Simulation of Electrodialysis with Bipolar Membranes: Estimation of

ARTICLE pubs.acs.org/IECR

Simulation of Electrodialysis with Bipolar Membranes: Estimation of Process Performance and Energy Consumption Yaoming Wang, Anlei Wang, Xu Zhang, and Tongwen Xu* Laboratory of Functional Membranes, School of Chemistry and Materials Science, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China ABSTRACT: A mathematical model of a typical three-compartment electrodialysis with bipolar membranes (EDBM) process has been developed to calculate the energy consumption and total cost of the process. In particular, gluconic acid was chosen as a model product, the energy consumption was calculated on the basis of the NernstPlanck equation, Donnan equilibrium, and electroneutrality assumption. The concentration profiles and resistance distributions across the respective layers were also displayed. Results indicated that the resistances of the solutions, diffusion layers, and Donnan interfaces were highly dependent on the applied current. The resistances in the diffusion layers were the dominant resistances, while the resistances due to Donnan interfaces and resistances of the membranes could be neglected. The energy consumption of an EDBM process was increased with an increase in current. The energy consumption in the validation experiment was in good agreement with the prediction, suggesting the reliability of the model.

1. INTRODUCTION Electrodialysis with bipolar membranes (EDBM) is an electromembrane process integrating the functions of conventional electrodialysis and bipolar membranes. It can realize salt conversion without second salt pollution and provide H+ and OH (or CH3O for alcohol splitting) in situ without the introduction of salts. Because of the technical advance, economical advantage, and environmental benignity of EDBM technology, it has been attracting more and more attention from all over the world, and also, it has found many applications in chemical synthesis, biofood processing, and environmental protection.16 However, EDBM technology has not developed at a desirable pace, because of the insufficient recognition of the role of EDBM plays in sustainable development, and many obstacles exist when this technology is brought to industrialization. The performance of an EDBM process is affected by several design parameters, such as current density, flow velocity, construction of cell and spacers, membrane characteristics, and stack design. To improve the performance of an EDBM process and bring this technology to perfection, it requires the collaborative efforts of academia, industry, and government to solve problems related to material and apparatus design and process control, integration, optimization, and simulation. Many developments, including those from our group, have been made on the aspects of material design and process optimization and integration,710 but relatively little effort has been directed toward dealing with process simulation. Besides, the reported models are mainly focused on the changes in product concentration with the time or the current efficiency of the process,1115 while models concerned with energy consumption, which is directly related to the total cost of the process, are especially lacking in the literature. In this research, a simple mathematical model of a typical three-compartment EDBM process for the production of gluconic acid has thus been developed based on some simplifications and assumptions. During the application of EDBM technology, r 2011 American Chemical Society

the mass transfer zone can be divided into the diffusion layer, the Donnan interfacial layer, and the membrane phase. An overall description of the resistance distribution across the respective layers was developed, and the energy consumption and total cost of the EDBM process were calculated therein. A confirmation experiment was also conducted to verify the adequacy of the model. A process simulation of energy consumption is important to obtain information on the process cost with respect to the operating conditions. The developed approach here can be easily extended to the modeling of some other electromembrane processes, such as the conventional electrodialysis (ED), reverse electrodialysis (RED), electro-deionization (EDI), and membrane capacitive deionization (MCDI). 1.1. Theoretical. Figure 1 shows a schematic graph of the basic transport of a typical three-compartment (BPAC) EDBM process. Taking the production of gluconic acid (HGlu) using EDBM technology as an example, in the acid compartment (i.e., the compartment between bipolar membrane and the anion exchange membrane), the desired transports consist of the migration of gluconate ion through the anion exchange membrane and the generation of hydrogen ion generated from the watersplitting of the bipolar membrane. However, undesired transports also exist, which are also the reason for the decrease in current efficiency in the acid compartment. The undesired transports consist of many terms, such as the transport of co-ions, the diffusion of acid molecules through the membranes, and the back-diffusion of salts. For the production of weak acid by using EDBM, it was reported that the diffusion of acid molecules through bipolar and anion exchange membranes is the dominant component.13 Herein, the molecular diffusion of gluconic acid Received: March 9, 2011 Accepted: November 8, 2011 Revised: November 1, 2011 Published: November 08, 2011 13911

dx.doi.org/10.1021/ie200467s | Ind. Eng. Chem. Res. 2011, 50, 13911–13921

Industrial & Engineering Chemistry Research

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the several hundred micrometers thickness of the diffusion layer. The basic equations describing the transport of the mobile ions through the diffusion boundary layer are the NernstPlanck equations, which can be expressed as eq 1: ∂Ci zi Ci F ∂j1 þ ð1Þ þ Ci Jv Ji ¼ Di RT ∂x ∂x

Figure 1. Setup of the EDBM unit (BPAC). BP, bipolar membrane; A, anion exchange membrane; C, cation exchange membrane.

where Di, zi, and Ci are the diffusion efficient, valence, and concentration of ion i, respectively; j1 is the potential drop in the diffusion layer of the acid compartment; and x is the distance. The origin of the coordinate x is placed at the boundary of the diffusion layer. t is the time. F, R, and T are the Faraday constant, the gas constant, and the absolute temperature, respectively. Furthermore, it is assumed that the electroconvection phenomena are neglected in the diffusion layers and membrane; that is, Jv = 0. The increase in the concentration of hydrogen ion in the acid compartment is due to the water dissociation of the bipolar membrane. The mechanism for water dissociation in the bipolar membrane remains a matter of controversy, and the second Wien effect and chemical reaction model are often used to explain the water-splitting phenomena of bipolar membrane. The second Wien effect assumes that water dissociation mainly occurs in the depletion layer of the bipolar membrane and the dissociated ions removed from this region are replenished by water dissociation equilibrium. The water dissociation is accelerated by an electric field, which describes the influence of a strong electric field E on the water dissociation rate K1, while the recombination rate constant K1 is not affected by the electric field, as shown in eq 2.16 K1

