VLE Qualitative Behavior

Vapor/liquid equilibrium (VLE) is the state of coexistence of liquid and vapor phases. In this qualitative discussion, we limit consideration to systems comprised of two chemical species, because systems of greater complexity cannot be adequately represented graphically. 

When N = 2, the phase mle becomes F = 4 — n. Since there must be at least one phase (n= 1), the maximum number of phase-mle variables which must be specified to fix the intensive state of the system is three namely, P, T, and one mole (or mass) fraction. All equilibrium states of the system can therefore be represented in three-dimensional P-T-composition space. Within this space, the states of pairs of phases coexisting at equilibrium (F=4 — 2 = 2) define surfaces. A schematic three-dimensional diagram illustrating these surfaces for VLE is shown in Fig. 10.1. 

This figure shows schematically the P-T-composition surfaces which contain the equilibrium states of saturated vapor and saturated liquid for a binary system. The under surface contains the saturated-vapor states it is the P-T-y] surface. The upper surface contains the saturated-liquid states it is the P-T-xi surface. These surfaces intersect along the lines U BHCi 

The subcooled-liquid region lies above the upper surface of Fig. 10.1 the superheated-vapor region hes below the under surface. The interior space between the two surfaces is the region of coexistence of both liquid and vapor phases. If one starts with a liquid at F and reduces the pressure at constant temperature and composition along vertical hue F G, the first bubble of vapor appears at point L, which hes on the upper surface. Thus, L is a bubblepoint, and the upper surface is the bubblepoint surface. The state of the vapor brrbble in equilibrium with the hquid at L mrrst be represented by a point on the under surface at the temperature and pressure of L. This point is indicated by V. Line VL is an example of a tie line, which cormects points representing phases in equilibrium. 

As the pressure is further reduced along line F G, more and more hquid vaporizes until at W the process is complete. Thus W hes on the under surface and represents a state of saturated vapor having the mixture composition. Since W is the point at which the last drops of hquid (dew) disappear, it is a dewpoint, and the lower surface is the dewpoint surface. Continued reduction of pressure merely leads into the superheated vapor region. 

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In most industrial processes coexisting phases are vapor and liquid, although liquid/liquid, vapor/solid, and liquid/solid systems are also encountered. In this chapter we present a general qualitative discussion of vapor/liquid phase behavior (Sec. 12.3) and describe the calculation of temperatures, pressures, and phase compositions for systems in vapor/liquid equilibrium (VLE) at low to moderate pressures (Sec. 12.4).t Comprehensive expositions are given of dew-point, bubble-point, and P, T-flash calculations. 

Equation (1.5-10), nolike Eq- (1.5-9). can reprodnce all the qualitative features of subcritical VLE illustrated in Fig. 1.5-1. If we take (1.5-10) as representing actual behavior, then subtraction of (I.S-9) from (, 5-10) and summation over all components gives... 

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