Page 204 - Materials Chemistry, Second Edition

Vadose Zone Soil Remediation 187

The term on the left-hand side of Equation (5.22) represents the total COC
mass in soil before washing, which includes the mass adsorbed on the soil
surface and that dissolved in the soil moisture (shown as the middle section
of the equation). The terms in the last section of the equation represent the
mass left on the soil surface and the mass dissolved in the liquid phase at
the end of washing (the total volume of the liquid is equal to the sum of the
washing fluid, V, and the soil moisture, V moisture ). Assuming the mass in the
l
soil moisture is relatively small when compared to mass adsorbed on the soil
V
surface before washing (i.e., C initial soil moisture << S initial M s,dry ) and the mass in
soil moisture is relatively small compared to the sum of the mass adsorbed
V
on the soil surface and that in the washing fluid after washing (i.e., C final soil
<< (S M + C V ), Equation (5.22) can be simplified to
moisture final s,dry final 1
M s,dry ≈ M s,dry + (5.23)
S initial S final C final V l

These two assumptions are valid when the soil before washing is relatively
dry and/or the COC is relatively hydrophobic.
If an equilibrium condition is achieved at the end of the washing, the COC
concentration on the soil and that in the liquid can be related by the partition
equation described in Chapter 2, Equation 2.24:

S final = (5.24)
p
K C final
where K is the partition equilibrium constant. By inserting Equation (5.24)
p
into Equation (5.23), the relationship between the initial and final COC
concentrations on the soil surface can be expressed by Equation (5.25) or
Equation (5.26) as:

1
= (5.25)
S final
V l
S initial 1+ ( M s,dry )
K p
1
S final = × S initial (5.26)
1+ ( M s,dry )
V l
K p
For a sequence of washers in series, the final COC concentration can be
determined by:

1 1 1
S final
= × × ×  (5.27)
V l,1
V l,3
V l,2
S initial 1+ ( M s,dry ) 1+ ( M s,dry ) 1+ ( M s,dry )
K p K p K p