Dynamic Relative Permeabilities for Partially Saturated Porous Media Accounting for Viscous Coupling Effects: An Analytical Solution

被引:5
作者
Solazzi, Santiago G. [1 ]
Jougnot, Damien [2 ]
Rubino, J. German [3 ]
Holliger, Klaus [1 ]
机构
[1] Univ Lausanne, Inst Earth Sci, CH-1015 Lausanne, Vaud, Switzerland
[2] Sorbonne Univ, EPHE, CNRS, UMR7619,METIS, F-75005 Paris, Ile De France, France
[3] Ctr Atom Bariloche CNEA, CONICET, R8402AGP, San Carlos De Bariloche, Rio Negro, Argentina
基金
欧盟地平线“2020”;
关键词
Viscous coupling; Dynamic relative permeability; Frequency-dependent effects; Porous media; Analytical solution; Partial saturation; IMMISCIBLE 2-PHASE FLOW; GOVERNING EQUATIONS; WAVE-PROPAGATION; ELASTIC WAVES; COEFFICIENTS; MODEL; ORIGIN; PHASES; IMPACT;
D O I
10.1007/s11242-023-01920-w
中图分类号
TQ [化学工业];
学科分类号
0817 ;
摘要
We 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.
引用
收藏
页码:653 / 677
页数:25
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