Approximate Design and Costing Methods for Heat Exchangers

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Approximate Design and Costing Methods for HeatExchangersGeoff F. Hewitt a & Simon J. Pugh ba Department of Chemical Engineering & Chemical Technology, Imperial College of Science,Technology & Medicine , London, UKb ESDU International plc , London, UKPublished online: 05 Oct 2011.

To cite this article: Geoff F. Hewitt & Simon J. Pugh (2007) Approximate Design and Costing Methods for Heat Exchangers,Heat Transfer Engineering, 28:2, 76-86, DOI: 10.1080/01457630601023229

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Heat Transfer Engineering, 28(2):7686, 2007Copyright C Taylor and Francis Group, LLCISSN: 0145-7632 print / 1521-0537 onlineDOI: 10.1080/01457630601023229

Approximate Design and CostingMethods for Heat Exchangers

GEOFF F. HEWITTDepartment of Chemical Engineering & Chemical Technology, Imperial College of Science, Technology & Medicine,London, UK

SIMON J. PUGHESDU International plc, London, UK

Methodologies for the rapid sizing and costing of heat exchangers have been developed under the aegis of ESDU Internationalplc, London. This paper is a summary of a group of design guides (referred to as data items) that cover a wide range of heatexchanger configurations. These data items are aimed at providing rapid selection, sizing, and costing at the process designstage. For two-stream exchangers, the C value method has been adopted in which the costs are expressed per unit (Q/Tm),where Q is the heat load and Tm the mean temperature difference. The development and applications of this method arereviewed, with an emphasis on comparisons between various types of exchanger. The nature of variations from the standardcases considered are also discussed. Though the C value method can be applied to two-stream plate-fin exchangers, suchexchangers often operate with multiple streams. Approximate calculations for the design of such multistream exchangerscan be made using the concept of the volumetric heat transfer coefficient. This methodology can be combined with standardcurves of the cost per unit volume as a function of volume to obtain an approximate costing of such exchangers.

BACKGROUND

The conservation of thermal energy by the use of heat ex-changers is of vital importance in any scenario for sustainabledevelopment. The most important step in the design process forheat exchangers within a process plant occurs at the initial pro-cess design stage. At this stage, the fundamental decisions aremade about the incorporation of heat recovery networks withinthe process leading to the placement and specification of heatexchangers. There are many types of heat exchanger availableand, depending on the process, a range of heat exchanger types isfeasible to meet the physical conditions (pressure, temperature,corrosion resistance, size, etc.) imposed by the process. The de-signer then has to choose between feasible types; ideally, thiswould be done on the basis of cost, but there is often a great dealof conservatism in industry in choosing heat exchanger typesoutside the normal range of experience. However, if approxi-mate cost data are available for all the feasible types, then thismakes the selection process much more focused. It was with this

Address correspondence to Mr. Simon J. Pugh, ESDU International plc, 27Corsham Street, London, N1 6UA, UK. E-mail: [email protected]

general background that ESDU International plc, in collabora-tion with heat exchanger manufacturers and under the guidanceof independent committees, embarked upon a series of their dataitems on the topic of selection and costing of heat exchangers in1992.

The first data item in the series [1] presented data allowingthe selection between feasible types and also gave approximatecost data for the majority of the types considered. Starting in1994, further data items were issued developing the methodol-ogy further for specific heat exchanger types. These further dataitems include ones dealing with shell-and-tube exchangers [2],air-cooled heat exchangers [3], plate-and-frame heat exchang-ers [4], and plate-fin heat exchangers [5]. Work on the seriesis ongoing [6, 7], and ESDU is incorporating the methods intocomputer codes for rapid access by process designers.

The objective of the present article is to briefly survey some ofthe work that has been done. The data items are quite extensiveand cover more than 200 pages of detailed information. Clearly,it is impossible to present any more than a brief summary in thepresent article, but it is hoped that this will give a feel for thekind of work being done.

In what follows, a description is given of the initial selectionprocedure, and the bases of the methods used for costing to allow

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G. F. HEWITT AND S. J. PUGH 77

decisions between feasible types are described. Comparisons incosts between various forms of heat exchangers are presented,these cost comparisons being derived from the data obtained.The effect of variations (e.g., changes in tube material, heat ex-changer geometry, etc.) from the standard types used in the initialselection are discussed. The development of methodologies formultistream exchangers, which are of increasing importance inpromoting economic heat recovery, are described. Finally, somebrief conclusions are drawn.

