Activity liquid phase

To illustrate calculations for a binary system containing a supercritical, condensable component. Figure 12 shows isobaric equilibria for ethane-n-heptane. Using the virial equation for vapor-phase fugacity coefficients, and the UNIQUAC equation for liquid-phase activity coefficients, calculated results give an excellent representation of the data of Kay (1938). In this case,the total pressure is not large and therefore, the mixture is at all times remote from critical conditions. For this binary system, the particular method of calculation used here would not be successful at appreciably higher pressures. 

GET LIQUID PHASE ACTIVITY COEFF 1C IEISTTS t GAM 130 CALL GAMMAtNfI0F,KEY,XF T GAM,ERG)... 

GAMMA CALCULATES LIQUID PHASE ACTIVITY COEFFICIENTS, GAM, FOR ALL N... 

Table 5. Liquid-Phase Activated Carbon Consumption, 10 t...

The binary interaction parameters are evaluated from liqiiid-phase correlations for binaiy systems. The most satisfactoiy procedure is to apply at infinite dilution the relation between a liquid-phase activity coefficient and its underlying fugacity coefficients, Rearrangement of the logarithmic form yields... 

These equations when combined with Eq. (13-5) lead to the following equations for liquid-phase activity coefficients in terms of measurable quantities ... 

There are many types of phase diagrams in addition to the two cases presented here these are summarized in detail by Zief and Wilcox (op. cit., p. 21). Solid-liquid phase equilibria must be determined experimentally for most binaiy and multicomponent systems. Predictive methods are based mostly on ideal phase behavior and have limited accuracy near eutectics. A predic tive technique based on extracting liquid-phase activity coefficients from vapor-liquid equilib-... 

Adsorption This is the most widely used of the physical-chemical treatment processes. It is used primarily for the removal of soluble organics with activated carbon serving as the adsorbent. Most liquid-phase-activated carbon adsorption reactions follow a Freundlich Isotherm [Eq. (25-21)]. 

Table 2. Liquid phase activated carbon consumption [11,16]. copyright 1992 John Willey Sons, Inc., with permission.

The Redlich-Kister [55, 57] equations provide a good technique for representing liquid phase activity and classifying solutions. 

In the previous sections, we emphasized that at constant temperature, the liquid-phase activity coefficient is a function of both pressure and composition. Therefore, any thermodynamic treatment of gas solubility in liquids must consider the question of how the activity coefficient of the gaseous solute in the liquid phase varies with pressure and with composition under isothermal conditions. 

The difficulties encountered in the Chao-Seader correlation can, at least in part, be overcome by the somewhat different formulation recently developed by Chueh (C2, C3). In Chueh s equations, the partial molar volumes in the liquid phase are functions of composition and temperature, as indicated in Section IV further, the unsymmetric convention is used for the normalization of activity coefficients, thereby avoiding all arbitrary extrapolations to find the properties of hypothetical states finally, a flexible two-parameter model is used for describing the effect of composition and temperature on liquid-phase activity coefficients. The flexibility of the model necessarily requires some binary data over a range of composition and temperature to obtain the desired accuracy, especially in the critical region, more binary data are required for Chueh s method than for that of Chao and Seader (Cl). Fortunately, reliable data for high-pressure equilibria are now available for a variety of binary mixtures of nonpolar fluids, mostly hydrocarbons. Chueh s method, therefore, is primarily applicable to equilibrium problems encountered in the petroleum, natural-gas, and related industries. 

Any convenient model for liquid phase activity coefficients can be used. In the absence of any data, the ideal solution model can permit adequate design. 

The estimation of the two parameters requires not only conversion and head space composition data but also physical properties of the monomers, e.g. reactivity ratios, vapor pressure equation, liquid phase activity coefficients and vapor phase fugacity coefficients. 

The liquid phase activity coefficient, yi, is a function of pressure, temperature and liquid composition. At conditions remote from the critical conditions it is virtually independent of pressure and, in the range of temperature normally encountered in distillation, can be taken as independent of temperature. 

At pressures above a few atmospheres, the deviations from ideal behaviour in the gas phase will be significant and must be taken into account in process design. The effect of pressure on the liquid-phase activity coefficientmustalso be considered. A discussion of the methods used to correlate and estimate vapour-liquid equilibrium data at high pressures is beyond the scope of this book. The reader should refer to the texts by Null (1970) or Prausnitz and Chueh (1968). 

ACT = correlation for liquid-phase activity coefficient such as, Wilson, NRTL, UNIQUAC, UNIFAC. 

Unless liquid phase activity coefficients have been used, it is best to use the same equation of state for excess enthalpy that was selected for the vapour-liquid equilibria. If liquid-phase activity coefficients have been specified, then a correlation appropriate for the activity coefficient method should be used. 

The liquid-phase activity coefficient y, can be defined by the expression ... 

This expression provides the basis for vapor-liquid equilibrium calculations on the basis of liquid-phase activity coefficient models. In Equation 4.27, thermodynamic models are required for cf>y (from an equation of state) and y, from a liquid-phase activity coefficient model. Some examples will be given later. At moderate pressures, the vapor phase becomes ideal, as discussed previously, and fj = 1. For... 

Given a prediction of the liquid-phase activity coefficients, from say the NRTL or UNIQUAC equations, then Equations 4.69 and 4.70 can be solved simultaneously for x and x . There are a number of solutions to these equations, including a trivial solution corresponding with x[ = x[. For a solution to be meaningful ... 

The solubility values are functions of pure component properties of the solute (a// /uv, 7ffl ) and the liquid phase activity coefficients of the components in solution. Solubility is calculated using the following equation... 

The liquid phase activity coefficient, which is a function of the subgroups, composition and temperature, can be evaluated using the UNIFAC group contribution method (Freedunslund et al., 1975). 

Sucii coefficients are needed for the effect of ammonium bicarbonate, carbamate, and hydrosulfide salts on the liquid phase activities of ammonia, carbon dioxide, and hydrogen sulfide. 

Understanding of phase behavior in concentrated salts systems requires liquid-phase activity coefficients for the electrolytes and for water in the multicomponent system. 

Equations 11 and 19 express the necessary liquid-phase activity coefficients for the calculation of vapor-liquid equilibria in the HCl-NaCl-HgO system. Equation 11 is very convenient... 

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. 

The liquid phase activity coefficients y and y2 depend upon temperature, pressure and concentration. Typical values taken from Perry s Chemical Engineers Handbook114) are shown in Figure 11.8 for the systems m-propanol-water and acetone-chloroform. In the former, the activity coefficients are considered positive, that is greater than unity, whilst in the latter, they are fractional so that the logarithms of the values are negative. In both cases, y approaches unity as the liquid concentration approaches unity and the highest values of y occur as the concentration approaches zero. 

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