Numerical Calculation of Equivalent Permeability Tensor for Fractured Vuggy Porous Media Based on Homogenization Theory
Zhaoqin Huang 1*, Jun Yao 1, Yajun Li 1, Chenchen Wang 1, Xinrui Lv 11 School of Petroleum Engineering, China University of Petroleum (Huadong), Qingdao 266555, China.
Received 15 July 2009; Accepted (in revised version) 13 April 2010
Available online 5 August 2010
A numerical procedure for the evaluation of equivalent permeability tensor for fractured vuggy porous media is presented. At first we proposed a new conceptual model, i.e., discrete fracture-vug network model, to model the realistic fluid flow in fractured vuggy porous medium on fine scale. This new model consists of three systems: rock matrix system, fractures system, and vugs system. The fractures and vugs are embedded in porous rock, and the isolated vugs could be connected via discrete fracture network. The flow in porous rock and fractures follows Darcy's law, and the vugs system is free fluid region. Based on two-scale homogenization theory, we obtained an equivalent macroscopic Darcy's law on coarse scale from fine-scale discrete fracture-vug network model. A finite element numerical formulation for homogenization equations is developed. The method is verified through application to a periodic model problem and then is applied to the calculation of equivalent permeability tensor of porous media with complex fracture-vug networks. The applicability and validity of the method for these more general fractured vuggy systems are assessed through a simple test of the coarse-scale model.AMS subject classifications: 35B27, 35Q30, 76S05
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Key words: Fractured vuggy porous media, equivalent permeability tensor, homogenization, upscaling.
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