Solubility Determination and Thermodynamic Modeling for the System

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

pubs.acs.org/jced

Solubility Determination and Thermodynamic Modeling for the System NaCl−NH4Cl−Diethanolamine−H2O Qiaoxin Wang†,‡ and Zhibao Li*,† †

Key Laboratory of Green Process and Engineering, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China ‡ Department of Chemical Engineering, University of Chinese Academy of Sciences, Beijing 100049, China

J. Chem. Eng. Data Downloaded from pubs.acs.org by UNIV DE BARCELONA on 02/07/19. For personal use only.

S Supporting Information *

ABSTRACT: In this work, the solubility behavior of salts NaCl and NH4Cl was investigated in aqueous diethanolamine (DEA) solution by varying both temperature and the solvent composition. DEA has been prevalently used in the postcombustion process to capture CO2, but a limited amount of references can be found pertaining to any solid−liquid system containing DEA. It was experimentally determined that the solubility of NaCl decreases, whereas the solubility of NH4Cl increases with the addition of DEA (x′DEA = 0−0.2). The solubility of both salts increases if temperature is raised from 283 to 353 K. The common-ion effect was examined for the quaternary system when both salts are present in the solution. By the regression of solubility data with the Mixed Solvent Electrolyte model, we proved that readjusting the middle-range interaction parameters between Cl−-DEA and DEAH+-Cl− would lower the relative deviation (within 5%) for each proposed ternary system. A comprehensive chemical model was further constructed based on the newly adjusted interaction parameters, provided to further analyze system equilibria, as well as the activity coefficients for aqueous electrolytes.

■

data of CO2 include (a) NRM characterization,13 (b) protonation method,14 (c) COSMO-RS methods,15 etc., a limited amount of work is found pertaining to any solubility data for a solid−liquid equilibria (SLE) system containing DEA. Recently, we had proven the accuracy of utilizing the MixedSolvent Electrolyte (MSE) model embedded in the OLI Stream Analyzer to predict the solubility behavior of NaCl and NH4Cl in a mixed, monoethanolamine (MEA) solution. Solubility data yielded direct information that furnished a base for the understanding of salt properties in a mixed solvent system, and the use of these data may help provide engineering solutions in real, industrial applications. The MSE model, after parameters are adjusted for electrolytes, will be vital in the effort to design a typical, salt separation process with the presence of DEA.9,16,17 As such, the primary objectives of this research were to first, conduct a multiple sets of solubility experiments for both ternary and quaternary systems containing inorganic salts, DEA, and water. Second, to create a chemical model by regressing the solubility data, this was achieved by adjusting the ion−ion interaction parameters using the OLI Engine Solver. Third, to perform standardized statistical analysis, followed by the construction of a

INTRODUCTION Amid the fear of climate change led by the increasing concentration of carbon content in the atmosphere, researchers and scientists are on the lookout for the better, standalone technology to address environmental concerns. Here the most rigorous challenge is attributed to the postcombustion capture of CO2 generated from fossil fuels,1,2 and the recent research orientation of using amine absorbents to remove CO2 from coal-fired flue gases is opening windows of operation.3,4 They are in fact the cheapest removal method currently available.5 Notable industrial applications of amine scrubbing technologies include, but are not limited to, natural gas treatments,6,7 acidic gas removal,8 even extending the scope of utilization into a modified Solvay’s process for dense soda ash manufacturing.9 Among a range of amine absorbents selections, diethanolamine (DEA) has been identified as one of the most efficient solvents to capture CO2.10 DEA is a secondary amine, showing more advantages over ternary alkanolamines in the treatment of acidic gas due to its high capacity. It has been proven that natural gas can be scrubbed using an ∼58 wt % of DEA solution.8 Other studies have found that DEA is often blended with other amines to foster the formation of carbamate, which is a key, intermediate product to enhance the CO2 adsorption process.11,12 Though the vapor−liquid equilibria (VLE) data for systems containing DEA are becoming readily available, for which the experimental methods for obtaining the solubility © XXXX American Chemical Society

Received: June 21, 2018 Accepted: January 23, 2019

A

DOI: 10.1021/acs.jced.8b00515 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

comprehensive thermodynamic model for the NaCl-NH4ClDEA-H2O system using the MSE model.

■

EXPERIMENTAL SECTION Materials. Analytical-grade sodium chloride (NaCl), ammonium chloride (NH4Cl), and pure DEA were supplied by XiLong Scientific. We ensured both the magnetic stirring system (84-1A, Shanghai Sile Instrument Co.) and the water bath (CK-4005GD, Scientz) functioned properly. Granulated solutes were employed in anhydrous solid state. Deionized water with a specific conductivity of 0.1 μS·cm−1 was used throughout this experiment. All chemicals reagents listed in Table 1 were used with no further purification. Prior to the Table 1. Chemical Reagents chemical compound

formula

CAS No.

analytical purity

DEA sodium chloride ammonium chloride

C4H11NO2 NaCl NH4Cl

111-42-2 7647-14-5 12125-02-9

≥99% ≥99.5% ≥99.5%

Figure 1. Solubility of NaCl in the aqueous solution of DEA at (■) 283 K, (●) 298 K, (▲) 313 K, (◆) 333 K, (▶) 353 K; p = 0.1 MPa; dashed lines: old model calculation; dots: experimental data; solid lines: new model calculation.

