this paper studies oil displacement from a porous reservoir with water. It is assumed there is a fracking fracture near the production well. It is known that as a viscous fluid is displaced by a less viscous fluid, the Saffman–Taylor instability occurs: the less viscous fluid breaks through the layer of the fluid being displaced, forming so-called “viscous fingers” (channels). After such a channel is ruptured and connected to a production well, the oil quality (i.e., the fraction of hydrocarbons in the production fluid) deteriorates dramatically. The paper describes the simulation and numerical modeling of viscous fluid unstable displacement from a porous medium. The displacement is modeled with Darcy’s law also considering capillary effects. The Brooks–Corey model is used to estimate the relative phase permeabilities. A fracking fracture is modeled as an area with elevated porosity and permeability. We consider the fracking fracture cleaning from the fracking fluid: a reservoir area filled with fracking fluid around the fracture is modeled; then the fluid is displaced with lower viscosity oil. The process is unstable and the displacement is uneven, so some of the fracturing fluid may remain inside the reservoir.
Darcy H. The Public Fountains of the City of Dijon. Experience and Application. Paris, 1856.
Buckley S. E., Leverett M. S. Mechanism of Fluid Displacement in Sands. Journ. Petr. Technology. 1941.
Saffman P. G., Taylor G. J. The Penetration of a Fluid into a Porous Medium of Hele-Shaw Cell Containing a More Viscous Fluid. Proc. R. Foc. Zond. 1958, A 245, 312.
Smirnov N. N., Nikitin V. F., Skryleva E. I. Microgravity Investigation of Seepage Flows in Porous Media. Microgravity Science and Technology. 2019:31(5):629–639.
Dushin V. R., Skryleva E. I., Nikitin V. F. Microgravity Investigation of Capillary Forces in Imbibition of Fluid into Porous Media. Proceedings of 69th International Astronautical Congress, 2018, Bremen, Germany.
Logvinov O. A. Skryleva E. I. Displacement of a Viscous Fluid from a Hele-Shaw Cell with a Sink. Moscow University Mechanics Bulletin. 2016;71(4):77–81.
Козлов И. В., Скрылева Е. И. Математическое моделирование и обработка эксперимента по вытеснению нефти водой из неокомских песчаников. Вестник кибернетики. 2016;2:139–146.
Душин В. Р., Никитин В. Ф., Скрылева Е. И. Вычислительное моделирование вытеснения флюида из пористой среды. Вестник кибернетики. 2017;4:62–82.