Calibrating Lattice Boltzmann Flow Simulations and Estimating Uncertainty in the Permeability of Complex Porous Media: Lattice Boltzmann Flow Simulations and Estimating Uncertainty

A common way to simulate fluid flow in porous media is to use Lattice Boltzmann (LB) methods. Permeability predictions from such flow simulations are
controlled by parameters whose settings must be calibrated in order to produce
realistic modelling results. Herein we focus on the simplest and most commonly
used implementation of the LB method: the single-relaxation-time BGK model.
A key parameter in the BGK model is the relaxation time which controls flow
velocity and has a substantial influence on the permeability calculation. Currently
there is no rigorous scheme to calibrate its value for models of real media.
We show that the standard method of calibration, by matching the flow profile
of the analytic Hagen-Poiseuille pipe-flow model, results in a BGK-LB model
that is unable to accurately predict permeability even in simple realistic porous
media (herein, Fontainebleau sandstone). In order to reconcile the differences
between predicted permeability and experimental data, we propose a method to
calibrate using an enhanced Transitional Markov Chain Monte Carlo method,
which is suitable for parallel computer architectures. We also propose a porosity dependent calibration that provides an excellent fit to experimental data and
which creates an empirical model that can be used to choose for new samples
of known porosity. Our Bayesian framework thus provides robust predictions of permeability of realistic porous media, herein demonstrated on the BGK-LB
model, and should therefore replace the standard pipe-flow based methods of
calibration for more complex media. The calibration methodology can also be
extended to more advanced LB methods.