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International Journal of Research in Engineering and Innovation Vol-1, Issue-4 (2017), 135-147 __________________________________________________________________________________________________________________________________

International Journal of Research in Engineering and Innovation

(IJREI) journal home page: http://www.ijrei.com

ISSN (Online): 2456-6934

_______________________________________________________________________________________

Corresponding author: R.S. Mishra

Email Id: [email protected] 135

Exergy analysis of dual compressor linde system

Mishra. R. S, Devendra Kumar

Department of Mechanical, Production Industrial and Automobiles Engineering, Delhi Technological University Delhi-110042

Corresponding author: [email protected]

_______________________________________________________________________________________

Abstract

The present studies concern on energy and exergy analyses of Dual Compressor Linde System. A parametric study is conducted to

investigate the effects of variation of various system input parameters such as pressure ratio, expander mass flow ratio, compressor

output temperature on different performance parameters like COP , work input ,liquefaction rate ,specific heat and exergy. The

numerical computations have been carried out for Dual Compressor Linde System are study with six different gases for liquefaction

like oxygen, argon, methane, fluorine, air and nitrogen respectively. Effect of different input gas also studies carefully and behaviour

of different gases in different system is presented in this paper. © 2017 ijrei.com. All rights reserved

Keywords: First and second law Analysis Dual Compressor Linde System, Thermodynamic (Energy-Exergy) Analysis

__________________________________________________________________________________________________________

1. Introduction

To achieve a very low temperature for refrigeration process

the gas must be liquefied .To do so mainly two methods i.e.

isentropic expansion in which the gas is expanded

isentropically to produce low temperature, basically used in

aircraft refrigeration system and cryogenic technology is used

for production of liquefied gases for industrial and commercial

applications. In the cryogenic process, the liquefaction and

purification of gases are done. Although the cryogenic process

is very critical for aerospace application and this technology

is also used for wind tunnel testing because high performance

wind tunnel required rapid movement of nitrogen gas around

the aerodynamic circuit. Cryogenic process is required for

Frozen Food Industries for preservation of food item

depending upon type of food item and whether they are

cooked or not before freezing. Cryogenic has got lot of

application in medical field. It is wildly used in MRI

equipment for diagnosis of diseases. Linde Hampson cycle is

enable to liquefy large number of gas but in a very inefficient

way. Compression in one stage consumes more work than the

work used in multi compression system. Dual pressure Linde

system is a modification of simple Linde system. It

modification based on the concept that multi-compression is

more efficient than the single stage compression system. In

Dual compressors Linde system two compressors L.P and H.P

are used with two separation units employing single heat

exchanger unit as comparison of simple Linde system. The

whole modification is done to get high output of liquefaction

gas with high efficiency. Fig shows the block and T-S diagram

of Dual Pressure Linde system.

Figure 1(a): Schematic of Dual compressor Linde system

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R.S. Mishra et al/ International journal of research in engineering and innovation (IJREI), vol 1, issue 4 (2017), 135-147

136

Figure 1(b): T-S diagram of Dual compressor Linde system

2. Use of entropy generation method for computing

exergy for finding irreversibility in the system

Whole part of heat energy can never be converted completely

into work, there some part of energy which used and second

which get waste, the useful part of energy that is able to

convert into heat is called available energy or exergy and

unavailable part which get destroyed is called unavailable

energy or exergy. As the first law of thermodynamics state that

the energy is always conserved but the content of that energy

which is capable of producing useful work is not constant that

is exergy. The maximum useful work or exergy at a particular

state is a composite property depending upon the state of

system and surrounding. A dead state having Zero exergy that

is equilibrium state. The exergy analysis allows us to identify

and quantify the sites with the losses of exergy, and therefore

showing the direction for the minimization of exergy losses to

approach the reversible COP.

R. Agrawal,et.al [1] carried out exergy analysis for efficient

cryogenic nitrogen generators: Gadhiraju Venkatarathnam

[2], also carried out Simulation of cryogenic processes , J.

Rizk, M.et.al, [3] carried out exergy optimization of a

cryogenic air separation unit,

Yasuki Kansha, et.al [4], developed novel cryogenic air

separation process based on self-heat recuperation. R.L.

Cornelissen, [5], carried out the energy-exergy analysis of

cryogenic air separation system.

From literature it noticed that exergy efficiency depend upon

mainly upon the inlet condition of the system but which inlet

condition best suit for a particular type of the system except to

increase the whole system efficiency stress are done on

particular parts of system From the literature review, it

conclude that every part of system has its own and equal

importance because ones effect on another whether it is small

or big create a lot of difference in proper analysis of system.

