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 CCHHEEMMIICCAALL  EENNGGIINNEEEERRIINNGG  TTRRAANNSSAACCTTIIOONNSS  
 

VOL. 45, 2015 

A publication of 

 
The Italian Association 

of Chemical Engineering 

www.aidic.it/cet 
Guest Editors: Petar Sabev Varbanov, Jiří Jaromír Klemeš, Sharifah Rafidah Wan Alwi, Jun Yow Yong, Xia Liu  

Copyright © 2015, AIDIC Servizi S.r.l., 

ISBN 978-88-95608-36-5; ISSN 2283-9216 DOI: 10.3303/CET1545108 

 

Please cite this article as: Fu C. , Gundersen T., 2015, Appropriate placement of compressors and expanders in above 

ambient processes, Chemical Engineering Transactions, 45, 643-648  DOI:10.3303/CET1545108 

643 

Appropriate Placement of Compressors and Expanders in 

Above Ambient Processes 

Chao Fu*, Truls Gundersen 

Norwegian University of  Science and Technology, Department of Energy and Process Engineering, Kolbjoern Hejes vei 

1.A, NO-7491, Trondheim, Norway 

chao.fu@ntnu.no 

The appropriate placement of compressors and expanders is studied in this paper. Since both heat and 

work are involved, the topic is extended from heat integration to the integration of both heat and work. The 

objective is to minimize exergy consumption for the integrated processes. A set of theorems have been 

proposed for assisting the design. A graphical design methodology using the Grand Composite Curve is 

developed that achieves the target of minimum exergy consumption. 

1. Introduction 

The concept of Appropriate Placement, also referred to as Correct Integration, is fundamental in Pinch 

Analysis, and a special case of the plus/minus principle (Linnhoff and Vredeveld, 1984). A quantitative 

approach is based on the Grand Composite Curve (GCC) that gives the amount of heat that can be 

correctly integrated. While this type of analysis is simple for reactors (Glavič et al., 1988), distillation 

columns (Linnhoff et al., 1983), evaporators (Smith and Linnhoff, 1988), heat pumps and heat engines 

(Townsend and Linnhoff, 1983), it is considerably more complicated for compressors and expanders since 

both heat and work are involved. The problem is extended to the integration of both heat and work. In 

addition, the shape of the GCC will change since the streams to be compressed or expanded are included 

when drawing the GCC. The placement of compressors was shortly discussed in the work by Glavič et al. 

(1988) with focus on reactor systems. Aspelund et al. (2007) formulated two heuristic rules for the 

placement of compressors and expanders in heat exchanger networks (HENs): (i) compression adds heat 

to the system and should preferably be done above Pinch, and (ii) expansion provides cooling to the 

system and should preferably be done below Pinch. The rules were stated more specifically by Gundersen 

et al. (2009) in the sense that both compression and expansion should start at the pinch temperature. An 

application example is the recuperative vapour recompression cryogenic air distillation process developed 

by Fu and Gundersen (2013). Another application is the N2 Brayton cycle in oxy-combustion processes (Fu 

and Gundersen, 2014). On the basis of the heuristic rules proposed by Gundersen et al. (2009), 

Wechsung et al. (2011) presented an MINLP optimization formulation for the synthesis of sub-ambient 

HENs including compression and expansion. The work is further extended by Onishi et al. (2014) using a 

superstructure with the objective of minimizing total annualized cost.  

The integration of compressors and expanders into HENs is not a straightforward task following the 

heuristic rules proposed by Gundersen et al. (2009). This paper presents a systematic methodology for 

such integration in above ambient processes. The objective is to minimize exergy consumption. A 

straightforward graphical design procedure is proposed on the basis of a set of theorems. 

2. Problem statement 

The following problem is to be solved: “Given a set of process streams with supply and target states 

(temperature and pressure), as well as utilities for power, heating and cooling, design a network of heat 

exchangers, compressors and expanders in such a way that the exergy consumption is minimized or the 

exergy production is maximized”. 



