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FUNDAMENTALS OF ENERGY BALANCES
Example 3.13
In the high-pressure process for the production of polyethylene, ethylene is compressed in
a two-step process. In the primary step, the gas is compressed in a two-stage compressor to
25 to 30 MPa. This is followed by compression in a hypercompressor to 150 to 320 MPa.
Estimate the work required to compress ethylene to 25 MPa in a two-stage compressor.
Ž
A reciprocating compressor will be used. The gas is at an initial temperature of 15 Cand
Ž
is cooled to 25 C after the first-stage compression.
Solution
As the calculations will be repetitive, use a spreadsheet.
Data T in 288 K P in 1bar P out 250 ba R D 8.1345 J/mol K
T c 282.4 K P c 50.4 bar M 28.05 C p data from Appendix D

First stage
Intermediate pressure P 2 D 15.811388 bar eqn 3.39
Compression ratio D P 2 /P 1 D 15.814

C p for ethylene T in D 288 use eqn 3.11a
A B C D
Coeff. 3.806 0.15359 8.35E-05 1.755E-08
3.806 44.23392 6.924165 0.419256
C p
sum,C p D 41.535011 kJ/kmol K
gamma D C p / C p R D 1.2502821
From Figure 3.7, extrapolated, Ep D 0.86.
m D 0.232768 eqn 3.36a
T 2 D 547.52197 eqn 3.35
Mean temp D T 1 C T 2 /2 D 417.76099
C p at mean temp of 419.6K

3.806 0.15359 8.35E-05 1.755E-08
3.806 64.446364 14.69784 1.2966068
sum, C p D 54.851135 kJ/kmol K
new gamma D 1.1786657

revised m D 0.1811049
revised T 2 D 474.76117
revised mean temp D 381.38058
little change so leave T mean at 419.6 K
T r D T mean /T c D 1.4858357 1.5