experiment, each individual piece of equipment was fully cleaned, with flasks thoroughly rinsed and dried for over 24 h to ensure no moisture was present inside. Procedure. Solubilities for the proposed systems NaClDEA-H2O, NH4Cl-DEA-H2O, and NaCl-NH4Cl-DEA-H2O were determined via the “dynamic method” with two independent variables, namely, temperature and the concentration of DEA. x′DEA was set to change between 0 and 0.2. We intend to only conduct solubility experiments for the ternary systems and the quaternary system, as they are of the greatest interest. The solubility experiments for the ternary systems NaCl-DEA-H2O and NH4Cl-DEA-H2O were completed first, followed by the common-ion effect investigations for the quaternary system NaCl-NH4Cl-DEA-H2O. During the experiment, we used a mass balance with the precision of 0.001 and a thermostat to control the temperature of our interest within ±0.1 °C. The magnetic stirring apparatus was turned on and placed under the jacketed reactor to allow constant stirring motion of the mixed solution. All experiments were conducted at the atmospheric pressure: 101 kPa. To ensure that the experiment yielded the most accurate data possible when the temperature was raised, we made certain that the jacketed reactors were tightly sealed; no water was flashed into steam when temperature approached 353 K. After the dependence of solubility on temperature and the solvent composition were quantitively confirmed, we established a series of relevant, unitless parameters by incorporating the ion pair interactions.16,17 It is highly desirable to use OLI Analyzer Studio 9.518a software developed by OLI Systems Inc. as a computational tool to make solubility predictions at first. It can be seen from Figures 1 and 2 that the predictions for the solubility of salts in ternary systems deviate much from the results collected from the actual experimentation; as such, modification and/or adjustment of the Mixed Solvent Electrolyte (MSE) interaction parameters were necessary; this is essentially the most important step toward building a comprehensive thermodynamic model for the system of our interest. The collected solubility data were fitted using the newly adjusted interaction parameters; a chemical model was built after parameters were imported into the OLI Stream Analyzer interactions. From this, the activity coefficient for

Figure 2. Solubility of NH4Cl in the aqueous solution of DEA at (■) 283 K, (●) 293 K, (▲) 303 K, (▼) 313 K, (◆) 323 K, (◀) 333 K, (▶) 343 K; p = 0.1 MPa; dashed lines: old model calculation; dots: experimental data; solid lines: new model calculation.

each cation and anion can be calculated, which is also dependent on temperature and solvent composition.

■

THERMODYNAMIC FRAMEWORKS Thermochemistry for the SLE Systems. In general, each salt-equilibrated dissociation in a solution can be quantified using a temperature-dependent only constant: the equilibrium solubility product, denoted as Ksp.19,20 Ksp can be derived from the Van’t Hoff equation, which is determined by the basic, standard state properties as listed in Table 2. In this work, the approach of calculating Ksp for solid species is to correlate it using the Mixed-Solvent Electrolyte, activity coefficient model, for which the calculation method is shown in eq 1. K sp =

∏ ai ν

i

=

∏ γ±∑ ν mi ν ·aH O i

i

2

(1)

Equations 2 and 3 are the corresponding Ksp equations for NaCl and NH4Cl. B



Article

Table 2. Dissociation Equations for the System NaClNH4Cl-C4H11NO2-H2O: OLI Generated speciesa H2O C4H11NO2 HCl(aq) NaOH(aq) NH4OH(aq) NH3(aq) HCl(aq) NaCl(s) NH4Cl(s)

Table 3. Standard-State Thermodynamic Properties (OLI MSE Model)

dissociation equations species

−

+

2H2O = H3O + OH C4H11NO2 + H2O = C4H12NO2+ + OH− HCl + H2O = H3O+ + Cl− NaOH = Na+ + OH− NH4OH = NH4+ + OH− NH3 + H2O = NH4+ + OH− HCl + H2O = H3O+ + Cl− NaCl(s) = Na+ + Cl− NH4Cl(s) = NH4+ + Cl−

H2O Na+ Cl− NH4+ NH3(aq) OH − C4H11NO2(aq) C4H12NO2+ NaOH(aq) NaCl(aq) NH4Cl(aq) HCl(aq) NH4OH(aq) Ksp (T)

a

DEA is equivalent to C4H11NO2.

K sp,NaCl = a Na+ ·aCl− = (m Na+ ·γNa+) ·(mCl− ·γCl−)

(2)

K sp,NH4Cl = a NH+ ·aCl− = (m NH4+ ·γNH +) ·(mCl− ·γCl−)

(3)

4

NH4Cl(s) NaCl(s)

The empirical approach of calculating Ksp is shown in eq 4, where parameters A, B, C, and D were experimentally determined and stored in the OLI Analyzer databank. Figure 3 shows the dependency of the log(Ksp) value with the change in temperature from 283 to 353 K. Parameters for each solute are further listed in Table 3. log(K sp) = A +

B + CT + DT 2 T

ΔG f , 2 09 8 (J/mol) −237 190 −261 881 −131 290 −79 454 −6383 −37 595 −56 477 −68 583 −91 992 −384 224 −203 184 −20 898 −62 442 A −3.787 −2.2852

ΔH f , 2 09 8 (J/mol) −285 830 −240 300 −167 080 −133 260 −19 440 −54 968 −103 499 −113 380 −95 863 −411 706 −314 550 −21 417 −88 214 B 0 532.06

ΔS 2 90 8 (J/mol/K)

ΔCp0298 (J/mol/K)

