A stochastic permeability model for the shale-gas systems

The pore network in shale reservoirs consists of pores associated with both organic matter and inorganic matrix. The range of pore sizes within the organic matter is usually an order of magnitude smaller than pore sizes within the inorganic matrix, causing a bimodal pore-size distribution for the total system revealed in nitrogen adsorption tests. 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 organic and inorganic media. This treatment of different pore sizes in organic and inorganic enables us to assign sorption process only in organic matter. The model can be used to calculate the apparent gas permeability (AP) in shale from a combination of nitrogen-adsorption and SEM-image data. We validate the model with data from the literature, and use it to determine permeability and tortuosity from pulse-decay experimental data. The model results show that AP 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. (C) 2015 Elsevier B.V. All rights reserved.