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    Thermal design of shell-and-tube

    heat exchangers (STHEs) isdone by sophisticated computersoftware. However, a good un-

    derstanding of the underlying principlesof exchanger design is needed to use thissoftware effectively.

    This article explains the basics of ex-changer thermal design, covering suchtopics as: STHE components; classifica-tion of STHEs according to constructionand according to service; data needed forthermal design; tubeside design; shellsidedesign, including tube layout, baffling,and shellside pressure drop; and mean

    temperature difference. The basic equa-tions for tubeside and shellside heattransfer and pressure drop are well-known; here we focus on the applicationof these correlations for the optimum de-sign of heat exchangers. A followup arti-cle on advanced topics in shell-and-tubeheat exchanger design, such as allocationof shellside and tubeside fluids, use ofmultiple shells, overdesign, and fouling,is scheduled to appear in the next issue.

    Components of STHEsIt is essential for the designer to have a

    good working knowledge of the mechani-cal features of STHEs and how they in-fluence thermal design. The principalcomponents of an STHE are:

    shell; shell cover; tubes; channel; channel cover; tubesheet;

    baffles; and

    nozzles.Other components include tie-rods andspacers, pass partition plates, impinge-ment plate, longitudinal baffle, sealingstrips, supports, and foundation.

    The Standards of the Tubular Ex-changer Manufacturers Association(TEMA) (1) describe these various com-ponents in detail.

    An STHE is divided into three parts:the front head, the shell, and the rearhead. Figure 1 illustrates the TEMAnomenclature for the various constructionpossibilities. Exchangers are described by

    the letter codes for the three sections for example, a BFL exchanger has a bon-net cover, a two-pass shell with a longitu-dinal baffle, and a fixed-tubesheet rearhead.

    Classificationbased on construction

    Fixed tubesheet. A fixed-tubesheetheat exchanger (Figure 2) has straighttubes that are secured at both ends totubesheets welded to the shell. The con-struction may have removable channelcovers (e.g., AEL), bonnet-type channelcovers (e.g., BEM), or integral tubesheets(e.g., NEN).

    The principal advantage of the fixed-tubesheet construction is its low cost be-cause of its simple construction. In fact,the fixed tubesheet is the least expensiveconstruction type, as long as no expan-sion joint is required.

    Other advantages are that the tubes canbe cleaned mechanically after removal of

    SHELL-AND-TUBE HEAT EXCHANGERS

    CHEMICAL ENGINEERING PROGRESS FEBRUARY 1998 Copyright 1997 American Institute of Chemical Engineers. All rights reserved. Copying and downloading permitted withrestrictions.

    Effectively DesignShell-and-TubeHeat Exchangers

    Rajiv Mukherjee,

    Engineers India Ltd.

    To make the mostof exchanger

    design software,

    one needs to

    understand STHE

    classification,

    exchanger

    components, tube

    layout, baffling,

    pressure drop, and

    mean temperature

    difference.

    http://www.aiche.org/docs/publication/permiss.htmhttp://www.aiche.org/docs/publication/permiss.htmhttp://www.aiche.org/docs/publication/permiss.htmhttp://www.aiche.org/docs/publication/permiss.htm
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    CHEMICAL ENGINEERING PROGRESS FEBRUARY 1998

    SHELL-AND-TUBE HEAT EXCHANGERS

    s Figure 1. TEMA designations for shell-and-tube heat exchangers.

    E

    F

    G

    H

    J

    K

    X

    One-Pass Shell

    Two-Pass Shellwith Longitudinal Baffle

    Split Flow

    Double Split Flow

    Divided Flow

    Cross Flow

    Kettle-Type Reboiler

    A

    B

    Removable Channel and Cover

    C

    N

    Bonnet (Integral Cover)

    Integral With TubesheetRemovable Cover

    D

    Special High-Pressure Closures

    T

    U

    W

    U-Tube Bundle

    Pull-Through Floating Head

    Floating Head with Backing Device

    S

    P

    N

    Outside Packed Floating Head

    Fixed Tube SheetLike "C" Stationary Head

    Fixed Tube SheetLike "B" Stationary Head

    Externally SealedFloating Tubesheet

    Fixed Tube SheetLike "A" Stationary Head

    Stationary Head Types Shell Types Rear Head Types

    M

    L

    Channel Integral With Tubesheetand Removable Cover

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    the channel cover or bonnet, and thatleakage of the shellside fluid is mini-mized since there are no flanged joints.

    A disadvantage of this design is

    that since the bundle is fixed to theshell and cannot be removed, the out-sides of the tubes cannot be cleanedmechanically. Thus, its application islimited to clean services on the shell-side. However, if a satisfactory chem-ical cleaning program can be em-ployed, fixed-tubesheet constructionmay be selected for fouling serviceson the shellside.

    In the event of a large differentialtemperature between the tubes andthe shell, the tubesheets will be un-

    able to absorb the differential stress,thereby making it necessary to incor-porate an expansion joint. This takesaway the advantage of low cost to asignificant extent.

    U-tube. As the name implies, thetubes of a U-tube heat exchanger(Figure 3) are bent in the shape of aU. There is only one tubesheet in a U-tube heat exchanger. However, thelower cost for the single tubesheet isoffset by the additional costs incurredfor the bending of the tubes and thesomewhat larger shell diameter (due

    to the minimum U-bend radius), mak-ing the cost of a U-tube heat ex-changer comparable to that of a fixed-tubesheet exchanger.

    The advantage of a U-tube heatexchanger is that because one end isfree, the bundle can expand or con-tract in response to stress differen-tials. In addition, the outsides of thetubes can be cleaned, as the tube bun-dle can be removed.

    The disadvantage of the U-tubeconstruction is that the insides of thetubes cannot be cleaned effectively,since the U-bends would require flex-ible-end drill shafts for cleaning.Thus, U-tube heat exchangers shouldnot be used for services with a dirtyfluid inside tubes.

    Floating head. The floating-headheat exchanger is the most versatiletype of STHE, and also the costliest.In this design, one tubesheet is fixedrelative to the shell, and the other is

    free to float within the shell. Thispermits free expansion of the tubebundle, as well as cleaning of boththe insides and outsides of the tubes.

    Thus, floating-head SHTEs can beused for services where both theshellside and the tubeside fluids aredirty making this the standard con-struction type used in dirty services,such as in petroleum refineries.

    There are various types of float-ing-head construction. The two mostcommon are the pull-through withbacking device (TEMA S) and pull-through (TEMA T) designs.

    The TEMA S design (Figure 4) isthe most common configuration in

    the chemical process industries (CPI).The floating-head cover is securedagainst the floating tubesheet by bolt-ing it to an ingenious split backingring. This floating-head closure is lo-cated beyond the end of the shell andcontained by a shell cover of a largerdiameter. To dismantle the heat ex-

    changer, the shell cover is removedfirst, then the split backing ring, andthen the floating-head cover, afterwhich the tube bundle can be re-

    moved from the stationary end.In the TEMA T construction (Fig-

    ure 5), the entire tube bundle, includ-ing the floating-head assembly, canbe removed from the stationary end,since the shell diameter is larger thanthe floating-head flange. The floating-head cover is bolted directly to thefloating tubesheet so that a split back-ing ring is not required.

    The advantage of this constructionis that the tube bundle may be re-moved from the shell without remov-

    ing either the shell or the floating-head cover, thus reducing mainte-nance time. This design is particular-ly suited to kettle reboilers having adirty heating medium where U-tubescannot be employed. Due to the en-larged shell, this construction has thehighest cost of all exchanger types.

    FEBRUARY 1998 CHEMICAL ENGINEERING PROGRESS

    SupportBracket

    StationaryTubesheet

    StationaryTubesheet

    Bonnet(Stationary

    Head)

    Bonnet(Stationary

    Head)

    Baffles Tie Rodsand Spacers

    s Figure 2. Fixed-tubesheet heat exchanger.

    Tubeplate Shell Tubes BafflesHeader

    s Figure 3. U-tube heat exchanger.

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    There are also two types of packedfloating-head construction outside-packed stuffing-box (TEMA P) andoutside-packed lantern ring (TEMA

    W) (see Figure 1). However, sincethey are prone to leakage, their use islimited to services with shellside flu-ids that are nonhazardous and non-toxic and that have moderate pres-sures and temperatures (40 kg/cm2

    and 300C).

