Modeling of Potassium Sulfate Production from Potassium Chloride by

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Research Article pubs.acs.org/journal/ascecg

Modeling of Potassium Sulfate Production from Potassium Chloride by Electrodialytic Ion Substitution Xiaoyao Wang,† Xiaozhao Han,† Xu Zhang,*,† Qiuhua Li,‡ and Tongwen Xu*,‡ †

School of Chemistry and Chemical Engineering, Hefei University of Technology, Hefei 230009, People’s Republic of China Laboratory of Functional Membranes, School of Chemistry and Materials Science, University of Science and Technology of China, Hefei 230026, People’s Republic of China

‡

S Supporting Information *

ABSTRACT: An experimental study was carried out on the preparation of potassium sulfate from potassium chloride by electrodialytic ion substitution. Effects of sulfate species, current density, and molar ratio of ammonium sulfate to potassium chloride were investigated. Results showed that ammonium sulfate was regarded as the optimum sulfate source because of the lowest energy consumption and cheap raw materials. When current density was set as 20 or 30 mA/cm2, the generated products can conform to the Chinese Government standard (GB20406-2006). A higher molar ratio can promote the substitution reaction more completely but results in larger loss of K+ ions and more increment of NH4+ ions in products. Moreover, a mathematical model was established to predict the product concentration. Results showed that there is a good agreement between experimental and computational concentrations. KEYWORDS: Potassium sulfate, Electrodialysis, Ion substitution, Model, Ion exchange membrane

■

large. Thus, it is urgent and important to find a new, simple, eco-friendly, and energy-efficient process for preparing potassium sulfate. Electrodialysis (ED) is an important electromembrane process based on the selective migration of aqueous ions through ion exchange membranes under a direct current (DC) electric field.9 Nowadays, ED has been proven to be a simple, energy-efficient, and eco-friendly technology.10−12 Hence, it has been used mainly to concentrate and desalt industrial feeds or effluents, purify and recover organic compounds, desalinize seawater, and so on.13−18 In our previous work, converting potassium chloride into potassium sulfate by four-compartment metathesis electrodialysis was investigated.4 Results showed that the process is of low cost, low energy consumption, and environmentally friendly. However, some impurity ions (such as Cl− and NH4+) still existed in the product, and the product purity could not meet the Chinese Government standard (GB20406-2006, as shown in Table 1). Pisarska studied the mass transfer process of electrodialytic metathesis (MgSO4 + 2KCl → K2SO4 + MgCl2), and results showed that the flow of co-ions was the main reason for product contamination and that ion exchange membranes with high selectivity should be required for the

INTRODUCTION Potassium sulfate is a kind of important chloride-free potash fertilizer for chloride-sensitive crops.1 Traditionally, potassium sulfate is generated by converting potassium chloride, which is easily recoverable from naturally potassium raw materials.2 Two main technique routes are available in industry.3 One is the well-known Mannheim method, which produces more than 50% of potassium sulfate in the world.4 However, it has some disadvantages, such as strong corrosiveness, high investment, and high energy consumption.4 The other is the double decomposition method in which potassium chloride reacts with a double salt (such as K2SO4·MgSO4·6H2O, K2SO4·2MgSO4, and KCl·MgSO4·2.75H2O),1,3 but double salt mineral resources are relatively rare in China;5 furthermore, the mother liquor quantity is too large to handle. Thus, more efforts have been made to prepare potassium sulfate. Krishna et al. developed a viable scheme in which tartaric acid was employed as a benign and recyclable K+ precipitant. The scheme mainly included three steps: selective precipitation of potassium bitartrate, decomposition of the bitartrate salt, and recovery of residual tartaric acid.6,7 Though the product yield was high, the process was relatively complicated. Maria et al. studied KCl conversion to K2SO4 using a chemical reactor coupled with direct contact membrane distillation.8 The highest potassium conversion coefficient could attain 93%. However, the potassium conversion coefficient was easily influenced by membrane temperature. Moreover, the mother liquor quantity was too © 2017 American Chemical Society

Received: June 18, 2017 Revised: August 29, 2017 Published: September 5, 2017 9076

DOI: 10.1021/acssuschemeng.7b01992 ACS Sustainable Chem. Eng. 2017, 5, 9076−9085

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ACS Sustainable Chemistry & Engineering Table 1. Requirements of Potassium Sulfate for Agricultural Use21 powder crystal items K2O content, wt % Cl− content, wt % H2O content, wt % free acid (H2SO4) content, wt % granularity (size 1.00−4.75 mm or 3.35−5.60 mm), %

particle

superior product

first grade product

qualified product

superior product

first grade product

qualified product

≥50.0 ≤1.0 ≤0.5 ≤1.0

≥50.0 ≤1.5 ≤1.5 ≤1.5

≥45.0 ≤2.0 ≤3.0 ≤2.0

≥50.0 ≤1.0 ≤0.5 ≤1.0 ≥90

≥50.0 ≤1.5 ≤1.5 ≤1.5 ≥90

≥40.0 ≤2.0 ≤3.0 ≤2.0 ≥90

Figure 1. Schematic diagram of preparing potassium sulfate by EIS (take the case that (NH4)2SO4 was selected as the sulfate source for example). AEM, anion exchange membrane; CEM, cation exchange membrane; MAEM, monovalent anion exchange membrane.

