Coupled Hydraulic and Mechanical Analysis at the Pore-Scale Domain for Reliable Assessment of Mechanical Properties in Anisotropic and Heterogeneous Formations
Authors: Teymouri Mehdi , Heidari Zoya 
Published: October 2020

Abstract
Reliable characterization of mechanical behavior (e.g., elastic properties) in anisotropic and heterogeneous formations require advanced methods for understanding the impacts of spatial distribution of rock components, pore structure, and pore pressure on mechanical properties. However, the existing methods for assessment of mechanical properties (e.g., effective elastic properties) such as effective medium models, assume constant stiffness values and idealized shapes for rock constituents and pores. These models also do not take into account coupled hydraulic and mechanical (HM) processes, which cause significant uncertainties in geomechanical evaluation. The objective of this paper is to investigate the effects of realistic spatial distribution of minerals, pore pressure, and pore structure on the effective elastic properties of rock-fluid systems.
In order to pursue this objective, we developed a pore-scale numerical simulator by satisfying conservation equations and considering the coupling among relevant HM processes. We adopted peridynamic theory to discretize the micro-/nano-scale medium. The inputs to the numerical modeling include pore-scale images of rock samples as well as mechanical and hydraulic properties of each rock constituent. We used micro-computed tomography (micro-CT) scan and focused ion beam (FIB) scanning electron microscope (SEM) images of rock samples to obtain a realistic micro-/nano-scale structure of both rock matrix and pore space. We then assigned realistic mechanical and hydraulic properties to each rock constituent within the pore-scale medium. The outcomes of numerical modeling include the variation of effective stress and the evolution of corresponding strain by honoring the variability in mechanical properties of rock components caused by their spatial distribution, size, pore pressure, and pore structure at the micro-/nano-scale level.
We successfully tested the reliability of the developed framework using results of an analytical solution for the case of consolidation. We then performed sensitivity analyses to quantify the effects of concentration and spatial distribution of rock components, divergence in mechanical properties of minerals, and pore structure on variations in effective elastic properties of rock components. For instance, the deformation of clay minerals dispersed in between the quartz minerals was approximately 60% less than that in clay minerals colonized next to the quartz under the same load. In the next step, we compared these mechanical characterizations with estimates obtained from the effective medium models. We observed measurable uncertainties (more than 15% depending on mineral content and distribution) in elastic properties of rock components estimated by the effective medium models such as self-consistent approximation. These uncertainties are associated with spatial distribution, shape, and size of minerals, which are not considered in those models. Such effective medium models also overlook the effects of pore structure and pore pressure on the mechanical properties. The results of coupled HM analysis for cases with the same mineral concentration but different pore structure revealed more than 12% error in estimates of effective mechanical properties.