Experiment and model for isochoric heat capacity of CO2-hydrocarbon liquid phase mixtures

doi:10.11949/0438-1157.20221032

Abstract

Abstract:

Carbon dioxide (CO₂) enhanced oil recovery (EOR) technology has been extensively studied in recent years. A full understanding of the heat capacity properties of CO₂-hydrocarbon mixtures is critical for the successful implementation of this project, while there is limited research on this. An adiabatic calorimeter was set up based on the adiabatic calorimetry method, and the isochoric heat capacity (C_v ) data of CO₂-hydrocarbon (n-hexane, n-octane, undecane, cyclohexane, ethylbenzene) binary liquid phase mixtures were measured at temperatures range from 317.15 K to 353.15 K and pressures up to 29.49 MPa, and a total of 335 data points were obtained. In addition, a predictive model (PR equation of state combined with thermodynamic relationships) and an empirical model were applied for calculating the C_v data, and the calculation average absolutely relative deviations (AARD) were 0.81%—3.66%, and less than 2.56%, respectively. The empirical model has a simpler form, while the prediction ability of PR model is powerful. These experimental C_v data and the developed two models are crucial for the implementation of CO₂-EOR project.

Key words: carbon dioxide, hydrocarbon, binary mixtures, isochoric heat capacity, PR model, empirical model

摘要：

近年来，二氧化碳(CO₂)提高原油采收率(CO₂-EOR)技术得到了广泛的研究。充分了解CO₂-烃类混合物的热容性质是该项目能够成功实施的基础，但是目前对此性质的研究非常有限。基于绝热量热法，搭建了一个绝热量热计，测量了温度为317.15~353.15 K，压力高达29.49 MPa时，CO₂-碳氢化合物(正己烷、正辛烷、十一烷、环己烷、乙苯)二元液相混合物的比定容热容(C_v )数据，共获得335个数据点。此外，采用预测模型(结合热力学关系的PR状态方程)和经验模型计算C_v，计算平均绝对相对偏差(AARD)分别为0.81%~3.66%和小于2.56%。经验模型的形式简单，但PR模型有较强的预测能力。实验测得的C_v 数据以及建立的两种计算模型对CO₂-EOR项目的实施至关重要。

关键词: 二氧化碳, 碳氢化合物, 二元混合物, 比定容热容, PR模型, 经验模型

CLC Number:

TE 09

Yahui GAO, Shuqian XIA. Experiment and model for isochoric heat capacity of CO₂-hydrocarbon liquid phase mixtures[J]. CIESC Journal, 2022, 73(11): 4838-4849.

高亚慧, 夏淑倩. CO₂-烃类液相混合物比定容热容的实验与模型研究[J]. 化工学报, 2022, 73(11): 4838-4849.

Figures/Tables 15

References 31

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参数	回归值
a×10^-2	7.5665
b×10^-2	-3.0678
c×10^-2	2.3821

参数	回归值
a×10^-2	7.5665
b×10^-2	-3.0678
c×10^-2	2.3821

T/K	p/MPa	C_v-_exp/(J∙g^-1∙K^-1)	T/K	p/MPa	C_v-_exp/(J∙g^-1∙K^-1)
317.15	4.69	4.108	337.15	9.82	3.921
319.15	5.15	4.079	339.15	10.46	3.912
321.15	5.60	4.039	341.15	11.16	3.904
323.15	6.07	4.017	343.15	11.86	3.892
325.15	6.54	4.010	345.15	12.58	3.885
327.15	7.03	3.987	347.15	13.40	3.883
329.15	7.58	3.958	349.15	14.70	3.881
331.15	9.09	3.939	351.15	15.00	3.877
333.15	8.60	3.928	353.15	15.87	3.866
335.15	9.20	3.919

T/K	p/MPa	C_v-_exp/(J∙g^-1∙K^-1)	T/K	p/MPa	C_v-_exp/(J∙g^-1∙K^-1)
317.15	4.69	4.108	337.15	9.82	3.921
319.15	5.15	4.079	339.15	10.46	3.912
321.15	5.60	4.039	341.15	11.16	3.904
323.15	6.07	4.017	343.15	11.86	3.892
325.15	6.54	4.010	345.15	12.58	3.885
327.15	7.03	3.987	347.15	13.40	3.883
329.15	7.58	3.958	349.15	14.70	3.881
331.15	9.09	3.939	351.15	15.00	3.877
333.15	8.60	3.928	353.15	15.87	3.866
335.15	9.20	3.919

