This sample calculation for methanol+benzene shows how to quickly generate the Tx binodal in Excel (uakron, 11min) using the Margules Acid-Base (MAB) model and the Excel iteration feature.(10min, uakron.edu) You generally need to start manually by setting the initial guess for the dilute component in each phase equal to the reciprocal of its infinite dilution activity coefficient. After a couple of iterations, you can set the "guess" cell equal to the "calculated" cell, and let Excel do the rest. Once you get one temperature right, you can usually just drag the fill handle to get the complete Tx diagram in short order. It is best to start at a low temperature to ensure that you detect LLE if it exists.

Note: This is a companion file in a series. You may wish to choose your own order for viewing them. For example, you should implement the first three videos before implementing this one. Also, you might like to see how to quickly visualize the Txy analog of the Pxy phase diagram. If you see a phase diagram like the ones in section 11.8, you might want to learn about LLE phase diagrams. The links on the software tutorial present a summary of the techniques to be implemented throughout Unit3 in a quick access format that is more compact than what is presented elsewhere. Some students may find it helpful to refer to this compact list when they find themselves "not being able to find the forest because of all the trees."

Comprehension Questions
1. Continue the temperature range to 380K with a feed composition of 60mol% methanol. What are the phase compositions and phase amounts in that case? (ANS. 0.299, 0.701, 75%beta-rich).
2. Continue the temperature range to 400K with a feed composition of 45mol% methanol. What are the phase compositions and phase amounts in that case?
3. Generate the binodal for methanol+nPentane for T=[400-460]. At 400K with a feed composition of 60mol% methanol, what are the phase compositions and phase amounts in that case?

Txy Phase Diagram Showing LLE and VLE Simultaneously (9min,uakron.edu)

The binary Txy phase diagram of methanol+benzene is visualized with sample calculations of the SSCED model with several values of the nonideality (k_ij) parameter. The calculations show the liquid-liquid equilibrium (LLE) phase boundary as well as the vapor-liquid equilibrium (VLE) boundary. As the estimated nonideality (k_ij) increases, the LLE boundary crashes into the VLE. It is so exciting that it makes a thermo nerd wax poetic about the "valley of Gibbs."

Comprehension Questions:

1. The LLE phase boundary moves up as the nonideality increases. Which way does the VLE contribution move? Explain how this relates to the molecules' escaping tendencies.
2. How would this phase diagram change if the pressure was increased to, say, 10 bars?
3. What value of k_ij is required to make the LLE binodal barely touch the VLE at 1 bar?
4. What value of k_ij is required to make the LLE binodal barely touch the VLE at 10 bars?

Plotting Ternary Data (6:25) (msu.edu)

This screencasts discusses equilateral and Cartesion plots, the one- and two-phase regions, Plait point, lever rule, interpolation of tie lines using the tie line plot, and the relation of the tie-line slope to the K ratio at small concentrations.

Hints for Generating LLE Envelopes (2:25) (msu.edu)

This screencasts makes several recommendations that help generate LLE phase envelopes most successfully.

LLE Calculations: UNIFAC from Actcoeff.xlsx Calculation of LLE. (5 min) (LearnChemE.com)
See also - Supplement on Iteration of LLE with Excel and Matlab. Hints on converging LLE using Excel with the method presented in the textbook. For details, see LLE by UNIFAC Details.

LLE flash using Matlab/Chap14/LLEflash.m (5:54) (msu.edu)

An overview of the LLE flash routine in Matlab, including an overview of the program logic and then an example of how to run the program.

See also - Supplement on Iteration of LLE with Excel and Matlab.

Details for calculating LLE using UNIFAC (7:45 msu.edu) from Actcoeff.xlsx.

This screencast provides details on setting up the macro in Excel. See also - Supplement on Iteration of LLE with Excel and Matlab. Hints on converging LLE using Excel with the method presented in the textbook. For an overview without all the details see the comment  LLE Calculations: Unifac.xls.

Solid-Liquid Equilibria using Matlab (7:17) (msu.edu)

The strategy for solving SLE is discussed and an example generating a couple points from Figure 14.12 of the text are performed. Most of the concepts are not unique to UNIFAC or MATLAB.

Solid-liquid Equilibria using Excel (7:38min, msu)

The strategy for solving SLE is discussed and an example generating a couple points from Figure 14.12 of the text are performed. Most of the concepts are not unique to UNIFAC or Excel. This screeencast shows how to use the solver tool to find solubility at at given temperature.