Upscaling of Two-phase Immiscible Flows in Communicating Stratified Reservoirs

A new analytical upscaling method is described. It is applicable for stratified reservoirs or with vertically distributed properties. The inter-layer communication is assumed to be perfect, corresponding to viscous or gravity dominant regimes. We apply asymptotic analysis to 2D flow equations of two incompressible immiscible fluids and reduce 2D Buckley-Leverrett system to 1D flow problem. Flow velocities in the layers depend on saturations of other layers, which reflects interaction between layers; the exchange terms between the layers may be expressed explicitly. The resulting quasilinear hyperbolic equations allow a self-similar solution, which makes it possible to express the pseudo-fractional flow function as a function of average saturation. The system is solved by the finite difference method. Both cases of discontinuous and continuous (lognormal) distributed layer permeabilities are studied. As comparison, the complete 2D waterflooding problems with very good vertical communication are solved in COMSOL. Generally, saturation profiles of the pseudo 1D model are only slightly different from the 2D simulation result by Comsol. The difference between recovery curves is marginal. This proves validity of the proposed method. Our method is much more advantageous over the classical Hearn-Kurbanov procedure. It is better at predicting displacement fronts and oil recovery.