Отправлено: 06.10.22 11:38. Заголовок: Determining effective permeability at reservoir scale: Application of critical path analysis

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

Critical path analysis (CPA) is applied to estimate the effective permeability keff.

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We find that CPA accurately estimates keff in two and three dimensions.

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CPA results are compared with estimations of five other models.

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Renormalization group theory also estimates keff precisely in two and three dimensions.


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 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 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.