Identification Of Kinetic Models Research Articles

An optimal experimental design framework for fast kinetic model identification based on artificial neural networks

The development of mathematical models to describe reaction kinetics is crucial in process design, control, and optimisation. However, distinguishing between different candidate kinetic models presents a non-trivial challenge. Recent works on this topic introduced an approach that employs artificial neural networks (ANNs) to identify kinetic models. In this paper, the ANNs-based model identification approach is expanded by introducing an optimal experimental design procedure. The performance of the method is evaluated through a case study related to the identification of kinetics in a batch reaction system, where different combinations of experimental design variables and noise level on the measurements are compared to assess their impact on kinetic model identification. The proposed experimental design methodology effectively reduces the number of required experiments while enhancing the artificial neural network's ability to accurately identify the appropriate set of equations defining the kinetic model structure.

An optimization-free Fisher information driven approach for online design of experiments

Developing mathematical models used to elucidate reaction kinetics plays a crucial role in the design, control, and optimization of chemical processes. One of the most challenging tasks in kinetic model identification is the precise estimation of unknown kinetic model parameters. This challenge can be effectively addressed through the application of Model-Based Design of Experiments (MBDoE) techniques, which enable the design of experiments facilitating precise model parameter estimation with minimal runs and analytical resources. Nevertheless, MBDoE techniques rely on an optimization procedure that is susceptible to parametric uncertainty, making the design procedure computationally intensive and prone to issues of local optimality. MBDoE techniques are also employed in online procedures to expedite the identification of kinetic models in autonomous platforms. As a result, ensuring rapid convergence becomes imperative to mitigate numerical issues during operational processes. In this paper a Fisher Information Matrix Driven (FIMD) approach is introduced to tackle these challenges. The methodology integrates a sampling-based experimental design approach with experiment ranking based on FIM to select the most informative experiment at each iteration. The effectiveness of the proposed design methodology is examined and discussed via two different case studies of increasing complexity: a fed-batch reactor in which the fermentation of baker’s yeast is carried out and a nucleophilic aromatic substitution in a flow reactor system.

Semi-supervised machine learning approach for reaction stoichiometry and kinetic model identification using spectral data from flow reactors

The semi-supervised machine learning approach is an integrated calibration-free modelling framework for identifying reaction systems from spectral data using minimal prior information and it is validated with experimental data obtained in a micro-reactor.

Closed-loop identification of enzyme kinetics applying model-based design of experiments

This study presents an automated reactor platform for the identification of enzyme kinetic models using model-based design of experiments on the example of the reduction of NAD+ by formate dehydrogenase from Candida boidinii.

Automated kinetic model identification via cloud services using model-based design of experiments

Industry 4.0 has birthed a new era for the chemical manufacturing sector, transforming reactor design and integrating digital twin into process control.

Diastereomer salt crystallization: Comprehensive process modeling and DoE-driven comparison of custom-coded and user-friendly simulators

Process modeling is gaining attention in the pharmaceutical industry due to the promise of exploring the design space with less experimentation. However, the associated numerical apparatus can be prohibitive for many, undermining the attainable benefits. This study aims to demonstrate the readiness of modeling by guiding the reader through the essential steps of model development, from experimentation to kinetic model identification and in-silico DoE execution, implemented and executed in a user-friendly but restrictive simulator and a highly technical, custom-coded environment. The crystallization of (S)-pregabalin l-tartrate from a racemic aqueous solution is applied as a surrogate system, involving secondary nucleation, growth, and agglomeration. The distomer may act as an impurity. This process is sufficiently complex to be representative but straightforward enough to be familiar to a broad audience. Despite their differences, both modeling environments resulted in the same kinetic model structure and fitted the measurements well. The models are compared based on the in-silico DoE outcomes rather than the goodness of fit. The analysis revealed that the key conclusions are identical, which validates the utilization of the user-friendly simulator in time-constrained applications.

