Multiscale Modeling and Simulations of Flows in Naturally Fractured Karst Reservoirs (Communications in Computational Physics, 2009)
Modeling and numerical simulations of fractured, vuggy, porus media is achallenging problem which occurs frequently in reservoir engineering. The problemis especially relevant in flow simulations of karst reservoirs where vugs and caves areembedded in a porous rock and are connected via fracture networks at multiple scales.In this paper we propose a unified approach to this problem by using the Stokes-Brinkmanequations at the fine scale. These equations are capable of representingporous media such as rock as well as free flow regions (fractures, vugs, caves) in a singlesystem of equations. We then consider upscaling these equations to a coarser scale.The cell problems, needed to compute coarse-scale permeability of Representative Elementof Volume (REV) are discussed. A mixed finite element method is then used tosolve the Stokes-Brinkman equation at the fine scale for a number of flow problems,representative for different types of vuggy reservoirs. Upscaling is also performed bynumerical solutions of Stokes-Brinkman cell problems in selected REVs. Both isolatedvugs in porous matrix as well as vugs connected by fracture networks are analyzed bycomparing fine-scale and coarse-scale flow fields. Several different types of fracturenetworks, representative of short- and long-range fractures are studied numerically.It is also shown that the Stokes-Brinkman equations can naturally be used to modeladditional physical effects pertaining to vugular media such as partial fracture withfill-in by some material and/or fluids with suspended solid particles.