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3. Upscaling of Adsorbing Solutes; Pore Scale
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and Brantley, 2003, Maher et al., 2004]. Then the question arises as to what
extent pore scale reaction models and parameters are applicable at the macroscale.
Recently, Meile and Tuncay [2006] addressed this question for the case of mineral
dissolution and homogenous reaction with the aid of a pore-scale numerical
model. They found that macro-scale descriptions of these processes are different
from pore-scale descriptions because of the effect of small-scale gradients
in concentration fields. To investigate these effects, they numerically generated
virtual porous media using random placement of identical spherical particles
and solved diffusion and reaction in the resulting pore spaces. They showed
that upscaled values of reaction and dissolution rates depend on the type of
reaction, pore geometry, and macroscopic concentration gradient. They found
that differences between these two scales become more significant for surface
reactions as compared to homogeneous reactions. A limitation in the work
of Meile and Tuncay [2006] is that they considered only diffusion transport
and neglected advection. Other modeling studies have shown that the role
of advection on the distribution of chemicals at the pore level is very important
(e.g., Bryant and Thompson [2001], Knutson et al. [2001a], Robinson and
Viswanathan [2003], Szecsody et al. [1998]).
Li et al. [2006b] studied the effect of pore-scale concentration gradients on a
mineral dissolution rate influenced by advection. They introduced two kinds of
models for minerals that could dissolve at different rates. First, they developed
a Poiseuille flow model that coupled the reaction rate to both advection and
diffusion within a pore space. Next they developed a “well-mixed reaction”
model that assumed complete mixing within the pore. They have shown that
concentration gradients could cause scale dependence of reaction rates. Significant
concentration gradients would develop when diffusion is slower than the
advection process, provided that rates of advection and reaction are comparable.
This shows the effect of pore-scale gradients and residence times on the
transport of reactive solutes. The effect of residence times on reactive transport
was also addressed by Robinson and Viswanathan [2003], who showed the importance
of pore-scale gradients, especially for nonlinear reactions; solute pulses
of short duration; and systems with broad residence time distribution curves.
Characteristic timescales of reaction processes pose constraints for transport
models [Mo and Friedly, 2000, Cao and Kitanidis, 1998].
Experimental studies (e.g., Guo and Thompson [2001]) as well as pore-scale
numerical models [Knutson et al., 2001a] have shown the dependence of mass
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