QUICK MANUAL DESIGN OF SHELL AND
TUBE HEAT EXCHANGERS
By
JAYESHMODI
Bachelor of Engineering
B.V.College of Engineering
University of Poona
Pune, India
1991
Submitted to the Faculty of the
Graduate College of the
Oklahoma State University
in partial fulfilment of
the requirements for
the Degree of
MASTER OF SCIENCE
May, 1995
QUICK MANUAL DESIGN OF SHELL AND
TUBE HEAT EXCHANGERS
Thesis Approved:
ean of the Graduate College
ii
PREFACE
The purpose of this thesis is to provide a general procedure to, quickly estimate the
approximate size of a shell and tube heat exchanger, including multiple shells in series
and/or parallel, and dimensions required for entering rating calculations. This procedure
is an expansion and refinement of the procedure given in Section 3.1.4 ofthe Heat
Exchanger Design Handbook (Bell, 1983). The procedure is useful for a preliminary
plant layout, cost estimation, and as a check on the output of computer-based design
procedures.
Chapter 1 discusses the general usefulness of an approximate design method for
shell and tube heat exchangers and describes both the essential and desirable features of
such a method. A brief description of the components of a shell and tube heat exchanger,
the various types of shell and bundle constructions, and the general selection criteria are
also presented.
Chapter 2 deals with the basic structure ofthe design method. It includes a brief
description of the concepts of conduction, convection and radiation. Also presented are
procedures for the estimation ofQ (total heat duty), MTD (mean temperature difference),
individual film heat transfer coefficients (a's) and overall heat transfer coefficient (Uo),
and the number of shells required to perform the specified duty. The existing version of
the design method, with its limitations, is also described.
In Chapter 3, the relationship of the heat transfer area, A, to the basic shell dimensions
(shell inside diameter and effective tube length) is developed. A. generalization of the
outside area/shell dimensions relationship for the reference case to other tube sizes and
iii
layouts, bundle types, number of tube side passes and finned tube dimensions is also
developed.
Chapter 4 presents a procedure for the estimation of tube counts. An approximate
method for estimating the baffle cut and baffle spacing as a function of the shell inside
diameter is also presented. Vibration limitations are also described.
The Summary and Conclusions are given in Chapter 5 and Recommendations in
Chapter 6. The use of the approximate design method is illustrated in the form of an
example problem in the appendix. Also given are various tables for the estimation of
film and overall coefficients for various cases, fouling factors, dimensions of bare and
finned tubes and detailed tables and plots for the estimation of the correction factors.
iv
ACKNOWLEDGMENTS
At the very outset, I would like to thank my major advisor, Dr. Ken Bell for his
invaluable comments, constructive criticism and guidance and unlimited patience. My
sincere appreciation extends to Dr. Karen High and Dr. Rob Whiteley, for agreeing to
serve on my committee. I would like to thank Dr. Arland Johannes (A J) whose
guidance, encouragement, and friendship are also invaluable.
I would also like to take this opportunity to thank my family for their
encouragement. I would also like to give my special appreciation to my friends,
especially Lindsay, Steven, Kanchana, Suresh and Rohit for their precious suggestions to
my research.
Last but not the least, I would like to thank all the secretaries of the School of
Chemical Engineering for their immense help and CEAT for the use of their facilities.
v
Chapter
TABLE OF CONTENTS
Page
I. SHELL AND TUBE HEAT EXCHANGERS 1
Introduction.......................................................................................................... 1
Shell and Tube Heat Exchangers......................................................................... 3
Components ;................................... 9
Selection Criteria 12
Finned Tube Heat Exchangers 12
II. BASIC STRUCTURE OF THE DESIGN METHOD 15
Modes of Heat Transfer....................................................................................... 15
Film Heat Transfer Coefficient 17
Overall Heat Transfer Coefficient........................................................................ 18
Basic Design Equation......................................................................................... 24
Calculation of Total Heat Duty 26
Logarithmic Mean Temperature Difference 26
Mean Temperature Difference 30
Number of Shell Required 34
Heat Transfer Area 36
Extension of "Base Case" to Other Shell/Bundle/Tube Geometries 39
Limitations ofthe Existing Version 40
III. CORRECTION FACTORS ESTIMATION 41
Introduction.......................................... 41
Correction Factor for Unit Cell Tube Array 42
Correction Factor for Number of Tube-side Passes 46
Correction Factor for Shell Construction/Tube-bundle Layout Type 48
Correction Factor for Finned-tube Heat Exchangers 50
Estimation of Equivalent Area 53
Effective Tube Length and Shell Diameter 54
VI
Chapter Page
IV. PARAMETER ESTIMATION 55
Estimation of Tube Counts 55
Estimation of Baffle Cut and Baffle Spacing 57
Tube Vibrations................................................................................................... 61
Mechanisms of Tube Vibrations.......................................................................... 62
V. SUMMARY AND CONCLUSIONS 64
Summary 64
Conclusions 66
VI. RECOMMENDATIONS 68
BIBLIOGRAPHY 69
APPENDICES 73
APPENDIX A--TYPICAL OVERALL AND INDIVIDUAL DESIGN
COEFFICIENTS FOR SHELL AND TUBE
HEAT EXCHANGERS .......................................•................................... 74
APPENDIX B--EXAMPLE PROBLEM............................................................. 84
APPENDIX C--CHARACTERISTICS OF TUBING 91
APPENDIX D--DIMENSIONS OF FINNED TUBES 92
APPENDIX E--TUBE COUNT TABLES 95
APPENDIX F--CALCULATIONS FOR FACTOR F1 101
APPENDIX G--DETAILED TABLES FOR F2 104
APPENDIX H--DETAILED TABLES FOR F3 110
APPENDIX I--TABLES AND PLOTS FOR ESTIMATION OF Fp 115
APPENDIX J--PLOTS FOR ESTIMATION OF BAFFLE SPACING 122
VII
··
LIST OF TABLES
Table Page
I. Features of Principal Shell and Tube Heat Exchanger Designs '10
II. Correction Factor F1 for Unit Cell Tube Array 43
III. Correction Factor F2 for Number of Tube-side Passes 47
IV. Correction Factor F3 for Various Tube Bundle Layouts 49
V. Correction Factor Fffor Low-finned Tubes 51
VI. Typical Overall Heat Transfer Coefficients for
Shell and Tube Heat Exchangers ; 75 · VII. Typical Film Heat Transfer Coefficients and Fouling Factors for
Shell and Tube Heat Exchangers......................................................................... 78
VIII. Characteristics of Tubing 91
IX. Dimensions of Finned Tubes................................................................................ 92
X. Tube Count for Fixed Tubesheet Heat Exchangers 96
XI. Tube Count for Split Ring Floating Head Heat Exchangers................................ 97
XII. Tube Count for V-Tube Heat Exchangers 98
XIII. Tube Count for PTFH Heat Exchangers (1000 KPa Pressure) 99
XIV. Tube Count for PTFH Heat Exchangers (2000 KPa Pressure) 100
XV. Correction Factor F2 for Fixed Tubesheet Heat Exchangers 104
XVI. Correction Factor F2 for SRFH Heat Exchangers 106 ·· XVII. Correction Factor F2 for U-Tube Heat Exchangers 106
viii
Table Page
XVIII. Correction Factor F2 for PTFH Heat Exchangers (1000 KPa Pressure) 108
XIX. Correction Factor F2 for PTFH Heat Exchangers (2000 KPa Pressure) 108
XIX. Factor F3 for SRFH Heat Exchangers 111
XX. Factor F3 for V-Tube Heat Exchangers 111
XXI. Factor F3 for PTFH Heat Exchangers (1000 KPa Pressure) 113
XXII. Factor F3 for PTFH Heat Exchangers (2000 KPa Pressure) 113
XXIII. Packing Factor for Fixed Tubesheet Heat Exchangers 116
XXIV. Packing factor for V-Tube Heat Exchangers ~ 117
XXV. Packing F~ctor for SRFH Heat Exchangers ~ 118
XXVI. Packing Factor for PTFH Heat Exchangers (1000 KPa Pressure) 119
XXVII. Packing Factor for PTFH Heat Exchangers (2000 KPa Pressure) 120
ix
Figure
LIST OF FIGURES
Page
1. TEMA Designation of Front End, Shell, and Rear End Types of
Shell and Tube Heat Exchangers......................................................................... 4
2. Fixed Tubesheet Design with Expansion Joint.......................................................... 5
3. V-Tube Design........................................................................................................... 6
4. Split-ring Floating Head Design 7
5. Pull-through Floating Head Design 8
6. Outside Packed Lantern-ring Design 8
7. Outside Packed Stuffing Box Design........................................................................ 9
8. Types of Commercial Finned Tubing 14
9. Cross-section of Fluid-to-fluid Heat Transfer Through a Tube Wall 18
10. Block Diagram of a Single Pass Shell and Tube Heat Exchanger with
Counter-current Flow of Fluids ~... 27
11. Temperature Profiles in a Single Pass Shell and Tube Heat Exchanger with
Counter-current Flow of Fluids 27
12. Block Diagram of a Single Pass Shell and Tube Heat Exchanger with
Co-current Flow of Fluids.............................. 28
13. Temperature Profiles in a Single Pass Shell and Tube Heat Exchanger with
Co-current Flow of Fluids 28
14. Temperature Profiles for a Single Pass, Counter-current Flow,
Shell and Tube Heat Exchanger with Varying Fluid Properties 30
15. 1-2 Shell and Tube Heat Exchanger 31
16. Temperature Profile in a 1-2 Shell and Tube Heat Exchanger 31
x
Figure Page
17. LMTD Correction Factor for a 1-n
Shell and Tube Heat Exchanger 33
18. Estimation ofNumber of Shells Required in Series 35
19. Equivalent Area as a Function of Shell Inside Diameter and Effective Tube
Length for 19.05 mm. OD Tubes on 23.81 mm. Equilateral Triangular
Tube Layout, Fixed Tubesheet, One Tube-side Pass,
Fully Tubed Shell................................................................................................. 38
20. Dimensional Nomenclature Used for Type SIT Trufin Finned Tubes 50
21. Baffle Cut Angle....................................................................................................... 59
22. Unit Cell Array for Triangular Pitch Layout 101
23. Unit Cell Array for Square and Rotated Square Layouts 103
24. Correction Factor F2 for Fixed Tubesheet Heat Exchangers: 105
25. Correction Factor F2 for SRFH Heat Exchangers 107
26. Correction Factor F2 for V-Tube Heat Exchangers 107
27. Correction Factor F2 for PTFH Heat Exchangers (1000 KPa Pressure) 109
28. Correction Factor F2 for PTFH Heat Exchangers (2000 KPa Pressure) 109
29. Correction Factor F3 for SRFH Heat Exchangers 112
30. Correction Factor F3 for U-Tube Heat Exchagers 112
31. Correction Factor F3 for PTFH Heat Exchangers (1000 KPa Pressure) 114
32. Correction Factor F3 for PTFH Heat Exchangers (2000 KPa Pressure) 114
33 Packing Factor as a Function of the Diameter of Outer Tube Limit and
Tube Pitch Layout for Various Exchanger Configurations 121
34 Baffle Spacing as a Function of Baffle Cut and Shell Inside Diameter for
Fixed Tubesheet Heat Exchangers : 124
35 Baffle Spacing as a Function of Baffle Cut and Shell Inside Diameter for
U-Tube Heat Exchangers 124
xi
Figure Page
36 Baffle Spacing as a Function of Baffle Cut and Shell Inside Diameter for
Split Ring Floating Head Exchangers 125
37 Baffle Spacing as a Function of Baffle Cut and Shell Inside Diameter for
Pull-through Floating Head Heat Exchangers (1000 KPa Pressure) 126
38 Baffle Spacing as a Function of Baffle Cut and Shell Inside Diameter for
Pull-through Floating Head Heat Exchangers (2000 KPa Pressure) 127
39 Baffle Spacing as a Function of Baffle Cut and Shell Inside Diameter for
Fixed Tubesheet Heat Exchangers 128
40 Baffle Spacing as a Function of Baffle Cut and Shell Inside Diameter for
Fixed Tubesheet Heat Exchangers 129
xii
A
Cp
D
d
hf
k
L
NOMENCLATURE
Area·, A' "equivalent" area, ft2 or m2
Specific heat at constant pressure, BTU/Ibm of or KJ/kg K
Diameter of shell, in. or m
Diameter of tube, in. or mm
Diameter of outer tube limit, in. or mm
Root diamet~r of finned tube, in. or mm
Correction factor for unit cell tube array
Correction factor for number of tube-side passes
Correction factor for the shell construction/tube bundle layout type
Correction factor for finned tubes
Configuration correction factor on LMTD
Gravitational conversion constant, 4.17xl 08 Ibm-ftllbf-hr2
Height of fin for low finned tubes, in. or mm
Thermal conductivity, BTU/hr ft2 (OF/ft) or W/m2 (Kim)
Tube length, ft. or m
Baffle cut distance from baffle tip to shell inside diameter, in. or mm
xiii
LMTD
m
MTD
PTFH
p
Pn
~P
q
Q
Re
S
SRFH
t
T
U
v
Yf
Logarithmic Mean Temperature Difference, of or K
Central baffle spacing, in. or mm
Baffle spacing at inlet and exit sections, in. or mm
Mass flow rate, lbmlhr or kg/s
Mean Temperature Difference, of or K
Pull-through Floating Head
Tube layout pitch, in. or mm
Tube layout pitch normal to the direction of flow, in. or mm
Pressure drop, Ibtiin.2 or Pa
Heat flux, BTUIhr ft2 of or W/m2 K
Total heat duty, BTUIhr or W
Reynolds number
Fouling resistance to heat transfer on tube-side and shell-side
respectively, hr ft2 0FIBTU or m2 K/W
Cross-sectional area of tube or pipe, ft2 or m2
Crossflow area at or near the centerline for one crossflow section,
ft2 or m2
Split Ring Floating Head
Area for flow through window, ft2 or m2
Temperature of cold fluid, OF or K
Temperature of hot fluid, OF or K
Overall heat transfer coefficient, BTUIhr-ft2_oF or W/m2-K
Velocity of fluid, ft/s or mls
Fin thickness for low finned tubes, in. or mm
xiv
GREEK SYMBOLS
a Individual film heat transfer coefficient, BTU/hr-ft2 OF or W/m2 K
Efficiency
SUBSCRIPTS:
c Cold fluid
f Fin
h Hot fluid
Inside a tube or pipe
Liquid phase
0 Outside a tube
s Shell side
t Tube side
T Total
v Vapor phase
w Wall surface
xv
CHAPTER I
SHELL AND TUBE HEAT EXCHANGERS
Introduction
The need for a design procedure to quickly estimate the size of a shell and tube
heat exchanger arises in various situations. Most of these occur at the initial stages of a
project. For any project at this stage, a critical factor to be considered is the economic
feasibility. In this regard one has to determine the cost of major items of equipment. To
do this an estimate of the size of the major equipment is required. A second reason for a
quick estimate of the size of the equipment is for the preparatio~ of a preliminary plant
layout. This will give one a rough idea as to the amount of space that would be required
for the plant and of the placement of the major components. To perform a detailed
analysis to determine the size of all the heat exchangers in the plant at this stage would be
an unnecessary, time consuming activity.
