Study Questions for
“Separation Process Principles” by
J. D. Seader and Ernest J. Henley
Chapter 10
1. Why are rigorous solution procedures difficult and tedious for multicomponent, multistage separation operations?
Section 10.1:
2. What are the assumptions for the theoretical model of an equilibrium stage? What composition variables are used for the two phases? What types of equations are written? Why are they called the MESH equations?
3. In the model, can each stage have a feed, a vapor sidestream, and/or a liquid sidestream? How many independent equations apply to each stage for C components?
4. In the model equations, are K-values and enthalpies counted as variables? Are the equations used to compute these properties counted as equations?
5. For a cascade of N countercurrent equilibrium stages, what is the number of variables, number of equations, and number of degrees of freedom? What are typical specifications, and what are the typical computed variables? Why is it necessary to specify the number of equilibrium stages and the locations of all sidestream withdrawals and heat exchangers?
Section 10.2:
6. Early attempts to solve the MESH equations were the Lewis-Matheson and Thiele-Geddes methods. Why are they not favored for computer calculations?
7. What are the four methods most widely used to solve the MESH equations?
8. How do equation-tearing and simultaneous-correction procedures differ?
Section 10.3:
9. What is a tridiagonal matrix (TDM) equation? How is it developed from the MESH equations? In the matrix equation, what are the variables and what are the tear variables? What is a tear variable? Is there one TDM equation for each component? If so, can each equation be solved independently of the others?
11. Why is the Wang-Henke method called the Bubble-Point (BP) method? For what types of problems does it work? Are initial estimates of the tear variables required? If so, how is that accomplished?
12. What is meant by normalization of a set of variables?
13. In the BP method, which of the MESH equations are used to compute a new set (i.e. update) of total molar vapor flow rates leaving each stage?
14. What criterion is used to determine convergence of the BP method?
15. Is convergence of the BP method sensitive to the initial guesses for the tear variables?
16. What types of plots are useful for displaying the results of the BP method?
17. Why is the modified McCabe-Thiele diagram of Fig. 10.14 useful?
18. Does the Sum-Rates (SR) method use tridiagonal matrix equations? How does the SR method differ from the BP method? For what types of problems is the SR method preferred over the BP method? What are the tear variables in the SR method?
19. Why does the set of stagewise enthalpy balances in the SR method have to be solved simultaneously by the Newton-Raphson method for a new set of temperatures?
20. What is the criterion for convergence of the SR method?
21. Are stagewise enthalpy balances important when solving multicomponent, multistage liquid-liquid extraction problems? If not, why not? What is the most difficult aspect of the isothermal sum-rates method?
Section 10.4:
22. What limitations of the BP and SR methods are overcome by the simultaneous correction (SC) methods? How do the SC methods differ from the BP and SR methods?
23. How do the Goldstein-Stanfield and Naphtali-Sandholm SC procedures differ?
24. Why does the SC procedure of Naphtali and Sandholm use, as composition variables, the component flow rates rather than mole fractions?
26. What is the difference between a tridiagonal matrix (TDM) equation and a block tridiagonal matrix (BTDM) equation? How do the algorithms for solving these two types of equations differ?
27. In the BP and SR methods, the TDM equations are linear in the variables. Is the BTDM equation of the Naphtali-Sandholm SC method linear? If not, how is it solved?
28. What is a Jacobian matrix? How is the Jacobian formulated?
29. What is the convergence criterion for the Naphtali-Sandholm SC method?
30. Is it always advisable to apply the full correction at each iteration of the Naphtali-Sandholm method? If not, how is the fraction of the correction to be applied best determined?
31. If the correction causes some variables to become negative, what should be done?
Section 10.5:
32. What types of calculations consume the most time in the BP, SR, and SC methods? How does the Inside-out method reduce this time?
33. How do the iteration variables in the Inside-out method differ from those in the SC methods?
34. Why is the Inside-out method sometimes referred to as a two-tier method?
35. To what types of problems can current implementations of the Inside-out methods be applied?
