NDLI: Three-Phase Permeabilities: Upscaling, Analytical Solutions and Uncertainty Analysis in Elementary Pore Structures

Content Provider	Springer Nature Link
Author	Bianchi Janetti, Emanuela Riva, Monica Guadagnini, Alberto
Copyright Year	2014
Abstract	Immiscible three-phase flow in a rigid porous medium is upscaled from the pore to the continuum (Darcy) scale through homogenization relying on multiple scale expansion. We solve the Stokes flow problem at the pore level upon imposing continuity of velocity and shear stress at the fluid–fluid interfaces. This enables one to explicitly account for the momentum transfer between the moving phases. A macroscopic model describing the system at the Darcy scale is then rigorously obtained. This allows defining a tensor of three-phase effective relative permeabilities, $$\mathbf{K}_{\alpha \eta ,r}$$ , as a function of the distribution of the fluids in the system, phase saturations and fluid viscosity ratios. We present an analytical solution for $$\mathbf{K}_{\alpha \eta ,r}$$ corresponding to a scenario where three-phase fluid flow takes place within (a) a plane channel and (b) a capillary tube with circular cross-section. These geometrical settings are typical of microfluidics applications and are archetypal to the analysis of key processes occurring in topologically complex porous or fractured systems. Our results show the relevance of the viscous coupling effects between the three phases on the continuum-scale system behavior and demonstrate that the traditional extension of Darcy’s law to model multiphase relative permeabilities might be inadequate. We then exploit our analytical solutions to investigate the way the uncertainty associated with the characterization of the phase viscosities propagates to $$\mathbf{K}_{\alpha \eta ,r}$$ through a global sensitivity analysis approach. We quantify the relative contribution of the considered uncertain parameters to the total variability of $$\mathbf{K}_{\alpha \eta ,r}$$ by relying on the variance-based Sobol indices which are derived analytically for the investigated settings.
Starting Page	259
Ending Page	283
Page Count	25
File Format	PDF
ISSN	01693913
Journal	Transport in Porous Media
Volume Number	106
Issue Number	2
e-ISSN	15731634
Language	English
Publisher	Springer Netherlands
Publisher Date	2014-10-12
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Three-phase flow Upscaling Relative permeability Viscous coupling Analytical solution Global sensitivity analysis Geotechnical Engineering & Applied Earth Sciences Industrial Chemistry/Chemical Engineering Hydrology/Water Resources Civil Engineering Hydrogeology Classical Continuum Physics
Content Type	Text
Resource Type	Article
Subject	Catalysis

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