Mathematical Modeling and Robust Multi-Objective Optimization of the Two-Dimensional Benzene Alkylation Reactor with Dry Gas

The benzene alkylation reactor using the dry gas is the most significant equipment in the ethylbenzene manufacturing process. In this paper, a two-dimensional homogeneous model is developed for steady state simulation of the industrial multi-stage catalytic reactor for ethylbenzene. The model validation on a practical benzene alkylation reactor shows the model is accurate and can calculate the hot spot temperatures. The composition of dry gas from upstream process varies with the operating conditions, which can cause unexpected hot spots in the reactor and catalyst deactivation. Considering the uncertainty in dry gas composition, a robust multi-objective optimization framework is proposed: first, the back-off in constraints is introduced to the multi-objective optimization problem to hedge against the worst case; then the optimal operating point can be selected using the multicriteria decision-making. The reactor optimization objectives are maximizing selectivity of ethylene and conversion of ethylbenzene, and the distribution ratios of dry gas are defined as decision variables. Results of robust multi-objective optimization show the selectivity and conversion at the optimal operating point are 90.88% (decreased by 0.24% compared to the practical condition) and 99.94% (increased by 0.72%). Importantly, the proportion of violations of the hot spot constraints decreases from 13.7% of the traditional method to 3.8% by applying the proposed robust multi-objective optimization method.