Page 425 - Analysis, Synthesis and Design of Chemical Processes, Third Edition

inappropriate. For complex liquid mixtures, activity-coefficient models are preferred, but only if all of
the binary interaction parameters (BIPs) are available.

Equations of State. The default fugacity model is normally either the SRK (Soave-Redlich-Kwong) or
the PR (Peng-Robinson) equation. They (like most popular equations of state) normally use three pure-
component parameters per substance and one binary-interaction parameter per binary pair. Although they
give qualitatively correct results even in the supercritical region, they are known to be poor predictors of
enthalpy changes, and (except for light hydrocarbons) they are not quantitatively accurate for phase
equilibria.

The predicted phase equilibrium is a strong function of the binary interaction parameters (BIPs). Process
simulators have regression options to determine these parameters from experimental phase-equilibrium
data. The fit gives a first-order approximation for the accuracy of the equation of state. This information
should always be considered in estimating the accuracy of the simulation. Additional simulations should
be run with perturbed model parameters to get a feel for the uncertainty, and the user should realize that
even this approach gives an optimistic approximation of the error introduced by the model. If BIPs are
provided in the simulator and the user has no evidence that one equation of state is better than another,

then a separate, complete simulation should be performed for each of these equations of state. The
difference between the simulations is a crude measure of the uncertainty introduced into the simulation by
the uncertainty in the models. Again, the inferred uncertainty will be on the low side.

Monte-Carlo simulations (see Section 10.7) can be done with the results of the regression; however,
present process simulators are not equipped to perform these directly. A simpler approach is to perform
the simulation with a few different values of the BIPs for the equation of state. These values are typically
0.01 to 0.10. Larger values are rare, except in highly asymmetric systems. However, the difference
between results calculated with values of, say, 0.01 and 0.02 can be large.

If BIPs are available for only a subset of the binary pairs, caution should be exercised. Assuming the
unknown BIPs to be zero can be dangerous. Group-contribution models for estimating BIPs for equations
of state can be used with caution.

There are usually six to ten equation-of-state choices, and a few mixing-rule choices. For polar or
associating components or for heavy petroleum cuts, the help facility of the simulator should be consulted.
Because different choices are available on the different simulators, they will not be covered here.

For most systems containing hydrocarbons and light gases, an equation of state is the best choice. One
should initially choose the Peng-Robinson or Soave-Redlich-Kwong equation. (Note that neither the van
der Waals nor Redlich-Kwong equation is a standard choice in simulators. These two equations of state
were tremendous breakthroughs in fluid property models, but they have long ago been supplanted by other
models that give better quantitative results.) VLE (vapor-liquid equilibrium) data for each binary system
can then be used with the regression utility to calculate the BIPs for the binary pairs and to plot the
resulting model predictions against the experimental data. This regression is done separately for each
equation of state. The equation that gives a better fit in the (PTxy) region of operation of the unit operation
of interest is then used. If phase equilibrium data are available at different temperatures, the temperature-
dependent BIP feature of the simulator can be used. In the simulator databank, many BIPs are already

regressed and available.

If neither simple equation of state adequately reproduces the experimental data, one of the other equations