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Upscaled model for unsteady slip flow in porous media

Published online by Cambridge University Press:  02 August 2021

Didier Lasseux Open the ORCID record for Didier Lasseux [Opens in a new window] ,
Francisco J. Valdés-Parada Open the ORCID record for Francisco J. Valdés-Parada [Opens in a new window]  and
Alessandro Bottaro Open the ORCID record for Alessandro Bottaro [Opens in a new window]
Didier Lasseux
Affiliation:
I2M, UMR 5295, CNRS, Univ. Bordeaux, 351, Cours de la Libération, 33405 Talence CEDEX, France
Francisco J. Valdés-Parada*
Affiliation:
División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, col. Vicentina, 09340, Mexico
Alessandro Bottaro
Affiliation:
Dipartimento di Ingegneria Civile, Chimica e Ambientale, Scuola Politecnica, Università di Genova, Via Montallegro 1, Genova 16145, Italy
*
†Email address for correspondence: iqfv@xanum.uam.mx
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Abstract

This work reports on modelling unsteady gas flow in porous media at the macroscopic scale in the slip regime, a topic of interest in a wide range of applications. The slip effect is modelled by means of a Navier-type boundary condition. A macroscopic model is derived from the initial-boundary-value problem governing unsteady, single-phase flow of a Newtonian fluid through homogeneous porous media in the creeping, isothermal and slightly compressible slip regime. For momentum transport, the macroscopic model involves two terms. The first consists of a convolution product between the macroscopic pressure gradient and the temporal derivative of an apparent dynamic permeability tensor; the second accounts for the memory of the initial condition. Both contributions are predicted from the solution of a unique closure problem that is independent of the initial flow configuration and of the macroscopic pressure gradient. The accuracy of the model is assessed by comparisons with direct numerical simulations performed at the pore-scale, which find excellent agreement. The simulations also show that a classical heuristic model, which is the consequence of assuming a separation of time scales between the pore-scale and the macroscale, is inadequate, in general, to correctly predict the macroscopic velocity. Results from this work provide a formal clear insight about unsteady flow in porous media in the slip regime, motivating further theoretical and experimental work.

JFM classification

Low-Reynolds-number flows: Porous media Low-Reynolds-number flows: Stokesian dynamics Mathematical Foundations: General fluid mechanics

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 923 , 25 September 2021 , A37
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© The Author(s), 2021. Published by Cambridge University Press

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