H2 O T Hþ þ OH K 1

Figure 2. Schematic graph of concentration (solid line) profiles of the EDBM stack. The dotted line represents the boundary of the diffusion layer. The dash-dotted line represents the boundary of the Donnan interface. Each feed compartment consists of a diffusion layer and a Donnan layer. 1, diffusion layer of the acid compartment; 2, Donnan interfacial layer of the acid compartment; 3, membrane phase of the anion exchange membrane; 4, left Donnan interfacial layer of the salt compartment; 5, left diffusion layer of the salt compartment; 6, right diffusion layer of the salt compartment; 7, right Donnan interfacial layer of the salt compartment; 8, membrane phase of the cation exchange membrane; 9, Donnan interfacial layer of the base compartment; 10, diffusion layer of the base compartment; C0, concentration of bulk solution; CR,A, fixed charge density of the anion exchange membrane; CR,C, fixed charge density of the cation exchange membrane.

through bipolar and anion membranes is considered as the undesired transport, while the other influences are neglected. Ci denotes the concentration of the ith species in the acid compartment (i = 1 for hydrogen ion; i = 2 for hydroxyl ion, i = 3 for sodium ion; i = 4 for gluconate ion). As a result of the surface charge of the ion exchange membrane when contacting with an aqueous solution, a Donnan interfacial layer is formed at the membranesolution interface, which will significantly influence the ion distribution across the membrane. Besides, concentration gradient layers (or diffusion layers) are also developed in the electrolyte solution adjacent to the membrane under a current field, which is ascribed to the difference of the ion transport rate between the membrane and solution. Therefore, the membrane domain of each compartment consists of a diffusion layer and a Donnan interfacial layer, as shown in Figure 2. The thickness of the Donnan interfacial layer is in the order of Debye length, which can be neglected compared with

K1 ¼ K10

1=2 pffiffiffiffi 2 ð8bÞ3=4 e 8b , π

b ¼ 0:09636

E εr T 2

ð2Þ

where εr is the relative permittivity, K1 is the forward water dissociation rate, K10 is the water dissociation rate when no electrical field is applied. In comparison, the chemical reaction model assumes that water dissociation can be considered as a type of proton-transfer reaction between water molecules and functional groups or chemicals,17 as symbolized in the following reactions. B þ H2 O T BHþ OH T BHþ þ OH BHþ þ H2 O T BH3 Oþ T B þ H3 Oþ A þ H2 O T AHOH T AH þ OH AH þ H2 O T A H3 Oþ T A þ H3 Oþ where BH+ and A stand for the positive and negative catalytic centers, respectively. Both the second Wien effect and the chemical reaction model can explain the water-splitting phenomena for some circumstances, but they both also have limitations. In fact, we find that generated acid concentrations are linearly dependent on current densities in the practical application of bipolar membranes.18 Herein, we introduce a constant (Kspl) to depict the dependence of the water-splitting rate on current density. C1 0 ¼ Kspl It

ð3Þ

where C10 is the concentration of hydrogen ion generated by water-splitting of the bipolar membrane; I is the current, 13912

dx.doi.org/10.1021/ie200467s |Ind. Eng. Chem. Res. 2011, 50, 13911–13921


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and t is the time. The value of Kspl is about 5 102 (mol 3 m3 3 A1 3 h1) for Neosepta BP-1 (Tokuyama, Co., Japan) bipolar membrane. The fluxes of gluconic acid molecules through the bipolar and anion exchange membrane can be expressed from the diffusion constants, as shown in eq 4. ∂CHGlu J5 ¼ Kaem A ∂t

ð4aÞ

∂CHGlu J6 ¼ Kbpm A ∂t

ð4bÞ

where J5 and J6 are the molecular diffusion flux of gluconic acid through the anion exchange and bipolar membrane, respectively. Kbpm and Kaem are the diffusion constants of acid through bipolar and anion exchange membranes, respectively. The value of Kbpm and Kaem can be determined from a diffusion dialysis stack,19,20 which is about 1.6 107 and 2 107 m1 for the selected membranes, respectively. The effective membrane surface area of the diffusion dialysis stack was 6.15 cm2. One chamber was filled with 100 mL gluconic acid solution, and the other was filled with 100 mL distilled water. Diffusion was allowed to occur for 2 h, and then, the solutions were removed from both sides of the cell and analyzed. A is the effective area of the membrane. The differential of the concentration of gluconic acid can be directly determined from the water splitting rate in eq 3. Gluconic acid is a weak acid; there is a weak-acid equilibrium in the acid compartment during the model calculation. HGlu a Hþ þ Glu The concentration of hydrogen ion can be calculated from the dissociation constant of gluconic acid, as shown in eq 5. pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ka þ Ka 2 þ 4Ka C0 0 ð5Þ C1 ¼ 2

Combining eqs 1, 4, and 9 and arranging the algebra gives the following equation. I ∂C1 C1 F ∂j1 ¼ ðD4 D1 Þ ðD4 þ D1 Þ F RT ∂x ∂x ðKaem þ Kbpm ÞKspl IA

