MULTI-SCALE, MULTI PHYSICS MODELING OF THERMO-CHEMICAL IRON/IRON OXIDE CYCLE FOR FUEL PRODUCTION
By
ABHISHEK KUMAR SINGH
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2013
1
© 2013 Abhishek Kumar Singh
2
To my parents and my brother
3 ACKNOWLEDGEMENTS
First and foremost I would like to thank my family for always encouraging me to pursue knowledge, while being a constant support system during my successes and failures. I would like to thank Dr. Joerg Petrasch for guiding me throughout the course of my research by imparting his valuable knowledge and experience and Dr. James
Klausner for providing me with all the necessary inputs and resources needed to conduct my research efficiently. I also like to thank Dr. Renwei Mei for his contribution in my research. I would like to express my gratitude towards Dr. David Hahn and Dr.
Helena Weaver for being on my committee.
I would also take the opportunity to acknowledge the efforts of Like Li, Amay
Berde, Fotouh Al. Raqoum , Nima Rahamatani and Nick AuYeung for their contribution in my research in the form of experimental results and creative inputs. Lastly, special thanks to my lab mates at the Energy Park, especially Anupam Akolker and Midori
Takagi for making the last four years a memorial experience
4 TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS ...... 4
LIST OF TABLES ...... 8
LIST OF FIGURES ...... 9
NOMENCLATURE ...... 15
ABSTRACT ...... 16
CHAPTER
1 INTRODUCTION ...... 18
2 SYSTEM MODEL FOR A HYDROGEN PRODUCTION PLANT ...... 24
2.1 Hydrogen Production Process Overview ...... 24 2.2 Mathematical Model ...... 26 2.3 Syngas Production from the Gasifier ...... 28 2.4 Results and Discussion ...... 29 2.4.1 Energy Balance of the System ...... 29 2.4.2 System Layout ...... 30 2.5 Comparison of the Hydrogen Production Plants Using Iron/Iron Oxide Looping Cycle and the Conventional Process ...... 32 2.5.1 Plant Configuration ...... 34 2.5.2 Efficiency Comparison ...... 35 2.6 Summary ...... 36
3 THERMODYNAMIC ANALYSIS OF THE IRON/IRON OXIDE CYCLE ...... 47
3.1 Iron/Iron Oxide Looping Cycle Overview ...... 47 3.2 Mathematical Model ...... 49 3.3 Results and Discussion ...... 49 3.3.1 Hydrogen Production Step ...... 49 3.3.1.1 Closed system analysis ...... 49 3.3.1.2 Open system analysis ...... 49 3.3.2 Reduction Step ...... 50 3.3.2.1 Closed system ...... 50 3.3.2.2 Open system ...... 51 3.3.3 Effect of Iron Carbide Formation on Hydrogen Production ...... 51 3.3.4 Sulphur Present in Syngas ...... 52 3.3.5 Cyclic Operation of the Reactor ...... 53 3.3.6 Sulphur Laden Syngas ...... 53 3.4 Summary ...... 54
5 4 EXPERIMENTAL VALIDATION OF THE THERMODYNAMIC MODEL ...... 69
4.1 Thermodynamic Model Validation ...... 69 4.2 Mathematical Model ...... 69 4.3 Results and Discussion ...... 70 4.3.1 Comparison of the Theoretical Limit and the Experimental Hydrogen Production ...... 70 4.3.1.1 Experimental facility ...... 70 4.3.1.2 Description of experiments ...... 72 4.3.1.3 Error analysis ...... 73 4.3.1.4 Comparison results ...... 74 4.3.2 Comparison of the Theoretical Limit and the Experimental Magnetite Reduction Process ...... 77 4.3.2.1 Experimental facility ...... 77 4.3.2.2 Comparison results ...... 78 4.4 Summary ...... 81
5 WINDOWLESS HORIZONTAL CAVITY REACTOR MODELING ...... 98
5.1 Solar Thermochemical Fuel Production ...... 98 5.2 Radiation Model ...... 100 5.3 Radiation in the Porous Media Inside the Absorbers ...... 103 5.4 Convective Heat Transfer ...... 104 5.5 Conductive Heat Transfer ...... 104 5.6 Chemical Reaction Rate ...... 104 5.7 Lattice Boltzmann Simulation inside Absorbers ...... 105 5.8 Process Flow ...... 105 5.9 Results and Discussion ...... 105 5.10 Summary ...... 108
6 RADIATION MODELING ...... 123
6.1 Radiative Heat Transfer in Porous Media ...... 123 6.2 Monte Carlo Ray Tracing Model ...... 124 6.3 Diffusion Approximation ...... 127 6.4 P1- Approximation ...... 127 6.5 Radiative Properties ...... 128 6.6 Comparison of Different Radiation Models ...... 130
7 COUPLED MODEL ...... 132
7.1 Reactive Flows in Porous Media ...... 132 7.2 Mathematical Modeling ...... 133 7.3 Reaction Rate ...... 135 7.4 Numerical Methods ...... 136 7.4.1 Random Walk Transport ...... 136 7.4.2 Conduction ...... 137
6 7.4.3 Fluid Flow ...... 138 7.4.4 Radiation ...... 138 7.5 Results ...... 139 7.5.1 Temperature Effect ...... 139 7.5.2 Inlet Mass Flow ...... 140 7.5.3 Inlet Concentration of Steam ...... 140 7.6 Summary ...... 140
8 CONCLUSION ...... 145
LIST OF REFERENCES ...... 148
BIOGRAPHICAL SKETCH ...... 155
7 LIST OF TABLES
Table Page
2-1 Coal composition (by weight %) ...... 37
2-2 Species considered in the thermodynamic equilibrium model for the coal gasifier ...... 37
2-3 Molar syngas composition (%)...... 38
2-4 Assumptions considered for the study ...... 39
2-5 Comparison of co-production of hydrogen and electricity production plants ...... 40
4-1 WD experiment operating conditions ...... 83
4-2 Uncertainty in steam mass flow rate measurements ...... 83
4-3 Hydrogen yield measurement uncertainty and relative error ...... 84
5-1 Simulation parameters for cavity aspect ratio Lcav, in / Dcav = 0.75, 1.0, and 1.25 for Cases I, II and III...... 109
5-2 Reactor efficiency and various energy losses for different aspect ratios ...... 109
7-1 Operating parameters used in numerical simulation and experiments ...... 141
8 LIST OF FIGURES
Figure Page
1-1 Multiple length scales involved in the iron/iron oxide looping cycle...... 23
2-1 Equilibrium reactor diagram ...... 40
2-2 Conceptual looping plant layout...... 40
2-3 Variation of the gasifier output syngas composition with the increase of oxygen/coal mass ratio...... 41
2-4 Total heat released during the isothermal hydrogen production process for 1 mole of iron...... 41
2-5 Total heat released during the isothermal reduction process using syngas for 1/3 mole of Fe3O4 at 1 bar...... 42
2-6 Energy balance for the complete system...... 42
2-7 Process layout for the 500 to 855 K temperature range...... 43
2-8 Process layout for the 855 to 1025 K temperature range...... 44
2-9 Process layout for the 1025 K to 1080 K temperature range...... 45
2-10 Process layout for the 1080 K to 1200 K temperature range...... 46
2-11 Schematic layout of the conventional hydrogen production plant...... 46
3-1 Closed system thermodynamic equilibrium hydrogen composition for the hydrogen production step (stoichiometric conditions)...... 55
3-2 Closed system solid mole fractions for the hydrogen production step (stoichiometric conditions)...... 55
3-3 Open system hydrogen yield per mole of Fe as a function of temperature for different amounts of steam employed...... 56
3-4 Open system equilibrium solid mole fractions for the hydrogen generation step after passing stoichiometric amount of steam...... 56
3-5 Open system equilibrium solid mole fractions for the hydrogen generation step after passing 2 times stoichiometric amount of steam...... 57
3-6 Open system equilibrium solid mole fractions for the hydrogen generation step after passing 4 times stoichiometric amount of steam...... 57
9 3-7 Closed system thermodynamic equilibrium Fe yield (bold lines) and solid carbon content (thin lines) for the iron oxide reduction step using syngas (stoichiometric conditions). The pressure is the parameter...... 58
3-8 Closed system thermodynamic equilibrium iron/iron oxide composition for reduction by syngas at 1 bar (stoichiometric conditions)...... 58
3-9 Closed system thermodynamic equilibrium composition of the gas phase for the iron oxide reduction step using syngas at 1 bar...... 59
3-10 Open system solid phase composition for reduction of magnetite by syngas at 1 bar after passing stoichiometric amount of syngas...... 59
3-11 Open system solid phase composition for reduction of magnetite by syngas at 1 bar after passing 2 times the stoichiometric amount of syngas...... 60
3-12 Open system solid phase composition for reduction of magnetite by syngas at 1 bar after passing 4 times the stoichiometric amount of syngas...... 60
3-13 Open system gas phase composition for reduction of magnetite by syngas at 1 bar and stoichiometric conditions...... 61
3-14 Open system gas phase composition for reduction of magnetite by syngas at 1 bar and 2 times the stoichiometric amount of syngas...... 61
3-15 Open system gas phase composition for reduction of magnetite by syngas at 1 bar and 4 times the stoichiometric amount of syngas...... 62
3-16 Average open system gas phase composition for steam oxidation after passing stoichiometric amount of steam...... 62
3-17 Average open system gas phase composition for steam oxidation after passing 2 times stoichiometric amount of steam...... 63
3-18 Average open system gas phase composition for steam oxidation after passing 4 times stoichiometric amount of steam...... 63
3-19 Open system solid phase composition for steam oxidation after passing stoichiometric amount of steam...... 64
3-20 Average open system gas phase composition for steam oxidation after passing 2 times stoichiometric amount of steam...... 64
3-21 Average open system gas phase composition for steam oxidation after passing 4 times stoichiometric amount of steam...... 65
3-22 Open system solid phase composition for the reduction step at 1 bar pressure and stoichiometric ratio...... 65
10 3-23 Open system solid phase composition for the reduction step at 1 bar pressure and two times stoichiometric ratio...... 66
3-24 Open system solid phase composition for the reduction step at 1 bar pressure and four times stoichiometric ratio...... 66
3-25 Open system Iron yield as a function of temperature for varying number of cycles...... 67
3-26 Open system hydrogen production for 100 cycles at 1 bar and stoichiometric conditions...... 67
3-27 Open system FeS composition for 100 cyclic operations at 1 bar and stoichiometric condition...... 68
4-1 Pictorial view of hydrogen production experimental facility.(Photo courtesy of Fotouh Al Raqom.) ...... 84
4-2 Flow diagram of hydrogen production experimental facility...... 85
4-3 Schematic depiction of electrical furnace and tubular reactor...... 85
4-4 Iron and silica powder size distributions by weight...... 86
4-5 The open system hydrogen production at 660 oC for flow rates of 0.9, 1.9, and 3.5 g/min...... 86
4-6 The open system hydrogen production at 960 oC for flow rates of 0.9, 1.9, and 3.5 g/min...... 87
4-7 The open system solid molar composition for the hydrogen production step in a fluidized bed at 660 oC...... 87
4-8 The open system solid molar composition for the hydrogen production step in a fluidized bed at 960 oC...... 88
4-9 The open system solid molar composition for the hydrogen production step in a stationary bed reactor at 660 oC...... 88
4-10 The open system solid molar composition for the hydrogen production step in a stationary bed reactor at 960 oC...... 89
4-11 The open system final solid molar composition for the hydrogen production step in a stationary bed reactor at 660 oC...... 89
4-12 The open system final solid molar composition for the hydrogen production step in a stationary bed reactor at 960 oC...... 90
11 4-13 The open system solid molar composition for the hydrogen production step in a semi-batch fluidized bed reactor at 660 oC...... 90
4-14 The open system solid molar composition for the hydrogen production step in a semi-batch fluidized bed reactor at 960 oC...... 91
4-15 Predicted total mass of the solid phase for hydrogen production step at 660 oC...... 91
4-16 Predicted total mass of the solid phase for hydrogen production step at 960 oC...... 92
4-17 Schematic layout of the magnetite reduction process experimental facility...... 92
4-18 The open system oxygen extraction in the reduction process at 900 oC for flow rates of 0.5, 0.25, and 0.1 slpm...... 93
4-19 The open system oxygen extraction in the reduction process at 1000 oC for flow rates of 0.5, 0.25, and 0.1 slpm...... 93
4-20 The open system solid molar composition for the reduction process in a stationary bed at 900 oC...... 94
4-21 The open system solid molar composition for the reduction process in a stationary bed at 1000 oC...... 94
4-22 The open system solid molar composition along the discretized length of the stationary bed for the reduction process at 900 oC...... 95
4-23 The open system solid molar composition along the discretized length of the stationary bed for the reduction process at 1000 oC...... 95
4-24 The open system solid molar composition for the reduction process in a fluidized bed at 900 oC...... 96
4-25 The open system solid molar composition for the reduction process in a fluidized bed at 1000 oC...... 96
4-26 The open system solid molar composition for the reduction process in a semi-batch fluidized bed reactor at 900 oC...... 97
4-27 The open system solid molar composition for the reduction process in a semi-batch fluidized bed reactor at 1000 oC...... 97
5-1 Schematic layout (front view) of the windowless horizontal cavity reactor...... 110
5-2 Schematic layout (side view) of the windowless horizontal cavity reactor...... 110
12 5-3 Variation of fraction of transferred power from the solar simulator to the aperture with increase in the aperture radius...... 111
5-4 Geometrical configuration of the back plate and the aperture for view factor calculation ...... 111
5-5 Root mean square error between the calculated view factor using analytical solution and the view factor calculated using the radiation model along the radius of the back plate...... 112
5-6 Geometrical configuration of the cylindrical part and the aperture for the view factor calculation...... 112
5-7 Root mean square error between the calculated view factor using analytical solution and the view factor calculated using the radiation model along the length of the cylinder...... 113
5-8 Process flow diagram for the cavity coupled model...... 114
5-9 Steady state temperature contours at the surface of absorber 1 for the aspect ratio of 0.75...... 115
5-10 Steady state temperature contours at the surface of absorber 1 for the aspect ratio of 1.0...... 115
5-11 Steady state temperature contours at the surface of absorber 1 for the aspect ratio of 1.25...... 116
5-12 Steady state heat flux distribution at the surface of absorber 1 for the aspect ratio of 0.75...... 116
5-13 Steady state heat flux distribution at the surface of absorber 1 for the aspect ratio of 1.0...... 117
5-14 Steady state heat flux distribution at the surface of absorber 1 for the aspect ratio of 1.25...... 117
5-15 Steady state temperature contours at the surface of back plate of the cavity for the aspect ratio of 0.75...... 118
5-16 Steady state temperature contours at the surface of back plate of the cavity for the aspect ratio of 1.0...... 118
5-17 Steady state temperature contours at the surface of back plate of the cavity for the aspect ratio of 1.25...... 119
5-18 Steady state temperature contours at the surface of front plate of the cavity for the aspect ratio of 0.75...... 119
13 5-19 Steady state temperature contours at the surface of front plate of the cavity for the aspect ratio of 1.0...... 120
5-20 Steady state temperature contours at the surface of front plate of the cavity for the aspect ratio of 1.25...... 120
5-21 Steady state temperature contours at the surface of cylindrical part of the cavity for the aspect ratio of 0.75...... 121
5-22 Steady state temperature contours at the surface of cylindrical part of the cavity for the aspect ratio of 1.0...... 121
5-23 Steady state temperature contours at the surface of cylindrical part of the cavity for the aspect ratio of 1.25...... 122
6-1 Schematic layout of the porous matrix inside the reactor...... 131
6-2 Effect of different radiation models on the temperature profile of the porous medium...... 131
7-1 Model setup ...... 141
7-2 Various modules of the model ...... 142
7-3 Schematic of the reactor ...... 142
7-4 Effect of temperature on the hydrogen production rate...... 143
7-5 Effect of steam input flow rate on the hydrogen production rate...... 143
7-6 Effect of inlet steam molar fraction on the rate of hydrogen production...... 144
14 NOMENCLATURE
A - Surface area of the enclosure
-1 -1 cp - Specific heat capacity (kJ kmol K )
G - Gibbs free energy (kJ)
0 -1 gi - Reference Gibbs function of species i evaluated (kJ kmol )
H - Enthalpy (kJ kmol-1)
m - Mass flow rate (kg s-1)
M - Molar mass (kg kmol-1)
ni - Number of moles for a species i (kmol)
P - Total system pressure (N m-2)
-2 Pref - Reference pressure (N m )
PID - Proportional–integral–derivative
T - Time (s)
R - Universal gas constant (kJ kmol-1K-1)
sLPM - Standard liters per minute
T - Temperature (K)
yi, eq - Mole fraction at equilibrium
yi - Species i mole fraction
mFe - Mass of iron (kg)
mFe,init - Initial mass of iron (kg)
()r - Total hemispherical emittance of the surface at r.