Ignoring one small system due less effect can put research gap

in complete thermodynamic analysis of system that why it

quite important take all parts of system as one and finding out

the every part impact on another to calculate right equation for

high output. Therefore following objectives of present

investigations are thermodynamic (energy-exergy) analysis of

considered systems and finding exergy destruction in each and

there individuals components and to suggestion for reducing

exergy destruction losses in whole systems and there

components. The effects of pressure ratio and gas outlet

temperature of compressor on various energy- and exergy-

based performance parameters are investigated considering all

six gases as the gas being liquefied. Mathematical

3. Modelling of Dual Compressor Linde System

𝑅$ =′ 𝐺𝑎𝑠′

𝑚4 = 1

𝑚4 = 𝑚7 + 𝑚12

𝑇0 = 298

𝑇1 = 300 K

𝑇4 = 𝑇3

𝑇3 =𝑇2+𝑇13

2

𝑃1 = 1.013

𝑃2 =𝑃4

5

𝑃4 = 80 3.1 Analysis of Compressor

𝑄1 = 𝑚10 ∗ (ℎ2 − ℎ1) (12)

𝑊𝑐1 = (𝑚10 ∗ ((ℎ2 − ℎ1)) − 𝑇2 ∗

(𝑠2 − 𝑠1))

𝐸𝑑𝑐𝑜𝑚𝑝1 = (

𝑚10 ∗ 𝑇2 ∗ (𝑠1 − 𝑠2) −

(𝑄1 ∗ (𝑇0

𝑇2))

)

𝑄2 = 𝑚4 ∗ (ℎ4 − ℎ3)

𝑊𝑐2 = (𝑚4 ∗ ((ℎ4 − ℎ3)) −

𝑇4 ∗ (𝑠4 − 𝑠3))

𝐸𝑑𝑐𝑜𝑚𝑝2 = (

𝑚4 ∗ 𝑇4 ∗ (𝑠3 − 𝑠4) −

(𝑄2 ∗ (𝑇0

𝑇4))

)

𝑊𝑁𝑒𝑡 = 𝑊𝑐2 + 𝑊𝑐1

𝐶𝑂𝑃 =ℎ1−ℎ10

𝑊𝑁𝑒𝑡

3.2 Analysis of heat exchanger

𝑃5 = 𝑃4

𝑚ℎ = 𝑚4

𝑚𝑐 = 𝑚12

𝐶ℎ = 𝑚ℎ ∗ 𝑐𝑝ℎ𝑜𝑡𝑓𝑙𝑢𝑖𝑑𝐻𝑋

𝐶𝑐 = 𝑚𝑐 ∗ 𝑐𝑝𝐶𝑜𝑙𝑑𝑓𝑙𝑢𝑖𝑑𝐻𝑋

𝑞ℎ𝑥 = 𝐶ℎ ∗ (𝑇4 − 𝑇5)

𝑞ℎ𝑥 = 𝐶𝑐 ∗ (𝑇13 − 𝑇12)

http://link.springer.com/search?facet-author=%22Gadhiraju+Venkatarathnam%22


137

"𝑇𝑦𝑝𝑒𝐻𝑋$ =′ 𝑐𝑜𝑢𝑛𝑡𝑒𝑟𝑓𝑙𝑜𝑤′”

𝑞𝑚𝑎𝑥 = 𝐶𝑚𝑖𝑛 ∗ (𝑇4 − 𝑇12)

𝑒𝑝𝑠𝑖𝑙𝑜𝑛 =𝑞ℎ𝑥

𝑞𝑚𝑎𝑥

𝑒𝑝𝑠𝑖𝑙𝑜𝑛 = .85

𝑁𝑡𝑢 = 𝐻𝑋(𝑇𝑦𝑝𝑒𝐻𝑋$, 𝑒𝑝𝑠𝑖𝑙𝑜𝑛, 𝐶ℎ, 𝐶𝑐, 𝑁′ 𝑡𝑢′)

𝐸𝑥𝑖𝑛𝐻𝑋= 𝑚4 ∗ ((ℎ4 − ℎ5) − (𝑇0 ∗ (𝑠4 − 𝑠5)))

𝐸𝑥𝑜𝑢𝑡𝐻𝑋= 𝑚12 ∗ ((ℎ12 − ℎ13) − (𝑇0 ∗ (𝑠12 − 𝑠13)))

𝐸𝑑𝐻𝑋 = ((𝐸𝑥𝑖𝑛𝐻𝑋) − (𝐸𝑥𝑜𝑢𝑡𝐻𝑋

)) (33)

3.3 Thermodynamic Analysis of Valve

ℎ5 = ℎ6

𝐸𝑥𝑖𝑛𝑉𝑎𝑙= (ℎ5 − ℎ0) − 𝑇0 ∗ (𝑠5 − 𝑠0)

𝐸𝑥𝑜𝑢𝑡𝑣𝑎𝑙= (ℎ6 − ℎ0) − 𝑇0 ∗ (𝑠6 − 𝑠0)

𝐸𝑑𝑣𝑎𝑙1 = (𝐸𝑥𝑖𝑛𝑉𝑎𝑙− 𝐸𝑥𝑜𝑢𝑡𝑣𝑎𝑙

)

"Analysis of seperator"

𝑚4 ∗ ℎ6 = ((𝑚7 ∗ ℎ7) + (𝑚12 ∗ ℎ12))