    Classificationbased on service

    Basically, a service may be single-phase (such as the cooling or heatingof a liquid or gas) or two-phase (such

    as condensing or vaporizing). Sincethere are two sides to an STHE, thiscan lead to several combinations ofservices.

    Broadly, services can be classifiedas follows:

    single-phase (both shellside andtubeside);

    condensing (one side condens-ing and the other single-phase);

    vaporizing (one side vaporizingand the other side single-phase); and

    condensing/vaporizing (one sidecondensing and the other side

    vaporizing).The following nomenclature is

    usually used:Heat exchanger: both sides single-

    phase and process streams (that is,not a utility).

    Cooler: one stream a process fluidand the other cooling water or air.

    Heater: one stream a process fluidand the other a hot utility, such assteam or hot oil.

    Condenser: one stream a condens-ing vapor and the other cooling wateror air.

    Chiller: one stream a processfluid being condensed at sub-atmo-spheric temperatures and the other aboiling refrigerant or process stream.

    Reboiler: one stream a bottomsstream from a distillation column andthe other a hot utility (steam or hotoil) or a process stream.

    This article will focus specificallyon single-phase applications.

    Design data

    Before discussing actual thermaldesign, let us look at the data thatmust be furnished by the process li-

    censor before design can begin:1. flow rates of both streams.2. inlet and outlet temperatures of

    both streams.3. operating pressure of both

    streams. This is required for gases,especially if the gas density is notfurnished; it is not really necessaryfor liquids, as their properties do notvary with pressure.

    4. allowable pressure drop forboth streams. This is a very importantparameter for heat exchanger design.

    Generally, for liquids, a value of0.50.7 kg/cm2 is permitted per shell.A higher pressure drop is usually war-ranted for viscous liquids, especiallyin the tubeside. For gases, the allowedvalue is generally 0.050.2 kg/cm2,with 0.1 kg/cm2 being typical.

    5. fouling resistance for bothstreams. If this is not furnished, thedesigner should adopt values speci-fied in the TEMA standards or basedon past experience.

    6. physical properties of bothstreams. These include viscosity,

    thermal conductivity, density, andspecific heat, preferably at both inletand outlet temperatures. Viscositydata must be supplied at inlet andoutlet temperatures, especially forliquids, since the variation with tem-perature may be considerable and isirregular (neither linear nor log-log).

    7. heat duty. The duty specifiedshould be consistent for both theshellside and the tubeside.

    8. type of heat exchanger. If notfurnished, the designer can choosethis based upon the characteristics ofthe various types of construction de-scribed earlier. In fact, the designer isnormally in a better position than theprocess engineer to do this.

    9. line sizes. It is desirable tomatch nozzle sizes with line sizes toavoid expanders or reducers. Howev-er, sizing criteria for nozzles are usu-ally more stringent than for lines, es-pecially for the shellside inlet. Conse-

    quently, nozzle sizes must sometimesbe one size (or even more in excep-tional circumstances) larger than thecorresponding line sizes, especially

    for small lines.10. preferred tube size. Tube size

    is designated as O.D. thickness length. Some plant owners have apreferred O.D. thickness (usuallybased upon inventory considerations),and the available plot area will deter-mine the maximum tube length.Many plant owners prefer to stan-dardize all three dimensions, againbased upon inventory considerations.

    11. maximum shell diameter. Thisis based upon tube-bundle removal re-

    quirements and is limited by crane ca-pacities. Such limitations apply only toexchangers with removable tube bun-dles, namely U-tube and floating-head.For fixed-tubesheet exchangers, theonly limitation is the manufacturersfabrication capability and the avail-ability of components such as dishedends and flanges. Thus, floating-headheat exchangers are often limited to ashell I.D. of 1.41.5 m and a tubelength of 6 m or 9 m, whereas fixed-tubesheet heat exchangers can haveshells as large as 3 m and tubes

    lengths up to 12 m or more.12. materials of construction. If

    the tubes and shell are made of iden-tical materials, all components shouldbe of this material. Thus, only theshell and tube materials of construc-tion need to be specified. However, ifthe shell and tubes are of differentmetallurgy, the materials of all princi-pal components should be specifiedto avoid any ambiguity. The principalcomponents are shell (and shellcover), tubes, channel (and channelcover), tubesheets, and baffles.Tubesheets may be lined or clad.

    13. special considerations. Theseinclude cycling, upset conditions, al-ternative operating scenarios, andwhether operation is continuous orintermittent.

    Tubeside design

    Tubeside calculations are quitestraightforward, since tubeside flow

    CHEMICAL ENGINEERING PROGRESS FEBRUARY 1998

    SHELL-AND-TUBE HEAT EXCHANGERS

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    represents a simple case of flowthrough a circular conduit. Heat-trans-fer coefficient and pressure drop bothvary with tubeside velocity, the latter

    more strongly so. A good design willmake the best use of the allowablepressure drop, as this will yield thehighest heat-transfer coefficient.

    If all the tubeside fluid were toflow through all the tubes (one tubepass), it would lead to a certain veloc-ity. Usually, this velocity is unaccept-ably low and therefore has to be in-creased. By incorporating pass parti-tion plates (with appropriate gasket-ing) in the channels, the tubeside fluidis made to flow several times through

    a fraction of the total number of tubes.Thus, in a heat exchanger with 200tubes and two passes, the fluid flowsthrough 100 tubes at a time, and thevelocity will be twice what it wouldbe if there were only one pass. Thenumber of tube passes is usually one,two, four, six, eight, and so on.

    Heat-transfer coefficient

    The tubeside heat-transfer coeffi-cient is a function of the Reynoldsnumber, the Prandtl number, andthe tube diameter. These can be bro-

    ken down into the following funda-mental parameters: physicalpr op er ti es (namely viscosity, ther-mal conductivity, and specific heat);tube diameter; and, very important-ly, mass velocity.

    The variation in liquid viscosity isquite considerable; so, this physicalproperty has the most dramatic effecton heat-transfer coefficient.

    The fundamental equation for tur-bulent heat-transfer inside tubes is:

    Nu = 0.027 (Re)0.8 (Pr)0.33 (1a)

    or

    (hD/k) =0.027 (DG/)0.8 (c/k)0.33 (1b)

    Rearranging:

    h = 0.027(DG/)0.8(c/k)0.33(k/D) (1c)

    Viscosity influences the heat-trans-fer coefficient in two opposing ways as a parameter of the Reynoldsnumber, and as a parameter of Prandtl

    number. Thus, from Eq. 1c:

    h ()0.330.8 (2a)

    h ()0.47 (2b)

    In other words, the heat-transfercoefficient is inversely proportionalto viscosity to the 0.47 power. Simi-larly, the heat-transfer coefficient isdirectly proportional to thermal con-ductivity to the 0.67 power.

    These two facts lead to some inter-

    esting generalities about heat transfer.A high thermal conductivity promotesa high heat-transfer coefficient. Thus,

    cooling water (thermal conductivityof around 0.55 kcal/hmC) has anextremely high heat-transfer coeffi-cient of typically 6,000 kcal/hm2C,

    followed by hydrocarbon liquids(thermal conductivity between 0.08and 0.12 kcal/hmC) at 2501,300kcal/hm2C, and then hydrocarbongases (thermal conductivity between0.02 and 0.03 kcal/hmC) at50500 kcal/hm2C.

    Hydrogen is an unusual gas, be-cause it has an exceptionally highthermal conductivity (greater thanthat of hydrocarbon liquids). Thus,its heat-transfer coefficient is to-ward the upper limit of the range

    for hydrocarbon liquids.The range of heat-transfer coeffi-cients for hydrocarbon liquids is

    FEBRUARY 1998 CHEMICAL ENGINEERING PROGRESS

    Stationary-HeadChannel

    StationaryTubesheet Shell

    SupportSaddles

    FloatingTubesheet

    Floating-HeadCover

    ShellCover

    Tie Rodsand Spacers

    PassPartition

    Baffles

    s Figure 4. Pull-through floating-head exchanger with backing device (TEMA S).

    ShellWeir

    SupportSaddleBaffles

    SupportSaddle

    FloatingTubesheet

    Floating-HeadCover

    ShellCoverStationary-Head

    Channel

    Tie Rodsand Spacers

    PassPartition

    s Figure 5. Pull-through floating-head exchanger (TEMA T).

