01 POWER ISLAND / 01 CCPP / V. Ganapathy-Industrial Boilers and HRSG-Design (2003)

A:

Performance calculations are more involved than design calculations, because we do not know the gas exit temperature. The NTU method discussed in Q8.30 minimizes the number of iterations. However, for an evaporator, a simple procedure exists for predicting the performance.

Nu ¼ 0:229 11;6150:632 ¼ 84:9

or

hc ¼ 84:8 12 0:0252=2 ¼ 12:9 Btu=ft2 h F

The nonluminous heat transfer coefficient may be computed as before and shown to be 0.895 Btu=ft2 h F.

U1 ¼ 1=ð0:895 þ 12:9Þ þ 0:001 þ 0:0011 þ 0:000565 þ 0:0004 ¼ 0:0756 U ¼ 13:2 Btu=ft2 h F

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Using Eq. (34) with saturation temperature of 388 F, we have

or

t2 ¼ 578 F From eq. (32)

Q ¼ 230;000 0:99 0:28 ð1050 578Þ ¼ 30:0 MM Btu=h

Steam generation ¼ 29;770 lb=h

The tube wall temperature and gas pressure drop may be computed as before. It may be shown that the gas pressure drop is 1.5 in.WC and the tube wall temperature is 408 F. Thus off-design performance is predicted for the evaporator. With an economizer or superheater, more calculations are involved as the water or steam temperature changes. Also, the duty is affected by the configuration of the exchanger, whether counterflow, parallel flow, or crossflow. The NTU method discussed in Q8.29 and Q8.30 may be used to predict the off-design performance of such an exchanger.

8.15b

Q:

Discuss the logic for determining the off-design performance of a water tube waste heat boiler with the configuration shown in Fig. 8.4.

A:

In the design procedure one calculates the size of the various heating surfaces such as superheaters, evaporators, and economizers by the methods discussed earlier based on the equation A ¼ Q=ðU DTÞ. In this situation, the duty Q, logmean temperature difference DT, and overall heat transfer coefficient U are known or can be obtained easily for a given configuration.

In the off-design procedure, which is more involved, the purpose is to predict the performance of a given boiler under different conditions of gas flow, inlet gas temperature, and steam parameters. In these calculations several trial- and-error steps are required before arriving at the final heat balance and duty, because the surface area is now known. The procedure is discussed for a simple case, configuration 1 of Fig. 8.4, which consists of a screen section, superheater, evaporator, and economizer.

1.Assume a steam flow Ws based on gas conditions.

2.Solve for the screen section, which is actually an evaporator, by using the methods discussed in Q8.15a.

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FIGURE 8.4 Configurations for water tube boiler.

3.Solve for the superheater section, either using the NTU method or by trial and error. Assume a value for the duty and compute the exit gas=steam temperatures and then DT.

Assumed duty Qa ¼ WgCpðTgi TgoÞhlf

¼ Wsðhso hsiÞ

where

hso; hsi ¼ enthalpies of steam at exit and inlet Tgi; Tgo ¼ gas inlet and exit temperatures.

Compute U. Then transferred duty is Qt ¼ U A DT. If Qa and Qt are close, then the assumed duty and gas=steam temperatures are correct; proceed to the next step. Otherwise assume another duty and repeat step 3.

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4.Solve for the evaporator section as in step 1. No trial and error is required, because the steam temperature is constant.

5.Solve for the economizer as in step 3. Assume a value for the duty and then compute exit gas=water temperatures, DT, and Qt. Iteration proceeds until Qa and Qt match. The NTU method can also be used to avoid several iterations.

6.The entire HRSG duty is now obtained by adding the transferred duty of the four sections. The steam flow is corrected based on the actual total duty and enthalpy rise.

7.If the actual steam flow from step 6 equals that assumed in step 1, then the iterations are complete and the solution is over; if not, go back to step 1 with the revised steam flow.

The calculations become more complex if supplementary firing is added to generate a desired quantity of steam; the gas flow and analysis change as the firing temperature changes, and the calculations for U and the gas=steam temperature profile must take this into consideration. Again, if multipressure HRSGs are involved, the calculations are even more complex and cannot be done without a computer.

