Real‐time Dynamic Optimization of Non‐linear Batch Systems

In this paper, a methodology for designing and implementing a real time optimizing controller for non‐linear batch processes is discussed. The controller is used to optimize the system input and state trajectories according to a cost function. An interior point method with penalty function is used to incorporate constraints into a modified cost functional, and a Lyapunov‐based extremum seeking approach is used to compute the trajectory parameters. Smooth trajectories were generated with reduced computing time compared to many optimizations in literature. In this paper, the theory is applied to general non‐flat non‐linear systems in a true on‐line optimization.     

A comparative study on optimised and non‐optimised axial flow,spherical reactors in naphtha reforming process

In this study, the operating conditions of an axial flow spherical reactor have been optimised using a reliable optimisation technique and the results are compared with the results of non‐optimised conditions. The dynamic behaviour of the reactor has been considered in the optimisation process and orthogonal collocation method has been used in order to solve the obtained equations from mathematical modelling of the process. The goal of this study is to maximise the aromatics and hydrogen production rate. Therefore, the objective function is the combination of two terms which include the production rate of the mentioned components. The catalyst distribution for each reactor, the inlet pressure of the system, Length per radius for each reactor, the naphtha feed molar flow rate and the hydrogen mole fraction in the recycle stream as well as the inlet temperature of each reactor have been optimised in this study. © 2011 Canadian Society for Chemical Engineering     

Modelling and optimisation of a chemical industry wastewater treatment plant subjected to varying production schedules

Industrial wastewater treatment plants (WWTPs) have to provide 100% reliability and availability for the discharging facilities at an industrial site. Varying production schedules at these facilities and specific components occurring in the industrial wastewater considerably hinder the optimisation of industrial WWTPs. In this context it is shown in this paper that model‐based optimisation is an efficient and cost‐reducing way to ensure that an industrial WWTP functions well. The aim of the study presented was two‐fold. The first step was to show the usefulness of a proposed procedure to build and calibrate a model for the industrial WWTP. The second objective was to use the model for optimisation of the WWTP. As an example, a large set of possible production schedules in the different discharging facilities was simulated. Based on these simulations it could be predicted which schedules allow the effluent standards to be met and which do not. The calibrated and validated model was also used to investigate different operating strategies such as the in‐series operation of the two available aeration tanks. In fact, with the model it was shown that a 20% reduction of the degradable COD concentration in the effluent could be achieved by operating the tanks in series instead of in parallel. This case study shows how the approach presented can lead to fast and cost effective modelling and optimisation of an industrial WWTP. Copyright © 2004 Society of Chemical Industry     

A global optimization method based on multi-unit extremum-seeking for scalar nonlinear systems

Finding the global optimum of a nonlinear function is a challenging task that could involve a large number of functional evaluations. In this paper, an algorithm that uses tools from the domain of extremum-seeking is shown to provide an efficient deterministic method for global optimization. Extremum-seeking schemes typically find the local optimum by controlling the gradient to zero. In this paper, the multi-unit framework is used, where the gradient is estimated by finite difference for a given offset between the inputs. The gradient is pushed to zero by an integral controller. It is shown that if the offset is reduced to zero, the system can be made to converge to the global optimum of nonlinear continuous static, scalar maps. The result is extended to constrained problems where a switching control strategy is employed. Several illustrative examples are presented and the proposed method is compared with other methods of global optimization.     

Optimal control of batch processes using particle swam optimisation with stacked neural network models

An optimal control strategy for batch processes using particle swam optimisation (PSO) and stacked neural networks is presented in this paper. Stacked neural network models are developed form historical process operation data. Stacked neural networks are used to improve model generalisation capability, as well as provide model prediction confidence bounds. In order to improve the reliability of the calculated optimal control policy, an additional term is introduced in the optimisation objective function to penalize wide model prediction confidence bounds. The optimisation problem is solved using PSO, which can cope with multiple local minima and could generally find the global minimum. Application to a simulated fed-batch process demonstrates that the proposed technique is very effective.     

Extremum‐seeking control of retention for a microparticulate system

The operation of a paper machine relies on the close monitoring and control of several integrated units to ensure a high quality paper with the required specifications. In this paper, the retention control system in the wet‐end of a paper machine is considered. The control objective is to maximize the retention of fines and fibres in the paper sheet to prevent the accumulation of micro particles in the water system. We present an adaptive extremum‐seeking scheme for the optimization and control of retention in the wet‐end of a paper machine. An adaptive learning technique is introduced to construct an algorithm that drives the system to the optimal retention value. Lyapunov's stability theory is used in the design of the extremum‐seeking controller structure and the development of the parameter learning laws. The performance of the technique is illustrated via simulations based on a first‐principles dynamic model developed previously for a micro‐particulate system.     

