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Computers and Chemical Engineering 35 (2011) 1257–1264

Contents lists available at ScienceDirect

Computers and Chemical Engineering

journa l homepage: www.e lsev ier .com/ locate /compchemeng

ynthesis of multipass heat exchanger networks based on pinch technology

in Suna,b,∗, Xionglin Luoa

Research Institute of Automation, China University of Petroleum, Beijing, Box 260, 102249 Beijing, ChinaDepartment of Chemical and Biological Engineering, University of British Columbia, 2360 East Mall, Vancouver, BC V6T1Z3, Canada

r t i c l e i n f o

rticle history:eceived 6 January 2010eceived in revised form 21 August 2010ccepted 27 August 2010vailable online 9 September 2010

a b s t r a c t

The multipass heat exchanger is the most common type of heat transfer equipment used in heat exchangernetworks (HENs) by the chemical process industries. There are many methods that have been proposedfor the synthesis of HENs with multipass heat exchangers, which are mostly derived from the FT designmethod. In this paper, an alternative new method to synthesis multipass HENs is presented based onthe classical pinch technology. In the multipass heat exchanger, both countercurrent and co-current flow

eywords:eat exchanger networksinch technologyultipass

are involved. For the co-current flow, composite curves and problem tables are modified, and comparedwith that of the countercurrent flow. A proper minimum temperature difference is also selected con-sidering the energy-capital cost trade-offs, and then a multipass HEN is synthesized. Results of the casestudy demonstrate that the new approach meets operating requirements and minimizes the total cost

o-currentountercurrent

successfully.

. Introduction

In industrial practice, multipass heat exchangers are commonlysed because of advantages such as longer flow-paths for a givenxchanger length, allowance for thermal expansion, easy mechan-cal cleaning, as well as good heat transfer coefficients on theube side due to higher velocities (Ponce-Ortega, Serna-Gonzalez,alcedo-Estrada, & Jimenez-Gutierrez, 2006).

Research efforts on the synthesis of heat exchanger networksHENs) have been significant in the last few decades (Gundersen,000). However, most of the methods published for HENs synthesisroblem consider the use of single pass exchangers (Colbert, 1989;innhoff & Flower, 1978; Zhu, O’Nell, Roach, & Wood, 1995). In theseethods, the pinch technology-based techniques have found appli-

ations in a wide range of designs for the countercurrent exchangeretworks. Pinch technology is a sequential graphical HENs methodased on the first law of thermodynamics and some constrains orig-

nated from the second law of thermodynamics (Predrag & Sreten,009). The first law is concerned with the energy balance (i.e. theonservation of energy constraint), and the second law ensures theositive temperature difference between the hot stream and theold stream, in case they exchange the heat. Based on the conceptsf pinch technology, it is feasible to design multipass HENs with

he help of the first and second laws of thermodynamics.

The most common approach for the synthesis of multipass HENss based on the FT correction factor (Galli & Cerda, 2000; Jose,

∗ Corresponding author at: Research Institute of Automation, China University ofetroleum, Beijing, Box 260, 102249 Beijing, China. Tel.: +86 01089731708.

E-mail addresses: sunlin6666@yahoo.com.cn, linsun@chbe.ubc.ca (L. Sun).

098-1354/$ – see front matter © 2010 Elsevier Ltd. All rights reserved.oi:10.1016/j.compchemeng.2010.08.005

© 2010 Elsevier Ltd. All rights reserved.

Medardo, & Arturo, 2008; Kern, 1950). During the design process,the rule of keeping FT > 0.75 is used to calculate the number of shells.The size of the exchanger is then found from the basic design equa-tion. However, the evaluation of the FT correction factor dependson trial iterations and may be difficult to compute (Ponce-Ortega,Serna-Gonzalez, & Jimenez-Gutierrez, 2008). Fakheri (2003) haspresented some explicit expressions that avoid the difficulties asso-ciated with the use of the FT charts. Ahmad and Smith (1989)introduced a new parameter, Xp, and derived simple equations tocalculate the number of shells in series explicitly. Reddy, Rao, andDavies (1998) also proposed a set of rules for designing multipassHEN with a smaller number of 1–2 shells without the considera-tion of the trade-offs among the energy consumption, the numberof units, and the area. Ponce-Ortega et al. (2006) presented an opti-mization method for the design of multipass heat exchangers byusing the FT correction factor. In short, all of these studies are mainlybased on the FT correction factor to optimize the multipass HENs.

