Page 277 - Materials Chemistry, Second Edition

260 Practical Design Calculations for Groundwater and Soil Remediation

Use the discussions in part (a) to convert the capillary rise to the
capillary pressure:
 10 ft 
= (14.7 psi) = 4.33 psi
P capillary  
 33.9 ft 
Use Equation (6.31) to determine the minimum air injection
pressure:
+
= 4.33 4.33 = 8.66 psig
P injection = P hydrostatic + P capillary
Discussion:
1. The actual air injection pressure should be larger than the mini-
mum air injection pressure calculated here to cover the system
pressure loss such as head loss in the pipeline, fittings, and injec-
tion head.
2. For sandy aquifers, the air entry pressure is negligible compared
to the hydrostatic pressure. However, for clayey aquifers, the
entry pressure is of the same order of magnitude as the hydro-
static pressure.
3. The calculated injection pressures are in the ballpark of the
reported field values, 1–8 psig.

6.7.4 Power Requirement for Air Injection

Theoretical horsepower requirements (hp theoretical ) of gas compressors for
an ideal gas undergoing an isothermal compression (PV = constant) can be
expressed as [6]:

×
= 3.03 10 −5 PQ ln P 2 (6.34)
hp theoretical 1 1
P 1
where
P = intake pressure, lb /ft 2
1
f
P = final delivery pressure, lb /ft 2
f
2
Q = air flow rate at the intake condition, ft /min
3
1
For an ideal gas undergoing an isentropic compression (PV = constant),
k
the following equation applies for single-stage compressor [6]:
3.03 10× − 5 k   P 2  k ( − 1)/ k 

hp theoretical = k 1− PQ 1   P 1   − 1 (6.35)
1
   
where k is the ratio of specific heat of gas at constant pressure to specific heat
of gas at constant volume. For air-sparging applications, it is appropriate to
use k = 1.4.