Mathematical Modeling of Water Vapor Injection into a Saturated Porous Medium

IF 0.8 Q2 MATHEMATICS
M. K. Khasanov, S. L. Borodin, M. V. Stolpovsky
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引用次数: 0

Abstract

A mathematical model of the process of water vapor injection into a porous reservoir containing methane is proposed, taking into account vapor condensation in the porous medium. A self-similar solution of this problem is constructed and an algorithm for its numerical solution is developed. Calculations were carried out, which showed good agreement between the self-similar and numerical solutions at a sufficiently low reservoir permeabilities. It is noted that for high-permeability reservoirs, in order to obtain adequate results, it is necessary to carry out longer-term calculations using the proposed numerical algorithm. Based on the analysis of the numerical experiment results, it is shown that when vapor is injected into a reservoir containing methane, five characteristic regions can be formed, namely: region with superheated vapor; with vapor and water in state of phase equilibrium; with methane, vapor and water in state of phase equilibrium; with methane and vapor; and region that contains only methane. Also the results of numerical experiments on the effect of vapor injection pressure and temperature on a reservoir heating are presented.

Abstract Image

水蒸气注入饱和多孔介质的数学建模
摘要 考虑到多孔介质中的水汽凝结,提出了向含甲烷的多孔储层注入水汽过程的数学模型。构建了该问题的自相似解,并开发了数值解算法。计算结果表明,在储层渗透率足够低的情况下,自相似解与数值解之间具有良好的一致性。需要指出的是,对于高渗透率储层,为了获得充分的结果,有必要使用所提出的数值算法进行长期计算。基于数值实验结果的分析表明,向含有甲烷的储层注入蒸汽时,可形成五个特征区域,即:过热蒸汽区域;处于相平衡状态的蒸汽和水;处于相平衡状态的甲烷、蒸汽和水;甲烷和蒸汽;以及仅含有甲烷的区域。此外,还介绍了蒸汽注入压力和温度对储层加热影响的数值实验结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.50
自引率
42.90%
发文量
127
期刊介绍: Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.
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