Finite element modelling of the effective elastic properties of partially saturated rocks

Abstract

Simulation of effective physical properties from microtomographic 3D images of porous structures allows one to relate properties of rocks directly to their microstructure. A static FEM code has been previously used to estimate effective elastic properties of fully saturated monomineralic (quartz) rock under wet and dry conditions. We use the code to calculate elastic properties under partially saturated conditions. The numerical predictions are compared to the Gassmann theory combined with Wood's formula (GW) for a mixture of pore fluids, which is exact for a monomineralic macroscopically homogeneous porous medium. Results of the numerical simulations performed for two Boolean sphere pack distributions show significant deviation from the GW limit and depend on the spatial distribution of fluids. This is shown to be a numerical artefact caused by incomplete equilibration of fluid pressure, which is primarily due to insufficient spatial resolution. To investigate the effect of pore-size and pore geometry, we perform FEM simulations for a model with regular pore geometry, where all pore channels have the same size and shape. Accuracy of these simulations increases with the total cross-section area of the channels and the size of individual channels. For the case where the total cross-section of the channels is large enough (on the same order as total porosity), there is a minimum of 4 voxels per channel diameter required for adequate fluid pressure equilibration throughout the pore space. Increasing the spatial resolution of the digital models reduces the discrepancy between the simulations and theory, but unfortunately increases the memory and CPU requirements of the simulations.