C6~C10烷醇的SAFT-VR Mie状态方程参数回归及其热物性研究

doi:10.11949/0438-1157.20221438

摘要/Abstract

摘要：

统计缔合流体理论(SAFT)状态方程对长链烷醇的热物性研究具有重要意义，而状态方程参数的获取是流体热物性研究的基础。基于SAFT-VR Mie状态方程，采用Levenberg-Marquardt算法并结合相平衡、过冷液相密度和声速性质的参数回归策略，获取C₆~C₁₀烷醇的状态方程模型参数。进一步评估SAFT-VR Mie状态方程对C₆~C₁₀烷醇在宽温度和压力范围内的相平衡和热力学偏导特性的预测性能，并与PC-SAFT状态方程进行比较。结果表明，SAFT-VR Mie对五种烷醇整体具有更优的饱和蒸气压、饱和液相密度、蒸发焓、过冷液相密度、比定压热容和声速预测性能，平均预测偏差分别为0.74%、0.82%、3.02%、0.54%、2.88%和2.31%。同时，SAFT-VR Mie具有可靠的外推预测能力，其对高压声速的预测结果与实验数据具有较好的一致性。此外，SAFT-VR Mie对压力-密度导数的不合理描述是造成声速预测偏差的主要原因。改进分子间单体和缔合相互作用能够有效提高比热容的预测精度，为长链烷醇缔合流体的热物性预测提供更好的理论关联模型。

关键词: 醇, 状态方程, 热力学性质, 统计缔合流体理论, 统计热力学, 参数估值, 缔合流体

Abstract:

The statistical associating fluid theory (SAFT) equation of state (EoS) is of great significance for the thermodynamic properties study of long-chain alcohols. The acquisition of SAFT-type EoS parameters is the basis for the thermodynamic properties study of fluids. The SAFT-VR Mie EoS parameters for C₆—C₁₀ alcohols were obtained by using a parametric regression strategy based on the Levenberg-Marquardt algorithm and combining phase equilibrium, condensed-liquid density, and speed of sound properties. The predictive performance of SAFT-VR Mie EoS based on the new parameters for phase equilibrium and thermodynamic derivative properties over a wide temperature and pressure range was further evaluated. The results show that SAFT-VR Mie EoS exhibits excellent prediction performance of saturated vapor pressure, saturated liquid phase density, enthalpy of vaporization, condensed-liquid density, isobaric specific heat capacity, and speed of sound for C₆—C₁₀ alcohols with average prediction deviations of 0.74%, 0.82%, 3.02%, 0.54%, 2.88%, and 2.31%, respectively. Meanwhile, SAFT-VR Mie EoS provides reliable extrapolation prediction capability, and its prediction results of speed of sound for high pressure show satisfactory agreement with experimental data. In addition, the unreasonable description of the pressure-density derivative by SAFT-VR Mie EoS is the primary reason for the deviations of speed of sound predictions. Improving the intermolecular monomer and association interactions can effectively improve the prediction accuracy of specific heat capacity, and provide a better theoretical correlation model for the prediction of thermodynamic properties of long-chain alcohols associating fluids.

Key words: alcohol, equation of state, thermodynamic properties, statistical associating fluid theory, statistical thermodynamics, parameter estimation, associating fluid

中图分类号:

TQ 013.1

毛元敬, 杨智, 莫松平, 郭浩, 陈颖, 罗向龙, 陈健勇, 梁颖宗. C₆~C₁₀烷醇的SAFT-VR Mie状态方程参数回归及其热物性研究[J]. 化工学报, 2023, 74(3): 1033-1041.

Yuanjing MAO, Zhi YANG, Songping MO, Hao GUO, Ying CHEN, Xianglong LUO, Jianyong CHEN, Yingzong LIANG. Estimation of SAFT-VR Mie equation of state parameters and thermodynamic properties of C₆—C₁₀ alcohols[J]. CIESC Journal, 2023, 74(3): 1033-1041.

图/表 10

图1 SAFT-VR Mie状态方程分子构型和参数回归流程示意图

Fig.1 Schematic diagram of the molecular configuration and parameter regression procedure of SAFT-VR Mie equation of state (EoS)

表1 C6~C10烷醇SAFT-VR Mie状态方程参数回归及热物性预测结果

Table 1 Results of SAFT-VR Mie EoS parameter regression and thermodynamic properties prediction for C6—C10 alcohols

Substances	m	σ/Å^①	(ε/k)/K	r $c A B$ /σ	(ε^AB/k)/K	λ_r	AARD/%
Substances	m	σ/Å^①	(ε/k)/K	r $c A B$ /σ	(ε^AB/k)/K	λ_r	P_s	ρ_s	ΔH_vap	ρ_l	c_P	u
1-hexanol (C₆)	2.4364	4.2407	315.79	0.28852	3102.4	11.9366	0.81	1.06	1.64	0.23	1.60	2.09
1-heptanol (C₇)	2.4415	4.4413	336.05	0.26707	3404.3	12.2372	0.81	0.73	3.11	0.57	2.00	2.12
1-octanol (C₈)	2.7639	4.4240	342.37	0.29096	3180.6	12.9708	0.67	0.61	3.21	0.64	3.17	3.61
1-nonanol (C₉)	2.9172	4.4871	358.14	0.26918	3398.7	13.3660	0.57	1.05	3.84	0.48	2.12	1.77
1-decanol (C₁₀)	2.4778	4.9442	409.06	0.28053	3457.4	14.3970	0.83	0.66	3.29	0.77	5.51	1.98
average	—	—	—	—	—	—	0.74	0.82	3.02	0.54	2.88	2.31

