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

Abstract

This 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). Different polymer grades are defined in terms of their molecular weight distributions, so that state variables values during steady states are kept as degrees of freedom. The corresponding mathematical formulation includes the differential equations that describe the dynamic behavior of the system, resulting in a MIDO problem. The differential equations are discretized using the simultaneous approach based on orthogonal 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 programming problem with hourly product demands as uncertain parameter described by discrete distributions.2

Integration of process design and control: A review

“…They considered a superstructure of feedback and forward controllers, and the optimization included the determination of optimal initial and final steady states and the time trajectories between them. Recently, Terrazas-Moreno, et al (2008) studied a methyl-methacrylate continuous polymerization reactor. In this research, the design decisions (equipment size and steady-state operating conditions), the scheduling decisions (grade productions sequence, cycle duration, production quantities, inventory levels) and the optimal control decisions (grade transition time and profile) were made simultaneously.…”

Economic Benefit from Progressive Integration of Scheduling and Control for Continuous Chemical Processes

“…Economic benefit from integrating process dynamics into batch and semi-batch scheduling has also been demonstrated via mixed-logic dynamic optimization in state equipment networks and solution with Benders decomposition in resource task networks [7,39]. Potential for economic benefit from integrating process dynamics into design, scheduling, and control problems has also been demonstrated [41,44,52]. Computational reduction of incorporating process dynamics into scheduling has been investigated successfully, maintaining benefit from the incorporation of process dynamics into scheduling while reducing dynamic model order [10,15,16,33,42].…”

Combined Noncyclic Scheduling and Advanced Control for Continuous Chemical Processes

“…Terrazas-Moreno and Flores-Tlacuahuac examine combined design, scheduling, and control with dynamic process models nearly a decade ago [51]. Koller et al present an optimization framework for integrated scheduling, control, and design of multi-product processes with uncertainty.…”