system.19 Trivedi et al. represented a combination of metathesis electrodialysis and nanofiltration for high purity potassium fertilizer (99% K2SO4), yet the operation process was relatively complicated because of two different membrane modules being involved.20 Thus, in this study, a different and simple ED system called electrodialytic ion substitution (EIS) was designed to improve the product quality. Figure 1 shows the schematic diagram of preparing potassium sulfate by EIS. Under the action of a DC electric field, Cl− migrates from compartment III to compartment II, whereas SO42− migrates from compartment I to compartment III and is rejected by the monovalent anion exchange membrane (MAEM) effectively. Hence, Cl− in compartment III can be substituted with SO42− in situ, and the main product K2SO4 is gathered in this compartment. Meanwhile, NH4+, which migrates through the cation exchange membrane (CEM), combines with Cl− to form the byproduct NH4Cl in compartment II. Effects of sulfate species, current density, and molar ratio of ammonium sulfate to potassium chloride were investigated, and a mathematical model was established to predict the product concentration.

counterions and co-ions. The current in the membrane phase can be expressed as eq 123 I = F(∑ ziJik )

(1)

Jki

where I is the current, zi is the ion i valence, is the ion i molar flux through membrane k, and F is the Faraday constant. As reported in previous literature,24 the transport number of ion i that migrates through membrane k, i.e., εki , can be expressed through the fraction of current transported by these ions as

εik =

ziJik ∑i ziJik

(2)

Generally, membrane counterion transport represents the fraction of the current that is counterions.22 The relationship between the counterion transport number and ion transport Figure 1 can be expressed as T A = 1 − εKA

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DEVELOPMENT OF THE PRODUCT CONCENTRATION MODEL To our knowledge, co-ions can theoretically be completely excluded from the polymer matrix in an ideal ion-exchange membrane. However, as a matter of fact, the selectivity of the ion exchange membrane cannot attain 100%,22 and some coions still exist in the membrane phase. Hence, the quantity of electric charge across the membrane includes that carried by

(3)

S T S = 1 − εNH 4 A

number T carried by membrane number in

(4)

S

where T and T are the membrane counterion transport numbers of AEM and MAEM, respectively, εKA is the K+ S transport number through AEM, and εNH is the NH4+ 4 transport number through MAEM. Membrane counterion transport number T, which is determined under the specific standard conditions, is usually 9077

DOI: 10.1021/acssuschemeng.7b01992 ACS Sustainable Chem. Eng. 2017, 5, 9076−9085

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Combining with eqs 5, 7, and 10, eqs 11 and 12 can be rewritten into eqs 13 and 14).

provided by the membrane manufacturer. However, the actual T value may differ from the manufacturer’s specifications and be influenced by operation current density,19 external salt concentration,22 and counterion charge number.25 In this study, to simplify the calculation process, T is assumed as a constant and calculated from the experimental data. Combining eqs 1−4, the four ion molar fluxes shown in Figure 1 can be expressed as eqs 5−8. A 2JSO = 4

JKA =

IT A F

4

4

(7)

I(1 − T S) F

dC NH4(t )

(8)

SO4 PCl =

JAK

2−

+

(9)

■

(10)

As far as we know, during the ED process, the solution volume in each compartment varies with time because of the electro-osmosis phenomenon,28,29 and the variation extent can be influenced by membrane structures and properties, current density, and as well as ion species. In this study, all the membranes possess homogeneously dense structures, and the effective membrane area is relatively small; furthermore, the operational current density is low, so the solution volume is assumed to be invariable for the sake of simplicity. As shown in Figure 1, CSO4 in the product compartment is affected by JSSO4 and JASO4, whereas CCl is only influenced by JSCl. Thus, eqs 11 and 12 can be obtained.

dt

(17)

d C K (t ) NI(1 − T A ) =− dt VF

(18)

4

V

EXPERIMENTAL SECTION

Table 2. Properties of the Ion Exchange Membranes Used in This Studya membrane type

thickness (μm)

IEC (meq/g)

area resistance (Ω cm2)

transport number (%)

CJMC-2 CJMA-2 ASV

140−150 90−100 120

0.8−1.0 0.8−1.0

1.5−2.5 2.5−3.5 3.7

>98 >94 >97

a

Data were collected from the product brochure provided by the company.

