Release:
2021. Vol. 7. № 2 (26)About the authors:
Aleksandr I. Filippov, Dr. Sci. (Tech.), Professor, Chief Researcher, Sterlitamak Branch of Ufa University of Science and Technology, Sterlitamak, Russia; filippovai1949@mail.ru, https://orcid.org/0000-0002-0964-9805Abstract:
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.
Keywords:
References:
Aziz H., Settari E. 2004. Mathematical Modeling of Reservoir Systems. Moscow: Institut kompyuternyh issledovanij. 416 pp. [In Russian]
Verzhbitskiy V. M. 2002. Numerical Basics. Moscow: Vysshaya shkola. 839 pp. [In Russian]
Ditkin V. A., Prudnikov A. P. 1966. Operational Calculus. Moscow: Vysshaya shkola. 405 pp. [In Russian]
Karslou G., Eger D. 1964. Thermal Conductivity of Solids. Moscow: Nauka. 487 pp. [In Russian]
Kuznetsov D. S. 1965. Special Functions. Moscow: Vysshaya shkola. 423 pp. [In Russian]
Masket M. 2004. The Flow of Homogeneous Fluids in a Porous Medium. Moscow-Izhevsk: IKI. 628 pp. [In Russian]
Nikolaevskiy V. N., Basniev K. S., Gorbunov A. T., Zotov G. A. 1970. Mechanics of Saturated Porous Media. Moscow: Nedra. 339 pp. [In Russian]
Pudovkin M. A., Salamatin A. N., Chugunov V. A. 1977. Temperature Processes in Operating Wells. Kazan: Izdatelstvo Kazanskogo universiteta. 168 pp. [In Russian]
Rubinshtein L. I. 1972. Temperature Fields in Oil Reservoirs. Moscow: Nedra. 276 pp. [In Russian]
Filippov A. I., Kovalskiy A. A., Gubajdullin M. R. 2019. “Finite-difference and analytical models of filtration flow in an imperfectly penetrated reservoir”. Inzhenernaya fizika, no. 9, pp. 22-30. [In Russian]
Filippov A. I., Akhmetova O. V., Kovalskiy A. A. 2018. “Low-frequency deceleration of the filtration wave in layered heterogeneous permeable formations”. Prikladnaya mekhanika i tekhnicheskaya fizika, vol. 59, no. 3 (349), pp. 103-110. [In Russian]
Filippov A. I., Akhmetova O. V., Kovalskiy A. A., Zelenova M. A. 2020. “The pressure field in the reservoir at a given well flow rate”. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 6, no. 3 (23), pp. 58-78. DOI: 10.21684/2411-7978-2020-6-3-58-78 [In Russian]
Filippov A. I., Akhmetova O. V., Gubaydullin M. R. 2015. “Pressure field with radial filtration in a heterogeneous orthotropic formation in the asymptotic approximation”. Inzhenerno-fizicheskiy zhurnal, vol. 88, no. 6, pp. 1285-1296. [In Russian]
Khayrullin M. H., Shamsiev M. N., Gadilshina V. R., Morozov P. E., Abdullin A. I., Badertdinova E. R. 2016. “Determination of the parameters of the bottomhole zone of a vertical well based on the results of thermohydrodynamic studies”. Inzhenerno-fizicheskiy zhurnal, vol. 89, no. 6, pp. 1470-1474. [In Russian]
Charnyy I. A. 1963. Underground Hydrodynamics. Moscow: Gostoptekhizdat. 397 pp. [In Russian]
Den Iseger P. 2006. “Numerical transform inversion using Gaussian quadrature”. Probability in the Engineering and Informational Sciences, no. 20, pp. 1-44. DOI: 10.1017/S0269964806060013
