Modeling pressure fields in a petroleum reservoir taking into account the change of liquid level in the well

Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy


Release:

2021. Vol. 7. № 2 (26)

Title: 
Modeling pressure fields in a petroleum reservoir taking into account the change of liquid level in the well


For citation: Filippov A. I., Akhmetova O. V., Kovalskiy A. A., Zelenova M. A. 2021. “Modeling pressure fields in a petroleum reservoir taking into account the change of liquid level in the well”. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 7, no. 2 (26), pp. 95-112. DOI: 10.21684/2411-7978-2021-7-2-95-112

About the authors:

Aleksandr I. Filippov, Dr. Sci. (Tech.), Professor, Department of General and Theoretical Physics, Sterlitamak branch of the Bashkir State University; eLibrary AuthorID, filippovai@rambler.ru

Oksana V. Akhmetova, Dr. Sci. (Phys.-Math.), Professor, Department of General and Theoretical Physics, Sterlitamak branch of the Bashkir State University; eLibrary AuthorID, ahoksana@yandex.ru

Aleksei A. Kovalsky, Cand. Sci. (Phys.-Math.), Director, Sterlitamak Branch of the Bashkir State University; eLibrary AuthorID, aakov68@mail.ru

Marina A. Zelenova, Cand. Sci. (Phys.-Math.), Associate Professor, Department of General and Theoretical Physics, Sterlitamak Branch of Bashkir State University; marina_ag@inbox.ru

Abstract:

This article presents a numerical model of pressure fields during filtration of reservoir fluid, which accounts for the effect of the well. The mathematical formulation of the problem under consideration includes the equation of piezoconductivity in a cylindrical coordinate system and differs in a non-classical boundary condition obtained from the ratio of the balance of mass and momentum. The authors compare the numerical calculations and the analytical solution constructed in the Laplace — Carson image space. Den Iseger’s numerical algorithm is used to convert it to the original space. As a result of the comparison, the area of applicability of the computational experiment was determined. It is shown that in the case of a limited reservoir, the exact solution of the problem coincides with a numerical experiment over the entire domain of definition. In the case of an infinite reservoir, the numerical model is applicable only in the region of small times, the dimensions of which are determined by the values of the right boundary and the radial coordinate.

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