A joint model-based experimental design approach for the identification of kinetic models in continuous flow laboratory reactors

Continuous flow laboratory reactors are typically used for the development of kinetic models for catalytic reactions. Sequential model-based design of experiments (MBDoE) procedures have been proposed in literature where experiments are optimally designed for discriminating amongst candidate models or for improving the estimation of kinetic parameters. However, the effectiveness of these procedures is strongly affected by the initial model uncertainty, leading to suboptimal design solutions and higher number of experiments to be executed. A joint model-based design of experiments (j-MBDoE) technique, based on multi-objective optimization, is proposed in this paper for the simultaneous solution of the dual problem of discriminating among competitive kinetic models and improving the estimation of the model parameters. The effectiveness of the proposed design methodology is tested and discussed through a simulated case study for the identification of kinetic models of methanol oxidation over silver catalyst

Kinetic Intersections as a Source of Information on Rate Coefficients

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Continuous-flow reactors for the rapid evolution and validation of kinetic motifs

In this paper we apply the concept of a kinetic motif as a simple way to represent all the time-dependent behaviour in a single-step or multi-step reaction system. Small-scale continuous-flow reactors offer the potential to rapidly collect large amounts of data while accessing conventionally challenging experimental conditions. The scope of the approach is demonstrated on reaction case study examples

Closed-Loop Model-Based Design of Experiments for Kinetic Model Discrimination and Parameter Estimation: Benzoic Acid Esterification on a Heterogeneous Catalyst

An autonomous reactor platform was developed to rapidly identify a kinetic model for the esterification of benzoic acid with ethanol with the heterogeneous Amberlyst-15 catalyst. A five-step methodology for kinetic studies was employed to systematically reduce the number of experiments required to identify a practical kinetic model. This included (i) initial screening using traditional factorial designed steady-state experiments, (ii) proposing and testing candidate kinetic models, (iii) performing an identifiability analysis to reject models whose model parameters cannot be estimated for a given experimental budget, (iv) performing online Model-Based Design of Experiments (MBDoE) for model discrimination to identify the best model from a list of candidates, and (v) performing online MBDoE for improving parameter precision for the chosen model. This methodology combined with the reactor platform, which conducted all kinetic experiments unattended, reduces the number of experiments and time required to identify kinetic models, significantly increasing lab productivity

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

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 (BA) and ethanol in a microreactor

The Development of Microreactor Technology for the Study of Multistep Catalytic Systems and Rapid Kinetic Modelling

Microreactor technology was applied to the study of catalytic systems because their high rates of heat and mass transport, improved safety and ease of automation makes them particularly effective research tools in this area. A multistep flow system for the synthesis of benzylacetone from benzyl alcohol via oxidation, aldol condensation and reduction reactions was developed by utilising three micropacked bed reactors and a gas liquid membrane separator. This reaction had previously been conducted in batch cascade, however, the multistep flow system enabled the achievement of higher yields with lower catalyst contact times because separating each reaction into its own reactor allowed greater freedom to tailor the operating conditions for each reaction. The multistep system also allowed the catalysts to be studied in a process wide environment, leading to the identification of significant catalyst inhibition due to by and co-products from upstream reactions. An automated closed loop microreactor platform was developed which utilised Model-Based Design of Experiments (MBDoE) algorithms for rapid kinetic modelling of catalytic reactions. The automated platform was first applied to the homogenous esterification of benzoic acid with ethanol using a sulfuric acid catalyst, where a campaign of steady-state experiments designed by online MBDoE led to the estimation of kinetic parameters with much higher precision than a factorial campaign of experiments. This reaction was then conducted with MBDoE designed transient experiments, which dramatically reduced the experimental time required. The same reaction was studied using a heterogeneous Amberlyst-15 catalyst, and by combining factorial designs, practical identifiability tests and MBDoE for model discrimination and parameter precision, a practical kinetic model was identified in just 3 days. The automated platform was applied to the oxidation of 5-hydroxymethylfurfural in a micropacked bed reactor with gas-liquid flow using AuPd/TiO2 catalysts, however due to poor experimental reproducibility, a kinetic model was not identified

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

Catalytic 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

CO-PrOx over nano-Au/TiO2: Monolithic catalyst performance and empirical kinetic model fitting

