and configuration of the PV modules), for the desalination of brackish water, as well as the study of its behaviour in different geographical locations. © 2005 Elsevier B.V. All rights reserved. Keywords: Brackish water; Electrodialysis; Photovoltaic energy; Renewable energy

1. Introduction The shortage of drinking water is a major problem in the southern communities of Spain, especially on the Mediterranean coast. In these regions, precipitations are insufficient to meet the demand for water and it is therefore necessary to resort to underground resources. However, in recent times, most of these aquifers have been over exploited and also suffer serious problems of saline contamination [1–3]. This problem worsens in remote areas, where the supply of water and electricity is particularly expensive or even non-existent. Electrodialysis is a technique based in the transport of ions through selective membranes under the influence of an

∗

Corresponding author. Tel.: +34 96590 3356; fax: +34 96590 3537. E-mail address: [email protected] (V. Montiel).

0376-7388/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2005.08.006

electrical field [4–6]. This technique has proved its feasibility and high performance in the desalination of brackish water [7–10], the desalting of amino acids and other organic solutions [11–15], effluent treatment and or recycling of industrial process streams [16–18] and salt production [19–21]. In a conventional electrodialysis stack, cation- and anionexchange membranes are placed alternatively between the cathode and the anode. When a potential difference is applied between both electrodes, the cations move towards the cathode and anions towards the anode. The cations migrate through the cation-exchange membranes, which have negative fixed groups, and they are retained by the anion-exchange membranes. On the other hand, the anions migrate through the anion-exchange membranes, which have positive fixed groups, and they are retained by the cation-exchange membranes. This movement produces a rise in the ions concentration in some compartments

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(concentrate compartments) and the decrease in the adjacent ones (diluate compartments). Nowadays, the social concern about the environment is growing in the developed countries, and laws demanding environmental protection are being approved. This fact has led to the research and development of new forms of renewable energy. One of the most widespread and studied is the photovoltaic power [22–24]. The advantages of the use of the photovoltaic (PV) power are that it is non-polluting; it is also silent; the fuel – sunlight – is free, abundant and a renewable resource, decentralized; long-life and the low maintenance cost of these systems. Generally, a photovoltaic system consists of PV modules, batteries, a regulator or controller, an inverter (dc–ac) and loads (charges). The PV modules can be connected in series and/or parallel and the solar radiation incident on the surface of the PV array is transformed into electric energy (direct current) by the PV modules. The generated electricity is passed to the regulator, which protects the batteries from overcharging or an excessive discharge. The batteries store energy that can be used as electrical back-up during periods of low solar insolation—for example, during cloudy weather or at night. The inverter transforms the direct current into alternating current (ac) for those devices that work with the latter. These systems can be used in remote sites for the self-sufficiency of electrical power in a reliable and autonomous way [25]. The use of PV modules as a power supply for an electrodialysis system for brackish water desalination in remote areas is studied in previous papers [22–32]. However, up until now, most of these studies use photovoltaic systems with batteries. To carry the electrical energy supply to the electrodialyzer directly from the PV modules would substantially decrease the cost of investment of these systems, due to the high price of batteries. However, the absence of batteries means that the water production depends on and varies according to solar radiation, which depends on factors such as the meteorological conditions, geographical location, season, time of day, and PV array orienta-

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tion. In this paper, the feasibility of the desalination of brackish water using an electrodialysis system powered by photovoltaic energy and the influence of experimental parameters has been studied. In a previous paper [33], a mathematical model for the desalination of brackish water by means of an electrodialysis system was introduced, operating in batch recirculation and through controlled potential powered by a conventional power supply. In this paper, a mathematical model for the desalination of brackish water by means of an electrodialysis system operating in batch recirculation powered by photovoltaic energy has been developed. The equations and parameters used will be theoretically developed or, in the case in which this is not possible, empirically determined. The application of this model allows to predict the behaviour of the global system under different operation and meteorological conditions and to study their influence on the time required for a successful desalination until a given final concentration. Moreover, it allows optimizing parameters as the electrical consumption of the process or the number of modules and the configuration (series and/or parallel) of the array in order to treat a certain volume of water. 2. Experimental Fig. 1 shows a diagram of the experimental system used. Electrodialyzer is EUR-6-80 by EURODIA. The stack has 80 cells with cation-exchange membranes CMX-Sb and anion-exchange membranes ACS, both made by Tokuyama. The active membrane area per cell is 550 cm2 , and the overall effective surface area is 4.4 m2 . The electrodes used are Dimensionally Stable Electrodes (DSEs). The system has been designed to operate in batch with recirculation. The experiments were carried out at voltages lower than 1.0 V per cell, which is the maximum voltage recommended by the manufacturer [34]. For this reason, the experiments were running

Fig. 1. Schematic illustration of the experimental system.

