6.

2 Boiler Design

1. General
The purpose of this section is to present some of the problems encountered in the
actual design and to offer approximate solutions.
As a demonstration problem we shall assume that it is desired to find the efficiency of
an oil-fired boiler whose plan view is shown in Figure 1. An elevation view would be similar to
the boiler shown in Figure 2 except that the tube size and spacing are different.
Other data will be assumed to be:
Furnace waterwalls and roof: 3-in bare tubes
Convection section: 2-in tubes on 4-in. centers, diamond staggered arrangement
Working pressure: 250 psig
Water entering: 200 F
Air entering and room temperature:: 80 F
Steam leaving: saturated
Radiation and unaccounted-for loss: 3%
Oil heating value: 18,500 Btu per lb
Oil analysis: 84% C, 13% Hs, 2% S, 1% N
Flue gas: 12.5% CO2 on dry basis, corresponding to 20% excess air
Convection section: 32 tubes wide, 126 in. between walls
Furnace section: 18 tubes on front wall, sidewalls, and roofs; water screen in path of
gases to convection zone has tube staggered.
Load: 22,000 lb per hr of steam
An efficiency of 75.7% will be assumed and calculations will be made to check this efficiency.

1
2. Furnace Calculations.
The first step will be to determine the wall areas and the tube surface. To simplify the
problem, the heat transfer to the floor tubes will be neglected and the average tube height for
the wall will be taken as 12 ft. Then the furnace envelope surfaces will be as follows:

Front wall area = 12 x 10.5 = 126 sq ft

Side wall area = 2 x 12 x 10.25 = 246 sq ft
Rear wall area = 12 x 5 = 60 sq ft
Roof area = 10.5 x 10.25 = 108 sq ft
Screen tube area = 12(10.5 – 5) = 66 sq ft

The area of the furnace envelope backed by refractory is 126 + 246 + 60 + 108 = 540 sq ft, and
the envelope area represented by the screen is 66 sq ft.
Since the waterwall tubes are set immediately in front of the refractory, called tangent
refractory, there is radiation to the backs of the tubes from the refractory. Adjustment factors
for the furnace envelope area to account for the tube arrangement and spacing are given in
Figure 3. For the portion of the furnace envelope backed by refractory, the tube spacing (using
data for the front wall) is the distance between the centers of the end tubes (10.5 ft – 0.25 ft)
divided by the tube diameter in feet and divided by the number of spaces between the end
tubes, or
( 10. 5−0 .25 ) 12
=2 . 41 diam.
3×17

2
3
The adjustment factor is 0.81 from curve 5, and the adjusted surface for refractory-backed tubes
is 0.81 x 540 = 437 sq ft. The water screen contains 18 tubes in a distance of 5.5 ft; therefore,
these tubes are on approximately 1.2-diam projected centers (assuming 17.5 spaces). Using
curve 3, the factor is 0.96 and the adjusted surface us 66 x 0.96 = 63 sq ft. Then the adjusted
envelope surface is 437 + 63 = 500 sq ft.

Before the furnace exit gas furnace can be obtained from Figure 4, it is necessary to
determine the available energy. For simplicity, these losses will be charged to the furnace.

Available energy=[ HHV ( 1−Q 7 ) +0. 24 W aa ( t ah −t a ) −1040 ( 9 H 2 ) −14 , 600 ( C−C ab ) ] ( W f )

Where
Q7 = the radiation and unaccounted-for loss expressed as a decimal,
HHV = higher heating value of the fuel, Btu per lb
Waa = actual air, lb per lb fuel
ta = temperature of air surrounding the boiler, F
tah = temperature of the air leaving the air heater or entering the burners, F

Observe that the equation is an expression for the lower heating value of the fuel with
adjustments for preheated air, radiation and unaccounted-for loss, and the loss due to
incomplete combustion.
It is necessary to use the lower heating value of the fuel to determine gas temperatures,
since the latent heat of the water vapor from the combustion of hydrogen in the fuel does not
increase gas temperature. Also, it is impossible for the boiler to condense this vapor and to
make use of it to evaporate water in the tubes. From the combustion analysis of the fuel we find
that there is 6.5% water vapor in the gases by weight and on the wet basis and there is 18.1 lb of
wet gas per lb of wet gas per lb of fuel. By using the higher heating with the assumed boiler
efficiency, the fuel consumption is found to be
22 , 000 (1201 . 7−168 . 0 )
Wf= =1622 lb per hr
0 . 757×18 , 500
Available energy=[ HHV ( 1−Q 7 ) +0. 24 W aa ( t ah −t a ) −1040 ( 9 H 2 ) −14 , 600 ( C−C ab ) ] ( W f )
And
Waa = 18.1 – 1 = 17.1
H2 = 0.13
C- Cab = 0.84 – 0.84
tah = ta = 80 F

