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Gas flow in ultra-tight shale strata

Published online by Cambridge University Press:  27 September 2012

Hamed Darabi ,
A. Ettehad ,
F. Javadpour  and
K. Sepehrnoori
Hamed Darabi
Affiliation:
Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, 1 University Station, Austin, TX 78712, USA
A. Ettehad
Affiliation:
Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, 1 University Station, Austin, TX 78712, USA
F. Javadpour*
Affiliation:
Bureau of Economic Geology, Jackson School of Geosciences, The University of Texas at Austin, University Station, Box X, Austin, TX 78713, USA
K. Sepehrnoori
Affiliation:
Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, 1 University Station, Austin, TX 78712, USA
*
†Email address for correspondence: farzam.javadpour@beg.utexas.edu
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Abstract

We study the gas flow processes in ultra-tight porous media in which the matrix pore network is composed of nanometre- to micrometre-size pores. We formulate a pressure-dependent permeability function, referred to as the apparent permeability function (APF), assuming that Knudsen diffusion and slip flow (the Klinkenberg effect) are the main contributors to the overall flow in porous media. The APF predicts that in nanometre-size pores, gas permeability values are as much as 10 times greater than results obtained by continuum hydrodynamics predictions, and with increasing pore size (i.e. of the order of the micrometre), gas permeability converges to continuum hydrodynamics values. In addition, the APF predicts that an increase in the fractal dimension of the pore surface leads to a decrease in Knudsen diffusion. Using the homogenization method, a rigorous analysis is performed to examine whether the APF is preserved throughout the process of upscaling from local scale to large scale. We use the well-known pulse-decay experiment to estimate the main parameter of the APF, which is Darcy permeability. Our newly derived late-transient analytical solution and the late-transient numerical solution consistently match the pressure decay data and yield approximately the same estimated value for Darcy permeability at the typical core-sample initial pressure range and pressure difference. Other parameters of the APF may be determined from independent laboratory experiments; however, a pulse-decay experiment can be used to estimate the unknown parameters of the APF if multiple tests are performed and/or the parameters are strictly constrained by upper and lower bounds.

JFM classification

Low-Reynolds-number flows: Porous media Rarefied Gas Flow: Rarefied Gas Flow

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 710 , 10 November 2012 , pp. 641 - 658
Copyright
Copyright © Cambridge University Press 2012

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