In this work, the performance of ceramic monoliths washcoated with Au/TiO2 is studied on CO preferential oxidation (CO-PrOx) reaction in H2-rich environments under a wide range of operating conditions of practical interest. The parameter estimation of a nonlinear kinetic empirical model representing this system is made via genetic algorithms by fitting the model predictions against our laboratory observations. Parameter uncertainty leading to inaccurate predictions is often present when kinetic models with nonlinear rate equations are considered. Here, after the fitting was concluded, a statistical study was conducted to determine the accuracy of the parameter estimation. Activation energies of ca. 30 kJ/mol and 55 kJ/mol were adjusted for CO and H2 oxidations, respectively. The catalyst showed appropriate activity and selectivity values on the CO oxidation on a H2-rich environment. After ca. 45 h on stream the catalyst showed no deactivation. Results show that the model is suitable for reproducing the behavior of the CO-PrOx reactions and it can be used in the design of reactors for hydrogen purification.Peer ReviewedPostprint (author's final draft

Computational study on biomass fast pyrolysis: Hydrodynamic effects on the performance of a laboratory-scale fluidized bed reactor

Bubbling fluidized bed reactors are utilized in a wide range of chemical industries, including biomass conversion, petroleum refining, and pharmaceutical and commodity chemicals production. Establishing a comprehensive understanding of how the gas-solid hydrodynamics, specifically bubbling to slugging, affects interphase mixing and associated chemical reactions is critical for optimizing process performance. Characterization of bench scale bubbling bed hydrodynamics is vital for scaling up to pilot and industrial scale. This proposal outlines a plan to simulate a bench scale bubbling fluidized bed biomass fast pyrolysis process with emphasis on the effects of the bubbling-to-slugging transition on oil yield. Computational models of the hydrodynamics and the biomass fast pyrolysis reactions in a bubbling bed reactor are investigated using Geldart Group B particles. MFiX, an open-source software package, is utilized using the continuum (two-fluid) approach for modeling the reactor hydrodynamics. The effects of bubblies on oil yield along the reactor height is evaluated. The goal is to use pressure time series approaches to resolve previously unrecognized details of the underlying physics in hydrodynamics that affect oil yield.The implication of this work includes establishing a standard approach to optimize yield and composition from bench and industrial scale reactors