Analytical optimisation of industrial systems and applications to refineries, petrochemicals

A new method for optimising process networks is presented in this paper. The method uses economic analysis of existing systems based on the new value analysis method (Ph.D. Dissertation, UMIST, Manchester, UK, 2002) as the basis to derive the optimum network design. The analytical optimisation method comprises of three steps. Market integration is the first step that fully exploits the available market opportunities for selling and purchasing streams based on individual marginal contributions from productions and processing of streams. Market integration is an easy and straightforward way of achieving quick benefits. The second step deals with optimisation of network flowsheet/connections. The economic margins of various paths of network are used to determine the weaker paths and the stronger paths where the loads of weaker paths can be shifted. This load shifting among paths leads up to the overall benefits of a system. Finally, the non-profitable or less profitable process units are optimised to improve their individual marginal contributions. Analytical optimisation turns the traditional back box approach into a clear and transparent procedure and is simple to understand and easy to use. The application of analytical optimisation is demonstrated with industrial cases from refining. In the end, a generalised methodology has been illustrated on how to design the optimum flowsheet of a petrochemical complex in a changing market price scenario.     

Dependence of the Error in the Optimal Solution of Perturbation‐Based Extremum Seeking Methods on the Excitation Frequency

In perturbation‐based extremum‐seeking methods, an excitation signal is added to the input, and the gradient, computed from the correlation between the input and output variations, is forced to zero. The main drawback of the method is that the speed of convergence, which is linked to the dither frequency, is slow due to the low value of dither frequency typically chosen. Increasing the excitation frequency may cause instability, but that could be corrected by phase compensation. In this paper, it is shown that an additional problem exists, i.e., the distance between the optimum and solution reached by the perturbation method is proportional to the square of the frequency of excitation and does not go to zero even when the amplitude of the excitation goes to zero. However, for Wiener/Hammerstein approximations, the error will indeed go to zero with the excitation amplitude. Simulation results on a distributed reaction system are used to illustrate the concepts presented in this work.     

Common vulnerabilities of RTO implementations in real chemical processes

Real‐time optimisation (RTO) systems face challenging scenarios in industrial practice, such as incomplete and corrupted process information, uncertain large‐scale mathematical models and numerical optimisation issues. Proper design of RTO structure and robust diagnosis tools are keys for good performance, although they are neglected in commercial RTO software and not fully solved in the technical literature. This article reviews the concepts behind the two‐step RTO approach and suggests performance metrics. It also points out the large list of structural decisions and the consequences of intuitive, experience‐based RTO design choices. The discussed vulnerabilities are illustrated with some simulations and real industrial implementations. © 2012 Canadian Society for Chemical Engineering     

Optimal Design and Economic Evaluation of Dividing‐Wall Columns

In an effort to reduce costs, a systematic optimization approach is proposed to address the energy consumption of dividing‐wall columns (DWCs). This iterative optimization procedure begins by minimizing the overall heat duty using an innovative objective function within a constrained design space. A sensitivity analysis is then carried out on the manipulated variables to obtain their optimal ranges. Optimal operating parameters are obtained through the evaluation of the total annualized cost (TAC). For the separation process of benzene/toluene/o‐xylene, the optimal DWC flow sheet exhibits a significant decrease in TAC when compared to conventional flow sheet optimum designs. The applied optimization method and sensitivity analysis have proven to produce results at the global optimum. This method is both practical and easily applied to other systems, even to systems with more than three components.     

Optimal energy consumption in refrigeration systems ‐ modelling and non‐convex optimisation

