Abstract:
Discrete Element Methods (DEM) explicitly model the mechanics of the discontinuities of naturally fractured rock masses. However, due to the large number of degrees of freedom in DEM simulations and the requirement of small times steps, the application of DEM simulations to reservoir-scale problems and long-term fluid injection problems is often computationally prohibitive. In order to reduce the computational costs associated with full-scale DEM simulations, an up-scaling method is presented in which Representative Elementary Volume (REV) DEM simulations are used to calibrate the parameters of a Continuum Damage Mechanics (CDM) constitutive model that is then used for Finite Element Analysis (FEA). The CDM model empirically captures the effect of the degradation of the rock integrity due to the yielding and sliding of natural fractures in the rock mass. Up-scaling is achieved through homogenization, in which the spatially averaged stress-strain behavior of various DEM RVE simulations is computed. Subsequently, a CDM constitutive relationship is fitted using the Levenberg-Marquardt Algorithm (LMA) and the homogenized DEM simulation data. The CDM model is then used in FEA reservoir scale simulations. The CDM model is implemented in ABAQUSTM and DEM simulations were conducted using UDECTM. The up-scaling methodology is demonstrated through a case study on a naturally fractured carbonate reservoir in which the up-scaled CDM model compares well with a direct numerical simulation with the DEM model but requires an order of magnitude less computational time.
Introduction
Discrete Element Method (DEM) models are used commonly in geomechanics to explicitly model the mechanics of Naturally Fractured Rock (NFR) masses (Jing, 2003). NFR is often modeled as a multiscale material due to the vastly different length scales involved in the deformation process (Zhou et al., 2003). At the fracture scale (10-3 m), the physics is dominated by brittle fracture propagation and fracture-to-fracture contact force interaction, while one is normally interested in the reservoir scale (103 m) response as a result of the spatial extension of the fractures. Because these scales of interest span approximately six orders of magnitude, multiscale methods are required to assess the overall response as modelling with fracture scale resolution at the reservoir scale becomes computationally prohibitive.
DEM models, unlike standard continuum models, consider the fractures within the rock mass as a Discrete Fracture Network (DFN), which explicitly defines the geometry of the fracture network. The physics of block interaction is then governed by the motion, contact forces and traction-separation laws between the rock blocks and the fractures (Cundall and Strack, 1979). Because NFR behavior is complex, even sophisticated phenomenological constitutive relationships may be inadequate to describe the complete rock mass behavior. The DEM approach aims to address this continuum behavioral deficiency by only requiring constitutive relations for the block interactions. (Cundall, 2001).