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    rather large due to the large variationin their viscosity, from less than 0.1cP for ethylene and propylene to morethan 1,000 cP or more for bitumen.

    The large variation in the heat-transfercoefficients of hydrocarbon gases isattributable to the large variation inoperating pressure. As operating pres-sure rises, gas density increases. Pres-sure drop is directly proportional tothe square of mass velocity and in-versely proportional to density. There-fore, for the same pressure drop, ahigher mass velocity can be main-tained when the density is higher. Thislarger mass velocity translates into ahigher heat-transfer coefficient.

    Pressure drop

    Mass velocity strongly influencesthe heat-transfer coefficient. For tur-bulent flow, the tubeside heat-transfercoefficient varies to the 0.8 power oftubeside mass velocity, whereas tube-side pressure drop varies to the squareof mass velocity. Thus, with increas-ing mass velocity, pressure drop in-creases more rapidly than does theheat-transfer coefficient. Consequent-ly, there will be an optimum mass ve-locity above which it will be wasteful

    to increase mass velocity further.Furthermore, very high velocities

    lead to erosion. However, the pres-sure drop limitation usually becomescontrolling long before erosive veloc-ities are attained. The minimum rec-ommended liquid velocity insidetubes is 1.0 m/s, while the maximumis 2.53.0 m/s.

    Pressure drop is proportional tothe square of velocity and the totallength of travel. Thus, when the num-ber of tube passes is increased for agiven number of tubes and a giventubeside flow rate, the pressure droprises to the cube of this increase. Inactual practice, the rise is somewhatless because of lower friction factorsat higher Reynolds numbers, so theexponent should be approximately2.8 instead of 3.

    Tubeside pressure drop rises steeplywith an increase in the number of tubepasses. Consequently, it often happens

    that for a given number of tubes andtwo passes, the pressure drop is muchlower than the allowable value, butwith four passes it exceeds the allow-able pressure drop. If in such circum-stances a standard tube has to be em-ployed, the designer may be forced toaccept a rather low velocity. However,if the tube diameter and length may bevaried, the allowable pressure drop canbe better utilized and a higher tubesidevelocity realized.

    The following tube diameters areusually used in the CPI: w, , e, ,1, 1, and 1 in. Of these, in. and1 in. are the most popular. Tubessmaller than in. O.D. should not beused for fouling services. The use ofsmall-diameter tubes, such as in.,is warranted only for small heat ex-changers with heat-transfer areas lessthan 2030 m2.

    It is important to realize that thetotal pressure drop for a given streammust be met. The distribution of pres-sure drop in the various heat exchang-ers for a given stream in a particularcircuit may be varied to obtain goodheat transfer in all the heat exchang-ers. Consider a hot liquid stream flow-ing through several preheat exchang-ers. Normally, a pressure drop of 0.7kg/cm2 per shell is permitted for liq-uid streams. If there are five such pre-heat exchangers, a total pressure dropof 3.5 kg/cm2 for the circuit would be

    permitted. If the pressure dropthrough two of these exchangers turnsout to be only 0.8 kg/cm2, the balanceof 2.7 kg/cm2 would be available forthe other three.

    Example 1:Optimizing tubeside design

    Consider the heat exchanger ser-vice specified in Table 1. A TEMAType AES exchanger (split-ring pull-through floating-head construction)

    was to be employed. Tubes were tobe either 25 mm O.D. (preferred) or20 mm O.D., 2 mm thick, and 9 mlong (but could be shorter).

    A first design was produced using25-mm-O.D. 9-m tubes (Case A inTable 2). The tubeside pressure dropwas only 0.17 kg/cm2 even though0.7 kg/cm2 was permitted. Further,the tubeside heat-transfer resistancewas 27.71% of the total, which meantthat if the allowable pressure dropwere better utilized, the heat-transferarea would decrease. However, whenthe number of tube passes was in-creased from two to four (keeping theshell diameter the same and decreas-ing the number of tubes from 500 to480 due to the extra pass-partitionlanes), the tubeside pressure drop in-creased to 1.06 kg/cm2, which wasunacceptable. (The shellside designwas satisfactory, with the allowablepressure drop quite well utilized.)

    CHEMICAL ENGINEERING PROGRESS FEBRUARY 1998

    SHELL-AND-TUBE HEAT EXCHANGERS

    Shellside Tubeside

    Fluid Crude oil Heavy gas oil circulating reflux

    Flow rate, kg/h 399,831 277,200

    Temperature in/out, C 227 / 249 302 / 275

    Operating pressure, kg/cm2 (abs.) 28.3 13.0

    Allowable pressure drop, kg/cm2 1.2 0.7

    Fouling resistance, hm2C/kcal 0.0007 0.0006

    Heat duty, MM kcal/h 5.4945 5.4945

    Viscosity in/out, cP 0.664 / 0.563 0.32 / 0.389

    Design pressure, kg/cm2(gage) 44.0 17.0

    Line size, mm (nominal) 300 300

    Material of construction Carbon steel Tubes: Type 410 stainless steelOther: 5CrMo

    Table 1. Heat exchanger service for Example 1.

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    Since the overdesign in the four-pass configuration was 28.1%, an at-tempt was made to reduce the tube-side pressure drop by decreasing thetube length. When the tube lengthwas reduced to 7.5 m, the overdesignwas 5.72%, but the tubeside pressuredrop was 0.91 kg/cm2, which was

    stil l higher than that permitted.Next, a design with 20-mm-O.D.

    tubes was attempted (Case B in Table2). The shell diameter and heat-trans-fer surface decreased considerably,from 925 mm to 780 mm, and from343 m2 to 300 m2, respectively. Thetubeside velocity (2.17 m/s vs. 1.36

    m/s earlier), pressure drop (0.51kg/cm2 vs. 0.17 kg/cm2), and heat-transfer coefficient (1,976 vs. 1,285kcal/hm2C) were all much higher.

    The overall heat-transfer coefficientfor this design was 398 kcal/hm2Cvs. 356 for Case A.

    Stepwise calculationsfor viscous liquids

    When the variation in tubeside vis-cosity is pronounced, a single-pointcalculation for the tubeside heat-transfer coefficient and pressure dropwill give unrealistic results. This isparticularly true in cases where acombination of turbulent (or transi-

    tion) flow and laminar flow exist,since the thermal performance is verydifferent in these two regimes.

    In such cases, it will be necessaryto perform the calculations stepwiseor zone-wise. The number of steps orzones will be determined by the vari-ation in the tubeside viscosity andthus the Reynolds number.

    Example 2:Stepwise calculations

    The principal process parametersfor a kettle-type steam generator in a

    refinery are shown in Table 3. Theviscosity of the heavy vacuum gas oilvaries from 1.6 cP at the inlet to 6.36cP at the outlet.

    A design was produced withoutperforming the calculations stepwise that is, on the basis of a single av-erage temperature and correspondingphysical properties. Details of this de-sign are shown in Table 4.

    Performing the tubeside calcula-tions stepwise, in ten equal heat dutysteps, revealed that the original ex-changer was undersurfaced. The rele-vant performance parameters for thesingle-point and stepwise calculationsare compared in Table 5.

    The main reason for the differencewas the variation in Reynolds num-ber, from 9,813 in the first zone to2,851 in the last zone. In addition,the mean temperature difference(MTD) decreased drastically, from138.47C in the first zone to a mere

    FEBRUARY 1998 CHEMICAL ENGINEERING PROGRESS

    Case A Case B

    Shell I.D., mm 925 780Tube O.D. Number of tubes 25 500 2 20 540 2

    Number of tube passes

    Heat-transfer area, m2 343 300

    Tube pitchTube layout angle 32 90 26 90

    Baffle type Single-segmental Single-segmental

    Baffle spacing, mm 450 400

    Baffle cut, percent of diameter 25 30

    Velocity, m/s

    Shellside 1.15 1.52

    Tubeside 1.36 2.17

    Heat-transfer coefficient, kcal/hm2C

    Shellside 2,065 2,511Tubeside 1,285 1,976

    Pressure drop, kg/cm2

    Shellside 0.86 1.2

    Tubeside 0.17 0.51

    Resistance, %

    Shellside film 17.24 15.84

    Tubeside film 27.71 21.14

    Fouling 50.35 57.66

    Metal wall 4.69 4.87

    Overdesign 8.29 4.87

    Table 2. Details of two designs for Example 1.

