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

may be found, and the ratio of actual to average heat flux should be computed. For the sake of illustration, use the following ratios of actual to average heat flux at the locations mentioned.

We must determine the maximum inside heat flux at each of the locations and correct it for flux inside the tubes to check for DNB. Hence, considering the tube OD=ID ratio of 1.19 and the 25% nonuniformity at each furnace elevation, we have the following local maximum inside heat flux at the locations mentioned ðqi is taken as qp d=diÞ :

It is desirable to obtain allowable quality of steam at each of these locations and check to be sure actual quality does not exceed it.

DNB tests based on particular tube profiles, roughness, and water quality as used in the operation give the most realistic data for checking furnace tube burnout. Correlations, though available in the literature, may give a completely wrong picture because they are based on tube size, heating pattern, water quality, and tube roughness that may not tally with actual operating conditions. However, they give the trend, which could be useful. For the sake of illustrating our example, let us use Fig. 7.10. This gives a good estimate only, because

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extrapolation must be carried out for the low heat flux in our case. We see the following trend at Gi ¼ 480,000 lb=ft2 h and 2700 psia:

Figure 7.13 shows the actual quality (assuming linear variation, perhaps in reality quadratic) versus allowable quality. It shows that a large safety margin exists; hence, the design is safe. This exercise should be carried out at all loads (and for all circuits) before coming to a conclusion.

7.32a

Q:

How is the circulation system analyzed in fire tube boilers?

A:

The procedure is similar to that followed for water tube boilers in that the CR is assumed and the various losses are computed. If the losses associated with the assumed CR and the resulting mass flow are in balance with the available head, then the assumed CR is correct; otherwise another iteration is done. Because fire tube boilers in general use horizontal tubes, the allowable heat flux to avoid DNB is lower than when vertical tubes are used. With gas streams containing hydrogen and steam as in hydrogen plant waste heat boilers, the tube-side and hence the overall heat transfer coefficient and heat flux will be rather high compared to flue gas stream from combustion of fossil fuels. Typical allowable heat fluxes for horizontal tubes range from 100,000 to 150,000 Btu=ft2 h.

7.32b

Q:

Perform the circulation calculations for the system shown in Fig. 7.14 with the following data:

Assume that saturated water enters the drum.

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FIGURE 7.13 Actual quality vs. allowable quality along furnace height.

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FIGURE 7.14 Circulation scheme in fire tube boiler.

A:

From steam tables, vf ¼ 0.194 and vg ¼ 1.12 cu ft=lb. Assume there are two downcomers of size 4 in schedule 40 (di ¼ 4.026 in.) and two risers of size 8 in schedule 40 (di ¼ 7.981 in.). The total developed length of each downcomer is 22.5 ft, and each has two 90 bends; the riser pipes have a total developed length of 5 ft. Exchanger diameter is 6 ft, and the center distance between the exchanger and the steam drum is 8 ft.

1.Assume CR ¼ 15; then

Mixture volume ¼ 0:067 1:12 þ 0:933 0:0194

¼ 0:0931

The head available due to the column of saturated water is 11=(0.0194 144) ¼ 3.94 psi, where 11 ft is the height of the water column.

2.Losses in downcomers:

¼ 9 fps

Inlet plus exit losses ¼ 1:5 velocity head

9 ¼ 1:5 9 2 32 144 0:0194

¼ 0:68 psi

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¼ 0:98 psi

where 0.0165 is the friction factor. Equation (13) was used for pressure drop of single-phase flow.

Total downcomer losses ¼ 0:68 þ 0:98

¼ 1:66 psi

3.Friction and acceleration losses in the exchanger may be neglected for this first trial, because in a fire tube boiler they will be negligible due to the low mass velocity.

4.Gravity losses in the exchanger: Using Fig. 7.7, r4 ¼ 0.57.

0:57

DPg ¼ 0:00695 6 0:0194 ¼ 1:22 psi

5.Gravity loss in riser pipe:

Inlet plus exit losses ¼ 1:5 velocity head

1:5 11 11

¼ 2 32 0:0931 144 ¼ 0:21 psi

Friction loss ¼ 3:36 0:014 15 202 2

0:0931

5 ð7:981Þ5 ¼ 0:02 psi

where 5 ft is the developed length of the riser.

