Reactive Contaminant Transport in the Saturated Zone: Review of Some Upscaling Approaches

We extend the discussion of the previous chapter to a setting wherein the dissolved chemical reacts with its environment. The catalogue of natural geochemical reactions and transformations associated with man-made contaminants that have entered the saturated zone is essentially limitless, but for the most part these reactions can be categorized according to speed, reversibility, and phase association. A relevant subset of the classification scheme of Rubin (1983) includes the four cases (1) reactions that are fast (equilibrium) and reversible involving aqueous-aqueous or (2) aqueous-solid phase interactions; and (3) reactions that are not fast (nonequilibrium) involving aqueous-aqueous or (4) aqueous-solid phase interactions. The terms “fast” and “not fast” are defined relative to the other transformation processes involved, including other reactions and convective and dispersive transport on the observation time scale. Aqueous-aqueous (Categories 1 and 3) are termed “homogeneous” and aqueous-nonaqueous (2 and 4) are termed “heterogeneous” (regarding phase; not to be confused with spatial variability). This scheme is useful because there is a distinct mathematical approach for each of these categories. The chemical mechanisms driving general reactions and the mass balance approaches for formulating representative transformation models are beyond the present scope, and are summarized at various levels in for instance Rubin (1983), Fetter (1993), Marsily (1986), Sposito (1994), and Lichtner et al. (1996). Here we will be restricted to some of the simpler (but representative) reaction mechanisms in categories 2 (sorption) and 4 (biodegradation), and focus on scaling issues associated with transport in heterogeneous porous media. We begin with a brief summary of reaction-transformation formulations and then describe concepts of heterogeneity, scale, and upscaling. The remainder of the chapter describes current methods for scaling plume behavior involving linear reactions (Eulerian approaches), and for scaling contaminant arrival behavior involving nonlinear reactions (Lagrangian approaches).