Thermal efficiency of a gas turbine in industry 2

[somacast]

Hello ,

I was asked by my supervisors to find out the efficiency (I believe they mean the thermal efficiency) of a newly installed gas turbine in our plant, as they want to compare against the old one and against the datasheets supplied, and as I used to like thermo and power plants subjects back in days (graduated 12 years ago) and as we do everything in our sections (you can work for years on piping and all of a sudden you are in a totally different issue such like this), I remember that gas turbines do operate on the basis of brayton cycle, so I read a little about it and I almost remembered it now.

However my question is : this brayton cycle is about the ideal gas, however what I have here is a real case and a fuel burning in a combustion chamber etc, I do have fuel composition and mass flow rate of it, I do have the exhaust temperature, and I guess I can get something from datasheets once received about the compression ratio (not sure though), and I do have T3 after the burning, it is a GT used to drive a compressor in the process, and without regenerator or heat recovery just an open cycle (air in , compress, burn, expand , and exhaust).

so what do I have to do? I would appreciate any real life case solved not the too basic theoretical cases shown in many youtube videos.

Thank you very much.

 

[davefitz]

There are many asme technical papers and also many published books on this subject, and if you wanted to develop a sophisticated real time monitoring system then you would need to consider readign these. Also, there is an ASME test code PTC 22 that you can use to document a performance test of the gas turbine, but you would likely need to add and calibrate some test instrumentation . Fortunately there now exists remote monitoring wifi attachemnts to many test instruments which would simplify routing the instruments' signals to the monitoring PC. I would suggest obtaining a copy of ASME PTC 22 and review that to see if you can apply it to your case.

On the simplest level, if the CTG work output is based on generating electricity, a simple first law estimate would be the efficiency is roughly the electrical output MWe divided by the fuel heat input expressed in MWth.

A slight improvement might be to asssume the air and combusted gases behave as "perfect gases" wherein their internal energy is independent of pressure and is only a function of temperature, and thus the compressor work penalty is expressed as MWc=Wa*Cpa(Tco-Tbm), where Wa= compressor bellmouth airflow, Tco = compressor air outlet temp, and Tbm = bell mouth inlet air temp, and Cpa= air heat capacity. The turbine total power output would be estimated as MWt=(Wa+Wf)*Cpg*(Ttit-Tto), where Wf is fuel flow rate, CPg is the heat capacity of the combusted gases, Ttit is the turbine inlet temperature, and To-s the exhaust temperature. The net useful shaft power output from the machine would be estimated as MWn= MWt-MWc-MWa, where the MWa is the auxiliary components power loss ( from OEM data sheet). None of these simplified calcs can be used for anything other than estimates, and the full ASME PTC 22 test protocol woudl need to be used for commercial purposes.

"...when logic, and proportion, have fallen, sloppy dead..." Grace Slick

 

[MFJewell]

I was going to chime in, but I think Dave said everything I was going to say. All of my experience is in power utility project development engineering when we were evaluating various gas turbines for selection.

 

[davefitz]

You can calculate the airflow if you have an accurate reading of the fuel flow , fuel analysis, and the exhasut oxygen ( or CO2) content. Refer to the asme power test codes PTC for the method of calculating lb air/lb fuel knowing the exhuast O2 level.

The net power to the driven compressor can be estimated using the described "perfect gas" approximation.

"...when logic, and proportion, have fallen, sloppy dead..." Grace Slick

 

[somacast]

@davefitz : thanks alot , I wiil see what I can do about it

 

[georgeverghese]

Another approach would be as follows, which doesnt require detailed calcs on the GT side:

a) Estimate the power absorbed by the process gas compressor, MW
b) Add on other power demands from gearboxes, dynamic gas seals, couplings etc to get to total power at the LP power turbine shaft, MW
c) Heat rate due to combustion of fuel gas at GT = (fuel gas flow in sm3/sec) x (LHV in MJ/sm3)

Net GT eff = Power derived at (b) / GT Heat rate derived at (c).

 

[somacast]

@georgeverghese : thanks a lot , I can see that you have ignored the mass flow of the air to the combustion chamber, is it due to its low enthalpy compared to the LHV of fuel ?? thanks.

 

[somacast]

Also I have another question please , about the efficiency of the driven (the propane compressor), how to find its efficiency here?

I do have the actual conditions at which it operates, the pressure and temperature in and out, I have flow in m3/s and flow out in m3/s ,

I tried to find first the mass flow m. = P x v / R x T

and the work required to drive it = m. x (h out actual - h in) = m. x Cp (T out actual - T in)

however iam getting weird figures for work , I need some help here please, I used the inlet v to calculate the inlet m.

can someone explain to me how to get efficiency ?

 

[georgeverghese]

In this approach to get the turbine eff, the air rate to the combustion chamber doesnt matter - the overall turbine eff includes the debit from the GT side air compressor, and the only energy input is the chemical energy released on combustion of the fuel gas. This is the approach taken by oil/gas process engineers when having to monitor GT performance and from there to get an estimate of GT fouling to get forecast plans for GT scheduled maintenance.

There is too much to explain how you'd get the propane compressor's absorbed power - pls read up your college / university texts on how compression power for centrifugal compresors is obtained, which involves some knowledge of engineering thermodynamics. You also need to have the polytropic compression efficiency curves at various speeds from the compressor vendor in order to do these calcs. Polytropic eff varies with compressor speed, feed flow and gas mol wt.

 

[somacast]

Thank you very much