Modeling of thermophysical processes in an oil reservoir during heating in a stopped well

Objectives. An important and urgent task of the oil producing industry is the identification of patterns of thermophysical processes in reservoirs. One approach to improving the efficiency of oil recovery in conditions of hard-to-recover reserves involves thermal action on the reservoir. The construction of mathematical models for describing such processes to optimize production technologies is based on the formation of nonstationary heat flows in the reservoir when a stopped well is heated. The application of mathematical modeling methods considered in the work forms a basis for calculating the distribution dependencies of nonstationary fields of thermophysical characteristics in the reservoir when heating the well to its parameters and the properties of the environments.
Methods. The work is based on heat- and mass-transfer theory along with mathematical physics, analytical and numerical methods, as well as algorithms, computer modeling approaches, and the development of applications using modern programming languages and their libraries.
Results. A formation saturated with oil, water, and a steam–gas mixture is theoretically described. A closed system of heat and mass transfer equations is obtained taking into account diffusion-droplet and heat flows and phase transformations. A formulated mathematical statement of the model comprises an initial–boundary value problem for equations relating the temperature, saturation, and pressure of the components of the saturating fluid in the formation. Numerical algorithms for solving are developed and their software implementation carried out. An application developed for computer implementation of the model provides convenient visualization of the calculation results consisting of several components (modules). Numerical experiments were carried out using the developed software to study how various factors, such as the properties of the formation sketch and the saturating liquid phase and heater characteristics, affect the thermophysical processes in the formation. Conclusions. The developed model can be used to clearly describe nonstationary distributions of thermophysical characteristics formed by thermal and diffusion-droplet flows in the reservoir during heating of a shut-up well. The obtained results expand current understandings of the regularities of thermophysical processes and the properties of the saturating phase in the reservoir under thermal influence.

1. Gilmanov A.Ya., Kovalchuk T.N., Skoblikov R.M., Fedorov A.O., Khodzhiev Ye.N., Shevelev A.P. Analysis of the influence of thermophysical parameters of the reservoir and fluid on the process of cyclic steam stimulation. Vestnik Tyumenskogo gosudarstvennogo universiteta. Seriya: Fiziko-matematicheskoe modelirovanie. Neft’, gaz, energetika = Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy. 2023;9(3–35):6–27 (in Russ.). https://doi.org/10.21684/2411-7978-2023-9-3-6-27

2. Zagrivnyi E.A., Rudakov V.V., Bataev S.N. Electro thermal complex for thermal methods of extraction of high-viscosity oil. Zapiski Gornogo instituta = Journal of Mining Institute. 2004;158:226–229 (in Russ.).

3. Aminev D.A., Kravchenko M.N. Methods of thermal impact on the reservoir at the stage of well heating with pressure reduction. In: SNK-2020: Proceedings of the Anniversary 70th Open International Student Scientific Conference of the Moscow Polytech. Moscow. 2020. P. 198–201 (in Russ.).

4. Dumanskii Yu.G., Khlebnikov P.A., Mokropulo I.P., Gilaev G.G. Production of highly viscous oils by the method of thermal impact on reservoirs at the Okha field. In: Development of Resources of Hard-to-Recover and High-Viscosity Oils: Conference Proceedings. 1997. P. 142–165 (in Russ.).

5. Lapatin V.V. Analysis of the efficiency of thermal impact on a reservoir with highly viscous oil using a pair of simultaneously operating horizontal wells. Aktual’nye problemy sotsial’no-gumanitarnogo i nauchno-tekhnicheskogo znaniya = Actual Problems of Social, Humanitarian and Scientific-Technical Knowledge. 2023;4(35):18–20 (in Russ.).

6. Usmanov A.R. Thermal methods of influence on the formation. Akademicheskii zhurnal Zapadnoi Sibiri = Academic Journal of West Siberia. 2018;14(6–77):141–142 (in Russ.).

