Ion-Exchange Membrane Electrodialysis of Saline Water and Its

ARTICLE pubs.acs.org/IECR

Ion-Exchange Membrane Electrodialysis of Saline Water and Its Numerical Analysis Yoshinobu Tanaka* IEM Research, 1-46-3 Kamiya, Ushiku-shi, Ibaraki 300-1216, Japan ABSTRACT: A computer simulation program was developed for a continuous saline water electrodialysis process. A practical-scale electrodialyzer was operated for concentrating seawater, and its performance was observed. The operating results of the electrodialyzer were computed by using the operating conditions as input for the program. The computed data were generally the same as the observed data. Thus, the program enables the semiquantitative discussion of the performance of a practical-scale electrodialyzer. In addition, (1) the current density distribution; (2) the electric resistances of a membrane pair, a desalting cell, and a concentrating cell; (3) the pressure drops in a desalting cell and a concentrating cell; and (4) the limiting current density of an electrodialyzer are discussed.

1. INTRODUCTION Ion-exchange membrane electrodialysis is a technique for separating ionic species in a feed solution, and it is applied to saline water desalination.16 This technology is currently used in many fields such as drinking water treatment, wastewater treatment, demineralization of amino acids, demineralization of whey, demineralization of sugar liquor, and treatment of organic substances. Electrodialysis is also applied to concentrate seawater,7,8 and research on electrodialytic seawater concentration has been carried out.911 In a salt-manufacturing process, the concentrated brine obtained from an electrodialyzer is supplied to an evaporation process to produce edible salt. Currently, nearly 106 ton/year of edible salt is manufactured in Japan. The largest problem in seawater concentration is that the price of produced salt is higher than that of imported salt because of higher energy consumption. To reduce energy consumption, homogeneous ion-exchange membranes having excellent electrochemical properties have been synthesized. The mechanical strength of these membranes was increased by cross-linking and reinforcement.1214 Their performance was tested by the long-term endurance operation of an electrodialyzer.15 A diagonal net spacer was incorporated into an electrodialyzer to mix a solution flowing in desalting cells.16 The divalent ion permeability across the membranes was strongly suppressed to prevent CaSO4 scale precipitation.1720 To prevent CaCO3 scale precipitation, hydrochloric acid was added to concentrating cells.21 Small particles suspended in a feed solution were removed using sand filtration.22 However, extremely small particles passed through the filter, entered into the electrodialyzer, and allowed microorganisms to breed at the membrane surface.23,24 The deposits on the membrane were removed by stack disassembling or washing with a chemical reagent.2527 The electrodialysis process can be operated as a continuous, batch, and feed-and-bleed process. In previous investigations,2830 an electrodialysis program for these processes was developed to analyze the performance of an electrodialyzer. The program includes the model equations with ordinary principles such as mass transport, mass balance, and energy consumption. To develop the program further, it is necessary to compare the data r 2011 American Chemical Society

calculated by computer simulation with the operating results of an electrodialyzer. In this investigation, a practical-scale electrodialyzer was operated for seawater concentration under changing current density and solution temperature. The performance of the electrodialyzer was computed using the electrodialysis program with the same conditions as applied to the electrodialysis operation used as input. The reasonability of the program is discussed by comparing the operating results of the electrodialyzer with the calculated results.

2. ELECTRODIALYSIS PROGRAM The electrodialysis process considered in this investigation is a continuous process for concentrating seawater.31 The principle of the process is fundamentally the same as that of a continuous process for saline water desalination and has been investigated widely.3235 However, in this work, the program is developed in the following ways to describe the operating conditions more definitely: (1) The relationship between solution temperature and electrodialyzer performance is clarified by evaluating the influence of temperature on the solution physical properties and membrane characteristics. (2) The electric current screening ratio of a spacer is defined and calculated. (3) The ionic concentration ratio in a concentrated solution is calculated using empirical equations. (4) The hydrodynamic diameters and pressure differences in a desalting cell and a concentrating cell are calculated. (5) A concentrated solution is circulated. Taking account of the above revisions, the electrodialysis program (compiled in section 7) is developed on the basis of the following assumptions: (1) Mass transport across the membrane pair is expressed by the overall mass-transport equation. Received: March 18, 2011 Accepted: July 11, 2011 Revised: July 2, 2011 Published: July 11, 2011 10765

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Industrial & Engineering Chemistry Research

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Figure 1. Continuous process.

(2) The overall transport number, overall solute permeability, overall electro-osmotic permeability, and electric resistance of an ion-exchange membrane pair are determined from the overall hydraulic permeability (leading parameter). (3) The influence of the temperature on the performance of an electrodialyzer is determined on the basis of the relationship between temperature and overall hydraulic permeability. (4) Solution leakage and electric current leakage are assumed to be negligible. (5) The frequency distribution of the solution velocity ratio in desalting cells is assumed to be a normal distribution. (6) The current density i at a distance of x from the inlets of desalting cells is approximated by a quadratic equation. (7) The voltage difference between the electrodes at the entrance of desalting cells is assumed to be equal to the value at the exits. (8) The limiting current density of the electrodialyzer is defined as the average current density applied to the electrodialyzer when the current density reaches the limit of an ion-exchange membrane at the outlet of the desalting cell in which linear velocity and salt concentration are the lowest. (9) The salt concentration is assumed to be uniform in concentrating cells, and concentrated solutions are extracted from the concentrating cells to the outside of the process. The limitations of the program are as follows: (1) Saline water supplied to an electrodialyzer is a solution dissolving strong electrolytes. (2) Empirical equations are developed on the basis of experiments using homogeneous ion-exchange membranes manufactured by Japanese companies.

