Page 74 - Materials Chemistry, Second Edition

Site Assessment and Remedial Investigation 57

where ϕ is the volumetric water content and ϕ is the air porosity. (Note:
a
w
total porosity, ϕ = ϕ + ϕ .) The total mass of COC (M ) present in the plume
t
w
t
a
is the sum of the mass in the previously mentioned three phases and free
product, if any. Thus,
M t = φ C ) + ()()ρ SV()+ a φ G mass of thefreeproduct+ (2.32)
V
V( w b
The mass of free product is simply the volume of the free product multi-
plied by its mass density. If no free product is present, Equation (2.32) can be
simplified to:
M t = φ C ) + ()()ρ S ()()+ V φ G (2.33)
V
V( w b a
If the system is in equilibrium and both Henry’s law and the linear
adsorption apply, the concentration in one phase can be represented by the
concentration in another phase multiplied by a factor. The following rela-
tionships exist:

 S   H 
G = HC = H   =   S (2.34)
 K p   K p 

 S   G 
C =   =    (2.35)
 K p   H

 G   K p 
S = K C = K p   =   G (2.36)
p
 H   H 

Using these relationships, Equation (2.33) can be rearranged to:

M t =φ )( )+ρ K p +φ H C
( )]
V [( w b a
φ
 ( w ) ()ρ b K p 
=   H + H +φ a   G (2.37)
()
 φ ) H 
()
=  ( w +ρ b +φ a  S
 K p K P 

where M /V can be viewed as the average mass concentration of the plume.
t
The total mass of COCs in a plume can be readily determined by multiplying