COLLOCATION METHODS FOR DISTILLATION DESIGN .1. MODEL DESCRIPTION ANDTESTING

Fast and accurate distillation design requires a model that significan tly reduces the problem size while accurately approximating a full-ord er distillation column model. This collocation model builds on the con cepts of past collocation models for design of complex real-world sepa ration systems. Two variable transformations make this method unique. Polynomials cannot accurately fit trajectories which flatten out. In c olumns, flat sections occur in the middle of large column sections or where concentrations go to 0 or 1. With an exponential transformation of the tray number which maps zero to an infinite number of trays onto the range 0-1, four collocation trays can accurately simulate a large column section. With a hyperbolic tangent transformation of the mole fractions, the model can simulate columns which reach high purities. F urthermore, this model uses multiple collocation elements for a column section, which is more accurate than a single high-order collocation section.