Distinct element modeling of hydraulically fractured Lac du Bonnet granite

Abstract

[1] The aim of this study is to better understand the mechanics of fracture development and propagation during hydraulic fracturing. This paper presents some development and applications of discrete particle modeling of this problem. A discontinuum modeling approach idealizes the material as separate particles bonded together at their contact points and utilizes the breakage of individual structural units or bonds to represent damage. The numerical models are correlated with existing hydrofracture laboratory experiments, which are presented in other publications. A simulation of a laboratory-scale hydrofracture experiment and the acoustic emission (AE) data from the experiment is used to validate the synthetic AEs produced in the hydrofracture model. This technique has been used to examine the mechanics of fracture initiation and time and spatial distributions of AE. The modeling results demonstrate that the mechanism of hydraulically induced fracture in the Lac du Bonnet (LdB) granite core sample is predominantly tensile failure and that the shear cracks recorded in the hydrofracture experiment were due to slip on preexisting fractures. Numerical modeling of hydrofracture on homogeneous and heterogeneous synthetic samples seems to capture much of the behavior observed in the laboratory hydrofracture experiments.

Finite element modeling of hydraulic fracturing in 3D

“…This equation shows that the displacements in the rock are caused by the gradient of the pressure difference p (1) . Another point is that equation (14) has no explicit time dependence.…”

“…where τ (0) ij = σ (0) ij − αp (0) δ ij is the effective stress in the initial state and where τ (1) ij = σ (1) ij − αp (1) δ ij is the effective stress caused by recent changes in the fluid pressure. We are interested in the deformations caused by the difference in effective stress from the initial state.…”

“…The fluid pressure is now written as the sum of the initial fluid pressure p (0) and the difference from the initial fluid pressure, p (1) , as…”

“…Einstein summation convention is applied, by assuming summation over each pair of equal indices. The stress state in the subsurface is divided into two parts -the initial stress state σ (0) ij and the difference from the initial state, σ (1) ij , which is caused by fluid injection. We therefore have that…”

“…They can be viewed as 3D extensions of the pioneering analytical 2D models of hydraulic fracturing, like the PKN-and the GdK-models, see Geertsma [12] for a review. There are also 3D models of hydraulic fracturing based on the distinct element method, where the forces on each grain in the rock ensemble is accounted for [1].…”