Gas Emission Control - Mathematics and Statistics for the Environment - page 485

∆ T m = ∆ T lm = (∆ T 1 - ∆ T 2 )/ln(∆ T 1 ∆ T 2 ) (16.23)

where ∆ T lm is the log mean temperature.
The value calculated from Equation 16.23 is used for single-pass heat exchangers or condensers.
For multiple-pass exchangers, a correction factor for the log mean temperature must be included.
However, no correction factor is needed for the special case of isothermal condensation (no change
in temperature) when there is a single component vapor and the gas temperature is equal to the
dewpoint temperature. In order to size a condenser, Equation 16.22 must be rearranged to solve for
the surface area.

A = q / U ∆ T lm (16.24)

where
A = Surface area of a shell-and-tube condenser (ft 2 ).
q = Heat transfer rate (Btu/lb).
U = Overall heat transfer coefficient (Btu/°F⋅ft 2 ⋅hr).
∆ T lm = Log mean temperature difference (°F).

Equation 16.24 is valid only for isothermal condensation of a single component. This implies that
the pollutant is a pure vapor stream comprised of only one specific hydrocarbon, such as benzene,
and not a mixture of hydrocarbons. Nearly all air pollution control applications involve mulitcom-
ponent mixtures, which complicates the design procedure for a condenser. For preliminary rough
estimates of condenser size, the procedure in Example 16.12 for single-component condensation can
be used for condensing multicomponents. In choosing a heat transfer coefficient, the smallest value
should be used to allow as much over design as possible.

■ EXAMPLE 16.12
Problem: In a rendering plant, tallow is obtained by removing the moisture from animal matter in
a cooker. Exhaust gases from the cookers contain essentially steam; however, the entrained vapors
are highly odorous and must be controlled. Condensers are normally used to remove most of the
moisture prior to incineration, scrubbing, or carbon adsorption (USEPA, 1981, p. 6-15). The exhaust
rate from the continuous cooker is 20,000 acfm at 250°F. The exhaust gases are 95% moisture with
the remaining portion consisting of air and obnoxious organic vapors. The exhaust steam is sent
first to a shell-and-tube condenser to remove the moisture and then to a carbon absorption unit. If
the coolant water enters at 60°F and leaves at 120°F, estimate the required surface area of the con-
denser. The condenser is a horizontal, countercurrent flow system with the bottom few tubes flooded
to provide subcooling.

Solution: Compute the pounds of steam condensed per minute:

20,000 acfm × 0.95 = 19,000 acfm steam

From the ideal gas law,

P × V = n × R × T

n = ( P × V )/( R × T )

n = (1 atm)(19,000 acfm)/[0.73 atm-ft 3 /lb-mol-°R)(250 + 460)°R] = 36.66 lb-mol/min

m = (36.66 lb-mole/min)(18 lb/lb-mole) = 660 lb/min of steam to be condensed