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8.1 Introduction
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cluded that a parabolic velocity profile in pore throats must be implemented
to get a good agreement for a wide range of Peclet number.
In applying equations of mass balance to simulate solute transport, usually pore
scale mixing is assumed within each network element. Different definitions of
network element have been used in literature. The choice commonly depends
on the process under consideration as well as computational load. Acharya
et al. [2005a] modeled porous medium with a network of pore-units, as the
network element. Each pore unit comprised of pore bodies and bonds of finite
volume. Such a pore-unit was assumed to be a mixing cell with steady state flow
condition [Sun, 1996, Suchomel et al., 1998b, Acharya et al., 2005a]. By solving
the mixing cell model for each pore unit and averaging the concentrations for
a large number of pore units as a function of time and space, the dispersivity
was calculated.
Li et al. [2006b] considered pore bodies as network elements to simulate reactive
transport within porous media. They have simulated reactive transport by
applying the mass balance equation which accounted for advection, diffusion
between adjacent pores, and reaction in each pore. Considering the network
domain as a REV, the reaction rates from network models were compared to
rates from continuum scale models, that use uniform concentrations, to examine
the scaling behavior of reaction kinetics.
Commonly the similarity between numerical and physical dispersion is used to
represent dispersion in porous media. The numerically generated dispersion
is a function of time step. Such a dispersion could be analyzed by fitting
the numerical solution to the Taylor’s expansion [Sun, 1996, Suchomel et al.,
1998b].
To solve the transport equation within pore network, Suchomel et al. [1998b]
used a finite-difference approximation to the one-dimensional transport problem
in each pore. They discretized the space within each individual pore throat
to calculate mass transfer within a given pore. They have used upwind explicit
finite-difference method to discretize the advection term. This scheme is numerically
diffusive. They have used such a numerical diffusion to represent
physical diffusion. Through comparison with Taylor expansion, they have calculated
numerical dispersion due to scheme approximations.
In this chapter we use a deterministic approach by applying equations of mass
balance to each network element to simulate reactive/adsorptive transport under
(partially-) saturated conditions. Under saturated conditions we use pore
bodies and pore throats, both with finite volumes, as network elements. How-
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