Determining effective permeability at reservoir scale: Application of critical path analysis

Determining the effective permeability (k_eff) 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 k_eff at the reservoir scale using the critical path analysis (CPA), (2) to evaluate the accuracy of this new approach by comparing the estimated k_eff to the numerically simulated effective permeability, and (3) to compare the performance of CPA estimates of k_eff with 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 k_eff estimated via CPA to k_eff 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 k_eff estimations in rather homogeneous formations, they substantially overestimate the effective permeability in highly heterogeneous formations.