15 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy
MULTI-SCALE, MULTI PHYSICS MODELING OF THERMO-CHEMICAL IRON/IRON OXIDE CYCLE FOR FUEL PRODUCTION
By
Abhishek Kumar Singh
August, 2013
Chair: James F. Klausner Cochair: Jörg Petrasch Major: Mechanical Engineering
Present dissertation focuses on multi-scale, multi-physics modeling of thermochemical iron/iron oxide cycle for hydrogen production. Matlab/Fortran based numerical models are developed to study the thermochemical hydrogen production using iron/iron oxide looping process from the perspective of a system level, a reactor level and finally down to the reactive material itself. For the system scale study, a model is created to develop four different layouts of the overall hydrogen production plant based on the operating temperature ranges. An efficiency based comparison is also performed between a hydrogen production plant using the iron/iron oxide looping cycle and a hydrogen production plant using the conventional process involving a water gas shift reaction and a pressure swing adsorber. For the reactor scale study, an open system, quasi-steady state thermodynamic model is developed and is used to predict the optimum operating conditions for hydrogen production. The validation of the thermodynamic model with the experimental results is carried out for the hydrogen production step and the iron oxide reduction step. A collision based Monte Carlo ray tracing model is developed and coupled to the lattice Boltzmann conduction model to
16 optimize the geometry of the windowless horizontal cavity reactor. Finally, for the reactive material scale analysis, a participating medium Monte Carlo ray tracing code is created for the continuum model involving heat and mass transfer coupled with chemical kinetics to investigate the effect of various parameters (such as operating temperature, input steam flow rate, steam concentration) on hydrogen production.
17 CHAPTER 1 INTRODUCTION
Fuel production using renewable energy resources is essential to fill the growing gap between the worldwide energy demand and the availability of the fossil fuels.
Thermochemical fuel (e.g. hydrogen, Syngas etc.) production using solar energy is a promising route for a sustainable energy solution. Hydrogen produced using solar energy may be a viable, alternative clean fuel. Hydrogen can be produced by splitting water using various reactive metals [1]. In this process, pure hydrogen is produced and solid metal oxides are formed. To reduce these metal oxides, concentrated solar energy is used. Various metal/metal oxide cycles for hydrogen production have been investigated previously [2]. Some cycles using metal oxide pairs such as TiO2/TiOx,
MnO2/MnO, and Co3O4/CoO show less than 1 % of stoichiometric hydrogen yield [2]; hence they are not attractive for practical purposes. Fe3O4/FeO, CeO2/CeO2-x and
ZnO/Zn are considered to be of special interest due to their higher hydrogen yield [3,4].
At 1 bar operating pressure, the thermal reduction temperature of Fe3O4 and ZnO is
2500 K [5] and 2235 K [6] respectively. At high temperatures, reduction of ZnO is difficult because the gaseous products (Zn and O2) need to be quenched to avoid recombination. Furthermore, working at such a high temperature is difficult due to lack of refractory reactor materials, and radiation losses. Operating temperatures of the reduction process can be lowered by reducing the working pressure, which has practical limitations such as leakage, throughput, and slower kinetics [7, 8, 9].
The use of a reducing agent such as Syngas from a coal gasifier can be a stepping stone towards viable solar thermochemical fuel production. A Fe3O4/Fe redox pair is studied in the current work. In contrast to hydrogen production using a water gas
18 shift reaction [10, 11], this cycle does not require gas phase separation of hydrogen and carbon dioxide. Steam is passed over the iron producing hydrogen and iron oxides in the oxidation step. Left over steam can be condensed from the output gases of the oxidation step, producing high purity hydrogen. Syngas is then used to reduce the iron oxides to iron. The gaseous product of the reduction process is CO2, which may be sequestrated or used as a commodity.
In the current proposal, multiple length scales involved in the iron/iron oxide looping cycle are studied (Figure 1-1). On the system scale (Chapter 2), a model of the overall hydrogen production plant is developed. On the reactor scale (Chapter 3, 4, and
5), an open system- quasi steady state thermodynamic model is used to predict the optimum operating conditions for hydrogen production at the reactor level. Furthermore, a collision based Monte Carlo ray tracing model is developed to optimize the geometry of the cavity reactor. Finally, on the reactive material scale, a continuum model involving heat and mass transfer coupled with chemical kinetics is developed to investigate the effect of various parameters (such as operating temperature, input steam flow rate, steam concentration) on the hydrogen production.
In Chapter 2- system model for a hydrogen production plant, a system model for the hydrogen production plant is developed. An open system, quasi-steady state thermodynamic model is formulated for the hydrogen production and the iron oxide reduction process. The energy balance of the hydrogen production step and the iron oxide reduction step is carried out to assess the energy requirement of the overall looping process. The heat content of Syngas from a gasifier is used to obtain the required operational temperature of the reactor. Three plant layouts are developed
19 according to the temperature range since the energy balance of the looping process changes depending on the operating temperature. An efficiency based comparison is performed between a hydrogen production plant using the iron/iron oxide looping cycle and a hydrogen production plant using the conventional process involving a water gas shift reaction and a pressure swing adsorber.
In Chapter 3 – thermodynamic analysis of the iron/iron oxide cycle, the open system quasi-steady state thermodynamic model developed in Chapter 1 is used for the thermodynamic analysis of the iron/iron oxide looping cycle. Favorable operating conditions for hydrogen production are identified. Operating conditions to avoid coking and iron carbide formation are determined. The effect of iron carbide formation on the hydrogen production step is investigated. The effect of Sulphur, in the form of H2S and
COS, contained in the Syngas on the looping process is also studied. Hydrogen production for 100 cycles is predicted using the thermodynamic model. The effect of
Sulphur in the Syngas over the 100 looping cycle is also studied.
In Chapter 4 – the thermodynamic model developed in Chapter 1 is validated with experimental results. A comparison of the thermodynamic limit and the experimental results is carried out for the hydrogen production step using a fluidized bed reactor. With increasing residence time, the experimental results approach the thermodynamic limit. A comparison of the thermodynamic results of iron oxide (Fe3O4) reduction using CO in a stationary bed and the experimental results is carried out. A thermodynamic comparison of a stationary bed reactor, a fluidized bed reactor, and a semi-batch fluidized bed reactor is also performed for both hydrogen production step and iron oxide reduction step.
20 In Chapter 5- windowless horizontal cavity rector modeling, a FORTRAN based model for the radiative transfer inside the cavity reactor is developed. The cavity reactor consists of a closed horizontal cylinder (cavity) with an opening (aperture) and a number of horizontal tubular absorbers at the periphery of the cavity. A cell based Monte Carlo model (Vegas) [12] is used to optimize the aperture diameter. Two separate models are used to trace the rays from the solar simulator until they either get absorbed inside the cavity or leave the cavity through the aperture. The Vegas Monte Carlo ray tracing code
[12] is used to trace the rays originating from the solar simulator to the aperture of the cavity reactor. Similarly, a dedicated collision based Monte Carlo ray tracing (MCRT) model [13] is used to trace the rays from the aperture of the cavity reactor until they either get absorbed inside the cavity or leave the cavity through the aperture. Significant re-emission occurs at higher temperatures. Re-emission from the cavity surface and the absorber surface is also accounted for. A lattice Boltzmann conduction code [14] is used for the conduction modeling in the absorbers and also inside the cavity walls. A zero-order Arrhenius-type rate law is used to account for the heat consumption due to endothermic reaction inside the absorber. The MCRT model and the lattice Boltzmann model are coupled together to obtain the steady state temperature profile and the heat flux distribution in the absorbers and at the surface of the cavity. A parametric study using the coupled model is performed to obtain the optimized geometry of the cavity reactor.
Chapter 6- radiation modeling provides details of the radiation modeling in the porous medium of the redox reactor. A participating medium Monte Carlo ray tracing
21 (MCRT) method [13] is employed to trace the rays inside the porous medium of the reactor. Emission from the reacting gas inside the reactor is negligible due to the short length-scales of the porous structure. Anisotropic scattering is taken in account for the radiation modeling. Due to comparatively large particle size (around 100 micrometer) of the porous medium, geometric optics [13] is used to determine the extinction coefficient of the participating medium. MCRT is more accurate as compared to other radiation models but it is also computationally more expensive. Due to the large optical thickness of the medium a simpler radiation model, the diffusion approximation is then used. The diffusion approximation provides strongly temperature dependent radiative conductivity, reducing the radiation problem to a steady state diffusion problem [13]. The diffusion approximation is not accurate near the boundaries. So the more accurate P1- approximation is used. It further reduces the computational time as compared to that of
MCRT at the same time, increases the accuracy compared to that of diffusion approximation. The P1- approximation is a first order accurate spherical harmonic method [13]. Each of these models is used individually with the finite volume conduction model and the random walk transport-of-the-species model.
In Chapter 7- coupled model, the participating medium radiation model (see chp.
6) is integrated with the finite volume conduction model and the random walk transport of species model. This coupled model is then utilized to obtain temperature, velocity and composition of species inside the porous structure. The coupled model is validated against experiments at certain operating conditions of the lab scale reactor.
22
Figure 1-1. Multiple length scales involved in the iron/iron oxide looping cycle.
23 CHAPTER 2 SYSTEM MODEL FOR A HYDROGEN PRODUCTION PLANT1
2.1 Hydrogen Production Process Overview
The solar thermochemical production of hydrogen using metal/metal oxide looping processes has yet to be demonstrated on an industrial scale. Looping processes using natural gas [10, 11, 15, 16] or coal derived Syngas as the reducing agent constitute an important stepping-stone towards solar thermochemical hydrogen production. The current Chapter focuses on the overall looping process using iron/iron oxides [17]. This process may be advantageous compared to conventional coal gasification and subsequent water gas shift [10, 11] due to its potential to deliver highly pure hydrogen without gas-phase separation: Metallic iron is oxidized by steam, producing hydrogen and iron oxides. Coal derived Syngas is then passed through the oxides, reducing them back to iron. Since the gaseous products of the oxidation reaction consist of hydrogen and steam only, the process can generate highly pure hydrogen. An additional benefit is gained from the reduction step where highly concentrated CO2, suitable for sequestration, is produced. In contrast to hydrogen production via the steam-iron process [17, 18-26] that employs two separate reactors for hydrogen production and iron oxide reduction [27], the suggested process uses the same reactor for both reactions thus avoiding the transport of solids between reactors.
The solid reactants remain in the reactor while streams of steam and Syngas are swapped between reactors.
1 Material from this Chapter has been published in - Singh A, Al-Raqom F, Klausner J, Petrasch J. Production of hydrogen via an Iron/Iron oxide looping cycle: Thermodynamic modeling and experimental validation. International Journal of hydrogen energy 2012;37: 7442- 7450. - Singh A, Al-Raqom F, Klausner J, and Petrasch J. Hydrogen production via the iron/iron oxide looping cycle. Proceedings of ASME 2011 5th International Conference on Energy Sustainability & 9th Fuel Cell Science, Engineering and Technology Conference ESFuelCell;2011.
24 An open system thermodynamic equilibrium model, in which reactant gases are constantly added to and product gases are constantly removed from the reactor, is implemented to simulate the behavior of the looping reactors. Based on the open system thermodynamic equilibrium model, a plant model is implemented and used to integrate the high temperature Syngas feed stream into the system. Process configurations for four distinct temperature ranges, (i) 500-855 K, (ii) 855-1025 K, (iii)
1025-1080, and (iv) 1080-1200 K have been developed.
The ideal two-step iron based looping process for the production of hydrogen consists of the hydrogen production step [1]:
Fe + 4/3 H2O 1/3 Fe3O4 + 4/3 H2 , (2-1)
h=-31.75 kJ/mol at 960 C, followed by the reduction step:
1/3 Fe3O4 + 2/3 CO +2/3 H2 Fe + 2/3 CO2 + 2/3 H2O, (2-2)
h=+1.25 kJ/mol at 960 C.
High purity hydrogen and magnetite are produced during the first step. During the second step, magnetite is reduced back to iron using Syngas as the reducing agent. In the ideal process hydrogen is completely consumed in the reduction reaction. However, in real processes, significant fractions of the hydrogen will not react. The hydrogen and
CO2 in the off-gases of the reduction step may be separated via conventional techniques, such as pressure swing absorption (PSA) [28] leading to lower purity hydrogen.
Hydrogen production and the electricity generation efficiencies of a hydrogen production plant using iron/iron oxide looping cycle are also calculated.
25 2.2 Mathematical Model
An open system equilibrium model (Figure 2-1) for a single looping reactor is implemented. Small amounts of steam are incrementally added to the system and the ensuing equilibrium reactant gas mixture is removed from the system while solid material remains within the system. Assuming constant temperature and pressure and ideal gas behavior, the species balance for a gaseous component follows:
dyi, gas n yi,,,, gas in y i gas eqnn gas,,, solid T P dt (2-3) yi,,, solid y i solid eqnn gas,,, solid T p
Species considered in the thermodynamic reactor models are H2, H2O, CH4, C,
CO, CO2, Fe, FeO, Fe3O4, Fe2O3, FeCO3, O2, and Fe3C. In the oxidation step, formation of iron oxides due to reaction of steam with iron occurs at the surface of the iron particle. The solids are taken in the same phase in the oxidation step. In the reduction step, solid carbon is formed due to reaction between CO and CO2 (Boudouard reaction).
For the Gibbs free energy calculation carbon is taken in a separate elemental phase.
Other solids formed in the reduction step are considered in a separate solid phase.
Gases are considered in the same phase in the oxidation and the reduction steps.
Equilibrium compositions for the open system oxidation/reduction process are calculated using Gibbs free energy minimization,
For the oxidation step yi,/, gas solid eqn gas, n solid ,, T p argmin( G n gas , n solid ,,) T p (2-4) nngas, solid Where ngas n1, gas, n 2, gas ,..., n n , gas nsolid n1, solid, n 2, solid ,..., n m , solid (2-5)
ni, gas ni, solid yyi,, gasnn, i solid nn ii11i,, gas i solid
26 The Gibbs free energy is calculated assuming two separate phases in close contact, namely a mixture of ideal gases, and a perfectly mixed incompressible solid.
n m G G G (2-6) i1 i,gas i1 i,solid
0 G n g n RT ln( y P/P ) i,gas i i i i ref (2-7) G n g 0 n RT ln y i,solid i i i i
For the reduction step
yi,/, gas solid eqn gas, n solid , n element ,, T p argmin G ( n gas , n solid , n element ,,) T P (2-8) ngas,, n solid n element
Where
ngas n1, gas, n 2, gas ,..., n n , gas nsolid n1, solid, n 2, solid ,..., n m , solid (2-9) nelement n1, element, n 2, element ,..., n m , element
ni, gas nni,, solid i element yi,,, gasnn,, y i solid y i element n n n n i11i,,, gas i i solid i 1 i element
The Gibbs free energy is calculated assuming two separate phases in close contact, namely a mixture of ideal gases, and a perfectly mixed incompressible solid.
n m m GGGG (2-10) i1i,,, gas i 1 i solid i 1 i element
0 Gi, gas n i gi n i RT ln( y i P / P ref ) 0 Gi, solid n i g i n i RT ln y i (2-11) 0 Gi, element n i g i n i RT ln y i
The number of moles of all species, ni,gas and ni,solid is constrained such that the elemental balance of the total system is satisfied.
nn M n M n ii11i,,,,, gas i gas i gas i gas initial
27 nn M n M n ii11i,,,,, solid i solid i solid i solid initial (2-12)
nn M n M n ii11i,,,,, element i element i element i element initial
Reference values for enthalpy, entropy, and the temperature dependent specific heat, cp, have been obtained from the HSC 7.0 database [29].
A steady state model, programmed in Matlab [30], has been developed for the conceptual looping plant layout shown in Figure 2.2; the model features open system chemical equilibrium analysis, heat and mass balance on the reactors, and heat and mass balance on the heat exchangers. The model is used to predict reactor yields and identify the amount of reactant gases necessary to achieve satisfactory conversion.
Analyses have been carried out for the temperature range between 500 K and 1200 K, at an operating pressure of 1 bar. The model is also used to obtain the syngas production from a gasifier operating at 1673 K temperature and 40 bar pressure.
2.3 Syngas Production from the Gasifier
Coal gasification consists of a number of reactions. Main reactions in the gasification process are given below:
(2-13) C(s) + H2 O CO + H 2 h 298K +131 kJ/mol
C(s) + CO 2 2CO h 298K +172 kJ/mol (2-14) 1 C(s) + O2 CO h 298K -111 kJ/mol (2-15) 2 1 CO + O CO h -283 kJ/mol (2-16) 2 22 298K 1 (2-17) H + O H O h -242 kJ/mol 22 2 2 298K (2-18) CO + H2 O CO 2 + H 2 h 298K -41 kJ/mol The ultimate analysis of the considered coal is given in Table 2-1 [31]. The gasifier is fed with slurry of water to solid mass ratio 0.5 [31]. Pure oxygen needed for
28 coal gasification is separated from the air in an air separation unit. Separated oxygen is compressed and fed to the gasifier along with the coal slurry.
