Material Balance for continuous fractionating column

In above figure, the column is fed with F mol/h of concentration Xf and delivers D mol/h of overhead product of concentration XD and B mol/h of bottom product of concentration XB.

The material balance for the system is

F = D +B……………….. (i)

For distillation of two component system, let us consider component A is most volatile component (MVC). Then material balance for most volatile component is given by

F . Xf = D . XD + B . XB………… (ii)

Eliminating B from equation ii gives

F . Xf = D . XD + (F-D) XB

F . Xf = D . XD + F. XB  – D . XB

F . Xf – F. XB = D . XD  – D . XB

F(Xf – XB) = D (XD  – XB)







Net flow rate:

Difference between vapor and liquid anywhere in the column is given by net flow rate.

Control surface I: This section includes condenser and all plates above n+1. Material balance around condenser and accumulator is given by.






Thus net flow rate in this section (control surface I) is given by ‘D’. Regardless of changes in V and L, their difference is constant and equal to ‘D’. Material balance for component A around condenser and accumulator gives




Here, quantity  net flow of component ‘A’ upward in upper section of the column, which is constant throughout control surface I.

Control surface II: This is the lower section of column and includes reboiler and all plates below ‘m’. Here, material balance around reboiler is given by










About Author

Name : Pratiksha Shrestha

Ms. Shrestha holds masters degree in food engineering and bioprocess technology from Asian Institute of Technology (AIT) Thailand. She is currently working for Government of Nepal at Department of Food Technology and Quality Control (DFTQC), Kathmandu. She is also a teaching faculty in College of Applied food and Dairy Technology (CAFODAT) affiliated to Purbanchal university, Nepal.