Characterization of Nanoscale Gas Transport in Shale Formations

Non-Darcy flow behavior can be commonly observed in nano-sized pores of matrix. Most existing gas flow models characterize non-Darcy flow by empirical or semi-empirical methods without considering the real gas effect. In this paper, a novel layered model with physical meanings is proposed for both ideal and real gas transports in nanopores. It can be further coupled with hydraulic fracturing models and consequently benefit the storage evaluation and production prediction for shale gas recovery. It is hypothesized that a nanotube can be divided into a central circular zone where the viscous flow behavior mainly exists due to dominant intermolecular collisions and an outer annular zone where the Knudsen diffusion mainly exists because of dominant collisions between molecules and the wall. The flux is derived based on integration of two zones by applying the virtual boundary. Subsequently, the model is modified by incorporating slip effect, real gas effect, porosity distribution, and tortuosity. Meanwhile, a multi-objective optimization method (MOP) is applied to assist the validation of analytical model to search fitting parameters which are highly localized and contain significant uncertainties. The apparent permeability is finally derived and analyzed with various impact factors. The developed nanoscale gas transport model is well validated by the flux data collected from both laboratory experiments and molecular simulations over the entire spectrum of flow regimes. It has a decrease of as much as 43.8% in total molar flux when the real gas effect is considered in the model. Such an effect is found to be more significant as pore size shrinks. Knudsen diffusion accounts for more than 60% of the total gas flux when pressure is lower than 0.2 MPa and pore size is smaller than 50 nm. Overall, the apparent permeability is found to decrease with pressure, though it rarely changes when pressure is higher than 5.0 MPa and pore size is larger than 50 nm.