DOI: 10.5937/jaes0-27897

This is an open access article distributed under the CC BY 4.0

Volume 19 article 768 pages: 97 - 108

This paper is devoted to the development and investigation of methods of mathematical and computer simulation of
the process of fluid filtration in a porous medium. The methods of numerical solution of the problems of the filtration
theory of build-up of conditions in the catchment and discharge areas boundaries, identification of filtration-capacitive
parameters of the effective formation and determination of free (unknown) boundaries and creation of computational
algorithms for analysis and forecast of technological indicators of oil and gas fields are considered. Methods and
models of continum mechanics, filtration theories, and methods for solving ill-defined problems, numerical modeling
and computer programming were used. Approximate Numerical methods for solving direct and inverse problems of
filtration theory, mathematical models for single-phase isothermal filtration of a gas mixture in a horizontal formation
at small concentration gradients of components, studying the properties of self-similar solutions, as well as numerical
solving the problem of identifying the capacitive parameters of the water-bearing stratum.

1. Tikhonov, A.N. (1943). On the stability of inverse problems. Dokl. AN SSSR (Moscow), 39(5), 195- 198.

2. Lavrentev, M. (1978). About some incorrect problems of mathematical physics. Novosibisk: Science.

3. Marchuk, G.I. (1980). Methods of Computational Mathematics. Moscow: Science.

4. Romanov, V.G. (1984). Inverse problems of mathematical physics. Moscow: Science.

5. Alexeev, Yu.K. (1971). Method of refinement of parameters of the mathematical model of the oil-producing formation. NTS for oil production. Moscow: Nedra.

6. Ahmetzyanova, D.M. (1975). Investigation of ways of specification of parameters of oil layers on operational data. PhD dissertation. Moscow.

7. Ahmetzyanova, D.M. (1971). On the calculation of the hydraulic conductivity of an oil reservoir at wells. Proceedings of TatNIPIneft. Kuibyshev, 20, 328-334.

8. Baishev, V.Z. (1983). Creation of methods for solving direct and inverse problems of development of deposits with several objects of operation. PhD dissertation. Moscow.

9. Bulygin, V.Ya. (1964). One finite-difference method of restoration of the function of formation pressure and hydraulic conductivity of formation. Kazan: Publishing house of Kazan University.

10. Zholdasov, A., Zakirov, S.N., Kenzhebekov, D.U., Esedulaev, R. (1989). Restoration of conditions in catchment and discharge areas of a water basin. Geologyand Intelligence (Moscow), 4, 132-134.

11. Palatnik, B.М. (1987). Identification of the gas reservoir parameters according to the development data under the water-drive regime. MING. Moscow: Dep. In VNIIgazprom, 02.06.87, No. 947-gs.

12. Palatnik, B.M., Zakirov, I.S. (1990). Identifi cation of the parameters of gas reservoirs under the gas and water-drive development regimes, Survey. inf. VNIIEGAZPROM, ser.: Development and operation of gas and gas condensate fields, 2, 37.

13. Kaliev, I.A., Mukhambetzhanov, S.T., Razinkov, E.N. (1989). Correctness of the mathematical model of nonequilibrium phase transitions of water in porous media. Dynamics of a continuous medium (Novosibirsk), 93-94, 46-60.

14. Danaev, N.T., Shazhdekeeva, N.K. Mukhambetzhanov S.T. (2010). On a problem of the theory of filtration taking into account phase transitions. Bulletin of KazNU named after al-Farabi (Almaty), 3 (66): 192- 196.

15. Shazhdekeeva, N.K., Kammatov, K., Adieva, A.A. (2005). On the existence of stationary solutions of a certain type of quasinelinear systems. Messenger of ASU, 2: 31-36.

16. Shazhdekeeva, N.K. Mukhambetzhanov, S.T. (2010). On the properties of the solution of a certain problem of the theory of filtration with respect to phase transitions. Materials of the V international conference: "Mathematical modeling and information technologies in education and science", dedicated to the 25th anniversary of computer science in the school (Almaty), pp. 114-118.

17. Shazhdekeeva, N.K., Myrzasheva, A.N., Baimakhan, A.R., Abdiakhmetova, Z.M., Latipov, E. (2019). About identification of filtration-capacitive parameters of the water falled basin. VESTNIK of Kaz NRTU (Almaty), 1, 514-521.

18. Shazhdekeeva, N.K., Aujani, E. (2008). About one task of restoring conditions on the catchment discharge areas boundaries and identification of filtrational parameters. Izvestiya NAS RK, Seriya fi z-mat- Almaty, 5, 55-59.

19. Safina, G. (2019). Numerical solution of filtration in porous rock. E3S Web of Conferences, 97, 05016, DOI: 10.1051/e3sconf/20199705016

20. Ravshanov, N., Aminov, S., & Kravets, O.J. (2019). Mathematical model and numerical algorithms to analyze gas filtration process in a porous medium. Journal of Physics: Conference Series, 1399(5), 055036. DOI: 10.1088/1742-6596/1399/5/055036

21. Duan, C., Liu, C., Wang, C., & Yue, X. (2019). Numerical methods for porous medium equation by an energetic variational approach. Journal of Computational Physics, 385, 13-32. DOI: 10.1016/j. jcp.2019.01.055

22. Liu, H., Wu, D., Xie, M., Liu, H., & Xu, Z. (2019). Experimental and numerical study on the lean premixed filtration combustion of propane/air in porous medium. Applied Thermal Engineering, 150, 445- 455. DOI: 10.1016/j.applthermaleng.2018.12.155

23. Kuzmina, L., Osipov, Yu., & Zheglova, Yu. (2019). Global asymptotics of the filtration problem in a porous medium. International Journal for Computational Civil and Structural Engineering, 15(2), 77-85. DOI: 10.22337/2587-9618-2019-15-2-77-85

24. Fayziev, B., Ibragimov, G., Khuzhayorov, B., & Alias, I. A. (2020). Numerical Study of Suspension Filtration Model in Porous Medium with Modified Deposition Kinetics. Symmetry, 12(5), 696. DOI: 10.3390/ sym12050696

25. Printsypar, G., Bruna, M., & Griffiths, I. M. (2019). The influence of porous-medium microstructure on filtration. Journal of Fluid Mechanics, 861, 484-516. DOI: 10.1017/jfm.2018.875

26. Rybak, I., Schwarzmeier, C., Eggenweiler, E., & Rüde, U. (2020). Validation and calibration of coupled porous-medium and free-fl ow problems using pore-scale resolved models. Computational Geosciences, 1-15. DOI: 10.1007/s10596-020-09994-x

27. Mikishanina, E. A. (2019). Investigation of the filtration coefficient of elastic-porous medium at plane deformation. Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 29(3), 396-407. DOI: 10.20537/vm190309

28. Kholmatova, I. I. (2020). Mathematical modeling and numerical algorithm for the gas displacement by water in an in homogeneous porous medium. In Journal of Physics: Conference Series, 1546, 012084. DOI: 10.1088/1742-6596/1546/1/012084

29. Shazhdekeeva, N.K. (2008). On one direct and inverse problem of single-phase isothermal filtration of a gas mixture in a horizontal formation. Bulletin of Kaz NU named after al-Farabi (Almaty), 2 (57), 101- 109.

30. Maksimov, A.M., Tsypkin, G.G. (1987). Formation of a two-phase zone with the interaction of thawed and frozen rocks with a solution of salt. Moscow: Institute of Problems of Mechanics of the Academy of Sciences.