The PaSR consists of an adiabatic chamber having inlet streams and one outlet. Steady flows of reactants are introduced through the inlets with given gas compositions and temperatures. The reactor pressure is assumed to be constant. Since there is no surface reaction, the mass flow rate at the outlet must be equal to the sum of the mass flow rates of all inlets so that the mass is conserved. In order to represent the evolution of the PDF properly by a stochastic scheme, PaSR addresses all problems in a transient manner. The overall mass balance for the gas mixture inside the PaSR is

(10–11)

where is the mass flow rate of the i th inlet and is the through-flow mass flow rate. The average properties of the PaSR are obtained from the ensemble of particles inside the reactor. Each particle is regarded as an independent PSR and interacts with others only through the molecular mixing process. Therefore, the conservation of energy and species is applied to an individual particle rather than to the reactor.

The species equation for a particle is then similar to that of a PSR:

(10–12)

and similarly the energy equation for a particle is:

(10–13)

In the above equations, the angled bracket () indicates the ensemble average that we use to approximate the density-weighted average in the simulation. The average residence time of the reactor, , is calculated as

(10–14)