To account effects of co-current flows in heat exchangers, thesynthesis of the HEN with only co-current heat exchangers is firstlydeveloped in this paper. By taking this as a starting point, and usingclassical pinch technology (Linnhoff et al., 1982), an alternativenew method to synthesis the multipass HEN is proposed with theconsideration of energy-capital cost trade-offs.

2. Synthesis of co-current heat exchangers based on thepinch design method

Multipass heat exchangers involve part countercurrent andpart co-current flow. The pinch design method has been success-fully used to synthesis countercurrent heat exchangers (Linnhoff &Flower, 1978). However, for the case of co-current flow, the clas-

1258 L. Sun, X. Luo / Computers and Chemical

Nomenclature

ParametersA heat transfer area (m2)Cp heat capacity (kJ (kg ◦C)−1)D heat deficit (kW)I input heat flowm flow rate (kg h−1)n tubes numberO output heat flowQ heat loads (MW)T temperature (◦C)U heat transfer coefficient (kJ (m2 ◦C)−1)�Tmin minimum temperature difference (◦C)

Subscriptsc cold streamsco co-current flowcount countercurrent flowh hot streamsin inputj the jth tubek the kth temperature intervalLM the log mean temperature differenceo outputR target value

SuperscriptsL upper bound

sadtap

2

hphdadcamwtbatI

TB

H lower bound

ical pinch technology is modified. Through the composite curvesnd the problem table, a HEN with co-current exchangers is firstlyeveloped. The pinch location, the number of heat exchangers andhe minimum temperature difference for the co-current HEN arelso calculated, and then the modified pinch technology is com-ared with the classical one.

.1. Composite curves for HENs with co-current exchangers

Temperature–enthalpy (T–H) plots known as ‘Composite curves’ave been used for many years to set energy ahead of design. Com-osite curves consist of temperature (T)–enthalpy (H) profiles ofeat availability in the process (the hot composite curve) and heatemands in the process (the cold composite curve) together ingraphical representation. In the composite curves, the vertical

ifference between the hot composite curve and cold compositeurves denotes the driving forces for heat transfer. In the regionlong the horizontal axis where both curves are presented, heatay be recovered between hot and cold process streams. The pointhere the composite curves are closest to each other is known as

he pinch. With the smallest driving forces, the pinch represents theottleneck for heat transfer. For example, Glemmestad (1997) used

heat exchanger network to demonstrate the synthesis of coun-

ercurrent heat exchangers, and the basic data are given in Table 1.n Fig. 1, the dashed arrowhead line is the hot composite curve for

able 1asic data of heat exchanger networks.

Stream no. Tin (◦C) TR (◦C) CP (MW/◦C) �Q (MW)

Hot1 (H1) 190 30 0.10 16.0Cold1 (C1) 80 160 0.15 12.0Cold2 (C2) 20 130 0.05 5.5

Engineering 35 (2011) 1257–1264

the HEN with countercurrent heat exchangers, and the correspond-ing minimum temperature difference, �Tmin,count, is selected to be20 ◦C. Based on the analysis presented by Glemmestad, for the caseof countercurrent flow the pinch is measured from the diagram,where the hot stream temperature is 100 ◦C and the cold one is80 ◦C. The targets for utility consumption are identified to the min-imum hot utility requirement, QH,min = 5.5 MW, and the minimumcold utility requirement, QC,min = 4 MW.

For this 3 streams problem (see Table 1), in this section only theco-current exchanger is used. In Fig. 1, the hot composite curve ismodified according to the thermodynamics. In co-current exchang-ers, since the flow direction of the hot stream (H1) is the sameas the directions of cold streams (C1 and C2), the temperature ofcold streams increases while the corresponding temperature of hotstream (H1) decreases. In Fig. 1, the dashed hot composite curveis divided into several intervals. In each temperature interval, themodified hot stream curves are drawn by reversing the originalhot composite curve derived from the classical pinch technology(the dashed arrowhead line). The temperature intervals are definedbased on the heat requirements and the constraint to ensure thepositive temperature difference between the hot stream and thecold stream.

