Abstract The objective of the work is to develop efficient numerical methods for solving the problem of displacement of one fluid by another in a porous medium, arising during the development and operation of oil and gas fields, and creation and operation of underground gas storage facilities in aquifers. At present, when conducting hydrodynamic calculations of underground gas storage facilities, methods are used that do not fully take into account the real properties of the gas and water reservoir, as well as the specifics of the process. In this regard, there is a need to develop efficient numerical methods for conducting hydro gas dynamic calculations that allow to take into account the specified factors and thereby to model the process more accurately. All of the above also apply to problems arising during the operation of gas fields bordering active edge waters. The theoretical justification for the possibility of storing gas in horizontal aquifers with a sufficiently sealed clay roof was first given by Charny et al. (1969). Subsequently, various approximate methods were proposed, and hydrodynamic calculations of water displacement by gas were carried out on their basis. Numerical implementation of the algorithm was carried out by the finite difference method on a moving grid. The proposed difference-iteration method in moving grids can be used to determine a rational method of influencing the reservoir.
Gasimov et al. (Mon,) studied this question.