Effect of electrode area on demineralization performance and the distribution of current density in an industrial-scale electrodialysis stack

Desalination 412 (2017) 49–57

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Effect of electrode area on demineralization performance and the distribution of current density in an industrial-scale electrodialysis stack David Tvrzník MemBrain s.r.o., Pod Vinicí 87, 471 27 Stráž pod Ralskem, Czech Republic

H I G H L I G H T S • • • •

Reduction of electrode area negatively affects performance. Reduction of area generates current density peaks at the edges of the electrode. The macrohomogeneous 2D model can be used to study the effect of electrode area. The macrohomogeneous 2D model cannot be used for prediction of performance.

a r t i c l e

i n f o

Article history: Received 3 October 2016 Received in revised form 10 February 2017 Accepted 1 March 2017 Available online 8 March 2017 Keywords: Electrodialysis ED EDR Current density distribution Mathematical modeling

a b s t r a c t Effect of electrode area on demineralization performance and the distribution of current density in an industrialscale electrodialysis stack was studied. A segmented electrode was used for this purpose. Several combinations of active/inactive segments of the electrode were tested and results obtained were mutually compared. It was found that any reduction of the electrode area caused the demineralization performance to decline and generated extremely high local current densities at the edges of the electrode. The experimental results were qualitatively in correlation with a macrohomogeneous 2D model for computation of the distribution of electric potential, electrolyte concentration in the dilute and current density in the electrodialysis stack. © 2017 Elsevier B.V. All rights reserved.

1. Introduction Electrodialysis (ED) is an electromembrane separation process that is mainly used for partial demineralization of whey, low TDS waters and aqueous solutions such as river or brackish waters, municipal waste waters or some industrial waste waters. Current trends in development of conventional ED are toward a higher level of modularity and reliability, simplicity of operation and lower maintenance of the process modules. At the same time, competition of other (membrane) separation processes in the field of low TDS water treatment such as reverse osmosis (RO) or capacitive deionization (CapDI) requires significant reduction of costs for production of industrial-scale ED stacks. The research activities are mainly focused on the development of novel, low cost ion-exchange membranes in this field as the ion-exchange membranes are the major part of manufacturing costs. Ti/Pt plate electrodes are another important part of manufacturing costs of industrial-scale ED stacks, especially in cases

E-mail address: [email protected].

http://dx.doi.org/10.1016/j.desal.2017.03.002 0011-9164/© 2017 Elsevier B.V. All rights reserved.

when electrode polarity reversal is used. For instance, Ti/Pt electrodes constitute approximately 20% of manufacturing costs of EDR-III stacks with a higher number of cell pairs (above 400) available from MEGA a.s. (Czech Republic). These electrodes can be replaced with cheaper alternatives such as mixed metal oxide (MMO) electrodes in some applications. Recently, use of CapDI electrodes in ED is of particular interest in some applications, especially owing to the possibility of complete elimination of the electrode loop and associated equipment [1]. Those who are skilled in the art know that electrodes for electrochemical systems are available also in other than plate forms. For example, mesh or rod electrodes are available. These alternatives have been adopted on a limited scale or have never been adopted in ED, however. In some ED stacks available in the market, electrode area is reduced compared to the active area of an ion-exchange membrane. This might be an alternative way of reduction of manufacturing costs. To date, relatively little has been published on the effect of electrode area on demineralization performance of ED stacks. It is therefore the aim of this work to evaluate the feasibility of building industrial-scale ED stacks with conventional plate electrodes and reduced electrode area in order to reduce manufacturing costs. Successful completion of this

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D. Tvrzník / Desalination 412 (2017) 49–57

List of symbols C F JS L QD R RA T U ai cS dC dCP dM dstack j n x y xrel yrel w m ΛS α ϕ ρ

