Simultaneous solution and MINLP synthesis of DAE process problems: PFR networks in overall processes.

Abstract

The main aim of this contribution is to describe a more general procedure for simultaneous solution and MINLP synthesis of process problems that are represented in an equation oriented modelling environment, by differential-algebraic systems of equations (DAE). An Orthogonal Collocation on Finite Elements (OCFE) has been used to discretize differential equations by some reasonable polynomial approximation and embedded into an MINLP problem formulation. In the context of the problems, three modifications are proposed. The first one concerns the problem of discontinuities caused by inequality constraints or bounds on profiles. Based on recent investigations, a more general smoothing procedure has been proposed by which it is possible to efficiently solve problems with discontinuities. Since the optimal solution is bracketed in one of the FEs, with the second modification we overcome the problem of the optimal finite element location by an appropriate MINLP formulation. Finally, the third modification concerns a reasonable simplification of the OCFE model for the production rate in PFR chemical reactor, which in this way becomes suitable for simultaneous solution and MINLP synthesis. The proposed simultaneous solution of DAE and MINLP synthesis has been tested and applied to the synthesis of the PFR reactor network in the overall HDA process scheme. It has been shown that incorrect topology can be predicted in the reactor network as well as in the whole HDA process when the modelling approximation of DAEs is too weak.