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below limiting current [34–36], avoiding processes of water dissociation [37], pH variations or membrane degradation. The photovoltaic modules PQ 10/40/01-02 (AEG) were made from poly crystalline silicon and had a peak power of 38.4 W and a surface area of 0.5 m2 . Since these PV modules were used for 10 years in a solar energy plant placed in Tabarca Island (Alicante, Spain), each PV module was tested and verified in order to know its performance and yield [38] before using them. The experiments were carried out in the University of Alicante (latitude 38◦ 24 05 N, longitude 0◦ 31 W and altitude of 109 m above sea level). The tilt of the PV modules was 55◦ and the PV array was south-facing (0.4◦ W). The solar radiation incident on the surface of the PV array was measured using a pyranometer 80 SPC (SOLDATA INSTRUMENTS). A system of data acquisition connected to a PC computer was used to measure current and voltage. The wind speed, Vwind , and the ambient temperature, Tamb , values were provided by a meteorological station, which is located in the vicinity of the experimental system. All the experiments were carried out at room temperature using 34.22 mM of NaCl (2000 ppm) as concentrate and diluate solutions (similar to the concentrations of brackish water of the zone) and 0.05 M Na2 SO4 as electrolyte. The reagents used in the preparation of the solutions were NaCl Thick Salt Synthesis Grade (SCHARLAU) and Na2 SO4 of purity not lower than 99% (FLUKA). Cl− analysis was made by potentiometric titration using an automatic titrator 702 SM Titrino (METROHM). The Na+ concentration in the samples was measured by AAS using a SpectrAA 220 FS (VARIAN). A Matlab 6.5 (The Mathwork Inc.©) program was used for the simulations. 3. Mathematical model 3.1. PV modules model 3.1.1. Introduction In a study of simulation as the developed in this work, the choice of a mathematical model for the PV module is of great significance. This model must allow for the prediction of current and voltage variations of the PV module with both ambient temperature and the solar radiation level. Recently, a variety of mathematical models have been developed, with most of them being characterized by the PV module being described as an electrical equivalent circuit [39]. For the correct choice of the mathematical simulation model, some factors have to be taken into account, like the versatility of the model (to allow simulating PV modules with different characteristics), the precision to reproduce the experimental results and the computational speed (that depends on the complexity of the mathematical model). In this paper, the five parameter model has been chosen, due to his versatility and precision – to within 1% of the point of peak power [38], maximum power provided by the PV module at reference conditions of Gref = 1000 W/m2 and Tmodule,ref = 298 K, where Gref is the solar irradiation at reference conditions and Tmodule,ref is the PV module temperature at reference conditions

Fig. 2. Diagram of the equivalent circuit for the “five parameters model”.

– and because in this case the computational complexity is not a critical point. In the five parameter model, the current generated by PV module is dependent on the irradiation connected in parallel with a diode and a resistance shunt, Rsh (
), and in series with a resistance (Rs ) and the load (Rload ) [40]. The “five parameters” of the mathematical simulation model are the current dependence on the irradiation IL (A), the shunt resistance Rsh (
), the resistance in series Rs (
), and both characteristics of the diode, the inverse saturation current of the diode I0 (A) and the shape factor of the PV module, γ (dimensionless). These parameters are not directly measurable and they are generally not included in the technical data sheet provided by the manufacturer. For this reason, they have to be determined from the information of the characteristic I–V curves in various operation points, which it is usually provided by the manufacturer. Fig. 2 shows a diagram of the equivalent circuit for the “five parameters model”. 3.1.2. Mathematical model of a PV module The equation of the characteristic I–V curves for a PV module according to “the five parameters model” is [38,41]:
   q(Vmodule + Imodule Rs ) Imodule = IL − I0 exp −1 γkTmodule
 Vmodule + Imodule Rs − (1) Rsh where Imodule is the PV output current provided by the PV module (A), Vmodule the voltage in the module terminals (V), q the electrical charge of the electron (1.6 × 10−19 C), k the Boltzmann constant (1.38 × 10−23 J K−1 ), and Tmodule is the temperature of the PV module (K). It can be assumed that IL is principally a function of the incident solar irradiation [41]. The value of IL can be calculated using the following equation: IL = Isc,ref

