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4. Upscaling Adsorbing Solutes: Pore-Network Modeling
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4.1 Introduction
Transport of reactive/adsorptive solutes in soils and aquifers plays an important
role in a variety of fields, including leaching of agrochemicals from the soil
surface to groundwater, uptake of soil nutrients by plant roots, and remediation
of contaminated soils and aquifers. Geochemical modeling has been widely
employed to improve our understanding of the complex processes involved in
fluid-solid interactions [Steefel and Lasaga, 1994, Gallo et al., 1998, Bolton
et al., 1999] and to study environmental problems related to groundwater and
subsurface contamination [Saunders and Toran, 1995, Xu et al., 2000, Mayer
et al., 2002]. In reactive solute transport, we should, in general, model various
reaction processes including: adsorption-desorption; precipitation-dissolution;
and/or oxidation-reduction. Studies of many contaminated field sites have
demonstrated that adsorption-desorption is one of the most significant geochemical
process affecting the transport of inorganic contaminants [Kent et al.,
2008, Davis et al., 2004a, Kohler et al., 2004].
4.1.1 Discrepancy between observations
In practical applications, we are interested in describing solute transport phenomena
at scales larger than the scale at which the generic underlying processes
take place (e.g., the pore scale). Commonly, in field or in lab experiments, reactive
transport coefficients are employed which are obtained from experimental
data. Measurement of the reaction coefficients usually employs well-mixed
batch or flow-through reactors [Lasaga, 1998]. In batch systems, the assumption
is that the aqueous phase is stirred rapidly enough so that concentration
gradients are eliminated; this removes the effect of subscale transport by diffusion
and/or advection within the pore spaces. In such cases, reaction is
surface-controlled and depends only on the uniform chemistry of the aqueous
solution. In natural systems, however, reactions are inevitably subject to the
influence of transport via advection, molecular diffusion, and/or dispersion.
As such, adsorption rates are an outcome of the coupling between reaction
and hydrodynamic processes [Li et al., 2007b]. These potential discrepancies
between batch experiments and the field can be the reason for much larger,
laboratory-measured reaction rates for many minerals than those observed in
the field [White and Brantley, 2003, Maher et al., 2004].
For upscaling batch experimental results to the field, we need to know the
dependency of the macro scale sorption coefficients on flow velocity and pore-
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