A mathematical model that describes a partial differential equation with boundary, internal and initial conditions was developed in the article, to study the gas-dynamic parameters of the gas filtration process in a porous medium under isothermal conditions. The study was performed based on the reviews of research works related to mathematical modeling in recent years. Computational experiments (CE) were conducted on a computer to determine the response of the main parameters on the process of gas filtration in a porous medium on the basis of the developed mathematical tool (model, numerical algorithm, and software). The results of numerical calculations were presented in the form of tables and graphical objects for the purpose of developing oil and gas fields and increasing oil and gas recovery. With the analysis of the numerical calculations performed, it was established that when the parameters and properties of gas filtration are considered as functions of pressure, then the process of gas filtration in porous media can be adequately described, as a whole, and it correctly reflects the main point of the object under research. It could be concluded that with the mathematical tool developed, it became possible to conduct a comprehensive study of the process of gas filtration in a porous medium.
1. Palatnik, B.M., and T.N. Segin. A New Approach for Small-Scale Simulation of Multiphase Flow in Naturally Fractured Reservoirs. European Petroleum Computer Conference, Stavanger, Norway, May 1992. doi: https://doi.org/10.2118/24263-MS (https://onepetro.org/SPEEPCC/proceedings-abstract/92EPCC/All-92EPCC/SPE-24263-MS/53978)
2. Berveno E.V., Kalinkin A.A. and Laevsky Y.M. Simulation of Incompressible Fluid Filtration in Fractured-porous Oil Field // Conference Proceedings, 6th EAGE Saint Petersburg International Conference and Exhibition, Apr 2014, Volume 2014, p.1 – 5, DOI: 10.3997/2214-4609.20140248 (https://www.earthdoc.org/content/papers/10.3997/2214-4609.20140248)
3. Spiridonov D., Vasilyeva M. Simulation of filtration problems in fractured porous media with mixed finite element method (Embedded Fracture Model) // Mathematical notes of NEFU, 24(3), pp. 100-110. doi:10.25587/SVFU.2018.3.10893. (http://www.mzsvfu.ru/index.php/mz/article/view/simulation-of-filtration-problems-in-fractured-porous-media)
4. Vabishchevich P., Vasilyeva M. Iterative solution of the pressure problem for the multiphase filtration// Mathematical Modelling and Analysis. - 2012. - Vol. 17, Issue 4. - Pp. 532-548. - DOI: 10.3846/13926292.2012.706655 (https://www.tandfonline.com/doi/abs/10.3846/13926292.2012.706655)
5. Pyatkov A.A., Rodionov S.P., Kosyakov V.P. and Musakaev N.G. Study of filtration processes of a two-phase fluid in a zonal-inhomogeneous fractured-porous medium // Journal of Physics: Conference Series. - 2019. - Vol. 1404. - P. 012039. - DOI: 10.1088/1742-6596/1404/1/012039 (https://iopscience.iop.org/article/10.1088/1742-6596/1404/1/012039/meta)
6. Maksat, K., Kalipa, K., Kulyash, B., Orken, M., & Assel, A. (2018). Numerical simulation of two-phase filtration in the near well bore zone, Open Engineering, 8(1), 77-86. doi: https://doi.org/10.1515/eng-2018-0010 (https://www.degruyter.com/view/journals/eng/8/1/article-p77.xml?language=en)
7. Rasulov M., Kul R.H. (2009) The Study of Filtration of Two Phase Fluid in a Porous Medium in a Class of Discontinuous Functions. In: Margenov S., Vulkov L.G., Waśniewski J. (eds) Numerical Analysis and Its Applications. NAA 2008. Lecture Notes in Computer Science, vol 5434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00464-3_57 https://link.springer.com/chapter/10.1007/978-3-642-00464-3_57)
8. Kurbonov N., Aminov S. Computer modeling of filtration processes with piston extrusion // Journal of Physics: Conference Series. - 2020. - Vol. 1441. - P. 012147. - DOI: 10.1088/1742-6596/1441/1/012147
9. Ravshanov N., Kurbonov N., Mukhamadiev A. An Approximate Analytical Solution of the Problem of Fluid Filtration in the Multilayer Porous Medium // International Journal of Computational Methods. - 2016. — Vol. 13, № 6. — 1650042 [10 pages] DOI: http://dx.doi.org/10.1142/S0219876216500420
10. Kurbonov N., Ibragimova K. Numerical Modeling of the Filtration Process During Oil Displacement by Gas // International Journal of Advanced Trends in Computer Science and Engineering. - 2020. - Vol. 9, Issue 5. - P. 8526-8532. - DOI: 10.30534/ijatcse/2020/232952020.
