## Info

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table 4.1 Methods Summary

Method

Source

Best applications

Range of specifications

Boiling point

Sum rates

2N Newton

Global Newton

Global Newton

Wang and Henke (24) Holland (8)

Sujata (35) McNeese (36) Burningham and Otto (34)

Naphtali and Sandholm (42) Holland (8)

Goldstein and Stanfield (45)

Global Newton Ishii and Otto (47)

Relaxation

Relaxation

Inside-out lnside-out

Nonequilibrium

Rose. Sweeny, and Schrodt (60)

Ketchum (64) Drew and Franks (65)

Boston (70)

Russell (72)

Krishnamurthy and Taylor

Narrow-boiling systems Ideal or nearly ideal systems Best if few feeds and sidedraws, superfractionators. isostrippers

Absorbers and strippers, especially the widest-boiling systems

Steam strippers

Narrow- or middle-boiling systems

Nearly ideal, many trays a problem

Debutanizers, demethaniiers

High number of trays, few components

All type mixtures including nonideal

Requires good starting values

Chemical and reactive systems

Few trays and many components, mildly nonideal to nonideal

Refinery columns

Ideal to nonideal systems Has been applied to amine systems

Wide range of difficult to solve columns

Nonideal and reactive systems

Wide variety of boiling-point ranges, columns and specifications

Ideal to nonideal systems Superfractionators, petrochemical, chemical columns

Wide variety of boiling-point ranges, columns, and specifications

Ideal to nonideal systems Refinery columns, complex columns

Mass-transfer-inhibited systems, replacement for use of efficiencies

Highly nonideal and reactive systems

Product rates and reflux; or two of condenser duty, reboiler duty, reflux ratio, and boilup

All side products flows and duties must be specified

Two of condenser duty, reboiler duty, reflux, and boilup plus all side product flows, one purity allowed

Two of condenser duty, reboiler duty, reflux, and boilup plus all side product flows, one purity allowed

Variety but may allow only one purity

Variety but may allow only one purity

Same as Naphtali-Sandholm

Wide variety, multiple purity, allows for broad mix including least squares solution when ove (-specified

Wide variety, multiple purity must have balance between number of specifications and variables

Same as Naphtali-Sandbolm be the BP method (Sec. 4.2.5) for simple, tall, nearly ideal columns distilling narrow-boiling mixtures, the 2N Newton (Sec. 4.2.8) for shorter columns with wider boiling ranges, and the SR method (Sec. 4.2.7) for very wide boiling absorber-strippers. If you have a very specific problem, you may be able to tune any of the methods to solve your problem.

4.3.5 What to look for in choosing a package or a method

The conditions listed below are somewhat ordered from most important to least important. Chan et al. (5) provide a detailed overview in selecting distillation software.

1. The accuracy of the final results is the most important test of a rigorous method. At the solution, these are usually dependent on the if-value and enthalpy methods rather than the rigorous method itself. If the method converges on the wrong answer, the whole effort is worthless. The program should then allow the user to adjust, tune, or add his or her own if-value or enthalpy methods to fit the specific system and to interpolate basic VLE data.

2. The reliability or stability of a method covers its ability to reach a solution for a wide group of problems in a general range of mixtures, such as wide or narrow boiling, and if it can solve columns across the whole spectrum of boiling point ranges. It also covers the ability of the method to solve the same column with variations in some of the specifications such as number of trays, reflux ratio, or feed conditions.

3. Whether a method is robust is found by testing it for a variety of columns. Being robust also covers whether a program can still solve when starting with a minimum amount or poor initial values. The quality of the initial values can be very important for certain methods but usually an experienced engineer will know what conditions his or her column will run at. You should consider how much effort has been placed in producing the program. Most methods require a set of conditional tests, heuristics, or "tricks" that improve the method's initial profiles or ability to converge; these things are not always stated in the literature and do take time to develop. In spite of what some salespeople may tell you, a method does not yet exist that solves all columns and works every time.

4. The flexibility and ease of input cam make a major difference in encouraging an engineer to use the program. Covered within this is how difficult is the input to learn, the quality of any manual supporting the program, interactive power, how the program catches input mistakes, and how it responds when the program fails to reach a solution.

5. A variety of features and accepted column specifications are necessary. The spécifications are not just product rates or duties but also product compositions or properties and someone will always stretch the limits on stages and components in a program.

6. The ease of implementation of any method is important only if the program is being written rather than purchased complete. After studying these methods, though, you may find that differences in understanding each method may not be great.

7. The amount of computer time used by a method is overrated. Very overrated. As very fast computers become more available, the computer time used will hardly be noticeable.

4.4 Nomenclature

4.4.1 English letters

Aj Term of simple /f-value model in the inside-out methods, defined bv

Aj h Term in the pseudo-Clausius-Clapeyron equation of the Kb method, defined by Eq, (4.54),

Ay Absorption factor, component i, stage j, defined by Eq. (4.6).

aj Mass transfer surface area between two phases, stage j, Sec. 4.2.13.

Term of simple liquid activity model in inside-out methods, Eq. (4.88).

B Total bottoms rate.

B, Term of simple K- value model in the inside-out methods, defined by

Bj „ Term in the pseudo-Clausius-Clapeyron equation of the Kb method, defined by Eq. (4.54).

b, Component bottoms rate, component i.

b,j Term of simple liquid activity model in inside-out methods, defined by Eq. (4.88).

C Last or total number of components.

C Scalar used in a quasi-Newton update of a Jacobian, Sec. 4.2.6.

Cj Term of simple vapor enthalpy model in the inside-out methods, de fined by Eq. (4.92).

CpUj Heat capacity of the liquid holdup in the column, stage j, Sec. 4.2.11.

Dj Dew-point equation as an independent function for a stage in Sec.

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