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CHEMICAL ENGINEERING
Assuming that the coefficient changes linearly for the inlet to outlet, then the average
coefficient will be given by:
[inlet coefficient (all liquid) C outlet coefficient (liquid C vapour)]/2
ReL at inlet D 36,833 ð 0.4/0.3 D 49,111 4.9 ð 104 From Figure 12.23, jh D 3.2 ð 103
Nu D 3.2 ð 103 ð 49,111 ð 2.780.33 D 220.2
3
2Ž
hi D 220.2 ð 0.12/25 ð 10 D 1057 Wm
12.15
C
1
Mean coefficient D 1057 C 3880/2 D 2467 Wm2Ž C1
The overall coefficient, U, neglecting the resistance of the tube wall, and taking the steam
coefficient as 8000 Wm2Ž C1 , is given by:
1/U D 1/8000 C 1/2467 D 5.30 ð 104
U D 1886 Wm2Ž C1
The overall coefficient required for the design D duty/TLM
TLM D 158.8 120 D 38.8Ž C, taking both streams as isothermal
So, U required D 37,900/38.3 D 990 Wm2Ž C1
So the area available in the proposed design is more than adequate and will take care of
any fouling.
The analysis could be improved by dividing the tube length into sections, calculating
the heat transfer coefficient and pressure drop over each section, and totalling.
More accurate, but more complex, methods could be used to predict the two-phase
pressure drop and heat transfer coefficients.
The pressure drop over the inlet and outlet pipes could also be estimated, taking into
account the bends, and expansions and contractions.
An allowance could also be included for the energy (pressure drop) required to accelerate the liquid vapour mixtures as the liquid is vaporised. This can be taken as two
velocity head, based on the mean density.
12.11.6. Design of kettle reboilers
Kettle reboilers, and other submerged bundle equipment, are essentially pool boiling
devices, and their design is based on data for nucleate boiling.
In a tube bundle the vapour rising from the lower rows of tubes passes over the upper
rows. This has two opposing effects: there will be a tendency for the rising vapour to
blanket the upper tubes, particularly if the tube spacing is close, which will reduce the
heat-transfer rate; but this is offset by the increased turbulence caused by the rising vapour
bubbles. Palen and Small (1964) give a detailed procedure for kettle reboiler design in
HEAT-TRANSFER EQUIPMENT
751
which the heat-transfer coefficient calculated using equations for boiling on a single tube
is reduced by an empirically derived tube bundle factor, to account for the effects of
vapour blanketing. Later work by Heat Transfer Research Inc., reported by Palen et al.
(1972), showed that the coefficient for bundles was usually greater than that estimated for
a single tube. On balance, it seems reasonable to use the correlations for single tubes to
estimate the coefficient for tube bundles without applying any correction (equations 12.62
or 12.63).
The maximum heat flux for stable nucleate boiling will, however, be less for a tube
bundle than for a single tube. Palen and Small (1964) suggest modifying the Zuber
equation for single tubes (equation 12.64) with a tube density factor. This approach was
supported by Palen et al. (1972).
The modified Zuber equation can be written as:
pt
p
qcb D Kb
[ gL v v2 ]0.25
12.74
do
Nt
where qcb D maximum (critical) heat flux for the tube bundle, W/m2 ,
Kb D 0.44 for square pitch arrangements,
D 0.41 for equilateral triangular pitch arrangements,
pt D tube pitch,
do D tube outside diameter,
Nt D total number of tubes in the bundle,
Note. For U-tubes Nt will be equal to twice the number of actual U-tubes.
Palen and Small suggest that a factor of safety of 0.7 be applied to the maximum flux
estimated from equation 12.74. This will still give values that are well above those which
have traditionally been used for the design of commercial kettle reboilers; such as that
of 37,900 W/m2 (12,000 Btu/ft2 h) recommended by Kern (1950). This has had important
implications in the application of submerged bundle reboilers, as the high heat flux allows
a smaller bundle to be used, which can then often be installed in the base of the column;
saving the cost of shell and piping.
General design considerations
A typical layout is shown in Figure 12.8. The tube arrangement, triangular or square pitch,
will not have a significant effect on the heat-transfer coefficient. A tube pitch of between
1.5 to 2.0 times the tube outside diameter should be used to avoid vapour blanketing.
Long thin bundles will be more efficient than short fat bundles.
The shell should be sized to give adequate space for the disengagement of the vapour
and liquid. The shell diameter required will depend on the heat flux. The following values
can be used as a guide:
Heat flux W/m2
Shell dia./Bundle dia.
25,000
25,000 to 40,000
40,000
1.2 to 1.5
1.4 to 1.8
1.7 to 2.0
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CHEMICAL ENGINEERING
The freeboard between the liquid level and shell should be at least 0.25 m. To avoid
excessive entrainment, the maximum vapour velocity uO v (m/s) at the liquid surface should
be less than that given by the expression:
L v
uO v < 0.2
v
1/2
12.75
When only a low rate of vaporisation is required a vertical cylindrical vessel with
a heating jacket or coils should be considered. The boiling coefficients for internal
submerged coils can be estimated using the equations for nucleate pool boiling.
Mean temperature differences
When the fluid being vaporised is a single component and the heating medium is steam (or
another condensing vapour), both shell and tubes side processes will be isothermal and the
mean temperature difference will be simply the difference between the saturation temperatures. If one side is not isothermal the logarithmic mean temperature difference should be
used. If the temperature varies on both sides, the logarithmic temperature difference must
be corrected for departures from true cross- or counter-current flow (see Section 12.6).
If the feed is sub-cooled, the mean temperature difference should still be based on the
boiling point of the liquid, as the feed will rapidly mix with the boiling pool of liquid;
the quantity of heat required to bring the feed to its boiling point must be included in the
total duty.
