Thermal design of multi-stream heat exchangers

M. Picoon-Nuu~nnez a,*, G.T. Polley b, M. Medina-Flores c

a Institute for Scientic Research, University of Guanajuato, Lascurain de Retana no. 5, Guanajuato, Gto., Mexicob 96 Park Road, Swarthmoor, Ulverston, Cumbria, LA12 0HJ, UK

c Faculty of Mechanical Electrical and Electronic Engineering, University of Guanajuato, Guanajuato, Gto., Mexico

Received 15 August 2001; accepted 22 March 2002

Abstract

The thermal design of multi-stream heat exchangers of the plate and n type is presented. Althoughoriginally used in low temperature processes, their application is extrapolated to above temperature pro-cesses and it is shown that, conceptually, multi-stream exchangers could replace whole heat recoverynetworks. The approach is based on the use of temperature vs. enthalpy diagrams or composite curves,which show how a multi-stream exchanger can be subdivided into block sections that correspond toenthalpy intervals and indicate the entry and exit points of the streams. A design methodology for plate andn exchangers in countercurrent arrangement, characterized by the maximization of allowable pressure as adesign objective is extended to the design of multi-uid exchangers. The methodology uses a thermo-hydraulic model which relates pressure drop, heat transfer coecient and exchanger volume. The potentialapplicability of the methodology is demonstrated on a case study. 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Multi-stream exchangers; Platen exchangers; Composite curves; Thermo-hydraulic model

1. Introduction

The rst applications of exchangers for the simultaneous transfer of heat between more thantwo streams were developed for cryogenic processes [1]. The type of exchangers employed for thispurpose were shell and helical tubes and plate and n. Shell and helical exchangers are able to

Applied Thermal Engineering 22 (2002) 16431660www.elsevier.com/locate/apthermeng

*Corresponding author. Tel.: +52-473-73-27519; fax: +52-473-73-26252.

E-mail address: picon@quijote.ugto.mx (M. Picoon-Nuu~nnez).URL: http://www.pinchtechnology.com (G.T. Polley).

1359-4311/02/$ - see front matter 2002 Elsevier Science Ltd. All rights reserved.PII: S1359-4311(02)00074-1

Nomenclature

A supercial heat transfer area (m2)Ac free ow area (m2)a coecient in heat transfer vs. Re correlation (Eq. (8))b exponent in heat transfer vs. Re correlation (Eq. (8))Cp heat capacity (J/kg C)CP heat capacity-ow rate (W/C)dh hydraulic diameter (m)f friction factorfs ratio of secondary surface area to total surface areaH enthalpy (kW)HT exchanger height (m)h heat transfer coecient (W/m2 C)hA total surface areaheat transfer coecient product (W/C)j Colburn factor (StPr2=3)k uid thermal conductivity (W/m C)Kh constant in heat transfer coecient equation (thermo-hydraulic model)Kp constant in pressure drop equation (thermo-hydraulic model)L exchanger length (m)_mm mass ow rate (kg/s)Np number of passages per streamPr Prandtl numberDP pressure dropQ heat load (W)R thermal resistance due to fouling (m2 C/W)Re Reynolds numberRW wall thermal resistance (m2 C/W)St Stanton numberT temperature (C)V passage or channel volume (m3)VT total volume of heat exchanger (m3)W exchanger width (m)x coecient in friction factor vs. Re correlation (Eq. (9))y exponent in friction factor vs. Re correlation (Eq. (9))

Subscripts1 side 1 of exchanger2 side 2 of exchangerw wall conditions

Greek lettersa total heat transfer area of one side of exchanger to total exchanger volume (m2/m3)

1644 M. Picoon-Nuu~nnez et al. / Applied Thermal Engineering 22 (2002) 16431660

handle one cold and two or more hot streams or vice versa, whereas the geometrical features ofplate and n exchangers make them suitable for handling more than two hot and more than twocold stream in the same unit.As it has been suggested, heat recovery networks require a minimum of N 1 individual ex-

changers, where N is the number of streams plus utilities that take part in the process [2], thenpotential savings in terms of space, weight and supporting structure could be achieved if all theseheat duties were to be processed in a single unit. There is therefore an incentive for developingdesign methodologies for multi-stream exchangers.The main concerns regarding the widespread use of heat exchangers of the plate and n type for

multi-uid applications are the limited range of temperature and pressure at which they canoperate and the restrictions regarding their application to relatively clean uids.Since a multi-stream exchanger represents a single unit where a number of dierent streams will

exchange heat, it is expected that a complex set of heat transfer paths will take place within theunit [3]. This complexity arises as a result of the participating streams not having the same entryand exit temperatures; not having the same physical properties and, therefore, not having thesame heat transfer capabilities.A multi-stream heat exchanger may consist of a large number of passages or channels with

