Measurements and Modeling of the Phase Equilibria in AlCl3 + NaCl +

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Measurements and Modeling of the Phase Equilibria in AlCl3 + NaCl + CaCl2 + H2O and AlCl3 + CaCl2 + NH4Cl + H2O Systems Xiangzhao Zeng,†,§ Yan Zeng,‡ and Zhibao Li*,† †

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Key Laboratory of Green Process and Engineering, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China ‡ Materials Engineering, McGill University, 3610 University Street, Montreal, QC H3A 0C5, Canada § School of Chemistry and Chemical Engineering, University of Chinese Academy of Sciences, Beijing 100049, China S Supporting Information *

ABSTRACT: Solid−liquid phase equilibrium for chloride salt systems plays a vital role in the utilization of liquid wastes generated from soda ash production by the Solvay process. The equilibrium data for ternary systems AlCl3−NaCl−H2O, AlCl3−NH4Cl−H2O, and CaCl2−NH4Cl−H2O from 283 to 353 K were determined by a dynamic method. A chemical model for these systems was developed with the mixed-solvent electrolyte model parameterization with the average absolute relative deviation less than 5%. The new model is capable of calculating solubilities of NaCl and NH4Cl in the AlCl3−CaCl2−H2O system, and the average absolute relative deviation of predicted points is less than 6%. The experimental and calculated phase equilibria have been used in developing a recovery method for NaCl and CaCl2 in the liquid wastes from the Solvay process and the subsequent utilization of CaCl2.

However, during the Solvay process, 8−10 m3 of liquid wastes is generated per ton of Na2CO3 produced.7 The liquid wastes mainly consist of CaCl2, NaCl, and NH3 with concentrations about 95−115, 50−51, and 0.006−0.03 kg·m−3, respectively. In the industry, liquid wastes are usually discharged to nearby rivers, while solid wastes are usually left and allowed to accumulate without undergoing further treatment to obtain other useful materials. To tackle the environmental issues and utilize the valuable chloride sources in liquid wastes, the effective separation of NaCl and CaCl2 from the liquid wastes and their transformation to other chlorides are promising strategies. In this context, it is very important to understand the thermodynamic properties, particularly solid−liquid equilibrium properties in the salt-water systems, associated with various chlorides system. Once separated, NaCl can be reused as a reactant in the Solvay process. However, CaCl2 requires subsequent utilization to increase its additional value, considering its excess global production capacity. For instance, more valuable aluminum chloride hexahydrate (AlCl3·6H2O) can be produced from CaCl2. For the design of this salt transformation, it is necessary to study the solid−liquid equilibria in the AlCl3−NaCl−CaCl2− NH4Cl−H2O system. There have been number of reports on the phase equilibria related to NaCl, CaCl2, or AlCl3·6H2O in aqueous chloride

1. INTRODUCTION Sodium carbonate (Na2CO3), often referred to as soda ash, is utilized as an essential raw material in the industrial manufacturing of many products.1,2 The Solvay process, named after the inventor Ernest Solvay, is one of the most famous synthesis techniques for the production of Na2CO3. In parts of the world where no natural sodium carbonate, carbonaceous minerals, or naturally occurring sodium carbonate bearing brines are available, the Solvay process is generally applied to produce Na2CO3.3 In 2017, 45% of China’s sodium carbonate productions was accomplished using the Solvay process, while expecting a rise in demand accompanied by a modest growth in production each year. The Solvay process produces soda ash from brine (predominantly sodium chloride) and limestone (calcium carbonate).4−6 In the first step, carbon dioxide (CO2) is bubbled through a concentrated aqueous solution containing sodium chloride (NaCl) and ammonia (NH3). During this step, sodium bicarbonate (NaHCO3) is precipitated out and then separated from the hot ammonium chloride (NH4Cl) solution. Following the solid−liquid separation, the residual NH4Cl solution is utilized to produce NH3 and calcium chloride (CaCl2) via reaction with quicklime (CaO). While CaCl2 is a major byproduct of the Solvay process, NH3 is recycled in the carbonation process. CaO is converted from CaCO3, during which CO2 is also produced and can be used for the carbonation process. Finally, Na2CO3 is produced from the calcination of NaHCO3. A comprehensive Solvay flowsheet diagram of the manufacturing process is shown in Figure 1. © XXXX American Chemical Society

Received: February 22, 2019 Accepted: April 24, 2019

A

DOI: 10.1021/acs.jced.9b00175 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

solutions. For instance, a wide range of phase equilibrium data of the binary CaCl2−H2O and AlCl3−H2O systems can be found in literature.8−16 However, for the ternary systems, AlCl3−CaCl2− H2O from 278.15 to 363.15 K17 and AlCl3−KCl−H2O from 298 and 333 K18 have been investigated. Zhou19 studied the solubilities of NaHCO3 and NH4HCO3 in the NH3−CO2− NaCl−H2O system and proved that thermodynamic modeling from the experimental data at ambient pressure could enable the prediction of phase equilibria at high pressures. Moreover, Gao20 developed a comprehensive thermodynamic model for calculating the thermodynamic and transport properties of a variety of chloride-containing systems, including AlCl3−FeCl2− H2O and AlCl3−KCl−H2O. However, the solid−liquid equilibria in the AlCl3−NaCl−CaCl2−NH4Cl−H2O system, which are indispensable for the process of AlCl3·6H2O crystallization from the liquid wastes in the Solvay process, has never been reported. In this work, the solid−liquid phase equilibria in the AlCl3− NaCl−CaCl2−NH4Cl−H2O system are measured from 283 to 353 K. The experimentally determined data are used to construct a comprehensive thermodynamics model that can represent the phase equilibria in the AlCl3−NaCl−CaCl2− NH4Cl−H2O system. The mixed-solvent electrolyte (MSE) model embedded in the OLI Software is applied for data correlation and regression regarding middle-range interaction parameters for aqueous electrolytes, as the modification of these parameters significantly improved the accuracy of the solubility calculations. This article provides reliable data and a comprehensive thermodynamic model to assist the separation process and subsequent utilization of NaCl and CaCl2 from liquid wastes.