69.95 58.41 56.74 111.17 25.77 −2.56 91.52 98.93 39.38 70.63 94.85 40.49 38.94 C

0.23 37.91 −123.18 65.86 17.90 −32.79 69.54 69.54 −3.20 50.50 86.50 16.14 23.24 D

0.023 471 0.009 082

−2.21 × 10−5 −7.03 × 10−6

property temperature, which is equivalent to 228 K. ε is the dielectric constant for water. ΔG°P , T = ΔG°Pr , Tr − ΔS°Pr , Tr (T − Tr) ÄÅ ÉÑ ÅÅ ÑÑ ij T yz Å j z Å − c1ÅÅT lnjj zz − T + Tr ÑÑÑÑ + a1(P − Pr ) jT z ÅÅ ÑÑ k r{ ÅÇ ÑÖ ÄÅ ij Ψ + P yzij Ψ + P yz ÅÅÅ zj z + Åa (P − Pr ) + a 2 lnjjj j Ψ + P zzzjjj Ψ + P zzz ÅÅÅÅ 3 r {k r{ k ÅÇ ÉÑ Ñ jij Ψ + P zyzÑÑÑij 1 yz j z + a4 lnjj j Ψ + Pr zzzÑÑÑÑjk T − Θ z{ k {ÖÑ ÄÅ ÅÅÅiji 1 y ij 1 yzyzi Θ − T y zz zz − j zzzjj − c 2ÅÅÅjjjjjjj ÅÅ k T − Θ z{ jjj T − Θ zzzzzjk Θ z{ ÅÅÇk k r {{É Ñ T (T − Θ) ÑÑÑÑ T i1 y ÑÑ + ωjjj − 1zzz − 2 ln r Ñ ( ) T T − Θ ε Ñ Θ k { r ÑÑÖ

(4)

ij 1 yz − ω Pr , Trjjjj − 1zzzz + ω Pr , TrYPr , Tr(T − Tr) j εP , T z k r r {

Figure 3. log(Ksp) for solid species NH4Cl and NaCl.

(5)

At a certain temperature and pressure, the difference between the Gibbs’ free energy of the real mixture and the ideal mixture of the same system is known as the excess Gibbs free energy,24 denoted by Gex. Herein three major components are included to fully describe a real, dissociated electrolyte model. Gex LR in eq 6 represents the long-range electrostatic interactions,25 which accounts for the direct effect of charge interactions originated from the Debye−Hückel theory, strictly valid in dilute solutions. Gex SR represents the local composition model (UNIQUAC) for neutral or no-charge molecular interactions, also known as the short-range interactions.26 It considers the size r and the surface area q of molecules through the structural parameters to generate the short-range binary interactions aij and aji between pairs; subsequent algorithms are shown in eqs 12 and 13. By calculating Gex, the activity coefficient of ion can be calculated as shown in eq 7; this variable accounts for the ion deviations from ideality.

Solution Nonideality. The Helgeson-Kirkham-Flowers (HFK) equation of states21−23 is often employed to calculate for the standard thermodynamic properties of the aqueous species at specific temperature and pressure. From the HFK equation as shown in eq 5, the standard partial molal Gibbs Free Energy can be obtained. Without the ground, standard state reference, excess properties cannot be determined. ΔG°Pr , Tr , ΔS°Pr , Tr are the standard partial molal Gibbs energy of formation and entropy. Tr and Pr are the reference state values for temperature (298.15 K) and pressure (1 bar). a1, a2, a3, and a4 are the pressure related coefficients. c1 and c2 are the temperature-related constants. ω is the temperature- and pressure-dependent term for electrostatic nature of electrolytes. Ψ is equivalent to 2600 bar; the term Θ represents the C


Journal of Chemical & Engineering Data G ex G ex G ex Gex = LR + MR + SR RT RT RT RT ÄÅ É ÅÅ ∂nGex /RT ÑÑÑ ÑÑ ln γi = ÅÅÅÅ ÑÑ ÅÅÇ ÑÑÖ ∂ni P , T , nj

Article

Table 4. Experimental Solubility of NaCl in the Aqueous DEA Solution at pa = 0.1 MPa

(6)

mb (NaCl), mol·kg−1

(7)

x′ (DEA)a,c

mb (DEA), mol·kg−1

283 K

298 K

313 K

333 K

353 K

0 0.025 0.050 0.075 0.100 0.114 0.125 0.135 0.150 0.159 0.174 0.185 0.200

0.000 1.423 2.937 4.519 6.169 7.175 7.908 8.633 9.791 10.527 11.705 12.628 13.847

6.140 5.762 5.371 5.098 4.601 4.222 3.844 3.742 3.247 3.086 2.831 2.513 2.279

6.193 5.850 5.595 5.303 4.886 4.652 4.385 4.263 3.918 3.783 3.532 3.335 3.104

6.224 5.927 5.651 5.424 5.083 4.949 4.806 4.735 4.560 4.460 4.255 4.118 3.930

6.366 5.995 5.699 5.532 5.292 5.135 5.058 4.961 4.884 4.811 4.713 4.594 4.475

6.518 6.108 5.885 5.656 5.526 5.422 5.411 5.314 5.250 5.172 5.150 5.010 4.980

In thermodynamics, we are more concerned with Gex MR, which accounts for all middle-range interactions between ion ex pairs, molecule-ion, and molecule pairs.20,24 GMR in a multicomponent system can be correlated using eq 8. Each individual ion contribution is directly related to the molal ionic strength Ix (mol/kg), for which an increase in the ionic strength results in a smaller activity coefficient value of the strong electrolyte. ex ij yz GMR = −jjjj∑ ni zzzz ∑ ∑ xixjBij (Ix) j i z i j RT k {

(8)

The molal ionic strength dependence of Bij (Ix) is given in eq 9. T0 refers to the reference temperature of 298.15 K. Note that Bij (Ix) is a symmetrical parameter; that is, Bij (Ix) = Bji (Ix), Bii = Bjj = 0; this implies that the sequence of inputting for data regression would not alter the parameter values. Data regressions performed to determine these numerical values were done by utilizing the formulated algorithms shown in eqs 10−13. These objective functions are formulated based on the maximum likelihood of a successful modeling.

a

Standard uncertainties u are u(T) = 0.15 K, u(p) = 0.5 kPa, and u(m) = 0.2 mol·kg−1. bm is the unit in molality (mol·kg−1). cx′ is the mole fraction of DEA on a salt-free basis.