Salt removal (%) Faraday constant (= 96485 C mol−1) Local flux density (mol m−2 s−1) Active length of an ion-exchange membrane (flow path length) (m) Dilute flow rate (m3 s−1) Molar gas constant (= 8.31446 J K−1 mol−1) Sheet resistance of an ion-exchange membrane (Ω m2) Thermodynamic temperature (K) Voltage (V) i-th coefficient of the kinetics of electrolyte separation from the dilute (mol1−i m3i−2 s−1) Molar concentration of an electrolyte (mol m−3) Thickness of a flow chamber (m) Thickness of a cell pair (m) Thickness of an ion-exchange membrane (m) Thickness of a membrane (electrodialysis) stack (m) Current density vector (A m−2) Number of cell pairs Horizontal coordinate (m) Vertical coordinate (m) Relative horizontal coordinate xrel ¼ d x (-) stack Relative vertical coordinate yrel ¼ yL (-) Active width of an ion-exchange membrane (m) Degree of a polynomial (-) Molar conductance of an electrolyte (S m2 mol−1) Coefficient related to the effect of a spacer on ohmic resistance of a flow chamber in the ED stack (-) Electric potential (V) Electric resistance of an ion-exchange membrane (Ω m)

Subscripts AM Related to the anion-exchange membrane C Related to the concentrate CIN Relatied to the concentrate inlet into the ED stack CM Related to the cation-exchange membrane D Related to the dilute DIN Related to the dilute inlet into the ED stack

distribution of current density and the limiting current density in an ED stack [2]. Kodým et al. used an electrode divided into 6 segments in order to verify their 2D mathematical model of mass and charge transfer in an ED stack [3]. In this work, each electrode was formed of 10 segments. The active surface area of each electrode segment was 350 × 125 mm. Adjacent segments were separated with a 5 mm wide gap. A power cable to each electrode segment was equipped with an on/off switch and an ammeter, see Fig. 1, which allowed for different combinations of active/inactive segments of the electrode to be tested and mutually compared. An overview of the studied combinations of active/inactive electrode segments is shown in Table 1. All tested combinations of active/inactive electrode segments are symmetrical about the two planes that bisect the ED stack vertically and horizontally. Case S1 is equal to the standard full-area electrode. Case S2 simulates reduction of electrode area by 20% and cases S3, S5 and S6 simulate reduction of electrode area by 40%. Case S6 was not tested, but its potential benefits are only discussed based on prediction of its performance using a mathematical model. Described segmentation and tested combinations of active/inactive segments of the electrode were chosen with regard to the potential replacement of the standard electrodes with alternative electrode arrangements, which requires a small number (2 to 3) of segments and easy installation in the end-plate of the ED stack. Both diluting and concentrating loops of the ED stack were fed with the same aqueous solution of NaCl at a temperature of 25 °C from a tank. After one pass of the liquid through the stack, both dilute and concentrate were returned back to the tank, thus maintaining constant composition of the feed solution. To avoid chlorine formation during the tests, the electrode loop was separated from the diluting and concentrating one and an aqueous solution of 10 kg m−3 Na2SO4 was circulated in the electrode loop. Electric potential was applied on the electrode terminals from the external DC power supply. The ED stack was gradually tested at all combinations of the following operating conditions: ◦ ◦ ◦ ◦

an aqueous feed solutions of 17.11, 51.33 and 85.56 mol m−3 NaCl, a dilute flow rate of 24, 32 and 40 m3 h−1, a voltage of 0.25 to 1.25 V/cell pair with a step of 0.25 V/cell pair, an electrode configuration of S1, S2, S3 and S5, see Table 1.

task requires that the potential performance loss associated with the reduction of electrode area is lower than the reduction of manufacturing costs.

The total electric current, electric current in the respective electrode segments, dilute and concentrate pH and conductivity at the outlet from the stack were monitored during the tests. The ED stack was operated under each combination of operating conditions for at least 10 min, although much less time was required to reach the steady state operation. Experimental data readings obtained at the steady state were used for further evaluation.

2. Experimental

3. Mathematical modeling

EDR-III/400–0.68 Type 13 industrial-scale ED stack available from MEGA a.s. (Czech Republic) was used in this work. The stack comprised 400 cell pairs of RALEX® CM-PES and AM-PES heterogeneous ion-exchange membranes available from the same manufacturer. Standard electrodes are divided into two parts, each part having a size of approximately half of the membrane active area in this stack. The purpose for this solution is a quite large membrane active area (350 × 1300 mm) and limited commercial availability of anodes of that size, but also mechanical issues such as bending of large electrodes manufactured from a relatively thin (2 mm) titanium plate and practical issues when installing such electrodes. In order to evaluate the effect of an electrode with reduced area in the stack, the standard two part electrodes were replaced with segmented electrodes. This is a common technique frequently used in electrochemistry including characterization of ED stacks. For example, Tanaka used an electrode divided into 8 segments to study the