    Shellside Tubeside

    Fluid Boiler feedwater, Steam Heavy vacuum gas oil

    Flow rate, kg/h 23,100 (fully vaporized) 129,085

    Temperature in/out, C 154 / 154 299 / 165

    Allowable pressure drop, kg/cm2 Negligible 1.4

    Fouling resistance, hm2C/kcal 0.0002 0.0006

    Viscosity in/out, cP 0.176 / 0.176 1.6 / 6.36

    Design pressure, kg/cm2(gage) 6.5 21.3

    Heat duty, kcal/h 11,242,000 11,242,000

    Table 3. Process parameters for Example 2.

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    17.04C in the last. Thus, while theinitial zones (the hot end) had both ahigh heat-transfer coefficient and ahigh MTD, these decreased progres-

    sively toward the outlet (cold) end ofthe exchanger. Consequently, whilethe first zone required a length ofonly 2.325 m, the last zone requireda length of 44.967 m, even thoughthe heat duties were the same. Thetubeside pressure drop was onlymarginally higher by the stepwisemethod, because the tubeside is en-tirely in the transition regime (Re be-tween 2,851 and 9,813).

    Shellside design

    The shellside calculations are farmore complex than those for thetubeside. This is mainly because onthe shellside there is not just one flowstream but one principal cross-flowstream and four leakage or bypassstreams. There are various shellsideflow arrangements, as well as varioustube layout patterns and baffling de-signs, which together determine theshellside stream analysis.

    Shell configuration

    TEMA defines various shell pat-

    terns based on the flow of the shell-side fluid through the shell: E, F, G,H, J, K, and X (see Figure 1).

    In a TEMA E single-pass shell, theshellside fluid enters the shell at oneend and leaves from the other end.This is the most common shell type more heat exchangers are built tothis configuration than all other con-figurations combined.

    A TEMA F two-pass shell has alongitudinal baffle that divides theshell into two passes. The shellsidefluid enters at one end, traverses theentire length of the exchangerthrough one-half the shell cross-sec-tional area, turns around and flowsthrough the second pass, then finallyleaves at the end of the second pass.The longitudinal baffle stops wellshort of the tubesheet, so that thefluid can flow into the second pass.

    The F shell is used for tempera-ture-cross situations that is, where

    the cold stream leaves at a tempera-ture higher than the outlet tempera-

    ture of the hot stream. If a two-pass(F) shell has only two tube passes,this becomes a true countercurrent ar-rangement where a large temperaturecross can be achieved.

    A TEMA J shell is a divided-flowshell wherein the shellside fluid en-ters the shell at the center and dividesinto two halves, one flowing to theleft and the other to the right andleaving separately. They are thencombined into a single stream. This isidentified as a J 12 shell. Alterna-tively, the stream may be split intotwo halves that enter the shell at thetwo ends, flow toward the center, andleave as a single stream, which isidentified as a J 21 shell.

    A TEMA G shell is a split-flowshell (see Figure 1). This constructionis usually employed for horizontalthermosyphon reboilers. There is onlya central support plate and no baffles.A G shell cannot be used for heat ex-

    changers with tube lengths greaterthan 3 m, since this would exceed the

    limit on maximum unsupported tubelength specified by TEMA typical-ly 1.5 m, though it varies with tubeO.D., thickness, and material.

    When a larger tube length is need-ed, a TEMA H shell (see Figure 1) isused. An H shell is basically two Gshells placed side-by-side, so thatthere are two full support plates. Thisis described as a double-split config-uration, as the flow is split twice andrecombined twice. This construction,too, is invariably employed for hori-zontal thermosyphon reboilers. Theadvantage of G and H shells is thatthe pressure drop is drastically lessand there are no cross baffles.

    A TEMA X shell (see Figure 1) isa pure cross-flow shell where theshellside fluid enters at the top (orbottom) of the shell, flows across thetubes, and exits from the oppositeside of the shell. The flow may beintroduced through multiple nozzles

    CHEMICAL ENGINEERING PROGRESS FEBRUARY 1998

    SHELL-AND-TUBE HEAT EXCHANGERS

    Number of kettles 2 (in parallel)Kettle/port I.D., mm 1,825 / 1,225

    Tubes per kettle 790 tubesType 316 stainless steel25 mm O.D. 2 mm thick 9 m long

    Number of tube passes 12

    Tube pitch 32 mm square (90)

    Baffling Full support plates only

    Connections, mm (nominal) Shellside: inlet 75, outlet 3 200Tubeside: 150

    Heat-transfer area, m2 1,104 (2 552)

    Table 4. Design produced for Example 2without stepwise calculations.

    Single-point StepwiseCalculations Calculations

    Tubeside heat-transfer coefficient, kcal/hm2C 347.9 229.2

    Overall heat-transfer coefficient, kcal/hm2C 244.7 179.3

    Tubeside pressure drop, kg/cm2 1.28 1.35

    Overdesign, % 24.03 9.11

    Table 5. Performance parameters for Example 2 usingsingle-point and stepwise calculations.

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    located strategically along the lengthof the shell in order to achieve a bet-ter distribution. The pressure dropwill be extremely low in fact,

    there is hardly any pressure drop inthe shell, and what pressure dropthere is, is virtually all in the noz-zles. Thus, this configuration is em-ployed for cooling or condensing va-pors at low pressure, particularlyvacuum. Full support plates can belocated if needed for structural in-tegrity; they do not interfere with theshellside flow because they are par-allel to the flow direction.

    A TEMA K shell (see Figure 1) isa special cross-flow shell employed

    for kettle reboilers (thus the K). Ithas an integral vapor-disengagementspace embodied in an enlarged shell.Here, too, full support plates can beemployed as required.

    Tube layout patternsThere are four tube layout pat-

    terns, as shown in Figure 6: triangular(30), rotated triangular (60), square(90), and rotated square (45).

    A triangular (or rotated triangular)pattern will accommodate more tubesthan a square (or rotated square) pat-

    tern. Furthermore, a triangular pat-tern produces high turbulence andtherefore a high heat-transfer coeffi-cient. However, at the typical tube

    pitch of 1.25 times the tube O.D., itdoes not permit mechanical cleaningof tubes, since access lanes are notavailable. Consequently, a triangularlayout is limited to clean shellsideservices. For services that requiremechanical cleaning on the shellside,square patterns must be used. Chemi-cal cleaning does not require accesslanes, so a triangular layout may beused for dirty shellside services pro-vided chemical cleaning is suitableand effective.

    A rotated triangular pattern sel-dom offers any advantages over atriangular pattern, and its use isconsequently not very popular.

    For dirty shellside services, asquare layout is typically employed.However, since this is an in-linepattern, it produces lower turbu-lence. Thus, when the shellsideReynolds number is low (< 2,000),it is usually advantageous to em-ploy a rotated square pattern be-cause this produces much higherturbulence, which results in a high-

    er efficiency of conversion of pres-sure drop to heat transfer.

    As noted earlier, fixed-tubesheetconstruction is usually employed forclean services on the shellside, U-tube construction for clean serviceson the tubeside, and floating-headconstruction for dirty services onboth the shellside and tubeside. (Forclean services on both shellside andtubeside, either fixed-tubesheet orU-tube construction may be used, al-though U-tube is preferable since itpermits differential expansion be-tween the shell and the tubes.)Hence, a triangular tube pattern maybe used for fixed-tubesheet exchang-ers and a square (or rotated square)pattern for floating-head exchangers.For U-tube exchangers, a triangularpattern may be used provided theshellside stream is clean and asquare (or rotated square) pattern ifit is dirty.

    Tube pitch

    Tube pitch is defined as the shortestdistance between two adjacent tubes.

    For a triangular pattern, TEMA

    specifies a minimum tube pitch of1.25 times the tube O.D. Thus, a 25-mm tube pitch is usually employedfor 20-mm O.D. tubes.

    For square patterns, TEMA addi-tionally recommends a minimumcleaning lane of in. (or 6 mm) be-tween adjacent tubes. Thus, the mini-mum tube pitch for square patterns iseither 1.25 times the tube O.D. or thetube O.D. plus 6 mm, whichever islarger. For example, 20-mm tubesshould be laid on a 26-mm (20 mm +

    6 mm) square pitch, but 25-mm tubesshould be laid on a 31.25-mm (25mm 1.25) square pitch.

