The heat loss method disused in ASME PTC 4.1 may be used for evaluating the efficiency of steam generators. For quick estimates of oil and natural gas fired steam generators, however, the following equations may be used. These equations were arrived at by the author after performing several calculations.

1. Natural gas 

Efficiency (%, HHV) = 89.4 - (0.001123 + 0.0195 * EA)*(Tg - Ta)
Efficiency (%, LHV) = 99.0 - (0.001244 + 0.0216 * EA)*(Tg - Ta)

Tg = exit gas temperatures, degF
Ta = reference air temperatures, degF
EA = excess air, EA = K * 21/(21-O2), K = 0.98 for natural gas 

2. Fuel Oil

Efficiency (%, HHV) = 92.9-(0.001298 + 0.0195 * EA) * (Tg-Ta) 
Efficiency (%, LHV) = 99.0-(0.001383 + 0.0203 * EA) * (Tg-Ta) 

Tg = exit gas temperatures, degF
Ta = reference air temperatures, degF
EA = excess air, EA = K * 21/(21-O2), K = 1.00 for fuel oil

Example-1:

A natural gas fired boiler with 15% excess air has an exit gas temperature of 380 degF, ambient = 90 degF. Determine efficiency on LHV basis. 

EA = 1.15
Efficiency (%, LHV) = 99.0 - (0.001244 + 0.0216 * EA)*(Tg - Ta)
Efficiency (%, LHV) = 99.0 - (0.001244 + 0.0216 * 1.15)*(380 - 90) = 91.4%

Example-2:

A natural gas fired boiler with 3% excess oxygen has an exit gas temperature of 350 degF, ambient = 85 degF. Determine efficiency on LHV basis. 

EA = K * 21/(21-O2) = 0.98 * 21/(21-3) = 1.143
Efficiency (%, LHV) = 99.0 - (0.001244 + 0.0216 * EA)*(Tg - Ta)
Efficiency (%, LHV) = 99.0 - (0.001244 + 0.0216 * 1.143)*(350 - 85) = 92.1%