Constant Pressure Reactor#

For this reactor model, the pressure is held constant and the energy equation is defined in terms of the total enthalpy. This model is implemented by the C++ class ConstPressureReactor and available in Python as the ConstPressureReactor class. A constant pressure reactor is defined by the state variables:

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

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

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

Equations 1-3 below are the governing equations for a 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 superscripted 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#

Writing the first law for an open system gives:

dUdt=pdVdt+Q˙+inm˙inhinhoutm˙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:

(3)#dHdt=Q˙+inm˙inhinhoutm˙out