Table 1. Chemical Reagents chemical name

CAS No.

aluminum chloride hexahydrate calcium chloride anhydrous sodium chloride

7784-13-6

ammonium chloride

sources Sinopharm Chemical Reagent Co., Ltd Sinopharm Chemical Reagent Co., Ltd Sinopharm Chemical Reagent Co., Ltd Sinopharm Chemical Reagent Co., Ltd

10043-52-4 7647-14-5 12125-02-9

mass fraction purity (%) ≥97 ≥96 ≥99.5 ≥99.5

2. EXPERIMENTAL SECTION 2.1. Experimental Materials. Aluminum chloride hexahydrate (AlCl3·6H2O, 97 wt %), calcium chloride (CaCl2, 96 wt %), sodium chloride (NaCl, 99.5 wt %), and ammonium chloride (NH4Cl, 99.5 wt %) were purchased from Sinopharm Chemical Reagent Co., Ltd. All reagents used in this work are listed in Table 1. Laboratory-made deionized water (0.1 μS· cm−1) was used to prepare aqueous solutions. 2.2. Experimental Procedure. The solubilities of salts in aqueous solutions were measured by a dynamic method. Detailed experimental procedure and apparatus can be found in our previous works.17−20 In the experiment, solution containing known concentration of AlCl3 or CaCl2 was first added to the jacketed reactor, each having a maximum volume of 250 mL. A certain amount of NaCl or NH4Cl was then gradually added to the solution. The addition was repeated until undissolved solid was observed over a sufficient equilibrium duration. The temperature of the solution was controlled by a circulating water bath, which was kept at the desired temperature within ±0.1 K. The solution was well-mixed by a magnetic stirring plate. The mass of the chemicals was measured using a digital balance (Mettler Toledo, model AL104) with a sensitivity of 0.0001 g. All experiments were repeated at least three times, and the final results reported here are the averages of all of the determined results under the same conditions. Standard uncertainties u are u(T) = 0.15 K, u(p) = 0.5 kPa, and u(m) = 0.2 mol·kg−1. 3. FRAMEWORK OF THERMODYNAMIC MODELING 3.1. Chemical Equilibrium in the AlCl3−NaCl−H2O, AlCl3−NH4Cl−H2O, and CaCl2−NH4Cl−H2O Systems. Table 2. Empirical Parameters of Ksp species

A

B

C

D

AlCl3·6H2O NaCl NH4Cl CaCl2·6H2O

19.9558 −2.2852 −3.787 14.5298

−1815.79 532.06 0.0 −10.7601

−0.0262205 0.009082 0.023471 −0.0239804

0.0 −7.0327 × 10−6 −0.000022061 0.0

There are some chemical equilibria in the AlCl3−NaCl−H2O, AlCl3−NH4Cl−H2O, and CaCl2−NH4Cl−H2O systems, such as the dissolution equilibria of AlCl3, CaCl2, NaCl, and NH4Cl. The main dissolution reactions can be described by the following

Figure 1. Flowsheet of the Solvay process for the production of sodium carbonate.

B

AlCl3·6H 2O(s) = Al3 + + 3Cl− + 6H 2O

(1)

CaCl 2(s) = Ca 2 + + 2Cl−

(2)

NaCl(s) = Na + + Cl−

(3) DOI: 10.1021/acs.jced.9b00175 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 3. Experimental Solubilities of Salts in the AlCl3−NaCl−H2O System from 283.15 to 353.15 Ka AlCl3 (mol·kg−1)

NaCl (mol·kg−1)

AlCl3 (wt %)

0 0.2519 0.5000 0.7506 1.0001 1.2465 1.5003 1.7473 2.0000 2.2479 2.5007 2.7514 2.9981 3.2490 3.3462

6.1126 5.3719 4.6171 3.8807 3.2184 2.5145 1.9467 1.3943 1.0026 0.6609 0.4664 0.2499 0.1722 0.0931 0.0524

283.15 K 0 2.4939 4.9919 7.5493 10.0978 12.6686 15.2348 17.7374 20.1329 22.4062 24.5169 26.5696 28.3694 30.1268 30.8014

3.3771

0

0 0.2519 0.5000 0.7506 1.0001 1.2465 1.5003 1.7473 2.0000 2.2479 2.5007 2.7514 2.9981 3.2490 3.3781

6.1537 5.4404 4.6955 3.9916 3.2868 2.6042 2.0490 1.5128 1.1052 0.7719 0.5450 0.3200 0.2438 0.1471 0.0945

3.3998 3.4309

0.0584 0

0 0.2519 0.5000 0.7506 1.0001 1.2465 1.5003 1.7473 2.0000 2.2479 2.5007

6.2234 5.4886 4.7746 4.1014 3.3796 2.7182 2.1981 1.6468 1.1927 0.8804 0.6359

31.0633 298.15 K 0 2.4865 4.9748 7.5126 10.0673 12.6184 15.1657 17.6446 20.0421 22.2981 24.4343 26.4909 28.2855 30.0608 30.9521 31.1339 31.4030 313.15 K 0 2.4813 4.9578 7.4767 10.0263 12.5551 15.0662 17.5410 19.9653 22.1932 24.3394

