Phase equilibria predictions

Figure 5.9 suggests the rule-of-thumb that one can expect the incipient hydrate temperature and pressure to be predicted to within 0.65 K and 10% of overall pressure, respectively. These values approximate the experimental accuracy of the measurements, and suggest that it may not be practical to increase the prediction accuracy until further progress is required for measurement accuracy. Such comparisons with data suggest that hydrate phase equilibria predictions are sufficiently established to permit the state-of-the-art to turn to time dependent phenomena (Sloan, 2005). 

To attempt phase equilibria predictions in regions where experimental results are not available, methods with no adjustable parameters for each binary system can be analyzed (M5, M6, Ml 1 and M12). The M12 method provides better predictions. 

Sum, A. K., Sandler, S. 1. (1999). A novel approach to phase equilibria predictions using ab initio methods. Industrial Engineering and Chemical Research, 38, 2849-2855. 

Keywords Bioreactors Fermentation Phase equilibria Predictive Soave-Redlich-Kwong Nomenclature... 

CRYOGENIC PHASE EQUILIBRIA PREDICTED BY BWR-11 He-N -C System at 2000 psia... 

Q When comparing the phase equilibria prediction methods you... 

While the method of the present chapter may appear comprehensive, the reader is cautioned that the calculation is limited by the available data, as in any prediction method. For each region of phase equilibrium prediction, the limitations on both the accuracy and data availability are discussed. The methods presented are useful for interpolations between available data sets. The reader is urged to use caution for extrapolations beyond the data range. Further experiments may be required in order to appropriately bound the P-T conditions of interest. 

E. Gubbins, "Applications of Molecular Tlieory to Phase Equilibrium Predictions" in Models for Thermodynamic and Phase Equilibrium. Calculations, S. /. Sandler, ed., pp. 507-600, Marcel Dekker, Inc., New York, 1994. Meaning from the beginning, i.e., from first principles. 

It is often necessary to add user components to complete a simulation model. The design engineer should always be cautious when interpreting simulation results for models that include user components. Phase equilibrium predictions for flashes, decanters, extraction, distillation, and crystallization operations should be carefully checked against laboratory data to ensure that the model is correctly predicting the component distribution between the phases. If the fit is poor, the binary interaction parameters in the phase equilibrium model can be tuned to improve the prediction. 

V. Use of ab Initio Energy Calculations for Phase Equilibrium Predictions... 

However, there are also cases in which it is difficult to define structure groups for the substances. This applies to refrigerants, for example. Their present categorization is set out in Tab. 1. Only one main group with a total of 8 subgroups is available for description. The quality of the phase equilibrium predictions made on this basis was unsatisfactory [7]. 

Those of us from industry on the week s program have been asked to describe, from the industrial side of the fence, the current activities, developments, and applications of particular assigned areas of phase equilibria or physical properties correlation. This paper pertains to equations of state, especially their application in phase equilibrium predictions. It is not the intention of this talk, nor would it be appropriate, to review all the equations of state that have been published. An excellent paper by Tsonopoulos and Prausnitz (jL) does make such a review. Instead, this paper will present the applications and limitations of some of the principal equations of state in current use. 

The most important industrial application of equations of state is, and will continue to be, in phase equilibrium predictions. All such calculations are based on the equilibrium criterion ... 

LIN 02] Lin S.-T., Sandler S.I., A priori phase equilibrium prediction from a segment contribution solvation model . Industrial Engineering Chemistry Research, vol. 41, pp. 899-913, 2002. 

Using UNIQUAC, Table 2 summarizes vapor-liquid equilibrium predictions for several representative ternary mixtures and one quaternary mixture. Agreement is good between calculated and experimental pressures (or temperatures) and vapor-phase compositions. ... 

