Page 75 - Materials Chemistry, Second Edition

58 Practical Design Calculations for Groundwater and Soil Remediation

(M /V), if known, with the total volume of the plume. Equation (2.37) can be
t
used to estimate the total mass of COC in a vadose zone if the average soil
moisture concentration, soil concentration, or vapor concentration is known,
and if no free product is present.
For a dissolved groundwater plume (ϕ = 0 and ϕ = ϕ ), Equation (2.37) can
w
a
t
be modified to
M t =φ ( ) KC]
[ +ρ
V b p
(2.38)
 φ 
=  +ρ b S
 K p 
To use the equations in this subsection, the following units are suggested: V
(in liters), G (mg/L), C (mg/L), S (mg/kg), M (mg), ρ (kg/L), K (L/kg), and
b
t
p
ϕ , ϕ , ϕ , and H (dimensionless).
a
w
t
As mentioned in Section 2.4.3, both S and X are used for COC concentra-
tions in soil in this book. S is the adsorbed concentration on the solid surface,
and X is used to represent the COC concentration of a soil sample. Symbol S
means “mass of COC/mass of dry soil,” while X means “mass of COC/mass
of soil plus moisture.” Assuming the mass of COC in the void is also cap-
tured in the analysis of the soil sample, the total mass of COC contained in a
unit volume of soil (M /V) can be related to COC concentration in soil (X) as
t
M t = X (2.39)
V × ρ t
where ρ is the total bulk density of the soil sample
t
As will be shown in Example 2.37, the mass in the void is relatively small
compared to that in the dissolved and adsorbed phases. Consequently,
the inclusion of mass in the void in Equation (2.39) is acceptable. Inserting
Equation (2.39) into Equation (2.37), the soil sample concentration (X) can be
related to G, C, and S as

φ
 [( w + ρ K p + φ H 
)( )
( )]
X =  b a  × C
 t ρ 
  ( w ) + ( b ) K p + ()  
ρ
φ
a φ

 ×
=   H H   G (2.40)
 t ρ 


] 
φ
( )
H
 [  ( w ) +ρ b +φ a K P 
=  K p  × S
  t ρ  