Thermodynamic modeling of refrigerants solubility in ionic liquids using original and ϵ*-Modified Sanchez–Lacombe equations of state

Accepted Manuscript Title: Thermodynamic Modeling of Refrigerants Solubility in Ionic Liquids Using Original and ∗ -Modified Sanchez–Lacombe Equations of State Author: Javad Hekayati Aliakbar Roosta Jafar Javanmardi PII: DOI: Reference:

S0378-3812(15)00307-6 http://dx.doi.org/doi:10.1016/j.fluid.2015.05.046 FLUID 10601

To appear in:

Fluid Phase Equilibria

Received date: Revised date: Accepted date:

26-4-2015 27-5-2015 28-5-2015

Please cite this article as: Javad Hekayati, Aliakbar Roosta, Jafar Javanmardi, Thermodynamic Modeling of Refrigerants Solubility in Ionic Liquids Using Original and epsilon*-Modified SanchezndashLacombe Equations of State, Fluid Phase Equilibria http://dx.doi.org/10.1016/j.fluid.2015.05.046 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Thermodynamic Modeling of Refrigerants Solubility in Ionic Liquids Using Original and

∗

-Modified Sanchez–Lacombe Equations of State

Javad Hekayati, Aliakbar Roosta*, Jafar Javanmardi Chemical Engineering, Oil and Gas Department, Shiraz University of Technology, Shiraz, Iran *

Corresponding author: [email protected] Tel: +98-7137354520 Fax: +98-7137354520

Highlights



P-T-x of a diverse set of refrigerants in different ionic liquid types are modeled.



Two equations of state based on lattice fluid theory are employed.



Use is made of 3086 experimental liquid density and 658 solubility datapoints.



Modeling of all the 88 isotherms studied are found to be acceptable.



AARDs of %5.773 and %5.771 for SL and ε*-Modified SL EOSs, respectively.

Abstract Ionic liquids can dramatically improve the efficiency of absorption refrigeration processes due to their negligibly small vapor pressure; where the IL absorbs the refrigerant gas in one stage and subsequently releases the high-pressure gas upon addition of heat. In the current study, phase equilibrium data (P-T-x) of a diverse set of refrigerants in different types of ionic liquids are modeled with the aid of two equations of state based on lattice fluid theory, i.e. SanchezLacombe and ε*-Modified Sanchez–Lacombe EOSs. The characteristic parameters of the pure components were determined from a database of 3086 experimental liquid density datapoints for 11 refrigerants and 12 ILs. According to the results obtained by considering the experimental data of 25 binary IL/refrigerant mixtures comprised of 88 isotherms with a total of 658 datapoints, both EOSs can successfully correlate the solubility data with AARDs of %5.773 and %5.771 for SL and ε*-Modified SL EOSs, respectively. 1

Keywords: Solubility; Ionic liquids; Sanchez–Lacombe EOS; Refrigerants; Lattice Fluid Theory 1. Introduction Ionic liquid (IL), also known as liquid electrolyte or liquid salt, is a term customarily used to refer to organic salts that form a stable and wide liquid range of over 300 K. Ionic liquids have a melting temperature below T=373.15 K and consist of a small organic or inorganic anion and a large asymmetric organic cation; the suitable choice of which could be used to adjust and tune the specific properties of the ionic liquids on demand. Due to their nonflammability, high thermal stability, recyclability and almost negligible vapor pressure, which essentially eliminates hazardous emissions to the atmosphere, these compounds are considered as environmentally benign solvents. Detailed reviews regarding ionic liquids synthesis and their various novel applications ranging from being used as alternatives to conventional organic solvents to their use as catalysts and catalytic supports are available in the literature [1–3]. In particular, Ionic liquids have found increasing application, alongside various refrigerant gases, both in separation and engineering applications; in which detailed phase equilibria and thermodynamics modeling are needed for their further development [4]. More specifically, Ionic liquids have been used to facilitate the separation of refrigerants and intermediates that often have very similar physico-chemical properties; for instance, the case of

an

azeotropic

hydrofluorocarbon

mixture

containing

difluoromethane

and

pentafluoroethane could be of note [5]. Also, ionic liquids can dramatically improve the efficiency of absorption refrigeration processes where the IL absorbs the refrigerant gas in one stage and subsequently releases the high-pressure gas upon addition of heat. Moreover, the major drawback of the current liquid solvents, with even low volatility, used in refrigeration processes is the necessity for costly and bulky equipment to remove their contamination from the high-pressure gas. In this regard, ionic liquids with their very low vapor pressure, help in preventing contamination of the refrigerant gas with solvent and hence