表1 C6~C10烷醇SAFT-VR Mie状态方程参数回归及热物性预测结果

Table 1 Results of SAFT-VR Mie EoS parameter regression and thermodynamic properties prediction for C6—C10 alcohols

Substances	m	σ/Å^①	(ε/k)/K	r $c A B$ /σ	(ε^AB/k)/K	λ_r	AARD/%
Substances	m	σ/Å^①	(ε/k)/K	r $c A B$ /σ	(ε^AB/k)/K	λ_r	P_s	ρ_s	ΔH_vap	ρ_l	c_P	u
1-hexanol (C₆)	2.4364	4.2407	315.79	0.28852	3102.4	11.9366	0.81	1.06	1.64	0.23	1.60	2.09
1-heptanol (C₇)	2.4415	4.4413	336.05	0.26707	3404.3	12.2372	0.81	0.73	3.11	0.57	2.00	2.12
1-octanol (C₈)	2.7639	4.4240	342.37	0.29096	3180.6	12.9708	0.67	0.61	3.21	0.64	3.17	3.61
1-nonanol (C₉)	2.9172	4.4871	358.14	0.26918	3398.7	13.3660	0.57	1.05	3.84	0.48	2.12	1.77
1-decanol (C₁₀)	2.4778	4.9442	409.06	0.28053	3457.4	14.3970	0.83	0.66	3.29	0.77	5.51	1.98
average	—	—	—	—	—	—	0.74	0.82	3.02	0.54	2.88	2.31

表2 热物性实验数据选取的温度和压力范围［7，31-34］

Table 2 The temperature and pressure range selected for the thermodynamic properties experimental data［7，31-34］

Substances	Vapor-liquid equilibrium			Compressed liquid phase
	T range/K			T range/K			P range/MPa
	P_s	ρ_s	ΔH_vap	ρ_l	c_P	u	ρ_l	c_P	u
1-hexanol	340—600	340—600	280—560	278—358	325—570	303—393	0.1—60	2—30	0.1—810
1-heptanol	320—620	320—620	280—580	278—358	325—570	303—393	0.1—60	2—30	0.1—810
1-octanol	320—640	320—640	280—630	278—358	325—570	291—433	0.1—60	2—30	0.1—811
1-nonanol	340—640	340—640	300—640	278—358	298—318	303—393	0.1—60	0.1—100	0.1—506
1-decanol	360—660	360—660	300—660	288—358	325—570	303—393	0.1—60	2—30	0.1—506

图2 SAFT-VR Mie和PC-SAFT状态方程对C6~C10烷醇热物性平均预测偏差比较

Fig.2 Comparison of the deviations of SAFT-VR Mie and PC-SAFT EoS for predicting the thermodynamic properties of C6—C10 alcohols

图3 SAFT-VR Mie和PC-SAFT状态方程对正己醇（C6）声速预测结果比较（1 bar=105 Pa）

Fig.3 Comparison of the results of SAFT-VR Mie and PC-SAFT EoS for predicting the speed of sound of 1-hexanol (C6)

图4 SAFT-VR Mie和PC-SAFT状态方程对正辛醇（C8）声速预测结果比较

Fig.4 Comparison of the results of SAFT-VR Mie and PC-SAFT EoS for predicting the speed of sound of 1-octanol (C8)

图5 SAFT-VR Mie和PC-SAFT状态方程对正癸醇（C10）声速预测结果比较

Fig.5 Comparison of the results of SAFT-VR Mie and PC-SAFT EoS for predicting the speed of sound of 1-decanol (C10)

图6 SAFT-VR Mie和PC-SAFT状态方程对正己醇（C6）压力-密度和压力-温度导数预测结果比较

Fig.6 Comparison of the results of SAFT-VR Mie and PC-SAFT EoS for predicting the pressure-density and pressure-temperature derivatives of 1-hexanol (C6)

图7 SAFT-VR Mie和PC-SAFT状态方程对正己醇（C6）剩余比定容热容不同微观贡献预测结果比较

Fig.7 Comparison of different microscopic contributions of SAFT-VR Mie and PC-SAFT EoS for predicting residual isochoric specific heat capacity of 1-hexanol (C6)

图8 SAFT-VR Mie和PC-SAFT状态方程对正己醇（C6）二阶温度导数不同微观贡献预测结果比较

Fig.8 Comparison of different microscopic contributions of SAFT-VR Mie and PC-SAFT EoS for predicting second-order temperature derivative of 1-hexanol (C6)

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C₆~C₁₀烷醇的SAFT-VR Mie状态方程参数回归及其热物性研究

Estimation of SAFT-VR Mie equation of state parameters and thermodynamic properties of C₆—C₁₀ alcohols

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