Prediction of Relative Air Permeability of Porous Media With Weibull Pore Size Distribution

Abstract

Modeling convective air movement in unsaturated porous media requires appropriate characterization of the relative air permeability (RAP). Adopting Assouline et al. (1998, https://doi.org/10.1029/97WR03039) water retention function that is based on the Weibull pore size distribution, this study was conducted to derive seven new predictive RAP models. These 7 new models, together with another 3 models developed by Assouline et al. (2016, https://doi.org/10.1002/2015WR018286), were then compared with data from 30 disturbed soil samples to investigate their predictive RAP performances. The model and data comparison results showed that the modified Burdine, modified Mualem, and modified Alexander and Skaggs relative permeability models proposed by Yang and Mohanty (2015, https://doi.org/10.1002/2014WR016190) had the highest accuracy for the RAP prediction among the 10 investigated models, which indicated that the tortuosity and connectivity exponent of water phase should be smaller than that of air phase for the disturbed soil samples. The modified Burdine, modified Mualem, and modified Alexander and Skaggs models were then the suggested RAP parameterizations for the subsurface multiphase flow numerical simulation.

Forced gas injection and water infiltration into sand — A two‐phase flow barrel and column experiment

“…This function is similar to Equation () (Ben‐Noah & Friedman, 2015), with a shift in the capillary pressure from h cr to h b , accounting for an air breakthrough threshold, which may be significant for air flow in wet soils. Several works (Clayton, 1999; Dury, Fischer, & Schalin, 1999; Rouf et al., 2012; Yang, Mohanty, Efendiev, & Sheng, 2019), including the current study (Figure 5), have shown a more linear relationship between the air conductivity and air content than that reported between hydraulic conductivity (i.e., for water) and water content. This can be explained by the fact that except for the extremum conditions of oven‐dry and water‐saturated soil, the relative conductivity for air K a,r (θ a ) was higher than K w,r (θ w ) and is closer to linear because, at a given saturation degree, the air occupies the larger pores, causing a more pronounced effect on the conductance of the water paths than the effect of the water, which occupies the smaller pores, to reduce the conductance of the air paths.…”

Comparison of Seven Weibull Distribution Models for Predicting Relative Hydraulic Conductivity

“…]\quad 0\le h\le {h}_{L}\,$ in which $${S}_{e}$$ is the effective water saturation; $$h$$ is the capillary pressure head, which for notational convenience is considered as being positive (i.e., absolute value); $$\theta $$ is the volumetric water content; $${\theta }_{s}$$ and $${\theta }_{r}$$, respectively, represent the saturated and residual volumetric water contents; $$\xi $$ and $$\mu $$ are two fitted parameters, and $${h}_{L}$$ is the capillary pressure head (absolute value) corresponding to a very low volumetric water content $${\theta }_{L}$$ such as wilting point (Assouline, 2001; Assouline et al., 1998; Assouline & Tartakovsky, 2001). In practice, $${h}_{L}$$ is generally considered to be equal to 153 m (i.e., 15 bars) and $${\theta }_{L}$$ can be set to equal to $${\theta }_{r}$$ (Assouline et al., 2016; Yang et al., 2019).…”

“… b The derivation of the AB model is given in Appendix , which is similar to that of Yang et al. (2019). …”

Effects of Water Retention Curves and Permeability Equations on the Prediction of Relative Air Permeability

“…(1998) was used by Yang et al. (2019) to develop seven RAP models such as Assouline et al. (1998)–Burdine (AB) model.…”

“…Recently, the WRC of Assouline et al (1998) was used by Yang et al (2019) to develop seven RAP models such as Assouline et al (1998)-Burdine (AB) model. The studies of Yang and Mohanty (2015) and Yang et al (2019) indicated that when using the Kosugi (1996) and Assouline et al (1998) WRCs, the Burdine (1953) and Mualem (1976) permeability equations should be modified (via optimum tortuosity-connectivity parameter) to improve their fit to the measured RAP data. However, the performances of the modified Burdine (Yang & Mohanty, 2015) and modified Mualem (Yang & Mohanty, 2015) permeability equations are not known yet for the RAP prediction when combining with the WRCs of Brooks and Corey (1964) and van Genuchten (1980).…”