2

maintaining the refrigeration capacity of the refrigerant. Furthermore, one of the major challenges imposed upon the prospective use of ILs as alternatives to conventional solvents is their relatively higher viscosity which in turn translates into slower mass transport rates and hence larger capital costs and process equipment, e.g. heat exchangers and contactors. In addressing this issue, dramatic improvements have been reported for the mass transport properties, i.e. viscosity and diffusivity, of ILs when used alongside refrigerants [6]. Proper designing, as well as optimization of these and other IL/refrigerant applications requires reliable quantitative modeling of the high-pressure phase behavior and equilibria data of the systems of interest. Especially, correlating and predicting the phase equilibria data, which essentially quantify the solubility of each component in all the contacting phases, could be very valuable in the design stage of the aforementioned processes. For instance, identification of the regions over which the IL/refrigerant systems are miscible, and hence not conducive to separation or absorption refrigeration, could be readily accomplished by way of thermodynamics modeling. Still and to the best of the author’s knowledge, use of equations of state in the thermodynamics modeling of IL/refrigerant mixtures is scarce in the published literature. Recently, Ren and Scurto [4] used a cubic equation of state, i.e. Peng-Robinson EOS [7] alongside the van der Waals 2-parameter mixing rule (PR-vdW2) to correlate the isothermal vapor-liquid equilibrium data for four binary mixtures of the type IL/refrigerant. Furthermore, Faúndez et al. (2013) correlated and tested for thermodynamic consistency the data of nineteen binary IL/refrigerant mixtures with the modified Peng-Robinson EOS proposed by Kwak and Mansoori [9]. The present study considers the data of 25 binary IL/refrigerant mixtures at pressures ranging from 0.01 to 12.05 MPa and temperatures spanning 283 to 449 K. These data include 88 isotherms with a total of 658 datapoints. An equation of state based on lattice fluid theory and a modified version of it are successfully employed and compared in their ability to correlate these experimental solubility data for the first time. Furthermore, in order to ascertain 3

their relative accuracy, the results obtained here are compared with the available published results of other authors who have employed other equations of state. 2. Thermodynamic Modeling

The lattice–fluid model was proposed by Sanchez and Lacombe [10] to describe thermodynamic properties of molecular fluids of arbitrary size. In this and other models based on lattice-hole theory [11,12], which are essentially based on statistical thermodynamics, the molecules are presumed to be consisting of repeating units called segments. This framework is similar to the concept of monomer in polymer sciences; the difference being that while the latter has its roots in physical reality, molecular segments are imaginary or mathematical units. Nonetheless, the common denominator between all such theories is that they consider the movement of each molecule segment to be restricted to the neighborhood of one of the lattice sites; so that, it is usual to consider only the effect of nearest neighbors on the molecule segment within its cell [13]. In the current study two variations of Sanchez-Lacombe (SL) equation of state [10,14,15], which are themselves based on lattice–fluid theory are employed. With three substance dependent characteristic parameters, the original SL EOS is represented by Eqs. (1, 2): 1  2  P  T (ln(1   )  (1  )  )  0 r

(1)

T P  T   , P   ,    T P 

(2)

RT  MP    RT ,    , r  P RT    

where



∗



,

∗

and

∗

are the characteristic parameters of the EOS for each pure component

that differ from the critical parameters, M is the molecular weight and R is the universal gas constant. The characteristic parameters, ε*, ν* and r represent the interaction energy, the characteristic volume and the segment length for pure substances, respectively; which are

4

themselves directly related to

∗

,

∗

and

∗

by Eqn. (2) and hence both constant sets could be

used interchangeably. In this form, the interaction energy, ε*, is treated as a constant. Following the original work of Sanchez and Lacombe, Machida et al. [16] proposed a simple modification to take into account the temperature dependence of hydrogen bonding and ionic interactions. In their work, a simple function in the form of the Langmuir equation was used that reduces to the original SL EOS at high temperatures; and introduces temperature dependence into the interaction energy parameter, ε*, as in Eq. (3):

  (T )   0

T 1  T

(3)

where α is a constant that gives temperature dependence to ε* and ε0 is the asymptotic value of the interaction energy, which ε* attains at the high temperature limit. For this formulation, which they dubbed as ε*-Modified SL EOS, the authors reported large improvements over the original SL EOS in the calculation of liquid densities of polar fluids and ionic liquids, especially in the high-pressure compressed-liquid region. For application of the original SL EOS, as well as the ε*-Modified SL EOS to mixtures, the combining rules, as presented in Eq. (4), were applied: P*   i j Pij * i

