化工学报 ›› 2019, Vol. 70 ›› Issue (9): 3228-3237.doi: 10.11949/0438-1157.20181314

• 热力学 • 上一篇    下一篇

CO2-C2H6共沸物分离的立方型状态方程选取

王海琴1,2(),范明龙2,张足斌1,2()   

  1. 1. 山东省油气储运安全省级重点实验室
    2. 中国石油大学(华东)储运与建筑工程学院, 山东 青岛 266580
  • 收稿日期:2018-11-12 修回日期:2019-05-17 出版日期:2019-09-05 发布日期:2019-06-24
  • 通讯作者: 张足斌 E-mail:whq@upc.edu.cn;zhangzubin_1@163.com
  • 作者简介:王海琴(1969—),女,博士,副教授,whq@upc.edu.cn
  • 基金资助:
    国家自然科学基金项目(51306210)

Selection of cubic equations of state for separation of CO2-C2H6 azeotrope

Haiqin WANG1,2(),Minglong FAN2,Zubin ZHANG1,2()   

  1. 1. Shandong Provincial Key Laboratory of Oil & Gas Storage and Transportation Safety
    2. School of Pipeline and Civil Engineering, China University of Petroleum, Qingdao 266580, Shandong, China
  • Received:2018-11-12 Revised:2019-05-17 Online:2019-09-05 Published:2019-06-24
  • Contact: Zubin ZHANG E-mail:whq@upc.edu.cn;zhangzubin_1@163.com

摘要:

汽液平衡热力学模型的准确选取对CO2-C2H6共沸物分离流程的设计和操作分析至关重要。在汽液平衡实验数据的基础上,依据逸度平衡原则,评估vdW、RK、SRK和PR立方型状态方程结合vdW、Margles和CVD混合规则预测CO2纯物质、CO2-C2H6共沸物和n-C5H12-CO2-C2H6三元体系汽液平衡的可靠性,采用平均绝对误差的方法进行状态方程的选取。结果表明:SRK状态方程计算CO2纯物质汽液平衡性质的精度最高;PR状态方程结合Margles混合规则可以准确计算CO2-C2H6共沸体系汽液平衡特性;对于n-C5H12-CO2-C2H6三元体系,SRK状态方程结合Margles混合规则计算精度明显优于vdW、RK和PR状态方程。通过试差迭代法优化CO2-C2H6共沸体系和n-C5H12-CO2-C2H6三元体系的二元交互作用参数,状态方程的计算精度得到明显提高。

关键词: CO2-C2H6共沸物, 立方型状态方程, 逸度平衡, 混合规则, 二元交互作用参数, 平均绝对误差

Abstract:

Accurate selection of vapor-liquid equilibrium thermodynamic model is essential to the design and operation of CO2-C2H6 azeotrope separation process. On the basis of collected experimental data, the reliabilities of four types of cubic equations of state including vdW, RK, SRK and PR combined with vdW, Margles and CVD mixing rules for predicting vapor-liquid equilibrium properties of CO2 pure substance, CO2-C2H6 azeotrope and n-C5H12-CO2-C2H6 ternary system are evaluated according to the principle of vapor-liquid fugacity equilibrium. In addition, average absolute deviation is adopted to select cubic state equations. The results show that the SRK equation of state calculates the vapor-liquid equilibrium property of CO2 pure material with the highest precision. The PR equation of state combined with Margles mixing rule can accurately calculate the vapor-liquid equilibrium characteristics of CO2-C2H6 azeotrope system. However, for n-C5H12-CO2-C2H6 ternary system, the calculating accuracy of SRK combined with Margles mixing rule is obviously better than that of vdW, RK and PR. Furthermore, binary interaction parameters have obvious effects on the calculating accuracy of cubic equations of state for the mixture system. In order to improve the calculation accuracy, the binary interaction parameter is calibrated for all of the studied EOSs regarding CO2-C2H6 azeotropic system and n-C5H12-CO2-C2H6 ternary system.

Key words: CO2-C2H6 azeotrope, cubic equation of state, fugacity equilibrium, mixing rule, binary interaction parameters, average absolute deviation

中图分类号: 

  • TE 645

表1

立方型状态方程以及纯物质、混合物质的逸度系数计算"

状态方程 公式形式 特征常数 纯物质逸度系数 混合物逸度系数
vdW p = R T V - b - a V 2

a = 27 64 R 2 T c 2 p c

b = 1 8 R T c p c

l n φ = V V - b - 2 a R T V - l n p V - b R T - 1 l n φ i = l n V V - b m + 1 V - b m ? n b m ? n i - 1 R T V ? n 2 a m ? n i - l n Z
RK p = R T V - b - a T 0.5 V V + b

a = 0.42748 R 2 T c 2.5 p c

b = 0.08664 R T c p c

l n φ = Z - 1 - l n p V - b R T - a b R T 1.5 l n 1 + b V l n φ i = 1 b m ? n b m ? n i Z - 1 - l n p V - b m R T + a m b m R T 1.5 1 b m ? n b m ? n i - 1 a m ? n 2 a m ? n i l n 1 + b m V
SRK p = R T V - b - a V V + b

a = 0.42748 R 2 T c 2 α T r , w p c

α T r , w 0.5 = 1 + m 1 - T r 0.5

m = 0.480 + 1.574 ω - 0.176 ω 2

T r = T T c ; ? b = 0.08664 R T c p c

l n φ = Z - 1 - l n p V - b R T - a b R T l n 1 + b V l n φ i = 1 b m ? n b m ? n i Z - 1 - l n p V - b m R T + a m b m R T 1 b m ? n b m ? n i - 1 a m ? n 2 a m ? n i l n 1 + b m V
PR p = R T V - b - a V V + b + b V - b

a = 0.457235 R 2 T c 2 α T r , w p c

α T r , w 0.5 = 1 + m 1 - T r 0.5

m = 0.37464 + 1.54226 ω - 0.26992 ω 2

T r = T T c ; ? b = 0.077796 R T c p c

l n φ = Z - 1 - l n p V - b R T - a 2 2 b R T × l n V + 2 + 1 b V - 2 - 1 b l n φ i = 1 b m ? n b m ? n i Z - 1 - l n p V - b m R T + a m 2 2 b m R T × 1 b m ? n b m ? n i - 1 a m ? n 2 a m ? n i l n V + 2 + 1 b m V - 2 - 1 b m

