A STUDY OF POROSITY AND PERMEABILITY USING A LATTICE BOLTZMANN SIMULATION

We explicitly calculate the absolute (single-phase) permeability of si mulated granular rocks as the pore space is evolved by various diagene tic schemes. Our goal is to match our computed curves to laboratory me asurements of porosity-permeability relationships in real rocks. To ac hieve this goal we model rock as a dense random pack of identical sphe rical grains with diagenetic cement deposited in the pore space. The p ositions of the sphere centers in our numerical model are taken from e xperimental measurements (the Finney pack). The diagenesis is simulate d in various ways: uniform cement deposition on the surface of each gr ain (uniform growth of the grains); cement deposition at grain contact s; cement deposition away from grain contacts; random filling of the p ore spaces; and various combinations of these. Permeability is compute d by explicitly modeling Stokes flow in the simulated pore space using a lattice Boltzmann method. Our simulations produce distinctively dif ferent porosity-permeability relationships which are characteristic of the cement deposition pattern. The distinctive porosity-permeability relationships found in laboratory measurements of real rocks are match ed by certain simulation schemes.