databank; the former parameter interactions between Cl−DEAH+ were readjusted to ensure the accuracy of solubility calculation and prediction. A full list of interaction parameters is shown in Table 5. The Solubility of NH4Cl in the (DEA-H2O) Ternary System. The solubility of NH4Cl in the DEA-H2O system was determined from 283 to 343 K with an increment of 10. The solubility behavior of NH4Cl appears to be much different from that of NaCl in the aqueous DEA solution. As seen in Figure 2 and Table 6, NH4Cl dissolves more with an increase in temperature. However, when temperature is kept at the same level, an increase in the concentration of DEA enhances the solubility of NH4Cl. DEA is formed by the reaction of ethanolamine (MEA) and 1 equiv of ethylene oxide, wherein MEA is formed by reacting ammonia and ethylene oxide. Ammonia serves as an important reactant to create the primary amine that is MEA; this explains the increased solubility behavior of NH4Cl in the aqueous DEA solution when coming to the fact of solvent dipole.29 Newly adjusted parameters from the previous ternary system were reused to correlate the SLE data for this system. Both Cl−-DEA and Cl−-DEAH+ are needed to fit experimental data. The initial predictions by OLI Analyzer are somewhat accurate, but results are much closer after parameters were adjusted. The Solubility of NH4Cl in the (NaCl-DEA-H2O) Quaternary System. Before determining the solubility of NH4Cl in the quaternary system, the solubility experiments of NH4Cl in the NaCl-H2O system were conducted at 283, 298, and 353 K. The purpose was to ensure whether the existing interaction parameters are accurate to study the common ion effect of adding double salts into pure water. As seen in Figure 4, we employed a fixed set of parameters, Na+−NH4+, previously reported by Zeng & Li,30 to correlate for the ternary system NH4Cl-NaCl-H2O. The regression values that belong to the intermediate temperature were further compared with the literature values.28−30 The relative deviations between the experimental and the regression results are within 1.5 ± 0.1%.

Bij (Ix) = [bij ,1 + bij ,2(T − T0)] + [cij ,1 + cij ,2(T − T0)] exp( − bij = b1, jiT +

cij = c1, jiT +

■

b2, ij T

c 2, ij T

Ix + 0.01 ) + b3, ijT 2 + b4, ij ln(T )

+ c3, ijT 2 + c4, ij ln(T )

(9)

(10) (11)

aij = a0, ij + a1, ijT + a 2, ijT 2

(12)

aji = a0, ji + a1, jiT + a 2, jiT 2

(13)

RESULTS AND DISCUSSION The Solubility of NaCl in the (DEA-H2O) Ternary System. The solubilities of NaCl were determined at the temperatures of 283, 298, 313, 333, and 353 K by varying the concentration of DEA. As seen in Figure 1 and Table 4, NaCl is more soluble at a higher temperature.27,28 This result indicates that, when solvents are heated, the kinetic energies of the bonded molecules are raised; hence, more solute particles tend to dissolve into the aqueous solution. At the same temperature, the solubility of NaCl is at the greatest when the amount of DEA added is the lowest, although the downward slope is not as steep when temperature approached 353 K. From these solubility patterns, we concluded that it is much easier to separate salt at a lower temperature and at a high concentration of DEA. The initial solubility predictions provided by the OLI Analyzer deviate much from the experimental values (shown in the form of dash lines in Figure 1). We discovered the interaction parameters between: Cl−-DEA was missing; as such, newly regressed values were later added into the MSE D



Article

Table 5. Binary Ion Interaction Parameters for the System NaCl-NH4Cl-DEA-H2O virial interaction parameters (middle-range) speciesa DEA DEA DEAH+ Na+ NH4+ Na+

BMD0 −

Cl Na+ Cl− Cl− Cl− NH4+

1672.964 −2.586 539 1360.641 −213.999 4369.664 55.389 67

species DEA NH3+

H2O H2O

BMD1

BMD2

−2.949 912 −236 672.9 0.001 364 01 0 −2.348 403 −217 727.0 1.863 23 16 036.8 2.325 859 −97 273.91 −0.102 8922 −12 536.67 UNIQUAC parameters (short-range)

CMD0

CMD1

CMD2

−2424.852 0 −2464.559 202.887 −9748.479 29.010 04

4.310 539 0 4.340 718 −2.153 91 −5.062 129 0

337 668.8 0 383 166.9 −9832.11 219 746 0

Q0IJ

Q0JI

Q1IJ

Q1JI

Q2IJ

Q2JI

−874.2494 −2226.92

−2178.758 4.742 67

12.288 52 −6.528 68

0.524 225 −6.616 42

0.002 0072 0.050 728

−0.005 172 −0.008 019

a Species pairs DEA-Cl− and DEAH+-Cl− are adjusted/created for regression; Na+-NH4− are taken from ref 30; others are kept as default parameters in OLI ESP.

Table 6. Experimental Solubility of NH4Cl in the Aqueous DEA Solution at pa = 0.1 MPa m (NH4Cl), mol·kg−1 x′ (DEA)a,b

mc (DEA), mol·kg−1

283 K

293 K

303 K

313 K

323 K

333 K

343 K

0 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.201

0 1.423 2.937 4.486 6.125 7.941 9.862 11.729 13.896

6.104 6.900 7.527 8.057 8.542 8.899 9.331 9.838 10.113

6.870 7.651 8.214 8.785 9.263 9.758 10.299 10.809 11.238

7.768 8.435 9.092 9.731 10.304 10.927 11.676 12.175 13.239

8.627 9.200 9.853 10.636 11.268 11.922 12.898 13.520 14.650

9.518 9.986 10.617 11.509 12.198 13.053 14.060 14.711 16.036

10.338 10.681 11.489 12.365 13.179 14.052 14.981 15.798 17.328

11.254 11.462 12.147 13.343 14.151 15.136 16.127 17.411 18.685

a Standard uncertainties u are u(T) = 0.15 K, u(p) = 0.5 kPa, and u(m) = 0.2 mol·kg−1. bx′ is the mole fraction of DEA on a salt-free basis. cm is the unit in molality (mol·kg−1).

