Design of Plug Flow Reactor (PFR)

Good morning all......!!

Hope everyone is doing good. Today i'm going to discuss on the design of Plug Flow Reactor (PFR). Actually this post is under making since many days and today its the day for publishing it.

As we already know PFR works on the principle of flow synthesis, where we will provide two liquid streams as inlet and get the desired output. However, there is a misconception in many Engineeer's that we'll get only desired products as output but the scenario is completely different as most of the times we may end up in getting low purity products, as this particular synthesis requires rigorous development. 

In my experience, even i've seen few managers who have tried converting batch process into flow process using a simple tube by just calculating the flow-rate against the batch process and injecting the reactants into the tubes, at the end they faced a severe consequence as the tube used as a reactor got blasted filling the total fumehood with fumes. The point that i want to make here is that, if we are proceeding with flow synthesis especially using the tubular reactor without backup, it might lead to catastrophic results (however, it depends on the scale of execution).

Here we are going to see the basic way of estimating the PFR capacity in terms of liters. This can be a foundation for further understanding of the flow synthesis.

A Plug Flow Reactor is a type of continuous reactor where reactants flow through a pipe without axial mixing. This design mimics the movement of discrete “plugs” of fluid, making it ideal for pharmaceutical processes involving reactions like hydrolysis, oxidation, or hydrogenation.

Key characteristics:

• Reactants move in one direction

• No mixing in the flow direction

• Concentration and rate vary along the length

What is a Plug Flow Reactor (PFR)?

A: A Plug Flow Reactor is a type of tubular reactor where the reactants flow in one direction with no axial mixing. The concentration and temperature vary along the reactor’s length, and each fluid element moves like a “plug.”

What is the main assumption behind PFR modeling?

A: The primary assumption is that there is no back-mixing. Each infinitesimal volume of fluid maintains its identity as it flows through the reactor, experiencing changing conditions along the length.

How does the concentration of reactants vary in a PFR?

A: The concentration of reactants decreases progressively along the length of the reactor as the reaction proceeds, unlike in a Continuous Stirred Tank Reactor (CSTR), where it is uniform throughout.

Is a PFR operated at steady state or dynamic conditions?

A: Most industrial PFRs operate under steady-state conditions, meaning that the inlet and outlet conditions remain constant with time.

What types of reactions are best suited for PFRs?

A: PFRs are suitable for:

• Fast reactions

• Exothermic reactions (with proper temperature control)

• Reactions where high conversion per unit volume is desired

What are some advantages of PFRs?

A:

• Higher conversion per volume compared to CSTR for many reaction orders

• Ideal for large-scale continuous processes

• Simpler construction for tubular flow systems

What are the limitations of PFRs?

A:

• Poor temperature control in long reactors

• Hot spots may form in exothermic reactions

• Not ideal for slow reactions due to long reactor lengths needed

What is the design equation for a PFR?

A: The general mole balance is:

Where:

• $V$ = reactor volume

• $F_{A\mathrm{0 }}$= molar flow rate of A

• $X$ = conversion

• $-r_{\mathrm{A }}$= rate of reaction of A

Can a PFR be used for multiple reactions?

A: Yes, but the design becomes more complex. PFRs can handle parallel, series, and reversible reactions, but kinetic modeling and heat/mass transfer considerations must be included.

Now, it think we can dive deep into the design by assuming an experimental data. Here we got conversion / disappearance of reactant A:

We assume the following experimental data for reactant A:

Time (min)	[A] (mol/L)
0	1.00
5	0.82
10	0.67
15	0.55
20	0.45
25	0.37
30	0.30
35	0.22
40	0.15
45	0.10
50	0.06
55	0.04
60	0.02

Integral Method – Identifying Reaction Order

We test three common rate laws:

• Zero-order:     

$$[A] = [A]_0 - kt$$

• First-order:

$$\ln[A] = \ln[A]_0 - kt$$

• Second-order:

$$\frac{1}{[A]} = \frac{1}{[A]_0} + kt$$

Now, we'll go with trial & error method in identifying the order of reaction by plotting the graphs for 

Plot 1: [A] vs time

Inference: The line is not straight, indicating it is not zero-order.

Plot 2: ln[A] vs time

Inference: This graph shows a near-linear relationship, confirming a first-order reaction.

Plot 3: 1/[A] vs time

Inference: This graph deviates from linearity, ruling out second-order kinetics.

From the slope of the first-order plot:

k = ( ln⁡[A]0−ln[A] ) / t

k = (ln(1.00)−ln(0.02)) / 60 ​= (0−(−3.912)) / 60 ​= 3.912 / 60 ​= 0.0616 min−1​

​

The rate equation will be -r_A = 0.0616 [A]

Now, lets calculate the PFR capacity for an assumed molar flow-rate:

Given:

• Molar flow rate $F_{A0}=10\text{mol/min}$

• Initial concentration $C_{A0}=1.00\text{mol/L}$

Then:

$$v_0 = \frac{F_{A0}}{C_{A0}} = 10 \, \text{L/min}$$

Reactor Volume Calculation (PFR Design)

For a first-order PFR:

$$V = \frac{F_{A0}}{kC_{A0}} \cdot [-\ln(1 - X)]$$

Assuming desired conversion $X = 0.98$;

$$V = \frac{10}{0.0616 \cdot 1} \cdot [-\ln(1 - 0.98)]$$

$$V = 162.34 \cdot 3.912 = \boxed{635.07 \, \text{L}}$$

Thats it....!!

This is quite simple, however we have other techniques to identify the reactor volume based on Maximization of reactangles method, which is defined very clearly in Octave Levenspiel 3rd Edition by plotting

$\frac{1}{-r_A}$ vs. conversion $X$$X$. This will be shown in the next post.

Thanks for reading the complete post.

Comments are most appreciated....!!

PollMaker

About The Author

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Hi! I am Ajay Kumar Kalva, Currently serving as the CEO of this site, a tech geek by passion, and a chemical process engineer by profession, i'm interested in writing articles regarding technology, hacking and pharma technology.
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