Benchmarking chemical neural ordinary differential equations to obtain reaction network-constrained kinetic models from spectroscopic data

Kinetic model identification relies on accurate concentration measurements and physical constraints to limit solution multiplicity. Not having these measurements and prior knowledge of species and reactions creates considerable challenges that are currently unresolved. We address these by developing a data-driven framework using realtime spectroscopic data, comprising: (i) multivariate curve resolution to deconvolve the spectra of the reacting mixture into those of its pseudocomponents and their corresponding concentrations, which enables species identification without prior information, (ii) Bayesian structure learning among the pseudocomponent spectra to enable hypothesizing reaction pathways, and (iii) neural ordinary differential equations (ODE) that are physically constrained by the hypothesized reaction network and the laws of mass action and temperature dependence to learn kinetic models from the temporal concentration projections of the realtime spectra. The predictive performance of the constrained neural ODEs is limited by the accuracy of spectral deconvolution in the presence of noise, and has been benchmarked against a constrained regression approach by varying signal:noise ratios in the synthetic spectroscopic data of reacting mixtures. Although the hypothesized reaction network differs from the actual reaction template, owing to noise, the network-constrained neural ODEs are seen to result in a 75.2% and 68.15% decrease in the root mean squared error (RMSE) of the concentration profile predictions as compared to the constrained regression method, when trained on time projected concentration data of the synthetic spectra generated at a signal to noise ratio of 35 and 100, respectively.

Autonomous kinetic model identification using optimal experimental design and retrospective data analysis: methane complete oxidation as a case study

An uncertainty-aware autonomous flow reactor platform was developed by combining automation and feedback optimization. The platform was applied to identify appropriate kinetic models online for a gas–solid catalytic reaction.

Oxidation of carbon monoxide over supported nickel oxide catalyst: kinetic model development and identification

The kinetics of carbon monoxide oxidation over alumina supported nickel oxide was studied using a mechanistic approach to model development and identification. Langmuir-Hinshelwood and Eley-Rideal reaction schemes, together with an alternative scheme were investigated, using low temperature, differential rate measurements. Experimental results were found to be most consistent with the alternative scheme, supporting a reaction mechanism based on non-competitive adsorption of carbon monoxide and oxygen onto different catalyst sites without mutual displacement. The resulting kinetic model was observed to have reasonable agreement with the experimental findings and was found representative of the system.

Enhanced kinetic model identification for gas–solid reactions through Computational Fluid Dynamics

Gas–solid reactions often play key roles in chemical engineering applications. To understand and design processes featuring such heterogeneous reactions, kinetic models are crucial. One way to identify kinetic models is via thermal analysis experiments. Even if those experiments are carried out meticulously, there will be some deviation between nominal reaction conditions and the actual reaction conditions directly at the reaction site. For situations, where these deviations are not negligible, we propose a new approach to compute the reaction conditions directly at the sample, based on the experimental data. A key feature of our approach is that no kinetic model is required for the simulation. For this reason, the enhanced data can be used for kinetic model identification. Though, a kinetic modeling method that can process arbitrary data is required, because the enhanced kinetic data will not obey the idealized assumptions of constant temperature or constant heating rate.To showcase our approach, we applied it to the reaction system CuO/Cu2O. Kinetic models with nominal and simulated values are derived with the TensorNPK method, showing the influence of the enhanced kinetic data on the identified reaction kinetics.

