Cantera/Integral and Differential Reactors

(Why integral vs. differential is useful/important)

Main difference between integral and differential reactors is in the assumptions about what's going on inside the reactor control volume. This changes the form of equations being solved.

A Word on Gradients

Really, ultimately, the difference is all about gradients. Whether you resolve them, or integrate over them; whether you ignore them, or treat them rigorously; not just which directions the gradients are in, but also which quantities the gradients are for.

Integral Reactors

Integral reactors: effects are integrated, conditions are wide, changing

Integral reactors may be isothermal - simply having an isothermal temperature profile does not mean a reactor is differential

Essentally an integral reactor is characterized by having gradients, or changes, in its thermodynamic state throughout the reactor volume. This necessitates either integrating over the multiple different zones of the reactor, each of which has a different temperature, pressure, composition, reaction rate, etc., or modeling the reactor as multiple interacting zones.

Differential Reactors

Differential reactors are the differential control volumes over which material/energy balances are written when deriving from, e.g., Reynolds Transport Theorem.

These are small enough, relative to the gradients in the system, that the control volume can be assumed to be perfectly uniform over the entire control volume.

In a differential chemical reactor, then, the entire reactor could be described with a single thermodynamic state - a single temperature, pressure, and composition - and thus have a single reaction rate, a single kinetic rate coefficient, and so on.

Thus, (real) differential reactors are useful for measuring kinetic rate data. (See Froment Bischoff book on reactor design for more details.)

Cantera's Temporal Approach

Differential/integral reactor definitions fit into how Cantera is solving equations

• Single Cantera reactor with a single control volume over a single timestep is a differential reactor
• Shrinking differential element size (timestep) to be tinier and tinier
• assuming spatial step is not differential, because assuming perfect spatial mixing, so no variance, so no difference (integral over constant function is linear func)