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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.

A mathematical model, numerical algorithm, solution, and results of the computational experiment on a computer are developed to predict the process of heat and moisture transfer in porous media, taking into account such factors as the internal heat and moisture release of a porous natural product on the example of raw cotton and its products of hulling, seeds of various crops. It also considers the effect of temperature and moisture content changes in the environment on the storage and drying of porous materials. In this study, the developed mathematical support of the object under research makes it possible to predict the change in temperature and moisture content at arbitrary points of the porous body and serves to prevent the loss of quality and spontaneous combustion of materials under solar radiation and to analyze and make managerial decisions. Based on the method of coordinate-wise splitting, a numerical algorithm for calculating three-dimensional heat and moisture transfer problems in areas of the parallelepiped type is presented. An implicit second-order difference scheme for calculating the required functions is presented. Based on the numerical calculations performed, it was established that moisture and heat transfer and their exchange with the environment occurs in the upper layers of the cotton pile; in the inner layers, there is an increase in temperature and moisture due to the respiration of raw cotton and its seeds, which depends on the degree of moisture of the raw cotton and their products of hulling.