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On the Design of a Reactor for High Temperature Heat Storage by Means of Reversible Chemical Reactions

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On the Design of a Reactor for High Temperature Heat Storage by Means of Reversible Chemical Reactions On the Design of a Reactor for High Temperature Heat Storage by Means of Reversible Chemical Reactions Patrick Schmidt Master of Science Thesis KTH School of Industrial Engineering and Management Energy Technology EGI-2011-117MSC EKV 862 Division of Energy Technology SE-100 44 STOCKHOLM Abstract This work aims on the investigation of factors influencing the discharge characteristics of a heat storage system, which is based on the reversible reaction system of Ca(OH)2 and CaO. As storage, a packed bed reactor with embedded plate heat exchanger for indirect heat transfer is considered. The storage system was studied theoretically by means of finite element analysis of a corresponding mathematical model. Parametric studies were carried out to determine the influence of reactor design and operational mode on storage discharge. Analysis showed that heat and gas transport through the reaction bed as well as the heat capacity rate of the heat transfer fluid affect the discharge characteristics to a great extent. To obtain favourable characteristics in terms of the fraction of energy which can be extracted at rated power, a reaction front perpendicular to the flow direction of the heat transfer fluid has to develop. Such a front arises for small bed dimensions in the main direction of heat transport within the bed and for low heat capacity rates of the heat transfer fluid. Depending on the design parameters, volumetric energy densities of up to 309 kWh/m3 were calculated for a storage system with 10 kW rated power output and a temperature increase of the heat transfer fluid of 100 K. Given these findings, this study is the basis for the dimensioning and design of a pilot scale heat exchanger reactor and will help to evaluate the technical feasibility of thermo-chemical heat storage systems. ii Acknowledgement With these lines I want to express my gratitude to all the people who supported me in the last couple of months. First and foremost I want to thank my advisor Marc Linder. The joy and enthusiasm he has for research was contagious and motivational for me. I appreciate all the effort, time, and ideas he contributed to support my work. Thanks to his patience and guidance my time at DLR was a valuable experience. I also owe Inga Utz a debt of gratitude for her advice and patience with which she has helped setting up and mending the modelling part of this thesis. Also, I would like to thank Victoria Martin for her support at Kungliga Tekniska högskolan in Stockholm. Thanks goes also to the many people that became a part of my life over the last months. You have made sure that I still had a life besides this thesis. For the enjoyable time spent together I am grateful. Finally, I want to thank my family for their unconditional support throughout my life. iii Contents Abstract ii Ackowledgement iii List of Figures vi List of Tables viii Nomenclature ix 1 Introduction 1 1.1 Thesis outline ................................ 2 2 Thermal Energy Storage: State of the Art 3 2.1 Sensible Heat Storage ............................ 3 2.2 Latent Heat Storage ............................. 6 2.3 Chemical Heat Storage ........................... 8 2.3.1 Reversible chemical reactions: thermodynamic considerations 8 2.3.2 Calcium Hydroxide – Calcium Oxide System . 11 2.3.3 Principle of Le Chatelier and Process Control . 13 3 Motivation & Focus 15 4 Plate Heat Exchanger Reactor as Chemical Heat Storage 19 4.1 Simplified Model for Highly Permeable Packed Beds . 19 4.1.1 Governing Equations ........................ 19 4.1.2 Boundary & Initial Conditions . 22 4.1.3 Simulation Results ......................... 24 4.2 Extended Model for Poorly Permeable Beds . 36 4.2.1 Extended System of Governing Equations . 37 4.2.2 Boundary & Initial Conditions . 38 4.2.3 Simulation Results ......................... 38 iv Contents 4.3 Design Suggestion for a Plate Heat Exchanger Reactor . 44 5 Conclusion & Prospects 48 References 50 A Thermophysical Properties of the reactants of the Calcium Hydroxide – Calcium Oxide System 53 A.1 Enthalpy and Entropy of Formation ................... 53 A.2 Molar heat capacity at constant pressure . 54 B Results of Parametric Study 55 v List of Figures 2.1 Schematic of an Andasol-type solar thermal power plant . 4 2.2 Schematic of a proposed storage concept for direct steam generation 5 2.3 Typical T,h-diagram of a pure substance ................. 6 2.4 Plot of the van’t Hoff equation for the reversible reaction system of Ca(OH)2 – CaO ............................... 13 2.5 Principle of heat transformation in the system of Ca(OH)2 – CaO . 14 3.1 Schematic of reactor with direct heat transfer . 16 3.2 Schematic of reactor with indirect heat transfer . 16 3.3 Schematic of a shell and tube heat exchanger reactor . 17 3.4 Heat transfer coefficient and heat transfer area over inner diameter for pipe flow ................................... 17 3.5 Schematic of a plate heat exchanger reactor for energy storage . 