NDLI: Poro-viscoelasticity modelling based on upscaling quasistatic fluid-saturated solids

Content Provider	Springer Nature Link
Author	Rohan, Eduard Shaw, Simon Whiteman, John R.
Copyright Year	2013
Abstract	In this paper, quasistatic models are developed for the slow flow of compressible fluids through porous solids, where the solid exhibits fading memory viscoelasticity. Problems of this type are important in practical geomechanics contexts, for example, in the context of fluid flow through unconsolidated reservoir sands and of wellbore deformation behaviour in gas and oil shale reservoirs, all of which have been studied extensively. For slow viscous fluid flow in the poro-viscoelastic media we are able to neglect the dynamic effects related to inertia forces, as well as the dissipation associated with the viscous flows. This is in contrast to the vast body of work in the poro-elastic context, where much faster flow of the viscous fluids may give rise to memory effects associated with microflows in pores of the solid media. Such problems have been treated extensively in both the dynamic and quasistatic cases. We are taking a specific type of the porous medium subject to slow deformation processes possibly inducing moderate pressure gradients and flow rates characterised by negligible inertia effects. As the result of homogenisation of such a two-phase medium, we observe the fading memory behaviour in the Biot modulus which controls the pressure increase due to skeleton macroscopic deformation and pore fluid content. Although our derivation leads to a result which is consistent with the formal phenomenological approach proposed by Biot (J Appl Phys 23:1482–1498, 1962), we offer the reader more insight into the structure of the poro-viscoelastic constitutive relations obtained; in particular, we can show that the Biot compressibility evolves in time according to the creep function while the skeleton stiffness is driven by the relaxation function.
Starting Page	883
Ending Page	895
Page Count	13
File Format	PDF
ISSN	14200597
Journal	Computational Geosciences
Volume Number	18
Issue Number	5
e-ISSN	15731499
Language	English
Publisher	Springer International Publishing
Publisher Date	2013-08-10
Publisher Place	Cham
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Viscoelasticity Two-scale modelling Homogenisation Fluid-saturated porous media Biot model Perfusion Viscoelastic solid porous media Unconsolidated sands Wellbore deformation Earth Sciences Geotechnical Engineering & Applied Earth Sciences Hydrogeology Mathematical Modeling and Industrial Mathematics Soil Science & Conservation
Content Type	Text
Resource Type	Article
Subject	Computers in Earth Sciences Computational Theory and Mathematics Computer Science Applications Computational Mathematics

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Erratum to: Poro-viscoelasticity modelling based on upscaling quasistatic fluid-saturated solids

Erratum to: Poro-viscoelasticity modelling based on upscaling quasistatic fluid-saturated solids

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