G Gref

(2)

where G is the value of the solar irradiation (W/m2 ), Gref the value of the solar irradiation of reference (W/m2 ), and Isc,ref is the value of the short circuit current (A) at reference conditions (reference conditions: Tmodule,ref = 298 K, Gref = 1000 W/m2 ). The latter parameter, Isc,ref , is a value provided usually by the manufacturer in the technical data sheet of the PV modules. Similarly, it is possible to consider that I0 varies principally according to the module temperature, and its value can

J.M. Ortiz et al. / Journal of Membrane Science 274 (2006) 138–149

be calculated using the following equation [41]:   I0 Tmodule 3 = I0,ref Tmodule,ref

141

(3)

where I0,ref is the value of the inverse saturation current of the diode (A) for the reference conditions and Tmodule,ref is the temperature of reference of the PV module. The values of I0,ref , Rs , Rsh , and γ are difficultly measurable and are not provided by the manufacturer. For this reason, they must be estimated solving a system of four equations. The first one of these equations suggests the following expression for the calculation of Rsh [41]: Rsh ≈ − 

dImodule dVmodule

1 

(4) Vmodule =0

The three remaining equations are obtained replacing the values of reference in the conditions of short circuit, open circuit, and peak power (maximum power provided by the PV module at reference conditions). These three equations allow the values of I0,ref , Rs and γ to be determined. Imodule |V =0 = Isc,ref

(5)

Imodule |V =VOC,ref = 0

(6)

Imodule |V =Vmp,ref = Imp,ref

(7)

In the previous equations, Isc,ref is the short circuit current of the PV module at reference conditions (A), Voc,ref is the open circuit voltage of the PV module at reference conditions (V), Imp,ref is the current in the point of maximum power at reference conditions (A) – i.e. peak power – and Vmp,ref is the voltage of the PV module in the point of maximum power at reference conditions (V). These values are usually provided by the manufacturer in the technical data sheet of the PV modules. Finally, the temperature of the PV module, Tmodule , is a parameter that affects the PV module output current, and it can be calculated by means of an energy balance in the photovoltaic module. The absorbed solar energy is turned into electric power and thermal energy. In relation to the latter, one part is lost by radiation and convection, and another part is accumulated in the PV module, causing an increase of its temperature. The variation of Tmodule in the PV module can be calculated using the following equation [42]: dTmodule = Qin − Qrad − Qconv − Qelect (8) (mCpmodule ) dt where mCpmodule is the thermal global capacity of the PV module (J K−1 ) corresponding to the temperature Tmodule , Qin is the solar power absorbed by the PV module (W), Qrad are the losses of energy by radiation (W), Qconv are the losses of energy by convection (W) and Qelect is the produced electric power. The previous equations allow knowing the behaviour of the PV module for any condition of temperature and solar irradiation. 3.1.3. Mathematical model of a PV array When a group of identical PV modules are connected in series and/or in parallel in order to set up a PV array, the PV array output

Fig. 3. Diagram of the cell pair and concentration profiles. δ is the Nernst dif0 , C0 , C fusion layer (m) and L is the membrane gap (m). Cconc conc and Cdil are dil the concentrations of the concentrate and diluate solutions at the inlet and at the wa , C wa , C wc outlet of the electrodialysis reactor respectively (mol m−3 ). Cconc conc dil wc and Cdil are the concentrations on the surface of the anion- and cation-exchange membranes at the sides of the concentrate and diluate solutions (mol m−3 ).

current can be expressed as [43]:      I R N q NVarray + arrayM S  − 1 Iarray = MIL = MI0 exp  NγkTmodule  −

NVarray +

Iarray RS N M

NRsh M

 

(9)

where Iarray and Varray are the PV array output current (A) and the PV array terminal voltage (V), respectively, M is the number of module strings in parallel and N is the number of modules in each series string. The previous expression assumes that the solar irradiation, G, is uniform for all the PV modules in the array, as well as the PV module temperature, Tmodule . For a PV array directly connected to an electrodialysis reactor, the PV array output current and the PV array terminal voltage are fixed by the potential drop in the reactor in every moment. On the other hand, the potential drop of the electrodialysis reactor depends on a broad number of parameters [30,33]. 3.2. Electrodialysis system: mass balance Fig. 3 shows a diagram of the cell pair of the electrodialysis system used, where geometric parameters and symbols of NaCl concentration profiles at the inlet and at the outlet of concentrate and diluate compartments are shown. In order to calculate the changes in the concentration of NaCl in both of the reactor compartments and in the tanks, it is necessary to establish the mass balances for both solutions. If it is supposed that the electrodialysis reactor and the concentrate and diluate tanks conform to the model of perfectly mixed reactor, and that the concentrate and diluate compartments are equivalent, then the mass balance equations for the Cl− in the electrodialysis reactor for concentrate and diluate compartments

