Numerical modeling of the carbonate and the sandstone formations

It is of interest in various scientific and industrial contexts to make a reliable estimation of the transport properties of porous media via more accessible probes such as NMR that yield information on static pore geometry and porosity. When the pore geometry is simple, there are empirical recipes that have long proven reliable in bridging the gap. For heterogeneous systems, such recipes fail to give a consistent prediction and invite case-by-case modifications. This is just one of many indications that the complex pore geometry erodes the predictive power of empirical laws that work well in simpler situations. Heterogeneity combined with sizeable diffusive coupling in extended pore space further undermines the validity of the MR interpretation based on simple pore geometry. On top of this, possible spatial variation of surface relaxivity may further complicate the interpretation. Resolution of these issues for real life samples requires elaborate simulations in tandem with experimental verifications on the shared pore geometry. We report on a recent progress which allows combined parallel Lattice Boltzmann and random walk simulations to study transport and diffusion properties in various types of pore geometry, from simple 2D micro-fluidic mazes, 3D glass-bead packs and sandstones to more complex carbonates.