Simultaneous design, scheduling, and optimal control of a methyl‐methacrylate continuous polymerization reactor

Abstract

AbstractThis work presents a mixed‐integer dynamic optimization (MIDO) formulation for the simultaneous process design, cyclic scheduling, and optimal control of a methyl methacrylate (MMA) continuous stirred‐tank reactor (CSTR). This article makes two specific contributions. The first consists of incorporating process dynamics into grade transitions to determine changeover times and profiles, as opposed to using fixed changeover times as in previous works dealing with design, scheduling, and dynamic optimization. A second contribution is that the steady states that describe each polymer grade are left as functions of decision variables, which has not been done in the integration of design, scheduling, and dynamic optimization. Also, this work incorporates uncertainty in product demands. The corresponding mathematical formulation includes the differential equations that describe the dynamic behavior of the system, resulting in a MIDO problem. The differential equations were discretized using the simultaneous approach, based on ortogonal collocation on finite elements, rendering a mixed integer non‐linear programming (MINLP) problem, where a profit function is to be maximized. The objective function includes product sales, some capital and operational costs, inventory costs, and transition costs. The optimal solution to this problem involves design decisions: flow rates, feeding temperatures and concentrations, equipment sizing, variables values at steady state; scheduling decisions: grade productions sequence, cycle duration, production quantities, inventory levels; and optimal control results: transition profiles, durations, and transition costs. The problem was formulated and solved in two ways: as a deterministic model and as a two‐stage stochastic programming problem with hourly product demands as uncertain parameters described by discrete distributions. © 2008 American Institute of Chemical Engineers AIChE J, 2008