𝑥7 = 0

𝑥12 = 1

𝐸𝑑𝑠𝑒𝑝1= (𝑇0 ∗ (

((𝑚12 ∗ 𝑠12) − (𝑚4 ∗ 𝑠6)) +

((𝑚12∗ℎ12)−(𝑚7∗ℎ7)

𝑇12)

))

3.4 Thermodynamic Analysis of heat exchanger

𝑚12 ∗ ℎ12 + 𝑚10 ∗ ℎ10 = 𝑚12 ∗ ℎ13 + 𝑚10 ∗ ℎ11

"Analysis of Valve"

h7=h8

𝐸𝑥𝑖𝑛𝑉𝑎𝑙2= (ℎ7 − ℎ0) − 𝑇0 ∗ (𝑠7 − 𝑠0)

𝐸𝑥𝑜𝑢𝑡𝑣𝑎𝑙2= (ℎ8 − ℎ0) − 𝑇0 ∗ (𝑠8 − 𝑠0)

𝐸𝑑𝑣𝑎𝑙2 = 𝑎𝑏𝑠(𝐸𝑥𝑖𝑛𝑉𝑎𝑙2− 𝐸𝑥𝑜𝑢𝑡𝑣𝑎𝑙2

)

3.5 Thermodynamic Analysis of separator

𝑚7 ∗ ℎ8 = ((𝑚9 ∗ ℎ9) + (𝑚10 ∗ ℎ10))

𝑚7 = 𝑚9 + 𝑚10

𝑚9 = 𝑚𝑓

𝑚10 = 𝑚𝑔

𝑥9 = 0

𝑥10 = 1

𝐸𝑑𝑠𝑒𝑝2= 𝑎𝑏𝑠 (𝑇0 ∗ (

((𝑚10 ∗ 𝑠10) − (𝑚7 ∗ 𝑠8))

+ ((𝑚10∗ℎ10)−(𝑚9∗ℎ9)

𝑇10)

))

𝐸𝑑𝑐𝑜𝑚𝑝1%= (

𝐸𝑑𝑐𝑜𝑚𝑝1

𝐸𝑑𝐷𝑢𝑎𝑙𝐶𝑜𝑚𝑝𝐿𝑖𝑛𝑑𝑒

) ∗ 100

𝐸𝑑𝑐𝑜𝑚𝑝2%= (

𝐸𝑑𝑐𝑜𝑚𝑝2


) ∗ 100

𝐸𝑑𝐻𝑋%= (

𝐸𝑑𝐻𝑋


) ∗ 100

𝐸𝑑𝑣𝑎𝑙1%= (

𝐸𝑑𝑣𝑎𝑙1


) ∗ 100

𝐸𝑑𝑠𝑒𝑝1% = (

𝐸𝑑𝑠𝑒𝑝1


) ∗ 100

𝐸𝑑𝑣𝑎𝑙2%= (

𝐸𝑑𝑣𝑎𝑙2


) ∗ 100

𝐸𝑑𝑠𝑒𝑝2%= (

𝐸𝑑𝑠𝑒𝑝2


) ∗ 100

𝐸𝑡𝑎2𝑛𝑑%= 𝑎𝑏𝑠 ((𝑚9 ∗

(ℎ9 − ℎ1) − 𝑇0 ∗ (𝑠9 − 𝑠1)

𝑊𝑁𝑒𝑡

) ∗ 100)

𝐸𝑑𝐷𝑢𝑎𝑙𝐶𝑜𝑚𝑝𝐿𝑖𝑛𝑑𝑒= 𝐸𝑑𝑐𝑜𝑚𝑝1 + 𝐸𝑑𝑐𝑜𝑚𝑝2 +

𝐸𝑑𝐻𝑋 + 𝐸𝑑𝑣𝑎𝑙1 + 𝐸𝑑𝑣𝑎𝑙2 + 𝐸𝑑𝑠𝑒𝑝1+ 𝐸𝑑𝑠𝑒𝑝2

In Non-ideal gas any variable can be defined by two other

dependent variable on them:

𝑎𝑛𝑜𝑛−𝑖𝑑𝑒𝑎𝑙 𝑔𝑎𝑠 = 𝑓𝑥(𝑏, 𝑐)

Table 1: Variable Table (Dual Compressor system)

Variable

(a)

Gas Variable

(b)

Variable

(c )

