08.08 - Reference States

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Departure Functions: PREOS.xls Compressor and OVC Design (11min) (uakron.edu) Redesign the ordinary vapor compression cycle (OVC) using propane as discussed in Chapter 5, this time applying PREOS.xls instead of the chart. In this sample calculation, the cycle operates from -100F in the evaporator with a compressor that takes the saturated vapor from the evaporator to 10 bars and 180F. With this procedure, applying PREOS.xls could be adapted to any compound in the database, not just propane. So PREOS.xls represents the equivalent of charts for roughly 200 compounds, and that's just what it can do for pure fluids.
Comprehension Questions: Assume a reference state of the saturated liquid at 1 bar. Use Eqn. 2.47 (SCVP eq) to estimate saturation conditions.
1. Compute the enthalpy (J/mol) of saturated vapor N2O at -100F.
2. Compute the enthalpy (J/mol) of saturated liquid N2O at 80F.
3. Compute the enthalpy (J/mol) of N2O at 60 bars and 350F.
4. Compute the COP for this OVC cycle.

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Peng-Robinson Properties - Excel (6:56) (msu.edu)

Provides an overview of using the Peng-Robinson spreadsheet Preos.xlsx for calculation of H, U, S and use of solver.

Comprehension Questions:

1. For liquid propane at 298K and 1 MPa, and a reference state of 298K and 1bar propane vapor, what is the ideal gas contribution to "H-HR" (J/mol)?
2. For liquid propane at 298K and 1 MPa, and a reference state of 298K and 1bar propane vapor, what is the ideal gas departure contribution: "H-Hig" (J/mol)?
3. For liquid propane at 298K and 1 MPa, and a reference state of 298K and 1bar propane vapor, what is the tabulated value of "H" (J/mol)?
4. Explain the similarity and difference between the numerical values of "H" and "H-Hig".
5. Ethane at 350K and 5 bars is expanded through an adiabatic, reversible turbine to 1 bar. What is the temperature (K) at the turbine outlet?

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Peng-Robinson Properties - Matlab (13:10) (msu.edu)

This screencast shows the types of calculations that can be done usiing the Matlab GUI. Includes finding states at a given P and T, matching S, finding saturations, and developing a custom objective function. Selection of root stability is stressed and demonstrated several times.

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Heat Pump Design (20min) (uakron.edu) This sample calculation was adapted from a 1987 practice test. It walks carefully through the coefficient of performance (COP) determination for a heat pump that might be applied to a home in Ohio, and the practicality of a heat pump compared to a furnace. The problem assumes a desired indoor temperature of 70F and an average outdoor temperature of 45F, with a 10F approach temperature on both sides. Care is needed to adapt the COP to heat pump application because the quantity of interest is QH, not QC. This video applies Freon-12, which has since been outlawed because it contributed to the hole in the ozone layer that comprised what may be the first example of anthropogenic catastrophe on a global scale. The good news is that the ozone hole has begun to heal itself since the regulation of Freon-12. Nevertheless, Freon-12 did possess remarkable properties as a refrigerant, highlighting the motivation to contiuously search for its replacement. As an exercise, it is suggested that you redesign this heat pump using HFO1234yf, a new refrigerant with a global warming potential of 4, compared to 3800 for HFC134a and virtually infinity for Freon-12.

Comprehension Questions: Assume a reference state of the saturated liquid at 1 bar. Use Eqn. 2.47 (SCVP eq) to estimate saturation conditions.
1. Compute the enthalpy (J/mol) of saturated vapor HFO1234yf at 80F.
2. Compute the enthalpy (J/mol) of saturated liquid HFO1234yf at 35F
3. Compute the enthalpy (J/mol) of HFO1234yf exiting an adiabatic reversible compressor being fed saturated vapor at 80F.
4. Compute the COP for this OVC cycle.

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Real Gas Expansion (LearnChemE.com, 5min) determines the final state of a real gas that expands adiabatically into a vacuum by an energy balance. Real Gas Expansion Part 2: Excel Solver (LearnChemE.com, 5min) uses the Peng-Robinson equation of state to compute the necessary properties. This two-part series shows the solution of a fairly challenging problem. Nevertheless, the solution appears to be easy when using the right tool.

Comprehension Questions:

1. This problem involves the use of just the energy balance. Can you think of a similar problem that would use both the energy and entropy balance?

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Thermodynamic pathways of EOS's for arbitrary reference states (uakron.edu, 20min) The development of a thermodynamic pathway from an arbitrary reference state to a given state condition is independent of the thermodynamic model. It depends only on (1a) identifying the condition of the reference state (e.g. ideal gas, real vapor, or liquid) (1b) transforming from the reference state to the ideal gas, if necessary (2) transforming from the ideal gas at the condition of the reference state to the ideal gas at the given state condition (3a) identifying the condition at the given state (3b) transforming from the ideal gas at the given state to the real fluid at the given state. The methodology is illustrated for two thermodynamic models: the Psat/Hvap model of Figure 2.6c,Eqs 2.45,47 vs. the PR EOS. The screencast is a bit long, but it covers 16 sample calculations (8 for H and 8 for S) and comparisons between PREOS vs Psat/Hvap. You might like to refer back to Sections 2.10 and 3.6 to review the Psat/Hvap model and the elemental reference state. Push pause before each sample calculation and check whether you can predict the next answer.

Comprehension Questions:

1. Compute "H" by hand for propane at 80C and 3 MPa relative to a reference at 230K and 1bar, assuming Cpig/R = 8.85 and the PR EOS. You may use PREOS.xlsx to compute H-Hig, but you must show your hand calculations for each step (1a-3b). Compare your answer to the result tabulated in PREOS.xlsx.
2. Compute "S" by hand for propane at 80C and 3 MPa relative to a reference at 230K and 1bar, assuming Cpig/R = 8.85 and the PR EOS. You may use PREOS.xlsx to compute S-Sig, but you must show your hand calculations for each step (1a-3b). Compare your answer to the result tabulated in PREOS.xlsx.
3. Compute "H" by hand for propane at 80C and 3 MPa relative to a reference at 230K and 1bar, assuming Cpig/R = 8.85 and the Psat/Hvap model. Show your hand calculations for each step (1a-3b). Compare your answer to the result tabulated in PREOS.xlsx.
4. Compute "S" by hand for propane at 80C and 3 MPa relative to a reference at 230K and 1bar, assuming Cpig/R = 8.85 and the Psat/Hvap model. Show your hand calculations for each step (1a-3b). Compare your answer to the result tabulated in PREOS.xlsx.

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This sample calculation shows how to compute the liquefaction in the Linde process for methane as the operating fluid. (uakron, 8min) The Linde process is a slight variation on the OVC cycle wherein the liquefied fraction exiting the throttle is captured as product and removed from the process. There is also heat integration in the sense that the cold vapor is used to precool the feed to the throttle.

FYI: Since natural gas is mostly methane, this process could be easily adapted to the production of liquefied natural gas (LNG) or liquified petroleum gas (LPG, mostly propane). Liquefied gases may seem impractical when you first encounter them, but they are more efficient for transport because they are so much more dense than the gases. Keeping them as liquids is basically a reflection of the effectiveness of the insulation. If any gas leaks from the relief valve (~1.1 bar), then liquid must evaporate to fill the space. The requisite heat of vaporization in that case cools the remaining below the boiling temperature. No heat = no vaporization.

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