An analytical model for real gas flow in shale nanopores with non‐circular cross‐section

Abstract

An analytical model for gas transport in shale media is proposed on the basis of the linear superposition of convective flow and Knudsen diffusion, which is free of tangential momentum accommodation coefficient. The present model takes into the effect of pore shape and real gas, and is successfully validated against experimental data and Lattice-Boltzmann simulation results. Gas flow in noncircular nanopores can be accounted by a dimensionless geometry correction factor. In continuum-flow regime, pore shape has a relatively minor impact on gas transport capacity; the effect of pore shape on gas transport capacity enhances significantly with increasing rarefaction. Additionally, gas transport capacity is strongly dependent of average pore size and streamline tortuosity. We also show that the present model without using weighted factor can describe the variable contribution of convective flow and Knudsen diffusion to the total flow. As pressure and pore radius decrease, the number of molecule-wall collisions gradually predominates over the number of intermolecule collisions, and thus Knudsen diffusion contributes more to the total flow. The parameters in the present model can be determined from independent laboratory experiments. We have the confidence that the present model can provide some theoretical support in numerical simulation of shale gas production.Where a is the geometry correction factor, dimensionless, with a 5 1 for a circular; r e is equivalent pore radius, m.

A Comprehensive Model for Real Gas Transport in Shale Formations with Complex Non-planar Fracture Networks

“…A higher Knudsen number indicates the distances between gas molecules are comparable to the pore dimension, resulting in rarefied gas3437, thus more gas production could be obtained. Besides, the slippage effect could accelerate the gas molecules transport speed because there is less drag or no stationary layer to slow them34.…”

A Theoretical Analysis of Pore Size Distribution Effects on Shale Apparent Permeability

“…Figure 2 also shows that the apparent permeability is high initially, drops steeply with increasing pore pressure, and approaches a constant value at high pore pressure (>5 MPa). This is because, at low pore pressure, the dominant transport mechanism is Knudsen diffusion, which enhances gas transport in shale [40]. With increasing pore pressure, the effect of Knudsen diffusion vanishes, which results in the decrease of the apparent permeability.…”

“…The Knudsen number for producing shale gas reservoirs is less than unity, which corresponds to the Darcy flow, slip flow, and early transitionflow regimes [39]. In this work, we consider slip flow as a part of Knudsen diffusion [40]. Moreover, we do not consider the surface diffusion in this work.…”

“…The flow regimes for producing shale gas reservoirs include continuum flow, slip flow, and transition flow [40]. The present model incorporates viscous flow and Knudsen diffusion to cover these flow regimes.…”

Review on gas flow and recovery in unconventional porous rocks

“…They found that both the type of crosssection and the shape of nanopores affected gas transport capacity. Ren et al (2016) proposed an analytical model for real gas transport in nanopores of shale reservoirs based on the linear superposition of convective flow and Knudsen diffusion. The model was established to be free of tangential momentum accommodation coefficient and taken into the effect of pore shape and real gas.…”