Calculating the current displacement efficiency and recoverable oil reserves in hydrodynamic models with dynamic relative permeability

UDK: 622.276.21.011.4:550.822.3

DOI: 10.24887/0028-2448-2026-6-50-55

Key words: oil brownfields, allocation of the current oil reserves, current displacement efficiency, dynamic phase permeability, non-linear flow, deviations from the linear Darcy's law, hydrodynamic model

Authors: S.V. Kostyuchenko (RN-GRD LLC, RF, Tyumen; Industrial University of Tyumen, RF, Tyumen); N.A. Cheremisin (RN-GRD LLC, RF, Tyumen); S.A. Velikopolsky (RN-GRD LLC, RF, Tyumen); I.I. Zaripov (RN-GRD LLC, RF, Tyumen)

The article describes the principles of building hydrodynamic models with dynamic relative permeabilities of oil, water, and gas and the use of such models for calculating the current displacement efficiency. The key difference between dynamic relative permeability and static relative permeability is the dependence of shape and endpoints of relative permeability not only on the saturation of pore space with oil, water and gas, but also on the filtration rate. This feature enables to model flow processes with deviations from the linear Darcy’s law and to solve tasks that usually can’t be solved using conventional simulation models with static relative permeability. Moving from models with static relative permeability to models with dynamic relative permeability brings them in line with the actual development features and enables the implementation of new capabilities in digital simulation models: separating drained and undrained areas of oil deposits and oil reserves within them; directly calculating cumulative and current displacement efficiency; building maps of oil reserves not covered by displacement processes. The estimated oil recovery factor in models with dynamic relative permeability is defined by the endpoints of relative permeability for small and large capillary numbers and may differ from the oil recovery factor in models with static relative permeability both upwards and downwards. Solving these tasks is relevant for justifying the efficiency of infill well pattern, flooding technologies, profiles of horizontal and multilateral wells, and other technologies of enhanced oil recovery both for oil and gas brownfields and for fields with hard-to-recover reserves.

References

1. Mikhaylov N.N., Polishchuk V.I., Khazigaleeva Z.R., Modeling of residual oil distribution in flooded heterogeneous formations (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2014, No. 8, pp. 36–39.

2. Mikhaylov N.N., Ostatochnoe neftenasyshchenie razrabatyvaemykh plastov (Residual oil saturation of developed reservoirs), Moscow: Nedra Publ., 1992, 270 p.

3. Popkov V.I., Zatsepina S.V., Shakshin V.P., Using relative permeabilities dependent on capillary number in hydrodynamic models of oil and gas fields (In Russ.), Matematicheskoe modelirovanie, 2005, V. 17, No. 2, pp. 92–102.

4. Baykov V.A., Kolonskikh A.V., Makatrov A.K. et al., Development of ultra low-permeability oil reservoirs (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2013,

no. 10, pp. 52–56.

5. Basak P., Non–Darcy flow and its implications to seepage problems, Journal of the Irrigation and Drainage Division, 1977, V. 103, Issue 4, pp. 459–473,

DOI: https://doi.org/10.1061/jrcea4.0001172

6. Fjelde I., Lohne A., Abeysinghe K.P., Critical aspects in surfactant flooding procedure at mixed–wet conditions, SPE-174393-MS, 2015,

DOI: https://doi.org/10.2118/174393-MS

7. Blom S.M.P., Hagoort J., How to include the capillary number in gas condensate relative permeability functions, SPE-49268-MS, 1998,

DOI: https://doi.org/ 10.2118/49268–MS

8. Amaefule J.O., Handy L.L., The Effect of interfacial tensions on relative oil/water permeabilities of concolidated porous media, SPE-8793-PA, 1982, pp. 371–381,

DOI: https://doi.org/10.2118/9783-PA

9. Cheremisin N.A., Sonich V.N., Baturin N.E., Medvedev N.Ya., Basic physics of increasing the efficiency of developing granulated reservoirs (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2002, no. 8, pp. 38–42.

10. Kostyuchenko S.V., Cheremisin N.A., Direct calculation of sweep efficiency and localization of current recoverable oil reserves in digital models (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2019, no. 7, pp. 94–98, DOI: https://doi.org/10.24887/0028-2448-2019-7-94-98

11. Kostyuchenko S.V., Cheremisin N.A., Dynamic phase permeability for calculating oil locations in digital models (In Russ.), Izvestiya vysshikh uchebnykh zavedeniy. Neft’ i gaz, 2021, No. 5, pp. 168–176, DOI: https://doi.org/10.31660/0445-0108-2021-5-168-176

12. Pyatibratov P.V., About the physical meaning and definition of the volumetric sweep efficiency in the binomial formula for calculating oil recovery factor (In Russ.), Neftyanoe khozyaystvo = Oil Industry,   2024, No. 4, pp. 80–83, DOI: https://doi.org/10.24887/0028-2448-2024-4-80-83