Tired of using multiple equations and charts to check the performance of your fired heaters? Use this simple method

Well known published methods are employed to design or

rate fired heaters. These methods are based on the work

done by:

1. Wilson, Lobo & Hottel (1932)

2. Hottel (1938)

3. Mekler (1938)

4. Lobo & Evans (1939) and others

These have a generic equation as below:

Qr = σ Aeffectiveεeffective (Tg4 – Tt

4) + hcAo(Tg

4 – Tt

4)

Where

Qr = Radiant Section Heat Absorbed

σ = Stefan Boltzmann constant

Aeffective = Effective tube heat absorption area

εeffective = Effective emissivity based on source & sink

Tg = Radiating gas cloud temperature

Tt = Absorbing tube metal temperature

hc = Convective heat transfer coefft gas to tube

Ao = Radiant tubes outer surface area

Aeffective and εeffective are decided by excess air level, tube

spacing, fire box geometry etc, involving a trial & error

method employing multiple equations and/or charts to get

the solution.

Lobo - Evans method is based on 85 tests on 19 different

furnaces with excess air ranging from 6 to 170%, heat

transfer rates or flux ranging from 9.5 to 170.3 kW/h.m2

(3,000 to 54,000 Btu/h.ft2) with reradiating refractory

surface 0.45 to 6.65 times the effective tube area. It is

reported to have an error of 5-16%.

The above charts/ methods attempt to relate fired duty

including air-preheat against unit heat transfer rate or flux.

The fired duty can easily be determined separately by the

thermal efficiency chart for the fuel fired and excess air

levels, as shown here.

Modern compact furnaces have a narrow range in design

and operation, for instance excess air from 5 to 40% and

refractory area 0.5 to 1 times effective tube area.

Sample Calculation: Duty = 25 MW; T in/out = 250/375°C.

Xs Air = 20% Radiant Av Flux = 35,000 W/h.m2

Solution: VC Heater. Single side fired. 2 pass - 6"NB tubes.

Exit flue gas approach to inlet fluid temperature = 100°C

Stack gas temperature = 250 + 100 = 350°C

Thermal efficiency - read from chart, 83.5%

Deduct 1.5% casing loss, net efficiency = 82%

Assume radiant duty is 65% of total.

Radiant inlet temperature = 294°C

Average radiant fluid temperature = (294+375)/2 = 334°C

Tube metal temperature, take 50°C above = 384°C

Radiant gas temperature, read from chart = 940°C

Radiant section thermal efficiency, from chart = 53%

Deduct 1.0% firebox casing loss, net efficiency = 52%

Radiant section duty = 52/82 = 63.4% Vs 65% assumed

= 15.85 kW

If you want to size this heater,

Radiant heat transfer area = 15.85e6/35,000 = 453 m2

Radiant coil length = 453/(π*6.625*0.0254) = 856 m

Take 60 tubes, 30 per pass,

• even number; top inlet / top outlet

Each tube, effective length = 14.3 m

Credit for 180° bend, tube weld to weld = 13.8 m

Tube Circle Diameter 60 tubes on 12” pitch on circle

= 60*12*0.0254/ π = 5.8 m

L/D ratio = 2.5

What if there is air-preheat and box heater?

Say flue gas out of air preheater = 200°C

Thermal efficiency - read from chart, 91.5%

Deduct 2% casing loss, net efficiency = 89.5%

Hot air contribution to radiant duty = 89.5 – 82 = 7%

Radiant duty = (52 +7)/89.5 = 65.9% = 16.5 MW

Radiant Tube Area = 471 m2.

Radiant coil length = 471/(π*6.625*0.0254) = 891 m

Take 60 tubes, 30 per pass, Tube C to C = 3.3m

Each tube, effective length = 14.8 m

No credit for 180° bend, tube weld to weld = 14.8 m

With 3 tubes/ pass on roof, 27 tubes/wall on 12” pitch

Coil bank height = 27*12*0.0254 = 8.2 m

W:H:L ratio = 3.3:8.2:14.8 = 1:2.5:4.5 OK

The method shown is good for estimates and thermal

efficiency calculations and studies within accuracy levels

common in heat transfer correlations.

Energy Environment Engineers

Basis: Hydrocarbon Oil or Gas. 15°C Ambient Temperature. No heat loss

Fuel Thermal Efficiency * Orsat Analysis

Fuel

C/H Ratio

Amb

Xs Air, % 10 30 50 100 10 30 50 100

C02, % 14.9698 12.57324 10.83813 8.058081 10.55276 8.786611 7.526882 5.540897

O2, % 2.001389 5.042939 7.245019 10.77326 2.110553 5.271967 7.526882 11.08179

FGT

93.33333 96.55% 96.01% 95.47% 94.12% 96.53% 95.99% 95.44% 94.07%

204.4444 91.50% 90.18% 88.87% 85.57% 91.48% 90.15% 88.81% 85.46%

315.5556 86.30% 84.18% 82.07% 76.77% 86.29% 84.13% 81.98% 76.61%

426.6667 80.93% 77.99% 75.05% 67.70% 80.92% 77.93% 74.95% 67.48%

537.7778 75.40% 71.62% 67.84% 58.38% 75.39% 71.55% 67.71% 58.11%

648.8889 69.74% 65.10% 60.45% 48.85% 69.73% 65.02% 60.30% 48.52%

760 63.96% 58.45% 52.94% 39.16% 63.95% 58.36% 52.76% 38.77%

871.1111 58.11% 51.72% 45.33% 29.35% 58.09% 51.60% 45.11% 28.88%

982.2222 52.19% 44.92% 37.64% 19.45% 52.16% 44.77% 37.38% 18.91%

1093.333 46.23% 38.07% 29.90% 9.48% 46.17% 37.88% 29.59% 8.86%

1204.444 40.24% 31.18% 22.12% 40.16% 30.96% 21.76%

60

Oil & Gas Fuels - Thermal Efficiency

Oil

9.1

Gas

3

50.00%

60.00%

70.00%

80.00%

90.00%

100.00%

10%Xs Air

30%

50%

Flue Gas Temperature, °C

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

80.00%

90.00%

100.00%

0 200 400 600 800 1000 1200 1400

10%Xs Air

30%

50%

100%

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

45.00

50.00

300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500

Av

Flu

x -

ba

sed

on

OD

, k

W/m

²

Tube Metal Temperature, °C

TMT Vs BWT & Flux - Single Side Firing 2D Spacing

1,000°C BWT

950°C

900°C

850°C

800°C

750°C

700°C

650°C