Page 248 - Separation process engineering

Chapter 6. Exact Calculation Procedures for Multicomponent

Distillation

Since multicomponent calculations are trial and error, it is convenient to do them on a computer. Because
stage-by-stage calculations are restricted to problems where a good first guess of compositions can be
made at some point in the column, matrix methods for multicomponent distillation will be used. These
methods are not restricted to cases where a good guess of compositions can be made.

6.1 Introduction to Matrix Solution for Multicomponent Distillation

Since distillation is a very important separation technique, considerable effort has been spent in devising
better calculation procedures. Details of these procedures are available in a variety of textbooks (Seader
and Henley, 2006; Holland, 1981; King, 1980; Smith, 1963; and Wankat, 1988).
The general behavior of multicomponent distillation columns (see Chapter 5) and the basic mass and
energy balances and equilibrium relationships do not change when different calculation procedures are
used. (The physical operation is unchanged; thus, the basic laws and the results are invariant.) What
different calculation procedures do is rearrange the equations to enhance convergence, particularly when
it is difficult to make a good first guess. The most common approach is to group and solve the equations

by type, not stage by stage. That is, all mass balances for component i are grouped and solved
simultaneously, all energy balances are grouped and solved simultaneously, and so forth. Most of the
equations can conveniently be written in matrix form. Computer routines for solution of these equations
are easily written. The advantage of this approach is that even very difficult problems can be made to
converge.

A convenient set of variables to specify are F, z, T , N, N , p, T reflux , L/D, and D. Multiple feeds can be
F
F
i
specified. This is then a simulation problem with distillate flow rate specified. Because the matrices
require that N and N be known, for design problems, a good first guess of N and N must be made (see
F
F
Chapter 7), and then a series of simulation problems are solved to find the best design.
In Section 2.7 we looked at solution methods for multicomponent flash distillation. The questions asked in
that section are again pertinent for multicomponent distillation. First, what trial variables should we use?
As noted, because N and N are required to set up the matrices, in design problems we choose these and
F
solve a number of simulation problems to find the best design. We select the temperature on every stage T j
because temperature is needed to calculate K values and enthalpies. We also estimate the overall liquid L j
and vapor V flow rates on every stage because these flow rates are needed to solve the component mass
j
balances.

Next, we need to decide if we should converge on all the trial variables in a sequential or simultaneous
fashion. Since commercial simulators often allow the user to select either of these approaches, we
consider both sequential and simultaneous approaches. The simultaneous approach is discussed in
Section 6.6.
If we decide to use a sequential approach, we must decide which trial variable to converge on first:
temperatures or flow rates. The answer depends on the type of problem we wish to solve. Distillation
problems, which tend to be narrow boiling, usually converge best if temperature is converged on first.
This method is illustrated in this chapter. Wide-boiling feeds such as flash distillation (Section 2.7) and

absorption and stripping (Chapter 12) tend to converge best if the sum-rates method that converges on
flow rates first is used.