We have encountered liquefaction since our first quality calculation in dealing with turbines. In refrigeration, throttling or isentropic expansion results in a partially liquid stream. The point of a liquefaction process is simply to recover the liquid part as the primary product.
Linde Liquefaction
The Linde process works by throttling high-pressure vapor. The Joule-Thomson coefficient, 
, must be such that the gas cools on expansion,2 and the temperature must be low enough and the pressure high enough to ensure that the expansion will end in the two-phase region. Since less than 100% is liquefied, the vapor phase is returned to the compressor, and the liquid phase is withdrawn. Multistage compression is usually used in the Linde liquefaction process to achieve the required high pressures. An example of the process pathways on a T-S diagram is shown in Fig. 5.12. The actual state of the gas entering the multistage compressor depends on the state of the feed.
Figure 5.12. Linde liquefaction process schematic. The system boundaries shown on the left are used in Example 5.5.
Example 5.5. Liquefaction of methane by the Linde process
Methane is to be liquefied in a simple Linde process. The feed and recycle are mixed, compressed to 60 bar, and precooled to 300 K. The vapor then passes through a heat exchanger for additional cooling before being throttled to 1 bar. The unliquefied fraction leaves the separator at the saturation temperature, and passes through the heat exchanger, then exits at 295 K. (a) What fraction of the gas is liquefied in the process; and (b) what is the temperature of the high-pressure gas entering the throttle valve?
Solution
The schematic is shown in Fig. 5.12. To solve this problem, first recognize that states 3, 6, 7, and 8 are known. State 3 is at 300 K and 60 bar; state 6 is saturated liquid at 1 bar; state 7 is saturated vapor at 1 bar; and state 8 is at 295 K and 1 bar. Use the furnished methane chart from Appendix E.
a. The System I energy balance is: H3 – [qH8 + (1 – q)H6] = 0
b. The energy balance for System II is: H4 – H3 = –q(H8 – H7) = –0.9286(1195 – 796.1) = –370.5 ⇒ H4 = 780
⇒ H4 = 780 @ 60 bar ⇒ chart gives –95°F = 203 K
Claude Liquefaction
The throttling process between states 4 and 5 in the Linde process is irreversible. To improve this, a reversible expansion is desirable; however, since the objective is to liquefy large fractions of the inlet stream, turbines are not practical because they cannot handle low-quality mixtures. One compromise, the Claude liquefaction, is to expand a portion of the high-pressure fluid in an expander under conditions that avoid the two-phase region, as shown in Fig. 5.13. Only a smaller fraction of the compressed gas enters the irreversible throttle valve, so the overall efficiency can be higher but more sophisticated equipment is required.
Figure 5.13. The Claude liquefaction process.
5.6. Engines
Steam is not the only working fluid that can be used in a power producing cycle. A common alternative is to use air, mixed with a small amount of fuel that is burned. The heat of combustion provides energy to heat the gas mixture before it does work in an expansion step. A major benefit of using air is that a physical loop is not necessary; we can imagine the atmosphere as the recycle loop. This approach forms the basis for internal combustion engines like lawn mowers, jet engines, diesels, and autos. An online supplement introduces the gas turbine, the turbofan jet engine, the internal combustion engine, and the diesel engine.
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