Pij*  (1  kij )( Pi* Pj * )1/2

j

i 0Ti* T  P  ( * )  *   (i 0 i* ) Pi i i *

*

rx  i i r r   ( xi ri 0 ) i

(4)

r0x i  i i r * ri  ri0 i*  0

where ϕi0 and ϕi represent the closed-packed volume fraction of component i in pure state and mixture, respectively, ri0 and ri represent the segment length of component i in pure state and mixture, respectively, and kij is a binary interaction parameter between component i and j. In comparing the original Sanchez-Lacombe EOS with its ε*-Modified formulation in

5

representing the solubility of refrigerants in ILs, comparisons are made between the two EOSs by determining from experimental data the kijs that minimize the average absolute relative deviations (AARDs [%]) between calculated and experimental refrigerant solubilities in the ionic liquid phase. When using SL EOS, chemical potentials are usually derived on the basis of the Helmholtz energy obtained from the partition function of mixtures, in order to compute phase equilibrium conditions at various temperature and pressure conditions. However, as demonstrated by Neau [17] the chemical potentials derived in this way are thermodynamically inconsistent, regardless of what combining rules are used. To redress this issue, a consistent expression for the fugacity coefficient that satisfies the ideal gas limit was derived directly from the equation-of-state as in Eq. (5): *      z  1  nr      ln i   ln z  ri 0  2  ln(1   )   ( ) *   r   ni n  T  T  j  

 nr   *    *      ni  n j   

(5)

where z is the compressibility factor. Based on the combining rules of Eq. (4), which are in fact the recommended combining rules of Sanchez and Lacombe [15], and the relations presented in Eq. (2), the terms containing derivative in Eq. (5) are evaluated and Eq. (6) results [18]:    z 1  1 0  ln i   ln z  ri 0  2  ln(1   )   ( )  * ri (  *   i* )   r   T     1   *   *     *  2ri   P    j Pij*     * ri 0 ( *   i* )   T       j   

(6)

In order to evaluate the characteristic parameters of the pure components considered in this study for both of the two EOSs, a comprehensive database comprised of 3086 experimental liquid density datapoints, as listed in Table 1, was gathered. The choice of the data sources was based on the inclusion of a high-pressure liquid region and a wide range of

6

liquid density data; in order to ensure that the obtained characteristic parameters of the pure components are representative over these expanded regions. Table 1 – Data sources used for evaluating the pure component characteristic parameters of the EOSs. In the table the pressure and temperature values have been rounded to the closest integer.

Substance

Fitting range P (MPa) T (K)

N.D. Reference

Refrigerants R-14 R-23 R-41 R-50 R-124 R-125 R-E125 R-134 R-161 R-290 R-134a

0-57 0-4 7-70 0-35 1-36 1-68 5-35 1-5 0-3 1-51 1-80

0-224 121-295 130-315 91-191 104-400 180-350 243-326 274-367 231-343 207-353 283-363

86 94 220 267 149 178 161 59 45 79 32

[19] [20] [21] [22] [23] [24] [21] [25] [26] [27] [28]

Ionic liquids [Hmim][Tf2N] [Emim][PF6] [Emim][TFSI] [Bmim][PF6] [Bmim][Tf2N] [Bmim][CH3SO4] [Emim][EtSO4] [Bmim][NO3] [Hmim][BF4] [Omim][BF4] [Emim][BF4] [Hmim][PF6]

0-65 10-200 1-100 0-200 0-60 0-35 0-140 0.1 10-200 0-60 10-200 10-200

293-338 353-472 283-373 313-472 293-473 283-353 283-413 283-363 313-473 283-323 313-472 313-472

162 129 84 181 237 261 151 15 180 117 180 180

[29] [30] [31] [32] [33] [34] [35] [36,37] [30] [38] [30] [30]

Cation: [Hmim], 1-Hexyl-3-Methylimidazolium; [Emim], 1-Ethyl-3methylimidazolium; [Bmim], 1-Butyl-3-methylimidazolium; [Omim], 3Methyl-1-Octylimidazolium. Anion: [Tf2N], Bis(TrifluoroMethylSulfonyl); [PF6], Hexafluorophosphate; [TFSI], Bis(TrifluoroMethylSulfonyl); [CH3SO4], Methyl Sulfate; [EtSO4], Ethyl Sulfate; [NO3], Nitrate; [BF4], Tetrafluoroborate.

