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A computer simulation of batch ion exchange membrane electrodialysis for desalination of saline water
Desalination 249 (2009) 1039–1047
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Desalination j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / d e s a l
A computer simulation of batch ion exchange membrane electrodialysis for desalination of saline water Yoshinobu Tanaka IEM Research, 1-46-3 Kamiya, Ushiku-shi, Ibaraki 300-1216, Japan
a r t i c l e
i n f o
Article history: Accepted 19 June 2009 Available online 6 October 2009 Keywords: Ion exchange membrane Batch electrodialysis Saline water desalination Energy consumption Limiting current density Reverse osmosis
a b s t r a c t A computer simulation program is developed for predicting desalinating performance of a batch electrodialysis process. The program includes the principle of ① mass transport, ② current density distribution, ③ cell voltage, ④ mass balance/energy consumption and ⑤ limiting current density. In this simulation the following parameters are inputted; ① membrane characteristics such as overall transport number, overall solute permeability, overall electro-osmotic permeability, overall hydraulic permeability, direct current electric resistance etc., ② electrodialyzer specifications such as flow-pass thickness, flow-pass width and flow-pass length in a desalting cell etc. and ③ electrodialytic conditions such as voltage, electrolyte concentration in a feeding solution, linear velocity in desalting cells, standard deviation of normal distribution of solution velocity ratio etc. The following phenomena were computed and discussed; ① Changes of electrolyte concentration and current density with operation time. ② Influence of cell voltage on operation time (batch duration), water recovery and energy consumption. ③ Influence of volume of an electrolyte solution prepared at first on operation time. ④ Influence of cell voltage, electrolyte concentration and standard deviation of solution velocity ratio in desalting cells on limiting current density. ⑤ Energy consumption in a reverse osmosis process. ⑥ Excepting limiting current density, the performance of an electrodialyzer is never influenced by the standard deviation of normal distribution of solution velocity ratio in desalting cells. ⑦ Energy consumption in electrodialysis is less than that in reverse osmosis at feeding saline water concentration less than about 2000 mg/l. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Ion exchange membrane electrodialysis is commercially available to saline water desalination and 5% of total water production in the world is now supplied by electrodialysis [1]. This is because electrodialysis is energy saving and advantageous to desalination of low concentration saline water. Recently, General Electric Co. constructed a 200,000 m3/day electrodialysis-reversal (EDR) plant at Barcelona Spain to desalinate river water (salinity; 2000 mg/l) [2]. This plant operates at a 90% recovery, a salt reduction ranging from 60 to 80% and an electrical consumption of less than 0.8 kWh/m3. The electrodialysis process is classified to a continuous (one-pass flow), a batch and a feed and bleed (partially circulation) process [3,4]. Among these processes, a batch process is applicable to the operation of a small- or middle-scale electrodialysis such as; seawater desalination in an island [5,6]; seawater desalination in a vessel [7]; desalination of brackish ground water [8,9]; waste water treatment [10,11]; demineralization of whey [12]; removal of nitrate [13], boron [14] etc. The performance of a batch process has been discussed from
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various view points as follows; Demircioglu et al. introduced equations expressing the ionic mass balance around a dilute circulation tank and discussed energy consumption in a batch process [15]. Parulekar investigated energy consumption of batch operations such as (1) constant current, (2) constant voltage, (3) constant current followed by constant voltage, (4) constant voltage followed by constant current, and (5) operation with time-variant current and voltage [16]. Moon et al. predicted the performance of one- and two-dimensional continuous and batch electrodialysis processes based on the fundamental principles of electrochemistry, transport phenomena, and thermodynamics [17]. Ortiz et al. developed a mathematical model for a batch process and discussed mass balance, ohmic drop and membrane potential [18]. In the previous investigation, we developed the computation program including the principle of ① mass transport, ② current density distribution, ③ energy consumption and ④ limiting current density and predicted the performance of a continuous process [19]. The above simulation model was developed on the basis of many fundamental experiments and its reasonability was supported by the performance of actual electrodialyzers operating in salt-manufacturing plants for seawater concentration [19,20]. In this investigation, a similar computer simulation program is applied for predicting desalinating performance of a batch process.
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2. Theoretical 2.1. Batch process In Fig. 1, a definite volume Q′ = Q ′start of an electrolyte solution ′ start ) is prepared in the circulation tank at (concentration; C′in = Cin, first. Next, we open valve V1, close valve V2, and then the solution is supplied to the inlets of desalting cells in an electrodialyzer setting ′ respectively linear and volume velocities of the solution at uin and qin and applying constant cell voltage Vcell. Effective membrane area and number of desalting cells are respectively S and N. Flow-pass thickness and length in a desalting cell are a and l respectively. Current density in an electrodialyzer decreases from iin at the inlets (x = 0), via i = I/S (average current density of an electrodialyzer, I: electric current, S: membrane area) at x = pl and i at x to iout at the outlets (x = l) in desalting cells. Voltage difference between a cathode and anode is maintained at Vin (x = 0) = Vp (x = pl) = Vout (x = l). JS and JV are respectively flux of ions and solutions across the membrane pairs from desalting cells to concentrating cells at x = pl. C′ is the electrolyte concentration in ′ , uout and qout ′ are respectively electrolyte desalting cells at x = pl. Cout concentration, linear velocity and volume velocity of solutions at the outlets of desalting cells. u and q′ are respectively average median linear and volume velocity in desalting cells (u = (uin + uout) / 2, q′ = ′ ) / 2). C″ and q″ are respectively electrolyte concentration (q′in + qout and volume flow velocity of a concentrated solution, which is
extracted at x = pl to the outside of the process. Electrodialysis is performed until electrolyte concentration of a desalted solution in the tank C′in changes from C′in,start at operating time t = 0 to a definite value C′in,final at t = tope and then valve V1 is closed, valve V2 is opened and the solution is discharged to the outside of the process to obtain a desalted solution (potable water).
