Off-Design Performance with Addition of Economizer

Very often, a boiler designed for a given set of gas and steam conditions operates at dif- ferent gas inlet conditions and steam parameters in the field. Plant requirements often dictate the gas inlet conditions. Appendix A describes the NTU method for evaluating off-design conditions and a simplified approach for evaporator performance evaluation. One may apply the same methods for fire tube boilers also. Sometimes plants would like to improve the efficiency of the existing boilers by adding an economizer. Hence, plant engineers should know how to evaluate their boiler for off-design conditions with change in gas parameters and steam conditions and addition or deletion of components. The following is a good example of the situation often faced by plant engineers.

Example 4.10

A plant using the boiler described earlier wants to add an economizer to improve its efficiency and steam generation. Gas inlet conditions are 52,000 kg/h at 850°C, same

analysis as before. Steam pressure is 12 kg/cm 2 g. An economizer is added: 50.8 × 44 mm

plain tubes, 76 mm square spacing, 4 streams, 20 tubes/row, 20 deep, 4 m long tubes. Feed water to economizer is as before at 104°C. Determine the performance of the boiler. Assume clean conditions (normal fouling). Surface area of economizer = 3.14 × 0.0508 ×

20 × 20 × 4 = 255 m 2 .

Solution

First we have to determine the duty of the evaporator at the new conditions. Since we have added an economizer, the feed water temperature to the evaporator is unknown and has to be computed and then the steam generation. Then we have to check if the economizer will deliver that feed water temperature matching the steam flow to the evaporator. Thus, an iterative process is involved.

As discussed in Appendix A, the performance of a water tube or fire tube evaporator may be obtained using the following equation:

ln 

 = UA

  ( WC

g pg )

One can compute U as shown in the earlier example. However, for illustration, let us

assume that U o is proportional to (gas flow) 0.8 . Hence, U o = 47.8 × (52,000/45,370) 0.8 = 53.3 kcal/m 2 h °C. Assume T 2 = 270°C. Average gas temperature in the boiler = 560°C. C p = 0.29 kcal/kg °C from Appendix F. Saturation temperature at 12 kg/cm 2 g = 191°C.

Waste Heat Boilers 239

Use 3% blowdown. Hence, ln[(850 − 191)/(T 2 − 191)] = 53.3 × 575/(52,000 × 0.99 × 0.29) = 2.05 or exit gas temperature from evaporator T 2 = 276°C. Hence, evaporator duty = 52,000 × 0.99 × 0.29 × (850 − 276) = 8.57 MM kcal/h = 9964 kW. The revised steam generation is obtained using an iterative process. Assume that feed water temperature leaving the economizer is 170°C. Enthalpy

pickup in evaporator = (665.4 − 171.8) + 0.03 × (193.6 − 171.8) = 494.3 kcal/kg. (Enthalpies of saturated steam, saturated water, and feed water entering the evaporator are, respec- tively, 665.4, 193.6, and 171.8 kcal/kg from steam tables. Hence, steam generation = 8,570,000/494.3 = 17,337 kg/h. Flow through economizer = 1.03 × 17,337 = 17,857 kg/h.

For the plain tube bundle, one may use the methods discussed in Appendix C to

estimate the value of U. It may be shown that U = 56 kcal/m 2 h C. Surface area of the economizer = 255 m 2 . Let us use the NTU method to determine the performance of the economizer as explained in Appendix A. Let us assume that C p in the economizer = 0.267 kcal/kg °C (flue gas). W g C pg = 52,000 × 0.267 × 0.99 = 13,745 (0.99 refers to the 1% heat loss). W i C pi = 17,857 ×

1.025 = 18,303 (where 1.025 is the average specific heat of water in the economizer).

C = 13,745/18,303 = 0.75. NTU = 56 × 255/13,745 = 1.0389

{ 1 − exp

 − NTU ( 1 − C )  } =

C exp − NTU ( 1 − C ) }

Q = 0.543 × 13,745 × (276 − 104) = 1.283 MM kcal/h. Enthalpy pickup of water = 1.283 ×

10 6 /17,857 = 71.8 kcal/kg or exit water enthalpy = 104.3 + 71.8 = 176.1 kcal/kg or temperature of water at economizer exit = 174oC from steam tables. Close to that assumed. Hence, steam generation will be slightly more.

The exit gas temperature from the economizer = 276 − 1.283 × 10 6 /(52,000 × .99 ×

0.267) = 182°C. One may check the gas pressure drop in the evaporator as discussed earlier and in the economizer as discussed in Appendix C. Thus, plant engineers may obtain the performance of their boiler with the addition of economizer at any inlet gas condition. One can also develop a computer code or an Excel program using the logic discussed here. As mentioned earlier, due to variations in steam and gas properties with temperature, a few iterations are required. As an exercise, plant engineers may add superheater upstream of the evaporator and see how to evaluate this option!

The computer output from a vendor is shown in Table 4.23. Slight variations may be seen due to approximations made.

Off-Design Performance with Addition of Economizer