New formulation of optimization-based simulation of a pressure swing adsorption process: Hybrid dynamic optimization

In this paper, the simulation based on optimization of a four-step pressure swing adsorption (PSA) process is considered. The simulation problem which consists in the determination of the cyclic steady-state (CSS) is formulated as an optimization problem where the performance index is the CSS condition, the decision variables are the state variables at the start of the cycle and the constraints are given by the process model along with associated initial and boundary conditions. More specifically, the optimization problem is formulated as a hybrid dynamic optimization problem involving four modes (PSA steps) where each mode is characterized by model equations, transition condition and transition functions. The necessary conditions of optimality for the hybrid dynamic system using the adjoint system method are derived and the gradients of the performance index and constraints with respect to decision variables are computed for the non linear programming (NLP) solver used. The case study is a non isothermal PSA process studied and presented in details in Liu and Ritter1 and Liu et al.2. The optimization results are compared to those obtained with gradients computed by means of a finite differences method.