A New Scaling-Up Method To Compute Relative Permeability and Capillary Pressure for Simulation of Heterogeneous Reservoirs

Abstract

Abstract Recent high-resolution tools and novel characterization techniques lead to simulate very detailed geological descriptions of heterogeneous reservoirs. To perform full-field displacement simulations, scaling-up techniques must be used because of the required coarser grids. Pseudoization methods are commonly used to get the relative permeability and capillary pressure curves. But they all consider 2D flow to realize the scaling-up. We propose a three-dimensional approach. When capillary forces are important inside the reservoir, the capillary pressure may be considered as nearly constant inside a coarse grid-block. This assumption enables to compute directly the fine grid-block saturations and the average coarse grid-block saturation for a given capillary pressure. For each fluid phase, we then compute the effective phase permeabilities of the coarse grid-block by means of an absolute permeability scaling-up method applied to phase permeabilities of the fine grid-blocks in 3D. Then renormalizing the resulting phase permeabilities by the average absolute permeability yields the average relative permeabilities curves for the three directions of space. Application of this technique, using an algebraic computation of average permeability adapted to heterogeneous media, will be presented for complex fluviatile cases, characterized by a large amount of shale inclusion at small-scale. Comparison of numerical simulations of oil-water flow on high-resolution descriptions, and on the corresponding scaled-up coarse models, shows the efficiency of this method. We recommend to apply this method to reservoir with low gravity segregation, with rocks exhibiting medium to low permeability and high capillary forces, and moderate injection rates.