Scaling Law For Slip Flow Of Gases In Nanoporous Media From Nanofluidics, Rocks, And Pore-Scale Simulations

Abstract

Summary In unconventional reservoirs, as the effective pore size becomes close to the mean free path of gas molecules, gas transport behavior begins to deviate from Darcy’s law. The objective of this study is to explore the similarities of gas flows in nanochannels and core samples as well as those simulated by direct simulation BGK (DSBGK). a particle-based method that solves the Bhatnagar-Gross-Krook (BGK) equation. Due to fabrication difficulties, previous work on gas flow experiments in nanochannels is very limited. In this work, steady-state gas flow was measured in reactive-ion etched nanochannels on a silicon wafer, which have a controlled channel size. A core-flooding apparatus was used to perform steady-state gas flow measurements on carbonate and shale samples. Klinkenberg permeability was obtained under varying pore pressures but constant temperature and effective stress. Same gas was used in nanofluidic and rock experiments, making them directly comparable. Results from both experiments were then compared to gas flow simulations by DSBGK method carried out on several independently constructed geometry models. DSBGK uses hundreds of millions of simulated molecules to approximate gas flow inside the pore space. The intermolecular collisions were handled by directly integrating the BGK equation along each molecule’s trajectory, rather than through a sampling scheme like that in the direct simulation Monte-Carlo (DSMC) method. Consequently, the stochastic noise is significantly reduced, and simulation of nano-scale gas flows in complex geometries becomes computationally affordable. The Klinkenberg factors obtained from these independent studies varied across three orders of magnitude, yet they all appear to collapse on a single scaling relation where the Klinkenberg factor in the slip flow regime is inversely proportional to the square root of intrinsic permeability over porosity. Our correlation could also fit the data in the literature, which were often obtained using nitrogen, after correcting for temperature and gas properties. This study contributes to rock characterization, well testing analysis as well as the understanding of rarefied gas transport in porous media.