A S N (JSO − JSO )

NJ S dCCl(t ) = − Cl dt V

NI(1 − T S) FV

=

Materials. The membranes used were CJMA-2 (AEM, Hefei Chemjoy Polymer Materials Co., Ltd., China), CJMC-2 (CEM, Hefei Chemjoy Polymer Materials Co., Ltd., China), and ASV (Asahi Glass Co., Ltd., Japan). Their main properties are listed in Table 2. The chemicals, such as K2SO4, KCl, and NH4Cl, were of analytically pure grades. Distilled water was used throughout.

4

=

(16)

where the initial conditions are CNH4(0) = 0 and CK(0) = CKCl(0). Thus, the final product concentrations can be predicted by eqs 13, 14, 17, and 18.

S S 2JSO /JCl

dCSO4(t )

NJ A d C K (t ) =− K dt V

dt

CSO4 /CCl

4

(15)

dC NH4(t )

where εSSO4 and εSCl are SO42− and Cl− ion transport numbers through MAEM and C SO4 and C Cl are SO 42− and Cl − concentrations in the product compartment. Combining this equation and eq 2, the permselectivity expression can be also rewritten into eq 10. SO4 PCl =

=

S NJNH

On the basis of eqs 6 and 8, eqs 15 and 16 can be rewritten into eqs 17 and 18.

S /εClS εSO 4

CSO4 /CCl

(14)

V

dt

where and are the molar fluxes of SO4 and K ions through the anion exchange membrane (AEM), JSSO4, JSCl, and JSNH4 (mol/s) are the molar fluxes of SO42−, Cl−, and NH4+ ions through the MAEM. Here, the current direction from left to right in Figure 1 is regarded as positive. Referring to previous literature,26,27 permselectivity of 4 MAEM between SO42− and Cl−, i.e., PSO Cl , can be expressed as JASO4

(13)

Eqs 13 and 14 are first order differential equations. Usually, they can be solved by the Runge−Kutta method with four steps, and the initial conditions are CSO4(0) = 0 and CCl(0) = CKCl(0). Similarly, CNH4 in the product compartment is dependent on S JNH4, whereas CK is only affected by JAK. Thus, eqs 15 and 16 can be obtained.

(6)

IT S F

SO4 ⎛ ·CSO4(t ) ⎞ T S·PCl NI ⎜ A ⎟ − T SO4 2FV ⎜⎝ ·CSO4(t ) ⎟⎠ CCl(t ) + PCl

⎛ ⎞ dCCl(t ) CCl(t ) NIT S ⎜ ⎟ =− SO4 dt FV ⎜⎝ CCl(t ) + PCl ·CSO4(t ) ⎟⎠

A

S S 2JSO + JCl =

=

dt

(5)

I(1 − T ) F

S JNH =

dCSO4(t )

Experimental Apparatus. Figure 2 illustrates the experiment flow sheet. The EIS membrane module (1) was provided by Hefei Chemjoy Polymer Materials Co., Ltd., China. The effective area of each membrane was approximately 20 cm2, and the entire module included two pieces of CEMs, three pieces of AEMs, and two pieces of MAEMs constituting two electrode compartments, two chlorate compartments (i.e., byproduct compartments), two KCl compartments (i.e., product compartments), and two sulfate compartments.

4

(11)

(12)

where N is the repeating unit number of EIS membrane stack and V is the solution volume in the product compartment. 9078

DOI: 10.1021/acssuschemeng.7b01992 ACS Sustainable Chem. Eng. 2017, 5, 9076−9085

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Figure 2. Flow diagram of the experimental process. (1) EIS module, (2) DC power supply, (3) electrode tank, (4) sulfate tank, (5) chlorate tank, (6) product (K2SO4) tank; (7−10) peristaltic pump. V are the K2SO4 concentration and volume in the product compartment at time t, respectively. The K2SO4 purity P (wt %), which represents the product quality, can be calculated through the equation

