Digital-Rock-Physics Modelling of Carbonates and Sandstones

Abstract

This thesis seeks to investigate the influence of porosity and pore geometry on the macroscopic parameters of a porous rock saturated with fluid. These macroscopic parameters, also known as Biot's parameters, include the drained and undrained bulk moduli which characterize the rock’s resistance to compression (or expansion), the pressure parameter needed to increase the fluid content by a unit value at constant total dilatation, and the so-called Biot-Willis coefficient. This study also seeks to examine the effects of porosity and pore geometry on the stored solid elastic energy in the rock. To achieve these goals, I develop numerical simulations of compression tests of digital rock models. These simulations allow me to calculate Biot’s parameters for samples with known pore geometries. The numerical model results are shown to be in good agreement with an analytical model for a spherical rock sample with a single spherical pore. I investigate the variation of the macroscopic parameters as a function of the porosity and of the solid and fluid material properties. In particular, I show that, apart from the Biot-Willis coefficient, the other macroscopic parameters, as well as the total and compression solid energy densities, decrease with an increase in porosity. Whereas Biot's parameters are generally influenced by both porosity and pore geometry, the pressure parameter is only influenced by porosity but remains the same regardless of changes in pore geometry. Also, the results reveal that the carbonate pore geometries have some similarity to the simple pore geometries but are generally softer, while sandstone pore geometries are even softer than carbonate ones.