Stress Strain Characterization of Sand Packs Under ?Uniform Loads As Determined From , . Computer Assisted Tomography
Authors: Kantzas A. 
Published: March 2010

Abstract
The local changes in the density and. porosity of dry sand packs as a function of the imposed overburden were determined using Computer Assisted Tomography. Pressure cycles were imposed on sands with different characteristics. The density and porosity was measured at a resolution of 0.075 cm × 0.075 cm × 0.3 cm. Hysteresis in the densityand porosity was observed. The imposed overburden and pore volume changes were translated to stress and strain, respectively. The data was used to calculate material properties such as the bulk compressibility and the formation compaction. The results were compared with information available in the literature. Good agreement was obtained.

Introduction and Theory
Computer Assisted Tomography (CAT) scanning has been use in the characterization of unconsolidated core material(1, 2) and has been found very useful in identifying core heterogeneities and areas of formation damage. Physical properties such as bulk density and porosity can be calculated using simple models(3, 4). However, the porosity measurements will be in error if the core is not compressed back to reservoir pressure. With this in mind, it was decided to perform a series of tests that would demonstrate the effect of overburden pressure on porosity. At the same time, methods using CAT scanners in the study of fracturing and the measurement of material properties appeared in the literature(5). The data collected from the porosity under various overburden pressures could then be translated into stress strain data and physical properties such as the bulk modulus could actually be measured(5, 6).
The CAT scanner provides normalized values of the linear attenuation coefficient of each volume element (voxel) which are usually called CT numbers (CTn) at a resolution that varies depending on the scanner used. The resolution of the measurements in this work is 0.075 cm × 0.075 cm × 0.3 cm. The bulk density is calculated from the CT number from the following equation:
(1) ρ b = 1.119 + 0.00163 * CT n
The porosity of a dry sand pack is calculated from the bulk density through:
Equation (2) Available In Full Paper.
where 2.649 is the grain density of quartz. Therefore, from a single scan of a given cross section, the bulk density and porosity maps of the cross section can be derived at the given resolution. If the sand pack is saturated with a single liquid (e.g., water) the bulk density can still be calculated using Equation (1). The porosity will be given through:
Equation (2a) Available In Full Paper.
where the subscript L denotes the liquid phase. When doing a compaction test, uniaxial stress or hydrostatic pressure is applied to the sample while images of the sample are taken before and after each change of pressure. Since density and porosity are mapped in each pressure step, density and porosity change (compression) curves can be generated for a given sand as a function of the imposed pressure. Density changes can be related to volume changes through the following equation:
Equation (3) Available In Full Paper.