The composite electrodes, made of titanium coated with ruthenium, were connected with a DC power supply (2) (RLD-3005D1, Suzhou WTKS Elec. &Tech. Co., Ltd., China). (NH4)2SO4 (or Na2SO4, MgSO4) solution (200 mL, 0.61−1.10 mol/L), NH4Cl solution (200 mL, 0.15 mol/L), and KCl solution (200 mL, 1.10 mol/L) were added to tanks 4−6, respectively. Tank 3 was filled with 200 mL of 0.3 mol/L K2SO4 as electrode rinse. Each circulation was equipped with a peristaltic pump (7−10) (BT100S, Baoding Lead Fluid Tech. Co., Ltd., China), and the flow rates were set at 184 L/h. Constant current and batch operation mode were adopted in this work, and once the voltage drop increased suddenly (reached at ∼3-fold of the initial voltage drop), the operation was stopped. Before the current was applied, the solution in each compartment was circulated for several minutes until all of the visible gas bubbles were eliminated. At different running times, voltage drops across the EIS module were recorded, and samples in tanks (4−6) were taken to analyze the ions concentrations. All of the operations were conducted at room temperature (25 ± 3 °C). Analyses and Data Treatment. Determination of Ion Concentration. Cl− concentration was measured by potentiometric titrator (ZDJ-400, Beijing Xianqu-Weifeng Technology Co. Ltd., China) with standard AgNO3 solution. K+ and Na+ concentrations were measured by an atomic absorption spectrophotometer (WFX130B, Beijing Beifen-Ruili Analytical Instrument (Group) Co., Ltd., China). NH4+ concentration was determined through oxidization first by formaldehyde and then titrating with a calibrated NaOH solution with phenolphthalein as an indicator. Mg2+ concentration was determined by ethylene diamine tetraacetic acid (EDTA) with Eriochrome Black T as an indicator. SO42− concentration was analyzed by barium chromate spectrophotometry with a visible spectrophotometer (VIS-7220G, Beijing Beifen-Ruili Analytical Instrument (Group) Co., Ltd., China). Calculations. The energy consumption E (kW·h/kg K2SO4) is the electricity power consumption of the EIS membrane module, which can be calculated as

E=

P=

∑i MiCi(t )

× 100% (20)

where Mi is the molar molecular weight of solute i in the product compartment and Ci(t) is the concentration of solute i. The K2SO4 yield Y (%), which represents the product quantity, can be calculated as Y=

C K2SO4(t ) C KCl(0)

× 100%

(21)

where CKCl(0) is the KCl concentration at time 0 in the product compartment.

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RESULTS AND DISCUSSION Effect of Sulfate Species. During this EIS process, additional sulfate was used to provide SO42− ions to replace the Cl− ions in the product compartment, and different sulfate species may result in different process performance and product qualities. Thus, in this case, sodium sulfate (Na2SO4), ammonium sulfate ((NH4)2SO4), and magnesium sulfate (MgSO4) were selected to conduct the EIS process. The initial molar ratio of (NH4)2SO4 to KCl was set at 0.55:1 to promote the complete transformation of KCl. The initial KCl concentration was set as ∼1.1 mol/L, and the current density was set at 30 mA/cm2. Figure 3 shows the voltage drops across the EIS module. The three voltage drop-time curves appear first decreased, then remain stable, and eventually increase. At the start of the operation, the solution concentration (∼0.15 mol/L) in the NH4Cl tank was at a low level to result in a high solution resistance. Then, as the operation proceeded, ion concentrations in the four tanks were high enough to provide stable solution resistance. Finally, the solution in the sulfate tank was significantly diluted to suddenly increase the voltage drop. At

∫ U (t )I dt M K2SO4C K2SO4(t )V

M K2SO4C K2SO4(t )

(19)

where U(t) is the voltage drop across the EIS module at time t, I is the current, and M is the molar molecular weight of K2SO4. CK2SO4(t) and 9079

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start to 300 min, SO42− concentrations increase linearly, whereas Cl− concentrations decrease linearly. Then, Cl− concentrations are at low levels, and SO42− concentrations present as stable. This means that nearly all of the Cl− ions have been replaced with SO42− in the product compartment. Moreover, both Cl− concentration−time curves and SO42− concentration−time curves are very close, suggesting that sulfate species have no apparent effect on Cl− and SO42− concentrations. Table 3 shows the ion content in product, product purity, product yield, and energy consumption for different sulfate species. Ion content, product purity, and product yield were calculated from relative ion concentrations in product solution. According to the Chinese Government standard GB204062006, all K2SO4 products shown in this table can meet the standard. The order of product yield in the three cases is YNa2SO4 < Y(NH4)2SO4 < YMgSO4, and the order of energy consumption is E(NH4)2SO4 < ENa2SO4 < EMgSO4. In addition, nitrogen is one of the three essential elements for plants, so byproduct NH4Cl can be used as nitrogen fertilizer. Furthermore, the price of (NH4)2SO4 in industry is friendly. Table S1 depicts the effect of sulfate species on ion content in the byproduct (NH4Cl, NaCl, MgCl2). The amount of Cl− ion accounts for nearly half of the total ion amount, and cations such as NH4+, Na+, and Mg2+ occupy the second position. Moreover, ∼16 wt % of SO42− ions exist in the byproduct compartment, suggesting that the SO42− ion can migrate through MAEM under a DC electric field. In addition, it is very exciting that only 2.15−3.29 wt % of K+ ions are in the byproduct, indicating that counterion selectivity of AEM used in this study is high. On the basis of these discussions, (NH4)2SO4 can be regarded as the optimum sulfate to conduct the EIS process in this study. Effect of Current Density. The experiment was also investigated using different current densities of 20, 30, 40, and 50 mA/cm2. In this case, (NH4)2SO4 was selected as the sulfate source, and the initial molar ratio of (NH4)2SO4 to KCl was the same as that in the above section. The changes in voltage drops across the EIS module are shown in Figure 5. As the current density increases from 20 to 50 mA/cm2, the voltage drop presents an upward tendency, and the operation time decreases from 497 to 197 min because of higher driving force.30 Figure 6 shows the SO42− and Cl− concentrations in the product compartment under different current densities. It is obvious that the transport fluxes of the two ions increase as current density increases, and the movement of Cl− becomes faster than that of SO42−. Table 4 illustrates the effects of current density on the ion content in product, product purity, product yield, and energy consumption. It can be seen that the Cl− content increases as the current density increases because the MAEM permselectivity decreases with the increment of current density.