T/K	p/MPa	C_v/(J∙g^-1∙K^-1)	T/K	p/MPa	C_v/(J∙g^-1∙K^-1)	T/K	p/MPa	C_v/(J∙g^-1∙K^-1)
ρ/(g∙cm^-3)=0.5678 x₁=0.1834			343.15	8.26	1.792	329.15	10.68	1.633
317.15	3.22	1.749	345.15	9.00	1.812	331.15	11.27	1.642
319.65	3.74	1.759	347.15	9.78	1.815	333.15	11.94	1.644
321.15	4.07	1.765	349.15	10.70	1.819	335.15	12.74	1.649
325.15	5.15	1.774	351.15	11.30	1.836	337.15	13.54	1.651
327.65	6.38	1.779	353.15	12.03	1.865	339.15	14.35	1.658
329.65	6.87	1.787	ρ/(g∙cm^-3)=0.6045 x₁=0.3351			341.15	15.17	1.661
331.15	7.40	1.794	317.15	9.98	1.687	343.15	16.00	1.663
333.15	8.14	1.803	319.15	10.78	1.688	345.15	16.78	1.665
335.15	8.87	1.816	321.15	11.63	1.689	347.15	17.72	1.669
337.15	9.67	1.831	323.15	12.49	1.694	349.15	18.57	1.670
339.15	10.38	1.835	325.15	13.29	1.700	351.15	19.42	1.673
341.15	11.21	1.842	327.15	14.07	1.705	353.15	19.97	1.681
343.15	11.92	1.856	329.15	14.73	1.707	ρ/(g∙cm^-3)=0.6276 x₁=0.5020
345.15	12.73	1.865	331.15	15.45	1.714	317.15	5.43	1.531
347.15	13.52	1.871	333.15	16.25	1.721	319.65	5.92	1.540
349.15	14.28	1.884	335.15	17.09	1.723	321.15	6.39	1.557
351.15	15.06	1.892	337.15	18.02	1.725	323.15	7.15	1.569
353.15	15.85	1.908	339.15	18.89	1.734	325.15	7.94	1.588
ρ/(g∙cm^-3)=0.5807 x₁=0.2417			341.15	19.76	1.736	327.15	8.68	1.601
317.15	3.66	1.697	343.15	20.68	1.738	329.15	9.37	1.617
319.15	3.71	1.709	345.65	21.87	1.748	331.15	9.96	1.626
321.15	3.86	1.713	347.15	22.37	1.751	333.15	10.61	1.631
324.15	4.19	1.721	349.15	23.16	1.764	335.15	11.48	1.636
326.15	4.38	1.727	351.15	23.99	1.772	337.15	12.27	1.640
327.15	4.46	1.728	353.15	24.83	1.776	339.15	12.97	1.642
329.15	4.72	1.739	ρ/(g∙cm^-3)=0.6174 x₁=0.4476			341.15	13.78	1.654
331.15	5.01	1.749	317.15	5.93	1.557	343.15	14.52	1.655
333.15	5.33	1.758	319.15	6.68	1.567	345.15	15.34	1.659
335.15	5.65	1.763	321.15	7.53	1.583	347.15	16.08	1.660
337.15	6.11	1.769	323.15	8.32	1.596	350.15	17.31	1.665
339.15	6.73	1.771	325.15	9.12	1.618	351.15	17.70	1.668
341.15	7.58	1.787	327.15	9.84	1.622	353.15	18.44	1.670

Experiment and model for isochoric heat capacity of CO₂-hydrocarbon liquid phase mixtures

