A Darcy-Cahn-Hilliard model of multiphase fluid-driven fracture

TL;DR

This paper introduces a coupled Darcy-Cahn-Hilliard and damage model to simulate multiphase flow and fluid-driven fracturing in porous media, validated against experiments and used to explore new flow regimes.

Contribution

The paper develops a novel thermodynamics-based multiphase fracture model with damage and phase fields, validated by experiments and capable of predicting new flow behaviors.

Findings

Recovered experimental phase diagram of flow regimes

Calibrated model accurately with finite element simulations

Predicted new flow regime beyond current experiments

Abstract

A Darcy-Cahn-Hilliard model coupled with damage is developed to describe multiphase-flow and fluid-driven fracturing in porous media. The model is motivated by recent experimental observations in Hele-Shaw cells of the fluid-driven fracturing of a synthetic porous medium with tunable fracture resistance. The model is derived from continuum thermodynamics and employs several simplifying assumptions, such as linear poroelasticity and viscous-dominated flow. Two distinct phase fields are used to regularize the interface between an invading and a defending fluid, as well as the ensuing damage. The damage model is a cohesive version of a phase-field model for fracture, in which model parameters allow for control over both nucleation and crack growth. Model-based simulations with finite elements are then performed to calibrate the model against recent experimental results. In particular, an experimentally-inferred phase diagram differentiating two flow regimes of porous invasion and fracturing is recovered. Finally, the model is employed to explore the parameter space beyond experimental capabilities, giving rise to the construction of an expanded phase diagram that suggests a new flow regime.