Permeability is a measure of the ability of a rock to transmit a single
fluid phase through its pore structure.
Unlike the bulk density and
sonic travel time, it is difficult to measure permeability directly in
a well. It is traditionally measured in the laboratory on regularly
shaped rock samples by forcing a fluid through the rock and recording
the resulting fluid flux and pressure drops.
Ingrain complements and
vastly expands laboratory permeability data sets by numerically
simulating fluid flow through a direct digital representation of a real
pore space obtained by high-resolution 3D imaging. Such imaging and
simulations can be rapidly and massively conducted on physical samples
of irregular shapes and sizes that are impossible to handle in the
The slow viscous flow needed for such permeability
estimates is simulated using the lattice Boltzmann method (LBM). LBM
mathematically mimics the Navier-Stokes equations of viscous flow by
treating the fluid as a set of particles with certain interaction
rules. Its great advantage over directly solving the equations of flow
is that it directly handles the boundary conditions on a complex
realistic pore surface. The outcomes are consistent datasets of
permeability versus porosity correlations and pore geometries for
various rock types, including tight gas sandstone, carbonates, and
friable tar sands.
Computational set-up for permeability determination
The absolute permeability is computed in a manner analogous to a
laboratory measurement: a pressure head or body force is directly
applied to a digital sample. The resulting fluid flux is then computed
and permeability is calculated according to the Darcy's equation.