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When referring to this work, full bibliographic details including the author, title, awarding institution and date of the thesis must be given e.g. AUTHOR (year of submission) "Full thesis title", University of Southampton, name of the University School or Department, PhD Thesis, pagination http://eprints.soton.ac.uk UNIVERSITY OF SOUTHAMPTON FACULTY OF ENGINEERING AND THE ENVIRONMENT Mathematical Modelling and Simulation of Biofuel Cells by Mohamad Hussein Osman Thesis submitted for the degree of Doctor of Philosophy December 2013 UNIVERSITY OF SOUTHAMPTON ABSTRACT FACULTY OF ENGINEERING AND THE ENVIRONMENT MATHEMATICAL MODELLING AND SIMULATION OF BIOFUEL CELLS by Mohamad Hussein Osman Bio-fuel cells are driven by diverse and abundant bio-fuels and biological catalysts. The production/consumption cycle of bio-fuels is considered to be carbon neutral and, in princi- ple, more sustainable than that of conventional fuel cells. The cost benefits over traditional precious-metal catalysts, and the mild operating conditions represent further advantages. It is important that mathematical models are developed to reduce the burden on labo- ratory based testing and accelerate the development of practical systems. In this study, recent key developments in bio-fuel cell technology are reviewed and two different ap- proaches to modelling biofuel cells are presented, a detailed physics-based approach, and a data-driven regression model. The current scientific and engineering challenges involved in developing practical bio-fuel cell systems are described, particularly in relation to a fundamental understanding of the reaction environment, the performance and stability requirements, modularity and scala- bility. New materials and methods for the immobilization of enzymes and mediators on electrodes are examined, in relation to performance characteristics and stability. Fuels, mediators and enzymes used (anode and cathode), as well as the cell configurations em- ployed are discussed. New developments in microbial fuel cell technologies are reviewed in the context of fuel sources, electron transfer mechanisms, anode materials and enhanced O2 reduction. Multi-dimensional steady-state and dynamic models of two enzymatic glucose/air fuel cells are presented. Detailed mass and charge balances are combined with a model for the reac- tion mechanism in the electrodes. The models are validated against experimental results. The dynamic performance under different cell voltages is simulated and the evolution of the system is described. Parametric studies are performed to investigate the effect of vari- ous operating conditions. A data-driven model, based on a reduced-basis form of Gaussian process regression, is also presented and tested. The improved computational efficiency of data-driven models makes them better candidates for modelling large complex systems. Contents Abstract . .i Contents . iii List of Tables . ix List of Figures . xi Accompanying Material . xv Author's Declaration . xvii Nomenclature . xix 1 Introduction 1 1.1 The definition of a fuel cell . .1 1.2 Inorganic fuel cells . .3 1.3 Bio-fuel cells . 10 iv Contents 1.3.1 Operating principles of a bio-fuel cell . 11 1.3.2 Applications of bio-fuel cells . 14 1.4 Thesis scope . 16 2 Literature Review 19 2.1 Enzymatic fuel cells . 19 2.1.1 Physical immobilisation of enzymes and mediators . 24 2.1.2 Enzyme immobilisation in polymers . 26 2.1.3 Covalent linking . 33 2.1.4 Nanostructured electrodes . 35 2.1.5 Fuel oxidation . 38 2.2 Microbial fuel cells . 44 2.2.1 Exoelectrogenesis . 44 2.2.2 Electron transport . 46 2.2.3 Biocatalyst source . 48 2.2.4 Anode materials . 51 2.2.5 O2 reduction . 52 Contents v 2.2.6 Reactor design . 53 2.3 Summary and outlook . 61 3 Numerical model of an all biological enzymatic fuel cell 67 3.1 Introduction . 67 3.2 Enzyme kinetics . 68 3.3 Model development . 71 3.3.1 Reaction kinetics . 73 3.3.2 Reactant mass balances . 77 3.3.3 Charge balance . 80 3.3.4 Initial and boundary conditions . 81 3.3.5 Half-cell models . 83 3.4 Results and discussion . 84 3.5 Conclusions . 95 4 Numerical model of Pt-cathode and enzymatic-anode fuel cell 97 4.1 Introduction . 97 4.2 Fuel cell model . 98 vi Contents 4.2.1 Reaction kinetics . 98 4.2.2 Reactant mass balances . 102 4.2.3 Charge balances . 