What is Differential Distillation, Simple Distillation, Rayleigh distillation,Rayleigh equation, material Balance equation

Differential Distillation:

Simple distillation, also known as Rayleigh distillation or differential distillation, is the most elementary example of batch distillation. In this distillation system, the vapor is removed from the

still during a particular time interval and is condensed in the condenser. The more volatile component is richer in the vapor than in the liquid remaining in the still. Over time, the liquid remaining in the still begins to experience a decline in the concentration of the more volatile component, while the distillate collected in the condenser becomes progressively more enriched in the more volatile component.

Schematic representation of differential distillation is as shown in in fig.1

Fig:1 Differential distillation

No reflux is returned to the still, and no stages or packing materials are provided inside the column; therefore, the various operating approaches are not applicable to this distillation system. 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 still (mol) and x_F be the mole fraction of the more volatile component (A) in the feed. Let B be the amount of compound remaining in the still, x_B be the mole fraction of component A in the still, and x_D be the mole fraction of component A in the vapor phase. The differential material balance for component A can then be written as:

x_D dB = d ( B x_B ) = B dx_B + x_B dB

Upon integration:

or

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 (x_D) is related to the liquid composition (x_B) by an equilibrium relation of the form x_D = F(x_B). 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 x_D) and liquid composition X (or x_B) of the more volatile component in a binary mixture can be approximated using the concept of constant relative volatility (α), which is given by:

Substitution of the above equation in Equation (2)

Although the analysis of simple distillation historically represents the theoretical start of batch distillation research, a complete separation using this process is impossible unless the relative volatility of the mixture is infinite. 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.