Vapor system, deviations

In most binary liquid-vapor systems, Raoult s law is a good approximation for a component only when its mole fraction is close to unity. Large deviations from this law are com-... 

Example 1.9 shows that, for certain systems, deviations from Raoult s law can cause a maximum or a minimum in the vapor pressure to exist at a certain temperature and composition. At constant pressure, the boiling point or bubble point temperature curve could have a maximum or a minimum. Liquid mixtures whose vapor pressure curve or surface exhibits a maximum or a minimum are said to form azeotropes. The composition at which the azeotrope occurs is the azeotropic composition. Binaries are likely to form azeotropes if they deviate from Raoult s law and if their boiling points are not too far apart (within about 8°C). Azeotropes caused by positive deviations from Raoult s law are minimum boiling, that is, the azeotrope boils at a... 

Fig. ll.S. Total vapor pressures and partial pressures in liquid-vapor systems showing (a) negative deviation and (b) positive deviation from Raoult s law. 

Many or even most liquid mixtures encountered in industrial practice exhibit a nonideal equihbrium behavior. In high-pressure systems both the vapor phase and the liquid phase can deviate fiom Dalton s and Raoult s laws (e.g., Prausnitz et al. 1998). In low-pressure systems deviations from Raoult s law prevail. The fundamental principles for formulating the thermodynamics of nonideal systems are presented in Chap. 2. 

That is the reason for the abnormally high boiling point, heat capacity and values of other physical parameters. One can suppose that in polyaromatics solutions the associates from the alcohol molecules are partly destroyed, the concentration of individual alcohol molecules grows and therefore the volatility of alcohol in the form of individual molecules increases, thus resulting in the increase of the alcohol vapor partial pressure above its solution in termolan. This phenomenon can explain the positive alcohol-termolan system deviation fix>m Raoult s law. 

Jonquieres, A. and Fane, A. 1998. Modified BET models for modeling water vapor sorption in hydrophilic glassy polymers and systems deviating strongly from ideality. J. Appl. Polym. Sci. 67 1415—1430. Jonscher, A.K. 1983. Dielectric Relaxation in Solids. London, U.K. Chelsea Dielectric Press. 

For the modeled high pressure Westinghouse experiments, the system conditions were such that the SFe vapor properties deviated a considerable amount from ideal gas property relations. Because of the ideal gas property inaccuracies, non-ideal gas property models for SFe vapor were developed and implemented in the RELAP5/M0D3 code calculations. These models were developed for the specific volume, v, the coefficient of thermal expansion, isothermal compressibility, /c, and heat capacity at constant pressure, Cp. The non-ideal property models were obtained using a five coefficient Martin-Hou type equation of state and thermodynamic relations [8]. 

Figure 4-4. Representation of vapor-liquid equilibria for a binary system showing moderate positive deviations from Raoult s law.

Figure 4-9. Vapor-liquid equilibria for a binary system where one component dimerizes in the vapor phase. Activity coefficients show only small deviations from liquid-phase ideality.

In Equation (24), a is the estimated standard deviation for each of the measured variables, i.e. pressure, temperature, and liquid-phase and vapor-phase compositions. The values assigned to a determine the relative weighting between the tieline data and the vapor-liquid equilibrium data this weighting determines how well the ternary system is represented. This weighting depends first, on the estimated accuracy of the ternary data, relative to that of the binary vapor-liquid data and second, on how remote the temperature of the binary data is from that of the ternary data and finally, on how important in a design the liquid-liquid equilibria are relative to the vapor-liquid equilibria. Typical values which we use in data reduction are Op = 1 mm Hg, = 0.05°C, = 0.001, and = 0.003... 

In systems that exhibit ideal liquid-phase behavior, the activity coefficients, Yi, are equal to unity and Eq. (13-124) simplifies to Raoult s law. For nonideal hquid-phase behavior, a system is said to show negative deviations from Raoult s law if Y < 1, and conversely, positive deviations from Raoult s law if Y > 1- In sufficiently nonide systems, the deviations may be so large the temperature-composition phase diagrams exhibit extrema, as own in each of the three parts of Fig. 13-57. At such maxima or minima, the equihbrium vapor and liqmd compositions are identical. Thus,... 

