Multivariate nonlinear regression model of methanol to aromatics by two-state fixed bed for product prediction

doi:10.11949/0438-1157.20211405

Abstract

Abstract:

Aiming at the problems of multiple assumptions about the mechanism modeling of methanol-to-aromatics, complex product prediction process, and high computational cost, a data-driven modeling method based on multiple nonlinear regression analysis was proposed. The influence of reaction pressure, methanol volume space velocity, central temperature, running time, effects of cumulative methanol feed and its interaction on aromatic products is studied in the two-stage fixed bed reaction system. The least square method is used to estimate the parameters and four regression models of quadratic nonlinear product distribution are established. The test results show that the overall decisive indicator of the test sample is 0.9576 and the mean square error MSE is 0.0037, which shows the high prediction accuracy of the product, time saving and strong generalization compared with the traditional kinetic model; The interaction between air speed and pressure influences the hydrocarbon selectivity significantly, and the pressure peak corresponding to the maximum hydrocarbon proportion in the product also increases with the airspeed increases.

Key words: two-stage fixed bed, methanol to aromatic, multivariate nonlinear regression, model, prediction

摘要：

针对甲醇制芳烃机理建模假设多、产物预测过程复杂、计算成本高等问题，提出了一种多元非线性回归分析的数据驱动建模方法。在两段法固定床反应系统中研究了反应压力、甲醇体积空速、一段中心温度、二段中心温度、装置运行时间、累计甲醇进料量及其交互作用对芳烃产物的影响。利用最小二乘法进行参数估计，建立四个六元二次非线性产物分布回归模型。测试结果表明，测试样本的总体决定性指标 $ρ 2$ 为0.9576，均方误差MSE为0.0037，相比于传统的动力学模型，具有产物预测精确度高、计算量小以及泛化性强的特点；空速和反应压力的交互作用对产物中芳烃选择性影响显著，在空速增大的情况下，产物中最大芳烃占比对应的压力峰值也随之增高。

关键词: 两段法固定床, 甲醇制芳烃, 多元非线性回归, 模型, 预测

CLC Number:

TQ 018

Xiongfei XU, Penglong LIU, Wei ZHANG, Xin XU, Kan ZHANG, Junwen WANG. Multivariate nonlinear regression model of methanol to aromatics by two-state fixed bed for product prediction[J]. CIESC Journal, 2022, 73(2): 838-846.

许雄飞, 刘鹏龙, 张玮, 许鑫, 张侃, 王俊文. 两段法固定床甲醇制芳烃产物预测多元非线性回归模型[J]. 化工学报, 2022, 73(2): 838-846.

Figures/Tables 10

Fig.1 Small test unit for methanol to aromatic in two-stage fixed bed

Table 1 Change scope of process conditions of MTA in two-stage fixed bed

工艺条件	上限	下限
p/MPa	0	0.8
τ/h^-1	0.1	0.5
T₁/℃	390	510
T₂/℃	450	510

Fig.2 Distribution of MTA products in two-stage fixed bed with device running time

Table 2 MTA partial experimental data

序号	p/MPa	τ/h^-1	T₁/℃	T₂/℃	TOS/min	M/g	w(甲醇)/%	w(C₁)/%	w(烷烃)/%	w(烯烃)/%	w(芳烃)/%
1	0	0.1	390.2	450	15118	2332.92	0.20	2.97	41.46	18.75	36.63
2	0	0.1	389	510	13751	1881.81	0.10	10.25	32.93	17.95	38.76
3	0	0.3	450.4	480	16075	3162.62	0.29	2.79	36.63	25.88	34.41
4	0	0.1	510	450	1443	476.19	0.01	48.30	16.59	3.58	31.53
5	0.22	0.4	426.1	460.5	5469	4354.77	0.13	4.00	34.16	8.23	53.48
6	0.23	0.4	422.5	490	5947	4990.51	0.24	5.13	37.21	12.25	45.16
7	0.24	0.2	423.4	462.6	7495	6180.13	0.08	4.67	36.75	8.91	49.59
?	?	?	?	?	?	?	?	?	?	?	?
68	0.46	0.3	458.8	480	16445	14527.90	0.18	15.72	30.65	8.66	44.79
69	0.46	0.3	457.3	480	16643	14725.90	0.76	16.04	30.21	8.10	44.89
70	0.44	0.3	454.1	480	17608	13879.3	0.45	10.86	32.06	6.63	50.00
71	0	0.3	394.9	510	18112	14383.3	0.17	6.50	25.55	30.87	36.91

