Global-nonlinear stochastic dynamics of a class of two-state two-parameter non-isothermal continuous stirred tank reactors

The global-nonlinear stochastic dynamics of a class of two-state two-parameter continuous exothermic chemical reactors subjected to noise disturbances is studied with Fokker-Planck's (FP's) partial differential equation (PDE) theory. The dependency of the stochastic on deterministic dynamics is formally established, and the fundamental characteristics of the associated two-state probability density function (PDF) are described in analytic form, including: (i) stationary state PDF, (ii) convection, diffusion, and metastability time scales along which the state PDF transient occurs, as well as (iii) conditions for PDF metastability. The correspondence between the determination of stochastic stationary state PDF and the assessment of deterministic multiplicity via Van Heerden's (VH) diagram is established. The developments and results are illustrated with numerical solution of FP's PDE, and put in perspective with typical and atypical results drawn with Monte Carlo (MC) method.