Multistage Compression

1. G.H.Raisoni College of Engineering
Submitted to :Prof kishor rambhad
Subject: Energy conversion-2
TOPIC: Multistage Compression
SUBMITTED BY: Abhishek Gawande
ROLL NO. :04

2. MULTISTAGE COMPRESSION:
Multi staging is simply the compression of air or gas in two or more cylinders
in place of a single cylinder compressor. It is used in reciprocating compressors
when pressure of 300 KPa and above are desired, in order to:
1) Save power
2) Limit the gas discharge temperature
3) Limit the pressure differential per cylinder
4) Prevent vaporization of lubricating oil and to prevent its ignition if the tem-
perature becomes too high.
It is a common practice for multi-staging to cool the air or gas between stages
of compression in an intercooler, and it is this cooling that affects considerable
saving in power.

3. 2 Stage Compressor without pressure drop in the intercooler:
1 2 3 4
Suction
Discharge
Qx
Intercooler
1
st
stage 2
nd
stage
For an ideal multistage compressor, with perfect inter-cooling and minimum
work, the cylinder were properly designed so that:
a) the work at each stage are equal
b) the air in the intercooler is cooled back to the initial temperature
c) no pressure drop occurs in the intercooler

4. Work of 1
st
stage cylinder (W
1
): Assuming Polytropic compression on
both stages.
11'1
n
1n
1
21'1
1
mRTVP
1
P
P
1n
VnP
W
=
ú
ú
ú
û
ù
ê
ê
ê
ë
é
-
÷
÷
ø
ö
ç
ç
è
æ
-
=
-
Work of 2
nd
stage cylinder (W
2
): Assuming Polytropic compression on
both stages.
33'3
n
1n
3
43'3
2
mRTVP
1
P
P
1n
VnP
W
=
ú
ú
ú
û
ù
ê
ê
ê
ë
é
-
÷
÷
ø
ö
ç
ç
è
æ
-
=
-

5. P
V
P
4
P
1
P
x
1
4
3
2
5
6
7
8
PV
n
= C
W
1
W
2
S
T
4
3
2
1
P
4
P
x
P
1
Q
x
For perfect inter-cooling and minimum
work:
W
1
= W
2
T
1
= T
3
W = W
1
+ W
2
W = 2W
1
P
2
= P
3
= P
x
therefore
P
1
V
1’
= P
3
V
3’
2
1
1
4
1
2
41x
32x
3
4
1
2
P
P
P
P
PP P
then ; P P Pbut ;
P
P
P
P
÷
÷
ø
ö
ç
ç
è
æ
=
=
===
Where:
Px – optimum intercooler
pressure or interstage
pressure

6. ú
ú
ú
û
ù
ê
ê
ê
ë
é
-
÷
÷
ø
ö
ç
ç
è
æ
-
=
ú
ú
ú
û
ù
ê
ê
ê
ë
é
-
÷
÷
ø
ö
ç
ç
è
æ
-
=
-
-
1
P
P
1n
V2nP
W
1
P
P
1n
V2nP
W
2n
1n
1
41'1
n
1n
1
21'1
Then the work W for an ideal 2-stage compressor is:
Heat losses calculation:
1.Heat loss during compression at 1
st
stage cylinder
Q
1
= mC
n
(T
2
– T
1
)
2. Heat loss during compression at 2
nd
stage cylinder
Q
2
=
mCn
(T
4
– T
3
)
3. Heat loss in the intercooler
Q
x
= mC
p
(T
2
– T
3
)

7. 2 Stage Compressor with pressure drop in the intercooler:
1 2 3 4
Suction
Discharge
Qx
Intercooler
1
st
stage 2
nd
stage
With pressure drop in the intercooler:
T
1
¹ T
3
and P
2
¹ P
3
W = W
1
+ W
2
P
1
V
1’
¹ P
3
V
3’
ú
ú
ú
û
ù
ê
ê
ê
ë
é
-
÷
÷
ø
ö
ç
ç
è
æ
-
=
ú
ú
ú
û
ù
ê
ê
ê
ë
é
-
÷
÷
ø
ö
ç
ç
è
æ
-
=
-
-
1
P
P
1n
VnP
W
1
P
P
1n
VnP
W
n
1n
3
43'3
2
n
1n
1
21'1
1

