Page 184 - Materials Chemistry, Second Edition

Vadose Zone Soil Remediation 167

Discussion:
All three approaches yield the same result.

5.2.4 Vapor Flow Rates

The radial Darcy velocity, u , in homogeneous soil systems can be expressed
r
as [2]:
−
P RI
P w
 k    r ln( w R   1 ( ) 2   
R / ) I   
P w
u r =   0.5 (5.4)
2µ

rR )
1+  1 ( ) 2  ln(/ w
−
P RI
R / ) I
  P w   ln( w R
where u is the vapor flow velocity at a radial distance r away from the extrac-
r
tion well. The velocity at the wellbore, u , can be found by replacing r with
w
R in Equation (5.4):
w
 k      P RI  2 
u w =    P w   1−     (5.5)
R I   
w
w
 2µ  R ln( R /) P w   
The volumetric vapor flow rate entering the extraction well, Q , can then
w
be found as:
)(
Q w = (2π R Hu )
w
w
 π k   P w    P RI  2  (5.6)
= H  µ    ln( R / )   1−   P w   
  w R I     
where H is the perforation interval of the extraction well.
To convert the vapor flow rate entering the well to the flow rate discharged
to the atmosphere (Q atm ), where P = P atm = 1 atm, the following relationship
can be used:
 P well 
Q atm =   Q well (5.7)
 P atm 
Example 5.10: Estimate the Extracted Vapor Flow
Rate of a Soil-Venting Well
A soil-venting well (4-in. diameter) was installed at a site. The pressure in the
extraction well is 0.9 atm and the radius of influence of this soil-venting well
has been determined to be 50 ft.