Numerical Simulation of Two-Phase Flow Using Locally Refined Grids in Three Space Dimensions

Capillary pressure is modeled as difiusion and treated inl- This paper presents a numerical method for solving incom- plicitly by mixed finite elements and multigrid. pressible, immiscible, two-phase flow problems in three space dimensions. The grid consists of rectangular blocks. Blocks The solution method permits large time steps, if the flow field does not change substantially between time steps, Ac- can iteratively be refined in areaa with active wells, with steep saturation fronts, or with large permeability contrasts, curate results can be o~~ained with only a limited number of The grid is dynamically adapted as the numerical simulation grid blocks. The method has been used vu study both sta- ble and unstable, immiscible displacement of oil by water. proceeds, Results for some test problems are given. The equations governing two-phase flow are treated sepa- rately, which leads to an elliptic. equation for pressure and Introduction velocity, and a parabolic equation for the water saturation. The objective of reservoir simulation is the computation of The solution technique combines mixed finite elements with fluid flow through porous media with an accuracy that is suf- the method of characteristics. Multigrid is wed to solve pres- ficient for the prediction of the hydrocarbon recovery. The sure ancl velocity from the mixed finite element discretiza- mathematical model for porous media flow consists of a cou- tion. The water saturation is determined by a convection- pled system of nonlinear partial differential equations that dominated parabolic equation. Operator splitting allows a represents the basic physical properties of the true solution. separate t rest ment of convect )on and diffusion. Numerical methods are required to determine an approxi-