Propagation of Elongated Fluid-Driven Fractures: Rock Toughness vs. Fluid Viscosity

TL;DR

This paper analyzes how rock toughness influences the propagation of elongated fluid-driven fractures using an extended PKN model, providing analytical solutions and insights into the roles of viscous and toughness-related dissipation.

Contribution

It introduces a self-consistent analysis of tough fractures with arbitrary injection laws using the `tough PKN' model and offers simplified equations for fracture propagation during injection and shut-in periods.

Findings

Toughness significantly affects fracture propagation regimes.

Analytical solutions are derived for different limiting regimes.

Viscous and toughness dissipation contributions are compared.

Abstract

This paper studies the effect of the rock fracture toughness on the propagation of elongated fluid-driven fractures. We use the `tough PKN' model of Sarvaramini and Garagash (2015), an extension of the classical PKN model(Perkins and Kern, 1961; Nordgren, 1972), which allows for a non-zero energy release rate into the advancing fracture front(s). We provide a self-consistent analysis of a `tough' elongated fracture driven by arbitrary fluid injection law under the assumption of negligible fluid leak-off. We use scaling considerations to identify the non-dimensional parameters governing the propagation regimes and their succession in time, provide a number of analytical solutions in the limiting regimes for an arbitrary power-law injection, and also posit a simplified, equation-of-motion, approach to solve a general elongated fracture propagation problem during the injection and shut-in periods. Finally, we use the developed solutions for a tough elongated fracture to surmise the relative importance of the viscous and toughness-related dissipation on the fracture dynamics and broach the implications of the possible toughness scale-dependence.