To evaluate a dilute flow rate needed to achieve a certain salt removal per a single pass of the liquid through the ED stack at the given feed concentration and voltage, means of approximating the dependence of salt removal on the dilute flow rate is required. Since only three experimental data points are available for three flow rate conditions, linear regression with an univariate quadratic function can be used. It can be shown that this approach provides sufficient accuracy for the purposes of this work. This is only due to a relatively narrow range of tested flow rates, however. Therefore, an alternative and generally better approach was used in this work and is described below. The local mass balance of an electrolyte in a volume element of the diluting chamber is

∂cS;D nwJ S : ¼− QD ∂y

ð1Þ

D. Tvrzník / Desalination 412 (2017) 49–57

51

Fig. 1. Diagram of electrode segmentation and electric connection. CM – cation-exchange membrane, AM – anion-exchange membrane.

Further suppose the local kinetics of electrolyte separation from the dilute can be expressed by a polynomial functions as follows. m

J S ¼ ∑ ai ciS;D

ð2Þ

i¼0

and the change of QD along the liquid flow path is negligible. Differential Eq. (1) can be transformed and solved analytically up to m = 2 under these assumptions. Due to practical reasons (possibility to express the local kinetics of the process by a polynomial of a higher degree or by another function, to incorporate separation of a solvent etc.), we maintain the original differential form of the equation and solve it numerically with an initial condition of cS,D(0) = cS,DIN. Thus it is possible to obtain the following symbolic function. cS;DOUT ¼ f ðQ D ; aÞ

ð3Þ

for the given combination of feed concentration, voltage and electrode configuration and to calculate vector a from experimental data using nonlinear regression. This approach to evaluating parameters in differential equations from integral data is described for example in literature [5]. Data obtained for selected combinations of operating conditions was further compared with the results from a mathematical model. Given the plate-and-frame geometry of the ED stack and electrode area Table 1 Studied combinations of active/inactive electrode segments. Electrode segment

S01A,B S02A,B S03A,B S04A,B S05A,B S06A,B S07A,B S08A,B S09A,B S10A,B

State of connection Case S1

Case S2

Case S3

Case S5

Case S6

On On On On On On On On On On

Off On On On On On On On On Off

Off Off On On On On On On Off Off

On On Off Off On On Off Off On On

On Off On Off On On Off On Off On

reduced in the longitudinal direction only, the studied problem was considered as a two-dimensional (2D). The mathematical model for computation of the distribution of electric potential, electrolyte concentration in the dilute and current density used was similar to that one that was described in literature [6]. Some major changes to the model were performed for the purposes of this work, however. See Fig. 1 for the coordinate system considered in this work. Model assumptions: ◦ the electrode area is reduced in the direction of y axis only, ◦ the distribution of the liquid flow among the respective flow chambers is uniform, ◦ the volume flow rates of the dilute and concentrate are equal and constant along the whole flow path length (transfer of water through the membranes is negligible), ◦ based on the previous point, the following local mass balance applies between the dilute and concentrate flow phases cS , D(x, y) +cS , C(x, y) = const., ◦ piston flow of the liquid through the flow chambers, ◦ shunt current is negligible (otherwise it would be necessary to use a 3D model), ◦ ions are transported only by migration through ion-exchange membranes, ◦ properties of ion-exchange membranes are constant, i.e. independent on composition of the liquid phases, which they are in contact with, ◦ ideal selectivity of ion-exchange membranes, ◦ conductivity of the solution is proportional to the electrolyte concentration, ◦ a binary uni-univalent electrolyte is used. The elements of the current density vector are:   cS;C ∂ϕ 2RT dCP þ ln c F ∂x  S;D ; jx ¼ − αdC 1 1 þ RA;CM þ RA;AM þ ΛS cS;D cS;C

ð4Þ

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D. Tvrzník / Desalination 412 (2017) 49–57




jy ¼ −

ΛS dC cS;D þ cS;C þ dM dCP

 1 1 þ ρCM ρAM ∂ϕ : ∂y

Table 2 Demineralization performance of EDR-III/400–0.68 Type 13 stack (experiment).