Computer programs are now available for the detailed design of heat exchangers
for which numerous parameters have to be specified. These programs are written by
specialized computer programmers and the exact contents are usually unknown to the
design engineer who actually implements them. This can be dangerous in that an error in
the program or in the input of data, if not detected at the early stages, can lead to errors
that could prove expensive at a later stage. This makes it desirable for the design
engineer to make a quick check ofthe computer design by hand and confirm the validity
of that design. This gives us a third reason to have an approximate design method with
which one could quickly estimate the size of the shell and tube heat exchanger.
A fourth reason is related to the computer analysis and other detailed methods in
that the quick method of estimation of the size of the shell and tube heat exchanger can
give the input parameters for the computer programs. This would almost certainly speed
up the detailed analysis as fewer iterations would be required to complete the design. The
data from the preliminary method will also provide the variables for detailed hand rating
procedures in the event this is required.
In any process plant, in layman's terms, there is a need to heat things up and cool
things down. This can be successfully accomplished by the use.of heat exchangers, the
most commonly used ones being the shell and tube type. In these cases a lot of heat
energy is either input into the system or released from it and much precious energy was
and probably still is being wasted. Of late, research is being carried out in the field of
effectively using this heat by a method called HENS (Heat Exchanger Network
Synthesis), which was first studied by Linnhoff (1982). This has added a whole new
dimension to the theory of heat exchangers and their importance in the process industry.
In any process plant a large number of heat exchangers are in service which has a direct
bearing on the equipment and operating cost of the plant. Again, a detailed analysis at
this stage would be quite an unnecessary task requiring a lot of time and money, the two
things usually not available in abundance.
Taking into account all the above factors, it is evident thllt a quick manual
estimate of the size ofthe shell and tube heat exchangers will be a very useful tool for
successful design and running ofthe plant.
The present version of this method has been in existence for the past quite a few
years (at least 20) and has worked reasonably well. However, the method has some
deficiencies and also some inconsistencies that have to be dealt with. Also, in recent
years, emphasis has been laid on the system of units used. Until a few years ago, the U.S.
2
Customary system was used. The present thesis incorporates the S.I. units into the design
method.
Shell and Tube Heat Exchangers •
There are several types of heat exchangers used in the Chemical Process Industry
(CPI), the most common type being the shell and tube heat exchanger. This thesis deals
exclusively with this type.
Shell and tube heat exchangers are composed of four principal sub-assemblies:
1) Front end
2) Rear end
3) Tube bundle
4) Shell
These sub-assemblies can be arranged in different combinations. These sub-assemblies
are of various types, which are designated by alphabetic charact~rs. These are shown in
figure 1.1 (TEMA, 1988). The resulting exchanger is designated by a three-letter
combination characterizing, in order, the stationary front end, the shell, and the rear end,
for example, AES.
There are three principal types of shell and tube heat exchangers.
A) Fixed-Tubesheet Design:
The fixed-tubesheet exchanger is the most common, and typically has one of the lowest
capital costs per m2 of heat transfer area, the lowest being that of the V-tube type. As
shown in figure 1.2, this design employs straight tubes secured at both ends into
tubesheets that are either welded to the shell or attached by flanged joints. To account for
any thermal expansion, Le., the expansion caused in the tubes and the shell due to
3
c:-;---:;: __ :J : __
w~~rr
EXTERNALLY SEALED
FLOATING TUseSHEET
FIX!O TUBE 3He:r
lJKE '"N" STArICNARY HEAD
f~1-~
'-.oJ
lUll END
HEAD TYPES
fiXED TUSeSHE:T
UKE H"." SiATICN~KY HEAO
U·TUBE BUNOL!
PUll THROUGH FlOAnNG HeAoO
";:'1f~ ,
I I '-~ ..... ~ __ ~"
___.I .J'Wf:,'::" " ,----- h\\ ;~~;:=-
"",--0__,....!i"i \\__'-=;;~. __
- GL.! -- _. -- ----
FlOATlNCi HUO
WITH BACXINCi OEVICE
~v-~,-.:
-2r~ ~J
Flxeo TUBE3HEEi
UK! "S" STAnCN~RY H!AD
c:.,,:--;..:.:
5~WIT
OUTSloe PAc<eo FlOATING HEAe
L
p
T
N
u
5
M
SHEll TYPES
~I T E ll~
ONE PASS SHE!.!..
~t~ .-----.---.. I] F
T'NO PASS SHeu.
WITH LONGiTUCINAl 3AFFlE
~I T G -----~-----~- I]
.1
S?!.IT FLOW
~I T I H --~--- I~ --_...-
J.. I~
COUBl! SPUT Fl.Ow
~II T I] J
I
..L
DIVIOED Flew
T
~ ·, I)
K
,·
.L
KETTlE TYPE R!!OllER
~I T X I~
I
Si'EOAL HIGH PRESSURE CLOSURE CROSS fLOW
o
FRONT END
S7'ATtONAIlY HEAD TYP~
r~rl-
A W~l;~I
C.t.fANNEt.
AND RE.lAOVAalE COVER CI-B
~~
.1', ~-
I'lt
t~_:::
BONNei' (JNrcO~L COVER)
-~-J1~-=-T
II k~
c ~11--J1
S::Z -~~llJ;"':.-
CiANNel. INTe<:iitAL WITH TUse-
SHEET AND REMOVASLE COVER
-=--~ --- I~
N ~~L?
CHANNEL tNTEG~AL WITH TUse-
SHE:T AND REMOVA8lE COVER
Figure 1.1 TEMA Designation of Front End, Shell, and Rear End Types of Shell and
Tube Heat Exchangers (TEMA, 1988).
4
different temperatures, an expansion joint such as a bellows may be incorporated in the
shell, allowing it to expand or contract. Because there are neither flanges nor packed or
gasketed joints inside the shell, potential leak points are elimina.ted, making the design
suitable for higher pressure or potentially lethal service. However, since the tube bundle
cannot be removed, the shell-side of the exchanger can be cleaned only by chemical
means. In this configuration, any practical number of tube-side passes, odd or even, are
possible. For multi-pass arrangement, partitions are built into both the heads. Common
TEMA designations are BEM, AEM, and NEN.
~-
''1'
Figure 1.2 Fixed Tubesheet Design with Expansion Joint (The Patterson-Kelley Co.,
1959).
B) v-tube Design:
In this type of design, figure 1.3, the differential expansion is taken care ofby the Ushape
of the tubes. As the name implies, the tubes have a "hairpin" shape, with both ends
of the tubes fastened to one tubesheet. This design allows each tube ~o expand and
contract independently. The U-tube bundle can be withdrawn to provide access to the
inside of the shell, and to the outside of the tubes. However, mechanical cleaning of the
inside of the tubes is not possible as there is no way to physically access the V-bend
region inside each tube, so chemical methods are required for tube-side maintenance. In
this type of exchanger, a single pass is not possible because the fluid must traverse the
length of the tube bundle at least twice. Any practical even number of passes can be
5
obtained by building partition plates in the front head. Common TEMA designations are
BEUandAEU.
Figure 1.3 U-Tube Design (The Patterson-Kelley Co., 1959). •
C) Floating Head Designs:
This type meets the expansion problem by having one stationary tubesheet and one free to
move or "float" back and forth as the tubes expand and contract under the influence of
temperature changes. Since the entire tube bundle is removable, maintenance is easy and
inexpensive. Floating head designs are generally not used with odd number of tube-side
passes as it poses severe sealing problems. This is due to the fact that with odd number
of passes, arrangements have to be made to account for the nozzle on the floating head.
This could be achieved by providing a packed joint on the floating cover. This does no~
guarantee a leak-proofjoint and hence, is generally avoided. There are four common
variations of this design:
i) Split-Ring Floating Head Design: In this type (figure 1.4), to separate the
shell- and tube-side fl~ids at the floating head end, the tube-side of the floating tubesheet
is fitted with a flanged, gasketed cover at its periphery which is held in position by
bolting it to a split backing ring on the other side ofthe tubesheet. The backing ring is
made in two halves and runs around the periphery of the tube bundle. The complete
floating head assembly (flange, cover, tubesheet and backing ring) is located beyond the
6
Xa I a
main shell cover of larger diameter. Service and maintenance costs are higher than the
pull-through type since the shell cover, split-ring and floating head cover must be .
removed before the tube bundle can be removed. Any practical even number of passes is
possible. Common TEMA designations are AES and BES.
fLoohn:=J J:1~.6~~~ ..p~,/\.cL-:
~[---1r----
q
Figure 1.4 Split-Ring Floating Head Design (The Patterson-Kelley Co., 1959)
ii) Pull-through Floating Head Design: Here (figure 1:5), a separate head or
cover is placed over the floating tubesheet within the head on the shell side, Le., the
diameter of the tubesheet is less than the shell inside diameter. The floating head is
internally gasketed to prevent leakage between the tube and shell sides. The split backing
ring is not required in this case and the floating tubesheet diameter must be increased to
match the outside diameter of the floating-head flange. As a result, the shell diameter
becomes approximately the same as that of the enlarged shell cover of the split backing
ring type to accommodate the same number of tubes. Internal pressure has a significant
effect in this case; the flange diameter increases as the pressure increases so that the area
available for tubes in a given shell diameter is reduced. This configuration is ideal for
applications that require freque~t cleaning; however, it is among the most expensive
designs. With this type, only an even number of tube-side pasSCiS is possible. For single
pass operation, however, a packed joint must be installed on the shell cover, which is
rarely done. The packed joint for odd number ofpasses has to be provided to account for
7
main shell cover of larger diameter. Service and maintenance costs are higher than the
pull-through type since the shell cover, split-ring and floating head cover must be .
removed before the tube bundle can be removed. Any practical even number of passes is
possible. Common TEMA designations are AES and BES.
fLoJin3 Jj~_6~~~ _p~~~-
Figure 1.4 Split-Ring Floating Head Design (The Patterson-Kelley Co., 1959)
ii) Pull-through Floating Head Design: Here (figure 1:5), a separate head or
cover is placed over the floating tubesheet within the head on the shell side, i.e., the
diameter of the tubesheet is less than the shell inside diameter. The floating head is
internally gasketed to prevent leakage between the tube and shell sides. The split backing
ring is not required in this case and the floating tubesheet diameter must be increased to
match the outside diameter of the floating-head flange. As a result, the shell diameter
becomes approximately the same as that of the enlarged shell cover of the split backing
ring type to accommodate the same number of tubes. Internal pressure has a significant
effect in this case; the flange diameter increases as the pressure increases so that the area
available for tubes in a given shell diameter is reduced. This configuration is ideal for
applications that require freque~t cleaning; however, it is among the most expensive
designs. With this type, only an even number of tube-side pasSiS is possible. For single
pass operation, however, a packed joint must be installed on the shell cover, which is
rarely done. The packed joint for odd number of passes has to be provided to account for
7
the floating tube-bundle and the possibility of the shell-side and tube-side mixing of
fluids. Common TEMA designations are AET and BET.
/
Figure 1.5 Pull-through Floating Head Design (The Patterson-Kelley Co., 1959)
iii) outside Packed Lantern-ring Design: This employs a lantern ring around
the floating tubesheet to seal the individual fluids as the floating tubesheet moves back
and forth. As shown in figure 1.6, the lantern ring is packed on both sides and weep
holes are provided so that any leakage is open to the atmosphere for ease of detection.
This type can be made only single or two-pass on the tube side. Since these types of heat
exchangers employ a packed joint, they are rarely used. Common TEMA designations
are AEP and BEP.
~~Rln
_._------_. -_._---_.•. __ .~ --------..-.
[
---------d1I!-.-------
Figure 1.6 Outside Packed Lantern-ring Design (The Patterson-Kelley Co., 1959)
8
iv) outside Packed Stuffing Box Design: This uses the outer skirt of the
floating tubesheet as part ofthe floating head as shown below in figure 1.7. A packed
stuffing box seals the shell-side fluid while allowing the floating head to move back and
forth. Since the stuffing box is in contact with the shell-side fluid only, the possibility of
mixing of the shell-side and tube-side fluids does not exist. This type has no practical
tube pass limitations but poses severe sealing problems with any odd number of passes.
Common TEMA designation is AJW and AEW.
Table 1.1 shows a comparison of the above discussed types of shell and tube heat
exchangers for various conditions.
S\:u.ffln~ Box Asse.mbL~
Figure 1.7 Outside Packed Stuffing Box Design (The Patterson-Kelley Co., 1959)
components of Shell and Tube Heat Exchangers
Shell: Up to 24 inches in diameter, ~hells are usually seamless or welded pipes. Larger
shells are usually made out of plates rolled to the specific diameter. TEMA Standards
(TEMA, 1988) specify the minimum thickness to be used for the particular class of
exchanger and the material of construction.
Tubes: These are the basic component ofthe shell and tube heat exchanger. They
provide the heat transfer surface between one fluid flowing inside the tubes and another
flowing across the outside. The tubes can either be plain (Le., bare) or have an extended
9
Type of
Design "U"-Tube Fixed
Tubesheet
Floating Head I Floating Head I Pull.Through Outside Packed
Bundle lantern-Ring
!-Ioallng Heaa IFloating Head
Split Outside Packed
Backing Ring Stuffing Box
Relative Cost
Increases From
(A) least Expen- A B C C sive through C E
(E) Most
Expensive
Provision for
Differential individual tubes expansion joint
floating head floating head floating head floatinc head
Expansion free to expa nd in sheff
Removable
I Bundle
yes no yes yes yes yes
Replacement'
Bundle yes not practical yes yes yes yes
Possible
I
Individual
only those in I Tubes outside row
yes yes
I
yes yes yes
Replaceable
difficult to yes. yes. yes. yes. yes.
Tube Interiors do mechanically mechanically mechanically mechanically mechanically mechanically
Cleanable can do or chemically or chemically or chemicaHy or chemically or chemically
chemically
Tube Exteriors
With Triangular chemically only chemically only chemically only chemicaJly only chemically only chemically only
Pitch Cleanable
Tube Exteriors yes, yes. yes. yes, yes.
With Square mechanically chemically only mechanicany mechanically mechanically mechanicaUy
Pitch Cleanable or chemically or chemically or chemically or chemically or chemically
Double
Tubesheet yes yes no no no yes
Feasible
no no
any practical
practical limita· practical limita-
Number of no practical tion (for single limited to single tion (for single no practical even
Tube Passes number possible limitations pass. floating or 2 pass pass, floa ting limitation
head requires head requires
packed joint) packed joint)
Internal Gaskets yes yes no yes no yes
Eliminated
Table 1.1 Features ofPrincipal Shell and Tube Heat Exchanger Designs (The Patterson-
Kelley Co., 1959).
10
surface. There are various types of extended surfaces in service; the most common type
being finned tubes.
Tubesheets: The tubes are held in place by being inserted into the holes in the tubesheet
and then rolled and/or welded. Tubesheets are in contact with both the shell-side and
tube-side fluids and must withstand the pressure on both sides. Tubesheets also function
as a partition between the two fluids, Le., they do not allow the mixing of the two fluids.
Bames: These are used on the shell side. Baffles are used primarily to support the tubes
along the length of the heat exchanger. They also direct the flow of the shell-side fluid
causing increased turbulence and higher heat transfer coefficients. The TEMA Standards
(TEMA, 1988) specify the minimum baffle thickness and spacing for a particular class of
heat exchanger.
Tie rods and spacers: Tie rods extend from one tubesheet to th~ last baffle. Their
primary purpose is to hold the spacers. Spacers are small tubes of the appropriate length
used to maintain the distance between adjacent baffles. In some cases tie rods are also
placed in place of the tubes underneath the nozzles to perform as impingement plates.
