Page 261 - Separation process engineering

The bubble-point method works well for narrow-boiling feeds, but is inherently unstable for wide boiling
feeds. The sum-rates method (Chapter 12) works well for wide-boiling feeds such as most absorbers but
is unstable for narrow-boiling feeds. The Naphtali-Sandholm approach often works well for both narrow-
and wide-boiling feeds, but Newtonian methods are notorious for diverging for nonlinear problems if the
first guess is not close to the final answer. Since distillation problems can be extremely nonlinear, the
first guess can be very important for all of these methods. If a good first guess is difficult to find, try
finding a simpler set of conditions where convergence does occur (e.g., fewer stages or larger L/D) and
then approach the desired condition by slowly changing the values of the variables. Since commercial
simulators use the previous run as an initial guess for the current run, this method should make the initial
guess closer to the answer, which means convergence is more likely.

A number of methods to make the convergence schemes more stable have been developed and are
employed in commercial process simulators. As a result, commercial simulators are quite robust,
particularly if an appropriate method (bubble-point, sum-rates or Naphtali-Sandholm) is chosen and a
good first guess has been used, although they occasionally still have difficulty converging. When there is a
convergence difficulty, first check that the basic solution approach chosen appears to be appropriate.

Then try increasing the number of iterations allowed. If this does not work, try reducing the tolerance on
convergence. Finally, most simulators have a number of options to make convergence more stable, such as
damping the predicted change in variables, and these options can be tried. With a combination of these
approaches, almost all equilibrium-staged multicomponent distillation problems can be solved. This is
one of the great advances in chemical engineering in the last 100 years. Rate-based models for distillation
are considered in Chapters 15 and 16.
The matrix approach is easily adapted to partial condensers and to columns with side streams (see
Problems 6.C2 and 6.C1). The approach will converge for normal distillation problems. Extension to

more complex problems such as azeotropic and extractive distillation or very wide boiling feeds is
beyond the scope of this book; however, these problems will be solved with a process simulator.
In some ways, the most difficult part of writing a multicomponent distillation program has not been
discussed. This is the development of a physical properties package that will accurately predict
equilibrium and enthalpy relationships (Barnicki, 2002; Carlson, 1996; Sadeq et al., 1997; Schad, 1998).

Sadaq et al. (1997) compared three process simulators and found that relatively small differences in the
parameters and in the VLE correlation can cause major errors in the results. Fortunately, a considerable
amount of research has been done (see Table 2-2 and Fredenslund et al., 1977; and Walas, 1985) to
develop accurate physical property correlations. Very detailed physical properties packages can be
purchased commercially and are included in the commercial process simulators.
Most companies using distillation have available computer programs using one of the advanced
calculation procedures. Several software and design companies sell these programs. The typical engineer
will use these routines and not go to the large amount of effort required to write his or her own routine.

However, an understanding of the expected profiles and the basic mass and energy balances in the column
can be very useful in interpreting the computer output and in determining when that output is garbage.
Thus, it is important to understand the principles of distillation calculations even though the details of the
computer program may not be understood.

6.8 Summary—Objectives

In this chapter we have developed methods for multicomponent distillation. The objectives for this
chapter are as follows:

1. Use a matrix approach to solve the multicomponent mass balances