ChemE. Degree of Freedom analysis & recycled stream

[worryingchem]

Homework Statement

The problem want me to do a degree of freedom analysis on the following process using the information provided.
There are two chemical rx in the process.
The desired production rate of DEA (D) is 105,000 kg/h.
The air composition is 21% mol% O₂ and 79 mol% N2[/SUB.
25% of ethylene (E) is converted in the first reaction.

Homework Equations

DOF = # of independent variables - # of independent equation

The Attempt at a Solution

When doing the problem, I put all the process units into one system and drew an overall diagram below.
For my DOF analysis of the bottom system to match the table in the top, I had to include the recycled stream, #10. Otherwise, I would be one stream variable short and get a DOF of -1. So my question is was it right to include the recycled stream when putting all the process units into one system?

For the bottom system, I had 9 independent variables (7 stream variables + 2 chemical rx) and 9 independent equations (1 flow, 1 stream composition, 1 system performance, and 6 material balance equations).

 

[BvU]

Hello WC,

Reason I didn't reply when having read your post is that I don't see a clear question: you have a summary of the DOF analysis in front of you (Is that the solutions manual ?)

Or was the question to do an analysis of the system as a whole (as a kind of black box) ? The recycle flow is an internal degree of freedom, and it has to be dealt with, one way or another (Which is relevant: equation solvers such as Aspen Custom Modeller can have trouble with this type of flowsheets if you're not careful).

I'd say you were right in treating this recycle as shown in your over-all diagram.

 

[worryingchem]

Ah, yes, thank you BvU, the picture is indeed the solution manual when treating each process unit as its own system. But I wanted to treat all the process units as one system. I should still get the same answer for my DOF analysis. However, unless, I draw my whole system like the bottom diagram of post 1, I won't be able to get the right DOF. So I was wondering if I was right to add the recycle stream to the diagram.

Thank you for clarifying that BvU.