Also, Table 2 enumerates the experimental solubility data used in this study, alongside the literature source for each data set. This table lists the isotherms of each IL/refrigerant system,

7

giving the solubility and pressure ranges for each one. Here, subscript 1 denotes the refrigerant and the solubilities are expressed as mole fractions. Table 2 - Details alongside sources of the phase equilibrium data for the IL/Refrigerant systems considered in this study. In the table the temperature values have been rounded to the closest integer.

System R14 + [Hmim][Tf2N]

R-23 + [Emim][TFSI] R-23 + [Bmim][PF6]

R-41 + [Bmim][PF6]

R-50 + [Bmim][Tf2N]

R-50 + [Bmim][CH3SO4]

R-50 + [Hmim][Tf2N]

R-50 + [Emim][EtSO4] R-124 + [Emim][TFSI]

R-125 + [Bmim][PF6]

R-125 + [Emim][TFSI]

T (K) N.D. 293 333 373 413 298 323 283 298 323 348 283 298 323 348 314 333 352 371 391 410 430 449 293 333 373 413 293 333 373 413 292 293 283 298 323 348 283 298 323 348 283

8 6 6 7 18 17 7 8 9 9 9 7 8 9 4 4 4 5 4 5 5 4 6 6 6 6 6 6 6 6 4 4 5 7 7 7 9 9 9 9 9

Data range x(1)

P (MPa)

0.023-0.089 0.017-0.071 0.012-0.073 0.012-0.077 0.007-0.481 0.008-0.333 0.010-0.419 0.008-0.373 0.000-0.231 0.001-0.149 0.002-0.637 0.014-0.484 0.006-0.332 0.002-0.238 0.030-0.163 0.056-0.163 0.056-0.163 0.030-0.163 0.056-0.163 0.056-0.163 0.030-0.163 0.030-0.163 0.038-0.193 0.040-0.188 0.037-0.173 0.037-0.184 0.063-0.511 0.084-0.488 0.100-0.450 0.079-0.422 0.004-0.041 0.001-0.010 0.050-0.757 0.028-0.665 0.010-0.322 0.001-0.171 0.013-0.660 0.003-0.363 0.000-0.154 0.000-0.088 0.008-0.681

1.633-9.580 1.428-7.700 1.127-8.390 1.202-9.010 0.027-1.997 0.048-1.999 0.050-1.500 0.050-2.000 0.010-1.999 0.010-2.000 0.010-2.000 0.050-1.999 0.050-1.999 0.010-1.999 1.510-9.900 3.080-10.500 3.240-10.980 1.740-11.350 3.510-11.650 3.580-11.850 1.910-11.980 1.940-12.050 1.363-8.510 1.604-8.853 1.603-8.206 1.645-8.814 0.886-8.250 1.440-9.210 1.966-9.300 1.660-9.240 1.014-10.150 0.198-2.029 0.010-0.200 0.010-0.300 0.010-0.300 0.010-0.300 0.010-0.800 0.010-1.000 0.010-1.000 0.010-1.000 0.010-0.800

8

Reference [39]

[40] [41]

[42]

[43]

[44]

[45]

[46] [47]

[41]

[48]

R-E125 + [Emim][TFSI]

R-134 + [Emim][TFSI]

R-134 + [Bmim][PF6]

R-161 + [Bmim][PF6]

R-290 + [Bmim][NO3]

R-290 + [Bmim][Tf2N]

R-290 + [Hmim][BF4]

R-290 + [Omim][BF4]

R-290 + [Emim][BF4]

R-290 + [Hmim][Tf2N] R-134a + [Emim][TFSI]

R-134a + [Hmim][Tf2N]

R-134a + [Hmim][BF4] R-134a + [Hmim][PF6]

298 323 348 283 298 323 348 283 298 323 348 283 298 323 348 283 298 298 323 348 288 298 308 288 298 308 288 298 308 288 298 308 288 298 308 298 298 323 348 298 323 348 298 323 298 323 348

9 9 9 7 8 8 6 6 8 8 8 6 8 8 8 6 2 6 8 8 8 8 8 7 7 7 7 7 7 7 7 7 6 6 6 10 14 14 17 10 14 5 5 7 6 10 5

0.006-0.521 0.004-0.285 0.004-0.171 0.010-0.565 0.006-0.383 0.004-0.187 0.002-0.074 0.246-0.960 0.033-0.716 0.016-0.421 0.006-0.250 0.031-0.789 0.024-0.689 0.006-0.346 0.006-0.196 0.009-0.575 0.007-0.420 0.073-0.496 0.005-0.270 0.003-0.170 0.008-0.047 0.005-0.030 0.004-0.025 0.021-0.137 0.014-0.099 0.014-0.077 0.012-0.082 0.017-0.069 0.008-0.052 0.017-0.113 0.015-0.102 0.011-0.086 0.005-0.028 0.004-0.017 0.003-0.012 0.096-0.241 0.016-0.767 0.011-0.697 0.009-0.693 0.025-0.758 0.028-0.764 0.243-0.716 0.044-0.522 0.031-0.707 0.059-0.651 0.029-0.768 0.200-0.637 9