several cold and hot streams. Heat transfer calculations of such systems performed on a channelby channel basis is complicated due to the number of channels involved and the interaction be-tween them. Previous work on multi-stream exchangers has been based on a simplication knownas the common wall temperature assumption which implies that at any position normal to thedirection of the ow, all separating plates are at the same temperature [4]. Subsequent studies havereplaced the common wall temperature assumption for a more exhaustive analysis that include allpossible paths for the ow of heat within a multi-stream unit such as the heat conduction throughns of non-adjacent layers [3,57].Current design approaches for multi-uid exchangers consider the design of block sections per

stream in an independent way [810]. The result of this design exercise is a set of ow lengths thatcorrespond to the heat duty and pressure drop of each stream. A single ow length is arrived at byselecting a common length and iteratively changing n type on the other streams until nal di-mensions match within a reasonable limit.The thermal design of a plate and n multi-stream heat exchanger must reveal the following:

total exchanger volume; exchanger dimensions (height, width and length); number of channels or

b total heat transfer area of one side of exchanger to volume between plates in that side(m2/m3)

d plate spacing (m)e plate thickness (mm)j n thermal conductivity (W/m C)l viscosity (kg/m s)q density (kg/m3)g n temperature eectivenesss n thickness (mm)

M. Picoon-Nuu~nnez et al. / Applied Thermal Engineering 22 (2002) 16431660 1645

passages per stream; type of ns per stream; heat transfer coecients and pressure drop. In thiswork, the basic elements and basic understandings that lead to the development of a rationaldesign methodology are presented.The design methodology developed in this paper involves the following ve major steps: (1) The

construction of temperature vs. enthalpy diagrams or composite curves to determine the enthalpyintervals, their temperature eld, heat load and stream population [1114]; (2) stream ramicationper interval to achieve uniform passage heat load; (3) the use of a volume design equation [15] todetermine block length and width; (4) appropriate selection of ns or secondary surfaces per streamfor achieving uniform eective (hA) values [13,14]); (5) determination of block height, number ofpassages and pressure drops; and (6) reconciliation of block dimensions by pressure drop relax-ation.The main assumptions made in the development of this work are: steady state operation, single

phase heat transfer process, adiabatic operation, constant uid properties, constant heat transfercoecients, negligible longitudinal heat conduction through walls, and no ow mal-distribution isconsidered. Also it is assumed that the thermal and friction performance data for the ns reportedby Kays and London [16], which will be used in this work, are valid for uids with Prandtl numbergreater than 1.

2. Graphical representation of a multi-stream heat exchanger

The composite curves, as those shown in Fig. 1, represent the heat balance of an entire process.They are composed of a hot and a cold composite curve. The hot composite curve represents thetotal heat that must be removed and is obtained by the thermal summation of all hot streams thattake part in the process; on the other hand, the cold composite curve, represents the total amountof heat that must be added to the process and is obtained by the thermal summation of all coldstreams present in the process. When both curves are superimposed, the overlap between themindicates the amount of heat that can be recovered within the process, whereas the overshoot onboth ends indicates the amount of external heating and cooling required for the process to be inthermal balance. When constant physical properties are assumed, composite curves are formed bystraight lines where each change in slope is related to the entry and exit of a stream. If a verticalline is drawn whenever a change in slope occurs, the whole heat recovery process is sectioned intovarious intervals. These are called enthalpy intervals and are characterized by a temperature eld(inlet and outlet temperatures), a heat load and a stream population. Techniques for the con-struction of these curves are well established [17]. The point of closest approximation between thecurves is termed the Pinch.The heat transfer needs of a process are met through a heat exchanger network. Considering

that the minimum number of two stream heat exchangers needed to fulll the thermal duty of theprocess is calculated from N 1, where N is the total number of process streams plus utilities [2],then performing all these duties in a single unit, potential savings in the form of space, weight andsupporting structure could be achieved.Overall, the whole heat duty of the process could be met if a single heat exchanger was able

to accommodate all of the hot and cold streams involved. Fig. 2a shows how every enthalpyinterval is characterized by a stream population and each interval could be thought of and de-

1646 M. Picoon-Nuu~nnez et al. / Applied Thermal Engineering 22 (2002) 16431660

signed as a block where the entry and exit temperatures of the streams are xed. Once everyblock has been sized, they are put together to become the multi-stream exchanger, as shown inFig. 2b.

Fig. 1. Temperature vs. enthalpy diagrams or composite curves for the representation of the energy balance of a

process.

Fig. 2. Representation of the stream population within enthalpy intervals and its relation to entry and exit points in a

multi-stream heat exchanger. (a) Stream population in enthalpy intervals and (b) multi-stream exchanger entry and exit

points.