A thermodynamic equilibrium at 1673K temperature and 40 bar pressure is considered in the gasifier [35]. The open system, quasi-steady state thermodynamic equilibrium model is used to obtain the syngas molar composition in the gasifier. For the gasifier equilibrium analysis 43 different species are considered (Table 2-2) [36].
Input oxygen to coal mass ratio is varied to obtain the maximum CO production
(maximum carbon conversion to CO) at the thermodynamic equilibrium of the gasifier.
Figure 2-3 shows the variation of the gasifier output syngas composition with the oxygen to coal mass ratio. Maximum CO production is obtained at the oxygen to coal mass ratio = 0.3. The syngas composition at oxygen to coal mass ratio = 0.3 is used for the iron oxide reduction process. Table 2-3 shows the composition of the output syngas from the gasifier at 1673 K and 40 bar pressure and oxygen to coal mass ratio = 0.3.
2.4 Results and Discussion
Plants layouts that efficiently integrate Syngas feed streams from conventional gasifiers and maximize hydrogen production are developed.
2.4.1 Energy Balance of the System
In Figure 2-4, the total heat released for 1 mole of iron reacting with various stoichiometric amounts of steam in an open system equilibrium reactor is shown. Steam is injected at the reactor temperature. The reaction is exothermic throughout the temperature range considered.
Figure 2-5 shows the total heat released for 1/3 mole of magnetite reacting with various stoichiometric amounts of Syngas in an open system equilibrium reactor. At
29 lower temperatures, heat is released. At higher temperatures the reaction becomes slightly endothermic. Syngas is injected at the reactor temperature.
In Figure 2-6, the energy necessary to obtain the steam at the input temperature necessary for the hydrogen production step is shown (solid). Below 855 K, it is sufficient to supply saturated steam to the hydrogen production reactor. The exothermic reaction will then heat the fluidized bed to the desired temperature. Above 855 K, steam must be superheated to the reactor input temperature; the exothermic reaction will then further heat the fluidized bed to the desired reaction temperature. The dashed line shows the total amount of energy recovered from the raw Syngas and the exhaust of redox reactors, which includes the evaporation/superheating of water and reheating of cleaned Syngas. Below 855 K, energy recovered is only used for evaporating and superheating of water. Above 855 K Syngas is also used to reheat the cleaned Syngas.
2.4.2 System Layout
An entrained flow gasifier with a typical Syngas temperature of 1673 K is considered as the source of Syngas. The Syngas composition for the system model is taken from Table 2-3. Since the energy released or required in the looping process strongly depends on the process temperatures, four system layouts for four distinct temperature ranges are developed.
Layout 1 (500-855K): Figure 2-7 shows the system layout for operating temperatures between 500 K and 855 K. Raw Syngas at 1673 K and water at ambient conditions enter the system. The excess energy of the hot Syngas is used to generate steam for the hydrogen production step. The hydrogen production step is always exothermic. For the given temperature range, the reduction process is also exothermic.
The energy released in both processes is sufficient to attain the required reaction
30 temperature by autothermal heating. The high pressure syngas is expanded in a syngas expander to obtain work output. The product gases of both the hydrogen production step and the iron oxide reduction step are used to generate excess steam. The produced hydrogen is compressed so that it can be transported. The product gases of the iron oxide reduction process are fed to a combined cycle for power generation.
Layout 2 (855-1025K): Figure 2-8 shows the system layout for temperatures between 855 and 1025 K. The energy content of the Syngas and the heat released in the oxidation step is sufficient to drive the system. Steam at the desired temperature is obtained by using high temperature raw Syngas. Similarly, treated Syngas is reheated to the reduction temperature using the raw Syngas. Thermal energy from the high temperature redox reactor product gases are recovered by generating excess steam.
The output hydrogen is compressed and ready to transport. The product gases from the reduction step are burned in a combined cycle to obtain power output.
Layout 3(1025-1080K): In Figure 2-9, the system layout for temperatures between 1025 K and 1080 K is shown. In this range, the reduction process is slightly endothermic: the energy content of the raw Syngas and the heat released in the oxidation step are insufficient to obtain steam and Syngas at the required reaction temperatures. Therefore, product gases from the oxidation and the reduction reactors are used for steam generation. No excess thermal energy is available in the system for this temperature range.
Layout 4(1080-1200K): In Figure 2-10, the system layout for temperatures between 1080 K and 1200 K is shown. In this range, the reduction process is slightly endothermic: the energy content of the raw Syngas, the heat released in the oxidation
31 step and the energy of product gases from the redox reactors are insufficient to obtain steam and Syngas at the required reaction temperatures. Therefore, some supplementary syngas firing (SF) is used for steam generation.
2.5 Comparison of the Hydrogen Production Plants Using Iron/Iron Oxide Looping Cycle and the Conventional Process
An efficiency based comparison is performed between a hydrogen production plant using the iron/iron oxide looping cycle and a hydrogen production plant using the conventional process involving a water gas shift (WGS) reaction and a pressure swing adsorber (PSA). For the conventional plant, already performed studies [31-34] are used as a basis of comparison.
A schematic layout of the plant using the conventional process is shown in Figure
2-11. The gasifier considered for the comparison produces syngas at 1673K and 40 bar pressure [35]. The raw syngas produced in the gasifier contains H2, H2O, CO, CO2,
CH4, H2S, COS, particulate matter and water soluble contaminants. After gasification the raw syngas produced is exposed to both quenching and a syngas scrubber for the removal of the particulate matter and the water- soluble contaminants (HCN, NH3, and chlorides) [31]. Quenching is a less expensive, more reliable but less efficient process because in this process the temperature of the raw syngas decreases, thereby decreasing the opportunity to generate high pressure steam by using the high thermal energy of the raw syngas [31].After quenching, raw syngas is passed through the WGS reactor in which water reacts with CO of the raw syngas and forms H2 and CO2. During the water gas shift reaction COS also reacts with water and gets converted to H2S. The shifted syngas is then sent for physical absorption in dimethyl ether of polyethylene glycol (Selexol) for sulphur removal [31]. After cleaning, the syngas is passed again
32 through Selexol for CO2 removal. In a hydrogen and electricity co-production plant, after
CO2 removal the clean syngas is sent to PSA for the extraction of hydrogen [31]. The separation efficiency of PSA is considered 75 % [31-34]. The extracted Hydrogen is at high pressure (60 bar and 308 K) and ready to be transported for further use [31].The purge gas output of the PSA is sent to the combined cycle for the power generation
[31]. For the electricity generation only plant, the syngas after removal of CO2 is directly fed to the combined cycle for power generation [31]. The high and intermediate pressure steam generated in the quenching and the water gas shift reactor is also used to generate power by expanding in a steam turbine.
Plant configurations for the hydrogen production using iron/iron oxide looping cycle are developed and optimized by incorporating efficient heat recuperation from the high temperature syngas output of the gasifier and the thermal energy of the oxidation/reduction product gases. The open system thermodynamic equilibrium model described in section 2-2 is used to obtain the output syngas composition. The thermodynamic equilibrium model is also used to estimate the hydrogen production and the iron oxide reduction process. The heat balance is carried out to estimate the energy requirement for the oxidation/reduction process. The combined cycle is used to estimate the power production for both co-production and the electricity generation only plant. A gas turbine is used to expand the HP syngas to generate the power output. Energy consumed in the separation of oxygen from the air and the compression of oxygen for the gasification process is also considered. The required work in the compression of the output hydrogen to 60 bar pressure is also accounted for in the efficiency calculations.
The exhaust CO2 from the power cycle is also compressed to 121 bar and energy
33 consumed for this is also considered in the study. Assumptions considered in the study are given in Table 2-4.
2.5.1 Plant Configuration
Plant configurations developed in section 2.4.2 are used for the iron/iron oxide looping cycle. The redox reactors are assumed to operate isothermally at temperature
1073 K and pressure 1 bar [38] for both the hydrogen and electricity co-production plant and the electricity production only plant. For the oxidation process 1 mole of Fe and the stoichiometric amount of steam is considered. 1/3 mole of Fe3O4 and the stoichiometric amount of syngas is used in the reduction process .The heat balance of the oxidation and the reduction process is carried out to obtain the energy requirement for each process. The temperature of the input steam for the oxidation process and the input syngas for the reduction process is calculated based on the energy released/required for the respective process.
Plant layout described in Figure 2-9 is used for the co-production plant. Oxygen is separated from the air in an air separation unit and then compressed to 48 bar before being delivered to the gasifier. The gasification process is carried out at 1673 K temperature and 40 bar pressure. The raw syngas contains impurities in the form of
H2S, COS and particulates. For the particulate and sulphur removal process raw syngas is required to cool down [37]. The high thermal energy of the raw syngas is used to increase the temperature of the clean syngas before supplying to the reduction reactor.
Exhaust gases from the oxidation reactor and the reduction reactor are used to generate steam for the oxidation process. The thermal energy in the exhaust gases, however, is not enough to raise the temperature of the generated steam to the input steam temperature needed for the oxidation step. The superheated steam from the
34 steam generator is also passed through superheater (SH) that uses the thermal energy of the high temperature raw syngas. The raw syngas is again used to increase the temperature of the clean syngas right after sulphur and particulate removal process.
Raw syngas is then expanded in a syngas expander to obtain the expansion work output. For the removal of sulphur raw syngas is then cleaned by physical absorption in
Selexol in a syngas cleaning unit.
For the co-production plant output gases from the reduction reactor are fed to the combined cycle for the power generation. The hydrogen produced from the oxidation reactor is compressed to 60 bar for further transportation. The output CO2 from the power cycle is also compressed to 121 bar (liquidized) and is ready for the sequestration.
2.5.2 Efficiency Comparison
Efficiency calculations are carried out using below formulations:
m LHV Net electric power (2-19) H22 ,produced H H2 m LHV elec m LHV coal,used coal coal,used coal
Net electric power Net CC power – W O2, sep – W O2, comp – W H2, comp – W CO2, comp W syngas expander (2-20)
Co-production of Hydrogen and electricity plant
Table 2-5 provides efficiencies of co-production plants using iron/iron oxide looping cycle, the conventional process and the FeO/Fe3O4 looping cycle. Efficiencies of the co-production plant using the iron/iron oxide cycle are calculated using Equations 2-
19 and 2-20. The co-production plants, using the conventional process, considered here for comparison purposes, assumed 75 % separation efficiency of PSA. The efficiency values for the co-production plant using the conventional process are taken from previous studies [31-34]. The conventional process plants shows higher hydrogen
35 production efficiency then the currently investigated process plant. In the conventional process plants the total amount of hydrogen in the syngas is increased in the water gas shift reactor before extraction in the PSA. In the current process hydrogen along with
CO in the syngas is used for the reduction of iron oxide and not extracted for the total hydrogen production purpose. Hydrogen output in the current process comes only from the oxidation process which is not enough to bridge the gap between the hydrogen production efficiency of the current and the conventional process. But in the current process the exhaust of reduction process contains higher amount of hydrogen and CO as compared to the purge gas of the conventional process so the electric power generation of the current plant is much higher than the conventional plants.
2.6 Summary
Four system layouts for different temperature ranges have been devised and analyzed. Below 1080 K temperature, all reactions can be driven by sensible heat of the reducing Syngas and heat generated in the exothermic hydrogen production step. CO- firing of Syngas is necessary after 1080 K temperature. Below 1080 K temperature no external energy is needed for looping cycle based hydrogen production but system configurations vary with temperature. As process temperatures increase, heat recovery requirements increase. For the temperature range between 500 K and 855 K, surplus energy is available and for 855 K to 1025 K sufficient energy is available to run the complete process while only recovering heat from the high temperature Syngas supplied to the process. For 1025 K to 1080 K, high temperature gaseous output from the oxidation and the reduction step is used to fulfill the energy need of the system. For
1080 K to 1200 K temperature range some syngas has to burn to obtain the steam at the input oxidation reactor temperature.
36 Efficiency calculations for a co-production of hydrogen and the electricity plant are performed. A comparison of efficiencies of this plant with the corresponding efficiencies of the conventional process plant is performed. Hydrogen production efficiency of the co-production plant using iron/iron oxide looping cycle is 41.2 % which is slightly less than that of the conventional co-production plant. In the conventional plant hydrogen present in the syngas is increases by the WGS reaction and then extracted in the PSA but in the current process hydrogen present in the syngas is not extracted which led to lower hydrogen production efficiency. But the higher amounts of the unreacted hydrogen and CO in the product gases of the reduction step provide 17.4
% electricity production efficiency which is higher than that of the conventional process.
Table 2-1. Coal composition (by weight %) Element Composition C 61.27 H 4.69 O 8.83 N 1.1 S 3.41 Moisture 12 Ash 8.7 LHV (MJ/kg) 24.826
Table 2-2. Species considered in the thermodynamic equilibrium model for the coal gasifier List of species
C(g),CH,CH2,CH3,CH4,C2H2,C2H4,C2H6,C3H8 H,H2,O,O2,CO,CO2,OH,H2O,H2O2,HCO,HO2 N,N2,NCO,NH,NH2,NH3,N2O,NO,NO2,CN,HCN,HCNO S(g),S2(g),SO,SO2,SO3,COS,CS,CS2,HS,H2S C(s),S(s)
37 Table 2-3. Molar syngas composition (%) Species Composition (%)
CO 61.48
CO2 1.5
H2 30.5
H2O 2.4
CH4 0.4
H2S 3.2 COS 0.2
38 Table 2-4. Assumptions considered for the study Assumptions
Gasification process [35] Temperature 1673 K ,Pressure 40 bar Water/coal mass ratio 0.5
Air separation unit [31,35] Power consumption 0.261 kWhel/kg pure O2
O2 purity 95 % vol.
Pressure of O2 separated 1.05 bar
Pressure of O2 to gasifier 48 bar
Temperature of O2 to gasifier 480.4 K Syngas expander (SE)[31] Polytropic efficiency of syngas expander 88 % Syngas cleaning conditions [37] Temperature 313 K , Pressure 25.7 bar Oxidation reactor [38] Temperature 1073 K, Pressure 1 bar, 1 mole Fe and stoichiometric ratio of steam Reduction reactor [38] Temperature 1073 K, Pressure 1 bar,
1/3 mole Fe3O4 and stoichiometric ratio of syngas Combined cycle performance Siemens V94.3 a , Net efficiency (LHV) 57.30 % [31]
H2 compression [35] Single stage compression ratio of H2 compressor, 3.5 Compressor stage isentropic efficiency, 82 % High purity hydrogen output, 303 K and 60 bar pressure
CO2 compression [35] Single stage compression ratio of CO2 compressor, 3.5 Compressor stage isentropic efficiency, 82 %
Liquid CO2 output, 303 K and 121 bar pressure
39 Table 2-5. Comparison of co-production of hydrogen and electricity production plants Process Source (%) (%) H2 elec
Iron/iron oxide cycle Current study 41.2 17.4 Conventional P. Chiesa et al.[31] 50.7 5.7 Conventional Foster Wheeler [32] 43.4 0.0 Conventional Klett et al. [33] 51.9 1.4 Conventional Spath and Amos [34] 45.4 0.7
Figure 2-1. Equilibrium reactor diagram
Figure 2-2. Conceptual looping plant layout
40
Figure 2-3. Variation of the gasifier output syngas composition with the increase of oxygen/coal mass ratio.
Figure 2-4. Total heat released during the isothermal hydrogen production process for 1 mole of iron.
41
Figure 2-5. Total heat released during the isothermal reduction process using syngas for 1/3 mole of Fe3O4 at 1 bar.
Figure 2-6. Energy balance for the complete system.
42
Figure 2-7. Process layout for the 500 to 855 K temperature range.
43
Figure 2-8. Process layout for the 855 to 1025 K temperature range.
44
Figure 2-9. Process layout for the 1025 K to 1080 K temperature range.
45
Figure 2-10. Process layout for the 1080 K to 1200 K temperature range.
Figure 2-11. Schematic layout of the conventional hydrogen production plant.
46
CHAPTER 3 THERMODYNAMIC ANALYSIS OF THE IRON/IRON OXIDE CYCLE2
3.1 Iron/Iron Oxide Looping Cycle Overview
Thermodynamic analysis of various metal/metal oxide cycle has been carried out previously [2]. Roeb et. al [45] conducted a thermodynamic analysis for two-step water splitting with mixed iron oxides including nickel-iron-oxide and zinc-iron-oxide to evaluate the maximum hydrogen production potential of coating materials using
FactSage software [46]. Their analysis showed that maximum hydrogen yield is realized when (i) the reduction temperature is raised to 1300 oC, (ii) the water splitting temperature is lowered below 800 ºC, and (iii) the oxygen partial pressure during reduction is minimized. This is consistent with similar findings by Singh et al. [47]. Roeb et al. have also validated the effect of reduction temperature and oxygen partial pressure in experimental studies. However, they could not experimentally verify the increased hydrogen yield at lower water splitting temperatures of approximately 800 ºC.
