Reactive distillation has significant economic and environmental advantages compared to conventional processes. However, the optimal design of a reactive distillation system is far from mature. This work proposed a novel equation-oriented optimization framework based on a rigorous equilibrium stage model for the optimization of reactive distillation systems. A pseudo-transient continuation (PTC) reactive distillation model was developed to solve the convergence problem of simulations. The bypass efficiency method was incorporated into the PTC model to avoid the intractable mixed integer optimization. The developed model can be integrated well with a steady-state optimization algorithm assisted by PTC models. Two cases demonstrated that the proposed model and optimization framework were robust and fast. However, the bypass efficiency method caused physically meaningless solutions, but they were found to be convertible to physically meaningful solutions without influencing the accurate optimization of number of stages according to the intrinsic properties of the bypass efficiency method introduced in the current work. (C) 2018 Elsevier Ltd. All rights reserved.