Ideal Reactors (CSTR and PFR)

In chemical reaction engineering, reactors are the vessels where chemical transformations take place. The two fundamental models for continuous, steady-state flow reactors are the Continuous Stirred-Tank Reactor (CSTR) and the Plug Flow Reactor (PFR).

These "ideal" models represent opposite extremes of mixing behavior, allowing engineers to size reactors and predict conversions without relying on complex computational fluid dynamics.

Continuous Stirred-Tank Reactor (CSTR)

The ideal CSTR assumes perfect mixing, meaning that the moment reactants enter the tank, they are instantaneously and uniformly distributed throughout the entire reactor volume.

Consequently, the temperature, concentration, and reaction rate are identical at every point inside the reactor, and are exactly equal to the conditions in the exit stream.

The design equation for a CSTR, derived from a steady-state mass balance (In - Out + Generation = 0), is:

Plug Flow Reactor (PFR)

The ideal PFR is modeled as a cylindrical tube with no radial mixing and no axial back-mixing. The fluid flows through the reactor as a series of infinitely thin "plugs," each spending the exact same amount of time in the reactor.

Because the reactant concentration decreases as the fluid travels down the length of the tube, the reaction rate continuously changes along the reactor length.

The design equation for a PFR requires integration over the changing conversion:

$V = F_{A0} \int_0^X \frac{dX}{-r_A}$

Residence Time ($\tau$)

The residence time ($\tau$), or space-time, is the time required to process one reactor volume of fluid, based on the inlet volumetric flow rate ($v_0$):

$\tau = \frac{V}{v_0}$

This is a useful measure of how long, on average, a molecule stays inside the reactor.

Engineering Check

For reactions with normal kinetics (where the rate decreases as reactant concentration drops), a PFR will always require less volume than a CSTR to achieve the same conversion. This is because the PFR operates at a higher average concentration (and thus a higher average rate) along its length, whereas the CSTR operates entirely at the lowest concentration (the exit concentration). Real-world reactors (which often suffer from dead zones or channeling) will always exhibit behavior somewhere between these two ideal limits.