Earth Science and Engineering, Imperial College London
Doi
Abstract
I present a new finite element (FE) simulation method to simulate pore-scale
flow. Within the pore-space, I solve a simplified form of the incompressible
Navier-Stoke’s equation, yielding the velocity field in a two-step solution
approach. First, Poisson’s equation is solved with homogeneous boundary
conditions, and then the pore pressure is computed and the velocity field
obtained for no slip conditions at the grain boundaries. From the computed
velocity field I estimate the effective permeability of porous media samples
characterized by thin section micrographs, micro-CT scans and synthetically
generated grain packings. This two-step process is much simpler than solving
the full Navier Stokes equation and therefore provides the opportunity to
study pore geometries with hundreds of thousands of pores in a computationally
more cost effective manner than solving the full Navier-Stoke’s equation.
My numerical model is verified with an analytical solution and validated on
samples whose permeabilities and porosities had been measured in laboratory
experiments (Akanji and Matthai, 2010). Comparisons were also made with
Stokes solver, published experimental, approximate and exact permeability
data. Starting with a numerically constructed synthetic grain packings, I also
investigated the extent to which the details of pore micro-structure affect the
hydraulic permeability (Garcia et al., 2009). I then estimate the hydraulic
anisotropy of unconsolidated granular packings.
With the future aim to simulate multiphase flow within the pore-space, I also compute the radii and derive capillary pressure from the Young-Laplace
equation (Akanji and Matthai,2010