6
water through a defined volume (Antelmi et al. 2020).
Contaminant transport is assumed to be dominated by
advection and linear sorption processes with negligible dis-
persion. For this analysis, the batch pore flushing model
was first fit to the column test effluent uranium data to
estimate the soil partitioning coefficient (Kd) and to cal-
culate the number of pore volumes flushed to reach the
40 CFR 192 groundwater standard of 44 µg/L (Figure 4).
Insufficient detections of ammonia in the column efflu-
ent data prevented calculation of Kd for ammonia. Next, a
plume-scale batch pore flushing model was used with the
average Kd for uranium derived from the column tests and
a previous estimate of the Kd for ammonia (0.5 L/kg, DOE
2003) to estimate the remediation timeframe for natural
flushing of uranium and ammonia.
The batch pore flushing model effluent concentrations
were calculated using Equation 1,
C
C e e (/n )
*
R K
Q t/PV
0
1
b d e ==#t
-NPV
+
-(1)
where C is contaminant concentration at time, t C0 is the
initial concentration, NPV is the number of pore volumes
at time, t R is the retardation factor Q is the flowrate
through the column PV is the pore volume of column,
derived from bromide tracer test ρb is the bulk density of
soil in column, calculated as the dry mass of soil divided by
the volume of soil in the column ne is the effective porosity,
derived from bromide tracer test and Kd is the soil parti-
tioning coefficient.
C, C0, Q, and ρb were measured for each column, and
ne and PV were derived from the bromide tracer test for each
column. Kd is the only unknown and was varied to fit the
model to the normalized measured effluent concentration
data. The Excel solver tool was used to minimize the sum of
the squared residuals between the measured and calculated
normalized uranium concentrations by varying the values
for Kd.
For columns with effluent concentrations exceeding the
40 CFR 192 groundwater uranium standard of 44 µg/L,
the number of pore volumes flushed to reach the ground-
water standard (NPVtarget) was calculated using Equation 2,
lnd NPV C
C
f
0
target #=-R n (2)
where,
R =retardation factor, R ne
Kd 1 tb =++
Cf =target concentration
C0 =initial concentration
The fitted Kd values for each column ranged from 0.99
to 7.45 liters per kilogram (L/kg), with an average of 3.62
L/kg. The range for the six columns with effluent concentra-
tions greater than the uranium groundwater standard was
from 0.99 to 2.75 L/kg, with an average Kd of 1.71 L/kg.
The average Kd for the columns with lower effluent concen-
trations was 6.14 L/kg. This suggests that sorption is non-
linear over the entire concentration range at the Site, and
at lower concentrations (below the 40 CFR 192 ground-
water standard) uranium may be more tightly sorbed to
solids. This observation also indicates that the estimated Kd
of 1.71 L/kg may be representative of the low concentra-
tion plume area (average concentration of 0.29 mg/L), but
the column test results may not be representative of the
sorption coefficient for the high concentration plume area
(average concentration of 1.8 mg/L). Based on the batch
pore flushing model, the calculated number of pore vol-
umes to achieve the 40 CFR 192 groundwater standard in
each column ranged from 5.2 to 19.8 with an average of
14.3 pore volumes.
The plume-scale batch pore flushing model used the
same equations as described above, but the parameters were
based on the groundwater plume. For example, one pore
volume is defined by the plume extent, and the flow rate
is the estimated natural flushing rate through the plume
(Antelmi et al. 2020). The plume-scale model results using
parameters derived from the column tests show that pro-
posed groundwater standards may be reached under natu-
ral flushing conditions within 100 years for the ammonia
plume, but longer than 100 years may be required for the
uranium plume. The plume-scale model indicates the pro-
posed groundwater standard of 3 mg/L for ammonia may
be reached in 50 years for expected natural flushing flow
rates (140 gallons per minute [gpm]) and 58 years for the
Figure 4. Time series of normalized effluent uranium
concentrations in the BH-03 (23-24 feet bgs) column. The
batch pore flushing model (green line) was fitted to the data
by adjusting the value of Kd in Equation 1
water through a defined volume (Antelmi et al. 2020).