The NernstPlanck equation, which is similar to the linear equation of nonequilibrium thermodynamics under the assumption that the frictional interactions between the mobile ions are neglected, can also be used to describe the transport of ions through the membrane as eq 11:21 ∂C̅ i Zi Ci F ∂j0 þ J̅ i ¼ D̅ i ð11Þ þ C̅ i Jv RT ∂x ∂x where Di and Ci are the diffusion coefficient and concentration of species i in the membrane, respectively, and j0 is the potential drop in the membrane. For simplicity, the electroconvection of ions through the membrane is neglected; that is, Jv = 0. Taking the transport number of counterion in the anion exchange membrane (TA) into eq 11, the gluconate ion fluxes within the anion exchange membrane can be expressed as eq 12. ∂C̅ 4 F ∂j0 ITA ð12Þ J̅ 4 ¼ D̅ 1 ¼ ∂x RT ∂x F As a result of the continuity of the flux at the membrane interface, the flux of ions in the bulk side of bulk-membrane interface should be equal to that of the membrane side. Thus, ∂C4 C4 F ∂j1 ITA ð13Þ D4 ¼ RT ∂x ∂x F Combining eqs 12 and 13, the differential concentration of hydrogen ion and the differential potential in the acid compartment can be expressed as eq 14. ∂C1, A ∂x

where C10 is the concentration of hydrogen ion comes from the dissociation of gluconic acid; C0 is the initial concentration of gluconic acid; and Ka is the dissociation constant of gluconic acid, the value of which is 1.99 104 at 25 °C. If the initial concentration of gluconic acid is higher than 0.1 mol 3 dm3 (C/Ka > 500), eq 5 can be simplified as following equation: pffiffiffiffiffiffiffiffiffiffi C1 0 ¼ K a C0 ð6Þ The concentration of hydrogen ion in the acid compartment is a sum of the dissociated gluconic acid and the water-splitting of the bipolar membrane, which can be expressed as eq 7: pffiffiffiffiffiffiffiffiffiffi C1 ¼ Ka C0 þ Kspl It ð7Þ CHGlu is the concentration of gluconic acid in the acid compartment, which can be expressed as eq 8: CHGlu ¼ C0 C1 0 þ Kspl It pffiffiffiffiffiffiffiffiffiffi ¼ C0 Ka C0 þ Kspl It

I ¼ Fð

∑ zi Ji þ ∑ JjÞ

ði ¼ 1, 4; j ¼ 5, 6Þ

D4 þ TA ðD1 þ D4 Þ ¼ I þ ðKaem þ Kbpm ÞKspl AD4 =2D1 D4 F

ð14aÞ ∂j1 ∂x ¼

RTI D4 þ TA ðD4 D1 Þ þ ðKaem þ Kbpm ÞKspl AD4 2D1 D4 C1 F F

ð14bÞ Assuming the concentration gradient of ions in the diffusion layer is linearly dependent on the thickness of diffusion layer (δ), the concentration of hydrogen ion at the boundary of the Donnan interfacial layer of the acid compartment at time t can be expressed as eq 15. C1, A jx ¼ δ ¼

ð8Þ

Here, C0 is the initial concentration of gluconic acid in the acid compartment. The current in the diffusion layer is a sum contribution of the entire fluxes, which can be expressed as eq 9: ð9Þ

ð10Þ

pffiffiffiffiffiffiffiffiffiffi Ka C0 þ Kspl It

D4 þ TA ðD1 þ D4 Þ Iδ F

þ ðKaem þ Kbpm ÞKspl AD4

=2D1 D4

ð15Þ

For the interface between the diffusion layer and the membrane, Donnan equilibrium is established between an electrolyte solution and an ion exchange membrane. As well-known, the concentrations of ions in a charged membrane and in an 13913



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external aqueous solution obey the following Donnan equilibrium relationship:

The dependence of current on the fluxes in the left diffusion layer of the salt compartment can be written as the following: I ¼ FðJ3, SL J4, SL þ J5 Þ

1=zi C̅ i Q ¼ Ci

ð16Þ

Combining eqs 21, 22, and 23 gives the concentration profile of ions in the left diffusion layer of the salt compartment. ∂C4, SL ∂x D4 þ TA ðD3 þ D4 Þ ¼ I þ Kaem Kspl AD4 =2D3 D4 F

where zi is the valence of i ion and Q is the Donnan equilibrium constant and is irrelevant to the ions existing in the solution. In the case of the ions in the acid compartment, the Donnan equilibrium of the ions can be written as eq 17. C4 C̅ 1 ¼ C1 C̅ 4

ð23Þ

ð17Þ

ð24Þ

where C1 and C4 are the concentration of hydrogen ion and gluconate ion in the membrane, respectively. The electroneutrality principle is also obeyed in the membrane, as shown in eq 18:

With the same assumption that the concentration gradient in the diffusion layer is linearly dependent on the thickness of this layer, the concentration of gluconate ion at the boundary of bulk side of the Donnan interface in the left diffusion layer of the salt compartment can be expressed as eq 25.

∑ zi C̅ i þ εCR ¼ 0

where ε is the sign of the fixed charge group and CR is the concentration of the fixed charge group. The fixed charge density, CR, of the membrane could be calculated from the concentration of ion exchange groups attached to polymer matrix (IEC) and the swelling degree.22 CR,A and CR,C are the fixed charge density of anion and cation exchange membrane, respectively. For the anion exchange membrane, ε is positive, and the electroneutrality inside the anion exchange membrane leads to following equation: C̅ 1 þ CR, A C̅ 4 ¼ 0

ð19Þ

In fact, the fixed charged density of the membrane is usually much higher than the concentration of bulk solution. Thus, the concentration of counterions in the membrane can be considered equal to the fixed charged density of the membrane. The electric potential drop (Donnan potentials) at the Donnan interface of the acid compartment is as follows: jdon

RT C4 RT C4 ln ln ¼ ≈ F F CR, A C̅ 4

J4, SL

∂C3 C3 F ∂j2 þ RT ∂x ∂x

∂C4 C4 F ∂j2 ¼ D4 RT ∂x ∂x

ð25Þ where CS is the concentration of feed salt in the salt compartment, which is a time-dependent variance. As a result of the electroneutrality requirement in the diffusion layer, we assume that the desalination rate of salt in the salt compartment is equal to the generation rate of hydrogen ion in the acid compartment. Meanwhile, we should acknowledge that such presumption is not precise enough, because the water dissociation rate in the bipolar membrane is not always equal to salt transport. However, this presumption is still acceptable for convenience because the commercial bipolar membranes usually have a water dissociation efficiency of higher than 98%, according to the product brochure. The concentration of gluconate ion at the boundary of left diffusion layer of the salt compartment at time t can be rewritten as the following: C4, SLjx ¼ δ ¼ CS, 0 D4 þ TA ðD3 þ D4 Þ þ Kaem Kspl AD4 2D3 D4 Kspl It Iδ F

