Application Of New Homotopy Algorithm In The Field Of Distillation Simulation

On the base of analysis and research to different kinds of distillation simulation Methods, two new algorithms, homotopy-simultaneous-correction united (HSCU) algorithm and homotopy-simultaneous-correction mixed (HSCM) algorithm, are put forward and are successfully used to simulate non-ideal system, extractive distillation and heterogeneous distillation. HSCU adopts the homotopy parameter continuation method to supply excellent initial value for SC algorithm and develops a new universal algorithm which combinesthe advantages of global convergence and quick convergent rate. In HSCU, sparse matrix technology is made the best to solve nonlinear equations so that the calculative procedure is enormously simplified. In addition, the calculative efficiency of the homotopy parameter continuation method is promoted by only one correction iterate at correction step.In HSCM, the homotopy arclength continuation method is improved in three aspects. First, SC methods is used to the corrector of the homotopy arclength continuation method. Second, the direction consistent condition has been adopted to keep the path tracking direction consistent in the work. Finally, a simple practical variable step size control strategy is used in the article. After these improvement, the calculative efficiency and stability are greatly increased.A new algorithm using homotopy continuation method is put forward to solve the liquid-phase stability analysis on the base of Michlesen stability analysis, which overcomes the local convergence of Newton-type methods and increases stability of the simulation program. The article shows that the convergent region of the Newton homotopy method has very simple topological structures. Thus, the global convergence of the Newton homotopy method is theoretically demonstrated.Finally, EXCMAT data base is built to make convenience for the usage of the simulation program.