SELECTING FEASIBLE DESIGNS

In any given process, the streams between which heat is tobe exchanged will have specific properties (temperature, pres-sure, compatibility with construction materials), and a feasibleheat exchanger is one that can meet the requirements to con-tain the respective streams. In consultation with manufacturers,the specifications of the capability of various heat exchangerswere collected together and presented in tabular form [1]. A to-tal of 19 alternative heat exchanger types were considered, andTable 1 is a small section of the table appearing for these var-ious types in ESDU [1]. In this same reference, more detaileddescriptions of the construction, capability, and limitations ofeach type were presented. Although this tabulation cannot beclaimed to be totally complete, it certainly covered the most im-portant types. Sometimes, there are no feasible standard typesof heat exchangers that can meet the process requirement; inthis case, special heat exchanger designs must be developed forthe application. However, in most cases, several alternative de-signs are feasible, and the final selection has to be made betweenthem. The obvious basis for choice is cost but, far too often, theselection is made on the basis of tradition within the particular

Table 1 Sample from ESDU [1] tables summarizing characteristics of heat exchanger types (construction material: carbon steel)

Heat exchanger Maximum pressure Temperature Fluid Normal size rangestype (bar, absolute) range (C) limitation for individual units Special features

Rotary regenerators Near atmospheric Up to 980 Low-pressure gases Inter-stream leakage mustbe tolerated

Scraped-surface 10 Up to 300 Liquids subject only tomaterials ofconstruction.

510 m height, 0.5 mdiameter

Suitable for viscous andcrystallization systems.

Shell-and-tube 300 (shell) 25 to 600 (lower andhigher with specialmaterials).

Subject only to materialof construction.

10 to 1000 m2 (pershellmultiple shellscan be used).

Very adaptable and can beused for nearly allapplications.

Spiral 18 Up to 400 Subject only to materialof construction. Oftenused for fouling duties.

Up to 200 m2 High heat transferefficiency. Cylindricalgeometry useful asintegral part ofdistillation tower.

Welded-plate 60 (higher in shells) In excess of 650 Subject only to materialof construction. Notsuitable for foulingduties.

>1000 m2 Differential pressureshould be less than30 bar. Differentialexpansion should beborne in mind.

industry. Shell-and-tube type heat exchangers have a reputationfor reliability and flexibility and are the most usual choice. How-ever, other forms of heat exchangers can often be more suitablefor particular applications: for very small duties, the double-pipeexchanger, which is manufactured from standard components,may be cheaper, and where sealing gaskets do not give riseto difficulties, plate-and-frame heat exchangers are often lessexpensive.

In many applications, the physical size of a heat exchanger isimportant. For a given heat exchanger surface area, shell-and-tube exchangers have an order of magnitude larger volume thando compact exchangers, such as plate-fin exchangers and printedcircuit exchangers. Using more compact exchangers, it is pos-sible, for instance, to use internal reboilers in many distillationapplications. Compact exchangers are also important in caseswhere space is at a premium (e.g., in offshore platforms in thepetroleum industry).

Thus, it is important to have cost and geometry data availablein making the all-important initial selection.

COSTING FOR SELECTION BETWEENFEASIBLE TYPES

The C Value Method

Conventionally, the approximate costing of heat exchangershas been done in terms of the cost per unit area. If the overallheat transfer coefficient (U ), heat load of the exchanger ( Q), andmean temperature difference (Tm) are known, then the area (A)is calculated simply from:

A =Q

U Tm(1)

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78 G. F. HEWITT AND S. J. PUGH

However, for various forms of heat exchangers, the defini-tion of area is often complex and, of course, the definition of Uis linked to this. In the Cvalue method (first suggested by He-witt et al. [8]), C is defined as the cost per unit ( Q/Tm). Thisavoids difficulties in defining area and overall coefficient andallows a direct comparison between heat exchangers in termsof the duty ( Q) and the available temperature driving force(Tm), which are related to the process specification. In both ap-proaches, care has to be exercised in specifyingTm because thismay depart significantly from its value for pure counter-currentflow.

Determination of Q / Tm

The heat load Q is readily determined from the enthalpychange of either of the streams. For pure counter-flow exchang-ers with single phase streams of constant specific heat capacity,the mean temperature difference Tm is equal to the logarithmicmean temperature difference TL M given by:

Tm = TL M = (Th,in Tc,out) (Th,out Tc,in)ln (Th,inTc,out)(Th,outTc,in)

(2)

where Th,in and Th,out are the inlet and outlet temperatures of thehot stream and Tc,in and Tc,out are the inlet and outlet tempera-tures of the cold stream.

