Vapour/liquid relationships

Fig. 16.3 Vapour/liquid relationships for ethanol/water and ethanol/water/calcium chloride at 1 bar., Experimental ---, calculated ---- ethanol/water system.

Problems with the determination of chemical equilibria in multiphase systems are solved in practice by assuming that the reaction takes place in any phase and all components are also equilibrated between phases. Accordingly, for a single reaction any of Eqns. (5.4-32) and (5.4-33) must be solved, while the relationships of Eqn. (5.4-31) must also be fulfilled. Since vapour-liquid equilibrium coefficients are functions of the compositions of both phases, the search for the solution is an iterative procedure. Equilibrium compositions are assumed, vapour-liquid equilibrium coefficients are then estimated, and new equilibrium compositions are evaluated. If the new equilibrium compositions are close to those assumed initially one may consider the assumed values to be the solution of the problem. Otherwise the evaluated compiositions are taken as the start for repetition of the procedure until a reasonable agreement between tissumed and evaluated comfiositions has been reached. 

If he selects the still pressure (which for a binary system will determine the vapour-liquid-equilibrium relationship) and one outlet stream flow-rate, then the outlet compositions can be calculated by simultaneous solution of the mass balance and equilibrium relationships (equations). A graphical method for the simultaneous solution is given in Volume 2, Chapter 11. 

This example illustrates the use of phase equilibrium relationships (vapour-liquid) in material balance calculations. 

It is convenient to carry out the analysis in terms of equilibrium stages . In an equilibrium stage (theoretical plate) the liquid and vapour streams leaving the stage are taken to be in equilibrium, and their compositions are determined by the vapour-liquid equilibrium relationship for the system (see Chapter 8). In terms of equilibrium constants ... 

If the vapour-liquid equilibrium relationship is expressed in terms of equilibrium constants, equation 11.7 can be written in a more useful form ... 

Roult s law is known to fail for vapour-liquid equilibrium calculations in polymeric systems. The Flory-Huggins relationship is generally used for this purpose (for details, see mass-transfer models in Section 3.2.1). The polymer-solvent interaction parameter, xo of the Flory-Huggins equation is not known accurately for PET. Cheong and Choi used a value of 1.3 for the system PET/EG for modelling a rotating-disc reactor [113], For other polymer solvent systems, yj was found to be in the range between 0.3 and 0.5 [96],... 

Another frequently used relationship for vapour-liquid equilibrium is the simple equation ... 

Fauske s method14,51 (given below) is based on emptying the reactor (or achieving vapour/ liquid disengagement) before the pressure has risen from the relief pressure to the maximum accumulated pressure in a vented system. The method incorporates the simplified equilibrium rate model, ERM, for saturated liquid inlet (see 9.4.2) together with the Clausius-Clapeyron relationship (discussed in 6.3.3). The method makes use of adiabatic experimental rate data for the runaway, whose measurement is described in Annex 2. 

Data on the vapour-liquid equilibrium relationships for the system. 

The height of a distillation column depends on the feed conditions, the product purity specifications and the extent of separation through the vapour-liquid equilibrium relationship, but also on the type of tray or packing used in the column as this affects the rate of separation. Column vendors will normally provide information on tray or packing efficiencies.9,10... 

As previously mentioned, one of the main degrees of freedom in absorption operations is the amount of solvent which is required to achieve the required absorption. This amount depends on how well the undesired gas component (the solute) is absorbed into the solvent. The vapour liquid equilibrium relationship for absorption of a gas component into a liquid solvent is expressed as ... 

The vapour liquid equilibrium relationship is same as the equation (III.7) with j = N. 

Because pressure and temperature are two readily measured experimental quantities (e.g. Griesser etal. 1999), the relationships among the vapour, liquid, and polymorphs of a substance are often represented on diagrams of pressure vs temperature. These are also very useful in summarizing the polymorphic behaviour of a system. 

Density or the pressure-volume-temperature (P-V-T) relationship is considered along with enthalpy and vapour-liquid equilibria as the three most essential thermophysical properties in the petroleum refining industry. The compressibility or density is commonly used in the petroleum industry to determine the volumetric properties of gases and liquids, information that is vital for transportation, safety and sale of petroleum fluids. 

In a one-component, or unary, system, only one chemical component is required to describe the phase relationships, for example, iron (Fe), water (H2O) or methane (CH4). There are many one-component systems, including all of the pure elements and compounds. The phases that can exist in a one-component system are limited to vapour, liquid and solid. Phase diagrams for one-component systems are specified in terms of two variables, temperature, normally specified in degrees centigrade,... 