    Designers prefer to employ theminimum recommended tube pitch,because it leads to the smallest shelldiameter for a given number of tubes.However, in exceptional circum-stances, the tube pitch may be in-creased to a higher value, for exam-ple, to reduce shellside pressure drop.This is particularly true in the case ofa cross-flow shell.

    BafflingType of baffles. Baffles are used to

    support tubes, enable a desirable ve-locity to be maintained for the shell-side fluid, and prevent failure of tubesdue to flow-induced vibration. Thereare two types of baffles: plate and rod.Plate baffles may be single-segmental,double-segmental, or triple-segmen-tal, as shown in Figure 7.

    Baffle spacing. Baffle spacing isthe centerline-to-centerline distancebetween adjacent baffles. It is themost vital parameter in STHE design.

    The TEMA standards specify theminimum baffle spacing as one-fifthof the shell inside diameter or 2 in.,whichever is greater. Closer spacingwill result in poor bundle penetrationby the shellside fluid and difficulty inmechanically cleaning the outsides ofthe tubes. Furthermore, a low bafflespacing results in a poor stream dis-tribution as will be explained later.

    FEBRUARY 1998 CHEMICAL ENGINEERING PROGRESS

    Square(90 )

    RotatedSquare

    (45 )

    Triangular(30 )

    RotatedTriangular

    (60 )

    s Figure 6. Tube layout patterns.

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    The maximum baffle spacing isthe shell inside diameter. Higher baf-fle spacing will lead to predominantlylongitudinal flow, which is less effi-cient than cross-flow, and large un-supported tube spans, which willmake the exchanger prone to tubefailure due to flow-induced vibration.

    Optimum baffle spacing. For tur-bulent flow on the shellside (Re >1,000), the heat-transfer coefficientvaries to the 0.60.7 power of veloci-ty; however, pressure drop varies tothe 1.72.0 power. For laminar flow(Re < 100), the exponents are 0.33 forthe heat-transfer coefficient and 1.0for pressure drop. Thus, as bafflespacing is reduced, pressure drop in-creases at a much faster rate thandoes the heat-transfer coefficient.

    This means that there will be anoptimum ratio of baffle spacing toshell inside diameter that will resultin the highest efficiency of conver-sion of pressure drop to heat transfer.This optimum ratio is normally be-tween 0.3 and 0.6.

    Baffle cut. As shown in Figure 8,baffle cut is the height of the segmentthat is cut in each baffle to permit theshellside fluid to flow across the baffle.This is expressed as a percentage of

    the shell inside diameter. Althoughthis, too, is an important parameter forSTHE design, its effect is less pro-found than that of baffle spacing.

    Baffle cut can vary between 15%and 45% of the shell inside diameter.

    Both very small and very largebaffle cuts are detrimental to effi-

    cient heat transfer on the shellsidedue to large deviation from an idealsituation, as illustrated in Figure 9. Itis strongly recommended that onlybaffle cuts between 20% and 35% beemployed. Reducing baffle cutbelow 20% to increase the shellsideheat-transfer coefficient or increas-ing the baffle cut beyond 35% to de-crease the shellside pressure dropusually lead to poor designs. Otheraspects of tube bundle geometryshould be changed instead to achievethose goals. For example, double-segmental baffles or a divided-flowshell, or even a cross-flow shell,may be used to reduce the shellsidepressure drop.

    For single-phase fluids on theshellside, a horizontal baffle cut (Fig-ure 10) is recommended, because thisminimizes accumulation of depositsat the bottom of the shell and alsoprevents stratification. However, in

    the case of a two-pass shell (TEMAF), a vertical cut is preferred for easeof fabrication and bundle assembly.

    Baffling is discussed in greater de-tail in (2) and (3).

    Equalize cross-flowand window velocities

    Flow across tubes is referred to ascross-flow, whereas flow through thewindow area (that is, through the bafflecut area) is referred to as window flow.

    The window velocity and thecross-flow velocity should be as closeas possible preferably within 20%

    CHEMICAL ENGINEERING PROGRESS FEBRUARY 1998

    SHELL-AND-TUBE HEAT EXCHANGERS

    Baffle

    BaffleCut

    s Figure 8. Baffle cut.

    s Figure 7. Types of baffles.

    Double SegmentalBaffles

    Triple SegmentalBaffles

    Single SegmentalBaffles

    Rod BaffleNo-Tubes-in-Window Segmental Baffles

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    of each other. If they differ by morethan that, repeated acceleration and

    deceleration take place along thelength of the tube bundle, resulting ininefficient conversion of pressuredrop to heat transfer.

    Shellside stream analysisOn the shellside, there is not just

    one stream, but a main cross-flowstream and four leakage or bypassstreams, as illustrated in Figure 11.Tinker (4) proposed calling thesestreams the main cross-flow stream(B), a tube-to-baffle-hole leakagestream (A), a bundle bypass stream

    (C), a pass-partition bypass stream(F), and a baffle-to-shell leakagestream (E).

    While the B (main cross-flow)stream is highly effective for heat

    transfer, the other streams are not aseffective. The A stream is fairly effi-

    cient, because the shellside fluid isin contact with the tubes. Similarly,the C stream is in contact with theperipheral tubes around the bundle,and the F stream is in contact withthe tubes along the pass-partitionlanes. Consequently, these streamsalso experience heat transfer, al-though at a lower efficiency than theB stream. However, since the Estream flows along the shell wall,where there are no tubes, it encoun-ters no heat transfer at all.

    The fractions of the total flow rep-

    resented by these five streams can bedetermined for a particular set of ex-changer geometry and shellside flowconditions by any sophisticated heat-exchanger thermal design software.Essentially, the five streams are inparallel and flow along paths of vary-ing hydraulic resistances. Thus, theflow fractions will be such that the

    pressure drop of each stream is iden-tical, since all the streams begin and

    end at the inlet and outlet nozzles.Subsequently, based upon the effi-ciency of each of these streams, theoverall shellside stream efficiencyand thus the shellside heat-transfercoefficient is established.

    Since the flow fractions dependstrongly upon the path resistances,varying any of the following con-struction parameters will affectstream analysis and thereby the shell-side performance of an exchanger:

    baffle spacing and baffle cut; tube layout angle and tube

    pitch; number of lanes in the flow di-

    rection and lane width; clearance between the tube and

    the baffle hole; clearance between the shell I.D.

    and the baffle; and location of sealing strips and

    sealing rods.

    FEBRUARY 1998 CHEMICAL ENGINEERING PROGRESS

    Horizontal Cut

    Vertical Cut

    s Figure 10. Baffle cut orientation.

    BB

    BB

    F

    E

    A

    B

    EA

    C

    B

    C

    A

    CC

    s Figure 11. Shellside flow distribution.

    s Figure 9. Effect of small and large baffle cuts.

    Main Flow

    Eddies

    Baffle

    ShellDiameter

    a. Small Baffle Cut

    Eddies

    MainFlow

    b. Large Baffle Cut

    Baffle

    c. Ideal Baffle Cut and Baffle Spacing

    Baffle

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    CHEMICAL ENGINEERING PROGRESS FEBRUARY 1998

    SHELL-AND-TUBE HEAT EXCHANGERS

    Using a very low baffle spacingtends to increase the leakage and by-pass streams. This is because all fiveshellside streams are in parallel and,

    therefore, have the same pressuredrop. The leakage path dimensionsare fixed. Consequently, when bafflespacing is decreased, the resistance ofthe main cross-flow path and therebyits pressure drop increases. Since thepressure drops of all five streams mustbe equal, the leakage and bypassstreams increase until the pressuredrops of all the streams balance out.The net result is a rise in the pressuredrop without a corresponding increasein the heat-transfer coefficient.

    The shellside fluid viscosity alsoaffects stream analysis profoundly. Inaddition to influencing the shellsideheat transfer and pressure drop per-formance, the stream analysis alsoaffects the mean temperature differ-ence (MTD) of the exchanger. Thiswill be discussed in detail later. First,though, lets look at an example thatdemonstrates how to optimize baffledesign when there is no significanttemperature profile distortion.