 
644 

 
Table 1: Stream data 

Stream  
s

T , 
o
C tT , 

o
C pmc , kW/

o
C H , kW sp , bar tp , bar 

H1 400 35 2 730 2 1 

H2 320 160 4 640 - - 

H3 110 35 3 225 - - 

C1 15 380 3 1095 1 2 

C2 190 250 10 600 - - 

Hot utility 400 400 - - - - 

Cold utility 15 15 - - - - 

 

As an illustrative example, the stream data is shown in Table 1, where sT  and tT  are the supply and 

target temperatures, sp  and tp  are the supply and target pressures, pmc  is the heat capacity flowrate, and 

ΔH  is the enthalpy change due to temperature change. The following assumptions are made: (1) 

polytropic efficiency for compressors and expanders = 1, (2) minimum temperature difference for heat 

transfer minT = 20 °C, (3) ambient temperature  0T = 15 °C, (4) cold utility at CUT  =1 5 °C and hot utility at 

HU
T  = 400 °C are available, and (5) the fluid to be compressed/expanded is ideal gas with constant 

specific heat ratio  = 1.4. The question to be addressed is at what temperatures C1 and H1 should be 

compressed/expanded so that the exergy consumption is minimised. 

3. Theorems 

The following four theorems are proposed for the integration of compressors in above-ambient HENs (the 

proof is not included due to space limitation): 

(1) A HEN design with Pinch Compression (compression starts at pinch temperature 
PI

T ) consumes 

the smallest amount of exergy if the following conditions are satisfied: (i) the outlet temperature of 

Ambient Compression (compression starts at 
0

T ), 
comp,0

T , is lower than 
HU

T , and (ii) Pinch 

Compression does not produce more heating than required. 

(2) If the heating demand has been satisfied by Pinch Compression, Ambient Compression is used 

for the remaining portion if 
comp,0 PI

T T . 

(3) If the heating demand has been satisfied by Pinch Compression and 
comp,0 PI

T T , Ambient 

Compression is used for the remaining portion and the corresponding heat (above pinch) should 

be utilized to reduce the portion using Pinch Compression. 

(4) The compression is done at 
0

T  if 
comp,0 HU

T T . 

T’ (
o
C)

H (kW)

T’0

T’PI

Qcomp,max
T’comp,PI

QHU,0

a
b

cd

Qexp,max

T’exp,PI

a'

b'

c'

d'

e'

f'

QCU,0

T’HU

 

Figure 1: GCC without pressure manipulation 



 
645 

Calculate                comp,0T

exp,HU 0
[T T ?]

Compression at 

Yes No

Draw the GCC without 

pressure manipulation, 

determine 

YesNo

0
T

p exp,PI,max
[(mc ) ]

p p exp,PI,max
[(mc ) (mc ) ?]

Pinch Compression [Pinch 

Expansion] is implemented 
The  stream is split. The 

portion for Pinch Compression 

[Expansion] is   

p exp,PI,max
[(mc ) ]

Draw new GCC without 

pressure manipulation for the 

remaining portion, find new 

p exp,PI,max
[(mc ) 0 ?]

[Expansion at      or      ]
0

T

YesNo

exp,HU PI
[T T ?]

No

Yes
New GCCs are produced 

and pressure is manipulated 

only for the portion with 

compression [expansion] at        

              , find 

The          is reduced by 

the portion compressed 

[expanded] at  

p
mc

exp,HU
[T ]

HU comp,0
T T ?

[Expansion at        ]HUT
p comp,PI,max

(mc )

p p comp,PI,max
(mc ) (mc ) ?

p comp,PI,max
(mc )

p exp,PI,max
[(mc ) ]p comp,PI,max(mc )

p comp,PI,max
(mc ) 0 ? PI comp,0T T ?

