A perspective on the impact of process systems engineering on

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Process Systems Engineering

A perspective on the impact of process systems engineering on reaction engineering Kaushik Sivaramakrishnan, Anjana Puliyanda, Dereje Tamiru Tefera, Ajay Ganesh, Sushmitha Thirumalaivasan, and Vinay Prasad Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.9b00280 • Publication Date (Web): 04 Apr 2019 Downloaded from http://pubs.acs.org on April 5, 2019

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Industrial & Engineering Chemistry Research

A perspective on the impact of process systems engineering on reaction engineering Kaushik Sivaramakrishnan, Anjana Puliyanda, Dereje Tamiru Tefera, Ajay Ganesh, Sushmitha Thirumalaivasan, and Vinay Prasad∗ Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada E-mail: [email protected] Phone: 1 780 2481595 Abstract Process systems engineering (PSE), as the name suggests, emphasizes an approach to understanding the behaviour of systems as a whole with a view to improving decision making for optimization and control of process systems. The discipline emphasizes the application of mathematical techniques in this effort, and a plausible claim has been made that is at the very core of the discipline of chemical engineering. Being a generalized approach to process systems in general, it finds wide application to many areas in chemical engineering. This work reviews the application of PSE to the area of reaction engineering, which is also at the core of chemical engineering. We highlight the impactful applications of PSE in reaction engineering, and discuss applications related to model building and analysis, reactor control, optimization, chemometrics and chemoinformatics.

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Introduction Sargent, in his perspective on the future directions of process systems engineering (PSE) in 1988, 1 argued that process systems engineering is not just a specialized area for mathematically minded chemical engineers, but is the very core of the discipline of chemical engineering itself. That assertion was based primarily on the modeling-related aspects of process systems engineering, including model development, identification, estimation and adaptation. Klatt and Marquardt, 2 citing Takamatsu, 3 define PSE as being concerned with methodologies for chemical engineering decisions including how to plan, how to design, how to operate and how to control any kind of unit operation, chemical or other production process or the chemical industry itself. Grossman and Westerberg, 4 in their perspective on research challenges in PSE, assert that PSE is concerned with the improvement of decision-making processes for the creation and operation of the chemical supply chain, and that it deals with the discovery, design, manufacture and distribution of chemical products in the context of many conflicting goals. Stephanopoulos and Reklaitis 5 reviewed the history and future prospects for PSE and highlighted its emphasis on studying how the components of the system and their interactions contributed to the behaviour of the system as a whole. They also pointed to the focus of PSE on mathematical models, numerical methods for their solution, optimization theory, and dynamic systems and control theories. These perspectives have established the relatively recent pedigree of PSE as a separate research discipline and highlighted its broad range of application to all aspects of chemical engineering. In addition, they have highlighted recent successes and future prospects in broad classes of problems such as process and product synthesis and design, process operations and process control, while advocating the expansion of the scope and boundaries of the systems that are considered, such as for the enterprise-wide management of products and manufacturing systems. It is the purpose of the current work to provide a perspective on the impact of PSE on problems in reaction engineering and chemistry, and on its future prospects in this important 2


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application area that is at the heart of chemical engineering. At this point, it would be prudent to set the stage by providing our definition of PSE and the types of research problems it tackles. We define PSE to include any research tackling one of the three major types of research problems: prediction, identification/estimation and control/optimization. Prediction, broadly speaking, deals with the problems where the behaviour of the outputs of the system is predicted with knowledge of inputs and a model of the system. We include systems analysis based on the properties of the models in this class of problems (e.g., dynamic analysis, parametric sensitivity, uncertainty analysis). The next class of problems, identification or estimation, is an inverse problem related to identifying the model of the system (or its parameters/characteristics) based on input-output data. The development of surrogate or proxy models can also be considered in this category. The third class of problems is also an inverse problem of specifying the optimal inputs given a model and desired characteristics for the outputs; in addition to control and optimization, model-based experimental design can also be considered to fall into this category. In this work, we consider reaction engineering to include investigations of reactions and reactors and their interactions and behaviour. The complex nature of systems of reactions and their interplay with transport in reactors and the difficulty in comprehensive analytical characterization of the entire set of species in the complex product mixtures produced make this an important area of application for PSE, and to review this is the motivation behind the current work. We would like to highlight the fact that this review focuses on the impactful use of PSE techniques in reaction engineering without stipulating that the researchers conducting the research are within what might traditionally be considered as the PSE community, i.e. all PSE-oriented work related to this application area is considered. Also, this is a perspective rather than an exhaustive review, and we highlight what we feel are the most impactful areas of contribution of PSE to reaction engineering. Finally, the organization of the rest of the sections of this document is based both on the application area and the type of PSE problem being solved. We highlight the impact of PSE on dynamic and uncertainty analysis

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of reacting systems, advanced reactor control, global optimization, and in chemometrics and chemoinformatics. It is our contention that the major impact of process systems engineering on reaction engineering has been related to tackling the challenges in analysis and optimization posed by high dimensionality and the coupled nature of the systems and their variables, nonlinearity and uncertainty in the models. In this context, chemometrics and chemoinformatics address the issues of model building, analysis and updating (soft sensing). Global optimization is particularly important given the nonlinear nature of reacting systems. Reactor control addresses control of yield and selectivity, which are of paramount importance in chemical processes. Given the large scale nature of many reaction mechanisms (e.g. related to combustion), dynamic and sensitivity analysis provide a way to identify important species and reactions at the time scale of importance. Given the lack of identifiability of kinetic parameters in many reaction networks based on the measurements available, uncertainty analysis gains importance in the context of using kinetic models in process design and optimization.