0.010-1.000 0.010-1.000 0.010-1.000 0.010-0.500 0.010-0.600 0.010-0.600 0.010-0.400 0.050-0.300 0.010-0.350 0.010-0.351 0.011-0.351 0.010-0.250 0.011-0.350 0.011-0.351 0.011-0.350 0.010-0.499 0.010-0.600 0.100-0.699 0.010-0.701 0.010-0.700 0.101-0.643 0.108-0.646 0.114-0.666 0.067-0.495 0.074-0.495 0.081-0.502 0.076-0.451 0.129-0.500 0.088-0.509 0.066-0.481 0.080-0.494 0.070-0.489 0.094-0.561 0.098-0.578 0.099-0.587 0.322-0.731 0.028-0.624 0.034-1.174 0.051-2.16 0.042-0.586 0.053-1.192 0.502-1.878 0.081-0.512 0.086-1.227 0.081-0.576 0.089-1.283 0.623-2.057

[48]

[47]

[42]

[42]

[49]

[49]

[49]

[49]

[49]

[50] [51]

[4]

[4] [4]

3. Results and Discussion The characteristic parameters of the two equations of state for each pure component were determined by minimizing the average absolute relative deviations (AARDs [%]) between calculated and experimental density data according to the objective function given in Eq. (7): Calc .   Exp. 100 N  AARD (%)    Exp. N i 1

(7)

Tables 3 and 4 give the characteristic parameters determined for the original and the ε*-Modified Sanchez–Lacombe equations of state, respectively. A quick comparison between the evaluated parameters reveals interesting trends. Considering the refrigerants, the values of the evaluated characteristic parameters for both the original and the ε*-Modified SL EOSs are close and the calculated deviations are similar. The same trend cannot be observed in ionic liquids, where the evaluated parameters, as well as the calculated average absolute relative deviations are in marked contrast; especially, ε*-Modified SL EOS, with introduction of temperature dependence into the interaction energy parameter, ε*, exhibits large improvements over the original SL EOS. Also, the much larger values of ε0, which are at the same time offset to some extent by the relatively smaller α values, indicate the higher temperature dependence of the ε* parameter of ionic liquids. Moreover, in the ε*-Modified SL EOS the interaction energy parameter, ε*, has either a monotonic increasing or a monotonic decreasing trend with temperature for the components studied; observable from the sign of the fitted α values. Table 3 - Characteristic parameters for the Sanchez–Lacombe equation of state.

Substance Refrigerants R-14 R-23 R-41 R-50 R-124 R-125 R-E125 R-134

ε* (J/mol)

ν* (cm3/mol)

1910.957 2654.812 2717.077 1770.44 3053.786 2817.176 2992.006 3516.183

6.457 7.706 5.301 7.574 6.362 8.665 10.193 11.393 10

r 7.116 5.351 6.148 4.436 11.662 7.547 7.274 5.326

%AARD 0.520 0.712 0.917 0.574 1.157 0.649 0.163 0.164

R-161 R-290 R-134a

3325.541 3212.731 3139.668

9.187 10.538 8.345

5.533 6.181 7.373

Average for refrigerants Ionic liquids [Hmim][Tf2N] [Emim][PF6] [Emim][TFSI] [Bmim][PF6] [Bmim][Tf2N] [Bmim][CH3SO4] [Emim][EtSO4] [Bmim][NO3] [Hmim][BF4] [Omim][BF4] [Emim][BF4] [Hmim][PF6]

5086.913 12.721 5724.515 9.997 4985.756 10.9 5599.609 10.615 5599.413 12.486 5572.764 10.122 5596.353 9.905 5692.476 9.986 5447.809 10.759 5197.697 12.034 5691.799 9.328 5378.185 10.62 Average for ionic liquids Overall average

0.171 0.168 0.236 0.494

23.845 16.532 21.887 18.473 22.14 19.351 18.188 16.512 19.324 19.826 15.65 21.257

0.055 0.232 0.177 0.334 0.234 0.046 0.247 0.050 0.352 0.044 0.315 0.336 0.202 0.341

Table 4 - Characteristic parameters for the ε*-modified Sanchez–Lacombe equation of state.

