A multi-stage compressor compresses air or gas in two or more cylinders instead of a single cylinder to save power, limit gas discharge temperature, limit pressure differential per cylinder, and prevent issues with lubricating oil. It is common for multi-stage compressors to cool the air between stages using an intercooler. For a two-stage compressor with perfect intercooling and no pressure drops, the work of each stage is equal, the temperature is cooled back to initial levels, and the total work is equal to twice the work of one stage. For three or more stages, similar conditions apply where the work, pressures, and temperatures are equal between stages and the total work is the work of one stage multiplied by the number

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 temperature 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:
Qx
Suction
1
2
3
4
Discharge
Intercooler
1st stage
2nd 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 1st stage cylinder (W1): Assuming Polytropic compression on
n−1
both stages.


n
nP1V1'
W1 =
n −1
 P2 
 
 P1 
 

− 1



P1V1' = mRT1
Work of 2nd stage cylinder (W2): Assuming Polytropic compression on
both stages.
n−1


n
nP3 V3'  P4 
  − 1
W2 =

n − 1  P3 
 




P3 V3' = mRT3

5. P
P4
T
5
4
PVn = C
W2
Px
P4
3
6
7
2
P1
8
4
3
W1
1
V
Px
P1
2
Qx
1
S
For perfect inter-cooling and minimum
work:
P2 P4
= ; but Px = P2 = P3 ; then
W1 = W 2
P1 P3
T1 = T3
Where:
Px = P1P4
W = W1 + W2
Px – optimum intercooler
1
W = 2W1
pressure or interstage
P2  P4  2
P2 = P3 = Px
= 
pressure
P1  P1 
 
therefore
P1V1’ = P3V3’

6. Then the work W for an ideal 2-stage compressor is:
2nP1V1'
W=
n −1
2nP1V1'
W=
n −1
n−1


n
 P2  − 1
 
 P1 

 




n−1


2n
 P4  − 1
 
 P1 

 




Heat losses calculation:
1. Heat loss during compression at 1st stage cylinder
Q1 = mCn(T2 – T1)
2. Heat loss during compression at 2nd stage cylinder
Q2 = mCn(T4 – T3)
3. Heat loss in the intercooler
Qx = mCp(T2 – T3)

7. 2 Stage Compressor with pressure drop in the intercooler:
Qx
Suction
1
2
3
4
Discharge
Intercooler
1st stage
With pressure drop in the intercooler:
T1 ≠ T3 and P2 ≠ P3
W = W1 + W2
P1V1’ ≠ P3V3’
2nd stage
n−1


n
nP1V1'  P2 
  − 1
W1 =

n − 1  P1 
 




n−1


n
nP3 V3'  P4 
  − 1
W2 =

n − 1  P3 
 





8. P
P4
5
P2
4
PVn = C
W2
P2
P3
P4
T
6
3
7
4
2
3
W1
P1
1
8
P1
P3
2
Qx
1
S
V
3 Stage Compressor without pressure drop in the intercooler:
1
2
Qx
3
4
Qy
5
6
Suction
Discharge
HP Intercooler
LP Intercooler
1st stage
2nd stage
3rd stage

9. P
P6
Py
T
7
W3
PVn = C
6
Py
4
6
Px
2
4
9
8
5
W2
Px
5
2
11
10
P1
P6
3
Qy
Qx
1
3
W1
12
1
V
For perfect inter-cooling and minimum work:
T1 = T3 = T5
Px = P2 = P3
W1 = W 2 = W 3
Py = P4 = P5
W = 3W1
P1V1’ = P3V3’ = P5V5’
mRT1 = mRT3 = mRT5
Therefore:
rP1 = rP2 = rP3
S
P1

10. Work for each stage:
1st Stage:
2nd Stage:
n−1


n
nP1V1'  P2 
  − 1
W1 =

n − 1  P1 
 




n−1


n
nP3 V3'  P4 
  − 1
W2 =

n − 1  P3 
 




3rd Stage:
Intercooler Pressures:
n−1


n
nP5 V5'  P6 
  − 1
W3 =

n − 1  P5 
 




P2 P4 P6
= =
P1 P3 P5
or
Px Py P6
= =
P1 Px Py
hence
2
1 6
Px = P P
3
;
Py = P1P6
3
2

11. Total Work:
W = 3W1
n−1


3n
3nP1V1'  P6 
  − 1
W=

n − 1  P1 
 




P1V1' = mRT1
Heat Losses during compression:
Q1 = mCn(T2 – T1)
Q2 = mCn(T4 – T3)
Q3 = mCn(T6 – T5)
Heat loss in the LP and HP intercoolers:
LP Intercooler
Qx = mCp(T2 – T3)
HP Intercooler
Qy = mCp(T4 – T5)
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 T1
4. the total work W is equal to
n−1


'
2S
SnP1V1  P2S 

 − 1
W=

n − 1  P1 






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!