Fractal-based real gas flow model in shales: An interplay of nano-pore and nano-fracture networks

Abstract

Characterizing fluid flow in shale is challenging due to the existence of small-sized pores, variable wettability conditions, and different pore fluid occupancies. Majority of the sub-irreducible water saturation is stored inside the hydrophilic inorganic material (iOM) nanopores in the form of bound water film or capillary water at initial reservoir condition. During production, gas is transported through nano-pores and nano-fractures where a water film covers iOM’s walls and crevices. That gives rise to the existence of multiphase fluid occupancies in pores and fractures. In this paper, we present an improved gas permeability model by taking into account the impacts of nanoscale (i.e., slippage effect, Knudsen diffusion) and sub-irreducible water saturations. To do so, the gas flow is modeled in hydrophilic iOM consisting of two types of pore networks (i.e., porous matrix and fracture network). We expand gas transport equations for nano-capillaries and nano-slits by taking into account pore size distribution (PSD) and fracture aperture distribution (FAD) using fractal theory. The proposed model is compared against the relevant experimental data and other analytical models available from the literature. The results show that by neglecting the nanoscale effect, the existence of water film could lead to an underestimation of flow capacity while ignoring the PSD/FAD would overestimate the calculated gas conductance. At higher pressures (>10 MPa), the gas apparent permeability rises as we increase the percentage of nano-capillary pores in the pore space. This trend reverses at lower pressures. For all pressures lower than 10 MPa, the apparent permeability decreases with increasing contribution of nano-capillary pores in the pore space. Real gas effect can significantly enhance gas flow capacity in nano-capillaries and nano-slits at higher pressures and lower temperatures. This effect is particularly significant in small pore sizes.