Graduation date: 2007
In this paper we develop an upscaling technique for non-Darcy flow in porous media.
Non-Darcy model of flow applies to flow in porous media when large velocities occur. The
well-posedness results for theory of quasilinear elliptic partial differential equations. To
discretize the model we used lowest order Raviart-Thomas mixed finite element spaces.
The resulting non-linear system is solved using fixed point iteration; we provide sufficient
conditions for this iteration to converge. Then we formulate an upscaling method for
non-Darcy flow extending a method by Durlofsky originally given for Darcy flow. The
method computes effective coefficients which can be used to simulate the Darcy flow on a
coarse grid. We compare numerical results for Darcy and non-Darcy flow and upscaling
results for two scenarios; in all cases results apply to a problem with rate-specified wells.