ð20Þ

Similarly, in the salt compartment, there are two diffusion layers and two Donnan interfacial layers in the membrane domain. The NernstPlanck equation can also be used to describe the ion distributions in these regions. J3, SL ¼ D3

C4, SLjx ¼ δ ¼ CS D4 þ TA ðD3 þ D4 Þ Iδ þ Kaem Kspl AD4 =2D3 D4 F

ð18Þ

ð26Þ where CS,0 is the initial concentration of feed salt in the salt compartment. The Donnan potential at the left Donnan interface of the salt compartment can be written similarly to eq 20 as eq 27. jdon, SL ≈

ð21aÞ

ð21bÞ

The continuity of fluxes stipulates that the fluxes of ions at the bulk side of the Donnan interface equal that of the membrane side. Thus, the concentration of gluconate ion at the boundary of the Donnan interface can be described as eq 22. ∂C4 C4 F ∂j2 ITA ð22Þ ¼ J4, SL ¼ D4 RT ∂x ∂x F

RT C4, SL ln F CR, A

ð27Þ

In the right diffusion layer of the salt compartment, the fluxes of ions can be developed according to the above route, which is described in the following equations: ∂C3 C3 F ∂j ITc þ ð28aÞ ¼ J3, SR ¼ D3 RT ∂x ∂x F J4, SR

∂C4 C4 F ∂j ¼ D4 RT ∂x ∂x

I ¼ FðJ3, SR J4, SR þ J5 Þ 13914

ð28bÞ ð28cÞ



ARTICLE

Here, Tc is the transport number of counterion in the cation exchange membrane. The differential of the concentration profile of the sodium ions in the right diffusion layer of the salt compartment can be solved as follows: ∂C3, SR ¼ ∂x

D3 Tc ðD3 þ D4 Þ I þ Kaem Kspl AD3 =2D3 D4 F

ð29Þ The concentration of sodium ion at the boundary of the right diffusion layer of the salt compartment at time t can be described as eq 30. C3, SRjx ¼ δ ¼ CS, 0 Kspl It D3 Tc ðD3 þ D4 Þ þ Kaem Kspl AD3 =2D3 D4 þ Iδ F

ð30Þ The Donnan potential at the right Donnan interface of the salt compartment can be written as eq 31. jdon, SR ≈

RT C3, SR ln F CR, C

J3, B ¼ D3

∂C3 C3 F ∂j þ RT ∂x ∂x

I ¼ FðJ2, B J3, B þ J6 Þ

E ¼ I 2 Rtot t

¼

ITc F

Rtot ¼ NðRsol þ Rmem þ Rdif þ Rdon Þ þ Rel

Combining eqs 32a, 32b, and 32c gives the differential concentration of the ions in the diffusion layer of the base compartment. ∂C3, B ¼ ∂x D3 þ Tc ðD2 þ D3 Þ þ Kbpm Kspl AD3 =2D2 D3 I F ð33Þ For the same generation rate of hydrogen ion and hydroxide ion due to water-splitting of the bipolar membrane, the concentration of sodium ion at the boundary of the diffusion layer near the base compartment at time t can be written similarly as eq 34. C3, Bjx ¼ δ ¼ CB, 0 þ Kspl It D3 þ Tc ðD2 þ D3 Þ Iδ þ Kbpm Kspl AD3 =2D2 D3 F

þ Rdif , SL þ Rdif , SR þ Rdif , B þ Rdon, A þ Rdon, SL þ Rdon, SR þ Rdon, B Þ

Rsol ¼

dδ ΛC

ð39Þ

where d is the distance of the spacers, Λ is equivalent conductance of the bulk solution, and C is the concentration of bulk. The equivalent conductance is assumed to be independent of concentration over the range of interest. For an estimation of the resistance of the solutions, the equivalent conductance at infinite dilution can be used. The equivalent conductances of gluconic acid, gluconate sodium, and sodium hydroxide at infinite dilution are about 380, 80.5, and 280 S 3 cm2 3 equiv1, respectively.24 In fact, the concentration of bulk is a time-dependent variance. Therefore, a natural logarithmic mean value is taken, which can be calculated by eq 40. C̅ ¼

C0 Ct C0 ln Ct

ð40Þ

The logarithmic mean concentrations of the acid, salt, and base compartments can be described by the following equations. C̅ A ¼

where CB,0 is the initial concentration of feed in the base compartment. The Donnan potential of the Donnan interface near the base compartment can be described as eq 35. RT C3, B ln F CR, C

ð38Þ

where the superscripts “A”, “S”, and “B” refer to the acid compartment, the salt compartment, and the base compartment, respectively. “L” and “R” denote the left side and the right side, respectively. The resistance of the solution can be expressed from the conductance and concentration of the bulk solution in eq 39.

ð34Þ

jdon, B ≈

ð37Þ

where N is the repeating unit of the EDBM stack. In the practical application of EDBM technique, the resistance of the electrode can be neglected because hundreds of repeating unit of stack can reduce the contribution of the electrode resistance to less than 2%.23 The resistance of the individual component is the sum of the corresponding resistance of the entire compartments, that is, the resistance in the acid compartment, the salt compartment, and the base compartment. Thus, the total resistance of a typical three-compartment EDBM stack can be described as eq 38. Rtot ¼ NðRsol, A þ Rsol, S þ Rsol, B þ Rmem þ Rdif , A

ð32bÞ ð32cÞ

ð36Þ

The total resistance equals the sum of the resistances of the individual stack components: the resistance of the solution, Rsol; the resistance of the membrane, Rmem; the resistance of the diffusion layer, Rdif; the resistance due to the Donnan interface, Rdon; and the resistance of the electrode, Rel.