with a constant electric current I as illustrated in Figure 1. An electrolyte solution (of concentration C0in) is supplied to the inlets of desalting cells (De) at an average linear velocity of u0in. Electrolytes and solutions transfer from desalting cells to concentrating cells (Con) across an ion-exchange membrane pair with fluxes of JS and JV, respectively. The concentrated solution is circulated through the circulation tank equipped at the outside of the electrodialyzer, with the solution velocity adjusted to u00in at the inlets and u00out at the outlets of concentrating cells. The salt concentration in the concentrated solution, C00 , is maintained at a steady state in the flow system. In desalting cells, the electrolyte concentration decreases from C0in under an applied average current density of I/S and reaches an average electrolyte concentration of C0out at the outlets of desalting cells. The change in the electrolyte concentration in desalting cells causes a change in current density along the flow pass from iin at the inlets to iout at the outlets. The current density becomes i at a distance of x from the inlets of desalting cells. I/S, JS, JV, C0 , C00 , u0 , and u00 are the values of the corresponding quantities at a distance of pl from the inlets of desalting cells; x = pl. Vin, Vout, and Vp are the voltage differences between the electrodes at the inlets (x = 0), outlets (x = l), and x = pl, respectively, for the desalting cells.

4. ELECTRODIALYSIS PROGRAM The performance of the electrodialyzer illustrated in Figure 1 is computed according to the electrodialysis program presented in Figures 24. The program consists of the following steps, as explained in the algorithm in section 7: Figure 2 shows steps 13. Step 1.

Simulation of the mass transport (sections 7.17.3) Step 2. Simulation of the current density distribution (section 7.7) Step 3. Simulation of the cell voltage (sections 7.5 and 7.8)

3. ELECTRODIALYSIS PROCESS An electrodialyzer (effective membrane area, S; flow-pass width, b; flow-pass length, l; flow-pass thickness, a) is operated 10766

dx.doi.org/10.1021/ie2005498 |Ind. Eng. Chem. Res. 2011, 50, 10765–10777


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Figure 2. Simulation of mass transport, current density distribution, and cell voltage (steps 13).

• average linear velocities at the inlets of desalting and concentrating cells, u0in and u00in, respectively; • current density, I/S • flow-pass thicknesses in desalting and concentrating cells, a0 and a00 , respectively; • flow-pass widths in desalting and concentrating cells, b0 and b00 , respectively; • flow-pass lengths in desalting and concentrating cells, l0 and l00 , respectively; • standard deviation of the normal distribution of solution velocity ratio in desalting cells, σ = 0.1; • and so on.

Figure 3 shows step 4. Step 4. Simulation of the NaCl concentration and energy consumption (sections 7.4 and 7.10) Figure 4 shows step 5. Step 5. Simulation of the limiting current density (section 7.11) Computation of the electrodialysis program is performed by substituting the following inputs and control keys in Figures 24: Inputs • temperature of the feed solution, T; • salt concentration at the inlets of desalting cells, C0in; 10767



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Figure 4. Simulation of limiting current density (step 5). Superscript # indicates the lowest value in an electrodialyzer. Figure 3. Simulation of the NaCl concentration in a concentrated solution and energy consumption (step 4).

Control Keys • average salt concentration in desalting cells at x = pl, C*; • position at which the current density becomes I/S in an electrodialyzer, p*; and • salt concentration at the outlet of the desalting cell0 at #* , which linear velocity becomes the lowest in a stack, Cout In the computation, if the algorithm reaches a decision point (diamond symbol), it is adjusted by changing control keys to realize the equations given at the decision points. Then, it loops back to an earlier portion in the algorithm. The trial-and-error calculation repeats until all equations are satisfied. The computation finished within 10 min to obtain one group of plots in the figures.

5. ELECTRODIALYSIS EXPERIMENTS In the electrodialysis experiments, 45 or 90 pairs of ionexchange membranes, Aciplex K172/A172 or Aciplex K182/ A182 (Asahi Chemical Co.), were integrated in an electrodialyzer (effective membrane area, 48.5 dm2 = 50 cm width 97 cm length; distance between the membranes, 0.05 cm). An electrodialysis system was formed as illustrated in Figure 5. In this system, the temperature of sand-filtered seawater was controlled to T ( 0.3 °C by a temperature controller and supplied to the seawater feeding tank. It was further supplied to the electrodialyzer at an average linear velocity at the inlets of the desalting cells

of u0in. The desalted seawater was extracted to the outside of the process. Seawater was supplied to the concentrating cells at an average linear velocity at the inlets of the concentrating cells of u00in and circulated through the concentrated solution circulating tank. The pH of the concentrated seawater was adjusted to less than 5.8 by adding sulfulic acid to prevent CaCO3 precipitation on the anionexchange membranes. The anode chamber was supplied with seawater (desalted seawater) in which sodium thiosulfate had been added to remove Cl2 generated at the anode. To avoid deterioration of the membrane due to Cl2, the washing chamber was incorporated between the anode chamber and the membrane stack. Seawater was also supplied to the cathode chamber into which hydrochloric acid had been added to maintain pH 2.0 to prevent Mg(OH)2 precipitation on the cathode. Next, an electric current was passed between electrodes as the stack voltage was observed. After steady state was achieved, the cell voltage was measured with Pt electrodes inserted into the concentrating cells integrated at both ends of the stack. The solutions were sampled at the inlets of the desalting cells and the outlets of the desalting and concentrating cells to analyze the concentrations of Na+, K+, Mg2+, Ca2+, and SO42 ions. In seawater electrodialysis, the electrolyte concentration C is given as C = CNa + CK + CMg + CCa = CCl + CSO4. Tables 1 and 236 list the specifications of the electrodialyzer and electrodialysis conditions, respectively.

