Recent progress on equation-oriented optimization of complex chemical processes

Process optimization in equation-oriented(EO)modeling environments favors the gradient-based optimization algorithms by their abilities to provide accurate Jacobian matrices via automatic or symbolic differentiation.However,computational inefficiencies including that in initial-point-finding for Newton type methods have significantly limited its application.Recently,progress has been made in using a pseudo-transient(PT)modeling method to address these difficulties,providing a fresh way forward in EO-based optimization.Nevertheless,research in this area remains open,and challenges need to be addressed.Therefore,understanding the state-of-the-art research on the PT method,its principle,and the strategies in composing effective methodologies using the PT modeling method is necessary for further developing EO-based methods for process optimization.For this purpose,the basic concepts for the PT modeling and the optimization framework based on the PT model are reviewed in this paper.Several typical applications,e.g.,complex distillation processes,cryogenic processes,and optimizations under uncertainty,are presented as well.Finally,we identify several main challenges and give prospects for the development of the PT based optimization methods.

Optimal design of extractive dividing-wall column using an efficient equation-oriented approach

The extractive dividing-wall column(EDWC)is one of the most efficient technologies for separation of azeotropic or close boiling-point mixtures,but its design is fairly challenging.In this paper we extend the hybrid feasible path optimisation algorithm(Ma Y,McLaughlan M,Zhang N,Li J.Computers&Chemical Engineering,2020,143:107058)for such optimal design.The tolerances-relaxation integration method is refined to allow for long enough integration time that can ensure the solution of the pseudo-transient continuation simulation close to the steady state before the required tolerance is used.To ensure the gradient and Jacobian information available for optimisation,we allow a relaxed tolerance for the simulation in the sensitivity analysis mode when the simulation diverges under small tolerance.In addition,valid lower bounds on purity of the recycled entrainer and the vapour flow rate in column sections are imposed to improve computational efficiency.The computational results demonstrate that the extended hybrid algorithm can achieve better design of the EDWC compared to those in literature.The energy consumption can be reduced by more than 20%compared with existing literature report.In addition,the optimal design of the heat pump assisted EDWC is achieved using the improved hybrid algorithm for the first time.