Figure 3. Effect of sulfate species on voltage drops across the EIS module.

that moment, the operation was immediately stopped. Comparing the three voltage drop-time curves, the MgSO4 process has the highest voltage drop, which may be interpreted as that Mg2+, which migrates through the CEM, combines with OH− generated by the electrode reaction to form the insoluble Mg(OH)2 in the electrode compartment. The voltage drop of the (NH4)2SO4 process is lower than that of the Na2SO4 process. The reason is that Na+ (0.358 nm) has a larger hydrated ion radius than that of NH4+ (0.331 nm),28 and the larger hydrated ion radius will result in higher resistance. Figure 4 illustrates the effect of sulfate species on Cl− and SO42− concentrations in the product compartment. From the

Figure 4. Effect of sulfate species on Cl− and SO42− concentrations in the product compartment.

Table 3. Effect of Sulfate Species on Ion Content in Product, Product Purity, Product Yield, and Energy Consumption ion content in product (wt %) sulfate species

Cl−

SO42−

K+

NH4+

(NH4)2SO4 Na2SO4 MgSO4

1.84 1.54 1.80

53.28 53.34 53.51

44.57 44.77 44.49

0.31

Na+

Mg2+

product purity (wt %)

product yield (%)

energy consumption (kWh/kg K2SO4)

0.21

95.7 95.8 96.1

84.9 83.3 88.3

1.87 2.08 2.43

0.36

9080

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product purity is P20 > P30 ≈ P40 > P50, and the order of product yield is Y50 > Y30 ≈ Y40 > Y20. The irregular trend of product yield suggests that more sulfate ions in the product were lost under higher current density. Furthermore, when the current density was set as 20 or 30 mA/cm2, the generated products can meet the requirements of the GB20406-2006 standard. In addition, like most electrodialysis processes,4,10,31,32 energy consumption in this case increases with the increment of current density. The effect of current density on ion content in the byproduct is shown in Table S2. First, higher current density can lead to lower Cl− ion content and higher SO42− ion content in the byproduct compartment; thus, it is again confirmed that the MAEM permselectivity decreases with the increment of current density. Second, because of higher AEM selectivity under higher current density, K + ion content decreases from 3.09 to 1.92 wt % as current density increases from 20 to 50 mA/cm2. Third, because higher current density may bring about a higher driving force, the NH4+ ion content increases with the increment of current density. Effect of Molar Ratio of (NH4)2SO4 to KCl. In this case, the current density was set as 30 mA/cm2, and (NH4)2SO4 was selected as the sulfate source. Effect of molar ratio of (NH4)2SO4 to KCl was investigated using different molar ratios of 0.55:1, 0.6:1, 0.7:1, and 1:1. Figure 7 illustrates the effect of the molar ratio of (NH4)2SO4 to KCl on voltage drops across the EIS module. It seems that,

Figure 5. Effect of current density on voltage drops across the EIS module.

Figure 6. Effect of current density on Cl− and SO42− concentrations in the product compartment.

Moreover, there exists some NH4+ ions in the product compartment, and the NH4+ content decreases from 0.35 to 0.17% as the current density increases from 20 to 50 mA/cm2. The main reason is that the counterion selectivity of MAEM cannot achieve 100%, and NH4+ ions can migrate through the MAEM under the DC electric field. In addition, as we know, a higher current density can result in a stronger driving force for ion migration. As seen in Figure 1, three spieces of ions (SO42−, Cl−, and NH4+) transport through MAEM. However, the migration flux increasing range of SO42− and Cl− through MAEM is larger than that of NH4+ in this study, which is similar to that reported in previous literature.19 Therefore, NH4+ content in the product decreases. Moreover, the order of

Figure 7. Effect of the molar ratio of (NH4)2SO4 to KCl on the voltage drop across the EIS stack.

as the molar ratio increases, the voltage drop decreases, indicating that excessive (NH4)2SO4 can reduce membrane module electrical resistance. Moreover, the operation time is extended with the increment of the molar ratio. As mentioned in the Experimental Apparatus section, a rule was set that once

