Mathematical model and numerical algorithms to analyze gas filtration process in a porous medium

  • № 3 (51) 2019

Страницы: 

47

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67

Язык: английский

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Аннотация

В статье рассматривается задача, связанная с исследованием процесса фильтрации газа в пористой среде с помощью математической модели объекта, описывающая нелинейное уравнение в частных производных и соответствующих им краевых и внутренних условий. В работе для выбора стратегии решения вышеуказанной задачи проанализированы научно-исследовательские работы, связанные с математическим моделированием и их численными методами решения, выполненные за последние 5-10 лет. В статье приведены основные этапы построения математической модели процесса фильтрации газа в пористых средах с учетом изменения гидродинамических параметров объекта исследования. Для решения вышеуказанной задачи, использованы численные методы: локально-одномерные схемы и схемы продольно-поперечных направлений. Получены системы одномерных уравнений в конечных разностях, аппроксимирующие краевую задачу теории фильтрации на семействах прямых линий. Для решения процесса нелинейной фильтрации газа в пористой среде были проверены некоторые способы построения итерационного процесса. В статье для исследования откликов основных параметров процесса приведены серия вычислительных экспериментов на компьютерах, анализов, связанных с ними.

The paper deals with the problem of gas filtration process in a porous medium using a mathematical model of an object; the model is described by a nonlinear partial differential equation and the corresponding boundary and internal conditions. To select a strategy for solving the above-mentioned problem, scientific-research studies over the last 5-10 years have been analyzed related to mathematical modeling and numerical methods of solution. The paper presents the main stages in construction of mathematical model of the process of gas filtration in porous media, taking into account the changes in hydrodynamic parameters of the object of study. To solve the above problem, the following numerical methods have been used: local-one-dimensional schemes and longitudinal-transverse direction schemes. Systems of one-dimensional equations in finite differences have been obtained; they approximate the boundary value problem of the theory of filtration on straight lines. To solve the problem of nonlinear gas filtration in a porous medium, several methods of constructing an iterative process have been checked. To study the responses of the principal parameters of the process, a series of computational experiments on a computer, their analyses and conclusions are given in the paper.

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