Collocation methods for distillation design.

Abstract: "Fast and accurate distillation design requires a model that significantly reduces the problem size while accurately approximating a full order distillation column model. Variable number of trays and variable feed tray location make optimization possible. This collocation model builds on the concepts of past collocation models for design of complex real-world separation systems. Two variable transformations make this method unique. Polynomials cannot accurately fit trajectories which flatten out. In columns, flat sections occur in the middle of large column sections, or where concentrations go to zero or one. With an exponential transformation of the tray number which maps zero to an infinite number of trays onto the range zero to one, two 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. Furthermore, this model uses multiple collocation elements for a column section, which is more accurate than a single high order collocation section."