Ideal Gas Constant Pressure Mole Reactor#

An ideal gas constant pressure mole reactor, as implemented by the C++ class IdealGasConstPressureMoleReactor and available in Python as the IdealGasConstPressureMoleReactor class. It is defined by the state variables:

  • T, the temperature (in K)

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

Equations 1 and 2 below are the governing equations for an ideal gas 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 homogeneous gas phase species and reactions on the reactor surfaces. The rate at which species k is generated through homogeneous phase reactions is Vω˙k, and the total rate at which moles of species k changes is:

(1)#dnkdt=Vω˙k+inn˙k,inoutn˙k,out+n˙k,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:

dUdt=pdVdt+Q˙+inn˙inh^inh^outn˙out

where positive 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:

dHdt=dUdt+pdVdt+Vdpdt

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

dHdt=Q˙+inn˙inh^inh^outn˙out

As for the ideal gas mole reactor, we replace the total enthalpy as a state variable with the temperature by writing the total enthalpy in terms of the species moles and temperature:

H=kh^k(T)nk

and differentiating with respect to time:

dHdt=dTdtknkc^p,k+h^kn˙k

Making this substitution and rearranging yields an equation for the temperature:

(2)#knkc^p,kdTdt=Q˙h^kn˙k