Review on mixing rules in vapor-liquid equilibrium of mixtures

doi:10.11949/0438-1157.20181508

Abstract

Abstract:

The vapor-liquid phase equilibrium data are the critical thermophysical property in chemistry industry. Since the mixing rules are the key factor to calculate the vapor-liquid equilibrium property of mixtures, they have been studied for more than one hundred years. The representative mixing rules are summarized, including the original quadratic form, non-quadratic type, density type, state equation-excess free energy type and other mixing rules. The ability to describe the vapor-liquid equilibrium in the fluid is evaluated. The mathematical derivation of these mixing rules are given in an understandable way and the motivation of their development and their strengths and weaknesses are analyzed.

Key words: mixing rule, phase equilibrium, vapor-liquid equilibrium, equation of state, activity coefficient model, virial coefficient boundary conditions

摘要：

混合工质汽液相平衡学术内涵丰富且应用广泛，而混合规则是决定混合物性描述准确与否的关键因素。综述了具有代表性的混合规则，包括原始的二次型、非二次型、密度型、状态方程-超额自由能型等混合规则，评价了其在流体汽液相平衡的描述能力，辅以数学推导介绍了其发展的动机及存在的优劣，以期对将来混合规则发展提供思路。

关键词: 混合规则, 相平衡, 汽液平衡, 状态方程, 活度系数模型, 维里系数边界条件

CLC Number:

TK 123

Yanxing ZHAO, Xian WANG, Xiaoyu YAO, Xueqiang DONG, Jun SHEN, Maoqiong GONG. Review on mixing rules in vapor-liquid equilibrium of mixtures[J]. CIESC Journal, 2019, 70(6): 2036-2050.

赵延兴, 王宪, 姚晓宇, 董学强, 沈俊, 公茂琼. 流体汽液相平衡混合规则研究进展[J]. 化工学报, 2019, 70(6): 2036-2050.

Figures/Tables 3

Table 1 Some modified forms based on vdW mixing rule

混合规则	类型	混合规则数学形式
Stryjek-Vera^[35,36]	Margules型	$k i j = x i K i j + x j K j i$
Stryjek-Vera^[35,36]	Van laar型	$k i j = K i j K j i / (x i K i j + x j K j i)$
Panagiotopoulos-Reid^[33]		$k i j = K i j - (K i j - K j i) x i$
Adachi-Sugie^[23,32]		$k i j = L i j - M i j (x i - x j)$
Sandoval等^[34]	GMR2	$k i j = K i j x i + K j i x i + 1 / 2 (K i j + K j i) (1 - x i - x j)$
Sandoval等^[34]	GMR3	$k i j = K i j x i + K j i x i + 1 / 2 (K i j + K j i) (1 - x i - x j) + L i j x i (1 - x i) + x j (1 - x j)$
Schwartzentruber-Renon^[31]		$k i j = K i j + L i j M i j x i - M j i x j M i j x i + M j i x j (x i + x j)$
Schwartzentruber-Renon^[38]		$a N Q = ∑ i ∑ j (x j - x i) x i x j a i a j L i j$
Twu等^[39]		$a N Q = ∑ i x i (∑ j x j a i a j 13 L i j 13 G j i 13) 3 / ∑ j G i j x j$
Mathias等^[40]		$a N Q = ∑ i x i ∑ j x j a i a j 13 L j i 13 3$
Luedecke-Prausnitz^[41]		$a N C = ρ / R T ∑ i ∑ j x i x j (x i L i j + x j L j i)$
Panagiotopoulos ^[42]		$a N C = b / v R T ∑ i ∑ j x i x j (x i L i j + x j L j i)$
Wilczek-Vera^[43]	Margules型	$k i j = (v L / v) (x i K i j + x j K j i)$
Wilczek-Vera^[43]	Van laar型	$k i j = (v L / v) [K i j K j i / (x i K i j + x j K j i)]$

