Averaging-based approach to toughness homogenisation for radial hydraulic fracture

TL;DR

This paper introduces a temporal-averaging homogenisation method for fracture toughness in radial hydraulic fractures, accounting for viscosity-toughness transition and step-wise crack growth, validated through numerical simulations.

Contribution

It proposes a novel averaging-based homogenisation strategy that incorporates fracture velocity, improving toughness modeling in radial hydraulic fractures.

Findings

Effective for periodic toughness distributions

Handles unbalanced toughness scenarios

Maintains accuracy with step-wise crack growth

Abstract

The homogenisation of the fracture toughness is considered in the context of a propagating hydraulic fracture. The radial (penny-shape) model is utilized, in order to incorporate the impact of the viscosity-toughness regime transition over time. A homogenisation strategy based upon temporal-averaging is investigated. This approach incorporates the instantaneous fracture velocity, meaning that it should remain effective in the case of step-wise crack advancement. The effectiveness of the approach is demonstrated for periodic toughness distributions, including those which are unbalanced, utilizing a highly accurate solver.