Mass transfer of phases in the flow of oil-water-gas mixture on the core scale

About the authors:

Aleksandr B. Shabarov, Dr. Sci. (Tech.), Professor, Honored Scientist of the Russian Federation, Professor, Department of Applied and Technical Physics, School of Natural Science, University of Tyumen, Tyumen, Russia; a.b.shabarov@utmn.ru, https://orcid.org/0000-0002-5374-8704
Dmitry E. Igoshin, Cand. Sci. (Phys.-Math.), Head of the Reservoir Physics Laboratory, Corporate Center for the Study of Reservoir Systems (Core and Fluids), Gazprom VNIIGAZ (Moscow); Associate Professor, Department of Fundamental Mathematics, Institute of Physics and Technology, University of Tyumen; d.e.igoshin@utmn.ru

Polina M. Rostenko, Postgraduate Student, Department of Applied and Technical Physics, Institute of Physics and Technology, University of Tyumen; stud003991636@study.utmn.ru

Anastasia P. Sadykova, Postgraduate Student, Department of Applied and Technical Physics, Institute of Physics and Technology, University of Tyumen; stud0000217819@study.utmn.ru

Abstract:

The study of three-phase fluid filtration in the pore space is one of the urgent tasks in the development of oil and gas and gas condensate fields. In the study of three-phase flows, semi-empirical methods for calculating relative phase permeabilities (RPP) are used in practice, which do not consider the structure of the pore space and the fundamental equations of hydrodynamics. The paper proposes and substantiates a physical and mathematical model of mass transfer in the filtration flow of an oil-water-gas mixture in a porous medium. The pore space structure model is based on the distribution of pore diameters obtained from capillary pressure curves (CCP). In the core, clusters are identified, consisting of a large channel through which oil, water and gas move in a “beaded” mode; channels of medium diameter filled with water and gas and channels of small radius in which gas moves. A system of equations is presented and solved that determines the distribution of moving volumes and volumetric flows over channels and phases. When determining pressure losses in the system of pore channels, friction losses, local losses, and also losses due to interfacial interaction are taken into account. For the first time, on the basis of a hydrodynamic model, analytical expressions were obtained to determine the RPP for oil, water and gas. The calculation-experimental method is based on three model experiments, the results of which determine the properties of the cluster channels in relation to the separately filtered phases. It is shown that the developed theory and calculation method, in the particular case of an oil-water mixture, coincide with the previously developed theory of two-phase filtration on the core scale.

References:

1. Altunin A. E., Sokolov S. V., Stepanov S. V., Cheremisin N. A., Shabarov A. B. 2013. “Calculation method of receiving relative phase permeability based on solution of Bernoulli generalized equations for a system of porous channels”. Oilfield Engineering, no. 8, pp. 40-46. [In Russian]
2. Afanaskin I. V., Volpin S. G., Korolev A. V., Lomakina O. V., Yalov P. V. 2018.
   “Super-element model of three-phase filtration of oil, gas and water taking into account performance of producing wells at bottomhole (and reservoir) pressure below bubble point pressure”. Proceedings in Cybernetics, no. 1 (29), pp. 9-19. [In Russian]
3. Akhmetov R. T., Mukhametshin V. V., Kuleshova L. S. 2019. “A dumbbell model application for the absolute permeability of reservoirs by capillary pressure curves determining”. Geology, Geophysics and Development of Oil and Gas Fields, no. 4 (328), pp. 52-56. DOI: 10.30713/2413-5011-2019-4(328)-52-56 [In Russian]
4. Benson L. A.-L. 2018. “Physical and mathematical model of inflow to a well in a gas condensate reservoir”. Cand. Sci. (Tech.) diss. Saint-Petersburg. 133 p. [In Russian]
5. Gafarov S. A., Ibragimov R. R., Latypov A. G., Karimov M. F., Mullagalieva L. M. 2012. “The gravityhydrodynamic filtering mechanism of three-phase mixture increasing of hydrocarbon recovery with creating underground gas storage (UGS) in depleted oil fields”. Petroleum Engineering, vol. 10, no. 3, pp. 45-49. [In Russian]
6. Igoshin D. E., Nikonova O. A., Mostovoy P. Ya. 2014. “Simulation of porous medium in the form of systematically packed intersecting spheres”. Tyumen State University Herald. Physical and Mathematical Sciences. Informatics, no. 7, pp. 34-42. [In Russian]
7. Igoshin D. E., Nikonova O. A. 2015. “The permeability of the porous medium with a periodic structure branching channels”. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 1, no. 2 (2), pp. 131-141. [In Russian]
8. Igoshin D. E., Gubkin A. S., Gubaidullin A. A. 2019. “Calculation of the relative phase permeabilities of a porous medium with a rhombohedral structure”. Proceedings of the XVI All-Russian Seminar with international participation “Dynamics of Multiphase Media” (30 September  — 5 October 2019, Novosibirsk, Russia), pp. 64-65. [In Russian]
9. Geologika. 2009. Operating instructions for the automated software-measuring complex for petrophysical examination of cores PIK-OFP/EP-3. Novosibirsk: Geologika. 43 p. [In Russian]
10. Kuzina O. A., Potochnyak I. R., Puldas L. A. 2022. “Features of the modernization of the petrophysical research complex for the implementation of the possibility of gas filtration together with water-oil fluids”. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 8, no. 1 (29), pp. 75-87. DOI: 10.21684/2411-7978-2022-8-1-75-87 [In Russian]
11. Kuzina O. A., Shabarov A. B. 2020. “Calculation and experimental method for determining the filtration parameters of the mixture ‘oil — aqueous solution of surfactants’”. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 6, no. 1 (21), pp. 41-64. DOI: 10.21684/2411-7978-2020-6-1-41-64 [In Russian]
12. Lozhkin M. G. 2015. “The method of relative phase permeability determination in the laboratory conditions at the sequential pseudo-steady filtration”. Exposition Oil & Gas, no. 7 (46), pp. 51-53. [In Russian]
13. Lozhkin M. G. 2015. “A relative permeability model of gas displacement by water and condensate and oil displacement by water and gas”. Exposition Oil & Gas, no. 1 (40), pp. 39-41. [In Russian]
14. Lozhkin M. G. 2017. “The experimental checking of mathematical models of relative permeabilities for three-phase core saturation”. Trofimuk Readings — 2017: Proceedings of the All-Russian Youth Scientific Conference (8-14 October 2017. Novosibirsk, Russia), pp. 214-217. [In Russian]
15. Manasyan A. E., Ustinov A. S., Kurapova I. G., Sarvaretdinov R. G., Melnikov M. N. 2008. “Method of formation and selection of curves of relative phase permeabilities with insufficient knowledge of the object”. Automation and Informatization of the Fuel and Energy Complex, no. 12, pp. 27-35. [In Russian]
16. Ovcharov V. V. 2014. “Review of calculation and correction methods of relative permeability curves for reservoir simulation of hydrocarbon deposits”. Proceedings in Cybernetics, no. 1 (13), pp. 10-16. [In Russian]
17. Orlov D. M., Fedoseev A. P., Savchenko N. V., Korchazhkina I. Yu., Grigoryev B. A., Ryzhov A. Ye., Perunova T. A., Maksimova N. Yu., Kalashnikova Ye. P. 2015. “Estimation of filtration velocity influence on relative phase permeabilities using method of unsteady filtration”. Vesti gazovoy nauki, no. 3 (23), pp. 8-14. [In Russian]
18. OST 39-235-89. 1989. Oil. Method for determining phase permeabilities in laboratory conditions with joint stationary filtration. Moscow. [In Russian]
19. Rassokhin S. G., Troitsky V. M., Mizin A. V. et al. 2010. “Experimental study of three-phase filtration processes under thermobaric conditions of the Aptian deposits”. Vesti gazovoy nauki, no. 1 (4), pp. 167-178. [In Russian]
20. Stepanov S. V., Shabarov A. B., Bembel G. S. 2016. “Computer technology for determination of interphase interaction function based on flow simulation in capillary cluster”. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 2, no 1, pp. 63-71. DOI: 10.21684/2411-7978-2016-2-1-63-71 [In Russian]
21. Stepanov S. V. 2006. “Use of oil field development data to obtain phase permeability curves”. Oil Industry, no. 4, pp. 112-114. [In Russian]
22. Stepanov S. V., Shabarov A. B., Bembel G. S., Shatalov A. V. 2015. “Investigation of dynamic phase permeabilities based on numerical simulation of two-phase flow in pore channels”. Proceedings of the XI All-Russian Congress on Fundamental Problems of Theoretical and Applied Mechanics, pp. 3600-3601. [In Russian]