ð31Þ

In the diffusion layer of the base compartment, the fluxes of the respective ions can be written as eq 32: ∂C2 C2 F ∂j J2, B ¼ D2 ð32aÞ RT ∂x ∂x

resistance (Rtot) and current, as described in eq 36.

C̅ S ¼

ð35Þ

C̅ B ¼

The energy consumption of the one unit of EDBM stack can be calculated from Ohm’s law, which is a function of the total 13915

Kspl It CA, 0 ln CA, 0 þ Kspl It

ð41aÞ

Kspl It CS, 0 ln CS, 0 Kspl It

ð41bÞ

Kspl It CB, 0 ln CB, 0 þ Kspl It

ð41cÞ



ARTICLE

The resistance of the diffusion layer is related to concentration of bulk in the diffusion layer, and it is given by eq 42.

The concentration of bulk is also a time-dependent variance. For simplicity, an average mean value of the bulk concentration is taken. Thus, the resistance of the individual diffusion layer during δZ δ 1 the EDBM process with a processing time of t can be given as the dx ð42Þ Rdif ¼ Λ 0 CðxÞ following equation: D4 þ TA ðD1 þ D4 Þ þ ðKaem þ Kbpm ÞKspl AD4 Rdif , A ¼ 2D1 D4 = IΛA F 9 9 88 D4 þ TA ðD1 þ D4 Þ > > > > > > > > þ ðK Iδ þ K ÞK AD aem bpm spl 4 = > > A, 0 > 2D1 D4 2 > > > ; ; : :> ð43aÞ

Rdif , SL

9 88 9 D4 þ TA ðD3 þ D4 Þ > > > > > > > þ K Iδ K AD aem spl 4 > < < = = Kspl It D4 þ TA ðD3 þ D4 Þ F þ Kaem Kspl AD4 ¼ 2D3 D4 = IΛS ln CS, 0 =CS, 0 > > > > F 2D3 D4 2 > > > :> : ; ;

ð43bÞ Rdif , SR ¼

9 9 88 D3 Tc ðD3 þ D4 Þ > > > > > > > > þ K Iδ K AD aem spl 3 = = > > > 2 F 2D3 D4 > > > ; ; :> :

ð43cÞ

Rdif , B

9 88 9 D3 þ Tc ðD2 þ D3 Þ > > > > > > > þ K Iδ K AD bpm spl 3 > < < = = Kspl It D3 þ Tc ðD2 þ D3 Þ F þ Kbpm Kspl AD3 ¼ 2D2 D3 = ΛB I ln CB, 0 þ =CB, 0 > > > > F 2D2 D3 2 > > > :> : ; ;

ð43dÞ The resistance due to Donnan interface (Rdon) can be calculated from the value of Donnan potential divided by the

Rdon, A

current, the resistance of the respective layer during the EDBM process with a processing time of t can be written as eq 44.

9 9 88 D4 þ TA ðD1 þ D4 Þ > > > > > > > > þ ðK Iδ þ K ÞK AD aem bpm spl 4 = = pffiffiffiffiffiffiffiffiffiffiffiffiffi Kspl It RT > > IF > 2D1 D4 2 > > > ; ; :> : 9 9 D4 þ TA ðD3 þ D4 Þ > > > þ Kaem Kspl AD4 > Iδ = = Kspl It RT F =CR, A ln CS, 0 ¼ > > > IF > 2D3 D4 2 > > > ; ; :> : 9 9 88 D3 Tc ðD3 þ D4 Þ > > > > >> > þ Kaem Kspl AD3 > Iδ = = Kspl It RT > > IF > 2D3 D4 2 > > > ; ; :> : 88 > > >
> > > > > > > þ Kbpm Kspl AD3 = Iδ = Kspl It RT > > IF > 2D2 D3 2 > > > ; ; :> :

13916

ð44aÞ

ð44bÞ

ð44cÞ

ð44dÞ



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Table 1. Properties of the Membranes Used in the EDBM Processa membrane type

a

thickness (μm)

IEC (meq 3 g1)

area resistance (Ω 3 cm2)

swelling degree (gH2O/gdry)

transport no.

0.98

Neosepta BP-1

300

FuMA-Tech FTBM

450

1.5

Neosepta CMX

164

1.62

2.91

0.18

Neosepta AMX

134

1.25

2.35

0.16

DF120(anion-exchange)

250

1.96

2.0

0.98

DF120(cation-exchange)

220

1.57

1.4

0.92

0.91

The data are collected from the product brochure provided by the company.

The energy consumption E (kWh 3 kg1) for the production of 1 kg of gluconic acid using EDBM technology can calculated by extrapolating the results in eq 45. NRtot t IRtot A ¼ E¼ Kspl IðNAÞtBM Kspl A2 BM I2

ð45Þ

where N is the repeating number of the EDBM stack; I is the current (A); Rtot is the total resistance for one unit EDBM stack (Ω); A is the area of the membrane (m2); B is the volume of the acid compartment (m3); M is the molecular weight of the gluconic acid (196.14 g 3 mol1); and Kspl is the water-splitting constant of the bipolar membrane (mol 3 m3 3 A1 3 h1). Bearing in mind the energy of consumption of the EDBM process, the total process cost can be calculated according to the literature.25 The thickness of the diffusion layer (δ), which can be determined from the well-known limiting current density (ilim) of the membrane through the following eq 46.26 δ¼