They concluded that kinetics play an important role in the oxidation step. Svoboda et al., have carried out a thermodynamic study of the potentials and limitations of iron based chemical looping processes for the production of high purity hydrogen. They studied the
Fe-Fe3O4 system for cyclic hydrogen production in the temperature range of 400-800 K
[18]. In their analysis, they have evaluated the hydrogen yield at equilibrium for the steam oxidation of pure iron to magnetite (Fe3O4). In accordance with Singh et al. and
2 Material from this Chapter has been published in - Singh A, Al-Raqom F, Klausner J, Petrasch J. Production of hydrogen via an Iron/Iron oxide looping cycle: Thermodynamic modeling and experimental validation. International Journal of hydrogen energy 2012; 37: 7442-7450. - Singh A, Al-Raqom F, Klausner J, and Petrasch J. Hydrogen production via the iron/iron oxide looping cycle. Proceedings of ASME 2011 5th International Conference on Energy Sustainability & 9th Fuel Cell Science, Engineering and Technology Conference ESFuelCell; 2011
47 Roeb et al., [45, 47] their theoretical results showed that lower oxidation temperatures are favorable for attaining higher hydrogen yields. They have also indicated that at lower temperatures, the reaction is limited by kinetics.
In the beginning of current Chapter, a closed system analysis of the iron/iron oxide cycle using HSC 7.0 [29] is performed. However, the complete looping process resembles more closely an open system. To evaluate the theoretical potential of the suggested two-step process, an open system incremental thermodynamic equilibrium model has been developed for both the hydrogen production (oxidation) step and the regeneration (reduction) step. The model is used to study the oxidation of iron by steam and reduction of magnetite by Syngas. Reaction conditions that favor hydrogen production and avoid the formation of undesired carbon compounds in the reduction process are determined.
The effect of iron carbide (Fe3C) formation on hydrogen production is also analyzed. The maximum amount of Fe3C formed in the reduction step, is used to determine its effect on the hydrogen production in the oxidation step.
Sulphur is present in the form of H2S and COS in Syngas from coal gasifier. The effect of Sulphur impurities on the looping cycle is analyzed. Iron sulphide (FeS) formed in the reduction process remains stable in the oxidation step thereby reducing the availability of iron for the hydrogen production. Cleaned Syngas is recommended for the reduction process.
Cyclic operation of the looping process is simulated. Quasi-steady operation is reached after approximately 5 cycles provided sulfur is absent from the system.
48 3.2 Mathematical Model
The mathematical model described in Chapter 2 (section 2.2) is used for the iron/iron oxide looping cycle.
3.3 Results and Discussion
3.3.1 Hydrogen Production Step
3.3.1.1 Closed system analysis
In Figure 3-1, the equilibrium hydrogen yield for the stoichiometric reaction
Fe + (4/3) HO2 (1/3)FeO+ 3 4 (4/3) H 2 (3-1) is given as a function of temperature : 90% Steam to hydrogen conversion is attained at
570 K . Thermodynamically, the temperature range between 550 K and 650 K is commendable.
In Figure 3-2, the updated equilibrium compositions of the solid phase for reaction (Equation 3-1) are given. At low temperatures magnetite (Fe3O4) dominates. As temperature increases, ferrous oxide (FeO) is formed. Elemental iron is only present in the equilibrium at temperatures above 1050 K.
3.3.1.2 Open system analysis
The open system equilibrium model is applied to the oxidation of iron by steam (
Equation 3-1). The overall hydrogen yield as a function of temperature, for different total steam amounts reacting with 1 mole of Iron, is shown in Figure 3-3. Hydrogen production increases as the total amount of steam increases; it decreases with increasing temperature. However, chemical kinetics imposes practical limitations at low temperatures. Conversion is independent of pressure. For a stoichiometric amount of steam, 1.2 mole of hydrogen per mole of Fe, i.e., 90% conversion, are attained at 680
K.
49 After passing different amounts of steam through initially pure iron, solid phase compositions are shown in Figures 3-4, 3-5, and 3-6. Fe3O4 formation decreases and
FeO content increases with increase in temperature. While some elemental iron is present at high temperatures for stoichiometric conditions, increased amounts of steam lead to an increase in highly oxidized species.
3.3.2 Reduction Step
3.3.2.1 Closed system
In Figure 3-7, the equilibrium Fe yield for the stoichiometric reaction:
Fe O + 2 CO + 2 H 3Fe + 2CO 2H O 3 4 2 2 2 (3-2) is shown as a function of temperature and pressure. Fe yields are relatively constant at elevated temperatures. For a total pressure of 1 bar the updated Fe yield is approximately 28% for temperatures ranging between 1000 and 1200 K. The extent of coking is significant at low temperatures. Low pressures are advantageous for iron oxide reduction by Synthesis gas because they lead to higher Fe yields, lower optimal temperature and less coking.
The composition of iron and iron oxides in the solid phase as a function of temperature at 1 bar is shown in Figure 3-8. At low temperatures magnetite prevails, elemental iron yield is relatively constant at higher temperatures and ferrous oxide prevails at elevated temperatures.
The composition of the gas phase as a function of temperature at 1 bar is shown in Figure 3-9. At low temperatures, the gas phase consists mainly of methane, water and CO2. The H2O fraction is minimal at approximately 900 K.
50 3.3.2.2 Open system
After passing different amounts of Syngas through initially pure Fe3O4, solid phase compositions are shown in Figures 3-10,3-11, and 3-12. Temperatures above approximately 900 K are favorable since they avoid carbon formation and lead to significant amounts of reduced species (Fe and FeO). Carbon formation occurs at temperatures below 900 K due to the Boudouard reaction. Small amounts of FeCO3 are formed below 450 K. Iron carbide (Fe3C) is formed between 950 K and 1050 K. Open system iron yields increase with the amount of Syngas used. However, as the Syngas amount increases, formation of Fe3C in the temperature range between 950 K and 1100
K also goes up. Around 1050 K the formation of ferrite is maximal.
When the reduced iron contains Fe3C, it may react with steam during the hydrogen production step, leading to CO, CH4, CO2, and H2 in the products. At an operating pressure of 1 bar and under stoichiometric conditions, the 1050 to 1200 K temperature range is favorable for the reduction of magnetite by Syngas.
The open system mean composition of the gas phase as a function of temperature at 1 bar is shown in Figures 3-13, 3-14, and 3-15. At lower temperatures, primarily methane, CO2, and H2O are formed. In the temperature range above 900 K, relatively high amounts of CO2 and H2O are observed.
3.3.3 Effect of Iron Carbide Formation on Hydrogen Production
In the reduction of magnetite by Syngas, iron carbide (Fe3C) is formed. Reactions leading to Fe3C formation [27] are given by:
Fe O +3CO+3H Fe C+2CO +3H O (3-3) 3 4 2 3 2 2
Fe O +6COFe C+5CO (3-4) 3 4 3 2
51 Fe O +CO+5H Fe C+5H O (3-5) 3 4 2 3 2
When steam is passed through the reduced iron containing iron carbide, CO, CO2, and
CH4 are formed along with H2, reducing the hydrogen yield and contaminating the H2 produced. One mole of Fe and a maximum amount of Fe3C formed in the reduction step
(Figure 3-12 at 960 K), are considered in the solid phase for the oxidation step.
In Figure 3-16 the gas phase composition is given for the stoichiometric amount of steam. The hydrogen yield maximal at 840 K. At lower temperatures, CH4 occurs in the product gases. At higher temperatures, CO and CO2 occur in the product gases.
In Figures 3-17 and 3-18, gas phase composition as a function of temperature for
2 times and 4 times of steam employed is shown. Figures 3-19, 3-20, and 3-21 show the solid phase composition as a function of temperatures for various amounts of steam used. At stoichiometric condition relatively large amount of Fe remain unreacted. Lower amounts of carbon and Fe3C form at intermediate temperatures.
3.3.4 Sulphur Present in Syngas
The effect of sulphur, present in the Syngas in the form of H2S and COS on the looping process is assessed. The Syngas composition for the study is taken from Table
2-3.
Reduction step
In Figures 3-22, 3-23, and 3-24, open system solid composition for reduction process using Syngas is given as a function of temperature. Formation of FeS is approximately constant at intermediate and higher temperatures. Formation of FeS increases with the increase in the amount of Syngas supplied.
52 The formation of FeS during the reduction step is significant. Due to the chemical stability of FeS, hydrogen production decreases in the oxidation process. Only treated
Syngas should be used for reduction process to avoid formation of Iron sulfides.
3.3.5 Cyclic Operation of the Reactor
An open system assessment of the looping process for 100 complete cycles is performed. Solid products of the hydrogen production step are used as initial reactants for the reduction process and vice versa. For every step, stoichiometric amounts of steam and Syngas are used. For this arrangement, both reactors are assumed to work at the same temperature and pressure. This eliminates the need for cyclic heating or cooling the reactors and the associated energy losses.
Figure 3-25 shows the Iron remaining in the system after 100 cycles. Steady state is reached after approximately 5 cycles. At 1200 K and steady state, 58 % of the
Iron present is recovered in the metallic form in every cycle. Iron recovery is negligible at lower temperatures.
Figure 3-26 shows the hydrogen production for 100 cycles. Since elemental iron is only partly recovered in the reduction process hydrogen production drops significantly after the first cycle. At lower temperatures there is little H2 production as the reduction process is incomplete. Hydrogen production is maximal around 1000 K. Note that a quasi- steady cyclical operation is reached after approximately 5 cycles.
3.3.6 Sulphur Laden Syngas
Syngas often contains Sulfur in the form of H2S and COS, in which case FeS is formed in the magnetite reduction process. Figure 3-27 shows the formation of FeS over a number of cycles. FeS accumulates in the reduction step and remains stable in
53 the Hydrogen production step. Consequently, removal of H2S and COS from the reducing gases is necessary for stable cyclic operation.
3.4 Summary
Hydrogen production via the iron/iron oxide looping cycle has been studied theoretically. An incremental thermodynamic equilibrium open system model has been developed. The model has been used to predict hydrogen yields, and solid compositions for the oxidation step and off-gas as well as solid composition for the reduction step. The thermodynamic analysis of the iron/iron oxide looping cycle at 1 bar for temperatures between 300 and 1200 K has been performed. Hydrogen production is thermodynamically favored at lower temperature (below 680 K). However, slow chemical kinetics at low temperatures is likely to compel higher temperatures for industrial scale processes. The quality of hydrogen produced depends on the formation of carbon- soot, FeCO3 and Fe3C in the solid phase during the reduction process.
The reduction of Fe3O4 is favored at higher temperatures (above 1050 K). In this temperature range, soot formation is relatively insignificant. As the Syngas amount increases, more Fe3O4 is reduced to Fe, and the production of Fe3C and soot increases.
For the reduction process, temperatures between 1050 and 1200 K are suitable for the reactor operating at 1 bar and at stoichiometric conditions.
The system has been studied for 100 complete redox cycles. Quasi-steady operation with a Hydrogen yield of approximately 0.8 moles of Hydrogen per mole of iron is achieved after approximately 5 cycles. Sulfur must be removed from Syngas to avoid the accumulation of FeS in the solid phase.
54
Figure 3-1. Closed system thermodynamic equilibrium hydrogen composition for the hydrogen production step (stoichiometric conditions).
Figure 3-2. Closed system solid mole fractions for the hydrogen production step (stoichiometric conditions).
55
Figure 3-3. Open system hydrogen yield per mole of Fe as a function of temperature for different amounts of steam employed.
Figure 3-4. Open system equilibrium solid mole fractions for the hydrogen generation step after passing stoichiometric amount of steam.
56
Figure 3-5. Open system equilibrium solid mole fractions for the hydrogen generation step after passing 2 times stoichiometric amount of steam.
Figure 3-6. Open system equilibrium solid mole fractions for the hydrogen generation step after passing 4 times stoichiometric amount of steam.
57
Figure 3-7. Closed system thermodynamic equilibrium Fe yield (bold lines) and solid carbon content (thin lines) for the iron oxide reduction step using syngas (stoichiometric conditions). The pressure is the parameter.
Figure 3-8. Closed system thermodynamic equilibrium iron/iron oxide composition for reduction by syngas at 1 bar (stoichiometric conditions).
58
Figure 3-9. Closed system thermodynamic equilibrium composition of the gas phase for the iron oxide reduction step using syngas at 1 bar.
Figure 3-10. Open system solid phase composition for reduction of magnetite by syngas at 1 bar after passing stoichiometric amount of syngas.
59
Figure 3-11. Open system solid phase composition for reduction of magnetite by syngas at 1 bar after passing 2 times the stoichiometric amount of syngas.
Figure 3-12. Open system solid phase composition for reduction of magnetite by syngas at 1 bar after passing 4 times the stoichiometric amount of syngas.
60
Figure 3-13. Open system gas phase composition for reduction of magnetite by syngas at 1 bar and stoichiometric conditions.
Figure 3-14. Open system gas phase composition for reduction of magnetite by syngas at 1 bar and 2 times the stoichiometric amount of syngas.
61
Figure 3-15. Open system gas phase composition for reduction of magnetite by syngas at 1 bar and 4 times the stoichiometric amount of syngas.
Figure 3-16. Average open system gas phase composition for steam oxidation after passing stoichiometric amount of steam.
62
Figure 3-17. Average open system gas phase composition for steam oxidation after passing 2 times stoichiometric amount of steam.
Figure 3-18. Average open system gas phase composition for steam oxidation after passing 4 times stoichiometric amount of steam.
63
Figure 3-19. Open system solid phase composition for steam oxidation after passing stoichiometric amount of steam.
Figure 3-20. Average open system gas phase composition for steam oxidation after passing 2 times stoichiometric amount of steam.
64
Figure 3-21. Average open system gas phase composition for steam oxidation after passing 4 times stoichiometric amount of steam.
Figure 3-22. Open system solid phase composition for the reduction step at 1 bar pressure and stoichiometric ratio.
65
Figure 3-23. Open system solid phase composition for the reduction step at 1 bar pressure and two times stoichiometric ratio.
Figure 3-24. Open system solid phase composition for the reduction step at 1 bar pressure and four times stoichiometric ratio.
66
Figure 3-25. Open system Iron yield as a function of temperature for varying number of cycles.
Figure 3-26. Open system hydrogen production for 100 cycles at 1 bar and stoichiometric conditions.
67
Figure 3-27. Open system FeS composition for 100 cyclic operations at 1 bar and stoichiometric condition.
68
CHAPTER 4 EXPERIMENTAL VALIDATION OF THE THERMODYNAMIC MODEL3
4.1 Thermodynamic Model Validation
In the current Chapter, the incremental thermodynamic equilibrium model described in Chapter 2 is employed to predict the maximum attainable reaction yields.
The model is validated experimentally for the oxidation case using an externally heated tubular fluidized bed reactor. With increasing residence time, the experimental results approach the thermodynamic limit. A comparison of the theoretical hydrogen production limit of a fluidized bed, a stationary bed and a semi-batch fluidized bed reactor is also carried out. The thermodynamic hydrogen production of a stationary bed reactor is higher than that of a fluidized bed reactor and a semi-batch fluidized bed reactor. A validation of the model with experiments is also carried out for the magnetite reduction process using an externally heated tubular stationary bed reactor. In a stationary bed reactor concentration gradient along the bed has major impact over the reduction process. The limit of magnetite reduction is assessed by calculating the extracted oxygen from the stationary bed. The theoretical magnetite reduction limit of the stationary bed reactor is also compared with the theoretical reduction limits of a fluidized bed and a semi-batch reactor.
4.2 Mathematical Model
The mathematical model described in Chapter 2 (section 2.2) is used for the iron/iron oxide cycle.
3 Material from this Chapter has been published in - Singh A, Al-Raqom F, Klausner J, Petrasch J. Production of hydrogen via an Iron/Iron oxide looping cycle: Thermodynamic modeling and experimental validation. International Journal of hydrogen energy 2012; 37: 7442-7450.
69 4.3 Results and Discussion
4.3.1 Comparison of the Theoretical Limit and the Experimental Hydrogen Production
A comparison between theoretical model and the experimental results is carried out for the hydrogen production step. Experiments are carried out at University of
Florida by Al-Raqom et al. [49].
4.3.1.1 Experimental facility
A bench scale experimental facility featuring a 21 mm inner diameter tubular fluidized bed reactor for the iron/iron-oxide hydrogen production looping process has been fabricated. A pictorial view of the hydrogen production experimental facility is shown in Figure 4-1 and a corresponding flow diagram is shown in Figure 4-2. The facility includes a 21 mm inner diameter, 0.6 m long fused quartz tube. Fused quartz is a non-crystalline form of silica with a melting point of 1665 °C [50]. To prevent powder carry-over, a 20 m pore size stainless steel frit is inserted at the top of the tube as depicted in reactor diagram (Figure 4-3). The powder is placed on a distributor made of a Cotronics ceramic blanket thermal insulation material that can withstand a temperature up to 1650 °C [51].