Based on the classical pinch technology, the boundaries of tem-perature intervals are firstly defined by using the supply and targettemperatures of the hot stream (H1) and cold streams (C1 and C2),as well as the minimum temperature difference �Tmin,count = 20 ◦C,as shown in Fig. 1. In this case, the hot composite curve is firstlydivided into 5 intervals, and the boundaries are defined as {190,180, 150, 100, 40, 30} (see Fig. 1). The dash-dotted arrowheadcurves are the corresponding hot composite curves. However, insuch a case the �Tmin,co becomes negative (�Tmin,co < 0) whichis unfeasible in practice. Graphically, to ensure the positive tem-perature difference between the hot stream and the cold stream(�Tmin,co > 0) we can either horizontally move cold curves in theH-positive direction or increase temperature intervals. Althoughby horizontally moving cold curves the �Tmin turns out positive,the total utility consumption is obviously increased. To minimizethe utility consumption and make the design feasible, the num-ber of temperature intervals is increased. In industrial practice, thetemperature interval functions as a single pass exchanger or oneof the tubes/shells in the multipass heat exchanger. For a multi-pass exchanger, tubes are commonly equal in length, and the logmean temperature differences (LMTD) are similar in each tube.Therefore, in this case the temperature interval is equally dividedinto 2 parts to increase the �Tmin,co. As Fig. 1 shows, since thetemperature difference in the interval I and that in interval II arenegative, to ensure the positive temperature difference both inter-vals are equally divided. Graphically, the number of temperatureintervals is depended on the value of the �Tmin,co. If the mini-mum temperature difference �Tmin,co is set to be 20 ◦C, the numberof temperature intervals will be increased into infinity, which isunfeasible in practice. Therefore, in this case the minimum tem-perature difference (�Tmin,co) is selected between 0 ◦C and 20 ◦C.In Fig. 1, the solid arrowhead lines are hot composite curves when�Tmin,co = 5 ◦C. Compared with the countercurrent HEN, none of thecomposite curves is moved horizontally, thus the minimum utilityrequirement remains unchanged.

The example illustrates that the minimum utility requirementfor the co-current HEN equals the requirement of the HEN withcountercurrent exchangers, and the minimum temperature differ-ence is 0 ◦C < �Tmin,co < 20 ◦C. The results indicate that the moreintervals are divided, and the more closed to 20 ◦C the value of the

�Tmin,co will be. On the other hand, the increment of temperatureintervals which is directly related to the number of heat transferunits will increase the capital cost, and decrease the energy con-sumption at the same time. Therefore it is very necessary to select

L. Sun, X. Luo / Computers and Chemical Engineering 35 (2011) 1257–1264 1259

N with

ac

2e

tceHHurmcindm

t

Q

wpe

�

at(cbf

U

p

HEN with co-current exchangers; Ac is the heat transfer area ofthe HEN with countercurrent exchangers, and the Ap is the heattransfer area of the HEN with co-current exchangers. Compared

Fig. 1. Composite curves of the HE

proper �Tmin,co, considering both the capital cost and the energyonsumption to minimize the total cost.

.2. Minimum temperature difference of HENs with co-currentxchangers

Linnhoff et al. (1982) proposed that the optimum minimumemperature difference exists where the total cost of energy andapital investments are minimized. As we known, the heat transferfficiency of the HEN with co-current exchangers is lower than theEN with countercurrent exchangers. For the case of the co-currentEN, if the number of co-current heat exchangers is decreased, thetility consumption will be increased in order to meet the heatequirement. On the other hand, if the utility consumption and theinimum temperature difference remain the same as that of the

ountercurrent HEN, the number of units will be increased intonfinity. However, this is not feasible in practice. Therefore, it isecessary to increase the number of heat exchangers properly andecrease the minimum temperature difference �Tmin,co to mini-ize the total utility consumption.The relationship among the heat requirement, the area and the

emperature difference is described by the following equation.

= UA �TLM (1)

here the temperature difference �TLM is the log mean tem-erature difference (LMTD). For the HEN with countercurrentxchangers, it is calculated by Eq. (2).

