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

From Eq. (73),

Q¼ 0:86 19;875 ð1000 250Þ ¼ 12:8 106 Btu=h

Let us calculate the exit water and gas temperatures.

Copyright © 2003 Marcel Dekker, Inc.

8.31

Q:

How is the natural or free convection heat transfer coefficient in air determined?

A:

The situations of interest to steam plant engineers would be those involving heat transfer between pipes or tubes and air as when an insulated pipe runs across a room or outside it and heat transfer can take place with the atmosphere.

Simplified forms of these equations are the following [12]. 1. Horizontal pipes in air:

DT ¼ temperature difference between the hot surface and cold fluid, F

do ¼ tube outside diameter, in. 2. Long vertical pipes:

3.Vertical plates less than 2 ft high:

5.Horizontal plates facing upward:

6.Horizontal plates facing downward:

Example

Determine the heat transfer coefficient between a horizontal bare pipe of diameter 4.5 in. at 500 F and atmospheric air at 80 F.

Copyright © 2003 Marcel Dekker, Inc.

Note that the above equations have been modified to include the effect of wind velocity in the insulation calculations; see Q8.51.

8.32

Q:

How is the natural or free convection heat transfer coefficient between tube bundles and liquids determined?

A:

One has to determine the free convection heat transfer coefficient when tube bundles such as desuperheater coils or drum preheat coils are immersed in boiler water in order to arrive at the overall heat transfer coefficient and then the surface area. Drum coil desuperheaters are used instead of spray desuperheaters when solids are not permitted to be injected into steam. The heat exchanger is used to cool superheated steam (Fig. 8.12), which flows inside the tubes while the cooler water is outside the tubes in the drum. Drum heating coils are used to keep boiler water hot for quick restart or to prevent freezing.

In this heat exchanger, steam condenses inside tubes while the cooler water is outside the tubes. The natural convection coefficient between the coil and drum water has to be determined to arrive at the overall heat transfer coefficient and then the size or surface area.

The equation that relates hc with other parameters is [2]

FIGURE 8.12 Exchanger inside boiler drum.

Copyright © 2003 Marcel Dekker, Inc.

Simplifying the above we have

m ¼ viscosity of fluid, lb=ft h r ¼ fluid density, lb=ft3

In Eq. (77) all the fluid properties are evaluated at the mean temperature between fluid and tubes except for the expansion coefficient, which is evaluated at the fluid temperature.

Fluid properties at saturation conditions are given in Table 8.26.

Example

1 in. pipes are used to maintain boiler water at 100 F in a tank using steam at 212 F, which is condensed inside the tubes. Assume that the pipes are at 200 F, and estimate the free convection heat transfer coefficient between pipes and water.

Solution. From Table 8.26, at a mean temperature of 150 F,

¼ 188 Btu=ft2 h F

8.33

Q:

Estimate the surface area of the heat exchanger required to maintain water in a boiler at 100 F using steam at 212 F as in the example of Q8.32. Assume that the heat loss to the cold ambient from the boiler is 0.5 MM Btu=h. Steam is condensed inside the tubes. 1 in. schedule 40 pipes are used.

Copyright © 2003 Marcel Dekker, Inc.

TABLE 8.26 Properties of Saturated Water

A:

The overall heat transfer coefficient can be estimated from

Copyright © 2003 Marcel Dekker, Inc.

or

Uo ¼ 177 Btu=ft2 h F

DT ¼ log-mean temperature difference ¼ 212 100 ¼ 112 F

Then,

8.34

Q:

Can we determine gas or steam temperature profiles in a heat recovery steam generator (HRSG) without actually designing it?

A:

Yes. One can simulate the design as well as the off-design performance of an HRSG without designing it in terms of tube size, surface area, etc. The methodology has several applications. Consultants and plant engineers can determine for a given set of gas inlet conditions for an HRSG how much steam can be generated and what the gas=steam temperature profile will look like, and hence write better specifications for the HRSG or select auxiliaries based on this simulation without going to a boiler firm for this information. Thus several options can be ruled out or ruled in depending on the HRSG performance. The methodology has applications in complex, multipressure cogeneration or combined cycle plant evaluation with gas turbines. More information on HRSG simulation can be found in Chapters 1 and 3 and Refs. 11, 12.

Copyright © 2003 Marcel Dekker, Inc.

Example

140,000 lb=h of turbine exhaust gases at 980 F enter an HRSG generating saturated steam at 200 psig. Determine the steam generation and temperature profiles if feedwater temperature is 230 F and blowdown ¼ 5%. Assume that average gas specific heat is 0.27 at the evaporator and 0.253 at the economizer.

Two important terms that determine the design should be defined here (see Fig. 8.13). Pinch point is the difference between the gas temperature leaving the evaporator and saturation temperature. Approach point is the difference between the saturation temperature and the water temperature entering the evaporator. More information on how to select these important values and how they are influenced by gas inlet conditions is discussed in examples below.

For unfired gas turbine HRSGs, pinch and approach points lie in the range of 15–30 F. The higher these values, the smaller will be the boiler size and cost, and vice versa.