CO₂-烃类液相混合物比定容热容的实验与模型研究

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T/K	p/MPa	C_v/(J∙g^-1∙K^-1)	T/K	p/MPa	C_v/(J∙g^-1∙K^-1)	T/K	p/MPa	C_v/(J∙g^-1∙K^-1)
ρ/(g∙cm^-3)=0.6153 x₁=0.1434			345.15	16.99	1.928	343.15	18.86	1.801
331.15	5.07	1.913	347.15	17.81	1.933	345.15	19.75	1.809
333.15	5.87	1.920	349.15	18.65	1.945	347.15	20.55	1.813
335.15	6.64	1.925	351.15	19.48	1.957	349.15	21.34	1.817
337.15	7.40	1.939	353.15	20.27	1.962	351.15	22.20	1.825
339.15	8.18	1.946	ρ/(g∙cm^-3)=0.6410 x₁=0.3228			353.15	22.98	1.829
341.65	9.15	1.949	340.15	7.04	1.821	ρ/(g∙cm^-3)=0.6639 x₁=0.5337
343.15	9.73	1.960	341.65	7.39	1.829	317.65	6.64	1.600
345.15	10.42	1.964	344.15	8.36	1.838	319.15	7.17	1.614
347.15	11.16	1.971	345.15	8.65	1.842	321.15	7.90	1.626
349.15	11.97	1.986	347.15	9.39	1.854	323.15	8.61	1.639
351.15	12.72	1.993	349.15	10.15	1.868	325.15	9.39	1.656
353.15	13.51	2.001	351.15	10.89	1.880	327.15	10.08	1.666
ρ/(g∙cm^-3)=0.6240 x₁=0.2209			353.15	11.68	1.889	329.15	10.84	1.671
317.15	6.09	1.814	ρ/(g∙cm^-3)=0.6584 x₁=0.4160			331.15	11.62	1.674
319.15	6.72	1.830	317.15	8.57	1.739	333.15	12.39	1.679
321.15	7.50	1.837	319.15	9.39	1.742	335.15	13.04	1.686
323.15	8.25	1.846	321.15	10.22	1.741	337.15	13.66	1.688
325.15	9.05	1.852	323.15	10.99	1.747	339.15	14.35	1.694
327.15	9.86	1.865	325.15	11.82	1.751	341.15	15.10	1.698
329.15	10.61	1.871	327.15	12.66	1.754	343.15	15.68	1.700
331.15	11.31	1.876	329.15	13.58	1.762	345.15	16.71	1.702
333.65	12.34	1.886	331.15	14.37	1.766	347.15	17.61	1.706
335.15	12.95	1.889	333.15	15.03	1.773	349.15	18.39	1.712
337.15	13.75	1.895	335.15	15.84	1.776	351.15	19.18	1.718
339.15	14.59	1.902	337.15	16.54	1.782	353.15	19.99	1.723
341.15	15.42	1.915	339.15	17.25	1.786
343.15	15.98	1.924	341.15	18.02	1.792

T/K	p/MPa	C_v/(J∙g^-1∙K^-1)	T/K	p/MPa	C_v/(J∙g^-1∙K^-1)	T/K	p/MPa	C_v/(J∙g^-1∙K^-1)
ρ/(g∙cm^-3)=0.7285 x₁=0.1609			ρ/(g∙cm^-3)=0.7292 x₁=0.2602			ρ/(g∙cm^-3)=0.7363 x₁=0.4350
317.15	13.39	1.896	317.15	9.52	1.896	323.15	7.10	1.761
319.15	14.21	1.906	319.65	10.52	1.902	325.15	7.84	1.772
321.15	14.99	1.913	321.15	11.06	1.903	327.15	8.64	1.783
323.15	15.78	1.926	323.15	11.80	1.912	329.15	9.33	1.793
325.15	16.64	1.931	325.15	12.60	1.918	331.15	10.07	1.803
327.15	17.42	1.931	327.15	13.39	1.921	333.15	10.81	1.811
329.15	18.22	1.944	329.15	14.20	1.928	335.35	11.69	1.819
331.15	19.10	1.946	331.15	15.03	1.936	337.15	12.33	1.824
333.15	19.97	1.956	333.15	15.86	1.941	339.15	13.00	1.830
335.15	20.80	1.967	335.15	16.72	1.951	341.15	13.74	1.836
337.15	21.72	1.971	337.15	17.57	1.958	343.15	14.58	1.840
339.15	22.61	1.978	339.15	18.37	1.963	345.15	15.27	1.846
341.15	23.47	1.986	341.15	19.24	1.972	347.15	16.08	1.852
343.15	24.31	1.994	343.15	20.12	1.979	349.15	16.88	1.856
345.15	25.22	1.997	345.15	20.96	1.991	351.15	17.60	1.861
347.15	26.03	2.000	347.15	21.75	1.995	353.15	18.32	1.869
349.15	26.96	2.019	349.15	22.63	2.008
			351.15	23.48	2.018
			353.15	24.28	2.021