NaCl (wt %) 26.3200 23.3138 20.1875 17.0774 14.2306 11.1628 8.6630 6.1828 4.4249 2.8899 2.0063 1.0587 0.7131 0.3780 0.2112 0 26.4500 23.5409 20.4601 17.4801 14.4894 11.5151 9.0768 6.6733 4.8557 3.3587 2.3365 1.3515 1.0064 0.5963 0.3793 0.2343 0 26.6700 23.7002 20.7332 17.8752 14.8377 11.9588 9.6736 7.2215 5.2202 3.8131 2.7156

AlCl3 (mol·kg−1)

solid phase NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl + AlCl3·6H2O AlCl3·6H2O NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl + AlCl3·6H2O AlCl3·6H2O AlCl3·6H2O NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl

AlCl3 (wt %)

NaCl (wt %)

2.7514 2.9981 3.2490 3.3912

0.4219 0.3428 0.2337 0.1445

313.15 K 26.3774 28.1705 29.9557 30.9725

1.7742 1.4091 0.9438 0.5779

3.4119 3.4480

0.0904 0

0 0.2519 0.5000 0.7506 1.0001 1.2465 1.5003 1.7473 2.0000 2.2479 2.5007 2.7514 2.9981 3.2490 3.4032

6.3386 5.5379 4.8913 4.1959 3.4851 2.8298 2.2970 1.7934 1.3209 0.9811 0.7619 0.5259 0.4304 0.3044 0.2028

3.4291 3.4750

0.1210 0

0 0.2519 0.5000 0.7506 1.0001 1.2465 1.5003 1.7473 2.0000 2.2479 2.5007 2.7514 2.9981 3.2490 3.4249 3.4629 3.5090

31.1702 31.5100 333.15 K 0 2.4760 4.9328 7.4460 9.9801 12.4938 15.0009 17.4289 19.8539 22.0969 24.2091 26.2626 28.0693 29.8704 30.9758

0.3616 0 27.0300 23.8623 21.1329 18.2119 15.2305 12.3889 10.0649 7.8142 5.7492 4.2308 3.2366 2.2016 1.7631 1.2258 0.8086

6.4906 5.6454 5.0001 4.3010 3.5771 3.0841 2.4167 2.0164 1.4625 1.1747 0.8760 0.6859 0.5376 0.3948 0.2674

31.2397 31.6786 353.15 K 0 2.4646 4.9097 7.4122 9.9401 12.3562 14.9227 17.2612 19.7323 21.9139 24.0923 26.0878 27.9466 29.7622 31.0325

0.4829 0 27.5000 24.2132 21.5020 18.5833 15.5698 13.3537 10.5342 8.7014 6.3264 5.0236 3.7034 2.8525 2.1926 1.5838 1.0610

0.1426 0

31.4241 31.8897

0.5668 0

solid phase NaCl NaCl NaCl NaCl + AlCl3·6H2O AlCl3·6H2O AlCl3·6H2O NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl + AlCl3·6H2O AlCl3·6H2O AlCl3·6H2O NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl + AlCl3·6H2O AlCl3·6H2O AlCl3·6H2O

a

Standard uncertainties u are u(T) = 0.15 K, u(p) = 0.5 kPa, and u(m) = 0.2 mol·kg−1.

NH4Cl(s) = NH4 + + Cl−

(4)

NH4 + + H 2O = NH3 + H+

(5)

where Ksp is the dissolution equilibrium constant, m is the concentration (mol·kg−1) of a species, and γ is the activity coefficient of a species. Ksp can be calculated by Δr G 0 = −RT ln K

The dissolution equilibrium constant of a solid, also known as the solubility product, taking AlCl3·6H2O as an example, can be expressed as K sp(AlCl3·6H 2O) = (m Al3+γ Al3+)(mCl−γCl−)3 a H2O6

NaCl (mol·kg−1)

(7)

where Δr G 0 is the standard-state Gibbs free energy of a reaction (J·mol−1), R is the universal gas constant (J·K−1·mol−1), and T is the temperature (K). Ksp can also be calculated using an empirical equation, such as

(6) C

DOI: 10.1021/acs.jced.9b00175 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 4. Solubility of NH4Cl in the Aqueous Solution of AlCl3 from 283.15 to 353.15 Ka AlCl3 (mol·kg−1) 0 0.2500 0.5000 0.7501 1.0001 1.2518 1.5005 1.7483 2.0030 2.2485 2.4984 2.7426 3.0002 3.2574 3.3455 3.3771 0 0.2500 0.5000 0.7501 1.0001 1.2518 1.5005 1.7483 2.0030 2.2485 2.4984 2.7426 3.0002 3.2574 3.3977 3.4309 0 0.2500 0.5000 0.7501 1.0001 1.2518 1.5005 1.7483 2.0030 2.2485

log K = A +

NH4Cl (mol·kg−1) 283.15 K 6.2716 5.5881 4.8520 4.0973 3.4395 2.8452 2.3311 1.8983 1.5362 1.3690 1.1502 0.9405 0.7253 0.4998 0.5360 0 298.15 K 7.3935 6.6205 5.8372 5.0082 4.3343 3.6359 3.0566 2.5666 2.0903 1.8548 1.6200 1.3372 1.0694 0.8298 0.8362 0 313.15 K 8.5811 7.6861 6.8506 5.9995 5.2437 4.5202 3.8960 3.3529 2.8054 2.5064