Substance Refrigerants R-14 R-23 R-41 R-50 R-124 R-125 R-E125 R-134 R-161 R-290 R-134a

Ionic liquids [Hmim][Tf2N] [Emim][PF6] [Emim][TFSI] [Bmim][PF6] [Bmim][Tf2N] [Bmim][CH3SO4] [Emim][EtSO4]

1/α (K)

ε0 (J/mol) ν* (cm3/mol) r

%AARD

23.925 2032.007 5.14 80.043 3367.73 7.266 124.982 3417.55 3.004 40.017 1976.897 4.919 165.097 3978.372 3.476 -37.577 2647.057 11.411 -56.838 2881.104 19.385 -47.076 3217.986 13.492 -40.792 2929.95 8.876 26.153 3319.327 8.714 -37.493 2989.808 11.227 Average for refrigerants

8.654 5.337 9.794 6.445 18.994 5.983 4.125 4.695 5.891 7.28 5.707

0.426 0.434 0.448 0.419 0.512 0.556 0.238 0.091 0.186 0.126 0.224 0.333

494.573 516.39 433.445 619.495 732.084 406.535 496.321

122.716 52.723 81.079 65.053 136.101 69.754 67.545

0.179 0.067 0.034 0.082 0.118 0.013 0.053

8389.657 9724.201 8295.304 10599.5 10066.4 8667.292 9630.752 11

2.126 2.805 2.624 2.681 1.642 2.535 2.4

[Bmim][NO3] [Hmim][BF4] [Omim][BF4] [Emim][BF4] [Hmim][PF6]

848.709 11188.83 1.312 571.575 10074.19 2.919 457.814 8547.961 2.363 632.075 10617.62 2.175 479.234 9376.201 3.418 Average for ionic liquids Overall average

101.055 63.714 89.136 59.117 60.139

0.055 0.084 0.010 0.081 0.074 0.071 0.196

In the phase equilibrium calculations, it was assumed that the ionic liquid does not dissolve into the vapor phase and hence the vapor phase is presumed to be pure refrigerant. Accordingly, the solubility of the refrigerant in the ionic liquid phase is determined by the isofugacity criterion of the refrigerant in both the liquid and the pure vapor phases. Furthermore, the binary interaction parameters, kijs, are fitted to the experimental data by minimizing an objective function based on average absolute relative deviations (AARDs [%]) between calculated and experimental refrigerant solubilities as in Eq. (8). As it was determined that the binary interaction parameter of each IL/refrigerant system is highly temperature dependent, which is actually expected due to the relatively extended temperature range of the experimental solubility data of each system, the kijs fitted for each isotherm were ultimately correlated using a second degree polynomial, the coefficients of which are reported in Tables 5 and 6 for Sanchez-Lacombe and ε*-modified Sanchez– Lacombe equations of state, respectively. As can be seen from these tables, in a certain majority of the IL/refrigerant systems studied, the temperature dependence of the binary interaction parameters could well be represented using only a linear equation. Hence, only in those cases where the augmented accuracy was appreciable enough to warrant it, the kijs were fitted on a nonlinear second degree polynomial. Also tabulated are AARDs [%] between calculated and experimental mole fractions of refrigerants in the ionic liquid phase as defined in Eq (8). Also keep in mind that to test both the predictive and correlative capabilities of the two EOSs considered in this study, the refrigerant solubility data were reproduced with and 12

without the fitted binary interaction parameters. But and as the results obtained from the latter case were found to be far from acceptable, which is expected due to the fact that the binary systems are comprised of vastly different components, no attempt is made here to tabulate those results. Calc.  xi Exp. 100 N xi AARD (%)   x Exp. N i 1 i

(8)

Table 5 – Binary interaction parameter correlation parameters, alongside average absolute relative deviation values for the Sanchez–Lacombe equation of state.

=

System A R14 + [Hmim][Tf2N] 6.258×10-07 R-23 + [Emim][TFSI] 0 R-23 + [Bmim][PF6] -3.476×10-06 R-41 + [Bmim][PF6] -7.562×10-07 R-50 + [Bmim][Tf2N] 3.633×10-07 R-50 + [Bmim][CH3SO4] 0 R-50 + [Hmim][Tf2N] 6.392×10-07 R-50 + [Emim][EtSO4] 0 R-124 + [Emim][TFSI] -3.214×10-06 R-125 + [Bmim][PF6] 0 R-125 + [Emim][TFSI] 0 R-E125 + [Emim][TFSI] 0 R-134 + [Emim][TFSI] 0 R-134 + [Bmim][PF6] 0 R-161 + [Bmim][PF6] 0 R-290 + [Bmim][NO3] -5.000×10-05 R-290 + [Bmim][Tf2N] 0 R-290 + [Hmim][BF4] 0 R-290 + [Omim][BF4] 0 R-290 + [Emim][BF4] 3.000×10-05 R-290 + [Hmim][Tf2N] 0 R-134a + [Emim][TFSI] 3.200×10-06 R-134a + [Hmim][Tf2N] -4.000×10-06 R-134a + [Hmim][BF4] 1.200×10-05 R-134a + [Hmim][PF6] -4.000×10-06