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are respectively [33]: Nk V k

Nk Vk

dCconc Nk ϕI 0 = Qconc Cconc − Qconc Cconc + dt zF −

wa − C wa ) Nk ADa (Cconc dil la

−

wa − C wa ) Nk ADc (Cconc dil lc

(10)

dCdil Nk ϕI 0 = Qdil Cdil − Qdil Cdil − dt zF wa − C wa ) Nk ADa (Cconc dil + la wa − C wa ) Nk ADc (Cconc dil + lc

(11)

where Nk is the number of cell pairs, Vk the compartment volume 0 , C0 , C (m3 ), Cconc dil conc and Cdil are the concentrations of the concentrate and diluate solutions at the inlet and at the outlet of the electrodialysis reactor respectively (mol m−3 ), Qconc and Qdil are the flow rates of concentrate and diluate solutions (m3 h−1 ), φ the current efficiency, I the current (A), z the charge of the ion, F the Faraday constant (C mol−1 ), A the active membrane area (m2 ), Da and Dc are the average diffusion coefficients of the NaCl in the anion- and cation-exchange membranes respectively (m2 s−1 ), la and lc are the thicknesses of the anion-exchange and

wa , C wa , cation-exchange membranes (m), t the time (s), and Cconc dil wc wc Cconc and Cdil are the concentrations on the surface of the anionand cation-exchange membranes at the sides of the concentrate and diluate solutions (mol m−3 ). According to the previous equations, the variation of the number of Cl− moles in concentrate and diluate solutions inside the electrodialyzer is given by: the moles that enter and exit the electrodialysis reactor, together with those that are transferred across the membranes (by migration and by back-diffusion). Likewise, the mass balance in the tanks is given as 0 VT ) d(Cconc conc 0 = Qconc Cconc − Qconc Cconc dt

(12)

0 VT ) d(Cdil 0 dil = Qdil Cdil − Qdil Cdil dt

(13)

T and V T are respectively the volumes of concentrate where Vconc dil and diluate solutions in the tanks (m3 ). During electrodialysis process, water is transported across the membranes due both migration of water molecules associated with ions (electroosmosis) and to osmosis caused by the difference in concentration across the membrane. Nevertheless, during the experiments it was observed that this transport is not quantitatively important in this case. For this reason, we will suppose that the volume of all the solutions remains constant [33]. Eqs. (10) and (11) are observed that Cl− concentration in concentrate and diluate streams during the experiments is a

Fig. 4. Flow diagram of the simulation program.

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function of the circulating current. Provided that the electrodialysis system is connected to a photovoltaic array, the intensity that circulates through the system in every moment depends on the global potential drop inside the electrodialysis reactor for a given instant [33]. The potential drop in the electrodialysis reactor can be expressed as the sum of a series of terms: dil dil Vstack = Istack Rstack = Nk (Eohm + Eohm + Emem ) + Eel (14) dil refers to the ohmic drops in a diluate comwhere the term Eohm conc partment, Eohm to the ohmic drop in a concentrate compartment, Emem the potential of membrane in each cell pair, and Eel refers to the electrode potentials.

Table 1 Values of the parameters used in the mathematical simulation model Parameter

