In this work, computer simulation of filtration processes based on the laws of hydrodynamics is considered. The adequacy of the developed models was verified by conducting a series of computational experiments. Created mathematical and software serves the purpose of research, forecasting and decision-making in the development and design of oil and gas fields.
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. 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. 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.
A mathematical model was developed to numerically study the process of fluid and gas filtration in three-layer interacting pressure porous formations. It is based on the reviews related to the mathematical modeling developed in recent years; it describes a system of partial differential equations with boundary and initial conditions and a conservative numerical algorithm for conducting a computational experiment (CE) on a computer. In this article, to analyze and make managerial decisions, the results of numerical calculations are presented in the form of graphical objects, which can be used to propose schemes for the location and capacity of vertical drainage wells to protect irrigated and non-irrigated areas from flooding. Using the proposed mathematical tool, it is possible to obtain the predicted groundwater levels of any area for the required period of time, taking into account some factors, such as the inhomogeneity of the reservoir in a plan, the slope of the confining layer, and other hydrogeological, hydro-technical, and natural conditions, or to calculate the thickness and the optimal location of vertical drainage wells to protect the territory, and to develop oil and gas fields and increase their oil and gas recovery. Analysis of the results of a numerical study of the process made it possible to establish the degrees of influence of the elastic filtration regime in a weakly permeable layer on the overflow into adjacent layers.
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