Table 4. Effect of Current Density on Ion Content in Product, Product Purity, Product Yield, and Energy Consumption ion content in product (wt %) current density (mA/cm2)

Cl−

SO42−

K+

NH4+

product purity (wt %)

product yield (%)

energy consumption (kWh/kg K2SO4)

20 30 40 50

1.29 1.84 2.33 2.92

54.64 53.28 53.38 52.39

43.73 44.57 44.09 44.52

0.35 0.31 0.20 0.17

98.1 95.7 95.9 94.1

81.2 84.9 84.7 79.0

1.51 1.87 2.33 2.89

9081

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ACS Sustainable Chemistry & Engineering the voltage drop increased suddenly (reached at ∼3-fold of the initial voltage drop) operation should be stopped immediately. When the molar ratio was set as 0.55:1, 0.6:1, or 0.7:1, operations followed the rule. With regard to the molar ratio of 1:1, when the operation time reaches 480 min, the voltage drop is still slow as shown in Figure 8. Considering a higher molar

the longer operation time and more SO42− ions in the ammonium sulfate compartment can lead to more SO42− ions diffusing through the CEM. The influence of the molar ratio on NH4+ and K+ ion content is not obvious. As the molar ratio increases from 0.55 to 1, the NH4+ ion content varies from 28.15 to 29.24 wt % and the K+ ion content changes from 2.05 to 2.17 wt %. In short, a higher molar ratio can bring about a lower voltage drop and more complete substitution reaction but results in a longer operation time, more significant loss of K+ ions, and an incremented number of NH4+ ions. After considering these aspects comprehensively, 0.6 and 0.7 are regarded as suitable molar ratios in this case. Validity of Product Concentration Model. As stated above, membrane counterion transport number T and permselectivity P, which are affected by many operation parameters, among which are external salt concentration22,33 and current density,34 are two important parameters. On the basis of the experimental results shown above, TS and TA can be directly calculated by solving eqs 17 and 18 with the measured 4 ion concentration data, and PSO Cl can be estimated by solving eqs 13 and 14 through the Runge−Kutta fourth-order method. The calculation steps are summarized as below. The detailed calculation procedures for P are summarized as follows: exp (1) Experimental values Cexp SO4 and CCl are obtained through analyzing the solution in the product compartment. (2) Estimation of P values and then calculation of Ccalc SO4 and calc CCl . The differential eqs 13 and 14 are numerically integrated through the Runge−Kutta fourth-order method. The residual calc exp calc error R between Cexp SO4, CCl and CSO4, CCl can be calculated by

Figure 8. Effect of the molar ratio of (NH4)2SO4 to KCl on Cl− and SO42− concentrations in the product compartment.

ratio may consume more materials and electric energy, extending the operation time (molar ratio of 1:1) does not seem to make sense. Figure 8 indicates SO42− and Cl− concentrations in the product compartment at different molar ratios. As shown in the figure, the molar ratio has almost no effect on Cl− concentrations, and the difference among the four SO42− concentration−time curves is slight. Effects of the molar ratio on the ion content in product, product purity, product yield, and energy consumption are shown in Table 5. First, a higher molar ratio results in less Cl− ion content and more SO42− ion content. Thus, it could be concluded that a higher molar ratio could promote the replacement of Cl− into SO42− more completely. As discussed above, a higher molar ratio would extend the operation time but lead to larger loss of K+ ion in the product compartment. Second, as the molar ratio increases from 0.55 to 1, the NH4+ ion content increases from 0.30 to 2.48%, suggesting that coion flux of MAEM will increase with the increment of external salt concentration.22 In particular, when the NH4+ ion content reaches 2.48%, it results in a decrease in the product purity. Third, all products generated in this case conform to the GB20406-2006 standard. Fourth, as the molar ratio increases, the product yield changes between 84.0 and 87.8% and the energy consumption varies between 1.87 and 2.12 kWh/kg K2SO4. Table S3 shows the effects of the molar ratio on ion content in the byproduct. As the molar ratio increases, Cl− ion content decreases while SO42− ion content increases. This is because

⎛ C exp, x − C calc, x ⎞2 i ⎟⎟ R = ∑ ⎜⎜ i exp, x C ⎝ ⎠ i x=1 n

(22)

where i = SO42− and Cl−. (3) Changing the estimation of P values and repeating step (2). Eventually, the optimum P value can be received according to the obtained relationship between R and P. Here, N = 2, V = 0.2 L, and the Faraday constant F = 96485 C/mol. For the model to be further validated, detailed calculation procedures are summarized: (1) When the current density is set as 20, 30, 40, or 50 mA/ SO cm2, the corresponding T and PCl 4 can be calculated based on the experimental results shown above. Subsequently, the relationship between T and current density and that between 4 PSO Cl and current density can be established. SO (2) On the basis of the established relations, T and PCl 4 data 2 of any current density from 20 to 50 mA/cm can be obtained. (3) Once the current density is determined, the ion concentrations in the product compartment can be calculated according to eqs 13−16.