ð5Þ

Charge balance is ∇ j¼0

ð6Þ

and the mass balance of a volume element of the diluting chamber is. ∂cS;D nwjx ; ¼− FQ D ∂y

ð7Þ

which was derived from Eq. (1) by taking the above mentioned model assumptions into account. Eqs. (6) and (7) form a system of two partial differential equations with the following boundary conditions: ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦

ϕ(0, y) = U for any y occupied by the anode, ϕ(dstack, y) = 0 for any y occupied by the cathode, jx(0, y) = 0 for any y out of the anode, jx(dstack, y) = 0 for any y out of the cathode, jy(x,0)=0, jy(x,L) = 0, cS,C(x,0)=cS,CIN, cS,D(x,0)= cS,DIN, The following parameters were used in the model:

◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦

L = 1.3 m, RA,AM =RA,CM = 7 × 10−4 Ω m2, U = 400 V, QD = 8.89 × 10−3 m3 s−1, cS,CIN =cS ,DIN = 17.11 mol m−3, dC = 0.68 × 10−3 m, dCP =2(dC + dM) = 2.52 × 10−3 m, dM = 0.58 × 10−3 m, dstack = ndCP = 1.008 m, n = 400, w = 0.35 m, ΛS = 1.17 × 10−2 S m2 mol−1, α = 1.5, ρAM =ρCM = 1.2 Ω m2,

which correspond to the real properties of the ED stack and its parts and selected operating conditions used. 4. Results and discussion The demineralization performance of the ED stack was expressed as percentage of salt removed from the liquid by a single pass of the dilute through the ED stack provided that the flow rate is constant. C¼

  cS;DOUT  100%: 1− cS;DIN

ð8Þ

NaCl concentrations were calculated from dilute conductivities at the inlet to the stack and at the outlet from the stack using data published in literature [4]. An overview of the results related to the demineralization performance of the ED stack for all combinations of operating conditions and cases of electrode connection is shown in Table 2. An example of evaluation of demineralization performance for all tested cases of electrode connection and its comparison for a selected operating conditions and salt removal (65%) is shown in a graphical form in Fig. 2. The respective curves (salt removal vs. dilute flow rate)

Feed concentration

Dilute flow rate

Voltage

[mol m−3]

[m3 h−1]

[V/cell pair]

S1

S2

S3

S5

17.11 17.11 17.11 17.11 17.11 17.11 17.11 17.11 17.11 17.11 17.11 17.11 17.11 17.11 17.11 51.33 51.33 51.33 51.33 51.33 51.33 51.33 51.33 51.33 51.33 51.33 51.33 51.33 51.33 51.33 85.56 85.56 85.56 85.56 85.56 85.56 85.56 85.56 85.56 85.56 85.56 85.56 85.56 85.56 85.56

24 24 24 24 24 32 32 32 32 32 40 40 40 40 40 24 24 24 24 24 32 32 32 32 32 40 40 40 40 40 24 24 24 24 24 32 32 32 32 32 40 40 40 40 40

0.25 0.5 0.75 1 1.25 0.25 0.5 0.75 1 1.25 0.25 0.5 0.75 1 1.25 0.25 0.5 0.75 1 1.25 0.25 0.5 0.75 1 1.25 0.25 0.5 0.75 1 1.25 0.25 0.5 0.75 1 1.25 0.25 0.5 0.75 1 1.25 0.25 0.5 0.75 1 1.25

30.19 54.44 68.95 77.63 82.82 22.03 42.90 57.17 66.94 73.62 18.57 35.47 48.58 58.76 66.66 18.56 39.45 55.12 66.87 75.68 14.01 30.00 43.67 55.36 65.37 10.91 23.79 35.80 46.99 57.41 14.01 30.88 45.69 58.70 70.13 10.47 22.86 34.95 46.76 58.28 8.89 19.60 29.56 38.80 47.38

28.48 53.29 67.99 76.70 81.87 21.61 41.92 55.98 65.71 72.44 17.27 35.04 48.09 57.67 64.71 18.00 38.06 53.55 65.52 74.77 13.66 29.49 43.04 54.63 64.55 10.81 23.42 35.10 45.93 55.96 13.99 29.15 44.04 58.67 73.03 10.59 22.69 34.30 45.44 56.11 8.93 18.24 27.78 37.58 47.63

