Information Technology Reference
In-Depth Information
For extraction columns the equations are identical to those of distillation columns if
one recognizes that the vapor terminology now refers to the lighter of the two phases.
Additionally, since there are no reboilers or condensers, the degrees of freedom are
zero except that one additional degree of freedom is introduced for each sidestream,
as in distillation columns.
The set of equations described above lend themselves to solution simultaneously
by means of the Newton-Raphson method, such as the algorithm of Naphtali and
Sandholm (1971). This method has the advantage of permitting the use of all possible
end and sidestream specifications; however, it has the disadvantage of requiring starting
estimates for all independent variables.
There are many arrangements of the equations with an accompanying convenient
selection of variables that lead to a variety of algorithms to generate a solution. For
example, one could employ total flows and mole fractions. There are a group of algo-
rithms that alternately solve the locally linear material balances and then the nonlinear
energy balances, adjusting the
K
values between iterations. The method used in Aspen
Plus's Distil block is the inside-out algorithm of Boston and Britt (1974). Details of
many of the methods may be found in Seader and Henley (1998).
11.2 THE DESIGN PROBLEM
To simulate a distillation column within a process it is necessary initially to solve a
design problem: that is for a given service, to establish the number of stages required
and the location of the feeds and sidestreams, and to define suitable end specifications.
Since the rigorous distillation models in Aspen Plus do not calculate directly such
design parameters as the number of stages and the feed location, it is necessary to
explore many possible rating solutions. Prior to the use of a rigorous model, it is useful
to estimate the design by less rigorous methods, including the manual McCabe-Thiele
method (1925). Prior to any design work, it is imperative that the vapor-liquid equilib-
rium diagrams and/or liquid-liquid equilibrium diagrams be reviewed. In many cases
the data stored in the Aspen Plus database will be suitable, but this may not be the
case and a literature search or experimental work may be required.
A brief review of the McCabe-Thiele method is given below. Unlike the models
in Aspen Plus, the McCabe-Thiele method can be used to solve the design problem:
that is, given the feed composition, flow rate, thermal state, and product composition
targets, determine feed location and the number of stages above and below the feed
stage. The following features are at the heart of the method.
1. All stages are at steady state and the stage products are at equilibrium.
2. The column operates under equal molal overflow conditions; that is, within a
section of a distillation column where there is no feed, no product takeoff, and
no interstage heat exchangers, the flow rates of all liquids leaving a stage are
identical, as are the flow rates of all vapors.
3. After a solution has been obtained, the reboiler and condenser duties are calcu-
lated by a manual energy balance around each device.
The McCabe-Thiele method can also be used to rate columns by a trial-and-error
procedure.