Table 5. Effects of Molar Ratio on Ion Content in Product, Product Purity, Product Yield, and Energy Consumption ion content in product (wt %) molar ratio

Cl−

SO42−

K+

NH4+

product purity (wt %)

product yield (%)

energy consumption (kWh/kg K2SO4)

0.55:1 0.6:1 0.7:1 1:1

1.82 1.23 0.59 0.36

52.81 53.57 54.54 55.94

45.06 44.59 43.76 41.22

0.30 0.61 1.10 2.48

95.7 97.1 97.6 91.9

84.9 87.0 87.8 86.0

1.87 1.87 2.12 2.10

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DOI: 10.1021/acssuschemeng.7b01992 ACS Sustainable Chem. Eng. 2017, 5, 9076−9085

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ACS Sustainable Chemistry & Engineering (4) Finally, the model will be verified by comparing experimental and computational ion concentrations in the product compartment. Figure 9 shows T−current density curves, and it can be seen that the actual transport number T increases with current

Figure 9. Calculational membrane counterion transport number T of AEM and MAEM.

density, and this is in accordance with that reported in previous literature.24 Furthermore, the T data in Figure 9 is as much as that provided by the manufacturers shown in Table 2. Figure 10

Figure 11. Experimental and calculated CSO4 and CCl in the product compartment. Experiment conditions: (a) 25 and (b) 35 mA/cm2. (NH4)2SO4 was selected as the sulfate source, and the molar ratio of (NH4)2SO4 to KCl was 0.55:1.

tration values in Figure 11. Hence, the conclusion can be drawn that the established mathematical model is reasonable and reliable.

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CONCLUSIONS An EIS process was proposed to prepare potassium sulfate, which is a kind of important chloride-free potash fertilizer. First, various operation parameters such as sulfate species, current density, and molar ratio of ammonium sulfate to potassium chloride were investigated. Results showed that all the generated products can meet the GB20406-2006 standards regardless of the sulfate used. Ammonium sulfate was regarded as the optimum sulfate source because of the lowest operation energy consumption and cheap raw materials. When the current density was set as 20 or 30 mA/cm2, the generated products can meet the requirements of the GB20406-2006 standard. Furthermore, the operation energy consumption increases with the increment of current density. A higher molar ratio can completely promote the substitution reaction, but an excessive molar ratio can result in larger loss of potassium ion and larger increase of ammonium ion in the product. Second, a product concentration mathematical model was established. SO The calculated T and PCl 4 data increase as current density increases, which is in accordance with that reported by previous literature. Furthermore, calculated results showed that there is a

4 Figure 10. Calculational membrane permselectivity factor PSO Cl of MAEM.

4 shows the PSO Cl , which increased with the increment of current density. The variation trend is also in accordance with that reported by previous literature,34 and this is the reason that the product with lower Cl− ion content can be generated under a higher current density. Figure 11 shows the experimental and computational SO42− and Cl− concentrations in the product compartment. Current densities were set as 25 and 35 mA/cm2, which are different SO from those stated above. TS, TA, and PCl 4 values used here were calculated with the interpolation method from Figures 9 and 10 and show good agreement between the two series concen-

