Evaluating Fuel Quantity Required to Raise Turbine Exhaust Gas Temperature

Evaluating Fuel Quantity Required to Raise Turbine Exhaust Gas Temperature

The following example shows how this is done. A computer program is ideal for this exercise as one has to obtain a rough estimate of the fuel quantity and fine-tune it using the enthalpy of the exhaust gas obtained after combustion. The gas analysis will vary with the firing temperature assumed, and hence several iterations may be required. However, the following manual calculation shows the procedure.

Example 1.8

Let us compute the fuel quantity required to raise the temperature of 500,000 kg/h of gas turbine exhaust gases from 500°C to 800°C and the final exhaust gas analysis.

Exhaust gas analysis entering the burner is % volume CO 2 = 3, H 2 O = 7, N 2 = 75, and

O 2 = 15. Fuel analysis is: methane = 97%, ethane = 2%, and propane = 1%. HHV = 55,335 kJ/kg and LHV = 49,867 kJ/kg.

Solution

This is a trial and error process. One has to assume the fuel input, perform combustion calculations and arrive at the exhaust gas analysis, calculate the gas enthalpies at inlet and exit of the burner, and do the following energy balance:

W 1 h g1 +Q f = (W 1 +W f )h g2 (Q f in kJ/h, h g1 ,h g2 in kJ/kg) where

W 1 ,W 2 are the exhaust gas flows entering and leaving the burner, kg/h h g1 ,h g2 are the enthalpies of the exhaust gas before and after the burner

Note that the gas analysis will be different after combustion, and hence a few iterations are required to obtain the gas enthalpy, which is again a function of gas analysis and temperature. Also,

W 2 =W 1 +W f

where W f is the fuel flow, kg/h. Let us first convert the incoming exhaust gas analysis from volumetric to mass basis.

MW = 0.03 × 44 + 0.07 × 18 + 0.75 × 28 + 0.15 × 32 = 28.38

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Fraction weight of CO 2 = 0.03 × 44/28.28 = 0.0465, H 2 O = 0.07 × 18/28.28 = 0.044.

N 2 = 0.75 × 28/28.38 = 0.74 and O 2 = 0.15 × 32/28.38 = 0.169.

Enthalpy at 500°C: From Table F.11, h g1 = 0.0465 × 118.2 + 0.044 × 231 + 0.74 × 124.5 + 0.169 × 113.8 = 127 kcal/kg = 531.75 kJ/kg. Mass of CO 2 in incoming exhaust gases = 0.0465 × 500,000 = 23,250 kg/h. Mass of H 2 O = 0.044 × 500,000 = 22,000 kg/h. Mass of N 2 = 0.74 × 500,000 = 370,000 kg/h. Mass of O 2 = 84,750 kg/h by difference.

Now convert the fuel analysis to mass basis. MW f = 97 × 0.16 + 2 × 0.3 + 1 × 0.44 = 16.56. Fraction weight of CH 4 = 97 × 0.16/16.56 = 0.937. C 2 H 6 = 2 × 0.3/16.56 = 0.036 and C 3 H 8 = 1 × 0.44/16.56 = 0.027. Let the burner duty = 160 GJ/h on LHV basis. (One may estimate the burner duty as W g × 1300 × (800 – 500) GJ/h where 1300 refers to the approximate specific heat of the flue gas in J/kg°C. Here Q = 195 GJ/h). But let us continue with our assumed value of 160 GJ/h and see what the final temperature is.

W f = 160 × 10 6 /49,867 = 3,208 kg/h. CH 4 in fuel = 0.937 × 3208 = 3007 kg/h. C 2 H 6 in fuel =

0.036 × 3208 = 116 kg/h and C 3 H 8 = 0.027 × 3208 = 86.6 kg/h. CH 4 of 1 kg requires 3.99 kg of oxygen for combustion from Tables 1.1 and 1.2. So

3007 kg/h requires = 11,998 kg/h. Similarly 1 kg of C 2 H 6 requires 3.725 kg oxygen and so 116 kg/h requires = 116 × 3.725 = 432 kg/h and C 3 H 8 requires = 86.6 × 3.629 = 314 kg/h oxygen. Hence, oxygen in exhaust gas after combustion will be reduced and will be 84,750 – 11,998 – 432 – 314 = 72,006 kg/h.

