First-Order Indicators for the Estimation of Discrete Fractures in Porous Media

TL;DR

This paper introduces a computationally efficient method for estimating the location and properties of large fractures in porous media using first-order indicators, improving accuracy without complex remeshing.

Contribution

It presents a novel fracture detection algorithm that leverages first-order indicators to identify and estimate fractures from flow data without remeshing or shape derivatives.

Findings

Algorithm effectively identifies fractures in numerical tests.

Method does not require remeshing or shape derivatives.

Numerical examples demonstrate stability and accuracy.

Abstract

Faults and geological barriers can drastically affect the flow patterns in porous media. Such fractures can be modeled as interfaces that interact with the surrounding matrix. We propose a new technique for the estimation of the location and hydrogeological properties of a small number of large fractures in a porous medium from given distributed pressure or flow data. At each iteration, the algorithm builds a short list of candidates by comparing fracture indicators. These indicators quantify at the first order the decrease of a data misfit function; they are cheap to compute. Then, the best candidate is picked up by minimization of the objective function for each candidate. Optimally driven by the fit to the data, the approach has the great advantage of not requiring remeshing, nor shape derivation. The stability of the algorithm is shown on a series of numerical examples representative of typical situations.