Porous grain model and equivalent elastic medium approach for predicting effective elastic properties of sedimentary rocks

This dissertation presents the results of using different inclusion and granular effective medium models and poroelasticity to predict the elastic properties of rocks with complex microstructures. Effective medium models account for the microstructure and texture of rocks, and can be used to predict the type of rock and microstructure from seismic velocities and densities. We introduce the elastic equivalency approach, using the differential effective medium model, to predict the effective elastic moduli of rocks and attenuation. We introduce the porous grain concept and develop rock physics models for rocks with microporosity. We exploit the porous grain concept to describe a variety of arrangements of uncemented and cemented grains with different degrees of hydraulic connectivity in the pore space.;We first investigate the accuracy of the differential effective medium and self-consistent estimations of elastic properties of complex rock matrix using composites as analogs. We test whether the differential effective-medium (DEM) and self-consistent (SC) models can accurately estimate the elastic moduli of a complex rock matrix and compare the results with the average of upper and lower Hashin-Shtrikman bounds. We find that when the material microstructure is consistent with DEM, this model is more accurate than both SC and the bound-average method for a variety of inclusion aspect ratios, concentrations, and modulus contrasts.;Based on these results, we next pose a question: can a theoretical inclusion model, specifically, the differential effective-medium model (DEM), be used to match experimental velocity data in rocks that are not necessarily made of inclusions (such as elastics)? We first approach this question by using empirical velocity-porosity equations as proxies for data. By finding a DEM inclusion aspect ratio (AR) to match these equations, we find that the required range of AR is remarkably narrow. Moreover, a constant AR of about 0.13 can be used to accurately match empirical relations in competent sand, shale, and quartz/calcite mixtures.;The porous grain model treats marine sediment as pack of porous elastic grains. The effective elastic moduli of the porous grains are calculated using the differential effective-medium model (DEM), where the intragranular ellipsoidal inclusions have a fixed aspect ratio and are filled with seawater. Then the elastic moduli of a pack of these spherical grains are calculated using different granular medium models and a modified (scaled to the critical porosity) upper Hashin-Shtrikman bound above the critical porosity, and modified lower and upper Hashin-Shtrikman bounds below the critical porosity. In this study, the modified lower and upper bounds were found to be appropriate for carbonate marine sediment and diatomaceous sediment, respectively.;The porous-grain model is also applied to estimate the effective elastic properties of three basic porous grain-aggregate scenarios, depending on the effective fluid connectivity of the intragranular porosity and in the grains. To determine the effective elastic properties of the saturated porous-grain material in the three different porous-grain-aggregate scenarios, we use two models: the differential effective medium approximation (DEM) and the combination DEM-Gassmann, depending on whether we wish to obtain the high frequency or the low frequency effective elastic moduli, respectively. In this approach, low and high frequency refer to fluid-related effects; but the wavelengths are still much longer than any scale of grains or intergranular pores.;A similar staged approach is used to determine the elastic moduli of a cemented porous grain aggregate at low cement concentration. This is achieved by introducing the porous grain concept into the cementation theory. Then, the combination of the cementation theory for porous grain material with a self-consistent approximation, specifically, the coherent potential approximation (CPA), allows us to estimate the elastic properties of cemented porous grain aggregates at all cement concentrations. Therefore, the porous grain model allows for (a) varying the grain contact friction coefficient gamma in the whole range from 0 to 1, for smooth to infinitely rough grains, respectively; (b) combining the self-consistent approximation with the cementation theory to account for intergranular cement volume fractions from 0 to 1; and (c) considering porous grain textures and the effect of frequency. (Abstract shortened by UMI.)...