TLM = (T2i − T1o) − (T2o − T1i)ln ((T2i − T1o)/(T2o − T1i))

(2)

For the HEN with countercurrent exchangers, the temper-ture differences are (T1, T2), as shown in Fig. 2(a). Forhe case of co-current, the temperature differences becomeT1 + T2 − �Tmin,co,�Tmin,co). When the heat requirement of theountercurrent HEN equals the co-current HEN, the relationshipetween the heat transfer area and the LMTD is described in the

ollowing equation.

cAcT2 − T1

ln T2/T1= UpAp

T1 + T2 − 2 �Tmin,co

ln ((T1 + T2 − �Tmin,co)/�Tmin,co)(3)

co-current heat exchangers only.

where Uc is the heat transfer coefficient of the HEN with counter-current exchangers, and U is the heat transfer coefficient of the

Fig. 2. Illustrations of the temperature differences: (a) one temperature interval and(b) the temperature interval is divided.

1260 L. Sun, X. Luo / Computers and Chemical

Fa

wpTfdacvedcff�wdtwmcwtt

c�EescFtattutba�ttn

k

ig. 3. The relationship between the temperature difference and the heat transferrea.

ith the case of countercurrent flow, although the minimum tem-erature difference in this temperature interval is decreased from1 to �Tmin,co, graphically the other side of the temperature dif-erence is obviously increased. Therefore the average temperatureifference and the heat exchange required area in each intervalre closed to that of the HEN with countercurrent exchangers. Theomposite curves in Fig. 2 are zoomed in from Fig. 1 shown pre-iously, and this temperature interval will be used as a simplexample. In the case of the countercurrent flow, the temperatureifferences of 2 sides are (20 ◦C and 35 ◦C), and the LMTD is cal-ulated by Eq. (2), as �TLM = (35 − 20)/(ln 35/20) = 26.8 ◦ C. Whileor the case of co-current flow in Fig. 2(a), the temperature dif-erences are (5 ◦C and 50 ◦C), and the LMTD is also calculated as

TLM = (50 − 5)/(ln 50/5) = 19.5 ◦ C. The results indicate comparedith the case of countercurrent flow, the minimum temperatureifference for the case of co-current flow is decreased from 20 ◦Co 5 ◦C. However, the LMTD is only decreased by 7.3 ◦C. In Fig. 2(b),hen the temperature interval is divided into 2 sub-intervals, theinimum temperature is increased to 12.5oC, and the LMTD is cal-

ulated as �TLM = ((100 − 65) − 12.5)/(ln (100 − 65)/12.5) = 21.9 ◦ C,hich is more closed to 26.8 ◦C. The results demonstrate the more

emperature intervals divided, the more closed the �Tmin,co andhe LMTD are to that of the countercurrent HEN.

Based on the above calculations, assuming the heat transferoefficient Uc equals Up, the minimum temperature differenceTmin,co and the corresponding heat transfer area are calculated by

q. (3), and indicated in Fig. 3. For the HEN with co-current exchang-rs, the LMTD decreases while the heat transfer area increases. Themaller the minimum temperature difference is selected, the lessorresponding number of units is added, vice versa. As shown inig. 3, when there is only 1 in the number of units in this tempera-ure interval, the �Tmin,co calculated is 5 ◦C, and the correspondingrea is increased by 26%; when the �Tmin,co is selected to be 20 ◦C,he area Ap equals the area Ac which is used for the case of the coun-ercurrent flow, and the corresponding number of heat exchangenits is increased to infinity which is unfeasible. Through calcula-ions based on the above equations, if the �Tmin,co is selected toe 12.5 ◦C while there are 2 units in this temperature interval, therea will be increased by 9.3%. If the number of units is set as 4, theT will be selected as 16.25 ◦C and compared with the case of

min,co

he countercurrent flow, the area will be increased by 3.5%. In ordero minimize the capital cost and utility consumption, balancing theumber of units and the heat exchange area, the �Tmin,co is recom-

Engineering 35 (2011) 1257–1264

mended to select to be 12.5 ◦C in this paper, and the correspondingtotal utility requirement is 9.5 MW.

