Analysis of the Claude process in liquefying natural gas

Assume that kinetic and potential energy changes are negligible, and this is a steady-state process. The whole operation is adiabatic, and the surroundings are at 290 K. 

It is economic to cool the compressed methane for liquefaction by the gas that does not liquefy in the throttling process. In the Claude process, the gas at an intermediate temperature splits into two parts. One of them enters the expander and exhausts as a saturated or slightly superheated vapor, and produces work. The remaining gas is further cooled in the second heat exchanger and throttled to liquefy. The portion that is not liquefied is combined with the output vapor of the expander and recycled into the compressor. 

Mass and energy balances for the control volume and adiabatic expander yield 

Wout =mgH9 +rhl5Hl5-m4H4 =mu(Hn-Hs) The combination of (a) and (b) yields the portion y that is liquefied 

For isentropic expansion S5 = S12s = 8.590 kJ/(kgK), and we have the quality at state 12  

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Example 4.23 Analysis of the Claude process in liquefying natural gas We wish to partially liquefy natural gas in a Claude process shown in Figure 4.28. It is assumed that the natural gas is pure methane, which is compressed to 80 bar and precooled to 300 K. In the expander and throttle the methane is expanded to 1.325 bar. The methane after the first heat exchange at state 5 is at 80 bar and 250 K. Thirty percent of the first heat exchangers output is sent to the expander. Only 10% of the first heat exchange is liquefied. The expander efficiency is 0.8. Determine the work loss in the liquefaction section excluding compression and precooling. 

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