Effective Relative Permeability in Scale-Up and Simulation

ABSTRACT In modern reservoir characterization, detailed heterogeneous models of reservoir properties are routinely scaled-up for flow simulation. In addition to single-phase flow properties, two-phase flow properties, relative permeability and capillary pressure functions must also be scaled up. Here techniques for determination and assignment of effective relative permeability and capillary pressure on different scales of heterogeneities are presented and discussed. Many authors have considered scales of heterogeneities, their influence on fluid flow, and calculation of effective properties at a particular scale. In this paper, however, we present a unified approach to this problem; we consider effective relative permeability and capillary pressure on multiple scales of heterogeneities, and discuss a procedure for considering these heterogeneities at each level so that the overall influence is represented in the flow simulation model, results of which are used for economic decisions. A simulation technique and an analytical method for calculation of effective relative permeability and capillary pressure are presented. Scale-up of relative permeabilities results in a set of effective relative permeability curves and an effective capillary pressure curve for each larger-scale simulation grid block. We show how these relative permeabilities, and the corresponding effective capillary pressure curves, can be grouped together to yield a manageable number of effective relative permeability and capillary pressure curves for flow simulation. The application of these techniques is demonstrated through 2D and 3D scale-up and flow simulation examples.