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:

\begin{equation*} \frac{dU}{dt} = - p \frac{dV}{dt} + \dot{Q} + \sum_{in} \dot{n}_{in} \bar{h}_{in} - \bar{h} \sum_{out} \dot{n}_{out} \tag{1} \end{equation*}

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:

\begin{equation*} \frac{dV}{dt} = \sum_w f_w A_w v_w(t) \tag{2} \end{equation*}

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:

\begin{equation*} \frac{dn_k}{dt} = V \dot{\omega}_k + \sum_{in} \dot{n}_{k, in} - \sum_{out} \dot{n}_{k, out} + \dot{n}_{k, wall} \tag{3} \end{equation*}

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.