Hot Gases to Electrical Power

Silas,

This is not my normal field, and I suspect that a few power plant engineers will add comments in the next 24 hours or so. However, I believe that typical thermal efficiencies of a steam turbine based electrical power plant have only about 30-40% of the thermal energy content of the fuel being converted to electricity, with about equal losses through the exhaust stack and the cooling tower. There are many methods used to improve the thermal efficiency of a system, such as a second turbine operating at low pressure. The best thermal efficiency occurs when the plant is located so its low-pressure steam can be used for process or building heating applications. When this is done, the overall thermal efficiency rises dramatically.

--JMM

The power station associated with it will have a nominal power output, which is usually in the public domain. Use that figure.

<....2,244,545 lb/hr of exhaust gases....>

It is rare to require an Engineering estimate to be based upon a number with seven significant digits.

It is rare to require an Engineering estimate to be based upon a number with seven significant digits.

Yep! Especially since the efficiency numbers are likely accurate +/- 5%.

Thank all for their responses.

I do not quite understand the 7 significant figures term but what I have is 2.3 million lb/hr of gases at 1990 degrees F.

That is an estimate of the gases produced by an RDF incinerator. If these gases are used to create steam (boiler= efficiency factor #1) that will drive a steam turbine (second efficiency factor) which will drive a generator (third efficiency factor).

Could electrical power output (240V 50 Hz) be calculated given average efficiencies for the boiler, turbine and generator? I have no particular hardware in mind, obviously would prefer ( and willing to pay for) the most efficient hardware.

Silas,

The phrase "significant figures" means how many places or digits were used to express the precision of your number. 2.3 million lb/hr has 2 significant figures, but 2.244 million lb/hr would have 4. The very correct concern mentioned by others is that the type of answer you are asking for has so many assumptions and approximations behind it, that its accuracy is likely to be only about 5% or 1 part in 20. This is an answer with (at best) two significant figures. Therefore, the original posting's giving an input energy with 7 places of precision was way out of line with the possible precision of the answer you wanted.

Remember that the word "precision" refers to how something is stated, but "accuracy" refers to a quite different thing--how reliable or "good" it is.

Back to your original question. 2.3x10⁶ lbs/hr of combustion gases at 1990°F gives an estimated 100MW of electrical output capacity. Here's how I got this, so someone else can see if I've slipped a decimal place or made any significant errors:

1. I don't have any values for heat content of exhaust gases, so I used the specific heats for each of these gases at 25°C, but checked the variation for saturated steam at atmospheric pressure and temperatures of 100-500°C.

2. Exhaust gases are assumed to be 78% N₂, 11% CO₂, and 11% H₂O. This is based on combustion of cellulose with nominal molecular formula of C₆H₁₂O₆ and input air with 80% N₂. C_p for N₂ is 0.25 cal/g/°C, for H₂O is 0.50 cal/g/°C, and CO₂ is 0.20 cal/g/°C. Therefore C_p for exhaust is approximately 0.27 cal/g/°C.

3. Thermal content of exhaust is assumed to be for a temperature change from 1990 to 100 °F, which is 1100 °C. This gives a total thermal content of:

(2.3x10^6 lb/hr)( 4.5x10^2 g/lb )( 0.27 cal/g/deg-C )( 0.0011 W hr )(1100 deg-C) = 3.4 x 10⁸ W.

4. With overall thermal efficiency of 30%, this means an available energy output of 1x10⁸W or 100MW.

Someone please check this number, because I don't normally do this type of engineering calculation.

--JMM

Bravo jmueller.- You please brush up more for now I'd be asking you to help me out with electrical output from exhaust gases of generators & turbines.

Rgds.

Ducon

JMM

Thanks! Your answer covered my question thoroughly, exactly what I was asking !

Thanks again

Silas