Development of group-contribution equation of state and theoretical prediction of thermodynamic model parameters

doi:10.11949/0438-1157.20191149

Abstract

Abstract:

Thermodynamic model is an important tool to study fluid phase behaviour and thermodynamic properties.The effective application of theoretical model is inseparable from the determination of model parameters. To endow the prediction function of the thermodynamic model, the current strategy is to establish the group contribution(GC) equation of state(EOS), and to explore the theoretical prediction method of the parameters of the thermodynamic model. Based on the previously developed equations of state for square-well chain fluids with variable well-width range(GC-SWCF-VR ), the group contribution equations of state for square-well chain fluids(GC-SWCF) were established, and the contribution values of different groups to model parameters were obtained by using group contribution method. It was proved that the density of pure substences can be predicted satisfactorily by GC-SWCF. Combining conductor-like screening model(COSMO) with SWCF, the model parameters of SWCF equation for 192 organic compounds were obtained based on COSMO method, which is a theoretical method to determine model parameters without relying on experimental data. It is found that COSMO+SWCF can predict the density of pure substences. Using one temperature-independent binary interaction adjustable parameter, both GC-SWCF and COSMO+SWCF can be applied to the calculation of densities and vapor-liquid equilibrium for binary mixture.

Key words: thermodynamics, group-contribution, equation of state, model, parameter

摘要：

热力学模型是研究流体相行为和热力学性质的重要工具。理论模型的有效应用离不开模型参数的确定。为赋予热力学模型的预测功能，目前的策略一是建立基团贡献(GC)状态方程(EOS)，二是探索热力学模型参数的理论预测方法。围绕先前开发的变阱宽方阱链流体状态方程(SWCF-VR)，采用基团贡献法思路获得了不同基团对模型参数的贡献值，建立了GC-SWCF方程，证实GC-SWCF方程能满意预测纯物质的密度。进一步将似导体屏蔽模型(COSMO)与SWCF结合，基于COSMO方法获得了192种有机化合物的SWCF方程的模型参数，这是一种不依赖实验数据确定模型参数的理论方法。发现COSMO+SWCF能较好地预测纯物质的密度。引入一个与温度无关的二元交互作用可调参数后，GC-SWCF与COSMO+SWCF都可应用于二元混合物密度与气液相平衡的计算中。

关键词: 热力学, 基团贡献, 状态方程, 模型, 参数

CLC Number:

TQ 013.1

Shaoguang QU, Changhao WANG, Yunhai SHI, Changjun PENG, Honglai LIU, Ying HU. Development of group-contribution equation of state and theoretical prediction of thermodynamic model parameters[J]. CIESC Journal, 2020, 71(1): 200-208.

屈绍广, 王昶昊, 施云海, 彭昌军, 刘洪来, 胡英. 基团贡献状态方程的开发与热力学模型参数的理论预测[J]. 化工学报, 2020, 71(1): 200-208.

