Checking Boiler Performance

Often a plant buys a steam generator without obtaining process data as shown earlier. However, if such data are obtained from the boiler supplier, the plant engineer can check the performance not only at full load but at off-design conditions as well.

The plant engineer can learn a lot on thermal performance of boilers by verifying the thermal performance data given by the boiler supplier, or even if he has not been

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provided the data at a particular load, the plant engineer, using the methods discussed here, can generate the complete performance data. Let us assume that the boiler described earlier is operating at 100% load with the stated fuel and at stated excess air of 15%; gas temperature measurements at the furnace exit and in high gas temperature regions will not be typically accurate. We can reasonably assume that the boiler exit gas temperature is accurate and also the water and steam temperatures. Measurement errors will

be lesser as the gas temperatures become lower. Using this premise, let us analyze the complete boiler to check the aforementioned data. One can independently calculate the heat transfer coefficients at various surfaces using the methods described in Appendices

B through E; combustion and efficiency calculations as discussed in Chapter 1 should

be performed to arrive at the air and flue gas quantities and the flue gas analysis. The oxygen measurement dry or wet may be used to obtain the operating excess air as discussed in Chapter 1.

Then one may obtain the flue gas properties such as specific heat, viscosity, and thermal conductivity as a function of gas temperature as discussed in Appendix F. These basic data will help one start doing the heat transfer calculations to check the boiler performance at any load. Here, since we have the data from the boiler supplier at 100% load, let us see if these are reasonable. If we do not have the boiler supplier’s data, there should be some field measurements of gas temperatures and water–steam temperature in an operating unit. These data may be used for verifying the calculations.

Solution

Economizer Performance Let us start from the economizer and work backward. Flue gas flow = 123,000 kg/h and

analysis is % volume CO 2 = 8.56, H 2 O = 17.3, N 2 = 71.65, O 2 = 2.48. The exit gas temperature is 154°C at 100% load (the summary of performance given in Table 3.14 includes some margin and hence shows a 4°C higher exit gas temperature). Water inlet and exit temperatures are 116 °C and 222 °C. Water flow through the economizer will be steam flow × blowdown-spray water flue = 101,000 − 3,260 = 97,740 kg/h.

The specific heat of water may be taken as 1.04 kcal/kg °C and that of flue gas as 0.2815 kcal/kg °C. One can confirm these from steam tables and flue gas data given in Appendix F.

Duty of economizer = 97,740 × 1.04 × (222 − 116) = 10.81 × 10 6 kcal/h. We will check this using the number of transfer units (NTU) method.

1. Assume the gas inlet temperature to the economizer (or use the measured field data. Exit gas temperature is an important data in any steam generator or HRSG, and there should be provisions to measure it accurately). Then the duty of the economizer is established as both the exit and inlet fluid temperatures are known. The exit water temperature may be calculated knowing the water flow. Since we have measured the water and steam temperatures, we may also use that information to confirm the estimates.

2. Calculate the U value applying the heat transfer correlations discussed in Appendix E on finned tubes. 3. Using the NTU method, obtain the duty of the economizer. If this matches the assumed duty, then iteration stops; else, inlet gas temperature is varied till con- vergence occurs. (The procedure provided earlier applies to all heat transfer surfaces.)

144 Steam Generators and Waste Heat Boilers: For Process and Plant Engineers

Let us, for illustration, use U values shown in Table 3.13 as the purpose is to illustrate how to check the boiler performance and not the calculation for U, which is detailed elsewhere.

W g = 123,000 kg/h, C pg = 0.2815 kcal/kg °C, t wo = 222°C, t wi = 116°C Water flow through the economizer = steam flow × blowdown-spray water flow. Initially,

we may assume zero spray and proceed. Here we know the spray water flow and so let us use that.

Duty = 97,740 × (h 222 –h 116 ) = 97,740 × (227.7 − 117) = 10.81 × 10 6 kcal/h (enthalpy of steam from steam tables). The gas inlet temperature = 154 + 10.81 × 10 6 /(123,000 × 0.2815) = 466°C. Specific heat of water = 1.044 kcal/kg °C. Using the NTU method,

WC p for flue gas = 123,000 × 0.2815 = 34,624 and for water = 97,740 × 1.044 = 102,040 WC min = 34,624 and C = WC min /WC max = 34,624/102,040 = 0.339

NTU = UA/C min = 40.6 × 2395/34,624 = 2.808

∈ = [1 – exp{–NTU × (1 – C)}]/[1 – C exp{–NTU × (1 – C)}] = [1 – exp{–2.808 × 0.661}]/[1 − 0.339 × exp{–2.808 × 0.661}] = [1 − 0.1563]/[1 – .339 × 0.1563] = 0.89

Duty Q = 0.89 × 34,624 × (466 − 116) = 10.79 × 10 6 kcal/h; this closely agrees with the provided data. We may also apply the Q = UAΔT method and verify the results.

Evaporator Performance See the method discussed in Appendix A for evaporator performance evaluation. The

following equation may be used for the performance of the evaporator (see Equation A.13b).

ln[(t g1 –t s )/(t g2 –t s )] = UA/(W g C pg ) In our case, U = 105 kcal/m 2 h °C, A = 322 m 2 ,C pg = 0.3024, t s = 256°C,

Hence, ln[(t g1 − 256)/(466 − 256)] = 105 × 322/(123,000 × 0.3024) = 0.909 [(t g1 − 256)/(466 − 256)] = exp(0.909) = 2.482 or t g1 = 777°C Duty of evaporator = 123,000 × (777 − 466) × 0.3024 = 11.57 × 10 6 kcal/h

Primary Superheater The steam flow is 100,000 − 3,260 = 96,740 kg/h. U = 105 kcal/m 2 h °C, A = 77 m 2 .

