We use a stochastic classification method based on a mixture of Gaussian assumption to separate two distributions of pores in organic matter and inorganic matrix. We construct an ensemble-based stochastic model conditioned to total organic content (TOC) and the characteristics of pore-size distributions in both organic and inorganic media. This treatment of different pore sizes in organic and inorganic enables us to assign sorption process only in organic matter. We incorporate a novel permeability model for shale rock that overcomes the limitation of Maxwell slip condition and includes higher order slip effects on gas flow. We validated our model using a set of in-house detailed experimental data on Eagle Ford shale samples. The model results show that apparent permeability is more sensitive to the mean of pores within inorganic matrix than within organic matter. These results suggest that pore sizes corresponding to each compartment; organic and inorganic should be considered to estimate permeability. The model results also confirm permeability enhancement owing to the sorption process in organic matter below critical sorption pressure.
Gas flow in shale strata is complicated due to small size of the interconnected pores (a.k.a. nanopores) and heterogeneity of the medium at different scales. A good body of recent literature studied gas flow in shale nanopores (Javadpour 2009; Civan 2010; Darabi et al. 2012; Akutlu and Fathi 2012; Shabro et al. 2012; Sakhaee-pour and Bryant 2012; Mehmani et al. 2013; Singh et al 2014; Rezaveisi et al. 2014; Kelly et al. 2015; Chen et al. 2015; Naraghi and Javadpour 2015; Tahmasebi et al. 2015a, 2015b, 2016; Singh and Javadpour 2016; Alfi et al., 2015, 2016). These studies showed that Darcy equation is not valid for shale system and additional processes such as Knudsen diffusion and gas slippage should be included in the gas flow equations.
Newly developed gas flow equations for shale system, a term called tangential momentum accommodation constant (TMAC) appears to correct gas slippage on inner pore walls. TMAC is an empirical term which depends on gas type, pressure, temperature, and pore material and roughness. TMAC measurement is normally difficult especially for natural composites such as shale samples. Singh and Javadpour (2016) in a recent study showed a methodology to determine TMAC from readily available Langmuir sorption isotherms of shale samples. This novel approach alleviates the limitations of slip-corrected gas flow models for shale systems.