Gas Turbine Exhaust Heat Recovery (WHR)

[moezcan]

Dear experts,

This is my first year as energy engineer; so I am continuously learning new things... My question is how can I calculate the waste heat potential from the exhaust gases of gas turbine?

For a waste heat recovery project, I need to calculate the waste heat potential of the exhaust gases from the a turbine. So far, I am unable to take measurements; therefore I must make a rough calculation based on gas turbines technical data:
Output Power: 15.290 kW
Heat Rate: 9940 kJ/kWh
Exhaust Flow: 180.050 kg/h
Exhaust Temp: 505 °C
Engine Efficiency: 36,2 %
LHV Natural gas: 9,722 kWh/m³

Since yesterday, I read the posts in the forum; but I am confused.
I calculate Input energy as 42217 kW.
if the engine efficiency is 36,2%, then the heat losses must be 63,8%.
Heat losses (63,8%): Cooling system, radiation, exhaust heat.
This means, the share of exhaust heat must be smaller than 62,8%.

Assuming:
Exhaust temperature:505°C
Dew Point:120°C
deltaT=505-120=385

Exhaust energy must be smaller than 42217*62,8/100 = 26.512,3 kW (in 505 °C)
If the dew point is 120°C, then the usable heat will be lower than 26.512,3*385/505 = 20.212,3 kW

Cp_flue_gas:1,099 kJ/kg-K
m_exhaust:180.050 kg/h = 50,014 kg/s

Q=m*Cp*deltaT
Q_exhaust=50,014*1,099*385 = 21.161.6 kW

So, as you can see based on Cp=1,099 kJ/kg-K, my assumption is wrong. I am looking for a way to calculate exhaust heat potential correctly. Please help me if there is a simple way (any online source, ampyrical correlation etc.)

Kind regards,
Moezcan.

 

[racookpe1978]

But, the only energy you can work is EITHER mass flow (kilogram/sec) inside your exhaust pipe - but you cannot use that exhaust flow directly WITHOUT causing backpressure that will ruin the turbine performance, OR heat flow:
Exhaust Flow: 180.050 kg/h
Exhaust Temp: 505 °C

Thus the only available energy for your heat reciovery is 180 kg/hr (at what thermal capacity for air?) at 505 C. That will be the energy that heat the heat recovery steam generator.

Thumb rules: Usually, you can run one 200 MegaWatt steam generator from two 200MegaWatt gas turbines. You can get one 75-100 MegaWatt steam generator from one 150 CT generator.

I have worked on several 1 CT + 1 ST generators as well, and sometimes the CT is "sized" to serve the heat recovery steam generator entirely: A refinery for example, will build a series of "slightly inefficient" gas turbines tuned so the steam from the HRSG's IS the desired product for the refinery, and the electricity being provided from the CT is simply extra profit, not the desired product.

 

[moezcan]

Hi racookpe, thanks for replying.

Those are catalogue values (V_exhaust 180 kg/s, T_exhaust=505°C); so the ambient conditions are ISO T_amb=15°C, at sea level, relative humidity 60%.

In these conditions, how can I calculate the capacity of my heat recovery steam generator?

 

[davefitz]

Simple estimates can be had if we assume the fluegas heat capacity is Cp=0.255 btu/lb/F and the lowest permitted stack gas temperature is 180 F ( 82 C). The maximum heat available for recovery ( excluding casing radiation loss) in the HRSG is :

Wg*Cp*(505-82)*1.8 = 397 kpph*0.255*423.*1.8= 77.08E6 btu/hr = 22.59 MWth

The steam cycle effiency would need to be separately calculated. If we assumed for estimating purposes it is 33% efficient (steam cycle HR=10,340 btu/KW-hr) then the add'l steam turbine power would be STG output = 0.333*22.59 = 7.45 MWe, gross.

Other losses need to be addressed, today's modern software easily and accurately can be used to configure the combined cycle .

The major cycle losses are the heat rejected at the condenser ( 22.59-7.45= 15.1 MWth) and at the stack (397e3*.255*1.8*(180-60) =21.87E6 btu.hr=6.4 MWth)

"Whom the gods would destroy, they first make mad "

 

[davefitz]

Stack loss is incorrect; it should be 12.1 E6 BTU/hr = 3.55 MWth

"Whom the gods would destroy, they first make mad "

 

[racookpe1978]

That small a turbine (realistically) cannot economically support a HRSG - There just isn't enough hot gas flow to make enough steam quick enough to pay for the expense of buying, building and running a HRSG.

If you can find a use for a little bit of hot air ....