Model development and analysis The most obvious examples of model development in reaction engineering are related to the development of kinetic models and coupling them with reactor and process-scale models. Without being exhaustive, we highlight the development of multiscale microkinetic models as a framework for understanding and simulating heterogenous metal-catalyzed systems in particular. 6–13 Another important set of contributions relates to automated reaction mechanism generation, 14–17 which also enables model development. The analysis of models for reacting systems takes many forms: here, we highlight the analysis of the steady-state and dynamic properties of the models, model reduction approaches, sensitivity analysis and uncertainty quantification. The most prominent application of steady-state analysis relates to the multiplicity of steady states, 18–23 which has

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significant implications for reactor design and process operation. The most common approach for determining multiplicity and identifying all the steady states is to use bifurcation analysis, which monitors changes in the qualitative structure of solutions to the governing equations for the system, to characterize the global multiplicity behaviour in terms of important dimensionless parameters such as the Damkohler number and the dimensionless heat of reaction. In dynamic analysis, the most important development has probably been computational singular perturbation (CSP), which separates the system model into dynamic modes and contributing reactions in a rigorous automated manner, which can then be used to build a reduced-order model at every instant. 24–28 This reduced model is obtained by performing modal decomposition and separating the dynamic modes into active, exhausted and dormant modes. The exhausted and dormant modes do not contribute to the current dynamics of the process in a significant manner, and their contribution can be neglected; this is used to generate the reduced-order model. Other approaches for dynamic analysis include graph theoretic approaches for time scale decomposition 29,30 and methods based on extents of reaction, 31–34 which can also be used in identification problems. The graph theoretic approaches describe the reaction mechanism as a bipartite graph, following which fast and equilibriated reactions identified; fast sub-graphs are identified as closed walks over the fast edges in the graph. The approach involving extents of reaction identifies reaction variants/invariants and identifies transformations that allows viewing a complex nonlinear chemical reaction system via decoupled dynamic variables, each associated with a distinct reaction. This allows for the decoupling of reactions and transport phenomena. There are also other effective approaches for model reduction in reacting systems. In situ adaptive tabulation 35–37 has been used to determine rate controlled constrained equilibrium manifolds and reduced order mechanisms with successful applications in combustion chemistry, where CSP has also been used extensively. Other approaches include integer programming, 38 which considers the impact of including or excluding specific species and the reactions in which they take part, and elemental flux analysis, 39 which provides an index of

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the importance species play across the entire range of validity of the mechanism. Other important aspects of analysis of models include sensitivity analysis, which is very useful in model-based experiment design, among other things, and uncertainty quantification. Rabitz et al. 40 have provided a review on the application of sensitivity analysis in kinetics, including local and global sensitivity, and stochastic and distributed systems; this is truly a comprehensive review on methods. There is a wide body of literature in this area, including many applications related to parameter estimation in kinetic models. 41–44 Worthy of notice are the efforts related to sensitivity analysis of reaction mechanisms, 15,45–48 the use of sensitivity analysis to construct skeletal reaction mechanisms, 49,50 and global sensitivity analysis of reaction mechanisms. 51–53 Another important application is the use of sensitivity analysis and Lyapunov exponents to detect the onset of thermal runaway in batch reactors. 54–56 Uncertainty analysis is used to capture the effect of uncertainty in parameters or inputs on the outputs of the system (typically, species composition in these cases); while sensitivity analysis has been used for this purpose 45,57 and Monte Carlo simulation 58,59 offers a straightforward but computationally expensive approach, approaches based on polynomial chaos expansion (PCE) 60–62 and probabilistic approaches 63–66 have shown much promise. Other approaches include the use of power series expansions. 67,68 Polynomial chaos expansion quantifies the effect of uncertain (kinetic) parameters on the outputs (usually the rates of reactions or product yields/composition) using orthogonal stochastic polynomial expansions. Collocation or least squares methods can be used to estimate the coefficients of the polynomial expansions based on a small number of Monte Carlo simulations sampling the distributions of the uncertain parameters. The power series expansion approach uses the sensitivity of the vector of rates of reactions in the system to the uncertain kinetic parameters to develop an expression for the probability distribution function of the rate vector. Monte Carlo sampling of uncertain parameters are then used to compute the distribution for the rate vector and its confidence intervals. In the context of application to uncertain reacting systems, PCE has been found to be more computationally efficient and accurate

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than power series expansion. 69–72 An important application of uncertainty analysis in catalytic systems is in quantifying the effect of uncertainty in binding energies calculated using density functional theory or semiempirical methods such as group additivity methods or Bronsted-Evans-Polanyi correlations on predictions of catalyst behaviour and system performance. 73–76

