The hybrid lumping macroscopic kinetic model for cobalt-based fischer-tropsch synthesis and its application in industrial single-tube simulation

doi:10.11949/0438-1157.20250514

CIESC Journal ›› 2025, Vol. 76 ›› Issue (12): 6398-6409.DOI: 10.11949/0438-1157.20250514

• Catalysis, kinetics and reactors • Previous Articles Next Articles

The hybrid lumping macroscopic kinetic model for cobalt-based fischer-tropsch synthesis and its application in industrial single-tube simulation

Ming XIA¹(), Shuai HUANG², Hui SHI³, Congcong NIU⁴, Debao LI⁵, Xu QIAO¹^,⁶

^1.State Key Laboratory of Materials-Oriented Chemical Engineering, College of Chemical Engineering, Nanjing Tech University, Nanjing 211816, Jiangsu, China
^2.Tianhua Institute of Chemical Machinery and Automation Co. , Ltd, Lanzhou 730060, Gansu, China
^3.School of Chemistry and Molecular Engineering, Nanjing Tech University, Nanjing 211816, Jiangsu, China
^4.Sinopec Research Institute of Petroleum Processing Co. , Ltd. , Beijing 100083, China
^5.Institute of Coal Chemistry, Chinese Academy of Sciences, Taiyuan 030001, Shanxi, China
^6.Jiangsu National Synergetic Innovation Center for Advanced Materials, Nanjing 211816, Jiangsu, China

Received:2025-05-09 Revised:2025-06-13 Online:2026-01-23 Published:2025-12-31
Contact: Ming XIA

钴基费托合成复合集总宏观动力学模型及工业单管模拟

夏铭¹(), 黄帅², 石慧³, 牛丛丛⁴, 李德宝⁵, 乔旭¹^,⁶

^1.南京工业大学化工学院，材料化学工程全国重点实验室，江苏南京 211816
^2.天华化工机械及自动化研究设计院有限公司，甘肃兰州 730060
^3.南京工业大学化学与分子工程学院，江苏南京 211816
^4.中石化石油化工科学研究院有限公司，北京 100083
^5.中国科学院山西煤炭化学研究所，山西太原 030001
^6.国家“江苏先进生物与化学制造协同创新中心”，江苏南京 211816

通讯作者: 夏铭
作者简介:夏铭（1987—），男，博士，副研究员，Sciengart@163.com, mxia@njtech.edu.cn
基金资助:
国家自然科学基金项目(22202225);国家自然科学基金项目(22208361);国家自然科学基金项目(22208154);南京工业大学新进人才启动项目(39801177);南京工业大学2025年校级教改课题(20250132);南京工业大学本科课程思政示范课程建设项目(20240030);南京工业大学化学与分子工程学院教育教学改革拔尖创新人才项目(2024YB02)

Abstract

Abstract:

Using the lumped kinetics concept and the chain growth probability model, combined with industrial single-tube experimental data, a composite lumped macrokinetic model for cobalt-based Fischer-Tropsch synthesis, including the syngas consumption rate and lumped component selectivity model, was established. Research results indicate that the CO single-pass conversion calculated by the established macroscopic lumping kinetic model aligns well with experimental values, and the calculated space-time yields of lump components such as methane, C₃ hydrocarbons, C₁₂ hydrocarbons, and C₂₉ hydrocarbons also show good agreement with experimental values under corresponding operating conditions, with maximum relative deviations usually <15%. Furthermore, the hybrid lumping macroscopic kinetic model was applied to modeling and simulation of the entire industrial single-tube unit process, it is demonstrated good performance in calculating the flow rates of wax oil and water, as well as the single-pass and overall CO conversion rates under different operating conditions. The hybrid lumping macroscopic kinetic model and its full-process modeling method for the cobalt-based Fischer-Tropsch synthesis proposed in this paper have the advantages of a moderate number of undetermined parameters and the ability to simultaneously simulate syngas conversion rate and lump component generation rates, showing good application value and academic significance. The presented hybrid lumping model could be extended to other similar reaction systems.

