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UBC Theses and Dissertations

A theoretical treatment of microscopic phenomena in porous rocks Endres, Anthony Lee


This thesis makes five significant contributions to the theoretical analysis of the connection between microscopic phenomena and the macroscopic physical properties of porous rocks. A random sphere packing model permitting contact generation during hydrostatic compression is derived. It is demonstrated that the closure of near-contact gaps with an extremely small mean width significantly alters the elastic properties of granular media from those predicted by previous models in the pressure range used in laboratory measurements. Generalized forms of the inclusion-based formulations are obtained; major classes of these formulations are defined according to the manner in which interactions between inclusions in the heterogeneous system are simulated. Each class possesses an associated microstructure that determines the topological relationship between the various components. Inclusion-based formulations are obtained that describe the effects of pore-scale fluid distribution on the dielectric and elastic responses of a partially saturated rock. It is found that the pore fluid configuration within the individual pores and the pore geometries in which saturation conditions are varying are critical factors in determining the dielectric and elastic properties of partially saturated rocks. In addition, it is observed that the effect of saturation condition variations in a particular pore geometry increases as the pore shape becomes more crack-like. The theoretical formulations describing the effects of pore-scale fluid distribution are used to analyze experimental data for a partially saturated tight gas sandstone and glass bead packing. Simple models that incorporate only the basic geometrical elements of the resulting pore-scale fluid distributions accurately predict the experimental data. It is also found that the same geometrical model can be used simultaneously to estimate the dielectric and elastic responses of a partially saturated porous medium. The effect of surface phenomena (e.g. electrical double layers and surface conduction) at the solid-fluid interface are incorporated into inclusion-based formulations of the dielectric response by employing the limiting case of a confocally-layered ellipsoid. It is found that the effect of surface phenomena varies as a function of both inclusion size and shape.

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