Steam temperature at exit = 313°C. Hence, the duty of superheater = 96,740 × (714.0 −

668.4) = 4.41 × 10 6 kcal/h, where 714.0 and 668.4 kcal/kg are enthalpies of steam at the exit and the inlet of superheater. The inlet gas temperature is 4,410,000/(123,000 × 0.3163) + 777 = 891°C Specific heat of steam = (714.0 − 668.4)/(313 − 256) = 0.80

WC min = 123,000 × 0.3163 = 38,905 WC max = 96,740 × 0.8 = 77,392

C = 38,905/77,392 = 0.502

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NTU = UA/WC min = 105 × 77/38,905 = 0.2078

∈ = [1 – exp(–0.2078 × 0.498)]/[1 − 0.502 × exp(–0.2078 × 0.498)] = 0.179 Q = 0.179 × (891 − 256) × 38,905 = 4.43 × 10 6 kcal/h

(agrees with value shown in Table 3.13)

Final Superheater A spray desuperheater cools the steam from 313°C to 286°C in order to attain 400°C at

the exit. Let us check the spray quantity.

96,240 × 714 + W s × 117 = (96,240 + W) × 695.1 or W s , the spray flow = 3146 kg/h, or final steam = 99,886 kg/h or close to 100,000 kg/h.

U = 109.3 kcal/m 2 h °C A = 103 m 2

Duty of superheater = 100,000 × (766.8 − 695.1) = 7.17 × 10 6 kcal/h Gas inlet temperature = 891 + 7.17 × 10 6 /(123,000 × 0.3244) = 1071°C

Specific heat of steam in the range 286°C – 400°C = (766.8 − 695.1)/(400 − 286) = 0.629 C min = 123,000 × 0.3244 = 39,901. C max = 100,000 × 0.629 = 62,900. C = 39,901/62,900 = 0.634

NTU = UA/C min = 109.3 × 103/39,901 = 0.282

∈ = [1 – exp(–0.366 × 0.282)]/[1 – 0.634 × exp(–0.366 × 0.282)] = 0.229 Q = 0.229 × (1071 − 286) × 39,901 = 7.17 × 10 6 kcal/h

(agrees with value shown in Table 3.13)

Screen Section The performance is obtained as for the evaporator.

ln[(t g1 –t s )/(t g2 –t s )] = UA/(W g C pg ) U = 117.8 kcal/m 2 h °C; A = 105 m 2 C pg = 0.3328 kcal/kg °C ln[(t g1 − 256)/(1071 − 256)] = 117.8 × 105/(123,000 × 0.3328) = 0.302 or t g1 = 1359°C Screen duty Q = 123,000 × 0.3328 × (1359 − 1071) = 11.79 × 10 6 kcal/h

The furnace duty may be estimated as shown in Chapter 2, or obtained by difference from total energy absorbed.

The boiler efficiency on LHV basis is 92.56%. Energy absorbed by steam = 64.68 MM kcal/h. The energy absorbed by economizer, evaporator, superheater, screen = 10.79 +

11.57 + 4.43 + 7.17 + 11.79 = 45.75 MM kcal/h. Enthalpy of gas at 1360°C from Table F.10 = 414 kcal/kg.

146 Steam Generators and Waste Heat Boilers: For Process and Plant Engineers

Furnace duty = [(64.68/0.9256) – 0.123 × 414] × 0.99 = 18.77 MM kcal/h. Total energy to steam = 45.75 + 18.77 = 64.52 MM kcal/h, which is close to the total duty of steam. This is a simplified approach and the results give a good estimate of performance. Note that these calculations are iterative in nature. Heat transfer coefficients are functions of gas temperatures, and hence, the U values have to be corrected based on actual average gas or film temperatures. Similarly, the steam-side heat transfer coefficients are a function of the average steam or water temperature, which is again obtained through an iterative process. A few iterations will correct these U values and provide reasonable performance results. A computer program will help speed up these iterations.

One may use this method to evaluate the furnace exit gas temperature and relate it with the correlations or typical charts available for estimating the furnace exit gas temperature. We may then compute the furnace duty using the method discussed in Chapter 2 and then the total duty and steam generation. If there are gas or steam temperatures measurements available at intermediate points, they may also be verified or used as data for cross-checking the calculations. Note that these calculations may be done at any load even if the boiler supplier has not provided the data for that load . For example, if a superheater is having high tube wall temperatures, the performance calculations may be done to check the duty as shown earlier using the exit gas temperature measurement alone. Then, the tube wall temperature may be computed as shown in Example 3.6. Comparisons may be made with field data, if any.

The purpose of this exercise is to show that plant engineers can independently perform the complete boiler calculations and verify the proposal data given by the boiler supplier or check the field data and compare the results with similar calculations and see if there are major deviations in duty or gas or steam temperatures at any heating surface, which should be brought to the attention of the boiler supplier.

A procedure to check the boiler performance from exit gas and fluid temperatures is discussed in Appendix A, and the same example is completely worked out.

Checking Boiler Performance