26.18 51.03 65.82 74.62 79.85 19.38 39.74 54.04 64.08 71.13 15.66 31.81 44.67 54.91 63.05 15.67 35.15 50.43 62.41 71.81 12.39 26.55 39.01 49.99 59.65 10.17 21.23 31.83 42.00 51.75 10.49 25.35 38.58 50.35 60.84 9.70 20.56 31.19 41.59 51.76 7.81 16.41 25.11 33.92 42.83

26.97 52.22 67.04 75.73 80.83 20.25 41.02 55.34 65.20 72.00 15.88 32.95 46.16 56.39 64.29 17.29 37.00 52.34 64.26 73.54 12.91 28.49 41.68 52.84 62.28 9.98 22.88 34.21 44.14 52.86 13.27 28.39 42.27 55.01 66.71 10.45 21.97 33.19 44.12 54.77 8.66 18.25 27.56 36.62 45.42

Salt removal [%]

were evaluated using the method discussed in the beginning of Section 3. This form of evaluation of data represents comparison of throughputs of ED stacks with the respective electrode arrangements in single pass applications. All experimental data presented in Table 2 was processed and evaluated in the same way. The dilute flow rates needed to achieve a certain salt removal for the respective cases of electrode connection were mutually compared in a whole range of salt removals corresponding to the minimum and maximum dilute flow rate in case S1 and for all tested combinations of feed concentration and voltage. An overview of measurements of the distribution of electric current in the respective segments of the electrode is shown in Fig. 3. The data presented is an average of values measured in segments SxxA and SxxB. Because of the large amount of experimental data obtained and similar trends of the electric current in the respective segments of electrode at different feed concentrations and dilute flow rates, data for just one combination of operating conditions (an aqueous solution of 17.11 mol m−3 NaCl and a dilute flow rate of 32 m3 h−1) is presented here. It was found that the demineralization performance of the ED stack was negatively affected in all studied cases with reduced electrode

D. Tvrzník / Desalination 412 (2017) 49–57

Fig. 2. Graphical representation of ED stack performance evaluation for an aqueous solution of 17.11 mol m−3 NaCl and a voltage of 1 V/cell pair.

Fig. 3. Distribution of electric current in the respective electrode segments for an aqueous solution of 17.11 mol m−3 NaCl and a dilute flow rate of 32 m3 h−1.

53

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D. Tvrzník / Desalination 412 (2017) 49–57

Table 3 Demineralization performance of EDR-III/400–0.68 Type 13 stack (model). Feed concentration [mol m−3]

Dilute flow rate [m3 h−1]

Voltage

Salt removal [%]

[V/cell pair]

S1

S2

S3

S5

S6

17.11 17.11 17.11 17.11 17.11 17.11 17.11 17.11 17.11 17.11 17.11 17.11 17.11 17.11 17.11

24 24 24 24 24 32 32 32 32 32 40 40 40 40 40

0.25 0.5 0.75 1 1.25 0.25 0.5 0.75 1 1.25 0.25 0.5 0.75 1 1.25

32.15 58.79 77.27 88.33 94.27 24.87 47.14 65.03 78.06 86.79 20.24 39.06 55.35 68.52 78.53

31.45 57.80 76.39 87.68 93.73 24.31 46.17 63.99 77.16 86.09 19.77 38.20 54.30 67.48 77.62

29.59 55.11 73.86 85.58 91.45 22.73 43.39 60.93 74.43 83.92 18.47 35.68 51.19 64.34 74.81

30.66 56.47 75.08 86.76 93.33 23.67 45.02 62.59 75.84 85.06 19.25 37.19 52.98 66.06 76.30

