Stochastic axial dispersion model for tubular equipment

•A stochastic model is proposed for the fluid dynamics of tubular equipment.•The SDE was built by inserting randomness in the dispersion coefficient.•A convergence analysis was carried out for numerically solving of SDE.•An estimator function was developed to calculate the stochastic term.•The computational confidence intervals were calculated using the Monte Carlo method.

A stochastic model based on the axial dispersion model was proposed for the mathematical representation of the fluid dynamics of tubular equipment with irregular behavior. The differential equation was built by inserting randomness in the dispersion coefficient, which added a stochastic term to the model. This term was capable of simulating fluctuations that may arise in the characterization of tubular equipment using the stimulus-response technique. The model was validated by comparing sample paths and computational confidence intervals with three experimental data sets of a tubular milli-reactor for polystyrene production with different configurations. A convergence analysis was carried out in order to determine the number of elements needed for time discretization. An estimator function was developed to calculate the parameter of the stochastic term, while the parameter of the deterministic term was estimated by the least squares method. The stochastic differential equation was discretized and solved by the Euler-Maruyama method. The computational confidence intervals were calculated using the Monte Carlo method. The results were considered satisfactory, once the model was capable of representing the irregular fluid dynamics of a tubular reactor.