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.
Funder
National Natural Science Foundation of China
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics,Applied Mathematics
Cited by
1 articles.
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