AlCl3 (wt %)

AlCl3 (mol·kg−1)

NH4Cl (wt %)

0 2.5039 5.0306 7.5864 10.1291 12.6615 15.1117 17.4762 19.8051 21.8471 23.8987 25.8387 27.8171 29.7419 30.2622 31.0633

25.1200 22.4360 19.5688 16.6129 13.9649 11.5362 9.4113 7.6069 6.0893 5.3326 4.4108 3.5521 2.6957 1.8294 1.9438 0

0 2.4042 4.8383 7.3162 9.7739 12.2682 14.6817 17.0203 19.3794 21.4414 23.4758 25.4572 27.4658 29.3870 30.2623 31.4030

28.3400 25.5230 22.6429 19.5830 16.9812 14.2842 11.9890 10.0169 8.1078 7.0905 6.1022 4.9761 3.9245 3.0009 2.9859 0

0 2.3093 4.6553 7.0432 9.4377 11.8562 14.2137 16.5135 18.8564 20.9203

31.4600 28.4619 25.5685 22.5837 19.8373 17.1623 14.7946 12.6962 10.5878 9.3487

B + CT + DT 2 T

2.4984 2.7426 3.0002 3.2574 3.4138 3.4480 0 0.2500 0.5000 0.7501 1.0001 1.2518 1.5005 1.7483 2.0030 2.2485 2.4984 2.7426 3.0002 3.2574 3.4277 3.4750 0 0.2500 0.5000 0.7501 1.0001 1.2518 1.5005 1.7483 2.0030 2.2485 2.4984 2.7426 3.0002 3.2574 3.4637 3.5090

1815.79 − 0.0262205T T

313.15 K 2.2433 1.9727 1.6330 1.3843 1.3812 0 333.15 K 10.2850 9.0688 8.0912 7.3001 6.4698 5.7974 5.0459 4.4036 3.8781 3.4850 3.2272 2.9538 2.6149 2.4522 2.4494 0 353.15 K 12.1549 10.7174 9.8685 8.8941 8.0437 7.2852 6.4769 5.8228 5.3301 4.7849 4.4784 4.0997 3.8171 3.5219 3.1168 0

AlCl3 (wt %)

NH4Cl (wt %)

22.9373 24.8692 26.9091 28.8092 29.7832 31.5100

8.2563 7.1710 5.8717 4.9081 4.8306 0

0 2.1969 4.4493 6.7144 9.0193 11.3079 13.6190 15.8817 18.1227 20.1836 22.1357 24.0127 25.9916 27.7582 28.7942 31.6786

35.4900 31.9465 28.8626 26.1970 23.3909 20.9937 18.3594 16.0367 14.0667 12.5410 11.4626 10.3678 9.0814 8.3770 8.2485 0

0 2.0763 4.1840 6.3512 8.5337 10.7298 12.9450 15.1012 17.2160 19.2816 21.1939 23.0842 24.9499 26.7796 28.3732 31.8897

39.4000 35.6817 33.1036 30.1901 27.5154 25.0325 22.3999 20.1629 18.3660 16.4494 15.2296 13.8336 12.7252 11.6072 10.2351 0

a Standard uncertainties u are u(T) = 0.15 K, u(p) = 0.5 kPa, and u(m) = 0.2 mol·kg−1.

the OLI platform are capable of calculating the thermodynamic properties of an aqueous solution.21−27 The MSE model is more flexible without component limitations, hence it was applied in this work. In the MSE model, the activity coefficient of a species in the aqueous solution can be expressed by the excess Gibbs free energy of the species, which is the sum of the three terms as described by

(8)

where A, B, C, and D are the empirical parameters and T is the temperature in K. The empirical parameters for AlCl3, NaCl, NH4Cl, and CaCl2 are summarized in Table 2. For example, Ksp of AlCl3·6H2O can be expressed as log K AlCl3·6H2O = 19.9558 +

NH4Cl (mol·kg−1)

GE GE GE GE = LR + SR + MR RT RT RT RT

(9)

(10)

GELR

3.2. Activity Coefficient Model. To calculate solubility, we need to know not only the equilibrium constant at a given temperature but also the activity coefficients γ of the involved species. The Aqueous model and the MSE model embedded in

where represents the long-range electrostatic interactions that can be calculated by the Pitzer−Debye−Hückel equation28 E and GSR represents the short-range interactions between molecule−molecule, molecule−ion, and ion−ion, which can D

DOI: 10.1021/acs.jced.9b00175 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 5. Experimental Solubilities of Salts in the CaCl2−NH4Cl−H2O System from 283.15 to 353.15 Ka CaCl2 (mol·kg−1)

NH4Cl (mol·kg−1)

0 0.5016 1.0022 1.5091 2.0029 2.4876 2.9931 3.4988 3.9570 4.4895 4.9947 5.5000

6.2716 5.5038 4.7601 4.0890 3.4132 2.7682 2.4723 2.2015 1.8458 1.5209 1.3327 1.1359

5.9112

0

0 0.5016 1.0022 1.5091 2.0029 2.4876 2.9931 3.4988 3.9570 4.4895 4.9947 5.5000 5.9888 7.1115

7.3935 6.5285 5.7286 4.9603 4.2723 3.4963 3.0779 2.7361 2.4438 2.1713 1.9645 1.6669 1.4790 1.4457

7.4620

0

0 0.5016 1.0022 1.5091 2.0029 2.4876 2.9931 3.4988 3.9570 4.4895 4.9947 5.5000 5.9888 7.1115 7.9783 9.0117 10.0240

