# PFR model with n order reactions

1. Feb 19, 2015

### Kevin Bacon

• This is a homework problem that was posted in another forum, so there is no template
I have this problem for my reactor design course and I need some help wrapping my head around it.

We have to design a plug flow reactor (PFR), which can be modeled as five equal volume CSTR's in series. The PFR has an inlet volumetric flow rate of $q_{in}$ which contains species $A_i, i = 1...n$ having concentration $C_{Ai,in}$ (also the whole PFR is operated at a constant temperature $T_{ref}$).

The PFR is initially filled with solution containing species at concentration $C_{Ai,0}$. The density of the inlet stream is constant at $\rho$. There are $m$ reactions taking place within the PFR, each defined by the stoichemetric coefficients $v_{i,j}$ where $i = 1...n, j = 1...m$.

Our goal is to design the smallest possible PFR to achieve steady state conversion of $X_{A1} = 0.75$.

We are given a matrix of the stoichometric coefficients:
$$v = \begin{bmatrix} -a & -b & 0 & d\\ -a & 0 & 0 & d\\ a & 0 & -c & -d\\ 0 & b & c & 0 \end{bmatrix}$$

Basic rate laws:
$$r_{A1,1} = -kC_{A1}C_{A2}^2\\ r_{A5,2} = kC_{A1}\\ r_{A4,3} = -kC_{A4}^2\\ r_{A3,4} = -kC_{A3}^2C_{A4}^2$$
All k = 1, the inlet volumetric flow rate is given and a vector of five values for $C_{Ai,in}$ and $C_{Ai,0}$ are given.

My approach so far is to create the net generation term being:

r = [-k*(c(1)*c(2)^2+c(1)^2+c(3)^2*c(4)^2-0.5*c(4)^2);
k*(c(1)-c(1)*c(2)^2);
k*(c(1)-c(4)^2);
k*(c(1)*c(2)^2-c(1)^2+c(3)^2*c(4)^2-0.5*c(4)^2)]

But do I take the CSTR approach or the PFR approach? A general idea would be very helpful. Thank you!

2. Feb 20, 2015

### Staff: Mentor

You are approximating the PFR as a set of set of 5 CSTRs in s

3. Feb 20, 2015

### Kevin Bacon

Yes, I understand this concept, I would have 5 CSTRS which means I'll have a mass and mole balance equation written around each, but how do I incorporate the reactions that are occurring?

4. Feb 20, 2015

### Staff: Mentor

Are you saying that you don't know how to solve a CSTR in which chemical reactions are occurring?

Chet