Ideal Gas Constant Pressure Reactor#

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

  • m, the mass of the reactor’s contents (in kg)

  • T, the temperature (in K)

  • Yk, the mass fractions for each species (dimensionless)

Equations 1-3 below are the governing equations for an ideal gas constant pressure reactor.

Mass Conservation#

The total mass of the reactor’s contents changes as a result of flow through the reactor’s inlets and outlets, and production of homogeneous phase species on surfaces:

(1)#dmdt=inm˙inoutm˙out+m˙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.

Species Equations#

The rate at which species k is generated through homogeneous phase reactions is Vω˙kWk, and the total rate at which species k is generated is:

m˙k,gen=Vω˙kWk+m˙k,wall

The rate of change in the mass of each species is:

d(mYk)dt=inm˙inYk,inoutm˙outYk+m˙k,gen

Expanding the derivative on the left hand side and substituting the equation for dm/dt, the equation for each homogeneous phase species is:

(2)#mdYkdt=inm˙in(Yk,inYk)+m˙k,genYkm˙wall

Energy Equation#

As for the ideal gas reactor, we replace the total enthalpy as a state variable with the temperature by writing the total enthalpy in terms of the mass fractions and temperature and differentiating with respect to time:

H=mkYkhk(T)dHdt=hdmdt+mcpdTdt+mkhkdYkdt

Substituting the corresponding derivatives into the constant pressure reactor energy equation (3) yields an equation for the temperature:

(3)#mcpdTdt=Q˙khkm˙k,gen+inm˙in(hinkhkYk,in)