Fluctuating fast chemical reactions in a batch process modelled by stochastic differential equations

In this paper, we report on results of investigations of the effects of fluctuations in the kinetics of a batch chemical reactor on the time trend of both concentration and temperature. Mixing problems and the relevant lack of ideality in the stirred tank may produce inhomogeneity in the chemical and physical properties of the global reacting system. The process is modelled by a system of stochastic ordinary differential equations whose weak solution is numerically determined by the Euler–Maruyama method. In particular, the role of the reaction order and the amplitude of fluctuation is analysed with respect to the first order moments of the concentration and temperature, respectively. The simulations have pointed out a considerable bias between the solution of the deterministic problem and the corresponding first moment trend of the stochastic approach in cases of nonlinear kinetics.