A Matlab 6.5 (The Mathwork Inc.©) program has been developed that is able to give a theoretical simulation of the system. The developed program contains both the mathematical equations of PV array subsystem and electrodialysis reactor subsystem. A flow diagram of the simulation program is shown in Fig. 4. The model uses the instantaneous values of solar irradiation (G) and meteorological information as the ambient temperature (Tamb ) and the wind speed (Vwind ) to calculate the temperature of the PV module (Tmodule ). With this information (G and Tmodule ), and the known electrodialysis reactor potential drop (Vstack ), the PV array output current (Iarray ) is predicted by the simulation program. Simultaneously, the model of the subsystem of electrodialysis calculates the overall resistance of the electrodialysis reactor (Rstack ) from the initial composition of concentrate and diluate (Cdil , Cconc ). Then, electrodialysis reactor voltage, Vstack , is recalculated using the values of Rstack and Iarray . On the other hand, the input concentration of the concentrate and diluate streams in electrodialysis reactor (Cdil and Cconc ) and the PV array output current (Iarray ) are used to calculate the output concentrations in the electrodialysis reactor, which will serve to recalculate the concentrations inside the tanks. It should be noted that in order to run the simulation program, small time intervals are used to recalculate all the variables of the system during the process. It is assumed that the system immediately reaches steady state in each interval of time. The differential equations are solved using a finite-differences method. The simulation of the global system ends when either the final diluate tank concentration or final simulation time is reached. 4. Parameters estimation Table 1 shows the values of the parameters used in the mathematical simulation model developed. Specific parameters that depend on the experimental system used (i.e. number of PV modules connected in series, characteristics of the electrodialyzer), or general parameters are usually available in bibliography (for example, membrane resistances, technical specifications of the photovoltaic modules). The values of the parameters involved in the simulation can be obtained as it is described below.

Value (γ)a

Shape factor PV series resistance (Rs )a (
) Shunt resistance (Rsh )a (
) Diode reverse saturation current at reference conditions (I0,ref )a (A) Short circuit current at reference conditions (Isc,ref )b (A) Open circuit voltage at reference conditions (Voc,ref )b (V) Peak power current (Imp,ref )b (A) Peak power voltage (Vmp,ref )b (V) a

3.3. Simulation model description

143

b

38.59 2.28 250 1.43 × 10−5 2.41 22.4 2.20 17.45

Calculated from the manufacturer data sheet. Obtained from the manufacturer data sheet [44].

Firstly, the parameters corresponding to the mathematical model of the PV modules (I0,ref , Rs , Rsh and γ) are calculated using Eqs. (4)–(7) and the information provided by the manufacturer (Isc,ref , Voc,ref , Imp,ref , Vmp,ref and the characteristic I–V curves at reference conditions). A detailed method of derivation of these equations suggested by B. Fry is available in Ref. [40]. The value of these parameters and the group of Eqs. (1)–(3) and (8) allow to predict the behaviour of a generic PV module on different meteorological conditions of solar irradiation (G) and ambient temperature (Tamb ). In this paper, the characteristic I–V curves for the eight PV modules used in the experiments were experimentally obtained in various meteorological conditions. Moreover, the characteristic I–V curves of generic PV module—with manufacturer specifications- was theoretically calculated under the same meteorological conditions, using Eqs. (1)–(3) and (8). The divergence between the theoretical and the experimental values of the peak power for each PV module tested was within 10%, compared to the manufacturer’s specification sheet [44]. For this reason, in this study the PV modules are considered to have the same characteristics that the generic PV module. So, the long useful life of the PV modules has been verified—life of the PV modules can overcome 30 years with a suitable maintenance of the PV system [45]. About the parameters of Eqs. (10)–(14), these are specified in a previous paper [33]. Therefore, a mathematical model for the global studied system has been described, which allows to know the variations of the stack current, Istack , and the concentrations of the ions in the concentrate and in the diluate tanks (Cdil , Cconc ) as a function of time, if the number of PV modules used (N and M) and the meteorological input data (G, Tamb , Vwind ) are specified. The theoretical data obtained from the simulation model will be compared with experimental results, in order to estimate the accuracy of the simulation model. 5. Results and discussion 5.1. Experimental results As we previously noted, the principal aims of this paper are verify the viability of brackish water desalination process using

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Table 2 Experimental conditions Experiment no. 1

2

3

Diluate volume (L) Concentrate volume (L) Electrolyte volume (L) Initial diluate concentration (ppm NaCl) Initial concentrate concentration (ppm NaCl) Electrolyte initial concentration (M Na2 SO4 ) Diluate mass flow rate (kg h−1 ) Concentrate mass flow rate (kg h−1 ) Electrolyte mass flow rate (kg/h) Number of PV modules

100 100 50 2000 2000 0.05 750 750 500 Eight (two blocks connected in parallel, four modules in series per block)

100 100 50 2000 2000 0.05 750 750 500 Four (four modules connected in series)

Day and initial hour of the experiments Tilt and orientation of the PV modules Atmospheric conditions

