Modeling and numerical simulations of fractured,vuggy,porus media is a challenging problem which occurs frequently in reservoir engineering.The problem is especially relevant in flow simulations of karst reservoirs wh...Modeling and numerical simulations of fractured,vuggy,porus media is a challenging problem which occurs frequently in reservoir engineering.The problem is especially relevant in flow simulations of karst reservoirs where vugs and caves are embedded 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 StokesBrinkman equations at the fine scale.These equations are capable of representing porous media such as rock as well as free flow regions(fractures,vugs,caves)in a single system of equations.We then consider upscaling these equations to a coarser scale.The cell problems,needed to compute coarse-scale permeability of Representative Element of Volume(REV)are discussed.A mixed finite element method is then used to solve 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 by numerical solutions of Stokes-Brinkman cell problems in selected REVs.Both isolated vugs in porous matrix as well as vugs connected by fracture networks are analyzed by comparing fine-scale and coarse-scale flow fields.Several different types of fracture networks,representative of short-and long-range fractures are studied numerically.It is also shown that the Stokes-Brinkman equations can naturally be used to model additional physical effects pertaining to vugular media such as partial fracture with fill-in by some material and/or fluids with suspended solid particles.展开更多
基金The authors would like to thank the China Petroleum&Chemical Corporation(SINOPEC),for supporting this work.
文摘Modeling and numerical simulations of fractured,vuggy,porus media is a challenging problem which occurs frequently in reservoir engineering.The problem is especially relevant in flow simulations of karst reservoirs where vugs and caves are embedded 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 StokesBrinkman equations at the fine scale.These equations are capable of representing porous media such as rock as well as free flow regions(fractures,vugs,caves)in a single system of equations.We then consider upscaling these equations to a coarser scale.The cell problems,needed to compute coarse-scale permeability of Representative Element of Volume(REV)are discussed.A mixed finite element method is then used to solve 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 by numerical solutions of Stokes-Brinkman cell problems in selected REVs.Both isolated vugs in porous matrix as well as vugs connected by fracture networks are analyzed by comparing fine-scale and coarse-scale flow fields.Several different types of fracture networks,representative of short-and long-range fractures are studied numerically.It is also shown that the Stokes-Brinkman equations can naturally be used to model additional physical effects pertaining to vugular media such as partial fracture with fill-in by some material and/or fluids with suspended solid particles.