8.5811 7.5517 6.6608 5.8425 5.1706 4.3232 3.9530 3.5711 3.1457 2.8542 2.5989 2.4071 2.3213 2.2070 2.0351 2.0047 1.9987

CaCl2 (wt %) 283.15 K 0 4.1236 8.1433 12.0819 15.8223 19.3855 22.6828 25.7824 28.5556 31.5425 34.0988 36.5251 39.6144 298.15 K 0 3.9627 7.8457 11.6889 15.3211 18.8695 22.1918 25.3020 27.9738 30.8628 33.4044 35.9147 38.1155 42.2826 45.2994 313.15 K 0 3.8141 7.5791 11.3162 14.8300 18.3157 21.5189 24.5865 27.3204 30.1799 32.7349 35.0971 37.1555 41.3798 44.3984 47.4584 50.1251

NH4Cl (wt %) 25.1200 21.8062 18.6419 15.7785 12.9959 10.3971 9.0303 7.8190 6.4199 5.1502 4.3852 3.6359 0 28.3400 24.8569 21.6148 18.5181 15.7516 12.7824 10.9992 9.5367 8.3266 7.1942 6.3325 5.2463 4.5369 4.1429 0 31.4600 27.6745 24.2783 21.1160 18.4523 15.3417 13.6981 12.0949 10.4679 9.2476 8.2097 7.4035 6.9412 6.1896 5.4584 5.0885 4.8171

CaCl2 (mol·kg−1)

solid phase NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl + CaCl2·6H2O CaCl2·6H2O

10.3260 0 0.5016 1.0022 1.5091 2.0029 2.4876 2.9931 3.4988 3.9570 4.4895 4.9947 5.5000 5.9888 7.1115 7.9783 9.0330 9.9713 11.0008 12.0078

NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl + CaCl2·6H2O CaCl2·6H2O

12.3270 0 0.5016 1.0022 1.5091 2.0029 2.4876 2.9931 3.4988 3.9570 4.4895 4.9947 5.5000 5.9888 7.1115 7.9783 9.0330 9.9713 11.0008 12.0078 13.0352

NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl + CaCl2·4H2O

13.2460

0 10.2850 8.9837 8.1014 7.2182 6.4780 5.6006 5.1792 4.7824 4.3361 4.0618 3.8020 3.5887 3.5190 3.4719 3.4580 3.3523 3.1540 3.1228 2.9774 0 12.1549 10.5761 9.7770 8.8850 8.1805 7.2637 6.8342 6.4430 5.8868 5.5245 5.4264 5.1607 5.1155 4.9494 4.9303 4.8592 4.7356 4.7330 4.4550 4.0444 0

CaCl2 (wt %) 313.15 K 53.4012 333.15 K 0 3.6239 7.2010 10.7802 14.1689 17.5215 20.6418 23.6175 26.2793 29.0435 31.5364 33.8664 35.8707 39.9622 42.7662 45.9475 48.6355 51.1272 53.4786 57.7712 353.15 K 0 3.4336 6.8061 10.1951 13.3915 16.5851 19.5654 22.4070 25.0367 27.7767 30.0509 32.3568 34.2903 38.4246 41.1991 44.3105 46.8919 49.3473 51.8346 54.3244 59.5148

NH4Cl (wt %) 0 35.4900 31.2807 28.0559 24.8524 22.0877 19.0127 17.2158 15.5593 13.8795 12.6647 11.5705 10.6504 10.1589 9.4035 8.9340 8.2187 7.4146 6.9952 6.3913 0 39.4000 34.8908 32.0018 28.9308 26.3623 23.3409 21.5325 19.8874 17.9520 16.4741 15.7358 14.6331 14.1172 12.8893 12.2709 11.4886 10.7337 10.2330 9.2689 8.1238 0

solid phase CaCl2·4H2O NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl + CaCl2·2H2O CaCl2·2H2O NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl + CaCl2·2H2O CaCl2·2H2O

a

Standard uncertainties u are u(T) = 0.15 K, u(p) = 0.5 kPa, and u(m) = 0.2 mol·kg−1.

be calculated by the UNIQUAC model.29 GEMR represents the middle-range interactions and can be calculated by an ionic strength-dependent, symmetrical, second-virial-coefficient-type expression8,24 ji zy = jjjj∑ ni zzzz ∑ ∑ xixjBij (Ix) j i z i j RT k {

NH4Cl (mol·kg−1)

where x is the mole fraction of a species and Bij(Ix) is a parameter for binary interactions between species i and j. Bij(Ix) is a function of ionic strength I, as follows Bij (Ix) = bij + cij exp( − Ix + 0.01 )

E GMR

(12)

where bij and cij are the temperature-dependent parameters, which can be described as

(11) E

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bij = BMD0 + BMD1 × T + BMD2/T + BMD3 × T 2 + BMD4 × ln T

(13)

cij = CMD0 + CMD1 × T + CMD2/T + CMD3 × T 2 + CMD4 × ln T

(14)

where BMD0, BMD1, BMD2, BMD3, BMD4, CMD0, CMD1, CMD2, CMD3, and CMD4 are adjustable parameters.

4. RESULT AND DISCUSSION 4.1. Phase Equilibrium Determination of the AlCl3− NaCl−CaCl2−NH4Cl−H2O System. Solubilities of NaCl and

Figure 4. Phase equilibria of the CaCl2−NH4Cl−H2O system. (■) 283 K, (red circle solid) 298 K, (blue triangle up solid) 313 K, (pink triangle down solid) 333 K, and (green tilted square solid) 353 K. Symbols represent experimental solubility data, dash lines are calculated with old (OLI) parameters, and solid lines are calculated with new parameters.