Contaminant transport is assumed to be dominated by
advection and linear sorption processes with negligible dis-
persion. For this analysis, the batch pore flushing model
was first fit to the column test effluent uranium data to
estimate the soil partitioning coefficient (Kd) and to cal-
culate the number of pore volumes flushed to reach the
40 CFR 192 groundwater standard of 44 µg/L (Figure 4).
Insufficient detections of ammonia in the column efflu-
ent data prevented calculation of Kd for ammonia. Next, a
plume-scale batch pore flushing model was used with the
average Kd for uranium derived from the column tests and
a previous estimate of the Kd for ammonia (0.5 L/kg, DOE
2003) to estimate the remediation timeframe for natural
flushing of uranium and ammonia.
The batch pore flushing model effluent concentrations
were calculated using Equation 1,
C
C e e (/n )
*
R K
Q t/PV
0
1
b d e ==#t
-NPV
+
-(1)
where C is contaminant concentration at time, t C0 is the
initial concentration, NPV is the number of pore volumes
at time, t R is the retardation factor Q is the flowrate
through the column PV is the pore volume of column,
derived from bromide tracer test ρb is the bulk density of
soil in column, calculated as the dry mass of soil divided by
the volume of soil in the column ne is the effective porosity,
derived from bromide tracer test and Kd is the soil parti-
tioning coefficient.
C, C0, Q, and ρb were measured for each column, and
ne and PV were derived from the bromide tracer test for each
column. Kd is the only unknown and was varied to fit the
model to the normalized measured effluent concentration
data. The Excel solver tool was used to minimize the sum of
the squared residuals between the measured and calculated
normalized uranium concentrations by varying the values
for Kd.
For columns with effluent concentrations exceeding the
40 CFR 192 groundwater uranium standard of 44 µg/L,
the number of pore volumes flushed to reach the ground-
water standard (NPVtarget) was calculated using Equation 2,
lnd NPV C
C
f
0
target #=-R n (2)
where,
R =retardation factor, R ne
Kd 1 tb =++
Cf =target concentration
C0 =initial concentration
The fitted Kd values for each column ranged from 0.99
to 7.45 liters per kilogram (L/kg), with an average of 3.62
L/kg. The range for the six columns with effluent concentra-
tions greater than the uranium groundwater standard was
from 0.99 to 2.75 L/kg, with an average Kd of 1.71 L/kg.
The average Kd for the columns with lower effluent concen-
trations was 6.14 L/kg. This suggests that sorption is non-
linear over the entire concentration range at the Site, and
at lower concentrations (below the 40 CFR 192 ground-
water standard) uranium may be more tightly sorbed to
solids. This observation also indicates that the estimated Kd
of 1.71 L/kg may be representative of the low concentra-
tion plume area (average concentration of 0.29 mg/L), but
the column test results may not be representative of the
sorption coefficient for the high concentration plume area
(average concentration of 1.8 mg/L). Based on the batch
pore flushing model, the calculated number of pore vol-
umes to achieve the 40 CFR 192 groundwater standard in
each column ranged from 5.2 to 19.8 with an average of
14.3 pore volumes.
The plume-scale batch pore flushing model used the
same equations as described above, but the parameters were
based on the groundwater plume. For example, one pore
volume is defined by the plume extent, and the flow rate
is the estimated natural flushing rate through the plume
(Antelmi et al. 2020). The plume-scale model results using
parameters derived from the column tests show that pro-
posed groundwater standards may be reached under natu-
ral flushing conditions within 100 years for the ammonia
plume, but longer than 100 years may be required for the
uranium plume. The plume-scale model indicates the pro-
posed groundwater standard of 3 mg/L for ammonia may
be reached in 50 years for expected natural flushing flow
rates (140 gallons per minute [gpm]) and 58 years for the
Figure 4. Time series of normalized effluent uranium
concentrations in the BH-03 (23-24 feet bgs) column. The
batch pore flushing model (green line) was fitted to the data
by adjusting the value of Kd in Equation 1