Page 424 - Analysis, Synthesis and Design of Chemical Processes, Third Edition

enthalpy of vaporization is an important part of a calculation, simple equations of state should not be
used. In fact, the “latent heat” or “ideal” options would be better. If the substance is above or near its
critical temperature, equations of state must be used, but the user must beware, especially if polar
substances such as water are present, as shown in Example 13.3.

Example 13.3

A gas stream at 3000°F of the following concentration is to be cooled by evaporation of 500 kg/h of
water entering at 70°F. Assume atmospheric pressure.

Perform a simulation to determine the final temperature of the cooled gas stream with the default
thermodynamic model and with the ideal model.

The default on most process simulators is an equation of state, either PR (Peng-Robinson) or SRK
(Soave-Redlich-Kwong). These models give an outlet temperature of 480°F. The ideal model gives an
outlet temperature of 348°F. The value calculated by the ideal model is closer to reality in this case
because the equations of state do a poor job of estimating the enthalpy of vaporization of water, which is
the most important property for the energy balance. The ideal model uses the experimentally determined

value of this enthalpy of vaporization (from the databank).

13.4.3 Phase Equilibria

Extreme care must be exercised in choosing a model for phase equilibria (sometimes called the fugacity
coefficient, K-factor, or fluid model). Whenever possible, phase equilibrium data for the system should

be used to regress the parameters in the model, and the deviation between the model predictions and the
experimental data should be studied.

There are two general types of fugacity models: equations of state and liquid-state activity-coefficient

models. An equation of state is an algebraic equation for the pressure of a mixture as a function of the
composition, volume, and temperature. Through standard thermodynamic relationships, the fugacity,
enthalpy, and so on for the mixture can be determined. These properties can be calculated for any density;
therefore, both liquid and vapor properties, as well as supercritical phenomena, can be determined.

Activity-coefficient models, however, can only be used to calculate liquid-state fugacities and enthalpies
of mixing. These models provide algebraic equations for the activity coefficient (γ ) as a function of
i
composition and temperature. Because the activity coefficient is merely a correction factor for the ideal-
solution model (essentially Raoult’s Law), it cannot be used for supercritical or “noncondensable”
components. (Modifications of these models for these types of systems have been developed, but they are
not recommended for the process simulator user without consultation with a thermodynamics expert.)

Equations of state are recommended for simple systems (nonpolar, small molecules) and in regions
(especially supercritical conditions for any component in a mixture) where activity-coefficient models are