Key words: Fischer-Tropsch synthesis, macrokinetics, lumped kinetics, cobalt-based catalyst

摘要：

采用集总动力学思想与链增长概率模型，结合工业单管试验数据，建立了钴基费托合成包含合成气消耗速率和集总组分选择性模型的复合集总宏观动力学模型。研究结果表明，建立的宏观集总动力学模型计算的单管CO单程转化率与试验值吻合良好，计算的集总组分CH₄、C₃H₈、C₁₂H₂₆和C₂₉H₆₀的时空收率与对应工况的试验值亦符合良好，大多数相对偏差在15%以内；将该复合集总宏观动力学模型应用于工业单管装置的全流程建模与模拟，结果表明，该模型较好地计算不同工况下蜡油、水的流率以及CO的转化率。本文提出的钴基费托合成复合集总宏观动力学模型及其全流程模型方法，具有待定参数数量适中，能够同时模拟合成气转化率和集总组分生成速率的优点，表现出较好的应用与学术价值，有望拓展应用至其他类似的反应体系。

关键词: 费托合成, 宏观动力学, 集总动力学, 钴基催化剂

CLC Number:

TQ 021

Ming XIA, Shuai HUANG, Hui SHI, Congcong NIU, Debao LI, Xu QIAO. The hybrid lumping macroscopic kinetic model for cobalt-based fischer-tropsch synthesis and its application in industrial single-tube simulation[J]. CIESC Journal, 2025, 76(12): 6398-6409.

夏铭, 黄帅, 石慧, 牛丛丛, 李德宝, 乔旭. 钴基费托合成复合集总宏观动力学模型及工业单管模拟[J]. 化工学报, 2025, 76(12): 6398-6409.

Figures/Tables 10

Fig.1 Illustration diagram of material balance in integral reactor

Table 1 Industrial single-tube test data and their conversion to lumped kinetics data

时间	M₀	反应条件					放料间隔/h	产物生成质量/g					CO 总转化率/ %	CO单程转化率/%		进料中各组分与 CO的摩尔比				单程转化的 CO物质的量/mol	系数						实验数据计算的平均分子量/(g/mol)
时间	M₀	T/K	P/MPa	U	V	V₀/L	t	CH₄	C₃H₈	C₁₂H₂₆	C₂₉H₆₀	H₂O	x	x_exp	x_calc	R₁	R₂	R₃	R₄	m_CO	A	B	C	D	E	$M C H 4$	$M C 3$	$M C 12$	$M C 29$	$M H 2 O$
2019.06.02	3.914	464.05	6.07	2.121	141.346	141346	8	1771.64	601.57	2948.62	2964.91	9924	79.18	31.378	30.97	2.414	0	0.295	0.205	1276.53	0.087	3.821	4.761	1.707	140.862	16	40.22	158.24	443.8	18
2019.06.05	4.087	467.85	6.08	2.009	137.583	137583	8	2026.62	773.86	3573.76	2482.79	10898	75.69	36.038	36.46	2.431	0	0.444	0.212	1137.498	0.111	4.616	5.335	1.443	148.139	16	41.02	163.9	420.89	18
2019.06.09	3.534	473.35	6.07	1.994	136.235	136235	8	1871.86	684.61	4503.84	2803.50	11687	77.48	34.439	33.94	1.921	0	0.421	0.192	1333.259	0.088	4.799	7.632	1.963	183.702	16	40.36	166.96	404.16	18
2019.06.10	3.303	473.45	6.06	2.102	139.371	139371	8	1735.6	658.86	3798.21	3561.24	11469	74.36	30.922	30.48	1.804	0	0.312	0.187	1400.732	0.077	4.977	7.082	2.418	192.905	16	40.08	162.37	445.87	18
2019.06.12	3.150	473.65	6.08	1.971	139.147	139147	8	1241.75	545.73	3890.46	3719.36	11437	74.07	29.439	29.98	1.675	0	0.244	0.231	1460.689	0.053	4.422	7.346	2.580	201.711	16	39.18	168.13	457.73	18
2019.06.13	3.001	473.65	6.08	1.996	142.245	142245	8	1273.47	561.31	3882.04	3647.42	11252	73.37	28.011	27.96	1.598	0	0.207	0.196	1552.535	0.051	4.893	7.859	2.824	208.301	16	38.23	164.6	430.31	18
2019.06.21	3.085	484.05	6.07	2.076	140.504	140504	8	1226.43	503.67	4221.75	4793.27	12939	83.38	30.848	32.24	1.520	0	0.307	0.258	1695.303	0.045	4.044	7.531	3.497	233.009	16	40.37	181.72	444.36	18
2019.06.24	3.280	488.95	6.07	2.005	132.947	132947	8	1314.00	374.07	5383.6	4094.02	13514	88.25	33.178	33.63	1.380	0	0.503	0.397	1596.877	0.051	2.873	9.407	3.000	228.896	16	39.69	174.48	415.99	18
2019.07.01	3.009	493.55	6.04	2.063	139.369	139369	8	1167.82	620.68	5413.03	5152.76	15192	87.66	35.540	33.23	1.310	0	0.35	0.349	1812.581	0.040	5.290	10.832	3.837	280.492	16	38.99	166.08	446.34	18
2019.07.08	3.062	493.85	6.05	1.97	145.156	145156	8	1479.35	708.24	4875.58	5282.83	15253	85.89	35.684	37.09	1.440	0	0.372	0.25	1817.709	0.051	6.122	9.904	3.915	276.744	16	37.78	160.77	440.72	18
2019.07.12	3.049	498.95	6.05	2.044	148.188	148188	8	1626.57	724.48	5405.9	6390.77	17146	86.10	37.749	37.66	1.400	0	0.362	0.287	1868.146	0.054	6.196	11.422	4.466	312.416	16	38.35	155.22	469.36	18

