Dynamic Optimization of Batch Reactors Using Adaptive Stochastic Algorithms

Abstract

The dynamic optimization (optimal control) of chemical batch reactors is considered. The solution of these types of problems is usually very difficult due to their highly nonlinear and multimodal nature. In fact, although several deterministic techniques have been proposed to solve these problems, convergence difficulties have been frequently found. Here, two algorithms based on stochastic optimization are proposed as reliable alternatives. These stochastic algorithms are used to succesfully solve four difficult case studies taken from the recent literature: the Denbigh's system of reactions, the oil shale pyrolysis problem, the optimal fed-batch control of induced foreign protein production by recombinant bacteria, and the optimal drug scheduling of cancer chemotherapy. The advantages of these alternative techniques, including ease of implementation, global convergence properties, and good computational efficiency, are discussed.

Dynamic Surrogate Modeling for Multistep-ahead Prediction of Multivariate Nonlinear Chemical Processes

“…66−69 The third case study involves the model for a shale-oil pyrolysis batch system that has been frequently addressed as an example of batch process dynamic optimization. 70,71 As previously mentioned, in all these case studies, two application scenarios will be considered: the first one would mimic a realistic situation where only input−output signals are available for training the models (see Section 3.4), and thus, the FPM is used as the process plant from which these signals are collected. The second scenario assumes that the FPM is available for the application of the proposed DOCE procedure in order to optimally select the training data (see Section 3.3).…”

“…71 The mathematical model in eq 11 describes the evolution of the concentrations, C Kr , C Pb , C Og , and C Cr , where k i is the specific reaction rate, k i0 is its initial value, E i is the activation energy, R is the gas constant, and T is the temperature that can be manipulated within the range of [698.15 ≤ T ≤ 748.15]. 70…”

“…The first case involves the model of a continuous bioreactor system that has been considered in different dynamic modeling and control studies, e.g., for data-driven univariate dynamic modeling, Quasi-sliding model control, and the design of nonlinear observers . The second application considers the model of a three-tank system that has been commonly used as a benchmark in different monitoring, control, and fault detection and diagnosis studies. − The third case study involves the model for a shale-oil pyrolysis batch system that has been frequently addressed as an example of batch process dynamic optimization. , …”

Design of dynamic trajectories for efficient and data-rich exploration of flow reaction design spaces

“…The concept of transient flow experiments is an extension of batch dynamic experiments, for which the aim is to obtain a trajectory of the optimization parameters in order to optimize some performance function. [16][17][18] While batch reactors optimized in such a way are then operated with dynamic variations even after obtaining the optimal conditions, continuous reactors optimized using dynamic experiments are run at constant conditions (those obtained dynamically at the optimal conditions).…”

An Adaptive Pseudospectral Method for Constrained Dynamic Optimization Problems in Chemical Engineering

“…The dynamic process in chemical engineering is often described by a set of differential equations and initial conditions. As physical bounds on the safety requirement and environmental regulations are necessary during the process, the dynamic optimization problems (DOPs) in chemical engineering are often associated with constraints on the variables 7–11.…”