Pure-component vapor pressures can be used for predicting solu-bihties for systems in which RaoiilFs law is valid. For such systems Pa = Pa a, where p° is the pure-component vapor pressure of the solute andp is its partial pressure. Extreme care should be exercised when attempting to use pure-component vapor pressures to predict gas-absorption behavior. Both liquid-phase and vapor-phase nonidealities can cause significant deviations from the behavior predicted from pure-component vapor pressures in combination with Raoult s law. Vapor-pressure data are available in Sec. 3 for a variety of materials. 

Multicomponent distillations are more complicated than binary systems due primarily to the actual or potential involvement or interaction of one or more components of the multicomponent system on other components of the mixture. These interactions may be in the form of vapor-liquid equilibriums such as azeotrope formation, or chemical reaction, etc., any of which may affect the activity relations, and hence deviations from ideal relationships. For example, some systems are known to have two azeotrope combinations in the distillation column. Sometimes these, one or all, can be broken or changed in the vapor pressure relationships by addition of a third chemical or hydrocarbon. 

To accommodate the step-by-step, recycling and checking for convergences requires input of vapor pressure relationships (such as Wilson s, Renon s, etc.) through the previously determined constants, latent heat of vaporization data (equations) for each component (or enthalpy of liquid and vapor), specific heat data per component, and possibly special solubility or Henry s Law deviations when the system indicates. 

Deviations in which the observed vapor pressure are smaller than predicted for ideal solution behavior are also observed. Figure 6.8 gives the vapor pressure of. (CHjCF XiN +. viCHCfi at T — 283.15 K, an example of such behavior,10 This system is said to exhibit negative deviations from Raoult s law. 

On the meniscus surface the deviation of vapor pressure from the saturation pressure Psat depends on the surface tension a, liquid density p( gas constant R, temperature T, and radii of curvature r. When p( > -Psat(T) < (2[Pg.354]

Data at two temperatures were obtained from Zeck and Knapp (1986) for the nitrogen-ethane system. The implicit LS estimates of the binary interaction parameters are ka=0, kb=0, kc=0 and kd=0.0460. The standard deviation of kd was found to be equai to 0.0040. The vapor liquid phase equilibrium was computed and the fit was found to be excellent (Englezos et al. 1993). Subsequently, implicit ML calculations were performed and a parameter value of kd=0.0493 with a standard deviation equal to 0.0070 was computed. Figure 14.2 shows the experimental phase diagram as well as the calculated one using the implicit ML parameter estimate. 

Whenever the solute and solvent exhibit significant degrees of mutual attraction, deviations from the simple relationships will be observed. The properties of these nonideal solutions must be determined by the balance of attractive and disruptive forces. When a definite attraction can exist between the solute and solvent, the vapor pressure of each component is normally decreased. The overall vapor pressure of the system will then exhibit significant deviations from linearity in its concentration dependence, as is illustrated in Fig. 10B. 

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... 

Chapter 17 - Vapor-liquid equilibrium (VLE) data are important for designing and modeling of process equipments. Since it is not always possible to carry out experiments at all possible temperatures and pressures, generally thermodynamic models based on equations on state are used for estimation of VLE. In this paper, an alternate tool, i.e. the artificial neural network technique has been applied for estimation of VLE for the binary systems viz. tert-butanol+2-ethyl-l-hexanol and n-butanol+2-ethyl-l-hexanol. The temperature range in which these models are valid is 353.2-458.2K at atmospheric pressure. The average absolute deviation for the temperature output was in range 2-3.3% and for the activity coefficient was less than 0.009%. The results were then compared with experimental data. 

NH4NH2C00, DNH4HC03.NH3. D(NH4)2C03,NH3,and DNH4NH C00,NH3 as adjustable parameters. Experimental data and calculated results are shown in Figure 2. The average percent deviation of calculated versus measured partial pressure is 11% for CO2 and 3.9% for NH3. The same system and the same least squares objective function have been studied by Beutier and Renon (9J. Their results, on the same basis, were 16% for C02 and 5% for NH3. Edwards, et al. (10) also studied vapor-liquid equilibrium of a NH3 C02 aqueous system at 373.15°K. 

---