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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
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)
R.S. Mishra et al/ International journal of research in engineering and innovation (IJREI), vol 1, issue 4 (2017), 135-147
137
"𝑇𝑦𝑝𝑒𝐻𝑋$ =′ 𝑐𝑜𝑢𝑛𝑡𝑒𝑟𝑓𝑙𝑜𝑤′”
𝑞𝑚𝑎𝑥 = 𝐶𝑚𝑖𝑛 ∗ (𝑇4 − 𝑇12)
𝑒𝑝𝑠𝑖𝑙𝑜𝑛 =𝑞ℎ𝑥
𝑞𝑚𝑎𝑥
𝑒𝑝𝑠𝑖𝑙𝑜𝑛 = .85
𝑁𝑡𝑢 = 𝐻𝑋(𝑇𝑦𝑝𝑒𝐻𝑋$, 𝑒𝑝𝑠𝑖𝑙𝑜𝑛, 𝐶ℎ, 𝐶𝑐, 𝑁′ 𝑡𝑢′)
𝐸𝑥𝑖𝑛𝐻𝑋= 𝑚4 ∗ ((ℎ4 − ℎ5) − (𝑇0 ∗ (𝑠4 − 𝑠5)))
𝐸𝑥𝑜𝑢𝑡𝐻𝑋= 𝑚12 ∗ ((ℎ12 − ℎ13) − (𝑇0 ∗ (𝑠12 − 𝑠13)))
𝐸𝑑𝐻𝑋 = ((𝐸𝑥𝑖𝑛𝐻𝑋) − (𝐸𝑥𝑜𝑢𝑡𝐻𝑋
)) (33)
3.3 Thermodynamic Analysis of Valve
ℎ5 = ℎ6
𝐸𝑥𝑖𝑛𝑉𝑎𝑙= (ℎ5 − ℎ0) − 𝑇0 ∗ (𝑠5 − 𝑠0)
𝐸𝑥𝑜𝑢𝑡𝑣𝑎𝑙= (ℎ6 − ℎ0) − 𝑇0 ∗ (𝑠6 − 𝑠0)
𝐸𝑑𝑣𝑎𝑙1 = (𝐸𝑥𝑖𝑛𝑉𝑎𝑙− 𝐸𝑥𝑜𝑢𝑡𝑣𝑎𝑙
)
"Analysis of seperator"
𝑚4 ∗ ℎ6 = ((𝑚7 ∗ ℎ7) + (𝑚12 ∗ ℎ12))
𝑥7 = 0
𝑥12 = 1
𝐸𝑑𝑠𝑒𝑝1= (𝑇0 ∗ (
((𝑚12 ∗ 𝑠12) − (𝑚4 ∗ 𝑠6)) +
((𝑚12∗ℎ12)−(𝑚7∗ℎ7)
𝑇12)
))
3.4 Thermodynamic Analysis of heat exchanger
𝑚12 ∗ ℎ12 + 𝑚10 ∗ ℎ10 = 𝑚12 ∗ ℎ13 + 𝑚10 ∗ ℎ11
"Analysis of Valve"
h7=h8
𝐸𝑥𝑖𝑛𝑉𝑎𝑙2= (ℎ7 − ℎ0) − 𝑇0 ∗ (𝑠7 − 𝑠0)
𝐸𝑥𝑜𝑢𝑡𝑣𝑎𝑙2= (ℎ8 − ℎ0) − 𝑇0 ∗ (𝑠8 − 𝑠0)
𝐸𝑑𝑣𝑎𝑙2 = 𝑎𝑏𝑠(𝐸𝑥𝑖𝑛𝑉𝑎𝑙2− 𝐸𝑥𝑜𝑢𝑡𝑣𝑎𝑙2
)
3.5 Thermodynamic Analysis of separator
𝑚7 ∗ ℎ8 = ((𝑚9 ∗ ℎ9) + (𝑚10 ∗ ℎ10))
𝑚7 = 𝑚9 + 𝑚10
𝑚9 = 𝑚𝑓
𝑚10 = 𝑚𝑔
𝑥9 = 0
𝑥10 = 1
𝐸𝑑𝑠𝑒𝑝2= 𝑎𝑏𝑠 (𝑇0 ∗ (
((𝑚10 ∗ 𝑠10) − (𝑚7 ∗ 𝑠8))
+ ((𝑚10∗ℎ10)−(𝑚9∗ℎ9)
𝑇10)
))
𝐸𝑑𝑐𝑜𝑚𝑝1%= (
𝐸𝑑𝑐𝑜𝑚𝑝1
𝐸𝑑𝐷𝑢𝑎𝑙𝐶𝑜𝑚𝑝𝐿𝑖𝑛𝑑𝑒
) ∗ 100
𝐸𝑑𝑐𝑜𝑚𝑝2%= (
𝐸𝑑𝑐𝑜𝑚𝑝2
𝐸𝑑𝐷𝑢𝑎𝑙𝐶𝑜𝑚𝑝𝐿𝑖𝑛𝑑𝑒
) ∗ 100
𝐸𝑑𝐻𝑋%= (
𝐸𝑑𝐻𝑋
𝐸𝑑𝐷𝑢𝑎𝑙𝐶𝑜𝑚𝑝𝐿𝑖𝑛𝑑𝑒
) ∗ 100
𝐸𝑑𝑣𝑎𝑙1%= (
𝐸𝑑𝑣𝑎𝑙1
𝐸𝑑𝐷𝑢𝑎𝑙𝐶𝑜𝑚𝑝𝐿𝑖𝑛𝑑𝑒
) ∗ 100
𝐸𝑑𝑠𝑒𝑝1% = (
𝐸𝑑𝑠𝑒𝑝1
𝐸𝑑𝐷𝑢𝑎𝑙𝐶𝑜𝑚𝑝𝐿𝑖𝑛𝑑𝑒
) ∗ 100
𝐸𝑑𝑣𝑎𝑙2%= (
𝐸𝑑𝑣𝑎𝑙2
𝐸𝑑𝐷𝑢𝑎𝑙𝐶𝑜𝑚𝑝𝐿𝑖𝑛𝑑𝑒
) ∗ 100
𝐸𝑑𝑠𝑒𝑝2%= (
𝐸𝑑𝑠𝑒𝑝2
𝐸𝑑𝐷𝑢𝑎𝑙𝐶𝑜𝑚𝑝𝐿𝑖𝑛𝑑𝑒
) ∗ 100
𝐸𝑡𝑎2𝑛𝑑%= 𝑎𝑏𝑠 ((𝑚9 ∗
(ℎ9 − ℎ1) − 𝑇0 ∗ (𝑠9 − 𝑠1)
𝑊𝑁𝑒𝑡
) ∗ 100)
𝐸𝑑𝐷𝑢𝑎𝑙𝐶𝑜𝑚𝑝𝐿𝑖𝑛𝑑𝑒= 𝐸𝑑𝑐𝑜𝑚𝑝1 + 𝐸𝑑𝑐𝑜𝑚𝑝2 +
𝐸𝑑𝐻𝑋 + 𝐸𝑑𝑣𝑎𝑙1 + 𝐸𝑑𝑣𝑎𝑙2 + 𝐸𝑑𝑠𝑒𝑝1+ 𝐸𝑑𝑠𝑒𝑝2
In Non-ideal gas any variable can be defined by two other
dependent variable on them:
𝑎𝑛𝑜𝑛−𝑖𝑑𝑒𝑎𝑙 𝑔𝑎𝑠 = 𝑓𝑥(𝑏, 𝑐)
Table 1: Variable Table (Dual Compressor system)
Variable
(a)
Gas Variable
(b)
Variable
(c )
ℎ0 𝑅$ 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.
R.S. Mishra et al/ International journal of research in engineering and innovation (IJREI), vol 1, issue 4 (2017), 135-147
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
P4 (Compressor pressure ratio)(HP) bar)
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
P4 (Compressor pressure ratio)(HP) bar)
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
P4 (Compressor pressure ratio)(HP) bar)
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)
R.S. Mishra et al/ International journal of research in engineering and innovation (IJREI), vol 1, issue 4 (2017), 135-147
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
P4 (Compressor pressure ratio)(HP) bar)
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
P4 (Compressor pressure ratio)(HP) bar)
Ed