表2

立方型状态方程的不同混合规则"

混合规则 混合物特征常数
a m b m
vdW a m = i = 1 N j = 1 N y i y j a i j ; ? a i j = a i a j 1 - k i j ; ? ? ( n 2 a m ) ? n i = 2 j = 1 N y j a i j

b m = i = 1 N j = 1 N y i y j b i j ; ? b i j = b i + b j 2 ;

? ( n b m ) ? n i = 2 j = 1 N y j b i j

Margles a m = i = 1 N j = 1 N y i y j a i j ; ? a i j = a i a j 1 - y i k i j - y j k j i ; ? ? ( n 2 a m ) ? n i = 2 j = 1 N y j a i j

CVD

a m = i = 1 N j = 1 N y i y j a i j b b i j k i j ; ? a i j = a i a j ; ? b i j = b i b j

? ( n 2 a m ) ? n i = 2 j = 1 N y i a i j b m b i j k i j + b i b m - 1 i = 1 N j = 1 N y i y j a i j k i j b b i j k i j

图1

CO2纯物质汽液平衡的p-T图"

图2

二氧化碳汽液逸度系数的平均绝对误差"

图3

CO2-C2H6体系汽液平衡数据的p-xy图"

图4

不同温度下二氧化碳和乙烷平衡常数的平均绝对误差之和"

表3

CO2-C2H6共沸体系优化后的二元交互作用参数kij "

温度、压力

范围

混合

规则

状态方程 k C O 2 , C 2 H 6 k C 2 H 6 , C O 2 A A D C O 2 + A A D C 2 H 6
优化后 优化前

244.6~288 K,

1.43~5.63 MPa

vdW vdW 0.1589 0.1424 0.2243 0.4435
RK 0.2137 0.2937 0.2889 0.3212
SRK 0.3257 0.2077 0.2406 0.2691
PR 0.2850 0.1901 0.2160 0.2541
Margles vdW 0.1981 0.0948 0.2212 0.4460
RK 0.2384 0.1600 0.2224 0.3122
SRK 0.2754 0.1618 0.1889 0.2500
PR 0.2668 0.1445 0.1841 0.2765
CVD vdW 0.1707 0.1994 0.3943 0.3952
RK 0.1002 0.1661 0.3872 0.3894
SRK 0.0099 0.2212 0.3854 0.3914
PR 0.1779 0.1485 0.3859 0.3876

图5

n-C5H12-CO2-C2H6体系汽液平衡数据的三元图"

图6

不同温度下二氧化碳、乙烷和正戊烷平衡常数的平均绝对误差之和"

表4

n-C5H12-CO2-C2H6三元体系优化后的二元交互作用参数kij "

温度、压力范围 混合规则 EOS k C O 2 , C 2 H 6 k C 2 H 6 , C O 2 k C O 2 , n - C 5 H 12 k n - C 5 H 12 , C O 2 k C 2 H 6 , n - C 5 H 12 k n - C 5 H 12 , C 2 H 6 A A D C O 2 + A A D C 2 H 6 + A A D n - C 5 H 12
优化后 优化前

253~283 K,

0.6896~5.46 MPa

vdW vdW -0.6837 0.0875 0.9587 -0.3942 0.3495 0.3443 1.8261 2.9008
RK -0.6438 0.0921 0.9977 0.8328 0.2997 0.6939 1.8108 2.4772
SRK -0.4869 0.2656 1.0962 -0.4959 0.3834 3.4815 2.3790 2.5333
PR -0.3722 0.1694 1.0288 -0.4821 0.3716 3.3173 2.1855 2.5360
Margles vdW 1.7717 -0.4295 1.0937 0.0148 0.4679 -0.0955 1.6319 2.2090
RK 1.9416 -0.5333 1.2083 0.3128 0.3289 -0.0739 1.0382 2.2478
SRK 0.8621 -0.0888 1.3591 0.3986 0.3603 0.3035 0.9192 2.3850
PR 0.9872 -0.1547 1.3165 0.3438 0.3594 0.2123 0.9584 2.3725
CVD vdW -0.2764 -0.1711 -0.4405 -0.3684 0.3663 0.3177 2.9648 2.9725
RK -2.8909 -2.8909 -0.1320 -0.1320 -0.2929 -0.2929 2.1863 2.2646
SRK 0.2875 0.3152 0.8591 0.8564 0.3805 0.3737 2.3533 2.3741
PR 0.3293 0.3422 0.8850 0.8874 0.3924 0.3877 2.3303 2.3547

图7

萃取精馏流程"

表5

塔顶二氧化碳和乙烷产品的摩尔分数以及回收率"

状态

方程

产品摩尔分数/% 产品回收率/%
CO2 C2H6 CO2 C2H6
计算值 实验值[38] 相对误差
vdW 83.75 95.5 12.3 81.83 93.82 94.96
RK 94.63 0.91 95.46 98.08 96.56
SRK 95.19 0.32 96.93 98.68 98.09
PR 95.01 0.51 96.56 98.53 97.53
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