In practice, the number of tubes in multipass heat exchangers iscommonly not larger than 6. The specific procedure for selecting aproper �Tmin is concluded as the following 5 steps.

(1) Based on the pinch design method, define temperature inter-vals and analyze the temperature difference.

(2) If the temperature difference is negative, the correspondingtemperature intervals are equally divided until it turns out pos-itive (�Tmin,co > 0).

(3) If the number of units in each temperature interval equalsor less than 6, the �Tmin,co is positive, and the correspond-ing increment of heat exchange area is less than 20% (see theshadow parts in Fig. 3), continue to step 4, or else use step 5.

(4) Balancing the area and the number of units, select a properminimum temperature difference �Tmin,co by using the aboveequations (Eqs. (1)–(3)).

(5) Increasing the total utility consumption until the minimumtemperature difference becomes positive, and then the proper�Tmin,co is estimated based on the above analysis.

2.3. Problem table algorithm

Graphical constructions are not the most convenient means ofdetermining energy needs, and a numerical approach called the“Problem Table Algorithm” (PTA) was developed to calculate theutility needs of a process and the location of the process pinch. Forco-current HENs, the theory of HENs synthesis is consistent withthe classical methods. Based on the previous analysis, the problemtable algorithm is developed for the HEN with co-current exchang-ers. In this algorithm, compared with the classical problem tableswhich are developed for the case of the countercurrent exchang-ers, the sub-networks are increased and the minimum temperaturedifference is decreased.

The presentation of the PTA for the co-current HEN is illustratedusing the problem described by Glemmestad, and the correspond-ing data are displayed in Table 1. The minimum temperaturedifference for the problem is 12.5 ◦C. As shown in Fig. 1, thestreams data are divided into 10 temperature intervals correspond-ing to “sub-networks” and called SN(1)–SN(10). These intervals aredefined based on the classical PTA and the analysis of the com-posite curves. As shown in Table 2, in each temperature intervalthe upper boundary of the hot stream (H1) is defined correspond-ing with the lower boundary of the cold streams (C1 and C2). Toensure the feasibility of complete heat exchange, the temperaturedifference between the upper boundary and the lower boundary ismaintained as the value of �Tmin,co.

In Table 2, the first column indicates the temperature intervals;the second column indicates the temperature boundaries for hotstreams and the third column indicates the temperature bound-aries for cold streams; the arrowhead lines indicate the directionof temperature variations. Taking the SN(3) as an example, for hotstreams the temperature interval is set to be [150 → 120], while forcold streams the corresponding interval is [100 → 107.5], and theminimum temperature difference during this interval is 12.5 ◦C. Thenet heat deficit or surplus figures are shown in column 4. The signconvention is such that a surplus is negative and a deficit positive.The calculation of the heat deficit or surplus is also based on theclassical PTA, for the sub-network SN(3), it is calculated as

D = (107.5 − 100) × (0.05 + 0.15) − (150 − 120) × 0.1 = −1.5

The amount of accumulated heat input and output is performed inthe column 5 and the column 6, and the calculation of heat flowsinput and output are shown in column 7 and column 8. In the case of

L. Sun, X. Luo / Computers and Chemical Engineering 35 (2011) 1257–1264 1261

Table 2Problem table for the HEN with co-current heat exchangers.

Sub-networks

Streams Heat Load

“Deficit”

D ,k MW

Accumulated Heat Flows

Hot Temperature Cold Input

Ik

Output

Ok

Input Output

(1) Hot Cold (1) (2)

180 167.5

SN(1) (190) 150 137.5 2.375 0 -2.375 5.5 3.125

SN(2) (180) 120 107.5 2.625 -2.375 -5 3.125 0.5

SN(3) (150) 112.5 100 -1.5 -5 -3.5 0.5 2

SN(4) (120) 100 87.5 1.75 -3.5 -5.25 2 -0.25SN(5) (112.5) 92.5 80 0.25 -5.25 -5.5 -0.25 0

SN(6) (100) 85 72.5 -0.375 -5.5 -5.125 0 0.375

SN(7) (92.5) 70 57.5 0 -5.125 -5.125 0.375 0.375

SN(8) (85) 40 27.5 0 -5.125 -5.125 0.375 0.375

cPe

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2

stmopdm

bsIt

SN(9) (70) 30 17.5

SN(10) (40)

o-current exchangers, the principle is consistent with the classicalTA which is proposed for synthesis of HENs with countercurrentxchangers.

