Degree-of-Freedom Analysis on a Distillation Process

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

In this Demonstration, a degree-of-freedom analysis is performed on a distillation process to determine whether the system has sufficient information to solve for the unknown variables. Use buttons to select the unit on which to do mass balances (distillation column, condenser or reboiler) or to do a balance on the overall system. When the condenser is selected, use buttons to select a partial or total condenser. Set the total number of unknowns with a slider; unknown variables are blue on the diagram and known variables are black. The known variables are selected randomly and change when you click the "new problem" button. Use buttons to select how species is represented: as or as ; the degree-of-freedom analysis is different for each representation. An explanation of the analysis is shown on the right. For zero degrees of freedom, the balances are solvable. The system is overspecified if it has more equations than unknowns and it is underspecified if it has more unknowns than equations. For the reboiler, the equilibrium ratio is known, and for a partial condenser the equilibrium ratio is known. Temperatures and pressures are known for this analysis. Mass balances and phase-equilibrium relations are solved to determine unknown variables.

Contributed by: Rachael L. Baumann (March 2016)
Additional contributions by: Janet deGrazia, John L. Falconer, Nathan S, Nelson and Nick Bongiardina
(University of Colorado Boulder, Department of Chemical and Biological Engineering)
Open content licensed under CC BY-NC-SA



When solving material balances for this distillation process, start with a unit that has zero degrees of freedom or start with the complete system if it has zero degrees of freedom. Then, do a degree-of-freedom analysis on another unit to see if it now has zero degrees of freedom. Repeat this procedure until all of the unknown variables are determined.

View the screencast videos [1, 2] for more examples of degree-of-freedom analysis.


[1] Degree of Freedom Analysis on a Single Unit [Video]. (Nov 14, 2011)

[2] Multiple Unit Material Balance: Degree of Freedom Analysis [Video]. (Oct 30, 2013)

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.