Let us choose a pinch point of 20 F and an approach point of 15 F. Saturation temperature ¼ 388 F. Figure 8.14 shows the temperature profile. The gas temperature leaving the evaporator ¼ 388 þ 20 ¼ 408 F, and water temperature entering it ¼ 388 7 15 ¼ 373 F.

Evaporator duty ¼ 140;000 0:99 0:27 ð980 408Þ

¼ 21:4 MM Btu=h

(0.99 is the heat loss factor with a 1% loss.)

Enthalpy absorbed by steam in evaporator

¼ð1199:3 345Þ þ 0:05 ð362:2 345Þ

¼855:2 Btu=lb

(1199.3, 345, and 362.2 are the enthalpies of saturated steam, water entering the evaporator, and saturated water, respectively. 0.05 is the blowdown factor for 5% blowdown.)

FIGURE 8.13 Pinch and approach points.

Copyright © 2003 Marcel Dekker, Inc.

FIGURE 8.14 Temperature profile in an HRSG.

Hence

Steam generated ¼ 21:4 106 ¼ 25;000 lb=h 855:2

Economizer duty ¼ 25;000 1:05 ð345 198:5Þ

¼ 3:84 MM Btu=h

3;840;000

Gas temperature drop ¼ 140;000 0:253 0:99 ¼ 109 F

Hence gas temperature leaving economizer ¼ 408 7 109 ¼ 299 F. Thus the thermal design of the HRSG is simulated.

8.35a

Q:

Simulate the performance of the HRSG designed in Q8.34 when a gas flow of 165,000 lb=h enters the HRSG at 880 F. The HRSG will operate at 150 psig. Feedwater temperature remains at 230 F.

A:

Gas turbine exhaust flow and temperature change with ambient conditions and load. As a result the HRSG has to operate at different gas parameters, and hence simulation is necessary to determine how the HRSG behaves under different gas and steam parameters.

Copyright © 2003 Marcel Dekker, Inc.

The evaporator performance can be determined by using Eq. (37). Based on design conditions, compute K.

Under the new conditions,

"#

Hence tg2 ¼ 388 F.

Evaporator duty ¼ 165;000 0:99 0:27 ð880 388Þ

¼ 21:70 MM Btu=h

In order to estimate the steam flow, the feedwater temperature leaving the economizer must be known. This is arrived at through a series of iterations. Try tw2 ¼ 360 F. Then

21:70 106

Steam flow ¼ ð1195:7 332Þ þ 0:05 ð338:5 332Þ

¼ 25;110 lb=h

Economizer assumed duty Qa ¼ 25;110 1:05

ð332 198:5Þ

¼ 3:52 MM Btu=h

Compute the term ðUSÞdesign ¼ Q=DT for the economizer based on design conditions.

Q ¼ 3:84 106

DT ¼ ð299 230Þ ð408 373Þ ¼ 50 F lnð69=35Þ

Hence ðUSÞdesign ¼ 3;840;000=50 ¼ 76;800. Correct this for off-design conditions.

Copyright © 2003 Marcel Dekker, Inc.

The economizer transferred duty is then ðUSÞperf DT. Based on 360 F water leaving the economizer, Qa ¼ 3.52 M Btu=h and the exit gas temperature is

Hence tg2 ¼ 388 7 85 ¼ 303 F, and

DT ¼ ð303 230Þ ð388 360Þ ¼ 47 F lnð73=28Þ

Transferred duty Qt ¼ 85;200 47 ¼ 4:00 MM Btu=h

Because the assumed and transferred duty do not match, another iteration is required. We can show that at duty of 3.55 MM Btu=h the, assumed and transferred duty match. Water temperature leaving the economizer ¼ 366 F (saturation); exit gas temperature ¼ 301 F. Steam generation ¼ 25,310 lb=h.

Because the calculations are quite involved, I have developed a software program called HRSGS that can simulate the design and off-design performance of complex, multipressure fired and unfired HRSGs. More information can be had by writing to V. Ganapathy, P.O. Box 673, Abilene, TX 79604.

8.35b

Q:

In the above case, how much fuel is required and at what firing temperature if 35,000 lb=h steam at 200 psig is to be generated? Gas flow is 140,000 lb=h at 980 F as in Q8.35a.

A:

A simple solution is given here, though the HRSG simulation would provide more accurate evaluation and temperature profiles. We make use of the concept that the fuel efficiency is 100% and all of that goes to generating the additional steam as discussed earlier.

Energy absorbed by steam ¼ 35;000 ð1199:3 198:5Þ

¼ 35:1 MM Btu=h

Additional energy to be provided by the burner ¼ 35.1 7 25.24 ¼ 9.86 MM Btu=h (the HRSG absorbs 25.24 as shown in Q8.34).

The oxygen consumed in the process of combustion (see Q6.27) is 9:86 106=ð140;000 58:4Þ ¼ 1:2%

Copyright © 2003 Marcel Dekker, Inc.