6. RESULTS AND DISCUSSION 6.1. Calculated Values versus Observed Values. The observed experimental values, Xobs, were plotted versus the values 10768



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Table 2. Electrodialysis Conditions temperature (°C)

20, 30, 40

current density (A/dm2)

1.0, 2.0, 3.0, 4.0

linear velocity (cm/s) desalting cells concentrating cells solution flow system

5 0.5

desalting cells

one-pass flow

concentrating cells

circulation flow

Figure 5. Electrodialysis system.

Table 1. Specifications of the Electrodialyzer ion-exchange membrane

Aciplex K172/A172, Aciplex K182/

thickness of the membrane (mm)

0.080.10 (K172, K182)

A182 0.090.11 (A172, A182) electric resistance of the membrane

1.92.2 (K172), 1.72.1 (A172)

(Ω cm2) number of membrane pairs in the

1.51.8 (K182), 1.41.7 (A182) 45 (K172/A172), 90 (K182/A182)

stack (pair) effective membrane area

48.5 dm2 (50 cm width 97 cm

distance between the membranes

0.5

length) (mm) fastening frame

stainless steel plate fastened with

gasket (desalting and concentrating

bolts and nuts synthetic rubber (0.5 mm thick)

Figure 6. Ion flux across a membrane pair.

cells) spacer

polyethylene net (diagonalnet)

anode

titanium (3 mm thick) + platinum

cathode

stainless steel (SUS316, 3 mm thick)

(3 μm thick)

calculated by means of simulations, Xcal, taking temperature T and current density I/S as parameters. The results are shown in Figure 6 (JS), Figure 7 (JV), Figure 8 (η, ηNaCl), Figure 9 (C0out), Figure 10 (C00 ), Figure 11 (C00 NaCl), Figure 12 (θ), Figure 13 (Vcell), and Figure 14 (ENaCl). Compared with the Xcal = Xobs line plotted in the figures, the observed values are seen to be generally equivalent to the calculated ones. However, there are some cases where considerable deviations arise. The deviations are estimated to be due to (1) errors in the assumptions and empirical equations applied in the computer program and/or (2) errors in the electrodialysis experiments. Inspecting the assumptions described in section 2, one can see that the computed results cannot be exactly the same as the experimental results. However, the deviations do not eliminate the usefulness of the program because the performance of a practical-scale electrodialyzer can be discussed semiquantitatively based on this program. 6.2. Current Density Distribution. Figure 15 shows distributions of the current density i taking the average current density

Figure 7. Solution flux across a membrane pair. 10769



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Figure 10. Electrolyte concentration in a concentrated solution. Figure 8. Current efficiency.

Figure 9. Electrolyte concentration in a desalted solution.

I/S as a parameter. Current density increased at the inlets (x/l = 0) of the desalting cells and decreased at the outlets (x/l = 1) of the desalting cells. The current density changes in Figure 15 are rather small. This is because the salt concentration in the feed solution, namely, seawater, is high. If dilute saline water were supplied to an electrodialyzer, the current density change would be greater. i becomes equivalent to I/S at x = pl, and p is plotted against I/S in Figure 16. 6.3. Electric Resistances of a Membrane Pair, a Desalting Cell, and a Concentrating Cell. The electric resistances of a membrane pair (rmemb), a solution in a desalting cell (r0 ), and a solution in a concentrating cell (r00 ) were calculated at x = pl (Figure 17). rmemb is greater than r0 and r00 . To decrease the

Figure 11. NaCl concentration in a concentrated solution.

energy consumption in a seawater concentration process, it is necessary to reduce the electric resistances of the ion-exchange membranes. 6.4. Pressure Differences in a Desalting Cell and a Concentrating Cell. Figure 18 shows the pressure drops in a desalting cell (ΔP0 ) and a concentrating cell (ΔP00 ). 6.5. Limiting Current Density. Limiting current density, (I/S)lim, is plotted against current density, I/S, in Figure 19. It should be noticed that (I/S)lim was computed using the standard deviation of the normal distribution of the solution velocity ratio, σ = 0.1. The actual limiting current density of the electrodialyzer can be estimated from the intersection of the (I/S)lim and I/S = (I/S)lim lines in the figure and is approximately 9 A/dm2 in this electrodialyzer. 10770



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Figure 12. NaCl purity in a concentrated solution.

Figure 14. Energy consumption.

Note that eq 1 involves two equations. The first expresses the material conservation law for the concentrating compartment, and its general form is 00

00

00

00

00

00

Cin uin þ JS S ¼ Cout uout ¼ Cout ðuin þ JV SÞ C00in

C00out

ðaÞ 00

Equation 1 is obtained by setting = = C in eq a. The second part presents the ion transfer into this compartment.39 Equation 2 is one of the KedemKatchalsky equations.40 The electrolyte concentration in concentrating cells, C00 , is obtained from eqs 1 and 2 as38 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi A2 þ 4FB A C00 ¼ ð3Þ 2F

Figure 13. Cell voltage.

