Transient quasi-static gas flow through a rigid porous medium with double porosity

Abstract

The highly compressible fl uid fl ow through a three-scales rigid porous medium (pore, fracture, macroscopic sample) is investigated using a homogenization method. The macroscopic description is strongly dependent on the separation of the different scales, and three cases are considered. The pores either play the role of a compressible fluid reservoir, introduce a memory effect, or are ignored, respectively. The homogenization result is compared to classical phenomenological models that are available in the case of slightly compressible fl uids. Pseudo-steady state models are shown to give a rough description of the phenomenon.(</J)o, (</J)oe = volume averages of the quantity qy on n, n', respectively.( </J) eff = particular volume average on n'.

Flow of low pressure gas through dual-porosity media

“…scale. In the present work we consider either Klinkenberg's or Knudsen's local flow regimes in the porous matrix and we then compare the results with those obtained in Darcy's regime by (Royer and Auriault 1994). The method used for upscaling the local descriptions is the homogenization method for periodic structures-also called method of multiple scales-that has been introduced by (Bensoussan et al 1978) and (Sanchez-Palencia 1980).…”

“…It should also be underlined that model II l cannot be expressed as a twoequation model including a matrix-fracture exchange term as in the pioneering work of (Barenblatt et al 1960) on dual-porosity modeling. When considering a slightly compressible fluid, a linearized form of model II l is obtained (Royer and Auriault 1994). An analytical expression of F can then be determined.…”

“…Royer and Auriault (1994) have considered gas flow in the above described medium, with Darcy's regime in the matrix and a non-slip flow in the fractures. For simplicity, a gas of linear equation of state has been considered: p = Aρ, where p and ρ denote the pressure and the density, respectively, and A is a constant.…”

“…After describing the medium under consideration for the study, we then present the results obtained in Darcy's regime by (Royer and Auriault 1994). Next, we focus on the derivation of the macroscopic models in Klinkenberg's and Knudsen's regime.…”

Macroscopic behavior of gas flow with adsorption through a fractured porous medium

“…The largest coupling effects between the pore-flow and the fracture-flow appear when the scales are equally separated, i.e. when [4], [5], [6). This is the case under consideration hereafter for the investigation of gas flow with adsorption in a rigid fractured porous medium.…”