Available energy=[ 18 ,500 ( 1−0 .03 )+0. 24 ( 17 . 1 ) ( 80−80 )−1040 ( 9 ) ( 0 .13 )−14 , 600 ( 0 . 84−0 .84 ) ] ( 1622 )
Available energy=27 ,150 ,000 Btu per hr

4
Then the available energy, the abscissa of Figure 4, is 27,150,000 ÷ 500 = 54,300 Btu per sq ft per
hr of adjusted envelope surface. From Figure 4, the gas temperature leaving the water screen
and entering the convection section is 1770 F.

5
 In order to determine the sensible energy of the gases leaving the furnace, the values of
constant pressure instantaneous specific heats are plotted in Figure 5 by using the flue gas
analysis. With these data, a curve of sensible energy above 80 F can be plotted, Figure 6. While
these curves are for the particular flue gas analysis of this problem, they would not materially
different for many other flue gas analyses.

From Figure 6, the sensible energy of the flue gas leaving the water screen is 478 Btu per lb
of gas and the energy transferred in the furnace (Qf) is

6
 Q f =27,150,000−18.1×1622×478=13,130,000 Btu per hr
The amount of water evaporated in the waterwalls is 13,139,000 ÷ (1201.7 – 168) – 12,700 lb
per hr, based on the inlet feedwater temperature.

The total projected area of the furnace envelope tubes is:

3−in. diam
Front wall=18 tubes× ×12 ft long=54 sq ft
12
3−in. diam
Side walls=17 tubes× ×12 ft long×2 walls=102 sq ft
12
3−in. diam
Re ar wall=7 tubes× ×12 ft long=21 sq ft
12
3−in. diam
Roof =18 tubes× ×12 ft long=54 sq ft
12
3−in. diam
Screen=18 tubes× ×10 . 25 ft long=46 sq ft
12
Total projected tube area = 277 sq ft

Therefore the radiant-heat transfer rate is 13,130,000 ÷ 277 = 47,400 Btu per (hr)(sq ft of
projected surface), or 47,400 ÷ π = 15,100 Btu per (hr)(sq ft of outside tube surface).
The assumption of boiler efficiency cannot be checked until the convection-surface
calculations have been complete.

7
3. Convection-Surface Calculations
Inspection of Figure 1 shows that there are 401 tubes in the convection zone. Assuming an
average tube length of approximately 12.5 ft to account for bent tubes and the longer tubes at
the rear of the cavity, the convection zone tube surface will be
2
A o=401 π × ×12 . 5=2625 sq ft
12
Heat transfer in the convection zone takes place both by convection and radiation. For the
convection heat transfer for boiler tubes it is not unusual to neglect the resistance of the water
film inside the tubes and the resistance of the metal; Uo then becomes equal to h from Table 1,
Eq. F.