By raising the temperature from 283 to 333 K, the solubility of NH4Cl in the quaternary systems increased by 20% at each elevated temperature level. The measured solubility data are presented in Figures 5 and 6 and in Tables 7 and 8. At each temperature level, an invariant point was encountered, which symbolizes the phase transition from NH4Cl to NaCl. We can

Figure 4. Solubility of NH4Cl in the NaCl-H2O system at (■) 283 K, (◆) 298 K, (blue line) 313 K, regression only, (magenta line) 333 K, regression only, (●) 353 K, (○) Zeng & Li;30 p = 0.1 MPa; dots: experimental data; solid lines: new model calculation.

Afterward, a quaternary system was proposed to examine phase equilibria for the two ternary systems combined: NH4ClNaCl-DEA-H2O. Specifically, the solubility of NH4Cl was determined by adding different amounts of NaCl into an aqueous DEA solution at first. In this experiment, the composition of DEA was fixed at xDEA′= 0.1 and 0.2, which are equivalent to 39.4 and 59.4 wt % of DEA, respectively.

Figure 5. Solubility of NH4Cl in the system NaCl-DEA-H2O, when x′DEA = 0.1, or 39.4 wt % for temperature at (■) 283 K, (●) 298 K, (▲) 313 K, (▼) 333 K; p = 0.1 MPa; dots: experimental data; solid lines: new model calculation. E



Article

Table 7. Experimental Solubility of NH4Cl in the System NaCl-DEA-H2O (The Common-Ion Effect) at x′DEA= 0.1a (39.4 wt %), pb = 0.1 MPa NaClc

NH4Clc

solid

NaClc

NH4Clc

solid

mol/kg

mol/kg

phase

mol/kg

mol/kg

phase

0 0.500 1.009 1.492 1.996 2.277 2.397 2.495 2.683

T = 283 K 8.542 7.972 7.733 7.328 7.089 6.984 6.899 6.684 6.578

NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl

0 0.500 1.009 1.492 1.996 2.277 2.397 2.495 2.683

T = 313 K 11.268 11.054 10.830 10.204 10.143 9.832 9.758 9.739 9.440

2.830

6.315

2.830

9.015

3.010 3.499 4.018 4.319 4.411

5.937 4.389 3.115 2.129 1.29

NH4Cl + NaCl NaCl NaCl NaCl NaCl NaCl

3.010 3.499 4.018 4.319 4.639 4.865 5.085

0 0.500 1.009 1.492 1.996 2.277 2.397 2.495

T = 298 K 9.800 9.520 9.361 8.808 8.613 8.448 8.416 8.483

2.683

8.290

2.830 3.010 3.499 4.018 4.319 4.639 4.865

7.881 7.174 5.635 3.812 2.475 1.463 0.481

Figure 6. Solubility of NH4Cl in the system NaCl-DEA-H2O, when x′DEA = 0.2, or 59.4 wt % for temperature at (■) 283 K, (●) 298 K, (▲) 313 K, (▼) 333 K; p = 0.1 MPa; dots: experimental data; solid lines: new model calculation.

infer form these data that the effect of adding NaCl impacts the solubility of NH4Cl insignificantly before reaching the invariant point. Because of the common-ion effect of the chlorine ion, the solubility of NH4Cl drops more as shown by the solubility curves immediately after encountering the invariant points. Unlike the ternary system that consists of only NaCl-NH4ClH2O, a certain amount of NH4Cl can be dissolved even if the amount of NaCl added was at its maximum under each temperature. The X-ray diffraction (XRD) technique was utilized to check for the transitions between solid phases as shown in Figure S1. We witnessed that similar to the commonion effect of adding in double salts into pure water, the invariant points at a higher temperature come before those at the lower temperature. Statistical Analysis. As seen in Figures 7−10, box plots were constructed to analyze the standard deviations between the experimental data and the regression results. For each system, a whisker was drawn to extend the difference between 25th percentile to the 75th percentile. The 50th percentile is shown inside of the whisker as indicated by a line. We employed eq 1431 to calculate for the averaged, relative standard deviation σ̅ between the experimental denoted by Xi,exp and the regressed values denoted by Xi,calc. Letter n represents the total number of experimental data. For the system NaCl-DEA-H2O, σ̅ was calculated to be 1.44 ± 0.10%. For the system NH4Cl-DEA-H2O, σ̅ was found to be 2.12 ± 0.10%. Lastly, for the quaternary system NaCl-NH4Cl-DEAH2O, σ̅ was determined to be 5.67 ± 0.10% at x′DEA = 0.1 and 4.97 ± 0.10% at x′DEA = 0.2. For all systems, the standard uncertainties for temperature are u(T) = 0.15 K, and the standard uncertainties for solubilities are u(m) = 0.2 mol·kg−1. n

σ ̅ = 100/n ∑ i=1

0 0.500 1.009 1.492 1.996 2.277 2.397 2.495

NH4Cl + NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl

2.683

10.724

2.830 3.010 3.499 4.018 4.319 4.639 4.865 5.085 5.306

9.956 9.958 8.064 5.833 5.365 3.863 2.862 1.779 0.250

NaCl NaCl NaCl NaCl NaCl NaCl NaCl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl + NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl

a

x′ is the mole fraction of DEA on a salt-free basis. bStandard uncertainties u are u(T) = 0.15 K, u(p) = 0.5 kPa, and u(m) = 0.2 mol·kg−1. cm is the unit in molality (mol·kg−1).

are readily available.13−15,32 We had proven that readjusting the middle-range interactions between Cl−-DEA and DEAH+Cl− would lower σ̅ for each of the proposed systems, indicating a more accurate modeling has been constructed.

