Comparison of Two-Dimensional and Three-Dimensional Macroscopic Invasion Percolation Simulations with Laboratory Experiments of Gas Bubble Flow in Homogeneous Sands

摘要

The upward flow of gas plays a role in many subsurface systems, including those related to oil and gas recovery, carbon dioxide storage, and ground-water remediation. Macroscopic invasion percolation (macro-IP) is a modeling approach suitable for the simulation of upward gas flow, including bubble flow, in porous media, but few studies have compared simulations with experiments. Monte Carlo suites of macro-IP simulations in two- and three-dimensional domains were compared with small-scale (similar to 10 cm) thin-tank experiments of gas injection in homogeneous, initially water-saturated sand, where transient gas saturations were quantified at the local scale. Comparisons were based on gas saturations and the spatial moments of the gas distribution and were performed for resolutions between 1 by 1 mm and 5 by 5 mm. Simulations were conducted both with and without a stochastic selection modification of the macro-IP approach. Two-dimensional simulations without stochastic selection were able to reproduce the spatial moments of the experimental gas distributions using reasonable estimates of local gas saturations at resolutions coarser than or equal to 2 by 2 mm. Three-dimensional simulations were also able to reproduce the spatial moments at a resolution of 4 by 4 mm, but required higher-than-expected gas saturations to accurately represent the injected gas volume. Finer discretizations in two- and three-dimensional simulations were unable to reproduce injected gas volumes without considering stochastic selection or without the use of unreasonably high local gas saturations. This suggests a lower limit on the grid block size for macro-IP without stochastic selection of approximately three to four grain diameters. By including stochastic selection of the next invaded site in the macro-IP simulations, observed gas saturations could be reproduced using finer discretization.