Rigorous Simulation And Optimization Of A Distillation Column Considering Stage Hydraulics

The economic performance of a distillation column is affected by its structure and operating variables,a rigorous and reliable method to find the optimal values of these parameters is needed.Although the rigorous equilibrium stage model has been widely used in distillation,it is still difficult to optimize the continuous operating variables and discrete structural variables of the column simultaneously based on the model due to the convergence problem and the integer optimization for stage number.To alleviate the problem,the hydraulic equations are usually ignored or simplified in the existing optimal design method,and the tray pressure drop is taken as a fixed value based on experience.Accurately describing the pressure profile,however,is crucial to the optimal design of the column.While considering the hydraulics in the column,the simultaneous optimization of all the decision variables remains an open question that needs an in-depth study.In present study,a rigorous distillation model considering stage hydraulics was established based on the rigorous MESH equations(material balance,equilibrium,summation,and heat balance).The mixed-integer nonlinear programming(MINLP)problem caused by the optimization of trays was converted into a traditional nonlinear programming(NLP)problem by the bypass efficiency method,which effectively solved the simultaneous optimization problem of continuous variables and integer variables;A pseudo-transient(PT)distillation model considering stage hydraulics was established based on pseudo-transient continue method,which effectively solved the convergence problem of the Newton-type algorithms for solving the nonlinear model equations in each optimization step of the NLP problem under equation-oriented environment.By applying the steady-state optimization algorithm assisted by the PT models,the simultaneous optimization of structural variables and operating variables was completed.Using the rigorous distillation model established in this study,for two cases of a traditional distillation column and a dividing wall column(DWC),optimal designs without considering stage hydraulics and considering stage hydraulics were carried out.Comparing the results of the two methods,it was proved that the pressure profiles in the column have the impact on the optimization results of the decision variables.The distillation column operated according to the design results without considering the hydraulics cannot meet the product requirements.This effect is more obvious on DWC.Finally,an optimization framework for DWC was proposed,which can consider stage hydraulics.And the operating flexibility of DWC was studied.It was found that the main factor limiting the operating flexibility was the column diameter,and thus the diameter requires a trade-off between operating flexibility and economy.