Similarly, CO 2 formed due to combustion of the fuel = 3007 × 2.744 + 116 × 2.927 + 86.6 × 2.994 = 8850 kg/h. After the burner = 23,250 + 8,850 = 32,100 kg/h.

H 2 O after combustion = 3007 × 2.246 + 116 × 1.798 + 86.6 × 1.634 + 22,000 = 29,105 kg/h

Hence products of combustion contain CO 2 = 32,100 kg/h, H 2 O = 29,105 kg/h, N 2 = 370,000 kg/h and O 2 = 72,006 kg/h. Total = 503,211 kg/h. Converting to mass fractions, CO 2 = 32,100/503,211 = 0.0637, H 2 O = 29,105/503,211 = 0.0578, N 2 = 370,000/503,211 = 0.7353, and O 2 = 72,006/503,211 = 0.143. From energy balance around the burner, neglecting heat losses,

500,000 × 531.75 + 160 × 10 6 = 503,208 × h g2 or h g2 = 846.32 kJ/kg = 202.1 kcal/kg. h g2 from the earlier flue gas analysis at 800°C = 0.0637 × 205.4 + 0.0578 × 391.6 + 0.7353 ×

207 + 0.143 × 190.7 = 215.2 kcal/kg. Hence exhaust gas temperature after firing is short of 800°C. Hence another iteration is required. From computer program, one can show that the fuel input required is 189 GJ/h on LHV basis.

W f = 189 × 10 6 /49,867 = 3,790 kg/h; CH 4 = 0.937 × 3,790 = 3,551 kg/h, C 2 H 6 = 0.036 × 3,790 = 136 kg/h and C 3 H 8 = 102.3 kg/h

O 2 required = 3551 × 3.99 + 136×3.725 + 3.629 × 102.3 = 15,046. O 2 after burner = 84,750–15,046 = 69,704 kg/h. CO 2 after burner = 23,250 + 2.744 × 3551 + 2.927×136 + 102.3 × 2.994 = 33,698 kg/h. H 2 O = 22,000 + 3551 × 2.246 + 136 × 1.798 + 102.3 × 1.634 = 30,387 kg/h. N 2 = 370,000 kg/h. Total flue gas after burner = 503,789 kg/h. Converting to mass fractions, CO 2 = 33,685/503,789 = 0.067, H 2 O = 30,380/503,786 = 0.06

N 2 = 370,000/503,786 = 0.734, O 2 = 69,704/503,789 = 0.138.

Enthalpy h g2 after burner = (500,000 × 531.75 + 189 × 10 6 )/503,789 = 902.9 kJ/kg.

h g2 at 800°C = 0.067 × 205.4 + 0.06 × 391.6 + 0.734 × 207 + 0.138 × 190.7 = 215.7 kcal/kg = 903 kJ/kg. This agrees with the fuel input of 189 GJ/h (LHV basis). Hence, 189 GJ/h is the fuel consumption required to raise the exhaust gas to 800°C.

Moles of flue gas: (33,698/44) + (30,387/18) + (370,000/28) + (69,704/32) = 17,846 % volume CO 2 = 100 × (33,698/44)/17,845 = 4.29%. H 2 O = (30,387/18)/17,846 = 9.46% N 2 = (370,000/28)/17,846 = 74% O 2 = (69,704/32)/17,846 = 12.2% or by difference 12.25%.

Combustion Calculations

TABLE 1.10

Flue Gas Analysis at Burner Inlet and Exit

Gas flow, kg/h

503,770 % volume CO 2 3 4.29

7 9.46 N 2 75 74.00 O 2 15 12.25

Temperature, °C

A summary of the burner performance is shown in Table 1.10. Using the simplified formula Q = 0.0001400 W g × O, we have Q = 0.000140 × 500,000 ×

(15 – 12.25) = 192.5 GJ/h (46 MM kcal/h). In British units, Q = 60 × 500,000 × 2.204 ×

2.75 = (182 MM Btu/h). Note that it is easy to get a good estimate of fuel consumption simply based on oxygen difference in the turbine exhaust gas. One may also obtain the firing temperature once the fuel analysis is known. Since measurement of gas temperature after the burner is not very accurate due to measurement errors and variation gas temperatures across the cross section of the duct, either the detailed combustion calculation for the fuel input based on exhaust gas oxygen content or the simplified procedure as described earlier will be an added check.