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A Framework for Modeling Subgrid Effects for Two-Phase Flows in Porous Media

Hou, Thomas Y. and Westhead, Andrew and Yang, Danping (2006) A Framework for Modeling Subgrid Effects for Two-Phase Flows in Porous Media. Multiscale Modeling & Simulation, 5 (4). pp. 1087-1127. ISSN 1540-3459. doi:10.1137/050646020.

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In this paper, we study upscaling for two-phase flows in strongly heterogeneous porous media. Upscaling a hyperbolic convection equation is known to be very difficult due to the presence of nonlocal memory effects. Even for a linear hyperbolic equation with a shear velocity field, the upscaled equation involves a nonlocal history dependent diffusion term, which is not amenable to computation. By performing a systematic multiscale analysis, we derive coupled equations for the average and the fluctuations for the two-phase flow. The homogenized equations for the coupled system are obtained by projecting the fluctuations onto a suitable subspace. This projection corresponds exactly to averaging along streamlines of the flow. Convergence of the multiscale analysis is verified numerically. Moreover, we show how to apply this multiscale analysis to upscale two-phase flows in practical applications.

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Additional Information:©2006 Society for Industrial and Applied Mathematics. Received by the editors November 24, 2005; accepted for publication (in revised form) June 30, 2006; published electronically December 5, 2006. The first author’s [T.Y.H.] research was in part supported by NSF ITR grant ACI-0204932 and NSF FRG grant DMS-0353838. This author’s [D.Y.] research was supported in part by the National Basic Research Program of China under grant 2005CB321703, by the NSFC under grants 10571108 and 10441005, and by the Research Fund for Doctoral Program of High Education of the Education Ministry of China under grant 2005042203.
Subject Keywords:porous media, upscaling, homogenization, hyperbolic, numerical modeling
Issue or Number:4
Record Number:CaltechAUTHORS:HOUmms06
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7553
Deposited By: Archive Administrator
Deposited On:03 Mar 2007
Last Modified:08 Nov 2021 20:43

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