Chapter 18 Problems Are

Chapter 18 – Mathematical Analysis of Solvent Extraction Columns

In this problem set you are given ternary systems (translation: three chemicals) that form two immiscible liquids phases. One phase (the solvent) will be used to extract a third chemical (the solute) from the other phase (the diluent) in a multi-stage column.

18.1 100 mol/min of methanol with 15 mol% benzene is extracted in a two-stage column with 100 mol/min of pure heptane at 20^{o}C.

a. You may have already done this part in problem 17.1. If so, skip to part b. Construct an LLE graph with benzene mole fraction on the ordinate (y-axis) and methanol on the abscissa (x-axis). For your convenience, the data and a formatted graph are found in Excel "MBH Data" below. Fit the extract and raffinate curves with polynomial functions: y = f(x). Also, construct a graph of tie line slope vs. the corresponding extract benzene composition and fit it with a polynomial. These will represent your equilibrium data - the compositions of any phases in equilibrium will satisfy all three polynomial equations.

b. For your convenience, a DIY PFD for a two-stage column is already set up in Excel "MBH Data". Find the compositions and amounts of all streams using mathematical methods. Compare the performance with the one-stage extractor in problem 17.1.

c. Plot lines connecting compositions of passing (e.g. R1 – E2) and leaving streams (e.g. R1 – E1) as discussed in Chapter 18. Note that the passing stream lines intersect outside the graph if extended. This will be the basis of a graphical method (Hunter-Nash) developed in Chapter 19.

Why this system? See problem 17.1.

18.2 100 mol/min of a mixture with 70 mol% benzene with 30 mol% ethanol is contacted with pure glycerol at 25

^{o}C in a 3-stage extraction column. The desired purity of the raffinate is 94.8 mol% benzene.

a. You may have already done this part in problem 18.1. If so, skip to part b. Construct an LLE graph with ethanol mole fraction on the ordinate (y-axis) and benzene mole fraction on the abscissa (x-axis). For your convenience, the data and a formatted graph are found in Excel "BEG Data" below. Fit the extract and raffinate curves with polynomial functions: y = f(x). Also, construct a graph of tie line slope vs. the corresponding extract methanol composition and fit it with a polynomial. These will represent your equilibrium data - the compositions of any phases in equilibrium will satisfy all three polynomial equations.

b. For your convenience, a DIY PFD for a 3-stage column is already set up in Excel "BEG Data". Find the compositions and amounts of all streams using mathematical methods. Compare the flow rate of glycerol required compared with the one-stage extractor in problem 17.2.

c. Plot lines connecting compositions of passing and leaving streams as discussed in Chapter 18. Note that the passing stream lines intersect outside the graph (~x=2.1) if extended. This will be the basis of a graphical method (Hunter-Nash) developed in Chapter 19.