Figures/Tables 8

References 49

1	张锁江, 韩世钧 . 电解质活度系数与溶剂化数[J]. 化工学报, 1994, 45(3): 293-297.
	Zhang S J , Han S J . Electrolytic activity coefficient and solvated number[J]. Journal of Chemical Industry and Engineering(China), 1994, 45(3): 293-297.
2	蒋文华, 刘华, 韩世钧 . 双流体配位状态方程在共聚物及共混物体系中的应用[J]. 化工学报, 1997, 48(5): 540-546.
	Jiang W H , Liu H , Han S J . New Equation of state and pVT relationships for copolymers and blends[J]. Journal of Chemical Industry and Engineering(China), 1997, 48(5): 540-546.
3	Xuan A , Wu Y , Peng C , et al . Correlation of the viscosity of pure liquids at high pressures based on an equation of state[J]. Fluid Phase Equilibria, 2006, 240(1): 15-21.
4	Li J , Ma J , Peng C , et al . Equation of state coupled with scaled particle theory for surface tensions of liquid mixtures[J]. Industrial & Engineering Chemistry Research, 2007, 46(22): 7267-7274.
5	许映杰, 王从敏, 李浩然, 等 . 用双液理论局部组成模型关联缔合体系核磁共振化学位移[J]. 化工学报, 2006, 57(9): 2021-2026.
	Xu Y J , Wang C M , Li H R , et al . Correlation of ¹H NMR chemical shift for associated systems by local composition model and two-liquid theory[J]. Journal of Chemical Industry and Engineering(China), 2006, 57(9): 2021-2026.
6	Huang S H , Radosz M . Equation of state for small, large, polydisperse, and associating molecules: extension to fluid mixtures[J]. Industrial & Engineering Chemistry Research, 1991, 30(8): 1994-2005.
7	Gross J , Sadowski G . Application of perturbation theory to a hard-chain reference fluid: an equation of state for square-well chains[J]. Fluid Phase Equilibria, 2000, 168(2): 183-199.
8	Felipe J . Thermodynamic behaviour of homonuclear and heteronuclear Lennard-Jones chains with association sites from simulation and theory[J]. Molecular Physics, 1997, 92(1): 135-150.
9	Karakatsani E K , Spyriouni T , Economou I G . Extended statistical associating fluid theory (SAFT) equations of state for dipolar fluids[J]. AIChE Journal, 2005, 51(8): 2328-2342.
10	Kroon M C , Karakatsani E K , Economou I G , et al . Modeling of the carbon dioxide solubility in imidazolium-based ionic liquids with the tPC-PSAFT equation of state[J]. The Journal of Physical Chemistry B, 2006, 110(18): 9262-9269.
11	Gil-Villegas A , Galindo A , Whitehead P J , et al . Statistical associating fluid theory for chain molecules with attractive potentials of variable range[J]. The Journal of Chemical Physics, 1997, 106(10): 4168-4186.
12	Li J , He H , Peng C , et al . A new development of equation of state for square-well chain-like molecules with variable width 1.1≤ λ≤ 3[J]. Fluid Phase Equilibria, 2009, 276(1): 57-68.
13	Tamouza S , Passarello J P , Tobaly P , et al . Application to binary mixtures of a group contribution SAFT EOS(GC-SAFT)[J]. Fluid Phase Equilibria, 2005, 228: 409-419.
14	Tihic A , Kontogeorgis G M , von Solms N , et al . A predictive group-contribution simplified PC-SAFT equation of state: application to polymer systems[J]. Industrial & Engineering Chemistry Research, 2007, 47(15): 5092-5101.
15	Rozmus J , de Hemptinne J C , Mougin P . Application of GC-PPC-SAFT EoS to amine mixtures with a predictive approach[J]. Fluid Phase Equilibria, 2011, 303(1): 15-30.
16	Zeng Z Y , Xu Y Y , Hao X , et al . Application of the simplified perturbed-chain SAFT to hydrocarbon systems with new group-contribution parameters[J]. Industrial & Engineering Chemistry Research, 2009, 48(12): 5867-5873.
17	Hu Y , Liu H , Prausnitz J M . Equation of state for fluids containing chainlike molecules[J]. The Journal of Chemical Physics, 1996, 104(1): 396-404.
18	Liu H , Hu Y . Molecular thermodynamic theory for polymer systems(Ⅱ): Equation of state for chain fluids[J]. Fluid Phase Equilibria, 1996, 122(1/2): 75-97.
19	Liu H , Hu Y . Molecular thermodynamic theory for polymer systems(Ⅲ): Equation of state for chain-fluid mixtures[J]. Fluid Phase Equilibria, 1997, 138(1/2): 69-85.
20	Liu H L , Zhou H , Hu Y . Molecular thermodynamic model for fluids containing associated molecules[J]. CJChE, 1977, (3): 20-30.
21	Li J , He H , Peng C , et al . Equation of state for square-well chain molecules with variable range(I): Application for pure substances[J]. Fluid Phase Equilibria, 2009, 286(1): 8-16.
22	何清, 李进龙, 何昌春, 等 . 状态方程模拟醇胺系统的密度和气液相平衡[J]. 化工学报, 2010, 61(4): 812-819.
	He Q , Li J L , He C C , et al . Modeling of density and vapor-liquid equilibrium for alcohol-amine systems with equation of state[J]. CIESC Journal, 2010, 61(4): 812-819.
23	李进龙, 彭昌军, 刘洪来 . 变阱宽方阱链流体状态方程模拟制冷剂的汽液平衡[J]. 化工学报, 2009, 60(3): 545-552.
	Li J L , Peng C J , Liu H L . Modeling vapor-liquid equilibrium of refrigerants using an equation of state for square-well chain fluid with variable range[J]. CIESC Journal, 2009, 60(3): 545-552.
24	Tamouza S , Passarello J P , Tobaly P , et al . Group contribution method with SAFT EOS applied to vapor liquid equilibria of various hydrocarbon series[J]. Fluid Phase Equilibria, 2004, 222: 67-76.
25	Mattedi S , Tavares F W , Castier M . Group contribution equation of state based on the lattice fluid theory: alkane-alkanol systems[J]. Fluid Phase Equilibria, 1998, 142(1): 33-54.