2.2. Electrodialysis (ED) program 2.2.1. Steps 1–3 Before discussing the performance of a batch electrodialyzer, it is necessary to make clear the relationship between electrolyte concentration at the inlets of desalting cells C′in and current density I/S, electrolyte concentration in concentrating cells C″ and electrolyte concentration in desalting cells C′ in Fig. 1. The relationship is determined using the electrodialysis simulation program which is applicable to a batch process as shown in Fig. 2. The algorithm in Fig. 2 consists of the following steps including respectively the principle of ① step 1: mass transport, ② step 2: current density distribution and ③ step 3: cell voltage. The program is performed with trial and error calculation and it is considerably similar to the program for the continuous electrodialysis process, which was explained in detail in the previous investigation [19] based on the fundamental investigation [21–26]. Computation of the electrodialysis program in Step 1–Step 3 is performed with substituting the following input and control keys in Fig. 2.
Fig. 1. Batch electrodialysis process.
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Fig. 2. Simulation of mass transport, current density distribution and cell voltage.
a) Input Overall hydraulic permeability ρ Electrolyte concentration at the inlets of desalting cells C′in Average linear velocity at the inlets of desalting cells uin Flow-pass thickness in a desalting cell a Flow-pass width in a desalting cell b Flow-pass length in a desalting cell l and others. b) Control key Average current density I/S*
Current efficiency η* Average median linear velocity in desalting cells u* Average electrolyte concentration in desalting cells at x=pl C′* Position at which current density becomes I/S in an electrodialyzer p* * . Cell voltage Vcell Computation is carried out using a trial and error calculation by ① adjusting I/S* to realize Vcell =V*cell ② adjusting C′* to realize C ′ = Cp′ =
1 N
Jmax
∑ Yj Cj = C ′*
j=1
③ adjusting η* to realize η=FJS /(I/S)=η*
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④ adjusting u* to realize u=(uin +uout)/2=u* ⑤ adjusting p to realize ζinout =ζinp ⑥ and determine every parameter being included in Fig. 2. ′ and I/S, C″ and C′ in Fig. 1 is exemplified Relationship between Cin in Fig. 3 and introduced as follows. ′ 0:5
I = S = X1 Cin ″
′ 0:5
′
′ 0:5
C = Y1 Cin C = Z1 Cin
′
′ 1:5
ð1Þ
+ X2 Cin + X3 Cin ′
′ 1:5
ð2Þ
+ Y2 Cin + Y3 Cin ′
+ Z2 Cin :
ð3Þ
The coefficients X1, X2, X3, Y1, Y2, Y3, Z1 and Z2 are computed in this simulation. 2.2.2. Step 4 Mass balance and energy consumption (Step 4) in the batch process (Fig. 4) is expressed as follows. ′ I dCin I ′ ″ ′ ″ ′ = λ −μðC −C Þ NS: − Qstart − ϕ + ρðC −C Þ NS dt S S
ð4Þ
N is the number of desalting cells integrated in an electrodialyzer. ′ decreases from Cin,start ′ ′ Operation time tope during which Cin to Cin,final , i.e. batch duration is introduced from Eq. (4) as follows ′
tope =
0:5
′
B2 = λX2 −μðY2 −Z2 Þ
1:5
′ 1 Cin;start Qstart −ðA1 C′in + A2 Cin + A3 C′in ÞNS ′ dCin : ∫ ′ ′ NS Cin;final B1 C′in0:5 + B2 Cin + B3 C′in1:5
Fig. 4. Simulation of mass balance and energy consumption (Step 4).
ð5Þ B3 = λX3 −μY3 :
in which A1 = ϕX1 + ρðY1 −Z1 Þ A2 = ϕX2 + ρðY2 −Z2 Þ A3 = ϕX3 + ρY3 B1 = λX1 −μðY1 −Z1 Þ
X1, X2, X3, Y1, Y2, Y3, Z1 and Z2 are determined in Section 2.2.1. Volume of a solution being discharged from concentrating cells to ′ the outside of the process Q″ and output of a desalted solution Q final are given as follows. I t t ″ ″ ′ 0:5 ′ 1:5 Q = ∫0ope ϕ + ρðC −C Þ NSdt = ∫0ope ðA1 C′in + A2 Cin + A3 C′in ÞNSdt ð6Þ S ′
′
Q final = Q start −Q
″
ð7Þ
Water recovery Re is
Re =
Q ′final : ′ Q start
ð8Þ
Energy consumption to obtain 1 m3 of a desalted solution (potable water) E (kWh/m3) and production rate of a desalted solution PR (m3/h) are respectively presented as follows.
E=
Vcell NS tope I ∫ dt Q ′final 0 S
′
PR =
Fig. 3. C′in versus I/S, C″ and C′, Vcell = 0.4 V/pair. I/S = 0.11811C′0.5 in + 184.00C′in 0.5 −3 − 4.541 × 103C′1.5 − 10.983C′in + 109.14C′1.5 C in . C″ = 0.3758C′ in . C′ = −1.1421 × 10 ′0.5 in + 0.9678C′in.
Q final : tope
ð9Þ
ð10Þ
2.2.3. Step 5 Simulation program of limiting current density (Step 5) is illustrated in Fig. 5 and explained in detail in the previous investigation [19] based on the fundamental investigation [23,25].
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Fig. 5. Simulation of limiting current density (Step 5). Super script # means the least value in an electrodialyzer.
2.3. Assumption The program described above is developed on the following assumptions, which are the same with the assumption in the continuous process [19]. ① Solution leakage and electric current leakage in an electrodialyzer are negligible. ② Direct current electric resistance of a membrane includes the electric resistance of a boundary layer formed on the desalting surface of the membrane due to concentration polarization. ③ Frequency distribution of solution velocity ratio in desalting cells is equated by the normal distribution. ④ Current density i at x distant from the inlets of desalting cells is approximated by the quadratic equation. ⑤ Voltage difference between the electrodes at the entrance of desalting cells is equal to the value at the exits. ⑥ Limiting current density of an electrodialyzer is defined as average current density applied to an electrodialyzer when current density reaches the limit of an ion exchange membrane at the outlet of a
desalting cell in which linear velocity and electrolyte concentration are the least. ⑦ Concentrated solution is extracted from concentrating cells to the outside of the process. 2.4. Fundamental experiment The simulation model is developed on the basis of various fundamental experimental measurements described below. (1) Membrane characteristics (λ, μ, ϕ, ρ) [21] (2) Alternating and direct current electric resistance of membranes [21,22] (3) Solution velocity distribution between desalting cells and current density distribution in an electrodialyzer [22,23] (4) Voltage difference between electrodes at the inlets and outlets of desalting cells in an electrodialyzer [23] (5) Physical properties of desalted and concentrated saline water [22] (6) Limiting current density of ion exchange membranes [23] (7) Solution leakage in an electrodialyzer [24,28].
