Computational rock physics at the pore scale: Transport properties and diagenesis in realistic pore geometries

Abstract

Transport properties, such as permeability, are important in many geophysical and petroleum applications. However, complex pore geometry often makes modeling and simulation of transport properties in porous media very difficult. Conventional methods are usually based on partial differential equations, but the implementation of these techniques becomes very complicated when the geometry is extremely complex. As a result, simplified geometry is often used; thus the implementation depends heavily on the model. Solving the same problem in a different geometry often means that many parts of the implementation have to be changed. Therefore, a more robust and simple tool, which can handle complex pore space without oversimplification or modification of the model, is needed. The Lattice-Boltzmann method (LBM), based on statistical description of microscopic phenomena, is one alternative. LBM describes fluid motion as collisions of imaginary particles, which are much bigger than the real fluid molecules. These particles have nearly nothing in common with real fluids, but they show almost the same behavior at a macroscopic scale. This simple collision rule is exactly equivalent to the Navier-Stokes equation within certain appropriate limits. Figure 1 shows a synthetic pore geometry (a random dense pack of identical spheres) and the corresponding digital 3-D structure. Uniform spheres in a random dense pack are a reasonable first approximation to real sandstones. Another advantage for this model is that changing porosity is relatively easy, and laboratory measurements can be mimicked using sintered glass beads. Figure 2 shows electric flux (current) calculated by the finite-element method (FEM) and hydraulic flux calculated by LBM. Both are normalized by each maximum value. The hydraulic flux shows much more sensitivity to the grain boundary than the electric current; the hydraulic flux decreases rapidly near the boundary. Also, the high flux regions are different in Figure 2, even though pore geometry …