Where there is significant departure from pure counter-current flow operation, then the mean temperature differenceis given by:

Tm = FTL M (3)where F is a correction factor. Extensive information on valuesof F for various heat exchanger configurations is given, for in-stance, by Taborek [9] and Hewitt et al. [10]. Thus, it is possibleto use this information to obtain values of F and hence, calculateTm and determine Q/Tm .

An alternative approach to calculating Q/Tm is to use therelationship between heat exchanger effectiveness (E) and thenumber of transfer units (NTU). Effectiveness is defined asthe ratio between the heat load Q and the maximum feasibleheat load Qmax, the latter being defined as the maximum heattransfer achieved if the outlet temperature of one of the streamsreaches the inlet temperature of the other stream. The streamreaching the inlet temperature of the other stream is that withthe lowest value of Mcp, and it follows that

E = |Tin Tout|larger(Th,in Tc,in) (4)

where |Tin Tout|larger is the larger of the temperature changesoccurring either on the hot side or cold side of the exchanger.The number of transfer units NT U is defined as:

NTU = UA( Mcp)smaller(5)

Figure 1 Relationship between E and NTU with R as a parameter. Shell-and-tube heat exchangers with E-type shells and an even number of tube-side passes[11].

where ( Mcp)smaller is the product of the flow rate ( M) and thespecific heat capacity (cp) of the stream having the lower productof M and cp. Defining a parameter R as:

R = (Mcp)smaller

( Mcp)larger, (6)

it is possible (for given heat exchanger configuration) to relate Eto NTU and R. ESDU has published extensive plots of this type[11], and the results are exemplified by those for shell-and-tubeheat exchangers with an E-type shell and an even number oftube side passes, as shown in Figure 1. Calculating R from Eq.(6) and E from Eq. (4), the NTU value can be established by theinterpolation of such charts and the value of Q/Tm establisheddirectly from the result as follows:

QTm

= UA = ( Mcp)smallerNTU (7)

Basic Information on Heat Transfer Coefficients and Costs

In developing approximate design and costing methods,ESDU has had the benefit of a large amount of industrial ad-vice and data. Recognizing that Q/Tm is equal to UA, dataare required on overall heat transfer coefficients and costs perunit area that can be converted to the required form. There is along tradition of ascribing standard values to film and over-all heat transfer coefficients in heat exchangers, and the ESDUapproach has continued this tradition. At first sight, the tradi-tion seems somewhat illogical, as the heat transfer coefficientwill obviously be strongly related to the available pressure drop.However, in process specifications, the pressure drop tends tolie within a restricted range (typically around 1 bar for liquidsand around 1% of the gas pressure for gases), which means thatthe coefficients encountered are often also in a restricted range.Thus, from the point of view of approximate design, it is legit-imate to take standard values for the coefficients. For tubularexchangers, the overall film coefficients shown in Table 2 rep-resent the collective judgment of a committee of experts withlong experience in heat exchanger design.


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Table 2 Film coefficients, fouling factors and overall film coefficient for tubular exchangers [8]

Cold side Hot side

Film coefficient Fouling factor Overall film Film coefficient Fouling factor Overall filmW/m2K (clean) Km2/W coefficient W/m2K W/m2K (clean) Km2/W coefficient W/m2K

Low pressure gas, 1 bar 112 0.0002 110 112 0.0002 110High pressure gas, 20 bar 682 0.0002 600 682 0.0002 600Process water 6000 0.0005 1500Treated cooling water 5000 0.0002 2500 Low viscosity organic liquid 1667 0.0004 1000 1667 0.0004 1000High viscosity liquid 210 0.0008 180 170 0.0008 150Condensing steam 8182 0.0001 4500Condensing hydrocarbon 1410 0.0002 1100Condensing hydrocarbon, 1 bar 435 0.0002 400Boiling treated water 5676 0.0003 2100 Boiling organic liquid 1667 0.0004 1000

For such exchangers, the sum of the reciprocals of the overallfilm coefficients is equal to 1/U , allowing U to be determined. Asimilar approach has been pursued for the other heat exchangergeometries covered in the in ESDU studies.

The other constituent information required in establishing Cvalues is the cost per unit area; the data for this is typified by thatshown in Figures 2 and 3 for shell-and-tube and plate-and-frameexchangers, respectively.

