Steam Inlet and Exit Nozzle Location

The steam nozzle inlet in a superheater header should preferably be located in the middle of the header or if it is long (say, above 4 m) at two quarter points with 50% of flow in each inlet to ensure steam flow is uniform inside the tubes. End inlet or exit connection as shown in Figure 3.34 is not recommended though it may be convenient from piping layout viewpoint. The static head difference between headers impacts the steam flow through each tube, and end connection as shown in arrangement 1 of Figure 3.34 shows the largest difference in steam flow between the first and last tubes, resulting in overheating of tubes close to steam inlet end.

Steam Generators 131

Gas

A B C D E Steam

Temperature distribution across various resistances at superheater exit. Note: (A) gas film, (B) gas-fouled layer, (C) tube wall, (D) steam-fouled layer, and (E) steam film.

Off-Design Performance of Superheater

Example 3.6

The following details are available for an inverted-loop superheater shown in Figure 3.27a, and the plant engineer wants to evaluate the performance when the gas flow and inlet conditions to the superheater are known. That is, compute the duty, exit gas temperature, exit steam temperature, and tube wall temperature. The superheater is located beyond several rows of screen tubes in a D-type boiler, and hence, direct radiation from the furnace is not considered.

Solution

Steam pressure at superheater exit = 100 kg/cm 2 a. Gas flow entering the superheater

(based on natural combustion calculations) = 250,000 kg/h at 1100°C (measured).

% volume of flue gas is CO 2 = 8.29, H 2 O = 18.17, N 2 = 71.08, O 2 = 2.46. Saturated

steam of 200,000 kg/h is entering the superheater, and flow direction is counter-

flow. Fouling factor on steam side = 0.0002 m 2 h °C/kcal and that on gas side is 0.0004 m 2 h °C/kcal. Superheater tube geometry details: 50.8 × 44 mm T11 tubes, 14 tubes/row, 15 rows deep, S T =S L = 100 mm. Average (height) length of tube is 8 m, 35 streams. For the mean-

ing of streams, see Appendix B. Surface area = 3.14 × 0.0508 × 14 × 15 × 8 = 268 m 2 . Let us assume a steam-side pressure drop of 4 kg/cm 2 . Hence, steam pressure at inlet = 104 kg/cm 2 a. Saturation temperature is 312°C. Assume an average gas temperature of 970°C in the superheater (to be checked later).

The flue gas properties have to be evaluated at the average film temperature. As

a first trial, we may assume it as 0.475 (tg 1 + ts 1 ) = 0.475 × (1100 + 312) = 670°C. From

Appendix F, the flue gas properties are C p = 0.3075 kcal/kg °C, µ = 0.1373 kg/m h, and k = 0.055 kcal/m h °C.

Using the Grimson’s correlation for convective heat transfer coefficient from Appendix C, we have Nu = 0.229 × Re 0.632 using B and N values of 0.229 and 0.632, respectively.

Gas mass velocity G = 250,000/[14 × (0.1 − 0.0508) × 8] = 45,369 kg/m 2 h (9,258 lb/ft 2 h). Hence, Re = Gd/µ = 45,369 × 0.0508/0.1373 = 16,786

Nu = h c d/k = 0.229 × 16,786 0.632 = 107.1 or h c = 107.1 × 0.055/0.0508 = 116 kcal/m 2 h °C Calculate the nonluminous heat transfer coefficient as discussed in Appendix D. Beam length L = 1.08 × [0.1 × 0.1 − 0.785 × 0.0508 × 0.0508]/0.0508 = 0.1695 m.

Factor K = (0.8 + 1.6 × 0.181) × (1 − 0.00038 × 1243) × (0.0829 + 0.1817)/[(0.0829 + 0.1817) × 0.1695] 0.5 = 0.719. ∈ g = 0.9 × (1 – e 0.719 × 0.1695 ) = 0.103. h n = 5.67 × 10 −8 × 0.103 ×

(1243 4 − 6.6 4 )/(1243 − 660) = 18.59 kcal/m 2 h °C.

