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HEAT TRANSFER IN THE RADIANT SECTION OF PETROLEUM HEATERS (part2): 1 - 2 - 3 - 4

 
 

EXAMPLE

Find the total net heat input (i.e., the enthalpy of the incoming fuel and air above 60° F., water as vapor) to the following furnace :

Data
Dimensions of combustion chamber 15' x 30' x 40'
Tube outside diameter 5: O.D.
Center to center spacing 10"
Number of tubes in section 90 arranged in a single row
Circumferential tube surface 4710 sq. ft.
Total wall area, Ar 4300 sq. ft. *
Conditions
Net heat input to oil 70,650,000 B.t.u./hr.
Desired radiant rate 15,000 B.t.u./hr./sq.ft. circumferential surface
Cracked gas fuel 20,000 B.t.u./lb. (L.H.V.)
Excess air 30%
Temperature of air leaving preheater 460° F.
Estimated tube skin temperature 1000° F.
Calculation of effective surface, aAcp Reference
Center to center distance/tube O.D. 2
a to one row 0.88 Fig. 5
Acp = (90 tubes)(10"C/12)(40' long) 3,000 sq.ft. of Acp
aAcp = 0.88(3000) 2,640 sq.ft. of aAcp
Calculation of exchange factor, f
Radiant section dimension ratio, 15/15 x 30/15 x 40/15 = 1 x 2 x 2.67
L = 2/3(volume)1/3 = 2/3(15x30x40)1/3 17.5 feet Table I
P, partial pressure CO2 + H2O 0.22 atmospheres Fig. 7
PL = 0.22(17.5) 3.84 (atm.) (ft.)
Assume tg (temp. flue gas leaving) 1,800° F.
PF, flame emissivity 0.495 Fig. 6
AR = Ar-aAcp = 4300-2640 1,660 sq.ft.
AR/aAcp = 1600/2640 0.63
f = 0.56 Fig. 8
q/aAcpf = 15,000(4710/2640)(1/0.56) 47,900 B.t.u./hr./aAcpf
Calculation of Total Net Heat Input Results Reference
tg 1,850° F. Fig. 2
PF, as previously calculated ** is close enough 0.495
t'F at 30% excess air, 460-60=400°
air preheat, 1850° F. tg 3,620° F. Fig. 3
0.98 H/aAcpf 94,000 B.t.u./hr./aAcpf Fig. 2
H/aAcp (94,000/0.98) x 0.56 53,700 B.t.u./hr./aAcp
H = Total net heat input (53,700)(2,640) 142,000,000 B.t.u./hr.
* Area of opening to convection section equals 200 sq.ft. so Ar = 4500-200.
** When assumed temperature of flue gases leaving radiant section is in
error by 100° or more, PF and f should be revised.

RESULTS

The results of the investigation are summarized in Tables II and III. Table II gives the characteristics of the furnaces studied and the ratio of the actual heat to the oil to that calculated by the proposed theoretical equation, as well as by the empirical equation of Wilson, Lobo and Hottel. Sketches of the general types of furnaces studied are shown in Figures 16 through 22 in the Appendix. These should be considered as diagrammatic only.
 

Table II. - Characteristics of Furnaces and Tests
Total Total Mean Ratio:
Tube Circum Effective Furnace Effective Length
Outside Tube ferential Tube Wall Refractory Ratio Radiant Air Flue Gas No.of Actual/Calculated
Furnace Diameter Spacing TubeArea Area Surface Surface AR/Acp Beam Preheat Recirculation Fuel Tests Heat to Oil
(h) (g)
Symbol General O.D. C-C Ac aAcp AT AR   L         Empirical Theoretical
Unit Type Inches Inches Sq.Ft. Sq.Ft. Sq.Ft. Sq.Ft.   Feet         Equation Equation
*1 A 5 10 2,389 1,340 3,080 1,740 1.30 14.3 Yes & No Yes & No Gas 16 1.03 1.02
*2 B 4 6.75 1,496 756 3,271 1,515 2.00 19.6 Yes No Oil 17 0.93 0.94
*3 C 5 10 2,945 2,255 3,855 1,600 0.71 17.0   No Gas 10 0.95 0.99
4 B 5 10 2,394 1,343 4,277 2,934 2.18 17.8 Yes No Gas 7 0.94 0.97
*5 D 5 17.3(a) 4,443 2,303 3,362 1,059 0.46 24.0(c) Yes No Gas 3 0.92 1.00
6(d) E 5 9 3,060 1,608 3,174 1,566 0.97 12.8 No No Gas 2 1.02 0.99
7(d)#1 E 5.5 9.75 12,467(b) 3,610 6,560 2,950 0.82 22.2 No No Gas 1 1.18 1.11
7 #2 E 5 9.25 7,153 3,698 6,560 2,862 0.77 22.2 No No Gas 1 1.11 1.14
*8 F 4 8.75 284 216 1,628 1,412 6.55 11.2 No No Gas 7 1.04 0.98
9 B 5 8.75 4,775 1,844 2,976 1,132 0.61 14.7 Yes No Gas 4 1.04 1.03
10 G 4 8.75 1,347 465 1,875 1,410 3.04 11.2 No No Oil 3 0.94 0.99
11 G 4 8.75 1,466 498 1,608 1,110 2.23 8.28(e) No No (f) 3 0.77 1.07
12 B 5 8.75 2,314 1,197 3,423 2,226 1.86 15.9 No No Oil 2 0.98 1.08
13 D 5 10.25 5,780 2,108 3,333 1,225 0.58 22.5(c) Yes No Gas 1 1.02 0.99
14 D 5 10.25 5,780 2,108 3,049 941 0.45 22.5(c) Yes No Gas 1 0.94 0.91
15 D 5 10.25 2,890 1,928 3,067 1,139 0.59 22.5(c) Yes No Gas 1 0.99 0.93
16 D 5 10.25 5,780 2,108 3,049 941 0.45 22.5(c) Yes No Gas 1 0.99 0.98
17 B 5 8.75 1,718 887 2,369 1,482 1.67 13.2 No No Gas 1 0.92 0.94
18 B 5 8.75 1,867 965 2,143 1,178 1.22 12.6 No No Gas 3 0.96 1.02
19 E 5.5 9.25 3,616 1,820 3,885 2,065 1.14 17.1 No No Oil 1 0.90 1.08
FOOTNOTES :
(a) Two rows with center lines 2.62 inches apart.
(b) Double row of tubes.
(c) Circular furnace, L = diameter.
(d) Double radiant type furnace.
(e) L = 1.8 (minimum distance).
(f) Products of combustion from furnace No. 10.
(g) Wilson, Lobo, and Hottel Empirical Equation.
(h) For sketches of general type of furnace see Figs. 16 through 22 in the Appendix.
* Furnaces used by Wilson, Lobo and Hottel (2).

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