Radial infusion models for permeability measurements of compressed fibrous beds

A summary, new development on analytic solutions of models of the Darcy problem for liquid progression through porous media, and some experimental results obtained by these models are presented. Two anisotropic cases, 2D in-plane and 3D axisymetric transverse injection, are analyzed and compared with a reference case that is represented by the widely used closed-form solution of radial in-plane injection. The analytic solutions of the two analyzed models were originally interpreted as the approximate ones, since they were derived assuming that one component of pressure gradients, in the governing equations, may be neglected. It is shown that the assumption regarding pressure gradients in both cases may be released, that the original results present closed-form solutions of the imposed quasi-steady models, and through numerical experiments, that these models are not sensitive to the radius of the injection port within the range in which relevant parameters usually vary in experiments. With these findings and the results obtained experimentally, it is also show that the two models are equally accurate and reliable as the reference one. They can be employed for the evaluation of all three permeability tensor components utilizing a relatively simple apparatus and as such may be utilized as standard models.