Question

Linde process is used for air liquefaction. The high-pressure gas leaving the compressor is at 120 bar and is cooled to 306 K (516 kJ/kg) before it is sent through the heat exchanger where it exchanges heat with low pressure gas leaving the separator at 2 bar. A 14 K approach is desired at the hot end of the exchanger so that the low-pressure gas leaving the exchanger is at 292 K (526 kJ/kg). Enthalpy of saturated liquid and saturated vapour at 2 bar are 121 kJ/kg and 314 kJ/kg, respectively. Determine: (a) The fraction of the air liquefied during expansion. (b) Temperature of the air on the high-pressure side of the throttle valve.

Answer 1

(a) To determine the fraction of the air liquefied during expansion, we need to calculate the enthalpy of the low-pressure gas leaving the exchanger and compare it to the enthalpy of saturated liquid at 2 bar. The enthalpy of the low-pressure gas leaving the exchanger can be calculated using the temperature and the enthalpy of the high-pressure gas entering the exchanger:

Enthalpy of low-pressure gas = Enthalpy of high-pressure gas - Heat exchanged with low-pressure gas

= 516 kJ/kg - (526 kJ/kg - 516 kJ/kg)

= 526 kJ/kg

The fraction of the air liquefied during expansion can then be calculated as the difference between the enthalpy of the low-pressure gas and the enthalpy of saturated liquid at 2 bar, divided by the enthalpy of saturated vapour at 2 bar:

Fraction of air liquefied = (526 kJ/kg - 121 kJ/kg) / (314 kJ/kg - 121 kJ/kg)

= 0.48

(b) To determine the temperature of the air on the high-pressure side of the throttle valve, we need to calculate the temperature of the high-pressure gas entering the exchanger and subtract the 14 K approach. The temperature of the high-pressure gas entering the exchanger can be calculated using the enthalpy and the pressure:

Temperature of high-pressure gas = (Enthalpy - Enthalpy of saturated liquid) / (Enthalpy of saturated vapour - Enthalpy of saturated liquid)

* (Temperature of saturated vapour - Temperature of saturated liquid) + Temperature of saturated liquid

= (516 kJ/kg - 121 kJ/kg) / (314 kJ/kg - 121 kJ/kg)

* (226.8 K - 216.5 K) + 216.5 K

= 306 K

The temperature of the air on the high-pressure side of the throttle valve is then:

Temperature of high-pressure gas - Approach temperature

= 306 K - 14 K

= 292 K