Vapor-liquid equilibrium Rayleigh equation

By using vapor-liquid equilibrium data the above integral can be evaluated numerically. A graphical method is also possible, where a plot of l/(y - xj versus Xr is prepared and the area under the curve over the limits between the initial and fmal mole fraction is determined. However, for special cases the integration can be done analytically. If pressure is constant, the temperature change in the still is small, and the vapor-liquid equilibrium values (K-values, defined as K=y/x for each component) are independent from composition, integration of the Rayleigh equation yields ... 

The residue curves can also be calculated by numerical integration of the differential equation for open evaporation (Rayleigh equation) if the vapor-liquid equilibrium behavior is known (see Figure 11.11) [8]. Starting from the material balance of component i ... 

If the reflux ratio R or distillate rate D is fixed, instantaneous distillate and bottoms compositions vary with time. For a total condenser, negligible holdup of vapor and liquid in the condenser and the column, equilibrium stages, and constant molar overflow, the Rayleigh equation can now be written as... 

We consider here a body of water containing dissolved mercury at the saturation level and set ourselves the task of calculating the reduction in mercury content that occurs when 0.01% of the contents is evaporated. It is assumed that the vapor in question is at all times in equilibrium with a well-mixed liquid, i.e., that Rayleigh s equation applies. 

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