Pass partition plates: These are used only when multiple passes on the tube-side are
required. These plates are welded to the head.
Sealing strips: These are typically flat metallic strips either notched into or welded to the
baffles. Their use is to minimize the bypass stream between the shell and the tube
bundle. They are usually attached in pairs.
Impingement plates: These are plates placed directly under the inlet nozzle on the shellside.
Their purpose is to break up and divert the incoming jet of fluid from the nozzle,
thus protecting the tubes from erosion and vibration. They are p.laced such that the area
between the plate and the shell, called the escape area, is larger than the inlet nozzle area
in order to reduce the velocity.
11
Selection criteria
There are no strict rules that are followed for the selection of a particular type of
shell and tube heat exchanger. In general, the following broad statements can be made:
1) The heat exchanger must satisfy the process requirements. This includes meeting the
desired change in the thermal conditions of the process streams within the allowable
pressure drops.
2) The heat exchanger must withstand the service conditions including mechanical and
thermal stresses developed during installation and operation, corrosion and to some
extent fouling.
3) The heat exchanger must be maintainable for the particular service conditions. This
implies choosing a configuration that permits cleaning - tube-side and/or shell-side, as
required - and replacement of tubes, gaskets and other components vulnerable to
corrosion, erosion or fouling.
4) Cost of the heat exchanger. This is basically the initial equipment cost. In some cases
a trade-off is required between higher initial cost of the equipment and the long term
advantages for the selection of a particular configuration.
Finned Tube Heat Exchangers
The need for enhanced tube configuration arises from the fact that, for certain
services in the industry, the heat transfer coefficients achieved are very low. This means
that a large surface area will be required to perform the specified duty. This warrants the
use of enhanced tube geometry for such an application. Virtualiy every heat exchanger is
a potential candidate for enhanced heat transfer. However, each application must be
tested to see if enhanced heat transfer "makes sense." An enhanced surface geometry
may be used for one of the following three objectives:
12
-- 1) Size Reduction: For a constant rate of heat exchange, the exchanger length and/or
diameter may be reduced. This will provide a smaller heat exchanger.
2) Reduced Mean Temperature Difference: For constant rate of heat exchange and tube
length, the Mean Temperature Difference (MTD) may be reduced. This provides
increased thermodynamic process efficiency and yields a savings of operating costs.
3) Increased Heat Exchange: For constant length of the exchanger and fixed fluid inlet
temperatures, an increase in the rate of heat exchange results.
4) Reduced Pumping Powerfor Fixed Heat Duty: This is theoretically possible.
However, this will typically require that the enhanced heat exchanger operate at a
velocity smaller than that of the competing plain surface. This will require increased
frontal area, which is normally not desired.
Enhanced surfaces can be used to provide any of the above mentioned
performance improvements. How much improvement is obtained depends on the
designer's objectives. The subject of enhanced heat transfer is dealt with in great detail
by Webb (1987).
Low finned tubes are used extensively in conventional shell and tube heat
exchangers. Such types of enhanced surfaces are used primarily for gas-gas or gas-liquid
systems, and for condensing and vaporizing services. The choice of a finned-tube size .
and arrangement is governed by numerous factors such as the finned-tube diameter, fin
height and thickness, number of fins per inch and the material of the fin and the bare tube.
In the case ·of shell and tube exchangers, finned tubes used are almost always integral,
i.e., fins and tube are the same metal. The geometry and the performance factors include
the transverse and longitudinal pitch, the shell and the tube-side mass velocity, metal
temperature of the fin tip, and the allowable pressure drops for the shell- and the tubeside.
The first low-fin condenser tube was developed in 1940. The first, and still the
most common one, has 19 fins/inch with a fin height of slightly less than 1/16 inch. The
fins on a low-fin tube are radially extruded from a fairly thick walled tube in a lathe-like
13
fmning machine. The resulting fins provide up to 5 times the outside surface area of a
bare tube with the same nominal diameter. Figure 1.8 shows various types of finned
tubes.
Figure 1.8 Types of Commercial Finned Tubing: (a) Wolverine Type SIT Trufin®
Low Finned Tube With 19 Fins per In. (b) Wolverine Type srr Trufin® Medium
Finned Tube With 11 Fins per In.; (c) Wolverine Type Turbo-Chil® Finned Tube.
14
CHAPTER II
BASIC STRUCTURE OF THE DESIGN METHOD
Modes of Heat Transfer
There are three modes of heat transfer: Conduction, convection, and radiation.
For engineering calculations, it is always convenient to consider the three modes
separately and then combine the results into an overall solution.
Conduction:
In a solid body, the flow of heat is the result of a process in which kinetic energy
is transferred from one molecule to another. This mode of heat transfer is called
conduction. In liquids and gases the molecules are not confined to their locations, but
move around and in this way transport energy. This process is still classified as
conduction as long as no macroscopic movement can be detected. The fundamentals of
heat conduction were established over a century ago with pioneering work by Biot and
Fourier. The equation defining the rate of 1-D conduction heat transfer, first given by
Biot (1804) and later solved by Fourier (c. 1824) for a number of complicated cases is
15
dT
Q= -kA- (2.1)
dx
where Q = Rate of heat transfer in the x direction, BTU / hr or W
dT
= Temperature gradient in the x direction at the point under consideration,
dx
(oF / ft) or (K / m)
A = Cross - sectional area perpendicular to the x direction, ft2 or m2
k = Thermal conductivity of the solid,
BTU / hr ft2 (oF / ft) or W / m2 (K/ m)
Thermal conductivity is a characteristic of the material and is determined experimentally
(Hutchinson, 1945).
For the case of shell and tube heat exchangers, we have to consider conduction through a
cylindrical tube. The equation for conduction, on integration, becomes
21tLkw (Ti -To)
Q= l{r;;;J (2.2)
where L = Length of the tube, ft or m
kw = Thermal conductivity of the tube material,
ro , ri = Outside and inside radii of the tube, respectively, ft or m
To, Ti = Outside and inside wall surface temperatures, respectively, OF or K
Convection:
Heat transfer by convection occurs due to the motion of a fluid, the heat being
carried as internal energy. This mode of heat transfer takes place when the fluid flow is
16
either laminar or turbulent. Convective heat exchange is enhanced by the fluctuating
motions, called eddies, in the turbulent stream. This is not the case with laminar flows
and hence the heat transfer by convection in turbulent flow is c;nsiderably higher than in
laminar flow.
Radiation:
Radiation is the transfer of energy through space by means of electromagnetic
waves. Radiation heat transfer, as opposed to conduction and convection, does not
require the presence of a medium to convey the heat from the source to the receiver, i.e.,
heat can be transmitted by radiation across an absolute vacuum. Radiation heat transfer
can normally be ignored unless temperatures are very high, as in flames, combustion
systems, or solids heated to red heat. It is also very important in low temperature
(cryogenic) systems where the cold bodies are isolated in high-vacuum enclosures to
eliminate convection and conduction effects. Such systems are hot considered in this
thesis.
Film Heat Transfer Coefficients
For many convective heat transfer processes, it is found that the local heat flux is
approximately proportional to the temperature difference between the wall and the bulk
of the fluid, i.e.,
~ ex: (Tb - Tw ) (2.3)
or
Q=a. (Tb - Tw ) (2.4)
A •
17
The constant of proportionality, 'a', is called the "film coefficient of heat transfer," and
has the units BTU/hr ft2 OF or W/m2 K. The value of a depends on the geometry of the
system, the physical properties ofthe fluid, and the velocity of flow.
The overall Heat Transfer coefficient
The various processes described above can be described as resistances to heat
transfer. Hence,
For conduction through a cylindrical wall:
In(r;<)
Rcond = 2nLk
w
(2.5)
For convection:
1
Rconv = - (2.6)
aA
In a typical shell and tube heat exchanger with no fouling and no fins, these resistances
act in series in the following way (refer to figure 2.1):
Figure 2.1 Cross-section of Fluid-to-fluid Heat Transfer Through a Tube Wall (Bell,
1993).
18
1) Convective resistance from the bulk of the fluid inside the tube to the wall of the tube,
2) Conductive resistance through the wall of the tube and
3) Convective resistance from the outer surface of the tube to the bulk of the fluid
flowing across the tube.
In most heat exchangers in actual service, after some period of use, the amount of
heat transferred for a given temperature difference decreases. This occurs because
deposits accumulate on the heat exchange surface and interpose an additional barrier to
heat flow. These deposits include sedimentation from dirty water, scale, organic growth,
etc.. Heat transfer across these films is predominantly by conduction, but the thickness of
the deposit or its thermal conductivity are seldom known for the designer to treat it as an
individual conduction problem. The deposits are generally termed "fouling". Based on
past experience of manufacturers and users, tables of "fouling factors" (typical units of
hr-ft2_oF/BTU or m2-K/W) have been prepared by TEMA (TEM. A, 1988) and are
presented in Appendix A. The reciprocals of the fouling factors are the heat transfer
coefficients for the fouling material. These values cannot be determined directly by
calculations, but are established experimentally and more so with experience. Fouling
factors or fouling resistances are a measure of the resistance to heat transfer due to the
presence of the fouling.
Extended surfaces or fins are frequently employed in shell and tube heat
exchangers. Fins will be beneficial if they are applied to the fluid stream having the
dominant thermal resistance (lower heat transfer coefficient). The fins provide reduced
thermal resistance for this stream by providing increased surface area. The heat transfer
coefficient on the extended surfaces may be either higher or lower than that which would
occur on the unfinnedlplain surface. Because of the temperature gradient in the fin
material over its length, the amount of heat transferred by the fin is less than the amount
that would be transferred by a fin of infinite thermal conductivity. Thus, the heat
19
conductance of a finned surface (aA) must be multiplied bya fin efficiency factor to
account for the temperature gradient in the fin.
The fin efficiency, 11f, is defined as the ratio of the actual heat transfer from the
fin to that which would occur if the entire fin were at its base temperature. The efficiency
of the fin is a function of its cross-sectional shape, its length, and the geometry of the
base surface. Appendix D gives the dimensions of typical finned tubes. Fin efficiency
equations for a number of specialized fin geometries are discussed in detail by Kern and
Kraus (1972) and Bell and Mueller (1984).
For most shell and tube heat exchanger applications, this efficiency can be
calculated as follows (Bell & Mueller, 1984):
1
llf = 2 (2.7)
1+ m ~df
3 dr
2
where m = hf (1 J
-+Rf kfYf
0.0 0
........................................................ (2.8)
d f = Outside diameter of finned tube, ft or m
d r = Root diameter of finned tube, ft or m
h f = Fin height, ft or m
Yf = Fin thickness, ft or m
kf = Thermal conductivity of fin material, BTU / hr ft2 (OF / ft) or W / m2 (K / m)
An inspection of Eqs. (2.7) and (2.8) indicates that the fin efficiency is higher for the
better-conducting fin materials, and higher as the outside heat transfer coefficient
becomes lower. Finned tubes are not generally used in applications where the fin
20
efficiency is lower than 0.65. For estimation purposes, the following simple guidelines
could be followed:
1) The higher the thermal conductivity of the fin material, the higher the fin efficiency.
2) The smaller the fin height, the higher the fin efficiency.
3) The lower the outside heat transfer coefficient, the higher the fin efficiency.
For most finned-tube applications, over normal operating ranges, the efficiency lies
between 0.9 and 1.0.
The heat flow can be considered to occur as a consequence of a driving force
through a resistance. In this case, the driving force is the overall temperature difference
and the resistance is the sum of all the above mentioned thermal resistances. The
equation for the heat duty then becomes
................... (2.9)
where Rfi, Rfo = Resistance due to fouling on the inner and outer surface of the tube
respectively, hr - ft2 _o F / BTU or m2 - K / W
Rfin = Fin resistance, hr - ft2 _OF / BTU or m2 - K / W
kw = Thermal conductivity of the tube material,
BTU / hr - ft2 - (0 F / ft) or W / m2 - (K / m)
ai, a 0 = Film coefficients for inside and outside the tube respectively,
BTUIhr-ft2 _0 For WIm2 -K
Ai, Ao = Inside and outside surface areas of the clean tubes
independent of fouling, ft2 or m2
21
In Equation (2.9), the temperatures T and t are the bulk fluid temperatures at a given
"point" in the heat exchanger and Q, Ao' and Ai are associated with that point. The
fouling is assumed to have negligible thickness and hence ro, ri, Ao, and Ai are those of
the clean tube and independent ofthe buildup of fouling (refer to figure 2.1). Hence the
values determined using the above equation are the "local values" corresponding to the
"local point" in the heat exchanger.
The fin resistance term can be evaluated using the equat~on (Bell & Mueller,
1984)
1
Rfin = Ar~:tT)f {a~ +Rfo } (2.10)
A +l1f
fin
where Aroot
Afin
Heat transfer area of the root portions between the fins, ft2 or m2
Heat transfer area of all the fins on the tube, ft2 or m2
We can now define an 'overall' heat transfer coefficient U* based on any
reference area, A* as
Q=U*A*(T-t) (2.11)
where U* = Overall heat transfer coefficient based on area A*, BTU / hr ft2 OF or
A* = Reference area, ft2 or m2
Comparison of equations (2.9) and (2.11) gives
22
u* =--------.......1".--~----------
A* * A* 1 (rO/) * * * RfiA ~lri RfoA RfinA A • --+ + + + +--
uiAi Ai 27tLkw Ao Ao uoAo
................ (2.12)
The reference area can be chosen as any convenient area. This area need not be any area
associated with the heat exchanger itself, but it should be one that is completely defined.
In most cases, but not necessarily, this area is chosen to be the outside area of all the
tubes in the heat exchanger, Ao. In this case,
U*=Uo
and
............................. (2.13)
and
Q=UoAo(T-t) (2.14)
The overall heat transfer coefficientcan also be written in terms of the fin efficiency
instead of the fin resistance and the wall resistance term can be written using arithmetic
mean instead of the logarithmic mean. Equation (2.13) then becomes:
1
Do = A
o
RfiA
o
A
o
,1.x Rfo 1 (2.15)
--+ + +--+--
a.iAi Ai kwAm 11f 11 fa. 0
In the above equation, the wall conduction term has been written in terms of the
arithmetic mean area and is evaluated for that portion of the tube wall that lies between
23
the inside diameter and the root diameter, i.e., exclusive of the fins. The term ~x refers to
the wall thickness of the tube.
Typical values of the overall heat transfer coefficient can be found tabulated in
various references (Bell, 1993; Kern, 1950; McKetta, 1992; Bell, 1983) and are presented
in Appendix A, Table A.l (Bell, 1993). This procedure can be highly inaccurate because
the tabulated values generally include the entire range encountered in practice. A better
procedure to estimate Vo is to estimate the values of the individual film coefficients
characteristic of the specific service; typical values are given in Appendix A, Table A.2.
The fouling factors are estimated either from the problem specification, personal
experience, or typical values for the fluid and service (refer to Appendix A, Table A.2).
For the case of finned tubes being employed, the fin efficiency is also estimated. The
overall heat transfer coefficient is then estimated by using either Equation (2.13) or
(2.15).
Basic Design Equation
Constant temperature difference, (T - t), was assumed in the above discussion. In
most exchanger applications, this is not true. One or both of the stream temperatures
change along the length of the exchanger. Taking this factor into consideration, the
design equation (2.11) is written in the differential form as:
dA* = u*(~;-t) (2.16)
This equation is then integrated over the entire heat duty of the exchanger. Hence,
24
QT
* J dQ
A = U*(T-t)
o
........................................................... (2.17)
This is the basic heat exchanger design equation. The required heat transfer area can then
be calculated by plotting Qvs. * 1 and evaluating the area under the curve or by
U (T -t)
using any of the available numerical methods.