복잡한 동특성을 갖는 다상 반응기의 설계를 위한 계산 효율적인 모사 및 최적화 전략

학위논문(박사)--서울대학교 대학원 :공과대학 화학생물공학부,2020. 2. 이종민.본 박사학위논문에서는 멀티 스케일 모델링, 실험 결과를 이용한 모델 보정법, 최적화 순으로 진행되는 산업용 화학 반응기의 설계 전략을 제시한다. 반응기는 화학 공정에서 제일 중요한 단위이지만, 그 설계에 있어서는 최신 수치적 기법들보다는 여전히 간단한 모델이나 실험 및 경험 규칙에 의존하고 있는 현실이다. 산업 규모의 반응기는 물리, 화학적으로 몹시 복잡하고, 관련 변수 간의 스케일이 크게 차이나는 경우가 많아 수학적 모델링 및 수치적 해법을 구하기가 어렵다. 모델을 만들더라도 부정확하거나 시뮬레이션 시간이 너무 긴 문제가 있어 최적화 알고리즘에 적용하기가 힘들다. 반응기 내 현상의 복잡성과 스케일 차이 문제는 멀티 스케일 모델링을 통해 접근할 수 있다. 전산유체역학 기반 구획 모델(CFD-based compartmental model)을 이용하면, 불균일한 혼합 패턴을 보이는 대형 반응기에서도 긴 시간 동안의 동적 모사가 가능하다. 이 모델은 큰 반응기를 완벽하게 균일한 작은 구획들의 네트워크로 간주하고, 각 구획을 반응 속도식들과 CFD 결과로부터 가져온 유동 정보가 포함된 질량 및 에너지 균형 방정식으로 표현한다. 기체, 액체, 고체 3상이 상호작용하며 복잡한 유동을 보이는 수성 광물 탄산화 반응기를 이 방법을 사용해 모델링하였다. 이 때 모델은 미분 대수 방정식(DAE)의 형태를 띠며, 메커니즘 상 모든 반응들(기-액 간 물질 전달 반응, 고체 용해 반응, 이온 간 반응, 앙금 침전 반응)과 유체 역학, 반응열, 열역학적 변화 및 운전 상의 이벤트 발생을 모두 고려할 수 있다. 모델을 이용해 이산화탄소 제거 효율, pH 및 온도 변화를 예측하여 실제 운전 데이터와 비교한 결과, 파라미터를 통한 보정이 전혀 없이도 7 % 이내의 오차를 보여주었다. 모델의 부정확성 문제는 모델링 후 실험 결과를 이용한 모델 보정으로 극복 할 수 있다. 본 논문에서는 광물 탄산화 반응기 모델을 베이지안 보정(Bayesian calibration)을 통해 강화하는 방법을 제시한다. 먼저 모델 중 불확실한 부분에 8개의 파라미터를 도입한 후, 베이지안 파라미터 추정법(Bayesian parameter estimation) 및 실험실 규모에서의 실험 결과들을 이용하여 파라미터들의 사후 확률 분포를 추정하였다. 얻어진 파라미터의 확률 분포들은 모델 및 실험의 불완전성으로 인해 나타나는 파라미터의 불확실성 및 다중 봉우리 특성을 반영하고 있다. 이를 이용하여 실험 결과를 잘 따라가는 확률론적 모델 예측치(stochastic model response)를 얻을 수 있었다. 16개의 실험 데이터셋 및 테스트셋의 피팅 에러(fitting error)는 결정론적인 최적화 알고리즘(deterministic optimization)을 사용할 때보다 비슷하거나 낮은 것으로 측정되었다. 수학적 최적화에 쓰이기에 너무 긴 시뮬레이션 시간 문제는 베이지안 최적화 알고리즘을 적용하여 해결할 수 있다. 화학 반응기 설계 최적화를 위해 본 논문에서는 다중 목적 베이지안 최적화(Multi-objective Bayesian Optimization, MBO)를 사용해 시뮬레이션 횟수를 최소화 하는 CFD 기반 최적 설계 방법을 제안하였다. 여섯 가지 설계 변수를 가지는 기-액 교반 탱크 반응기에서 전력 소비를 최소화하고 가스 분율(gas holdup)를 극대화하기 위해 이 방법을 이용한 결과, 단 100 회의 시뮬레이션 만으로 최적 파레토 커브(Pareto curve)를 얻을 수 있었다. 제안된 최적 설계안들은 문헌에 보고된 기존 반응기들과 비교해 뛰어난 성능을 보여주었다. . 본 논문을 통해 제안된 CFD 기반 구획 모델링법, 베이지안 모델 보정법 및 베이지안 최적화 방법은 복잡한 물리적 및 화학적 특징을 갖는 산업 규모의 화학 반응기에 적용될 수 있을 것으로 기대된다.This thesis presents a design strategy for industrial-scale chemical reactors which consists of multi-scale modeling, post-modeling calibration, and optimization. Although the reactor design problem is a primary step in the development of most chemical processes, it has been relied on simple models, experiments and rules of thumbs rather than taking advantage of recent numerical techniques. It is because industrial-size reactors show high complexity and scale differences both physically and chemically, which makes it difficult to be mathematically modeled. Even after the model is constructed, it suffers from inaccuracies and heavy simulation time to be applied in optimization algorithms. The complexity and scale difference problem in modeling can be solved by introducing multi-scale modeling approaches. Computational fluid dynamics (CFD)-based compartmental model makes it possible to simulate hours of dynamics in large size reactors which show inhomogeneous mixing patterns. It regards the big reactor as a network of small zones in which perfect mixing can be assumed and solves mass and energy balance equations with kinetics and flow information adopted from CFD hydrodynamics model at each zone. An aqueous mineral carbonation reactor with complex gas–liquid–solid interacting flow patterns was modeled using this method. The model considers the gas-liquid mass transfer, solid dissolution, ionic reactions, precipitations, hydrodynamics, heat generation and thermodynamic changes by the reaction and discrete operational events in the form of differential algebraic equations (DAEs). The total CO2 removal efficiency, pH, and temperature changes were predicted and compared to real operation data. The errors were within 7 % without any post-adjustment. The inaccuracy problem of model can be overcome by post-modeling approach, such as the calibration with experiments. The model for aqueous mineral carbonation reactor was intensified via Bayesian calibration. Eight parameters were intrduced in the uncertain