4 February 2004, 13 h 35 min 55◦ , South (0.4◦ West) Sunny

6 February 2004, 12 h 13 min 55◦ , South (0.4◦ West) Cloudy

500 100 50 2000 2000 0.05 750 750 500 Eight (two blocks connected in parallel, four modules in series per block) 8 February 2004, 12 h 42 min 55◦ , South (0.4◦ West) Sunny

an electrodialysis system powered directly with photovoltaic energy – without batteries – as well as the development of a mathematical model to simulate the global system. For this reason, a series of experiments were carried out, where the influence of PV modules configuration – connection in series and parallel

– and of the meteorological conditions in the functioning of the system – sunny day and cloudy days – were studied. Table 2 shows the experimental conditions of the experiments. Provided that electrodialyzers have a maximum voltage to apply that it must not be overcome, these equipments will deter-

Fig. 5. Experimental results of (1) G and Iarray vs. t, (2) G and Varray vs. t, (3) Cdil and Cconc (ppm Cl− ) vs. t (horizontal line indicates legal limit to drinkable water).

J.M. Ortiz et al. / Journal of Membrane Science 274 (2006) 138–149

mine the maximum number of PV modules in series that can be connected. In the electrodialyzer used in this paper (EUR-6-80 of EURODIA), the manufacturer advises not to exceed the value of 1 V per cell (80 V total). The PV modules used (PQ10/40/01-02 of AEG) have an open circuit voltage just over 20 V at reference conditions. This fact forces to use arrays with a maximum of four PV modules in series. So, an eventual overcharge of voltage in the electrodialyzer will be avoided. Fig. 5 shows the experimental results obtained for the experiments. In Fig. 5a, a double representation of the solar irradiation incident on the PV modules surface (G) and the PV array output current (Iarray ) as function of time (t) is showed for the experiment (EXPERIMENT 1) (eight PV modules, sunny day). The solar irradiation values are approximately constant, due to the fact that the experiment was carried out in the central hours of a day and with short duration (approx. 1 h). Fig. 5b shows the voltage established across the system (Varray = Vstack ) as function of time (t). Fig. 5c shows the composition in the diluate and Cl− and C Cl− versus t). concentrate tanks (Cdil conc Fig. 5d–f are analogous to previously mentioned for the experiment (EXPERIMENT 2) (four PV modules, day with cloudy intervals). Fig. 5d and e shows clearly how the behaviour of the PV array output current (Iarray ) and the PV array voltage (Varray ) of the system are strongly dependent on the solar irradiation (G). However, this dependence is not so marked on the compositions of the diluate and concentrate tanks. Finally, Fig. 5g–i correspond to the experiment with longer duration (EXPERIMENT 3), which was carried out during the central hours of a sunny day. The behaviour of the curves of G, Iarray and Varray versus t can be explained by the following reason. Fig. 6 shows a pair of characteristic I–V curves of the two PV generators for the same module temperature and incident solar irradiation, and different array configuration, corresponding to the experiments carried out on a sunny day (EXPERIMENT 1, eight PV modules: two blocks in parallel,

Fig. 6. Characteristic I–V curves at reference conditions (Gref = 1000 W/m2 , Tmodule,ref = 298 K) of the PV arrays for Experiments 1 and 2.

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four modules connected in series in each block) and on a cloudy day (EXPERIMENT 2, four PV modules: four modules connected in series). In order to explain these figures, it is necessary to indicate that the point of functioning of the system in every instant – defined by the values of voltage and current – is determined by the intersection of the operative straight line of the reactor – that depends principally on the overall reactor resistance, Rstack , with the characteristic I–V curves of the photovoltaic generator—which depends principally on G and Tamb . For this reason, in the experiment carried out on a cloudy day (EXPERIMENT 2), the electrical resistance of the electrodialyzer has an initial value R0 , which depends principally on the conductivity of the solutions, membrane resistance [33]. In Fig. 6 EXPERIMENT 2, the operative curve of the reactor is shown for the initial moment, being the point A (IA , VA ) the working point of the system. During the experiment, the electrical resistance of the electrodialyzer grows up and the working point of the system moves (points B–D). Fig. 6 shows two clearly differentiated regions. The first one is between the points A and C and fits with low values of potential drop of the electrodialyzer. The current circulating across the system is constant and independent from the potential drop and it will only depend on the meteorological conditions (solar irradiation and ambient temperature). This zone is characterized principally by the proportionality between incident solar irradiation (G) and the PV array output current. When the point C is reached, the process enters into the second region—indicated in the figure as the zone between the point C and the point D. In this second region, the voltage increases and the PV array output current decreases until the point D is reached, which is the final instant of the process. As it is shown in this part of Fig. 6, the current is much less dependent proportional to the incident solar irradiation on the PV modules. In Fig. 5, it can be noted that the initial current in Experiments 1 and 3 is twice that current given by the PV array output current generated in Experiment 2, due to the fact that two PV modules blocks connected in parallel were used in the latter (see points A–A in Fig. 6). Similarly, the final voltage tends to the same value for all cases due to the fact that blocks with equal number of PV modules connected in series were used to carry out the experiments (see points D–D in Fig. 6). It is important to note that in this experiment the solar irradiation is very irregular due to the meteorological variable conditions. This can be seen in the first part of the curves, where it is observed clearly as the PV array output current is proportional to the solar irradiation. This proportionality is kept until the zone 2 is reached where the current begins to decrease. The previous explanation is also applicable to the experiment carried out on a sunny day (EXPERIMENT 1). In order to verify the reliability of the mathematical model for a longer period of functioning of the system, a third experiment was carried out, in which a volume of diluate five times greater T = 500 L, Fig. 5g–i) was treated. During this experiment, a (Vdil progressive decay of the solar irradiation as the day advance can be observed.