Reactor control The inherent nonlinearity of chemical reactions and their kinetics presents challenges for the control of chemical reactors; in addition, uncertain model parameters and unmeasured disturbances, complex kinetics and a lack of comprehensive measurements for all species present in the reaction mixture make the problem more difficult. Also, interest in reactor control has moved beyond the traditional measured or easy to measure variables to control of product quality (e.g. composition, particle features) which is often difficult to measure. In this section, we review the main advances in addressing these challenges, focusing on developments in nonlinear, robust and stochastic reactor control problems. Proportional-integral-derivative (PID) control 77,78 has traditionally been used for basic regulatory control for linear systems; however, researchers have attempted to extend the use of these and similar simple controllers for nonlinear reacting systems. Jones 79 accounted for nonlinearity using optimum feedback control systems for nonlinear processes by using nonlinear control elements. He compared the results of nonlinear and linear controllers using a CSTR as the base case and concluded that nonlinear control was superior. Marini and Georgakis 80 were able to show that the unstable dynamics of low density polyethylene reactors are associated with the deviation from the steady state of the reaction rate and used a nonlinear controller that was able to adjust the initiator concentration to keep the reaction rate at its steady-state value. Luyben 81 introduced nonlinear feedforward control for batch CSTR and tubular reactors. He compared nonlinear feedforward control with linear feedforward and

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open-loop control strategies and showed that the nonlinear feedforward controller performed well even with model uncertainty. Georgakis 82 used variable transformation approaches to address nonlinear control and used the physical interpretation of the slow and fast modes of process dynamics and the synthesis of multivariable and/or nonlinear control structures using extensive thermodynamic variables. By doing so, he developed dynamic modes related to the total energy or mass content of the systems and to the deviation of the reaction rate from its steady-state value for chemical reactors 80 . The method was tested on an isothermal and adiabatic CSTR and a catalytic cracking process. Related to this approach, Waller and Makila 83 used chemical reaction invariants and variants for nonlinear reactor control design. The advantage of these methods is that there is no need to have accurate knowledge of the nonlinear model of the reactor, and such ad hoc strategies are still very common in the chemical process industry. Other efforts on extensions of linear control include the extension of the internal model control principle (IMC) 84 to nonlinear systems. Economou et al. 85,86 extended IMC to the nonlinear case (NLIMC) using operator theory. This was tested for adiabatic, exothermic CSTRs operating in a region where the linearized process gain changes sign. Economou et al. noted that the operator inversion method of Hirschorn 87 failed in many practical cases to provide a satisfactory approximation to the exact inverse. Other investigations also showed the drawbacks of this operator theory approach; for example, Kravaris and Kantor 88 showed that the Hirschorn inverse suffers from internal instability due to pole-zero cancellations at the origin. The main disadvantage of NLIMC is that open-loop unstable processes can not be handled since the formulation is equivalent to an open-loop observer on the state variables. Interested readers may need to consult Rivera’s review on IMC 89 for more details. Parrish and Brosilow 90 then developed nonlinear inferential control (NLIC) to estimate unmeasured disturbances which was later extended by Hidalgo and Brosilow 91 to handle an open-loop unstable styrene polymerization reactor by replacing the Euler-based method with a Runge-Kutta integration technique. In their approach, Hidalgo and Brosilow lumped the

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disturbance effect and modeling errors into a single variable. Control action was calculated using a one-step-ahead approach to bring the output to its desired value at the end of the time horizon. The key strength of the approach was that since state variable identification is implicit in the output matching technique, the method could effectively be used for open-loop unstable processes. The next major development in advanced reactor control was model predictive control (MPC). 92,93 94–96 In the context of reactor control, MPC has focused on nonlinear control and robustness. 94,97 Once the stability theory for constrained receding horizon control and the state space formulation was established, 98,99 the main research focus in recent years has been the nonlinear formulation of MPC and design for uncertain systems. Formulation of nonlinear MPC (NMPC) involved direct use of first principles-based models or, in some cases, nonlinearly identified models using neural networks or other methods, 100 which was very important for problems such as polymer reactor control with grade changeovers and for handling modeling errors and parameter uncertainty. In practical application, however, this change resulted in a nonconvex online mathematical optimization and poses numerical difficulties. For this reason, a major focus of the research in NMPC has been to develop a reliable nonlinear optimization solver suitable for real-time implementation 101,102 and formulation of algorithms to ensure stability and/or near-optimality can be achieved when global optimal solution is not possible. 103–105 With respect to nonlinear reactor control and generally chemical process systems, NMPC is the most popular and powerful nonlinear control method 95,106 and has performed favourably in comparison with other nonlinear control algorithms. 107 One of the practical research results on NMPC is due to Ricker and Lee, 108 applied to the Tennessee Eastman challenge process consisting of an exothermic, 2-phase reactor, a flash separator, a compressor, and a stripper with a reboiler. In their work they showed that NMPC (based on successive linearization and quadratic programming) improved the performance of the control significantly, especially in cases involving multiple constraints and/or large set-point changes for