31.34 57.55 76.12 87.52 93.79 24.22 46.00 63.74 76.90 85.89 19.70 38.05 54.09 67.22 77.36

area. With respect to the increasing negative impact of the electrode with reduced area on demineralization performance, the tested cases of the electrode with reduced area can be sorted as follows: S1 b S2 b S5 b S3. Namely, the dilute flow rate needed to achieve a certain salt removal was lower by 2.5 to 3.5% in case S2, by 7 to 20% in case S3 and by 5 to 10% in case S5 than in case S1. Predictions of salt removal by the macrohomogeneous 2D model, discussed in Section 3, for the feed solution of 17.11 mol m−3 NaCl are

shown in Table 3. Case S6 with electrode area reduced by 40% gives similar results as case S2 with electrode area reduced by 20%. The differences between the experimental and calculated data in Table 2 and Table 3, respectively, are relatively small at low voltages and mainly due to the selection of parameter α, see Section 3. The model predicts significantly higher salt removals than the real data for higher voltages, however. This is a result of simplifications assumed in the model, namely the piston flow of the liquid through the flow chambers for which the effect of concentration polarization is not defined. It was shown in other works such as [7] that the best correlation between experimental data and a mathematical model could be achieved by considering the boundary diffusion layers at the interfaces between the liquid and ion-exchange membranes and ideal transverse mixing of the flow phases. This approach cannot be used here due to computational complexity, however. Other causes of differences between experimental and computed data might be, to a certain extent, nonideal selectivity of the ion-exchange membranes, non-uniform distribution of the liquid flow among the respective flow chambers that was observed by the author in another work, shunt currents which deform the electric field at the inlet and outlet portions of the flow chambers and real behavior of electrolyte solutions. Therefore, the presented macrohomogeneous 2D model should not be used for quantitative prediction of demineralization performance of industrial-scale ED stacks, especially at higher voltages. It is obvious, that the model at least maintains the same sort order of the studied cases of the electrode with reduced area with respect to their increasing negative impact on demineralization performance of the ED stack as the experimental data does.

S1

S2

S3

S5

S6 Fig. 4. Distribution of current density in the ED stack according to the mathematical model for an aqueous solution of 17.11 mol m−3 NaCl, a dilute flow rate of 32 m3 h−1 and a voltage of 1 V/cell pair.

D. Tvrzník / Desalination 412 (2017) 49–57

It is evident from comparison of cases S3, S5 and S6, all with electrode area reduced by 40%, that it is possible at least partially to eliminate the negative impact of the electrode with reduced area on demineralization performance by a suitable arrangement of the electrode segments. It means that two inactive segments of the electrode should not be located next to each other and segments S01A,B and S10A,B should be active. The distribution of electric current in the respective segments of the electrode, see Fig. 3, is as expected in case S1, ie. electric current (current density) decreases along the dilute flow path due to decreasing electrolyte concentration in the dilute and consequentially increasing ohmic resistance of the membrane stack. This is logically more obvious at higher voltages. Significantly increased electric current was observed in the active electrode segments in cases with the reduced electrode area (S2, S3 and S5), especially in those facing the inactive segments. It is obvious from the distribution of electric current in the respective segments of the electrode, that an extremely high current density

55

must occur at the edges of the active segments facing the inactive segments. An example of computation of current density in an ED stack using the mathematical model discussed in Section 3 for the same combination of operating conditions is shown in Fig. 4. Gnuplot Version 4.6 computer program was used to create 2D visualization of the distribution of current density. Domains of extremely high current density propagate into the first and last 5 to 10% cell pairs according to the mathematical model. In reality, the area of these domains might be reduced due to the real kinetics of mass transfer between the dilute and ion-exchange membranes, especially at low electrolyte concentrations. The corresponding distribution of current density on the electrode is shown in Fig. 5 and the distribution of electric current in the respective electrode segments is shown in Fig. 6. Mathematical model in correlation with experiments predicts generation of current density extremes at the edges of the electrode with reduced area. These extremes are 2.5 to 5-times higher than current

Fig. 5. Distribution of current density on the electrode according to the mathematical model for an aqueous solution of 17.11 mol m−3 NaCl, a dilute flow rate of 32 m3 h−1 and a voltage of 1 V/cell pair.

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D. Tvrzník / Desalination 412 (2017) 49–57

Fig. 6. Distribution of electric current in the respective electrode segments according to the mathematical model for an aqueous solution of 17.11 mol m−3 NaCl and a dilute flow rate of 32 m3 h−1.

densities that would normally exist here in case of use of the full-area electrode. The distribution of electric current among the respective electrode segments computed by the model, as shown in Fig. 6, is also in a good agreement with experiments, although the computed electric currents do not match the experimental values exactly (compare Fig. 6 with Fig. 3 for the same voltage). Again, these differences are results of simplifications assumed in the model as discussed above. Combination of demineralization performance drop and generation of current density extremes, which may cause local precipitation of insoluble compounds such as CaCO3 or Mg(OH)2 (scaling) due to operation at overlimiting current densities or local overheating and demage to the parts of the ED stack, especially ion-exchange membranes, makes reduction of electrode area an unpromising way of reduction of the manufacturing costs.

