Question

A process flow sheet analysis results in the degree of freedom having a value of $2$. Which one of the following steps must be carried out?

• A. Identify and add two new independent equations from process model
• B. Remove two equations that have been wrongly assumed to be independent
• C. Assign values of two variables in the process
• D. Assign value to one variable and remove one equation that was wrongly assumed to be independent

Hint:

Always remember: $DF$ represents the number of external design choices a process engineer must specify to uniquely define a steady-state process simulation.

Answer 1

The Correct Option is C

Concept: The Degree of Freedom ($DF$) in process simulation and flowsheeting design is calculated using the formula: \[ DF = N_{\text{variables}} - N_{\text{independent equations}} \] The value of $DF$ indicates the design flexibility of the system:

• If $DF = 0$, the system is completely specified and has a unique solution.

• If $DF \gt 0$, the system is underspecified, meaning there are more unknown variables than available independent governing equations.

Step 1: Interpret a degree of freedom value of $2$.
We are given $DF = 2$. This tells us that the system has $2$ extra degrees of freedom. To solve the system and obtain a unique operating point, a designer must manually specify or assign fixed values to exactly $2$ independent design variables. This reduces the remaining degrees of freedom to zero ($DF = 0$), allowing the system of equations to be solved. This matches Option C.