Numerical model for flow in rocks composed of materials of different permeability

Abstract

In the oil and gas industry permeability measurements on rock samples give an indication of the capacity to produce the output (oil/gas etc). Permeability of small samples can be derived from x-ray Computed Tomography (CT) scans which yields a three-dimensional (binary) digital image of the sample. Then using suitable numerical tools, one can use this digital data to compute a velocity field and hence the permeability of the sample. Up to now, this has been done on the assumption that fluid can only flow in pores (with no flow in solid regions). However, if the sample is made up of different materials, each material can have a different permeability to fluid flow. Hence, here we consider numerical modelling of flow through such a material. We use the Lattice Boltzmann method to model this flow, but need to change the usual streaming and collision steps to account for the partial permeability of voxels. We first implement this new algorithm on some well-known test cases, with excellent agreement with analytic results and then use our algorithm on some real CT digital data. Our results clearly show the effect of increasing the local fraction of a high permeability material within a sample on the global permeability.