EDUCATIONAL CODE TO COMPUTE PERMEABILITY OF POROUS MATERIALS USING HOMOGENIZATION, MICRO-CT AND FEM

Resumo

In this work, we present a description of the method and an educational program to
determine permeability of a porous media considering the microstructure of pores provided by micro
computed tomography (micro-CT) images using numerical homogenization based on finite element
(FE) implementation. Permeability is a very important parameter for transport analysis that is
commonly determined in laboratorial tests using the Darcy’s law. However, laboratorial tests can be
expensive, time-consuming and do not offer a deep understanding of the internal structure of the
material. An alternative and efficient strategy to determine permeability of porous materials
considering their microstructures is by means of numerical homogenization technique. In this strategy,
determining permeability requires dealing with a multiscale problem, where the determination of the
macro parameter relies on the simulation of a fluid flowing through canals created by connected pores
presented in the material’s internal microstructure. This paper aims to explain how to model a Stokes
flow through the porous media using FE code implemented in MatLab/Octave to compute materials’
permeability. The boundary value problem is modeled with periodic boundary conditions and a unit
gradient pressure applied in the desired direction to obtain the macro parameter. The velocity field
caused by the prescribed pressure gradient is determined solving the Stokes equation. Lastly, the micro
and macro scales are linked together with the average volume flow rate and the unit pressure gradient
using Darcy’s law. The accuracy of the method depends on reliable computational models, therefore
micro-CT has an important role in numerical homogenization generating representative virtual models
for numerical simulations.