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3. Computation 3.1. Specifications and operating conditions of an electrodialyzer A batch process is assumed to be operated by applying constant voltage between electrodes for obtaining potable water. In this situation, we assume the following specifications of an electrodialyzer and operating conditions with constant cell voltage Vcell: Linear velocity at the inlets of desalting cells uin = 10 cm/s Standard deviation of solution velocity ratio in desalting cells σ = 0.05, 0.10, 0.15, and 0.20 Flow-pass thickness in a desalting cell a = 0.05 cm Flow-pass width in a desalting cell b = 100 cm Flow-pass length in a desalting cells l = 100 cm Membrane area S = bl = 104 cm2 = 1 m2 Number of desalting cells N = 300 cells Overall hydraulic permeability ρ = 1 × 10− 2 cm4/eq s Electric current screening ratio of a spacer ε = 0.15 Cell voltage Vcell = 0.2, 0.25, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8 V/pair Electrolyte concentration of a solution supplied to an electro′ = 500, 1,000, 2,000, dialyzer at the beginning of operation Cin,start 3,000, and 4,000 mg/l (ionic constituent ratio is the same to that of seawater) Electrolyte concentration of a desalted solution C′in,final = 300 mg/ l (potable water) Volume of a solution prepared in a circulation tank Q ′start = 5, 10, 15, 20 m3.
Fig. 7. Current density changes with operating time. C′in, start; ○ 4000, △ 3000, □ 2000, ▽ 1000, 500 mg/l, Vcell = 0. 4 V/pair, Q′start = 10 m3.
′ as a parameter and of potable water E are computed taking Cin,start shown in Figs. 9–11 which are not influenced by Q ′start . 3.2.3. Influence of volume of an electrolyte solution prepared at first on operation time Fig. 12 shows the relationship between Q ′start and tope.
3.2.2. Influence of cell voltage on the performance of a batch process Operation time (batch duration) tope versus Vcell computed setting Q ′start = 10 m3 is given in Fig. 8. Vcell versus potable water production rate PR, water recovery Re and energy consumption to obtaining 1 m3
3.2.4. Limiting current density Limiting current density (I/S)lim versus current density I/S is given in Fig. 13 setting Vcell and C′in as parameters. A I/S = (I/S)lim line is indicated in the figure showing that I/S approaches (I/S)lim at increased Vcell and decreased C′in . Fig. 14 gives I/S versus (I/S)lim taking σ and C′in as parameters and shows that (I/S)lim decreases with increasing σ. Fig. 15 indicates that ion flux JS, solution flux JV and ′ are electrolyte concentration at the outlets of desalting cells Cout independent of σ. σ is influenced extremely by precision of part dimensions of a stack and skill of stack assembling work of an electrodialyzer. Fig. 14 suggests that σ should be reduced as much as possible for increasing limiting current density and operating an
′ start; Fig. 6. Electrolyte concentration changes in a feeding solution with operating time. Cin, ○ 4000, △ 3000, □ 2000, ▽ 1000, ⋄ 500 mg/l, Vcell = 0. 4 V/pair, Q′start = 10 m3.
′ start; ○ 4000, △ 3000, Fig. 8. Relationship between cell voltage and operation time. Cin, □ 2000, ▽ 1000, ⋄ 500 mg/l, Q′start = 10 m3.
3.2. Result and discussion 3.2.1. Changes of electrolyte concentration and current density with operating time Figs. 6 and 7 exemplify the changes of C′in and I/S with operating time t setting Q ′start = 10 m3 and Vcell = 0.4 V/pair.
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′ ,start; ○ 4,000, △ Fig. 9. Relationship between cell voltage and water production rate. Cin 3,000, □ 2,000, ▽ 1,000, ⋄ 500 mg/l.
Fig. 11. Relationship between cell voltage and energy consumption. C′in, start; ○ 4000, △ 3000, □ 2000, ▽ 1000, ⋄ 500 mg/l.
electrodialyzer stably. However, Figs. 14 and 15 show that excepting limiting current density, the performances of an electrodialyzer are hardly influenced by σ.
Array: 6–3 Membrane area: 222 m2/vessel, 2000 m2/plant Specific design flux: 0.5 m3/m2 day Feed TDS and temperature: 1000, 2000, 3000, 3500, 4000 mg/l, 25 °C Energy recovery device: incorporated with and without PX-220B (Energy Recovery Inc.).
3.2.5. Comparison of energy consumption between electrodialysis process and reverse osmosis process Energy consumption of a reverse osmosis plant is computed using RO membrane System Simulation Software: IMS Design developed by Hydranautics Nitto denko Company [27]. Parameters inputted in this simulation are as follows. Capacity: 1000 m3/day potable water Pump motive efficiency: 0.780 (pump efficiency: 0.83 × motor efficiency 0.94) RO membrane: polyimide composite low pressure type membrane CPA5 Water recovery: 75% Vessel and element: 8 in× 40in vessel incorporated with 6 elements (spiral wound)
Fig. 10. Relationship between cell voltage and water recovery. C′in, start; ○ 4000, △ 3000, □ 2000, ▽ 1000, ⋄ 500 mg/l.
′ and energy Fig. 16 gives the relationship between Cin,start consumption E in an electrodialysis (ED) process taking Vcell as a parameter. The energy consumption in a reverse osmosis (RO) process with the energy recovery device (ERD) and without ERD is also plotted in the figure. Energy consumption in ED is recognized to become less than that in RO at a feeding saline water concentration ′ ) less than about 2000 mg/l. (Cin,start 4. Conclusion The performance of a batch electrodialysis process is analyzed based on the principle of ① mass transport, ② current density distribution, ③
Fig. 12. Relationship between volume of a solution prepared and operation time. C′start = 2000 mg/l.
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Fig. 15. Influence of σ on JS, JV and C′out. Vcell = 0.4 V/pair, C′in = 1000 mg/l.