co
mp
1 (K
J/K
g)
Edcomp1(Oxygen)
Edcomp1(Argon)
Edcomp1(Methane)
Edcomp1(Fluorine)
Edcomp1(Air)
Edcomp1(Nitrogen)
R.S. Mishra et al/ International journal of research in engineering and innovation (IJREI), vol 1, issue 4 (2017), 135-147
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
pressure compressor ratio
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
P4 (Compressor pressure ratio)(HP) bar)
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
P4 (Compressor pressure ratio)(HP) bar)
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
P4 (Compressor pressure ratio)(HP) bar)
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
P4 (Compressor pressure ratio)(HP) bar)
Ed
val2 (K
J/K
g)
Edval2(Oxygen)
Edval2(Argon)
Edval2(Methane
Edval2(Fluorine)
Edval2(Air) Edval2(Nitrogen)
R.S. Mishra et al/ International journal of research in engineering and innovation (IJREI), vol 1, issue 4 (2017), 135-147
141
Figure 11: Exergy destruction rate of first separator versus high
pressure compressor ratio
Figure 12 Exergy destruction rate of second separator versus high
pressure compressor ratio
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
pressure compressor ratio
0 50 100 150 200 250
0
40
80
120
160
200
240
280
320
360
P4 (Compressor pressure ratio)(HP) bar)
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
P4 (Compressor pressure ratio)(HP) bar)
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
P4 (Compressor pressure ratio)(HP) bar)
Ed
co
mp
1%
Edcomp1,%(methane)Edcomp1,%(Oxygen)Edcomp1,%(Argon)Edcomp1,%(Fluorine)
Edcomp1,%(Nitrogen)
R.S. Mishra et al/ International journal of research in engineering and innovation (IJREI), vol 1, issue 4 (2017), 135-147
142
Figure 14: Exergy destruction of Compressor 2 % versus high
pressure compressor ratio
Figure 15: Exergy destruction of heat exchanger 1% versus high
pressure compressor ratio
Figure 16: Exergy destruction of expansion valve 1 % versus high
pressure compressor ratio
Figure 17: Exergy destruction of expansion valve 2 % versus high
pressure compressor ratio
40 80 120 160 200
10
15
20
25
30
35
40
P4 (Compressor pressure ratio)(HP) bar)
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
P4 (Compressor pressure ratio)(HP) bar)
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
P4 (Compressor pressure ratio)(HP) bar)
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
P4 (Compressor pressure ratio)(HP) bar)
Ed
val2
%
Edval2,%(Nitrogen)
Edval2,%(Air)
Edval2,%(Methane)
Edval2,%(Oxygen)
Edval2,%(Fluorine)
Edval2,%(Argon)
R.S. Mishra et al/ International journal of research in engineering and innovation (IJREI), vol 1, issue 4 (2017), 135-147
143
Figure 18: Exergy destruction of Separator 1 % versus high
