天然气水合物热分解Stefan相变数学模拟研究

doi:10.11949/0438-1157.20201573

化工学报 ›› 2021, Vol. 72 ›› Issue (6): 3252-3260.DOI: 10.11949/0438-1157.20201573

天然气水合物热分解Stefan相变数学模拟研究

李明川¹(),樊栓狮²,徐赋海³,严科⁴,黄爱先³

^1.中国石油大学（华东）石油工程学院，山东青岛 266580
^2.华南理工大学化学与化工学院，广东广州 510641
^3.中国石化胜利油田分公司东辛采油厂，山东东营 257094
^4.中国石化胜利油田分公司胜利采油厂，山东东营 257051

收稿日期:2020-11-03 修回日期:2020-11-27 出版日期:2021-06-05 发布日期:2021-06-05
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)

Mathematical modeling of Stefan phase change for thermal dissociation of natural gas hydrate

LI Mingchuan¹(),FAN Shuanshi²,XU Fuhai³,YAN Ke⁴,HUANG Aixian³

^1.School of Petroleum Engineering, China University of Petroleum (East China), Qingdao 266580, Shandong, China
^2.School of Chemistry and Chemical Engineering, South China of Technology, Guangzhou 510641, Guangdong, China
^3.Dongxin Production Plant, Shengli Oil Field, Sinopec, Dongying 257094, Shandong, China
^4.Shengli Production Plant, Shengli Oilfield, Sinopec, Dongying 257051, Shandong, China

Received:2020-11-03 Revised:2020-11-27 Online:2021-06-05 Published:2021-06-05
Contact: LI Mingchuan

摘要/Abstract

摘要：

天然气水合物热分解过程是一个移动边界的Stefan相变问题。在单相连续水合物控制体的守恒积分热传导模型基础上，建立了考虑尖锐移动边界的天然气水合物热分解控制体的界面耦合Stefan能量守恒条件。利用Boltzmann相似变量求得了一半无限大天然气水合物热分解Stefan相变模型的Neumann解，对超越方程进行了单调性证明，确定了Stefan模型解的唯一性。通过实例分析验证了超越方程的单调性和Stefan模型解的唯一性，MATLAB编程实现了水合物体热分解相变过程温度、分解前缘规律性，参数敏感性拟合研究表明，随着温度的升高，λ（超越方程的解）和x_f（界面位置）逐渐增大，x_d（穿越深度）和t_d（穿透时间）逐渐减小。

关键词: Stefan相变, 天然气水合物, 数学模拟, 分解前缘, Neumann解

Abstract:

The thermal dissociation process of natural gas hydrate is a Stefan phase change problem with moving boundaries. Based on the conservation integral heat conduction model of the single-phase continuous hydrate control body, the paper establishes the interface coupling Stefan energy conservation condition of the natural gas hydrate thermal decomposition control body considering the sharp moving boundary. Using Boltzmann's similar variables, the Neumann solution of the Stefan phase transition model for the thermal decomposition of half infinite natural gas hydrate was obtained. The monotonicity of the transcendental equation was proved, and the uniqueness of the Stefan model was confirmed. By example analysis, the monotonicity of the transcendental equation, and the uniqueness solution of Stefan model have been verified. By MATLAB programs, the laws of temperature distribution, dissociation frontal brim have been studied during the thermal dissociation process into a hydrate reservoir. The sensitivity fitting studies have shown that λ (the solution of transcendental equation) and x_f (interface position) increased gradually, x_d (the penetrated depth) and t_d (the penetrated time) decreased gradually with the temperature increasing.

Key words: Stefan phase change, natural gas hydrate, mathematical modeling, dissociation frontal brim, Neumann solution

中图分类号:

TQ 511.1

李明川, 樊栓狮, 徐赋海, 严科, 黄爱先. 天然气水合物热分解Stefan相变数学模拟研究[J]. 化工学报, 2021, 72(6): 3252-3260.

LI Mingchuan, FAN Shuanshi, XU Fuhai, YAN Ke, HUANG Aixian. Mathematical modeling of Stefan phase change for thermal dissociation of natural gas hydrate[J]. CIESC Journal, 2021, 72(6): 3252-3260.

图/表 8

图1 连续水合物控制体

Fig.1 Continuous hydrate control volume

图2 界面不连续水合物控制体

Fig.2 Interface discontinuous hydrate control volume

表1 水合物热分解一维模型基础数据[26-27]

Table 1 One dimensional model basic data for thermal dissociation hydrate[26-27]

初始压力/MPa

初始温度/℃

密度/ (kg/m³)

液相水合物分解区

热扩散系数/(m²/s)

固相水合物区热

扩散系数/(m²/s)

液相水合物分解区

热导率/(W/(m·K))

图3 超越方程单调性及解关系曲线

Fig.3 Relationship curves of the monotonicity and the solution of the transcendental equation

图4 水合物体温度随距离关系曲线

Fig.4 Relationship curves of temperature of hydrate control body vs. distance

图5 水合物体温度随时间关系曲线

Fig.5 Relationship curves of temperature of hydrate control body vs. time

图6 水合物分解前缘随时间关系

Fig.6 Relationship curves of the dissociation frontal brim of hydrate vs. time

图7 温度敏感性参数关系

Fig.7 Relationship curves of the sensitivity analysis of temperature

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天然气水合物热分解Stefan相变数学模拟研究

Mathematical modeling of Stefan phase change for thermal dissociation of natural gas hydrate

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