M. Picoon-Nuu~nnez et al. / Applied Thermal Engineering 22 (2002) 16431660 1647

3. Pressure drop and heat load distribution

The stream population per enthalpy interval is characterized by a set of streams each with agiven ow rate, permissible pressure drop, and heat load. In this work it is assumed that theallowable pressure drop per stream corresponding to a particular enthalpy interval is distributedlinearly according to the fraction of heat load. Thus:

DPi;interval DPi;Total DHi;intervalDHi;Total

1

where i is the stream number.Now for the heat load per stream to be uniform, streams need to be split in such a way that the

total number of hot branches be equal to the total number of cold branches. One way of ac-complishing this is by using the simple approach of Fig. 3, where the stream population and heatcapacity-ow rate (CP) of streams for a given enthalpy interval are shown. Each stream has beensplit so that every passage or channel exhibits the same heat load and the total number of hotpassages equals the total number of cold passages. In Fig. 3,

PCPhot 8 W/C and

PCPcold

16 W/C. This indicates that the heat capacity-ow of the cold passages must be twice as big as theheat capacity-ow rate of the hot passages. One way of achieving this is by having eight hotpassages, each with a CP of 1 W/C, and eight cold passages each with a CP of 2 W/C. In ageneral form, the ratio of the CP any hot passage to the CP of any cold passage can be expressedby:

CPhot passage

CPcold passage

1P

CPcold=P

CPhot2

Fig. 3. CP distribution per passage for achieving uniform heat load.

1648 M. Picoon-Nuu~nnez et al. / Applied Thermal Engineering 22 (2002) 16431660

As will be seen later, the nal number of passages on the hot and cold side is a function of theblock width, which is specied at some stage in the design approach. Besides, in a typical ap-plication, most streams will end up with a fractional number of passages. Since fractional passagesmust be changed to an integer value. A rating analysis, that is beyond the scope of this paper,must be conducted in order to consider the eect of this change upon performance.

4. Volume design equation for plate and n exchangers

The geometrical features of plate and n heat exchangers make them capable of performingheat duties where simultaneous heat transfer between more than two streams takes place. Fig. 4shows a countercurrent arrangement of this type of construction.A typical assembly is composed of plates between which, ns are tted. The function of these

ns is threefold: to increase heat transfer surface area, to increase heat transfer coecient bypromoting turbulence and to provide mechanical support between plates. The channels formedbetween the plates constitute the passages through which, in an alternate manner, hot and colduid circulate in countercurrent ow arrangement. The main geometrical parameters of a plateand n exchanger are: ratio of total surface area of one side of the exchanger to volume betweenplates (b), plate spacing (d), ratio of secondary surface area to total surface area (fs), hydraulicdiameter (dh), n thickness (s) and n thermal conductivity (j). Once the surface type is specied,all these parameters are automatically known.A design methodology for plate and n exchangers in countercurrent arrangement character-

ized by the maximization of allowable pressure as a design objective, as developed by Picon et al.[15] is extended here for a multi-uid application. In countercurrent arrangement, only one uid isable to fully utilize its allowable pressure drop. This stream is referred to as the critical stream[15]. The design of the exchanger proceeds by specifying the type of n (or secondary surface) foreach stream. In the case of a multi-stream application, a critical stream must be chosen for

Fig. 4. Typical assembly of a plate and n exchanger and a multi-stream application. (a) Plate and n exchanger and

(b) multi-stream heat exchanger in countercurrent ow arrangement.

M. Picoon-Nuu~nnez et al. / Applied Thermal Engineering 22 (2002) 16431660 1649

every enthalpy interval. The critical stream will be matched with an opposing stream which will betermed the reference stream. This allows the relevant block dimensions (length and width) to becomputed so that the rest of the streams will have to accommodate their heat load within thesedimensions. The basis of the sizing approach is a volume design equation. This model is presentedbelow.The basic heat transfer design equation for a two stream heat exchanger

Q UAF DTLM 3can be combined with the denition of overall heat transfer coecient to give

A1 QF DTLM1

g1

1

h1

R1

1

g2

A1A2

1

h2

R2

Rw

4

where A1 and A2 represent the total heat transfer area; h1 and h2, the clean heat transfer coecientsand R1 and R2, the thermal resistance due to fouling on sides 1 and 2 respectively. Rw is the wallthermal resistance and F is the log mean temperature dierence correction factor. For a counterow arrangement F has the value of 1.The application of this equation to the case of compact heat exchangers of the plate and n type

requires that total heat transfer areas for each side be expressed in terms of volume. A parameterthat relates total surface area of one side of the exchanger to total exchanger volume is a. Fromthis denition, A1 and A2 are related to total exchanger volume from:

A1 a1VT and A2 a2VT 5where a can be expressed by:

a1 b1d1

d1 d2

and a2 b2

d2d1 d2

6

where b is the total surface area of one side to the volume of that side and d is the plate spacing forside 1 and 2 respectively.After substitution of (5) into (4) we have

VT QDTLM1

g1a1

1

h1

R1

1

g2a2

1

h2

R2

Rw

7

Eq. (7) represents the total exchanger volume as a function of heat duty, surface geometry andheat transfer coecients; g1 and g2 are the temperature eectiveness of the total surface area ofside 1 and 2 respectively and they can be calculated from

g 1 fstanh 2hks

1=2 d2

h i2hks

1=2 d2

h i8