26	Reamer H H , Sage B H . Phase equilibria in hydrocarbon systems. Volumetric and phase behavior of the propane-n-decane system[J]. Journal of Chemical and Engineering Data, 1966, 11(1): 17-24.
27	Orge B , Iglesias M , Rodriguez A , et al . Mixing properties of (methanol, ethanol, or 1-propanol) with (n-pentane, n-hexane, n-heptane and n-octane) at 298.15 K[J]. Fluid Phase Equilibria, 1997, 133(1): 213-227.
28	Hirata M , Ohe S , Naga K . Computer Aided Data Book of Vapor-Liquid Equilibria [M]. Tokyo: Kodansha Limited Elsevie, 1975.
29	Peng Y , Goff K D , dos Ramos M C , et al . Developing a predictive group-contribution-based SAFT-VR equation of state[J]. Fluid Phase Equilibria, 2009, 277(2): 131-144.
30	Dos Ramos M C , Haley J D , Westwood J R , et al . Extending the GC-SAFT-VR approach to associating functional groups: alcohols, aldehydes, amines and carboxylic acids[J]. Fluid Phase Equilibria, 2011, 306(1): 97-111.
31	Papaioannou V , Adjiman C S , Jackson G , et al . Simultaneous prediction of vapour-liquid and liquid-liquid equilibria (VLE and LLE) of aqueous mixtures with the SAFT-γ group contribution approach[J]. Fluid Phase Equilibria, 2011, 306(1): 82-96.
32	Kim Y S , Jang J H , Lim B D , et al . Solubility of mixed gases containing carbon dioxide in ionic liquids: measurements and predictions[J]. Fluid Phase Equilibria, 2007, 256(1-2): 70-74.
33	Nguyen-Huynh D , Tran T K S , Tamouza S , et al . Modeling phase equilibria of asymmetric mixtures using a group-contribution SAFT (GC-SAFT) with a k_ij correlation method based on London’s theory（2）： Application to binary mixtures containing aromatic hydrocarbons, n-Alkanes, CO₂, N₂, and H₂S[J]. Industrial & Engineering Chemistry Research, 2008, 47(22): 8859-8868.
34	Tran T K S , NguyenHuynh D , Ferrando N , et al . Modeling VLE of H₂+ hydrocarbon mixtures using a group contribution SAFT with a k_ij correlation method based on London’s Theory[J]. Energy & Fuels, 2009, 23(5): 2658-2665.
35	Mourah M , NguyenHuynh D , Passarello J P , et al . Modelling LLE and VLE of methanol+ n-alkane series using GC-PC-SAFT with a group contribution kij[J]. Fluid Phase Equilibria, 2010, 298(1): 154-168.
36	Breure B , Bottini S B , Witkamp G J , et al . Thermodynamic modeling of the phase behavior of binary systems of ionic liquids and carbon dioxide with the group contribution equation of state[J]. The Journal of Physical Chemistry B, 2007, 111(51): 14265-14270.
37	Neau E , Escandell J , Nicolas C . Modeling of highly nonideal systems: 2. Prediction of high pressure phase equilibria with the group contribution NRTL-PR EoS[J]. Industrial & Engineering Chemistry Research, 2010, 49(16): 7589-7596.
38	Escandell J , Neau E , Nicolas C . A new formulation of the predictive NRTL-PR model in terms of k_ij mixing rules. Extension of the group contributions for the modeling of hydrocarbons in the presence of associating compounds[J]. Fluid Phase Equilibria, 2011, 301(1): 80-97.
39	Hsieh C M , Lin S T . Determination of cubic equation of state parameters for pure fluids from first principle solvation calculations[J]. AIChE Journal, 2008, 54(8): 2174-2181.
40	Panayiotou C . Toward a COSMO equation-of-state model of fluids and their mixtures[J]. Pure and Applied Chemistry, 2011, 83(6):1221-1242.
41	Hsieh C M , Lin S T . First-principles prediction of vapor-liquid-liquid equilibrium from the PR+ COSMOSAC equation of state[J]. Industrial & Engineering Chemistry Research, 2010, 50(3): 1496-1503.
42	Oh S Y , Bae Y C . Phase equilibrium calculations of ternary liquid mixtures with binary interaction parameters and molecular size parameters determined from molecular dynamics[J]. The Journal of Physical Chemistry B, 2010, 114(27): 8948-8953.
43	Oh S Y , Bae Y C . Understanding liquid mixture phase miscibility via pair energy parameter behaviors with respect to temperatures determined from molecular simulations[J]. The Journal of Physical Chemistry B, 2011, 115(19): 6051-6060.
44	Abbott M M , Prausnitz J M . Generalized van der Waals theory: a classical perspective[J]. Fluid Phase Equilibria, 1987, 37: 29-62.
45	Lin S T , Hsieh C M , Lee M T . Solvation and chemical engineering thermodynamics[J]. Journal of the Chinese Institute of Chemical Engineers, 2007, 38(5/6): 467-476.
46	屈绍广 . 方阱链流体状态方程的应用及其模型参数的理论预测[D]. 上海: 华东理工大学, 2015.
	Qu S G . Application of equation of state for square well chain fluid and theoretical prediction of model parameters[D]. Shanghai: East China University of Science and Technology, 2015.
47	Smith B D , Srivastava R . Thermodynamic Data for Pure Compounds: Part A Hydrocarbons and Ketones[M]. Netherland: Elsevier, 1986.
48	Voutsas E C , Pappa G D , Magoulas K , et al . Vapor liquid equilibrium modeling of alkane systems with Equations of State: "simplicity versus complexity"[J]. Fluid Phase Equilibria, 2006, 240(2): 127-139.
49	Calvar N , Gomez E , Gonzalez B , et al . Experimental densities, refractive indices, and speeds of sound of 12 binary mixtures containing alkanes and aromatic compounds at T = 313.15 K[J]. Journal of Chemical Thermodynamics, 2009, 41(8): 939-944.

