The simulation of two-phase fluid flow in a layered oil reservoir under a nonlinear filtration law

About the authors:

Damir A. Gubaidullin, Dr. Phys. and Math. Sci., Corresponding Member of The Russian Academy of Sciences, Director of Institute of Mechanics and Engineering, Kazan Science Center, The Russian Academy of Sciences
Grigory A. Nikiforov, Dr. Phys. and Math. Sci., Research Associate, Institute of Mechanics and Engineering, Kazan Science Center, The Russian Academy of Sciences

Abstract:

Deviation from the linear filtration law is observed in the oil in low permeability reservoirs, at high oil viscosity, as well as both at high and low oil velocity. Among the non-Newtonian fluids it is possible to distinguish two groups—nonlinear viscous liquids and liquids with memory. In this paper we suggest a numerical solution to the problem with the laws for the liquids of the first group. The cases of motion of the fluid with maximum shear rate and of the pseudo plastic fluid have been studied, with capillary and gravitational forces taken into consideration. The reservoir that has the impermeable top and bottom and consists of two interlayers with lithologic contact has been calculated. The results obtained with the same initial and boundary conditions have been compared. It has been shown that when the nonlinear filtration law is applied in calculation, the oil recovery rate differs substantially from the rate calculated linearly, while the results of the calculations by the selected nonlinear laws are close.

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