ℎ0 𝑅$ 𝑇0 𝑃1

ℎ1 𝑅$ 𝑇1 𝑃1

ℎ2 𝑅$ 𝑇2 𝑃2

𝑠0 𝑅$ 𝑇0 𝑃1

𝑠1 𝑅$ 𝑇1 𝑃1

𝑠2 𝑅$ ℎ2 𝑃2

𝑠3 𝑅$ 𝑇3 𝑃2

ℎ3 𝑅$ 𝑇3 𝑃2

𝑠4 𝑅$ ℎ4 𝑃2

ℎ4 𝑅$ 𝑇4 𝑃2

𝑐𝑝(ℎ𝑓)𝐻𝑋 𝑅$ 𝑇4 𝑃4

𝑐𝑝(𝑐𝑓)𝐻𝑋 𝑅$ 𝑇13 𝑃2

𝐶𝑚𝑖𝑛 - 𝐶ℎ𝑜𝑡_𝐻𝑋 𝐶𝑐𝑜𝑙𝑑_𝐻𝑋

ℎ7 𝑅$ 𝑋7 𝑃2

𝑠7 𝑅$ 𝑋7 𝑃2

𝑠6 𝑅$ ℎ6 𝑃2

𝑋6 𝑅$ ℎ6 𝑃2

𝑋8 𝑅$ ℎ8 𝑃1

𝑇6 𝑅$ ℎ6 𝑃2

𝑠5 𝑅$ ℎ5 𝑃4

𝑇5 𝑅$ ℎ5 𝑃4

𝑇8 𝑅$ ℎ8 𝑃1

𝑠8 𝑅$ ℎ8 𝑃1

ℎ9 𝑅$ 𝑋9 𝑃1

𝑠9 𝑅$ 𝑋9 𝑃1

ℎ10 𝑅$ 𝑋10 𝑃1

𝑠10 𝑅$ ℎ10 𝑃1

𝑇10 𝑅$ ℎ10 𝑃1

ℎ12 𝑅$ 𝑋12 𝑃2

𝑠12 𝑅$ ℎ12 𝑃2

𝑇12 𝑅$ ℎ12 𝑃2

ℎ13 𝑅$ 𝑇13 𝑃2

𝑠13 𝑅$ 𝑇13 𝑃2

The effects of pressure ratio and gas outlet temperature of

compressor on various energy- and exergy-based performance

parameters are investigated considering all six gases as the gas

being liquefied.


138

4. Result and Discussion

Figure 2(a): COP and second law efficiency versus high pressure

compressor ratio

Figure 2(b): Liquefaction rate versus high pressure compressor

Ratio

Figure 3: Net work done versus high pressure compressor ratio

Figure 4: Specific heat of hot fluid of heat exchanger versus high

pressure compressor ratio

40 60 80 100 120 140 160 180 200 220

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

0

2

4

6

8

10

12

14

16

18

20

22

24

P4 (Compressor pressure ratio)(HP) bar)

CO

P

h2

nd

,%

COPoxygen

COP argon

COP methane

COP Fluorine

COP AirCOP

Nitrogen

h2nd,%oxygen

h2nd,%Argon

h2nd,% Methane

h2nd,%Fluorine

h2nd,%Airh2nd,%

Nitrogen

40 60 80 100 120 140 160 180 200 2200.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0.14


mf(L

iq m

ass)(kg

/s)

mf(Oxygen)

mf(Argon)

mf(Methane)

mf(Fluorine)

mf(Air)

mf(Nitrogen)

40 60 80 100 120 140 160 180 200 220

200

250

300

350

400

450

500

550

600

650

700

750

800


Wn

et(N

et.w

ork)(K

J/K

g)

Wnet(Oxygen)

Wnet(Argon)

Wnet(Methane)

Wnet(Fluorine)

Wnet(Air)

Wnet(Nitrogen)

40 60 80 100 120 140 160 180 200 2200.50.70.91.11.31.51.71.92.12.32.52.72.93.13.33.53.73.94.14.34.5


cp

hf(H

X)(K

j/K

g-K

)

cphot,fluid,HX(Oxygen)

cphot,fluid,HX(Argon)

cphot,fluid,HX(Methane)

cphot,fluid,HX(Fluorine)

cphot,fluid,HX(Air)

cphot,fluid,HX(Nitrogen)


139

Figure 5: NTU versus high pressure compressor ratio

Figure 6: Exergy destruction rate versus high pressure compressor

ratio

In fig.2 the optimum pressure ratio 0.4 gases like nitrogen, air

and methane is 60PR while for the fluorine oxygen, argon it is

80PR the air nitrogen second law efficiency first increasing up

to 60PR but after further increase in pressure ratio it show

decrement up to 140PR. While other gases achieving after

their optimum PR they show continuous decrement or fall in

second law efficiency. While in COP case all gases show

decrease in COP by increasing the PR. In fig.3 the liquefaction

rate start decreasing after achieving their optimum PR but

gases like air and nitrogen show huge decrease in liquefaction

rate but after 140PR they show almost negligible rate of

liquefaction fig. 4 show net work done for liquefaction of

gases with increase in pressure ratio. It is very important factor

to know how much work done is required for liquefaction to

cost optimization and system design parameters. From

thermodynamic analysis, it depicts that almost all gases show

increase in work done as the pressure ratio of the system

increases. For Dual Linde compressor system argon show

least work requirement while gases like methane and nitrogen

require highest work done for liquefaction specific heat of hot

side fluid play very important role in analysis part of system,

In fig.4 show the specific heat of all gases show increment

with increase in PR while specific heat in case of methane gas

show first increase up to 160PR. Then it starts decreasing with

in very less marginal rate.

