10.4122/1.1000000233
Berentsen, Cas
Cas
Berentsen
berentsen@geo.uu.nl
Hassanizadeh, Majid
Majid
Hassanizadeh
hassanizadeh@geo.uu.nl
Berentsen, Cas
Cas
Berentsen
berentsen@geo.uu.nl
Modelling of two-phase flow in porous media including non-equilibrium capillary pressure effects
XVI International Conference on Computational Methods in Water Resources
2006
2006
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.