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Raoof, A. and Hassanizadeh S. M., “Dispersivity under Partially-Saturated Conditions;
Pore-Scale Processes”, prepared for submission to Water Resources Research.
CHAPTER 6
DISPERSIVITY UNDER PARTIALLY-SATURATED
CONDITIONS; PORE-SCALE PROCESSES
Make everything as simple as possible, but not simpler.
Albert Einstein
Abstract
It is known that in unsaturated porous media, the dispersion coefficient depends on
the Darcy velocity and soil water saturation. In 1D flow, it is commonly assumed
that the dispersion coefficient is a linear function of velocity with the coefficient of
proportionality being the dispersivity. However, there is not much known about its
dependence on saturation. The purpose of this study is to investigate how the longitudinal
dispersivity varies non-linearly with saturation using a pore network model. We
discretize the porous medium as a network of pore bodies and pore throats of finite
volumes. The pore space is modeled using a MDPN which allows for a distribution
of coordination numbers ranging between zero and 26.
This topological, property
together with geometrical distributions, are used to mimic the microstructure of real
porous media. The dispersivity was calculated by solving the mass balance equations
for solute concentration in all network elements and averaging the concentrations over
a large number of pores.
We have introduced a new formulation of solute transport within a pore network
which helps to capture the effect of limited mixing within the pores under partiallysaturated
conditions. This formulation allows a very detailed description of solute
transport processes within the pores by accounting for limitations in mixing within
drained pore bodies and pore throats as a result of reduced water content. We found
that dispersivity increases with the decrease in saturation, reaches a maximum value,
and then decreases with further decrease in saturation.