Information Technology Reference
In-Depth Information
and
n
comp
x
i
−
1
=
0
(6.28)
i
n
comp
y
i
−
1
=
0
(6.29)
i
Aspen Plus documentation does not provide information on the details of the imple-
mentation of the minimization procedure; however, the papers of Anderson et al. (1976)
and Fabries and Renon (1976) describe possibilities.
6.5 PRACTICAL ASPECTS OF REGRESSION OF VLE OR LLE DATA
The first question that arises when activity coefficient equations are employed is
whether to use a two- or four-parameter approach. With the NRTL equation it would
be either three or five. Aspen Plus recommends that the NRTL
c
parameter be fixed
according to the following rules:
0.2 for saturated hydrocarbons with polar nonassociated liquids and systems that
exhibit liquid - liquid immiscibility
0.3 for nonpolar substances; nonpolar with polar nonassociated liquids; small
deviations from ideality
0.47 for strongly self-associated substances with nonpolar substances
When using two parameters, a question arises as to the selection of the constant
a
i,j
or the temperature-dependent
b
i,j
version of the parameters. Prausnitz et al. (1999)
discuss this point and no clear advice is available; however, experience has shown
that the difference between the two approaches in quality of fit is very small. Often,
the difference between the two- and four-parameter approach is also very small. When
regressing four parameters simultaneously, steps taken during the regression are related
to the current values. It is important to note that relative to the
b
i,j
values, the
a
i,j
values vary sometimes by two orders of magnitude. Aspen Plus provides the ability
to assign a scaling factor to any parameter so that step sizes during the regression are
not dominated by a particular parameter.
In most cases of nonlinear data regression, more than one set of values that satisfy
the equations can be found. It is imperative that results be checked to assure that the
results produce calculated values of the independent values that fit the data consistent
with the requirements of the simulation for which the results will be employed. In
many cases the values calculated by the regression will depend on the starting values
of the parameters. In some cases a regression that employs Aspen Plus's default values
will suffice.
6.5.1 Regression of VLE Data
A useful technique for providing starting values for vapor - liquid equilibrium regression
using
T
-
P
-
x
-
y
data is to estimate the infinite dilution activity coefficients by calcu-
lating activity coefficients using equation (6.18), plotting versus
x
1
and extrapolating to
