07.06 Solving The Cubic EOS for Z
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- Chapter 1 - Basic concepts
- Chapter 2 - The energy balance
- Chapter 3 - Energy balances for composite systems.
- Chapter 4 - Entropy
- Chapter 5 - Thermodynamics of Processes
- Chapter 6 - Classical Thermodynamics - Generalization to any Fluid
-
Chapter 7 - Engineering Equations of State for PVT Properties
- 07.01 Experimental Measurements
- 07.02 Corresponding States
- 07.05 Cubic Equations of State
- 07.06 Solving The Cubic EOS for Z
- 07.07 Implications of Real Fluid Behavior
- 07.08 Matching The Critical Point
- 07.09 -The Molecular Basis of Equations of State: Concepts and Notation
- 07.10 Molecular Basis of Equations of State: Molecular Simulation
- 07.11 - The molecular basis of equations of state: analytical theories
- Chapter 8 - Departure functions
- Chapter 9 - Phase Equlibrium in a Pure Fluid
- Chapter 10 - Introduction to Multicomponent Systems
- Chapter 11 - An Introduction to Activity Models
- Chapter 12 - Van der Waals Activity Models
- Chapter 13 - Local Composition Activity Models
- Chapter 14 - Liquid-liquid and solid-liquid equilibria
- Chapter 16 - Advanced Phase Diagrams
- Chapter 15 - Phase Equilibria in Mixtures by an Equation of State
- Chapter 17 - Reaction Equilibria
- Chapter 18 - Electrolyte Solutions
Solving the PR EOS for Z . (8
Using Preos.xlsx and Interpreting
3. Using Preos.xlsx and Interpreting Output (11:38) (msu.edu)
This screencast includes discussion of what we mean by the casual terminology 'three root region' and 'one root region', and how to interpret screen output. Also, the screencast spends time dicussing selection of stable roots using fugacity.
Comprehension Questions:
1. Is it possible to have a 1-root region below the critical temperature?
2. Is it possible to have a 3-root region above the critical temperature?
3. How does fugacity help us to identify the proper root to select?
4. Would argon at 5 MPa be in the 1-root or 3-root region?
Peng-Robinson PVT Properties
1. Peng-Robinson PVT Properties - Excel (3:30) (msu.edu)
Introduction to PVT calculations using the Peng-Robinson workbook Preos.xlsx. Includes hints on changing the fluid and determining stable roots.
Comprehension Questions:
1. At 180K, what value of pressure gives you the minimum value for Z of methane? Hint: don't call solver.
2. At 30 bar, what value of pressure gives Z=0.95 for methane?
3. Compute the molar volume(s) (cm3/mol) for argon at 100K for each of the following?
(a) 3.000 bars (b) 4.000 bars (c) 3.26903 bars.
Peng Robinson Using Solver fo
5. Peng Robinson Using Solver for PVT and Vapor Pressure - Excel (4:42) (msu.edu)
Describes use of the Goal Seek and Solver tools for Peng-Robinson PVT properties and vapor pressure.
Comprehension Questions:
1. Which of the following represents the vapor pressure for argon at 100K?
(a) 3.000 bars (b) 4.000 bars (c) 3.26903 bars.
Selecting Stable Roots
4. Selecting Stable Roots (1:11) (msu.edu)
Selecting stable roots is often one of the confusing aspects in working with cubic equations of state. This screencasts gives a visual picture of how the roots and stability are related to the vapor pressure and EOS humps at subcritical temperatures.
Solving vdW EOS for density
6. Solving for density (uakron.edu, 9min) An alternative to solving directly for Z is to solve for density then compute Z=P/(ρRT). This requires iterative solution and it is not very expedient for repetitive calculations, but it requires no rearrangement of the EOS and it is easy to visualize. This sample calculation is illustrated here for the vdW EOS, solving for the density of propane as: (a) liquid 25C,11bars (b) liquid 62C,35bars (c) vapor at 80C and 30bars.
Comprehension Questions:
1. Solve for the liquid density (mol/cm3) of n-pentane at 62C and 2.5 bars using the vdW EOS.
2. Solve for the Z-factor of liquid n-pentane at 62C and 2.5 bars using the vdW EOS.
3. What's the value of the Z-factor at 80C and 30 bars according to this presentation?
Using a Macro to Create an Isotherm (Excel)
Using a macro to create an isotherm (Excel) (msu.edu, 14:31) The tabular Excel display is convenient for viewing all the intermediate values, but no so good for building a table such as for an isotherm. This screencast shows how to write/edit a macro to build a table by copying/pasting values. The screencast creates an isotherm on a Z vs. Pr plot over 0.01 < Pr < 10.