Phase Equilibria Data

Phase equilibrium data are needed for the design of all separation processes that depend on differences in concentration between phases. 

Experimental data have been published for several thousand binary and many multi-component systems. Virtually all the published experimental data has been collected 

The criterion for thermodynamic equilibrium between two phases of a multicomponent mixture is that for every component, / 

P = total system pressure d , = vapor fugacity coefficient  

Substituting from equations 8.29 and 8.30 into equation 8.28 and rearranging gives 

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One of the limitations of most phase-equilibrium data is that variances of experimental measurements are seldom known. 

The maximum-likelihood method is not limited to phase equilibrium data. It is applicable to any type of data for which a model can be postulated and for which there are known random measurement errors in the variables. P-V-T data, enthalpy data, solid-liquid adsorption data, etc., can all be reduced by this method. The advantages indicated here for vapor-liquid equilibrium data apply also to other data. 

Repeat the calculation from Example 4.2 with actual phase equilibrium data in the phase split instead of assuming a sharp split. 

This database provides thermophysical property data (phase equilibrium data, critical data, transport properties, surface tensions, electrolyte data) for about 21 000 pure compounds and 101 000 mixtures. DETHERM, with its 4.2 million data sets, is produced by Dechema, FIZ Chcmic (Berlin, Germany) and DDBST GmhH (Oldenburg. Germany). Definitions of the more than SOO properties available in the database can be found in NUMERIGUIDE (sec Section 5.18). 

Landolt-Bornstein Physikalische-chemische TabeUen, Eg. I, p. 303, 1927. Phase-equilibrium data for the binary system NH3-H2O are given by Clifford and Hunter,y. Fhys. Chem., 37, 101 (1933). 

Enthalpy and phase-equilibrium data for the binary system HCI-H2O are given by Van Nuys, Trans. Am. Inst. Chem. Engts., 39, 663 (1943). 

This subsec tion summarizes and presents examples of phase equilibrium data currently available to the designer. The thermodynamic concepts utilized are presented in the subsection Thermodynamics of Sec. 4. 

Ternary-phase equilibrium data can be tabulated as in Table 15-1 and then worked into an electronic spreadsheet as in Table 15-2 to be presented as a right-triangular diagram as shown in Fig. 15-7. The weight-fraction solute is on the horizontal axis and the weight-fraciion extraciion-solvent is on the veriical axis. The tie-lines connect the points that are in equilibrium. For low-solute concentrations the horizontal scale can be expanded. The water-acetic acid-methylisobutylketone ternary is a Type I system where only one of the binary pairs, water-MIBK, is immiscible. In a Type II system two of the binary pairs are immiscible, i.e. the solute is not totally miscible in one of the liquids. 

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). 

The term pt is a binary interaction parameter which must be determined from phase equilibrium data. We will discuss determination of p 9 values in more detail later. 

Values of p can be determined, in principle, from any phase equilibrium data. A small table of p 2 values is available in reference (2). However, one of the most straightforward ways of determining pf values is to fit phase equilibrium data for solvent sorption in concentrated polymer solutions. To do this, equations (2) and (13) are combined to solve for p utilizing experimental partial pressure data. 

There are relatively few phase equilibrium data relating to concentrated polymer solutions containing several solvents. Nevertheless, In polymer devolatilization, such cases are often of prime Interest. One of the complicating features of such cases Is that. In many Instances, one of the solvents preferentially solvates the polymer molecules, partially excluding the other solvents from Interaction directly with the polymer molecules. This phenomenon Is known as "gathering". 

The algorithm we used for solvent/polydisperse polymer equilibria calls for only one solvent/polymer interaction parameter. The interaction parameter (pto) i ed in the algorithm can be determined from essentially any type of ethylene/polyethylene phase equilibrium data. Cloud-point data have been used (18). while Cheng (16) and Harmony ( ) have done so from gas sorption data. 

PARAMETER ESTIMATION USING THE ENTIRE BINARY PHASE EQUILIBRIUM DATA... 

It was shown by Englezos et al. (1998) that use of the entire database can be a stringent test of the correlational ability of the EoS and/or the mixing rules. An additional benefit of using all types of phase equilibrium data in the parameter estimation database is the fact that the statistical properties of the estimated parameter values are usually improved in terms of their standard deviation. 