Again, these data were obtained with the assistance of ex-changer manufacturers and are based on actual cost data for avariety of exchangers.

Using data such as those shown in Table 2 and Figures 2 and3, it is possible to construct tables of C values for two-streamexchangers, and these are exemplified by the results shown inTable 3. Though the values of U that are also tabulated are notnecessary from the point of view of costing, such values arehelpful from the point of view of approximate sizing. The heatexchanger surface area can be calculated as Q/UTm and thevolume of the exchanger estimated if the area per unit volumeis known. Thus, for shell-and-tube exchangers, the surface areaper unit volume is of the order of 50100 m2/m3, whereas forcompact exchangers such as plate-fin exchangers, the value isaround 500 m2/m3.

Figure 2 Cost per unit area as a function of area for BEM-type shell-and-tubeheat exchangers [2].

COST COMPARISONS USING C VALUE METHOD

The tables of C values (exemplified by Table 3) can be inter-polated logarithmically. Thus, the value of C is given by:

C = exp{

ln C1 + ln(C1/C2) ln[(Q/Tm)/( Q/Tm)1]

ln[( Q/Tm)1/( Q/Tm)2]

}(8)

where C1 and C2 are the C values of the particular hot-side/cold-side fluid pairing at ( Q/Tm)1 and ( Q/Tm)2, respectively. Therelative cost of one exchanger type against another varies with( Q/Tm), as is exemplified by the following values taken forthe case of treated cooling water on the cold-side and a lowviscosity organic fluid on the hot-side.

For small duties, the double-pipe heat exchanger is more eco-nomical than the shell-and-tube heat exchanger, reflecting theability to mass-produce its components. The reverse is true forlarge duties. Over the range shown, the plate-and-frame heat ex-changer is notably more economical than the other types, though,of course, there are potential problems with sealing. A fullywelded plate exchanger, on the other hand, is more expensivethan the tubular types for small duties but less expensive for largeduties. The printed circuit heat exchanger is highly compact and

Figure 3 Cost per unit area as a function of area for plate-and-frame heatexchangers [4].


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Table 3 Table of C values and U values for double-pipe exchangers [1]

Hot-side fluid

Low- Medium- High- Low Highpressure pressure pressure viscosity viscosity Condensing

Q/T gas gas gas Process hydrocarbon hydrocarbon Condensing Condensing hydrocarbon(W/K) Fluid Parameter (


Figure 5 Comparison of costs of stainless steel shell-and-tube exchangersand stainless steel plate-and-frame exchangers [2, 4].

boiling/condensing duties) at larger surface areas. If, on the otherhand, comparisons are made between stainless steel shell-and-tube exchangers and stainless steel plate-and-frame exchangers,then the latter have a considerable cost advantage over the fullrange of sizes, as is shown in Figure 5.

COST VARIATIONS

The numbers given in C value tables exemplified by Table 3are for standard designs. For example, in the case of the tablefor shell-and-tube exchangers, the standard is a fixed tube sheet,two-pass carbon steel exchanger with a E-type shell (desig-nated BEM in the TEMA [12] standards). Real designs depart,of course, from these standard configurations, and allowancemust be made for these variations in assessing costs. A simplis-tic way of doing this is to use fixed multipliers, and this hasbeen adopted in the ESDU studies where appropriate. Table 5shows the effect of various changes from the standard design forplate-and-frame exchangers.

The cost-factor approach leads to serious errors where man-ufacturing costs are a significant proportion of the total cost. Inthis case, the effect of the variation increases with an increasingsurface area. Examples of such variations are shown in Figures6 and 7, both for the case of shell-and-tube heat exchangers.

In Figure 6, the effect of tube material is shown. For lowsurface areas, manufacturing costs represent a bigger proportionof the total costs, and the cost ratio is lower than the relative cost

Table 5 Effect of various factors on costs of plate-and-frameexchangers [4]

Factor onChange C value

Design pressure increased from 10 to 16 bar 1.1Design pressure increased from 10 to 25 bar 1.4Material changed from AISI 316 stainless steel to titanium 1.7Material changed from AISI 316 to AISI 304 stainless 0.9Gaskets changed from EPDMTM to VitonTM 1.5Plates changed to semi-welded design 1.6

Figure 6 Effect of tube material on costs of shell-and-tube heat exchangers[2]: (a) stainless steel to carbon steel, (b) Monel to carbon steel.

of the tube materials. As the surface area increases, however,the ratio of costs increases, ultimately asymptoting to a constantvalue corresponding to the ratio of tube costs.

