The local changes in the porosity of dry sand packs as a function of the imposed overburden were determined using computer Assisted Tomography. Pressure cycles were imposed on sands of different characteristics and the porosity was measured at a resolution of 0.075 cm × 0.075 porosity was measured at a resolution of 0.075 cm × 0.075 cm × 0.3 cm. Hysteresis in the porosity was observed. The imposed overburden and pore volume change were translated to stress and strain respectively. The local porosity changes depict the local strain under a given load. porosity changes depict the local strain under a given load. A two dimensional finite element model was developed to predict the microscopic behavior of sand. The model predict the microscopic behavior of sand. The model provided an excellent correlation between measured and provided an excellent correlation between measured and calculated strains. The mean and standard deviation differed by 0.509 % and 0.35 % strain respectively, from the measured data. However, the model had difficulty in predicting dilation and extreme compression (5 to 6 % predicting dilation and extreme compression (5 to 6 % volumetric strain). It was also found that, in terms of elastic moduli, the model indicated that a macroscopically homogeneous sand is highly heterogeneous on the macroscopic scale. Under these conditions, local stresses varied sharply and stress components on an element tended to be non-hydrostatic.
Computer Assisted Tomography (CAT) scanning has been use in the characterization of unconsolidated core material and it was found very useful in identifying core heterogeneities and areas of formation damage. Physical properties such as the bulk density and the porosity can properties such as the bulk density and the porosity can be calculated using simple models Pie However, the porosity measurements will be in error if the core is not 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 for the use of CAT scanners in the study of fracturing and the measurement of material properties appeared in the literature. The data collected properties appeared in the literature. 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 physical properties such as the bulk modulus could actually be measured.
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 was 0.075 cm × 0.075 cm × 0.3 cm.