## Mole Reactor¶

This page shows the derivation of the governing equations used in Cantera's Mole Reactor model.

More information on the Mole Reactor class can be found here.

## Mole Reactor¶

A homogeneous zero-dimensional reactor. By default, they are closed (no inlets or outlets),
have fixed volume, and have adiabatic, chemically-inert walls. These properties may all be
changed by adding appropriate components such as `Wall()`

, `ReactorSurface()`

,
`MassFlowController()`

, and `Valve()`

.

A Mole Reactor is defined by the three state variables:

\(U\), the total internal energy of the reactor's contents (in J)

\(V\), the reactor volume (in m

^{3})\(n_k\), the number of moles for each species (in kmol)

The equation for the total internal energy is found by writing the first law for an open system:

Where \(\dot{Q}\) is the net rate of heat addition to the system.

The reactor volume changes as a function of time due to the motion of one or
more `Wall()`

s:

where \(f_w = \pm 1\) indicates the facing of the wall (whether moving the wall increases or decreases the volume of the reactor), \(A_w\) is the surface area of the wall, and \(v_w(t)\) is the velocity of the wall as a function of time.

The moles of each species in the reactor's contents changes as a result of flow through
the reactor's inlets and outlets, and production of homogeneous gas phase species and reactions on the reactor `Wall()`

.
The rate of moles of species \(k\) generated through homogeneous phase
reactions is \(V \dot{\omega}_k\), and the total rate at which moles of species
\(k\) changes is:

Where the subscripts *in* and *out* refer to the sum of the corresponding property
over all inlets and outlets respectively. A dot above a variable signifies a time
derivative.

Equations 1-3 are the governing equations for a Mole Reactor.