8
 The area between tubes that is available for flow of the gases varies throughout the
convection zone, but at any point the area is the number of tube spaces times the width and
height of each space. Because of the tube bends, the length of the area will be smaller than the
tube length; take 12 ft as the length of the area. The first convection row is 5 ft 5 in. long and
must contain 17 tubes or 16 spaces. The area is
2 in. width
16 spaces× ×12 ft high=32 sq ft
12
For the next to the last row, the area is
2 in. width
7 spaces× ×12 ft high=14 sq ft
12
The average area of 23 sq ft will be used. A more exact method would be to design each section
separately.
The gas flow is 1622 x 18.1 = 29,400 lb per hr and the density is
P 144×14 . 7
ρ0 = = =0 .0808 lb per cu ft
RT 53 .3×492
Then the mass flow based on the average flow area is
29 , 400
G= =0 .356 lb per ( sqft ) ( sec)
3600×23
G 0 . 356
V 0= = =4 . 4 fps
ρ0 0 . 0808
0. 91 V 00 . 69 0 . 91 ( 4 . 4 )0. 69
U 0 =h= = =4 . 41 Btu per ( hr ) ( sqft ) ( F )
D0 .31
( ) 2 0. 31
12
The next step is to estimate the final gas temperature so that the LMTD may be calculated.
Since the furnace was calculated to evaporate 12,700 lb per hr, the convection zone should
evaporate 22,000 – 12,700 = 9,300 lb per hr. Each pound of flue gases should then transfer to
the tubes in the convection zone by radiation and convection.
9300 ( 1201 .7−168 . 0 )
=328 Btu per lb
1622×18 . 1
The energy of the flue gases entering the convection zone was calculated to be 478 Btu per
lb. Then the energy leaving the convection zone will be 478 – 328 = 150 Btu per lb. From Figure
6, this would represent a temperature of 670 F.
This flue gas temperature is too high for an economical steam generator as it is 264 F above
the saturated steam temperature of 406 F. For typical conditions, the exit flue gas temperature
should be roughly 100 above the saturation temperature.
If the tube temperature is taken to be the same as the water temperature (406 F), in
accordance with previous assumptions of negligible resistance through the water film and the
metal, LMTD is
1770−670
θm =LMTD= =669 F
1770−406
ln
670−406

9
Convection heat transfer is
Qc =U 0 A 0 θm=4 . 41×2625×669=7 , 740 ,000 Btu per hr

Gases radiate and absorb energy at intermittent wave-length bands. Radiation in the
infrared band from gases has been recognized as important to the design of some heat-transfer
apparatus. While the radiation considered for the furnace is from luminous flames and
suspended particles, the convection-zone radiation is from inactive nonluminous gases that are
not undergoing a chemical change and that carry very little, if any, suspended solids.
Of the constituents in the flue gases, carbon dioxide and water vapor are the only ones that
have sufficiently strong radiating characteristics to merit consideration. Sulfur dioxide and
carbon monoxide have strong radiating tendencies but usually are present in flue gas in such
small quantities that they need not be considered.
The radiation from gases containing carbon dioxide and water vapor may be approximated
by

[ ( ) ( )]
Tg 4 4
T
Qr =0. 1723 Aε s ε g −α s
100 100
In which
Qr = heat transfer by radiation from gases, Btu per hr
A = outside tube surface area, sq ft
Es = tube emissivity, 0.80 for boiler and superheater tubes
Eg = emissivity of the gases at temperature Tg
Tg = absolute gas temperature, R
A = emissivity of the gases at temperature Ts
Ts = absolute tube surface temperature, R

When the gases are at standard atmosphere, as is the case in nearly all boilers, the gas
emissivities can be evaluated (other assumptions for these equations are that PcL + PwL < 0.3 and
that Tg/Ts > 1.25)
ε g =ε cg +ε wg C w
And α =ε cs +ε ws C w
In which
cg = emissivity of carbon dioxide at temperature Tg from Figure 7.
wg = emissivity of water vapor at temperature Tg from Figure 8.
cs = emissivity of carbon dioxide at temperature Ts from Figure 7.
wg = emissivity of water vapor at temperature Ts from Figure 8.
Cw = correction factor for water vapor emissivity from Figure 9.

The average gas temperature may be estimated from the equation

t +t
T g =460+θm + 1 2
2

10
Where
m = log mean temperature difference between gas and surface, F
t1 and t2 = surface temperature at sections where fluid enters and leaves tubes, respectively, F.

11
 In the convection zone, water is being evaporated and therefore the tube-surface
temperature is constant throughout the zone. This would not be true for superheaters or
economizers. Also, it is sufficiently accurate to say that the tube-surface temperature is the
same as the water and steam temperature within the tube.
Observe that the values c and w, shown in Figure 7 and Figure 8, are plotted with values of
PL as parameters. For each set of curves, P is the partial pressure of the gas expressed in
atmospheres and L is the radiant beam length for the gas, expressed in feet. Subscripts c and w
indicate carbon dioxide and water vapor, respectively, as before. Values of L should be
determined from the expressions given in Table 2.