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Fig. 7. Experimental and theoretical results of (1) G and Iarray vs. t, (2) G and Varray vs. t, (3) Cdil and (ppm Cl− ) vs. t (horizontal line indicates legal limit to drinkable water).

5.2. Simulation results As pointed out in the previous paragraph, the influence of various parameters in the process of desalination have been studied. The results of the simulation model are shown as follows. Fig. 7 shows the variation of Iarray and G versus t during the experiments, as well as the theoretical curves provided by the mathematical model. Likewise, Fig. 7 shows a group of curves Cl− and versus t for the experiments carried out and the theoCdil retical curves obtained with the application of the mathematical model (the maximum legal limit for drinkable waters according to [46] is indicated). The figures show how the mathematical developed model reproduces satisfactorily the experiments in the range of experimental conditions studied—concentrations from 20 ppm Cl− up to 4500 ppm of Cl− [33] and solar irradiation above the threshold value of 100 W/m2 . The maximum divergence between theoretical and experimental concentrations is no more than 5% (during the experiments) in all the experiments carried out. The good agreement shown between theoretical and experimental data confirm the validity of the simulation model. Fig. 7 shows as the curve of Iarray versus t obtained in the simulation is more sensitive to the changes of irradiation that

the PV array output current obtained experimentally. A sudden change in the solar irradiation (see Fig. 7c) is immediately detected by the model and the theoretical PV array output current is adjusted instantaneously to a new calculated value. Nevertheless, experimentally, these sudden changes are slowly detected by the system. For this reason, the experimental curve obtained is softer than the theoretical curve. The reason for this fact is that the real potential drop in the reactor depends on processes [33] that are not immediately established. On the other hand, a difference is observed between theoretical and experimental behaviour in the beginning of the experiments, where the predicted PV array output current for the model of simulation is slightly greater than the current obtained experimentally. The mathematical model was developed assuming that (i) all the PV modules are electrically equivalent and with the technical specifications of the manufacturer, (ii) the electrodialysis reactor and the concentrate and diluate tanks conform to the model of perfectly mixed reactor, (iii) all the cells of the electrodialysis reactor are equivalent (equal length, area, flow rate) and (iv) the system reaches immediately the steady state for every interval of time. The obtained results show the validity of the previous assumptions in the experimental studied conditions. However, in

J.M. Ortiz et al. / Journal of Membrane Science 274 (2006) 138–149

the beginning of the experiments, a slightly divergence between theoretical and experimental data is showed in Fig. 7. This fact is explained because of the existence of a transient period until the steady state is reached. This transient period is due to certain phenomena related to the saline balance of the membranes (internal diffusion processes, membrane potential) need a specific period of time to become stable. Nevertheless, it is verified experimentally that this transient period does not have great influence in Cl− disappearance in the diluate stream. The steady state is reached as soon as t > 30τ in all the experiments, being τ the residence time in the electrovolume /Q dialyzer, τ = Vstack stack (s). Therefore, the approximation is valid as long as the process duration is greater than indicated transient period.

