Slip in natural gas flow through nanoporous shale reservoirs

Abstract

It is observed that to assess the shale gas flow in nanopores the recent literature relies on the flow regimes discovered by Tsien (1946). Tsien classified fluid flow systems based on the range of Knudsen number (Kn), the ratio of the mean free path to average pore diameter. The flow regimes are: continuum flow for Kn<0.01, slip flow for 0.001<Kn<0.1, transition regime for 0.1<Kn<10, and free molecule flow for Kn>10. This scale was originally developed from the physics of rarefied gas flow. Is it then appropriate to use the classical Kn scale to develop models of shale gas flow in tight reservoirs where the nanopores are in the range of 1–1000nm, and pore pressures can be as high as 10,000psi? The present work explores answers to this question. We provide an analysis based on classical slip flow model. We validate the Kn scale incorporating PVT (Pressure–Volume–Temperatures) schemes. Our results show that in very tight shale (order of 1nm pore size) there can be substantial slip flow based on the characteristics of pore walls in the reservoirs of high temperatures and low pressures. In the case of large pore size (∼1000nm) there is zero slip flow irrespective of temperature and pressure. The Kn scale which was designed for rarefied gases cannot be true for the natural gas flow regimes at all temperatures and pressures. Therefore we must be careful in referring this scale to model the shale gas flows. Results presented here from simple calculations agree with those obtained from expensive molecular dynamics (MD) simulations and laboratory experiments.