Figure 2. Phase equilibria of the AlCl3−NaCl−H2O system: (■) 283 K, (red circle solid) 298 K, (blue triangle up solid) 313 K, (pink triangle down solid) 333 K, and (green tilted square solid) 353 K. Closed symbol represents experimental solubility data, open symbols are literature values,18 dash lines are calculated with old (OLI) parameters, and solid lines are calculated with new parameters. Figure 5. Relative deviations of the calculated values of the phase equilibria in the AlCl3−NaCl− H2O system.

Figure 3. Phase equilibria of the AlCl3−NH4Cl−H2O system: (■) 283 K, (red circle solid) 298 K, (blue triangle up solid) 313 K, (pink triangle down solid) 333 K, and (green tilted square solid) 353 K. Symbols represent experimental solubility data, open symbols are literature values,11 dash lines are calculated with old (OLI) parameters, and solid lines are calculated with new parameters.

Figure 6. Relative deviations of the calculated values of the phase equilibria in the AlCl3−NH4Cl −H2O system.

AlCl3·6H2O in the AlCl3−NaCl solution at 283−353 K by experimental determination are listed in Table 3 and plotted in Figure 2. As shown in Figure 2, the solid−liquid equilibrium at

each temperature is represented by two curves connected by an invariant point. X-ray diffraction (XRD) (Figure S1) confirms that the equilibrium solid phases are NaCl for the long curve on F

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Figure 7. Relative deviations of the calculated values of the phase equilibria in the CaCl2−H4Cl−H2O system.

Figure 8. Solubility of NaCl in the aqueous solution of CaCl2 + AlCl3. (■) 283 K, (red circle solid) 298 K, (blue triangle up solid) 313 K, (pink triangle down solid) 333 K, and (green tilted square solid) 353 K. Symbols represent the experimental solubility data, and solid lines are calculated with new parameters.

the left side and AlCl3·6H2O for the short curve at the right bottom. These two solid phases coexist at the invariant points. The solubility of NaCl experiences a moderate increase with temperature but a substantial decrease with the concentration of AlCl3. The solubility of AlCl3·6H2O, as can be seen from the bottom right of Figure 2 and more clearly from the inset graph, increases with increasing temperature and decreases with increasing NaCl concentration. At the invariant points, AlCl3 concentrations are 3.35, 3.38, 3.39, 3.40, and 3.42 mol·kg−1, respectively, at 283, 298, 313, 333, and 353 K. The experimental data determined in the present study (solid symbols) are compared to those reported by Farelo18 (open symbols) with minimal differences. For the AlCl 3−NH4Cl−H2O system, the determined solubility data at 283−353 K are given in Table 4 and Figure 3. It is clearly shown that the solubility of NH4Cl increases obviously with increasing temperature and decreases with AlCl3 concentration. Reported solubility of NH4Cl in pure water11 is also labeled in Figure 3 and shows consistency in the trend with the rest of the data. For the CaCl2−NH4Cl−H2O system, the solubility data at 283−353 K are given in Table 5 and Figure 4. Apparently, the solubilities of NH4Cl and CaCl2 increase with temperature and decrease with the concentration of each other. In Figure 4, the long univariant curve is the saturation curve of solid NH4Cl, whereas the short one is that of CaCl2·6H2O at 283 and 298 K, CaCl2·4H2O at 313 K, and CaCl2·2H2O at 333 and 353 K. XRD results of the coexisting solids at the invariant points of 313 and

Figure 9. Solubility of NH4Cl in the aqueous solution of CaCl2 + AlCl3. (■) 283 K, (red circle solid) 298 K, (blue triangle up solid) 313 K, (pink triangle down solid) 333 K, and (green tilted square solid) 353 K. Symbols represent the experimental solubility data, and solid lines are calculated with new parameters.

333 K are shown in Figure S2. The solid-phase compositions at the invariant points under different temperatures were also reported in the literature.7,30−32

Table 6. New MSE Model Parameters for the Al3+−Na+, Ca2+−Na+, Al3+−NH4+, Ca2+−NH4+, and NH4+−CaCl2 Interactionsa species

BMD0

BMD1

BMD2

CMD0

CMD1

CMD2

Al3+−Na+ Ca2+−Na+ Al3+−NH4+ Ca2+−NH4+ NH4+−CaCl2 Na+−Cl− Ca2+−Cl− Al3+−Cl− NH4+−Cl−

6566.768 76.75154 189.3155 −158.8153 27.97895 −213.999 −95.9932 32.07073 4369.664

−9.825896 −0.1554948 0 0.2386682 −0.2120578 1.86323 0.470226 0 2.325859

−1 120 721 −22 919.88 −71 361.20 36 700.55 3838.230 16 036.8 −17 370.9 −25 552.14 −96 273.91

−10 646.74 −20.32925 −262.6868 5.268895 37.04635 202.887 −0.694366 −99.52161 −9748.479

16.00759 0.094363714 0 −0.002252 0.1406685 −2.15391 −0.421581 0 −5.062129

1 817 317 16 617.73 112 990.2 −16 021.45 1737.603 −9832.11 43 725.9 35 686.79 219 746

Species pairs Al3+−Na+, Ca2+−Na+, Al3+−NH4+, Ca2+−NH4+, and NH4+−CaCl2 are adjusted/created for regression; other are kept as default parameters in OLI Engine Solver. a

