Insights into Calculating Boiler Efficiencies
Prospective industrial boiler buyers should question what a boiler’s stated efficiency values are based upon in order to accurately compare products.
Efficiency is the name of the game today, and the boiler world is no exception. If you can squeeze half a percent of efficiency out of a boiler, it can amount to a significant cost savings on an annual basis. It should come as no surprise, therefore, that creative ways of calculating efficiency sometimes are used. Boiler buyers should not be misled, however. There are those methods that have a logical precedent behind them — the heat loss method and the input-output method — and there are those methods that may provide misleading or incorrect information.
One misleading method that may be gaining popularity lately needs to be identified before it can go any further. This method is a modification of the input-output method. It takes the input energy of natural gas (1,020 BTU/ft3) and the energy of the steam output (BTU/lb at a given saturated pressure) and compares them directly to arrive at what has been called fuel-to-steam boiler efficiency. While at first glance this may appear to be a logical approach, a key factor is missing. The energy in this steam — based on the enthalpy of the saturated vapor at its given pressure — is the final state of the steam. The state of the condensate or feedwater being returned to the boiler, however, is not accounted for. This is the critical flaw in this fuel-to-steam method.
All things have an energy associated with them. Those of most interest to the boiler industry are:
• The energy in the fluid on the gas side.
• The energy of the fluid on the water/steam side.
What determines the efficiency of the boiler is how well the energy is transferred between these two fluid flows.
The flue gases lose energy as they pass through the boiler while the condensate/water gains this exact same amount of energy. The energy left over in the flue gases when exiting the boiler is waste. This is the other side of the efficiency equation. This is the first law of thermodynamics at work: energy can neither be created nor destroyed.
A simple example can illustrate this point. Imagine a boiler where the enthalpy of the condensate/water returned to the boiler is neglected. For the purposes of analysis, the following properties of the boiler will be assumed:
• The input firing is 16,000 ft3/hr of natural gas, which equates to an input of 16.32 MMBTU/hr.
• The furnace temperature is 2400°F (1316°C).
• The ambient (combustion) air temperature is 70°F (21°C).
• The operating steam pressure is 90 psig.
• The steam output is 12,400 lb/hr.
Using the method that compares the energy of the gas side directly with the energy of the steam, this results in a 90.1 percent efficiency (table 1).
For our imaginary boiler to operate at 90.1 percent efficiency, the exit temperature of the gases would have to be 325°F (163°C). Now, at a saturated steam pressure of 90 psig, steam has a temperature of 330°F (166°C). This then means that the flue gases leaving the boiler are cooler than the steam being produced. However, in order to obey the first law of thermodynamics with a parallel flow heat exchanger (the industry standard), the flue gases leaving the boiler must be hotter than the steam leaving the boiler; otherwise, energy is being created inside the boiler. Clearly, something is wrong with this calculation.
Now, let us reevaluate this scenario including the enthalpy of the condensate. Assume that the condensate enters the boiler as liquid at 230°F (110°C), and this liquid has an enthalpy of 198 BTU/lb. This would mean that the steam would not gain the full 1,186 BTU/lb as it passed through the boiler; instead, it would gain only 988 BTU/lb. The input energy remains the same as before, but the energy transferred is decreased. Reworking the above problem with this in mind, the flue gases exiting the boiler are now 703°F (373°C). The efficiency is calculated in table 2.
The calculations for the sample system show it is not 90.1 percent efficient; instead, it is 75.1 percent efficient.
Despite the errors associated with the efficiency calculation, it is being used and is affecting engineering specifications. To protect against calculation errors such as this, prospective boiler buyers should question what a boiler’s stated efficiency values are based upon in order to accurately compare products. Before deciding which boiler is the most efficient, do some calculations of your own to determine if the values stated are even physically possible.
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