Apparent Pyrolysis Kinetics and Index-Based Assessment of Pretreated Peach Seeds

To better understand pyrolysis for upscaling purposes, a kinetic characterization of the process is necessary for every feedstock. Laboratory experiments allow identification of apparent kinetic models. This paper aims at the apparent kinetic investigation of peach seeds’ slow pyrolysis. Peach seeds from Greek peach fruits pyrolyzed under inert atmospheric conditions at different temperatures (475–785 °C), heating rates (100–250 °C/min) and N2 flow rates (25–200 cc/min). Prior to pyrolysis, they submitted to hexane extraction for the recovery of 36.8% wt. of the contained oils. Determination of the specific rate constant (k) and activation energy (Ea) for each considered reaction was made by using the Coats–Redfern integral non-isothermal fitting model that requires an assumption of the reaction order (n). Results revealed that a 3rd order reaction model best fits the process, the increasing of the pyrolysis temperature leads to a decrease of the activation energy (E) and pre-exponential factor (A), while nitrogen flow rate and heating rate had an opposite impact. E and A values ranged from 23 to 56 kJ/mol and 1.82 × 106 to 1.13 × 106 min−1, respectively, at different pyrolysis conditions. Furthermore, estimation of combustion and pyrolysis indexes were made to assess the suitability of peach seeds as a fuel, using isothermal thermogravimetric analyses (TGA). Results revealed that peach seeds are a suitable feedstock for pyrolysis, while prior submission of peach seeds to oils extraction, in a cascade biorefinery approach, can increase the energy and material recovery efficiency and potentially the environmental and economic benefit of the agri-food industrial sector.

Design, operation and evaluation of an improved refractory wear testing technique

A newly developed Continuous Wear Testing Device (CWTD) based on a rotating cylinder specimen enables in-situ wear rate measurements of fine ceramic dissolution in slags. A corroding fine ceramic sample is measured several times during a corrosion test with a high precision 3D laser measurement system. Mass loss derived from this measurement is compared with direct determination by load cells. Optimal flow conditions for static and dynamic measurements are achieved by a high ratio of slag mass to immersed sample mass and by an adjustable rotation speed. Corrosion of Al2O3 fine ceramic cylinders in a CaO-MgO-Al2O3-SiO2 slag at 1550 °C demonstrated the occurrence of Marangoni convection and lower corrosion rate for a static measurement, while Taylor vortices appeared with a dynamic setup. The accuracy of the wear measurement was assessed and evaluated for corrosion profiles which enable the identification of kinetic models for the calculation of diffusivities.

Safe model-based design of experiments using Gaussian processes

The construction of kinetic models has become an indispensable step in developing and scale-up of processes in the industry. Model-based design of experiments (MBDoE) has been widely used to improve parameter precision in nonlinear dynamic systems. Such a framework needs to account for both parametric and structural uncertainty, as the physical or safety constraints imposed on the system may well turn out to be violated, leading to unsafe experimental conditions when an optimally designed experiment is performed. In this work, Gaussian processes are utilized in a two-fold manner: 1) to quantify the uncertainty realization of the physical system and calculate the plant-model mismatch, 2) to compute the optimal experimental design while accounting for the parametric uncertainty. The proposed method, Gaussian process-based MBDoE (GP-MBDoE), guarantees the probabilistic satisfaction of the constraints in the context of model-based design of experiments. GP-MBDoE is assisted with the use of adaptive trust regions to facilitate a satisfactory local approximation. The proposed method can allow the design of optimal experiments starting from limited preliminary knowledge of the parameter set, leading to a safe exploration of the parameter space. This method’s performance is demonstrated through illustrative case studies regarding the parameter identification of kinetic models in flow reactors.

A Multi-Objective Optimal Experimental Design Framework for Enhancing the Efficiency of Online Model Identification Platforms

Abstract Recent advances in automation and digitization enable the close integration of physical devices with their virtual counterparts, facilitating the real-time modeling and optimization of a multitude of processes in an automatic way. The rich and continuously updated data environment provided by such systems makes it possible for decisions to be made over time to drive the process toward optimal targets. In many manufacturing processes, in order to achieve an overall optimal process, the simultaneous assessment of multiple objective functions related to process performance and cost is necessary. In this work, a multi-objective optimal experimental design framework is proposed to enhance the efficiency of online model-identification platforms. The proposed framework permits flexibility in the choice of trade-off experimental design solutions, which are calculated online—that is, during the execution of experiments. The application of this framework to improve the online identification of kinetic models in flow reactors is illustrated using a case study in which a kinetic model is identified for the esterification of benzoic acid and ethanol in a microreactor.

