Introduction

Chemical reactor design is fundamental to chemical engineering. The two most common ideal reactor models are the Continuous Stirred Tank Reactor (CSTR) and the Plug Flow Reactor (PFR). Each has distinct characteristics that affect reactor sizing and performance.

CSTR Design Equation

In a CSTR, the contents are perfectly mixed, so the exit concentration equals the concentration throughout the reactor:

Where:

• V = Reactor volume (L)
• F_A0 = Molar flow rate of reactant A (mol/min)
• X = Fractional conversion
• (-r_A) = Reaction rate at exit conditions (mol/L/min)

PFR Design Equation

In a PFR, there is no radial mixing - the fluid flows as a "plug" through the reactor:

The integral must be evaluated numerically for most kinetics expressions.

Levenspiel Plot

The Levenspiel plot is a graphical method for comparing CSTR and PFR volumes. It plots 1/(-r_A) versus conversion X:

• CSTR: The required volume is proportional to the area of a rectangle from (0,0) to (X, 1/(-r_A) at X)
• PFR: The required volume is proportional to the area under the curve from X=0 to the target conversion

For positive-order reactions, the PFR always requires less volume than a CSTR for the same conversion, because the reaction rate is higher at higher concentrations.

Reaction Kinetics

This calculator supports several reaction rate expressions:

Space Time

Space time (τ) is a measure of the average time a fluid element spends in the reactor:

Where v₀ is the volumetric flow rate. Note that space time equals mean residence time only for constant-density systems.