18 4.1 Schematic of the implemented geometric model with corresponding boundaries and domains .......................... 23 4.2 Temperature profile of the reaction bed for various bed dimensions at t = 30 min................................... 27 4.3 Conversion profile of the reaction bed for various bed dimensions at t = 30 min................................... 27 4.4 Transferred heat per flow channel over time for various reaction bed dimensions .................................. 28 4.5 Average HTF outlet temperature over time for various reaction bed dimensions .................................. 28 4.6 Averaged conversion over time for various reaction bed dimensions 29 4.7 Temperature profile of the reaction bed for various HTF inlet velocities at t = 60 min .................................. 31 4.8 Conversion profile of the reaction bed for various HTF inlet velocities at t = 60 min .................................. 31 vi List of Figures 4.9 Transferred heat per flow channel over time for various HTF inlet velocities ................................... 32 4.10 Average HTF outlet temperature over time for various HTF inlet velo- cities ..................................... 32 4.11 Averaged conversion over time for various HTF inlet velocities . 33 4.12 Volumetric energy density at rated power as a function of HTF inlet velocity and reaction bed width ...................... 35 4.13 Conversion at rated power as a function of HTF inlet velocity and reaction bed width ............................. 35 4.14 Effective volumetric energy density at rated power as a function of HTF inlet velocity and reaction bed width . 36 4.15 Conversion after 15 min versus bed permeability . 39 4.16 Characteristic temperatures along the boundary of reaction bed and flow channel .................................. 41 4.17 Average HTF outlet temperature over time for countercurrent flow configuration ................................ 42 4.18 Conversion profile across the reaction bed in countercurrent flow at various times ................................. 43 4.19 Temperature profile across the reaction bed in countercurrent flow at various times ................................. 43 4.20 Schematic of a horizontal reaction bed . 44 4.21 Average HTF outlet temperature over time for various design parame- ters of a horizontal reaction bed ...................... 46 4.22 Transferred heat per flow channel over time for various design para- meters of a horizontal reaction bed .................... 47 vii List of Tables 2.1 Selection of reversible reactions proposed for high temperature energy storage ..................................... 11 4.1 Boundary conditions of the simplified model . 25 4.2 Initial conditions of the simplified model . 25 4.3 Reactor key data for various reaction bed dimensions . 30 4.4 Reactor key data for various HTF inlet velocities . 33 4.5 Additional boundary & initial conditions for the extended model . 38 4.6 Key data of a reactor with vertical reaction bed for various design parameters .................................. 45 4.7 Key data of a reactor with horizontal reaction bed for various design parameters .................................. 47 viii Nomenclature Acronyms CSP Concentrating Solar Power DLR Deutsches Zentrum für Luft- und Raumfahrt HEX Heat exchanger HTF Heat transfer fluid NIST National Insitute of Standards and Technology PCM Phase change material SEGS Solar Energy Generating System Latin Letters DrG Change in Gibbs free energy of reaction [J/mol] Dr H Enthalpy of reaction [J/mol] DrS Entropy of reaction [J/(mol · K)] q˙ Heat flux [W/m2] cp Specific heat capacity at constant pressure [J/(kg · K)] d Diameter [m] E Energy content [kWh] h Height [m] h Specific enthalpy [J/kg] K Equilibrium constant [-] K Permeability [m2] ix Nomenclature k Reaction rate constant [1/s] M Molar mass [kg/mol] m Mass [kg] n Number [-] Nu Nusselt number [-] p Pressure [Pa] pv Volumetric power density [kW/m3] Pr Prandtl number [-] Q Heat [J] R Gas constant [J/(mol · K)] r Reaction rate [mol/(m3 · s)] Rth Thermal resistance [K/W] Re Reynolds number [-] s Thickness [m] W 3 SQ˙ Heat source/sink [ /m ] Sm Mass source/sink [kg/(m3 · s)] T Temperature [K] t Time [s] U Overall heat transfer coefficient [W/(m2 · K)] ug Velocity of gaseous phase [m/s] uv Volumetric energy density [kWh/m3] V Volume [m3] v Velocity [m/s] x Nomenclature w Width [m] X Conversion [-] Greek Letters a Heat transfer coefficient [W/(m2 · K)] # Porosity [-] h Dynamic viscosity [kg/(m · s)] l Thermal conductivity [W/(m · K)] n Stoichiometric coeffient [-] r Density [kg/m3] Subscripts 95% Conversion of 95% bed Reaction bed eff Effective eq Equilibrium fc Flow channel g Gaseous phase H Hydration h Hydraulic ht Heat transfer HTF Heat transfer fluid in Inlet init Initial m Mean xi Nomenclature out Outlet p Particle pc Phase change r Reaction, reactant rp Rated power s Solid phase y y-direction in coordinate system Superscripts q Standard condition xii CHAPTER 1 Introduction Economic growth and the quality of life in the developed world depend critically on reliable, affordable energy. It drives industrial production and the information economy. Access to it is also vital for lifting people out of poverty.
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