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Master in Chemical Engineering Influence of Operating Conditions

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  • Master in Chemical Engineering

    Influence of Operating Conditions on the precision of the kinetic parameters for different

    kinetic laws

    Masters Thesis

    of

    David Armando de Oliveira Pinto

    Developed for the Course of Dissertation

    In

    IFP Energies Nouvelles

    Supervisor in FEUP: Prof. Jos Miguel Loureiro

    Supervisors in IFPen: Doctor Alberto Silva Servia

    Doctor Jan Verstraete

    Chemical Engineering Department

    Julho 2016

  • Influence of Operating Conditions on the precision of the kinetic parameters for different kinetic laws

    Acknowledgments

    Here I want to express my gratitude to all the people that made this masters thesis, possible.

    To Dr. Dominique Humeau, director of the Process Experimentation division, and Dr. Herv

    Cauffriez, department head of the Experimentation Intensification department, I thank you

    for the opportunity to make my internship in IFPEN.

    To my supervisors at IFPEN, Doctor Jan Verstraete Doctor Alberto Silva Servia, for all the

    attention, support, guidance and knowledge given.

    To Prof. Jos Miguel Loureiro, Im very grateful for his availability, knowledge sharing and all

    the corrections and important suggestions about this work.

    To all my friends here in Lyon, Gonalo and Paulo, for the support in the hardest moments

    and for all the time we shared that made this great experience.

    To all my family, for their love and support.

    To all my friends in Portugal, Eduardo, Daniela and Ana, for all the unconditional support,

    even hundreds of kilometers away.

    To all the people I met during my stay here, for making this ERASMUS experience one of the

    unforgettable experiences in my life.

  • Influence of Operating Conditions on the precision of the kinetic parameters for different kinetic laws

    Resumo

    Na indstria, recursos tcnicos e econmicos so normalmente limitados. Para determinar

    qual o modelo cintico para cada reao ento crucial otimizar o nmero de experincias

    realizadas.

    Neste trabalho, a influncia de diferentes condies foram testadas, nomeadamente a funo

    objetivo, modelo cintico e o uso de rudo para a gerao de dados pseudo-experimentais.

    Utilizando um conjunto de 196 experincias, diferentes mtodos para determinar as

    experincias mais informativas e o melhor mtodo para as determinar.

    Deste trabalho, possvel concluir que utilizando menos de oitenta experincias os intervalos

    de confiana e os valores dos parmetros no variam significativamente com a adio de mais

    experincias, permitindo reduzir o seu nmero para menos de metade do habitual.

    Palavras Chave: Modelao cintica, Design Experimental, mtodo

    D-optimal , mtodo I-optimal

  • Influence of Operating Conditions on the precision of the kinetic parameters for different kinetic laws

    Abstract

    In the industrial world, economical and technical resources are often limited. To determine

    the kinetic model for different reactions it is then crucial to optimize the number of

    experiments performed.

    In this work, the influence of different conditions was tested, such as the objective function,

    kinetic model and the use of noise to generate pseudo-experimental data.

    Using a Data Set of 196 experiments, different methods were tested in order to determine the

    most informative experiments and the best method to determine them.

    From this work, it is possible to conclude that eighty experiments allow to obtain confidence

    intervals and parameter values that do not vary significantly after the addition of more

    experiments. This enables to reduce the number of experiments performed to less than half.

    Keywords: Kinetic Modeling, Experimental Design, D-optimal

    method, I-optimal method

  • Influence of Operating Conditions on the precision of the kinetic parameters for different kinetic laws

    Honor Declaration

    I hereby certify and declare on my honor, that the present work is my own and

    everything coming from external sources has been properly referenced.

    Sign and Date

  • Influence of Operating Conditions on the precision of the kinetic parameters for different kinetic laws

    i

    Contents

    1 Introduction ........................................................................................... 1

    1.1 Project Presentation .......................................................................... 1

    1.2 Company presentation ........................................................................ 1

    1.3 Work contributions ............................................................................ 2

    1.4 Thesis Structure ................................................................................ 2

    2 State of Art ............................................................................................ 3

    2.1 Dehydrogenation of Methyl-Cyclohexane ................................................. 3

    2.2 Types of kinetic laws .......................................................................... 3

    2.2.1 Power Law Model .........................................................................................4

    2.2.2 Adsorption Models.........................................................................................4

    2.3 Optimization for kinetic parameters determination .................................... 6

    2.3.1 Newtons Method ..........................................................................................6

    2.3.2 Levenberg-Marquardt Method ...........................................................................6

    2.4 Kinetic parameters statistical analysis ..................................................... 7

    2.4.1 Jacobian matrix ...........................................................................................7

    2.4.2 Hessian Matrix .............................................................................................7

    2.4.3 Confidence Interval .......................................................................................7

    2.4.4 F-Distribution value .......................................................................................7

    2.5 Experimental Design........................................................................... 7

    3 Objective Function .................................................................................. 9

    3.1 Sum of the Squares of the Absolute Deviations .......................................... 9

    3.2 Sum of the squares of the relative deviations .......................................... 10

    3.3 Conclusions .................................................................................... 11

    4 Kinetic Model ....................................................................................... 13

    4.1 Power Law ..................................................................................... 13

    4.1.1 5 Parameters Power Law .............................................................................. 13

    4.2 Adsorption Models ........................................................................... 14

  • Influence of Operating Conditions on the precision of the kinetic parameters for different kinetic laws

    ii

    4.2.1 Dual site surface reactions with generation of molecular hydrogen, with the generation of

    the second hydrogen molecule as controlling step ......................................................... 14

    4.2.2 Single site surface reactions according to the Eley-Rideal mechanism, with the generation

    of the second hydrogen molecule as controlling step ...................................................... 15

    4.3 Conclusions .................................................................................... 16

    5 Noise Influence in Parameter Estimation ..................................................... 17

    5.1 Fixed Relative Noise ......................................................................... 17

    5.2 Random Relative Noise ...................................................................... 19

    5.3 Gaussian Error Distribution ................................................................ 21

    5.4 Conclusions .................................................................................... 21

    6 Experimental Design .............................................................................. 23

    6.1 Experimental Design using the Jacobian Matrix Calculated using the Initial

    Parameter Estimation ................................................................................ 23

    6.1.1 Model parameters using D-optimal method ........................................................ 23

    6.1.2 Plausible estimations using D-Optimal .............................................................. 28

    6.1.3 Model parameters using I-optimal ................................................................... 33

    6.2 Experimental Design Recalculating the Jacobian Matrix using the Calculated

    Parameter .............................................................................................. 38

    6.3 Conclusions .................................................................................... 43

    7 Conclusion ........................................................................................... 45

    7.1 Accomplished objectives ................................................................... 45

    7.2 Limitations and Future Work ..........................

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