Pore-scale analysis of grain shape and sorting effect on fluid transport phenomena in porous media
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Macroscopic transport properties of porous media depend on textural rock parameters such as porosity, 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 other textural rock properties can be tedious, time-consuming, or impossible to obtain without special methods such as X-ray microtomography and scanning electron microscopy. However, by using digital three-dimensional pore-scale rock models and physics-based algorithms researchers can calculate both geometrical and transport properties of porous media. Therefore, 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 at the pore-scale level the effects of grain shapes and spatial cement distribution on macroscopic rock properties for improved understanding of various petrophysical correlations. Deposition and compaction of grains having arbitrary angular shapes and various sizes is modeled using novel sedimentation and cementation pore-scale algorithms. Additionally, the algorithms implement numerical quartz precipitation to describe preferential cement growth in pore-throats, pore-bodies, or uniform layers. Subsequently, petrophysical properties such as geometrical pore-size distribution, primary drainage capillary pressure, absolute permeability, streamline-based throat size distribution, and apparent electrical formation factor are calculated for several digital rock models to evaluate petrophysical correlations. Furthermore, two geometrical approximation methods are introduced to model irreducible (connate) water saturation at the pore scale. Consolidated grain packs having comparable porosities and grain size distributions but various grain shapes indicate that realistic angular grain shape distribution gives the best agreement of petrophysical properties with experimental measurements. Cement volume and its spatial distribution significantly affect pore-space geometry and connectivity, and subsequently, macroscopic petrophysical properties of the porous media. For example, low-porosity rocks having similar grain structure but different cement spatial distribution could differ in absolute 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 provide sufficient rock-structure character to describe absolute permeability correlations. In comparison to surface-to-volume ratio, capillary trapped (irreducible) water saturation exhibits better correlation with absolute permeability due to weak pore space connectivity in low-porosity samples near the percolation threshold. Furthermore, in grain packs with fine laminations and permeability anisotropy, pore-scale analysis reveals anisotropy in directional drainage capillary- pressure curves and corresponding amounts of capillary-trapped wetting fluid. Finally, results presented in this dissertation indicate that pore-scale modeling methods can competently capture the effects of porous media geometry on macroscopic rock properties. Pore-scale two- and three-phase transport calculations with fast computers can predict petrophysical properties and provide sensitivity analysis of petrophysical properties for accurate reservoir characterization and subsequent field development planning.