The opposite trend is observed when comparing floating head(AES) and fixed tube sheet (BEM) designs. For small surfaceareas, the increased manufacturing costs of a floating head givea high cost ratio, as shown in Figure 7. However, as the surfacearea increases, the additional cost has less of an effect, and thecost ratio decreases.

The advantage of the now-extensive cost data available inthe ESDU data item series is that cost variation issues can bequantified more accurately.

MULTISTREAM EXCHANGERS

The use of pinch technology (process integration) techniquesfor the optimization of heat exchanger networks has givenan increased emphasis on techniques such as stream splittingto achieve maximum heat recovery. Making connections be-tween a multiplicity of heat exchangers can be expensive, andthere is a considerable premium on the use of multistream heatexchangers. Such exchangers are traditionally typified by brazed

Figure 7 Rates of costs of floating head (AES) and fixed tube sheet (BEM)shell-and-tube exchangers as a function of surface area [2].


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Figure 8 Typical multistream plate-fin heat exchanger (Courtesy ofALPEMA, [13]).

aluminum plate-fin exchangers, the type commonly used in thecryogenic industry in applications such as gas-liquifaction. Atypical plate-fin unit is shown in Figure 8.

A useful source of information on such exchangers is thestandards of the Aluminum Plate Exchangers Manufacturers As-sociation (ALPEMA) [13], from which Figure 8 is taken.

Though multistream exchangers can simplify the problemsof implementing heat exchanger networks and achieve an econ-omy of scale relative to having a number of separate two-streamexchangers, they do present a challenge in design. There are anumber of commercial computer codes for the design of suchexchangers, such as the MUSE code developed by the HeatTransfer and Fluid Flow Service (HTFS). These are based onthe detailed integration of local transport equations. However,there seems to be a dearth of quick design methods for the appli-cation at the process design stage. As part of the ESDU devel-opment work on selection and costing of heat exchangers, a newmethodology for rapid design evolved. The key feature in thedevelopment of the methodology was the definition of volumet-ric heat transfer coefficients. These coefficients could be used inconjunction with the methodology of process integration (pinchtechnology) to obtain an estimate of the heat exchanger volume.Using manufacturers curve of costs per unit volume as a func-tion of volume [5], it is possible to obtain estimates of costs di-rectly. The derivation of volumetric heat transfer coefficients andthe application in the design methodology is described below.

It should be stressed that the use of pinch technology tech-niques and the associated heat exchanger network optimization

methods is an active and advancing field. In the present context,the objective has been to use the techniques at a rather elemen-tary level to give a structure for approximate process design. Forinstance, it has been assumed that single phase streams have aconstant specific heat capacity, and that phase change occurs atconstant temperature. These assumptions can be relaxed in moreadvanced methods (see [14, 15]) but simplicity was the order ofthe day in the present work.

Volumetric Heat Transfer Coefficients

If one considers the schematic diagram of a plate-fin heatexchanger geometry, as illustrated in Figure 9, a volumetric heattransfer coefficient B may formally be defined such that:

d Q = BV (T1 T2) (8)where d Q is the amount of heat transferred between adjacentstreams at temperatures T1 and T2, respectively, in a volumeV . Volume is defined as:

V = s yz (9)where s is the distance between the centers of the passages (seeFigure 9), y is the distance along the width of the plate (alsosee Figure 9), and z is a distance into the plate parallel withthe streams (i.e., perpendicular to the plane of Figure 9). Thevalue of d Q can also be written conventionally in terms of localarea-based heat transfer coefficients as:

d Q = zy au f 1 +f 1a f 12

(T1 TW 1)1 (10)

d Q = zy au f 2 +f 2a f 22

(TW 2 T2)2 (11)

d Q = W (TW 1 TW 2)yz/(tp + t f ) (12)where au f and a f are the unfinned and finned surface areasper unit area of plate in a given passage, is the conventionalarea-based heat transfer coefficient, f the fin efficiency, W theconstruction material thermal conductivity, TW the wall temper-ature, tp the plate thickness (see Figure 9), and t f the mean finthickness. Subscripts 1 and 2 refer to the channel carrying thehot fluid and the channel carrying the cold fluid, respectively(see Figure 9).

Figure 9 Plate-fin exchanger geometry [5].


