humidity – will have an effect on output and efficiency. Other factors that affect output and efficiency of a gas turbine include: shaft speed, fuel temperature, fuel composition (hydrogen to carbon ratio), the type of fuel – liquid or gas for a duel‐fuel unit – exhaust back pressure, and others. A manufacturer’s performance guarantee for a new unit will be valid only under specified ambient conditions, fuel quality, inlet and outlet pressure drops, running time on the machine, shaft speed, and perhaps others. Results of an acceptance test, conducted to verify a manufacturer’s guarantee, must be corrected to the guarantee conditions specified using the manufacturer‐provided correction curves. Likewise, regular performance monitoring mea- surements and results must be corrected to the same standard conditions for comparison.
That is, the performance of a gas turbine operating in the summer at 33 °C cannot be directly compared to the same machine operating during winter conditions at 2 °C.
Usually, for performance monitoring and analysis:
• the inlet and outlet pressure losses are fairly constant;
• fuel temperature is controlled to a set value;
• pipeline‐quality natural gas composition is nearly constant;
• shaft synchronous speed does not change appreciably; and
• the machine should operate at its specified firing temperature.
Therefore, the three main corrections to standard conditions can often be reduced to
• ambient temperature;
• barometric pressure; and
• relative humidity.
Of these, the primary correction is that for ambient temperature.
3.2.1 Derivative of the Cost Function
The owner has granted access to the CHP plant’s online data historian and you have been able to capture a few months of hourly averages for gas‐turbine temperatures and pressure for one of the units at the plant. This data begins at the end of April and extends to mid‐July. From this data, you have culled the points when the gas turbine was not at 100% load and on the designated firing curve. The unit was removed from service on April 29 for an offline water wash and returned to regular full load service by May 3. The plant is located in the United States. Economic data provided by the owner includes:
• price of natural gas: $4.50/MMBtu ($15.35/MWh);
• discount rate: 11%;
• average market heat rate: 10.27 MMBtu/MWh (10.835 GJ/MWh);
• plant operating HHV efficiency: 53.56%;
• gas turbine and steam turbine output: 284 MW;
• gas turbine gross output: 179.1 MW;
• water wash outage: 48 hours;
• offline water wash fixed labor and material costs: $20 000;
• reference ambient temperature: 50 °F (283.15 K);
• reference ambient pressure: 14.68 psia (101.24 kPa(a));
• average capacity factor: 92%.
Correction curves for the three identical gas turbines at the facility are shown in Figure 3.5, Figure 3.6, and Figure 3.7.
Ratio = –1.831E – 05T2– 7.661E – 04T + 1.085E + 00 0.80
0.85 0.90 0.95 1.00 1.05 1.10
0 20 40 60 80 100
Output ratio
Ambient temperature (°F) Effect of ambient temperature on output
Figure 3.5 Ambient temperature correction.
3.2.2 Exercise 2
1. Correct the measured gas‐turbine output to standard temperature, barometric pressure and relative humidity.
2. Plot the lost gas‐turbine output over the monitored period.
Ratio = −6.661E – 03*BP2+ 2.364E – 01*BP − 1.035E + 00 0.96
0.97 0.98 0.99 1.00 1.01 1.02 1.03
13.5 14.0 14.5 15.0 15.5
Output ratio
Barometric pressure (psia) Effect of ambient pressure on output
Figure 3.6 Ambient pressure correction.
25°F 50°F 75°F 100°F
0.9985 0.9990 0.9995 1.0000 1.0005
1.0010 Relative humidity effect on output
0 20 40 60 80 100 120
Effect on output
Relative humidity (%)
Slope = 7.099E – 07*T2– 6.388E – 05*T + 1.532E – 03 Intercept = −5.026E − 07*T2+ 4.519E − 05*T + 9.989E − 01 Ratio = slope*RH + Intercept
Figure 3.7 Relative humidity correction.
3. Determine an approximate rate of change for the gas turbine output due to compressor fouling.
4. Calculate the lost production costs for a 48‐hour offline water wash.
5. Write a general equation for the losses associated with compressor fouling, and offline water washing.
6. Find the general expression for the optimum period between offline water washes during a year. Calculated the optimum period for the case study.