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reactors and other units involved. In their comparison with linear MPC they also found that NMPC always performed better. Maner and Doyle 109 developed NMPC based on the autoregressive-plus Volterra model for the control of two polymerization reactors. They ensured semiglobal closed-loop stability and showed that NMPC outperformed PID and a linear MPC. Hidalgo and Brosilow 91 investigated NMPC for a styrene polymerization reactor (a nonlinear, open-loop unstable process) and found stable control and exact tracking of the set point at steady state despite significant model errors. Patwardhan et al. 110 compared NMPC against linear MPC for open-loop unstable CSTR reactors and showed that NMPC was able to bring the controlled variable to its set-point quickly and smoothly from a wide variety of initial conditions. Moreover, they found that compared to the other controllers, NMPC dealt with constraints in an explicit manner without any degradation in the quality of control and demonstrated superior performance in the presence of a moderate amount of error in the model parameters, and the process was brought to the set-point without steady-state offset. Their findings were also substantiated by others. 111,112 Schmid and Biegler 113 used the open-loop unstable fluid catalytic cracking unit and a multi-step approach to show the similar strengths of NMPC. Sistu and Bequette 112 performed a comprehensive analysis of NMPC of a CSTR, including operation at open-loop unstable operating conditions. The effect of dead time on reactor control using NMPC was also investigated, 112 with control formulations developed to account for its effect. 114 There are many such applications of NMPC to reactor control including practical applications. Interested readers are referred to 91,93,96,107,115–117 for details; these applications include polymer reactors, batch fermentation processes, solar plants and catalytic cracking units. Badgwell and Qin 118 provide a useful review on industrial NMPC formulations and applications, and another useful resource is Kouvaritakis and Cannon. 119 The most common application of NMPC in industrial practice is to polymerization reactors 120–126 and petroleum refining, 127 though applications to semiconductor reactors 128 and pH neutralization systems 129 are also documented. It is to be noted that classic reactor control problems such as constraint han-

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dling and dead time compensation are handled naturally using MPC, which is not always the case for other approaches. In addition to nonlinearity, another major challenge for chemical reactor control is model and/or parameter and measurement uncertainties and unmeasured disturbances. When the plant model is fully known (nominal case), the closed loop stability of MPC can be guaranteed using terminal state constraints. However, when there is uncertainty in the plant model, ensuring stability is a serious concern. In industrial MPC applications, it is common to address this issue is using extensive closed-loop simulation prior to implementation; however, it is expensive and relies on the control engineer to anticipate and test every important combination of plant dynamics and active constraints. Research has been conducted to treat this problem explicitly by modifying the MPC algorithm. 130–132 Depending on the nature of the model and/or measurement uncertainties, research in this regard is classified into robust and stochastic MPC. Robust control in general refers to the case where the uncertainty is assumed to have known bounds while stochastic MPC refers to a more general class, in which case the uncertainty is assumed to be random with a known probability distribution, and where some or all of the constraints are probabilistic in nature. 131 Unlike the extension of linear MPC to NMPC, extension to robust and stochastic model predictive control is not straightforward. First it requires assumptions on and/or a description of unmodeled dynamics. In the case of robust MPC, the disturbance is assumed to take values in the compact set that contains the origin in its interior. In the stochastic formulation, such a set is not necessarily compact, and it is assumed that there is an underlying probability space with a specific probability measure. 133 Second, the decision variable for the optimal control problem is considerably different. In conventional MPC (where the model of the system is assumed accurate), the decision variable is the control sequence. For the case of robust and stochastic MPC using the control sequence as the decision variable (even though this has been used in the literature) is not sufficient and often need to be

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re-parametrized. 134,135 Third, the definition of cost function is different and reformulation is required based on the desired design scheme. 94 Fourth, constraints require reformulation based on the design. For example, it is necessary in stochastic MPC to ‘soften’ the state and terminal constraints. 136–138 The other challenge with extension to robust and stochastic MPC is stabilizability. In the case of the nominal problem, addition of either a suitable terminal cost to the cost function or a terminal constraint ensures closed-loop stability; 99 alternately, a large horizon 139,140 may be used to ensure stability. For robust MPC, when the disturbance is bounded and additive, the terminal cost and terminal constraint need to be replaced by robust versions i.e. the terminal cost should be a robust local Lyapunov function and the terminal constraint set has to be robustly control invariant. 99 For stochastic MPC, there is not yet a satisfactory treatment of stabilizing terminal conditions when the disturbance is not bounded. 136 Constrained stochastic MPC also requires stochastic optimization to be employed for both linear and nonlinear cases. In the case of robust MPC the problem will reduce to the deterministic case. Fortunately, there has been considerable progress in this respect which may need fine tuning to develop a practically appealing algorithm. 141,142 In terms of the application of robust MPC to the reactor control problem, Zafiriou, 143 by using a contraction mapping principle, studied the robustness properties of linear MPC controllers subject to input and output constraints. He derived necessary and/or sufficient conditions for nominal and robust stability which were then used for other case studies including a subsystem of the Shell standard control problem. 144 Sistu and Bequette 112 investigated the effect of model structure uncertainty for an endothermic and an exothermic CSTR. Rawlings and co-workers 145 also computed the sensitivity of the optimal solution to model parameters and manipulated variables and showed the bounds on manipulated variable uncertainty for the corresponding variability in the objective function for a batch reactor control problem. Badgwell, 146 by a direct extension of the nominal stabilizing regulator presented by Rawlings and Muske, 146 developed linear robust MPC tested on a multivariable

