On the Importance of the Stokes-Brinkman Equations for Computing Effective Permeability in Karst Reservoirs (Communications in Computational Physics, 2011)
Cavities and fractures significantly affect the flow paths in carbonate reservoirsand should be accurately accounted for in numerical models. Herein, we considerthe problem of computing the effective permeability of rock samples based onhigh-resolution 3D CT scans containing millions of voxels. We use the Stokes-Brinkmanequations in the entire domain, covering regions of free flow governed by the Stokesequations, porous Darcy flow, and transitions between them. The presence of differentlength scales and large (ten orders of magnitude) contrasts in permeability leadsto highly ill-conditioned linear systems of equations, which are difficult to solve. Toobtain a problem that is computationally tractable, we first analyze the relative importanceof the Stokes and Darcy terms for a set of idealized 2D models. We find that,in terms of effective permeability, the Stokes-Brinkman equations are only applicablefor a special parameter set where the effective free-flow permeability is less than fourorders of magnitude different from the matrix permeability. All other cases can be accuratelymodeled with either the Stokes or the Darcy end-member flows, dependingon if there do or do not exist percolating free-flow regions. The insights obtained areused to perform a direct computation of the effective permeability of a rock samplemodel with more than 8 million cells.