6. Conclusions In this paper, the feasibility of the desalination of brackish water using an electrodialysis system powered directly by photovoltaic energy has been demonstrated. Moreover, in order to design and optimize these systems, it is necessary to consider parameters like the number and configuration of PV modules, meteorological conditions, charateristics of electrodialysis reactor or the required volume of brackish water to be processed. Likewise, a mathematical simulation model has been developed successfully to simulate the functioning of these systems. The simulation is carried out solving numerically a group of equations that describe the process. Using input variables like meteorological data and specifying the operation parameters of the system, streams flow rates and compositions, the required volume of brackish water to be processed, the model calculates the diluate and concentrate tanks concentration as a function of time and the electrical consumption of the process, as well as the variation of Istack and Vstack during the process. This model can be used to study the influence of design variables and the parameters of operation in the functioning of the system with the objective of finding the optimal design and operation conditions. From the above-mentioned data, a significant number of objectives to be calculated or optimised can easily be defined. For example, for a given electrodialysis reactor, the minimum necessary number of PV modules and the optimal configuration of the PV array to desalinate a specific volume of brackish water per day for a particular location can be calculated. The simulation of an electrodialysis system is a complex task, due to the process depending on several parameters. Some of these parameters are specifics to the equipment used (characteristics of PV modules, number of PV modules, membrane resistance, geometric measures of reactor compartments, material electrodes). Others parameters are variables of operation as the concentration and the streams flow rates, the volume of batches. Finally, the simulation model developed in this paper is the starting point for subsequent studies of design and optimization of these systems for different locations and for waters with different saline composition.

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Acknowledgements J.M. Ortiz is grateful to the Agencia Valenciana de Ciencia y Tecnolog´ıa for his scholarship and Instituto Alicantino de Cultura Juan Gil Albert for the economic support. The authors would like to thank Ministerio de Ciencia y Tecnolog´ıa (Project BQU2001-4458-E) and Generalitat Valenciana (Project CTIDIB/2002/147) for the economic support.

Nomenclature active membrane area (m2 ) concentration (mol m−3 ) diffusion coefficient (m2 s−1 ) ohmic potential drop across concentrated solution (V) dil Eohm ohmic potential drop across diluted solution (V) Eel measured or applied electrode potential (V) Emem membrane potential in each stack compartment (V) Eohm ohmic potential drop across bulk solution (V) F Faraday constant (C mol−1 ) G solar irradiation (W m−2 ) Gref solar irradiation at reference conditions (W m−2 ) I0 diode inverse saturation current (A) I0,ref diode inverse saturation current at reference conditions (A) Iarray photovoltaic array output current (A) IL photo-generated current (A) Imodule PV output current of a module (A) maximum power point current (A) Imp Imp,ref maximum power point current at reference conditions (A) Isc short circuit current (A) Isc,ref short circuit current at reference conditions (A) Istack eletrodialysis reactor current (A) k Boltzmann constant (J K−1 ) L membrane gap (m) l membrane thickness (m) mCpmodule thermal global capacity of the PV module (J K−1 ) M number of PV modules connected in parallel in each string of the array N number of PV modules connected in series in each string of the array Nk number of cells in the electrodialysis stack q electrical charge of the electron (C) Q flow rate (m3 h−1 ) Qconv losses of energy by convection (W) Qelec electric power produced by the PV module (W) Qin solar power absorbed by the PV module (W) Qrad losses of power by radiation (W) R resistance (
) Rload external load resistance (
)

A C D conc Eohm

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Rs resistance in series (
) Rsh shunt resistance (
) Rstack overall resistance of the electrodialysis stack (
) t time (s) Tamb ambient temperature (K) Tmodule PV module temperature (K) Tmodule,ref PV module temperature at reference conditions (K) Varray photovoltaic array output voltage (V) Vk compartment volume in stack cells (m3 ) Vmodule output voltage of a PV module (V) maximum power voltage (V) Vmp Vmp,ref maximum power voltage at reference conditions (V) Voc,ref open circuit voltage at reference conditions (V) Vstack total electrodialysis stack voltage (V) Vstack potential drop in the electrodialysis stack (V) volume total volume of the electrodialysis stack (m3 ) Vstack Vwind wind speed (m s−1 ) z ion charge Greek letters φ current efficiency γ shape factor δ Nernst diffusion layer (m) τ residence time (s) Subscripts a anion-exchange membrane amb ambient temperature array photovoltaic array c cation-exchange membrane conc concentrate dil diluate end end of process in initial k generic compartment in the electrodialyzer mem membrane module photovoltaic module mp maximum power oc open circuit ref reference conditions sc short circuit stack electrodialysis stack Superscripts 0 stack cell inlet T tank wa anion-exchange membrane surface wc canion-exchange membrane surface

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