Fig. 13. Limiting current density.
cell voltage, ④ mass balance/energy consumption and ⑤ limiting current density. Results obtained in this investigation are applicable to estimate the optimum operating conditions of a batch electrodialyzer. The model equations shown in this article is based on fundamental experiments. The computer program is developed by incorporating the model equations with ordinary principle such as mass transport, mass balance, energy consumption, etc. In another investigation [20], it was concluded that the reliability of the simulation program is supported by evaluating the performance of actual electrodialyzers for seawater concentration. In this investigation, energy consumption in batch electrodialysis is compared to that in reverse osmosis and a reasonable conclusion is introduced. However, the reliability of the theory must be further discussed in succeeding investigations by comparing with experimental results. Nomenclature a b C
flow-pass thickness in a desalting cell (cm) flow-pass width in a desalting cell (cm) electrolyte concentration (eq cm− 3)
Fig. 14. Limiting current density. Vcell = 0.4 V/pair.
E i I I/S JS JV l N p
PR q Q r Re S t tope u
energy consumption (kWh m− 3) current density (A cm− 2) electric current (A) average current density (A cm− 2) flux of ions across a membrane pair (eq cm− 2 s− 1) flux of a solution across a membrane pair (cm3 cm− 2 s− 1) flow-pass length in a desalting cell (cm) number of desalting cells in an electrodialyzer dimensionless distance from the inlet of a desalting cell at which current density is equal to the average current density I/S of an electrodialyzer production rate (m3 h− 1) solution volume across a membrane pair (cm3 s− 1) solution volume (m3) electric resistance (Ω cm2) water recovery ion exchange membrane area (cm2) transport number of ions in a membrane, operating time (s) operation time (batch duration) (s, h) linear velocity in desalting cells (cm s− 1)
Fig. 16. Relationship between electrolyte concentration. ED, Vcell; ○ 0.2, △ 0.3, □ 0.4, ▽ 0.5, ⋄ 0.6 V/pair Q′start = 10 m3, RO, ●: with ERD, ▲: without ERD.
Y. Tanaka / Desalination 249 (2009) 1039–1047
V Vcell Vmemb VΩ x Yj
voltage (V) cell voltage (V pair− 1) membrane potential (V pair− 1) ohmic potential (V pair− 1) distance from the inlet of a desalting cell (cm) number of desalting cells in group j
Greek letters ε electric current screening ratio of a spacer ζ current density non-uniformity coefficient η current efficiency λ overall transport number of a membrane pair (eq A− 1 s− 1) μ overall solute permeability of a membrane pair (cm s− 1) ξ linear velocity ratio of solutions in desalting cells Δξ half of ξ value range of desalting cells ρ overall hydraulic permeability of a membrane pair (cm4 eq− 1 s− 1) σ standard deviation of normal distribution of linear velocity ratio ξ in desalting cells ϕ overall electro-osmotic permeability of a membrane pair (cm3 A− 1 s− 1)
Subscript alter A final in j K lim out p start
alternating current anion exchange membrane ending of operation inlet of a desalting cell group j in the normal distribution within the range of ξj − Δξj <ξ <ξj +Δξj cation exchange membrane limiting current density outlet of a desalting cell point x = pl distant from the inlet of a desalting cell beginning of operation
Superscript ′ desalting cell ″ concentrating cell * control key # desalting cell in which solution velocity becomes the least
Acknowledgements We thank deeply Dr. H. Iwahori, Nitto Denko Corporation and Dr. T. Goto, Water Re-Use Promotion Center for discussing on the energy consumption in reverse osmosis and electrodialysis.
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References [1] A. Kumano, Operation of seawater desalination plants in the Middle and Near East, New Membrane Technology Symposium, Japan Membrane Society, December 5, 2007, Tokyo; IDA 2004 Tampa. [2] Water Desalination Report, vol. 45, No. 7, pp.1–2 (2009). [3] M.S. Mintz, Criteria for economic optimization are presented in the form of comparative performance equations for various methods of operation, Ind. Eng. Chem. 55 (1963) 19–28. [4] F.B. Leitz, Measurements and Control in Electrodialysis, Desalination, Elsevier Science Publishers B. V, Amsterdam, 1986, pp. 381–401. [5] T. Seto, L. Ehara, R. Komori, A. Yamaguchi, T. Miwa, Seawater desalination by electrodialysis, Desalination 25 (1978) 1–7. [6] O. Kuroda, S. Takahashi, K. Wakamatsu, S. Itoh, S. Kubota, K. Kikuchi, Y. Eguchi, Y. Ikenaga, N. Sohma, K. Nishinoiri, An electrodialysis sea water desalination system powered by photovoltaic cells, Desalination 65 (1987) 161–169. [7] Y. Tani, K. Doi, Y. Terada, M. Yokota, M. Wakayama, The marine desalination unit by electrodialysis, Industrial Water 239 (1978) 86–89. [8] K. Kusakari, F. Kawamata, N. Matsumoto, H. Saeki, Y. Terada, Electrodialysis plant at Hatsushima, Desalination 21 (1977) 45–50. [9] K. Walha, R.B. Amar, L. Firdaus, F. Quemeneur, P. Jaouen, Brackish groundwater treatment by nanofiltration, reverse osmosis and electrodialysis in Tunisia. Performance and cost comparison, Desalination 207 (2007) 95–106. [10] S. Resbeut, G. Pourcelly, R. Sandeaux, C. Gavach, Electrodialysis process for waste stream treatment: electrodialysis applied to the demineralization of phenylalanine solutions, Desalination 120 (1998) 235–245. [11] H.-J. Rapp, P.H. Pfromm, Electrodialysis for chloride removal from the chemical recovery cycle of a Kraft pulp mill, J. Membr. Sci. 146 (1998) 249–261. [12] B. T. Batchelder, Electrodialysis applications in whey processing, the 1986 International Whey Conference, October 28, 1986, Chicago, Illinois, USA. [13] F. Hell, J. Lahnsteiner, F. Frischherz, G. Baumgartner, Experience with full-scale electrodialysis for nitrate and hardness removal, Desalination 117 (1998) 173–180. [14] N. Kabay, O. Arar, F. Acar, A. Ghazai, U. Yuksel, M. Yuksel, Removal of boron from water by electrodialysis: effect of feed characteristics and interfering ions, Desalination 223 (2008) 63–72. [15] M. Demircioglu, N. Kabay, E. Ersoz, I. Kurucaovali, C. Safak, N. Gizli, Cost comparison and efficiency modeling in the electrodialysis of brine, Desalination 136 (2001) 317–323. [16] S.J. Parulekar, Optimal current and voltage trajectories for minimum energy consumption in batch electrodialysis, J. Membr. Sci. 148 (1998) 91–103. [17] P. Moon, G. Sandi, D. Stevens, R. Kizilel, Computational modeling of ionic transport in continuous and batch electrodialysis, Sep. Sci. Technol. 