There are numerous sources of phase equilibrium data available that serve as a database to those developing or improving equations of state. References to these databases are widely available. In addition, new data are added mainly through the Journal of Chemical and Engineering Data and the journal Fluid Phase Equilibria. Next, we give data for two systems so that the reader may practice the estimation methods discussed in this chapter. 

The activity coefficients are evaluated from the above phase equilibrium data by procedures widely available in the thermodynamics literature (Tassios, 1993 Prausnitz et al. 1986). Since the objective in this book is parameter estimation we will provide evaluated values of the activity coefficients based on... 

Englezos, P. and S. Hull, Phase Equilibrium Data on Carbon Dioxide Hydrate in the Presence of Electrolytes, Water Soluble Polymers and Montmorillonite , CanJ. Chem. Eng, 72, 887-893 (1994). 

Most of the interaction parameters employed were taken from other studies (20, 21), and are reportedly obtained by minimizing errors in the match of phase equilibrium data. However, in (21), the SRK equation employed was slightly different from that used here. The parameters for CO2 - H2O were chosen because they had been shown to give a critical line which is qualitatively correct. The H2O - CO interaction parameter is the value given in (20) for H2S - CO. For H2O - H2, kij was taken to be -0.25 in the absence of any literature studies. 

Design of extraction processes and equipment is based on mass transfer and thermodynamic data. Among such thermodynamic data, phase equilibrium data for mixtures, that is, the distribution of components between different phases, are among the most important. Equations for the calculations of phase equilibria can be used in process simulation programs like PROCESS and ASPEN. 

There are mainly four possibilities of acquiring the necessary phase equilibrium data for a certain system ... 

Ohmura, R. Uchida, T. Takeya, S. Nagao, J. Minagawa, H. Ebinuma, T. Narita, H. (2003 a). Clathrate hydrate formation in (methane + water + methylcyclohexanone) systems the first phase equilibrium data. J. Chem. Thermodynamics, 35, 2045-2054. 

More than half a century ago, Bawden and Pirie [77] found that aqueous solutions of tobacco mosaic virus (TMV), a charged rodlike virus, formed a liquid crystal phase at as very low a concentration as 2%. To explain such remarkable liquid crystallinity was one of the central themes in the famous 1949 paper of Onsager [2], However, systematic experimental studies on the phase behavior in stiff polyelectrolyte solutions have begun only recently. At present, phase equilibrium data on aqueous solutions qualified for quantitative discussion are available for four stiff polyelectrolytes, TMV, DNA, xanthan (a double helical polysaccharide), and fd-virus. 

Existing correlations of phase equilibrium data contain many regressed parameters, they are often semi-empirical, and they may be successful in fitting the data in parts of the phase diagram -even with high accuracy. As far as prediction is concerned, models developed for that purpose attempt to justify theoretically a link between the model parameters and real physical phenomena. However, the distinction between these two methods is often lost, since theoretically based models are forced to fit the data better by the introduction of additional adjustable parameters. 

Successful engineering design presupposes knowledge of reliable data on mass transfer, including thermodynamic properties, such as phase-equilibrium data and solubility, within a technically and economically possible range of pressure and temperature. 

Information about experimental solubility and equilibrium data are important, even when complex mixtures are extracted. Reviews of high-pressure phase-equilibrium data have been published by several authors, for example, by Knapp et al. [38] covering the period 1900 to 1980, by Fomari et al. [39] covering 1978 to 1987, and by Dohm and Brunner [40], between 1988 to 1993. 

Based on phase-equilibrium data in the Master diagram (Figure 9.8-12) (where S-l and 1-V equilibrium data are presented) the experiments for cocoa butter micronization using the PGSS process were carried out. The pre-expansion pressure was in the range of 60 to 200 bar and at temperatures from 20 to 80°C. The micronization with the nozzle D = 0.25 mm resulted in fine solid particles with median particle sizes of about 62 pm. In Figure 9.8-13 the morphology of a cocoa-butter particle is presented. 

DETHERM Dechema eV (also available on STN) thermophysical properties and phase equilibrium data... 

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