Flow of low pressure gas through dual-porosity media

Abstract

Using the theory of homogenization we derive macroscopic models for describing flow of gas at low pressure in dual-porosity media. The case of a fractured porous medium is under consideration for the study, and the existence of a representative elementary volume that consists of open connected fractures surrounded by porous matrix blocks is assumed. The local flow is governed by either Klinkenberg's law or Knudsen's diffusion law in the matrix while either a non-slip flow or a slip flow occurs in the fractures. Six new models are derived by homogenization, which are compared to the three models which were obtained for Darcy's regime in an earlier work. Each of these nine models is characterized by its macroscopic flow regime and by the type of macroscopic behavior it describes. Besides Darcy's and Klinkenberg's macroscopic flow regimes, a transition regime between Klinkenberg's and Knudsen's regimes is identified. The types of macroscopic behaviors include a dual and a single porosity description and an intermediate behavior that describes a single-porosity behavior, but in which the porosity of the entire fractured porous medium is accounted for.

Acoustical properties of double porosity granular materials

“…Rarefaction effects are therefore neglected. However, it has been shown that these effects do not change the form of the macroscopic isothermal acoustic description in single 26 and double 27 porosity materials but the way the effective quantities are calculated. To model the material as a homogenous equivalent fluid, the separation of scales assumption should be satisfied, e.g., e ¼ l p =L ( 1 and e 0 ¼ l m =l p ( 1.…”

Influence of sorption on sound propagation in granular activated carbon

“…For pores smaller than the molecular mean free path the Knudsen number becomes large and the dominant transport mechanism is Knudsen diffusion 9,16 rather than viscous slip flow. It states that the diffusive transport is proportional to the pressure gradient 2,9,16,29 and the filtration velocity is given by:…”

“…Diagram of the scales of a double porosity material (adapted from Ref 26 ). The wave equation in a rigid-frame double porosity granular material has the same general form6,7,25,26,29 as that of Eq.(35). However, E and k should be replaced by the dynamic bulk modulus db E and dynamic viscous permeability db k of the double porosity granular material.…”

Time Analysis of the Three Characteristic Behaviours of Dual-Porosity Media. I: Fluid Flow and Solute Transport

“…As it will be seen in §4.3, the result is of crucial importance for the determination of the order of magnitude of the velocity ratio for transient fluid flow in dualporosity media. Several empirical approaches have been made for determining this order of magnitude, but with no clear understanding on the rules which condition the result (Royer and Auriault 1994), (Chastanet et al 2007). Thanks to the above time analysis which suggests to examine the temporal regimes, we are in position to rigorously derive this fundamental result.…”