On modeling hydraulic fracture in proper variables: stiffness, accuracy, sensitivity

TL;DR

This paper introduces a modified formulation for hydraulic fracture modeling using proper variables, enhancing numerical efficiency, accuracy, and sensitivity analysis, demonstrated through the Nordgren problem.

Contribution

The paper presents a new formulation in proper variables that improves numerical stability, accuracy, and computational efficiency in hydraulic fracture modeling.

Findings

Enhanced numerical stability and accuracy demonstrated

Flexible handling of differential equation stiffness

Effective sensitivity analysis enabled

Abstract

The problem of hydraulic fracture propagation is considered by using its recently suggested modified formulation in terms of the particle velocity, the opening in the proper degree, appropriate spatial coordinates and $\varepsilon$-regularization. We show that the formulation may serve for significant increasing the efficiency of numerical tracing the fracture propagation. Its advantages are illustrated by re-visiting the Nordgren problem. It is shown that the modified formulation facilitates (i) possibility to have various stiffness of differential equations resulting after spatial discretization, (ii) obtaining highly accurate and stable numerical results with moderate computational effort, and (iii) sensitivity analysis. The exposition is extensively illustrated by numerical examples.