On microscale heterogeneity in granular media and its impact on elastic property estimation

Abstract

We emphasize the existence of stress-dependent microscopic heterogeneities in granular media and their influence on macroscopic property estimation using numerical simulations. Although numerical simulations based on contact mechanics successfully reproduce experimental stress-dependent acoustic response of granular media, most contact-mechanics-based effective medium theories (EMTs) fail. We have determined that the main reason for this discrepancy is an inadequate theoretical treatment of micro-heterogeneities in structure, force, and stress. Under infinitesimal perturbations used for estimating elastic moduli, microheterogeneities lead to displacements or relaxations — typically ignored in EMT. These infinitesimal granular relaxations are necessary to comply with detailed force balance, but do not involve grain slip and hence do not depend on friction. Furthermore, we have found that these relaxations primarily depend on the “amount” of heterogeneity, which to a first order are dependent on stress only and are independent of mineralogy. In the absence of an effective medium framework to estimate such relaxation corrections, we have provided simulation-based corrections to account for the impact of heterogeneity on elastic moduli calculations in EMT.

The Influence of Convex Particles' Irregular Shape and Varying Size on Porosity, Permeability, and Elastic Bulk Modulus of Granular Porous Media: Insights From Numerical Simulations

“…We begin with modeling of the granular assemblies based on the 3‐D random packing of regular (e.g., spheres and spheroids) or irregularly shaped convex particles using a discrete element method (DEM). The DEM is a robust method to simulate the interactions between discrete objects (Cundall & Strack, ; Jodrey & Tory, ; Makse et al, ; Sain et al, ; Tory et al, ) including irregularly shaped (Matuttis & Chen, ) objects. In the DEM‐based simulation, the materials (granular media) are approximated by assemblies of discrete elements (particles) bonded together by various models of cohesive forces.…”

“…In the absence of laboratory measurements, the theoretical elastic contact-mechanics-based effective medium theory models (Digby, 1981;Duffaut et al, 2010;Dvorkin & Nur, 1996;Norris & Johnson, 1997;Walton, 1987) are often used to predict the effective elastic moduli of granular aggregates modeled by random packings of identical elastic spherical particles. Makse et al (1999Makse et al ( , 2004 and Sain et al (2016) extensively studied the underlying assumptions of these effective medium theory models using the numerical molecular-dynamics simulation approach.…”

Scale and Boundary Effects on the Effective Elastic Properties of 2‐D and 3‐D Non‐REV Heterogeneous Porous Media

“…Similar procedures were applied on three‐dimensional compacted random packing of 5,000 spherical particles. The compacted random packing of spheres (Figure b) was generated at hydrostatic confining pressure of 100 MPa using the discrete element method‐based granular dynamics algorithm (Sain et al, ). In contrast to Berea digital rock, the standalone samples of random sphere packing had a minimum side length of 300 and maximum side length of 700 voxels with D grain / L voxel = 54.…”

7. Seismic, rock physics, spatial models, and their integration in reservoir geophysics

“…As with the HertzMindlin contact theory for loose granular media, the DvorkinNur contactcement model also is found to often overpredict shear stiffnesses in cemented sand stones. This could be related to heterogeneous mixture of nonspherical grain contacts, hetero geneous cementation, and tangential slip at loose contacts (Avseth and Skjei, 2011), or relative roll and torsion, and relaxation due to local stress heterogeneities not taken into account in the ef fective medium contact theory models (e.g., Elata and Berryman, 1996;Makse et al, 1999;Sain et al, 2016).…”

“…Shear moduli tend to be over predicted and often require heuristic corrections (e.g., Bachrach and Avseth, 2008). Numerical methods, referred to as "molecular dynamics" or "discrete element modeling," which simulate the motions and interactions of thousands of grains, appear to come closer to predicting ob served behavior (e.g., Garcia and Medina, 2006;Makse et al, 2004;Sain et al, 2016). Closedform effective medium models can be useful, because it is not always practical to run a numerical sim ulation; however, model predictions of the types presented in this section must be used with care.…”