Improved state transfer algorithm-based kinetics parameter estimation for cascaded plug flow reactors

doi:10.11949/j.issn.0438-1157.20181343

Abstract

Abstract:

The actual chemical process reaction system usually consists of several interconnected cascaded reactor. To establish its mechanism model and estimate its dynamic parameters, it is necessary to repeatedly solve large-scale nonlinear differential equations. The calculation is very expensive. Since this parameter optimization process involves solving large sets of differential equations, it is very time consuming. According to the problem that intelligent optimization algorithm always needs enormous computing resource while a satisfied solution is acceptable for an industrial application, an improved state transfer algorithm (STA) is proposed to estimate the kinetics parameters of the cascaded plug flow reactors model. This method uses an opposite operator to initialize the start status of STA, and a tolerable error threshold to break the optimization process. This improvement is helpful since much computing time is saved while the global search capability and fast convergence capability of standard STA are retained. Simulation study, whose target is optimization the kinetics parameters of the cascaded plug flow reactors of an industrial hydrocracking process, verified the effectiveness and superiority of this proposed method.

Key words: cascaded plug flow reactors, reaction kinetics, kinetic modeling, parameter estimation, state transfer algorithm, expensive optimization, satisfied solution

摘要：

实际化工过程反应系统通常由若干个相互关联的平推流反应器串级构成，要建立其机理模型，并估计其动力学参数，就必须反复求解大规模非线性微分方程组，计算代价较高。针对智能优化算法在求解昂贵优化问题时计算成本过高，而工业过程模型往往只需要找到一组满意解即可的特点，提出了一种基于改进状态转移算法的串级平推流反应器动力学参数估计方法。该算法在保留标准状态转移算法全局寻优能力和快速收敛能力的同时，利用对立算子优化初始种群，并根据误差阈值判定满意解中止条件，可有效节约计算时间。以实际炼油企业的加氢裂化装置为研究对象，采用所提方法对其反应系统的动力学参数进行估计，仿真结果表明了所提方法的有效性。

关键词: 串级平推流反应器, 反应动力学, 动力学模型, 参数估值, 状态转移算法, 昂贵优化, 满意解

CLC Number:

TP 273

Yongfei XUE, Yalin WANG, Bei SUN, Qianzhong LI, Jiazhou SUN. Improved state transfer algorithm-based kinetics parameter estimation for cascaded plug flow reactors[J]. CIESC Journal, 2019, 70(2): 607-616.

薛永飞, 王雅琳, 孙备, 李钱钟, 孙家舟. 基于改进状态转移算法的串级平推流反应器动力学参数估计[J]. 化工学报, 2019, 70(2): 607-616.

Figures/Tables 13

Fig.1 Diagram of plug flow reactor for modeling

Fig.2 Cascaded plug flow reactors

Fig.3 Optimization result of Michalewicz function by standard STA

Fig.4 Kinetics parameters estimation of cascaded plug flow reactors based on improved STA

Fig.5 Reaction network of six lumped components in four hydrocracking reactors

Table 1 Physical property data used for estimating kinetics parameters of hydrocracking

物性名称	本文取值
第1反应器中混合物的比定压热容 $c ˉ 1,1$	3.14 kJ?kg^-1?K^-1
第2反应器中混合物的比定压热容 $c ˉ 1,2$	2.48 kJ?kg^-1?K^-1
第3反应器中混合物的比定压热容 $c ˉ 1,3$	2.47 kJ?kg^-1?K^-1
第4反应器中混合物的比定压热容 $c ˉ 1,4$	2.26 kJ?kg^-1?K^-1
反应器级间冷氢的比定压热容 $c H 2$	14.32 kJ?kg^-1?K^-1
加氢裂化反应平均放热系数H_r	418.4 kJ?kg^-1
第1反应器中混合物的密度ρ₁	905 kg·m^-3
第2反应器中混合物的密度ρ₂	833 kg·m^-3
第3反应器中混合物的密度ρ₃	809.8 kg·m^-3
第4反应器中混合物的密度ρ₄	737.1 kg·m^-3

