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4. Upscaling Adsorbing Solutes: Pore-Network Modeling
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interface. They performed pore-scale simulations for a wide range of localscale
distribution coefficients and Peclet numbers. Through these simulations,
they found relationships for the upscaled parameters as a function of underlying
pore-scale parameters. Such relations are useful to perform upscaling by
means of pore-network model. They have shown that even if there is equilibrium
adsorption at the pore wall (i.e., at the grain surface), one may need to
employ a kinetic description at larger scales. They have also shown this kinetic
behavior through employed volume averaging method, yielding very similar results
for upscaled kinetic parameters. These kinetic expressions are sometimes
referred to as “pseudokinetics”, because they are a result of averaging to larger
scales, and are not inherent to the underlying surface reaction [Binning and
Celia, 2008]. Scale-dependent pseudokinetics has been observed for relatively
simple sorption systems, with local equilibrium [Burr et al., 1994, Espinoza and
Valocchi, 1997, Rajaram, 1997].
Li et al. [2006b] used pore-network modeling to investigate scaling effects in
geochemical reaction rates accounting for heterogeneities of both physical and
mineral properties. In particular, they upscaled anorthite and kaolinite reaction
rates under simulation conditions relevant to geological CO 2 sequestration.
They found that pore-scale concentrations of reactants and reaction rates could
vary spatially by orders of magnitude. Under such conditions, scaling effects
are significant and one should apply an appropriate scaling factor; i.e., using
lab-measured rates directly in the reactive transport models may introduce
errors. To find macro-scale reaction rates analogous to CO 2 injection conditions,
Algive et al. [2007b] have used pore-network modeling together with
experimental work (on a glass micromodel) to evaluate effects of deposition
regimes on permeability and porosity. Diffusion was taken into account in the
calculation of the effective reaction coefficient at the macro scale, so that masstransfer-limited
reaction could be studied. They found that both pore-scale
and macro-scale transport processes are needed for explaining deposition patterns;
while macroscopic parameters controlled the concentration field and its
variation, microscopic parameters determined the deposition rate for a given
macroscopic concentration field.
Although there are some studies on upscaling of reaction rate coefficients, many
of them do not provide an explicit relationship between pore scale and upscaled
parameters. In this work, we present a methodology for using a pore-network
model to investigate scaling effects in adsorption rates. The aim of this research
is to find a relation between macroscopic (Darcy scale) and local scale transport
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