Table 1 Industrial single-tube test data and their conversion to lumped kinetics data

时间	M₀	反应条件					放料间隔/h	产物生成质量/g					CO 总转化率/ %	CO单程转化率/%		进料中各组分与 CO的摩尔比				单程转化的 CO物质的量/mol	系数						实验数据计算的平均分子量/(g/mol)
时间	M₀	T/K	P/MPa	U	V	V₀/L	t	CH₄	C₃H₈	C₁₂H₂₆	C₂₉H₆₀	H₂O	x	x_exp	x_calc	R₁	R₂	R₃	R₄	m_CO	A	B	C	D	E	$M C H 4$	$M C 3$	$M C 12$	$M C 29$	$M H 2 O$
2019.06.02	3.914	464.05	6.07	2.121	141.346	141346	8	1771.64	601.57	2948.62	2964.91	9924	79.18	31.378	30.97	2.414	0	0.295	0.205	1276.53	0.087	3.821	4.761	1.707	140.862	16	40.22	158.24	443.8	18
2019.06.05	4.087	467.85	6.08	2.009	137.583	137583	8	2026.62	773.86	3573.76	2482.79	10898	75.69	36.038	36.46	2.431	0	0.444	0.212	1137.498	0.111	4.616	5.335	1.443	148.139	16	41.02	163.9	420.89	18
2019.06.09	3.534	473.35	6.07	1.994	136.235	136235	8	1871.86	684.61	4503.84	2803.50	11687	77.48	34.439	33.94	1.921	0	0.421	0.192	1333.259	0.088	4.799	7.632	1.963	183.702	16	40.36	166.96	404.16	18
2019.06.10	3.303	473.45	6.06	2.102	139.371	139371	8	1735.6	658.86	3798.21	3561.24	11469	74.36	30.922	30.48	1.804	0	0.312	0.187	1400.732	0.077	4.977	7.082	2.418	192.905	16	40.08	162.37	445.87	18
2019.06.12	3.150	473.65	6.08	1.971	139.147	139147	8	1241.75	545.73	3890.46	3719.36	11437	74.07	29.439	29.98	1.675	0	0.244	0.231	1460.689	0.053	4.422	7.346	2.580	201.711	16	39.18	168.13	457.73	18
2019.06.13	3.001	473.65	6.08	1.996	142.245	142245	8	1273.47	561.31	3882.04	3647.42	11252	73.37	28.011	27.96	1.598	0	0.207	0.196	1552.535	0.051	4.893	7.859	2.824	208.301	16	38.23	164.6	430.31	18
2019.06.21	3.085	484.05	6.07	2.076	140.504	140504	8	1226.43	503.67	4221.75	4793.27	12939	83.38	30.848	32.24	1.520	0	0.307	0.258	1695.303	0.045	4.044	7.531	3.497	233.009	16	40.37	181.72	444.36	18
2019.06.24	3.280	488.95	6.07	2.005	132.947	132947	8	1314.00	374.07	5383.6	4094.02	13514	88.25	33.178	33.63	1.380	0	0.503	0.397	1596.877	0.051	2.873	9.407	3.000	228.896	16	39.69	174.48	415.99	18