Number of transfer unit (NTU) help in the design of heat

exchanger, the size of heat exchanger can be predicting by

assessing the NTU of heat exchanger. Fig. 5 show NTU

variation of various gases with respect to increasing PR.

Except air and nitrogen all for gases first decreases up to

120PR then starts increasing at a very marginal rate by further

increasing in PR.

Fig.6 in dual compressor system the destruction in high

pressure and low pressure are different at the PR140 the

exergy destruction rate is minimum for five gases except

methane in these gases the destruction first increases up to

160PR and then decreases. Whereas in gases like air and

nitrogen show very sharp decrement at 140PR methane gas

show a straight slope of increase in exergy destruction up to

peak at 200PR then further increase in PR show decrease in

exergy destruction. Fig. 7 show high pressure compressor

exergy destruction rate with respect to PR.

The exergy destruction is continuously increasing for all six

gases with increase of PR the trend of exergy destruction in

heat exchanger is shown in fig. 8 the air and nitrogen gas show

highest rate of destruction among other gases.

The destruction rate for said gases first decrease up to 100PR

and then increase again by further increase in PR. Methane gas

show very sharp decrement in exergy destruction up to 160PR

then became constant and start rise at very low rate at 200PR.

Argon show lowest exergy destruction rate in heat exchanger,

while fluorine and oxygen are continuous decrease by

increasing PR and become constant in range of 140 to 220PR

40 60 80 100 120 140 160 180 200 220

2.6

2.8

3

3.2

3.4

3.6

3.8

4

4.2

4.4

4.6

4.8


NT

U

NTUHX1(Oxygen)

NTUHX1(Argon) NTUHX1(Methane)

NTUHX1(Fluorine)NTUHX1(Air)

NTUHX1(Nitrogen)

40 60 80 100 120 140 160 180 200 220

0

10

20

30

40

50

60

70

80

90


Ed

co

mp

1 (K

J/K

g)

Edcomp1(Oxygen)

Edcomp1(Argon)

Edcomp1(Methane)

Edcomp1(Fluorine)

Edcomp1(Air)

Edcomp1(Nitrogen)


140

Figure 7: Exergy Destruction rate of High pressure compressor

versus high pressure compressor ratio

Figure 8: Exergy destruction rate of heat exchanger versus high


Figure 9: Exergy destruction of expansion valve versus high pressure

compressor ratio

Figure 10: Exergy Destruction rate of second expansion valve

versus compressor pressure ratio

40 60 80 100 120 140 160 180 200 220

120

150

180

210

240

270

300

330

360

390

420

450

480

510

540

570

600


Ed

co

mp

2(K

J/K

g)

Edcomp1(Oxygen)

Edcomp1(Argon)

Edcomp1(Methane)

Edcomp1(Fluorine)

Edcomp1(Air)

Edcomp1(Nitrogen)

40 60 80 100 120 140 160 180 200 220

75

90

105

120

135

150

165

180

195

210

225

240

255

270


Ed

HX

1 (K

J/K

g)

EdHX1(Oxygen)

EdHX1(Argon)

EdHX1(Methane)

EdHX1(Fluorine)

EdHX1(Air)

EdHX1(Nitrogen)

0 50 100 150 200 250

50

60

70

80

90

100

110

120

130

140

150

160

170


Ed

val1 (K

J/K

g)

Edval1(Oxygen)

Edval1(Argon)

Edval1(Methane

Edval1(Fluorine)

Edval1(Air) Edval1(Nitrogen)

40 60 80 100 120 140 160 180 200 220

20

40

60

80

100

120

140

160

180

200

220

240

260

280


Ed

val2 (K

J/K

g)

Edval2(Oxygen)

Edval2(Argon)

Edval2(Methane

Edval2(Fluorine)

Edval2(Air) Edval2(Nitrogen)


141

Figure 11: Exergy destruction rate of first separator versus high


Figure 12 Exergy destruction rate of second separator versus high


Dual compressor system contain two expansion valve (V1 and V2),

Valve V1 work on the high temperature while V2 is work on at lowest

temperature. Fig. 9 and 10 show exergy destruction rate of gases with

respect to PR (Pressure ratio) the destruction in valve 1 the

destruction rate for gases first decrease up to 80 PR then they become

constant, while on the other hand the lowest temperature working

valve V2 the destruction rate of exergy is high and it increase with

increase in PR of system. Methane gas in both valve show highest

rate of destruction among all six gases. Fig. 11 & 12 show exergy

destruction rate in separator 1 and 2. Dual compressor system having

two separator at different temperature level. In separator 1, the trend

of exergy destruction for five gases except methane show decreasing

trend in the range of 40-100 PR but after this range the exergy

destruction in separator start increasing again in methane gas case

separator 1 show unusual behaviour it decrease at very fast rate and

become minimum at 80PR then increase again with small rate up to

180PR then again decrease, At 200PR it show almost negligible

destruction for methane. In separator 2 the rate of destruction increase

up to 80PR for all six gases and then decreases in further increases in

PR.