parts of the rigorous reactor model. Then the calibration was performed by estimating the parameter posterior distribution using Bayesian parameter estimation framework and lab-scale experiments. The developed Bayesian parameter estimation framework involves surrogate models, Markov chain Monte Carlo (MCMC) with tempering, global optimization, and various analysis tools. The obtained parameter distributions reflected the uncertain or multimodal natures of the parameters due to the incompleteness of the model and the experiments. They were used to earn stochastic model responses which show good fits with the experimental results. The fitting errors of all the 16 datasets and the unseen test set were measured to be comparable or lower than when deterministic optimization methods are used. The heavy simulation time problem for mathematical optimization can be resolved by applying Bayesian optimizaion algorithm. CFD based optimal design tool for chemical reactors, in which multi-objective Bayesian optimization (MBO) is utilized to reduce the number of required CFD runs, is proposed. The developed optimizer was applied to minimize the power consumption and maximize the gas holdup in a gas-sparged stirred tank reactor, which has six design variables. The saturated Pareto front was obtained after only 100 iterations. The resulting Pareto front consists of many near-optimal designs with significantly enhanced performances compared to conventional reactors reported in the literature. It is anticipated that the suggested CFD-based compartmental modeling, post-modeling Bayesian calibration, and Bayesian optimization methods can be applied in general industrial-scale chemical reactors with complex physical and chemical features.1. Introduction 1 1.1. Industrial-scale chemical reactor design 1 1.2. Role of mathematical models in reactor design 2 1.3. Intensification of reactor models through calibration 5 1.3.1. Bayesian parameter estimation 6 1.4. Optimization of the reactor models 7 1.4.1. Bayesian optimization 9 1.5. Aqueous mineral carbonation process : case study subject 10 1.6. Outline of the thesis 12 2. Multi-scale modeling of industrial-scale aqueous mineral carbonation reactor for long-time dynamic simulation 14 2.1. Objective 14 2.2. Experimental setup 15 2.3. Mathematical models 19 2.3.1. Reactor model 19 2.3.2. CFD model 28 2.3.3. Numerical setting 30 2.4. Results and discussions 32 2.4.1. CFD-based compartmental model for industrial-scale reactor. 32 2.4.2. Design and simulation of higher-scale reactors 42 2.5. Conclusions 47 3. Model intensification of aqueous mineral carbonation kinetics via Bayesian calibration 50 3.1. Objective 50 3.2. Experimental methods 51 3.2.1. Solution and gas preparation 51 3.2.2. Laboratory-scale mineral carbonation process 53 3.3. Mathematical models 56 3.3.1. Kinetics of aqueous mineral carbonation process 56 3.3.2. Differential algebraic equation (DAE) model for the reactor 65 3.3.3. Discrete events for simulation procedure 71 3.3.4. Numerical setting 72 3.4. Bayesian parameter estimation 72 3.4.1. Problem formulation 73 3.4.2. Bayesian posterior inference 76 3.4.3. Sampling 81 3.5. Results and discussions 82 3.5.1. Stochastic output response 82 3.5.2. Quality of parameter estimtates 86 3.5.3. Assessment of parameter uncertainties 91 3.5.4. Kinetics study with the proposed model parameters 99 3.6. Conclusions 103 4. Multi-objective optimization of chemical reactor design using computational fluid dynamics 106 4.1. Objective 106 4.2. Problem Formulation 107 4.3. Optimization scheme 113 4.3.1. Multi-objective optimization algorithm 113 4.3.2. CFD-MBO optimizer 120 4.4. CFD modeling 125 4.4.1. Tank specifications 125 4.4.2. Governing equations 125 4.4.3. Simulation methods 127 4.5. Results and discussion 128 4.5.1. CFD model validation 128 4.5.2. Optimization results 130 4.5.3. Analysis of optimal designs 139 4.6. Conclusions 144 5. Concluding Remarks 146 Bibliography 149 Abstract in Korean (국문초록) 163Docto