  Determining the effective permeability (keff) of geological formations has
broad applications to site remediation, aquifer discharge or recharge,
hydrocarbon production, and enhanced oil recovery. The objectives of this study
are: (1) to explore an approach to estimating keff at the reservoir scale using
the critical path analysis (CPA), (2) to evaluate the accuracy of this new
approach by comparing the estimated keff to the numerically simulated effective
permeability, and (3) to compare the performance of CPA estimates of keff to
estimates by three other models i.e., perturbation theory (PT),
effective-medium approximation (EMA), and renormalization group theory (RGT).
We construct two- and three-dimensional random (uncorrelated) geologic
formations based on permeability measurements from the Borden site and assume
that the permeability distribution conforms to the log-normal probability
density function over a wide range of means and standard deviations. Comparing
keff estimated via CPA to keff values derived from numerical flow simulations
indicates that CPA provides accurate estimations in both two and three
dimensions over a wide range of heterogeneity levels, similar to RGT.
Inter-model comparisons show that although PT and EMA provide reasonable keff
estimations in rather homogeneous formations, they substantially overestimate
the effective permeability in highly heterogeneous formations.
