Gas relative permeability and its modeling in tight and ultra-tight porous rocks

Abstract Gas relative permeability, krg, is a key parameter to determine gas production in unconventional reservoirs. Several theoretical approaches were proposed to study gas relative permeability in tight and ultra-tight porous rocks. Some models are based on a “bundle of capillary tubes” concept. Some others were developed based upon a combination of universal scaling laws from percolation theory and the effective-medium approximation (EMA). Although applications from the EMA have been successfully used to estimate single-phase permeability in permeable media (Ghanbarian et al., 2017; Ghanbarian and Javadpour, 2017), non-universal scaling from the EMA has never been invoked to model gas relative permeability in tight and/or ultra-tight porous rocks. In this study, it was assumed that pore-throat sizes follow the log-normal distribution. It was further assumed that gas transport in shales is mainly controlled by molecular and hydraulic flow, two mechanisms contributing in parallel. Using the EMA, effective pore-throat radii, effective conductances, and gas relative permeabilities were determined at various gas saturations. Comparison with three-dimensional pore-network simulations showed that the proposed krg model estimated gas relative permeability accurately. We also compared our model with experimental data reported in Yassin et al. (2016) including three Montney tight gas siltstone samples from the Western Canadian Sedimentary Basin. Results showed that our model estimated krg reasonably well, although it slightly overestimated krg. This might be because the fitted log-normal probability density function underestimated the probability of small pore-throat sizes. References Ghanbarian, B., & Javadpour, F. (2017). Upscaling pore pressure‐dependent gas permeability in shales. Journal of Geophysical Research: Solid Earth, 122(4), 2541-2552. Ghanbarian, B., Torres-Verdin, C., Lake, L. W., & Marder, M. P. (2017). Upscaling gas permeability in tight-gas sandstones. AGU Fall Meeting Abstracts. New Orleans LA. Yassin, M. R., Dehghanpour, H., Wood, J., & Lan, Q. (2016). A theory for relative permeability of unconventional rocks with dual-wettability pore network. SPE Journal, 21(06), 1970-1980.