User:A.sharma95/sandbox

Introduction
Distillation is a process in which we separate two components one is overhead distillate and the other is the bottom product. The bottom product is mostly liquid while the distillate may be liquid or vapour. This separation basically requires following three things:

1.	A second phase must form, so that liquid and vapour can contact each other on each stage in the column.

2.	Both the components must different volatility.

3.	Two phases can be separated by gravity or other mechanical techniques.

The distillation column contains one feed component, xf. The top product is distillate which is represented by xD and the bottom product containing composition of xB of the light component. It consist of three sections: stripping section, rectification section, and feed section.

Overhead Condenser

 * This is a heat exchange equipment used for condensing the hot liquid leaving the top of the column. Either cooling water or air is used as a cooling agent.

Overhead Accumulator

 * This a horizontal pressure vessel where the condensed vapour is collected.

Pumps

 * They can be used to return the reflux liquid back to the distillation column.

Reboiler

 * Its purpose is to produce the vapour stream in the distillation column. It can be used internally and externally. Stream reboiler and fired reboiler are used.

Mathematical modelling
The total mole hold up in the nth tray Mn is considered constant but the imbalance in the input and output flows is taken into account for in the component and the heat balance equations- INLET: Phase	Flow rate	Concentration Liquid	$$L_(n+1)	X_(n+1)$$ Vapour	$$V_(n-1)   Y_(n-1)  $$

OUTLET: Phase	Flow rate	Concentration Liquid	$$V_n	y_n$$ Vapour	$$L_n	x_n$$

Component balance[1]: $$t (M_n x_n )=L_(n+1) x_(n+1)-L_n x_n+V_(n-1) y_(n-1)-V_n y_n$$                (1)

by differentiating and substituting above equation we get $$t (x_n )=[L_(n+1) x_(n+1)+V_(n-1) y_(n-1)-(L_(n+1)+V_(n-1) ) x_n-V_n (y_n-x_n ) ]/M_n$$ Energy Balance[2]:

$$t (M_n h_n )=h_(n+1) L_(n+1)-h_n L_n+H_(n-1) V_(n-1)-H_n V_n  $$                (2) substituting the mass balance equation in above equation we get the following expression: $$V_n=[h_(n+1) L_(n+1)+H_(n-1) V_(n-1)-(L_(n+1)+V_(n-1) ) h_n ]/(H_n-h_n)$$ where, V:- represents vapour flow, L:- is liquid flow, x:- is liquid concentration of light component, y:- represents vapour concentration of light component, h:- is enthalpy for liquid ; and H:-is enthalpy for vapour