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adiabatic CSTR. In this work model uncertainty was parametrized by a list of possible plants (the polytopic method). Robust stability was achieved by adding constraints that prevent the sequence of optimal controller costs from increasing for the true plant; the algorithm did not need new tuning parameters to achieve robustness. Oravec and Bakoov 147 developed robust MPC based on the optimization of convergence rate subject to the nominal system, and additional saturation of control inputs. The algorithm was used to stabilize an exothermic hydrolysis of propylene oxide to propylene glycol in a CSTR with multiple steady states, one of which was unstable. There are other recent applications of robust MPC to reactor control in the literature. 99,147–151 Robust 152 and stochastic 153 NMPC have also been applied to thin film vapour deposition reactors, where the spatially distributed nature of the systems provides added challenges. With respect to industrial practice, the main strategies (except for the min-max formulation) are ad hoc strategies. 94 For instance, some of the most common approaches are closed-loop simulation prior to implementation and suppressing input movement and appending additional constraints to a nominally stabilizing MPC algorithm. Stochastic MPC is a recent research topic and there is very little information on its industrial application. 94,154 It has been stated about robust and stochastic MPC that the algorithms are too complex for current implementation in the process industries and suggestions have been made for more research on demand-oriented simpler alternatives. 133,155 A fairly recent development related to MPC is economic model predictive control (EMPC), 156,157 which attempts to integrate economic process optimization and process control into a single optimization problem. This negates the need for a separate real time optimization framework that supplies set points to the model predictive controller. The cost function used in EMPC usually reflects the economic considerations of the process, and this approach can result in operating the process in time-varying fashion to optimize process economics in response to varying demand or price fluctuations. However, this formulation presents challenges related to providing guarantees of stability. Given the importance of chemical reactors to practically

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all process plants, EMPC has been applied to reacting systems. Lao et al. 158 apply EMPC to a non-isothermal tubular reactor with a second-order chemical reaction, with the governing parabolic partial differential equations being converted to finite dimensional systems using a Galerkin method before applying EMPC. Zavala and Biegler 159 present an NMPC formulation that accounts for economics that is applied to the control of low density polyethylene reactors, and couple the controller with a moving horizon estimator. Sildir et al. 160 describe a two-level EMPC scheme applied to the control of a fluid catalytic cracker. EMPC was used to identify the optimal riser and the regenerator temperature reference trajectories based on dynamic optimization of the plant profit in the face of product price changes, with a regulatory model predictive controller manipulating the catalyst circulation rate and the air flow rate based on reference trajectories provided by EMPC. Other chemical applications of EMPC are listed in Ellis et al. 161

Optimization Optimization has a wide range of applications in reaction engineering, including parameter estimation, optimization of process operations and optimization of catalysts (by identifying optimal properties for them). It would be a herculean task list all the approaches for and applications of optimization in these areas. Given the nonlinear nature of kinetic and reactor models, we will highlight the importance of global optimization methods in this section. This is an area that deserves more attention in terms of the application of global optimization methods to large-scale systems, but there still have been significant contributions in this area. An important contribution is by Singer et al., 162 who developed a method supposed to guarantee finding the best possible least-squares fit of experimental data by a nonlinear kinetic model, which is useful in identifying inconsistencies between the model and experimental data. Esposito and Floudas 163 explored global optimization of differential-algebraic

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systems with applications in the estimation of reaction kinetics. Katare et al. 164 proposed a hybrid heuristic optimization algorithm to solve a similar problem, which is also the approach followed by Saha et al. 165,166 Guillén-Gosálbez and co-workers 167,168 explored branch and bound methods and outer approximation for global optimization of kinetic models. Moles et al. 169 compared global optimization methods for parameter estimation in biochemical pathways and concluded that in the tradeoff between stochastic and deterministic optimization techniques, the robustness of the stochastic techniques provided significant benefits even if the globality of the optimal solution could not be established. Recently, some attention has been focused on process development and optimization in the framework of so-called self-optimization. This amounts to solving multi-objective blackbox optimization problems coupled with experiment design to generate and continuously update response surfaces. Coupled with online sensing and chemometric analysis, this closes between exploratory experimentation and optimization and can be a powerful enabler for robotic automated chemistry and process development and optimization. Examples of the application to chemical reaction optimization can be found in Jeraal et al. 170 and Schweidtmann et al. 171 Reactor design is an obvious application for optimization techniques, and has received significant attention; we only highlight a few important classes of problems here. Feinberg 172–174 developed a geometric approach for optimal reactor design that focuses on the identification of the attainable region. Jacobsen et al. 175 attempted to link density functional calculations for catalysts to optimal reactor design. Another important application is in the synthesis of optimal reactor networks. 176,177 Sundmacher and coworkers studied optimal design in the context of intensification using elementary process functions, which tracked a fluid element along the reaction coordinate while its thermodynamic states were optimized by manipulating external mass and energy fluxes. 178 Dynamic optimization approaches have found favour, especially in batch reactor operation and batch process scheduling. 179,180 Another aspect that has been explored extensively is simultaneous reactor design and control. 181,182

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Finally, given the uncertainty in kinetic parameters for many reacting systems, optimization under uncertainty has also received much attention. 182–185

