Vaporization vapor-phase mole fractions

Vapor-Phase Mole Fraction Propionic Acid... 

The sum of the squared differences between calculated and measures pressures is minimized as a function of model parameters. This method, often called Barker s method (Barker, 1953), ignores information contained in vapor-phase mole fraction measurements such information is normally only used for consistency tests, as discussed by Van Ness et al. (1973). Nevertheless, when high-quality experimental data are available. Barker s method often gives excellent results (Abbott and Van Ness, 1975). 

TRUE VAPOR-PHASE MOLE FRACTION. CALCULATED WHEN THE CHEMICAL THEORY IS USED. 

Y(I) vector of vapor-phase mole fractions of the components (I = 1, N). 

YF (I) Vector (length 20) of vapor-phase mole fractions (I =... 

The general XT E problem involves a multicomponent system of N constituent species for which the independent variables are T, P, N — 1 liquid-phase mole fractions, and N — 1 vapor-phase mole fractions. (Note that Xi = 1 and y = 1, where x, and y, represent liquid and vapor mole fractions respectively.) Thus there are 2N independent variables, and application of the phase rule shows that exactly N of these variables must be fixed to estabhsh the intensive state of the system. This means that once N variables have been specified, the remaining N variables can be determined by siiTUiltaneous solution of the N equihbrium relations ... 

Pressure (MPa) Liquid Phase Mole Fraction (x2) Vapor Phase Mole Fraction (yz)... 

Experimental values for the activity coefficients for components 1 and 2 are obtained from the vapor-liquid equilibrium data. During an experiment, the following information is obtained Pressure (P), temperature (T), liquid phase mole fraction (x, and x2=l-X ) and vapor phase mole fraction (yi and y2=l—yi). 

Temperature (K) Liquid Phase Mole Fraction of Ethylbenzene (X ) Vapor Phase Mole Fraction of o-Xylene (yi) Activity Coefficient of Ethylbenzene (Yi) Activity Coefficient of o-Xylene (Y2>... 

Separation systems include in their mathematical models various vapor-liquid equilibrium (VLE) correlations that are specific to the binary or multicomponent system of interest. Such correlations are usually obtained by fitting VLE data by least squares. The nature of the data can depend on the level of sophistication of the experimental work. In some cases it is only feasible to measure the total pressure of a system as a function of the liquid phase mole fraction (no vapor phase mole fraction data are available). 

In the book, Vapor-Liquid Equilibrium Data Collection, Gmehling and colleagues (1981), nonlinear regression has been applied to develop several different vapor-liquid equilibria relations suitable for correlating numerous data systems. As an example, p versus xx data for the system water (1) and 1,4 dioxane (2) at 20.00°C are listed in Table El2.3. The Antoine equation coefficients for each component are also shown in Table E12.3. A12 and A21 were calculated by Gmehling and colleaques using the Nelder-Mead simplex method (see Section 6.1.4) to be 2.0656 and 1.6993, respectively. The vapor phase mole fractions, total pressure, and the deviation between predicted and experimental values of the total p... 

The vapor-phase mole fractions of water of Olds et al. (19) can be represented very well using the Peng-Robinson equation of state in conjunction with a constant interaction parameter over the temperature range from 100°F to 460°F. The same interaction parameter can be used to reproduce the data of Sultanov et al. 

Figure 7 shows the predicted vapor-phase mole fractions of HC1 at 25°C as a function of the liquid-phase molality of HC1 for a constant NaCl molality of 3. Also included are predicted vapor-phase mole fractions of HC1 when the interaction parameter A23 is taken as zero. There are unfortunately no experimental vapor-liquid equilibrium data available for the HC1-NaCl-FLO system however, considering the excellent description of the liquid-phase activity coefficients and the low total pressures, it is expected that predicted mole fractions would be within 2-3% of the experimental values. 

Thermodynamic Foundation. An expression relating the vapor phase mole fraction (y2) of a low volatility component (subscript 2) in a compressed gas to the liquid (or solid) phase mole fraction (x2) is given by (8) ... 

X(H) heavy key mole fraction in distillate X(L) light key mole fraction in distillate Y component vapor phase mole fraction, liquid feed... 

K = mole fraction component in vapor phase/mole fraction component in liquid phase... 

Enter an alpha value if you have chosen F or T for the method. Enter a K value for a light key component if you chose A. Input the factor alpha or K. Alpha is defined as simply the light key K divided by the heavy key K component. The K factor is simply the particular component s vapor phase mole fraction divided by its liquid mole fraction. The alpha value is therefore a ratio of the chosen two key components. These key components should be those that readily point to how well the fractionator is doing its job of separation. For example, for a depropanizer tower, choose propane as the light key component and butane as the heavy key, since you wish to separate the propane from the butane to make a propane product specification. For a multicomponent system, you may try several components to determine a controlling alpha and/or to factor an average tray efficiency. 

A little reflection should convince anyone that there is no other way that BOTH the liquid-phase and vapor-phase mole fractions can sum to unity. 

In Eqs. (3) and (4), the vapor phase mole fractions y and the liquid phase mole fractions %i have to fulfil the vapor-liquid-liquid equilibrium conditions in case of heterogeneous liquid mixtures, and the vapor-liquid equilibrium conditions in homogeneous mixtures. For the latter case, the reaction term 0 in Eq. (5) simplifies to... 

Gas phase mass transfer fluxes (Stefan flux in the gas phase is negligible as long as the vapor phase mole fractions are below say 20 %, which means either moderate temperatures and/or high sweep gas flow rates) are ... 

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