As shown in the last section, R W>ult s and Henry s laws are permissible solutions of the differential expression (7 40) which governs vapour-liquid equilibria at constant temperature and constant (or effectively constant) total pressure. However, these laws are not the only functional relationships connecting and Xi which are compatible with (7 40), and in the present section we shall discuss some alternative relationships for the special case of a binary system. 

In the simplest case the vapour-liquid critical points of the two components may be connected by a continuous locus of vapour-liquid critical points of mixtures at various concentrations with or without additional liquid-liquid immiscibility. In other cases the locus of vapour-liquid critical points is interrupted and starting from one of the components may wonder off to higher temperatures or may crossover to an upper or a lower consolute point. The principle of isomorphic critical behaviour asserts that the thermodynamic behaviour associated with the critical behaviour in mixtures can still be described by the scaling-law expression of eq 10.1 in terms of two independent scaling fields, hi and hj, and a dependent scaling field hi. The different types of critical phenomena observed experimentally are caused by different relationship of these scaling fields with the actual physical fields. ... 

In this chapter, we have presented a survey of the major theoretical approaches that are available for dealing with the effects of critical fluctuations on the thermodynamic properties of fluids and fluid mixtures. Special attention has been devoted to our current insight in the nature of the scaling densities and how proper relationships between scaling fields and physical fields account for asymmetric features of critical behaviour in fluids and fluid mixtures. We have discussed the application of the theory to vapour-liquid critical phenomena in one-component fluids and in binary fluid mixtures and to liquid-liquid phase separation in weakly compressible liquid mixtures. Because of space limitations this review is not exhaustive. In particular for the interesting critical behaviour of electrolyte solutions we refer the reader to the relevant literature. 

The first argument concerns the exponent of the Marangoni number. In [4] and [9] a direct proportionality (n=l) was assumed. This is an arbitrary assumption, qitite inadequate to the generated function, hr a theoretical approach [12] hrat and mass transfer in gas (vapour)- liquid systems has been analyzed in terms of circulation intensities caused interfacial tiubulence. The formulation and solution of tire problem are correct and reveal the mechanism of interfacial turbulence in detail which shows (by examining the relationships derived) that in feet both values (R-1) and the characteristic difference Act are directly proportional to the circulation intensitj Act also depends on circulation cell size. Thus K in Eq. (8) is a function of Ag, that is, it includes... 

For non-associating liquids, has a value of about 17.7 J K mol and 7 e is about 6 K, but somewhat dependent on the substance under consideration, 7 ont is its critical temperature where the inteifacial tension between a liquid and a vapour phase becomes zero. According to the principles of corresponding states and to scaling theories, the temperature dependence just below the vapour-liquid critical point can be described by relationships like Eq. (9),... 

Permporometry is a characterisation technique for determining active pores of ceramic membranes that makes use of the capillary condensation phenomena. The method was first developed by (Eyraud et al, 1984) as gas-liquid permporometry and has subsequently been improved to the gas-vapour permporometry method (Cao et al, 1993). Permporometry is based on controlled blocking of pores by capillary condensation with a condensable vapour combined with a simultaneous measurement of counterdiffusion of non-condensable gases through the pores that are not blocked by the condensed vapour. The relationship between the real pore diameter, dp and the Kelvin radius is given by ... 

As with all thermodynamic relations, the Kelvin equation may be arrived at along several paths. Since the occurrence of capillary condensation is intimately, bound up with the curvature of a liquid meniscus, it is helpful to start out from the Young-Laplace equation, the relationship between the pressures on opposite sides of a liquid-vapour interface. 

In this equation, all of the terms except y +i and x but including x, are constant. Hence the relationship between and x is linear with a slope of L j(L + D) and a line representing the relationship on a graph of y vs jc must pass tlrrough y = jcd when x — jcd, since tire vapour and the liquid have the same composition in the product. This is called the rectifying operating line in a graphical representation of tire distillation process. 

An apparatus for testing enamel with acid and alkaline liquids (and their vapours) was later proposed in an attempt to standardise corrosion ratings on an international basis. After surveying enamel properties and their relationship with resistance to liquids of different pH values, the concept of modifying the resistance by including specific elements in the glass structure has been outlined. ... 

The liquid and vapour molar flow rate in the enriching section, are denoted by L and V, as previously and in the stripping section as L and V. The relationship between L, V, L and V is determined by the feed rate F and the thermal quality of the feed "q". 

Knowing the outlet liquid composition, the outlet vapour composition can be calculated from the v-l-e relationship. 

The relationship between the area for vapour flow, Av, and the height above the liquid level, hv, can been found from tables giving the dimensions of the segments of circles see Perry and Green (1984), or from Figure 11.32 and 11.33 in Chapter 11. 

---