The tube ends are sealed with stainless steel fittings using silicon O-rings that can withstand temperatures up to 300 oC. The quartz tube reactor extends through an
MTI electric furnace. The furnace has a continuous operational range of 100 to 1100 °C and can operate at 1200 °C for a short time span (less than one hour). The furnace has a heating rate of 10 °C/min. It is equipped with a PID controller and features 30 programmable segments (+/- 1 °C accuracy) [52]. The length of the furnace heating zone is 300 mm with a constant temperature zone length of 80 mm. A K-type
70 thermocouple is placed near the center of the furnace. A steam generator consisting of four 200 W cartridge heaters inside an aluminum chamber is used to generate vapor.
Stainless steel wool and a stainless steel screen are inserted in the aluminum chamber to separate out water droplets and to ensure dry steam discharges the steam generator.
The steam generator is thermally insulated with fiber glass insulation. The rate of steam generation is controlled with a pulse-width modulated signal (PMS) and solid-state relay at a frequency of 2 Hz. A 120 VAC power source provides power to the steam generator. The steam is superheated to about 200 °C by passing it through an Omega
Engineering, 1.37 cm outer diameter (0.25" NPT) 200 W in-line gas heater [53] that is mounted vertically and is capable of heating gas from an inlet temperature of 121 °C up to 540 °C with a maximum gas volumetric flow rate of 0.227 m3/min (8 CFM). Two water cooled condensers are used. One condenser is used to determine the steam mass flow rate based on the volume of condensate collected in a separate steady state measurement prior to the experiment. The other condenser is used to remove excess water from the hydrogen/steam mixture flow discharging the reactor. The condensed water is accumulated in a water trap and the weight of the water accumulated is used to determine the amount of unreacted steam. The volume of the produced hydrogen is determined by visual inspection of water displacement in an inverted graduated cylinder at normal conditions (NTP, 20 °C and 101 kPa). The inverted graduated glass cylinders with 2000 ml capacity are immersed in a water bath.
Stainless-steel sheathed E-type and J-type thermocouples are used to monitor and record the gas temperatures entering and exiting the tube reactor as well as the temperatures of the fittings. A K-type thermocouple is used to monitor the bed
71 temperature. A National Instruments data acquisition board, NI USAB-6225 [54], is used to collect the thermocouple and flow meter voltage signals. A Labview virtual instrument is used to observe, control and collect the experimental data.
4.3.1.2 Description of experiments
Experiments are carried out to evaluate the water dissociation (WD) step in the
Iron/Iron oxide looping cycle. Reactor bed temperatures of 660 and 960 oC and steam mass flow rates of 0.9, 1.9, and 3.5 g/min are considered. Table 4-1 lists the operating conditions for the six WD experiments.
The total duration of the WD experiments ranges between 35 and 50 minutes.
High purity Ancor MH-100 porous iron powder with 99.56% purity manufactured by
Hoeganaes Corporation is used [55].The iron is a porous powder with an average apparent density of 2.5 g/cm3, a material density of 7.87 g/cm3 and a melting point of
1536 °C. Results of the iron powder sieve analysis are shown in Figure 4-4. In each experiment approximately 25 grams of iron powder are used. The powder is mixed with
99.5% pure silica in a 2:1 silica to iron volume ratio to retard sintering. The silica (SIL-
CO-SIL 63, U.S. Silica) sieve analysis is also illustrated in Figure 4-5 [56]. The mixed iron/silica bed is placed on the distributor in the quartz tube, which is then sealed with stainless steel fittings. The quartz tube extends outside the electrical furnace. The bottom portion of the quartz tube is insulated with a ceramic blanket that is held in place with stainless steel bands to prevent steam condensation. A nitrogen flow is passed through the reactor with a volumetric flow rate of 2 sLPM to heat the system to at least
150 °C and to purge the air in the system, thus preventing oxidation of the iron powder.
Using a three-way valve, the steam is either directed to a condenser, which empties into
72 a graduated cylinder, or the steam is directed to the reaction chamber. The mass flow rate of steam is controlled via the heat input to the boiler.
The exact steam mass flow rate is determined by measuring the rate of condensate when steam is directed to the condenser prior to the actual experiment. The electrical furnace temperature is set for the desired reaction temperature and held at the temperature for the duration of the experiment. Once the stainless steel fitting temperatures reach 150 °C and the steam flow rate reaches steady state, the nitrogen is shut off, and the steam is directed into the gas heater section, where it is superheated and then directed to the reactor. Hydrogen and excess steam leave the reactor and pass through a condenser upon initiation of the oxidation reaction. The condensed water is collected in a sealed cylinder (water trap). After the removal of all excess water, pure hydrogen is directed into an inverted water-filled, graduated cylinder. The accumulated amount of hydrogen is determined by visual observation of the water displaced from the graduated cylinders.
4.3.1.3 Error analysis
An error analysis is used to assess the measurement uncertainty. The steam mass flow rate is determined from the rate of the steam condensate accumulation. The measurements are repeated, and the standard deviation () is used as a statistical measure of the absolute error. The measurement uncertainty is taken as . For each operating condition, the steam mass flow rate is measured twice. The standard deviation for the steam mass flow rate error is listed in Table 4-2.
The volumetric hydrogen yield is determined by measuring the displaced water volume in an inverted graduated cylinder. The uncertainty associated with the
73 measurement involves a visual inspection of the water meniscus. The water meniscus reading is affected by the disruption of hydrogen bubbles rising through the inverted cylinder. These disruptions are more frequent at higher rates of reaction. The measurement uncertainty and relative error (error in meniscus reading) are estimated and listed in Table 4-3.
4.3.1.4 Comparison results
The measured hydrogen yields using the fluidized bed of iron particles at different steam flow rates are compared to the theoretical open system incremental equilibrium yield at bed temperatures of 660 and 960 oC. Figures 4-5 and 4-6 show the hydrogen yield as a function of the cumulative steam fed to the reactor for the 660 and
960 oC respective bed temperatures. The abscissa shows the ratio of the cumulative steam mass flowing into the reactor to the stoichiometric steam mass necessary for complete conversion of Fe to Fe3O4,
mt. HO2 (4-1) HO2 M 4 HO2 mFe,initial 3 M Fe
The ordinate shows the ratio of the cumulative hydrogen mass discharging the reactor to the stoichiometric mass of hydrogen that can be produced from complete conversion from Fe to Fe3O4, t m dt H2 (4-2) 0 H2 M 4 H2 mFe,initial 3 M Fe Figure 4-5 shows that hydrogen yield increases with decreasing flow rate
(increasing residence time) and moves toward the thermodynamic limit with increasing cumulative mass of steam entering the reactor.
74 The influence of slow reaction kinetics at lower temperatures is clearly discernible. In Figure 4-6, the hydrogen production rate is observed to be relatively insensitive to the steam flow rate because reaction kinetics are enhanced at higher temperatures. The thermodynamic limit is approached, particularly at high cumulative steam throughput. The cumulative steam throughput is quite important since there is an energy cost for water to steam conversion.
Most of the theoretical steam to hydrogen conversion occurs with small cumulative amounts of steam. This allows for high theoretical energy efficiencies, since little excess steam needs to be produced. However, even at high temperatures, experiments do not match the steep initial rise in cumulative H2 production. The theoretical hydrogen production limit of a stationary bed is higher than that of a fluidized bed. In a stationary bed reaction, completion depends on the concentration of the reactants along the bed. In the oxidation process, fresh steam reacts with the iron particles in the beginning of the stationary bed. The product of this reaction moves along the bed and again reacts with the fresh iron. As a result, utilization of same amount of steam is higher in a stationary bed as compared to the fluidized bed which in turn increases the hydrogen production in a stationary bed. The semi-batch fluidized bed shows less hydrogen production due the closed system nature of this type of reactor.
Figures 4-7 and 4-8 show the variation of the theoretical solid phase composition as a function of the cumulative amount of steam employed for the 660 and 960 oC respective fluidized bed temperatures. At higher temperature (960 oC) relatively more
Fe3O4 and Fe2O3 are formed.
75 Figures 4-9 and 4-10 show the solid molar composition variation with the cumulative steam used for the oxidation process at 660 oC and 960 oC stationary bed temperatures. More Fe2O3 formation occurs in a stationary bed as compared to that in a fluidized bed. No Fe is present at higher cumulative steam amount.
Figure 4-11 and 4-12 show the final solid molar composition in a stationary bed along the bed length. The abscissa shows the ratio of the discretized iron mass to the initial mass of iron, n mi (4-3) i1 l m Fe,initial
Due to the exposer to the fresh steam, more Fe2O3 is formed in the beginning of the stationary bed. A higher amount of Fe3O4 is formed at the end of the bed at both temperatures.
In Figures 4-13 and 4-14, solid molar composition for a semi-batch fluidized bed reactor at 660 oC and 960 oC temperatures is shown. Due to lower reaction completion, some Fe still persists at both temperatures. Formation of Fe3O4 is quite lower in this case as compared to that of a stationary bed and a fluidized bed reactor.
Figures 4-15 and 4-16 show the total solid phase mass normalized by the initial iron mass as a function of the cumulative mass of steam into the reactor for the 660 and
960 oC respective bed temperatures. Both the theoretical limit of solid phase mass and that inferred from experimental hydrogen production data via a gas-phase mass balance are shown. In both Figures, the large symbols at the end of the experimental curves denote the final mass determined via weighing at the end of the experiment. The
76 discrepancy is attributed to the breakdown of Fe-particles swept away during the experiment as well as incomplete extraction of the solid phase after the experiment.
4.3.2 Comparison of the Theoretical Limit and the Experimental Magnetite Reduction Process
A comparison between theoretical model and the experimental results for the magnetite reduction process is performed. Experiments are carried out at University of
Florida by Barde et al.
4.3.2.1 Experimental facility
Figure 4-17 shows the schematic of the experimental set up. It comprises of quartz tube that serves as a reactor. The tube is 45 cm in length and 5.08 cm in diameter with integrated frit that acts as a support for a mixture of magnetite and alumina. The tube can sustain temperatures up to 1200 oC. The tube is supported by gland seals at both ends and silicon O-rings are used for sealing purpose. The O-rings can sustain temperatures up to 250 oC. Radiative ceramic heater serves as the primary heater that can raise the bed temperature up to 1100 oC. Another radiative heater is installed below the primary heater which raises the gas temperature close to the bed temperature. The gas lines are heated using the rope heaters.
The gas line supplies various gases like CO, Ar, and He. Every individual gas line is provided with a gas flow controller. The independent gas lines are united together in a manifold. The combined gas line then connects the manifold to the inlet of the reactor. A pre-heater is installed on the gas line.
During the reduction process, a mixture of CO and CO2 is available at the exit of the reactor. Though the gas of interest is CO2, it is difficult to separate the CO from CO2; thus flow-meter measures flow of mixture and not CO2 alone. The mixture of gases is
77 supplied to a mass-spectrometer, which can register presence of gases independent of each other. A calibration is performed to convert data provided by the mass- spectrometer in the form of the partial pressures to flow rate data.
To measure temperature of the reactor bed, thermocouples are installed which records the temperature at different locations in the bed. That gives temperature distribution in the bed, both axially as well as radially. To register data for different parameters like flow rate, temperature etc. as well as to control the flow controllers on the gas line, LABVIEW is used. The program communicates with DAQ board to control the instruments as well as to register the data.
4.3.2.2 Comparison results
The oxygen extracted from the stationary bed of magnetite particles in the CO reduction process at different CO flow rates is compared to the theoretical open system incremental equilibrium CO2 production limit for a stationary bed. A comparison of the theoretical limit of the magnetite reduction in a stationary bed with that of a fluidized bed and a semi-batch fluidized bed reactor is also carried out.
Figures 4-18 and 4-19 show the cumulative CO2 produced for the cumulative CO used in a stationary bed at 900 oC and 1000 oC temperatures. The abscissa shows the ratio of the cumulative CO mass flowing into the reactor to the stoichiometric CO mass necessary for the complete conversion of Fe3O4 to Fe. mt. CO (4-4) CO M 4 CO m M Fe34 O ,initial Fe34 O
The ordinate shows the cumulative CO2 produced from the magnetite powder to the stoichiometric mass of CO2 that can be generated from the complete conversion of
Fe3O4 to Fe.
78 t m dt CO2 (4-5) 0 CO2 M 4 CO2 m M Fe34 O ,initial Fe34 O
Figure 4-18 shows the cumulative amount of CO2 generated from the magnetite powder stationary bed with various CO input flow rates. The cumulative amount of generated CO2 shows the extent of magnetite reduction to iron or other lower oxidation state iron oxides. At 900 oC experimental results are approaching the theoretical limit for the stationary bed. The CO2 production is insensitive towards the input CO flow rate variation which is due to the effect of high reaction kinetics at 900 oC temperature.
The experimental results at higher flow rates seam to outperform the theoretical limit of the magnetite reduction in a fluidized bed. The magnetite reduction in a semi- batch fluidized bed reactor is comparatively less due to the closed system nature of this type of reactor. In Figure 4-19, no further increase in the CO2 production for the various input CO flow rate at 1000 oC is depicted because theoretical limit is already reached at a lower temperature (900 oC) for the corresponding input CO flow rate.
Figure 4-20 shows the solid molar composition predicted by the thermodynamic model at 900 oC temperature for a stationary bed magnetite reduction process. Iron formation increases with increase of input CO amount. At higher cumulative CO input, amount some coking and Fe3C formation is anticipated which is subjected to verification by performing a XRD analysis of the experimental solid product of the magnetite reduction process. In Figure 4-21, solid molar composition of the magnetite reduction process in a stationary bed using the thermodynamic model at 1000 oC is shown.
Magnetite to Fe conversion is comparatively higher than that of at 900 oC temperature.
79 o Less amount of coking and Fe3C formation is predicted at 1000 C as compared to that at 900 oC temperature.
Figures 4-22 and 4-23 show the final solid molar composition in a stationary bed along the bed length. The abscissa shows the ratio of the discretized magnetite mass to the initial mass of the magnetite.
n mi (4-7) i1 l m Fe 34 O ,initial
In Figure 4-22 the variation of the final solid molar composition along the bed length for a stationary bed is shown. The carbon formation (in the form of coking) occurs in the beginning of the stationary bed. The magnetite reduction is higher in the beginning of the stationary bed because of the interaction of fresh CO with magnetite powder in this part of the bed. After most of the magnetite is reduced to iron or FeO, the chances of carbon formation due to Boudouard reaction increases thereby formation of
C occurs in the beginning of the reactor bed. Fe3C formation is also higher in the beginning of the stationary bed as compared to that at a larger length of the bed. Iron formation is higher at the end of the bed because of less amount of Fe3C formation in that part of the bed. Figure 4-23 shows the final solid molar composition along the
o stationary bed length at 1000 C temperature. Less formation of Fe3C enhances the iron formation at higher temperature.
Figures 4-24 and 4-25 show the solid molar composition in a fluidized bed reactor at 900 and 1000 oC temperatures. At higher temperatures, iron formation is slightly high as compared to that at lower temperature. Smaller amount of Fe3C as compared to the stationary bed case is predicted at both temperatures. No coking
80 formation at these temperatures for a fluidized bed reactor is anticipated. The iron formation is lower than that for a stationary bed which explains the lower oxygen extraction shown in Figures 4-18 and 4-19.
Figures 4-26 and 4-27 show the solid molar composition for a semi-batch fluidized bed reactor at 900 and 1000 oC temperatures. The solid molar compositions are comparable for both the temperature which shows the insensitivity of magnetite reduction towards temperature increase. Due to the closed system nature of this type of reactor, it shows lower iron formation as compared to that of the fluidized bed and the stationary bed reactor.
4.4 Summary
Theoretical predictions have been experimentally validated for the hydrogen production step in a fluidized bed reactor at 660 and 960 C for steam flow rates between 0.9 and 3.5 g/min. As the steam flow rate to the reactor decreases, i.e., as the residence time of steam in the reactor increases, the experimentally observed cumulative steam-to-hydrogen conversion approaches the theoretically predicted values. The initial steep rise of the theoretical yield shows the potential for efficient conversion of steam to hydrogen. However, particularly at low temperatures and during the initial reaction phase, experimental yields remain significantly below the theoretical limit. Increasing the residence time partially alleviates these issues. At higher temperatures, reduction of the flow rate (i.e., increasing the residence time) has only a marginal effect on conversion thereby indicating very slow effective kinetics beyond a certain Hydrogen yield. This is consistent with the ongoing kinetic modeling in which two distinct kinetic regimes, (i) a shrinking sphere regime, and (ii) a diffusion-limited regime,
81 have been identified. Based on this study, it is concluded that the diffusion limited regime proves an obstacle to efficient reactor operation and should be avoided. A combination of measures is suggested to overcome these obstacles: (i) minimize the particle size as far as possible without unacceptable mass losses to maximize the surface to volume ratio, (ii) increase the gas-phase residence time, e.g., via recirculation, and (iii) only partially reduce and oxidize the iron-based reactants to avoid the diffusion-limited regime. The theoretical hydrogen production limit for a stationary bed and a semi-batch fluidized bed reactor is also compared with the theoretical limit of the fluidized bed reactor. Theoretically stationary bed reactor predicted higher hydrogen production as compared to the fluidized bed and the semi-batch reactor. In a stationary bed reactor utilization of the same amount of steam is higher as compared to the other two considered reactor.