Supermarket refrigeration consumes substantial amounts of energy. However, due to the thermal capacity of the refrigerated goods, parts of the cooling capacity delivered can be shifted in time without deteriorating the food quality. In this study, we develop a realistic model for the energy consumption in super market refrigeration systems. This model is used in a Nonlinear Model Predictive Controller (NMPC) to minimise the energy used by operation of a supermarket refrigeration system. The model is non‐convex and we develop a computational efficient algorithm tailored to this problem that is somewhat more efficient than general purpose optimisation algorithms for NMPC and still near to optimal. Since the non‐convex cost function has multiple extrema, standard methods for optimisation cannot be directly applied. A qualitative analysis of the system's constraints is presented and a unique minimum within the feasible region is identified. Following that finding we propose a tailored minimisation procedure that utilises the nature of the feasible region such that the minimisation can be separated into two linear programs; one for each of the control variables. These subproblems are simple to solve but some iterations might have to be performed in order to comply with the maximum capacity constraint. Finally, a nonlinear solver is used for a small example without separating the optimisation problem, and the results are compared to the outcome of our proposed minimisation procedure for the same conceptual example. The tailored approach is somewhat faster than the general optimisation method and the solutions obtained are almost identical. © 2012 Canadian Society for Chemical Engineering     

Temporal clustering for order reduction of nonlinear parabolic PDE systems with time‐dependent spatial domains: Application to a hydraulic fracturing process

A temporally‐local model order‐reduction technique for nonlinear parabolic partial differential equation (PDE) systems with time‐dependent spatial domains is presented. In lieu of approximating the solution of interest using global (with respect to the time domain) empirical eigenfunctions, low‐dimensional models are derived by constructing appropriate temporally‐local eigenfunctions. Within this context, first of all, the time domain is partitioned into multiple clusters (i.e., subdomains) by using the framework known as global optimum search. This approach, a variant of Generalized Benders Decomposition, formulates clustering as a Mixed‐Integer Nonlinear Programming problem and involves the iterative solution of a Linear Programming problem (primal problem) and a Mixed‐Integer Linear Programming problem (master problem). Following the cluster generation, local (with respect to time) eigenfunctions are constructed by applying the proper orthogonal decomposition method to the snapshots contained within each cluster. Then, the Galerkin's projection method is employed to derive low‐dimensional ordinary differential equation (ODE) systems for each cluster. The local ODE systems are subsequently used to compute approximate solutions to the original PDE system. The proposed local model order‐reduction technique is applied to a hydraulic fracturing process described by a nonlinear parabolic PDE system with the time‐dependent spatial domain. It is shown to be more accurate and computationally efficient in approximating the original nonlinear system with fewer eigenfunctions, compared to the model order‐reduction technique with temporally‐global eigenfunctions. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3818–3831, 2017     

Simultaneous synthesis of structural‐constrained heat exchanger networks with and without stream splits

This paper presents a comprehensive simultaneous synthesis approach based on stage‐wise superstructure to design cost‐optimal heat exchanger network (HEN). It is well known that the simultaneous synthesis model has very complicated mixed integer nonlinear programming formulations, which are non‐convex, non‐continuous and have many local optima. Up till now, it cannot be expected that an algorithm can find, in polynomial time, the global solution to the simultaneous synthesis problem of HEN. In order to reduce computational complexity, some simplified assumptions for structures, such as no stream splits, stream splits with isothermal mixing, no stream split flowing through more than one exchanger, etc, are adopted to prune the search space at the expense of neglecting certain important alternatives in the network configuration. In this work, a flexible stage‐wise superstructure is proposed to control the solution performance and search space efficiently. At each stage of the superstructure, with or without stream splits is determined at random or by the experience of designers. In this way, various candidate series and split network designs featuring the lowest annual cost can be found. Moreover, an efficient two‐level optimisation algorithm is employed for solving the presented model utilising genetic algorithm and particle swarm optimisation algorithm. Three case studies are presented to show the applicability of the proposed methodology. In addition, the results show that the new approach is able to find more economical networks than those generated by other methods. © 2012 Canadian Society for Chemical Engineering     

Modelling and optimisation of continuous catalytic regeneration process using bee colony algorithm

The continuous catalytic regeneration (CCR) reforming process optimisation leads to nonlinear programming with nonlinear quality constraints such as octane number and coke concentration on the catalytic particles. A typical CCR reforming process consists of four reactors with recycle. The reaction patterns and reactors have been mathematically modelled on a base of 12‐lumped kinetics reaction network derived from literature. The bee colony optimisation (BCO) algorithm is one of the most recent and efficient swarm intelligence‐based algorithms which simulates the foraging behaviour of honey bee colonies. The performance of the BCO algorithm in the process optimisation was compared with the genetic algorithm (GA). In the present work, BCO algorithm was used for optimising the CCR reforming process. The results show that the BCO algorithm reaches a better optimum point in a lower evaluation time and higher convergence rate with respect to the GA. © 2012 Canadian Society for Chemical Engineering     

