Modelling of two-phase flow in porous media ...

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XVI International Conference on Computational Methods in Water Resources (CMWR-XVI) Ingeniørhuset

Modelling of two-phase flow in porous media including non-equilibrium capillary pressure effects
Paper
Author:Cas Berentsen <berentsen@geo.uu.nl> (Utrecht University, Earth Sciences Department, Geohydrology group)
Majid Hassanizadeh <hassanizadeh@geo.uu.nl> (Utrecht University, Earth Sciences Department, Geohydrology group)
Presenter:Cas Berentsen <berentsen@geo.uu.nl> (Utrecht University, Earth Sciences Department, Geohydrology group)
Date: 2006-06-18     Track: General Sessions     Session: General
DOI:10.4122/1.1000000233
DOI:10.4122/1.1000000234

Two-phase flow models commonly use equilibrium capillary-pressure relations. However, in core-flow experiments the time needed to reach capillary equilibrium is already in the order of days. Some recently developed theories [1],[2] account for non-equilibrium capillary pressure at the (upscaled) macro-scale, by proposing that capillary pressure is a function of saturation rate. There is plenty of experimental evidence on the significance of non-equilibrium effects in unsaturated media. However, there are very few experiments dealing with two-phase flow. Recently we have carried out a number of two-phase flow experiments consisting both drainage and imbibition in a small column set-up. The experimental data clearly indicates the existence of a local non-equilibrium effect. In this study, we investigated the necessity to account for non-equilibrium capillary pressure effects at the local scale. Moreover, we tried to obtain qualitative agreement between our experimental data and the non-equilibrium model proposed by [2]. We first developed a numerical code in which we simultaneously solve for the wetting phase saturation, wetting phase pressure and non-wetting phase pressure by solving the wetting phase mass balances and the non-equilibrium capillary pressure relation. Next the numerical model is compared to the data of the non-equilibrium two-phase capillary pressure experiments. Qualitative agreement between the numerical model and the physical experiments is obtained, which appears not to be possible without the addition of the local non-equilibrium capillary pressure term. [1] Barenblatt, G.I. and A.A. Gil’man (1987), “Non equilibrium counterflow capillary impregnation”, Journal of Engineering physics, Vol 52, p.335ff [2] Hassanizadeh, S. M. and W. G. Gray (1993) “Thermodynamic basis of capillary pressure in porous media”. Water Resources Research, V29, No.10, 3389–3405.