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

doi:10.11949/0438-1157.20201573

Abstract

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

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

CLC Number:

TQ 511.1

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.

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.

Figures/Tables 8

Fig.1 Continuous hydrate control volume

Fig.2 Interface discontinuous hydrate control volume

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))

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

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

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

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

Fig.7 Relationship curves of the sensitivity analysis of temperature

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