Simulations of Pressure Fluctuations and Acoustic Emission in Hydraulic Fracturing

TL;DR

This paper uses a 2D lattice model to simulate hydraulic fracturing, analyzing pressure, energy, and acoustic emissions in both homogeneous and heterogeneous materials, revealing scaling laws and fractal crack structures.

Contribution

It introduces a lattice simulation approach for hydraulic fracturing that captures pressure fluctuations, acoustic emissions, and crack fractal dimensions in heterogeneous environments.

Findings

Pressure and energy evolution match continuum mechanics in homogeneous cases

Distribution of acoustic emission energies follows a specific probabilistic pattern

Crack structures exhibit fractal dimensions depending on material heterogeneity

Abstract

We consider a two dimensional lattice model to describe the opening of a crack in hydraulic fracturing. In particular we consider that the material only breaks under tension and the fluid has no pressure drop inside the crack. For the case in which the material is completely homogeneous (no disorder) we present results for pressure and elastic energy as a function of time and compare our findings with some analytic results from continuum fracture mechanics. Then we investigate fracture processes in strongly heterogeneous cohesive environments. We determine the cummulative probability distribution for breaking events of a given energetical magnitude (acoustic emission). Further we estimate the probabilty distribution of emission free time intervals. %We present results for a scaling relation between the amount of %injected fluids, the crack pressures, the time dependent crack %extensions and the system sizes. Finally we determine the fractal dimension(s) of the cracks.