Mixtures
The equations for estimating nucleate boiling coefficients given in Section 12.11.1 can be
used for close boiling mixtures, say less than 5Ž C, but will overestimate the coefficient if
used for mixtures with a wide boiling range. Palen and Small (1964) give an empirical
correction factor for mixtures which can be used to estimate the heat-transfer coefficient
in the absence of experimental data:
hnb mixture D fm hnb single component
12.76
where fm D exp[0.0083Tbo Tbi ]
and Tbo D temperature of the vapour mixture leaving the reboiler Ž C,
Tbi D temperature of the liquid entering the reboiler Ž C.
The inlet temperature will be the saturation temperature of the liquid at the base of the
column, and the vapour temperature the saturation temperature of the vapour returned to
the column. The composition of these streams will be fixed by the distillation column
design specification.
Example 12.12
Design a vaporiser to vaporise 5000 kg/h n-butane at 5.84 bar. The minimum temperature
of the feed (winter conditions) will be 0Ž C. Steam is available at 1.70 bar (10 psig).
HEAT-TRANSFER EQUIPMENT
753
90
45
Tube outer limit dia.
420 mm
Tube O.D 30mm
52 Tube holes
26 u-tubes
Tube sheet layout, U-tubes, Example 12.9
Solution
Only the thermal design and general layout will be done. Select kettle type.
Physical properties of n-butane at 5.84 bar:
boiling point D 56.1Ž C
latent heat D 326 kJ/kg
mean specific heat, liquid D 2.51 kJ/kgŽ C
critical pressure, Pc D 38 bar
Heat loads:
sensible heat (maximum) D 56.1 02.51 D 140.8 kJ/kg
total heat load D 140.8 C 326 ð
5000
D 648.3 kW,
3600
add 5 per cent for heat losses
maximum heat load (duty) D 1.05 ð 648.3
D 681 kW
From Figure 12.1 assume U D 1000 W/m2 Ž C.
Mean temperature difference; both sides isothermal, steam saturation temperature at
1.7 bar D 115.2Ž C
Tm D 115.2 56.1 D 59.1Ž C
681 ð 103
D 11.5 m2
1000 ð 59.1
Select 25 mm i.d., 30 mm o.d. plain U-tubes,
Area (outside) required D
Nominal length 4.8 m (one U-tube)
Number of U tubes D
11.5
D 25
30 ð 103 4.8
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CHEMICAL ENGINEERING
Use square pitch arrangement, pitch D 1.5 ð tube o.d.
D 1.5 ð 30 D 45 mm
Draw a tube layout diagram, take minimum bend radius
1.5 ð tube o.d. D 45 mm
Proposed layout gives 26 U-tubes, tube outer limit diameter 420 mm.
Boiling coefficient
Use Mostinski’s equation:
heat flux, based on estimated area,
hnb
681
D 59.2 kW/m2
qD
11.5
5.84 0.17
5.84 1.2
5.84 10
0.69
3 0.7
D 0.10438 59.2 ð 10 1.8
C4
C 10
38
38
38
D 4855 W/m2 Ž C
12.63
Take steam condensing coefficient as 8000 W/m2 Ž C, fouling coefficient 5000 W/m2 Ž C;
butane fouling coefficient, essentially clean, 10,000 W/m2 Ž C.
Tube material will be plain carbon steel, kw D 55 W/mŽ C
30
30 ð 103 ln
1
30
1
1
1
1
25
C
C
C
C
D
Uo
4855 10,000
2 ð 55
25 5000 8000
12.2
Uo D 1341 W/m2 Ž C
Close enough to original estimate of 1000 W/m2 Ž C for the design to stand.
Myers and Katz (Chem. Eng. Prog. Sym. Ser. 49(5) 107 114) give some data on the
boiling of n-butane on banks of tubes. To compare the value estimate with their values
an estimate of the boiling film temperature difference is required:
D
1341
ð 59.1 D 16.3Ž C 29Ž F
4855
Myers data, extrapolated, gives a coefficient of around 3000 Btu/h ft2 Ž F at a 29Ž F temperature difference D 17,100 W/m2 Ž C, so the estimated value of 4855 is certainly on the
safe side.
Check maximum allowable heat flux. Use modified Zuber equation.
Surface tension (estimated) D 9.7 ð 103 N/m
L D 550 kg/m3
273
58
ð
ð 5.84 D 12.6 kg/m3
v D
22.4 273 C 56
Nt D 52
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HEAT-TRANSFER EQUIPMENT
For square arrangement Kb D 0.44
qc D 0.44 ð 1.5 ð
326 ð 103
p
[9.7 ð 103 ð 9.81550 12.612.62 ]0.25 12.74
52
D 283,224 W/m2
D 280 kW/m2
Applying a factor of 0.7, maximum flux should not exceed 280 ð 0.7 D 196 kW/m2 .
Actual flux of 59.2 kW/m2 is well below maximum allowable.
Layout
From tube sheet layout Db D 420 mm.
Take shell diameter as twice bundle diameter
Ds D 2 ð 420 D 840 mm.
Take liquid level as 500 mm from base,
freeboard D 840 500 D 340 mm, satisfactory.
340
420
500
From sketch, width at liquid level D 0.8 m.
Surface area of liquid D 0.8 ð 2.4 D 1.9 m2 .
1
1
5000
ð
ð
D 0.06 m/s
Vapour velocity at surface D
3600 12.6 1.9
Maximum allowable velocity
uO v D 0.2
550 12.6
12.6
1/2
D 1.3 m/s
12.75
so actual velocity is well below maximum allowable velocity. A smaller shell diameter
could be considered.