Separation process optimization calculations

A modified Newton-like method for nonlinearly constrained optimization calculations is presented and applied to a variety of separation process optimization problems. The nonlinear programming algorithm in this paper is similar to those of Wilson, Han and Powell. It differs only in the way in which approximations to the Hessian matrix of the Lagrangian function are built. For separation process applications, a large amount of reliable second-derivative information is available in analytical form. Much of the remaining second-derivative information is subject to certain thermodynamic constraints. Our algorithm exploits these two facts by building Hessian matrix approximations in two parts, a computed part which is built analytically, and an approximated part which is built by iterated projections and the Powell-symmetric-Broyden formula. Iterated projections are required so that the quasi-Newton matrix approximations satisfy the thermodynamic constraints at each iteration and a limiting secant condition. Further advantage is taken of the complete separability of the thermodynamic functions. This modified successive quadratic programming algorithm has been compared to various Newton-like methods on a number of separation process optimization problems. These include cost minimization calculations for one- and two-stage flash units and the optimization of the operating conditions of a distillation column. The numerical results show that our modified algorithm can compete favorably with existing methods, in terms of reliability and efficiency, on these applications.