A study of porosity and permeability using a lattice Boltzmann simulation

We explicitly calculate the absolute (single‐phase) permeability of simulated granular rocks as the pore space is evolved by various diagenetic schemes. Our goal is to match our computed curves to laboratory measurements of porosity‐permeability relationships in real rocks. To achieve this goal we model rock as a dense random pack of identical spherical grains with diagenetic cement deposited in the pore space. The positions of the sphere centers in our numerical model are taken from experimental measurements (the Finney pack). The diagenesis is simulated in various ways: uniform cement deposition on the surface of each grain (uniform growth of the grains); cement deposition at grain contacts; cement deposition away from grain contacts; random filling of the pore spaces; and various combinations of these. Permeability is computed by explicitly modeling Stokes flow in the simulated pore space using a lattice Boltzmann method. Our simulations produce distinctively different porosity‐permeability relationships which are characteristic of the cement deposition pattern. The distinctive porosity‐permeability relationships found in laboratory measurements of real rocks are matched by certain simulation schemes.