Parameter Estimation for the Reduced Fracture Model via a Direct Filter Method

TL;DR

This paper introduces a real-time numerical method using a direct filter to accurately estimate fracture widths in porous media from observational data, based on a reduced fracture model of diffusion.

Contribution

It presents a novel online parameter estimation technique for fracture width detection using a direct filter within a reduced fracture model framework.

Findings

High accuracy in parameter approximation demonstrated through numerical experiments

Effective real-time detection of fracture widths in porous media

Validation of the method's robustness and efficiency

Abstract

In this work, we present a numerical method that provides accurate real-time detection for the widths of the fractures in a fractured porous medium based on observational data on porous medium fluid mass and velocity. To achieve this task, an inverse problem is formulated by first constructing a forward formulation based on the reduced fracture model of the diffusion equation. A parameter estimation problem is then performed online by utilizing a direct filter method. Numerical experiments are carried out to demonstrate the accuracy of our method in approximating the target parameters.