The working lines are used for the graphical calculation of the stages in the rect. & strip. sections. The pinch point is introduced.
The McCabe-Thile approach is a graphical method which allows for the calculation of the number of stages of a column in the binary distillation case.
The method is appplied to both the sections of the column and it is based to the following observations:
xD is a data of the distillation design hence it is known. y1 ≡ xD for the hypothesis of total condenser.
The liquid and vapor streams leaving a stage are in equilibrium.
This means that e.g. for the stage 1, x1 and y1 are linked with each other by the equilibrium correlation and the compositions can be read graphically on the equilibrium curve in the x-y diagram.
The compositions of the two counter-current liquid and vapor streams are represented by the working line equation, e.g. for stage 1 they are x1 and y2.
These composition can be read graphically on the working line represented in the x-y diagram.
The same observations of above are valid for the stripping section. The McCabe-Thiele graphical construction is then possible, as shown in the following animation: