Macro-Scale Dynamic Effects in Homogeneous and Heterogeneous Porous Media Article Received: 29 April 2003 Accepted: 06 May 2004 DOI:
Cite this article as: Manthey, S., Majid Hassanizadeh, S. & Helmig, R. Transp Porous Med (2005) 58: 121. doi:10.1007/s11242-004-5472-6 Abstract
It is known that the classical capillary pressure-saturation relationship may be deficient under non-equilibrium conditions when large saturation changes may occur. An extended relationship has been proposed in the literature which correlates the rate of change of saturation to the difference between the phase pressures and the equilibrium capillary pressure. This linear relationship contains a damping coefficient, \tau, that may be a function of saturation. The extended relationship is examined at the macro-scale through simulations using the two-phase simulator MUFTE-UG. In these simulations, it is assumed that the traditional equilibrium relationship between the water saturation and the difference in fluid pressures holds locally. Steady-state and dynamic ‘‘numerical experiments’’ are performed where a non-wetting phase displaces a wetting phase in homogeneous and heterogeneous domains with varying boundary conditions, domain size, and soil parameters. From these simulations the damping coefficient
τ can be identified as a (non-linear) function of the water saturation. It is shown that the value of τ increases with an increased domain size and/or with decreased intrinsic permeability. Also, the value of τ for a domain with a spatially correlated random distribution of intrinsic permeability is compared to a homogeneous domain with equivalent permeability; they are shown to be almost equal. Keywords two-phase flow dynamic capillary pressure-saturation relationship macro-scale damping coefficient References Ataie-Ashtiani, B., Hassanizadeh, S. M., Oostrom, M., Celia, M. A., White, M. D. 2001 Effective parameters for two-phase flow in a porous medium with periodic heterogeneities J. Contam. Hydrol. 49 87 100 Google Scholar Barenblatt, G. I., Patzek, T. W., Silin, D. B. 2002The mathematical model of non- equilibrium effects in water-oil displacement. In proceedings of SPE/DOE 13th Symposium on improved oil recovery. SPE 75169 Tulsa OK USA Google Scholar
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