Simultaneous Cyclic Scheduling and Control of Tubular Reactors: Parallel Production Lines

Abstract

In this work we propose a simultaneous scheduling and control optimization formulation to address both optimal steady-state production and dynamic product transitions in multiproduct tubular reactors working in several parallel production lines. Because the problem involves integer and continuous variables and the dynamic behavior of the underlying system the resulting optimization problem is cast as a Mixed-Integer Dynamic Optimization (MIDO) problem. Moreover, because spatial and temporal variations are considered when modeling the addressed systems, the dynamic systems give rise to a system of one-dimensional partial differential equations. For solving the MIDO problems we transform them into a mixed-integer nonlinear programs (MINLP). We use the method of lines for spatial discretization, whereas orthogonal collocation on finite elements was used for temporal discretization. The proposed simultaneous scheduling and control formulation is tested using three multiproduct continuous tubular reactors featuring complex nonlinear behavior.2

Towards the Grand Unification of Process Design, Scheduling, and Control—Utopia or Reality?

“…The presented approach has been extensively studied in the following years to broaden its scope and effectiveness. Terrazas [96] and multiple production lines [97].…”

Stochastic back‐off algorithm for simultaneous design, control, and scheduling of multiproduct systems under uncertainty

“…Thus, back-off terms b are introduced to each inequality constraint g to approximate the effect of uncertainty, and force the solution to back off from the optimal nominal solution. Provided that firstorder KKT optimality conditions for the multiscenario optimization hold and critical realizations in the uncertain parameter set are active at the solution, the present back-off calculation is equivalent to the multiscenario problem, as long as assumptions (2) and (3) are satisfied. In the present analysis, the back-off terms b t ð Þ will be dependent on time, to allow for less conservatism in the solution.…”

“…All these aspects can impact each other, resulting in complex interactions. 2 The simple approach of optimizing each aspect individually is often found to be insufficient, as it can result in suboptimal or infeasible solutions. Integrated optimization of design, control, and/or scheduling frameworks are therefore sought, and deemed necessary to achieve optimal process integration.…”

A dynamic optimization framework for integration of design, control and scheduling of multi-product chemical processes under disturbance and uncertainty

“…Although the sequential method is fast, there are many limitations. Since each subproblem is solved independently, the interactions between design, control, and scheduling are typically neglected, even though it has been recognized that these interactions can be significant (Flores-Tlacuahuac and Grossmann, 2011;Zhuge and Ierapetritou, 2012). Furthermore, assumptions need to be made in each sub-problem, e.g.…”