基于物理信息神经网络的甲烷无氧芳构化反应的正反问题

doi:10.16085/j.issn.1000-6613.2023-1392

化工进展 ›› 2024, Vol. 43 ›› Issue (9): 4817-4823.DOI: 10.16085/j.issn.1000-6613.2023-1392

• 化工过程与装备 • 上一篇

基于物理信息神经网络的甲烷无氧芳构化反应的正反问题

李依梦¹(), 陈运全¹, 何畅²^,³(), 张冰剑¹^,³, 陈清林¹^,³

^1.中山大学材料科学与工程学院，广东广州 510006
^2.中山大学化学工程与技术学院，广东珠海 519082
^3.广东省石化过程节能工程技术研究中心，广东广州 510006

收稿日期:2023-08-11 修回日期:2023-10-02 出版日期:2024-09-15 发布日期:2024-09-30
通讯作者: 何畅
作者简介:李依梦（1999—），女，硕士研究生，研究方向为过程系统工程。E-mail：liym256@mail2.sysu.edu.cn。
基金资助:
广东省自然科学基金(2022A1515010479);国家自然科学基金(22078373)

Forward and reverse problems of methane dehydro-aromatization based on physics-informed neural network

LI Yimeng¹(), CHEN Yunquan¹, HE Chang²^,³(), ZHANG Bingjian¹^,³, CHEN Qinglin¹^,³

^1.School of Materials Science and Engineering, Sun Yat-sen University, Guangzhou 510006, Guangdong, China
^2.School of Chemical Engineering and Technology, Sun Yat-sen University, Zhuhai 519082, Guangdong, China
^3.Guangdong Engineering Center for Petrochemical Energy Conservation, Sun Yat-sen University, Guangzhou 510006, Guangdong, China

Received:2023-08-11 Revised:2023-10-02 Online:2024-09-15 Published:2024-09-30
Contact: HE Chang

摘要/Abstract

摘要：

解决化学反应动力学建模的正问题和反问题研究有助于更深地理解反应机理，降低实验成本。本研究以一维填充床甲烷无氧芳构化（MDA）反应为案例，利用物理信息神经网络（PINN）将化学反应机理方程耦合到损失函数中，以此构建动力学建模和参数反演的求解框架。首先，通过正问题求解确定最佳神经网络超参数方案，结果表明构建的正问题模型在求解MDA反应动力学方程上有良好的预测性能，训练和外推的L₂误差分别为0.19%和0.95%。在此基础上，在0、0.1%、0.3%高斯噪声下，利用标签数据反演反应速率常数，训练得到的预测值与真实值相对误差均在0.5%内，体现出了反问题模型在低质量数据下进行未知动力学参数反演的能力。

关键词: 甲烷无氧芳构化, 物理信息神经网络, 反应动力学模型, 反问题

Abstract:

Research on solving the forward and reverse problems of chemical reaction kinetics modeling can help to gain a deeper understanding of reaction mechanisms and reduce experimental costs. This study took the one-dimensional packed bed methane dehydro-aromatization (MDA) as an example and used a physics-informed neural network to couple the chemical reaction mechanism equations into the loss function. In this way, a solution framework for reaction kinetics modeling and parameter inversion was constructed. Firstly, the optimal neural network hyperparameters were determined by solving the forward problem. The results showed that the constructed model had good predictive performance in solving the MDA reaction kinetics model, with training error and extrapolation error L₂ of 0.19% and 0.95%, respectively. Based on this, the rate constants of MDA were inverted using labeled data under 0, 0.1%, and 0.3% Gaussian noise, and the predicted values obtained from training had a relative error within 0.5% of the true values, demonstrating the ability of physics-informed learning to perform inversion for unknown kinetic parameters under low-quality data.

Key words: methane dehydro-aromatization, physics-informed neural network, reaction kinetic model, inverse problem

中图分类号:

TQ013.2

李依梦, 陈运全, 何畅, 张冰剑, 陈清林. 基于物理信息神经网络的甲烷无氧芳构化反应的正反问题[J]. 化工进展, 2024, 43(9): 4817-4823.

LI Yimeng, CHEN Yunquan, HE Chang, ZHANG Bingjian, CHEN Qinglin. Forward and reverse problems of methane dehydro-aromatization based on physics-informed neural network[J]. Chemical Industry and Engineering Progress, 2024, 43(9): 4817-4823.

图/表 7

表1 MDA反应动力学参数与速率方程

反应j	ΔH_j /J·mol^-1	E_j /J·mol^-1	k_j /mol·(h·g)^-1	K_P_j /atm
反应速率		$d F C H 4 / d q = - 2 r 1$ $d F C 2 H 4 / d q = r 1 - 3 r 2 - 2 r 3$ $d F C 6 H 6 / d q = r 2 - r 3$ $d F C 10 H 8 / d q = r 3$ $d F H 2 / d q = 2 r 1 + 3 r 2 + 3 r 3$
1	2.089×10⁵	65580	0.188	6.149×10^-5
2	-58428	30840	0.194	1.234×10⁵
3	-41737	-190740	4.620	9432

表1 MDA反应动力学参数与速率方程

反应j	ΔH_j /J·mol^-1	E_j /J·mol^-1	k_j /mol·(h·g)^-1	K_P_j /atm
反应速率		$d F C H 4 / d q = - 2 r 1$ $d F C 2 H 4 / d q = r 1 - 3 r 2 - 2 r 3$ $d F C 6 H 6 / d q = r 2 - r 3$ $d F C 10 H 8 / d q = r 3$ $d F H 2 / d q = 2 r 1 + 3 r 2 + 3 r 3$
1	2.089×10⁵	65580	0.188	6.149×10^-5
2	-58428	30840	0.194	1.234×10⁵
3	-41737	-190740	4.620	9432

图1 基于PINN的化学反应正、反问题建模框架

表2 不同超参数下的L2误差

m	L₂误差
m	n=2	n=4	n=6	n=8
64	0.3284	0.0019	0.0020	0.0032
128	0.3274	0.0019	0.1400	0.0054
256	0.0023	0.0018	0.1690	0.6616

图2 不同超参数下的训练效果

图3 模型预测结果

表3 参数反演结果

速率常数	真实值	无噪声		含0.1%高斯噪声		含0.3%高斯噪声
速率常数	真实值	预测值	相对误差/%	预测值	相对误差/%	预测值	相对误差/%
k₁	0.188	0.189	0.5	0.188	0	0.184	2.1
k₂	0.194	0.191	1.5	0.205	5.7	0.184	5.2
k₃	4.620	4.623	0.06	4.760	3.0	4.770	3.2

图4 无噪声和含0.1%、0.3%高斯噪声的标签数据和对应的训练结果

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基于物理信息神经网络的甲烷无氧芳构化反应的正反问题

Forward and reverse problems of methane dehydro-aromatization based on physics-informed neural network

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