7. What are the annual saving for scheduling the offline water washes at the optimum cycle period rather than at a 5 MW loss on the gas turbine?
8. Discuss the variability of the test data. What factors may have influenced the scatter in the data and what techniques would you suggest to overcome uncertainties caused by the sample distribution?
3.2.3 Linear Programming
A linear programming model for this case is shown in Figure 3.8. In this method, it is easy to establish that the optimum water wash frequency occurs when the cost of lost generation due to fouling equals the cost to conduct the offline wash (lost production plus fixed labor costs.)
From either method, it is evident that the water‐wash frequency is only a function of the rate of change in output due to compressor fouling. The greater the rate of change, the more fre- quent washes should occur at a constant price of fuel. The challenge, as seen above, was to determine the rate of change given the real nature of the fouling and its variable impact on the output of the machine.
3.2.4 New Methods – New Thinking
Instead of optimizing an existing situation, you may consider another alternative. Optimization assumes that the basic conditions under which a system functions continue. It is not wrong to maintain this assumption. It is, after all, what the gas‐turbine manufacturer assumed given
$0.000
$0.200
$0.400
$0.600
$0.800
$1.000
$1.200
$1.400
$1.600
$1.800
$2.000
60 80 100 120 140 160
Annual costs ($ millions)
Water wash frequency (days) Lost generation Maintenance Total
Figure 3.8 Linear programming solution.
the recommendation to purchase an upgraded water wash system. However, it is not the only alternative.
Another alternative is to assume the constraints of the existing system can be changed.
That compressor fouling is not necessary for the future. That is, a given system of parame- ters does not have to remain the same, regardless of how long the process has continued.
Working to implement a project that changes the given situation can be a better alternative than simply optimizing the given system. As mentioned above, a higher grade filtration system could completely eliminate fouling and the resultant lost generation, and the need for online and offline washes. The reliability of the facility can be improved as well as its long‐term performance.
As stated earlier, the corporation has followed accepted good industry practices for opera- tions and the maintenance of its facilities. However, good industry practices developed over time based on technologies present in the past. Rethinking the constraints provides opportu- nities to improve margins and opens new avenues for corporations to grow their business.
3.2.5 Exercise 3: Gas Turbine Inlet Filtration Upgrade
Analysis of competitive bids from two qualified supplies yielded a lowest evaluated cost of a new filter system of $5 000 000, including removal of the old system, installation, and testing of the new system.
• Determine the net present value of a capital improvement assuming that compressor fouling can be reduced to 10% of the present rate. Use the following inputs:
∘ HEPA filter element life is the same as an F9 filter element: 3 years.
∘ Differential filter cost: $100 000 compared to F9 filter elements.
∘ Filter price escalation: 2.5% per year.
∘ Natural gas and power price escalation: 0.75% per year.
∘ Corporate tax rate: 28%.
∘ Discount rate for evaluation: 11%.
∘ Project life: 20 years.
∘ The filter supplier will install a three‐stage filtration system with a new filter house and connecting duct work during an upcoming scheduled outage. The regularly scheduled outage will need to be extended 18 days to allow for construction.
∘ Under what conditions would you recommend a filter upgrade?
3.2.6 Presenting Results
A presentation of the results of this case‐study analysis can be compressed into a few important points. A breakdown structure of the results can help organize the presentation and identify where the focus should be. Another method might be to create a storyboard of the presentation using the various elements that need to be presented. Writing down the elements on separate pieces of paper and using a magnetic board, you can rearrange the points, eliminate, modify or add points easily until a coherent presentation method is apparent.
There are two efficiency improvement alternatives to consider: one that can be implemented immediately, and the other an option for the near term. Figure 3.9 shows one possible
breakdown structure for the two options showing points to discuss and a suggested order.
Once the topics are clearly presented, your company will have the opportunity to propose working with the client to complete one or both of the alternatives. Having a meeting with the client to discuss the findings, as opposed to a written report only, would create a means to discuss your proposal without interference from competing companies.