7. ALGORITHM The algorithm is compiled in this section. It is explained in detail in the textbook by Tanaka.37 7.1. Mass Transport. The ion flux, JS, and volume flux, JV, transported across a membrane pair are expressed by the following overall mass-transport equation38 00

00

0

JS ¼ C JV ¼ λðI=SÞ μðC C Þ 00

0

JV ¼ ϕðI=SÞ þ FðC C Þ

ð4Þ

B ¼ λðI=SÞ þ μC0

ð5Þ

In a practical-scale electrodialyzer, solution leakage and electric current leakage are usually generated to greater or lesser degrees. However, in the above equation, the influence of both leakages is not taken into account. 7.2. Membrane Characteristics. The membrane-pair characteristics λ (equiv C1), μ (cm s1), and ϕ (cm3 C1) and the membrane-pair alternating-current electric resistance ralter (Ω cm2) (where 2ralter = rK + rA) are expressed by the following functions of F (cm4 equiv1 s1)38

ð1Þ ð2Þ

in which λ is the overall transport number, μ is the overall solute permeability, ϕ is the overall electro-osmotic permeability, and F is the overall hydraulic permeability.

A ¼ ϕðI=SÞ þ μ FC0

λ ¼ 9:208 106 þ 1:914 105 F

ð6Þ

μ ¼ 2:005 104 F

ð7Þ

ϕ ¼ 3:768 103 F0:2 1:019 102 F

ð8Þ

2ralter ¼ rK þ rA ¼ 1:2323F1=3

ð9Þ

F is the leading parameter representing the other membrane-pair characteristics. Each membrane must have its own F value. 10771



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Figure 17. Electric resistances of a membrane pair and a solution in a desalting cell and a concentrating cell.

Figure 15. Current density distributions.

concentration C (g of salt/kg of solution) d ¼ 1:001 1:101 104 T 3:356 106 T 2 þ ð7:881 1:368 102 T þ 8:978 105 T 2 Þ 104 C

ð11Þ

k ¼ ð0:9383 þ 3:463 102 TÞ 103 C ð1:655 þ 3:863 102 TÞ 106 C2 ð1:344 þ 3:160 102 TÞ 109 C3

ð12Þ

γ ¼ 0:5927 þ 0:4355C0:5 7:201 105 C þ 3:503 106 C2

ð13Þ

Equation 13 holds in the range from normal temperature to 70 °C. 7.4. Ionic Constituents in a Concentrated Solution41. In the electrodialysis of seawater, the equivalent ratio of Na+ ions to total ions, rNa, in the concentrated solution is expressed as the following function of current density (I/S) (A/dm2) and T (°C) rNa ¼ 0:9584 4:269 103 T

Figure 16. p values at which i becomes equal to I/S.

However, the F values of various commercially available membranes have been found to be nearly the same, and they can be expressed by the following empirical function of temperature T (°C)41 F ¼ 3:421 103 þ 3:333 104 T

þ ð0:7983 þ 9:824 102 TÞ 102 ðI=SÞ0:5 ð14Þ The relationships between rNa and rK, rMg, and rCa are

ð10Þ

This equation reveals the relationship between temperature and membrane characteristics. 7.3. Relationship between Temperature and Electrolyte Concentration of an Electrolyte Solution and Its Physical Properties. Density d (kg/dm3) can be obtained from ref 42; specific electric conductance k (S/cm), from ref 43; and electrolyte (NaCl) activation coefficient γ, from ref 44. They are given by the following functions of temperature T (°C) and electrolyte

rK ¼ 1:905 102 þ 8:838 103 rNa

ð15Þ

rMg ¼ 0:7405 0:7668rNa

ð16Þ

rCa ¼ 0:2460 0:2482rNa

ð17Þ

The relationship between (I/S) and rCl is approximated by the equation rCl ¼ 0:9929 þ 1:947 103 ðI=SÞ 10772

ð18Þ



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Figure 20. Structure of a diagonal net spacer.

because the solution stream fans out and solution mixing is promoted between the two channels. The electric current screening ratio, ε, of the diagonal net spacer in Figure 20 is represented by the equation41 Figure 18. Pressure drops in a desalting cell and a concentrating cell.

ε ¼ ðelectric current screening area of a unit meshÞ=ðtotal area of a unit meshÞ

¼

2rða=2Þ a ¼ r 2 sin R r sin R

ð20Þ

in which a is the flow-pass thickness of the cell, d = a/2 is the diameter of the spacer rod, r is the distance between the two rods, and R is the crossing angle of the two rods. The numeral 2 means that two screening parts are taken into account in four screening parts surrounding the unit net mesh. The electric resistances of a desalting cell (r0 ) and a concentrating cell (r00 ) are given as r0 ¼

a0 ð1 ε0 Þk0

ð21Þ

r 00 ¼

a00 ð1 ε00 Þk00

ð22Þ

7.6. Hydrodynamic Diameters and Pressure Differences in a Desalting and a Concentrating Cell. The hydrodynamic

diameter, dH, of a desalting or concentrating cell incorporated with a diagonal net spacer is expressed as45,46 Figure 19. Limiting current density.

dH ¼

in which T is not included. rCl and rSO4 are related through rSO4 ¼ 1 rCl

ð19Þ

7.5. Electric Current Screening Ratio of a Spacer and Electric Resistances of a Desalting Cell and a Concentrating Cell. Spacers partially screen the electric current and increase the

local current density. To discuss the energy consumption of an electrodialyzer, it is necessary to evaluate the electric current screening ratio of a spacer. The structure of the diagonal net spacer incorporated in the electrodialyzer of this work is illustrated in Figure 20, which shows that rods arranged in two directions are stacked on each other. The solution supplied to the cell flows along two channels, so solution stagnation is prevented

8 4π

d=2 r

4 1 d=2 1 þ þ 2π 1 b d=2 b r

ð23Þ

where d/2 is the radius of the spacer rods (d/2 = a/4), r is the distance between two spacer rods or mesh size, and b is the flowpass width of the cell. Assuming the flow pattern in the cell to be laminar, the pressure difference between the inlet and the outlet of the cell is46 ΔP ¼

