A 2D large eddy simulation of Darcy's experiment Using

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					   A 2D large eddy simulation of Darcy’s experiment: Using computational physics to
            assess effects of pore space properties on hydraulic conductivity

                                      Larry Winter

                     Department of Hydrology and Water Resources
                                University of Arizona

Hydraulic conductivity, K, is the parameter in Darcy’s Law that quantifies a saturated
porous volume’s resistance to flow. Despite its great practical and theoretical importance,
the basis for estimating K -- like the basis for Darcy’s Law itself -- is empirical:
estimating a value for K usually depends on making macroscopic measurements similar
in principle to Darcy’s original experiment of 1856. Although it seems reasonable that K
should depend on microscopic geometric and topological properties like pore radius and
length, tortuosity, and connectivity, the form of K’s dependence on these (or other) pore
space properties is unclear. One obstacle to developing a fundamental theory for K has
been the difficulty of observing pore-scale phenomena, but this is gradually being
overcome by advances in both computation and observation. Recent developments in
high performance computational fluid dynamics (HPCFD) make accurate simulations of
flow in realistic structures feasible (Smolarkiewicz et al., 2007; Prusa et al., 2008). At
the same time, advances in non-invasive experimental techniques have greatly improved
our ability to characterize pore-scale phenomena (Fourie et al., 2007; Piri and Karpyn,
2007). In this talk I will discuss the HPCFD approach to simulating Darcy’s experiment
that Piotr Smolarkiewicz (NCAR) and I are taking, which is based on immersed boundary
methods (IMB) of flow through artificial pore spaces having geometries and topologies
that appear realistic. After setting the context, I will motivate the method by discussing
some initial results. In particular, our computational experiments reproduce the linear
relation between fluid flux and the gradient of hydraulic pressure that is the essence of
Darcy’s Law; hence, our experiments yield estimates of K that can be related directly to
pore space properties. Since this is work in progress, I will also indicate some future
directions for theory and applications. Regarding the latter, the IMB methodology seems
especially promising for coupling flow through channels to porous media flow in
problems ranging from stream-aquifer interactions to carbon sequestration.

Fourie W., R. Said, P. Young and D. L. Barnes, “The simulation of pore scale fluid flow
with real world geometries obtained from X-Ray computed tomography,” Proc.
COMSOL Conf., Boston, 2007.
Piri M. and Z.T. Karpyn, “Prediction of fluid occupancy in fractures using network
modeling and x-ray microtomography: I & II,” Phys. Rev. E, 76 (1), 2007.
Prusa J.M., P.K. Smolarkiewicz and A.A. Wyszogrodzki, “EULAG, a computational
model for multiscale flows,” Computers and Fluids, 37 (9), 2008