Chemometrics This section introduces chemometrics and the main techniques it uses, and highlights applications in reaction engineering. In the context of PSE, the use of chemometrics in various soft sensing applications can be viewed in the terms of developing inferential models for estimating the system states from outputs. Specifically, it helps in obtaining compositions and chemical signatures of species from measurements (typically chromatographic and spectroscopic), which then enables state and parameter estimation related to kinetics and control of product composition and optimization of operational performance by developing relationships between response and input feed variables which are used for prediction purposes. 186–188 Chemometrics is a multivariate statistical process control (MSPC) tool used in process analytical technology (PAT) with a focus on the design, analysis and control of a process through timely measurements during processing, aimed at achieving the desired final product quality. 189–192 PAT has been widely used in the production areas of pharmaceutical, food and biotechnology industries and encompasses multivariate mathematical approaches on data 193 collected from analyzers that are built into a manufacturing process to relay the real time state of the process. 194 A majority of the analyzers are chromatographic and spectroscopic instruments (Fluorescence, Visual, NIR, IR, Raman,1 HNMR) built into the process by mean of flow cells, quartz windows and immersion probes and are popular because they are fast, non-invasive and have no sample preparation requirements. 195–198 Process data from spectral analyzers happen to be high dimensional, non-causal, non-full rank, noisy and have missing values; making multivariate statistical methods that analyze this data to build mathematical system inferential models (soft sensors) in latent variable space an ideal choice for monitoring 199–211 processes because of which chemometrics is growing to be

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a popular PAT tool in passive environments. A passive environment is an offline training environment whereby measurements from a process environment are gathered for the purpose of training a system model (soft sensors) by using a variety of chemometric techniques like calibration,multivariate analysis, curve resolution; for monitoring the process. 212 The model once built can be used actively to adjust the process environment to achieve optimization, control and product development. Multivariate calibration refers to the process of relating, correlating, or modeling analyte concentration or the measured value of a physical or chemical property to a measured response. 213 Partial least squares (PLS) regression is popular in multivariate calibration as it modifies relations between sets of the observed variables by a small number of latent variables that maximize covariance in predictor and response space (not directly observed or measured) by incorporating regression and dimension reduction techniques. 214 Curve resolution in spectral data is a factor analytical decomposition that works by resolving the data into concentration and spectral profiles eitherly bi-linearly or multi-linearly using the self modeling multivariate curve resolution - alternating least squares (SMCRALS) 215,216 and the parallel factor analysis (PARAFAC) 217,218 models, respectively. The initial estimates for the decision variables can be obtained by evolving factor analysis (EFA) on a row-wise augmented data matrix both in the forward and backward direction 219 if the data has an intrinsic order or by use of a global search technique in the feasible space using particle swarm optimization (PSO). 220 The concentration and spectral profiles are subject to physically meaningful constraints like non-negativity, closure, unimodality to obtain a unique decomposition free from rotational and intensity ambiguities. 221 The PARAFAC model is inherently free of these ambiguities and is a unique decomposition as it is in terms of independent components, not orthogonal as with SMCR-ALS. The two unidentifiables in the PARAFAC model are the lack of an inherent order and the scale of the components. There is no guarantee that a certain component would come out as the first, making second order calibration as a way to automatically identify which of the factors happens to be

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the analyte of interest should a pure sample be included, wherein the scores of that sample are forced to be zero for all but one factor that must ultimately pertain to the analyte of interest. 222–224 The issue of scaling can be addressed by fixing a reference scale so that if concentration is known in a sample the corresponding column could be scaled so that scores equal the concentrations. These decomposition methods depend on a parameter called the rank or the number of pseudo-components which capture most of the variance in the data. In orthogonal decomposition it is determined using empirical metrics 225 based on principles of singular value decomposition into principal uncorrelated directions; while in higher order PARAFAC decompositions methods like core consistency 226 and split half analysis are used for rank determination based on the principles of PARAFAC being a restricted Tucker3 227 model and the uniqueness of decomposition. Resolution methods are applied to complex mixtures and aim to extract information on the number of components that significantly contribute to the mixture properties, the concentration of the components and their respective spectra in the case of hyphenated analytical techniques employed without prior knowledge about the system, and they can then enable further chemical interpretation and understanding of reaction networks. 228 The original data matrix consists of the raw experimental data that can be two way or three way, i.e. retention/reaction times vs. wavelength channels vs. intensity of absorbance. Almost always, the matrix is decomposed to extract the number of components contributing to the majority of data variance and then one of the following optimization algorithms employed to calculate the individual concentrations and the spectra of the extracted pseudo-components: (i) rank annihilation factor analysis (RAFA); 229 (ii) Generalized rank annihilation method (GRAM); 198 (iii) Evolving factor analysis (EFA); 230 (iv) Alternating least squares (ALS); 231 (v) Orthogonal projection analysis (OPA). 232 The rank annihilation methods consist of bilinear data sets from which the relative concentrations of components in a mixture are derived. GRAM is a non-iterative method that requires only a single calibration sample to obtain the so- called second-order advantage, i.e., it can determine the analyte of interest in the presence