Although the above mentioned method can be used for any case, it is desirable to
have an easier method without a great loss in accuracy. This can be achieved by making
certain simplifying assumptions. One set of assumptions that is reasonably valid for a
wide range of cases and leads to a very useful result is the following (Bell & Mueller,
1984; Bowman, Mueller, & Nagle, 1940; Kern, 1950):
1) All elements of a given stream have the same thermal histo~. This simply means that
all elements of a given stream that enter an exchanger follow paths through the exchanger
that have the same heat transfer characteristics and have the same exposure to heat
transfer surface.
2) The heat exchanger is at steady state.
3) Each stream has a constant specific heat.
4) The overall heat transfer coefficient is constant.
5) There are no heat losses from the exchanger.
6) There is no longitudinal heat transfer in the exchanger.
7) The flow is either entirely co-current or entirely counter-current.
Once these assumptions are made, the heat transfer area can be calculated directly for the
case of co-current or counter-current flow using the equation (Bell & Mueller, 1984):
A* = U*(QMTTD) (2.18)
25
where MTD = Mean Temperature Difference, of or K
The equations for MTD and the case where the seventh assumption is violated is dealt
with in detail at a later stage.
Calculation of the Total Heat Duty, QT
For the case of single phase sensible heat transfer
QT =mhCph (T1 - T2) =mcCpc (t2 -t1) (2.19)
where fih = Mass flow rate of the hot fluid, Ibm / hr or kg / s
me = Mass flow rate of cold fluid, Ibm / hr or kg / s
Tl' T2 = Inlet and exit temperatures of the hot fluid, respectively, OF or K
t 1, t2 = Inlet and exit temperatures ofthe cold fluid, respectively, OF or K
Cp ,Cp = Specific heats of the hot and cold fluid respectively,
h c
BTU / Ibm-oF or kJ / kg - K
Logarithmic Mean Temperature Difference
In the general heat transfer equation (2.17), the temperature difference term ilT,
the local (at any given point in the heat exchanger) temperature difference between the
hot and the cold streams, cannot be used for the entire heat exchanger. After making the
simplifying assumptions, equation (2.18) can be used to calculate the heat transfer area.
For the case of pure co-current or counter-current flows, analytical evaluation of the
design integral of equation (2.1 7) can be carried out, leading to different forms of the
LMTD. The MTD concept is valid for many other flow configurations as will be seen
later. The procedure to calculate the MTD can be found in numerous references (Bell,
1993; Bowman, et aI., 1940; Jaw, 1964; Kern, 1950).
26
a) counter-current flow of fluids (Refer to figure 2.2)
Tt----....
~ ......----41
Figure 2.2 Block Diagram of a Single Pass Shell and Tube Heat Exchanger with
Counter-current Flow of Fluids.
Consider the cooling of a fluid which enters at temperature T1 and exits at T2•
This cooling is accomplished by a fluid entering at temperature tl and exiting at t2. The
temperature profiles along the length of the tube are given in fig.ure 2.3.
DISTANCE ALONG THE EXCHANGER
Figure 2.3 Temperature Profiles in a Single Pass Shell and Tube Heat Exchanger with
Counter-current Flow of Fluids.
27
The MTD for this case is then calculated as
(Tl -t2)-(T2 -t1)
(LMTD)counter-current = In{~~~ ~:~~} (2.21)
b) Co-currentlParallel flow of fluids (Refer to figure 2~4)
Tt------
t1 ------ .........------..~
Figure 2.4 Block Diagram of a Single Pass Shell and Tube Heat Exchanger with Cocurrent
or Parallel Flow of Fluids.
The same nomenclature is used for this case as the previous one. The temperature
profiles are as shown in figure 2.5.
DISTANCE ALONG THE EXCHANGER
Figure 2.5 Temperature Profiles in a Single Pass Shell and Tube Heat Exchanger with
Co-current or Parallel Flow of Fluids.
28
The MTD for this case is calculated by the equation:
(Tl - tl ) - (T2 - t2 )
(LMTD )co-current = In{ (~=:~)) } (2.22)
The definitions ofMTD's given in equations (2.20) and (2.21) are the logarithmic means
of the terminal temperature differences in each case. Hence, for the case of pure co-current
and counter-current flows, the MTD is referred to as the "Logarithmic Mean
Temperature Difference", abbreviated as LMTD.
For some cases, the LMTD can be reasonably approximated by the arithmetic
mean temperature difference, AMTD. Hence,
......................................................... (2.23)
The LMTD is always equal to or less than the AMTD. The difference between LMTD
and AMTD increases with decreasing ratio of the smaller terminal temperature difference
to the larger.
When the temperature difference varies greatly between the hot and cold
terminals, large changes in the physical properties of the fluids may occur. To some
extent changes in these properties can be compensated for by the application of the
"Caloric" temperature concept. With it an "overall" coefficient is calculated for each end
of the heat exchanger using equation (2.13) and incorporated into the general heat transfer
equation as (Colburn, 1933):
Q_ A U2~Tl- Ul~T2 - In{ ~~:~} (2.24)
29
where VI, V2 Overall heat transfer coefficients for each end of the heat exchanger,
~TI, ~T2 = Corresponding temperature difference between the hot and the
cold streams at each end of the heat exchanger, of or K
A possible temperature profile is shown in figure 2.6. In this ca;e, the term overall
temperature difference loses its meaning.
Temperature, T, t
of orK
Length along the exchanger, ft or m
Figure 2.6 Temperature Profiles for a Single Pass, Counter-current flow, Shell and Tube
Heat Exchanger with Varying Fluid Properties.
Mean Temperature Difference (MTD)
In the equations given above, true parallel or counter-current flow is assumed.
While this assumption usually works quite well for single pass exchangers, it is not true
for multi-pass ones. For example, consider the 1-2 shell and tube heat exchanger shown
30
in figure 2.7, i.e., one shell side pass and two tube side passes. The corresponding
temperature profile is shown in figure 2.8.
Figure 2.7 1-2 Shell and Tube Heat Exchanger (Bell, 1993).
Figure 2.8 Temperature Profile in a 1-2 Shell and Tube Heat Exchanger (Bell, 199
Here, the first pass is true parallel and the second pass is counter-current. In this ca!
LMTD cannot be applied directly. It then becomes necessary to develop a new
expression for the calculation of the effective or true temperature difference to repla
counter-current or parallel LMTD. The effective mean temperature difference for S\
case can be carried out along the lines similar to those used to obtain the LMTD. Tl
basic assumptions remain the same, except for the pure co-curre"nt or counter-curren
limitation. An additional assumption required is that each pass has the same amoun
heat transfer area. Rather than computing the MTD directly, it is preferable to coml
correction factor FT for the LMTD assuming pure counter-current flow, i.e.,
Ft = (LMTD)c=r-current (
31
where FT = 1 indicates pure counter-current flow.
Equations for FT were developed by Underwood and modified by Nagle (1933)
and Nagle, Bowman, and Mueller (1940) for a 1-2 shell and tube heat exchanger.
The final expression for the correction factor is :
and
To eliminate the necessity for solving the above complicated equation FT, has
been plotted as a function of the parameters Rand P. Such a plot is given in figure (2.9)
for a 1-n exchanger where tn' is any even number (Kern, 1950; Perry & Chilton, 1973;
Bell, 1983; TEMA, 1988). The total heat transfer area required for multi-pass exchangers
is then given by the equation:
A* =--..Q.,T;;~-
U*(MTD)
..................................................... (2.27)
where MTD = Mean Temperature Difference, of or K
= Fr(LMTD)counter-current
The value ofFT is always less than unity unless one stream is isothermal. This is
expected due to the fact that the tube passes in co-current flow with the shell side fluid do
not have as great a mean temperature difference as those in counterflow to it.
32
0: 00.9
t-
U«
LL.
zo
t= 0.8
u III:IV--
W
0:: a:
o
u
0 0 .7
.... £TTIIIIII •• II.
~
--J
.._.._---
------------ ••• t-fu
~~t"
~~~-
It!iiftt;11 r
-~~1+ ~·r -t·-.· --1.: ~;;:
~atmEh~ir
~
..1
rs
,-i§i..·--
4-
:~bt.i·,
f
~
tt
o
__ ~.d'
-I--
i-t+
t:
.-,
" :
~
~t\_I.:t\- ttl\"
·0 -1\-(lIIllll-",lll-~
HI"H1 ~HHrnw- ~
~mt:m~ U.
tt
I ~ ;1:-
1.0
..
tJ-'
0.6
Vol
Vol
...
0.50 0.1 0.2 0.3 0.4 0.5 0.6 0.7
P : TEMPERATURE EFFICIENCY
titltt::t.fj.!-II' ~'~ ,
0.8 0.9 1.0
r~' LMTD CORRECTION FACTOR
1~rJ: 1 SHELL PASS EVEN NUMBER OF TUBE PASSES
(
p: tl-t. RT:.-T-2 T.-t. ta-t.
Figure 2.9 LMTD Correction Factor for a I-n Shell and Tube Exchanger (TEMA, 1988).
The LMTD correction factor FT can be estimated to a good degree of accuracy without
the actual use of the plots. In general, for a single tube pass purely counter-current heat
exchanger, FT = 1. For the case of a single shell with any even number of tube-side
passes (1-2n heat exchanger), the value ofFT lies between 0.8 and 1.0. The value will be
close to 1.0 for the case of nearly isothermal temperature of one-stream, and close to 0.8
when the outlet temperatures of both the streams are equal.
Number of Shells Required
The thermodynamic feasibility of a multi-tube pass design has to be checked for
the case when the outlet temperature of the cold stream is higher than the hot stream
outlet temperature. This is called a temperature cross. Absolute limits for a quick check
are (Bell, 1993):
1) For hot fluid on the shell side:
2) For cold fluid on the shell side:
(Tc,in +Tc,out )
Th,out> 2
T. (\Th,in +Th,out)
c,out < -2
In the event that these limits are approached, it is necessary to use multiple 1-2n shells in
series. It is generally highly undesirable to design a one shell, 1-2n heat exchanger when
there is a temperature cross. The number of shells required to perform a specified duty
can be easily determined graphically as follows (Refer to figure 2.10):
i) Plot the hot fluid inlet and the cold fluid outlet temperatures on the left hand ordinate,
and the hot fluid outlet and cold fluid inlet temperatures on the right hand ordinate. The
distance between the ordinates is arbitrary.
ii) For constant specific heat systems, straight operating lines are drawn from the inlet to
the outlet temperature points of each stream. In case of changing specific heat of any
34
stream, calculate the temperature as a function of the amount of heat added or removed
by the other stream. In such a case the operating line(s) will be curved.
iii) Starting with the cold fluid outlet temperature, a horizontal line is drawn until it
intercepts the hot fluid line. From that point, a vertical line is drawn until it intercepts the
cold fluid line.
iv) This procedure is carried out until a vertical line intercepts the cold fluid operating
line at or below the cold fluid inlet temperature or a horizontal line crosses the right hand
ordinate.
v) The number of horizontal lines, including the one that crosses the right hand ordinate,
is the number of shells in series that is sufficient to perform the required duty. In the case
shown, this is three.
Temperature,
T, t, OF or K'
Heat Transferred, Q, BTU/hr or W
Figure 2.10 Estimation ofNumber of Shells Required in Series.
35
Figure 2.10 can also be used to estimate the temperatures of the intermediate
stages. Consider shell number 3. As seen in the figure, the hot stream inlet temperature
to this stage will be very close to the cold fluid inlet temperature to the second shell, and
the cold fluid inlet temperature will be determined by drawing (\ line parallel to the x-axis
until it meets the ordinate. The temperatures to the other stages can be determined in a
similar way.
Heat Transfer Area
Once the values of heat duty, QT, the mean temperature difference (MTD), and
the overall heat transfer coefficient are known, the required heat transfer area can be
calculated using the equation
QT
Ao = Uo(MTD) (2.28)
where the overall heat transfer coefficient, V0' is based on the total tube outer surface
area including fins if present.
Once the area Ao is determined, it can be related to the shell inside diameter, and
effective tube length through a tube count table. A plot of the heat transfer area in a shell
and tube heat exchanger as a function of the shell inside diameter and the effective tube
length is given as figure (2.11) for the special case of 19.05 tnm. tubes on a 23.81 tnm.
triangular pitch, fixed tubesheet type exchanger with one tube-side pass, fully tubed shell
(Bell, 1993). The term "effective tube length" implies the length ofa single straight
section from tubesheet to tubesheet for a straight tube exchanger and from tubesheet to
tangent line for a V-tube exchanger. As seen in figure (2.11), lines are shown indicating
the (L/Di) ratios (marked 3: 1, 6: 1, etc.). Shells shorter than thre.e times the shell diameter
36
(3: 1) may suffer from poor fluid distribution and excessive entry and exit losses, and are
likely to be more expensive than a unit with a higher L/Di but the same area, especially if
the shell-side fluid is under high pressure. Shells longer than 15 times the shell diameter
are likely to be difficult to handle mechanically, and require a large clearway for bundle
removal or retubing. Many heat exchangers fall in the 6: 1 to 8: 1 range, with a
pronounced trend towards higher values as pressure drop prediction procedures have
improved (Bell, 1993).
Hence, once the area Ao is known, figure (2.11) can be used to determine the
combinations of tube length and shell diameter that will provide. that area for a given tube
size and layout for a single shell, one pass fixed tubesheet exchanger. This then becomes
the "base case" for all further calculations.
37
100~-~.-.o.-~~~~~-..,;"",..~~~~1~~.......:..-..~~
o 4 8 12 16 20 28
EFFECTIVE TUBE LENGTH, m
Figure 2.11 Equivalent Area as a Function of Shell Inside Diameter and Effective Tube
Length for 19.05 nun. OD Tubes on 23.81 nun. Equilateral Triangular Tube Layout,
Fixed Tubesheet, One Tube-side Pass, Fully Tubed Shell (Bell, 1993).
38
Extension of the "Base Case" to other ShelIIBundleffube Geometries
The calculated area is corrected for the tube size and layout, the type of tubebundle/
shell construction, and the number of tube-side passes for the specific geometry. ,
An "equivalent" area, A is defined by
o
,
Ao = AoF1F2F3Ff (2.29)
where Ao = Actual heat transfer area required calculated from Equation (2.28), ft2 or m2
F1 = Correction factor f<?r unit cell tube array
= 1.00 for 19.05 mm. O.D. tubes on 23.81 mm. triangular pitch
F2 Correction factor for number of tube - side passes
1.00 for one tube - side pass
F3 Correction factor for shell construction / tube bundle layout type
1.00 for fixed tubesheet type heat exchangers
Ff Correction factor for finned - tube type exchangers
1.00 for plain tubes
,
The equivalent area A is the one used to enter on the ordinate of figure (2.11). A
o
horizontal line is drawn from this point and various values of the equivalent length and
shell diameters are determined. The corresponding LlDi ratios are also calculated.
Choice of a particular L-Di combination depends to some extent on the amount of space
that is available to place the equipment. Generally, the combination that gives an L/Di
ratio of6:1 to 8:1 is preferred as explained earlier (Bell, 1993). One such combination is
then selected for further calculations.
39
Limitations of the Existing Version of the Approximate Design Method
The existing version of the approximate design method; though it has worked
reasonably well for the past several years, has several deficiencies.