Evolutionary design of optimum distillation column sequence

Synthesis of the optimum distillation column sequence (DCS), which incorporates a huge search space composed of both conventional and complex arrangements, is a highly complicated combinatorial problem in the field of chemical process design and optimisation. In this study, a novel procedure for the synthesis of optimum DCS proposed by Boozarjomehry et al. [Boozarjomehry et al., Can. J. Chem. Eng. 87, 477–492 (2009)] is expanded to include the complex distillation arrangements. The method is based on evolutionary algorithms, and the total annual cost (TAC) is the main criterion used to screen alternatives. Efficient procedure has been proposed for encoding mechanism to include and classify various complex arrangements together with conventional distillation columns. All columns existing in each DCS alternative are designed using the most recommended short‐cut methods to estimate the TAC of the DCS. Four standard benchmark case studies are carried out to clearly demonstrate the excellent performance of the proposed method. The produced results for these problems indicate that the proposed method outperforms the other existing approaches in terms of flexibility, accuracy and comprehensiveness. © 2011 Canadian Society for Chemical Engineering     

On the accuracy of Landweber and Tikhonov reconstruction techniques in gas‐solid fluidized bed applications

As electrical capacitance tomography technique needs a sophisticated reconstruction, the accuracy of two of the most widely used reconstruction techniques (Landweber and Tikhonov) for gas‐fluidized bed applications were assessed. For this purpose, the results of two‐fluid model simulations were used as an input of reconstruction. After finding the optimum reconstruction parameters for the studied system, it is found that both techniques were able to obtain the radial profile and overall value of average volume fraction very well. Conversely, both methods were incapable to determine bubble sizes accurately especially small bubble sizes, unless the Landweber technique with inverted Maxwell concentration model is applied. The probability distribution of the reconstructed results was also smoother in transition between the emulsion and bubble phases compared to the reality. Finally, no significant differences in noise immunity of these two techniques were observed. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4102–4113, 2015     

Automated targeting for inter-plant water integration

Apart from in-plant water recovery, inter-plant water integration (IPWI) offers another promising mean for the reduction of fresh water and wastewater flowrates for process plants. This paper extends the automated targeting technique that was developed for single water network into IPWI. This optimisation-based technique is based on the concept of pinch analysis, which enables the setting of various network targets prior to detailed design. The automated targeting technique is formulated as a linear programming model for which global optimum is guaranteed. The proposed technique is demonstrated using several industrial and literature examples.     

Design and optimisation of batch and semi-batch reactors

This paper addresses a systematic methodology for batch and semi-batch reactor design and optimisation for both ideal and non-ideal mixing. It can be applied to non-isothermal and multiphase systems. The method starts from a general representation in the form of a temporal superstructure based on the similarity of between plug flow reactors and ideal batch reactors. The temporal superstructure of a batch reactor exists in both the space and time dimensions. For non-ideal mixing, this paper addresses a mixing compartment network model to represent mixing inside reactors. The mixing compartment network is then included into the temporal superstructure to model non-ideally mixed batch reactors and the mixing pattern optimised with the other variables. Besides the operation variables for batch reactors, this method can also suggest the optimum mixing pattern and promising reactor configurations for mechanical design. A profile-based approach is proposed to make a search of the profiles for temperature, pressure and feed addition. This approach starts from a set of initial profiles of temperature, pressure and feed addition. Then the performance of the batch reactor is evaluated against the objective function under different profiles. An optimal set of profiles is then found by this profile searching process. A stochastic optimisation technique based on simulated annealing is employed to obtain optimal solutions. This method is also extended to multiphase reaction systems based on the concept of shadow reactor compartments. A number of case studies are presented to illustrate the use of the proposed methodology.     

Extremum seeking control using a partial sum of input-output product

Recent extremum seeking control that uses a continuous perturbation and the integral feedback of perturbation- output product is based on a static nonlinear process. The method can be applied to dynamic nonlinear processes for tracking and maintaining the optimal operating points. It has several tuning parameters, such as the integral controller gain and the magnitude and frequency of the continuous perturbation signal. The frequency of the continuous perturbation signal should be low enough to ensure the time-scale separation between the real-time optimization and the process dynamics for the closed-loop stability. However, for some processes, fast perturbations are preferred because they can be attenuated easily in subsequent processes such as buffers and storages. For this, we propose an extremum seeking control method where the partial sum of perturbation-output product is used for a faster squarewave perturbation. Simulations for two processes of parallel competing reactions have been given, and a simple liquid level system to test extremum seeking control methods is suggested.