T/K	p/MPa	C_v/(J∙g^-1∙K^-1)	T/K	p/MPa	C_v/(J∙g^-1∙K^-1)	T/K	p/MPa	C_v/(J∙g^-1∙K^-1)
ρ/(g∙cm^-3)=0.7771 x₁=0.0966			ρ/(g∙cm^-3)=0.7783 x₁=0.1516			335.15	8.07	1.394
317.15	5.46	1.414	343.15	6.39	1.516	337.15	8.74	1.398
319.15	5.92	1.421	345.15	6.96	1.524	339.15	9.45	1.411
321.15	6.53	1.435	347.15	7.85	1.542	341.15	10.22	1.421
323.15	7.41	1.441	349.15	8.68	1.561	343.15	10.98	1.432
325.15	8.27	1.459	351.15	9.52	1.563	345.15	11.66	1.440
327.15	9.12	1.472	353.15	10.41	1.573	347.15	12.44	1.446
329.15	10.00	1.482	ρ/(g∙cm^-3)=0.7870 x₁=0.2928			349.15	13.20	1.454
331.15	10.92	1.491	337.15	6.66	1.434	351.15	13.97	1.460
333.15	11.68	1.511	339.15	7.22	1.439	353.15	14.77	1.472
335.15	12.62	1.521	341.15	7.99	1.446	ρ/(g∙cm^-3)=0.7923 x₁=0.4150
337.15	13.53	1.537	343.15	8.77	1.457	337.15	6.60	1.352
339.15	14.45	1.546	345.15	9.46	1.460	339.15	7.12	1.357
342.15	15.88	1.556	347.15	10.23	1.472	341.15	7.75	1.369
343.15	16.20	1.561	349.15	11.02	1.483	343.15	8.34	1.384
345.15	17.19	1.569	351.15	11.86	1.496	345.15	8.99	1.395
347.15	18.08	1.578	353.15	12.60	1.505	347.15	9.65	1.399
349.15	19.02	1.587	ρ/(g∙cm^-3)=0.7891 x₁=0.3646			349.15	10.30	1.416
351.15	19.93	1.601	331.15	6.69	1.377	351.15	11.02	1.425
353.15	20.88	1.613	333.15	7.30	1.385	353.15	11.98	1.432

T/K	p/MPa	C_v/(J∙g^-1∙K^-1)	T/K	p/MPa	C_v/(J∙g^-1∙K^-1)	T/K	p/MPa	C_v/(J∙g^-1∙K^-1)
ρ/(g∙cm^-3)=0.8215 x₁=0.1088			ρ/(g∙cm^-3)=0.8295 x₁=0.2122			ρ/(g∙cm^-3)=0.8326 x₁=0.3466
317.65	12.07	1.390	317.15	9.64	1.372	317.15	7.58	1.350
319.15	12.96	1.394	319.65	10.91	1.378	319.15	8.51	1.355
321.15	13.85	1.401	321.15	11.66	1.380	321.15	9.43	1.358
323.15	14.64	1.407	323.15	12.63	1.386	323.15	10.32	1.362
325.15	15.88	1.413	325.15	13.62	1.390	325.15	11.27	1.368
327.15	16.96	1.419	327.15	14.67	1.396	327.15	12.13	1.370
329.15	17.91	1.426	329.15	15.69	1.400	329.15	13.06	1.373
331.15	18.94	1.432	331.15	16.70	1.406	331.15	13.97	1.377
333.15	19.93	1.438	333.15	17.68	1.411	333.15	14.89	1.381
335.15	20.90	1.444	335.15	18.66	1.417	335.65	15.99	1.386
337.15	21.91	1.451	337.15	19.70	1.423	337.15	16.65	1.389
339.15	22.87	1.457	339.15	20.66	1.429	339.15	17.60	1.394
341.15	23.89	1.463	341.15	21.84	1.434	341.15	18.52	1.398
343.15	24.81	1.470	343.15	22.67	1.440	343.15	19.39	1.404
345.15	25.82	1.476	345.15	23.81	1.445	345.15	20.32	1.408
347.65	27.04	1.485	347.65	24.80	1.454	347.15	21.25	1.413
349.15	27.72	1.490	349.15	25.50	1.457	349.15	22.13	1.419
351.15	28.64	1.496	351.15	26.59	1.464	351.15	23.00	1.425
353.15	29.49	1.501	353.15	27.39	1.471	353.15	23.88	1.430

组分	a₀	a₁×10³	a₂×10⁵	a₃×10⁸	a₄×10¹¹
CO₂	3.259	1.356	1.502	-2.374	1.056
正己烷	8.831	-0.166	14.302	-18.314	7.124
正辛烷	10.824	4.983	17.751	-23.137	8.980
十一烷	15.285	5.485	24.990	-35.821	14.200
环己烷	4.035	-4.443	16.834	-20.775	7.746
乙苯	4.544	10.578	13.644	-19.276	7.885

PR模型		经验模型
体系	AARD/%	参数	数值	训练集	测试集
CO₂-正己烷	3.25	a	4.4095
CO₂-正辛烷	1.06	b	0.3246
CO₂-十一烷	0.81	c	0.1544
CO₂-环己烷	2.71	d	-2.3119
CO₂-乙苯	3.66	e	0.0718
		f	-2.2543×10^-4
		g	2.0609
		R²		0.9438
		RMSE/%		4.58	5.47
		AARD/%		2.45	2.56

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