1) Although a rough procedure for considering finned tubes is given in the footnote in
the existing version, no formal procedure is described to incorporate the finned tubes in
the tube diameter and layout factor. This present version of the approximate method
incorporates the finned tubes by separating the above mentioned factor F1 into two
correction factors, one relating directly to the tube outside diameter, pitch and layout, and
the other separately providing for the appropriate multipliers for typical finned tubes
(refer to equation 2.27).
2) The correction factors F2 and F3 are each functions of the shell diameter, but the
diameter ranges for each factor are different. This discrepancy is rationalized in the
present version.
3) The present method provides a means to estimate the number of tubes in a given shell
size. This depends on the use of a shell diameter-sensitive "packing factor." This allows
a more formal procedure for verifying the correct range of in-tube velocities and the
number of tube-side passes required, as a part of the approximate design.
4) There is no formal procedure for estimating the baffle cut and baffle spacing in the
existing version of the design method. The present version provides a method to estimate
the baffle spacing as a function of the shell inside diameter and the baffle cut.
5) The present version of the approximate design method incorporates the 8.1. units.
40
CHAPTER III
CORRECTION FACTOR ESTIMATION
Introduction:
At this stage we have the following information available to us:
i) The total heat load, QT.
ii) The mean temperature difference, MTD.
iii) The overall heat transfer coefficient, Vo.
iv) The number of shells needed to perform the required heat duty.
v) The total heat transfer area required, Ao based on total outside area of tubes including
fins.
As explained in the previous chapter, the "base case" needs to be corrected for
other shell and tube geometries. This is accomplished by the us~ of the correction factors
FI, F2, F3 and Ff(refer to equation 2.29).
Hence, the equation for calculating the "equivalent" area is:
,
Ao =AoFIF2F3Ff (3.1)
where Ao = Actual heat transfer area required, ft2 or m2
Fl Correction factor for unit cell tube array
F2 Correction factor for number of tube - side passes
F3 Correction factor for shell construction / tube bundle layout type
Ff Correction factor for finned tube type exchangers
41
The actual heat transfer area Ao in equation (3.1) is calculated using equation
(2.28). In order to use figure (2.11), this area has to be corrected for the particular shell
and tube geometry under consideration. This is accomplished by the use of the above ,
mentioned correction factors. The corresponding area estimated using equation (3.1), A
o
is the equivalent area. This value is used to enter the ordinate of figure (2.11) to estimate
the combinations of effective tube length and shell diameter.
We now consider each ofthe factors individually.
1) Correction Factor for the Unit cell Tube Array
This correction factor is applied to correct the area for the type of tube layout and
angle, tube size and pitch. The reference case for this factor is 19.05 mm. outside
diameter tubes on 23.81 mm. triangular pitch, and the factor is defined as:
(Heat transfer area / Cross - sectional area of unit cell)Re ference Case
F1 = ( . ) (3.2)
Heat transfer area / Cross - sectional area of unit cell New Case
Table 3.1 gives values of F1 for various tube sizes and layouts. The value of F1 is read
directly from the table for the particular tube size, type of tube layout and angle, and the
tube layout pitch for the case at hand. Appendix F gives the method to calculate the heat
transfer area and cross-sectional area of a unit cell.
42
~
VJ
Table 3.1: Correction Factor Fl for Unit Cell Tube Array
TUBE TUBE PITCH TUBE TUBE LAYOUT Fl
OlD in. OlD mm. RATIO PITCH in. PITCH mm.
0.250 6.350 1.25 0.313 7.938 ~ <l 0.334
1.25 0.313 7.938 ~ DO 0.385
1.33 0.333 8.446 ~ <l 0.378
1.33 0.333 8.446 ~ D<> 0.436
1.50 0.375 9.525 ~ <l 0.480
1.50 0.375 9.525 ~ DO 0.555
0.375 9.525 1.25 0.469 11.906 ~ <l 0.500
1.25 0.469 11.906 ~ DO 0.577
1.33 0.499 12.668 ~ <l 0.566
1.33 0.499 12.668 ~ DO 0.653
1.50 0.563 14.288 ~ <l 0.720
1.50 0.563 14.288 ~ DO 0.831
0.500 12.700 1.25 0.625 15.875 ~ <l 0.666
1.25 0.625 15.875 ~ DO 0.770
1.33 0.665 16.891 ~ <l 0.755
1.33 0.665 16.891 ~ D<> 0.871
1.50 0.750 19.050 ~ <l 0.960
1.50 0.750 19.050 ~ DO 1.108
0.625 15.875 1.25 0.781 19.844 ~ <l 0.833
1.25 0.781 19.844 ~ DO 0.962
1.33 0.831 21.114 ~ <l 0.943
1.33 0.831 21.114 ~ DO 1.089
1.50 0.938 23.813 ~ <l 1.200
1.50 0.938 23.813 ~ DO 1.385
~
~
Table 3.1 : Contd.
TUBE TUBE PITCH TUBE TUBE LAYOUT Fl
OlD in. OlD mm. RATIO PITCH in. PITCH mm.
0.750 19.050 1.25 0.938 23.813 --)- <l 1.000
1.25 0.938 23.813 --)- DO 1.155
1.33 0.998 25.337 --)- <l 1.132
1.33 0.998 25.337 --)- DO 1.307
1.50 1.125 28.575 --)- <l 1.440
1.50 1.125 28.575 --)- DO 1.663
0.875 22.225 1.25 1.094 27.781 --)- <l 1.166
1.25 1.094 27.781 --)- DO 1.347
1.33 1.164 29.559 --)- <l 1.320
1.33 1.164 29.559 --)- DO 1.525
1.50 1.313 33.338 --)- <l 1.679
1.50 1.313 33.338 --)- DO 1.939
1.000 25.400 1.25 1.250 31.750 --)- ~O 1.333
1.25 1.250 31.750 --)- 1.539
1.33 1.330 33.782 --)- <l 1.509
1.33 1.330 33.782 --)- 0<> 1.743
1.50 1.500 38.100 --)- <l 1.920
1.50 1.500 38.100 --)- DO 2.216
1.250 31.750 1.25 1.563 39.688 --)- <l 1.666
1.25 1.563 39.688 --)- DO 1.924
1.33 1.663 42.228 --)- <l 1.887
1.33 1.663 42.228 --)- 0<> 2.178
1.50 1.875 47.625 --)- <l 2.400
1.50 1.875 47.625 --)- DO 2.771
~
Vl
Table 3.1 : Contd.
TUBE TUBE PITCH TUBE TUBE LAYOUT Fl
OlD in. OlD Mm. RATIO PITCH in. PITCH mm.
1.500 38.100 1.25 1.875 47.625 ~ <] 1.999
1.25 1.875 47.625 ~ 00 2.309
1.33 1.995 50.673 ~ <l 2.264
1.33 1.995 50.673 ~ DO 2.614
1.50 2.250 57.150 ~ <l 2.879
1.50 2.250 57.150 ~ 00 3.325
2.000 50.800 1.25 2.500 63.500 ~ <l 2.666
1.25 2.500 63.500 ~ 00 3.078
1.33 2.660 67.564 ~ <] 3.018
1.33 2.660 67.564 ~ 00 3.485
1.50 3.000 76.200 ~ <l 3.839
1.50 3.000 76.200 ~ DO 4.433
2) correction Factor for Number of Tube-side Passes
This factor is applied when the number of tube-side passes is greater than 1(one),
Le., F2 = 1 for one tube-side pass. The correction factor is defined as
F2 = Number oftubes in heat exchanger with one tube - side pass (3.3)
Number of tubes in heat exchanger with' n' tube - side passes
where n = 2,4,6, , and the heat exchangers have the samelube layout
and inside shell diameter.
This factor is given in the existing version of the approximate design method but, it has
been recalculated here using a different, and relatively new database. The tube counts
used to calculate these values are different from those used in the existing version, and
hence, the values ofF2 are also somewhat different than those given in the existing
version. For a given exchanger configuration, F2 is a function of the shell inside
diameter and the number of tube-side passes. Table 3.2 gives values of factor F2 for
19.05 mm. outside diameter tubes on 23.81 mm. triangular pitch and a pitch ratio (PR) of
1.25 for various types of configurations. For any other tube size and layout, this factor
has to be used with the correction factor Fl. For a V-tube type b-eat exchanger, there is a
minimum of two tube-side passes, and hence, this factor has to be considered. Given in
Appendix G are the detailed tables for F2 and plots ofF2 vs. the shell inside diameter, Di.
The tube counts used for the evaluation of F2 are given in Appendix E (Saunders, 1988).
46
Table 3.2 : Correction Factor F2 for Number of Tube-side Passes.
n·I FACTORF2
m. 2 PASSES 4 PASSES 6 PASSES
0.203-0.337 1.113 1.400 1.613
0.387-0.540 1.059 1.173 1.244
0.591-0.737 1.038 1.109 1.151
0.787-0.940 1.029 1.080 1.109
0.991-1.219 1.022 1.061 1.083
1.295-1.524 1.017 1.047 1.063
As is seen in Appendix G, the values for F2 vary substantially for the different
configurations with the lowest being that for fixed tubesheet heat exchangers. As an
example consider F2 for 4 (four) tube-side passes over the diameter range of 0.203 m 0.337
m. The value ofF2 for the various configurations are as follows:
1) Fixed tubesheet exchangers = 1.113
2) V-tube exchangers = 1.165
3) Split backing ring floating head exchangers = 1.561
4) Pull-through floating head exchangers (1000 KPa pressure) = 1.692
5) .Pull-through floating head exchangers (2000 KPa pressure) = 1.754
This indicates that for the same diameter, more tubes can be accommodated in a fixed
tubesheet exchanger than any other configuration. It also indicates that as the number of
tube-side passes increase, more tubes are lost in the other confi~urations as compared to
the fixed tubesheet type. This implies that a smaller fixed tubesheet type exchanger
would be required to perform the same duty. It is not always possible to utilize this fact
as many factors affect the choice of the exchanger configuration such as differential
expanSIon.
47
3) Correction Factor for Shell constructiooffube-bundle Layout Type
This factor, F3, is defined as
F3 = Number of tubes in I nI tube - side passes of fixed tubesheet exchanger (3.4 )
Number of tubes in 'n' tube - side passes of other type of exchanger
where n = 1, 2, 4, , and the heat exchangers have the same tL1be layout, shell inside
diameters, and number of passes.
As is evident from the above equation, the reference case for this factor is the fixed
tubesheet type exchanger. Hence, for 1-2 split ring floating head type of exchanger,
factor F3 is estimated as
F3 = Number of tubes in 2 tube - side passes of fixed tubesheet exchanger (3.5)
Number of tubes in 2 tube - side passes of SRFH type of exchanger
The data used in the evaluation ofF3 is given in Appendix E and tables and plots
of F3 as a function of shell inside diameter are given in Appendix H. The value of F3 is
based on the data for 19.05 mm. outside diameter tubes on a 23.81 mm. triangular pitch
and a PR of 1.25 (Saunders, 1988). For other tube sizes and tub-e layouts, this factor is
used in conjunction with factor F1. Table 3.3 gives values of F3 for various types of shell
and tube heat exchangers over a range of shell inside diameters. As is evident from the
values indicated in Table 3.3 and Appendix H, more tubes can be accommodated in a
fixed tubesheet exchanger than any other configuration for the same shell inside diameter
and number of tube-side passes.
48
~
\0
Table 3.3 : Correction Factor F3 for Various Tube Bundle Constructions.
Type of F3
Tube Bundle Inside Shell
Construction Diameter m.
0.203-0.337 0.387-0.540 0.591-0.737 0.787-0.940 0.991-1.219 1.295-1.524
Fixed Tubesheet 1.000 1.000 1.000 1.000 1.000 1.000
(TEMA L, M, or N)
U-Tube (TEMA U) 1.065 1.072 1.047 1.034 1.024 1.020
Split Backing Ring 1.213 1.112 1.090 1.072 1.059 1.045
(TEMA S)
Pull-tlnough Floating 2.431 1.532 1.342 1.258 1.200 1.165
Head (1000 KPa
Pressure, TEMA T)
Pull-through Floating 2.500 1.589 1.395 1.311 1.244 1.201
Head (2000 KPa
Pressure, TEMA T)
4) Correction Factor for Finned-tube Tvpe Exchangers
This factor is applied when low fmned tubes are employed in the exchanger and is
defined as
F _ Outside surface area per unit length of plain tube
f - Outside surface area per unit length offinned tube (3.6)
Figure 3.1 shows the dimensional nomenclature used for the finned tube (Bell & Mueller,
1984).
I =nf
d - ---.--- • dj dr do
Lir:::::::==x
p
::::=.....----t~~
d - outside diameter of plain end
do· diameter over fins
d, - root diameter of finned section
d. - inside diameter of finned section
xp - wall thickness of plain section
XI • wall thickness of finned section
Figure 3.1 Dimensional Nomenclature Used for Type SIT Trufin Finned Tubes (Bell &
Mueller, 1984).
As is evident from equation (3.6), Ff= 1.0 for plain tubes. Values ofFfcan be read
directly from Table 3.4. The data used in the estimation ofFf(Bell & Mueller, 1984) is
given in Appendices C and D.
50
Vl
~
Table 3.4 : Correction Factor Fffor Low-finned Tubes
ROOT FACTOR
DIAMETER
OUTSIDE OUTSIDE FINS
DIA. DIA. PER dr Ff
in. mm. INCH in. mm.
0.375 9.525 19 0.250 6.350 0.436
0.500 12.700 19 0.375 9.525 0.411
0.500 12.700 19 0.375 9.525 0.318
0.500 12.700 16 0.375 9.525 0.504
0.625 15.875 16 0.500 12.700 0.482
0.625 15.875 19 0.500 12.700 0.399
0.625 15.875 19 0.500 12.700 0.410
0.625 15.875 26 0.500 12.700 0.299
0.625 15.875 32 0.557 14.148 0.415
0.750 19.050 11 0.500 12.700 0.373
0.750 19.050 16 0.625 15.875 0.402
0.750 19.050 19 0.625 15.875 0.392
0.750 19.050 19 0.625 15.875 0.390
0.750 19.050 19 0.625 15.875 0.390
0.750 19.050 26 0.625 15.875 0.306
0.750 19.050 26 0.640 16.256 0.311
0.750 19.050 28 0.672 17.069 0.377
0.750 19.050 32 0.682 17.323 0.390
0.750 19.050 40 0.675 17.145 0.304
0.750 19.050 40 0.625 15.875 0.212
(.../l
N
Table 3.4 : Contd.
OUTSIDE OUTSIDE FINS ROOT FACTOR
DIAMETER
DIA. DIA. PER dr
in. mm. INCH in. mm. Fe
0.875 22.225 11 0.625 15.875 0.361
0.875 22.225 16 0.750 19.050 0.458
0.875 22.225 19 0.750 19.050 0.385
0.875 22.225 19 0.750 19.050 0.385
0.875 22.225 28 0.797 20.244 0.375
0.875 22.225 32 0.807 20.498 0.387
1.000 25.400 11 0.750 19.050 0.353
1.000 25.400 16 0.875 22.225 0.452
1.000 25.400 19 0.875 22.225 0.381
1.000 25.400 26 0.890 22.606 0.298
1.000 25.400 26 0.875 22.225 0.293
1.000 25.400 28 0.922 23.419 0.374
1.000 25.400 32 0.932 23.673 0.386
5) Estimation of Equivalent Area
Once the actual heat transfer area, Ao is calculated using equation (2.26), and the
above mentioned factors are determined for the specific shell and tube geometry, the
"equivalent" area is estimated using Equation (2.29) as given below:
,
A = AoFIF2F3Ff (2.29)
o
where Ao = Actual heat transfer area required calculated from Equation(2.28), ft2 or m2
FI = Correction factor for unit cell tube array
F2 = Correction factor for number of tube- side passes
F3 = Correction factor for shell construction/ tube bundle type
Ff = Correction factor for finned tube exchangers
,
A plot has been prepared, figure (2.11), for the equivalent area, A as a function
o
of shell inside diameter, effective tube length, and the L/Di ratio for the special case of
19.05 mm. outside diameter plain tubes on a 23.81 mm. triangular pitch in a fixed
tubesheet type exchanger with one tube-side pass, fully tubed shell.