The validation of the theoretical model for the magnetite reduction using CO in a stationary bed reactor with the experiments is performed. The input CO flow rates are varied between 0.1 slpm and 0.5 slpm at 900 oC and 1000 oC stationary bed temperatures. A comparison of the cumulative amount of CO2 produced from experiments and the theoretical predictions for a magnetite powder stationary bed reactor is carried out. The CO2 production is insensitive towards the variation in the input CO flow rates at the considered temperatures. The experimental results approaches the theoretical limit at 900 oC temperature and no significant change in the experimental results are depicted at 1000 oC temperature. Theoretical predictions of the solid molar compositions for a stationary bed reactor show the formation of coking and
Fe3C. The formation of these carbon compounds should be verified by performing the
82 XRD analyses of the solid product of the magnetite reduction experiment. A comparison of the theoretical cumulative CO2 generation limit from magnetite powder for a fluidized bed and a semi-batch fluidized bed reactor with the stationary bed is also carried out.
The theoretical limit of magnetite reduction for a stationary bed reactor is higher than that of the fluidized bed reactor and the semi-batch fluidized bed reactor.
Table 4-1. WD experiment operating conditions Experiment Steam mass flow rate Bed T* # (g/min) (°C)
1 3.5 0.2 956 7 2 1.9 0.1 962 7 3 0.9 0.1 950 7 4 3.5 0.2 641 5 5 0.9 0.1 681 5 6 1.9 0.1 693 5
Table 4-2. Uncertainty in steam mass flow rate measurements Steam mass flow rate Uncertainty (g/min) (g/min) 3.5 0.2 1.9 0.1 0.9 0.1
83 Table 4-3. Hydrogen yield measurement uncertainty and relative error T m t Uncertainty H2 Volume Relative H2O error (C) (kg/min) (min) (ml) (ml) (%) 0-15 10 200 5.0 3.5 15-tfinal 5 200 2.5
0-15 5 200 2.5 660 1.9 15-tfinal 1 200 0.5
0-15 5 200 2.5 0.9 15-tfinal 1 200 0.5
0-6 20 200 10.0 3.5 6-20 10 200 5.0 20-tfinal 5 200 2.5
960 0-20 10 200 5.0 1.9 20-tfinal 5 200 2.5
0-20 5 200 2.5 0.9 20-tfinal 1 200 0.5
Figure 4-1. Pictorial view of hydrogen production experimental facility.(Photo courtesy of Fotouh Al Raqom.)
84
Figure 4-2. Flow diagram of hydrogen production experimental facility.
Figure 4-3. Schematic depiction of electrical furnace and tubular reactor.
85 100
90 SiO2SiO2 Fe 80 70 60 50 40
Weight Weight (%) 30 20 10 0 +150/-250 +45/-150 -45
US Standard Sieve (Micron)
Figure 4-4. Iron and silica powder size distributions by weight.
Figure 4-5. The open system hydrogen production at 660 oC for flow rates of 0.9, 1.9, and 3.5 g/min.
86
Figure 4-6. The open system hydrogen production at 960 oC for flow rates of 0.9, 1.9, and 3.5 g/min.
Figure 4-7. The open system solid molar composition for the hydrogen production step in a fluidized bed at 660 oC.
87
Figure 4-8. The open system solid molar composition for the hydrogen production step in a fluidized bed at 960 oC.
Figure 4-9. The open system solid molar composition for the hydrogen production step in a stationary bed reactor at 660 oC.
88
Figure 4-10. The open system solid molar composition for the hydrogen production step in a stationary bed reactor at 960 oC.
Figure 4-11. The open system final solid molar composition for the hydrogen production step in a stationary bed reactor at 660 oC.
89
Figure 4-12. The open system final solid molar composition for the hydrogen production step in a stationary bed reactor at 960 oC.
Figure 4-13. The open system solid molar composition for the hydrogen production step in a semi-batch fluidized bed reactor at 660 oC.
90
Figure 4-14. The open system solid molar composition for the hydrogen production step in a semi-batch fluidized bed reactor at 960 oC.
Figure 4-15. Predicted total mass of the solid phase for hydrogen production step at 660 oC.
91
Figure 4-16. Predicted total mass of the solid phase for hydrogen production step at 960 oC.
Mass Spectrometer
CO + CO2
Thermocouples Reactor
DAQ
Syst Magnetite Heater em
CO
Co
Gas flow ntr
Figure 4-17. Schematic layout of the magnetite reduction process experimental facility.
92
Figure 4-18. The open system oxygen extraction in the reduction process at 900 oC for flow rates of 0.5, 0.25, and 0.1 slpm.
Figure 4-19. The open system oxygen extraction in the reduction process at 1000 oC for flow rates of 0.5, 0.25, and 0.1 slpm.
93
Figure 4-20. The open system solid molar composition for the reduction process in a stationary bed at 900 oC.
Figure 4-21. The open system solid molar composition for the reduction process in a stationary bed at 1000 oC.
94
Figure 4-22. The open system solid molar composition along the discretized length of the stationary bed for the reduction process at 900 oC.
Figure 4-23. The open system solid molar composition along the discretized length of the stationary bed for the reduction process at 1000 oC.
95
Figure 4-24. The open system solid molar composition for the reduction process in a fluidized bed at 900 oC.
Figure 4-25. The open system solid molar composition for the reduction process in a fluidized bed at 1000 oC.
96
Figure 4-26. The open system solid molar composition for the reduction process in a semi-batch fluidized bed reactor at 900 oC.
Figure 4-27. The open system solid molar composition for the reduction process in a semi-batch fluidized bed reactor at 1000 oC.
97
CHAPTER 5 WINDOWLESS HORIZONTAL CAVITY REACTOR MODELING4
5.1 Solar Thermochemical Fuel Production
In Chapters 2, 3, and 4, a thermochemical fuel production using iron/iron oxide cycle is studied. In a solar thermochemical fuel production process, solar energy is used instead of Syngas for the reduction step [57, 58]. The reduction step is highly endothermic, requiring significant energy input at high temperatures [59]. For
Fe3O4/FeO redox pair the reaction equations are given by [60]
Reduction step
o1 Fe3 O 4 3FeO + (1 2)O 2 , H298K 319.5 kJ mol (5-1)
Oxidation step
o1 3FeO + H2 O Fe 3 O 4 + H 2 , H298K 33.6 kJ mol (5-2)
By reducing the operating pressure of the reduction process, the reduction temperature is lowered due to LeChatelier’s principle [60]. For the Fe3O4/FeO redox pair the thermal reduction temperature falls below to 1500 oC at 10-4 bar [61]. Steinfeld et al. [62, 63, 64] used a horizontal cavity reactor with a quartz window for solar thermochemical fuel production. They directly irradiated the reactant particles leading to an efficient energy transfer. The aperture window must be kept clean and cool using constant gas-flows.
4 Material from this Chapter has been published in - Li L, Singh A, AuYeung N, Mei R, Petrasch J, Klausner JF. Lattice Boltzmann simulation of high-diffusivity problems with application to energy transport in a high-temperature solar thermochemical reactor. Proceedings of the ASME 2013 Summer Heat Transfer Conference HT: 2013 (in publication).
- The lattice Boltzmann modeling of the conduction inside the absorber and the cavity walls by Li Like (Li 2013) is greatly appreciated.
98 Furthermore, scaling up the refractory windows is extremely challenging, making windowed reactors undesirable for commercial processes.
In the present work, a windowless horizontal cavity reactor (Figure 5.1) is considered. The windowless horizontal cavity reactor consists of an insulated horizontal cylinder (cavity) with a small opening (aperture) and a number of tubular cylinders
(absorbers) at the circumference of the cavity. The cavity allows multiple reflections of the rays so that the behavior of the cavity closely resembles that of a black body. Due to multiple reflections inside the cavity, the apparent absorptance of the cavity increases as compared to the actual absorptance of the cavity material [65]. The reactants inside the absorber are indirectly heated by the solar radiations. Low pressure inside the absorbers is created using a vacuum pump.
Melchior et.al [66] performed a Monte Carlo ray tracing analysis of a vertical cavity reactor for diffusely/specularly reflecting walls, containing either single tubes or multiple tubes, and a selective window or a windowless aperture. In the vertical cavity reactor, a large fraction of radiation hits the cavity walls leading to low efficiency of the reactor. In the current design, absorbers cover the periphery of the cavity maximizes the fraction of radiation hitting the absorbers. In their work, Melchior et al. did not stimulate the heat transfer inside the absorbers. Rather, they considered the net power absorbed by the reactor as a parameter and calculated the energy transfer efficiency based on the variation of this parameter. In contrast, the current analysis couples the radiation model with a lattice Boltzmann conduction model and the reaction rate of the reduction process.
99 For lab-scale experiments, the University of Florida high flux solar simulator is used as a radiation source. Modeling for radiative transfer from the simulator to the reactor is done using the Vegas Monte Carlo ray tracing code. The aperture diameter is optimized using the Vegas [12]. A collision based Monte Carlo ray tracing (MCRT) model is used to further trace the rays from the aperture of the cavity until they are either absorbed inside the cavity or escape the cavity through the aperture. Re-emission from the cavity surface and absorbers surfaces is also considered. The radiation model is coupled with the lattice Boltzmann model (LBM) [14] to obtain the temperature profile at the absorber/cavity surface. The LBM accounts for conduction inside the porous medium of the absorber and inside the cavity reactor walls. Losses due to re-emission and convection from the cavity surface are also considered while solving for the temperature profile at the cavity surface. A zero-order Arrhenius-type rate law is considered to account for the heat sink term due to the chemical reaction inside the absorber. The MCRT is coupled with the LBM and the heat sink term for the Fe3O4 reduction process is also accounted for. A parametric study is performed to optimize the geometry of the cavity reactor by using the coupled model. The coupled model is used to obtain steady state temperature profile and heat flux at the absorber and the cavity surface. The geometry of the cavity reactor is varied based on the aspect ratio
(Lcavity/Dinner, cavity) for a total solid reactant mass of 10 kg. Thermal efficiency of the cavity reactor is calculated for different aspect ratios. For an aspect ratio of 1.0, maximum thermal efficiency of 21 % is achieved.
5.2 Radiation Model
A schematic layout of the windowless horizontal cavity reactor with absorbers at the inner periphery is shown in Figure 5-1 and Figure 5-2. Ideally, the absorbers should
100 be touching each other so that all incoming rays will hit the absorbers. However, some clearance must be left between the absorbers due to manufacturing limitations. The
Vegas code is used for optimizing the aperture diameter. The fraction of the incident radiations at the aperture from the solar simulator varying with the diameter of the aperture is shown in Figure 5-3. As the size of the aperture increases, the fraction of incident radiation admitted into the cavity increases; however with increased aperture size, the radiation losses through the aperture also increase. Due to a part of radiations absorbed at the solar simulator mirror surfaces, incident power at the aperture never converges to 1. Approximately 75% of the solar simulator output radiative power is incident at a 5 cm diameter aperture. Rays from solar simulator are traced up to the aperture using Vegas. The MCRT code is used for further tracing the rays until they either get absorbed inside the cavity or escape through the aperture.
For a non-participating medium and assuming a refractive index of unity, the radiative heat flux leaving or going into a surface, using MCRT, is governed by the following equation [13].
dF ' q(r) (r) T4 (r) (r) ' T 4 (r) 'ddAA d A ' (5-3) A dA
The first term on the right hand side of Equation 5-3 represents the emission from the cavity/absorber surface at location r and the corresponding temperature T(r) . The second term represents the fraction of energy originally emitted from the surface at r' , which eventually absorbed at location .
Each ray is assumed to carry same amount of power. The power Qray carried by each ray from the simulator is given by
101 Qinput,simulator Qray (5-4) Nray,total
The cavity and the absorber surfaces are assumed to be diffusely reflecting / emitting.
The cavity surface and the absorber surfaces are divided in small elements of equal area.
The number of rays re-emitted by absorbers and the cavity surface are given by
4 TAi,cavity i NNi,cavity ray,total (5-5) Qcavity
4 TAi,absorber i NNi,absorber ray,total (5-6) Qabsorber
Where
n 4 (5-7) QTAcavity i,cavity i i1
n 4 QTAabsorber i,absorber i (5-8) i1
The lattice Boltzmann method (LBM) [14] is used for the calculation of the heat transfer inside the absorbers. The absorber heat flux calculated using MCRT is provided to the LBM to obtain temperature profile of the absorber and the cavity surface. Due to multiple number of absorbers used in the simulation, an average heat flux approach is used to reduce the computational time of simulation.
Radiation Model Validation
The radiation model is validated against the analytical solutions for comparatively simpler geometries. Equation 5-9 provides the analytical view factor for the geometry shown in Figure 5-4. 1 R r r 1 (R )2 FXX( 22 4(2 ) ) aprt 2 aprt bp RRX12 , , 1 2 (5-9) 2 R1 LLR()1
102 Figure 5-5 shows the root mean square error variation along the radial direction of the back plate between the radiation model solution and the analytical solution for the geometry shown by Figure 5-4. Equation 5-10 provides the analytical view factor for the geometry shown in Figure 5-6.
2 (5-10) 2Z ( X 2 R ) RdR dAcyl z raprt 22 dFaprt cyl 3 . ZRXZR, , 1 22 (XR 4 ) 2 Aaprt rrcavity cavity
Figure 5-7 shows the root mean square error variation along the length of the cylinder between the radiation model solution and the analytical solution for the geometry shown by Figure 5-6.
5.3 Radiation in the Porous Media Inside the Absorbers
The porous matrix (reactive material bed) considered in the present study is optically thick thus the Rosseland diffusion approximation for the radiation inside the reactive material bed is valid (13). The radiative heat transfer inside the absorber is then simplified to a diffusion process with an equivalent thermal conductivity
2 16n σ 3 kTR , (5-11) 3βR
where βR is the Rosseland-mean extinction coefficient, and n is the refractive index of the medium. Due to large the incident radiation attenuated mostly at the surface of the porous bed. Thus most of the radiative heat transfer inside the porous bed takes place due to the local emission and absorption, justifying the use of Rosseland diffusion approximation in the present case (13).
103 5.4 Convective Heat Transfer
In the iron oxide thermal reduction step only oxygen is released during the reaction. Since the released oxygen is removed from the system at a low speed, the convective heat transfer is neglected in the present calculations.
5.5 Conductive Heat Transfer
For the reduction step, the heat transfer inside the absorber is simplified to a conduction problem. Using Equation 5-11, the effective thermal conductivity for the conduction can be approximated as (13)
2 16n σ 3 keff kR k cond T k cond , (5-12) 3βR
where kcond , is the thermal conductivity for the porous medium
5.6 Chemical Reaction Rate
The heat consumption in the thermal reduction of the metal oxide is given by q''' r ''' ( h 0.5 h h ) chem MO M O2 MO , (5-13)
r ''' where MO is the volumetric reaction rate of the metal oxide MO such as FeO, h is the specific enthalpy of the reactants or products. The reaction rate is modeled by an
Arrhenius-type rate law (68). The reaction rate term is given by
''' Ea rMO k 0 exp f ( x ) RT , (5-14)
Where Ea, the activation energy for the reduction is determined experimentally, the pre- exponential factor, k0, is a constant fitted from experimental data, x is the mass fraction of the reacted material and f(x) is a dimensionless function that depends on the reaction mechanism.
104 5.7 Lattice Boltzmann Simulation inside Absorbers
The energy conservation equation for the cylindrical absorbers is given by
TTTT11 ''' ρcp rkeff 2 k eff k eff q chem , (5-15) t r r r r z z
where ρ and cp are the density and specific heat capacity of the solid matrix,
''' respectively, and qchem is the rate of volumetric heat sink given by Equations 5-13, and
5-14
5.8 Process Flow
The process flow of the coupled model is given in Figure 5-8.
5.9 Results and Discussion
The coupled model is used to perform a parametric study to optimize the efficiency of the reactor. The thermal efficiency of the reactor is given by:
Ploss thermal, reactor 1 (5-16) Pinput,simulator (5-17) PPPPloss loss,aprt loss,cavity surface loss,absorber For the optimization of the horizontal cavity reactor, a number of parameters such as aperture diameter, cavity inner diameter, length of the cavity, diameter of the absorbers, number of absorbers, and the thickness of the insulation are considered. For the purpose of simulation, absorbers of 2 inch diameter, 3 inch thick cavity material and
5 inch thick insulation material are considered. The aspect ratio (Lcavity/Dinner, cavity) is varied to optimize thermal efficiency of the cavity reactor. Three different aspect ratios,
0.75, 1.0, and 1.25 are considered for the study. The baseline parameters for the considered aspect ratios are given in Table 5-1. Since the absorbers are considered to be uniformly distributed along the azimuthal direction inside the cylindrical cavity, only
105 one absorber (absorber 1 as depicted in Figure 5-1) is selected for the purpose of simulation to reduce the computational effort. The heat flux boundary condition is assumed to be the average value of the heat fluxes at all absorbers.