Table 1 Physical property data used for estimating kinetics parameters of hydrocracking

物性名称	本文取值
第1反应器中混合物的比定压热容 $c ˉ 1,1$	3.14 kJ?kg^-1?K^-1
第2反应器中混合物的比定压热容 $c ˉ 1,2$	2.48 kJ?kg^-1?K^-1
第3反应器中混合物的比定压热容 $c ˉ 1,3$	2.47 kJ?kg^-1?K^-1
第4反应器中混合物的比定压热容 $c ˉ 1,4$	2.26 kJ?kg^-1?K^-1
反应器级间冷氢的比定压热容 $c H 2$	14.32 kJ?kg^-1?K^-1
加氢裂化反应平均放热系数H_r	418.4 kJ?kg^-1
第1反应器中混合物的密度ρ₁	905 kg·m^-3
第2反应器中混合物的密度ρ₂	833 kg·m^-3
第3反应器中混合物的密度ρ₃	809.8 kg·m^-3
第4反应器中混合物的密度ρ₄	737.1 kg·m^-3

Fig.6 Fitness function of improving STA

Table 2 Estimation results of kinetics parameters for hydrocracking reaction

反应速率常数	活化能E_i/(J·mol^-1)	指前因子k_i₀/s^-1
k₁	95700.39 95700.39 95700.39 95700.39 95700.39 95700.39	4585.95
k₂		2383.74
k₃		2373.56
k₄		417.33
k₅		39.32
k₆	97199.38 97199.38 97199.38 97199.38	473.33
k₇		96.48
k₈		2.65×10^-5
k₉		0
k₁₀	63753.57 63753.57 63753.57	0.20
k₁₁		0
k₁₂		9.92×10^-3
k₁₃	97292.32 97292.32	44.70
k₁₄	97292.32 97292.32	0
k₁₅	8018.36	11.70×10^-3

项目	标准STA	改进STA （平均值）	性能提升（平均值）/%
寻优迭代次数	200	41.7	79.15
计算总耗时/s	30477.12	6215.60	79.61
fitness调用耗时/s	30378.39	6108.06	79.89
ode15 s调用耗时/s	30416.73	6199.97	79.62

Table 4 Parameters setting of improved STA

参数名称	取值	参数名称	取值
伸缩算子γ	1	迭代次数iter	2.0×10²
旋转算子α	(1/2)^iterα_max	误差满意阈值ξ	3.0×10^-２
旋转算子初值α_max	1	活化能E_i上限	1.3×10⁵
旋转算子终值α_min	1.0×10^-3	活化能E_i下限	6.0×10³
轴向算子δ	1	指前因子k_i₀上限	7.0×10³
平移算子β	1	指前因子k_i₀下限	0
状态个数SE	30	所求问题状态维数	20

Fig.7 Prediction results on mass fraction of some key components at outlet of hydrocracking reactor

Fig.8 Prediction results of outlet temperature for cascaded hydrocracking reactors

Table 5 Statistical error of 16 hydrocracking testing samples which are adjacent

预测项目	标准STA		改进STA
预测项目	MAE	MRE	MAE	MRE
尾油质量分数	0.001948	1.0627%	0.002412	1.3155%
柴油质量分数	0.001188	0.3069%	0.001510	0.3899%
航煤质量分数	0.000220	0.1089%	0.000306	0.1513%
重石质量分数	0.000455	0.2386%	0.000629	0.3302%
轻石质量分数	0.000260	1.6356%	0.000339	2.1251%
轻端质量分数	0.000280	1.3670%	0.000378	1.8609%
1反出口温度	0.076543	0.0113%	0.111887	0.0166%
2反出口温度	0.106760	0.0158%	0.139421	0.0207%
3反出口温度	0.109646	0.0162%	0.143436	0.0212%
4反出口温度	0.098496	0.0146%	0.122468	0.0182%

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