Hydraulic Fracture

TL;DR

This paper analyzes hydrofracture growth considering fluid pressure dynamics, revealing how fracture growth depends on a compliance ratio and identifying conditions for spontaneous or controlled fracture expansion.

Contribution

It introduces a modified model of fracture growth that accounts for fluid pressure drop and compliance ratios, extending Griffith's analysis to hydrofracturing scenarios.

Findings

Fracture growth depends on the compliance ratio $oldsymbol{rac{C_f}{C_f+C_m}}$

For low $oldsymbol{\alpha_0 extless= 0.2}$, fractures grow spontaneously to a certain size

Higher $oldsymbol{\alpha_0 extgreater 0.2}$ requires more fluid for each growth increment

Abstract

We consider a variation of Griffith's analysis of rupture, one which simulates the process of hydrofracturing, where fluid forced into a crack raises the fluid pressure until the crack begins to grow. Unlike that of Griffith, in this analysis fluid pressure drops as a hydrofracture grows. We find that growth of the fracture depends on the ratio of the compliances of the fluid and the fracture, a non-dimensional parameter called $\alpha_0$ here. The pressure needed to initiate a hydrofracture is found to be the same as that derived by Griffith. Once a fracture initiates, for relatively low values of the model parameter $\alpha_0$ ($\alpha_0 \leq 0.2$) the fracture advances spontaneously to a new radius which depends on the value of $\alpha_0$. For $\alpha_0 \leq 0.2$ further fluid injection is required to increase the fracture radius after spontaneous growth stops. For the case where $\alpha_0 > 0.2$ each increment of fracture growth requires injection of more fluid. For the extreme case where $\alpha_0 = 0$ our results are the same as Griffith's, i.e., a fracture once initiated grows without limit.