The method of calculation of relative phase permeability functions based on the empirical interfacial interaction function

About the authors:

Mikhail A. Zagorovskiy, Specialist, Department of Scientific and Technological Development, Tyumen Petroleum Research Center, Tyumen, Russia; Postgraduate Student, Department of Applied and Technical Physics, School of Natural Science, University of Tyumen, Tyumen, Russia; mazagorovskiy2@tnnc.rosneft.ru

Sergei V. Stepanov, Senior Expert, Tyumen Petroleum Research Center, Tyumen, Russia; Dr. Sci. (Tech.), Professor, Tyumen Petroleum Research Center Specialized Department, School of Natural Sciences, University of Tyumen, Tyumen, Russia; svstepanov@tnnc.rosneft.ru

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

Abstract:

The article describes the results of research about the creation of an empirical method for calculation relative phase permeability functions (RPP). The method based on calculation of interfacial interaction function (IIF) from the experimental SCAL data and searching multi-parameter dependences for the parameters of the approximation dependence of IIF. It is proposed to use a function defined on two segments of the domain of definition, for approximation of IIF. The research had been carried out on laboratory data for group of terrigenous and carbonate samples. It had been established that the pressure losses due to interfacial interaction of oil and water during the joint flow of the water-oil mixture are at the maximum for the considered core samples from 60 to 90% of the total pressure losses. Multi-parameter dependences for IIF parameters were found for both groups of data. It was defined that using of multi-parameter dependences for IIF parameters provides the quality of RPP forecast with deviation by 30% for terrigenous samples and by 22% for carbonate samples. There was conducted the study of the influence of data set amount for multi-parameter dependences (training set) on the quality of RPP forecast (test set). It had been established that increasing of data set amount for multi-parameter dependences of IIF parameters has a positive effect on the quality of RPP functions forecast. At the same time, the increasing of data set amount in 2 times leads to decreasing of the average relative error of RPP calculation from 25.5 to 20.9% for terrigenous samples and from 70.3 to 23.6% for carbonate samples.

References:

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, (8), 40–46. [In Russian]

Baskakov, A. P., Berg, B. V., Vitt, O. K., Kuznetsov, Yu. V., & Fillipovskii, N. F. (1991). Heat engineering (2nd ed.). Energoatomizdat. [In Russian]

Isachenko, V. P., Osipova, V. A., & Sukomel, A. S. (1969). Heat transfer (2nd ed.). Energia. [In Russian]

Malshakov, A. V., & Efimov, V. A. (1991). Permeability and percolation properties of porous space in sedimentary rocks. Journal of Engineering Physics and Thermophysics, 61(4), 635–640. [In Russian]

Markov, P. V. (2020, October 26–29). New technology for inverse problem solving of digital core model construction using stochastic modeling and particle swarm optimization [Conference paper SPE-201944-MS]. SPE Russian Petroleum Technology Conference, Virtual. https://doi.org/10.2118/201944-MS

Mirzadzhanzade, A. H., Ametov, I. M., & Kovalev, A. G. (1992). Physics of the oil and gas reservoir. Nedra. [In Russian]

Orlov, D. M., Ryzhov, A. E., & Perunova, T. A. (2013). Method for determining relative permeabilities from data on unsteady filtration by combined physical and computer modeling. Journal of Applied Mechanics and Technical Physics, 54(5), 789–797. https://doi.org/10.1134/S002189441305012X

Pryazhnikov, M. I., Minakov, A. V., Pryazhnikov, A. I., & Iakimov, A. S. (2022). Map of water-oil flow regimes in a direct microchannel. Technical Physics Letters, 48(2), 1–4. https://doi.org/10.21883/TPL.2022.02.53572.19030

Salomatin, E. N., Borodin, D. A., & Shulga, R. S. (2021). Poorly consolidated core flow centrifugation experiments. Karotazhnik, 8(314), 69–82. [In Russian]

Stepanov, S. V., & Shabarov, A. B. (2021). Towards the presence of regularities between the function of interfacial interaction and the filtration capacity properties. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, 7(1), 92–111. https://doi.org/10.21684/2411-7978-2021-7-1-92-111 [In Russian]

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, 2(2), 50–72. https://doi.org/10.21684/2411-7978-2016-2-2-50-72 [In Russian]

Brooks, R. H., & Corey, A. T. (1964). Hydraulic properties of porous media. Hydrology Papers, (3).

Burdine, N. T. (1953). Relative permeability calculations from pore size distribution data. Journal of Petroleum Technology, 5(3), 71–78. https://doi.org/10.2118/225-G

Corey, A. T. (1954). The interrelation between gas and oil relative permeabilities. Producers Monthly, 19, 38–41.

Koroteev, D., Dinariev, O., Evseev, N., Klemin, D., Safonov, S., Gurpinar, O., Berg, S., van Kruijsdijk, C., Myers, M., Hathon, L., de Jong, H., & Armstrong, R. (2013, July 2–4). Application of digital rock technology for chemical EOR screening [Conference paper SPE-165258-MS]. SPE Enhanced Oil Recovery Conference, Kuala Lumpur, Malaysia. https://doi.org/10.2118/165258-MS

McPhee, C., Reed, J., & Zubizarreta, I. (2015). Core Analysis: А Best Practice Guide. Elsevier.

Raeini, A. Q., Yang, J., Bondino, I., Bultreys, T., Blunt, M. J., & Bijeljic, B. (2019). Validating the generalized pore network model using micro-CT images of two-phase flow. Transport in Porous Media, 130(2), 405–424. https://doi.org/10.1007/s11242-019-01317-8

Yakimchuk, I., Evseev, N., Korobkov, D., Ridzel, O., Pletneva, V., Yaryshev, M., Ilyasov, I., Glushchenko, N., & Orlov, A. (2020, October 26–29). Study of polymer flooding at pore scale by digi­tal core analysis for East-Messoyakhskoe oil field [Conference paper SPE-202013-MS]. SPE Russian Petroleum Technology Conference, Virtual. https://doi.org/10.2118/202013-MS

Zakirov, T. R., Galeev, A. A., & Khramchenkov, M. G. (2019). Haines jumps simulation in X-ray CT image of natural sandstone. Journal of Physics: Conference Series, 1158(4), Article 042042. https://doi.org/10.1088/1742-6596/1158/4/042042

Zhao, X., Feng, Y., Liao, G., & Liu, W. (2020). Visualizing in-situ emulsification in porous media during surfactant flooding: A microfluidic study. Journal of Colloid and Interface Science, 578, 629–640. https://doi.org/10.1016/j.jcis.2020.06.019