将二氧化碳注入饱含水合物、甲烷和水混合物的储层时用二氧化碳取代水合物中甲烷的数学模型

IF 0.4 4区数学 Q4 MATHEMATICS

Proceedings of the Steklov Institute of Mathematics Pub Date : 2023-12-20 DOI:10.1134/s0081543823040181

G. G. Tsypkin

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引用次数: 0

摘要

摘要针对储层中与水和游离甲烷处于热力学平衡状态的水合物中二氧化碳置换甲烷的情况，提出了一个数学模型。假设置换反应区域足够窄，可以用转换前沿来近似。找到的自相似解将问题简化为超越方程组的数值分析。数值实验表明，存在三种特征的注入状态，其实施取决于储层中处于自由状态的水量。

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Mathematical Model of Replacing Methane in Hydrate with Carbon Dioxide When It Is Injected into a Reservoir Saturated with a Mixture of Hydrate, Methane, and Water

Abstract

A mathematical model is proposed for the replacement of methane with carbon dioxide in a hydrate contained in a reservoir in thermodynamic equilibrium with water and free methane. The substitution reaction region is assumed to be narrow enough to be approximated by the conversion front. A self-similar solution is found that reduces the problem to the numerical analysis of a system of transcendental equations. Numerical experiments show that there exist three characteristic regimes of injection, whose implementation depends on the amount of water in the free state in the reservoir.

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来源期刊

Proceedings of the Steklov Institute of Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.90

自引率

20.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Proceedings of the Steklov Institute of Mathematics is a cover-to-cover translation of the Trudy Matematicheskogo Instituta imeni V.A. Steklova of the Russian Academy of Sciences. Each issue ordinarily contains either one book-length article or a collection of articles pertaining to the same topic.