Optimisation-based process synthesis is a systematic method to determine the optimal configuration and design and operation parameters of chemical processes. Ideally, rigorous unit operation models should be included in process synthesis to ensure the applicability of the optimisation results, which, however, leads to a large-scale strongly nonlinear and nonconvex MINLP problems and cannot be solved reliably by the existing algorithms. To address that problem, in this work, we proposed a feasible path algorithm-based branch and bound (B&B) algorithm with good convergence and reasonable efficiency. In the algorithm, a B&B tree is constructed with nodes generated by systematically fixing part of the binary variables while relaxing the other binary variables to be between 0 and 1. Since the nonlinear programming (NLP) problem in each node is intractable to solve, our previously developed hybrid steady-state and time-relaxation-based optimisation algorithm (Ma et al., 2020) is adopted, which has been proposed to have good convergence for process optimisation problems in the equation oriented (EO) modeling environment. To improve the efficiency of the MINLP algorithm, during B&B, the solution from a parent node is used to initialize the NLP subproblems in the children nodes recognizing that they only differ in whether fixing or relaxing one specific binary variable. The proposed MINLP algorithm is validated by three case studies. One case study is to determine the distillation sequence based on the state-equipment network (SEN) (Yeomans and Grossmann, 2000) incorporating rigorous material balance, phase equilibrium, summation and enthalpy balance equations (MESH) model for distillation columns. The total CPU time for determining the optimal distillation sequence of separating benzene, toluene and o-xylene is only 11 min compared to the result 101 min in the literature. In Yeomans and Grossmann paper, only a four product SEN is presented without case study. Specifically to test our algorithm, the optimal distillation sequence for the separation of methanol, ethanol, 1-propanol and 1-butanol is generated within 23 min. Another case study is to optimize the dividing wall columns also using rigorous MESH models, the solution of which was got within 6 min. Compared to the optimised DWC configuration in literature (Gianluca et al., 2021), our results gain at least 6% TAC reduction.
References
Yeomans, Hector, and Ignacio E. Grossmann. “Disjunctive Programming Models for the Optimal Design of Distillation Columns and Separation Sequences.†Industrial & Engineering Chemistry Research, vol. 39, no. 6, American Chemical Society, 2000, pp. 1637–48, https://doi.org/10.1021/ie9906520.
Ma, Yingjie, et al. “Novel Feasible Path Optimisation Algorithms Using Steady-State And/or Pseudo-Transient Simulations.†Computers & Chemical Engineering, vol. 143, Elsevier Ltd, 2020, p. 107058–, https://doi.org/10.1016/j.compchemeng.2020.107058.
Montonati, Gianluca, et al. “Dividedâ€wall Distillation Column Design Using Molecular Tracking.†AIChE Journal, vol. 68, no. 2, John Wiley & Sons, Inc, 2022, https://doi.org/10.1002/aic.17504.