Group	r	σ ³/(ml/mol)	(ε/k)/K
—CH₂—	0.177	0.060	10.697
—CH₃	0.560	1.754	139.214
—OH	0.337	1.738	233.906
CH₂ CH—	0.675	1.939	187.548
—CO—	0.202	0.178	118.739
—Cl	0.616	1.701	178.289
—Br	0.354	1.961	201.728
—I	0.706	1.806	219.982

Group	r	σ ³/(ml/mol)	(ε/k)/K
—CH₂—	0.177	0.060	10.697
—CH₃	0.560	1.754	139.214
—OH	0.337	1.738	233.906
CH₂ CH—	0.675	1.939	187.548
—CO—	0.202	0.178	118.739
—Cl	0.616	1.701	178.289
—Br	0.354	1.961	201.728
—I	0.706	1.806	219.982

Binary system	T/K	p/MPa	?p(?T)/%	?y/%	k_kl	?y/%(k_kl =0)
C₃H₈-C₅H₁₂	344.25	0.4～2.4	1.78	2.68	0.02323	4.14
	360.95	0.5～3.4	1.91	1.81		2.90
	377.55	0.7～4.1	1.91	1.18		2.39
	394.25	1.0～4.5	1.52	1.96		2.84
C₃H₈-C₁₀H₂₂	344.25	0.3～2.1	2.38	0.16	0.02858	0.28
C₄H₁₀-C₇H₁₆	339～430	0.69	(2.32)	4.00	-0.01939	2.46
C₆H₁₄-C₂H₅OH	332～338	0.1	(1.36)	3.76	0.05355	12.40
	263.15	0.002～0.004	9.56	2.55		8.09
	303.15	0.014～0.016	7.33	5.18		15.66
	308.15	0.03～0.04	1.33	3.83		12.04
	318.15	0.46～0.6	5.26	4.36		11.53
C₆H₁₄-C₃H₇OH	338.15	0.04～0.1	2.43	2.18	0.04249	8.57
C₆H₁₄-C₃H₇OH	348.15	0.04～0.12	2.15	1.92	0.04249	9.37
C₆H₁₄-C₇H₁₆	303.15	0.01～0.02	1.92	1.20	-0.00703	1.59
C₆H₁₄-C₇H₁₆	323.15	0.02～0.05	2.52	0.84	-0.00703	0.93
C₃H₇OH-C₇H₁₆	298.15	0.009～0.01	2.93	3.49	0.05215	12.62
C₄H₉OH-C₅H₁₂	303.15	0.005～0.08	5.50	0.15	0.02251	2.63
C₄H₉OH-C₆H₁₄	323.15	0.02～0.05	3.81	0.62	0.02604	1.79
C₅H₁₁OH-C₅H₁₂	303.15	0.003～0.08	4.30	0.26	0.01965	1.49
C₅H₁₁OH-C₆H₁₄	303.15	0.001～0.02	2.59	0.70	0.02191	4.44
C₅H₁₁OH-C₆H₁₄	323.15	0.003～0.05	2.43	0.60	0.02191	3.82
C₈H₁₇OH-C₆H₁₄	313.15	0.008～0.04	0.47	0.02	0.017661	0.05