Notice that the heat flow from SN(5) to SN(6) is 0, and the pointf zero heat flow represents the pinch location, where the temper-ture of the hot stream is 92.5 ◦C and that of the cold streams is0 ◦C. The minimum hot utility and cold utility requirement can beound from Table 2, which is 5.5 MW and 4 MW respectively. Theesults are consistent with the previous analysis.

For both the case of co-current and countercurrent flow, therocess of solving the problem table consists of dividing the tem-erature intervals, defining the number of sub-networks and theorresponding temperature boundaries, and applying the classicalTA to find the pinch location and the minimum utilities.

.4. Synthesis of HENs with co-current exchangers

Through the analysis of composite curves and PTA, the synthe-is of HENs with co-current exchangers is still based on the pinchheory, but heat transfer units is adjusted to ensure that the mini-

um temperature difference is positive. Therefore, the proceduref the synthesis mainly includes 2 steps, firstly performing theinch match based on the selection of a minimum temperatureifference, and then increasing the number of heat exchanges toinimize total cost.For HENs with co-current exchangers, the design is developed

ased on the classical pinch technology, as shown in Fig. 4. Thetreams data are used from the previous section as shown in Table 1.f heat exchangers in Fig. 4 are replaced by co-current ones directly,he HEN will no longer meet the heat requirement (12 MW). It is

Fig. 4. Flow chart of the HEN with countercurrent exchangers.

-2.625 -5.125 -2.5 0.375 3

-1 -2.5 -1.5 3 4

necessary to increase heat exchangers and decrease the minimumtemperature difference properly.

For the HEN with co-current exchangers, based on the prob-lem table shown in Table 2, the number of exchangers is increasedproperly (see Fig. 5).

In Fig. 5, the HEN meets the pinch matches rules. Compared withthe countercurrent HEN, the topology becomes more complicatedand the heat exchangers are increased. The area requirement foreach co-current exchanger is less than the countercurrent one. Forthe lower heat exchange efficiency, the co-current heat exchangersare seldom used in practical, but the above discussions establishedthe basis for solving the problem of multipass HENs.

The above results demonstrate that, for HENs with co-currentheat exchangers

(1) The hot and cold composite curves are modified, and the tem-perature intervals are increased based on the classical pinchtechnology. However, the principle of the HEN synthesis isconsistent with the classical pinch technology which was devel-oped for the HEN with countercurrent exchangers.

(2) The minimum temperature difference is lower than that ofthe countercurrent one but still positive. For multipass heatexchangers, the minimum temperature difference is not lowerthan the �Tmin,co of the HENs with co-current exchangers, andit is related to the heat transfer area and the number of tubes.

(3) A heat exchange unit functions as a tube or shell in a multipassHEN.

(4) The multipass HEN is synthesized through adjusting the num-ber of heat exchange units, and reselecting a proper minimumtemperature difference (�Tmin,co) based on the previous anal-ysis.

3. Synthesis of multipass HENs

3.1. Composite curves

For multipass HENs, both the co-current and the countercurrentflow are involved. The composite curves are drawn according to the

practical sequence of the co-current and the countercurrent flow.Take the HEN proposed by Glemmestad as an example, the param-eters are shown in Table 1. Assuming the shell side is cold streamsand the tube side is hot streams, the composite curves for the mul-

1262 L. Sun, X. Luo / Computers and Chemical Engineering 35 (2011) 1257–1264

EN wi

tie

cvcw�atth

fia

iifiptwT

Fc

Fig. 5. Flow chart of the H

ipass HEN are presented by properly combining the temperaturentervals based on the previous analysis of the HEN with co-currentxchangers only (see Figs. 6 and 7).

In Fig. 6, temperature intervals {I, II, III, IV, V} in the HEN witho-current exchangers are combined into interval I′, and the inter-als {VI, VII} are combined into interval II′. Compared with thease of co-current exchangers, temperature intervals are decreasedhich means the number of heat exchangers is decreased, while theTmin, the location of the pinch point and the utility consumption

re completely the same as that of the co-current HEN. Throughhe analysis of Fig. 6, since the temperature intervals function asubes or shells in multipass exchangers, the 2 tubes and 4 tubeseat exchangers are used.

