2.2.2 NAPL Phase Existence Determination
There are two basic kinds of partitioning theory implemented in
the source-term release module, depending on whether a NAPL phase exists.
When no NAPL phase is present, the theory required to describe the phase
partitioning behavior is much simpler. Because the contaminant loss
flux equations implemented in the module require a numerical solution procedure,
contaminant masses and loss fluxes are calculated at discrete time intervals.
At the beginning of each time step, the module determines if a NAPL phase
must exist based on the source zone properties and the contaminant inventories
in the source zone at that time. After this determination, the appropriate
type of phase partitioning theory is used for the calculations associated
with that time step.
The test criterion for the existence of a NAPL phase was developed
as follows. For a given source zone (i.e., for a source zone with
a given volumetric water content, volumetric air content, bulk density
of solid-sorbent, and overall volume), there is a maximum upper limit to
the amount of contaminant that can be accommodated in the aqueous, solid-sorbent,
and vapor phases. This limit depends on the contaminant's aqueous
solubility, saturated vapor pressure (or saturated vapor concentration),
and sorption coefficient. Therefore, summing up the maximum amounts
of contaminant that can be accommodated in each of these three phases,
and comparing this to the actual contaminant mass (or activity) in the
source zone is a way to determine whether a NAPL phase must exist.
A general way to express this criterion in mathematical terms is
where
Mi is the total mass or activity of contaminanti in the source zone (g or Ci)
qw is the volumetric water content of the soil (unitless)
is the aqueous solubility of contaminant i (g cm-3 or Ci cm-3)
qa is the volumetric air content of the soil (unitless)
is the saturated vapor concentration of contaminant i (g cm-3 or Ci cm-3)
ß is the bulk density of the solid-sorbent phase (g cm-3)
Kdi is the linear equilibrium sorption coefficient for contaminant i to a solid sorbent (cm3 g-1)
V is the overall volume of the contaminated source zone (cm3).
[All symbols used in this report are defined in Section 7.0.] This
expression (and all subsequent phase partitioning theory) is commensurate
with the conceptualization that the source zone is a "well-mixed reactor"
(i.e., its properties are spatially uniform throughout).
A criterion equivalent to the one in Equation 2.1 is checked for
each contaminant that could be part of a NAPL phase (i.e., all contaminants
with Henry's Law constants 10-7). If it is untrue for
all of them, the source-term release module assumes that a NAPL phase does
not exist. If it is true for one or more of them, the source-term
release module assumes that a NAPL phase exists (and that all of these
contaminants will partition into the NAPL phase to some degree).
The exact mathematical form of the criterion that is actually checked in
the source-term release module calculations varies 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).