Performance
of Evaporators
The performance of an evaporator(fire tube or water tube,bare or finned) may be obtained by solving the following equations:(The performance evaluation of superheater,economizers are more involved and readers may see my books,"Waste Heat Boiler Deskbook" or "Steam Plant Calculations Manual"). Q=W_{g}C_{pg}(tg_{1}tg_{2})hl =USDT=US[(tg_{1}ts)(tg_{2}ts)]/ln[(tg_{1}ts)/(tg_{2}ts)] Wg=gas flow,lb/h tg_{1,}tg_{2,}ts=gas inlet and exit temperatures and saturation steam temperature,F C_{pg}=gas specific heat,btu/lbF hl=heat loss,factor.1 % heat loss means hl=0.99 U=overall heat transfer coefficient,Btu/ft^{2}hF S=surface area,ft^{2} DT=logmeantemperature difference,F Simplifying the above,we have: ln[(tg_{1}ts)/(tg_{2}ts)]=US/(WgC_{pg}xhl) 

Example
of a Fire Tube Boiler
Let
us assume that a fire tube boiler is operating as shown below in clean
conditions:
gas
inlet temperature=1500 F
gas
flow=100,000 lb/h
gas
exit temperature in clean conditions=500 F
steam
pressure=150 psig (ts=366 F)
feed
water temperature=230 F
blow
down=5 %
tubes:
2x1.77in,600 tubes,20 ft long,surface area=6280 ft^{2}(OD basis)
Duty=100,000x.98x.287x1000=28.1
Mm Btu/h and steam=27,710 lb/h
Let
us compute U.
ln[(1500366)/(500366)]=Ux6280/(100,000x0.287x0.98)
or U=9.56 Btu/ft^{2}hF
Let
us assume that a scale has formed and the equivalent additional fouling=0.05
ft^{2}hF/Btu. What happens to the performance?
This
will decrease U to: 1/(1/9.56)+.05)=6.5 Btu/ft^{2}hF
This
in turn will affect the exit gas temperature as follows:
ln[(1500366)/(tg_{2}366)]=6.5x6280/(100,000x.98x0.287)
or tg_{2}=630 F
The
duty=100,000x0.98x0.287x(1500630)=24.4 Mm Btu/h and steam generation=24,100
lb/h
Table
below summarises the results.(For more detailed calculations of tube wall
temperatures,heat flux,see my books) Note
that even though the heat flux has reduced due to lower U in fouled condition,the
tube wall temperature is significantly higher!
item  clean  fouled 
fouling factor,ft^{2}hF/Btu  .001  .05 
U,Btu/ft^{2}hF  9.6  6.5 
heat flux,Btu/ft^{2}h  6086  4133 
drop across scale,F  6  207 
tube wall temp,F  377  577 
duty,MM Btu/h  28.13  24.47 
exit gas temperature,F  500  630 
steam flow,lb/h  27,710  24,100 
Effect of scale conductivity on tube wall temperatures
scale  ther cond,Btu in/ft^{2}h  fouling resistance  temperature rise,F 
calcium phospate  25  0.0008  8 
calcium sulfate  16  0.00125  13 
magnesium phospate  15  0.00133  14 
silicate  0.6  0.0333  333 
boiler steel  310  0.00006  0.6 
magnetic iron oxide  20  0.001  10 