23. Shabarov A. B., Shatalov A. V. 2016. “Geometric model of the pore space for calculating the filtration of oil and water”. Thermophysics, Heat Engineering, Hydrogas Dynamics. Innovative Technologies, pp. 25-36. Tyumen: University of Tyumen. [In Russian]
24. Shabarov A. B. 2013. Hydrogas dynamics: A tutorial. 2nd ed., revised. Tyumen: University of Tyumen. 460 p. [In Russian]
25. Shabarov A. B., Saranchin N. V., Chistyakova N. F., Shirshova A. V., Puldas L. A., Stupnikov A. A., Vetrov I. M., Shatalov A. V., Bembel G. S., Vakulin A. A., Varyukhin S. E., Berdyugin S. V., Medvedev D. N., Molchanov D. A., Vorobyov V. V. 2011. Final report on the topic “Numerical study of the displacement process on the scale of the core to obtain consistent curves of capillary pressure and relative phase permeabilities” (Framework Agreement of Tyumen Petroleum Research Center — University of Tyumen dated 16.06.2011). Tyumen: Tyumen Petroleum Research Center; University of Tyumen. [In Russian]
26. Shabarov A. B., Shatalov A. V., Markov P. V., Shatalova N. V. 2018. “Relative permeability calculation methods in multiphase filtration problems”. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 4, no. 1, pp. 79-109. DOI: 10.21684/2411-7978-2018-4-1-79-109 [In Russian]
27. Shabarov A. B., Shatalov A. V. 2016. “Pressure drops in water-oil mixture flow in porous channels”. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 2, no. 2, pp. 50-72. DOI: 10.21684/2411-7978-2016-2-2-50-72 [In Russian]
28. Shabarov A. B., Igoshin D. E., Rostenko P. M., Sadykova A. P. 2022. “Digital cluster model of pore space at flow of three-phase flow in porous medium”. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 8, no. 1 (29), pp. 88-108. DOI: 10.21684/2411-7978-2022-8-1-88-108 [In Russian]
29. Yuryev A. V., Belozerov I. P., Shulev V. E. 2014. “Determination of relative phase permeabilities and coefficients of oil displacement by water on full-size core samples”. Problems of Development of Deposits of Hydrocarbon and Ore Minerals, no. 1, pp. 342-345. [In Russian]
30. Aziz K., Settari A. 1979. Petroleum Reservoir Simulation. Applied Science Publishers. 476 p.
31. Blunt M. J. 2000. “An empirical model for three-phase relative permeability”. SPE Journal, vol. 5, no. 4, pp. 435-445. DOI: 10.2118/67950-PA
32. Brooks R. H., Corey A. T. 1964. “Hydraulic properties of porous media”. Hydrology Papers, no. 3, 37 p.
33. Burdine N. T., Gournay L. S., Reichertz P. P. 1950. “Pore size distribution of petroleum reservoir rocks”. Journal of Petroleum Technology, vol. 2, no. 7, pp. 195-204. DOI: 10.2118/950195-G
34. Corey A. T. 1954. “The interrelation between gas and oil relative permeabilities”. Producers Monthly, vol. 19, no. 1, pp. 38-41.
35. Delshad M., Delshad M., Pope G. A. 1987. “Two- and three-phase relative permeabilities of micellar fluids”. SPE Formation Evaluation, vol. 3, no. 2, pp. 327-337.
36. Element D. J., Masters J. H. K., Sargent N. C., Jayasekera A. J., Goodyear S. G. 2003. “Assessment of three-phase relative permeability models using laboratory hysteresis data”. Paper presented at the SPE International Improved Oil Recovery Conference in Asia Pacific (October 2003, Kuala Lumpur, Malaysia), paper SPE-84903-MS. DOI: 10.2118/84903-MS
37. Fatt I. 1956. “The network model of porous media”. AIME Petroleum Transactions, vol. 207, pp. 144-181. DOI: 10.2118/574-G
38. Gubkin A. S., Igoshin D. E., Filimonova L. N. 2019. “Calculation of two-phase flow in micro-channels of variable section with account of compressibility of one phase”. AIP Conference Proceedings, vol. 2125, no. 1, pp. 030111. DOI: 10.1063/1.5117493
39. Henry W., Banks J. 1803. “III. Experiments on the quantity of gases absorbed by water, at different temperatures, and under different pressures”. Philosophical Transactions of the Royal Society of London, vol. 93, pp. 29-274. DOI: 10.1098/rstl.1803.0004
40. Hustad O. S., Hansen A. G. 1995. “A consistent correlation for three phase relative permeabilities and phase pressures based on three sets of two phase data”. Paper presented at the 8th European IOR — Symposium (16-17 May 1995, Vienna, Austria). DOI: 10.3997/2214-4609.201406940
41. Leverett M. C., Lewis W. B. 1941. “Steady flow of gas-oil-water mixtures through
    unconsolidated sands”. Transactions of the AIME, vol. 142, no. 1, pp. 107-116. DOI: 10.2118/941107-G
42. Shahverdi H., Sohrabi M., Fatemi M., Jamiolahmady M. 2011. “Three-phase relative permeability and hysteresis effect during WAG process in mixed wet and low IFT systems”. Journal of Petroleum Science and Engineering, vol. 78, no. 3-4, pp. 732-739. DOI: 10.1016/j.petrol.2011.08.010
43. Stone H. L. 1973. “Estimation of three-phase relative permeability and residual oil data”. Journal of Canadian Petroleum Technology, vol. 12, no. 4, paper PETSOC-73-04-06. DOI: 10.2118/73-04-06
44. Stone H. L. 1970. “Probability model for estimating three-phase relative permeability”. Journal of Petroleum Technology, vol. 22, no. 2, pp. 214-218. DOI: 10.2118/2116-PA
45. Valavanides M. S. 2015. “ImproDeProF project: recent advances and new challenges in the development of the DeProF tentative theory for steady-state two-phase flow in porous media”. Paper presented at the International Conference “Science in Technology” SCinTE 2015 (5-7 November 2015, Athens, Greece).
46. Valavanides M. S. 2012. “Steady-state two-phase flow in porous media: Review of progress in the development of the DeProF theory bridging pore to statistical thermodynamics scales”. Oil & Gas Science and Technology, vol. 67, no. 5, pp. 787-804. DOI: 10.2516/ogst/2012056