8.16a

Q:

Determine the tube metal temperature for the case of a superheater under the following conditions:

Average gas temperature ¼ 1200 F Average steam temperature ¼ 620 F

Outside gas heat transfer coefficient ¼ 15 Btu=ft2 h F Steam-side coefficient ¼ 900 Btu=ft2 h F

(Estimation of steam and gas heat transfer coefficients is discussed in Q8.03 and Q8.04.)

Tube size ¼ 2 0.142 in. (2 in. OD and 0.142 in. thick) Tube thermal conductivity ¼ 21 Btu=ft h F (carbon steel)

(Thermal conductivity of metals can be looked up in Table 8.9.)

A:

Because the average conditions are given and the average tube metal temperature is desired, we must have the parameters noted above under the most severe conditions of operation—the highest gas temperature, steam temperature, heat flux, and so on.

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TABLE 8.9 Thermal Conductivity of Metals, Btu=ft h F

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TABLE 8.9 Continued

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Let us use the concept of electrical analogy, in which the thermal and electrical resistances, heat flux and current, and temperature difference and voltage are analogous. For the thermal resistance of the tube metal,

(Here we have applied the electrical analogy, where voltage drop is equal to the product of current and resistance.) Hence,

Average tube metal temperature ¼ ð1200 565Þ þ ð620 þ 9:3Þ ¼ 632 F 2

We note that the tube metal temperature is close to the tube-side fluid temperature. This is because the tube-side coefficient is high compared to the gas heat transfer coefficient. This trend would prevail in equipment such as water tube boilers, superheaters, economizers, or any gas–liquid heat transfer equipment.

An approximation of the tube metal temperature for bare tubes in a gas–

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8.16b

Q:

In a boiler air heater, ho ¼ 9, hi ¼ 12, ti ¼ 200 F, and to ¼ 800 F. Estimate the average tube wall temperature tm.

A:

Using Eq. (35), we have

tm ¼ 800 1212þ 9 ð800 200Þ ¼ 457 F

8.17

Q:

How is the performance of fire tube and water tube boilers evaluated? Can we infer the extent of fouling from operational data? A water tube waste heat boiler as shown in Fig. 8.5 generates 10,000 lb=h of saturated steam at 300 psia when the gas flow is 75,000 lb=h and gas temperatures in and out are 1000 F and 500 F. What should the steam generation and exit gas temperature be when 50,000 lb=h of gas at 950 F enters the boiler?

A:

It can be shown as discussed in Q8.15a that in equipment with a phase change [1,8],

which was given there as Eq. (34).

For fire tube boilers, the overall heat transfer coefficient is dependent on the gas coefficient inside the tubes; that is, U is proportional to Wg0:8. In a water tube boiler, U is proportional to Wg0:6. Substituting these into Eq. (34) gives us the following.

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Now the actual exit gas temperature is 520 F, which means that the fouling is severe.

The energy loss due to fouling is

Q¼ 50;000 0:26 ð520 471Þ ¼ 0:63 106 Btu=h

If energy costs $3=MM Btu, the annual loss of energy due to fouling will be 3 0.63 8000 ¼ $15,120 (assuming 8000 hours of operation a year).

8.18

Q:

When and where are finned tubes used? What are their advantages over bare tubes?

A:

Finned tubes are used extensively in boilers, superheaters, economizers, and heaters for recovering energy from clean gas streams such as gas turbine exhaust or flue gas from combustion of premium fossil fuels. If the particulate concentration in the gas stream is very low, finned tubes with a low fin density may be used. However, the choice of fin configuration, particularly in clean gas applications, is determined by several factors such as tube-side heat transfer coefficient, overall size, cost, and gas pressure drop, which affects the operating cost.

Solid and serrated fins (Fig. 8.6) are used in boilers and heaters. Finned surfaces are attractive when the ratio between the heat transfer coefficients on the outside of the tubes to that inside is very small. In boiler evaporators or

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