Optimal design of dispersive tubular reactors at steady-state using optimal control theory

Abstract

This paper studies the design of optimal temperature profiles for a class of exothermic, jacketed dispersive tubular reactors under steady-state conditions and subject to maximum temperature constraints. The studied class ranges from perfectly mixed continuous stirred tank reactors to plug flow reactors. The aim is to derive the Pareto optimal set of temperature profiles for conflicting conversion and energy costs, while extracting generic features from the obtained solutions. Hereto, a four step procedure which is based on a weighted sum of both costs and which combines indirect, analytical and direct, numerical optimal control techniques, is employed. The generic features are studied (i ) along the Pareto set by varying the weights and (ii ) along the reactor class by adapting the dispersion level.

Efficient deterministic multiple objective optimal control of (bio)chemical processes

“…This class includes the classic convex Weighted Sum (WS) of the different objectives, but also encompasses novel methods as Normal Boundary Intersection (NBI) (Das and Dennis, 1998), or Normalised Normal Constraint (NNC) (Messac and Mattson, 2004). The second class involves population based stochastic methods, e.g., genetic algorithms (Srinivas and Deb, 1995;Deb et al, 2002;Konak et al, 2006) and particle swarm optimisation (Coello et al, 2004), which have been found to be able to generate the Pareto set directly from the multiple objective formulation.…”

Optimal heating profiles in tubular reactors with solid‐phase axial wall conduction for isothermal operation

“…The use of optimal control to maximize conversion and/or minimize thermal excursions in tubular reactors neglecting solid-phase axial conduction have been studied previously. [19][20][21][22][23] Ko et al 19 used optimal control to identify optimal heat transfer coefficient profiles which maximize yield for an elementary reversible exothermic reaction. Since the heat transfer coefficient appeared linearly in the model equations, the problem was singular, and the input profile consisted of regions where the input was maximum/minimum (bang-bang control) and regions where the input lied inside the feasible region (singular control).…”

“…They showed that for plug flow reactors, with objective functions including running costs, the optimal input is bang-singular-bang and for objective functions with only terminal costs the optimal input is bangbang. More recently, Logist et al 22 conducted a similar analysis, extending to tubular reactors including axial dispersion and state variable constraints and observed that axial dispersion led to an increase in optimal objective function values. However, to-date, no rigorous analysis via optimal control theory has been applied to the case of finite and significant solid-phase axial heat conduction, commonly encountered in microreactors, and it is this gap the paper aims to fill.…”

Interactive NBI and (E)NNC methods for the progressive exploration of the criteria space in multi-objective optimization and optimal control

“…The$content$is$identical$to$the$published$paper,$but$without$the$final$typesetting$by$the$publisher.) Journal)homepage:)http://www.journals.elsevier.com/computers@and@chemical@engineering/))) Original)file)available)at:)http://www.sciencedirect.com/science/article/pii/S0098135415002355) ) ) ) conflicting ones treated in Logist et al (2009): (i) maximizing the conversion, which is related to minimizing the reactant concentration at the outlet:…”