Determining effective permeability at the reservoir scale: Numerical simulations compared with critical path analysis

Abstract:

Determining the effective permeability (k_eff) of geological formations is of great importance, particularly for site remediation, oil and gas production, and enhanced oil recovery. However, due to the presence of heterogeneity across scales, accurate calculation of k_eff requires precise characterization of reservoirs. In the literature, stochastic, theoretical, and numerical methods have been proposed to determine the value of k_eff but, very often, these methods are either too simple to capture the complexity of earth systems or too cumbersome to apply. In this study, we propose a simple but powerful technique for estimating k_eff at reservoir scales via the critical path analysis (CPA) approach. Conceptually, based on CPA, the permeability value corresponding to the mode of its probability density function should represent the effective permeability of a reservoir. To validate this hypothesis, we built up two-dimensional geologic structures using the measured permeability histogram of the Borden aquifer reported by Sudicky (1986) and simulated flow at the reservoir scale using COMSOL. We investigated the robustness of this hypothesis and effect of heterogeneity on it by altering the permeability geometric mean (1.2E-12 m² < k_g < 1.2E+9 m²) and standard deviation (0.04 <σ< 6.50) of the log-normal permeability distribution. We compared the numerically determined k_eff via COMSOL with the estimated effective permeability by CPA and two other models i.e., Gutjahr et al (1978) and Stepanyants and Teodorovich (2003). Results showed that the CPA approach estimated the effective permeability with RMSLE = 0.5, more accurately than the other two models studied here with RMSLE = 2.9 and 15.3 respectively for the Stepanyants and Teodorovich (2003) and Gutjahr et al (1978) models.