As explained earlier, once the required heat transfer area is calculated using
Equation (2.28), the equivalent area is estimated using the above mentioned correction
factors for the specific geometry. This area is then used to enter on the ordinate of Figure
(2.11) to determine the combinations of the effective tube length and shell inside diameter
that will provide the required area Ao (calculated using equation 2.28).
53
6) Estimation of Effective Tube Length and Shell Inside Diameter
The plot is entered on the ordinate of figure (2.11) at the value of the equivalent
area calculated by equation (2.29). For this value ofAo', various combinations of the
effective tube length, shell inside diameter, and the correspondin.g L/Di values are
determined. As is seen in the figure, the L/Di values range from 3: 1 to 15: 1.
54
CHAPTER IV
PARAMETER ESTIMATION
Introduction
Given below is a method to estimate the tube count for a given shell size and
tubesheet type and an estimation procedure for the baffle spacing as a function of the
baffle cut and shell inside diameter. The baffle spacing has a direct bearing on the shellside
fluid velocity and pressure drop and hence is an important factor to be considered in
the design of shell and tube heat exchangers. Both the above mentioned methods are not
given in the existing version ofthe design method.
1) Estimation of Tube Count for a Given Shell Inside Diameter and Exchanger
The number of tubes for a given shell size and tubesheet type depends on the tube
pitch, tube layout angle, number of tube-side passes and pass partition plates, diameter of
outer tube limit, tube diameter, tube bundle type (fixed tubesheet, V-tube bundle, floating .
head type, etc.), presence of impingement plate, tie rods, available pressure drop, etc..
Some standard tube count tables are compiled and are available in the open literature
(Kern, 1950; Perry & Chilton, 1973; Saunders, 1988). Computer programs are used to
layout the tube fields and count the tubes. Some manufacturers have their own standard
tables. In any case, accurate estimates are difficult to obtain due to the large number of
55
variables which must be considered. For an initial design, a. simple, but, a reasonably
accurate estimate can be made as follows:
As
Nt =Fp A
c
(4.1)
where Nt Total number of tubes
Fp = Packing factor
As = Area of outer tube limit, ft2 or m2
1t 2
4 DotI
Ac = Cross- sectional area of unit cell, ft2 or m2
Hence equation 4.1 can be expressed as
Nt =: ~ {~~;1}2 =O.785~~{~:1}2 (4.2)
where Dotl Diameter of outer tube limit, in. or mm
Tube layout pitch, in. or mm
Ct = Tube layout angle constant
0.866 for 300 angle
1.000 for 450 and 900 layout angles
The value ofFp depends mainly on the tube layout pitch, Ltp, and the diameter of
outer tube limit, Dotl.
Fp values for various heat exchanger configurations are given in Appendix I.
56
2) Estimation of Baffle cut and Spacing for a Given Shell Size.
Baffles have two very important functions.
i) To provide support for the tubes against sagging and damage due to vibrations caused
by the fluids flowing through and across them.
ii) To increase the heat transfer coefficient as much as possible by directing the flow and
increasing velocity without violating the available pressure drop limitations.
Several types of baffles are available but the most commonly used in shell and
tube exchangers is the single segmental type. These give higher heat transfer coefficients
and pressure drop by increasing the velocity of the shell-side fluid. The heat transfer
coefficient and the pressure drop across the exchanger also depend on the baffle spacing
and baffle cut and hence these are considered in some detail in this section. To do this,
we first define the terms baffle cut and baffle spacing.
Baffle Cut:
This is basically the size of the segment removed and is usually specified as a
percent of the shell inside diameter. As the baffle cut increases, the flow pattern deviates
increasingly from crossflow. The segment sheared off must be less than half the diameter
to insure that adjacent baffles overlap at least one full tube row. For liquid flows on the
shell-side, a baffle cut of 20-25 percent of the diameter is common; for low pressure gas
flows, 40-45 percent (i.e., close to the maximum allowable cut) is more common, in order
to minimize pressure drop (Bell & Mueller, 1984).
Baffle Spacing:
This is defined as the spacing between two adjacent baffles. For given shell and
tube diameters, tube layout, and the shell-side flow rate, the baffle cut determines the
flow velocity through the window (the space from the top of the baffle to the shell inside
diameter), whereas the baffle spacing determines the crossflow velocity. Hence, both
57
baffle cut and baffle spacing influence the fluid velocity and hence, the heat transfer
coefficient and pressure drop on the shell-side.
TEMA (TEMA, 1988) specifies a minimum baffle spacing of20% of the shell
diameter or 2 inches, whichever is greater. It also specifies the maximum allowable
spacing depending upon the tube outside diameter and materials of construction.
The underlying principle for the estimation of baffle spacing is that the velocities
in the window and crossflow regions should be approximately equal. The advantage of
having approximately equal velocities in the crossflow and window regions is that it
tends to maximize the effective use of the available pressure drop to create higher heat
transfer coefficients. It also tends to make the tube-bundle more rigid. This is
particularly important where tube vibration is expected to occur. This principle is also
used in the NTIW (No Tubes In the Window) design where every tube passes through
and is supported by every baffle guiding the flow. The loss in the number of tubes can be
minimized by having small baffle cuts and an increase in shell-side fluid velocity
(especially through the window) resulting in a significant increase in shell-side heat .
transfer coefficient (Bell, 1993). Based on the above principle, the following procedure is
used to determine the relationships between baffle cut, baffle spacing and shell inside
diameter.
a) Crossflow Area At or Near the Centerline for One Crossflow Section
i) For plain tubes on rotated and inline square layouts.
- {(. ) (Dotl - do J( )} 8m - Is D1 - Dotl + Pn P - do
58
.......................... (4.3)
where Sm = Crossflow area at or near centerline for one crossflow section,
ft2 or m2
Is = Baffle spacing, in. or nun
do = Outer diameter of plain tube, in. or nun
Pn = Tube pitch normal to flow, in. or nun
P = Tube pitch, in. or nun
ii) For plain tubes on triangular layouts
Sm=ls{<ni _DOtl)+(DOtlp-dO J[(P-do)]} (4.4)
The nomenclature is as in equation (4.3).
b) Baffle Cut Angle:
This is the angle suhtended by the intersection of the cut edge of the baffle with the inside
surface of the shell
e=2cos-1{1- ~~} (4.6)
where 8 = Baffle cut angle, radians
59
c) Area for Flow Through Window
Sw = Swg - Swt (4.6)
= Gross window area - Window area occupied by tubes.
Swg = ~r {~-[1-2;i]Si{~)} (4.7)
Swt == ~t (l-Fc}td~ (4.8)
where Fc is the fraction of total tubes in crossflow and can be calculated from
1 { JDi -21cJ.r -l(Di -2lc Jl r -l(Di -2Ic Jl} Fe = 7t 7t +~ Dot! SlItcos Dot! J-{cos Dot! J (4.9)
where lc = Baffle cut, in. or mm
Assuming that the area of crossflow is equal to the area for flow through the
window, we get the following relationship:
Sm =Sw = Swg -Swt (4.10)
This equation can be simplified to get a relationship for the baffle spacing as a
function of the shell inside diameter, and the baffle cut.
For plain tubes on triangular layouts,
........................................ (4.11)
60
For convenience, a plot of ls/Di vs. (lc/Di)* 100, for the various bundle configurations for
the special case of 19.05 mm. outside diameter plain tubes on 23.81 mm. triangular pitch,
is given in Appendix J. Also given are plots for 19.05 mm OD tubes on 25.4 mm
triangular pitch and 19.05 mm OD tubes on 25.4 mm square pitch. The results show that
the baffle spacing is not a very strong function of the tube size and pitch. It is more
dependent on the shell inside diameter, baffle cut, and diameter of outer tube limit.
Tube Vibrations
Damaging tube vibration can occur under certain conditions of shell-side flow
relative to baffle configuration and unsupported tube span (TEMA, 1988). The designer
should consider the use of shorter unsupported tube spans by a modification of the
internal baffle configuration. This includes the baffle spacing, the tube-tube hole
clearance and the use of the no-tube-in-window (NTIW) design. Another method used to
prevent failures due to flow induced vibration is the use of the RODbaffle (RBE) type of
shell and tube exchanger first developed and patented by the Phillips Petroleum Co. in
1970. As the name implies, the supports for the tubes are rods instead of the
conventional perforated plate baffles.
TEMA Standards specify the maximum unsupported tube span for a shell size.
The potential for tube vibration can occur at anyone or more of the following locations
within the heat exchanger:
1) Main section of the heat exchanger bundle where the baffles are generally of equal
spacing and there may be repeated impact between adjacent tubes at mid-span. Cutting at
the baffles can also occur, particularly if the baffles are thin or harder than the tubes or
there is a large baffle hole-tube clearance due to repeated impact between tubes and
baffles due to thermal expansion.
61
iii :~
2) Inlet and outlet sections of the tube bundle at or near the shell nozzles where the
unsupported tube span is usually the highest and the local velocities are highest due to the
nozzles.
3) U-bends.
4) Underneath the nozzles.
5) Tubes that pass through the window.
Mechanisms of Tube Vibration
Tube vibrations in shell and tube heat exchangers may be induced by the shell-side
fluid flow, tube-side fluid flow, or mechanically transmitted vibration from other
equipment. The most frequently encountered source of tube excitation is from shell-side
fluid flow. This source is solely dependent upon the design of the heat exchanger.
Several mechanisms that may cause tube vibration, as described in the literature
(Barrington, 1973; Chen & Weber, 1970; Kissel, 1973; TEMA,·1988; Walker & Reising,
1968), are as follows:
1) A natural frequency of the tubes may coincide with the vortex shedding frequency of
the fluid in crossflow to the tubes and excite large resonant vibration amplitudes.
2) Turbulent pressure fluctuations occurring in the wake of a cylinder or carried to the
cylinder from an upstream disturbance may provide a potential mechanism for tube
vibration. The tubes respond to that portion of the energy spectrum that is close to their
natural frequency. The amplitude of vibration may be very small at low flow rates and
increases in direct proportion to the dynamic head.
3) Fluidelastic coupling occurs when the fluid flowing past the tubes causes them to
vibrate with a large whirling motion. The vibration is self-excited and, once initiated,
will grow in amplitude.
62
"Ii II~
4) Tubes experiencing axial flow are subject to flow induced vibration resulting, in part
from the flow parallel to the tubes, and in part from the crossflow components that exist
in any real axial flow situation.
5) If the shell-side fluid is a low density gas, acoustic resonance or coupling may occur.
This happens when standing waves in the shell are in phase with the vortex shedding
from the tubes. These standing waves are perpendicular to the direction of crossflow and
the axis of the tubes. Although this phenomenon can result in a serious noise problem, it
usually does not cause significant tube vibration amplitude or damage. Standing waves
in a liquid or dense fluid are normally too small to produce the same effect.
All the above mentioned factors have to be considered in the event that there
exists a possibility of tube vibration problems during the operation of the heat exchanger.
63
CHAPTER V
SUMMARY AND CONCLUSIONS
Summary:
Shell and tube heat exchangers are the most common type of heat exchangers
used in the Chemical Process Industry. They are one of the most important components
in a process that can be used to achieve large amounts of energy savings. Numerous
computer programs as well as the hand-based Delaware method are available for the
detailed design but this is an unnecessary, time consuming activity at the initial stages of
a project. A "Quick Manual Design," though approximate, will give an experienced
designer a fair idea of the actual size of the heat exchanger after detailed design. This is
important in the initial stages in that it can be used to obtain an estimate ofthe cost of the
equipment which in turn is required at the time of the cost estimation of the project.
Another advantage of such an approximate design is in the preparation of the plant layout
and the piping and instrumentation diagram. The results from the approximate method
will also be good starting points for the detailed design that requires some iterative
solution. These results can also be used as a check for the results obtained using
computer programs. This thesis is a modification of such an approximate design method.
1) All the correction factors in the presented version of the design method have been
recalculated using a totally different database and hence there is-some difference in the
various values of the correction factors, as compared to the existing version.
64
2) The correction factor for the presence of finned tubes presented here was considered
only as a footnote for factor Fl. The present version gives a new factor Ff to account for
the presence of finned tubes.
3) No formal procedure is given in the existing version to estimate the tube counts or the
baffle spacing. These are covered in this thesis.
A summary of the approximate design method is as follows:
1) Calculate the total amount of heat to be transferred, i.e., the total heat duty, QT.
2) Estimate the individual heat transfer coefficients (u's) from ~vailable literature (also
given in Appendix A).
3) Estimate the fouling factors, if required, from available literature (also given in
Appendix A).
4) If finned-tubes are employed in the service, choose the fin dimensions, calculate the
fin efficiency using equation (2.7) or estimate it for the material of construction and
dimensions as explained in Chapter II (close to 1.0 for highly conducting materials and
low heat transfer coefficients), or calculate the resistance to heat transfer due to the
presence of fins using equation (2.10).
5) Calculate the thermal resistance of the tube wall.
6) Once the values of the resistances have been determined, calculate the overall heat
transfer coefficient using equation (2.13).
7) Estimate the number of shells required in series to perform the required heat duty.
8) Calculate the AMTD using equation (2.23).
9) Estimate the LMTD for the specified temperature conditions using the calculated
value of the AMTD.
10) Estimate the LMTD correction factor FT based on flow configuration (and outlet
temperatures for multi-pass designs).
11) Estimate the MTD using equation (2.25).
65
12) Once the values ofQT, Do, and MTD are known, calculate the required total outside
heat transfer area including fins using equation (2.28).
13) Estimate the correction factor Fl for the tube size, tube laY<2ut, and pitch from Table
(3.1).
14) Estimate correction factor F2 for number of tube-side passes as a function of the
shell inside diameter from Table (3.2).
15) Estimate the correction factor F3 for the shell construction/tube-bundle type from
Table (3.3).
16) Estimate correction factor Fffor finned tubes from Table (3.4).
17) Calculate the "equivalent" area to be used to enter the ordinate of Figure (2.11) using
Equation (2.29).
18) Determine the various length-shell inside diameter combinations from figure (2.11).
19) Select a value of the effective length and shell inside diameter which gives an L/Di
in the range of 6: 1 to 8: 1.
Conclusions
1) The approximate design method can be used to perform a quick preliminary design of
shell and tube heat exchangers. This can be useful at the initial stages of a project for
cost estimation and preparation of the plant layout and P & I diagrams.
2) The approximate design method will be a useful tool for performing a quick manual
check of any available design.
3) The approximate design method can be used to check the validity of computer based
designs.
4) The method works well for estimating various parameters which can be used as input .
variables in the detailed and iterative design methods thus saving time.
5) This approximate design method can be a useful pedagogical tool.