32μlu dH 2

ð24Þ

in which l is the flow-pass length in the cell. The viscosity coefficient of the solution, μ (g cm1s1), can be obtained from ref 43 and is given by the following function of temperature T (°C) and electrolyte concentration C (g of salt/kg of solution) of 10773



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7.8. Cell Voltage. The cell voltage, Vcell, is given by the equation49,50

the solution 2

4

μ ¼ 1:200 10 1:224 10 T þ ð2:107 105 1:529 107 TÞC þ ð 1:392 108 þ 1:123 1010 TÞC2 þ ð5:819 1010 6:769 1012 TÞC3

Vcell ¼ VΩ, in þ Vmemb, in ¼ VΩ, out þ Vmemb, out ð25Þ

The ohmic potential, VΩ,in, and membrane potential, Vmemb,in, at the inlets of desalting cells in eq 35 are given as

7.7. Current Density Distribution. Solution velocities in desalting cells vary between the cells, which gives rise to a solution velocity distribution. We assume here that the frequency, Yj, of the solution velocity ratio ξ of group j defined by

ξ¼

ub u u

To determine the coefficients a1, a2, and a3 in eq 27, the following three simultaneous equations are set up47,48 Vin ¼ Vout

ð28Þ

Vin ¼ Vp

ð29Þ

ζinout ¼ ζinp

ð30Þ

ζinout is introduced from eq 28 and expressed as ζinout ¼

R1 þ R2 p þ R3 p2 iout ¼ ζout ¼ β1 þ β2 p þ β3 p2 I=S

ð31Þ

As shown in eq 31, it equals the outlet current density nonuniformity coefficient ζout. ζinp is introduced from eq 29 and expressed as ζinp ¼

γ1 þ γ2 p þ γ3 p2 ¼ ζout ð2p 3p2 ÞðI=SÞ

0

VΩ, in ¼ ðrin þ rmemb, in þ r 00 Þiin

Vmemb, in

ð26Þ

where u is the average linear velocity in every desalting cell and ub is the linear velocity in each desalting cell, is approximated by the normal distribution. Here, the standard deviation of the normal distribution of ξ is defined as σ. Assuming the existence of this solution velocity distribution, the electrolyte concentration decreases along flow passes in desalting cells and gives rise to an electric resistance distribution and a current density distribution. We assume here that the current density i at a distance of x from the inlet of a desalting cell is approximated by 2 x x ð27Þ þ a2 i ¼ a1 þ a2 l l

ð32Þ

ζout ¼

iin a1 ¼ I=S I=S iout a1 þ a2 þ a3 ¼ I=S I=S

ð33Þ

ð34Þ

ð36Þ

RT γ00 C00 ¼ 2ðtK þ tA 1Þ ln 0 0 F γin Cin

ð37Þ

These potentials at the outlets of desalting cells in eq 35 are given by averaging the values for N cell pairs integrated in an electrodialyzer ! jmax jmax 1 0 00 VΩ, out ¼ Yj rout, j þ Yj rmemb, out, j þ r N N j¼0 j¼0

∑

∑

ð38Þ

Vmemb, out

jmax RT 1 γ00 C00 ¼ 2ðtK þ tA 1Þ ln 0 F N j ¼ 0 γout, j C0out, j

∑

ð39Þ in which Yj is the number of desalting cells in group j and subscript j denotes group j in the normal distribution within the range of ξj Δξj < ξj < ξj + Δξj. 7.9. Direct Electric Resistance of an Ion-Exchange Membrane Pair. rmemb,in in eq 36 and rmemb,out in eq 38 are membrane-pair direct-current electric resistance at the inlet and outlet, respectively, of a desalting cell and are evaluated as follows:50 The alternating-current electric resistance of an ionexchange membrane, ralter, given in eq 9 is equivalent to the electric resistance measured by the conventional method, but it is calculated from the overall hydraulic permeability F in this investigation. To measure the direct-current electric resistance of an ion-exchange membrane, the membrane is set in a two-cell apparatus, and a low-concentration NaCl solution [specific conductivity k0 (S/cm)] is supplied to both cells. The direct-current electric resistance of the membrane, rdire* (Ω cm2), is measured at 25 °C by passing a direct current. The relationship between k0 and rdire*/ralter is given by the empirical equation

It is also equal to ζout. We determined a1, a2, and a3 from the inlet current density nonuniformity coefficient ζin, outlet current density nonuniformity coefficient ζout, inlet current density iin, and outlet current density iout ζin ¼

ð35Þ

r log dire ralter

! ¼ 0:3380 þ 0:6386k0 þ 0:2961ðlog k0 Þ2 ð40Þ

A low-concentration NaCl solution (specific conductivity k0 ) is supplied to the desalting side, and a high-concentration solution (specific conductivity k00 ) is supplied to the concentrating side of the above apparatus. The direct-current electric resistance of the membrane, rdire, is measured at 25 °C by passing a direct current and subtracting the effect of membrane potential. 10774



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The empirical relationship between k00 /k0 and rdire/r*dire is 00 rdire k ¼ 1:000 0:1359 ð41Þ k0 rdire The direct electric current of a membrane pair, rmemb, is estimated by multiplying eq 40 by eq 41 ! ! rdire rdire ð42Þ rmemb ¼ rK þ rA ¼ 2ralter ¼ 2rdire ralter rdire rmemb is calculated by substituting ralter expressed in eq 9 into eq 42. 7.10. NaCl Concentration in a Concentrated Solution and Energy Consumption. The concentration of ion i, C00i (equiv/cm3), in a concentrated solution is calculated from ionic concentration ratio of ion i, ri (cf. section 7.4), and the concentration of electrolyte, C00 (equiv/cm3) (cf. eq 3), using the equation 00