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Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 2005, 476. (3) Dave, R.; Ghosh, P. Efficient Recovery of Potassium Chloride from Liquid Effluent Generated during Preparation of Schoenite from Kainite Mixed Salt and Its Reuse in Production of Potassium Sulfate. Ind. Eng. Chem. Res. 2006, 45, 1551. (4) Zhang, X.; Wang, X.; Liu, X.; Han, X.; Jiang, C.; Li, Q.; Xu, T. Conversion of Potassium Chloride into Potassium Sulfate by FourCompartment Electrodialysis: Batch Operation Process. Ind. Eng. Chem. Res. 2015, 54, 11937. (5) Zhang, Y.; Cao, J.; Ren, B.; Xie, Y. A General Description for Production Method of Potassium Sulfate (In Chinese). Chemical Fertilizer Design 2003, 41, 3. (6) Ghara, K.; Korat, N.; Bhalodia, D.; Solanki, J.; maiti, P.; Ghosh, P. Production of pure potassium salts directly from sea bittern employing tartaric acid as a benign and recyclable K+ precipitant. RSC Adv. 2014, 4, 34706. (7) Maiti, P.; Ghosh, P.; Ghara, K.; Solanki, J.; Brahmbhatt, H.; Chunawala, J.; Eringathodi, S.; Paul, P. Selective extraction of potassium chloride employing tartaric acid as safe, benign and recyclable extractant. US 9540248B2. (8) Tomaszewska, M.; Łapin, A. The influence of feed temperature and composition on the conversion of KCl into KHSO4 in a membrane reactor combined with direct contact membrane distillation. Sep. Purif. Technol. 2012, 100, 59. (9) Shi, S.; Lee, Y.; Yun, S.; Hung, P.; Moon, S. Comparisons of fish meat extract desalination by electrodialysis using different configurations of membrane stack. J. Food Eng. 2010, 101, 417. (10) Wang, Y.; Huang, C.; Xu, T. Which is more competitive for production of organic acids, ion-exchange or electrodialysis with bipolar membranes? J. Membr. Sci. 2011, 374, 150. (11) Ran, J.; Wu, L.; He, Y.; Yang, Z.; Wang, Y.; Jiang, C.; Ge, L.; Bakangura, E.; Xu, T. Ion exchange membranes: New developments and applications. J. Membr. Sci. 2017, 522, 267. (12) Asraf-Snir, M.; Gilron, J.; Oren, Y. Gypsum scaling of anion exchange membranes in electrodialysis. J. Membr. Sci. 2016, 520, 176. (13) Dong, Y.; Liu, J.; Sui, M.; Qu, Y.; Ambuchi, J.; Wang, H.; Feng, Y. A combined microbial desalination cell and electrodialysis system for copper-containing wastewater treatment and high-salinity-water desalination. J. Hazard. Mater. 2017, 321, 307. (14) Wang, Z.; Luo, Y.; Yu, P. Recovery of organic acids from waste salt solutions derived from the manufacture of cyclohexanone by electrodialysis. J. Membr. Sci. 2006, 280, 134. (15) Zhang, X.; Li, C.; Wang, X.; Wang, Y.; Xu, T. Recovery of hydrochloric acid from simulated chemosynthesis aluminum foils wastewater: An integration of diffusion dialysis and conventional electrodialysis. J. Membr. Sci. 2012, 409−410, 257. (16) de Groot, M.; Bos, A.; Lázaro, A.; de Rooij, R. Bargeman, G. Electrodialysis for the concentration of ethanolamine salts. J. Membr. Sci. 2011, 371, 75. (17) Zhang, X.; Wang, X.; Chen, Q.; Lv, Y.; Han, X.; Wei, Y.; Xu, T. Batch preparation of high basicity polyferric sulphate by hydroxide substitution from bipolar membrane electrodialysis. ACS Sustainable Chem. Eng. 2017, 5, 2292. (18) Sharma, P.; Gahlot, S.; Rajput, A.; Patidar, R.; Kulshrestha, V. Efficient and Cost Effective Way for the Conversion of Potassium Nitrate from Potassium Chloride Using Electrodialysis. ACS Sustainable Chem. Eng. 2016, 4, 3220. (19) Pisarska, B. Transport of co-ions across ion exchange membranes in electrodialytic metathesis MgSO 4 +2KCl→ K2SO4+MgCl2. Desalination 2008, 230, 298. (20) Trivedi, J.; Bhadja, V.; Makwana, B.; Jewrajka, S.; Chatterjee, U. Sustainable process for the preparation of potassium sulfate by electrodialysis and its concentration and purification by a nanofiltration process. RSC Adv. 2016, 6, 71807. (21) The requirements of potassium sulfate for agricultural use. Chinese Government Standard, GB20406-2006.

good agreement between experimental and computational SO42− and Cl− concentrations in the product compartment. In short, EIS is a simple, effective, and environmentally friendly process for preparing potassium sulfate.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acssuschemeng.7b01992. Additional information including effects of operation parameters on the quality of the byproduct (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*Tel.: +86-551-6290-5769. E-mail: [email protected]. *Tel.: +86-551-6360-1587. E-mail: [email protected]. ORCID

Tongwen Xu: 0000-0001-6000-1791 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research is supported by the National Natural Science Foundation of China (No. 21606063), International Partnership Program of Ch inese Academy of Sciences (No.21134ky5b20170010), the Fundamental Research Funds for the Central Universities (No. JZ2016HGTA0707), and the Natural Science Foundation of Anhui Province (Nos. 1508085QB34, 1608085QB41).

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NOMENCLATURE I: current, A z: charge of ion Jki : ion i molar flux through membrane k, mol s−1 εki : ion i transport number through membrane k T: membrane transport number, i.e., membrane counterion transport number 2− 4 PSO and Cl− Cl : permselectivity of MAEM between SO4 −1 C: concentration, mol L V: volume, L N: repeating unit number of EIS membrane stack F: Faraday constant, C mol−1 E: energy consumption, kW·h/kg K2SO4 M: molar molecular weight of K2SO4, kg mol−1 t: time, s R: residual error

Subscripts and Superscripts

k: membranes i: ions A: anion exchange membrane S: monovalent anion exchange membrane exp: experimental calc: calculational

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REFERENCES

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