Collocation methods for distillation design .1. Model description and testing

Fast and accurate distillation design requires a model that significantly reduces the problem size while accurately approximating a full-order distillation column model. 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 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. Furthermore, this model uses multiple collocation elements for a column section, which is more accurate than a single high-order collocation section.