Question

n-butane is to be liquefied to make liquid petroleum
gas (LPG). The butane is available at 25◦C and 1 bar,
it will be compressed to 15 bar in a compressor that
has an isentropic efficiency of 85%, cooled to 0◦C
in a heat exchanger, and then expanded adiabatically
to 1 bar, with the vapor recycled to the compressor.
Determine the work required per kg of LPG produced.

Answer 1

Initial temperature of n-butane, T₁ = 25⁰C

Initial pressure of n-butane, P₁ = 1 bar

Final pressure of n-butane after compressing = 15 bar

C_P of butane = 1.73 KJ/Kg

C_v of butane = 1.57 KJ/Kg

n = 1.1019

Work done to compress n-butane,W

But isentropic efficiency is 85% , hence

Net actual work required = 154.577 J/kg..........................................................................(1)

As we know that

Also

As the boiling point of butane is near 0⁰C, therefore

In order to cool butane, amount of heat Q rejected per kg of butane

So, 532712.65 J/kg of heat liberated by cooling n-butane

Then again this gas is expanded to 1 bar, hence work produced during the expansion is

................................................(2)

Net word required = 154.577 - 131.5173

= 23.0597 J/kg

Hence 23.0595 J/kg of work required per kg of LPG produced.