At equilibrium, in order to achieve equality of chemical potentials, not only tire colloid but also tire polymer concentrations in tire different phases are different. We focus here on a theory tliat allows for tliis polymer partitioning [99]. Predictions for two polymer/colloid size ratios are shown in figure C2.6.10. A liquid phase is predicted to occur only when tire range of attractions is not too small compared to tire particle size, 5/a > 0.3. Under tliese conditions a phase behaviour is obtained tliat is similar to tliat of simple liquids, such as argon. Because of tire polymer partitioning, however, tliere is a tliree-phase triangle (ratlier tlian a triple point). For smaller polymer (narrower attractions), tire gas-liquid transition becomes metastable witli respect to tire fluid-crystal transition. These predictions were confinned experimentally [100]. The phase boundaries were predicted semi-quantitatively. 

P. A. Gupte, M. Nagvekar, R. P. Danner, and T. E. Daubert, Documentation of the Basis for Selection of the Contents of Chapters Phase Equilibrium in Manualfor Predicting Chemical Process Design Data, Design Institute for Physical Property Data (AIChE), (1987). 

Critical Temperature The critical temperature of a compound is the temperature above which a hquid phase cannot be formed, no matter what the pressure on the system. The critical temperature is important in determining the phase boundaries of any compound and is a required input parameter for most phase equilibrium thermal property or volumetric property calculations using analytic equations of state or the theorem of corresponding states. Critical temperatures are predicted by various empirical methods according to the type of compound or mixture being considered. 

We are interested in comparing the effectiveness of the various equations of state in predicting the (p. V. T) properties. We will limit our comparisons to Tr > 1 since for Tr < 1 condensations to the liquid phase occur. Prediction of (vapor + liquid) equilibrium would be of interest, but these predictions present serious problems, since in some instances the equations of state do not converge for Tr< 1. 

From the outset, Flory (6) and Huggins (4,5 ) recognized that their expressions for polymer solution thermodynamics had certain shortcomings (2). Among these were the fact that the Flory-Huggins expressions do not predict the existence of the LCST (see Figure 2) and that in practice the x parameter must be composition dependent in order to fit phase equilibrium data for many polymer solutions 3,8). 

Using copolymerization theory and well known phase equilibrium laws a mathematical model is reported for predicting conversions in an emulsion polymerization reactor. The model is demonstrated to accurately predict conversions from the head space vapor compositions during copolymerization reactions for two commercial products. However, it appears that for products with compositions lower than the azeotropic compositions the model becomes semi-empirical. 

For the following mixtures, suggest suitable models for both the liquid and vapor phases to predict vapor-liquid equilibrium, a. H2S and water at 20° C and 1.013 bar. 

The phenomenon of critical flow is well known for the case of single-phase compressible flow through nozzles or orifices. When the differential pressure over the restriction is increased beyond a certain critical value, the mass flow rate ceases to increase. At that point it has reached its maximum possible value, called the critical flow rate, and the flow is characterized by the attainment of the critical state of the fluid at the throat of the restriction. This state is readily calculable for an isen-tropic expansion from gas dynamics. Since a two-phase gas-liquid mixture is a compressible fluid, a similar phenomenon may be expected to occur for such flows. In fact, two-phase critical flows have been observed, but they are more complicated than single-phase flows because of the liquid flashing as the pressure decreases along the flow path. The phase change may cause the flow pattern transition, and departure from phase equilibrium can be anticipated when the expansion is rapid. Interest in critical two-phase flow arises from the importance of predicting dis-... 

The isolation of crystalline products having mixed polymorphic compositions (often referred to as concomitant polymorphism) remains a topic of interest, even though the phase rule predicts that a system at equilibrium consisting two components (solvent + solute) and three phases (solution + Form I + Form II) is uni variant. Hence, for crystallizations performed at a fixed pressure (typically atmospheric) the system becomes nonvariant and genuine equilibrium can exist at only one temperature. Therefore, concomitant products must be obtained under nonequilibrium conditions. Flexibility in molecular conformation was attributed to the concomitant polymorphs of a spirobicyclic dione [34] and of 3-acetylcoumarin [35],... 

---