zFDC0 ilim ðTc Tc 0 Þlim

ð46Þ

where C0 is the molar concentration of the bulk solution and Tc and Tc0 are the transport number of counterions in the membrane and in the solution, respectively. The transport number of counterions in the membrane and in the solution can be measured using the static potential method. 1.2. EDBM Setup. As shown in Figure 1, an EDBM stack of BPAC configuration (BP, bipolar membrane; A, anion exchange membrane; C, cation exchange membrane) is used for calculation. The membranes include Neosepta BP-1(BP), FTBM (BP), Neosepta CMX (C), Neosepta AMX (A), and domestic DF120 serial monopolar membranes; their main properties are listed in Table 1. HGlu (200 mol 3 m3), NaGlu (2000 mol 3 m3), NaOH (200 mol 3 m3), and Na2SO4 (350 mol 3 m3) are added as the initial feeds for the cycles of acid, salt, base, and electrode rinse, respectively. Each compartment is connected to a separate external beaker (0.003 m3), and each circulation is equipped with a submersible pump. The thickness of the spacer is 1 103m. The effective membrane area is 2.4 m2 with a repeating unit number of 10 (0.3 m 0.8 m 10). In the confirmation experiment, the composite electrodes (Wuhan Nengshi Analytical Sensor Co., Ltd., China) were connected with a direct current power supply (WYL6050S, Hangzhou Yuhang Siling Electronics Co. Ltd., China). Each loop was equipped with an external beaker, allowing for continuous circulation by a submersible pump (1.2 m3 3 h1, CXB30, Wenzhou Erle Pump Co., Ltd., China). The validation experiment was completed at Jiangxi Xinhuanghai Medicine Food Chemical Co., Ltd. (Jiangxi Province, China). The experiment was conducted at

room temperature. The initial concentrations of sodium gluconate in the salt compartment, gluconic acid in the acid compartment, and sodium hydroxide in the base compartment are 1.69, 0.10, and 0.09 mol 3 dm3, respectively. Before the current was applied, the solution of each compartment was circulated for half an hour, and all the visible gas bubbles were eliminated.

3. RESULTS AND DISCUSSION 3.1. Concentration Profile of Feed in the Respective Layers during the EDBM Process. The diffusion coefficients

of H+, OH, Na+ and Glu at infinite dilute solutions are 9.34 109, 5.28 109, 1.33 109, and 7.41 1010 m2 3 s1, respectively.27 The thickness of the diffusion layers was assumed to be 2 104 m.28 The fixed charge density of Neosepta AMX and CMX membrane are about 7812.5 and 9000 mol 3 m3, respectively. In fact, the model is established with some kind of route guidance. Specially, the concentration distributions across the multiple layers of the EDBM stack are developed at first. Then, the resistance distribution profiles are calculated accordingly. Finally, the energy consumption and the total process cost are calculated. The figures are obtained according to the equations established in the theoretical part of the text. The concentration profiles are mainly referred to eqs 15, 26, 34, and 41. The resistance profiles are linked with eqs 43 and 44. The energy consumption is linked with eq 45. Figure 3 illustrates the simulated concentration profiles of electrolyte in the respective layers of the EDBM stack when the current is in the range 1050 A, with a period of 0.5 h. For the time-dependence of the electrolyte concentration, an average of the initial and final concentration is adopted. The concentration of the corresponding counterion of the membrane is regarded as equal to the fixed charge density; that is, the concentration of gluconate ion in the Neosepta AMX membrane and sodium ion in the Neosepta CMX are about 7812.5 and 9000 mol 3 m3, respectively. It should be pointed out that an overall description of the concentration profiles within the individual multiple regions of the membrane domains are not plotted in one figure because of the significant differences between these data. It is clearly indicated that electrolyte concentrations in the diffusion layers are increased with an increase in current, except in the salt compartment. This is normal, because the feed concentration in the salt compartment decreases with the passage of time. At the same time, the electrolyte concentrations in the diffusion layers are less than bulk concentration, except in the right diffusion layers of the salt compartment. There are two main reasons that account for this phenomenon. On one hand, the transport rate of ions within the membrane is faster than that in the solution, so that a concentration gradient is formed in the diffusion layer. The concentration gradient becomes more pronounced with an increase in 13917



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Figure 3. Effect of current density on the simulated concentration profile of EDBM stack with a period of 0.5 h.

current, as indicated by the NernstPlanck equation, so that the electrolyte concentration in the diffusion layer is less than the bulk concentration. On the other hand, the molecular diffusion of gluconic acid across the anion exchange membrane is accelerated with an increase in current as described by eq 4. The higher electrolyte concentration, compared with the bulk concentration, in the right diffusion layer of the salt compartment can be confirmed from eq 29, because the value of the term KaemKsplAD3 is higher than that of the term (D3 Tc(D3 + D4))/F. 3.2. Resistance Profile of the Respective Layer during the EDBM Process. Figure 4 shows the effect of current density on the simulated resistance of the individual layer of the EDBM stack with a period of 0.5 h. As shown in Figure 4, the resistances of the solutions, diffusion layers, and Donnan interfaces are highly dependent on the applied current of the EDBM process, while the resistances of membranes are independent of the current. The total diffusion resistances of the EDBM stack, which are sums of the resistance in the diffusion layers of the acid, salt, and base compartments, are decreased with an increase in current. In fact, there are two counteracting effects that influence the diffusion resistance in the acid or base compartment. On one hand, the concentration gradient, which becomes more pronounced with an increase in current, can lead to an increase of resistance in the diffusion layer. On the other hand, the migrations of the ions across the membranes are accelerated with an increase in current,

Figure 4. Effect of current density on the resistance distribution across the individual layers of the EDBM stack, with a period of 0.5 h.

which leads to an increase in the bulk concentration in the acid and base compartments and decreases the diffusion resistance 13918



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Table 2. Parameters for the Estimation of Process Cost of the EDBM Process EDBM process (BPAC) repeating units expt time (min)

10 30

effective memb. area (m2)

2.4

electrode rinse concn (mol 3 m3)

200

initial base concn (mol 3 m3)

200

monopolar memb. price ($ 3 m2)

Figure 5. Effect of current density on the energy consumption and total cost of the EDBM process, with a period of 0.5 h.

