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 m3)
\(n_k\), 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.