## Stochastic Reactor Modelling

Stochastic reactor models (SRM) are a stochastic extension of the deterministic plug flow (PFR) or continuous stirred tank (CSTR) reactor models which are often used in chemical engineering. The stochastic equivalents of these two generic models are the 'partially stirred plug flow reactor' (PaSPFR) and the 'partially stirred reactor' (PaSR).

In SRMs, global quantities such as the mass, volume, mean density
and mean pressure are assumed to be spatially homogeneous. The volume may be allowed to change with time according to a known function. Local quantities such as mass fractions and temperature are treated as *random variables*. The SRM gives the time evolution of the joint scalar mass density function, assuming statistical homogeneity. For these models the assumption of spatial homogeneity is replaced by the assumption of spatial statistical homogeneity. Statistical homogeneity means that the random variables describing mass fraction and temperature may be assumed to be sampled from the same probability density function throughout the domain.

The advantage of stochastic reactor models is that they can account for fluctuations of the quantities modelled by random variables within the reactor. So far the main application for the SRM is the HCCI engine but it has also been used to model a carbon black reactor. The CoMo Group are also active developing numerical algorithms for the solution of SRMs.