Table 1 Some modified forms based on vdW mixing rule

混合规则	类型	混合规则数学形式
Stryjek-Vera^[35,36]	Margules型	$k i j = x i K i j + x j K j i$
Stryjek-Vera^[35,36]	Van laar型	$k i j = K i j K j i / (x i K i j + x j K j i)$
Panagiotopoulos-Reid^[33]		$k i j = K i j - (K i j - K j i) x i$
Adachi-Sugie^[23,32]		$k i j = L i j - M i j (x i - x j)$
Sandoval等^[34]	GMR2	$k i j = K i j x i + K j i x i + 1 / 2 (K i j + K j i) (1 - x i - x j)$
Sandoval等^[34]	GMR3	$k i j = K i j x i + K j i x i + 1 / 2 (K i j + K j i) (1 - x i - x j) + L i j x i (1 - x i) + x j (1 - x j)$
Schwartzentruber-Renon^[31]		$k i j = K i j + L i j M i j x i - M j i x j M i j x i + M j i x j (x i + x j)$
Schwartzentruber-Renon^[38]		$a N Q = ∑ i ∑ j (x j - x i) x i x j a i a j L i j$
Twu等^[39]		$a N Q = ∑ i x i (∑ j x j a i a j 13 L i j 13 G j i 13) 3 / ∑ j G i j x j$
Mathias等^[40]		$a N Q = ∑ i x i ∑ j x j a i a j 13 L j i 13 3$
Luedecke-Prausnitz^[41]		$a N C = ρ / R T ∑ i ∑ j x i x j (x i L i j + x j L j i)$
Panagiotopoulos ^[42]		$a N C = b / v R T ∑ i ∑ j x i x j (x i L i j + x j L j i)$
Wilczek-Vera^[43]	Margules型	$k i j = (v L / v) (x i K i j + x j K j i)$
Wilczek-Vera^[43]	Van laar型	$k i j = (v L / v) [K i j K j i / (x i K i j + x j K j i)]$

Table 2 TC type mixing rules

分类	混合规则	$a m$	$b m$
无限压力	TC^[74]	$α m = α v d W + 1 C T C A n r E R T$	$b m = b v d W - a v d W R T 1 - α m$
零压参考	TCB^[75]	$α m = α v d W + 1 C T C B A 0 E R T - A 0 v d W E R T - l n b v d W b$	$b m = b v d W - a v d W R T 1 - α m$
常数r替代ε	TCB(r)^[75]	$α m = α v d W + 1 C r A 0 E R T - A 0 v d W E R T - l n b v d W b$	$b m = b v d W - a v d W R T 1 - α m$

Table 2 TC type mixing rules

分类	混合规则	$a m$	$b m$
无限压力	TC^[74]	$α m = α v d W + 1 C T C A n r E R T$	$b m = b v d W - a v d W R T 1 - α m$
零压参考	TCB^[75]	$α m = α v d W + 1 C T C B A 0 E R T - A 0 v d W E R T - l n b v d W b$	$b m = b v d W - a v d W R T 1 - α m$
常数r替代ε	TCB(r)^[75]	$α m = α v d W + 1 C r A 0 E R T - A 0 v d W E R T - l n b v d W b$	$b m = b v d W - a v d W R T 1 - α m$

Table 3 Dimensionless volume of some ACM-EoS models

模型	状态方程	ε=v/b	参考压力
HV^[48]	SRK/PR	1	无限压力
WS^[49]	SRK/PR	1	无限压力
CHV^[62]	SRK/PR	1	无限压力
HVOS^[61]	SRK/PR	1	无限压力
Fischer-Gmehling^[76]	SRK	1.1	无限压力
MHV1^[63]	SRK/PR	1.235/1.228	零压
MHV2^[64]	SRK	1.632	零压
Michelsen^[50]	SRK/PR	1.4~1.8	零压
Novenario ^[77]	PR	1.15	零压
TCB(r) ^[75]	SRK/PR	1.18	零压
VTPR^[78]	PR	1.225	101325 Pa
PSRK^[79]	SRK	1.099	101325 Pa
Noll-Fischer^[80]	SRK	1.189	0.23 MPa
LCVM^[68]	PR	1.164	无参考压力

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