On the other hand, when the multipass heat exchangers arerstly countercurrent and then co-current, the composite curvesre shown in Fig. 7.

In Fig. 7, temperature intervals {IV, V} are combined into thenterval II′, and temperature intervals {VI, VII, VIII} are combinednto the interval III′. In the temperature interval III′, the hot stream isrstly countercurrent flow and then co-current flow. The hot com-osite curves are drawn as the shown solid curves. The minimum

emperature difference in the temperature interval III′ is 20 ◦C,hile in the temperature interval II′ it decreased to be 13.75 ◦C.

herefore, compared with the composite curves shown in Fig. 6,

ig. 6. Composite curves of the multipass HEN which is firstly co-current and thenountercurrent.

th co-current exchangers.

the pinch location is changed, and the minimum temperature dif-ference is a little increased. The 2 tubes heat exchangers are used,and compared with the curves shown in Fig. 6 the heat transferefficiency is lower than that of the HEN with the co-current flowbefore the countercurrent flow.

The procedure to draw the composite curves for multipass HENsincludes 4 steps.

(1) Based on the basic streams data, draw the composite curvesaccording to the procedure proposed for the HEN with co-current exchangers only in the previous section, and combinethe adjacent temperature intervals.

(2) Reverse the hot composite curve according to the sequence ofthe co-current and the countercurrent flow.

(3) Select a proper minimum temperature difference �Tmin by themethod proposed for the HEN with co-current exchangers.

(4) Analyze the number of tubes in each temperature interval, if thenumber is more than 6, the corresponding temperature intervalwill be equally divided further (means increasing the numberof heat exchangers), and go to the step 3, or else the compositecurves for multipass HEN are performed.

3.2. Synthesis of multipass HENs

The synthesis of the multipass HEN is based on the HEN withco-current exchangers and the classical pinch technology used for

Fig. 7. Composite curves of the multipass HEN which is firstly countercurrent andthen co-current.

L. Sun, X. Luo / Computers and Chemical Engineering 35 (2011) 1257–1264 1263

Hc

ltIahcha

Q

wdhc

Iti

4

msbd

TB

Fig. 9. Composite curves of the multipass HEN in the case study.

TC

Fig. 8. Flow chart of the multipass HEN.

EN with countercurrent exchangers. Through the analysis of theomposite curves, the multipass HEN is obtained as shown in Fig. 8.

In Fig. 8, the number of heat exchangers is 3, the �Tmin, theocation of the pinch point and the total utility consumption arehe same as the case of co-current exchangers as shown in Fig. 5.n the multipass HEN, there are 2 tubes in heat exchangers I and II,nd 4 tubes in heat exchanger III. The flow direction in all of theseeat exchangers is firstly co-current and then countercurrent. Toalculate the heat loads and the area of each heat exchanger, theeat exchange area in each tube of the multipass heat exchanger isssumed equal, and the area is calculated by Eq. (4),

=n∑

j=1

1n

UA �TLM,j (4)

here j is the tube number; �TLM,j is the log mean temperatureifference of the jth tube; n is the number of the tubes; Q is theeat requirements. Assuming the flow rate of the heat capacity isonstant, the area is solved by the following equation.

1n

UA �TLM,j = Cphmh(Thj,i − Thj,o) (5)

n Fig. 8, the area of heat exchanger I is calculated as 148 m2, andhe area of heat exchanger II is 60 m2, the area of heat exchanger IIIs 137 m2.

. Case study

To illustrate the principles and the procedures of the proposed

ethod, a case study is presented, considering the following 4

treams problem. The streams data and cost data were introducedy Linnhoff and Hindmarsh (1983), and the minimum temperatureifference was selected to be 20 ◦C (Table 3).

able 3asic data of the heat exchanger network, case study.

