Abstract
AbstractWe present an analytical model to compute frequency-dependent relative permeability functions for partially saturated porous media accounting for viscous coupling effects. For this, we consider the oscillatory motion of two immiscible fluid phases and solve the Navier–Stokes equations at the pore scale using suitable interface conditions between fluids. These calculations are combined with the generalized two-phase flow Darcy equations to obtain the corresponding upscaled macroscopic fluxes. By means of an analog pore model consisting of a bundle of cylindrical capillaries in which pore fluids are distributed in a concentric manner, we find closed analytical expressions for the complex-valued and frequency- and saturation-dependent relative permeability functions. These expressions allow for a direct assessment of viscous coupling effects on oscillatory flow for all frequencies and saturations. Our results show that viscous coupling effects significantly affect flow characteristics in the viscous and inertial regimes. Dynamic relative permeabilities are affected by the pore fluid densities and viscosities. Moreover, viscous coupling effects may induce two critical frequencies in the dynamic relative permeability curves, a characteristic that cannot be addressed by extending the classic dynamic permeability definition to partially saturated scenarios using effective fluids. The theoretical derivations and results presented in this work have implications for the estimation and interpretation of seismic and seismoelectric responses of partially saturated porous media.
Funder
H2020 Marie Sklodowska-Curie Actions
University of Lausanne
Publisher
Springer Science and Business Media LLC
Subject
General Chemical Engineering,Catalysis
Reference67 articles.
1. Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions: With Formulas, Graphs and Mathematical Tables. Dover Publications, Mineola (1965)
2. Auriault, J.L., Borne, L., Chambon, R.: Dynamics of porous saturated media, checking of the generalized law of darcy. J. Acoust. Soc. Am. 77(5), 1641–1650 (1985)
3. Auriault, J.L., Lebaigue, O., Bonnet, G.: Dynamics of two immiscible fluids flowing through deformable porous media. Transp. Porous Media 4(2), 105–128 (1989)
4. Avraam, D., Payatakes, A.: Generalized relative permeability coefficients during steady-state two-phase flow in porous media, and correlation with the flow mechanisms. Transp. Porous Media 20(1), 135–168 (1995)
5. Avraam, D., Payatakes, A.: Flow mechanisms, relative permeabilities, and coupling effects in steady-state two-phase flow through porous media. The case of strong wettability. Ind Eng Chem Res 38(3), 778–786 (1999)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献