2.2.3 Partitioning Theory When No NAPL Phase Exists

If no NAPL phase exists, the phase partitioning theory for any individual contaminant is independent of the other contaminants.  In this case, an overall total contaminant concentration in the source is defined using the total contaminant mass (or activity) present in the source zone and the overall volume of the source zone:



where    C_ti is the overall total concentration of contaminant i in a bulk volume of source zone (g cm^-3 or Ci cm^-3).

This overall total concentration can be related to the amounts in each phase by



where

C_wi  is the concentration of contaminant i in the aqueous phase (g cm^-3 or Ci cm^-3)
C_vi  is the concentration of contaminant i in the vapor phase (g cm^-3 or Ci cm^-3)
C_si  is the concentration of contaminant i in the sorbed phase (g g^-1 or Ci g^-1).

If we assume that Henry's Law is valid for aqueous-vapor partitioning, and that the aqueous-sorbed partitioning is governed by linear equilibrium sorption, Equation 2.3 can be rewritten as



where    K_Hi is the modified Henry's Law constant for contaminant i (concen./concen. basis) for partitioning between aqueous solution and vapor (unitless).

If we define a parameter, R_i, to be



Equation 2.4 can be simplified to



where    R_i is the retardation factor, or phase apportionment factor, for contaminant i (unitless).

For the contaminated vadose zone and contaminated aquifer source zones, the parameter R_i can be identified as the commonly reported retardation factor. ^(a)  For the contaminated pond/surface impoundment source zone, the parameter R_i is more appropriately identified as a phase apportionment factor.^(b)

The source-term release module needs values of the aqueous and vapor concentrations of the contaminants for the mass loss flux calculations.  Combining Equations 2.2 and 2.6, these concentrations can be expressed as





Note that, because of the way NAPL phase nonexistence was determined (Equation 2.1), Equations 2.7 and 2.8 may result in an aqueous or vapor concentration that exceeds the contaminant's aqueous solubility or saturated vapor concentration.  It is possible for the aqueous concentration calculated by Equation 2.7 to be greater than the aqueous solubility if the value of the Henry's Law constant for the contaminant is less than the ratio of its saturated vapor concentration and its aqueous solubility (and if the total contaminant mass is near the saturation limit).  Conversely, it is possible for the vapor concentration calculated by Equation 2.8 to be greater than the saturated vapor concentration if the value of the Henry's Law constant for the contaminant is greater than the ratio of its saturated vapor concentration and its aqueous solubility (and if the total contaminant mass is near the saturation limit).  What this means is that Henry's Law is not really valid for concentrations all the way up to the saturation limit.  However, the source-term release module considers that Henry's Law is still valid over the entire concentration range, and merely limits the aqueous or vapor concentration to its saturated value when Equation 2.7 or 2.8 would predict an unrealistically high value.
 Equations 2.7 and 2.8 are only general forms of the equations used by the module.  The exact mathematical forms of the equations actually used in the calculations vary depending on the type of contaminant source zone under analysis (i.e., how the volume of the source zone, V, is explicitly described in terms of other source zone parameters).  These exact forms are presented in the report sections dedicated to the three different source zones (Sections 3.0, 4.0, and 5.0).

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(a)	In these scenarios, ß is more explicitly defined as ßs, the soil bulk density. In addition, for a contaminated aquifer, the volumetric air content, qa, is zero, and the volumetric water content, qw, is more explicitly defined as the total porosity, qt.
(b)	In this scenario, ß is more explicitly defined as ßss, the suspended sediment concentration.