correspondingly. The second effect overwhelms the first one that results in the decrease of the diffusion resistance in the acid and base compartments. In the case of the diffusion resistance in the salt compartment, the accelerated depletion of salt with ascending current is attributed to the increase of diffusion resistance. The resistances due to the Donnan interfaces, which are much less than those in the diffusion layers and feed solutions, are decreased swiftly with an increase in current. This is caused by an increase in ion concentration in the boundary of the Donnan interface, which can be confirmed from the concentration profiles in Figure 3. Because of a lower charge density of the anion exchange membrane compared with that of the cation exchange membrane, the Donnan resistance of the acid compartment is slightly higher than that of the base compartment. The resistances of the solutions in the acid and base compartments are decreased with the increase in current, while a reverse trend is observed for the solution resistance in the salt compartment. Figure 4 also gives a clear contribution of individual components to the total resistance of the stack. The resistance in the diffusion layers is the dominant component, which consumes nearly twothirds of the total resistance when the current is in the range 1050 A. At the same time, the total resistance in the EDBM stack is reduced by about 20% when the current is increased from 10 A to 50 A. 3.3. Energy Consumption and Total Cost of the EDBM Process. Figure 5 shows the effect of current density on the energy consumption and total cost of the EDBM process with a period of 0.5 h. Table 2 also lists some parameters for the estimation of the total cost in an EDBM process. As shown in Figure 5a, the energy consumption of the EDBM process for the production of gluconic acid is nearly linearly increased with the increase in current. The increased trend of the energy consumption is consistent with the Ohm’s law. The nearly proportional trend of the energy consumption is ascribed to the small difference between the total resistances of the stack, as indicated in Figure 4. Figure 5b illustrates that the total process cost decreases swiftly at first and then increases gradually with the increase in current. There is a minimum cost at the current of 33 A of about 0.603 $ 3 kg1. The energy consumption cost increases linearly with the increase in current, of which the contribution to the total process cost is increased from 13 to 73% when the current is increased from 10 to 50 A. It seems that the total fixed cost

350

initial acid concn (mol 3 m3) initial salt concn (mol 3 m3)

remarks

2000 135

bipolar memb. price ($ 3 m2) memb. cost ($)

1350 3888

stack cost ($)

5832

1.5 times membrane

peripheral equip. cost ($)

8748

1.5 times stack cost

total invest. cost ($)

14580

cost

amortization ($ 3 yr1)

4860

3 years

1166.4

interest rate, 8%

maintenance ($ 3 yr1)

1458

10% the investment cost

total fixed cost ($ 3 yr1)

7484.4

interest ($ 3 yr1)

electricity charge ($ 3 KWh1)

0.1

occupies the majority of the total cost of the EDBM process at low current density, while the energy consumption becomes the dominant factor at high current density. In fact, there is often a trade-off to be made between high and low current density during the practical applications of the EDBM process. Higher current densities are not attractive because of their high energy costs related to increased ohmic drop, and lower current densities are not attractive because of the large required membrane area. The range of the simulated energy consumption is consistent with our previous work on one repeating unit experimental stack.7,8 For the high price of a commercial Neosepta BP-1 bipolar membrane, a confirmation experiment with a FTBM bipolar membrane and DF120 serial monopolar membrane (Shandong Tianwei Membrane Technology Co., Ltd.) was carried out to verify the model. The energy consumption of the EDBM process at a current of 10 A is about 1.03 kWh 3 kg1, which is very similar to our predicted value of 1.01 kWh 3 kg1.

4. CONCLUSION A simple model to describe the energy consumption and total cost for a typical three-compartment (BPAC) EDBM process was developed on the basis of the NernstPlanck equation, the Donnan equilibrium, and the electroneutrality assumption in the diffusion layers and membrane phase. The results indicated that concentration gradients in all the diffusion layers increase with an increase in current, except in the salt compartment. The resistances of the solutions, diffusion layers, and Donnan interfaces are highly dependent on the applied current of the EDBM process. The resistances in diffusion layers are the dominant resistance, while the resistances due to Donnan interfaces and the resistances of the membranes can be neglected. With an increase in current, the energy consumption of the EDBM process increases and the total process cost decreases swiftly at first and 13919



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then increases gradually with a minimum cost at a current of 33 A. The energy consumption in the validation experiment is in good agreement with the prediction of the model. An explicit description of the energy consumption and the prediction of the process cost therein are of importance to the application of the EDBM technique. Modeling of the EDBM process can also give some inspiration to improve the performance of this technology and bring this technology to perfection.

don = donnan el = electrolyte L = left mem = membrane R = right s = salt solutions sol = solution

’ AUTHOR INFORMATION

’ REFERENCES

Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT This research is supported in part by the National Natural Science Foundation of China (No. 21025626), the Knowledge Innovation Program of the Chinese Academy of Sciences (No. KSCX2-YW-G-075-25), the Fundamental Research Funds for the Central Universities (No. WK2060190007), and Foundations of Educational Committee of Anhui Province (Nos. ZD200901, KJ2010A330, and KJ2008A69). ’ NOMENCLATURE A = effective area of the membrane (m2) C = concentration (mol 3 m3) CR = the concentration of the fixed charge group (mol 3 m3) d = distance of the spacer (m) D = diffusion coefficient (cm2 s1) F = Faraday constant (C 3 mol1) i = ions I = current (A) J = flux K1 = forward water dissociation constant K1 = water recombination constant Ka = the dissociation constant of acid Kaem = diffusion constants of acid through anion exchange membrane (m1) Kbpm = diffusion constants of acid through bipolar membrane (m1) Kspl = water-splitting constant of bipolar membrane (mol 3 m3 3 A1 3 h1) Q = Donnan equilibrium constant N = number of cell pairs R = gas constant (J 3 K1 3 mol1) t = time (h) T = temperature (K) TA = transport number of counterion in anion exchange membrane TC = transport number of counterion in cation exchange membrane U = voltage drop across the cell (V) x = distance (m) z = charge of ion j = potential (V) ε = sign of the fixed charge group εr = the relative permittivity δ = thickness of diffusion boundary layer (m) Λ = equivalent conductance (S 3 cm2 3 equiv1) Subscripts and Superscripts