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Combining Eqs. (812), the overall volumetric coefficient isgiven by:

1B

= 2s(au f 1 +f 1a f 1)1+ 2s(au f 2 +f 2a f 2)2

+ s(tp + t f )W

(13)

It is convenient to define local volumetric coefficients i wherei = 1 or 2 for the respective streams. Thus,1 and2 are definedsuch that:

11

= 2s(au f 1 +f 1 a f 1)1+ s(tp + t f )

2 W(14)

12

= 2s(au f 2 +f 2a f 2)2+ s(tp + tp)

2 W(15)

and1B

= 11

+ 12

(16)

Although a wide range of fin geometries are possible with plate-fin heat exchangers, the most common type is the serrated fin, anda suitable reference geometry would be one with a fin frequency( fn) of 708.7 fins/m (18 fins per inch), a fin thickness of 2.032 104 m (0.008 in), a plate gap/fin height (b) of 0.00635 m(0.25 inches), and a parting sheet thickness (tp) of 1.5 mm. Theprocedure used in ESDU [5] was to estimate typical values ofi for various streams for this reference design (analogous tothe values given for area-based film coefficients in Table 2 forshell-and-tube heat exchangers). In order to calculate guidelinecoefficients, pressure drops of 0.1 bars were assumed for liq-uid and two-phase streams and 1% of the gas pressure for gasstreams. The fin efficiency was calculated from the equation:

= tanh mm

(17)

where m is given by:

m = b(

2t f W

)(18)

The local film coefficients (1 and 2) were calculated usingj factor data given by Taylor [16]; the same source was usedfor friction factor data for the calculation of pressure drop. Astandard exchanger length of 6 m was assumed, and W wastaken as 130 W/m K. Using this procedure, the typical values of shown in Table 6 were obtained.

These can then be used in approximate calculations for two-stream exchangers, combining the values for the hot and coldstreams using Eq. (16) to give the relevant value of B. The activevolume (Va) of the heat exchanger can then be calculated fromthe expression:

Va =Q

BTm(19)

Table 6 Typical values of local volumetric coefficients [5]

(kW/m3K)

FluidHydrocarbons liquid 1100Boiling and condensing 1400Gaseous: low pressure (2 bar) 80Gaseous: medium pressure (20 bar) 400

Air-type (O2, N2, etc.)Liquid 1000Boiling and condensing 1200Gaseous: low pressure (2 bar) 60Gaseous: medium pressure (20 bar) 300

where Tm can be calculated from Eq. (2) for counter-currentflow or Eq. (3) for exchangers that do not have pure counter-current flow. The total volume of the exchanger V is then cal-culated by allowing a nominal 15% extra volume to account forthe headers (i.e., V = 1.15Va).

Having established the volume, the approximate cost of theheat exchanger can be determined using manufacturers data forcost per unit volume as a function of volume. In the specific workreported by ESDU [5], curves provided by IMI Marston Ltdwere presented that show a decreasing cost per unit volume asfunction of volume, with costs for multistream exchangers beingtypically 3040% higher than those for two-stream exchangers.Data can be represented in terms of C values for given valuesof Q/Tm , and tables of C values obtained in this way arepresented in ESDU [5].

Method For Multistream Exchangers

The volumetric heat transfer coefficient methodology can beextended to cover multistream plate-fin exchangers using thefollowing steps:

1. The stream data are represented in terms of hot and cold com-posite curves using the pinch analysis method (see Linhoffand Smith [17] for a detailed description of the methodology).A typical pair of composite curves is shown in Figure 10 forthe six stream example, which will be presented in more de-tail below. As will be seen, there is a pinch at which theminimum temperature difference Tmin is 6 K.

2. The composite curve is divided into zones corresponding toregions where the hot and cold composite curves are linear, asexemplified by Figure 10. Each of these zones is then treatedseparately.

3. A mean volumetric coefficient for a zone containing nstreams can be estimated from the expression:

QzBz

=n

i = 1

Qii

(20)

where Qz is the total heat transferred in zone z, Bz the meanvolumetric coefficient for the zone, Qi the heat lost or gainedby the ith stream in the zone and i the local volumetric heat


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Figure 10 Composite curves for six-stream example.

transfer coefficient for the ith stream. Obviously, Eq. (20)reduces to Eq. (16) for the case of a two-stream exchanger.

4. Calculate Tm,z for the zone. Often, multi-stream exchang-ers operate close to counter-current flow, and Tm,z can becalculated from Eq. (2) (i.e., as a logarithmic mean temper-ature difference) using the appropriate end temperatures ofthe zone.

Figure 11 Network of two-stream exchangers for heat recovery between the hot and cold streams for the six-stream example shown in Table 7. Note: Numbersin the diagram that are not assigned units are temperatures in C.