Table 3 Model statistical tests

模型	实验组数	参数维度	F	$F 0.05 (28,29)$
C₁	57	28	65.74	1.87
烷烃	57	28	181.03	1.87
烯烃	57	28	86.13	1.87
芳烃	57	28	192.41	1.87

Table 3 Model statistical tests

模型	实验组数	参数维度	F	$F 0.05 (28,29)$
C₁	57	28	65.74	1.87
烷烃	57	28	181.03	1.87
烯烃	57	28	86.13	1.87
芳烃	57	28	192.41	1.87

Table 4 Comparison of training and test sets

MVR model	Train set		Test set
MVR model	$ρ 2$	MSE	$ρ 2$	MSE
C₁	0.98	0.001	0.9	0.003
烷烃	0.99	0.0006	0.94	0.005
烯烃	0.99	0.0001	0.96	0.002
芳烃	0.99	0.001	0.97	0.005
总体	0.992	0.0007	0.9576	0.0037

Table 4 Comparison of training and test sets

MVR model	Train set		Test set
MVR model	$ρ 2$	MSE	$ρ 2$	MSE
C₁	0.98	0.001	0.9	0.003
烷烃	0.99	0.0006	0.94	0.005
烯烃	0.99	0.0001	0.96	0.002
芳烃	0.99	0.001	0.97	0.005
总体	0.992	0.0007	0.9576	0.0037

Fig.3 Parity plot of MTA product distribution

Fig.4 Parity plot of overall predicted sample

Table 5 Analysis of variance for aromatic model

方差来源	平方和	自由度	均方	F值	P值
模型	0.72	27	0.027	12.15	< 0.0001
A	2.72×10^-5	1	2.72×10^-5	0.012	0.9121
B	0.068	1	0.068	30.96	< 0.0001
C	0.021	1	0.021	9.48	0.0045
D	3.75×10^-4	1	3.75×10^-4	0.17	0.6821
E	8.65×10^-3	1	8.65×10^-3	3.95	0.0565
F	8.44×10^-3	1	8.44×10^-3	3.85	0.0593
AB	0.16	1	0.16	73.2	< 0.0001
AC	0.019	1	0.019	8.65	0.0064
AD	1.83×10^-4	1	1.83×10^-4	0.084	0.7745
AE	0.022	1	0.022	10.21	0.0034
AF	0.014	1	0.014	6.59	0.0157
BC	1.88×10^-7	1	1.88×10^-7	8.58×10^-5	0.9927
BD	2.71×10^-3	1	2.71×10^-3	1.24	0.2748
BE	2.44×10^-3	1	2.44×10^-3	1.11	0.2999
BF	3.02×10^-3	1	3.02×10^-3	1.38	0.2497
CD	4.87×10^-5	1	4.87×10^-5	0.022	0.8825
CE	6.59×10^-4	1	6.59×10^-4	0.3	0.5876
CF	5.18×10^-3	1	5.18×10^-3	2.37	0.1349
DE	3.05×10^-4	1	3.05×10^-4	0.14	0.7119
DF	2.65×10^-4	1	2.65×10^-4	0.12	0.7305
EF	2.37×10^-3	1	2.37×10^-3	1.08	0.3068
A²	0.013	1	0.013	6.16	0.0191
B²	3.92×10^-5	1	3.92×10^-5	0.018	0.8945
C²	2.59×10^-3	1	2.59×10^-3	1.18	0.2863
D²	0.011	1	0.011	5.12	0.0313
E²	8.00×10^-3	1	8.00×10^-3	3.65	0.0659
F²	1.91×10^-4	1	1.91×10^-4	0.087	0.7699
残差	0.064	29	2.19×10^-3
总偏差	0.78	56

Fig.5 Effect of the interaction among the various variables

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