Environmental Hydrogeology
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Hysteresis and dynamics effects in capillary pressure-saturation relationships
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Researchers: prof.dr.ir S. M. Hassanizadeh, dr. R.J. Schotting,
Alexei Beliaev, Hans van Duijn and Joost Hulshof
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Project description
This research aims at a better description of two-phase flow in a porous medium,
in general, and the
development of general relationships for capillary pressure, in particular. It is
well known that the capillary pressure-saturation
relationship is not unique and depends on the flow dynamics. In fact, it depends on
the direction as well as the rate of flow. The
dependence of capillary pressure-saturation curves on the direction of flow is known
as capillary pressure hysteresis; this is a
well-known effect and has been the subject of extensive investigations. The dependence
of capillary curves on the rate of flow
is due to dynamic effects and is less well known and not quantified properly. The
central goal of this research is the
development of capillary pressure-saturation relationships which simultaneously account
for both of these effects. The research
is based on a thermodynamic analysis of two-phase flow in porous media. Results from
this analysis combined with some ideas
from plasticity lead to some explicit representations of capillary hysteresis and
dynamic effects. The new capillary relationships,
combined with equations of conservation of mass and Darcy's law, yield new governing
equations for two-phase flow and
unsaturated flow. The mathematical properties of these new equations are investigated
in relation to their well-posedness or
concrete properties of particular solutions. Numerical solutions of the new equations
will be also investigated.
Alexei Beliaev is a visitor from the Water Problems Institute of the Russian Academy of
Sciences. His other research interest is
in the application of the homogenization theory to mechanics of heterogeous materials
and mixtures. He looks for exact bounds
for homogenized coefficents and he studies liquid flows in porous media with random
fields and structures.