Table 7 Six-stream example: low pressure hydrocarbon gases with = 80 kW/m3K

Stream Hot Inlet Outletnumber or cold Mcp(kW/K) temperature (K) temperature (K)

H1 Hot 10 300 150H2 Hot 5 250 100H3 Hot 8 200 150C1 Cold 15 90 130C2 Cold 5 120 210C3 Cold 20 170 250

5. The heat exchanger volume corresponding to the zone canthen be calculated using the expression:

Vz =Qz/Tm,z

z(21)

The total volume V is then calculated (allowing 15% againfor headers) from the expression:

V = 1.15n

i=1Vz (22)

Example of Multistream Calculation

As an example of the methodology described in the previoussection, one may consider the case shown in Table 7.


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Here, there are six hydrocarbon gas streams (three hot andthree cold). The composite curves for this example are as shownin Figure 10. Applying the procedure described above, a totalexchanger volume (V ) of 4.97 m3 is obtained, and using themanufacturers curves for cost per unit volume as function ofvolume, the cost of the multistream exchanger for this duty iscalculated as 95 k. It is interesting to compare the cost of a mul-tistream exchanger with the costs of solving the same problemusing a network of two-stream exchangers. The network can bedeveloped using the methods of pinch analysis (see Linhoff andSmith [17]) and is shown using the conventional grid diagramin Figure 11.

As can be seen, ten two-stream heat exchangers are required.The estimated cost of the exchangers is around 195 k, morethan double the cost of meeting the required duties in a singlemulti-stream exchanger.

CONCLUSIONS

The following main conclusions can be drawn from the stud-ies forming the basis of this article: the provision of informationfor selection and budget costing is important for the process de-signer at the initial stage of design of the process. This is thecrucial stage in achieving the most economic solutions.

The C value method has proved an invaluable tool in theselection and preliminary costing of heat exchangers, and isalready built into several proprietary computer codes.

The approximate design of multistream exchangers is aidedby using volumetric heat transfer coefficients, and a new method-ology for estimating these is presented.

Considerable cost savings can be achieved by using multi-stream exchangers rather than a multiplicity of two-stream ex-changers.

ACKNOWLEDGMENTS

The authors would like to gratefully acknowledge the assis-tance of Heat Transfer Steering Group of ESDU in advisingon the work described in this present article. They are also ex-tremely grateful for the assistance of various working parties(drawn mainly from industry) who advised on the work on thespecific heat exchanger types.

NOMENCLATURE

A heat transfer projected surface area of heat exchanger,m2

a surface areas between plates per unit area, m2B overall volumetric heat transfer coefficient, W/m3Kb plate gap or fin height, mC cost per unit Q/Tm , /(W/K)cp specific heat capacity, J/kgKE thermal effectiveness

F heat transfer correction factor in LMTD methodfn fin frequency, fins/lengthH enthalpy, kWm parameter given by Eq. (18)M mass rate of flow, kg/s

n number of streams within a zoneNTU number of heat transfer unitsQ rate of heat transfer (heat load) of heat exchanger, WR thermal capacity ratios element volume depth, mT fluid temperature, Ct f , tp mean fin and plate thickness, respectively, mT temperature difference, K or CU overall heat transfer coefficient, W/m2KV total heat exchanger volume, m3Va total active heat transfer volume of plate-fin exchanger,

m3

V element volume, m3y element width, mz element length, m

Greek Symbols

stream heat transfer coefficient, W/m2K film volumetric heat transfer coefficient, W/m3K thermal conductivity, W/mK fin efficiency

Subscripts

c, h cold and hot streams, respectivelyf, u f finned and unfinned surfaces, respectivelyin, out inlet and outlet conditions, respectivelyLM logarithmic meanm mean

max maximum valueW conditions at wallz zone1, 2 cold and hot streams, respectively

REFERENCES

[1] ESDU, Selection and Costing of Heat Exchangers, ESDU dataitem No. 92013, ESDU International plc, London, UK, 1992.

[2] ESDU, Selection and Costing of Heat Exchangers, Shell-and-TubeType, ESDU data item No. 94042, ESDU International plc, Lon-don, UK, 1994.

[3] ESDU, Selection and Costing of Heat Exchangers, Air-CooledType, ESDU data item No. 94043, ESDU International plc,London, UK, 1994.