Identification of kinetic models of methanol oxidation on silver in the presence of uncertain catalyst behavior

AbstractCatalytic oxidation of methanol to formaldehyde is an important industrial process due to the value of formaldehyde either as a final product or as a precursor of numerous chemicals. The study of kinetics in this system is hindered by sources of uncertainty that are inherently associated to the nature and state of the catalyst (e.g., uncertain reactivity level, deactivation phenomena), the measurement system and the structure of the kinetic model equations. In this work, a simplified kinetic model is identified from data collected from continuous flow microreactor systems where catalysts with assorted levels of reactivity are employed. Tailored model‐based data mining methods are proposed and applied for the effective estimation of the kinetic parameters and for identifying robust experimental conditions to be exploited for the kinetic characterization of catalysts with different reactivity, whose kinetic behavior is yet to be investigated.

Automated learning of chemical reaction networks

The identification of kinetic models from process measurements relies on obtaining expensive data from experimental designs in order to estimate kinetic rate parameters and discern which mechanisms fit the data most appropriately. This paper proposes an approach that utilizes a mixed-integer nonlinear programming formulation to estimate and identify kinetic rate parameters from a postulated superset of reactions. The proposed methodology can be applied to steady state systems, or dynamic systems through explicit derivative estimation. An adaptive design of experiments methodology is proposed to facilitate intelligent sampling across the experimental domain. The proposed methodology is applied to three problem settings: isothermal CSTRs where initial concentrations are varied to learn the reaction network, dynamic chemical looping combustion reactors where semi-empirical mechanistic models are used to model catalyst conversion, and an expanded example that considers alternative reaction mechanisms and stoichiometric relationships and applies the proposed adaptive sampling technique to a higher dimensional domain.

Analysis of Experimental Conditions, Measurement Strategies, and Model Identification Approaches on Parameter Estimation in Plug Flow Reactors

Continuous flow reactors such as plug flow reactors (PFRs) have been used in the identification of reaction systems (Moore, J. S.; Jensen, K. F. Angew. Chem. 2014, 126, 480−483). It is important to understand the impact of operating conditions, measurement strategies, and kinetic model identification methods on the identification of reaction systems in a PFR. Typically, for kinetic model identification using the simultaneous identification approach, concentrations are measured as a function of residence time under isothermal operating conditions in a PFR. On the other hand, concentrations and temperature are required to be measured as a function of residence time under non-isothermal conditions for kinetic model identification of multiple reaction systems in a PFR. In this work, we extend the incremental method for identification of kinetic and heat transport models using measurements from non-isothermal steady-state PFRs. This work investigates the role of experimental conditions, measurement strategies ...

On the Use of Online Reparametrization in Automated Platforms for Kinetic Model Identification

AbstractParameter estimation algorithms integrated in automated platforms for kinetic model identification are required to solve two optimization problems: i) a parameter estimation problem given the available samples; ii) a model‐based design of experiments problem to select the conditions for collecting future samples. These problems may be ill‐posed, leading to numerical failures when optimization routines are applied. In this work, an approach of online reparametrization is introduced to enhance the robustness of model identification algorithms towards ill‐posed parameter estimation problems.

An autonomous microreactor platform for the rapid identification of kinetic models

Rapid estimation of kinetic parameters with high precision is facilitated by automation combined with online Model-Based Design of Experiments.

Maximum-likelihood estimation of kinetic parameters via the extent-based incremental approach

For lumped homogeneous reaction systems, this paper presents a kinetic model identification scheme that provides maximum-likelihood parameter estimates and guarantees convergence to global optimality. The use of the extent-based incremental approach allows one to (i) identify each reaction individually, and (ii) reduce the number of parameters to be identified via optimization to the ones that appear nonlinearly in the investigated rate law. The approach results in maximum-likelihood parameter estimation if the experimental extents are uncorrelated and the rate estimates used to compute the modeled extents are unbiased. Furthermore, the identification problem can be rearranged via Taylor series expansion as a polynomial optimization problem. This optimization problem is then reformulated as a convex optimization problem that can be solved efficiently to global optimality. Different aspects of the approach are demonstrated via simulated examples.