    Example 3:

    Optimizing baffle designConsider the heat exchanger ser-

    vice specified in Table 6. Since thereare two independent variables baf-fle spacing and baffle cut we willfirst keep the baffle cut constant at25% and vary the baffle spacing(Table 7). Later, the baffle spacingwill be kept constant and the bafflecut varied (Table 8). In real practice,both parameters should be varied si-multaneously, but keeping one pa-rameter constant and varying theother will more vividly demonstratethe influence of each parameter.

    The first design developed is des-ignated Design A in Table 7. Here,the baffle cut is 25% and the bafflespacing is 300 mm. In Designs B andC, the baffle spacing was changed to350 mm and 400 mm, respectively.There is no temperature profile dis-tortion problem with these designs.

    Notice that as the baffle spacing is

    increased from 300 mm to 400 mm,the main cross-flow, bundle bypass,and pass-partition bypass streams in-crease progressively, whereas thetube-to-baffle-hole leakage and baf-fle-to-shell leakage streams decreaseprogressively. The overall heat-trans-fer efficiency of the shellside streamincreases progressively. Neverthe-

    less, since the shellside velocity andthe Reynolds number decrease, boththe shellside heat-transfer coefficientand the shellside pressure drop de-crease, but the former at a muchlower rate than the latter. Since theallowable shellside pressure drop is1.0 kg/cm2, Design A is ruled out, asits shellside pressure drop far ex-

    Shellside Tubeside

    Fluid Crude oil Heavy gas oil circulating refluxFlow rate, kg/h 367,647 105,682

    Temperature in/out, C 209 / 226 319 / 269

    Heat duty, MM kcal/h 4.0 4.0

    Density in/out, kg/m3 730 / 715 655 / 700

    Viscosity in/out, cP 0.52 / 0.46 0.27 / 0.37

    Specific heat in/out, kcal/kgC 0.63 / 0.65 0.78 / 0.73

    Thermal conductivity in/out, kcal/hmC 0.087 / 0.085 0.073 / 0.0795

    Allowable pressure drop, kg/cm2 1.0 0.7

    Fouling resistance, hm2C/kcal 0.0006 0.0006

    Design pressure, kg/cm2(gage) 36.6 14.0

    Design temperature, C 250 340

    Line size, mm (nominal) 300 150

    Material of construction Carbon steel 5CrMo

    Table 6. Process parameters for Example 3.

    Design A Design B Design C

    Baffle spacing, mm 300 350 400

    Tube-to-baffle-hole leakage (A), fraction 0.157 0.141 0.13

    Main cross-flow stream (B), fraction 0.542 0.563 0.577

    Bundle bypass stream (C), fraction 0.113 0.116 0.119

    Baffle-to-shell leakage stream (E), fraction 0.12 0.109 0.1Pass-partition bypass stream (F), fraction 0.069 0.072 0.075

    Overall shellside heat-transfer efficiency, % 71.3 73.4 74.9

    Shellside velocity, m/s

    Cross-flow 2.5 2.15 1.87

    Window flow 2.34 2.34 2.34

    Shellside pressure drop, kg/cm2 1.34 1.03 0.79

    Heat-transfer coefficient, kcal/hm2C

    Shellside 2,578 2,498 2,372

    Tubeside 1,402 1,402 1,402

    Overall 401.8 399.8 396.5

    Overdesign, % 7.58 7.08 6.21

    Table 7. Effects of varying baffle spacing for a constant 25%baffle cut for Example 3.

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    ceeds this limit. Designs B and C areboth acceptable. The overdesignvaries marginally. Thus, it would beprudent to adopt Design C, since ithas a lower pressure drop and a bet-ter stream analysis.

    Now consider the effect of varyingthe baffle cut while keeping the bafflespacing constant at 400 mm, asshown in Table 8. As the baffle cut isprogressively increased from 25% inDesign D to 36% in Design G, thefollowing changes are observed:

    the main cross-flow stream (B)fraction increases appreciably;

    the tube-to-baffle-hole (A), baf-fle-to-shell (E), and pass-partition (F)stream fractions decrease steadily;

    the bundle bypass (C) streamfraction remains steady;

    the overall heat-transfer effi-ciency of the shellside stream first de-creases and then increases; and

    as the window velocity decreas-es, the shellside heat-transfer coeffi-cient falls; the pressure drop also de-creases, but not as fast as the heat-transfer coefficient.

    These observations are reflected inthe overdesign values. Design E ap-

    pears to be the best choice, since De-sign D cannot be accepted because ofthe excessive shellside pressure drop.

    Reducing Pby modifying baffle design

    Single-pass shell and single-seg-mental baffles. The first baffle alter-native is the single-segmental bafflein a single-pass (TEMA E) shell.

    However, in many situations, theshellside pressure drop is too highwith single-segmental baffles in a sin-gle-pass shell, even after increasingthe baffle spacing and baffle cut to thehighest values recommended. Such asituation may arise when handling avery high shellside flow rate or whenthe shellside fluid is a low-pressuregas. In these cases, the next alterna-tive that should be considered is thedouble-segmental baffle (Figure 7).

    Single-pass shell and double-seg-mental baffles. By changing the baf-fling from single-segmental to double-segmental at the same spacing in anotherwise identical heat exchanger,the cross-flow velocity is reduced ap-proximately to half, because the shell-side flow is divided into two parallel

    streams. This greatly reduces thecross-flow pressure drop. However,the window velocity and therefore thewindow pressure drop cannot be re-duced appreciably (assuming that themaximum recommended baffle cut

    was already tried with single-segmen-tal baffles before switching to double-segmental baffles). Nevertheless,since cross-flow pressure drop is in-variably much greater than windowpressure drop, there is an appreciablereduction in the total pressure drop.There is also a decrease in the shell-side heat-transfer coefficient, but thisis considerably less than the reductionin the pressure drop. The use of dou-ble-segmental baffles is covered indepth in (3).

    Divided-flow shell and single-seg-mental baffles. If the allowable shell-side pressure drop cannot be satisfiedeven with double-segmental baffles ata relatively large spacing, a divided-flow shell (TEMA J) with single-seg-mental baffles (Figure 1) should be in-vestigated next. Since pressure drop isproportional to the square of the veloc-ity and to the length of travel, a divid-ed-flow shell will have approximately

    FEBRUARY 1998 CHEMICAL ENGINEERING PROGRESS

    Design D Design E Design F Design G Design H

    Baffle cut, percent of diameter 25 30 33 36 20

    Tube-to-baffle-hole leakage (A), fraction 0.13 0.106 0.093 0.08 0.159

    Main cross-flow stream (B), fraction 0.577 0.612 0.643 0.674 0.54

    Bundle bypass stream (C), fraction 0.119 0.122 0.118 0.117 0.126

    Baffle-to-shell leakage stream (E), fraction 0.1 0.091 0.085 0.078 0.114

    Pass-partition bypass stream (F), fraction 0.075 0.069 0.062 0.052 0.061

    Overall shellside heat-transfer efficiency, % 74.9 73.0 75.7 78.6 72.7

    Shellside velocity, m/s

    Cross-flow 1.87 1.87 1.87 1.87 1.87

    Window flow 2.34 1.86 1.65 1.48 3.09

    Shellside pressure drop, kg/cm2 0.79 0.69 0.65 0.6 0.98

    Heat-transfer coefficient, kcal/hm2

    CShellside 2,372 2,200 2,074 1,929 2,406

    Tubeside 1,402 1,402 1,402 1,402 1,402

    Overall 396.5 391.4 387.3 381.9 397.4

    Overdesign, % 6.21 4.86 3.76 2.33 6.43

    Table 8. Effects of varying baffle cut for a constant 400-mmbaffle spacing for Example 3.

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    one-eighth the pressure drop in an oth-erwise identical single-pass exchanger.

    The advantage of a divided-flowshell over double-segmental baffles is

    that it offers an even larger reductionin pressure drop, since not only cross-flow velocity but even window veloc-ity can be reduced. The disadvantageis the increase in cost due to the addi-tional piping required.

    Divided-flow shell and double-segmental baffles. If even a divided-flow shell with single-segmental baf-fles is unable to meet the allowableshellside pressure drop limit, it willbe necessary to adopt a combinationof a divided-flow shell and double-

    segmental baffles. With such a com-bination, a very large reduction inshellside pressure drop is possible to as low as 4% of the pressure dropin a single-pass exchanger with thesame baffle spacing and baffle cut. Insharp contrast, the heat-transfer coef-ficient will reduce to about 40%.