39 (2004) 2531–2555. [18] J.M. Ortiz, J.A. Sotoca, E. Exposito, F. Gallud, V. Garcia-Garcia, V. Montiel, A. Aldaz, Brackish water desalination by electrodialysis: batch recirculation operation modeling, J. Membr. Sci. 252 (2005) 65–75. [19] Y. Tanaka, A computer simulation of continuous ion exchange membrane electrodialysis for desalination of saline water, Desalination 249 (2009) 809–821. [20] Y. Tanaka, A computer simulation of ion exchange membrane electrodialysis for concentration of seawater, Membrane Water Treatment 1 (1) (in press). [21] Y. Tanaka, Irreversible thermodynamics and overall mass transport in ion exchange membrane electrodialysis, J. Membr. Sci. 281 (2006) 517–531. [22] Y. Tanaka, Current density distribution and limiting current density in ion exchange membrane electrodialysis, J. Membr. Sci. 173 (2000) 179–190. [23] Y. Tanaka, Limiting current density of an ion exchange membrane and of an electrodialyzer, J. Membr. Sci. 266 (2005) 6–17. [24] Y. Tanaka, Overall mass transport and solution leakage in an ion exchange membrane electrodialyzer, J. Membr. Sci. 235 (2004) 15–24. [25] Y. Tanaka, Ion Exchange Membranes: Fundamentals and Applications, Membrane Science and Technology Series 12, Elsevier, Amsterdam, 2007. [26] Y. Tanaka, Mass transport and energy consumption in ion-exchange membrane electrodialysis of seawater, J. Membr. Sci. 215 (2003) 265–279. [27] HYDRANAUTICS Nitto Denko Company, IMS (Integrated Membrane Solutions) Design, http:www.membranes.com. [28] Y. Tanaka, Pressure distribution, hydrodynamics, mass transport and solution leakage in an ion exchange membrane electrodialysis, J. Membr. Sci. 234 (2004) 23–39.
Contents lists available at ScienceDirect
Desalination j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / d e s a l
A computer simulation of batch ion exchange membrane electrodialysis for desalination of saline water Yoshinobu Tanaka IEM Research, 1-46-3 Kamiya, Ushiku-shi, Ibaraki 300-1216, Japan
a r t i c l e
i n f o
Article history: Accepted 19 June 2009 Available online 6 October 2009 Keywords: Ion exchange membrane Batch electrodialysis Saline water desalination Energy consumption Limiting current density Reverse osmosis
a b s t r a c t A computer simulation program is developed for predicting desalinating performance of a batch electrodialysis process. The program includes the principle of ① mass transport, ② current density distribution, ③ cell voltage, ④ mass balance/energy consumption and ⑤ limiting current density. In this simulation the following parameters are inputted; ① membrane characteristics such as overall transport number, overall solute permeability, overall electro-osmotic permeability, overall hydraulic permeability, direct current electric resistance etc., ② electrodialyzer specifications such as flow-pass thickness, flow-pass width and flow-pass length in a desalting cell etc. and ③ electrodialytic conditions such as voltage, electrolyte concentration in a feeding solution, linear velocity in desalting cells, standard deviation of normal distribution of solution velocity ratio etc. The following phenomena were computed and discussed; ① Changes of electrolyte concentration and current density with operation time. ② Influence of cell voltage on operation time (batch duration), water recovery and energy consumption. ③ Influence of volume of an electrolyte solution prepared at first on operation time. ④ Influence of cell voltage, electrolyte concentration and standard deviation of solution velocity ratio in desalting cells on limiting current density. ⑤ Energy consumption in a reverse osmosis process. ⑥ Excepting limiting current density, the performance of an electrodialyzer is never influenced by the standard deviation of normal distribution of solution velocity ratio in desalting cells. ⑦ Energy consumption in electrodialysis is less than that in reverse osmosis at feeding saline water concentration less than about 2000 mg/l. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Ion exchange membrane electrodialysis is commercially available to saline water desalination and 5% of total water production in the world is now supplied by electrodialysis [1]. This is because electrodialysis is energy saving and advantageous to desalination of low concentration saline water. Recently, General Electric Co. constructed a 200,000 m3/day electrodialysis-reversal (EDR) plant at Barcelona Spain to desalinate river water (salinity; 2000 mg/l) [2]. This plant operates at a 90% recovery, a salt reduction ranging from 60 to 80% and an electrical consumption of less than 0.8 kWh/m3. The electrodialysis process is classified to a continuous (one-pass flow), a batch and a feed and bleed (partially circulation) process [3,4]. Among these processes, a batch process is applicable to the operation of a small- or middle-scale electrodialysis such as; seawater desalination in an island [5,6]; seawater desalination in a vessel [7]; desalination of brackish ground water [8,9]; waste water treatment [10,11]; demineralization of whey [12]; removal of nitrate [13], boron [14] etc. The performance of a batch process has been discussed from
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various view points as follows; Demircioglu et al. introduced equations expressing the ionic mass balance around a dilute circulation tank and discussed energy consumption in a batch process [15]. Parulekar investigated energy consumption of batch operations such as (1) constant current, (2) constant voltage, (3) constant current followed by constant voltage, (4) constant voltage followed by constant current, and (5) operation with time-variant current and voltage [16]. Moon et al. predicted the performance of one- and two-dimensional continuous and batch electrodialysis processes based on the fundamental principles of electrochemistry, transport phenomena, and thermodynamics [17]. Ortiz et al. developed a mathematical model for a batch process and discussed mass balance, ohmic drop and membrane potential [18]. In the previous investigation, we developed the computation program including the principle of ① mass transport, ② current density distribution, ③ energy consumption and ④ limiting current density and predicted the performance of a continuous process [19]. The above simulation model was developed on the basis of many fundamental experiments and its reasonability was supported by the performance of actual electrodialyzers operating in salt-manufacturing plants for seawater concentration [19,20]. In this investigation, a similar computer simulation program is applied for predicting desalinating performance of a batch process.