Figure 13: Exergy destruction of Compressor 1 % versus high


0 50 100 150 200 250

0

40

80

120

160

200

240

280

320

360


Ed

sep

1(K

J/K

g)

Edsep(Oxygen)

Edsep(Argon)

Edsep(Methane)

Edsep(Fluorine)

Edsep(Air)

Edsep(Nitrogen)

40 60 80 100 120 140 160 180 200 2200

20406080

100120140160180200220240260280300320340360380400420440460


Ed

sep

,2(K

J/K

g)

Edsep2(Oxygen)

Edsep2(Argon)

Edsep2(Methane)

Edsep2(Fluorine)

Edsep2(Air)

Edsep2(Nitrogen)

40 60 80 100 120 140 160 180 200 220

0

1

2

3

4

5

6

7


Ed

co

mp

1%

Edcomp1,%(methane)Edcomp1,%(Oxygen)Edcomp1,%(Argon)Edcomp1,%(Fluorine)

Edcomp1,%(Nitrogen)


142

Figure 14: Exergy destruction of Compressor 2 % versus high


Figure 15: Exergy destruction of heat exchanger 1% versus high


Figure 16: Exergy destruction of expansion valve 1 % versus high


Figure 17: Exergy destruction of expansion valve 2 % versus high


40 80 120 160 200

10

15

20

25

30

35

40


Ed

com

p2%

Edcomp2,%(Methane)

Edcomp2,%(Air)Edcomp2,%(Air)

Edcomp2,%(Argone)Edcomp2,%(Argone)

Edcomp2,%(Nitrogen)Edcomp2,%(Nitrogen)

Edcomp2,%(Oxygen)Edcomp2,%(Oxygen)

Edcomp2,%(Fluorine)Edcomp2,%(Fluorine)

40 60 80 100 120 140 160

8

10

12

14

16

18

20

22

24

26

28

30

32

34

36


Ed

HX

%

EdHX,%(Nitrogen)

EdHX,%(Air)

EdHX,%(Fluorine)

EdHX,%(Oxygen)

EdHX,%(Argon)

EdHX,%(Methane)

40 60 80 100 120 140 160 180

6

7

8

9

10

11

12

13

14


Ed

val1

%

Edval1,%(Air)

Edval1,%(Nitrogen)

Edval1,%(Argon)

Edval1,%(Methane)

Edval1,%(Oxygen)

Edval1,%(Fluorine)

40 60 80 100 120 140 160

2

4

6

8

10

12

14

16


Ed

val2

%

Edval2,%(Nitrogen)

Edval2,%(Air)

Edval2,%(Methane)

Edval2,%(Oxygen)

Edval2,%(Fluorine)

Edval2,%(Argon)


143

Figure 18: Exergy destruction of Separator 1 % versus high


Figure 19: Exergy destruction of separator 2 % versus high


From Fig.13-19 show the exergy destruction in percentage

form of every component with six gases for easy

understanding. In fig.13 show methane has highest rate of

destruction followed by oxygen, argon, fluorine and nitrogen.

While, in fig 14 compressor 2 methane has highest oxygen

show lowest percentage of exergy destruction. In heat

exchanger nitrogen has highest followed by air, fluorine,

oxygen and methane shown in fig 15. Fig. 16-17 the valve 1

show air is the highest percentage destruction and fluorine has

the least value. In fig.18 separator 1 show fluorine has a

highest destruction of exergy, while methane has the least

value in the PR range of 40 to 80. Fig.19 show separator 2

percentage destruction form in this methane gas show highest

and nitrogen has the least value.

Figure 20: COP and second law efficiency versus high pressure

compressor temperature

Figure 21: Liquefaction rate versus high pressure compressor

temperature

40 60 80 100 120 140 160 180 200 220

0

5

10

15

20

25

30

35

40

45

50


Ed

sep

1%

Edsep,1%(Fluorine)

Edsep,1%(Oxygen)

Edsep,1%(Argon)

Edsep,1%(Nitrogen)

Edsep,1%(Air) Edsep,1%(Methane)

40 60 80 100 120 140 160 180 200 2200

5

10

15

20

25

30

35

40


Ed

sep

2%

Edsep,2,%(Methane)

Edsep,2,%(Argon)

Edsep,2,%(Oxygen)

Edsep,2,%(Fluorine)

Edsep,2,%(Air)

Edsep,2,%(Nitrogen)

280 300 320 340 360 380 400 420 440 460

0.30.320.340.360.38

0.40.420.440.460.48

0.50.520.540.560.58

0.60.620.640.660.68

0.70.720.740.760.78

0.8

0

2

4

6

8

10

12

14

16

T4( High pressure Compressor.Temp)(K)

CO

P

h2

nd

,%

COPoxygen COP argon COP methane

COP FluorineCOP AirCOPNitrogen

h2nd,%oxygen

h2nd,%Argon

h2nd,% Methane

h2nd,%Fluorine

h2nd,%Airh2nd,%

Nitrogen

280 300 320 340 360 380 400

0.02

0.04

0.06

0.08

0.1

0.12


mf(

Liq

mass)(k

g/s

)

mf(Oxygen)

mf(Argon)

mf(Methane)

mf(Fluorine)

mf(Air)


144

Figure 22: Net work done versus high pressure compressor

temperature

.