a = acid b = base dif = diffusion

(1) Huang, C. H.; Xu, T. W. Electrodialysis with bipolar membranes for sustainable development. Environ. Sci. Technol. 2006, 40, 5233. (2) Xu, T. W.; Huang, C. H. Electrodialysis-based separation technologies: A critical review. AIChE J. 2008, 54, 3147. (3) Bazinet, L.; Lamarche, F.; Ippersiel, D. Bipolar-membrane electrodialysis: Applications of electrodialysis in the food industry. Trends Food Sci.Technol. 1998, 9, 107. (4) Strathmann, H. Membrane separation processes: Current relevance and future opportunities. AIChE J. 2001, 47, 1077. (5) Kumar, M.; Tripathi, B. P.; Shahi, V. K. Electro-membrane process for in situ ion substitution and separation of salicylic acid from its sodium salt. Ind. Eng. Chem. Res. 2009, 48, 923. (6) Drioli, E.; Romano, M. Progress and new perspectives on integrated membrane operations for sustainable industrial growth. Ind. Eng. Chem. Res. 2001, 40, 1277. (7) Wang, Y. M.; Huang, C. H.; Xu, T. W. Optimization of electrodialysis with bipolar membranes by using response surface methodology. J. Membr. Sci. 2010, 362, 249. (8) Wang, Y. M.; Zhang, X.; Xu, T. W. Integration of conventional electrodialysis and electrodialysis with bipolar membranes for production of organic acids. J. Membr. Sci. 2010, 365, 294. (9) Mier, M. P.; Ibanez, R.; Ortiz, I. Influence of process variables on the production of bovine milk casein by electrodialysis with bipolar membranes. Biochem. Eng. J. 2008, 40, 304. (10) Wang, A. L.; Peng, S. C.; Wu, Y. H.; Huang, C. H.; Xu, T. W. A hybrid bipolar membrane. J. Membr. Sci. 2010, 365, 269. (11) Gao, L. H.; Liu, D. J.; Yang, J. Modeling of a three-compartment membrane electrodialysis in H2SO4(NH4)(2)SO4NH3 3 H2O system. J. Membr. Sci. 2009, 344, 252. (12) Jaime-Ferrer, J. S.; Couallier, E.; Viers, P.; Rakib, M. Two-compartment bipolar membrane electrodialysis for splitting of sodium formate into formic acid and sodium hydroxide: Modelling. J. Membr. Sci. 2009, 328, 75. (13) Jaime-Ferrer, J. S.; Couallier, E.; Viers, P.; Durand, G.; Rakib, M. Three-compartment bipolar membrane electrodialysis for splitting of sodium formate into formic acid and sodium hydroxide: Role of diffusion of molecular acid. J. Membr. Sci. 2008, 325, 528. (14) Roux-de Balmann, H.; Bailly, M.; Lutin, F.; Aimar, P. Modelling of the conversion of weak organic acids by bipolar membrane electrodialysis. Desalination 2002, 149, 399. (15) Zhang, Y.; Pinoy, L.; Meesschaert, B.; Van der Bruggen, B. Separation of small organic ions from salts by ion-exchange membrane in electrodialysis. AIChE J. 2011, 57, 2070. (16) Onsager, L. Deviations from Ohm’s law in weak electrolytes. J. Chem. Phys. 1934, 2, 599. (17) Simons, R. Strong electric fields effects on proton transfer between membrane-bound amines and water. Nature 1979, 280, 824. (18) Huang, C. H.; Xu, T. W.; Feng, H. Z.; Li, Q. H. Win-Win coupling in electrodialysis with bipolar membranes (EDBM) for cleaner production. Ind. Eng. Chem. Res. 2009, 48, 1699. (19) Luo, J. Y.; Wu, C. M.; Wu, Y. H.; Xu, T. W. Diffusion dialysis of hydrochloride acid at different temperatures using PPO-SiO2 hybrid anion exchange membranes. J. Membr. Sci. 2010, 347, 240. (20) Luo, J. Y.; Wu, C. M.; Xu, T. W.; Wu, Y. H. Diffusion dialysisconcept, principle and applications. J. Membr. Sci. 2011, 366, 1. (21) Koter, S.; Kultys, M. Electric transport of sulfuric acid through anion exchange membranes in aqueous solutions. J. Membr. Sci. 2008, 318, 467. 13920



ARTICLE

(22) Dlugolecki, P.; Nymeijer, K.; Metz, S.; Wessling, M. Current status of ion exchange membranes for power generation from salinity gradients. J. Membr. Sci. 2008, 319, 214. (23) Dlugolecki, P.; Gambier, A.; Nijmeijer, K.; Wessling, M. Practical potential of reverse electrodialysis as process for sustainable energy generation. Environ. Sci. Technol. 2009, 43, 6888. (24) Handbook of Chemistry and Physics. 74th ed.; Lide, D., Ed.; CRC Press, Inc.: Boca Raton, FL, 1993. (25) Strathmann, H.; Koops, G. H. Process economics of electrodialytic water dissociation for the production of acid and base. In Handbook on Bipolar Membrane Technology; Kemperman, A. J. B., Ed.; Twente University Press: Enschede, Sweden, 2000; pp 191220. (26) Choi, J. H.; Park, J. S.; Moon, S. H. Direct measurement of concentration distribution within the boundary layer of an ion-exchange membrane. J. Colloid Interface Sci. 2002, 251, 311. (27) Ramirez, P.; Gomez, V.; Cervera, J.; Schiedt, B.; Mafe, S. Ion transport and selectivity in nanopores with spatially inhomogeneous fixed charge distributions. J. Chem. Phys. 2007, 126, 194703. (28) Morf, W. E.; Pretsch, E.; de Rooij, N. F. Memory effects of ion-selective electrodes: Theory and computer simulation of the timedependent potential response to multiple sample changes. J. Electroanal. Chem. 2009, 633, 137.

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