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Inertial solution for high-pressure-difference pulse-decay measurement through microporous media

Published online by Cambridge University Press:  21 September 2023

Zhiguo Tian ,
Duzhou Zhang ,
Yue Wang ,
Gang Zhou ,
Shaohua Zhang  and
Moran Wang Open the ORCID record for Moran Wang [Opens in a new window]
Zhiguo Tian
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
Duzhou Zhang
Affiliation:
Beijing Institute of Control Engineering, Beijing, PR China
Yue Wang
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
Gang Zhou
Affiliation:
Beijing Institute of Control Engineering, Beijing, PR China
Shaohua Zhang
Affiliation:
Beijing Institute of Control Engineering, Beijing, PR China
Moran Wang*
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
*
†Email address for correspondence: moralwang@gmail.com
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Abstract

We present a theoretical asymptotic solution for high-speed transient flow through microporous media in this work by addressing the inertia effect in the high-pressure-difference pulse-decay process. The capillaric model is adopted, in which a bundle of straight circular tubes with a high length–radius ratio is used to represent the internal flow paths of microporous media so that the flow is described by a simplified incompressible Navier–Stokes equation based on the mean density, capturing the major characteristics of mass flow rate. By order-of-magnitude analysis and asymptotic perturbation, the inertial solution with its dimensionless criterion for the high-pressure-difference pulse-decay process is derived. To be compared with experimental data, the theoretical solution involves all three related effects, including the inertia effect, the slippage effect and the compressibility effect. A self-built experimental platform is therefore established to measure the permeability of microporous media by both pulse-decay and steady-state methods to validate the theoretical solution. The results indicate that the relative difference between two methods is less than 30 % even for permeability at as low as $48.2$ nD $(10^{-21}\,{\rm m}^2)$, and the present theoretical solution can accurately capture the inertia effect in the high-pressure-difference pulse-decay process, which significantly accelerates the measurements for ultra-low-permeability samples.

JFM classification

Low-Reynolds-number flows: Porous media
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 971 , 25 September 2023 , R1
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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