# 14.04 LLE Using Activities

### M1 Model for Tx LLE Phase Diagram in Excel

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?

### Crashing LLE and VLE Phase Boundaries As Nonideality Increases

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 (kij) parameter. The calculations show the liquid-liquid equilibrium (LLE) phase boundary as well as the vapor-liquid equilibrium (VLE) boundary. As the estimated nonideality (kij) 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 kij is required to make the LLE binodal barely touch the VLE at 1 bar?
4. What value of kij is required to make the LLE binodal barely touch the VLE at 10 bars?