Figure 23: Specific heat of heat exchanger versus high pressure


Figure 24: NTU versus high pressure compressor temperature

High pressure outlet temperature of high pressure compressor

affect the overall performance of the system. Fig.20 show the

effect of temperature variation on COP and second law

efficiency of dual compressor system from analysis, it is

noticed that COP of gas are continuously decreasing with

increasing outlet temperature of high pressure compressor the

mean temperature of all gases is the lowest temperature, i.e.

280K, but trend of decreasing COP and second law efficiency

for methane gas is highest as compare to other gases. The

lowest range of working temperature for methane and argon is

420K and, for air and fluorine is 360K. While, oxygen show

poor range of working temperature at 380K. Fig. 21 show

liquefaction rate variations with increasing outlet compressor

temperature. The liquefaction also affected by increasing

temperature range. From graph study, it has been noticed that

with increase of temperature the liquefaction rate decreasing

drastically. Gases like fluorine air and nitrogen cannot be

liquefied, if compressor outlet temperature increasing beyond

340K, and for oxygen, this temperature would be 380K.

Fig.22 show the work requirement for liquefaction either

increase continuously with increase of compressor

temperature. So it is desirable that compressor outlet

temperature should be minimum. Fig.23 show specific heat of

gases in heat exchanger is also affected by the increasing

outlet temperature of compressor. In this fig., it noticed that as

we increase the temperature the specific heat of five gases is

decreasing at a very minimum rate. While, in case of methane

it decrease first up to 340k and then start increasing again by

further increase in compressor outlet temperature. Fig. 24

280 300 320 340 360 380 400 420 440 460200220240260280300320340360380400420440460480500520540560580600620640660680700720740760780800820840


Wn

et(N

et.w

ork)(K

J/K

g)

Wnet(Oxygen)

Wnet(Argon)

Wnet(Methane)

Wnet(Fluorine)

Wnet(Air)

Wnet(Nitrogen)

280 300 320 340 360 380 400 420 440 4600.350.450.550.650.750.850.951.051.151.251.351.451.551.651.751.851.952.052.152.252.352.452.552.652.752.852.953.05


cp

hf(H

X)(K

j/K

g-K

)

cphot,fluid,HX(Oxygen)

cphot,fluid,HX(Argon)

cphot,fluid,HX(Methane)

cphot,fluid,HX(Fluorine)

cphot,fluid,HX(Air)

cphot,fluid,HX(Nitrogen)

280 300 320 340 360 380 400 420 440 460

3.15

3.5

3.85

4.2

4.55

4.9

5.25

5.6


NT

U

NTUHX1(Oxygen)

NTUHX1(Argon)

NTUHX1(Methane)

NTUHX1(Fluorine)

NTUHX1(Air)

NTUHX1(Nitrogen)


145

show NTU variation of heat exchanger with outlet temperature

of compressor. The graph analysis states that there is increase

in NTU value with increase in high pressure compressor

temperature up to 420K. But after that it start decreasing for

all gases, methane gas show lowest NTU with highest NTU

variations range in 4.2 to 5.6

Figure 25: Exergy destruction in compressor 1 versus high pressure


Figure 26: Exergy destruction in compressor 2 versus high pressure


Figure 27: Heat exchanger exergy destruction versus high pressure


Figure 28: Exergy destruction in expansion valve 1 versus high

pressure compressor temperature

280 300 320 340 360 380 400 420 440 460

3

6

9

12

15

18

21

24

27


Ed

co

mp (

KJ/K

g)

Edcomp(Oxygen)

Edcomp(Argon)

Edcomp(Methane)

Edcomp(Fluorine)

Edcomp(Air)

Edcomp(Nitrogen)

280 300 320 340 360 380 400 420 440 460110

130

150

170

190

210

230

250

270

290

310

330

350

370

390

410

430

450


Ed

co

mp

2 (

KJ/K

g)

Edcomp2(Oxygen)

Edcomp2(Argon)

Edcomp2(Methane)

Edcomp2(Fluorine)

Edcomp2(Air)

Edcomp2(Nitrogen)

280 300 320 340 360 380 400 420 440 4602030405060708090

100110120130140150160170180190200210220230240250260270


Ed

HX

1 (K

J/K

g)

EdHX(Oxygen)

EdHX(Argon)

EdHX(Methane)

EdHX(Fluorine)

EdHX(Air)

EdHX(Nitrogen)

280 300 320 340 360 380 400 420 440 460

60

75

90

105

120

135

150

165


Ed

val1 (K

J/K

g)

Edval(Oxygen)

Edval(Argon)

Edval(Methane

Edval(Fluorine)

Edval(Air) Edval(Nitrogen)


146

Figure 29: Exergy destruction in separator 2 versus high pressure


Figure 30: Exergy destruction in separator 2 versus high pressure


The low pressure and high pressure compressor have exergy

destruction in each other with variation in high compressor

outlet temperature. Fig.25 and 26 show exergy destruction of

low pressure and high pressure compressor with temperature

variations. The rate of exergy destruction is start decreasing

with increase of outlet compressor temperature. For gas air

and nitrogen, it is up to 350K. Where this decrement for

oxygen is 380K. Methane and argon show the decrement up

to 420K, then their destruction rate rise up again by further

increase in temperature of compressor. The exergy destruction

of high pressure compressor for all gases are increases with

increase in compressor temperature.