■

MODEL APPLICATIONS The Calculation of Speciation Distribution. It is often difficult to precisely analyze for the concentration of Na+ and NH4+ ion in the solutions using either chemical or instrument analysis. In conducting the solubility experiments, we weigh the amounts of DEA, H2O, and these solutes (NaCl and NH4Cl) on a mass balance to obtain the total amount of each in the units of grams. The total amount of water and DEA in

Xi ,calc − Xi ,exp Xi ,exp

NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl

8.801 6.440 4.678 3.098 2.290 2.093 0.917 T = 333 K 13.179 12.993 12.845 12.380 12.145 11.979 11.855 11.785

NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl + NaCl NaCl

(14)

There is indeed arbitrariness when picking the parameters of a given system. For a rule of thumb, the UNIQUAC parameters for the DEA-water interactions were left unchanged, because the reported VLE data of the DEA-water or DEA-water-CO2 F



Article

Table 8. Experimental Solubility of NH4Cl in the System NaCl-DEA-H2O (The Common-Ion Effect) at x′DEAa = 0.2 (59.4 wt %), pb = 0.1 MPa NaClc

NH4Cl

solid

NaCl

NH4Cl

solid

mol/kg

mol/kg

phase

mol/kg

mol/kg

phase

0 0.250 0.500 0.750 1.000 1.175

T = 283 K 10.113 10.063 9.895 9.829 9.704 9.213

NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl

0 0.250 0.500 0.750 1.000 1.250

T = 313 K 14.650 13.837 13.571 13.525 13.436 13.390

1.250 1.500

9.073 8.389

1.500 1.750

12.750 11.262

1.750 2.000 2.242

7.596 6.627 5.897

NH4Cl NH4Cl + NaCl NaCl NaCl NaCl

2.000 2.242 2.493 2.733 3.016 3.465 3.764 3.929

0 0.250 0.500 0.750 1.000 1.250

T = 298 K 12.244 11.912 11.807 11.806 11.514 11.416

NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl

0 0.250 0.500 0.750 1.000 1.250

10.878 9.704 8.331 7.670 5.431 4.068 2.393 1.367 T = 333 K 17.328 16.454 16.232 16.130 15.805 15.667

1.369

11.147

1.500

15.208

1.500 1.750 2.000 2.242 2.493 2.733 3.020

10.747 9.841 9.216 8.624 6.882 6.299 4.595

NH4Cl + NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl

NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl + NaCl NaCl

1.631 1.750 2.000 2.242 2.493 2.733 3.020 3.486 3.748 4.002 4.449

13.684 13.476 13.067 11.282 10.055 7.966 7.217 5.241 4.136 2.735 1.045

NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl

NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl NH4Cl + NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl

Figure 7. Relative deviation for the solubility of NaCl in the aqueous DEA solution (experimental vs regression) at (black ◆) 283 K, (red ◆) 298 K, (blue ◆) 313 K, (magenta ◆) 333 K, (green ◆) 353 K.

a

Figure 8. Relative deviation (experimental vs regression) for the solubility of NH4Cl in the aqueous DEA solution at (black ◆) 283 K, (red ◆) 293 K, (blue ◆) 303 K, (magenta ◆) 313 K, (green ◆) 323 K, (dark blue ◆) 333 K, (purple ◆) 343 K.

the reactor is fixed during the solubility measurements, so all units are further converted into the molal concentration scale (mol/kgH2O). In this paper, the detailed speciation occurred in solution due to complexing was determined by thermodynamic modeling. These chemicals were inputted as inflows into OLI platform to establish a new, thermodynamic model based on solubility regressions. With the aid of this model, OLI made it possible to compute for the aqueous concentration of each ion in molal scale, including those that form ion complexes. Figure 11a−d was drawn for illustration purposes. The effect of adjusting the inflow of DEA or temperature on the distribution of aqueous electrolytes was analyzed by OLI Analyzer Studio. First, shown in Figure 11a,c are for the ternary system NaCl-DEA-H2O; the absolute, molality

concentration for Na+ and Cl− are equivalent to each other, considering the dissolution process did not lead to the formation of complex ions. Conditions for calculation are either for a fixation of temperature at 298 K or the concentration of DEA at 5 mol/kg. In contrast, the dissolution process of NH4Cl in the aqueous DEA system is an example of the formation of complex ions, which influenced the solubility of NH4Cl positively, as DEA weighs more. Also, for the aqueous system NH4Cl-DEA-H2O shown in Figure 11b we witnessed the cease in NH4+ when mixing with the increased concentration of DEA, producing more of NH3 and NH4OH at a constant temperature. The Calculation of Activity Coefficient. By the regression of solubility data for the proposed ternary and quaternary systems, a comprehensive model was constructed. Not only does it allow a more accurate solubility prediction,

x′ is the mole fraction of DEA on a salt-free basis. bStandard uncertainties u are u(T) = 0.15 K, u(p) = 0.5 kPa, and u(m) = 0.2 mol·kg−1. cm is the unit in molality (mol·kg−1).

G



Article

Figure 9. Relative deviation for the solubility of NH4Cl in the system NaCl-DEA-H2O (experimental vs regression), when x′DEA = 0.1, or 39.4 wt % for temperature at (black ◆) 283 K, (red ◆) 298 K, (blue ◆) 313 K, (magenta ◆) 333 K.

