KAUST DepartmentNumerical Porous Media SRI Center (NumPor)
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
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AbstractIn this work we propose upscaling method for nonlinear Forchheimer flow in heterogeneous porous media. The generalized Forchheimer law is considered for incompressible and slightly-compressible single-phase flows. We use recently developed analytical results (Aulisa et al., 2009)  and formulate the resulting system in terms of a degenerate nonlinear flow equation for the pressure with the nonlinearity depending on the pressure gradient. The coarse scale parameters for the steady state problem are determined so that the volumetric average of velocity of the flow in the domain on fine scale and on coarse scale are close. A flow-based coarsening approach is used, where the equivalent permeability tensor is first evaluated following streamline methods for linear cases, and modified in order to take into account the nonlinear effects. Compared to previous works (Garibotti and Peszynska, 2009) , (Durlofsky and Karimi-Fard) , this approach can be combined with rigorous mathematical upscaling theory for monotone operators, (Efendiev et al., 2004) , using our recent theoretical results (Aulisa et al., 2009) . The developed upscaling algorithm for nonlinear steady state problems is effectively used for variety of heterogeneities in the domain of computation. Direct numerical computations for average velocity and productivity index justify the usage of the coarse scale parameters obtained for the special steady state case in the fully transient problem. For nonlinear case analytical upscaling formulas in stratified domain are obtained. Numerical results were compared to these analytical formulas and proved to be highly accurate. © 2014.
SponsorsThe authors are thankful to Dr. Luan Hoang for his valuable discussions, suggestions and recommendations. The research of this paper was supported by the NSF Grant DMS-0908177.
JournalAdvances in Water Resources