Page 201 - Materials Chemistry, Second Edition

184 Practical Design Calculations for Groundwater and Soil Remediation

where k is the ratio of specific heat of gas at constant pressure to specific
heat of gas at constant volume. For the typical soil-venting applications, it is
appropriate to use k = 1.4.
For reciprocating compressors, the efficiencies (E) are generally in the
range of 70% to 90% for isentropic and 50% to 70% for isothermal compres-
sion. The actual horsepower requirement can be found as:

hp actual = hp theoretical (5.21)
E

Example 5.19: Determine the Required Horsepower of
the Vacuum Pump in Soil Venting
Two vapor extraction wells are installed. The design flow rate of each well
is 40 ft /min, and the design wellhead pressure is 0.9 atm. A vacuum pump
3
is to serve both wells. Estimate the required horsepower of the vacuum
pump.

Solution:
(a) The pressure in the extraction well, P 1
= 0.9 atm = (0.9)(14.7) = 13.2 psi = (13.2)(144) psi = 1,905 lb/ft 2
(b) Assuming isothermal expansion, use Equation (5.19) to deter-
mine the theoretical power requirement as:

×
5
hp theoretical = (3.03 10 ) 1 1 P 2
−
PQ ln
P 1
(14.7)(144)
= (3.03 10 )[(14.7)(144)][(2)(40)]ln× − 5
(1905)
= 0.54hp

Assuming an isothermal efficiency of 60%, the actual horse-
power required is determined by using Equation (5.21) as:

0.54
hp actual = hp theoretical = = 0.9 hp
E 60%