Figure 10. Relative deviation for the solubility of NH4Cl in the system NaCl-DEA-H2O (experimental vs regression), when x′DEA = 0.2, or 59.4 wt % for temperature at (black ◆) 283 K, (red ◆) 298 K, (blue ◆) 313 K, (magenta ◆) 333 K.

more important is for it to further analyze the thermodynamic properties of these systems. For example, the relationship between the concentration of DEA and the respective activity coefficient of electrolytes can be calculated. γi is estimated by means of data correlation, not directly retrievable from experimental measurements. As seen in Figures 12 and 13, when γi approaches 1, the ion behaves as if it was ideal, as stated in Raoult’s law. For γi > 1 and γi < 1, the ion tends to show either a positive or a negative deviation from Raoult’s law, respectively. A negative deviation implies that ion is more volatile in that specific concentration, whereas a positive deviation indicates the opposite. Water activity is slightly higher at a lower temperature than at a higher temperature when either NaCl or NH4Cl is present in the solution. To illustrate the influence of temperature on the activity coefficient behavior of electrolyte, two temperature

Figure 11. Speciation distribution for the system (a) NaCl-DEA-H2O at 298 K; (b) NH4Cl-DEA-H2O at 298 K; (c) NaCl-DEA-H2O at DEA = 5 mol/kg; (d) NH4Cl-DEA-H2O at DEA = 5 mol/kg.

levels (283 and 353 K) were considered. For the ternary system NaCl-DEA-H2O, it is shown that γNa+ remains stable at H



Article

solubility of NH4Cl increases with the addition of DEA. The solubility of both salts increases if temperature was raised from 283 to 353 K. The common-ion effect was observed when both salts were present in the solution. With the Mixed-SolventElectrolyte model, this work provides a detailed thermodynamic analysis for the development and optimization toward the design of any salt separation process including NaCl and NH4Cl in the aqueous DEA solution. Most importantly, the solid−liquid equilibria (solubility of solutes) are of great importance not only for process design but also for the amine selection for CO2 adsorption when solid reactants are involved in a chemical reaction.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.8b00515. An XRD pattern. The characterization result corresponds to the system NaCl-NH4Cl-DEA-H2O at x′DEA = 0.2 for the precipitants obtained at the invariant point under 333 K (PDF)

Figure 12. Molality-based activity coefficient vs the concentration of DEA for the system NaCl-DEA-H2O.

■

AUTHOR INFORMATION

Corresponding Author

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

Zhibao Li: 0000-0002-5737-1289 Funding

The authors are grateful for the financial support provided by the National Science Foundation of China (Grant Nos. 21506218, 21476235, and U1407112). Notes

The authors declare no competing financial interest.

■

ABBREVIATIONS MSE = mixed-solvent-electrolyte DEA = diethanolamine wt % = weight percentage a = activity aij = UNIQUAC interaction parameter of species i and j a0,ij, a1,ij, a2,ij, a0,ji, a1,ji, and a2,ji = MSE model: short-range adjustable parameters Ax = Debye−Hückel parameter bij = middle-range interaction parameter of species i and j b0,ij, b1,ij, b2,ij, and b3,ij = MSE model: middle-range adjustable parameters Bij = middle-range interaction parameter between species i and j cij = middle-range interaction parameter between species i and j Gex = excess Gibbs’ free energy Ix = mole fraction based ionic strength Ksp = solubility equilibrium constant m = molality (mol/kg solvent) ni = number of moles of species i in qi = UNIQUAC surface area parameter of species i QiIJ, QiJI (i = 1, 2, ···) = short-range adjustable parameters of the MSE model ri = UNIQUAC molecular volume parameter of species i R = ideal gas constant (8.314 J·mol−1·K−1) T = absolute temperature (K)

Figure 13. Molality-based activity coefficient vs the concentration of DEA for the system NH4Cl-DEA-H2O.

298 K regardless of the change in DEA concentration, yet significantly increases at 353 K or at a higher temperature, when DEA is more concentrated. γCl− slightly reduces at 353 K, when the DEA concentration is high, but it exponentially increases at room temperature when the DEA concentration reaches 14 mol/kg (x′ DEA = 0.2). For the ternary system NH4Cl-DEA-H2O, γCl− slightly reduces at both temperature levels, whereas γNH4+ significantly increases at both temperature levels. Larger gaps are the results of changes in the ionic strength fraction of each ion, as the distinctions directly influence the interaction parameters.

■

CONCLUSION The experimental solubility of NaCl and NH4Cl were determined in the DEA-H2O system via the dynamic method. The experiments were conducted by varying both temperature and the concentration of DEA: xDEA′ from 0 to 0.2. With the aid of the OLI Analyzer software, a comprehensive chemical model was constructed based on the newly adjusted interaction parameters by the regression of solubility data, provided to further analyze system equilibria and thermodynamic properties. It was found the solubility of NaCl decreases, whereas the I



Article

High Pressures and Temperatures, 1st ed.; Kline Geology Laboratory, Yale University, 1981. (22) Helgeson, H. C.; Kirkham, D. H.; Flowers, G. C. Theoretical Prediction of the Thermodynamic Behavior of Aqueous Electrolytes at High Pressures and Temperatures. IV. Calculation of Activity Coefficients, Osmotic Coefficients, and Apparent Molar and Standard and Relative Partial Molar Properties to 600 °C and 5 kb. Am. J. Sci. 1981, 281, 1249−1516. (23) Tanger, J. C.; Helgeson, H. C. Calculation of Thermodynamic and Transport Properties of Aqueous Species at High pressures and Temperatures: Revised Equations of State for the Standard Partial Molal Properties of Ions and Electrolytes. Am. J. Sci. 1988, 288, 19− 98. (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) Abrams, D. S.; Prausnitz, J. M. Statistical Thermodynamics of Liquid Mixtures - New Expressions for Excess Gibbs Energy of Partly or Completely Miscible Systems. AIChE J. 1975, 21, 116−128. (26) Pitzer, K. S. Electrolytes. From Dilute Solutions to Fused Salts. J. Am. Chem. Soc. 1980, 102, 2902−2906. (27) Shock, E. L.; Helgeson, H. C. Calculation of the Thermodynamic and Transport Properties of Aqueous Species at High pressures and Temperatures: Correlation Algorithms for Ionic Species and Equation of State Predictions to 5 kb and 1000 °C. Geochim. Cosmochim. Acta 1988, 52, 2009−2036. (28) Silcock, H. L. Solubilities of Inorganic and Organic Compounds, 1st ed.; Pergamon Press: Oxford, UK, 1979. (29) D’Aprano, A.; Fuoss, R. M. Electrolyte-Solvent Interaction. X. Dipole Solvation. J. Phys. Chem. 1963, 67, 1722−1723. (30) Zeng, Y.; Li, Z. Solubility Measurement and Modeling for the NaCl−NH4Cl−Monoethylene Glycol−H2O System from (278 to 353) K. J. Chem. Eng. Data 2015, 60, 2248−2255. (31) Box, G. E. P.; Hunter, W. G.; Hunter, J. S. Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building; John Wiley & Sons: New York, 2005; Vol. 2, pp 1−14. (32) Lee, J. I.; Otto, F. D.; Mather, A. E. Solubility of Carbon Dioxide in Aqueous Diethanolamine Solutions at High Pressures. J. Chem. Eng. Data 1972, 17, 465−468.

