P-wave velocity-porosity relations and homogeneity lengths in a realistic deposition model of sedimentary rock

A realistic model of a porous rock is generated by simulating critical processes in sedimentary rock formation. The simulated processes include deposition of grains in different energy environments, compression with grain rearrangement effects due to the stratigraphic column pressure and cementation. It has been shown that such processes are fundamental in determining the appropriate correlations for the system to exhibit realistic electrical and hydraulic conductivities of sandstones. Here we analyse the theoretical model from the geometrical and acoustic standpoint, determining the relations of the homogenization volumes and sound speed to the resulting porosity of the model. For the quartz cemented contact model we find the correct velocity magnitudes and concavities in the velocity-porosity curves. We also show that using anisotropic rescaling as a compaction stage can lead to inadequate acoustic properties for the rock model, due to the importance of grain rearrangement.