On the global nonlinear stochastic dynamical behavior of a class of exothermic CSTRs

The problem of assessing the short and long time effects of stochastic fluctuations on the global-nonlinear dynamics of a class of closed-loop continuous exothermic reactors with temperature control and mono or bistable isothermal dynamics is addressed. The consideration of the problem within a Fokker-Planck (FP) stochastic framework yields: (i) the characterization of the global-nonlinear stochastic dynamics, and (ii) the connection between the deterministic and stochastic modeling approaches. The evolution of the state probability density function (PDF) is explained as the result of a complex interplay between deterministic dynamical features, initial PDF shape, and noise intensity. The correspondence between stationary PDF mono (or bi) modality and deterministic mono (or bi) stability is established, and the stochastic settling time is put in perspective with the deterministic, noise-diffusion, and escape times. The conditions for the occurrence of a retarded response, with respect to deterministic and noise-diffusion times, are identified. The proposed approach: (i) is illustrated with representative case class example, and (ii) constitutes an inductive step towards the development of a general-purpose stochastic modeling approach in chemical process systems engineering.