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Determine the chamber volume:
V =
ρ ×
r
×
2
L
= 3.14 × 0.75 m
2
× 3.5 m = 6.18 m
3
Calculate the residence time:
t = V/Q
= (6.18 m
3
)/(14.98 m
3
/s) = 0.41 s
■
EXAMPLE 16.11. INCINERATOR FUEL REQUIREMENT
Problem
: The exhaust from a meat smokehouse contains obnoxious odors and fumes. The company
plans to incinerate the 5000-acfm-exhaust stream. What quantity of natural gas is required to raise
the waste gas stream from a temperature 90°F to the required temperature of 1200°F? The gross
heating value of natural gas is 1059 Btu/scf. Assume no heat losses (USEPA, 1981, p. 3-14).
Given:
Standard condition (state 1)
T
1
= 60°F
Exhaust gas flow rate
V
2
= 5000 acfm at temperature
T
= 90°F
Exhaust gas initial temperature
T
2
= 90°F
Natural gas gross heating value = 1059 Btu/scf
Combustion temperature
T
3
= 1200°F
Solution:
Correct the actual waste gas volume (
V
a
) to standard condition volume (in standard cubic
feet per hour). The correction equation is
V
T
V
T
1
1
2
2
=
VV
T
T
=
460
+
+
60
=
1
2
=
5000
4727 scfm
=
283,620 scfh
1
2
460
90
Convert the volumetric flow rate to a mass flow rate by multiplying by the density:
Mass Flow Rate = Volume Rate × Density
The standard volume of an ideal gas at 60°F = 379.64 ft
3
/lb-mol. Assume that the waste gas molecu-
lar weight is the same as air, 29 lb/lb-mol:
Density = (Molecular Weight)/Volume = 29/379.64 = 0.076388 lb/ft
3
Mass Flow Rate = 4727 × 0.076388 = 361 lb/min
Calculate the heat rate by using the ideal gas equation:
Q = m
×
C
p
×
(T
3
- T
2
)
= 361 × 0.26 × (1200 - 90) = 104,185 Btu/min
Determine the heating value of natural gas. For natural gas, 1 scf contains 1059 Btu. Finally, deter-
mine the natural gas quantity:
W
= 104,185/1059 = 98 scfm
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