Fig.27 show exergy destruction rate in heat exchanger for

different gases with variation in compressor outlet

temperature, the exergy destruction for all gases almost

constant up to 360K. But onwards this temperature is start

decreasing. Methane gas show huge dip in exergy destruction

rate up to 340K. Fig.28 show that with increase in compressor

temperature, the rate of exergy destruction in HX also

increases for all gases. Fig. 29 show that in high temperature

separator, the exergy destruction trend for all six gases with

respect to variation in high pressure compressor temperature.

The argon, air and nitrogen show increment up to 420K. After

this temperature increment in exergy destruction rate

increases, the oxygen and fluorine gas show increasing curve

in slightly parabolic nature. While, methane gas show

exceptionally high rate of exergy destruction with increase in

compressor outlet temperature. Fig.30 show that in separator

2, exergy destruction is first decreases then increase with

increase of outlet compressor temperature.

5. Conclusion

Exergy analysis of Dual Compressor Linde System with

different gases are evaluated on the basis of pressure ratio,

compressor outlet temperature, and expander mass flow ratio.

Following results are concluded from study.

(1) During off design condition, performance of cycle does

not hamper within the specific range of cyclic pressure

ratio, for particular considered system there is always

appropriate operating pressure ratio range for each

working gas on which system work better

(2) Dual Compressor Linde system are compared on the basis

of performance parameters at different pressure ratio,

form the data observation it observed that heat exchanger

help in achieving more refrigerant effect which is in turn

optimize the performance of the system.

(3) During PR increase, there is an imbalance in mass flow of

forward and return stream of heat exchanger HX. Second

law efficiency with the help of increasing pressure ratio

which variant and create specific heat imbalance to

overcome the mass imbalance.

(4) Variation in expander mass flow has highly influence the

refrigeration effect of expander and overall performance

of system. Optimum range of expander flow fraction (r)

producing refrigeration effect is 0.55 to 0.7. Liquid

280 300 320 340 360 380 400 420 440 460

100

150

200

250

300

350

400

450


Ed

sep

1 (K

J/K

g)

Edsep1(Oxygen)

Edsep1(Argon)

Edsep1(Fluorine)

Edsep1(Methane)

Edsep1(Air)

Edsep1(Nitrogen)

280 300 320 340 360 380 400 420 440 4600

10

20

30

40

50

60

70

80

90

100

110


Ed

sep

2 (K

J/K

g)

Edsep2(Oxygen)

Edsep2(Argon)

Edsep2(Fluorine)

Edsep2(Methane)

Edsep2(Air)

Edsep2(Nitrogen)


147

production rate is highly influenced by refrigeration effect

of expander.

(5) Inlet temperature of expander also plays an important

factor to determine the refrigeration effect while

other parameters in the system are constant. As the

mass flow fraction increases through expander the

output temperature of expander 𝑇𝑒 also decreases

which in turn lower the inlet temperature of input

temperature of 𝑇𝑖𝑛 𝐸𝑋𝑃.

(6) In all gases methane gas show highest performance

parameters in most of system while argon show

lowest.

References

[1] R. Agrawal,et.al (1991) Efficient cryogenic nitrogen generators:

An exergy analysis, Gas Separation & Purification, Volume 5,

Issue 3, September 1991, Pages 139-150.

[2] Gadhiraju Venkatarathnam (2008), “Simulation of cryogenic

processes” , Cryogenic Mixed Refrigerant Processes

,International Cryogenics Monograph Series , Pages 51-63.

[3] J. Rizk, M.et.al, (2012) A real column design exergy

optimization of a cryogenic air separation unit, Energy, Volume

37, Issue 1, January 2012, Pages 417-429.

[4] Yasuki Kansha, et.al(2011) , A novel cryogenic air separation

process based on self-heat recuperation, Separation and

Purification Technology, Volume 77, Issue 3, 4 March 2011,

Pages 389-396.

[5] R.L. Cornelissen, G.G. Hirs, Exergy analysis of cryogenic air

separation, Energy Conversion and Management, Volume 39,

Issues 16–18, November–December 1998, Pages 1821-1826.

http://link.springer.com/search?facet-author=%22Gadhiraju+Venkatarathnam%22

http://link.springer.com/book/10.1007/978-0-387-78514-1

http://link.springer.com/bookseries/6086

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