    No-tubes-in-window segmentalbaffles. As baffle spacing is increasedto reduce the shellside pressure drop,an exchanger becomes more prone totube failure due to flow-induced vi-bration. Exchangers with double-seg-

    mental baffles are less likely to expe-rience such problems than those withsingle-segmental baffles.

    However, a vibration problem maypersist even with double-segmentalbaffles. In such cases, a no-tubes-in-window design (Figure 7) should beadopted. Here, each tube is supportedby every baffle, so that the unsupport-ed tube span is the baffle spacing. Inexchangers with normal single-seg-mental baffles, the unsupported tubespan is twice the baffle spacing.

    Should it become necessary to usea very large baffle spacing to restrictthe shellside pressure drop to the per-mitted value, intermediate supportsmay be used to increase the naturalfrequency of the tubes, thus produc-ing a design that is safe against tubefailure due to flow-induced vibration.

    The no-tubes-in-window designrequires a larger shell diameter for agiven number of tubes. This esclates

    its cost, typically by about 10%. Thehigher cost is offset to some extent bythe higher shellside heat-transfer co-efficient, since pure cross-flow is

    more efficient than the combinationof cross-flow and window flow inconventional designs.

    Cross-flow shell. There are someservices where the pressure drop limi-tation is so severe that none of theabove shell/baffling configurations canyield a satisfactory design. A steamejector condenser operating at a pres-sure of 50 mm Hg and having an al-lowable pressure drop of 5 mm Hg isan example. Such situations require theuse of a cross-flow shell (TEMA X).

    Here, pure cross-flow takes place ata very low velocity, so there is virtuallyno pressure drop in the shell. Whateverpressure drop occurs is almost entirelyin the nozzles. Support plates will beneeded to meet TEMA requirementsand prevent any possible flow-inducedtube vibration. Since the shellside flowis parallel to these support plates, shell-side pressure drop is not increased.

    Increasing tube pitch

    For a given number of tubes, thesmaller the tube pitch, the smaller the

    shell diameter, and therefore thelower the cost. Consequently, design-ers tend to pack in as many tubes asmechanically possible.

    As noted earlier, designers gener-ally set the tube pitch at 1.25 timesthe tube O.D. For square or rotatedsquare pitch, a minimum cleaninglane of in. or 6 mm is recommend-ed by TEMA.

    As far as thermal-hydraulics areconcerned, the optimum tube-pitch-to-tube-diameter ratio for conversionof pressure drop to heat transfer istypically 1.251.35 for turbulent flowand around 1.4 for laminar flow.

    Increasing the tube pitch to re-duce pressure drop is generally notrecommended for two reasons. First,it increases the shell diameter and,thereby, the cost. Second, reducingpressure drop by modifying the baf-fle spacing, baffle cut, or shell typewill result in a cheaper design.

    However, in the case of X shells, itmay be necessary to increase the tubepitch above the TEMA minimum tomeet pressure drop limitations, sincethere are no other parameters that canbe modified.

    Mean temperature difference

    Temperature difference is the driv-ing force for heat transfer.

    When two streams flow in op-posing directions across a tube wall,there is true countercurrent flow(Figure 12). In this situation, theonly limitation is that the hotstream should at all points be hotterthan the cold stream. The outlettemperature of the cold stream maybe higher than the outlet tempera-ture of the hot stream, as shown inFigure 12.

    CHEMICAL ENGINEERING PROGRESS FEBRUARY 1998

    SHELL-AND-TUBE HEAT EXCHANGERS

    s Figure 13. Cocurrent flow.

    Temperature

    Exchanger Length

    s Figure 12. Countercurrent flow.

    Temperature

    Exchanger Length

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    Since the temperature differencevaries along the length of the heatexchanger, it has to be weighted toobtain a mean value for single-point

    determination of heat-transfer area.The logarithmic mean temperaturedifference (LMTD) represents thisweighted value.

    If the hot and cold streams flow inthe same direction, flow is cocurrent(Figure 13). The mean temperaturedifference is still represented by theLMTD. However, the LMTD forcocurrent flow is lower than that forcountercurrent flow for the same ter-minal differences. This is because al-though one terminal temperature dif-

    ference is very high, the other is fartoo low that is, the temperaturedifferences along the path of heattransfer are not balanced.

    What is even more serious withcocurrent flow is that the outlet tem-perature of the cold stream must besomewhat lower than the outlet tem-perature of the hot stream, which is aserious limitation. Consequently,countercurrent flow is always pre-ferred to cocurrent flow.

    These principles apply only to sin-gle-pass exchangers. However, as

    noted earlier, shell-and-tube heat ex-changers invariably have two or moretube passes. Since the shellside fluidflows in one direction, half the tubepasses experience countercurrentflow and the other half experiencecocurrent flow. The MTD for this sit-uation is neither the LMTD for coun-tercurrent flow nor that for cocurrentflow, but a value between the two.

    A correction factor, Ft, which de-pends on the four terminal tempera-tures and the shell style can be deter-mined from charts in the TEMA stan-dards. The LMTD for countercurrentflow is multiplied by this factor to ob-tain the corrected MTD.

    An important limitation for 1-2shells (one shell pass and two or moretube passes) is that the outlet tempera-ture of the cold stream cannot exceedthe outlet temperature of the hotstream. This is because of the presenceof one or more cocurrent passes. In re-

    ality, a very small temperature differ-ence is possible, but this represents anarea of uncertainty and the credit isvery small, so it is usually ignored.

    When there is a temperature cross(that is, the outlet temperature of thecold stream is higher than the outlettemperature of the hot stream), andpure countercurrent flow is not possi-ble, multiple shells in series must beused. This will be discussed in detailin the followup article scheduled tobe published in the next issue.

    An F shell has two passes, so if thereare two tube passes, this is a pure coun-tercurrent situation. However, if an Fshell has four or more tube passes, it is

    no longer a true countercurrent situationand, hence, the Ft correction has to beapplied. An F shell having four or moretube passes is represented as a 2-4 shell.The Ft factor for a 2-4 shell is identicalto that for two 1-2 shells in series or twoshell passes. The TEMA Ft factor chartfor three shell passes really representsthree shells in series, that for four shellpasses four shells in series, and so on.

    It is important to realize that theLMTD and Ft factor concept assumesthat there is no significant variation inthe overall heat-transfer coefficient

    along the length of the shell. Howev-

    er, there are some services where thisis not true. An example of this is thecooling of a viscous liquid as theliquid is cooled, its viscosity increas-

    es, and this results in a progressivereduction in the shellside heat-trans-fer coefficient. In this case, the sim-plistic overall MTD approach will beinaccurate, and the exchanger mustbe broken into several sections andthe calculations performed zone-wise.

    Temperature profile distortionAn important issue that has not

    been considered so far is the tempera-ture profile distortion. As noted earli-er, the leakage and bypass streams are

    less efficient for heat transfer than themain cross-flow stream.Consider a case where the shellside

    stream is the cold fluid. Since themain cross-flow stream encounters avery large fraction of the total heat-transfer surface, it has to pick up avery large part of the total heat duty.Assume that the cross-flow stream is58% of the total shellside stream, butthat it comes in contact with 80% ofthe tubes. As a result, its temperaturerises more rapidly than if the entireshellside stream were to pick up the

    entire heat duty. Therefore, its temper-

    FEBRUARY 1998 CHEMICAL ENGINEERING PROGRESS

    s Figure 14. Temperature profile distortion factor due to bypass and leakage.

    Temperature

    Tubeside

    MainCros

    s-flowSt

    ream

    CStream

    E Stream

    Shellside

    LastBaffle

    Exchanger Length

    ApparentTemp

    eratureProfile

    C =Bundle-to-Shell Bypass

    E =Baffle-to-Shell Leakage

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    ature profile will be steeper than thatof the total stream (the apparent tem-perature profile) without consideringthe various flow fractions (Figure 14).

    The temperature profiles of thebaffle-hole-to-tube leakage, shell-to-bundle leakage, and pass-partition by-pass streams will depend on their re-spective flow fractions and the frac-tional heat-transfer area encountered.However, since the shell-to-baffleleakage stream does not experienceany heat transfer, the remaining fourstreams must pick up the entire heatduty, so that these four streams to-gether will have a temperature profilesteeper than that of the apparent

    stream. Consequently, the temperaturedifference between the hot and thecold streams will be lower all alongthe length of the heat exchanger,thereby resulting in the reduction ofthe MTD. This reduction in the MTDis known as the temperature profiledistortion (or correction) factor.

