New approach to approximation of quantities involving physical properties derivatives in equation‐oriented process design

A new method for approximating quantities that involve physical properties derivatives in equation‐oriented process design is presented. It is a hybrid algorithm that makes combined use of Newton's method and the Schubert update. In doing so, available analytical derivative information is used in an optimal way. This hybrid algorithm is surprisingly close, in terms of the number of iterations required for solution, to an implementation of Newton's method that uses finite difference approximations of any unavailable physical properties derivatives. However, the number of rigorous thermodynamics calculations is usually about 50% fewer for the hybrid method. This can result in a substantial savings for problems in which the physical properties calculations dominate the simulation time. Two examples are presented to support these claims.