132 Steam Generators and Waste Heat Boilers: For Process and Plant Engineers

Hence, h o = 18.59 + 116 = 134.59 kcal/m 2 h °C. Tube-side coefficient h i = 0.0278 × C × (200,000/35/3,600) 0.8 /0.044 1.8. Assume an average steam temperature of 360°C for estimating h i . C from Appendix B,

Table B.4, is 382. Then, h i = 4250 W/m 2 K = 3655 kcal/m 2 h °C (745 Btu/ft 2 h °F)

1/U o = 50.8/44/3655 + 0.0002 × (50.8/44) + 0.0508 ln(50.8/44)/2/35 + 0.0004 + 1/134.59

= 0.000316 + 0.000231 + 0.0001042 + 0.0004 + 0.00743 = 0.008481 or

U o = 117.9 kcal/m 2 h °C Let us use an average gas specific heat at 900°C and an average steam specific heat

between 400°C and saturation. Enthalpy at 100 kg/cm 2 a at 400°C = 740.8 kcal/kg and

that of saturated steam at 312°C is 650 kcal/kg. Hence, C ps = (740.8 − 650)/(400 − 312) = 1.0318 kcal/kg °C

∈ =[1 − exp{–NTU × (1 – C)}]/[1 – C exp{–NTU × (1 – C)}] W g C pg = 250,000 × 0.328 = 82,000 W s C ps = 200,000 × 1.0318 = 206,360. WC min = 82,000

C = WC min /WC max = 82,000/206,360 = 0.397. NTU = UA/WC min = 117.9 × 268/82,000 = 0.384

Hence, ∈ = [1 – exp{–0.384 × (1 − 0.397)}]/[1 − 0.397 exp{–0.384 × (1 − 0.397)}] = 0.301 Hence, energy transferred Q = 0.301 × 82,000 × (1100 − 312) = 19.45 × 10 6 kcal/h

Hence, T g2 = 1,100 – 19.45 × 10 6 /(250,000 × 0.328) = 863°C T s2 = 312 + 19.45 × 10 6 /(200,000 × 1.0318) = 406°C

We have to correct for the average specific heats of gas and steam at the revised gas and steam temperatures and make another run, but the duty will be close to the earlier one, and hence, let us proceed with the tube wall temperature estimation.

Tube Wall Temperature Estimation Let us compute the tube wall temperature at the superheater exit. Being counter-flow,

gas temperature = 1100°C, steam temperature = 406°C. Assume tube outer wall is 475°C. C factor at 406°C from Appendix B is 342. Note that the tube-side heat transfer coefficient decreases at higher steam temperatures at high pressures, while the gas-side heat transfer coefficient is higher at higher temperatures, compounding the problem of tube wall temperature (see Figure B.3).

h c = 3655 × 342/382 = 3272 kcal/m 2 h °C (taking the ratio of C values from previous calculation for h i ).

Assume the film temperature is 750°C (this has to be revised later). From Appendix F,

C p = 0.3127, µ = 0.1451, k = 0.059. G = 45,369. Re = 45,369 × .0508/.1451 = 15,883.

Nu = 0.229 × 15,883 0.632 = 103.5 = h c × 0.0508/.059 or h c = 120 kcal/m 2 h °C (24.4 Btu/ft 2 h °F)

Steam Generators 133

K = (0.8 + 1.6 × 0.181) × (1 – 0.000381 × 1373) × (0.0829 + 0.1817)/[(0.0829 + 0.1817) ×

0.1695] 0.5 = 0.649. ∈ g = 0.9 × (1 – e 0.649 × 0.1695 ) = 0.093. h n = 5.67 × 10 −8 × 0.093 × (1373 4 − 7.48 4 )/(1373 − 748) = 27.34 W/m 2 K = 23.5 kcal/m 2 h °C (4.8 Btu/ft 2 h °F)

1/U o = 50.8/44/3272 + 0.0002 × (50.8/44) + 0.0508 ln(50.8/44)/2/35 + 0.0004 + 1/143.5

= 0.0003529 + 0.000231 + 0.0001042 + 0.0004 + 0.006969 = 0.008057 or

U o = 124 kcal/m 2 h °C (25.3 Btu/ft 2 h °F)

Heat flux based on tube OD = 124 × (1100 − 406) = 86,135 kcal/m 2 h (31,646 Btu/ft 2 h). Temperature drop across inside steam film = 86,135 × 0.0003529 = 30°C (54°F)

Drop across inside fouling layer = 86,135 × 0.000231 = 19.9°C (36°F) Hence, tube inner wall temperature = 406 + 30 + 20 = 456°C (853°F) Drop across tube wall = 86,135 × 0.0001042 = 9°C (16°F)

Hence, tube outer wall temperature = 456 + 9 = 465°C (869°F) (used for checking oxida- tion limits). Table 3.10 shows the allowable temperatures of certain tube materials.