2019.07.01	3.009	493.55	6.04	2.063	139.369	139369	8	1167.82	620.68	5413.03	5152.76	15192	87.66	35.540	33.23	1.310	0	0.35	0.349	1812.581	0.040	5.290	10.832	3.837	280.492	16	38.99	166.08	446.34	18
2019.07.08	3.062	493.85	6.05	1.97	145.156	145156	8	1479.35	708.24	4875.58	5282.83	15253	85.89	35.684	37.09	1.440	0	0.372	0.25	1817.709	0.051	6.122	9.904	3.915	276.744	16	37.78	160.77	440.72	18
2019.07.12	3.049	498.95	6.05	2.044	148.188	148188	8	1626.57	724.48	5405.9	6390.77	17146	86.10	37.749	37.66	1.400	0	0.362	0.287	1868.146	0.054	6.196	11.422	4.466	312.416	16	38.35	155.22	469.36	18

Fig.2 (a),(b) Comparison of calculated conversion and experimental conversion within different ranges; (c) Conversion residual plot (d) Syngas consumption rate

Table 2 Statistical test results of the kinetics model

M_P	M_i	F	ρ²	F_0.05
3	11	341.306	0.992	34.406

Table 3 Calculated values of the carbon chain growth probability factor α1 for methane formation in comparison with the experimental values

T/K	P/MPa	GHSV/h^-1	R₁	α_{1, exp}	α_{1, calc}	W_{1, exp}	W_{1, calc}	RD/%
464.05	6.07	3715.27	2.414	0.5419	0.5262	0.2138	0.2245	-5.01
467.85	6.08	3728.25	2.431	0.5269	0.5260	0.2288	0.2246	1.82
473.35	6.07	3789.95	1.921	0.5604	0.5803	0.1898	0.1762	7.17
473.45	6.06	3786.64	1.804	0.5737	0.5954	0.1779	0.1637	7.99
473.65	6.08	3764.47	1.675	0.6309	0.6153	0.1321	0.1480	-12.02
473.65	6.08	3774.52	1.598	0.6260	0.6271	0.1360	0.1391	-2.25
484.05	6.07	3961.53	1.52	0.6574	0.6395	0.1141	0.1300	-13.88
488.95	6.07	4209.79	1.38	0.6525	0.6613	0.1177	0.1147	2.54
493.55	6.04	4193.09	1.31	0.6885	0.6772	0.0945	0.1042	-10.26
493.85	6.05	4204.55	1.44	0.6495	0.6513	0.1198	0.1216	-1.46
498.95	6.05	4336.51	1.4	0.6563	0.6579	0.1150	0.1170	-1.78

Table 4 Calculated values of the carbon chain growth probability factor α3 generated by C2-5 hydrocarbons （with a total set of C3） in comparison with the experimental values

