download pdf version of PhD book - Universiteit Utrecht

1. Introduction
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
our formulation in a MDPN model. Resulting saturation-relative permeability
relationships show very good agreement with measured curves.
Chapter 6 is devoted to the study of the dispersion coefficients under partially
saturated conditions using a new formulation. It is known that in unsaturated
porous media, the dispersion coefficient depends on the Darcy velocity as
well as saturation. The dependency of dispersion on velocity is fairly studied,
however, there is not much known about its dependence on saturation and the
underlying process. The purpose of this chapter is to investigate how the longitudinal
dispersivity varies with saturation. We have represented the porous
medium with our MDPN. Both pore bodies and pore throats have volumes and
we assign separate concentrations to each of them. Further, since pore geometry
and corner flows greatly influence transport properties, efforts are made
to include different angular cross sectional shapes for the pore throats. This
includes circular, rectangular, and irregular triangular cross sections, which
are important especially under unsaturated/two-phase flow and reactive transport.
After the construction of the pore network, 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 under partially-saturated
conditions. In this formulation we refine the discretization on the basis of the
saturation state of pores. We assign separate concentrations to different corners
of a given drained pore body and also assign different concentrations to
different corners of a drained angular pore throat. This formulation allows a
very detailed description of pore-scale solute transport processes by accounting
for limitations in mixing as a result of reduced water content. The numerically
computed dispersivities successfully explain the results obtained through experimental
studies, and show the underlaying pore scale processes contributing
to dispersion under unsaturated conditions.
Chapter 7 deals with transport of adsorptive solute under partially saturated
conditions. All of the modeling capabilities developed in previous chapters
are included in this chapter. Compared to column scale experimental
studies on adsorptive transport, there is lack of pore scale modeling studies,
especially under unsaturated porous media. Under unsaturated conditions, the
system contains three phases: air, water, and solid. The principal interactions
usually occur at the solid-water interfaces (sw) and air-water interfaces (aw)
and are thus greatly influenced by water content. In this chapter, we have for-
12