    The temperature profile distortionfactor is more pronounced when theleakage and bypass streams are high,especially the shell-to-baffle leakagestream, and the ratio of shellside tem-perature difference to the temperature

    approach at the shell outlet is high.The latter is because the closer thetemperature approach at the shell out-let, the sharper the reduction in MTD. The leakage and bypass streams

    tend to be high when the shellsideviscosity is high and when the bafflespacing is very low. Thus, care has tobe exercised in the design of viscousliquid coolers such as a vacuumresidue cooler in a crude oil refinery.

    The minimum recommended tem-perature profile distortion factor is0.75. Below this, two or more shellsin series must be employed. By usingmultiple shells in series, the ratio ofshellside temperature difference tothe temperature approach at the shelloutlet is reduced. The mixing of themain cross-flow stream with the by-pass and leakage streams after eachshell reduces the penalty due to thedistortion of the temperature profileand hence increases the temperatureprofile distortion factor.

    In many situations, a temperatureprofile distortion factor is unavoid-able, such as when cooling a viscousliquid over a large temperaturerange, and there is no alternative tothe use of multiple shells in series.However, in many other situations,improper baffle spacing unnecessar-ily imposes such a penalty where itis easily avoidable. Designers nor-mally tend to pack baffles as closeas possible to get the maximumshellside heat-transfer coefficient,pressure drop permitting. In manysuch cases, the use of somewhathigher baffle spacing will reduce theshell-to-baffle leakage stream (theprincipal culprit) and hence improvethe MTD correction factor appre-ciably, thereby producing a muchbetter design.

    CHEMICAL ENGINEERING PROGRESS FEBRUARY 1998

    SHELL-AND-TUBE HEAT EXCHANGERS

    Shell I.D. 500 mm

    Tubes 188 tubes, 20 mm O.D. 2 mm thick 6 m long

    Number of tube passes 2

    Tube pitch 26 mm square (90)

    Baffling Single-segmental, 140 mm spacing, 21% cut (diameter)

    Connections 75 mm on shellside, 150 mm on tubeside

    Heat-transfer area 70 m2

    Table 10. Construction parameters for Example 4.

    Nomenclature

    c = stream specific heat, kcal/kgC

    D = tube inside diameter, m

    Ft = LMTD correction factor,

    dimensionless

    G = stream mass velocity, kg/m2h

    h = stream heat-transfer coefficient,

    kcal/hm2C

    k = stream thermal conductivity,kcal/hmC

    Nu = Nusselt number = hD/k,

    dimensionless

    Pr= Prandtl number = c/k,

    dimensionless

    Re = Reynolds number =DG/,

    dimensionless

    Greek Letter

    = stream viscosity, kg/mh

    Shellside Tubeside

    Fluid Naphtha Cooling water

    Flow rate, kg/h 9,841 65,570

    Temperature in/out, C 114 / 40 33 / 40

    Heat duty, MM kcal/h 0.46 0.46

    Specific gravity in/out 0.62 / 0.692 1.0 / 1.0

    Viscosity in/out, cP 0.254 / 0.484 0.76 / 0.66

    Average specific heat, kcal/kgC 0.632 1.0

    Thermal conductivity in/out, kcal/hmC 0.092 / 0.101 0.542 / 0.546

    Allowable pressure drop, kg/cm2 0.7 0.7

    Fouling resistance, hm2C/kcal 0.0002 0.0004

    Design pressure, kg/cm2(gage) 12.0 6.5

    Design temperature, C 150 60

    Material of construction Carbon steel Admirality brass

    Table 9. Process parameters for Example 4.

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    Example 4: Temperaturedistortion and baffle spacing

    Consider an existing naphthacooler in a refinery and petrochemi-

    cal complex. The process parametersare listed in Table 9, and the con-struction parameters in Table 10.The existing design was undersur-faced by 21%, mainly because thetemperature profile distortion factorwas 0.6, which is lower than theminimum recommended value of0.75. The existing design had a baf-fle spacing of 140 mm and a bafflecut of 21% (of the diameter). Theshell-to-baffle leakage stream frac-tion was 0.24.

    To improve the design, the bafflespacing was progressively increased.The undersurfacing decreased withincreasing baffle spacing, up to aspacing of 190 mm; thereafter, per-formance again started to deteriorate.Thus, 190 mm is the optimum bafflespacing.

    The detailed results of the vari-ous iterations are compared inTable 11. CEP

    FEBRUARY 1998 CHEMICAL ENGINEERING PROGRESS

    Existing Design Alternative No. 1 Alternative No. 2 Alternative No. 3 Alternative No. 4

    Baffle spacing, mm 140 160 175 190 210Stream analysis, fraction of stream

    Baffle-hole-to-tube leakage (A) 0.189 0.173 0.163 0.154 0.143

    Main cross-flow (B) 0.463 0.489 0.506 0.521 0.539

    Shell-to-bundle leakage (C) 0.109 0.113 0.116 0.118 0.121

    Shell-to-baffle leakage (E) 0.24 0.225 0.215 0.207 0.196

    Pass-partition bypass stream (F) 0 0 0 0 0

    Overall shellside heat-transfer 62 64.7 66.4 67.9 69.7efficiency, %

    Temperature profile distortion factor 0.6 0.692 0.735 0.766 0.794

    Shellside velocity, m/s 0.15 0.14 0.13 0.13 0.12

    Shellside heat-transfer coefficient, 614 570 562 550 512kcal/hm2C

    Shellside pressure drop, kg/cm2 0.034 0.029 0.027 0.026 0.023

    Overall heat-transfer coefficient,kcal/hm2C 380 362 359 354 338

    Mean temperature difference, C 13.73 15.9 16.87 17.58 18.22

    Overdesign, % 21.1 12.8 8.26 5.73 6.61

    Table 11. Detailed results of Example 4 iterations.

    Literature Cited

    1. Tubular Exchanger Manufacturers

    Association, Standards of the Tubular

    Exchanger Manufacturers Associa-

    tion, 7th ed., TEMA, New York

    (1988).

    2. Mukherjee, R., Dont Let Baffling

    Baffle You, Chem. Eng. Progress, 92

    (4), pp. 7279 (Apr. 1996).

    3. Mukherjee, R., Use Double-Segmen-

    tal Baffles in Shell-and-Tube Heat Ex-

    changers, Chem. Eng. Progress, 88

    (11), pp. 4752 (Nov. 1992).

    4. Tinker, T., Shellside Characteristics of

    Shell-and-tube Heat Exchangers: A

    Simplified Rating System for Commer-

    cial Heat Exchangers, Trans. ASME,

    80, pp. 3652 (1958).

    Further Reading

    Kakac, S., et al., Heat Exchangers: Ther-

    mal-Hydraulic Fundamentals and De-

    sign, Hemisphere Publishing Corp.,

    New York (1981).

    Schlunder, E.V., et al., eds., Heat Ex-

    changer Design Handbook, Hemi-

    sphere Publishing Corp., New York

    (1983).

    R. MUKHERJEEis assistant chief consultant in

    the Heat and Mass Transfer Dept. of Engineers

    India Ltd., New Delhi (011-91-11-371-6171;

    Fax: 011-91-11-371-5059l; e-mail:

    [email protected]), where he has

    been employed since 1971. He has over 26

    years of experience in the design, revamping,

    and troubleshooting of air-cooled and shell-

    and-tube heat exchangers (especially for oil

    refineries, gas processing plants, and

    petrochemical plants), and also has

    considerable experience in heat-exchanger-

    network synthesis and optimization. He has

    written several articles in technical journals

    and has presented two papers in the Industrial

    Session of the 10th International Heat Transfer

    Conference at Brighton in August 1994.

    He has served as faculty for several courses in

    heat exchanger design, energy conservation,

    and heat exchanger network optimization.

    He is an honors graduate in chemical

    engineering from J adavpur Univ., Calcutta,

    and is a member of the Indian Institute of

    Chemical Engineers and the Indian Society

    for Heat and Mass Transfer.

    Acknowledgment

    The author is grateful to the management of

    Engineers India, Ltd., for permission to publish

    this article and acknowledges the use of Heat

    Transfer Research, Inc.s software for the

    worked-out examples and their design

    methodology.