66
6) The present version of the approximate design method takes into account the presence
of finned tubes by providing a correction factor Ff to estimate the "equivalent" area. In
the existing version of the approximate method, this factor was combined with factor F1,
and only as a footnote.
7) The existing version of the approximate design method gives factors F2 and F3 over
varying shell inside diameter ranges. The present version has rationalized this, i.e., it
gives the factors over the same diameter ranges.
8) The present version incorporates S.I units.
9) The present version provides a method to estimate the baffle spacing as a function of
baffle cut and shell inside diameter.
67
CHAPTER VI
RECOMMENDATIONS
1) The method presented to estimate the tube count using the packing factor is not very
useful as it stands. It needs to be worked on to get as few figures as possible without a
substantial loss of accuracy.
2) Some type of vibration analysis should be incorporated in this method.
3) The method should include some type of optimization criteria such as minimizing the
heat transfer area, utilizing maximum available pressure drop, etc.
4) Some guidelines need to be provided on the selection of velocities and hence number
of tubes in parallel, number of tube-side passes, etc.
68'
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Bell, K. J. (1963). Final Report of the Co-operative Research Pro~ram on Shell and Tube
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Bell, K. J. (1978). Estimate S & T Exchanger Design Fast. Oil and Gas
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Bell K.J. (1983). In Schlunder, E. U. (Ed.). Heat Exchan~er Desi~n Handbook.
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Bell, K. J. (1993). Overall Design Methodology for Shell and Tube Heat Exchangers.
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Bell K. J. (1993). Typical Overall Design Coefficients for Shell and Tube Heat
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Bell, K. J., & Mueller, A. C. (1984). En~ineerin~ Data Book II. Wolverine Tube, Inc.
Bowman, R. A., Mueller, A. C., & Nagle, W. M. (1940). Mean ~emperature Difference
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Briggs, D. E., Katz, D. L., & Young, E. H. (1963). How to Design Finned-Tube Heat
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69
Briggs, D. E., & Young, E. H. (1965). Convection Heat Transfer and Pressure Drop of
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~,~(41), pp.1-10.
Chen, Y. N., & Weber, M. (1970). Flow Induced Vibrations in Tube Bundle Heat
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Colburn, A. P. (1933). A Method of Correlating Forced Convection Heat Transfer Data
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Cook, E. M. (1964a). Comparison of Equipment for Removing Heat from Process
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Fischer, F. K. (1938). Mean Temperature Difference Correction in Multipass Exchangers.
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Gilmour, C. H. (1953a). Short Cut to Heat Exchanger Design- II. Chemical En~ineerin~
(March), pp. 226-229.
Gilmour, C. H. (1953b). Short Cut to Heat Exchanger Design- III. Chemical En~ineerin2
(April), pp. 214-218.
Gilmour, C. H. (1953c). Short Cut to Heat Exchanger Design- IV. Chemical En~ineerin2
(October), pp. 203-208.
Gilmour, C. H. (1954a). Short Cut to Heat Exchanger Design- V. Chemical Engineerin~
(February), pp. 190-195.
Gilmour, C. H. (1954b). Short Cut to Heat Exchanger Design- VI. Chemical Engineerin~
(March), pp. 209-213.
Gilmour, C. H. (1954c). Short Cut to Heat Exchanger Design- VII. Chemical Engineering
(August), pp. 199-206.
Hutchinson, E. (1945). On the Measurement of the Thermal Conductivity of Liquids.
TranS. Faraday Soc., 41, pp. 87-92.
Jaw, L. (1964). Temperature Relations in Shell-and-Tube Exchangers Having One-Pass
Split-Flow Shells. Trans. ASME. .8.Q (August), pp. 408-416.
70
Kern, D. Q. (1950). Process Heat Transfer. New York: McGraw Hill Book Co.
Kern, D. Q., and, & Kraus, A. D. (1972). Extended Surface Heat Transfer. New York:
McGraw-Hill.
Kissel, 1. H. (1973). Flow Induced Vibrations in Heat Exchangers-A Practical Look.
Machine Desi~n, ~(11), pp. 104-107.
Linnhoff, B. (1982). User Guide on Process Inte~ration for the Efficient Use of Ener2Y.
London: Institution of Chemical Engineers.
Lohrisch, F. W. (1963). What are Optimum Exchanger Conditions? Hydrocarbon
Process. Petrol. Refiner, 42(5), pp. 177-180.
Lord, R. C., Minton, P. E., & Slusser, R. P. (1970). Design of Heat Exchangers. Chemical
En2ineerin~, TI(2), pp. 96-118.
McAdams, W. H. (1954). Heat Transmission (3rd ed.). New York: McGraw Hill Book
Company inc.
McKetta, J. J. (Ed.). (1992). Heat Transfer Desi20 Methods. New York: Marcel Dekker
Inc.
Morton, D. S. (1962). Heat Exchangers Dominate Process Heat Transfer. Chern. En2.,
Q2(June, 11), pp. 170-176.
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En~. Chern., ~(6), pp. 604-608.
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Rohsenow, W. M., Hartnett, 1. P., & Ganic, E. N. (Ed.). (1985). Handbook of Heat
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Saha, & Srivastava (1935). Treatise On Heat. Calcutta: The Indian Press.
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Saunders, E. A. D. (1988). Heat Exchan2ers: Selection. Desi2n and Construction (1st
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Shah, R. K. (1984). What's New in Heat Exchanger Design. MechanicaLEn~ineerin~,
.ulQ(5), pp. 50-60.
71
Taborek, J. (1983). In Schlunder E.D. (Ed.), Heat Exchan~er Desi2n Handbook
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..
Ten Broeck, H. (1938). Multipass Exchanger Calculations. Ind. En2. Chern., 3.Q, pp.
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72
APPENDICES
73
APPENDIX A
TYPICAL OVERALL AND INDIVIDUAL DESIGN COEFFICIENTS
FOR SHELL AND TUBE HEAT EXCHANGERS
(Bell, 1993)
Given in Table A.l are typical values of the overall heat transfer coefficients for
shell and tube heat exchangers. These values can be used to estimate the heat transfer
area required in a shell and tube heat exchanger. The results using these values may not
be very accurate due to the fact that these values are derived to include a wide range of
process conditions. As explained earlier, a more accurate method would be to estimate
the overall heat transfer coefficient by estimating the individual resistances. To do so
typical values of the film heat transfer coefficients are required. Table A.2 presents these
values for various fluid conditions. Also given in Table A.2 are typical values of fouling
resistance for various fluid conditions. These values are as those given by Bell (Bell,
1993).
74
Table A.I : Typical Overall Heat Transfer Coefficients for Shell and Tube Heat
Exchangers (Bell, 1993).
FLUID I FLUID 2 Do
W/m2 K
Water (3,4) Water 1400-1700
Water (3,4) Gas, about 10 psig 85-115
" Gas, about 100 psig 170-230
" Gas, about 1000 psig 325-575
" Light organic liquids (5) 700-1000
" Medium organic liquids (6) 425-700
" Heavy organic liquids (7) 225-425
" Very heavy organic liquids
(8)
Heating 50-225
Cooling 25-85
Steam Gas, about 10 psig 85-115
" Gas, about 100 psig 200-250
" Gas, about 1000 psig 400-625
" Light organic liquids (5) 750-1100
" Medium organic liquids (6) 450-750
" Heavy organic liquids (7) 250-450
" Very heavy organic 85-250
liquids (8)
Steam (No non-condensables)
Water 1700-2275
75
Table A.I : Contd.
FLUID I FLUID 2 Uo
W/m2 K
Light organic liquids Light organic liquids (5) 575-750
" Medium organic liquids (6) 400-575
" Heavy organic liquids (7)
Heating 225-425
Cooling 140-285
" Very heavy organic
liquids (7)
Heating 115-285
Cooling 25-140
Medium organic Medium organic liquids 285-450
liquids (6) (6)
" Heavy organic liquids (7)
Heating 170-285
Cooling 85-200
" Very heavy organic
liquids (8)
Heating 85-170
Cooling 25-140
Heavy organic Heavy organic 50-170
liquids (7) liquids (7)
" Very heavy organic • 25-85
liquids
Gas, about 10 psig Gas, about 10 psig 50-85
" Gas, about 100 psig 85-115
" Gas, about 1000 psig 85-140
Gas, about 100 psig Gas, about 100 psig 110-170
" Gas, about 1000 psig 140-200
Gas, about Gas, about 1000 psig 200-350
1000 psig
76
Table A.I: Contd.
FLUID 1
Water
"
"
FLUID 2
Condensing light organic
vapors, pure component
(5,9)
Condensing medium
organIc vapors, pure
component (6,9)
Condensing heavy
organic vapors, pure
component (7,9)
Do
W/m2 K
850-1150
550-850
425-550
1. The total fouling resistance and the overall heat transfer coefficient are based on the total
outside tube area.
2. Allowable pressure drops on each side are assumed to be about 10 psi except for (a) low
pressure gas and condensing vapor where the pressure drop is assumed to be about 5 % of
the absolute pressure, and (b) heavy organics where the allowable pressure drop is assumed
to be about 20 to 30 psi.
3. Aqueous solutions give approximately the same coefficients as water.
4. Liquid ammonia gives about the same results as water.
5. "Light organic liquids" include liquids with viscosities less than about 0.5 cp, such as
hydrocarbons through Cg, gasoline, light alcohols and ketones, etc.
6. "Medium organic liquids" include liquids with viscosities between 0.5 cp and 1.5 cp, such as
kerosene, straw oil, hot gas oil, absorber oil, and light crudes.
7. "Heavy organic liquids" include liquids with viscosities greater than 1.5 cp, but not over 50 cp,
such as cold gas oil, lube oils, fuel oils, and heavy crudes.
8. "Very heavy organic liquids" include tars, asphalts, polymer melts, greases, etc., having liquid
viscosities greater than 50 cpo
77
Table A.2: Typical Film Heat Transfer Coefficients for Shell and Tube Heat
Exchangers (Bell, 1993).
FLUID CONDITIONS (l, W/mJ, Ka,b FOULING
RESISTANCE,
W/m2 Ka
Sensible heat transfer
Water c Liquid 5000-7500 lE-4-2.5E-4
Ammonia Liquid 6000-8000 0-IE-4
Light organics d Liquid 1500-20.00 0-2E-4
Medium organics e Liquid 750-1500 lE-4 -4E-4
Heavy organics f Liquid
Heating 250-750 2E-4-10E-4
Cooling 150-400 2E-4-10E-4
Very heavy organicsg Liquid
Heating 100-300 4E-3-30E-3
Cooling 60-150 4E-3-30E-3
Gash Pressure 100-200 kN/m2 abs. 80-125 0-IE-4
Gash Pressure 1 MN/m2 abs. 250-400 0-IE-4
Gash Pressure 10 MN/m2 abs. 500-800 0-IE-4
Condensing heat transfer
Steam, ammonia Pressure 10 kN/m2 abs. no 8000-12000 0-IE-4
noncondensables i, j
Steam, ammonia Pressure 10 kN/m2 abs, 1% 4000-6000 0-IE-4
noncondensables k
Steam, ammonia Pressure 10 kN/m2 abs 4% 2000-3000 0-IE-4
noncondensables k
Pressure 100 kN/m2 abs, no
.
Steam, ammonia 10000-15000 0-IE-4
noncondensables i,j,k,l
Steam, ammonia Pressure 1 MN/m2 abs, no 15000-25000 0-IE-4
noncondensables i,j,k,l
Light organics d Pure component, pressure 10 1500-2000 0-IE-4
kN/m2 abs, no
noncondensables I
Light organics d Pressure 10 kN/m2 abs 4% 750-1000 0-IE-4
noncondensables k
Light organics d Pure component, pressure 2000-4000 0-IE-4
100 kN/m2 abs, no
noncondensables I
78
Table A.2 : Contd.
FLUID CONDITIONS a., W/mJ, Ka,b FOULING
RESISTANCE,
W/m2 Ka
Light organics d Pure component, pressure 3000-4000 0-IE-4
1 MN/m2 abs
Medium organics e Pure component or narrow 1500-4000 lE-4-3E-4
condensing range, pressure
100 kN/m2 abs m, n
Heavy organics Narrow condensing range, 600-2000 2E-4-5E-4
pressure 100 kN/m2 abs m, n
Light multicomponent Medium condensing range, 1000-2500 0-2E-4
mixtures, all condensable e pressure 100 kN/m2
absk,m,o
Medium multicomponent Medium condensing range, 600-1500 lE-4-4E-4
mixtures, all condensable e pressure 100 kN/m2 abs
k,m,o
Heavy multicomponent Medium condensing range, 300-600 2E-4-8E-4
mixtures, all condensablef pressure 100 kN/m2 abs
k,m,o
Vaporizing heat transferp,q
Water r Pressure < 0.5 MN/m2 abs, 3000-10000 lE-4-2E-4
ATSH,max = 25 K
Water r Pressure> 0.5 MN/m2 abs, 4000-15000 lE-4-2E-4
pressure < 10 MN/m2 abs
ATSH,max = 20 K
Ammonia Pressure < 3 MN/m2 abs 3000-5000 0-2E-4
ATSH,max = 20K
Light organics d Pure component, pressure < 1000-4000 lE-4-2E-4
2
MN/m2 abs, ATSH max
=20K
,
Light organics d Narrow boiling ranges, 750-3000 0-2E-4
Pressure < 2 MN/m2 abs,
ATSH,max = 15 K
Medium organics e Pure component, pressure < 1000-3500 lE-4-3E-4
2
MN/m2 abs, ATSH,max
=20K
Medium organics e Narrow boiling ranges, 600-2500 lE-4-3E-4
Pressure < 2 MN/m2 abs,
ATSH..max = 15 K
79
Table A.2: Contd.
FLUID
Heavy organics f
CONDITIONS
Pure component, pressure <
2
MN/m2 abs, ATSH max
=20K '
a., W/ml Ka,b FOULING
RESISTANCE,
W/m2 Ka
750-2500 2E-4-5E-4
Heavy organics g
Very heavy organicsh
Narrow boiling ranges,
Pressure < 2 MN/m2 abs,
ATSH,max = 15 K
Narrow boiling ranges,
Pressure < 2 MN/m2 abs,
AT~H_m~x = 15 K
400-1500
300-1000
2£-4-8£-4
2E-4-10E-4
a. Heat transfer coefficients and fouling resistances are based on area in contact with fluid.
