Flash and distillation calculations by a Newton-Like method

Abstract

A hybrid approach, one based on the combined use of Newton's method and the Schubert update, is applied to flash and distillation problems. the main advantages of this approach are two-fold. First, it makes maximum use of readily available analytical first partial derivative information. Second, it approximates those derivatives which are both difficult and expensive to obtain, primarily K value and excess enthalpy-composition derivatives, cheaply yet accurately by using a quasi-Newton formula.This hybrid (or Newton-like) approach is compared to a partial Newton method (i.e. one that neglects those difficult and/or expensive derivatives), Schubert's method and a finite difference implementation of Newton's method.In short, our hybrid approach compares favorably with a finite difference Newton method and is usually both more efficient and more robust than either the partial Newton or Schubert method on these problems. In fact, it generally requires only a few more iterations than Newton's method to reach the desired accuracy. However, it usually uses between 60 and 70% fewer rigorous physical properties calculations than Newton's method. This, in our opinion, is important because rigorous physical properties calculations usuallly constitute the largest portion of the calculations (and therefore cost) associated with separation problems. Several examples are presented to support these claims.