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

burner can come on and fire to full capacity. The steam pressure decay during this period can be evaluated by this procedure.

8.44d

Q:

Let us assume that the boiler is operating at 45,000 lb=h and suddenly the demand goes to 50,000 lb=h.

Case 1: What happens to the steam pressure if we maintain the same heat input to the evaporator and the feedwater supply?

Case 2: What happens if the feedwater is cut off but heat input remains the same?

A:

Case 1: Q ¼ 45:0 106 Btu=h; Wf ¼ 45;000 lb=h; Wl ¼ 50;000 lb=h: First let us com-pute the steam generation. Using Eq. (86a),

h1 ¼ 471:6 Btu=lb and hf ¼ 189:5 Btu=lb

From Eq. (86a),

dp

45;000 ð471:6 189:6Þ þ Ws 730 þ 5580 dz ¼ Q also, dp=dz ¼ 4ðWs 50;000Þ,

Simplifying,

12:69 106 þ Ws 730 þ 5580 4ðWs 50;000Þ ¼ 45:9 106 Ws ¼ 49;857 lb=h

Thus,

dpdz ¼ 4 ð49;857 50;000Þ ¼ 572 psi=h ¼ 0:159 psi=s

Case 2: Wf ¼ 0 and Q ¼ 45:9 MM Btu=h: Using the above equations,

Ws 730 þ 5580 4ðWs 50;000Þ ¼ 45:9 106; or Ws ¼ 50;405 lb=h dpdz ¼ 1620 psi=h ¼ 0:45 psi=s

The pressure actually increases, because the cooling effect of the feedwater is not sensed.

In practice, controls respond fast and restore the balance among heat input, feedwater flow, and steam generation to match the demand. If we cannot adjust the heat input, as in unfired waste heat boilers, the pressure will slide as shown if we withdraw more steam than can be supplied by the boiler.

Copyright © 2003 Marcel Dekker, Inc.

8.45a

Q:

Discuss the parameters influencing the test results of an HRSG during performance testing.

A:

The main variables affecting the performance of an HRSG are the gas flow, inlet gas temperature, gas analysis, and steam parameters. Assuming that an HRSG has been designed for a given set of gas conditions, in reality several of the parameters could be different at the time of testing. In the case of a gas turbine HRSG in particular, ambient temperature also influences the exhaust gas conditions. The HRSG could, as a result, be receiving a different gas flow at a different temperature, in which case the steam production would be different from that predicted.

Even if the ambient temperature and the gas turbine load were to remain the same, it is difficult to ensure that the HRSG would receive the design gas flow at the design temperature. This is due to instrument errors. Typically, in large ducts, the gas measurement could be off by 3–5% and the gas temperatures could differ by 10–20 F according to ASME Power Test Code 4.4. As a result it is possible that the HRSG would receive 5% less flow at 10 F lower gas temperature than design conditions, even though the instruments recorded design conditions. As a result, the HRSG steam generation and steam temperature would be less than predicted through no fault of the HRSG design. Figure 8.18 shows the performance of an HRSG designed for 500,000 lb=h gas flow at 900 F; steam generation is 57,000 lb=h at 650 psig and 750 F. The graph shows how the same HRSG behaves when the mass flow changes from 485,000 to 515,000 lb=h while the exhaust temperature varies from 880 F to 902 F. The steam temperature falls to 741 F with 880 F gas temperature, whereas it is 758 F at 920 F. The steam flow increases from 52,900 to 60,900 lb=h as the gas mass flow increases. Thus the figure shows the map of performance of the HRSG for possible instrumental error variations only. Hence HRSG designers and plant users should mutually agree upon possible variations in gas parameters and their influence on HRSG performance before conducting such tests.

8.45b

Q:

Based on operating data, can we determine whether an HRSG is operating well?

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FIGURE 8.18 HRSG performance as a function of gas flow and temperature.

A:

It is possible to evaluate the operating data for possible deviations from predicted or guaranteed data as shown below. An HRSG supplier has guaranteed certain data for his HRSG in his proposal, which are shown alongside the measured data in Table 8.34. How are these data to be reconciled?

Note that the actual gas flow is difficult to measure and is not shown. However, using an energy balance, one can obtain the gas flow based on energy

TABLE 8.34 Proposed and Actual HRSG Performance

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absorbed by steam and the difference between gas temperatures at the inlet and exit. Note that the operating steam pressure is lower than that called for in the design.

From the energy balance, we have

Wg ðhi hoÞ 0:99 ¼ Ws Dh

where hi; ho refer to the enthalpy of gas at the inlet and exit of the HRSG corresponding to the gas temperatures measured. The steam flow, Ws, and the enthalpy absorbed by steam, Dh, are known from steam tables. Hence Wg, the gas flow, can be calculated. It can be shown to be 501,300 lb=h.

Now using the HRSGS program, one can simulate the design mode using the proposal data as shown in Fig. 8.19a. Then, using the calculated gas flow and the inlet temperature, run the HRSGS program in the off-design mode at the lower steam pressure. The results are shown in Fig. 8.19b. It may be seen that 69,520 lb=h of steam should have been generated at 690 F and the exit gas temperature should be 364 F, whereas we measured only 68,700 lb=h and exit gas at 380 F. Hence more analysis is required, but there is a prima facie concern with the HRSG performance.

8.46

Q:

Estimate the boiling heat transfer coefficient inside tubes for water and the tube wall temperature rise for a given heat flux and steam pressure.

