The impact of grain-scale changes in microstructure geometry on effective mechanical and transport properties of granular porous media

The effective physical properties can be used to simplify the large-scale macroscopic modeling of physical processes by considering the constitutive equations of the heterogeneous porous media as if it was a homogenous continuum. The estimation of effective physical properties of porous media requires the knowledge of the microstructure geometry. In the absence of microstructure geometry, numerous theoretical models or approximations based on simplified geometries (e.g., packings of spheres, circular pipes, etc.) are often used to predict effective properties, such as porosity, permeability and elastic moduli. For instance, one of the fundamental assumptions of the most theoretical contact-mechanics-based models to predict elastic moduli is that all of the spherical particles are elastic. Since most of the materials in nature are not perfectly elastic, especially at large strain; therefore, these models are unable to accurately describe the behavior of such materials. Additionally, the predictions of effective properties using the simplified theoretical models may fail to match observed properties because of numerous simplified assumptions about the shape and size of particles and pores, which can be violated in granular materials composed of complex irregularly shaped particles. The theoretical investigation of effective physical properties of such materials is extremely difficult due to the complex and non-unique shape, position, and orientation of these particles. In the presence of microstructure geometry, we can avoid oversimplification of the microstructure geometry of porous media to predict effective physical properties using theoretical models. Digital Rocks (DR) technology can provide with a digital 3D representation of a porous medium (microstructure geometry), which can be used as an input to physics-based numerical methods to obtain an estimate of the effective physical properties (e.g., porosity, permeability, and elastic moduli) of the complex rocks. It is important to note that computed effective physical properties, especially elastic moduli, from 3D digital microstructure geometry could be affected by the scale, choice of numerical method, and boundary conditions. The key contributions of this dissertation are: (1) developed contact-mechanics-based effective medium model to predict effective moduli of granular aggregates composed of spherical particles, which are no longer elastic, but rather elastic-perfectly plastic, (2) developed numerical-experimental workflow to investigate the influence of irregular particle shape and size distributions on porosity, permeability, and elastic moduli of computationally generated granular porous media, (3) inferred limited information about the extreme estimates of pore throat sizes of the connected pathways from particle size distribution of computationally generated granular media, and from numerical simulations of mechanical percolation/trapping of fine particles in these granular assemblies, (4) developed numerical methodology to minimize the scale and boundary effects on computations of effective elastic moduli from 3D digital microstructure geometry of porous media.

Keywords: Geophysics.
Advisor: Mavko Gary
Dunham Eric 
Mukerji Tapan