Knudsen-Like Scaling May Be Inappropriate for Gas Shales
Authors: Carpenter Chris 
Published: October 2018

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 187068, “Knudsen-Like Scaling May Be Inappropriate for Gas Shales,” by Tadeus W. Patzek, SPE, King Abdullah University of Science and Technology, prepared for the 2017 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, 9–11 October. The paper has not been peer reviewed.
The author writes that the generally accepted Knudsen diffusion in shales is based on a mistranslation of the flow physics and may give theoretically unsound predictions of the increased permeability of shales to gas flow. This increase of permeability comes from the micropores, fine-scale microfractures, and cracks. The nanopores in shales provide gas storage by sorption and capillary condensation of heavier gas components. In the smallest nanopores, even methane molecules are increasingly ordered and resemble liquid more than gas. These nanopores feed the macroscopic flow paths in ways that are not captured well by generally accepted equations.
Introduction
For gas pressures below 1 bar, gas permeability can exceed that of liquid substantially. Size distribution of a single pore is a distribution of radii of the largest spheres that can be fitted at each point along this pore. “Pore size” or “pore-body radius” is the radius of maximum sphere that can be inscribed into a pore, while “pore throat” refers to the radius of a minimum inscribed sphere common to two adjacent pores. In slit-like pores, pore throats and bodies are the same and pore widths are often reported to account for gas sorption. Pore sizes—whatever this term means to different authors—in the crushed samples of mudrocks are often inferred from small-angle and ultrasmall-angle neutron scattering, multistage desorption measurements, and molecular or statistical physics calculations; these sizes are not directly measured. A specific definition of pore size is provided in the complete paper.
The nanopores and micropores in sedimentary, compacted silicious and calcarious mudrocks (shales) are connected but have very low permeability. This low permeability results from the small cross sections of pore throats and the scale-dependent connectivity that ranges from strong at nanoscale to increasingly sparse at micro and higher scales. Methane in shales is produced through the highways of loosely connected micropores and multiscale cracks, both manmade and natural, into which a background continuum of the tiny nanopores feeds gas. This background continuum with the ordered, densely packed methane molecules can masquerade at times as multilayer methane adsorption.
Nanopore densities within grains of organic matter can be high. Grains containing hundreds of nanopores are common. The fractured gas-bearing mudrock formations (shales) are essentially multiscale and multiphysics systems, and their behavior is complex. Yet researchers frequently attempt to replace shale complexity with a set of slim cylindrical capillaries that flow methane with slip at the capillary walls. The majority of the complete paper describes a 180-year-long path of classical physics that has led to the models of Knudsen diffusion of gases in capillaries and the Knudsen flow regimes in the high-Reynolds-number flows of rarified gases, later transplanted to petroleum literature.