Parameters of PL are also used in Figure 9. This graph accounts for the effect of the water-
vapor partial pressure on radiation.
The tube-surface temperature for our problem is 406 F and the mean gas temperature is
T g =460+669+406=1535 R
Or
t g =1075 F
Partial pressure of gases are proportional to the volumetric analysis of the wet gas. In this
case we have 11.2% carbon dioxide and 10.4% water vapor. Therefore, evaluating L from Table 2
as 2/12 x 2.8, we get

12
 2
Pc L=0. 112× ×2. 8=0. 0523
12
2
Pw L=0 .104× ×2.8=0. 0486
12
And

13
 From Figure 9, Cw = 1.08. For a temperature t, of 406 F and PwL = 0.0486, ws is 0.064 from
Figure 8. Finding other values in similar manner, we get,
α =ε cs +ε ws C w

α=0 . 055+0 . 064 ( 1 .08 )=0 . 124

And
ε g =ε cg +ε wg C w
ε g =0 . 062+0 . 039 ( 1 . 08 )=0 . 104
Using these values,

[ ( ) ( )]
Tg 4 4
Ts
Qr =0. 1723 Aε s ε g −α
100 100

[ ( ) 1535 4
( )]
4
866
Qr =0. 1723 ( 2625 ) ( 0 .80 ) 0. 104 −0 . 124
100 100
Qr =1 , 835 , 000 Btu per hr

The total energy transferred for the entire boiler is

14
 Q=Q f +Qc +Qr

Q=13 ,130 ,000+7,740 ,000+1,835 ,000

Q=22,705,000 Btu per hr

And the evaporation is

22 , 705 ,000
=21 , 950 lb per hr
1201 .7−168 . 0

This shows that the assumed efficiency was correct. However, the temperature of the gases
entering the convection zone is low. A more economical unit would have less waterwall surface
and more convection surface to reduce the final flue-gas temperature.

Observe that the energy transferred by radiation from nonluminous gases in the convection
zone amounts to about 20% of the heat transfer in this zone.

4. Secondary Surface
Calculations for surfaces of the convection type of superheater, economizer, and tubular air
heater follow the same procedures that were used for the convection zone. Gas, air, and steam
film coefficients may be determined from Table 1. Water film coefficients for economizers offer
only token resistance to the flow of heat and may be neglected for economizers. Similarly, the
metal in the tube walls may be disregarded in calculating the heat flow.

Nonluminous radiant heat transfer from the water vapor and carbon dioxide in the flue
gases will amount to a small percentage of the total heat transfer for economizers and air
preheaters.

For secondary surface, the flow of water, steam, air, or gas is customarily given as the mass
flow in units of pounds per (hour) (square feet of flow area).

Superheaters, air heaters, and economizers use 2- or 2 1/2 - in. OD tubes. These tubes may
be placed on approximately 3- to 9-in. centers in superheaters. The wider spacing is to reduce
the possibility of slag bridging across the space. With either pendent or horizontal superheater
designs, the tubes are in-line and form several passes. Mass gas flows range from 1500 to 3000
lb per (hr) (sq ft) while mass steam flows are from 200,000 to 300,000 lb per (hr)(sq ft). Mass
steam flows may be higher, up to 700,000 or more, for very high-temperature superheaters.

15
 Air preheater tubes should have the air on the outside of the tubes to prevent plugging from
soot in the gases. In this way staggered tubes may be used effectively. The tubes are of either
No. 12 or No. 14 BWG (0.109 in. or 0.083 in., respectively) thickness and are arranged for at
least ½ in. space between tubes. Mass gas flows are from 5000 to 10,000 and mass air flows are
from 3000 to 5000 lb per (hr) (sq ft).

Economizers, being of the continuous tube design, are arranged with tubes in-line, and
there are many water passes. The tubes are on centers that provide 1 ½- to 2-in. lanes for gas
flow. The spacing parallel to the gas flow ranges from 1 to 3 in. Water velocities in the tubes
range from 3 to 8 fps and the mass flow of gases is about 4000 to 7000 lb per (hr)(sq ft).

5. Assignment

Assume that the pulverized coal furnace is rectangular in plan and elevation views. The
waterwalls are of 3-in. tangent tubes. Include floor surface (assume flat, horizontal floor) and calculate
temperature of the gas leaving the furnace, the heat transfer per hour for each square foot of projected
surface, the heat release per cubic foot of furnace volume, and the steam produced if the downcomers
carry saturated water.

Steam pressure, psia - 1650

Fuel, quantity, tons per hr - 49

Kind - Ill.l Christian

Furnace, height, ft - 70

Depth, ft - 27

Width, ft - 31

ta, F - 80

tah, F - 550

Radiation and unaccepted for - 1.8%

Excess air, % - 19

16