Control Volume Mole Reactor#

A control volume mole reactor, as implemented by the C++ class MoleReactor and available in Python as the MoleReactor class. It is defined by the 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)

Equations 1-3 are the governing equations for a control volume mole reactor.

Volume Equation#

The reactor volume changes as a function of time due to the motion of one or more walls:

(1)#\[ \frac{dV}{dt} = \sum_w f_w A_w v_w(t) \]

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.

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 homogeneous gas phase species 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:

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

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#

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

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

where \(\dot{Q}\) is the net rate of heat addition to the system and \(\hat{h}\) is the molar enthalpy.

On this page
Show Source