Premium
Distributed stream method for tray optimization
Author(s) -
Lang YD,
Biegler L. T.
Publication year - 2002
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690480315
Subject(s) - tray , reboiler , condenser (optics) , mathematical optimization , distillation , smoothing , column (typography) , computer science , fractionating column , pressure drop , process (computing) , mathematics , engineering , mechanical engineering , chemistry , mechanics , chromatography , geometry , light source , physics , optics , connection (principal bundle) , computer vision , operating system
Determining the optimum number of trays in a distillation column has been an important process optimization problem for over 50 years, which over the past decade has been addressed successfully as a mixed‐integer nonlinear‐programming (MINLP) problem. But tools for solving MINLPs are not widespread, especially in connection with detailed simulation models. In a differentiable distribution function (DDF), all streams around a column, except top and bottom products, are directed to all of the column trays and the distributed flow rate of entry or exit streams is directed to a specific tray based on the value of its DDF at that tray. It allows the placement of feeds, sidestreams, and number of trays in the column to be continuous variables in the DDF, and in the optimization problem it eliminates the need for integer variables. Instead, the tray optimization problem is formulated as an NLP using the original MESH model. It is critical to deal with trays that have no liquid or vapor flows. To describe this phenomenon properly in the optimization, complementary constraints are formulated and added to the NLP, by taking advantage of a smoothing algorithm developed by Gopal and Biegler for phase equilibrium. Also, since pressure in each tray affects distillation calculations substantially, the pressure drops across each tray depend on the optimal number of trays and a related smoothing function formulation removes the pressure drop on dry trays. Pressure in the condenser or reboiler is then adjusted accordingly. The results of the methods applied to three distillation problems show significant cost reductions in distillation design.