Table 5.2 shows the steady state thermal efficiency and various energy losses for the horizontal cavity reactor. The energy losses are calculated at the steady state and then the thermal efficiency is calculated by using Equations 5-16, 5-17. The aperture radiation loss considers radiation loss due to the rays leaving the cavity reactor through the aperture, either directly or after multiple reflections. The loss from the absorbers takes into consideration the radiation and convection losses from the inlet and outlet of the absorbers. The loss from the cavity considers radiation and convection losses from the cavity surface, excluding the losses from the inlet and the outlet of the absorbers.
For an aspect ratio of 0.75, the aperture radiation loss is comparatively higher than that of the other two aspect ratios because the comparatively shorter length of the cavity reactor hinders the multiple reflections of the incident/re-emitted rays inside the reactor. The aperture loss reduces with increase in the length of the cavity reactor. The cavity reactors based on the aspect ratios of 1.0 and 1.25 depicts lower aperture loss as compared to the aspect ratio of 0.75. Also, the nominal difference between aperture losses for the aspect ratios 1.0 and 1.25 implies that further increase in reactor length has lesser impact on the decrease in aperture loss.
With increase in aspect ratio, total energy loss from the absorbers decreases due to decrease in the number of absorbers which thereby decreases the total surface area available for convection and the radiation heat loss.
106 Figures 5-9, 5-10, and 5-11 show steady state surface temperature distribution of the representative absorber 1 for the aspect ratios 0.75, 1.0, and 1.25 respectively. For the aspect ratio of 0.75, the high temperature region is closer to the back plate of the cavity reactor due to comparatively shorter length of the reactor. For the aspect ratio of
1.0, the high temperature region is approximately in the middle of the reactor length and for the aspect ratio of 1.25; the high temperature region is towards the front plate of the reactor. The high temperature region in the proximity of the boundary (back plate) of the cavity reactor increases the radiation loss. The maximum absorber steady state temperature reached in all three cases is approximately 2000 K. The most uniform temperature profile is achieved for an aspect ratio of 1.0.
The steady state heat flux distribution at the surface of the representative absorber 1 for aspect ratios 0.75, 1.0, and 1.25 is shown in Figures 5-12, 5-13, and 5-14 respectively.
Figures 5-15, 5-16, and 5-17 show the steady state surface temperature distribution of the cavity reactor back plate for the aspect ratios 0.75, 1.0, and 1.25 respectively. The lower temperature region is seen at larger radius of the cavity back plate due to shadow effect of the absorbers. For the aspect ratio of 0.75, the cavity back plate temperatures are quite high because of the shorter length of the reactor in comparison to the other aspect ratios.
Figures 5-18, 5-19, and 5-20 show the steady state surface temperature distribution of the cavity reactor front plate for the aspect ratios 0.75, 1.0, and 1.25 respectively. For the aspect ratio of 0.75, high temperature region is quite close to the aperture of the cavity reactor. The insulation of the front plate near to the aperture
107 region is complex in geometry because of the accommodation for the angle of the incoming radiations. A special attention is given to the insulation of the region near to the aperture of the cavity reactor.
Figures 5-21, 5-22, and 5-23 show the steady state surface temperature distribution of the cavity reactor cylindrical part for the aspect ratios 0.75, 1.0, and 1.25 respectively.
5.10 Summary
A radiation model for a windowless horizontal cavity reactor is developed. The
Vegas code is used to determine the aperture diameter of the cavity reactor. The lattice
Boltzmann model developed at University of Florida by Li et.al is used for conduction modeling inside the absorbers and inside the cavity walls. The MCRT model and LBM are coupled together and the coupled model is used to obtain the steady state temperature and flux distribution at the surface of the absorber for different geometries of the cavity reactor. A parametric study is performed to optimize the geometry of the cavity reactor. The coupled model is used to obtain the thermal efficiency of the cavity reactor for different aspect ratios. Maximum efficiency of 21 % is obtained for an aspect ratio of 1.0. For a shorter length reactor (aspect ratio of 0.75) back plate receives higher amount of radiation which in turn increases the temperature of the back plate. Higher temperature increases the radiation losses from the back plate of the reactor. The shorter length of the reactor also increases the radiation loss through the aperture which can be decrease by using a comparatively larger length reactor. The aperture radiation loss seems insensitive for an aspect ratio higher than 1.0.
108 Table 5-1. Simulation parameters for cavity aspect ratio Lcav, in / Dcav = 0.75, 1.0, and 1.25 for Cases I, II and III. Parameter Value Solar power input 10 kW Absorber emissivity 0.8 Number of absorbers 17, 14, 12 Absorber diameter 50.8 mm Absorber length 246, 304.8, 337.8 mm Absorber thickness 3.18 mm Aperture diameter 50.0 mm Cavity diameter 355.4, 302, 266.4 mm
Table 5-2. Reactor efficiency and various energy losses for different aspect ratios Lcavity/Dinner,cavity = 0.75 Lcavity/Dinner,cavity = 1.0 Lcavity/Dinner,cavity = 1.25 ( no. of absorbers = ( no. of absorbers = ( no. of absorbers = 17) 14) 12) 0.1986 0.2101 0.1893 thermal, reactor
Aperture 0.0871 0.0643 0.0642 radiation loss
Loss from the 0.5662 0.3951 0.3333 absorbers
Loss from the 0.1478 0.3305 0.4132 cavity
109
Figure 5-1. Schematic layout (front view) of the windowless horizontal cavity reactor.
Figure 5-2. Schematic layout (side view) of the windowless horizontal cavity reactor.
110
Figure 5-3. Variation of fraction of transferred power from the solar simulator to the aperture with increase in the aperture radius.
Figure 5-4. Geometrical configuration of the back plate and the aperture for view factor calculation
111
Figure 5-5. Root mean square error between the calculated view factor using analytical solution and the view factor calculated using the radiation model along the radius of the back plate.
Figure 5-6. Geometrical configuration of the cylindrical part and the aperture for the view factor calculation.
112
Figure 5-7. Root mean square error between the calculated view factor using analytical solution and the view factor calculated using the radiation model along the length of the cylinder.
113
Figure 5-8. Process flow diagram for the cavity coupled model.
114
Figure 5-9. Steady state temperature contours at the surface of absorber 1 for the aspect ratio of 0.75.
Figure 5-10. Steady state temperature contours at the surface of absorber 1 for the aspect ratio of 1.0.
115
Figure 5-11. Steady state temperature contours at the surface of absorber 1 for the aspect ratio of 1.25.
Figure 5-12. Steady state heat flux distribution at the surface of absorber 1 for the aspect ratio of 0.75.
116
Figure 5-13. Steady state heat flux distribution at the surface of absorber 1 for the aspect ratio of 1.0.
Figure 5-14. Steady state heat flux distribution at the surface of absorber 1 for the aspect ratio of 1.25.
117
Figure 5-15. Steady state temperature contours at the surface of back plate of the cavity for the aspect ratio of 0.75.
Figure 5-16. Steady state temperature contours at the surface of back plate of the cavity for the aspect ratio of 1.0.
118
Figure 5-17. Steady state temperature contours at the surface of back plate of the cavity for the aspect ratio of 1.25.
Figure 5-18. Steady state temperature contours at the surface of front plate of the cavity for the aspect ratio of 0.75.
119
Figure 5-19. Steady state temperature contours at the surface of front plate of the cavity for the aspect ratio of 1.0.
Figure 5-20. Steady state temperature contours at the surface of front plate of the cavity for the aspect ratio of 1.25.
120
Figure 5-21. Steady state temperature contours at the surface of cylindrical part of the cavity for the aspect ratio of 0.75.
Figure 5-22. Steady state temperature contours at the surface of cylindrical part of the cavity for the aspect ratio of 1.0.
121
Figure 5-23. Steady state temperature contours at the surface of cylindrical part of the cavity for the aspect ratio of 1.25.
122
CHAPTER 6 RADIATION MODELING
6.1 Radiative Heat Transfer in Porous Media
Radiation is the predominant mode of heat transfer in many high temperature engineering applications [70]. Particularly in porous materials or media containing particulates radiation heat transfer [71, 72] plays an important role. Fluidized beds, packed beds, catalytic reactors, combustors, soot and fly ash, sprayed fluid, porous and reticulate ceramics, microspheres and multilayered particles are typical applications of porous media [73]. For the purpose of radiation modeling, only the porous matrix is considered as a participating medium. The reacting gases are ignored in modeling since they contribute less than 5 % to the radiation heat transfer [74].
The Monte Carlo ray tracing (MCRT) in a participating medium is used for the radiation modeling. In classical MCRT, photon bundles are traced until they are absorbed inside the system or lost to the surroundings [75]. MCRT can handle any arbitrary geometry of the system. For large numbers of photon bundles MCRT results converge towards the exact solution. MCRT can be used easily to solve non-gray, non- isothermal and anisotropic problems [71]. However, due to the statistical nature of
MCRT model, a large sample of photon bundles needs to be traced, making it computationally expensive [13].
The diffusion approximation is an efficient alternative method, which can be easily applied since the porous matrix considered is an optically thick medium. It is a simpler model and computationally less expensive [13]. The radiation heat transfer
123 inside the optically thick porous media is due to local emission and absorption of the thermal radiations [76] thereby justifying the use of diffusion approximation.
One major drawback of diffusion approximation is the inaccuracy at the system boundaries [77]. The P1- approximation, a first-order spherical harmonics method, is used to counter the deficiency of the diffusion approximation. In the P1-approximation, the integro-differential radiative transfer equation is converted to a set of partial differential equations [13]. These partial differential equations can be solved by employing the common numerical schemes. This method is computationally less expensive compared to the MCRT method and is more accurate at the boundaries than the diffusion approximation method.
The Radiative properties of the porous media are determined using geometrical optics for large particles [13]. An experimental specimen is used to determine the particle volume fraction of the porous medium. Linear anisotropic scattering is assumed inside the porous medium. Boundaries are assumed to be perfectly insulated and diffusely emitting/reflecting. All the above models are then individually integrated with the conduction model developed by Li et al. [14]. Since MCRT is the most accurate of the methods considered; a comparison of the diffusion approximation and the P1- approximation with the MCRT is performed. Figure 6-1 shows the schematic layout of the porous medium considered for the study.
6.2 Monte Carlo Ray Tracing Model
A Monte Carlo ray tracing (MCRT) method for a participating medium is used for the radiation modeling in a porous medium. A participating medium emits, absorbs and scatter radiations. The Radiative heat transfer in a participating medium is govern by the following equation (RTE) [13]
124 dI I I s I(sˆ ) (s ˆ ,s) ˆ d , b i i i (6-1) d4s 4
The first term on the RHS of above equation expresses the augmentation of intensity by emission. The second term expresses the reduction of intensity by extinction. The last term quantifies augmentation by in-scattering, where the phase
(sˆˆ ,s) sˆ function i is the probability that a ray is scattered from direction i into directionsˆ .The porous medium (Figure 6-1) is discretized into smaller sub-volumes.
Each sub-volume is supposed to have constant radiative properties. The divergence of heat flux is given by [75]
.q (4πII d )d (6-2) rb 04
The porous matrix is assumed to be non-gray, absorbing, emitting and linear anisotropically scattering participating medium. The medium particles are assumed to be opaque and spherical in shape - a reasonable assumption for irregularly shaped and randomly oriented particles [71].
Random Number Relations
The point of emission from the surface of a sub-volume is given by
In the r-direction r ri dr (6-3)
In the z-direction z z dz (6-4) i
Where is the random number between 0 and 1.
The emission direction of the ray from the emission point is given by
Azimuthal angle 2 (6-5)
1 And polar angle cos (1 2 ) (6-6)
125 By using the above random number relations for azimuthal angle and polar angle, the direction cosines can be used to obtain the direction of the emitted ray. The photon bundle emitted is traced until it is absorbed inside the medium or leaves the boundary.
The emitted photon bundle is not absorbed and allowed to move further until the below criterion is satisfied. s l 1 ds ds In( ) (6-7) 00
s Where ds s (for k sub-volumes of constant absorption coefficient). k k 0 k
11 The photon path length ( lk ) is given by lk In( ) .
Similarly for the scattering, the distance a ray travels before getting scattered is given by s l 1 ds ds In( ) (6-8) ss,, 00
11 Where l In( ) s
The azimuthal angle and polar angle of the scattered ray for linear anisotropic scattering is given by
Azimuthal angle 2 (6-9) r r
1 A1 2 Polar angle (1 cos sin ) (6-10) 22
The new direction vector can be found by introducing a local coordinate system at the point of scattering and using above angles.
126 6.3 Diffusion Approximation
s If the optical thickness of a medium is too high ( ds >> 1 ), the relatively 0 simpler diffusion approximation can be used for the radiation modeling inside a porous medium [13] . The below equation can be used to obtain the heat flux
16n23 T dT q (6-11) 3R dz
A strongly temperature dependent Radiative conductivity can also be defined from
Equation 6-11 as
16nT23 k R (6-12) 3R
Where the Rosseland mean extinction coefficient ( R ) is given by
11 dI b d (6-13) 3 R 4 T0 dT
This reduces the radiation problem to a simple diffusion problem with strongly temperature dependent conductivity. The diffusion approximation is not accurate at the system boundaries [66].
6.4 P1- Approximation
The Radiative transfer equation (Equation 6-1) is an integro-differential equation in six independent variables: 3 space coordinates, 2 direction coordinates and a wave length coordinate. The high dimensionality of the problem the method of spherical harmonics can be used to transform this equation into a set of partial differential equations with a higher order of accuracy. The P1-approximation is the lowest order and
127 most used spherical harmonics method. The governing equation is a Helmholtz equation:
2GAGAI (1 )(3 ) (1 )(3 )4 (6-14) 11b
The Incidence radiation is given by
G( ) I ( ,sˆ ) d (6-15) ii 4
s The single scattering albedo is given by (6-16)
Boundary Conditions
(2 ) 2 G BC)1 @ z=0 GI 4 b (6-17) (3Az1 )
(2 ) 2 G BC)2 @ z=h GI4 (6-18) (3Az ) b 1
(2 ) 2 G BC)3 @ r=R GI4 b (6-19) (3Ar1 )
A FORTRAN based finite difference model is developed to solve the governing equation using the boundary conditions.
6.5 Radiative Properties
Radiative properties of the material are calculated by using the experimental specimen of the porous media. Particle size of the medium is between 75 and 100 m .
Based on the particle size and the weight of the experimental specimen particle volume fraction (fv) is calculated assuming particles are spherical in shape with uniform distribution in the experimental specimen.
Vvoid fv (6-20) Vparticle
128 For the given particle size and fv geometric optics assumption is valid. Based on above assumptions, the extinction coefficient is calculated using below equations.
The DC resistivity ( dc ) for iron is given by [67]
(A BTTT C2 D 3 )10 6 dc 1 1 1 1 (6-21)
1 dc The DC conductivity is given by dc (6.22)
According to the Hagen-Rubens relation [79] the index of refraction (n) is given by n 30 dc (6-23)
For n >> 1, the spectral hemispherical reflectivity ( n, ) can be approximated by
22 n, 1 2 nn (6-24)
Using Equation 6-24 and Hagen-Rubens relation the spectral hemispherical reflectivity can be determine by
22 1 30 30 dc dc (6-25)
The absorption, scattering and extinction coefficient can be calculated by using the following equations
Na(1 ) 2 p (6-26)
Na 2 p (6-27)
(6-28)
129 6.6 Comparison of Different Radiation Models
The models described above are individually integrated with the conduction model developed by Li et al. [14] at University of Florida and the effect of these different radiation models on the temperature profile of the porous medium is analyzed. To test the transient evolution of conduction and radiation heat transfer, the following initial condition is applied:
T(z=0, r)=T(z=H, r)=1000K;
T(z/H=0.5, r)=250K and the initial temperature is linear in the z-direction.
Figure 6-2 shows the variation of the temperature with the increase of time based on the different radiation models employed. The MCRT model is the basis of comparison for other two models. In the beginning of the process, P1-approximation and diffusion approximation shows convergence to the MCRT model. As time increases, convergence of both P1-approximation and diffusion approximation decreases. The P1- approximation and the diffusion approximation give similar results. So for an optically thick participating medium, both the P1-approximation and the diffusion approximation can be used. Since the diffusion approximation is particularly easy to implement and computationally less expensive than the P1-approximation, the use of the diffusion approximation is recommended over P1-approximation in optically thick participating media. In Chapter 7, the diffusion approximation is integrated with the finite volume conduction model and the random walk transport of species model. The coupled model is used to investigate the effect of different input parameters on the hydrogen production.
130
Figure 6-1. Schematic layout of the porous matrix inside the reactor.
Figure 6-2. Effect of different radiation models on the temperature profile of the porous medium.
