A SIMPLE METHOD FOR DESCRIBING THE DEPENDENCE OF RETARDATION FACTORS ON MOISTURE CONTENT

Retardation of reactive solutes migrating through unsaturated porous media is dependent on the water content.  This dependence arises because the interfacial area (water-sorbing solid) changes with moisture content.  Traditional treatments for reactive transport have assumed that values of bulk distribution coefficient determined for saturated conditions can be used without modification for unsaturated calculations.  We have derived an expression that describes the distribution coefficient, K_d, as a function of water saturation, S, that explicitly accounts for changes in the wetted surface area.  In our derivation, the K_d can be represented as the product of two functions, one dependent on the interfacial processes (i.e., chemistry) and the other, the “relative partition coefficient” (analogous to relative permeability), K_d,rel=S/[S+K_R(1-S)], that is dependent on S and independent of chemistry.  K_R is an empirical constant that is dependent on the medium and the wetting characteristics of the fluid.  The equation is derived using a functional form for the reactive surface area that is analogous to the wetted surface area used in the petroleum industry (Embid and Lake, 1996).  Our derivation suggests that K_d,rel(S) will be the same for all reactive species in a given medium.  K_d,rel(S) values were calculated from data for U(VI) and Sr²⁺ sorption to Hanford soil reported by Lindenmeier et al. (1995).  A plot of K_d,rel versus saturation for both U(VI) and Sr²⁺ follow the theoretical form of the equation and yield K_R=0.81±0.20 (r²=0.72, df=10).  Thus, it appears that a single K_R valued can be used to describe the data and supports the assumptions in the development of the equation. This result implies that values for K_d(S) for any chemical species can be estimated from their K_d(S) value at saturation and a value of K_R derived using another chemical species. 

 

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