Ci ¼ ri C00

ð43Þ

The concentrations of NaCl, C00NaCl, and electrolyte, C00 , in a concentrated solution; the NaCl purity, θ, of the concentrated solution; the electrolyte output, JS, and the NaCl output, PNaCl, are given by49,50 00

00

CNaCl ðg=cm3 Þ ¼ 58:443CNa ðequiv=cm3 Þ

ð44Þ

C00 ðg=cm3 Þ ¼ 57:84C00 ðequiv=cm3 Þ

ð45Þ

as its limiting current density, (I/S)lim, introduced from eqs 34 and 50, which is expressed by51 I ilim ðm1 þ m2 u#out Þ 0 # n1 þ n2 u#out ¼ ¼ Cout ð51Þ S lim ζout ζout 0

# in which Cout is C0out at u = u#out. In eq 51, u#out is nearly equal to u#in for commercially available membranes. Substituting u#in = u#out in eq 51 leads to I m1 þ m2 u#in 0 # n1 þ n2 u#in ¼ Cout ð52Þ S lim ζout 0

in which Cin# is C0in at u = u#in, which is given by u#in ¼ u#in ð1 3σÞ

where σ is the standard deviation of the normal distribution of the solution velocity ratio defined by eq 26.0 # is also introduced The relationship between (I/S)lim and Cout as I a # 0 0 #Þ ¼ ð54Þ u ðC Cout S lim λl in in Setting eq 52 equal to eq 54 gives Z1 ¼

Z2 ¼

CNaCl ðg=cm3 Þ C00 ðg=cm3 Þ

ð46Þ

JS ½kg=ðm2 hÞ ¼ ½C00 ðkg=m3 Þ½JV ðm=hÞ

ð47Þ

PNaCl ½kg=ðm2 hÞ ¼ fJS ½kg=ðm2 hÞgθ

ð48Þ

The energy consumption to produce one ton of NaCl, ENaCl, is expressed using Vcell by the equation ENaCl ¼

Vcell I PNaCl

ð49Þ

7.11. Limiting Current Density. The limiting current density of a cation-exchange membrane is less than that of an anionexchange membrane, because the mobility of the counterions in solution for a cation-exchange membrane is less than that for an anion-exchange membrane. Therefore, the limiting current density of an ion-exchange membrane integrated in an electrodialyzer, ilim, is given by the following empirical equation established for a cation-exchange membrane51 0

n1 þ n2 uout ilim ¼ ðm1 þ m2 uout ÞCout

ð50Þ

When the current density reaches the limit of a cation-exchange membrane, ilim, at the outlet of the desalting cell in which the linear velocity is the lowest among the uoutvalues, that is, u#out, the average current density applied to the electrodialyzer is defined

0

# Cout

n1 þ n2 u#in ð55Þ

# C0in C0out

00

θ¼

ð53Þ

aζout λl

u#in m1 þ m2 u#in

!

Z1 ¼ Z2

ð56Þ ð57Þ

The limiting current density of the electrodialyzer, (I/S)lim, is computed by a0 trial-and-error calculation by substituting control 0 #* # for Cout in eq 55 to realize Z1 = Z2 (eq 57) to determine key Cout 0 0 # # into eq 52. Cout. (I/S)lim is calculated by substituting Cout

8. CONCLUSIONS Data computed with the electrodialysis program described in this work are generally equivalent to the data observed in electrodialyzer operation, but some deviations are found between the two data sets. The deviations do not eliminate the usefulness of the program because the program enables the performance of a practical-scale electrodialyzer to be discussed semiquantitatively. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT We are grateful to Mr. Masao Akiyama, Sea Water Science Research Laboratory, Japan Tobacco & Salt Public Corporation, for offering the experimental data and Ms. Noriko Nakai, Central Research Institute, Japan Tobacco & Salt Public Corporation, for assistance in the experimental work. We thank Mr. Goro Takahashi and Miss Aki Shinohara, Department of Chemistry, 10775


Industrial & Engineering Chemistry Research School of Hygienic Science, Kitasato University, for assistance in the fundamental investigation.

’ NOMENCLATURE a = flow-pass thickness in a cell (cm) b = flow-pass width in a cell (cm) C = electrolyte concentration (equiv cm3) d = diameter of a spacer rod (cm); solution density (kg dm3) dH = hydrodynamic diameter of a cell (cm) ENaCl = energy consumption to produce one ton of NaCl (kWh/t NaCl) F = Faraday constant (C equiv1) i = current density (A cm2) ilim = limiting current density of an ion-exchange membrane (A cm2) I = electric current (A) I/S = average current density of an electrodialyzer (A dm2) (I/S)lim = limiting current density of an electrodialyzer (A dm2) JS = ion flux across a membrane pair (equiv cm2 s1) JV = volume flux across a membrane pair (cm3 cm2 s1) l = flow-pass length in a cell (cm) N = number of cell pairs integrated in an electrodialyzer p = position at which current density becomes I/S in an electrodialyzer r = electric resistance (Ω cm2); concentration ratio of ion i to total ions in a concentrated solution (equiv equiv1); distance between two spacer rods (cm) ralter = alternating electric resistance of a membrane pair (Ω cm2) rdire = direct electric resistance of a membrane pair (Ω cm2) R = gas constant (J K1 mol1) t = transport number of ions in an ion-exchange membrane S = effective membrane area (cm2) T = temperature (°C, K) u = linear velocity of a solution (cm s1) Vcell = cell voltage (V pair1) Vmemb = membrane potential (V pair1) VΩ = ohmic potential (V pair1) Greek Letters