A:

Subcooled boiling heat transfer coefficient inside tubes for water can be estimated by the following equations.

According to Collier [13],

According to Jens and Lottes [13],

where

DT ¼ difference between saturation temperature and tube wall temperature,

F

P ¼ steam pressure, psia

q ¼ heat flux inside tubes, Btu=ft2 h

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FIGURE 8.19a Simulation of HRSG design data.

Copyright © 2003 Marcel Dekker, Inc.

FIGURE 8.19b Simulation of HRSG operating data.

Copyright © 2003 Marcel Dekker, Inc.

The heat transfer coefficient is then given by

hi ¼ q=DT

Example

What is the boiling heat transfer coefficient inside the tubes, and what is the tube wall temperature if the heat flux inside boiler tubes is 60,000 Btu=ft2 h and steam pressure ¼ 1200 psia?

Solution. Using Collier’s equation,

DT ¼ 0:072 e 1200=1260 60;0000:5 ¼ 6:8 F hi ¼ 60;000=6:8 ¼ 8817 Btu=ft2 h F

Using Jens and Lottes’s equation,

DT ¼ 1:9 e 1200=900 60;0000:25 ¼ 7:8 F hi ¼ 60;000=7:8 ¼ 7650 Btu=ft2 h F

The above expressions assume that the tube surface where boiling occurs is smooth and clean.

8.47a

Q:

What is the relationship among critical heat flux, steam pressure, quality, and flow in water tube boilers?

A:

Several variables influence the critical heat flux or the departure from nucleate boiling (DNB) condition. These are

Steam pressure

Mass velocity of mixing inside the tubes Steam quality

Tube roughness and cleanliness Tube size and orientation

Correlations such as the Macbeth correlation are available in the literature [13].

Copyright © 2003 Marcel Dekker, Inc.

where

qc ¼ critical heat flux, Btu=ft2 h hfg ¼ latent heat of steam, Btu=lb

Gi ¼ mass velocity inside tubes, lb=ft2 h x ¼ steam quality, expressed as a fraction di ¼ tube inner diameter, in.

Example

Estimate the critical heat flux under the following conditions:

Steam pressure ¼ 1000 psia

Tube inner diameter ¼ 1.5 in.

Mass velocity ¼ 600,000 lb=ft2 h

Steam quality ¼ 0.20

qc ¼ 0:00633 106 650 1:50 0:1 0:60:51ð1 0:2Þ ¼ 2:43 106 Btu=ft2 h

In real-life boilers, the allowable heat flux to avoid DNB is much lower, say 20– 30% lower, than the values obtained by laboratory tests under controlled conditions due to factors such as roughness of tubes, water quality, and safety considerations. Boiler suppliers have their own data and design boilers accordingly.

8.47b

Q:

How is the critical heat flux qc determined in pool boiling situations as in fire tube boilers?

A:

Several correlations are available in the literature, but only two will be cited. Motsinki suggests the simple equation [13]

where Ps; Pc are the steam pressure and critical pressure, both in psia.

Copyright © 2003 Marcel Dekker, Inc.

Zuber’s correlation takes the form [13]

where

s ¼ surface tension r ¼ density

hfg ¼ latent heat

g; g0 ¼ acceleration due to gravity and conversion factor g in force units all in metric units.

Example

Determine the critical heat flux for steam at 400 psia under pool boiling conditions.

Solution. The following data can be obtained from steam tables:

Saturation temperature at 400 psia ¼ 445 F

Density of liquid ¼ 51 lb=cu ft (827 kg=m3)

Density of vapor ¼ 0.86 lb=cu ft (13.8 kg=m3)

Latent heat of vaporization ¼ 780 Btu=lb (433 kcal=kg)

From Table 8.26 at a saturation temperature of 445 F, surface tension is 0.0021 lbf=ft (0.31 kgf=m).

¼ 1:102 MM Btu=ft2 h

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Using Eq. (88c),

qc ¼ 13:8 433 0:13 0:0031 813 9:82

¼ 2:95 106 kcal=m2 ¼ 1:083 MM Btu=ft2 h

Again, as before, factors such as surface roughness, water quality, scale formation, and bundle configuration play a role, and for conservative estimates, boiler designers use a value that is 20–30% of these values.

8.47c

Q:

Estimate the critical heat flux for a tube bundle of a fire tube boiler with the following data:

Tube OD ¼ 2 in.

Number of tubes ¼ 590

Length ¼ 29.5 ft

Tube spacing ¼ 2.75 in., triangular

Surface area ¼ 9113 ft2

Tube bundle diameter ¼ 78 in.

A:

The heat flux for a tube bundle is obtained by correcting the heat flux for pool boiling obtained from Q8.47b.

First compute a factor C ¼ DbL=A where

Db ¼ bundle diameter, ft L ¼ length of tubes, ft

A ¼ surface area of bundle, ft2

C ¼ 78 29:5 ¼ 0:021 12 9113

The correction factor F is obtained from the correlation log F ¼ 0:8452 þ 0:994 log C

For C ¼ 0:021; log F ¼ 0:8224; or F ¼ 0:15:

Hence,

Corrected heat flux ¼ 1:083 106 0:15 ¼ 162;500 Btu=ft2 h Typically a value such as 70–80% of this is used for tube bundles.

Copyright © 2003 Marcel Dekker, Inc.