Equation-Oriented Optimization Of Complex Distillation Systems

In the field of process industries,distillation is the most widely used separation unit operation.For the sake of saving energy and separating azeotropes,complex distillation systems are needed.In complex distillation systems,there often exists mass and energy cycles between units,which result in complex interaction between variables.Hence,to get more accurate results,a more rigorous optimization framework should be taken.In the field of process optimization,the rigorous optimization based on equilibrium stage can be roughly divided into two categories: sequential module method and equation-oriented method.The automatic or symbolic differentiation of variables can be obtained through the calculation of Jacobian matrixes in the environment of equation-oriented framework.Hence,from the perspective mentioned above,the equation-oriented method has a distinct advantage in the field of optimization.However,in the equation-oriented method,the difficulty in flow convergence and the immaturity of the mixed integer solving algorithm hinder the application of equation-oriented method.Recently,the raise of the pseudo-transient continuation(PTC)model has greatly overcome the above two shortcomings,providing a powerful tool for the equation-oriented optimization of complex distillation systems.In PTC model,the addition of dynamic process broadens the convergence basin greatly,and the use of bypass efficiency method overcomes the integer optimization problem.However,there is still room for improvement of this model,such as unintuitive expression of model equations and low calculation efficiency.In view of the above problems,this paper proposes an improved PTC model.In the aspect of model equation,this paper proposes a new PTC column tray model based on the concept of equivalent stream,which avoids the tedious trial and error process of hydraulic correlation parameters in the past research.In the aspect of optimization algorithm,this paper proposes a new mixed-steady state-time relaxation optimization algorithm,which combines the steady state simulation and time relaxation algorithm.Compared with the bulit in dynamic optimization algorithm,the new algorithm greatly reduces calculation time with the same accuracy.The improved model and algorithm mentioned above are then applied to the analysis and optimization of common complex flowsheets.A heat-integrated extractive distillation with a recycle feed and the pressure-swing distillation are optimized.In the optimization of pressure-swing distillation with equilibrium stage model,the air leakage is expressed as the function of pressure under the condition of equation-oriented,and then,the above function is taken as the constraint in the optimization solver.This method changes the convention of fixing the operating pressure of the distillation column at atmospheric pressure,which is of great significance to both theoretical research and engineering design of the distillation system.In addition,the model proposed in this paper is universal and can be extended to the optimization of other commonly used complex distillation systems.