Mixture phase equilibrium

Mixture phase equilibrium calculations, types of, 24 680-681 Mixture-process design type, 8 399 commercial experimental design software compared, 8 398t Mixtures. See also Multicomponent mixtures Nonideal liquid mixtures acetylene containing, 2 186 adsorption, 2 593-594 adsorption isotherm models,... 

The Lee-Kesler (7) generalized equation of state, which also applies to both phases, is the basis for the sixth thermodynamic properties method. As originally developed, the Lee-Kesler equation was for predicting bulk properties (densities, enthalpies etc.) for the entire mixture and not for calculating partial properties for the components of mixtures. Phase equilibrium was not one of the uses that the authors had in mind when they developed the equation. Recognizing the other possibilities of the Lee-Kesler equation, Ploecker, Knapp, and... 

Phase equilibrium. For a nc-component mixture phase equilibrium is determined when the Gibbs free energy G for the overall open system is at a minimum (Biegler et al, 1997),... 

In modern separation design, a significant part of many phase-equilibrium calculations is the mathematical representation of pure-component and mixture enthalpies. Enthalpy estimates are important not only for determination of heat loads, but also for adiabatic flash and distillation computations. Further, mixture enthalpy data, when available, are useful for extending vapor-liquid equilibria to higher (or lower) temperatures, through the Gibbs-Helmholtz equation. ... 

Given the estimate of the reactor effluent in Example 4.2 for fraction of methane in the purge of 0.4, calculate the.actual separation in the phase split assuming a temperature in the phase separator of 40°C. Phase equilibrium for this mixture can be represented by the Soave-Redlich-Kwong equation of state. Many computer programs are available commercially to carry out such calculations. 

Figure A2.5.15. The molar Gibbs free energy of mixing versus mole fraetionxfor a simple mixture at several temperatures. Beeause of the synuuetry of equation (A2.5.15) the tangent lines indieating two-phase equilibrium are horizontal. The dashed and dotted eiirves have the same signifieanee as in previous figures.

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). 

The criterion for phase equilibrium is given by Eq. (8.14) to be the equality of chemical potential in the phases in question for each of the components in the mixture. In Sec. 8.8 we shall use this idea to discuss the osmotic pressure of a... 

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. 

Note that this equation holds for any component in a multi-component mixture. The integral on the right-hand side can only be evaluated if the vapor mole fraction y is known as a function of the mole fraction Xr in the still. Assuming phase equilibrium between liquid and vapor in the still, the vapor mole fraction y x ) is defined by the equilibrium curve. Agitation of the liquid in tire still and low boilup rates tend to improve the validity of this assumption. 

I rcdici.s properties and lompuics ihcmical and solid-liquid phase equilibrium for aqueous mixtures. Up to 20 composition data sets may be handled in memory at once. Requires 512K memory. 

Various amines find application for pH control. The most commonly used are ammonia, morpholine, cyclohexylamine, and, more recently AMP (2-amino-2-methyl-l-propanol). The amount of each needed to produce a given pH depends upon the basicity constant, and values of this are given in Table 17.4. The volatility also influences their utility and their selection for any particular application. Like other substances, amines tend towards equilibrium concentrations in each phase of the steam/water mixture, the equilibrium being temperature dependent. Values of the distribution coefficient, Kp, are also given in Table 17.4. These factors need to be taken into account when estimating the pH attainable at any given point in a circuit so as to provide appropriate protection for each location. 

With a suitable equation of state, all the fugacities in each phase can be found from Eq. (6), and the equation of state itself is substituted into the equilibrium relations Eq. (67) and (68). For an A-component system, it is then necessary to solve simultaneously N + 2 equations of equilibrium. While this is a formidable calculation even for small values of N, modern computers have made such calculations a realistic possibility. The major difficulty of this procedure lies not in computational problems, but in our inability to write for mixtures a single equation of state which remains accurate over a density range that includes the liquid phase. As a result, phase-equilibrium calculations based exclusively on equations of state do not appear promising for high-pressure phase equilibria, except perhaps for certain restricted mixtures consisting of chemically similar components. 

In summary, we now have the tools for describing phase equilibrium for both pure materials and for mixtures, and for understanding chemical processes at equilibrium. We will rely upon the foundation developed in this chapter as we... 