Compression at      
0

T

The remaining portion is 

compressed [expanded] at       

                and added to the 

total portion for compression 

[expansion] at

0
T

HU
[T ]

p exp,PI,max
[(mc ) ]

p comp,PI,max
(mc )

HU
T

0
T

HU
[T ]

0
T

HU
[T ]

0
T

HU
[T ]

 

Figure 2: The design procedure 

Similarly, the following four theorems are proposed for the integration of expanders in above ambient 

HENs: 

(5) A HEN design with Pinch Expansion (expansion starts at 
PI

T ) consumes the smallest amount of 

exergy if the following conditions are satisfied: (i) the outlet temperature of expansion at 
HU

T , 

exp,HU
T , is higher than 

0
T , and (ii) Pinch Expansion does not produce more cooling than required. 

(6) If the cooling demand has been satisfied by Pinch Expansion, the remaining expansion should be 

done at 
HU

T  or 
0

T  if 
exp,HU PI

T T . 

(7) If the cooling demand has been satisfied by Pinch Expansion and 
exp,HU PI

T <T , the remaining 

expansion should be done at 
HU

T  and the corresponding cooling (below Pinch) should be utilized 

to reduce the portion using Pinch Expansion. 

(8) Expansion should be done at 
HU

T  if 
exp,HU 0

T T . 

4. Design procedure 

Figure 1 shows the GCC for process streams without pressure manipulation. Modified temperatures ( T ' ) 

are used (for cold streams minT' T 0.5 T   and for hot streams minT' T 0.5 T   ). The outlet temperature 

of Pinch Compression/Expansion is comp,PIT '  and exp,PIT ' . A temperature is defined as a Potential Pinch 



 
646 

 
Point if it may create a new pinch after the heating/cooling effect caused by Pinch Compression/Expansion 

is included. The following temperatures are Potential Pinch Points: (i) the convex kink points on the GCC 

in the region between exp,PIT T'  and comp,PIT T '  (such as points a, b, a’ and b’); (ii) the points comp,PIT T'  

and exp,PIT T '  on the GCC (points c and c’), or the point with the lowest temperature on the GCC (point d’)  

if exp,PIT '  is lower than this temperature and the point with the highest temperature if comp,PIT '  is higher than 

the temperature; (iii) the intersection point between the constant temperature line exp,PIT T'  (or 

comp,PI
T T' ) and a pocket (point e’) on the GCC. 

The maximum portion of the stream that can use Pinch Compression, p comp,PI,max(mc ) , is determined by the 

following steps: starting at the pinch point ( PIT' ), draw lines between the pinch point and Potential Pinch 

Points (above pinch) and extend the line with the largest slope until it intersects with the constant 

temperature line ( comp,PIT T' ). The corresponding heating demand at the intersection (point d in Figure 1), 

comp,max
Q , is equal to the maximum work resulting from Pinch Compression, and p comp,PI,max(mc )  can thus be 

determined as comp,max comp,PI PIQ / (T' T' ) . If the pmc  of the stream to be compressed is larger than 

p comp,PI,max
(mc ) , stream splitting is required and the fraction of the stream using Pinch Compression is 

p comp,PI,max
(mc ) . The maximum portion of the stream that uses Pinch Expansion, p exp,PI,max(mc ) , is 

determined in a similar way: starting at the Pinch Point, draw lines between the pinch point and Potential 

Pinch Points (below Pinch) and extend the line with the largest negative slope until it intersects with the 

constant temperature line ( exp,PIT T' ). The corresponding cooling demand exp,maxQ  at the intersection 

(point f’ in Figure 1) is equal to the maximum work resulting from Pinch Expansion, and p exp,PI,max(mc )  is 

determined as exp,max PI exp,PIQ / (T' T' ) . Stream splitting is required if p p exp,PI,maxmc (mc )  and the fraction of 

the stream using Pinch Expansion is p exp,PI,max(mc ) . 

On the basis of the theorems, a graphical design procedure has been developed and is illustrated in 

Figure 2. The case for the integration of expanders is presented in brackets and not explained in detail. 

