Simultaneously optimizing the structure and operating parameters of distillation columns based on rigorous rate-based models is critical for various process intensification technologies to achieve their intended purpose in real-world distillation columns. However, efficiently optimizing a distillation column based on rate-based models while considering the column hydraulics is far from practical. The biggest obstacle in using rigorous models for distillation columns in an equation-oriented environment is ensuring a robust solution for large-scale, strongly coupled nonlinear models, along with the simultaneous optimization of integer and continuous variables. In this study, a new optimization framework was introduced. It incorporated a pseudo-transient simulation method to ensure convergence of the simulation in equation-oriented environment. Additionally, an efficient relaxation method transformed the mixed integer nonlinear programming problem into a nonlinear programming problem, facilitating simultaneous optimization of both the integer variable representing column structure and the continuous variables governing column operation. Three examples, including a complex intensified catalytic distillation column, were optimized to demonstrate the efficiency of the proposed framework. Specifically, its advantages in terms of mathematical optimality and industrial feasibility were illustrated.
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