[4] ESDU, Selection and Costing of Heat Exchangers, Plate-and-Frame Type, ESDU data item No. 95007, ESDU Internationalplc, London, UK, 1995.


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[5] ESDU, Selection and Costing of Heat Exchangers, Plate-Fin Type,ESDU data item No. 97006, ESDU International plc, London, UK,1997.

[6] ESDU, Selection and Costing of Heat Exchangers, Spiral-PlateType, data item in Preparation, ESDU International plc, London,UK, 2005.

[7] ESDU, Selection and Costing of Heat Exchangers, Helixchangers,data item in Preparation, ESDU International plc, London, UK,2005.

[8] Hewitt, G. F., Guy, A. R., and Marsland, R. H., Heat TransferEquipment, in User Guide on Process Integration for the EfficientUse of Energy, eds. B. Linnhoff, D. W. Townsend, D. Boland, G. F.Hewitt, B. E. A. Thomas, A. R. Guy, and R. H. Marsland, 1st ed.rev., IChemE, Rugby, UK, 1982.

[9] Taborek, J., Charts for Mean Temperature Difference in Indus-trial Heat Exchanger Configurations, in Heat Exchanger De-sign Handbook, ed. G. F. Hewitt, Begell House, New York,1994.

[10] Hewitt, G. F., Shires, G. L., and Bott, T. R., Process Heat Transfer,CRC Press, Boca Raton, Florida, 1994.

[11] ESDU, Design and Performance Evaluation of Heat Exchang-ers: The EffectivenessNTU Method, Parts 15, ESDU dataitem Nos. 98003-98007, ESDU International plc, London, UK,1998.

[12] TEMA, Standard of Tubular Exchanger Manufacturers Asso-ciation, 7th ed. and 8th ed., TEMA, New York, 1988 and1999.

[13] ALPEMA, The Standards of the Brazed Aluminum Plate-FinHeat Exchanger Manufacturers Association, 2nd ed., Availableat: http://www.alpema.org, 2000.

[14] Zhu, X. X., ONeill, B. K., Roach, J. R., and Wood, R.M., A Method for Automated Heat Exchanger Network Syn-thesis Using Block Decomposition and Non-Linear Opti-mization, Trans. IChemE, vol. 73A, pp. 919930, November1995.

[15] Asante, N. D. K., and Zhu, X. X., An Automated and InteractiveApproach for Heat Exchanger Network Retrofit, Trans. IChemE,vol. 75A, pp. 349360, March 1997.

[16] Taylor, M. A., Plate-Fin Heat Exchangers: Guide to Their Spec-ification and Use, 1st ed., HTFS, Harwell Laboratory, England,1987.

[17] Linnhoff, B., and Smith, R., Pinch Analysis for Network De-sign, Heat Exchanger Design Handbook, ed. G. F. Hewitt, BegellHouse, New York, 1994.

Geoff Hewitt is Emeritus Professor of Chemical En-gineering at Imperial College, London. He was for-merly the head of the Thermal Hydraulics Divisionand founder of the Heat Transfer and Fluid FlowService (HTFS) at the Harwell Laboratory of theUKAEA. He moved to Imperial College (part-timein 1985 and full-time in 1990) and has continuedto work there on multiphase flow and heat transfer.He has authored and edited many books (including

Process Heat Transfer in 1994 and Encyclopedia of Heat and Mass Trans-fer in 1997) and published more than 400 papers and reports, mainly on gas-liquid flow and evaporative heat transfer. He is the editor of Multiphase Sci-ence and Technology, executive editor of the Heat Exchanger Design Hand-book, and one of the founding editors of Heat Transfer Engineering. He isthe recipient of the AIChE Donald Q. Kern Award, ASME Max Jakob Award,the Nusselt Reynolds Prize, the Luikov Medal, and the IChemE Council andArmstrong Medals. He has received honorary doctorates at Louvain, UMIST,and Heriot Watt. He is a fellow of the Royal Academy of Engineering, fellowof the Royal Society, and Foreign Associate of the US National Academy ofEngineering.

Simon Pugh is the head of thermofluids at ESDUInternational plc of London, UK. His current role in-cludes the management of all ESDUs heat transferwork, which is undertaken under the guidance of in-ternational independent committees of experts fromindustry and the universities. He is currently leadingthe group of engineers working on the developmentof a range of design guides to oil industry foulingproblems and computer programs for better selection,

design, and operation of heat exchangers. He holds a mechanical engineeringdegree from Brunel University in UK.


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Documents

Approximate Design and Costing Methods for Heat Exchangers