Ranges shown are typical, not all-encompassing. Temperatures are assumed to be in normal
processing range; allowances should be made for very high or low temperatures.
b. Allowable pressure drops on each side are assumed to be about 50-100 kN/m2 except for (1)
low-pressure gas and two-phase flows, where the pressure drop is assumed to be about 5%
of the absolute pressure; and (2) very viscous organics, where the allowable pressure drop
is assumed to be about 150-250 kN/m2.
c. Aqueous solutions give approximately the same coefficients as water.
d. "Light organics" include fluids with liquid viscosities less than about 0.5 x 10-3 Ns/m2, such
as hydrocarbons through C8, gasoline, light alcohols and ketones, etc.
e. "Medium organics" include fluids with liquid viscosities between about 0.5 x 10-3 Ns/m2
and 2.5 x 10-3 Ns/m2, such as kerosene, straw oil, hot gas oil, and light crudes.
f. "Heavy organics" include fluids with liquid viscosities greater than 2.5 x 10-3 Ns/m2, but not
more than 50 x 10-3 Ns/m2, such as cold gas oil, lube oils, fuel oils, and heavy and reduced
crudes.
g. "Very heavy organics" include tars, asphalts, polymer melts, greases, etc., having liquid
viscosities greater than about 50 x 10-3 Ns/m2. Estimation of co~fficientsfor these
80
materials is very uncertain and depends strongly on the temperature difference, because
natural convection is often a significant contribution to heat transfer in heating, whereas
congelation on the surface and particularly between fins can occur in cooling. Since many of
these materials are thermally unstable, high surface temperatures can lead to extremely
severe fouling.
h. Values given for gases apply to such substances as air, nitrogen, carbon dioxide, light
hydrocarbon mixtures (no condensation), etc. Because of the very high thermal
conductivities and specific heats of hydrogen and helium, gas mixtures containing
appreciable fractions of these components will generally have su~stantially higher heat
transfer coefficients.
i. Superheat of a pure vapor is removed at the same coefficient as for condensation of the
saturated vapor if the exit coolant temperature is less than the saturation temperature (at the
pressure existing in the vapor phase) and if the (constant) saturation temperature is used in
calculating the mean temperature difference. But see note k for vapor mixtures with or
without noncondensable gas.
j. Steam is not to be condensed on conventional low-finned tubes; its high surface tension
causes bridging and retention of the condensate and a severe reduction of the coefficient
below that of the plain tube.
k. The coefficients cited for condensation in the presence of noncondensable gases or for
multicomponent mixtures are only for very rough estimation purposes because of the
presence of mass transfer resistances in the vapor (and to some extent, in the liquid) phase.
Also, for these cases, the vapor-phase temperature is not constant, and the coefficient given
is to be used with the mean temperature difference estimated using vapor-phase inlet and
exit temperatures, together with the coolant temperatures.
l. As a rough approximation, the same relative reduction in low-pressure condensing
coefficients due to noncondensable gases can also be applied to higher pressures.
m. Absolute pressure and noncondensables have about the same effect on condensing
81
coefficients for medium and heavy organics as for light organics. Because of prior thermal
degradation, fouling may become quite severe for the heavier condensates. For large
fractions of noncondensable gas, interpolate between pure component condensation and gas
cooling coefficients.
D. "Narrow condensing range" implies that the temperature difference between dew point and
bubble point is less than the smallest temperature difference between vapor and coolant at
any place in the condenser.
o. "Medium condensing range" implies that the temperature difference between dew point and
bubble point is greater than the smallest temperature difference between vapor and coolant,
but less than the temperature difference between inlet vapor and outlet coolant.
p. Boiling and vaporizing heat transfer coefficients depend very strongly on the nature of the
surface and the structure of the two-phase flow past the surface in addition to all of the other
variables that are significant for convective heat transfer in other modes. The flow velocity
and structure are very much governed by the geometry of the equjpment and its connecting
piping. Also, there is a maximum heat flux from the surface that can be achieved with
reasonable temperature differences between surface and saturation temperatures of the
boiling fluid; any attempt to exceed this maximum heat flux by increasing the surface
temperature leads to partial or total coverage of the surface by film of vapor and a sharp
decrease in the heat flux. Therefore, the vaporizing heat transfer coefficients given in this
table are only for very rough estimating purposes and assume the use of plain or low-finned
tubes without special nucleation enhancement. ~TSH,max is the maximum allowable
temperature difference between surface and saturation temperature of the boiling liquid.
No attempt is made in this table to distinguish among the various types of vapor-generation
equipment, since the major heat transfer distinction to be made is propensity of
the process stream to foul. Severely fouling streams will usually call for a vertical
thermosiphon or a forced convection (tube-side) reboiler for ease of cleaning.
q. Subcooling heat load is transferred at the same coefficient as latent heat ~oad in kettle
82
reboilers, using the saturation temperature in the mean temperature difference. For
horizontal and vertical therrnosiphons, a separate calculation is required for the sensible heat
transfer area, using appropriate sensible heat transfer coefficients and the liquid temperature
profile for the mean temperature difference.
r. Aqueous solutions vaporize with nearly the same coefficient as pure water is attention is
given to boiling-point evaluation, if the solution does not become saturated, and if care is
taken to avoid dry wall conditions.
s. For boiling of mixtures, the saturation temperature (bubble point) of the final liquid phase
(after the desired vaporization has taken place) is to be used to calculate the mean
temperature difference. A narrow-boiling-range mixture is defined as one for which the
difference between the bubble point of the incoming liquid and the bubble point of the exit
liquid is less than the temperature difference between the exit hot stream and the bubble
point of the exit boiling liquid. Wide-boiling-range mixtures require a case-by-case analysis
and cannot be reliably estimated by these simple procedures.
83
APPENDIXB
EXAMPLE PROBLEM
Problem Statement
A shell and tube heat exchanger is cooling a low pressure gas (0.45 MN/m2 abs.)
from 376 K to 319 K, heating water from 300 K to 311 K. The gas flow rate is 86.55
kg/s, with a specific heat of 2311 J/kg K and the water flow rate is 246.64 kg/s with a
specific heat of 4179 J/kg K.
A split backing ring floating head type exchanger is to be used with water in the
tubes. The tubes are Wolverine Type SIT Trufin®, No. 60-195083 (19.05 mm. outside
diameter) on 25.4 mm. square pitch. The material of construction is 90-10 Cupronickel
(Alloy C70600), which has a thermal conductivity of 52 W/m K.
The specifications of the finned tubes are:
19 fins per inch (748 fins/m)
Outside diameter (over fins) : 19.05 mm. (0.75 in.)
Wall thickness (under fins) : 2.11 mm (0.083 in.)
Inside diameter (under fins) : 11.61 mm (0.457 in.)
Total external surface area per unit length: 0.151m2/m (0.496 ft2/ft)
Surface area ratio, external to internal: 4.14
Typical pressure drops allowable are 3 kPa and 86 kPA for the shell- and tubeside
respectively. Fouling resistances are given as 0.00035 m Klw for either side.
84
Estimate the effective tube length and shell inside diameter of the exchanger for this
servIce.
Solution:
Check the Heat Balance
Qgas =86.55(2311)(376-319)
=1.14x107W
Qwater = 246.64(4179)(311- 300)
=1.13xl07W
Mean Temperature Difference
We first estimate the LMTD by calculating the AMTD.
AMTD = !{(376-311)+(319 - 300)}
2
=42 K
Since the ratio of the smaller terminal temperature difference to the larger is quite low,
the difference between the AMTD and the LMTD is quite low aiso. Hence, we estimate
that the LMTD value is approximately 90% of the AMTD.
LMTD =0.9 x 42 =37.8 K
Since the temperatures of the outlet streams are not equal and neither stream is
isothermal, we estimate the value of the LMTD correction factor to be approximately
between 0.8 and 1.0. We estimate this value to be 0.9, i.e.,
FT= 0.9
85
Therefore, MTD = 0.9x 37.8 = 34.0 K
Estimation of Overall Heat Transfer Coefficient, Uo ·
Gas: Uo = 400 W/m2 K (from Appendix A, Table A.2)
Rfo= 0.00035 m2 K/W
Water: ui = 7000 W/m2 K (from Appendix A, Table A.2)
Rfi = 0.00035 m2 K/W
Fin Efficiency
This value can be calculated using equation (2.7) or can be estimated. We know
that the thermal conductivity of the fin material (90-10 Cupronickel) is quite high (52
W/m K). Also, the fin height is low, i.e., it is a low finned tube. The heat transfer
coefficient on the shell side is quite low (400 W/m2 K). Hence, the fin efficiency for this
case can be assumed to be high. As explained earlier, the fin efficiency lies between 0.95
and 1.0 for not very severe operating conditions. We estimate this value to be 0.98 for
the case at hand.
We now calculate the wall resistance.
L\x = 1.-(d r -di) = 1.-(15.875-11.61)
2 2
= 2.133 mm
Am ~ 7t(di + ~x)L
~ 7t(11.61+2.133)
~ 43.2 (mm2 / mm length)
86
Hence,
Lix A 2.133 (mm) 0.151 (m2 / m)
R 11 - w 0 =
wa - kwAm 52 (W / m K) 43.2 (mm2 / mm)
= 1.43 x 10-4 m2 K/ W
We now estimate the value ofUo using equation (2.15)
1
Uo = ------------------------
0.151 +0.00035 0.151 + 1.43 x 10-4 + 0.00035 + 1
7000(0.0365) 0.0365 0.98 400(0.98)
~200 W/m2 K
Calculation of the Required Area
7
A = 1.14 x 10 = 1690 m2
o 200(33.7)
This is the actual area required in the exchanger. However, in order to use figure
(2.11), it is necessary to use equation (2.29) and the associated tables to find the ,
equivalent area, Ao .
Calculation of the Equivalent Area
From Table 3.1, for 19.05 mm. OD tubes on 25.4 mm. square pitch,
Fl = 1.307
From Table 3.2, for 2 tube-side passes and assuming a shell diameter of about 1 m.,
F2 =1.018
87
From Table 3.3, for split backing ring type of exchanger, and a shell diameter of about 1
m.,
F3 = 1.06
From Table 3.4, for 748 fins/m (19 fins/in.), 19.05 nun. OD tubes,
Ff= 0.392
Therefore,
,
A = 1690 x 1.307 x 1.018 x 1.06 x 0.392
o
= 920 m2
From figure (2.11), for A~ == 920 m2,
the following combinations ofL vs. Di are obtained:
L m. n·I m. LlDj
5.0 1.372 3.6
6.5 1.219 5.3
7.9 1.143 6.6
9.2 1.067 8.6
9.8 0.991 9.9
As seen in the above table, the first two L-Di combinations need not be
considered to avoid operational problems. A good choice appears to be 1.067 m. inside
diameter shell and 9.2 m. effective tube length. Although the L/Di ratio is on the higher
88
side, detailed analysis may prove to give results within all prescribed limits. These may
include space constraints, pressure drop limitations, vibration limitations.
Calculation of the Area Provided
We now check whether the chosen configuration will provide the required heat
transfer area.
From Appendix E, for split-ring floating head exchanger, 1.067 m. shell inside
diameter and two tube-side passes:
Hence, the heat transfer area provided is:
Ao = 0.151 (m2 I m) x 9.2 (m) x 1223
= 1700 m2
Thus, the area provided by the chosen configuration is greater than that required and the
design is satisfactory in this respect.
Tube-side Velocity
Number of tubes per pass = 612
Internal flow area of one tube
Internal flow area of one pass
1t x (0.1161)2 = 1.059 x 10-4 m2
4
612 x 1.059 x 10-4 = 0.065 m2
Hence, velocity in tubes = 246.64 (kg/s) =3.81 m/s
997 (kg 1m3) x 0.065 (m2 )
The calculated velocity of water in the tubes seems to be a little on the higher side for
Cupronickel tubes.
89
We provide single segmental baffles for this configuration.
Two pairs of sealing strips would probably be adequate.
Provide a 25% baffle cut.
Minimum baffle spacing as per TEMA = 0.2 (1.067) = 0.215 m. = 8.5 inches
We provide a central baffle spacing of 0.375 m.
90
APPENDIXC
CHARACTERISTICS OF TUBING
(TEMA, 1988)
Tube
I
Inr.cm&1
Sq. Ft. Sq.Ft. wci&ht
External Inu:ma1 Pc'Ft. Tube Moment Sc:cticn lUdiUl eX Tnnavent:
0.0. B.W.O. I~wa. Area SwiaC8 Surfacc Lcnath I.D. oC lncni.a ModulUi Gynrim Consunr. ~ Me1&lAza
Inches Glle lnc:i1~ Sq. Inch Per Foot PcrFoot Su:d Inches lIIch~ Inches' Inches C·· 1.0. Sq.1ncb
Lcnlth LeniUs Lbc..
"4 I 22 0.028 0.0296 0.0654 0.0508 0.066 0.1;,& 0.(XX)12 0.0Cl098 O.ONl A6 1.280 0.0105
24 0.022 0.0333 O.~ 0.()53g O.~ 0.2C6 0.00010 0.0008:1 0.0810 52 1.214 0.0158
26 0.018 0.0:360 O.oeM 0.0560 0.045 0.214 O.OOCX)O 0.00071 0.082:3 56 1.168 0.0131
27 0.018 0.037'3 0.0650' 0.0571 0.00&0 0'::18 0.CXXX)8 0.(XX)65 0.C829 5& 1.147 0.0118
W 18
I
0.040 O.oeo3 0.0982 0.0725 0.171 ozn 0.00068 0.CC38 0.1168
I
~
I
1.354 0.0502
20 0.035 0.0731 0.0982 O.ONl 0.127 0.3)5 0.00055 0.0029 0.1208 114 1.230 0.0374
22 0.028 0.07;0 0.CN82 0.08:35 0.104 0.310 0.CXX)48 0.0025 0.12:31 125 1.118 0.0305
24 0.022 0.0860 0.CN82 0.0887 0.083 0.331 0.0CXX38 0.0020 0.1250 134 1.1~ 0.02~
112 18 0.065 0.1075 0.1309 0.096SJ CU22 0.370 0.0021 0.0088 0.1555 168 1.351 0.0888
18 0.G49 0.1269 0.1309 0.1052 0.2:)6 0.402 0.CCn8 0.0071 0.1604 198 1.2404 0.0694
20 0.~5 0.1452 0.13OG 0.1128 0.174 0.4:)0 0.0014 0.0056 0.1&49 227 1.163 0.0511
22 0.029 0.154a 0.13OG 0.1162 0.141 O.~ 0.0012 0.(X)46 0.16n 241 1.126 0.0415
&8 12 0.109 0.1~1 0.1638 0.1066 0.601 0.<C07 0.0081 0.0197 0.1865 203 1.5.36 O.ln
13 0.095 0.1AS8 0.1638 0.11:Jg Q.538 0.435 0.0057 0.0183 0.19()& 232 1.-'37 0.158
14 0.083 0.1855 0.1838 0.1202 0.481 0.459 0.0053 0.0170 0.193i 258 1~ 0.141
15 o.on 0.1817 0.1638 0.1259 0.426 O.tSl 0.0049 0.0156 0.1m 283 1.299 0.125
16 0.065 0.1924 0.1638 0.1296 0.389 0.495 0.0045 0.0145 0.1gg:) ~ 1.263 0.114
17 0.058 0.2035 0.18:)6 0.1333 0.352 0.509 0.0042 0.0134 0.2015 317 1.228 0.103
18 0.G49 0.2181 0.16:l6 0.1380 O.:m 0.527 0.0037 0.0119 0.2G&4 ~ 1.188 0.OS9
19 O.~ 0.2299 0.1838 0.1.,8 0.262 0.541 O.oem 0.0105 0.2067 358 1.155 o.on
20 0.035 0..2419 0.1638 ·0.1~ 0..221 0.555 0.cXl28 O.OOQl 0.2OQO 3n 1.128 0.065
3/4 10 0.134 0.1825 0.1983 0.1262 0.833 0.482 0.0129 0.0344 0.2229 285 1.556 0.259
11 0.120 0.2043 0.1963 0.1335 0.8C8 0.510 0.0122 0.032e 0.2267 3Ua 1.471 0.Z38
12 O.log 0.2223 0.1Q83 0.1393 0.747 0.532 0.0118 0.Q'Xl9 0.2299 347 1.410 0.219
1:1 0.095 0.2"63 0.1983 0.1468 0.665 O.sea 0.0107 0.0285 0.2340 384 1.339 0.195
14 0.083 0.2619 0.1963 0.1529 0.592 f).5&4 0.00SJ8 0.0262 02371 418 1.264 0.114
15