# PFR model with n order reactions

• Kevin Bacon
In summary, you need to design a PFR which can be modeled as a set of 5 CSTRS 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}. There are m reactions taking place within the PFR, each defined by the stoichemetric coefficients v_{i,j}. The goal is to design the smallest possible PFR to achieve steady state conversion of X_{A1} = 0.75.
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!

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

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

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?

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

Chet

## 1. What is a PFR model with n order reactions?

A PFR (Plug Flow Reactor) model with n order reactions is a mathematical model used to describe the behavior of a chemical reactor where the reactants flow through the reactor without any back-mixing. The reactions occurring in the reactor follow an n order kinetics, meaning the rate of the reaction is dependent on the concentration of the reactants raised to the power of n.

## 2. How is a PFR model with n order reactions different from other reactor models?

A PFR model with n order reactions differs from other reactor models in that it takes into account the flow of reactants through the reactor and the kinetics of the reactions. This model assumes that the composition of the reactants changes along the length of the reactor and the reaction rate is dependent on the concentration of the reactants at that specific point in the reactor.

## 3. What are the important parameters in a PFR model with n order reactions?

The important parameters in a PFR model with n order reactions are the reactor volume, the feed concentration of reactants, the reaction rate constants, and the order of the reactions. These parameters are used to calculate the conversion of reactants, the residence time, and the concentration profile of the reactants along the length of the reactor.

## 4. What are the limitations of a PFR model with n order reactions?

One limitation of a PFR model with n order reactions is that it assumes ideal plug flow and no back-mixing, which may not be the case in real reactors. This model also does not take into account any external effects such as heat transfer or pressure changes. Additionally, the model may become complicated and difficult to solve for reactions with more than one order.

## 5. How is a PFR model with n order reactions used in practical applications?

A PFR model with n order reactions is used in practical applications to design and optimize chemical reactors. It allows engineers to predict the behavior of a reactor and make adjustments to improve its performance. This model is also used to analyze reaction kinetics and determine the rate constants for different reactions. Additionally, it can be used to study the effects of different operating conditions on the reactor performance.

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