7. Gizzatullina A.A. Thermal impact on highly viscous oil in the reservoir using a pair of horizontal wells operating simultaneously. In: 12th All-Russian Congress on Fundamental Problems of Theoretical and Applied Mechanics: Conference Proceedings in 4 v. V. 2. 2019. P. 1178–1179 (in Russ.). https://www.elibrary.ru/qfwigl

8. Salavatov T.Sh., Mamedov F.F. The prospects of using devices of alternative energy sources towards thermal treatment of formation and bottomhole zone. Azerbaidzhanskoe neftyanoe khozyaistvo = Azerbaijan Oil Industry. 2019;4:37–44 (in Russ.).

9. Yangirov R.R. Dynamics of the temperature field in the reservoir during thermal impact on the productive reservoir on the example of the Russian field. In: West Siberian Oil and Gas Congress: Collection of Scientific Papers of the 13 International Scientific and Technical Congress of the Student Section of the Society of Petroleum Engineers (SPE). 2019. P. 181–183 (in Russ.). https://www.elibrary.ru/zgqxbb

10. Igtisanova G.R., Gabdullina G.I. Calculation of the parameters of the kust pump station with autonomous energy provision and heat, water-gas reservoir stimulation. In: Actual Issues of Higher Education – 2020: Proceedings of the All-Russian Scientific and Methodological Conference (with International Participation). 2020. P. 230–237 (in Russ.). https://www.elibrary.ru/dfeidr

11. Gizzatullina A.A., Fatkullin A.A., Abdulmanov A.A. Mathematical modeling of heat influence on a high-viscous oil in a layer through a horizontal well. In: Contemporary technologies in the oil and gas industry – 2020: Collection of Works of the International Scientific and Technical Conference. 2020. P. 45–49 (in Russ.). https://www.elibrary.ru/fvllkz

12. Kartashov E.M., Kudinov V.A. Analiticheskaya teoriya teploprovodnosti i prikladnoi termouprugosti (Analytical Theory of Heat Conduction and Applied Thermoelasticity). Moscow: URSS; 2018. 656 p. (in Russ.).

13. Kartashov E.M. Model representations of heat shock in terms of dynamic thermal elasticity. Russ. Technol. J. 2020;8(2): 85–108 (in Russ.). https://doi.org/10.32362/2500-316X-2020-8-2-85-108

14. Sayakhov F.L., Fatykhov M.A., Dyblenko V.M., Simkin E.M. Calculation of the main indicators of the process of highfrequency heating of the bottomhole zone of oil wells. Izvestiya vysshikh uchebnykh zavedenii. Seriya Neft’ i gaz = Oil and Gas Studies.1977;6:15–21 (in Russ.). https://elibrary.ru/nzemgp

15. Surguchev M.L., Simkin E.M., Zhdanov S.A. Influence of methods of thermophysical impact on bottomhole zones on increasing oil recovery. Neftyanoe khozyaistvo = Oil Industry. 1977;10:48–50 (in Russ.).

16. Vakhitov G.G., Simkin E.M. Ispol’zovanie fizicheskikh polei dlya izvlecheniya nefti iz plastov (The Use of Physical Fields to Extract Oil from Reservoirs). Moscow: Nedra; 1985. 231 p. (in Russ.).

17. Durkin S.M., Menshikova I.N. Assessment of the impact of method of accounting of non-reservoir rocks in the proce

18. Dieva N.N., Kravchenko M.N., Nabiullina A.A. Justification based on numerical modeling of the choice of thermal impact methods on kerogen-containing reservoirs. In: Actual Problems of Oil and Gas Geology in Siberia: Proceedings of the 2nd All-Russian Scientific Conference of Young Scientists and Students Dedicated to the 85th Anniversary of Academician A.E. Kontorovich. 2019. P. 37–39 (in Russ.). https://elibrary.ru/mukjjh

19. Tupysev M.K. Dynamics of hydrate formation in near-wellbore zone of wells while the development of low-temperature gas deposits. Georesursy, Geoenergetika, Geopolitika. 2010;2(2):20 (in Russ.). https://elibrary.ru/sikwul