8. P
V
P
4
P
1
P
3
1
4
3
2
5
6 7
8
PV
n
= C
W
1
W
2
S
T
4
3
2
1
P
4 P
1
Q
x
P
2
P
2
P
3
3 Stage Compressor without pressure drop in the intercooler:
1 2 3 4
Suction
Discharge
Qx
LP Intercooler
1
st
stage 2
nd
stage 3
rd
stage
5 6
Qy
HP Intercooler

9. S
T
4
3
2
1
P
6
P
x
P
1
Q
x
P
V
P
6
P
1
P
x
1
4
3
2
5
67
12
PV
n
= C
W
1
W
2
P
y
9
10
11
8
W
3
P
y
5
6
Q
y
For perfect inter-cooling and minimum work:
T
1
= T
3
= T
5
P
x
= P
2
= P
3

W
1
= W
2
= W
3
P
y
= P
4
= P
5
W = 3W1
P
1V
1’ = P
3V
3’ = P
5V
5’
mRT
1
= mRT
3
= mRT
5
Therefore:
r
P1
= r
P2
= r
P3

10. Work for each stage:
ú
ú
ú
û
ù
ê
ê
ê
ë
é
-
÷
÷
ø
ö
ç
ç
è
æ
-
=
-
1
P
P
1n
VnP
W
n
1n
1
21'1
1
1
st
Stage:
ú
ú
ú
û
ù
ê
ê
ê
ë
é
-
÷
÷
ø
ö
ç
ç
è
æ
-
=
-
1
P
P
1n
VnP
W
n
1n
3
43'3
2
2
nd
Stage:
3
rd
Stage:
ú
ú
ú
û
ù
ê
ê
ê
ë
é
-
÷
÷
ø
ö
ç
ç
è
æ
-
=
-
1
P
P
1n
VnP
W
n
1n
5
65'5
3
3
2
61y
3
6
2
1x
y
6
x
y
1
x
5
6
3
4
1
2
PPP ; PPP
hence
P
P
P
P
P
P
or
P
P
P
P
P
P
==
====
Intercooler Pressures:

11. Total Work:
W = 3W
1
11'1
3n
1n
1
61'1
mRTVP
1
P
P
1n
V3nP
W
=
ú
ú
ú
û
ù
ê
ê
ê
ë
é
-
÷
÷
ø
ö
ç
ç
è
æ
-
=
-
Heat Losses during compression:
Q
1
= mC
n
(T
2
– T
1
)
Q
2
= mC
n
(T
4
– T
3
)
Q
3
= mC
n
(T
6
– T
5
)
Heat loss in the LP and HP intercoolers:
LP Intercooler
Qx = mC
p
(T
2
– T
3
)
HP Intercooler
Qy = mC
p
(T
4
– T
5
)
Note:
1.For isentropic compression and expansion process, no heat loss during
compression.
2.For isothermal compression and expansion process, the loss during
compression is equivalent to the compression work, and no intercooler
is required.

12. For multistage compression with minimum work and perfect inter-cooling
and no pressure drop that occurs in the inter-coolers between stages, the
following conditions apply:
1. the work at each stage are equal
2. the pressure ratio between stages are equal
3. the air temperature in the inter-coolers are cooled to the original
temperature T
1
4. the total work W is equal to
ú
ú
ú
û
ù
ê
ê
ê
ë
é
-
÷
÷
ø
ö
ç
ç
è
æ
-
=
-
1
P
P
1n
VSnP
W
2S
1n
1
2S
'
11
Where: s – is the number of
stages.
Note: For multistage compressor with pressure drop in the intercoolers the
equation of W above cannot be applied. The total work is equal to the sum
of the work for each stage that is computed separately.

14. THANK YOU!THANK YOU!