A Theory for Relative Permeability of Unconventional Rocks With Dual-Wettability Pore Network

Recent studies show that the pore network of unconventional rocks, such as gas shales, generally consists of inorganic and organic parts. The organic part is strongly oil-wet and preferentially imbibes the oleic phase. In contrast, the inorganic part is usually hydrophilic and preferentially imbibes the aqueous phase. Conventional theories of relative permeability, which are based on uniform wettability, cannot be applied to determine phase permeability in unconventional rocks with dual-wettability behavior. The objective of this paper is to extend the previous theories to model relative permeability of dual-wettability systems in which oleic and aqueous phases can both act as wetting phases in hydrophobic and hydrophilic pore networks, respectively. In the first part of the paper, we review and discuss the results of scanning electron microscopy (SEM), organic petrography, mercury injection capillary pressure (MICP), and comparative water/oil imbibition experiments conducted on several samples from the Triassic Montney tight gas siltstone play of the Western Canadian Sedimentary Basin. We also discuss various crossplots to understand the reasons behind the observed dual-wettability behavior, and to investigate the spatial distribution and morphology of hydrophilic and hydrophobic pores. In the second part, Purcell's model (Purcell 1949) is extended to develop a conceptual model for relative permeability of gas and water in a dual-wettability system such as the Montney tight gas formation. Finally, the proposed model is compared with measured relative permeability data. The results suggest that the submicron pores within solid bitumen/pyrobitumen are strongly water-repellant; therefore, they prefer gas over water under different saturation conditions. This part of the pore network is usually represented by a long tail at the lower end of the pore-throat-size distribution determined from MICP. The proposed relative permeability model describes single-phase flow of gas through the tail part, and two-phase flow of gas and water through the remaining bell-shaped part of the pore-throat-size distribution, which dominantly represents inorganic micropores. On the basis of our model, by increasing the fraction of water-repellant submicron pores, gas relative permeability decreases for a fixed water saturation. This decrease is ascribed to the reduction of the average size of flow conduits for the gas phase.