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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: [email protected] (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
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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
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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
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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
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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
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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
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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
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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