The first step is to calculate comp,0T  and compare it with HUT . According to Theorems 1 and 4, compression 

should start at 0T  if comp,0 HUT T  and at PIT  if comp,0 HUT T . When Pinch Compression is used, according to 

Theorem 1, the entire stream is compressed at PIT  if its pmc  is less than p comp,PI,max(mc ) , which is 

determined using the concept of Potential Pinch Points. Otherwise, the stream is split and Pinch 

Compression is used for the portion p comp,PI,max(mc ) . A new GCC is then produced, where the pressure 

manipulation of the portion with Pinch Compression, i.e. the heating or cooling of the portion from sT  to 

PI
T  before compression and from comp,PIT  to tT  after compression are included. The pressure manipulation 

of the remaining portion should not be included. The portion available for compression at new pinch 

temperatures can then be determined. The procedure is repeated until either the entire stream has been 

compressed or the heating demand has been completely satisfied (i.e. the pinch problem has become a 

threshold problem, p comp,PI,max(mc ) =0). In the latter case, according to Theorem 2, the remaining portion of 

the stream is compressed at 0T  if comp,0 PIT T . Otherwise, and according to Theorem 3, the portion for 

compression at the original PIT  should be reduced and an iterative procedure is required: A new GCC is 

produced by including pressure manipulation only for the portion of the stream with compression at 0T  

(the other portion of the stream is included in the GCC without pressure manipulation), and the procedure 

for implementing Pinch Compression is repeated. The procedure stops if the entire stream has been 

compressed, otherwise the portion for compression at 0T  increases until comp,0T  is lower than the new 

Pinch temperatures (which means that the Pinches below comp,0T  have been removed). When the heating 

demand has been completely satisfied by compression at the new pinch point(s) above comp,0T , the 

remaining portion of the stream should be compressed at 0T . 

 



 
647 

(a) 

0
50

100
150
200
250
300
350
400
450

0 100 200 300 400 500

T
 '
 (

°C
)

H (kW)

T 'exp,PI =113.2
oC

Qexp,max=100 kW

T 'comp,PI =301.4
oC

Qcomp,max=270 kW

 
(b) 

0
50

100
150
200
250
300
350
400
450

0 200 400 600 800

T
 '
 (

°C
)

H (kW)  

(c) 

0
50

100
150
200
250
300
350
400
450

0 100 200 300 400

T
 '
 (

°C
)

H (kW)  (d) 

0
50

100
150
200
250
300
350
400
450

0 100 200 300

T
 '
 (

°C
)

H (kW)  

Figure 3: GCCs: (a) Case O; (b) Case I; (c) Case II; (d) Case III 

5. Illustrative example 

For the stream data presented in Table 1, the GCC for Case O without pressure manipulation is presented 

in Figure 3(a). The pinch temperature is 200 °C. The following three cases are studied: Case I - H1 is 

expanded at HUT  (the highest temperature) and C1 is compressed at 0T  (the lowest temperature); Case II 

- both compression and expansion start at PIT ; Case III - the proposed procedure is applied. For Cases I 

and II, the design is straightforward. For Case III,  comp,0T = 78.1 °C HU<T  and  exp,HUT = 279.1 °C 0>T , Pinch 

Compression/Expansion should be used (Theorems 1 and 5). The work resulting from Pinch 

Compression/Expansion is determined to be  comp,maxQ = 270 kW and  ,maxexpQ = 100 kW based on Figure 

3(a). The maximum portions are determined to be  p comp,PI,max(mc ) = 2.66 kW/°C and  p exp,PI,max(mc ) = 1.15 

kW/°C. Streams C1 and H1 should thus be split: the first portions (indexed α) are compressed/expanded at 

PI
T  while the remaining portions are temporarily not compressed/expanded. A new GCC is then drawn and 

two new pinch points are created at 100 and 310 °C. The maximum portions compressed/expanded at the 

new pinch temperatures can thus be determined with a similar procedure using the concept of Potential 

Pinch Points: p comp,PI,max,new(mc ) = 0.64 kW/°C and p exp,PI,max,new(mc ) = 2.18 kW/°C. The remaining portions 

(indexed β) of streams H1 and C1 can thus be completely compressed/expanded at the new PIT .  

