Various configurations of batch distillation column

The early analysis of this process for a binary system, proposed by Rayleigh, is given below. Let F be the initial binary feed to the stiU (moles), and xf be the mole fraction of the more volatile component A in the feed. Let B be the amount of compounds remaining in the still, xb the mole fraction of component A in the still, and xd the mole fraction of component A in the vapor phase. The differential material balance for component A can then be written as  

In this simple distillation process, it is assumed that the vapor formed within a short period is in thermodynamic equilibrium with the liquid. Hence, the vapor composition xp is related to the hquid composition xb by an equiUbrium relation of the form xp = fixs)- The exact relationship for a particular mixture may be obtained from a thermodynamic analysis depending on temperature and pressure. For a system following the ideal behavior given by Raoult s law, the equilibrium relationship between the vapor composition y (or xp) and liquid composition x (or xb) of the more volatile component in a binary mixture can be approximated using the concept of constant relative volatility a), and is given by  

Although the analysis of simple distillation historically represents the theoretical start of batch distUlation research, a complete separation using this process is impossible unless the relative volatihty of the mixtme is inhnite. Therefore, the application of simple distillation is restricted to laboratory scale distillation, where high purities are not required, or when the mixture is easily separable. 

Example 4.1 A mixture of components A and B with 0.4 mole fraction of A and relative volatility of 2.0 is distilled in a simple distillation. The feed is 100 moles, and 40% of mixture is distilled. Find the distillate composition at the end of operation. 

Solution Since 40% of feed is distilled, the residue amount in the reboiler is 60 moles. The bottom composition can be found using Equation 4.5 as given below. 

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