Binary system	T/K	p/MPa	?p(?T)/%	?y/%	k_kl	?y/%(k_kl =0)
C₃H₈-C₅H₁₂	344.25	0.4～2.4	1.78	2.68	0.02323	4.14
	360.95	0.5～3.4	1.91	1.81		2.90
	377.55	0.7～4.1	1.91	1.18		2.39
	394.25	1.0～4.5	1.52	1.96		2.84
C₃H₈-C₁₀H₂₂	344.25	0.3～2.1	2.38	0.16	0.02858	0.28
C₄H₁₀-C₇H₁₆	339～430	0.69	(2.32)	4.00	-0.01939	2.46
C₆H₁₄-C₂H₅OH	332～338	0.1	(1.36)	3.76	0.05355	12.40
	263.15	0.002～0.004	9.56	2.55		8.09
	303.15	0.014～0.016	7.33	5.18		15.66
	308.15	0.03～0.04	1.33	3.83		12.04
	318.15	0.46～0.6	5.26	4.36		11.53
C₆H₁₄-C₃H₇OH	338.15	0.04～0.1	2.43	2.18	0.04249	8.57
C₆H₁₄-C₃H₇OH	348.15	0.04～0.12	2.15	1.92	0.04249	9.37
C₆H₁₄-C₇H₁₆	303.15	0.01～0.02	1.92	1.20	-0.00703	1.59
C₆H₁₄-C₇H₁₆	323.15	0.02～0.05	2.52	0.84	-0.00703	0.93
C₃H₇OH-C₇H₁₆	298.15	0.009～0.01	2.93	3.49	0.05215	12.62
C₄H₉OH-C₅H₁₂	303.15	0.005～0.08	5.50	0.15	0.02251	2.63
C₄H₉OH-C₆H₁₄	323.15	0.02～0.05	3.81	0.62	0.02604	1.79
C₅H₁₁OH-C₅H₁₂	303.15	0.003～0.08	4.30	0.26	0.01965	1.49
C₅H₁₁OH-C₆H₁₄	303.15	0.001～0.02	2.59	0.70	0.02191	4.44
C₅H₁₁OH-C₆H₁₄	323.15	0.003～0.05	2.43	0.60	0.02191	3.82
C₈H₁₇OH-C₆H₁₄	313.15	0.008～0.04	0.47	0.02	0.017661	0.05

System(1) + (2)	T/K	p/MPa	k_kl	?T(?p)^①/%	?y ₁/%
n-butane + n-heptane	339.25～430.35	0.68	-0.0219	2.47	3.91
cyclopentane + benzene	322.75～352.85	0.1013	-0.0358	2.34	2.16
cyclohexane + benzene	350.64～353.34	0.1013	-0.0221	1.64	0.29
n-propane + benzene	344.25	0.136～2.38	0.1423	(0.24)	2.8
methanol + acetic acid	336.15～388.95	0.0941	-0.0021	0.29	5.07
methanol + n-heptane	331.96～333.75	0.1013	0.1042	6.64	5.31
methanol + cyclohexane	327.46～332.81	0.1013	0.0924	5.45	5.14
methanol + n-propanol	349.15～365.95	0.1013	0.0279	2.73	4.48
bromoethane + benzene	318.25～348.01	0.1013	0.0523	3.65	2.65
n-octane +ethylbenzene	323.15～408.25	0.00667～0.1013	0.095	0.71	1.88
n-heptane + benzene	326.15～368.65	0.03168～0.1013	-0.0665	2.18(0.7)	1.75
n-octane + benzene	328.15～380.25	0.01688～0.1013	-0.2012	0.56(0.62)	1.53