G.H.Raisoni College of Engineering

Submitted to :Prof kishor rambhad Subject: Energy conversion-2 TOPIC: Multistage CompressionSUBMITTED BY: Abhishek GawandeROLL NO. :04

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.

2 Stage Compressor without pressure drop in the intercooler:

1 2 3 4Suction DischargeQx

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

Work of 1st stage cylinder (W1): Assuming Polytropic compression on both stages.

11'1

n1n

1

21'11

mRTVP

1PP

1nVnP

W

Work of 2nd stage cylinder (W2): Assuming Polytropic compression on both stages.

33'3

n1n

3

43'32

mRTVP

1PP

1nVnP

W

P

V

P4

P1

Px

1

4

32

5

6

7

8

PVn = C

W1

W2

S

T

4

3

2

1

P4 Px P1

Qx

For perfect inter-cooling and minimum work:W1 = W2

T1 = T3

W = W1 + W2

W = 2W1

P2 = P3 = Px

thereforeP1V1’ = P3V3’

21

1

4

1

2

41x

32x3

4

1

2

PP

PP

PP P

then ; P P Pbut ; PP

PP

Where: Px – optimum intercooler pressure or interstage pressure

1PP

1nV2nP

W

1PP

1nV2nP

W

2n1n

1

41'1

n1n

1

21'1

Then the work W for an ideal 2-stage compressor is:

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)

2 Stage Compressor with pressure drop in the intercooler:

1 2 3 4Suction DischargeQx

Intercooler

1st stage 2nd stage

With pressure drop in the intercooler:T1 T3 and P2 P3

W = W1 + W2

P1V1’ P3V3’

1PP

1nVnP

W

1PP

1nVnP

W

n1n

3

43'32

n1n

1

21'11

P

V

P4

P1

P3

1

4

32

5

6 7

8

PVn = C

W1

W2

S

T

4

3

2

1

P4 P1

Qx

P2

P2 P3

3 Stage Compressor without pressure drop in the intercooler:

1 2 3 4

Suction Discharge

Qx

LP Intercooler

1st stage 2nd stage 3rd stage

5 6Qy

HP Intercooler

S

T

4

3

2

1

P6 Px P1

Qx

P

V

P6

P1

Px

1

4

3

2

5

67

12

PVn = C

W1

W2

Py 9

10

11

8

W3

Py

5

6

Qy

For perfect inter-cooling and minimum work:T1 = T3 = T5 Px = P2 = P3 W1 = W2 = W3 Py = P4 = P5

W = 3W1P1V1’ = P3V3’ = P5V5’

mRT1 = mRT3 = mRT5

Therefore: rP1 = rP2 = rP3

Work for each stage:

1PP

1nVnP

Wn

1n

1

21'11

1st Stage:

1PP

1nVnP

Wn

1n

3

43'32

2nd Stage:

3rd Stage:

1PP

1nVnP

Wn

1n

5

65'53

3 261y

36

21x

y

6

x

y

1

x

5

6

3

4

1

2

PPP ; PPP

hence

PP

P

P

PP

or PP

PP

PP

Intercooler Pressures:

Total Work:

W = 3W1

11'1

3n1n

1

61'1

mRTVP

1PP

1nV3nP

W

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 intercooleris required.

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

1PP

1nVSnP

W2S

1n

1

2S'

11Where: 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.

THANK YOU!THANK YOU!