+

B -4.672×10-04 3.195×10-04 2.666×10-03 5.084×10-04 -2.543×10-04 -4.248×10-04 -8.818×10-04 1.208×10-02 2.128×10-03 4.003×10-04 2.143×10-04 1.591×10-04 6.006×10-04 5.595×10-04 7.994×10-05 3.070×10-02 6.000×10-04 6.000×10-04 2.000×10-04 -1.648×10-02 0 -1.948×10-03 2.485×10-03 -7.456×10-03 2.485×10-03

+ C 2.142×10-01 -1.042×10-01 -4.939×10-01 -8.432×10-02 1.105×10-01 8.904×10-02 1.534×10-01 -3.410 -3.056×10-01 -1.054×10-01 -4.885×10-02 -2.507×10-02 -2.327×10-01 -2.291×10-01 -1.450×10-02 -4.603 -8.280×10-02 -8.980×10-02 4.373×10-02 2.349 9.500×10-02 3.234×10-01 -3.504×10-01 1.181 -3.604×10-01 Average

%AARD 1.184 5.492 8.282 5.711 2.269 2.159 9.313 13.807 15.146 10.668 4.091 6.264 4.661 8.569 6.424 1.497 3.497 3.133 3.243 7.255 3.450 4.020 4.591 5.587 4.011 5.773

Table 6 - Binary interaction parameter correlation parameters, alongside average absolute relative deviation values for the ε*-modified Sanchez–Lacombe equation of state.

=

System R14 + [Hmim][Tf2N]

A 8.048×10-07

+

B -1.326×10-03 13

+ C 1.807×10-01

%AARD 1.475

0 0 0 0 0 0 0 0 0 0 0 2.817×10-06 0 0 0 0 0 0 0 0 4.000×10-06 0 0 -1.600×10-06

-7.987×10-05 1.812×10-05 -9.999×10-05 -8.948×10-04 -9.097×10-04 -9.201×10-04 6.711×10-03 -1.200×10-04 -1.003×10-03 -8.368×10-04 -1.204×10-03 -2.512×10-03 -7.755×10-04 -9.729×10-04 -6.500×10-04 -6.500×10-04 -3.000×10-04 -6.500×10-04 4.300×10-19 0 -3.485×10-03 -1.128×10-03 -8.000×10-04 2.741×10-04

-1.622×10-01 -1.769×10-01 2.256×10-02 2.438×10-02 6.126×10-02 2.751×10-02 -2.083 3.177×10-02 2.498×10-02 -4.424×10-02 -1.194×10-01 1.879×10-01 -6.966×10-02 1.477×10-01 -1.570×10-01 -7.030×10-02 -1.267×10-03 1.937×10-02 -1.650×10-01 -1.990×10-01 4.435×10-01 3.531×10-02 3.852×10-02 -1.015×10-01 Average

P (MPa)

R-23 + [Emim][TFSI] R-23 + [Bmim][PF6] R-41 + [Bmim][PF6] R-50 + [Bmim][Tf2N] R-50 + [Bmim][CH3SO4] R-50 + [Hmim][Tf2N] R-50 + [Emim][EtSO4] R-124 + [Emim][TFSI] R-125 + [Bmim][PF6] R-125 + [Emim][TFSI] R-E125 + [Emim][TFSI] R-134 + [Emim][TFSI] R-134 + [Bmim][PF6] R-161 + [Bmim][PF6] R-290 + [Bmim][NO3] R-290 + [Bmim][Tf2N] R-290 + [Hmim][BF4] R-290 + [Omim][BF4] R-290 + [Emim][BF4] R-290 + [Hmim][Tf2N] R-134a + [Emim][TFSI] R-134a + [Hmim][Tf2N] R-134a + [Hmim][BF4] R-134a + [Hmim][PF6]

(a)

(b)

14

5.258 7.787 5.999 3.06 2.707 9.738 12.798 11.557 14.278 6.363 5.16 3.337 6.172 7.014 4.863 3.788 2.795 3.307 6.708 3.278 3.954 3.56 6.108 3.211 5.771

(c)

(d)

(e)

(f)

Fig. 1. Solubility of IL/refrigerant systems: (a), ‘R14 + [Hmim][Tf2N]’; (b), 'R-23 + [Emim][TFSI]'; (c), 'R-41 + [Bmim][PF6]'; (d), 'R-125 + [Emim][TFSI]'; (e), 'R-290 + [Bmim][Tf2N]'; (f), 'R-290 + [Omim][BF4]'. (Legend: SL; ε*-modified SL; Also, symbols denote experimental data.)