T/K	P/MPa	GHSV/h^-1	R₁	α_{3, exp}	α_{3, calc}	W_{3, exp}	W_{3, calc}	RD/%
464.05	6.07	3715.27	2.414	0.8120	0.8052	0.0726	0.0738	-1.65
467.85	6.08	3728.25	2.431	0.7868	0.7931	0.0874	0.0808	7.56
473.35	6.07	3789.95	1.921	0.8120	0.8103	0.0694	0.0709	-2.13
473.45	6.06	3786.64	1.804	0.8120	0.8141	0.0675	0.0687	-1.72
473.65	6.08	3764.47	1.675	0.8281	0.8274	0.0581	0.0612	-5.38
473.65	6.08	3774.52	1.598	0.8259	0.8366	0.0599	0.0561	6.48
484.05	6.07	3961.53	1.52	0.8492	0.8309	0.0469	0.0592	-26.35
488.95	6.07	4209.79	1.38	0.8754	0.8745	0.0335	0.0361	-7.80
493.55	6.04	4193.09	1.31	0.8436	0.8439	0.0502	0.0521	-3.63
493.85	6.05	4204.55	1.44	0.8289	0.8349	0.0574	0.0570	0.64
498.95	6.05	4336.51	1.4	0.8400	0.8417	0.0512	0.0533	-4.02

Table 5 Calculated values of the carbon chain growth probability factor α12 generated by C6-19 hydrocarbons （aggregated as C12） in comparison with the experimental values

T/K	P/MPa	GHSV/h^-1	R₁	α_{12, exp}	α_{12, calc}	W_{12, exp}	W_{12, calc}	RD/%
464.05	6.07	3715.27	2.414	0.9143	0.9155	0.3558	0.3840	-7.91
467.85	6.08	3728.25	2.431	0.9182	0.9177	0.4035	0.3840	4.84
473.35	6.07	3789.95	1.921	0.9232	0.9187	0.4566	0.3839	15.93
473.45	6.06	3786.64	1.804	0.9171	0.9170	0.3894	0.3840	1.39
473.65	6.08	3764.47	1.675	0.9232	0.9236	0.4140	0.3825	7.61
473.65	6.08	3774.52	1.598	0.9232	0.9244	0.4146	0.3821	7.84
484.05	6.07	3961.53	1.52	0.9174	0.9223	0.3929	0.3830	2.52
488.95	6.07	4209.79	1.38	0.9236	0.9248	0.4822	0.3819	20.80
493.55	6.04	4193.09	1.31	0.9232	0.9168	0.4381	0.3840	12.36
493.85	6.05	4204.55	1.44	0.9175	0.9179	0.3949	0.3839	2.78
498.95	6.05	4336.51	1.4	0.9165	0.9185	0.3821	0.3839	-0.47

Table 6 Calculated values of the carbon chain growth probability factor α29 generated by C20+ hydrocarbons （aggregated as C29） in comparison with the experimental values

T/K	P/MPa	GHSV/h^-1	R₁	α_{29, exp}	α_{29, calc}	W_{29, exp}	W_{29, exp}	RD/%
464.05	6.07	3715.27	2.414	0.9698	0.9650	0.3578	0.3743	-4.62
467.85	6.08	3728.25	2.431	0.9676	0.9678	0.2803	0.3734	-33.22
473.35	6.07	3789.95	1.921	0.9601	0.9681	0.2842	0.3732	-31.30
473.45	6.06	3786.64	1.804	0.9649	0.9673	0.3651	0.3738	-2.39
473.65	6.08	3764.47	1.675	0.9707	0.9687	0.3958	0.3726	5.86
473.65	6.08	3774.52	1.598	0.9705	0.9683	0.3895	0.3730	4.23
484.05	6.07	3961.53	1.52	0.9716	0.9703	0.4461	0.3704	16.98
488.95	6.07	4209.79	1.38	0.9649	0.9684	0.3667	0.3729	-1.71
493.55	6.04	4193.09	1.31	0.9711	0.9691	0.4171	0.3721	10.79
493.85	6.05	4204.55	1.44	0.9713	0.9703	0.4279	0.3703	13.46
498.95	6.05	4336.51	1.4	0.9717	0.9709	0.4517	0.3690	18.31

