Determining effective permeability at reservoir scale: Numerical simulations and theoretical modeling

TL;DR

This study introduces a critical path analysis (CPA) method to estimate effective permeability at the reservoir scale, compares it with numerical simulations and other models, and finds CPA to be accurate across various heterogeneity levels.

Contribution

The paper presents a novel application of critical path analysis for estimating reservoir-scale permeability and evaluates its accuracy against established models and simulations.

Findings

CPA provides accurate keff estimates across heterogeneity levels

PT and EMA overestimate keff in highly heterogeneous formations

CPA performs similarly to renormalization group theory (RGT) in accuracy

Abstract

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.