G

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Ca2+−Na+, and Ca2+−NH4+, play a key role in a successful modeling. Therefore, to improve the modeling accuracy, new MSE model parameters for these interactions were determined via regression of the solubility of the ternary systems determined in this work, together with data reported in literature.33−35 The newly obtained MSE model parameters of ionic interactions are presented in Table 6. The calculated results with the new parameters are plotted as solid curves in Figures 2−4. Figures 5−7 show the average absolute relative deviations (AARD) between the new model calculations and the experimental values for the AlCl3−NaCl−H2O, AlCl3− NH4Cl−H2O, and CaCl3−NH4Cl−H2O systems. AARD is calculated by n

AARD = 1/n ∑ i=1

|Xi ,calc − Xi ,exp| Xi ,exp

× 100% (15)

All of the studied systems have AARD less than 5%, while their maximum relative deviations are less than 15%. This indicates that the new parameters are capable of representing the experimental data. To further verify the new model, solubility in the quaternary system of CaCl2−AlCl3−NaCl−H2O at 283−353 K was predicted with the new set of parameters (Table 6) and compared with the experimental data. Figure 8 compares the predicted and experimental solubilities of NaCl in the CaCl2− AlCl3−H2O solution when CaCl2 concentration is 1 mol·kg−1. As can be seen, the prediction agrees well with the experimental measurement, showing that the solubility of NaCl increases insignificantly with temperature but reduces gradually with increasing AlCl3 concentration. The solubility data can be found in Table S1. Similarly, for the quaternary system CaCl2−AlCl3− NH4Cl−H2O (see Figure 9 and Table S2), the prediction results align well with the experiment. 4.3. Application of the MSE Model. To reuse NaCl of the liquid wastes from the Solvay process, three-effect evaporation process was modeled with the newly parameterized model. The three-effect evaporation process and the subsequent calculated results are shown in Figure 10. In the first effect evaporation, liquid wastes, containing 50 g·L−1 NaCl and 100 g·L−1 CaCl2, were concentrated to 118 and 236 g·L−1, respectively, by evaporation at 376 K and 0.8 atm. In the second effect evaporation, 374 g·L−1 NaCl would crystallize at 400 K and 0.8 atm, while 7 g·L−1 NaCl and 100 g·L−1 CaCl2 were still left in the solution. In the third effect evaporation, when the temperature increases up to 427 K, the supersaturated solutions would be produced by controlling the molar ratio of CaCl2 and H2O at 1:2. After that, when the solution cools after evaporation, standard CaCl2·2H2O solid would be produced. Meanwhile, heat can also be reused by heat exchangers for energy-saving purpose. Figure 11 illustrates the shift in ion dominance along with the change in temperature. With increasing temperature, the relative concentration of Ca2+ decreases, whereas the relative concentration of CaCl2 increases. During this evaporation, NaCl can be used in the carbonation of the Solvay process, and CaCl2· 2H2O can be used for the production of snow remover.

Figure 10. Three-effect evaporation process for separating NaCl and CaCl2 in liquid waste from the Solvay process.

Figure 11. Shift in ion dominance from Ca2+ to CaCl2(aq).

4.2. Calculation of Phase Equilibria Using New Parameters. The MSE model with the default values of interaction parameters in the OLI database was evaluated by comparing the calculated solubilities (dashed lines) with the experimental results (solid symbols), as shown in Figures 2−4. As shown in Figure 2, the MSE model with default parameters can reproduce the solubility of NaCl at very low or high concentration region of AlCl3 but yields significant deviations from the experimental results in the middle range with AlCl3 concentration ranging from 0.5 to 2.5 mol·kg−1. The default model results in remarkable discrepancies from the experimental results in solubility of the AlCl3−NH4Cl−H2O and CaCl2− NH4Cl−H2O systems (Figures 3 and 4). The discrepancies between the default model calculation and the experimental determination are mainly attributed to inaccurate activity coefficients. For the investigated systems, the interactions between species, such as Al3+−Na+, Al3+−NH4+,

5. CONCLUSIONS This work is a systematic study of the phase equilibrium measurements and thermodynamic modeling for the AlCl3− NaCl−CaCl2−NH4Cl−H2O system. Based on the solubility data for three ternary subsystems (AlCl3−NaCl−H2O, AlCl3− NH4Cl−H2O, and CaCl2−NH4Cl−H2O), a chemical model for H

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the AlCl3−NaCl−CaCl2−NH4Cl−H2O system was developed with new parameters containing Al3+−Na+, Ca2+−Na+, Al3+− NH4+, Ca2+−NH4+, and NH4+−CaCl2 interaction parameters, using in the MSE model. The new model is capable of calculating the solid−liquid equilibria in the AlCl3−NaCl− CaCl2−NH4Cl−H2O system over the temperature range of 283−353 K. This new model can provide the thermodynamic basis for the simulation of the three-effect evaporation process for separating NaCl and CaCl2 in liquid wastes from the Solvay process and subsequent utilization of CaCl2.

