Volume 6, Issue 1
Multiscale Modeling and Simulations of Flows in Naturally Fractured Karst Reservoirs

Peter Popov, Yalchin Efendiev & Guan Qin

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Commun. Comput. Phys., 6 (2009), pp. 162-184.

Published online: 2009-06

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  • Abstract

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.

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@Article{CiCP-6-162, author = {Peter Popov, Yalchin Efendiev and Guan Qin}, title = {Multiscale Modeling and Simulations of Flows in Naturally Fractured Karst Reservoirs}, journal = {Communications in Computational Physics}, year = {2009}, volume = {6}, number = {1}, pages = {162--184}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7676.html} }
TY - JOUR T1 - Multiscale Modeling and Simulations of Flows in Naturally Fractured Karst Reservoirs AU - Peter Popov, Yalchin Efendiev & Guan Qin JO - Communications in Computational Physics VL - 1 SP - 162 EP - 184 PY - 2009 DA - 2009/06 SN - 6 DO - http://dor.org/ UR - https://global-sci.org/intro/cicp/7676.html KW - AB -

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.

Peter Popov, Yalchin Efendiev & Guan Qin. (1970). Multiscale Modeling and Simulations of Flows in Naturally Fractured Karst Reservoirs. Communications in Computational Physics. 6 (1). 162-184. doi:
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