xi = mole fraction of species i xi′ = salt-free, mole fraction of solvent i γi = activity coefficient of species i

■

REFERENCES

(1) Anderson, K.; Peters, G. The Trouble with Negative Emissions. Science 2016, 354 (6309), 182−183. (2) Chu, S. Carbon Capture and Sequestration. Science 2009, 325 (5948), 1599−1599. (3) Kintisch, E. A Career CO2 Hunter Goes After Big Game. Science 2007, 317 (5835), 186−186. (4) Rochelle, G. T. Amine Scrubbing for CO2 Capture. Science 2009, 325 (5948), 1652−1654. (5) Lastoskie, C. Caging Carbon Dioxide. Science 2010, 330 (6004), 595−596. (6) Lawson, J. D.; Garst, A. W. Gas Sweetening Data: Equilibrium Solubility of Hydrogen Sulfide and Carbon Dioxide in Aqueous Monoethanolamine and Aqueous Diethanolamine Solutions. J. Chem. Eng. Data 1976, 21, 20−30. (7) Rinker, E. B.; Ashour, S. S.; Sandall, O. C. Kinetics and Modeling of Carbon Dioxide Absorption into Aqueous Solutions of Diethanolamine. Ind. Eng. Chem. Res. 1996, 35, 1107−1114. (8) OLI System Inc. Gas Sweetening Using DEA. 2014; http:// support.olisystems.com/. Accessed June 17, 2018). (9) Gärtner, R. S.; Witkamp, G. J. Mixed Solvent Reactive Recrystallization of Trona (Sodium Sesqi-carbonate) Into Soda (Sodium Carbonate). Hydrometallurgy 2007, 88, 75−91. (10) Vallée, G.; Mougin, P.; Jullian, S.; Fürst, W. Representation of CO2 and H2S Absorption by Aqueous Solutions of Diethanolamine Using an Electrolyte Equation of State. Ind. Eng. Chem. Res. 1999, 38, 3473−3480. (11) Aroua, M. K.; Benamor, A.; Haji-Sulaiman, M. Z. Equilibrium Constant for Carbamate Formation from Monoethanolamine and Its Relationship with Temperature. J. Chem. Eng. Data 1999, 44, 887− 891. (12) Aroua, M. K.; Amor, A. B.; Haji-Sulaiman, M. Z. Temperature Dependency of the Equilibrium Constant for the Formation of Carbamate From Diethanolamine. J. Chem. Eng. Data 1997, 42, 692− 696. (13) García-Abuín, A.; Gómez-Díaz, D.; López, A. B.; Navaza, J. M.; Rumbo, A. NMR Characterization of Carbon Dioxide Chemical Absorption with Monoethanolamine, Diethanolamine, and Triethanolamine. Ind. Eng. Chem. Res. 2013, 52, 13432−13438. (14) Abu-Arabi, M. K.; Al-Jarrah, A. M.; El-Eideh, M.; Tamimi, A. Physical Solubility and Diffusivity of CO2 in Aqueous Diethanolamine Solutions. J. Chem. Eng. Data 2001, 46, 516−521. (15) Yamada, H.; Shimizu, S.; Okabe, H.; Matsuzaki, Y.; Chowdhury, F. A.; Fujioka, Y. Prediction of the Basicity of Aqueous Amine Solutions and the Species Distribution in the Amine−H2O− CO2 System Using the COSMO-RS Method. Ind. Eng. Chem. Res. 2010, 49, 2449−2455. (16) Wang, P.; Kosinski, J. J.; Anderko, A.; Springer, R. D.; Lencka, M. M.; Liu, J. Ethylene glycol and its mixtures with water and electrolytes: Thermodynamic and transport properties. Ind. Eng. Chem. Res. 2013, 52, 15968−15987. (17) OLI System Inc. OLI ESP User Guide−A Guide to Using OLI ESP 9.X; http://support.olisystems.com. Accessed June 17, 2018. (18) OLI Systems, Inc., OLI Analyzer Studio−Stream Analyzer version 9.5; http://www.olisystems.com. Accessed August 10, 2017. (19) Yang, J. M.; Zhang, R. Z.; Liu, H.; Ma, S. H. Solid-Liquid Phase Equilibria at 50 and 75 °C in the NaCl + MgCl2 + H2O System and the Pitzer Model Representations. Russ. J. Phys. Chem. A 2013, 87, 2195−2199. (20) Zemaitis, J. F.; Clark, D. M.; Rafal, M.; Scrivner, N. C. Handbook of Aqueous Electrolyte Thermodynamics, 1st ed.; AIChE Inc.: New York, 1986. (21) Helgeson, H. C.; Kirkham, D. H.; Flowers, G. C. Theoretical Prediction of the Thermodynamic Behavior of Aqueous Electrolytes at J


Solubility Determination and Thermodynamic Modeling for the System

Recommend Documents