Comparison of Four Competing Invasion Percolation Models for Gas Flow in
Porous Media
Abstract
Numerous variations of Invasion-Percolation (IP) models can simulate
multiphase flow in porous media across various scales (pore-scale IP to
macroscopic IP); here, we are interested in gas flow in water-saturated
porous media. This flow occurs either as continuous or discontinuous
flow, depending on the flow rate and the porous medium’s nature.
Literature suggests that IP models are well suited for the discontinuous
gas flow regime; other flow regimes have not been explored. Our research
compares four existing macroscopic IP models and ranks their performance
in these “other” flow regimes. We test the models on a range of
gas-injection in water-saturated sand experiments from transitional and
continuous gas flow regimes. Using the light transmission technique, the
experimental data is obtained as a time series of images in a
2-dimensional setup. To represent pore-scale heterogeneities, we ran
each model version on several random realizations of the initial entry
pressure field. We use a diffused version of the so-called Jaccard
coefficient to rank the models against the experimental data. We average
the Jaccard coefficient over all realizations per model version to
evaluate each model and calibrate specific model parameters. Depending
on the application domain, we observe that some macroscopic IP model
versions are suitable in these previously unexplored flow regimes. Also,
we identify that the initial entry pressure fields strongly affect the
performance of these models. Our comparison method is not limited to
gas-water systems in porous media but generalizes to any modelling
situation accompanied by spatially and temporally highly resolved data.