Looks like an exam problem, something that doesn't belong here.

This is a genuine mass and energy balance problem... Efficiency loss during confiring is known in boilers operation.
 

The original posting does not provide enough information to serve as a basis for any meaningful advice, and I agree with davidbeach that, as stated, it does look a bit like a homework help question even though that may not be the case.

Valuable advice from a professor many years ago: First, design for graceful failure. Everything we build will eventually fail, so we must strive to avoid injuries or secondary damage when that failure occurs. Only then can practicality and economics be properly considered.

Could you be specific about the the alleged missing data here. That's becoming seriously concerning. Two post without a hint off answer....

How did you arrive at the boiler eff values?
What is the feed rate of fuel, heating value of fuel, steam output of the boiler, and so on.
Since the eff is a percentage you cant average them, you need to combing the actual input values and then estimate the effect of mixing fuels.

The other concern is a low boiler eff with coal, sounds like the pulverizers are way out of whack. That needs to be looked into also.

= = = = = = = = = = = = = = = = = = = =
Plymouth Tube

Thanks EdStaubkess for your input!
The Boiler efficiency were obtained from a third party study just after upgrading the boiler.
The boiler was run on respective fuels(Natural Gas, Wood(hog fuel) and the total energy imput was divided by the enthalpy of the steam output (h(T,P))
B_eff=m*GHV*(1-%moisture)/h(T,P).
What do you mean by:
"you need to combing the actual input values"?
Kind regards

Just to correct
The total enthalpy of the steam output (h(T,P)) was divided by the total energy imput
B_eff=h_steam(T,P)/m*GHV*(1-%moisture)

You can't average averages, you need to assign feed rates and heating values for each fuel component.

But first you have understand why there are differences between fuels. Was this very poor coal that was used? low heating value? high moisture? Not correct fineness?

= = = = = = = = = = = = = = = = = = = =
Plymouth Tube

The coal is fine with low moisture content (from QC lab).
I suspect that the coal feeder might be unreliable.
So I was trying to back calculate the coal mass flow rate using boiler energy output with the two other know fuel flow rate and heating values.

No missing important information? What about providing a description of the furnace and steam generator configuration and size? Suspension or stoker firing for solid fuels? Is fluidized bed firing involved? What about burner types? Is multi-stage combustion for emission control purposes involved?

Assuming that this system is for electric power production, what nominal size system is involved? 10 MW, 50 MW, 100 MW, 500 MW, ...? What range of loading conditions form the basis of the plant design, peaking duty, mid-rage, base load, or some blend of these?

If you are really seeking useful advice, you are only hampering yourself by not being as complete as practical in providing information to those from whom you are seeking the help.

Valuable advice from a professor many years ago: First, design for graceful failure. Everything we build will eventually fail, so we must strive to avoid injuries or secondary damage when that failure occurs. Only then can practicality and economics be properly considered.

- I have 3 boilers feeding steam to a main header at 10000kPag/475C... which feeds 1 BPTG@100MVAR and 1 CTG@75MVAR.
- The solid are fire through Stokers, The Natural Gas is through 8 burners controlled by alstom flame pilots.
- The system is for electric power production and process steam generation
- As EdStainless suggested the way to calculate the overall efficiency when co-firing blend of these 3 fuel, is not by averaging efficiencies but knowing the respective flow rate and GHV of each fuel stream.
- The investigation is to assess the accuracy of the coal feeder by back calculating the coal flow rate from energy and mass balance around the problematic boiler.
Thanks you for your suggestions

For clarification, is your configuration three separate boilers with one fired with coal, one fired with wood, and one fired with gas?

Valuable advice from a professor many years ago: First, design for graceful failure. Everything we build will eventually fail, so we must strive to avoid injuries or secondary damage when that failure occurs. Only then can practicality and economics be properly considered.

3 Boilers all capable of firing coal/hog fuel (wood bark)/Natural Gas.
The thermal efficiency study was done by observing the each boiler burning 100% off respective fuel.
During normal operation, the amount and ratio of each fuel (especially Nat. Gas) depends on Power Price and outages...

Can you "isolate" one boiler for testing purposes? What I have in mind is setting up tests to establish the effects of mixed fuel firing in your boilers. Let two of the three boilers handle all of the load variations and operate one at several different mixes of fuel flows for reasonable test periods of about two or three hours while carefully monitoring inputs and outputs for the test boiler. Most likely, gas firing will provide the most predictable results, and wood firing will probably provide the least predictable results. I would structure tests first using constant coal flow with several different constant gas firing rates.

After setablishing an understanding of the performance characteristics of the relationships of mixed gas and coal firing in the boiler, I would then repeat this sequence of test runs using wood instead of coal. After developing an understanding of the gas vs. wood firing characteristics, I would conduct another similar sequence of tests with different constant flow rates of coal and wood.

Since all of these tests can be conducted with the test boiler being fully operational and productive, the marginal costs for these tests should be very modest, and they will provide actual performance characteristic information for your actual system. This empirical information will be far more valuable than any theoretical estimates. No matter how well intentioned, theoretical estimates of boiler performance characteristics are really very elegant guesses. For the test sequences that I am suggesting, you should take care to assure that all of your test instruments are well calibrated and calibration corrections are properly included in your calculations.

Valuable advice from a professor many years ago: First, design for graceful failure. Everything we build will eventually fail, so we must strive to avoid injuries or secondary damage when that failure occurs. Only then can practicality and economics be properly considered.

I would suggest using the LHV lower heating value of the fuels and computing the LHV efficiency of the boiler- this automatically corrects for the varying moisture content of the various fuels.

"Nobody expects the Spanish Inquisition! "