CM 3230 Thermodynamics, Fall 2016 Lecture 16

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1 CM 3230 Thermodynamics, Fall 2016 Lecture Joule-Thomsom Expansion - For a substance flowing adiabatically through a throttle (valve or pourous plug): in > out and negligible change in kinetic and potential energy, h q in w s,by 0 isenthalpic - oints of interest: given in, T in and out, what is T out and/or phase condition? - If fluid is an ideal gas, T out T in : no cooling or heating will occur Joule-Thomson expansion effects are due to real gas behavior - can characterize the effect using the Joule-Thomson Coefficient, μ JT μ JT ( T ) h CM3230 Lecture 16 age 1 - Q: If we want temperature to decrease as the fluid goes through the adiabatic throttle, do we want μ JT > 0 or μ JT < 0? - Values of μ JT could be found from laboratory data/studies. Alternatively, could use thermodynamic estimation: dh c p dt + (v ( v T ) ) d ( T (( v ) T ) v) real h c p c p id gas (( v T ) v) ideal 2 v [T ( T 2)] d - Since c real is quite complicated to evaluate using cubic EOS (e.g. Van der Waals, eng Robinson, etc.), a more tractable alternative is to use the virial EOS based on pressure expansion (see example 5.9, pp ) - Main application: refrigeration and gas liquefaction CM3230 Lecture 16 age 2

2 - Joule-Thomson Inversion Curves (Figures taken from D. Miller, Joule-Thomson Inversion Curve, Corresponding States, and Simpler Equation of State, Ind. Eng. Chem. Fund., v 9, no. 4, 1970, pp ) Note: equation 5 referred to in Figure 2 is given by: r (18.54/T r ) T r 2 ) CM3230 Lecture 16 age 3 - Two competing molecular activity: a) μ JT > 0. When molecular attraction dominates, expansion increases potential energy and kinetic energy decreases decrease in temperature b) μ JT < 0. When molecular repulsion dominates, expansion decreases potential energy and kinetic energy increases increase in temperature - The inversion curve is when μ JT 0. For a given pressure, the temperature where μ JT 0 is known as the Boyle temperature, i.e. T Boyle [T()] μjt 0 - Inside the dome is where μ JT > 0. Note: this dome is not a vapor-liquid dome! CM3230 Lecture 16 age 4

3 2. Gas Liquefaction - Basic units: a) Compressor: this will increase the pressure to desired condition of the throttle (but temperature will increase) b) Cooler: reduces temperature before throttle process Compression+cooling must move the condition to be inside the JT-inversion dome. c) Throttle: Joule-Thomson (isenthalpic) expansion gas has cooled significantly to attain partial liquefaction d) Separator: extract the liquefied product CM3230 Lecture 16 age 5 Draw the gas liquefaction diagram: - Improvements (Linde process): a) Use cold vapor from the separator and cool the gas before it enters the throttle b) After the heat exchanger, mix with gas feed CM3230 Lecture 16 age 6

4 Example 5.10 (page 302) Given: N 2, enters throttle at T in 122 C and in 100 bar exits at out 1 bar. Data: T c 126.2K, c 33.8 bar, ω Required: Solution: percentage liquefaction (if any) use arture functions instead h T out ideal c T in dt + [ h Tout, out h Tin, in ] Assuming outlet is a vapor-liquid mixture, can use Antoine equation: ln( out ) T out 6.60 T out 77.15K T out ideal c At the inlet: T r,in 1.20 and r,in 2.96 h Tin, in dt 2270 J T in mol RT c ( (0.039)( 0.934)) 2983 J mol CM3230 Lecture 16 age 7 Since the process is isenthalpic, h 0 From arture plots, at r,out J mol + [ h T out, out J mol ] h Tout, out 713 RT c (8.314)(126.2) h Tout, out (vap) 0.1 h Tout, out (liq) (0.039)( 7.5) 5.7 x( 0.1) + (1 x)( 5.7) per cent liquefaction: 10% x 0.9 CM3230 Lecture 16 age 8

5 Figure 1. TS Diagram for nitrogen. from: Thomson_effect#/media/File:Throttling_in_Ts_diagram_01.jpg CM3230 Lecture 16 age 9 Some notable features of Figure 1: - Isenthalpic lines appear flat when < 2 bars ideal gas behavior, i.e. isenthalpic implies isothermal - Downward slopes in the T-s diagram locates the positive Joule-Thomson coefficients ( pressure decreases as entropy increases along the isenthalpic curves) - Just operating in the region where μ JT > 0 is not sufficient for liquefaction still needs the initial condition to be chosen such that the isenthalpic expansion path will enter the vapor-liquid dome while exiting to the outlet pressure CM3230 Lecture 16 age 10

Basic Thermodynamics Module 1

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