Modeling compaction effects on the elastic properties of clay-water composites

Abstract

Modeling the elastic properties of clay-bearing rocks (shales) requires thorough knowledge of the mineral constituents, their elastic properties, pore space microstructure, and orientations of clay platelets. Information about these variables and their complex interrelationships is rarely available for real rocks. We theoretically modeled the elastic properties of synthetic clay-water composites compacted in the laboratory, including estimates of pore space topology and percolation behavior. The mineralogy of the samples was known exactly, and the focus was on two monomineralic samples comprised of kaolinite and smectite. We used differential effective medium theory (DEM) and analysis of scanning electron microscope (SEM) images of the compacted kaolinite and smectite samples. Percolation behavior was included through calculations of critical porosities from measurements of the liquid limits of the individual clay powders. Quantitative analysis of the SEM images showed that the large scale (>0.1 μm) pore space of the smectite composite had more rounded pores (mean aspect ratio α ¼ 0.55) than the kaolinite composite (mean pore's aspect ratio α ¼ 0.44). However, models that used only these largescale pore shapes could not explain the compressional and shear velocity measurements. DEM simulations with a single pore aspect ratio showed that bulk and shear moduli are controlled by different pore shapes. Conversely, modeling results that combined critical porosity and dual porosity models into DEM theory compared well with the measured bulk and shear moduli of compacting kaolinite and smectite composites. The methods and results we used could be used to model unconsolidated clay-bearing rocks of more complex mineralogy.

Using small-angle X-ray scattering to investigate the compaction behaviour of a granulated clay

“…n = 1 for 1 st order reflections). This gave d ≈ 10•7 Å, which appears consistent with the expected basal spacing for a smectite without hydration (Bergaya et al 2006, Moyano et al 2012, Villar et al 2012.…”

“…Hence, the results obtained here for gMgSm agreed reasonably well with previously published results for compacted clays [Vanorio et al 2003, Mondol et al2007, Moyano et al 2012 and were somewhat larger than expected for sMCC, based on data previously reported by Han et al [2011]. The smaller modulus of sMCC suggests that it should exhibit greater strain during loading and unloading than gMgSm, which is counter to the observations.…”

Linking preferred orientations to elastic anisotropy in Muderong Shale, Australia

“…Several modeling approaches, assuming shale as a transverse isotropic body, have been proposed to explain anisotropic elastic properties, including selfconsistent theories and hypothetical assumptions of microstructures and preferred orientation (e.g., Rundle and Schuler, 1981;Hornby et al, 1994;Jakobsen et al, 2000;Draege et al, 2006;Ortega et al, 2007;Moyano et al, 2012). Although providing qualitatively convincing results, most of these modeling approaches have not fully taken clay preferred orientations, elastic anisotropy of minerals, and microstructural information into account.…”

Aspect ratio histograms of 3D ellipsoids and 2D ellipses — Analytical relations and numerical examples

“…Sometimes, 2D sections of a core sample are used as the basis for statistical estimation of the aspect ratio for a given rock sample. One recent example can be found in Moyano et al (2012), where histograms of pore aspect ratio are estimated based on 2D sections from several clay samples. Gupta et al (2011) estimate aspect ratios ranging from 9 to 165 for kaolinite particles.…”