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of unsuspected interferences. 233 It solves a specific eigenvalue problem whose eigenvectors constitute the transformation matrix that rotates the abstract factors from principal component analysis (PCA) into their physical counterparts. 234 EFA can provide initial estimates of concentration and spectra of the pure components in a mixture by an evolutionary process of applying PCA in backward and forward time directions to the data set. In this way, active concentration regions are detected. Another method quite similar to EFA is eigenstructure tracking analysis (ETA) where the window size starting with 2 is increased by a unit till the number of components is reached. 235 Analytical chemistry is one of the most common areas that benefits from the use of chemometric tools. This encompasses a variety of specialized disciplines like materials science, 236 pharmaceuticals, 203 food chemistry, 237 environmental chemistry, 238 biochemistry, 239 and geochemistry. 191 For example, in environmental science, it can used for tracking of impurities and pollutants in water and air. In food chemistry, it can be used to validate the authenticity of food products, trace origin of food classes, detection of adulteration and quality control, monitoring effects of processing on food components, and detection of food spoilage due to microbial growth. There has been extensive and critically reviewed research relating to the applications of chemometrics to food chemistry. 240–242 In biochemistry, the anti-bacterial potency of certain drugs can be quantitatively established. 243 Accurate information of source-rocks of certain crude oils and splitting of complex heavy oils into different pseudo-components tracking their evolution during thermal reactions make chemometrics an important technique in geochemistry and petroleum research. 216,244,245 Chemometrics has also been effective in eliminating the need for the use of hyphenated techniques like gas chromatography-mass spectrometry (GC-MS) by predicting reactor-output concentrations and product selectivity in processes involving conversion and oxidation of industrially important petrochemicals like propylene 246 and tetralin, 247 respectively. Early applications of chemometrics include the work of Christiansen et al., 248 and Wu and Malmstadt, 249 who integrate microcomputers with titrators for photometric and poten-

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tiometric purposes. A particular application was in nylon manufacturing where the titrant could be added at a user-determined flowrate automatically and equivalence points found out. Flow-injection analysis, which enables the study of interaction of a sample with a reagent, the kinetics of the reaction and the dispersion effects was also optimized using these techniques. 250–253 Hierarchical clustering analysis (HCA) was applied on emissions from materials like polymers to identify spectral groupings, followed by supervised techniques. 254 These chemometric approaches saved time and human effort to identify classes in complex spectra. It has been recorded in the literature that online pattern recognition techniques had been employed in the development of the present-day IR spectrometer by matching the spectral groups created with structural units of compound classes in standard libraries. 255 In petroleum chemistry, differentiation of crude oils and identification of their sources are significant areas where chemometric tools play a role. Eide et al. 256 used chemometric curve resolution methods on GC-MS characterization to identify individual components from diesel engines exhausts. Eide and Zahlsen 257 utilized electrospray ionization mass spectrometry (ESI-MS) as an improvement over GC as it ionizes the molecules without fragmentation. Mass spectra of crude oil mixtures are complex where each line can indicate different compound isomers of the same molecular weight; however, techniques such as PCA 258 can be used for chemical fingerprinting and classifying crude samples. However, the single quadrupole ESI-MS is inferior to high-resolution MS in terms of line resolution and thus requires significant assistance of pattern recognition and calibration techniques. 259 The impact of auto-scaling and range scaling on the PCA output was studied by Wang et al. 258 on biomarker data for matching the crude oils with their respective source rocks located in the Northern Wuerxun Depression, Hailar Basin. Mudge 260 utilized PLS regression to identify the possible sources for the hydrocarbons that constitute the sediment deposits in the Gulf of Alaska. A clear mapping of the sources to the hydrocarbons could not be identified in this analysis. PARAFAC, as a trilinear dimension reduction technique, is of immense importance in the analysis of fluorescence spectra. PARAFAC in combination with

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GRAM and SMCR-ALS was also used to decompose chromatograms for complex mixtures that are overlapped and drifted. 261 Bylund et al. 262 suggested the use of PARAFAC to deal with slight shifts in liquid chromatography-mass spectrometry to align the multidimensional data in the chromatographic direction. Resolution methods have found application in environmental chemistry. Comas et al. 261 determined the concentration of aromatic sulfonates in water using high performance liquid chromatography (HPLC) as the analytical technique. Due to the large amount of analytes present, GRAM was utilized, which quantifies all components simultaneously. The challenge here was the interference from the signatures of undesired material in HPLC. In order to resolve the overlapping excitation-emission maps from the fluorescence spectra of a complex poly-nuclear aromatic solution consisting of 6 constituent components, RAFA was employed as a resolution technique by Ho et al. 263 Impurities were detected in samples of tetracycline hydrochloride by decomposition of their HPLC data (collected with a diode array detector, DAD) into the respective spectra and concentration profiles. 264 Fixed size moving window EFA and OPA were the two methods used for this purpose. Multivariate curve resolution integrated with ALS optimization has been shown to solve issues of co-elution in chromatographic techniques in different kinds of compositionally complex samples. It was noticed by Salau et al. 265 that the pesticides, carbofuran and pirimicarb have comparable mass spectra, but SMCR-ALS could deal with the co-elution problem. SMCR-ALS was also particularly useful to resolve the FTIR spectra of Canadian oil sands-derived Cold Lake bitumen into 3 pseudo-component spectra and changes in their concentration over a range of temperatures and reaction times, with EFA being used to obtain the initial estimates of concentration and spectral profiles. A comparison of various chemometric calibration techniques was provided by Sivaramakrishnan et al. 246 where they compared the forecasting ability of LS-SVM (least squares support vector machine), PLS and interval-PLS for predicting the concentrations of the products from acid-catalyzed oligomerization of propylene at various temperatures and flow rates based on FTIR spectra. Four product streams based on PCA and hierarchical

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clustering analysis (HCA) were identified and regression models were built to establish relationships between inlet operating conditions of temperature and flowrate as well as the FTIR spectra of the products and the product concentrations, respectively. HCA was also used to find groups in the infrared spectra which were later used to predict the output concentrations as well.

