Control Volume Reactor#

This model represents a homogeneous zero-dimensional reactor, as implemented by the C++ class Reactor and available in Python as the Reactor class. A control volume reactor is defined by the state variables:

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

  • V, the reactor volume (in m3)

  • U, the total internal energy of the reactors contents (in J)

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

Equations 1-4 below are the governing equations for a control volume 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.

Volume Equation#

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

(2)#dVdt=wfwAwvw(t)

where fw=±1 indicates the facing of the wall (whether moving the wall increases or decreases the volume of the reactor), Aw is the surface area of the wall, and vw(t) is the velocity of the wall as a function of time.

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:

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

Energy Equation#

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

(4)#dUdt=pdVdt+Q˙+inm˙inhinhoutm˙out

Where Q˙ is the net rate of heat addition to the system.