From Tables 5 and 6 it can be seen that both of the equations of state are able to correlate the solubility data to within about 5.7% AARD deviation. In other words, by using only a single temperature-dependent fitting parameter, the AARD values for both EOSs are comparable. Nonetheless, considering all of the IL/refrigerant systems studied, the ε*-Modified SanchezLacombe equation of state generally shows moderately improved performance in representing the solubility data in comparison with the original Sanchez-Lacombe equation of state. In addition, Fig. 1 illustrates the P-T-x diagram for six of the binary IL/refrigerant mixtures studied. The generally comparable accuracy of both of the EOSs can also be inferred from these plots; nonetheless, both of the equations of state demonstrate higher precision in representing the solubility data at elevated temperatures. This trend can be seen more conspicuously in Fig. 2 where the average %AARD of all the experimental isotherms have

15

been plotted versus temperature. Essentially, as can be seen from Tables 5 and 6, in both of the equations of state the kijs generally get farther away from zero with increasing temperature. In the original Sanchez-Lacombe EOS where the kijs are generally positive, they tend to go towards +1 for higher temperatures. The exact opposite can generally be observed for the ε*modified Sanchez–Lacombe EOS, where the kij values are usually negative and go towards 1 for higher temperatures.

(a) (b) Fig. 2 – Average %AARD of isotherms vs. temperature: (a), Sanchez-Lacombe EOS; (b), ε*-modified Sanchez–Lacombe EOS

Also, in order to ascertain how the Sanchez-Lacombe and ε*-Modified Sanchez– Lacombe equations of state perform in comparison with other EOSs, Table 7 presents the average absolute relative deviations between calculated and experimental solubility data for eleven isotherms of the binary mixtures of R-134 and four different ionic liquids, obtained for PR-vdW2, SL and ε*-Modified SL equations of state. As can be seen, overall the ε*-Modified Sanchez–Lacombe equation of state shows higher accuracy than the other two EOSs. Also, one has to keep in mind the fact that as its name suggests, the van der Waals 2-parameter mixing rule (vdW-2) employs two fitted binary interaction parameters for representing the solubility data, in contrast with the combining rule used in this study which contains only one binary interaction parameter.

16

Table 7. Comparative study of the AARDs% of three EOSs in representing the solubility data of R-134a + IL binary mixtures.

System: R-134a + ILs

T (K)

N.D.

AARD% a

SLb 4.64 3.82 3.67

ε*-modified SLb 5.39 3.29 3.3

[Emim][TFSI]

298.15 323.15 348.15

14 14 17

PR-vdW2 7.41 3.95 3.11

[Hmim][Tf2N]

298.15 323.15 348.15

10 14 5

6.75 3.37 0.39

4.79 4.62 4.1

5.61 2.96 1.12

298.15 323.15

5 7

5.30 5.36

4.88 5.26

5.39 6.17

298.15 323.15 348.15

6 10 5 Average

2.74 5.97 2.05 4.22

4.64 3.87 3.51 4.35

3.72 3.56 1.89 3.85

[Hmim][BF4]

[Hmim][PF6]

a. [4] b. This study

4. Conclusions As demonstrated in this study, the solubilities of refrigerant gases in ionic liquids could conveniently be modeled, with acceptable accuracy, with the aid of both Sanchez-Lacombe and ε*-Modified Sanchez–Lacombe equations of state; using only one adjusted, temperaturedependent binary interaction parameter for each IL/refrigerant system. Hence, with relatively simple mathematical formulation and acceptable accuracy, both equations of state could readily be employed to model refrigerant-ionic liquid phase equilibria; and the insights gained could be used to develop and optimize absorption refrigeration processes which take advantage of the flexibility that the ionic liquids impart to the refrigeration process. Also, it was shown that although comparable in representing the solubility data of refrigerants in ionic liquids, with ε*-modified Sanchez–Lacombe EOS being moderately more accurate than the original Sanchez–Lacombe EOS, the former exhibits markedly improved performance in correlating the liquid density data of ionic liquids.

17

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