441 hw 6
A process engineer has specified the duty of the heat exchanger E37, the first stage intercooler in the ammonia synthesis compression system. He has also given you the physical
properties of the fluids on the tube and the shell sides. Design a heat exchanger that will
meet the duty specification and the pressure drop specifications of not more than 10 psi in
both the shell side and the tube side. The diameter of the shell and the tube length should
not exceed 60 inches and 24 feet respectively.
Excel calculation
Step (1) Assume the exchanger is 1 shell and 1 pass/shell. Use F = 0.65
Step (2) Assume Uo =120 Btu/ft2/hr/F.
Step (3) Calculate A from given temperatures and assumed Uo.
Step (4) Pick tube OD = 3/4 in and BWG=14 (Wall thickness = 0.083 in., ID = 0.584 in.
from Table D-12, p. 961, Ref. 1)
Step (5) Pick length = 24 feet and triangular pitch.
Step (6) Calculate No of tubes.
Step (7) Estimate the Shell ID (Ds, in) using the following relationship (valid only for
0.75” OD, 1” triangular pitch)
 N 
Ds = do  t 
 0.21 
1 / 2.15
+2
You also need the following equations for the Excel calculation
The area of flow (shell side) As = flow area at the center of the tube and between baffles
As =
Shell _ I .D.
 clearance between tube  baffle spacing
Tube _ pitch
Shell side heat transfer coefficient
k a
ho = f o
Do Fs
 DoGs 



 s 
0.6
k a
 Cp 

 = f o Re0.6Pr1/3
Do Fs
 k f
1/ 3
where
ao = 0.33 if tubes in tube bank are staggered (triangular pitch) and 0.26 if tubes are
inline (square pitch)
Fs = safety factor to account for bypassing effects = 1.6 (recommended value)
Gs = shell-side mass velocity across tubes, based on minimum free area between
baffles at shell axis, lb/hrft2.
Do = outside tube diameter
Subscript f refers to properties at average film temperature = (Ti + To)/2
Tube side heat transfer coefficient
25
hi = 0.023
kf
Di
Re0.8Pr1/3
The overall heat transfer coefficient is calculated from (neglecting heat resistance through
tube wall)
1
1
1
D 1
D 1
=
+
+ o
+ o
Di hid
Di hi
U o ho
hod
Note: fouling factor =
1
h
Stop the iteration when the assumed and calculated Uo’s are within 1% (|1  Uo,assu/Uo,cal|
 0.01)
Tube side pressure drop may be estimated from
- Pi =
Bi 2 f F G 2 Ln p
 i Dii
where
fF = Fanning friction factor for isothermal flow based on conditions at the
arithmetic-average temperature of the fluid.
L = tube length
np = number of tube passes
Bi = correction factor to account for friction due to sudden contraction, sudden
expansion, and reversal of flow direction = 1.2 for this assignment
i = correction for non-isothermal flow = 1.0 for this assignment
Use pipe roughness ( = 0.00015 ft) for carbon steel
The friction factor may be estimated from

 2.185 
 14.5  

ln  0.269 
fF =  1.737 ln 0.269 
 
D
Re
D Re  



Shell side pressure drop may be estimated from
- Po =
Bo 2 f s N r Gs2
o
where
fs = special friction factor for shell-side flow
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2
Nr = number of rows of tubes across which shell fluid flows
Bo = correction factor to account for friction due to reversal of flow direction,
recrossing of tubes, and variation in cross section; when flow is across
unbaffled tubes, Bo can be taken as 1.0; when flow is across baffled tubes, Bo
can be taken as the number of tube crosses
Nr = (number of tubes)0.5/2
Bo = number of baffles + 1
D G
fs = bo  o s
 s



0.15
For staggered tubes
bo = 0.23 +
0.11
( xT  1)1.08
xT = ratio of tube pitch to tube diameter
Table 1 lists the excel calculation for this assignment. The bold values in the shaded
boxes are the data used for the calculation. Starting with Uo =120 Btu/ft2/hr/F, we need
two iterations to reach agreement to within 1% between assumed and calculated Uo ‘s.
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Table 1. Excel calculation for heat exchanger E37
INLET TEMP(F)
OUTLET TEMP(F)
MASS FLOW (LB/HR)
Density, lb/ft3
VISCOSITY (cP)
CP (BTU/LB/oF)
k (BTU/HR/FT/oF)
PASSES
FOULING, F-hr-ft2/Btu
LENGTH, FT
TUBE O D,IN
TUBE I D, IN
PITCH TRIANGULAR, IN
NO OF BAFFLES
Shell
Tube
242.60 91.400
100.59 108.903
146605 941364
1.2105 62.519
0.012
0.748
0.815
1.030
0.066
0.360
1.000
2.000
0.00073 0.00195
24.000
0.750
0.583
1.000
12.000
Shell
115.55
ASSUME U, Btu/(hr.ft2.F)
Q (Btu/hr)
16974037
Delta Tlm (F)
46.50
F correction factor
0.65
Surface area, ft2
4860.07
O. Area/tube, ft2
4.71
No. of tube
1032.00
Shell ID, in.
41.09
Baffle spacing, in
22.15
Clearance tubes, in
0.25
X-area, in2
Tubes/pass
Total X-area, in2
Mass vel., lb/ft2/hr
Pr
Re
h, Btu/(hr.ft2.F)
Uo, Btu/(hr.ft2.F)
114.49723
No of iterations
1
Pressure drop calculation
e/D
Bo, # of tube cross
xT, pitch/OD
bo
Nr
16.062378
Friction factor
Pressure drop, psi
227.552
92774.8
0.34666
206624
236.483
Tube
0.26695
516
137.745
984110
5.18689
26407.4
1015.65
0.00309
13
1.33333
0.59032
0.09415 0.00763
4.65224 4.66642
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