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Advances in Applied Mathematics, Modeling, and Computational Science

Volume 66 of the series Fields Institute Communications pp 161-185

A Multiscale Method Coupling Network and Continuum Models in Porous Media II—Single- and Two-Phase Flows

  • Jay ChuAffiliated withDepartment of Mathematics, The University of Texas at Austin Email author 
  • , Björn EngquistAffiliated withDepartment of Mathematics, The University of Texas at AustinICES, The University of Texas at Austin
  • , Maša ProdanovićAffiliated withDepartment of Petroleum and Geosystems Engineering, The University of Texas at AustinCPGE, The University of Texas at Austin
  • , Richard TsaiAffiliated withDepartment of Mathematics, The University of Texas at AustinICES, The University of Texas at Austin

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Abstract

We present a numerical multiscale method for coupling mass conservation laws at the continuum scale with a discrete, pore scale network model for two-phase flow in porous media. Our previously developed single-phase flow algorithm is extended to two-phase flows, for the situations in which the saturation profile go through a sharp transition from fully saturated to almost unsaturated states. Our method evaluates the continuum equation by simulations using small representative networks centering at different physical locations, and thereby computes the effective dynamics of the two phase flow at the continuum scale. On the other hand, the initial and boundary data for the network simulations are determined by the variables used in the continuum model. We present numerical results for single-phase flows with nonlinear flux-pressure dependence, as well as two-phase flows.