水合物热分解Stefan相变模型解的存在性及Laplace变换求解

doi:10.11949/0438-1157.20221376

化工学报 ›› 2023, Vol. 74 ›› Issue (4): 1746-1754.DOI: 10.11949/0438-1157.20221376

水合物热分解Stefan相变模型解的存在性及Laplace变换求解

李明川¹^,²(), 樊栓狮³, 徐赋海⁴, 卢惠东⁴, 李晓军⁴

^1.中国石油大学（华东）石油工程学院，山东青岛 266580
^2.非常规油气开发教育部重点实验室（中国石油大学（华东）），山东青岛 266580
^3.华南理工大学化学与化工学院，广东广州 510641
^4.中国石化胜利油田分公司东辛采油厂，山东东营 257094

收稿日期:2022-10-18 修回日期:2023-03-01 出版日期:2023-04-05 发布日期:2023-06-02
通讯作者: 李明川
作者简介:李明川（1976—），男，博士，副教授，iceswpi@126.com
基金资助:
中国科学院知识创新工程基金项目(KGCX2-SW-309)

Existence and Laplace transform of the solution to Stefan phase change model in thermal dissociation hydrate

Mingchuan LI¹^,²(), Shuanshi FAN³, Fuhai XU⁴, Huidong LU⁴, Xiaojun LI⁴

^1.School of Petroleum Engineering，China University of Petroleum, Qingdao 266580, Shandong, China
^2.Key Laboratory of Unconventional Oil & Gas Development (China University of Petroleum), Ministry of Education, Qingdao 266580, Shandong, China
^3.School of Chemistry and Chemical Engineering, South China University of Technology, Guangzhou 510641, Guangdong, China
^4.Dongxin Production Plant, SINOPEC Shengli Oilfield, Dongying 257094, Shandong, China

Received:2022-10-18 Revised:2023-03-01 Online:2023-04-05 Published:2023-06-02
Contact: Mingchuan LI

摘要/Abstract

摘要：

天然气水合物热分解Stefan相变模型为二阶抛物线型偏微分方程(组)。开展了水合物热分解Stefan相变模型解的存在性、唯一性论证和Laplace求解方法的探索。演绎了简化的过程、细节的推导：应用微分方程的迭代格式，导出了最大、最小值引理和参数取值范围；通过边界上的交替条件映射对x_n (t)、T_n (x，t)的极限存在性的证明，证实了微分方程解的存在；采用反证法，证明了Stefan微分方程解的唯一性。运用Laplace变换、分离变量和Laplace逆变换法，求得了该Stefan模型的解析解，超越方程的单调性证明了方程解的唯一性。

关键词: Stefan模型, Laplace变换, 相变, 天然气水合物, 偏微分方程

Abstract:

Stefan phase change model is a second order partial differential equation (or set) in thermal dissociation natural gas hydrate. The demonstration of existence and uniqueness, and the probe of Laplace method of the solution to Stefan phase change model were discussed for the thermal dissociation natural gas hydrate. The simplification process and the detailed derivation for the model were deduced. By using the iterative scheme method of differential equations, the maximum and minimum lemma and the range of parameter values were derived. The proof of the existence of the limit of x_n (t), T_n (x,t) by alternating condition maps on the boundary confirms the existence of the solution of the differential equation. The uniqueness of the solution of Stefan differential equation is proved by contradictory method. Using Laplace transform, separation of variables and Laplace inverse transform method, the analytical solution of the Stefan model is obtained, and the monotonicity proof of the transcendental equation verifies the uniqueness of the solution of the equation.

Key words: Stefan model, Laplace transform, phase change, natural gas hydrate, partial differential equation

中图分类号:

TQ 511.1

李明川, 樊栓狮, 徐赋海, 卢惠东, 李晓军. 水合物热分解Stefan相变模型解的存在性及Laplace变换求解[J]. 化工学报, 2023, 74(4): 1746-1754.

Mingchuan LI, Shuanshi FAN, Fuhai XU, Huidong LU, Xiaojun LI. Existence and Laplace transform of the solution to Stefan phase change model in thermal dissociation hydrate[J]. CIESC Journal, 2023, 74(4): 1746-1754.

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水合物热分解Stefan相变模型解的存在性及Laplace变换求解

Existence and Laplace transform of the solution to Stefan phase change model in thermal dissociation hydrate

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