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2. Theoretical 2.1. Batch process In Fig. 1, a definite volume Q′ = Q ′start of an electrolyte solution ′ start ) is prepared in the circulation tank at (concentration; C′in = Cin, first. Next, we open valve V1, close valve V2, and then the solution is supplied to the inlets of desalting cells in an electrodialyzer setting ′ respectively linear and volume velocities of the solution at uin and qin and applying constant cell voltage Vcell. Effective membrane area and number of desalting cells are respectively S and N. Flow-pass thickness and length in a desalting cell are a and l respectively. Current density in an electrodialyzer decreases from iin at the inlets (x = 0), via i = I/S (average current density of an electrodialyzer, I: electric current, S: membrane area) at x = pl and i at x to iout at the outlets (x = l) in desalting cells. Voltage difference between a cathode and anode is maintained at Vin (x = 0) = Vp (x = pl) = Vout (x = l). JS and JV are respectively flux of ions and solutions across the membrane pairs from desalting cells to concentrating cells at x = pl. C′ is the electrolyte concentration in ′ , uout and qout ′ are respectively electrolyte desalting cells at x = pl. Cout concentration, linear velocity and volume velocity of solutions at the outlets of desalting cells. u and q′ are respectively average median linear and volume velocity in desalting cells (u = (uin + uout) / 2, q′ = ′ ) / 2). C″ and q″ are respectively electrolyte concentration (q′in + qout and volume flow velocity of a concentrated solution, which is
extracted at x = pl to the outside of the process. Electrodialysis is performed until electrolyte concentration of a desalted solution in the tank C′in changes from C′in,start at operating time t = 0 to a definite value C′in,final at t = tope and then valve V1 is closed, valve V2 is opened and the solution is discharged to the outside of the process to obtain a desalted solution (potable water).
2.2. Electrodialysis (ED) program 2.2.1. Steps 1–3 Before discussing the performance of a batch electrodialyzer, it is necessary to make clear the relationship between electrolyte concentration at the inlets of desalting cells C′in and current density I/S, electrolyte concentration in concentrating cells C″ and electrolyte concentration in desalting cells C′ in Fig. 1. The relationship is determined using the electrodialysis simulation program which is applicable to a batch process as shown in Fig. 2. The algorithm in Fig. 2 consists of the following steps including respectively the principle of ① step 1: mass transport, ② step 2: current density distribution and ③ step 3: cell voltage. The program is performed with trial and error calculation and it is considerably similar to the program for the continuous electrodialysis process, which was explained in detail in the previous investigation [19] based on the fundamental investigation [21–26]. Computation of the electrodialysis program in Step 1–Step 3 is performed with substituting the following input and control keys in Fig. 2.
Fig. 1. Batch electrodialysis process.
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Fig. 2. Simulation of mass transport, current density distribution and cell voltage.
a) Input Overall hydraulic permeability ρ Electrolyte concentration at the inlets of desalting cells C′in Average linear velocity at the inlets of desalting cells uin Flow-pass thickness in a desalting cell a Flow-pass width in a desalting cell b Flow-pass length in a desalting cell l and others. b) Control key Average current density I/S*
Current efficiency η* Average median linear velocity in desalting cells u* Average electrolyte concentration in desalting cells at x=pl C′* Position at which current density becomes I/S in an electrodialyzer p* * . Cell voltage Vcell Computation is carried out using a trial and error calculation by ① adjusting I/S* to realize Vcell =V*cell ② adjusting C′* to realize C ′ = Cp′ =
1 N
Jmax
∑ Yj Cj = C ′*
j=1
③ adjusting η* to realize η=FJS /(I/S)=η*
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④ adjusting u* to realize u=(uin +uout)/2=u* ⑤ adjusting p to realize ζinout =ζinp ⑥ and determine every parameter being included in Fig. 2. ′ and I/S, C″ and C′ in Fig. 1 is exemplified Relationship between Cin in Fig. 3 and introduced as follows. ′ 0:5
I = S = X1 Cin ″
′ 0:5
′
′ 0:5
C = Y1 Cin C = Z1 Cin
′
′ 1:5
ð1Þ
+ X2 Cin + X3 Cin ′
′ 1:5
ð2Þ
+ Y2 Cin + Y3 Cin ′
+ Z2 Cin :
ð3Þ
The coefficients X1, X2, X3, Y1, Y2, Y3, Z1 and Z2 are computed in this simulation. 2.2.2. Step 4 Mass balance and energy consumption (Step 4) in the batch process (Fig. 4) is expressed as follows. ′ I dCin I ′ ″ ′ ″ ′ = λ −μðC −C Þ NS: − Qstart − ϕ + ρðC −C Þ NS dt S S
ð4Þ
N is the number of desalting cells integrated in an electrodialyzer. ′ decreases from Cin,start ′ ′ Operation time tope during which Cin to Cin,final , i.e. batch duration is introduced from Eq. (4) as follows ′
tope =
0:5
′
B2 = λX2 −μðY2 −Z2 Þ
1:5
′ 1 Cin;start Qstart −ðA1 C′in + A2 Cin + A3 C′in ÞNS ′ dCin : ∫ ′ ′ NS Cin;final B1 C′in0:5 + B2 Cin + B3 C′in1:5
Fig. 4. Simulation of mass balance and energy consumption (Step 4).
