Tools › Fluids and Heat Transfer › Thermodynamic Cycles › Steam System and Boiler Efficiency › Example

50,000 lb/h natural-gas boiler at 150 psig: heat-loss efficiency from 3 % O2 and a 450 °F stack, blowdown and deaerator balance, trap, insulation and backpressure-turbine savings

Tool	Steam System and Boiler Efficiency
Source	Department of the Army (1989). Central Boiler Plants. TM 5-650, Tables 1-4 to 1-8 (fuel analyses) and Appendix D (blowdown arithmetic); U.S. Department of Energy, Advanced Manufacturing Office (2012). Energy Tips: Steam, Steam Tip Sheets #1, #2, #4, #9, #10, #15, #20 and #22. DOE/GO-102012-3401 to 3410; International Association for the Properties of Water and Steam (2007). IAPWS R7-97(2012).
Level	Professional

Problem

A boiler burns the natural gas of TM 5-650 Table 1-4 (C 70.8 %, H 23.4 %, N 3.8 %, O 1.2 %, CO2 0.8 %, HHV 21,700 Btu/lb) with 3 % oxygen in the dry flue gas and a 450 °F stack, 80 °F combustion air at 60 % humidity, 1 % radiation and 0.5 % unaccounted losses. It delivers 50,000 lb/h of saturated steam at 150 psig; 60 % of it returns as condensate at 180 °F, the makeup is 60 °F water of 150 ppm TDS against a 3,000 ppm boiler limit, the deaerator runs at 5 psig and the blowdown flashes to it. Find the efficiency by the heat-loss method, the blowdown, makeup and deaerator steam, the fuel input and its annual cost at $8/MMBtu for 8,000 h, the fuel cost of steam, the loss of one 1/8-in trap stuck open at 150 psig, the loss of 100 ft of bare 2-in line and the saving of 1.5 in of insulation, and the power a backpressure turbine (50 % isentropic, 95 % generator) would recover from 20,000 lb/h let down to 15 psig against purchased power at $0.06/kWh.

Inputs to Enter

Fuel: natural gas (TM 5-650 Table 1-4), excess air from 3.0 % O2 dry, no CO, no unburned carbon, stack 450 °F, air 80 °F at 60 % RH, radiation 1.0 %, unaccounted 0.5 %, $8.00/MMBtu, 8,000 h/yr
Steam: 50,000 lb/h at 150 psig saturated; deaerator 5 psig, vent 0.1 %; condensate 60 % at 180 °F; makeup 60 °F, TDS 150 / 3,000 ppm; flash tank 5 psig; no drain exchanger, economizer or preheater; water $4.00 per 1,000 gal; 30 ppm residual of a 40 % product at $2.00/lb
Traps and pipe: 1 failed trap, 1/8 in orifice, C_d 0.72, line 150 psig; 2.375-in OD pipe, 100 ft, 75 °F ambient, bare ε 0.8, 1.5 in of insulation at 0.31 Btu·in/(h·ft²·°F), jacket ε 0.1
Turbine: 20,000 lb/h to 15 psig, η_s 50 %, η_g 95 %, $0.06/kWh

Open the Steam System and Boiler Efficiency tool (loaded with this example)

Answers

Excess air 15.03 % (theoretical air 16.12, actual 18.55 lb per lb of fuel; dry CO2 10.16 %); losses dry gas 7.24 %, fuel water 11.73 %, air moisture 0.19 %, radiation 1.0 %, unaccounted 0.5 %: η = 79.34 % HHV (combustion efficiency 80.84 %, LHV basis 88.27 %, LHV 19,505 Btu/lb)
Blowdown 1,047 lb/h (1.87 % of the 55,876 lb/h feedwater, 20 cycles), makeup 20,947 lb/h, deaerator steam 4,829 lb/h (8.8 % of the 54,829 lb/h generation), flash 14.9 % = 156 lb/h; boiler duty 55.01 MMBtu/h, fuel input 69.33 MMBtu/h = 3,195 lb/h, $4,437,303.18 per year; fuel cost of steam $10.09 per 1,000 lb (effective $11.09); blowdown heat lost to the drain 0.149 MMBtu/h = $12,031 per year
Trap: Napier 0.72 × 0.01227 in² × 164.7 psia / 70 × 3,600 = 74.84 lb/h (Tip Sheet #1 table 75.8), $6,040 per year; bare 2-in pipe 581 Btu/(h·ft) (509 MMBtu/yr per 100 ft at 8,760 h; Tip Sheet #2 table 480), insulated 50.0 Btu/(h·ft) at a 114.5 °F jacket, saving $4,287 per year
Turbine: h_1 1,196.0, h_2s 1,066 (x 0.896), work 65.0 Btu/lb, 19.05 kW per 1,000 lb/h shaft (18.3 at 96 %, the Tip Sheet #20 line), 361.9 kW, 2,895,000 kWh/yr; 7.1 % more boiler steam for the same process heat, generated power $0.0397/kWh (Tip Sheet #20 form $0.0362), saving $58,757 per year

Notes

The tool's default inputs are this boiler; press Submit. The boiler is illustrative (stated on the page); the fuel is the TM 5-650 analysis, the trap, insulation, steam-cost and turbine figures are the DOE tip-sheet methods checked against their printed examples, and every balance is checked by test_steam_boiler_efficiency.php (524 checks) against an independent numpy script, the NIST WebBook water tables and the TM 5-650 Appendix D examples (References/Steam-Boiler/).