Constant Pressure Mole Reactor

A constant pressure mole reactor is implemented by the C++ class ConstPressureMoleReactor and is available in Python as the ConstPressureMoleReactor class. It is defined by the state variables:

• \(H\), the total enthalpy of the reactor’s contents (in J)

• \(n_k\), the number of moles for each species (in kmol)

Equations 1 and 2 below are the governing equations for a constant pressure mole reactor.

Species Equations

The moles of each species in the reactor changes as a result of flow through the reactor’s inlets and outlets and production of gas phase species through homogeneous reactions and reactions on the reactor surfaces. The rate at which species \(k\) is generated through homogeneous phase reactions is \(V \dot{\omega}_k\), and the total rate at which moles of species \(k\) changes is:

(1)\[ \frac{dn_k}{dt} = V \dot{\omega}_k + \sum_\t{in} \dot{n}_{k, \t{in}} - \sum_\t{out} \dot{n}_{k, \t{out}} + \dot{n}_{k, \t{wall}} \]

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.

Energy Equation

Writing the first law for an open system gives:

\[ \frac{dU}{dt} = - p \frac{dV}{dt} + \dot{Q} + \sum_\t{in} \dot{n}_\t{in} \hat{h}_\t{in} - \hat{h} \sum_\t{out} \dot{n}_\t{out} \]

where positive \(\dot{Q}\) represents heat addition to the system and \(h\) is the specific enthalpy of the reactor’s contents.

Differentiating the definition of the total enthalpy, \(H = U + pV\), with respect to time gives:

\[ \frac{dH}{dt} = \frac{dU}{dt} + p \frac{dV}{dt} + V \frac{dp}{dt} \]

Noting that \(dp/dt = 0\) and substituting into the energy equation yields:

(2)\[ \frac{dH}{dt} = \dot{Q} + \sum_\t{in} \dot{n}_\t{in} \hat{h}_\t{in} - \hat{h} \sum_\t{out} \dot{n}_\t{out} \]