Table 2: New stream data for H1 and C1 

Streams  
s

T , °C tT , °C pmc , kW/°C H , kW sp , bar tp , bar 

Case I       

H1 279.1 35 2 488.2 1 1 

C1 78.1 380 3 905.7 2 2 

Case II       

H1_1 400 210 2 380 2 2 

H1_2 123.2 35 2 176.4 1 1 

C1_1 15 190 3 525 1 1 

C1_2 291.4 380 3 265.8 2 2 

Case III       

H1_α1 400 210 1.15 218.5 2 2 

H1_α2 123.2 35 1.15 101.4 1 1 

H1_β1 400 110 0.85 246.5 2 2 

H1_β2 41.2 35 0.85 5.3 1 1 

C1_α1 15 190 2.66 465.5 1 1 

C1_α2 291.4 380 2.66 235.7 2 2 

C1_β1 15 300 0.34 96.9 1 1 

C1_β2 425.5 380 0.34 15.5 2 2 



 
648 

 
Table 3: Performance comparison 

Cases O I II III 

Hot utility demand, kW 350 591.8 119.4 37.6 

Cold utility demand, kW 250 439.3 150 91.7 

Pinch temperature, 
o
C 200 200 100 100; 200; 310 

Compression work, kW - 189.3 304.2 312.4 

Expansion work, kW - 241.8 173.6 158.3 

Exergy consumption, kW - 286.0 198.9 175.6 

 

Due to pressure manipulation, the new data for streams H1 and C1 are shown in Table 2 and the 

corresponding GCCs are shown in Figure 3. The performance comparison is presented in Table 3. 

Compared to Case I (compression at 0T  and expansion at HUT ), the exergy consumption is reduced by 

30.5 % when both compression and expansion start at PIT  (Case II) following the heuristic rules proposed 

by Gundersen et al. (2009). However, the original pinch has been removed according to Figure 3(c), 

indicating that too large portions have been compressed/expanded at PIT . Minimum exergy consumption is 

achieved when the proposed procedure is applied (Case III). The exergy consumption is reduced by 

38.6 % compared to Case I. The reason for exergy savings is that the heat resulting from both 

compression and expansion has been completely utilised. This fact can be observed by comparing Cases 

III and O. The heating/cooling demand in Case III is reduced by an amount equal to the 

compression/expansion work.  

6. Conclusions 

A systematic methodology for the integration of compressors and expanders into heat exchanger networks 

above ambient temperature has been developed. The objective has been to minimize exergy consumption 

since both heat and work are involved. The Grand Composite Curve has been used as a tool in the 

graphical design procedure. Considerable exergy savings (38.6 %) have been achieved in the illustrative 

example by maximum utilization of Pinch Compression/Expansion.   

References 

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utilizing pressure based exergy for subambient cooling, Appl. Therm. Eng., 27(16), 2633-2649. 

Fu C., Gundersen T., 2013, Recuperative vapor recompression heat pumps in cryogenic air separation 

processes, Energy, 59, 708-718. 

Fu C., Gundersen T., 2014, N2 Brayton cycle in oxy-combustion power plants, Chemical Engineering 

Transactions, 39, 223-228. 

Glavič P., Kravanja Z., Homšak M., 1988, Heat integration of reactors - I. Criteria for the placement of 

reactors into process flowsheet, Chem. Eng. Sci., 43(3), 593-608. 

Gundersen T., Berstad D.O., Aspelund A., 2009, Extending Pinch Analysis and Process Integration into 

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placement of heat engines and heat pumps in process networks, AIChE J., 29(5), 742-748. 

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