R = crossing angle of two spacer rods (deg) γ = activity coefficient of electrolyte (NaCl) in a solution ε = electric current screening ratio of a spacer ζ = current density nonuniformity coefficient η = current efficiency θ = NaCl purity of a concentrated solution k = specific electric resistance (S cm1) λ = overall transport number of a membrane pair (equiv C1) μ = overall solute permeability of a membrane pair (cm s1); viscosity coefficient of a solution (g cm1 s1) F = overall hydraulic permeability of a membrane pair (cm4 equiv1 s1) ϕ = overall electro-osmotic permeability of a membrane pair (cm3 A1 s1) Subscripts

A = anion-exchange membrane K = cation-exchange membrane in = inlet out = outlet Superscripts 0

= desalting cell

ARTICLE 00

= concentrating cell # = lowest * = control key

’ REFERENCES (1) Kusakari, K.; Kawamata, F.; Matsumoto, N.; Saeki, H.; Terada, Y. Electrodialysis plant at Hatsushima. Desalination 1977, 21, 45–50. (2) Koga, S.; Mitsugami, Y. Supply of potable water from brackish water by electrodialysis desalination process at Ohoshima island in Tokyo prefecture. Ind. Water 1978, No. 239, 41–47. (3) Kawahara, T. Construction and operation experience of a largescale electrodialysis water desalination plant. Desalination 1994, 96, 341–348. (4) Passanisi, J.; Persechino, J.; Reynolds, T. K. EDR, NF and RO at a brackish water reclamation facility. Presented at the 2000 AWWA Annual Conference, Denver, CO, Jun 1115, 2000; Paper AWWA 51518. (5) Ryabtsev, A. D.; Kotsupalo, N. P.; Titarenko, V. I.; Igumenov, I. K.; Gelfond, N. V.; Fedotova, N. E.; Morozova, N. B.; Shipachev, V. A.; Tibilov, A. S. Development of two-stage electrodialysis set-up for economical desalination of sea-type artesian and surface waters. Desalination 2001, 137, 207–214. (6) Walha, K.; Amar, R. B.; Firdaous, L.; Quemeneur, F.; Jaouen, P. Brackish groundwater treatment by nanofiltration, reverse osmosis and electrodialysis in Tunisia, Performance and cost comparison. Desalination 2007, 207, 95–106. (7) Tsunoda, Y. Electrodialysis for producing brine concentrates from sea water. In Proceedings of the First International Symposium on Water Desalination; U.S. Department of the Interior: Washington, DC, 1965; Vol. 3, pp 325339. (8) Watanabe, T.; Hiroi, I.; Azechi, S.; Tanaka, Y.; Fujimoto, Y. Concentration process by ion-exchange membrane method. Bull. Soc. Sea Water Sci. Jpn. 1980, 34, 61–90. (9) Kaho, M.; Watanabe, T.; Azechi, S.; Akiyama, M.; Nagatsuka, S.; Fujimoto, Y. Long-term concentration test by unit cell-type electrodialytic apparatus of practical use. Bull. Soc. Sea Water Sci. Jpn. 1969, 23, 3–20. (10) Watanabe, T.; Azechi, S.; Tanaka, Y.; Nagatsuka, S.; Yugi, N. Effects of the concentration and temperature of feed solution and of current density on the characteristics of electrodialytic concentration. Bull. Soc. Sea Water Sci. Jpn. 1970, 24, 104–128. (11) Azechi, S.; Fujimoto, Y.; Yuyama, T.; Itami, Y. Studies on electrodialytic equipment with ion exchange membrane on the improvement of the filter press-type concentrator. Bull. Soc. Sea Water Sci. Jpn. 1973, 26, 244–264. (12) Mizutani, Y.; Yamane, R.; Kimura, K. Production of ion exchange membrane. Japanese Patent S39-27861, 1964. (13) Mineki, Y.; Gunzima, T.; Arai, S. Production of an ion exchange membrane. Japanese Patent S47-40868, 1972. (14) Misumi, T.; Kawashima, Y.; Takeda, K.; Kamaya, M. Production of ion exchange membrane. Japanese Patent S49-34476, 1974. (15) Hanzawa, N.; Yuyama, T.; Suzuki, K.; Nakayama, M. Studies on durability of ion exchange membrane (IV): Long term electrodialytic concentration test. In Scientific Papers of the Odawara Salt Experiment Station; Japan Monopoly Corporation: Odawara, Japan, 1966; Vol. 11, pp 113. (16) Hanzawa, N.; Azechi, S.; Fujimoto, Y.; Nagatsuka, S. Studies on the electrodialytic equipment with ion exchange membrane X. Comparison of spacer used for electrodialytic equipment. In Scientific Papers of the Odawara Salt Experiment Station; Japan Monopoly Corporation: Odawara, Japan, 1966; Vol. 10, pp 1625. (17) Hani, H.; Nishihara, H.; Oda, Y. Anion-exchange membrane having permselectivity between anions. Japanese Patent S36-15258, 1961. (18) Mizutani, Y.; Yamane, R.; Sata, T.; Izuo, T. Permselectivity treatment of a cation-exchange membrane. Japanese Patent S56-42083, 1971. 10776