No. Cpm (kW/◦C) Tin (◦C) TR (◦C)

(1) Hot 2.0 150 60(2) Hot 8.0 90 60(3) Cold 2.5 20 125(4) Cold 3.0 25 100

able 4omparison of the characters for the HEN, case study.a

Type �Tmin (◦C) Location of thepinch point

Hot streams(◦C)

Cold str(◦C)

Countercurrent 20 Behind the heat exchanger 90 70Co-current 10.5 Behind the heat exchanger 80.5 70Multipass 13.8 End point of the tube 83.8 70

a For the HEN with co-current exchangers alone or countercurrent exchangers alone, th

Fig. 10. The flow chart of the multipass HEN in case study.

In this example, according to previous discussions, the mini-mum temperature difference �Tmin is selected between 0 ◦C and20 ◦C. In Fig. 9, the hot composite curves are divided into 4 tem-perature intervals, and in each interval the minimum temperaturedifference is positive. In the interval II, the temperature difference isminimum which is 13.8 ◦C, and the corresponding area is increasedabout 10% by using Eqs. (1)–(3). Considering the trade-off betweenthe utility consumption and the network area, the minimum tem-perature difference is selected to be 13.8 ◦C.

The hot utility requirement and the cold utility requirement canbe read from Fig. 9, which is 107.5 kW and 40 kW respectively. Atthe pinch point, the temperature of hot streams is 83.8 ◦C, and thetemperature of cold streams is 70 ◦C. The 2 tubes and 4 tubes heatexchangers are applied in this HEN. As a result, based on the pinchdesign method, the HEN is synthesized and shown in Fig. 10.

The multipass HEN shown in Fig. 10 follows the basic rules ofthe classical pinch technology. There is no external heating belowthe pinch, no external cooling above the pinch and no heat transferacross the pinch. To indicate the difference of synthesis between themultipass heat exchangers and the countercurrent heat exchang-

ers, the relative characters are compared based on the same streamsdata (see Table 4). The values of minimum temperature differenceand heat exchange required area of the multipass HEN are betweenthat of the countercurrent (�Tmin,count, Ac) and the co-current HEN

eams Hot utility(kW)

Cold utility(kW)

Number of heatexchangers

Number ofunits

Total area(m2)

107.5 40 6 6 874107.5 40 26 26 1023107.5 40 9 18 919

e number of tubes is presented as the unit number.

1 mical

(opmh

5

pfltapd

(

(

(

(

emai

A

d

Reddy, K. A., Rao, Ch. D. P., & Davies, G. S. (1998). Synthesis of multipass heatexchanger networks. AIChE Journal, 44, 999–1002.

Zhu, X. X., O’Nell, B. K., Roach, J. R., & Wood, R. M. (1995). A new method for heat

264 L. Sun, X. Luo / Computers and Che

�Tmin,co, Ap). The number of co-current heat exchangers is 4 timesf countercurrent heat exchangers in this case study. For the multi-ass HEN, although the number of tubes is increase, the number ofultipass heat exchangers is still closed to that of countercurrent

eat exchangers.

. Conclusions

The classical pinch technology is modified to synthesis multi-ass HENs, which involve part countercurrent and part co-currentow. Composite curves and problem tables are used to analyzehe pinch point location, the utility consumption, and the networkrea. By taking an account of the energy-capital cost trade-offs, therocess to select a proper minimum temperature difference is alsoeveloped.

Results of the case study indicate that,

1) The composite curves of multipass HENs are drawn based onthe composite curves of co-current HENs.

2) The multipass exchanger of which the flow direction is firstlyco-current and then countercurrent is recommended.

3) The value of the minimum temperature difference (�Tmin) andthat of the heat transfer area (A) of multipass HENs are alwaysbetween those of co-current and countercurrent HENs, whichmeans �Tmin,co ≤ �Tmin ≤ �Tmin,count, Ap ≤ A ≤ Ac.

4) The principle of the synthesis for multipass HENs is consistentwith the classical pinch design method.

This work mainly focused on the multi-tubes heat exchang-rs. For the multi-shells heat exchangers, base on the developedethod further calculations and optimizations are necessary to bal-

ncing the number of shells and the total cost, which will be studiedn the following researches.

cknowledgement

This work was supported by the National Natural Science Foun-ation of China under Grant 20976193.

Engineering 35 (2011) 1257–1264

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