20. Sharafutdinov R.F., Kanafin I.V., Khabirov T.R. Numerical Investigation of the temperature field in a multiple-zone well during gas-cut oil motion. J. Appl. Mech. Tech. Phys. 2019;60(5):889–898. https://doi.org/10.1134/S0021894419050122 [Original Russian Test: Sharafutdinov R.F., Kanafin I.V., Khabirov T.R. Numerical Investigation of the temperature field in a multiple-zone well during gas-cut oil motion. Prikladnaya mekhanika i tekhnicheskaya fizika. 2019;60(5–357):125–135 (in Russ.). https://doi.org/10.15372/PMTF20190512 ]

21. Ramazanov A.Sh., Parshin A.V. Temperature distribution in oil-water-saturated reservoir with account of oil degassing. Neftegazovoe delo = Oil and Gas Business. 2006;1:22 (in Russ.). https://elibrary.ru/twwnpx

22. Ramazanov A.S., Parshin A.V. Analytical model of temperature variations during the filtration of gas-cut oil. High Temp. 2012;50(4):567–569. https://doi.org/10.1134/S0018151X12040189 [Original Russian Test: Ramazanov A.Sh., Parshin A.V. Analytical model of temperature variations during the filtration of gas-cut oil. Teplofizika vysokikh temperatur. 2012;50(4):606–608 (in Russ.). https://elibrary.ru/kovvto ]

23. Shagapov V.Sh., Tazetdinov B.I. Modeling the dynamics of formation and decomposition of gas hydrate particles during their surfacing in water. Vestnik Samarskogo gosudarstvennogo universiteta. Estestvennonauchnaya seriya = Vestnik of Samara University. Natural Science Series. 2013;9-2(110):133–139 (in Russ.). https://elibrary.ru/rxwiiv

24. Ramazanova E.N., Aliverdiev A.A., Grigor’ev E.B., Zarichnyak Yu.P., Aliev R.M., Beibalaev V.D. Temperature field of an oil reservoir considering the effect of thermal methods of impact and thermal conductivity of rocks. Vesti gazovoi nauki. 2023;2(54):68–73 (in Russ.). https://elibrary.ru/wrwewp

25. Gil’manov A.Y., Shevelev A.P., Lagunov P.S., et al. Influence of the Thermophysical Properties of the Reservoir and Fluid on the Technological Parameters of the Cyclic Steam Stimulation. J. Eng. Phys. Thermophy. 2023;96(5):1311–1319. https://doi.org/10.1007/s10891-023-02797-8 [Original Russian Test: Gil’manov A.Ya., Shevelev A.P., Lagunov P.S., Gulyaev P.N., Petukhov A.S., Lyutoev P.A. Influence of the Thermophysical Properties of the Reservoir and Fluid on the Technological Parameters of the Cyclic Steam Stimulation. Inzhenerno-fizicheskii zhurnal. 2023;96(5):1323–1331 (in Russ.).]

26. Efimtsev S.V., Nustrov B.C., Okhezin S.P., Podoplelov V.V. Some problems of filtration in deformable media. Izvestiya Ural’skogo gosudarstvennogo universiteta. Seriya Matematika i mekhanika. 2003;5(26):66–76 (in Russ.).

27. Makarychev S.V., Mazirov M.A. Teplofizika pochv: metody i svoistva (Thermal Physics of Soils: Methods and Properties). Suzdal; 1996. V. 1. 231 p. (in Russ.).

28. Laptev A.G., Nikolaev N.A., Basharov M.M. Metody intensifikatsii i modelirovaniya teplomassoobmennykh protsessov (Methods of Intensification and Modeling of Heat and Mass Transfer Processes). Moscow: Teplotekhnik; 2011. 287 p. (in Russ.).

29. Goldobin D.S., Krauzin P.V. Saturation of aquifers with two-component gas mixture. Vestnik PNIPU. Mekhanika = PNRPU Mechanics Bulletin. 2013;4:33–41 (in Russ.).

30. Goldobin D.S., Krauzin P.V. Formation of bubbly horizon in liquid-saturated porous medium by surface temperature oscillation. Phys. Rev. E. 2015;92(6):063032(1–8). http://dx.doi.org/10.1103/PhysRevE.92.063032