Chemoinformatics Translating the information from chemometric models into knowledge of real chemistry by focusing on chemical database retrieval systems and chemical expert systems that map properties and activities deduced from the soft sensors to predict representative candidate molecule structures forms the basis of QSAR/QSPR (Quantitative Structure Activity Relationship/ Quantitative Structure Property Relationship) 266 models that largely encompass the growing discipline of chemoinformatics. 267 Chemoinformatics was first defined by Brown 268 as the transformation of data to information and knowledge for making better decisions in the process of drug discovery. Over the years, the set of techniques has been applied in many other application areas. Chemoinformatic methods in the context of reaction engineering largely include : identification of molecular descriptors (or functional groups) from chemometric models, stochastic reconstruction of candidate molecules using these structural indicators, 269 and molecular similarity measures used to query databases for structures whose fingerprints are most similar 270 to the ones obtained by chemometric models through deconvolution of data from spectral analyzers. Therefore, chemoinformatics can be used to build on the results of chemometric investigations to build advanced models and master equations to aid in system automation and further discovery. 271,272 Chemoinformatics also encompasses hypothesizing reaction network pathways as causal inferences between candidate molecules by mapping on to enegetics of real chemistry from a database, 273 and predicting novel reaction pathways by high throughput reaction prediction

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between nodes of reactants and products such that reactions in subsequent reaction pathways occur at the same functional group site. 274 Data driven heuristic score-based methods that make locally optimum choices can be used to construct Bayesian reaction networks among nodes of similar candidates in the absence of prior knowledge of system composition or chemistry by maximizing an information criterion. 275 The methods mentioned above for reaction network generation 273 or predicting pathways 274 are primarily data driven template-based approaches which have limited scalability to larger, more diverse datasets. This is overcome by a template-free approach 276 wherein molecules are represented as labelled graphs over atoms, whose pairwise interactions are computed to find the strongest one, which is designated as a reaction centre so that chemically feasible bond configurations among these atoms are enumerated to give a set of candidate products that are ranked using a Weisfeiler Lehman difference network to identify the most likely product. Recent chemoinformatic investigations have focused on the intelligent development of synthesis routes, 277 predictions of physical properties, 278 optimal reaction conditions, 279 reactivity and pathways, 280,281 and exploring identification of complexity. 282 Catalyst informatics has also emerged as a promising framework for the development and optimization of catalysts, the coupling of experiments and theory and the developments and analysis of microkinetic models; we refer readers to the review by Medford et al. 283 for details. Hence, it can be seen that chemometrics and chemoinformatics together can be used to demystify the composition, properties and chemistry of complex mixtures with innumerable unknown compounds that can be used in an online environment for property prediction, composition control, predicting reaction network pathways or hypothesizing novel pathways. While chemometrics focuses on the soft sensing aspects of PSE, chemoinformatics can be seen to belong to the model building and analysis aspect.

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Future prospects Complexity is prevalent in most chemical reacting systems, and this challenge is likely to increase in the future. This is driven both by the drive for process intensification 284–286 and the use of complex feeds (biomass, heavy organic residues such as bitumen, etc.). The aim is to achieve full compositional control (in terms of yield and selectivity) in real time with incomplete sets of experimental data characterizing the mixture analytically with processes made more complex by intensification. While this is a daunting prospect, there are aspects of PSE that can potentially help realize this goal. Data fusion, combined with chemoinformatic techniques, can enable the development of a joint framework of capturing complementary and orthogonal information of the process by integrating data from different instruments using stage-based, feature-based and semantic meaning-based fusion. 287 Stage-based fusion consists of sequential concatenation of scaled data matrices from different measurements. 288 Feature-based fusion consists of capturing common and distinct variance in a factor analytical framework. 289 Semantic meaningbased fusion consists of implementing joint factorization of matrices from different measurements while incorporating network regularization constraints that factor in the relationships between disparate matrices. 290 Semantic-based fusion can also be implemented through a Kalman filter framework of sequentially fusing incoming measurements to update the state predicted by earlier measurements, 291 with blockwise multisensor Kalman filtering applied to a fused block of measurements. Chemoinformatic techniques that build molecular representations can be used to generate the states that will be updated based on the data fusion methods. The key is to update structural molecular descriptions of the constituents of the mixtures based on the information from multiple sensors, and it appears that a general purpose, rigorous method needs to be developed. Uncertainties and inaccuracies in the different analytical techniques can be accounted for explicitly by incorporating a Bayesian framework. Once the data fusion approach provides a comprehesive (real time) description of the composition of the complex mixture, reaction mechanisms (networks) and the asso24


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ciated kinetics can be developed using the chemoinformatic methods for reaction network described earlier. 273,275 The discovery and synthesis of organic molecules as candidates in drug discovery and the discovery and optimization of (heterogeneous) catalysts are also likely to continue to be important areas of the application of PSE. As in the past, chemoinformatics techniques that focus on the prediction of the reactivity and reaction pathways of hypothetical synthesizable molecules based purely on their molecular structure and similarity to well-characterized molecules are likely to play a big role in this endeavour, and we believe machine learning approaches such as deep learning 292 will have significant impact.

Acknowledgement The authors thank Natalia Semagina and Arno de Klerk for useful discussions. We also acknowledge financial support from the Natural Sciences and Engineering Research Council (NSERC) of Canada through a Discovery grant.

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Process systems engineering 1 2 Sensitivity 3 4 Uncertainty 5 6 reactants 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

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