Influence of capillary and gravity forces on equilibrium and transport of oil and water in porous media

About the authors:

Nikolay S. Bakhtiy, Cand. Tech. Sci., Associate Professor, Department of Mathematical Modeling, Institute of Mathematics and Computer Sciences, Tyumen State University Head of Department of Petroleum Reservoir Simulation, Tyumen Branch of Surgut Research and Planning Institute, Surgutneftegas Open Joint Stock Company
Marina V. Abdulina, Cand. Phys. and Math. Sci., Head of laboratory, Department of Petroleum Reservoir Simulation, Tyumen Branch of Surgut Research and Planning Institute, Surgutneftegas Open Joint Stock Company
Yury I. Mokropulo, Engineer of the 1st grade, Department of Petroleum Reservoir Simulation, Tyumen Branch of Surgut Research and Planning Institute, Surgutneftegas Open Joint Stock Company

Abstract:

Influence of capillary and gravity forces is significant for both initial equilibrium and fluid dynamics during oil recovery. Analytical solutions of reservoir engineering problems can be rarely obtained due to complexity of the problems. Therefore, these problems are usually solved numerically. But analytical solutions are important for both better understanding of the physical process and verification of numerical schemes. Numerical solutions of three 1D two-phase reservoir simulation problems are obtained: equilibrium of oil and water in a heterogeneous reservoir, gravity flow of oil and water, imbibition in water-wet media. Comparison of these solutions and analytical solutions is presented, as well as the refinement test of the problems.

References:

1. Aziz, K., Settari, A. Petroleum Reservoir Simulation. London: Applied Science Publishers Ltd., 1979.

2. Aziz, K., Durlofsky, L., Tchelepi, H. Notes for petroleum reservoir simulation // Stanford: Stanford University. 2005. 490 p.

3. Charny, I.А. Fluid and gas dynamics in porous media. Moscow: State Scientific and Technical Publishers of Oil and Mining-Fuel Literature, 1963. 496 p. (in Russian).

4. Mayer, V.P. Gravity flow of two phases in finite porous media // Oil and Gas. 2001. № 2. Pp. 57–65. (in Russian).

5. Mayer, V.P. About testing of reservoir simulation models // Central Development Commission Rosnedra Herald. 2009. № 1. Pp. 68–78. (in Russian).

6. McWhorter, D., Sunada, D.K. Exact integral solutions for two-phase flow // Water Resour. Res. 1990. Vol. 26. Pp. 399.

7. Barenblatt, G.I. Entov, V.M., Ryzhik, V.M. Theory of nonstationary fluid and gas dynamics in porous media. Moscow: Nedra, 1972. 288 p. (in Russian).

8. Kashchiev, D., Firoozabadi, A. Analytical solutions for 1D countercurrent imbibition in water-wet media // SPEJ. 2003. 8(4). Pp. 401–408.

9. Bakhty, N.S. Particularities of multiphase multicomponent reservoir simulation and verification of numerical solutions of Tecscheme software: Ph.D. thesis, Tyumen, 2012. 136 p. (in Russian).

10. Rozhdestvensky, B.L., Yanenko, N.N. Systems of quasi-linear equations and their applications to gas dynamics. Moscow: Nauka, 1978. 688 p. (in Russian).