Tube mid-wall temperature = 460°C (860°F) (used for calculating tube wall thickness) Drop across gas fouling layer = 86,135 × 0.0004 = 34°C (61°F) Drop across gas film = 86,135 × 0.006969 = 600°C (1080°F)

Considering various nonuniformities due to gas flow, due to steam flow due to header arrangement (Figure 3.35), or variations in tube lengths and margin for safety, one may add a certain value based on experience. Let us use 25°C as margin, and so maximum tube wall temperature is 485°C (905°F) for tube mid-wall temperature and 490°C (914°F) for outer wall for design. The various thermal resistances are shown in Figure 3.34 at superheater exit.

Estimating the Tube Thickness Table 3.10 shows that the allowable temperature for T11 material is 565°C. Hence, T11

material is adequate for this superheater. Let us check the thickness.

Flow nonuniformity inside tubes due to header arrangements.

134 Steam Generators and Waste Heat Boilers: For Process and Plant Engineers

TABLE 3.10

Allowable Material Temperatures

Material

Composition

Temp., °F

SA 178A (erw)

Carbon steel

SA 178C (erw)

Carbon steel

SA 192 (seamless)

Carbon steel

SA 210A1

Carbon steel

SA 210C

Carbon steel

SA 213-T11

1.25Cr–0.5Mo–Si

SA 213-T22

2.25Cr–1Mo

SA 213-T91

9Cr–1Mo–V

SA 213-TP304H

18Cr–8Ni

SA 213-TP347H

18Cr–10Ni–Cb

SA 213-TP321H

18Cr–10Ni–Ti

SB 407–800H

33Ni–21Cr–42Fe

Per ASME Boiler and Pressure Vessel code sec 1, the following equation may be used to determine the thickness at 485°C (905°F):

t = Pd/(2S + P) + 0.005d Design pressure P is arrived at based on pressure drop in the superheater, desuper-

heater if used, and piping. Let us say the additional pressure drop in the piping and desuperheater is 1 kg/cm 2 . S is the allowable stress.

The superheater pressure drop in kPa is given by ΔP = 810 × 10 −6 × fL e vw 2/ d i 5.

w = flow per tube, kg/s = 20,000/3,600/35 = 1.587 kg/s. At average steam temperature of 360°C and at 103 kg/cm 2 a, specific volume = 0.023 m 3 /kg. The effective length of tube = 8 + 2.5 × 1.75/3.28 = 9.33 m (2.5 times inner diam- eter was taken for the bend loss in feet). (Number of tubes per row × number of rows deep)/streams = number of lengths of tube = 14 × 15/35 = 6. Hence, developed length = 6 × 9.33 = 56 m.

Δ P = 810 × 10 −6 × 0.02 × 56 × 0.023 × 1.587 2 /0.044 5 = 319 kPa = 3.25 kg/cm 2 . We have

to add the tube entrance and exit losses due to the connection at the inlet and exit headers.

At the entrance of tube saturated steam, specific volume = 0.0176 m 3 /kg, and at exit

where steam is at 100 kg/cm 2 a and 406°C, v = 0.0275 m 3 /kg. Inlet velocity = 1.587 × 0.0176 × 4/(3.14 × 0.044 × 0.044) = 18.3 m/s. Loss = 0.5 × velocity

head = 0.5 × 18.3 × 18.3/(2 × 9.8 × 0.0176) = 485 kg/m 2 = 0.0485 kg/cm 2. Steam velocity at exit = 1.587 × 0.0275 × 4/(3.14 × 0.044 × 0.044) = 28.7 m/s. Velocity head VH = 28.7 × 28.7/(2 × 9.8 × 0.0275) = 1529 kg/m 2 = 0.15 kg/cm 2 . Loss = 0.15 kg/cm 2. Total pressure drop inside tubes = 3.25 + 0.049 + 0.15 = 3.45 kg/ cm 2 (49 psi). Hence, assuming piping loss as 1.0 kg/cm 2 , design pressure may be taken as 1.1 × (100 + 3.45 + 1.0) = 115 kg/cm 2 . (It can range from 108 to 115 kg/cm 2 g.) At 485°C (905°F),

allowable stress for T11 is 13,100 psi (from Table 3.11) = 921 kg/cm 2 . Tube thickness = 115 × 50.8/(2 × 921 + 115) +0.005 × 50.8 = 3.23 mm. Thickness used is 3.4 mm. One may use a higher thickness after evaluating the flow in unequal tube lengths, or the design pressure may be slightly lowered to give some margin for corro- sion allowance if required.

Steam Generators 135

TABLE 3.11

Allowable Stress Values, ASME 2009, S

Temp., SA178a, SA213

SA213 SA213 SA213 °F

SA192 T11

T22

A1 T91

TP304H

TP316H TP321H TP347H

Steam Inlet and Exit Nozzle Location