Equilibrium vapor-liquid distribution ratio

In distillation the components are distributed between separable vapor and liquid phases. The distribution coefficients or K values are the ratios of the vapor-liquid compositions in the equilibrium phases. They are expressed as the liquid phase activity coefficients, y/s, the vapor... 

It follows, trivially, that, provided vapor-liquid equilibrium is indeed possible at the assigned values of temperature and pressure, pressure p is the first moment of the liquid-phase mole fraction distribution. It is therefore natural to define the dimensionless label X as bip, that is, as the ratio of the vapor pressure to the total pressure. This now requires the first moment of to be unity, = 1. Raoult s law takes the form... 

Eew multicomponent systems exist for which completely generalized equilibrium data are available. The most widely available data are those for vapor-liquid systems, and these are frequently referred to as vapor-liquid equilibrium distribution coefficients or K value. The K values vary with temperature and pressure, and a selectivity that is equal to the ratio of the K values is used. Eor vapor-liquid systems, this is referred to as the relative volatility and is expressed for a binary system as... 

It is convenient to define an equilibrium ratio as the ratio of mole fractions of a species in two phases in equilibrium. For the vapor-liquid case, the constant is referred to as the K-value or vapor-liquid equilibrium ratio as defined by (1-3) as Ki s yjxi- For the liquid-liquid case, the constant is frequently referred to as the distribution coefficient or liquid-liquid equilibrium ratio as defined by (1-6) as Kd, x ilx i. ... 

K-Values A measure of how a given chemical species distributes itself between liquid and vapor phases is the equilibrium ratio ... 

Because the equilibrium constant Keq ranges from zero, when the system is all solid, to infinity, when it is all liquid, (strictly, one should include vaporization, neglected here) it is convenient to introduce another related function, a ratio we call D (for distribution), which contains the same information but ranges from — 1 to +1 D = (Keq — l)/(Keq +1). This allows us to portray graphically the behavior of a system in terms of the amount of each of two phases as a function of temperature. This is done in Fig. 1, for a small system (a), a mid-size system (b), and a large but not truly macroscopic system (c). However, even case (c) in this figure does not... 

The fundamental basis of distillation is the physical eqnilibrinm between the liquid and vapor phases of a system. Eqnilibrinm is the condition reached after an infinite time of contact between the phases. In practice, liqnid-vapor systems normally reach a state close to equilibrinm in a comparatively short time of contact. At equilibrium, the composition in the vapor phase is nsnally different from that in the liqnid. (If this is not the case, then an azeotrope is present, as discnssed later.) The relationship of eqnilibrinm concentrations of a component between phases is described by the equilibrium ratio. Other terms used for this ratio can inclnde distribution coefficient, equilibrium constant, K-constant, or simply volatility. 

Equation (6-106) cannot be integrated analytically because the relationship between xD and xw depends on the liquid-to-vapor ratio, the number of theoretical stages, and the equilibrium distribution curve. However, it can be integrated graphically with pairs of values for xD and xw obtained from the McCabe-Thiele diagram for a series of operating lines of the same slope. 

If the gaseous phase can he considered as a vapor, then the distribution of a species between the vapor and liquid phase is of interest. Obviously, the species can be a major constituent of each phase here. The equilibrium ratio /C, of a component i is defined as (equation (1.4.1))... 

K is the distribution coefficient or K factor, defined as the ratio of mole fraction in the vapor phase i/ to the mole fraction in the liquid phase x at equilibrium. When Raoult s law and Dalton s law hold for the mixture, the K. factor is defined as the ratio of the vapor pressure to the total pressure of the system [2] ... 

To imderstand and evaluate methods of crude stabilization, one must be familiar with phase equilibrium. Almost every operation in the production of hydrocarbons involves some form of equilibrium between the vapor and liquid phases of multi-component hydrocarbon systems. The distribution of individual components between phases has heen correlated in terms of equilibrium ratios, or K values, which are functions of the temperature, pressure, and composition of the system. 

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