106 4.2.4 Initial and boundary conditions . 107 4.3 Results and discussion . 111 4.4 Conclusions . 117 5 Data-driven model using Gaussian process regression 119 5.1 Introduction . 119 5.2 Model development . 120 5.2.1 General linear regression . 121 5.2.2 Gaussian process regression . 123 5.2.3 Determining the hyperparamters . 124 5.2.4 Predicting a new output . 125 5.2.5 Reduced-basis approach . 127 5.3 Results and discussion . 131 5.4 Conclusion . 134 Contents vii 6 Conclusions 137 Bibliography 141 Appendix: Journal publications 155 List of Tables 1.1 Electrolyte type and operating temperature of some inorganic fuel cells . .3 2.1 Summary of key enzymatic fuel cell developments . 42 2.2 Summary of key microbial fuel cell developments . 59 3.1 Reaction kinetics parameters . 77 3.2 Source terms in mass and charge balances . 79 3.3 Mass and charge balance parameters . 81 4.1 Source terms for mass and charge balances. 103 4.2 The default parameters values used in the simulations. 108 List of Figures 1.1 Schematic of the operating principle of a generic bio-fuel cell . .3 1.2 Schematic of electrode structure . .5 1.3 Typical fuel cell voltage and power variations with current density . 12 2.1 Electron mediation: (a) structural example of a redox metallopolymer hy- drogel (PVP-Osmium complex). (b) method of apoenzyme reconsruction . 23 2.2 Effect of an applied magnetic field on the performance of a biofuel cell . 25 2.3 Enzyme retention on electrode using different immobalisation methods . 28 2.4 GOx activity and fuel cell performance using differen enzyme sources . 29 2.5 Electrical performance of two fuel cells using a biocatalyst and Pt . 30 2.6 Enhancement of electrical performance of a fuel cell using novel biocathode oxygen supply . 31 2.7 Scanning electron microscope images of different GOx/HQS immobalization methods using PPy nanowires . 33 xii List of Figures 2.8 Schematic of a fuel cell employing nano-structured bioelectrocatalytic elec- trodes . 38 2.9 Effect of electrode preparation method on the performance of a microbial fuel cell . 50 2.10 MFC reactor designs: (A) double chamber, (B) single-chamber, (C) single- chamber with cloth-electrode assembly, (D) cassette-electrode. 54 2.11 Microbial fuel cell performance using different carbon electrodes . 57 2.12 Power output of some electrochemical systems . 62 3.1 Schematic representation of the fuel cell showing the reaction mechanism. 72 3.2 (a) Fitted half-cell simulations with experimental results. And transient half-cell response of (b) the cathode at 0 V and (c) the anode at 0.1 V. 85 3.3 Numerical simulations and experimental polarization curve. 86 3.4 Normalized concentrations vs. jcell......................... 87 3.5 Time evolution at short-circuit (Vcell = 0 V) of (a) jcell and enzymatic rates and (b) averaged mole fractions. 88 3.6 Time evolution at Vcell = 0:3 V of (a) jcell and enzymatic rates and (b) averaged mole fractions. 89 3.7 pH variation across the cell (Vcell=0.3 V) compared to steady-state. 90 List of Figures xiii 3.8 Oxidized mole fraction of BOD and mediator, F, in the cathode at Vcell=0.3 V............................................. 91 3.9 Overpotentials in (a) the cathode and (b) the anode at Vcell=0 V. 91 0′ 3.10 Current curves for different mediator potentials (EK ). 92 0′ 3.11 Power curves for different mediator potentials (EK ). 93 3.12 Concentrations of Kred,Dox versus current for different mediator potentials 0′ (EK )........................................... 94 0′ 3.13 Anodic overpotential versus current for different mediator potentials (EK ). 94 4.1 A schematic of the modelled cell. 100 4.2 The pH dependence of enzymatic rate constants. 102 4.3 Simulated and experimentally determined polarization curves. 110 4.4 Enzyme and mediator mole fractions versus cell current density. 110 4.5 Enzyme and mediator mole fractions across the anode at different cell voltages.111 4.6 pH variation across the cell at different cell voltages. 112 4.7 Polarization curves for different initial pH. 113 4.8 (a) Maximum power output and short-circuit current, (b) electrochemical reaction rate for different cell voltages versus initial pH. 113 xiv List of Figures 4.9 Mediator and enzyme mole fractions for different cell voltages versus initial pH............................................ 114 4.10 Cell polarization curves for.