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

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) 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.