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

Abstract

The upward flow of gas plays a role in many subsurface systems, including those related to oil and gas recovery, carbon dioxide storage, and groundwater 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 (∼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.

Relative Permeability Measurements during the Exsolution and Dissolution of Hydrogen Gas Produced by the Hydrolysis of Sodium Borohydride

“…The best-fit values of I r /I s for the 12/20, 20/30, and mixed sands were 0.69, 0.56, and 0.67, respectively. These values are consistent with the values of 0.71 ± 0.08 and 0.63 ± 0.07 for the 12/20 and 20/30 sands, respectively, reported previously using this technique (Mumford et al, 2015) to fit a ratio of transmitted light intensities for a dry and water-saturated pack. The error bars in Fig.…”

“…Throughout the exsolution and relative permeability experiments, both following exsolution and following external drainage and imbibition, digital images were collected to quantify local gas saturations using a light transmission technique (Mumford et al, 2015; Niemet and Selker, 2001; Tidwell and Glass, 1994). The light transmission setup consisted of a light‐emitting diode (LED) panel (Led Go, CN‐1200H) behind the cell and a digital camera (Canon, EOS Rebel T3i) in front of the cell.…”

“…The light, camera, and cell were covered to reduce changes in ambient light intensity throughout the experiments, and camera settings and lighting conditions were held constant during each test. This method has been used in several previous studies to quantify gas saturations in thin flow cells (Hegele and Mumford, 2014; Mumford et al, 2015; Niemet and Selker, 2001; Norton, 1995; Tidwell and Glass, 1994; Ye et al, 2009), and gas saturations in similar acrylic cells have been verified against a total water mass balance during stable air–water drainage. The light intensity in the captured images is related to the water saturations using (Niemet and Selker, 2001) where S w is the water saturation, I is the local light intensity transmitted through a sand pack, I s is the light intensity transmitted through a completely water‐saturated sand pack, I r is the light intensity transmitted through a sand pack at residual water saturation, and S r is the residual water saturation.…”

“…Rather than measuring I r values using images of sand packs drained to residual water saturation, the I r / I s term in Eq. [2] was used as a fitting parameter (Mumford et al, 2015), obtained by matching the displaced water volume during the exsolution experiments to image‐based gas volumes. This is equivalent to calibrating light intensity values by fitting the average number of pores across the samples, as proposed by Tidwell and Glass (1994).…”

Electro‐Thermal Subsurface Gas Generation and Transport: Model Validation and Implications

“…The spatial domain (illustrated in Figure ) was divided into 4‐×4‐×10‐mm grid blocks. While IP‐style models are fractal in nature, a previous MIP study has indicated that a resolution of 4 mm is sufficient to produce reasonable estimates of both local gas saturations and spatial moments with a MIP model (Mumford et al, ). Grid independence of the continuum portion of the model (i.e., the ‘ET’ model) was confirmed by comparing temperature distributions of model simulations with gas production disabled across a range of resolutions.…”