It must be noted here, that the discussed evaluation might be, to some extent, affected by the number of cell pairs in the ED stack. The electrodes constitute a higher part of the manufacturing costs in ED stacks with a lower number of cell pairs, ie. the potential of manufacturing costs reduction is higher here, but also the negative impact of electrode with reduced area on demineralization performance and the distribution of current density is much larger. On the other hand, both potential of cost savings and negative impact of the electrode with reduced area are much lower in ED stacks with a higher number of cell pairs. In addition, decreasing the distance among the active electrode segments at least partially eliminates the negative impact of the electrode with reduced area. This leads to an unsuitable segmentation of the electrode or to a mesh electrode, however.

D. Tvrzník / Desalination 412 (2017) 49–57

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5. Conclusions

Acknowledgements

Reduction of electrode area negatively affects the distribution of current density in the EDR-III/400-0.68 Type 13 industrial-scale ED stack and thus negatively affects its demineralization performance. With respect to the increasing negative impact on demineralization performance, the studied cases of the electrode with reduced area can be sorted as follows: S1 (standard full-area electrode) b S2 (electrode area reduced by 20%) b S6 (electrode area reduced by 40%) b S5 (electrode area reduced by 40%) b S3 (electrode area reduced by 40%). The negative impact of the electrode with reduced area can be at least partially eliminated by a suitable arrangement of electrode segments, as follows from comparison of cases S3, S5 and S6. Reduction of area of the conventional plate electrode was evaluated as an unpromising way of reducing the manufacturing costs of industrial-scale ED stacks due to the performance drop and generation of current density extremes at the edges of the electrode with reduced area, which significantly increases the risk of scaling or demage to the stack by overheating or burning. The macrohomogeneous 2D mathematical model for computation of the distribution of electric potential, electrolyte concentration in the dilute and current density in the ED stack used is a suitable qualitative tool for studying effects of the electrode with reduced area as it correctly predicts not only the negative impact of reduced electrode area on performance of the stack, but it also predicts the current density extremes at the edges of the electrode. Due to the simplifications assumed in the model, it is not suitable for quantitative prediction of the demineralization performance of the ED stack, however.

This work was carried out within the framework of the project FRTI4/398 “Research, development and application of new generation electromembrane modules” supported by Ministry of Industry and Trade of the Czech Republic and project No. LO1418 “Progressive development of Membrane Innovation Centre” supported by the program NPU I Ministry of Education Youth and Sports of the Czech Republic, using the infrastructure of Membrane Innovation Centre. References [1] J. Barber, H. Yang, Electrodialysis reversal with capacitive electrodes, AIChE 2013 – Desalination and Water Management for Rural Communities, 2013. [2] Y. Tanaka, Current density distribution and limiting current density in ion-exchange membrane electrodialysis, J. Membr. Sci. 173 (2000) 179–190. [3] R. Kodým, M. Drakselová, P. Pánek, Novel approach to mathematical modeling of the complex electrochemical systems with multiple phase interfaces, Electrochim. Acta 179 (2015) 538–555. [4] H.J. DeWane, W.J. Hamer, Electrolytic conductivity of aqueous solutions of the sodium halides, National Bureau of Standards Report 9979, 1969. [5] M. Kubíček, Numerické algoritmy řešení chemickoinženýrských úloh, SNTL, Praha, 1983. [6] R. Kodým, P. Pánek, D. Šnita, D. Tvrzník, K. Bouzek, Macrohomogeneous approach to a two-dimensional mathematical model of an industrial-scale electrodialysis unit, J. Appl. Electrochem. 42 (9) (2012)http://dx.doi.org/10.1007/s10800-012-0457-6. [7] D. Tvrzník, L. Machuča, A. Černín, Mathematical model of mass transfer in an electrodialyzer with net-like spacers, Desalin. Water Treat. 14 (2010) 174–178.