Industrial & Engineering Chemistry Research (19) Mihara, K.; Misumi, T.; Yamauchi, H.; Ishida, Y. Anionexchange membrane having excellent specific permselectivity between anions. Japanese Patents S45-19980, S45-30693, 1970. (20) Mihara, K.; Misumi, T.; Yamauchi, H.; Ishida, Y. Production of a cation-exchange membrane having excellent specific permselectivity between cations. Japanese Patent S47-3081, 1972. (21) Watanabe, T.; Yamamoto, H.; Akiyama, M.; Yugi, N. Prevention of calcium-carbonate deposition by acid-adding method. Bull. Soc. Sea Water Sci. Jpn. 1972, 26, 83–90. (22) Tsunoda, S. Present status and latest trends of deep bed filtration. Bull. Soc. Sea Water Sci. Jpn. 1993, 48, 27–37. (23) Nagatsuka, S.; Kagiwada, K.; Soga, K.; Sugita, S. The influence of the sea water quality on the adhered matter of membrane. Bull. Soc. Sea Water Sci. Jpn. 1987, 40, 356–362. (24) Ohwada, K.; Shimizu, U.; Taga, N. Microorganism and organic matter deposited on the ion exchange membrane. Bull. Soc. Sea Water Sci. Jpn. 1981, 34, 367–372. (25) Yamashita, I. Removing method of fouling substances in an electrodialyzer. Japanese Patent S51-131477, 1976. (26) Ueno, K.; Ozawa, T.; Ooki, H.; Ishida, T.; Sudo, T. Washing method of ion-exchange membranes. Japanese Patent S55-33662, 1980. (27) Urabe, S.; Doi, K. Washing method of ion-exchange membranes. Japanese Patent S62-52624, 1987. (28) Tanaka, Y. A computer simulation of continuous ion exchange membrane electrodialysis for desalination of saline water. Desalination 2009, 249, 809–921. (29) Tanaka, Y. A computer simulation of batch ion exchange membrane electrodialysis for desalination of saline water. Desalination 2009, 249, 1039–1047. (30) Tanaka, Y. A computer simulation of feed-and-bleed ion exchange membrane electrodialysis for desalination of saline water. Desalination 2010, 254, 99–107. (31) Tanaka, Y. A computer simulation of ion exchange membrane electrodialysis for concentration of seawater. Membrane Water Treatment 2010, 1, 13–37. (32) Lee, H. J.; Sarfert, F.; Strathmann, H.; Moon, S. H. Designing of an electrodialysis desalination plant. Desalination 2002, 142, 267–286. (33) Moon, P.; Sandi, G.; Stevens, D.; Kizilel, R. Computational modeling of ionic transport in continuous and batch electrodialysis. Sep. Sci. Technol. 2004, 29, 2531–2555. (34) Fidaleo, M.; Moresi, M. Optimal strategy to model the electrodialytic recovery of a strong electrolyte. J. Membr. Sci. 2005, 260, 90–111. (35) Sadradeh, M.; Kaviani, A.; Mohammadi, T. Mathematical modeling of desalination by Electrodialysis. Desalination 2007, 206, 534–549. (36) Akiyama, M. Ion Exchange Membrane Electrodialysis for Seawater Concentration. The Influence of Seawater Temperature on the Performance of an Electrodialyzer; Technical Report; Sea Water Science Research Laboratory, Japan Tobacco & Salt Public Corp.: Kanagawa, 1995. (37) Tanaka, Y. Ion Exchange Membrane Electrodialysis: Fundamentals, Desalination, Separation; Nova Science Publishers: New York, 2010. (38) Tanaka, Y. Irreversible thermodynamics and overall mass transport in ion-exchange membrane electrodialysis. J. Membr. Sci. 2006, 281, 517–531. (39) Zabolotskii, V. I.; Shurdrenko, A. A.; Gnusin, N. P. Transport characteristics of ion-exchange membranes in electrodialytic concentration of electrolytes. Elektrokhimiya 1988, 6, 744–750. (40) Kedem., O.; Katchalsky, A. A physical interpretation of the phenomenological coefficients of membrane permeability. J. Gen. Physiol. 1961, 45, 143–179. (41) Tanaka, Y. Ion exchange membrane electrodialysis for saline water desalination and its application to seawater concentration. Ind. Eng. Chem. Res. 2011, 50, 7494–7503. (42) Sato, K.; Matsuo, T. Seawater Handbook; Society of Sea Water Science: Tokyo, 1974; p. 110. (43) Akiyama, M. Physical Properties of Saline Water in an IonExchange Membrane Electrodialysis Process; Technical Report; Sea Water

ARTICLE

Science Research Laboratory, Japan Tobacco & Salt Public Corp.: Kanagawa, 1992. (44) Harned, H. S.; Owen, B. B. The Physical Chemistry of Electrolyte Solutions, 3rd ed.; Reinhold: New York, 1958; p 726. (45) Zimmerer, C. C.; Kotte, V. Effects of spacer geometry on pressure drop, mass transfer, mixing behavior, and residence time distribution. Desalination 1996, 104, 129–134. (46) Tsiakis, P.; Papageorgiou, L. G. Optimal design of an electrodialysis brackish water desalination plant. Desalination 2005, 173, 173–186. (47) Tanaka, Y. Current density distribution, limiting current density in ion-exchange membrane electrodialysis. J. Membr. Sci. 2000, 173, 179–190. (48) Tanaka, Y. Current density distribution, limiting current density and saturation current density in an ion-exchange membrane electrodialyzer. J. Membr. Sci. 2002, 210, 65–75. (49) Tanaka, Y. Mass transport and energy consumption in ionexchange membrane electrodialysis of seawater. J. Membr. Sci. 2003, 215, 265–279. (50) Tanaka, Y.; Ehara, R.; Itoi, S.; Goto, T. Ion-exchange membrane electrodialytic salt production using brine discharged from a reverse osmosis seawater desalination plant. J. Membr. Sci. 2003, 222, 71–86. (51) Tanaka, Y. Limiting current density of an ion-exchange membrane and of an electrodialyzer. J. Membr. Sci. 2005, 266, 6–17.

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