  Determining the pressure differential required to achieve a desired flow rate
in a porous medium requires solving Darcy's law, a Laplace-like equation, with
a spatially varying tensor permeability. In various scenarios, the permeability
coefficient is sampled at high spatial resolution, which makes solving Darcy's
equation numerically prohibitively expensive. As a consequence, much effort has
gone into creating upscaled or low-resolution effective models of the
coefficient while ensuring that the estimated flow rate is well reproduced,
bringing to fore the classic tradeoff between computational cost and numerical
accuracy. Here we perform a statistical study to characterize the relative
success of upscaling methods on a large sample of permeability coefficients
that are above the percolation threshold. We introduce a new technique based on
Mode-Elimination Renormalization-Group theory (MG) to build coarse-scale
permeability coefficients. Comparing the results with coefficients upscaled
using other methods, we find that MG is consistently more accurate,
particularly so due to its ability to address the tensorial nature of the
coefficients. MG places a low computational demand, in the manner that we have
implemented it, and accurate flow-rate estimates are obtained when using
MG-upscaled permeabilities that approach or are beyond the percolation
threshold.