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Let the losses in drum internals ¼ 0.5 psi. This can vary depending on the type of internals used. Then

Total losses ¼ 1:66 þ 1:22 þ 0:37 þ 0:21 þ 0:02 þ 0:50 ¼ 3:98 psi

This is close to the available head; hence CR ¼ 15 is the circulation ratio for this system. The calculations can be fine-tuned with actual dimensions after the layout is done. One can compute the heat flux and compare it with the allowable heat flux to check if the circulation rate is adequate. Usually circulation is not a problem in this type of boiler, because the heat flux is low, on the order of 20,000–30,000 Btu=ft2 h, whereas the allowable flux could be 100,000– 150,000 Btu=ft2 h. See Chapter 8 for correlations for critical heat flux (CHF).

7.33

Q:

How is the flow in steam blowoff lines determined?

A:

Whenever steam flows to the atmosphere from a high pressure vessel, the flow reaches critical flow conditions, and beyond a certain pressure further lowering of pressure does not increase the steam discharge. The flow is given by the equation [17]

The value of DP to be chosen depends on K, the system resistance, where

K ¼ 12 f dLe

where

Le ¼ total equivalent length of all downstream piping including valves and fittings, ft

f ¼ Darcy friction factor

d ¼ pipe inner diameter, in.

Y ¼ expansion factor (see Table 7.13)

v ¼ specific volume of steam before expansion, cu ft=lb

DP ¼ pressure drop, lower of actual upstream pressure minus downstream pressure or that obtained from Table 7.13

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TABLE 7.13 Limiting Factors for Sonic

Velocity k ¼ 1.3

Example

Determine the flow of saturated steam from a vessel at 170 psia to the atmosphere if the total equivalent system resistance K ¼ 10 and pipe inner diameter ¼ 2.067 in.

or DP ¼ 170 0.773 ¼ 131.5 psia. Hence, use DP ¼ 131.5 psia. Also from Table 7.13 for K ¼ 10, Y ¼ 0.705. Hence

¼ 12;630 lb=h

7.34

Q:

How is the flow through boiler blowdown lines determined?

A:

Sizing of blowdown or drain lines is very important in boiler or process plant operations.

The problem of estimating the discharge rates from a boiler drum or vessel to the atmosphere or to a vessel at low pressures involves two-phase flow calculations and is a lengthy procedure [18].

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and

The term ðdP=dvÞs refers to the change in pressure-to-volume ratio at critical flow conditions at constant entropy.

Hence, in order to estimate mc, Eqs. (42) and (44) have to be solved. This is an iterative procedure. For the sake of simplicity, the term involving the height differences will be neglected. For high pressure systems the error in neglecting this term is marginal, on the order of 5%.

The problem is, then, given K and Ps, to estimate Pc and m. This is a trial- and-error procedure, and the steps are outlined below, followed by an example. Figs. 7.16 and 7.17 are two charts that can be used for quick sizing purposes.

1.Assume a value for Pc.

2.Calculate ðdP=dvÞs at Pc for constant-entropy conditions. The volume change corresponding to 2–3% of Pc can be calculated, and then ðdP=dvÞs can be obtained.

3.Calculate mc using Eq. (44).

4.Solve Eq. (42b) for m.

ðv2=v1Þ ¼ 2 ln ðrs=rcÞ is then found.

Then m is computed using Eq. (42b). If the m values computed using Eqs. (42b) and (44) tally, then the assumed Pc and the resultant mc are correct. Otherwise Pc has to be changed, and all steps have to be repeated until m and mc agree.

Example

A boiler drum blowdown line is connected to a tank set at 8 atm. Drum pressure is 100 atm, and the resistance K of the blowdown line is 80. Estimate the critical mass flow rate mc and the critical pressure Pc.

vl ¼ 0.001445 m =kg, or r ¼ 692 kg=m .

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¼0:1696

v ¼ vl þ xðvv vlÞ

¼0:001249 þ 0:1696 ð0:05078 0:001249Þ

¼0:009651 m3=kg

Again, compute v at 41 atm (2.5% more than Pc). Using steps similar to those described above, v ¼ 0.0093 m3=kg.

The dryness fraction at 40 atm at isenthalphic condition is

x¼ 334 258:2 ¼ 0:1845 669 258:2

vc ¼ 0:001249 þ 0:1845 ð0:05078 0:001249Þ

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