So far, we have described the effect of pressure and temperature on the phase equilibria of a pure substance. We now want to describe phase equilibrium for mixtures. Composition, usually expressed as mole fraction x or j, now becomes a variable, and the effect of composition on phase equilibrium in mixtures becomes of interest and importance. 

In our discussion of (vapor + liquid) phase equilibria to date, we have limited our description to near-ideal mixtures. As we saw in Chapter 6, positive and negative deviations from ideal solution behavior are common. Extreme deviations result in azeotropy, and sometimes to (liquid -I- liquid) phase equilibrium. A variety of critical loci can occur involving a combination of (vapor + liquid) and (liquid -I- liquid) phase equilibria, but we will limit further discussion in this chapter to an introduction to (liquid + liquid) phase equilibria and reserve more detailed discussion of what we designate as (fluid + fluid) equilibria to advanced texts. 

If we could prevent the mixture from separating into two phases at temperatures below Tc, we would expect the point of inflection to develop into curves similar to those shown in Figure 8.17 as the dotted line for /2, with a maximum and minimum in the fugacity curve. This behavior would require that the fugacity of a component decreases with increasing mole fraction. In reality, this does not happen, except for the possibility of a small amount of supersaturation that may persist briefly. Instead, the mixture separates into two phases. These phases are in equilibrium so that the chemical potential and vapor fugacity of each component is the same in both phases, That is, if we represent the phase equilibrium as... 

Effect of Pressure on Solid + Liquid Equilibrium Equation (6.84) is the starting point for deriving an equation that gives the effect of pressure on (solid + liquid) phase equilibria for an ideal mixture in equilibrium with a pure... 

A gas-liquid mixture will have a lower density than the liquid alone. Therefore, if in a U-tube one limb contains liquid and the other a liquid-gas mixture, the equilibrium height in the second limb will be higher than in the first. If two-phase mixture is discharged at a height less than the equilibrium height, a continuous flow of liquid will take place from the first to the second limb, provided that a continuous feed of liquid and gas is maintained. This principle is used in the design of the air lift pump described in Chapter 8. 

In processing, it is frequently necessary to separate a mixture into its components and, in a physical process, differences in a particular property are exploited as the basis for the separation process. Thus, fractional distillation depends on differences in volatility. gas absorption on differences in solubility of the gases in a selective absorbent and, similarly, liquid-liquid extraction is based on on the selectivity of an immiscible liquid solvent for one of the constituents. The rate at which the process takes place is dependent both on the driving force (concentration difference) and on the mass transfer resistance. In most of these applications, mass transfer takes place across a phase boundary where the concentrations on either side of the interface are related by the phase equilibrium relationship. Where a chemical reaction takes place during the course of the mass transfer process, the overall transfer rate depends on both the chemical kinetics of the reaction and on the mass transfer resistance, and it is important to understand the relative significance of these two factors in any practical application. 

Compression of a reaction mixture at equilibrium tends to drive the reaction in the direction that reduces the number of gas-phase molecules increasing the pressure by introducing an inert gas has no effect on the equilibrium composition. 

There are two types of multicomponent mixtures which occur In polymer phase equilibrium calculations solutions with multiple solvents or pol ers and solutions containing poly-disperse polymers. We will address these situations In turn. 

As the agitation of the reaction mixture was very intensive, interfacial mass transfer resistance is suppressed, and the concentration in gas and liquid are related by the phase equilibrium... 

Volumetric equations of state (EoS) are employed for the calculation offluid phase equilibrium and thermo-physical properties required in the design of processes involving non-ideal fluid mixtures in the oil, gas and chemical industries. Mathematically, a volumetric EoS expresses the relationship among pressure, volume, temperature, and composition for a fluid mixture. The next equation gives the Peng-Robinson equation of state, which is perhaps the most widely used EoS in industrial practice (Peng and Robinson, 1976). 

It should be kept in mind that an objective function which does not require any phase equilibrium calculations during each minimization step is the basis for a robust and efficient estimation method. The development of implicit objective functions is based on the phase equilibrium criteria (Englezos et al. 1990a). Finally, it should be noted that one important underlying assumption in applying ML estimation is that the model is capable of representing the data without any systematic deviation. Cubic equations of state compute equilibrium properties of fluid mixtures with a variable degree of success and hence the ML method should be used with caution. 

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