Permeability Estimates of Self-Affine Fracture Faults Based on Generalization of the Bottle Neck Concept

TL;DR

This paper introduces a fast and accurate method to estimate the permeability of self-affine fracture faults by generalizing the bottleneck concept, significantly improving computational efficiency over traditional methods.

Contribution

It extends the bottleneck concept to two-dimensional self-affine fields, providing a more efficient way to estimate fracture permeability with high accuracy.

Findings

Method remains accurate with mechanical overlap

Computational efficiency is comparable to simple averaging

Over two orders of magnitude faster than Reynolds equation solutions

Abstract

We propose a method for calculating the effective permeability of two-dimensional self-affine permeability fields based on generalizing the one-dimensional concept of a bottleneck. We test the method on fracture faults where the local permeability field is given by the cube of the aperture field. The method remains accurate even when there is substantial mechanical overlap between the two fracture surfaces. The computational efficiency of the method is comparable to calculating a simple average and is more than two orders of magnitude faster than solving the Reynolds equations using a finite-difference scheme.