ð5Þ B3 = λX3 −μY3 :
in which A1 = ϕX1 + ρðY1 −Z1 Þ A2 = ϕX2 + ρðY2 −Z2 Þ A3 = ϕX3 + ρY3 B1 = λX1 −μðY1 −Z1 Þ
X1, X2, X3, Y1, Y2, Y3, Z1 and Z2 are determined in Section 2.2.1. Volume of a solution being discharged from concentrating cells to ′ the outside of the process Q″ and output of a desalted solution Q final are given as follows. I t t ″ ″ ′ 0:5 ′ 1:5 Q = ∫0ope ϕ + ρðC −C Þ NSdt = ∫0ope ðA1 C′in + A2 Cin + A3 C′in ÞNSdt ð6Þ S ′
′
Q final = Q start −Q
″
ð7Þ
Water recovery Re is
Re =
Q ′final : ′ Q start
ð8Þ
Energy consumption to obtain 1 m3 of a desalted solution (potable water) E (kWh/m3) and production rate of a desalted solution PR (m3/h) are respectively presented as follows.
E=
Vcell NS tope I ∫ dt Q ′final 0 S
′
PR =
Fig. 3. C′in versus I/S, C″ and C′, Vcell = 0.4 V/pair. I/S = 0.11811C′0.5 in + 184.00C′in 0.5 −3 − 4.541 × 103C′1.5 − 10.983C′in + 109.14C′1.5 C in . C″ = 0.3758C′ in . C′ = −1.1421 × 10 ′0.5 in + 0.9678C′in.
Q final : tope
ð9Þ
ð10Þ
2.2.3. Step 5 Simulation program of limiting current density (Step 5) is illustrated in Fig. 5 and explained in detail in the previous investigation [19] based on the fundamental investigation [23,25].
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Fig. 5. Simulation of limiting current density (Step 5). Super script # means the least value in an electrodialyzer.
2.3. Assumption The program described above is developed on the following assumptions, which are the same with the assumption in the continuous process [19]. ① Solution leakage and electric current leakage in an electrodialyzer are negligible. ② Direct current electric resistance of a membrane includes the electric resistance of a boundary layer formed on the desalting surface of the membrane due to concentration polarization. ③ Frequency distribution of solution velocity ratio in desalting cells is equated by the normal distribution. ④ Current density i at x distant from the inlets of desalting cells is approximated by the quadratic equation. ⑤ Voltage difference between the electrodes at the entrance of desalting cells is equal to the value at the exits. ⑥ Limiting current density of an electrodialyzer is defined as average current density applied to an electrodialyzer when current density reaches the limit of an ion exchange membrane at the outlet of a
desalting cell in which linear velocity and electrolyte concentration are the least. ⑦ Concentrated solution is extracted from concentrating cells to the outside of the process. 2.4. Fundamental experiment The simulation model is developed on the basis of various fundamental experimental measurements described below. (1) Membrane characteristics (λ, μ, ϕ, ρ) [21] (2) Alternating and direct current electric resistance of membranes [21,22] (3) Solution velocity distribution between desalting cells and current density distribution in an electrodialyzer [22,23] (4) Voltage difference between electrodes at the inlets and outlets of desalting cells in an electrodialyzer [23] (5) Physical properties of desalted and concentrated saline water [22] (6) Limiting current density of ion exchange membranes [23] (7) Solution leakage in an electrodialyzer [24,28].
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3. Computation 3.1. Specifications and operating conditions of an electrodialyzer A batch process is assumed to be operated by applying constant voltage between electrodes for obtaining potable water. In this situation, we assume the following specifications of an electrodialyzer and operating conditions with constant cell voltage Vcell: Linear velocity at the inlets of desalting cells uin = 10 cm/s Standard deviation of solution velocity ratio in desalting cells σ = 0.05, 0.10, 0.15, and 0.20 Flow-pass thickness in a desalting cell a = 0.05 cm Flow-pass width in a desalting cell b = 100 cm Flow-pass length in a desalting cells l = 100 cm Membrane area S = bl = 104 cm2 = 1 m2 Number of desalting cells N = 300 cells Overall hydraulic permeability ρ = 1 × 10− 2 cm4/eq s Electric current screening ratio of a spacer ε = 0.15 Cell voltage Vcell = 0.2, 0.25, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8 V/pair Electrolyte concentration of a solution supplied to an electro′ = 500, 1,000, 2,000, dialyzer at the beginning of operation Cin,start 3,000, and 4,000 mg/l (ionic constituent ratio is the same to that of seawater) Electrolyte concentration of a desalted solution C′in,final = 300 mg/ l (potable water) Volume of a solution prepared in a circulation tank Q ′start = 5, 10, 15, 20 m3.
Fig. 7. Current density changes with operating time. C′in, start; ○ 4000, △ 3000, □ 2000, ▽ 1000, 500 mg/l, Vcell = 0. 4 V/pair, Q′start = 10 m3.
′ as a parameter and of potable water E are computed taking Cin,start shown in Figs. 9–11 which are not influenced by Q ′start . 3.2.3. Influence of volume of an electrolyte solution prepared at first on operation time Fig. 12 shows the relationship between Q ′start and tope.
3.2.2. Influence of cell voltage on the performance of a batch process Operation time (batch duration) tope versus Vcell computed setting Q ′start = 10 m3 is given in Fig. 8. Vcell versus potable water production rate PR, water recovery Re and energy consumption to obtaining 1 m3
3.2.4. Limiting current density Limiting current density (I/S)lim versus current density I/S is given in Fig. 13 setting Vcell and C′in as parameters. A I/S = (I/S)lim line is indicated in the figure showing that I/S approaches (I/S)lim at increased Vcell and decreased C′in . Fig. 14 gives I/S versus (I/S)lim taking σ and C′in as parameters and shows that (I/S)lim decreases with increasing σ. Fig. 15 indicates that ion flux JS, solution flux JV and ′ are electrolyte concentration at the outlets of desalting cells Cout independent of σ. σ is influenced extremely by precision of part dimensions of a stack and skill of stack assembling work of an electrodialyzer. Fig. 14 suggests that σ should be reduced as much as possible for increasing limiting current density and operating an
′ start; Fig. 6. Electrolyte concentration changes in a feeding solution with operating time. Cin, ○ 4000, △ 3000, □ 2000, ▽ 1000, ⋄ 500 mg/l, Vcell = 0. 4 V/pair, Q′start = 10 m3.
′ start; ○ 4000, △ 3000, Fig. 8. Relationship between cell voltage and operation time. Cin, □ 2000, ▽ 1000, ⋄ 500 mg/l, Q′start = 10 m3.
