Reliable Computation of Equilibrium Cascades with Affine Arithmetic

Computing the steady state of multistage counter-current processes like distillation, extraction, or absorption is the equivalent to finding solutions for large scale non-linear equation systems. The conventional solution techniques are fast and efficient if a good estimation is available but are prone to fail, and do not provide information about the reason for the failure. This is the main motive to apply reliable methods in solving them. Reliable computations are usually realized with interval methods. This paper presents a reliable root finding method based on affine arithmetic (AA), a recently developed linearization technique and interval method. AA is compared here to another linearization technique, the widely known Interval Newton method. The studied examples seem to indicate superiority of the novel method over the traditional one. The comparison is made with a pruning technique not state-of-the-art but analogous in the two compared methods. AA can be combined with constraint propagation (CP) or linear programming (LP) aided CP, as pruning techniques. The combined techniques, AA/CP and AA/LP are studied and compared. AA/LP proves to be preferable because of its robustness. Short distillation columns are successfully computed with the proposed AA/LP method. Topical heading: Separations