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(4) Zeng, Y.; Li, Z. Solubility measurement and modeling for the NaCl−NH4Cl− monoethylene−H2O system from (278 to 353) K. J. Chem. Eng. Data 2015, 60, 2248−2255. (5) Wisniak, J. Sodium carbonate e from natural resources to Leblanc and back. Indian J. Chem. 2003, 10, 99−112. (6) Steinhauser, G. Cleaner production in the Solvay Process: general strategies and recent developments. J. Cleaner Prod. 2008, 16, 833−841. (7) Jiang, H.; Zhang, W. Research on the utilization of waste liquid from Solvay process as resource in the combined circulation of salt and sodium carbonate. China Well Rock Salt 2009, 40, 9−12. (8) Zemaitis, J. F.; Clark, D. M.; Rafal, M.; Scrivner, N. C. Handbook of Aqueous Electrolyte Thermodynamics: Theory & Application; American Institute of Chemical Engineers: New York, 1986. (9) He, L. L.; Yu, D. X.; Lv, W. Z.; et al. A novel method for CO2 sequestration via indirect carbonation of coal fly ash. Ind. Eng. Chem. Res. 2013, 52, 15138−15145. (10) Krumgalz, B. S. Mineral Solubility in Water at Various Temperatures; Israel Oceanographic and Limnological Research Ltd.: Haifa, Israel, 1994. (11) Linke, W. Solubilities Inorganic and Metal-Organic Compounds, 4th ed.; American Chemical Society: Washington, DC, 1958; Vol. 1. (12) Atherton, S. Solubilities of Inorganic and Metal Organic Compounds, 3th ed.; National Institutes of Health: Bethesda: MD, 1953; Vol. 1. (13) Guthrie, F. On salt solutions and attached water, IV. Separation of ice, or of a hydrate, or of the anhydrous salt, from solutions of salts below 0 °C. London, Edinburgh Dublin Philos. Mag. J. Sci. 1876, 1, 354− 369. (14) Rodebush, W. H. The freezing points of concentrated solutions and the free energy of solution of salt. J. Am. Chem. Soc. 1918, 40, 1204− 1213. (15) Yanatieva, O. K. Polytherms of solubility of salts in the tropic system CaCl2−MgCl2−H2O and CaCl2−NaCl−H2O. Zh. Prikl. Khim. 1946, 19, 709−722. (16) Clynne, M. A.; Potter, R. W. Solubility of some alkali and alkaline earth chlorides in water at moderate temperatures. J. Chem. Eng. Data 1979, 24, 338−340. (17) Wang, J.; Petit, C.; Zhang, X.; Cui, S. Phase equilibrium study of the AlCl3−CaCl2−H2O system for the production of aluminum chloride hexahydrate from Ca-rich flue ash. J. Chem. Eng. Data 2016, 61, 359−369. (18) Farelo, F.; Fernandes, C.; Avelino, A. Solubilities for six ternary systems: NaCl+NH4Cl+H2O, KCl+NH4Cl+H2O, NaCl+LiCl+H2O, KCl+LiCl+H2O, NaCl+ AlCl3+H2O, and KCl+AlCl3+H2O at T = (298 to 333). J. Chem. Eng. Data 2005, 50, 1470−1477. (19) Zhou, J.; Zeng, Y.; Demopoulos, G. P.; Li, C.; Li, Z. Solubility of NaHCO3 and NH4HCO3 in the relevant media and prediction of highpressure phase equilibria for the NH3−CO2−NaCl−H2O system. J. Chem. Eng. Data 2017, 62, 4401−4410. (20) Gao, W.; Li, Z.; Asselin, E. Solubility of AlCl3·6H2O in the Fe(II)+Mg+Ca+K+ Cl+H2O system and its salting-out crystallization with FeCl2. Ind. Eng. Chem. Res. 2013, 52, 14282−14290. (21) OLI System Inc. OLI ESP User Guide−A Guide to Using OLI ESP 9.X. http://support.olisystems.com (accessed June 17, 2018). (22) OLI Systems, Inc. OLI Analyzer Studio−Stream Analyzer version 9.5. http://www.olisystems.com (accessed Aug 10, 2017). (23) Gerbino, A.; Wang, P. An Overview of Data Analysis and Data Entry for OLI Programs; OLI Systems Inc.: Morris Plains, NJ, 2006. (24) Wang, P.; Anderko, A.; Young, R. D. A speciation-based model for mixed- solvent electrolyte systems. Fluid Phase Equilib. 2002, 203, 141−176. (25) Kosinski, J. J.; Wang, P.; Springer, R. D.; Anderko, A. Modeling acid-base equilibria and phase behavior in mixed-solvent electrolyte systems. Fluid Phase Equilib. 2007, 256, 34−41. (26) Wang, P.; Anderko, A.; Young, R. D. Modeling viscosity of concentrated and mixed-solvent electrolyte systems. Fluid Phase Equilib. 2004, 226, 71−82.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.9b00175. XRD patterns of the obtained solid phases from the NaCl−AlCl3−H2O and CaCl2−NH4Cl−H2O systems (Figures S1 and S2); solubility data of NaCl and NH4Cl in the CaCl2−AlCl3 solution (Tables S1 and S2) (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel/Fax: +86 10 62551557. ORCID

Zhibao Li: 0000-0002-5737-1289 Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS The authors are grateful for the financial support provided by the National Science Foundation of China (Grant 21776279). ABBREVIATIONS MSE, mixed-solvent electrolyte wt %, weight percentage a, activity Bij, parameter for the middle-range interaction between species i and j bij, parameter for the middle-range interaction between species i and j cij, parameter for the middle-range interaction between species i and j BMD0, BMD1, BMD2, BMD3, BMD4, CMD0, CMD1, CMD2, CMD3, adjustable middle-range interaction parameters Gex, excess Gibbs free energy Ix, mole-fraction-based ionic strength Ksp, solubility equilibrium constant m, molality (mol·kg−1 solvent) ni, number of moles of species i in mol R, the universal gas constant (8.314 J·mol−1·K−1) T, temperature (K) xi, mole fraction of species i γi, activity coefficient of species i

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REFERENCES

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