pressure compressor ratio
Figure 19: Exergy destruction of separator 2 % versus high
pressure compressor ratio
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
P4 (Compressor pressure ratio)(HP) bar)
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
P4 (Compressor pressure ratio)(HP) bar)
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
T4( High pressure Compressor.Temp)(K)
mf(
Liq
mass)(k
g/s
)
mf(Oxygen)
mf(Argon)
mf(Methane)
mf(Fluorine)
mf(Air)
R.S. Mishra et al/ International journal of research in engineering and innovation (IJREI), vol 1, issue 4 (2017), 135-147
144
Figure 22: Net work done versus high pressure compressor
temperature
.
Figure 23: Specific heat of heat exchanger versus high pressure
compressor temperature
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
T4( High pressure Compressor.Temp)(K)
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
T4( High pressure Compressor.Temp)(K)
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
T4( High pressure Compressor.Temp)(K)
NT
U
NTUHX1(Oxygen)
NTUHX1(Argon)
NTUHX1(Methane)
NTUHX1(Fluorine)
NTUHX1(Air)
NTUHX1(Nitrogen)
R.S. Mishra et al/ International journal of research in engineering and innovation (IJREI), vol 1, issue 4 (2017), 135-147
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
compressor temperature
Figure 26: Exergy destruction in compressor 2 versus high pressure
compressor temperature
Figure 27: Heat exchanger exergy destruction versus high pressure
compressor temperature
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
T4( High pressure Compressor.Temp)(K)
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
T4( High pressure Compressor.Temp)(K)
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
T4( High pressure Compressor.Temp)(K)
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
T4( High pressure Compressor.Temp)(K)
Ed
val1 (K
J/K
g)
Edval(Oxygen)
Edval(Argon)
Edval(Methane
Edval(Fluorine)
Edval(Air) Edval(Nitrogen)
R.S. Mishra et al/ International journal of research in engineering and innovation (IJREI), vol 1, issue 4 (2017), 135-147
146
Figure 29: Exergy destruction in separator 2 versus high pressure
compressor temperature
Figure 30: Exergy destruction in separator 2 versus high pressure
compressor temperature
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
T4( High pressure Compressor.Temp)(K)
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
T4( High pressure Compressor.Temp)(K)
Ed
sep
2 (K
J/K
g)
Edsep2(Oxygen)
Edsep2(Argon)
Edsep2(Fluorine)
Edsep2(Methane)
Edsep2(Air)
Edsep2(Nitrogen)
R.S. Mishra et al/ International journal of research in engineering and innovation (IJREI), vol 1, issue 4 (2017), 135-147
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.