Numerical Calculation of Piton-like Oil Displacement for Different Schemes of Flooding

Abstract eng:
Prediction of the motion of oil-water contact has great importance in the problems of oilfield development by flooding. We consider a piston-like model of oil-water displacement, which takes into account differences in viscosity of two fluids. Filtration of liquids is described by Darcy's law. Both fluids are weakly compressible and the pressure in the reservoir satisfies the quasi-stationary diffusion equation. Pistonlike model leads to discontinuity of the tangential velocity at the boundary L of oil-water contact. Using the generalized Cauchy integral we reduce the problem of finding the current boundary of oil-water contact to the system of singular integral equations for the velocity components and to the Cauchy problem for the boundary motion of oil-water contact. An algorithm for numerical solution of this problem is developed. The monitoring of oil-water boundary motion for different schemes of flooding (four-point, five-point, seven-point, nine-point, etc.) is carried out.

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