Liquid phase mole fraction

Unfortunately, many commonly used methods for parameter estimation give only estimates for the parameters and no measures of their uncertainty. This is usually accomplished by calculation of the dependent variable at each experimental point, summation of the squared differences between the calculated and measured values, and adjustment of parameters to minimize this sum. Such methods routinely ignore errors in the measured independent variables. For example, in vapor-liquid equilibrium data reduction, errors in the liquid-phase mole fraction and temperature measurements are often assumed to be absent. The total pressure is calculated as a function of the estimated parameters, the measured temperature, and the measured liquid-phase mole fraction. 

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

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 ... 

Here Klx a (kmol/m s) is the overall mass transfer coefficient for the liquid phase, based on mole fraction in the L-phase, x is the equilibrium liquid phase mole fraction, and Ac is the cross-sectional area of the column (m ). Hence... 

Liquid temperature Mole ratio c in the liquid phase Mole fraction in the liquid phase Mole ratio in the gas phase Mole fraction in the gas phase Height of packing Exothermic heat of adsorption... 

Figure 5.220. Liquid phase mole fractions of components A, B, C and D in the reflux drum.

Figure 5.221. Liquid phase mole fractions in the bottom plate in the same run as Fig. 5.220.

In practice, VLE data are available as sets of isothermal measurements. The number of isotherms is usually small (typically 1 to 5). Hence, we are often left with limited information to perform interpolation with respect to temperature. On the contrary, one can readily interpolate within an isotherm (two-dimensional interpolation). In particular, for systems with a sparingly soluble component, at each isotherm one interpolates the liquid mole fraction values for a desired pressure range. For any other binary system (e.g., azeotropic), at each isotherm, one interpolates the pressure for a given range of liquid phase mole fraction, typically 0 to 1. 

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

Leu and Robinson (1992) reported data for this binary system. The data were obtained at temperatures of 0.0, 50.0, 100.0, 125.0, 133.0 and 150.0 °C. At each temperature the vapor and liquid phase mole fractions of isobutane were measured at different pressures. The data at 133.0 and 150.0 are given in Tables 14.9 and 14.10 respectively. The reader should test if the Peng-Robinson and the Trebble-Bishnoi equations of state are capable of describing the observed phase behaviour. First, each isothermal data set should be examined separately. 

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>... 

X Liquid-phase mole fraction (-) or variable in optimization problem (-) ... 

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). 

X component liquid phase mole fraction, liquid feed... 

This factor should be inputted if you have chosen the two-film method. Enter the value of the chosen light key component liquid phase mole fraction. This value should be obtained from an equilibrium curve, a two-component binary system, or a tray-to-tray computer program printout. The program uses this factor to calculate the slope of the equilibrium curve. Be sure to select the liquid light key mole fraction at the proper curve point or tray condition that corresponds to the K value used. 

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... 

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