Liquid-phase nonidealities analysis

Since Raoulrs Jaw is p, = x-pf, the liquid-phase activity coefficient in Eq. (3.2-9) is a "Raouh s law correction factor that lakes info account liquid-phase nonideality. Since most distillations are carried out at relatively low pressure and moderate-lo-high temperature, Eq- (5.2-9) is the most generally used relationship in distillation system analysis and design. 

In the analysis and correlation of vapor-liquid equilibrium (VLE) data it is essential, especially at superatmospheric pressures, to take into account the effect of vapor-phase nonideality. This is expressed by the fugacity coefficient which, as long as the density of the mixture is not greater than one fourth of its critical value, can be calculated reliably with the following equation (for a binary mixture) ... 

The sodium-lithium phase system has been studied by thermal analysis in the liquid and solid regions to temperatures in excess of 400°C. Two liquid phases separate at 170.6°C. with compositions of 3.4 and 91.6 atom % sodium. The critical solution temperature is 442° zt 10°C. at a composition of 40.3 atom % sodium. The freezing point of pure lithium is depressed from 180.5°C. to 170.6°C. by the addition of 3.4 atom % sodium, and the freezing point of pure sodium is depressed from 97.8° to 92.2°C. by the addition of 3.8 atom % lithium. From 170.6° to 92.2°C. one liquid phase exists in equilibrium with pure lithium. Regardless of the similarity in the properties of the pure liquid metals, the binary system deviates markedly from simple nonideal behavior even in the very dilute solutions. Correlation of the experimentally observed data with the Scatchard-Hildebrand regular solution model using the Flory-Huggins entropy correction is discussed. 

For liquids in near-critical fluids the analysis is generally more complicated than the above development for solids because the equilibrium liquid phase is not pure. To the degree that the solvent dissolves in the liquid, the solubility of the solute can decrease. But such solutions may be nonideal, and if the corresponding activity coefficients are greater than unity, then they may partially compensate for the decrease in solubility. 

In their analysis of two-component bubbly systems, Sankaranarayanan et al. [116] set the function S, which means that component 1 (the gas component) obeyed the ideal gas law. The function j/ was chosen to produce a nonideal equation of state so that component 2 could exist as a liquid phase. 

The extension of ideal phase analysis of the Maxwell-Stefan equations to nonideal liquid mixtures requires the sufficiently accurate estimation of composition-dependent mutual diffusion coefficients and the matrix of thermodynamic factors. However, experimental data on mutual diffusion coefficients are rare, and prediction methods are satisfactory only for certain types of liquid mixtures. The thermodynamic factor may be calculated from activity coefficient models such as NRTL or UNIQUAC, which have adjustable parameters estimated from experimental phase equilibrium data. The group contribution method of UNIFAC may also be helpful, as it has a readily available parameter table consisting of mam7 species. If, however, reliable data are not available, then the averaged values of the generalized Maxwell-Stefan diffusion coefficients and the matrix of thermodynamic factors are calculated at some mean composition between x0i and xzi. Hence, the matrix of zero flux mass transfer coefficients [k ] is estimated by... 

Since thermodynamic nonidealities are of the essence for phase separation in liquid-liquid systems, and such nonidealities contribute to multicomponent interaction effects, it may be expected that liquid-liquid extraction would offer an important test of the theories presented in this book. Here, we present some experimental evidence to show the significance of interaction effects in liquid-liquid extraction. The evidence we present is largely based on experiments carried out in a modified Lewis batch extraction cell (Standart et al., 1975 Sethy and Cullinan, 1975 Cullinan and Ram, 1976 Krishna et al., 1985). The analysis we present here is due to Ej-ishna et al. (1985). The experimental system that will be used to demonstrate multicomponent interaction effects is glycerol(l)-water(2)-acetone(l) this system is of Type I. The analysis presented below is the liquid-liquid analog of the two bulb gas diffusion experiment considered in Section 5.4. 

An important first step in any model-based calculation procedure is the analysis and type of data used. Here, the accuracy and reliability of the measured data sets to be used in regression of model parameters is a very important issue. It is clear that reliable parameters for any model cannot be obtained from low-quality or inconsistent data. However, for many published experimentally measured solid solubility data, information on measurement uncertainties or quality estimates are unavailable. Also, pure component temperature limits and the excess GE models typically used for nonideality in vapor-liquid equilibrium (VLE) may not be rehable for SEE (or solid solubility). To address this situation, an alternative set of consistency tests [3] have been developed, including a new approach for modehng dilute solution SEE, which combines solute infinite dilution activity coefficients in the hquid phase with a theoretically based term to account for the nonideality for dilute solutions relative to infinite dilution. This model has been found to give noticeably better descriptions of experimental data than traditional thermodynamic models (nonrandom two liquid (NRTE) [4], UNIQUAC [5], and original UNIversal Eunctional group Activity Coefficient (UNIEAC) [6]) for the studied systems. 

Distillation is a countercurrent process in which equihbrium is maintained between Uquid and vapor, normally in a vertical column containing packing, thin wetted walls, or bubble cap plates. The single-stage separation factor for distillation is given by the vapor pressure isotope effect. Because mixtures of isotopic molecules show little or no nonideality in either liquid or vapor phase (Jancso et al. 1993), liquid vapor separation factors should be virtually independent of isotope enrichment (plate number), and the analysis of the distillation process is... 

In practice, the data needed to generate the liquidus and vaporus curves of a nonideal binary system are usually obtained by allowing liquid mixtures of various compositions to boil in an equilibrium still at a fixed temperature or pressure. When the hquid and gas phases have become equihbrated, samples of each are withdrawn for analysis. The partial pressures shown in Fig. 13.8(a) were calculated from the experimental gas-phase compositions with the relations pa = y p and Pb = P — Pa-... 

A challenging task faced by the analytical chemist when dealing with raw samples is extracting/isolating the analyte of interest from the sample matrix. It is fair to say that the majority of nonideal samples arrive in a format incompatible with most analytical instrumentation, and requires some degree of clean-up. Even well-defined samples (e.g. aqueous solutions) require basic filtration prior to analysis. Other desirable techniques may include liquid/liquid extraction and solid phase extraction. 

---