Fig.3 A simplified diagram of the full-process simulation of the industrial single-tube device for cobalt-based Fischer-Tropsch synthesis using Aspen PlusHEAT—feed preheater; RPLUG—fixed-bed reactor; COOL-V1—normal-temperature cooler; COOL-V2—water cooler; CUB-V3—subcooler; COMP—recycle compressor;FF1—fresh feed; REC-S—recycle stream; SYNGAS-M—synthesis gas mixed; FRIN—inlet stream of the reactor; FROUT—outlet stream of the reactor; FT-WAT1—FT synthesized water; FT-WAX1—FT synthesized wax1; FT-V1—vapor stream from the COOL-V1; FT-WAT2—FT synthesized water2; FT-OIL2—FT synthesized oil2; FT-OIL3—FT synthesized oil3; REC1—stream to recycle and purge

Table 7 Comparison of simulated and experimental values of key material data for the entire process of cobalt-based Fischer-Tropsch synthesis industrial single-tube equipment

对比组		新鲜气（FF1)	循环气 (REC-S)	入器气 (FRIN)	费托蜡1 (FT-WAX1)	费托油2 (FT-OIL2)	费托油3 (FT-OIL3)	费托水1 (FT-WAT1)	费托水2 (FT-WAT2)	弛放气 (PURGE)
模拟值	流量/(kg/h)	4.052	5.507	9.558	0.763	0.067	0.003	1.077	0.273	1.868
	流量/(kg/h)	4.052	5.507	9.558	SUM = 0.833			SUM=1.350		1.868
	组分	摩尔分数	摩尔分数	摩尔分数	质量分数	质量分数	质量分数	质量分数	质量分数	摩尔分数
	H₂	0.6703	0.5636	0.6138	0.0005	0.0004	0.0004	0	0	0.5636
	CO	0.2886	0.2245	0.2547	0.0044	0.0050	0.0061	0	0	0.2245
	N₂	0.0281	0.0723	0.0515	0.0086	0.0214	0.0418	0.0010	0.0006	0.0723
	CH₄	0.0129	0.1269	0.0732	0.0026	0.0039	0.0055	0	0	0.1269
	C₃H₈	0	0.0114	0.0060	0.0038	0.0131	0.0308	0	0	0.0114
	C₁₂H₂₆	0	0	0	0.4719	0.9530	0.9047	0	0	0
	C₂₉H₆₀	0	0	0	0.4991	0.0001	0	0	0	0
	H₂O	0	0.0014	0.0007	0.0092	0.0031	0.0108	0.9989	0.9993	0.0014
试验值	流量/(kg/h)	3.814	—	—	SUM = 0.713, 各组分已全分析，不便列出			SUM = 1.241, 不便列出		1.822
	组分	摩尔分数	摩尔分数	摩尔分数	—	—	—	—	—	摩尔分数
	H₂	0.6728	0.5875	0.6114	—	—	—	—	—	0.5875
	CO	0.2990	0.2334	0.2533	—	—	—	—	—	0.2334
	N₂	0.018	0.0460	0.0518	—	—	—	—	—	0.0460
	CH₄	0.0023	0.1060	0.0747	—	—	—	—	—	0.1060
	C₂H₆+	—	—	—	—	—	—	—	—	—
	H₂O	—	—	—	—	—	—	—	—	—
相对误差/%	(模拟值-试验值)/试验值×100	6.24	—	—	16.8	—	—	8.87	—	2.52

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The hybrid lumping macroscopic kinetic model for cobalt-based fischer-tropsch synthesis and its application in industrial single-tube simulation

钴基费托合成复合集总宏观动力学模型及工业单管模拟

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