11.06 - Redlich-Kister and the Two-parameter Margules Models

Binary VLE Flash Calculations Using the Lever Rule (uakron.edu, 6min)

When you want to perform flash calculations with one activity model and many components, you should use the methods of Section 10. 4 or Section 12.7. When you want to perform flash calculations with two components and many activity models, this video shows the best method. Starting with a Txy or Pxy binary phase diagram, the procedure of Section 10.1 is easily adapted. Since binary Pxy and Txy diagrams are the first thing you do for any activity model, you can simply apply this procedure any time for any activity model. This example shows how to interpret the phase diagram for 2-propanol+water at 30C, similar to Figure 11.5.

Comprehension Questions: Use the SCVP model of vapor pressures and the M2 activity model for the following. (Hint: you might want to watch the videos below before answering these.)
1. Sketch the Pxy diagram for methanol+benzene at 373K with A12=1.5 and A21=2.0.
At P = 2683mmHg and zM = 0.4, the mole fraction methanol in the liquid phase is closest to:
(a) 0.25 (b) 0.33 (c) 0.66 (d) 0.75.
2. Sketch the Pxy diagram for methanol+benzene at 373K with A12=1.5 and A21=2.0.
At P = 2683mmHg and zM = 0.4, the molar amount of the liquid phase is closest to:
(a) 0.25 (b) 0.33 (c) 0.66 (d) 0.75.
3. Sketch the Txy diagram for mtbe+ethanol at 760mmHg with A12=1.5 and A21=1.2.
At T = 333K and zM = 0.3, the mole fraction mtbe in the liquid phase is closest to:
(a) 0.25 (b) 0.33 (c) 0.66 (d) 0.75.
4. Sketch the Txy diagram for mtbe+ethanol at 760mmHg with A12=1.5 and A21=1.2.
At T = 333K and zM = 0.3, the molar amount of the liquid phase is closest to:
(a) 0.25 (b) 0.33 (c) 0.66 (d) 0.75.

Fitting the M2 model parameters using Excel. (uakron.edu, 6min) You can type Eqns. 11.2 and 11.38 directly into Excel then it is a simple matter to compute the A12 and A21 values from a single data point and compute the γ's, P's, and y's at all compositions assuming constant values for A12 and A21. This generates a phase diagram in short order. The procedure is illustrated in this presentation for the 2-propanol+water system at 30C, similar to Examples 11.1 and 11.5 in the textbook. It would be a simple matter to adapt this spreadsheet to fit the experimental data in Example 11.8 by computing the deviations at each composition. With this tool readily available, you should be able to apply the M2 model to any binary mixture in short order.

Comprehension Questions: You may assume the SCVP model for purposes of the calculations below (but you should use more accurate vapor pressure estimates for more professional purposes).

1. At 760 mm Hg the system acetone(1)+hexane(2) exhibits an azeotrope at 68 mole percent acetone with a boiling point of 49.8°C. 
a. Estimate the A12 and A21 parameters.
b. Estimate the bubble point pressure and vapor composition of 10 mole percent acetone at this temperature.
2. Acetonitrile+water forms an atmospheric pressure azeotrope at 70 mole% acetonitrile, 76°C.
a. Estimate the A12 and A21 parameters.
b. Estimate the bubble point pressure and vapor composition of 80 mole percent acetonitrile at this temperature.

The extension to the multicomponent M2 flash spreadsheet (uakron.edu, 10min) adapts the multicomponent M1 spreadsheet by recognizing that summing rows of a matrix times mole fractions involves a simple matrix multiplication. (Matrix operations involve highlighting the cells of interest, typing the MMULT function, and hitting ctrl+shift+enter.) The column multiplication simply applies the sumproduct function. In this way, we just need to insert one more column relative to the multicomponent M1 spreadsheet, then change the expression for gi, and we are done.

Comprehension Questions:
1. Find the bubble and dew temperatures of an equimolar mixture of 2-propanol, water, and methanol at 2 bars using the M2 model. Then compute V/F x and y at the temperature that is halfway between dew and bubble. Is it what you expected?
2. Find the bubble and dew temperatures of an equimolar mixture of 2-propanol, water, and methanol at 3 bars using the M2 model. Then compute V/F x and y at the temperature that is halfway between dew and bubble. Is it what you expected?
3. Find the bubble and dew temperatures of an equimolar mixture of 2-propanol, water, and methanol at 4 bars using the M2 model. Then compute V/F x and y at the temperature that is halfway between dew and bubble. Is it what you expected?
4. Find the bubble and dew temperatures of an equimolar mixture of 2-propanol, water, and methanol at 5 bars using the M2 model. Then compute V/F x and y at the temperature that is halfway between dew and bubble. Is it what you expected?