Distillation Process Simulation By Homotopy Algorithm

Distillation is a very important and efficient method of separating liquidmixture . Currently, the continuous, steady-state distillation problema is solved bysome form of Newton's method, which requires a good starting guess.however, theonly class of methods whose success is independent of a starting guess is thehomotopy-continuation methods described in this paper.This paper describes two homotopies and their use in the solution of difficultdistillation prosess simulation problems on the basis of analysis and research topresent different kinds of distillation simulation methods. The first, the Newtonhomotopy, is able to solve problems successfully in the equilibrium stage separationprocess, such as ideal system, non-ideal system, azeotropic distillation, extractivedistillation. Because of the global convergence of homotopy and the quick rate of SCalgorithm (simultaneous correction algorithm), these two methods are combined.Excellent initial values for SC algorithm are provided by the homotopy, that isNewton homotopy. A general algorithm is put forward and spares matrix techniquesallow the use of these methods.The non-equilibrium stage model equations are also developed in a creativeway by the author and his advisor. Its form is convenient and easy to be solved. It isnot found in the documents at present.Since the equations being solved do not always model a separation process unitin the equilibrium stage equations,the Newton homotopy sometimes suffers fromintermediate solutions that are physically meaningless, simultaneously,to test thereliability of the non-equilibrium stage model equations in this paper, the second,physical homotopy algorithm (who takes the plate efficiency as the homotopyparameter) is adopted .The calculation results is satisfactory .