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Pore-Scale Numerical Study of Grain Shape and Sorting Effects on Fluid-Transport Phenomena in Porous Media

Tatyana Torskaya, Ph.D.

The University of Texas at Austin, 2013

Supervisor: Carlos Torres-Verdín

Abstract:

Macroscopic fluid transport properties of porous rocks depend not only on porosity but also on textural properties such as grain size and grain shape distributions, surface-to-volume ratios, and spatial distributions of cement. Although porosity is routinely measured in the laboratory, direct measurements of textural rock properties can be tedious, time-consuming, or impossible without special methods, for example X-ray micro-tomography. However, digital three-dimensional pore-scale rock models and physics-based algorithms one can be used to calculate both geometrical and transport properties of porous media. Pore-scale modeling techniques provide a unique opportunity to explore explicit relationships between pore-scale geometry and fluid and electric flow properties.

The primary objective of this dissertation is to investigate the effects of grain shape and spatial cementation distribution at the pore-scale level on macroscopic rock properties for improved quantification of petrophysical correlations. Using new sedimentation and cementation pore-scale algorithms developed in this research project, I model deposition and compaction of grains having arbitrary angular shapes and sizes. Additionally, the algorithms implement numerical quartz precipitation to describe preferential cement growth in pore-throats, pore-bodies, or uniform layers. Petrophysical properties such as geometrical pore-size distribution, primary drainage capillary pressure, permeability, streamline-based throat size distribution, and apparent electrical formation factor are subsequently calculated for several digital rock models to infer petrophysical correlations. Furthermore, two geometrical approximation methods are examined to model irreducible (connate) water saturation at the pore scale.

Consolidated grain packs with comparable porosity and grain size distribution constructed from different grain shapes indicate that an angular grain shape distribution gives rise to the best agreement of petrophysical properties with experimental measurements. Cement volume and its spatial distribution significantly affect pore-space geometry and connectivity, hence macroscopic petrophysical properties of porous rocks. For example, low-porosity rocks exhibiting identical detrital grain structure and total cement volume but different cement spatial distribution could differ in permeability by two orders of magnitude and in capillary trapped water saturation by a factor of three. For clastic rocks with porosity much higher than percolation threshold porosity, pore-scale modeling results confirm that surface-to-volume ratio and porosity embody sufficient information to infer permeability correlations. In low-porosity samples near the percolation threshold, capillary trapped (irreducible) water saturation in comparison to surface-to-volume ratio exhibits better correlation with permeability due to weak pore-space connectivity. In addition to permeability anisotropy in grain packs constructed with fine grain laminations, pore-scale analysis revealed anisotropy in directional drainage capillary- pressure curves and corresponding volumes of capillary-trapped wetting fluid.

Results described in this dissertation indicate that pore-scale modeling can be used for practical sensitivity analysis of pore- and throat-size distributions on macroscopic rock properties.