11. Liu W. Exact analytical solution of a generalized multiple moving boundary model of one-dimensional non-Darcy flow in heterogeneous multilayered low-permeability porous media with a threshold pressure gradient // Applied Mathematical Modelling. - 2020. — Vol. 81. — Pp. 931-953. - DOI: 10.1016/j.apm.2020.01.028
12. Ford R.A., Abu Zaytoon M.S., Hamdan M. H. Simulation of flow Through Layered Porous Media // IOSR Journal of Engineering (IOSRJEN). - 2016. — Vol. 06, № 06. — Pp. 48-61.
13. Hajji M.A. Multi-Point Special Boundary-Value Problems and Applications to Fluid Flow Through Porous Media // Proceedings of the International MultiConference of Engineers and Computer Scientists (IMECS 2009). Vol II. - Hong Kong, 2009.— Pp. 18-20.
14. Zhu J., Ma J. An Improved Gray Lattice Boltzmann Model for Simulating Fluid Flow in Multi-scale Porous Media // Advances in Water Resources. - 2013. — Vol. 56. — Pp. 61-76. DOI: 10.1016/j.advwatres.2013.03.001
15. Allan F.M., Hajji M.A. Multi-layer parallel shooting method for multi-layer boundary value problems // 2009 International Conference on Innovations in Information Technology (IIT), Al Ain, 2009, pp. 289-293, doi: 10.1109/IIT.2009.5413402.
16. Yehya A., Naji H., Sukop M.C. Simulating flows in multi-layered and spatially-variable permeability media via a new Gray Lattice Boltzmann model // Computers and Geotechnics. - 2015. — Vol. 70. — Pp. 150-158. DOI: 10.1016/j.compgeo.2015.07.017
17. Almalki W., Hamdan M. H., Kamel M.T. Analysis of flow through layered porous media // Conference: Proceedings of the 12th WSEAS international conference on Mathematical methods, computational techniques and intelligent systems. - 2010. — Pp. 182-189.
18. Batista M.R., Da Mota J.C. Monotone iterative method of upper and lower solutions applied to a multilayer combustion model in porous media// Nonlinear Analysis: Real World Applications - 2021. - Vol. 58. -P.103223. – Doi: 10.1016/j.nonrwa.2020.103223
19. Ravshanov N., Aminov S., and Kravets O.Ja. Mathematical model and numerical algorithms to analyze gas filtration process in a porous medium // Journal of Physics: Conference Series. - 2019. - Vol. 1399, Issue 5. - P. 055036. - DOI: 10.1088/1742-6596/1399/5/055036
20. Ravshanov, N., Nazirova, E.S., Pitolin, V.M. Numerical modelling of the liquid filtering process in a porous environment including the mobile boundary of the oil-water section // Journal of Physics: Conference Series. - 2019. - Vol. 1399, Issue 2. - P. 022021. - DOI: 10.1088/1742-6596/1399/2/022021 (https://iopscience.iop.org/article/10.1088/1742-6596/1399/2/022021)
21. Ravshanov, N., Nazirova, E.S., Aminov, S.M. Mathematical model and numerical algorithms to analyze gas filtration process in a porous medium // TUIT Bulletin. - 2019. - Issue 3(51). - Pp. 45-65. (https://www.researchgate.net/publication/337945326_Mathematical_model_and_numerical_algorithms_to_analyze_gas_filtration_process_in_a_porous_medium)
22. Ravshanov N., Nazirova E. Numerical simulation of filtration processes of strongly polluted oil in a porous medium // Ponte. – 2018. – vol. 74. – № 11/1. – рр. 107-116.
23. Ravshanov N., Orifjonova U. 2020. Modeling the process of fluid filtration in interacting pressure porous layers. Problems of Computational and Applied Mathematics.
Ravshanov, N and Nazirova, Elmira
"MODELING AND ANALYSIS OF NONSTATIONARY GAS FILTRATION UNDER GAS DYNAMIC PARAMETERS VARIATION,"
Bulletin of TUIT: Management and Communication Technologies: Vol. 4
, Article 3.
Available at: https://uzjournals.edu.uz/tuitmct/vol4/iss2/3