3.2. Result and discussion 3.2.1. Changes of electrolyte concentration and current density with operating time Figs. 6 and 7 exemplify the changes of C′in and I/S with operating time t setting Q ′start = 10 m3 and Vcell = 0.4 V/pair.
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′ ,start; ○ 4,000, △ Fig. 9. Relationship between cell voltage and water production rate. Cin 3,000, □ 2,000, ▽ 1,000, ⋄ 500 mg/l.
Fig. 11. Relationship between cell voltage and energy consumption. C′in, start; ○ 4000, △ 3000, □ 2000, ▽ 1000, ⋄ 500 mg/l.
electrodialyzer stably. However, Figs. 14 and 15 show that excepting limiting current density, the performances of an electrodialyzer are hardly influenced by σ.
Array: 6–3 Membrane area: 222 m2/vessel, 2000 m2/plant Specific design flux: 0.5 m3/m2 day Feed TDS and temperature: 1000, 2000, 3000, 3500, 4000 mg/l, 25 °C Energy recovery device: incorporated with and without PX-220B (Energy Recovery Inc.).
3.2.5. Comparison of energy consumption between electrodialysis process and reverse osmosis process Energy consumption of a reverse osmosis plant is computed using RO membrane System Simulation Software: IMS Design developed by Hydranautics Nitto denko Company [27]. Parameters inputted in this simulation are as follows. Capacity: 1000 m3/day potable water Pump motive efficiency: 0.780 (pump efficiency: 0.83 × motor efficiency 0.94) RO membrane: polyimide composite low pressure type membrane CPA5 Water recovery: 75% Vessel and element: 8 in× 40in vessel incorporated with 6 elements (spiral wound)
Fig. 10. Relationship between cell voltage and water recovery. C′in, start; ○ 4000, △ 3000, □ 2000, ▽ 1000, ⋄ 500 mg/l.
′ and energy Fig. 16 gives the relationship between Cin,start consumption E in an electrodialysis (ED) process taking Vcell as a parameter. The energy consumption in a reverse osmosis (RO) process with the energy recovery device (ERD) and without ERD is also plotted in the figure. Energy consumption in ED is recognized to become less than that in RO at a feeding saline water concentration ′ ) less than about 2000 mg/l. (Cin,start 4. Conclusion The performance of a batch electrodialysis process is analyzed based on the principle of ① mass transport, ② current density distribution, ③
Fig. 12. Relationship between volume of a solution prepared and operation time. C′start = 2000 mg/l.
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Fig. 15. Influence of σ on JS, JV and C′out. Vcell = 0.4 V/pair, C′in = 1000 mg/l.
Fig. 13. Limiting current density.
cell voltage, ④ mass balance/energy consumption and ⑤ limiting current density. Results obtained in this investigation are applicable to estimate the optimum operating conditions of a batch electrodialyzer. The model equations shown in this article is based on fundamental experiments. The computer program is developed by incorporating the model equations with ordinary principle such as mass transport, mass balance, energy consumption, etc. In another investigation [20], it was concluded that the reliability of the simulation program is supported by evaluating the performance of actual electrodialyzers for seawater concentration. In this investigation, energy consumption in batch electrodialysis is compared to that in reverse osmosis and a reasonable conclusion is introduced. However, the reliability of the theory must be further discussed in succeeding investigations by comparing with experimental results. Nomenclature a b C
flow-pass thickness in a desalting cell (cm) flow-pass width in a desalting cell (cm) electrolyte concentration (eq cm− 3)
Fig. 14. Limiting current density. Vcell = 0.4 V/pair.
E i I I/S JS JV l N p
PR q Q r Re S t tope u
energy consumption (kWh m− 3) current density (A cm− 2) electric current (A) average current density (A cm− 2) flux of ions across a membrane pair (eq cm− 2 s− 1) flux of a solution across a membrane pair (cm3 cm− 2 s− 1) flow-pass length in a desalting cell (cm) number of desalting cells in an electrodialyzer dimensionless distance from the inlet of a desalting cell at which current density is equal to the average current density I/S of an electrodialyzer production rate (m3 h− 1) solution volume across a membrane pair (cm3 s− 1) solution volume (m3) electric resistance (Ω cm2) water recovery ion exchange membrane area (cm2) transport number of ions in a membrane, operating time (s) operation time (batch duration) (s, h) linear velocity in desalting cells (cm s− 1)
Fig. 16. Relationship between electrolyte concentration. ED, Vcell; ○ 0.2, △ 0.3, □ 0.4, ▽ 0.5, ⋄ 0.6 V/pair Q′start = 10 m3, RO, ●: with ERD, ▲: without ERD.
Y. Tanaka / Desalination 249 (2009) 1039–1047
V Vcell Vmemb VΩ x Yj
voltage (V) cell voltage (V pair− 1) membrane potential (V pair− 1) ohmic potential (V pair− 1) distance from the inlet of a desalting cell (cm) number of desalting cells in group j
Greek letters ε electric current screening ratio of a spacer ζ current density non-uniformity coefficient η current efficiency λ overall transport number of a membrane pair (eq A− 1 s− 1) μ overall solute permeability of a membrane pair (cm s− 1) ξ linear velocity ratio of solutions in desalting cells Δξ half of ξ value range of desalting cells ρ overall hydraulic permeability of a membrane pair (cm4 eq− 1 s− 1) σ standard deviation of normal distribution of linear velocity ratio ξ in desalting cells ϕ overall electro-osmotic permeability of a membrane pair (cm3 A− 1 s− 1)
Subscript alter A final in j K lim out p start
alternating current anion exchange membrane ending of operation inlet of a desalting cell group j in the normal distribution within the range of ξj − Δξj <ξ <ξj +Δξj cation exchange membrane limiting current density outlet of a desalting cell point x = pl distant from the inlet of a desalting cell beginning of operation
Superscript ′ desalting cell ″ concentrating cell * control key # desalting cell in which solution velocity becomes the least
Acknowledgements We thank deeply Dr. H. Iwahori, Nitto Denko Corporation and Dr. T. Goto, Water Re-Use Promotion Center for discussing on the energy consumption in reverse osmosis and electrodialysis.
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