131
CHAPTER 7 COUPLED MODEL5
7.1 Reactive Flows in Porous Media
The study of reactive flows in porous media is necessary for a comprehensive understanding of the thermochemical fuel production process [80]. The reactive flow in porous media is influenced by a various factors. These factors include a large range of geometrical length scales, the thermochemical and thermophysical properties, heat and mass transfer phenomenon and flow of the reactive gases [81]. Due to a large range of length and time scale, the relevance of non-equilibrium in reactive flows in porous media increases [82]. To model the fuel production in such type of systems, coupling of heat and mass transfer with chemical kinetics is essential. A coupling of conduction, convection and radiation with chemical kinetics in a packed bed of large reactive particles has been studied in [83]. A model of heat and mass transfer coupled to chemical kinetics in an irradiated, catalytic RPC matrix has been investigated in [82].
In this Chapter, a magnetically stabilized fluidized bed is considered for the iron/iron oxide redox cycle. In the magnetically stabilized bed, the iron particles form a porous structure of chains as a result of sintering in presence of a magnetic field. This porous chain structure is robust and stable at high temperatures and, serves as a medium for thermochemical reactions [84]. A range of complex coupled unsteady phenomena proceed on a range of time and length scales. Simulating these phenomena in their entirety on all relevant scales is not feasible. Therefore a continuum
5 The flow and transport modeling inside the porous structure by Nima Rahmatian and the lattice Boltzmann modeling of the conduction inside the absorber and the cavity walls by Li Like (Li 2013) is greatly appreciated.
132 scale description of governing equations and variables is developed using the method of volume averaging.
The model considers transient heat and mass transfer coupled to endothermic or exothermic chemical reactions. The fluidized bed reactor is cylindrical in shape; therefore a 2D model is developed. A schematic representation of the model setup and the relevant boundary conditions is given in Figure 7-1.
Relevant physical phenomena are:
Fluid dynamics (Darcy or Forchheimer-type static momentum equations) Fluid phase mass transfer (Diffusion/Dispersion) Chemical kinetics (an Arrhenius type kinetic model) Transient conduction heat transfer (primarily porous matrix/ solid phase) Convection heat transfer (solid/fluid interface) Radiative transfer
The coupled model consists of four distinct modules 1) A finite difference finite volume module for unsteady conduction in the solid phase, 2) a Lagrangian PDF based- random walk module to simulate transport and reaction in the fluid phase, 3) a static fluid flow module to simulate Darcy or Forchheimer type fluid flow, and 4) A radiation model. The coupled model structure is depicted in Figure 7-2. The model considers the process as a 2-D, unsteady, exothermic reaction with reactive solid. The porous matrix is considered as a continuous, anisotropic, uniform, absorbing, emitting, and scattering participating media. Three different radiation models described in Chapter 6 are used in the coupled model. The effect of all three models on the coupled model output is investigated in the current Chapter.
7.2 Mathematical Modeling
The conservation laws hold for each phase in the system. But in order to develop a continuum model for the reaction in the porous medium the volume averaging
133 technique is used [82]. Conservation of mass for solid and fluid phases is satisfied within each phase and they are linked by the chemical reaction equation. Thus the total mass inside the reactor is conserved.
For fluid phase the volume-averaged conservation of mass equation is:
F d u F r dt (7-1) where r is mass generation due to chemical reaction.
The fluid flow is governed by the Darcy’s law:
F p F u K (7-2)
Fluid transport of chemical species is modeled by the transport equation for a compressible mean flow field . For constant porosity ε one can obtain:
FF jju F 1 F .j .D . F Mr j j 0, t (7-3) where D is the macroscopic dispersion tensor, and M r R is production rate of j j j species j due to chemical reaction.
In this study a transient formulation of species is adopted to allow for a
Lagrangian description where individual fluid particles are traced as they are transported through porous medium. By neglecting pressure work, viscous dissipation, conduction and radiation in gas phase and assuming ideal gas behavior energy equation in fluid phase can be written as:
ns P P dT SsVA c nPPPP n( h ( T ) h ( T )) 0 h ( T T ) P, j j j j j sf (7-4) j1dt j , nj 0
134 Where solid to fluid convective heat transfer is expressed by interfacial heat transfer coefficient hfg and superscript P denotes fluid particle properties.
In solid phase energy equation is written in transient conduction format with volume-averaged source terms that account for the solid-fluid convection and radiation heat transfer and reaction heat generation:
Ts s sc p, s () k s T s I s t (7-5)
np fluid solid np p s 11pp P s VA0 P Isnj h jT n i h i T h sf(). T T q r VV cellp j i cell p Radiation Heat Transfer Reaction Heat Convection Heat Transfer (7-6)
Radiation source term is given by: dI III s sˆ sˆ,d sˆ sˆ (7-7) b i i i d4s 4
.qs 4 II dˆ d (7-8) rb 04
7.3 Reaction Rate
The complete oxidation of Fe is governed by the following reaction:
3Fe+4H O Fe O +4H 2 3 4 2 (7-9)
Reaction rate equation is assumed to be first order and have Arrhenius type temperature dependency. It is further known that reaction rate is proportional to the active surface area of the porous structure. Thus the combined form of the reaction rate equation is expressed as:
E dH[] a a 2 k eRT [ H O ] S (1 )2/3 dt 0 2 0 1/3 2 2 (1 (1 ) ) a (7-10)
135 where S0 is the initial surface area of the porous structure and is Fe conversion factor defined as:
reacted mass of Fe initial mass of Fe and a is a parameter that indicates when the diffusion becomes the dominant rate- determining mechanism. a is found by comparing the results with the experimental data.
7.4 Numerical Methods
7.4.1 Random Walk Transport
The transport of the species can be simulated by tracing the paths of many particles. This Lagrangian approach evaluates chemical rate locally and consequently the errors due to averaged temperatures and compositions in rate law expression decrease. One step of a particle in 1D is expressed as:
xp tu 2 D t (7-11) where is a normally distributed random number with zero mean and standard deviation of one and u is the velocity of the base flow. The transport equation
(Equation 7-3) can be rewritten similar to Fokker-Planck equation:
F F 2 j u DD FF D M r 0 (7-12) t x F x xj x2 j j j
Thus species transport equation can be satisfied by moving the fluid particle in the form of Equation 7-11. To obtain smooth results the time-step δt has to be chosen sufficiently small. In other words a single stochastic step must be small compared to the cell size.
Molecular diffusion is neglected therefore species conservation in a fluid particle only depends on chemical reaction.
136 7.4.2 Conduction
Finite Volume formulation is adopted to solve the conduction equation in 2D cylindrical coordinate with source terms due to reaction, convection and radiation.
s s s TTT1 cs()() rk s k s I s p, st r r s r z s z s (7-12)
The finite volume formulations are:
j1 j j j j j aTPPSSNNEEWWPP aT aT aT aT aT b (7-13)
kSP aS 2 dz (7-14)
kNP aN 2 dz (7-15)
2krEP E aE drp() dr E dr p r P (7-16)
2krWP W aW drp() dr W dr p r P (7-17)
c s p, s P aP dt (7-18) bI s P (7-19)
The conductivity at the finite volume interfaces is written as:
kSPNP k k k kkSP, NP kSPNP k k k (7-20)
kEPEP k() dr dr kNPNP k() dr dr kkEP, NP kEEPPNNPP dr k dr k dr k dr (7-21)
137 It should be noted that due to ui-spaced grid in z-direction the finite volume coefficient and the conductivity at the interfaces in z-direction are different from ones in r-direction
(see Figure 7-3).
7.4.3 Fluid Flow
Assuming the fluid phase behaves according to the ideal gas equation, the mass conservation and Darcy’s law are combined and the equation of state is used to express the density in terms of pressure and temperature. The resultant equation is a nonlinear
PDE for the pressure field inside the porous structure (Equation 7-23).
F 11 p K FF p p r RT tF RT (7-22)
To treat the nonlinearity in Equation 7-23 the nonlinear coefficients are obtained from previous time step i.e. they are lagging one time step but since the time step is small and the nonlinearity is weak the solution converges. Thus the PDE which is solved can be written as:
F 11 p K FF pr RT t Old Old F (7-23)
The PDE for pressure (Equation 7-23) is expanded for 2D cylindrical coordinate system and it results in an elliptic diffusion equation. The Alternating Direction Implicit scheme is adopted to solve Equation 7-23 with the second order accuracy in space and time.
7.4.4 Radiation
The diffusion approximation model described in Chapter 6 is used in the coupled model.
138 7.5 Results
The fluid flow and transport model is developed by Rahmatian et al. and the conduction model is developed by Li et al. at University of Florida. Coupled model results are validated with the experimental result. Three input parameters temperature, inlet steam flow rate, inlet steam concentration are varied to assess their effect on the hydrogen production.
7.5.1 Temperature Effect
The predicted hydrogen production rate computed with continuum model code for three different temperatures are compared against corresponding experimental data and are shown in Figure 7-4. The operating parameters for both experiments and numerical simulation are given in Table 7-1.
The simulation results follow the trend and shows very good agreement. The deviation from the actual experiment is mainly due to fluctuations in temperature of the structure. Moreover there is always some uncertainty about the state of the sample after reduction step. The duration of the reduction step is kept the same for all redox cycles but slight changes in temperature or CO2 flow rate, which acts as the reducing agent, can cause a meaningful difference in the final state of the sample which is only partially reduced back to elemental iron. Thus the sample for the next oxidation contains more/less reactive material and as a result the hydrogen production is different.
Due to lack of required technique to directly measure how much of iron oxide is reduced back to the elemental iron between cycles, the simulation is run based on the estimated amount of iron which is extracted from the amount of hydrogen produced in that oxidation step experiment.
139 As proposed in the chemical rate law, the rate at which hydrogen comes out of the reactor shows a significant dependence on the temperature and the peak value has been captured by the numerical results.
7.5.2 Inlet Mass Flow
Another parameter of interest is the steam flow rate at the inlet of the reactor.
Since the steam generation is expensive, its effect on the hydrogen production is studied to be able to find the optimum operating condition for the reactor in which energy is consumed efficiently. In Figure 7-5 the results of the simulation are shown versus the experimental data for steam flow rates of 1, 3 and 4 g/min. During this set of experiments the temperature of the bed is kept constant at 800 oC.
7.5.3 Inlet Concentration of Steam
As it is shown in the proposed rate law for oxidation of the iron structure
(Equation 7-18), the production rate is proportional to the concentration of steam. This effect can be seen in all the experiments due to the length of the reactor. The inlet steam starts reacting with the iron and production hydrogen. As a result the gas phase will be a mixture of the steam and hydrogen so the partial pressure or equivalently the concentration of the steam decreases along the reactor.
Further investigations are preformed to test the effect of the steam concentration on the production rate by changing the inlet concentration of the steam. Thus the inlet steam is diluted with Helium to reduce the concentration. In Figure 7-6 the impact of lower steam concentration on hydrogen production rate is shown.
7.6 Summary
The transient heat and mass transfer model is coupled with the chemical kinetics for the hydrogen production step. Diffusion approximation is used for the radiation
140 model. Finite volume method is used to model the conduction inside the porous medium. The random Walk method is used to simulate the transport of species. All three models are integrated together. Results are obtained using coupled model for three different input parameters: temperature, inlet steam flow rate and inlet steam concentration. The coupled model is validated against the experimental results. The coupled model simulation results show good agreement with the experimental results.
Table 7-1. Operating parameters used in numerical simulation and experiments Parameters Numerical simulation Lab-scale reactor Reactor size D=0.04 m, L=0.02 D=0.046m, L=0.10m Reactive material Iron=100 g Iron=100 g, Silica=100 g Initial temperature 800oC 800oC Inlet steam mass flow rate 3 g/min 3g/min Porosity 0.63 0.63
Figure 7-1. Model setup
141
Figure 7-2. Various modules of the model
Figure 7-3. Schematic of the reactor
142 )
M 3 o P Experiment 800 C
L o
S Experiment 700 C ( 2.5 Experiment 600 oC e o t Model 800 C a o
R Model 700 C 2 o
n Model 600 C
o
i
t c
u 1.5
d
o
r P
1
n
e
g o
r 0.5
d
y H
0 5 10 15 20 Time (min)
Figure 7-4. Effect of temperature on the hydrogen production rate.
3.5 )
M Experiment 1 g/min
P 3
L Experiment 3 g/min S
( Experiment 4 g/min
e 2.5 Model 1 g/min t
a Model 3 g/min R Model 4 g/miin
n 2
o
i
t
c u
d 1.5
o
r P
n 1
e
g o
r 0.5
d
y H 0 5 10 15 20 Time (min)
Figure 7-5. Effect of steam input flow rate on the hydrogen production rate.
143 ) 2.5 Inlet Steam Molar Fraction
M Exp. data 0.8
P Exp. data 0.6 L
S Exp. data 0.4 ( 2
e Model 0.8 t
a Model 0.6
R Model 0.4
n 1.5
o
i
t
c
u d
o 1
r
P
n
e g
o 0.5
r
d
y H 0 0 5 10 15 20 Time (min)
Figure 7-6. Effect of inlet steam molar fraction on the rate of hydrogen production.
144
CHAPTER 8 CONCLUSION
Multi-scale, multi-physics modeling of thermochemical iron/iron oxide cycle for hydrogen production is performed. Matlab/Fortran based numerical models are developed to study the thermochemical hydrogen production using iron/iron oxide looping process from the perspective of a system level, a reactor level and finally down to the reactive material itself.
For the system scale study, a Matlab based model is created to develop four different layouts of the overall hydrogen production plant based on the operating temperature ranges. Below 1080 K temperature hydrogen production plant is self- sustaining but for operating temperature higher than 1080 K some syngas firing is needed. An efficiency based comparison is also performed between a hydrogen production plant using the iron/iron oxide looping cycle and a hydrogen production plant using the conventional process involving a water gas shift reaction and a pressure swing adsorber. Hydrogen production efficiency of the co-production plant using iron/iron oxide looping cycle is 41.2 % which is slightly less than that of the conventional co-production plant. In the conventional plant hydrogen present in the syngas is increases by the WGS reaction and then extracted in the PSA but in the current process hydrogen present in the syngas is not extracted which led to lower hydrogen production efficiency. But the higher amounts of the unreacted hydrogen and CO in the product gases of the reduction step provide 17.4 % electricity production efficiency which is higher than that of the conventional process.
145 For the reactor scale study, an open system, quasi-steady state thermodynamic model is developed and is used to predict the optimum operating conditions for hydrogen production. Hydrogen production is thermodynamically favored at lower temperature (below 680 K). However, slow chemical kinetics at low temperatures is likely to compel higher temperatures for industrial scale processes. The quality of hydrogen produced depends on the formation of carbon- soot, FeCO3 and Fe3C in the solid phase during the reduction process. Theoretical predictions have been experimentally validated for the hydrogen production step in a fluidized bed reactor at
660 and 960 C for steam flow rates between 0.9 and 3.5 g/min. As the steam flow rate to the reactor decreases, i.e., as the residence time of steam in the reactor increases, the experimentally observed cumulative steam-to-hydrogen conversion approaches the theoretically predicted values. The initial steep rise of the theoretical yield shows the potential for efficient conversion of steam to hydrogen. However, particularly at low temperatures and during the initial reaction phase, experimental yields remain significantly below the theoretical limit. Increasing the residence time partially alleviates these issues. At higher temperatures, reduction of the flow rate (i.e., increasing the residence time) has only a marginal effect on conversion thereby indicating very slow effective kinetics beyond a certain Hydrogen yield. The validation of the theoretical model for the magnetite reduction using CO in a stationary bed reactor with the experiments is performed. The input CO flow rates are varied between 0.1 slpm and 0.5 slpm at 900 oC and 1000 oC stationary bed temperatures. A comparison of the cumulative amount of CO2 produced from experiments and the theoretical predictions for a magnetite powder stationary bed reactor is carried out. The CO2 production is
146 insensitive towards the variation in the input CO flow rates at the considered temperatures. The experimental results approaches the theoretical limit at 900 oC temperature and no significant change in the experimental results are depicted at 1000 oC temperature. Theoretical predictions of the solid molar compositions for a stationary bed reactor show the formation of coking and Fe3C. A collision based Monte Carlo ray tracing model is developed and coupled to the lattice Boltzmann conduction model to optimize the geometry of the windowless horizontal cavity reactor. The coupled model is used to obtain the thermal efficiency of the cavity reactor for different aspect ratios.
Maximum efficiency of 21 % is obtained for an aspect ratio of 1.0. For a shorter length reactor (aspect ratio of 0.75) back plate receives higher amount of radiation which in turn increases the temperature of the back plate. Higher temperature increases the radiation losses from the back plate of the reactor. The shorter length of the reactor also increases the radiation loss through the aperture which can be decrease by using a comparatively larger length reactor. The aperture radiation loss seems insensitive for an aspect ratio higher than 1.0.
Finally, for the reactive material scale analysis, a participating medium Monte
Carlo ray tracing code is created for the continuum model involving heat and mass transfer coupled with chemical kinetics to investigate the effect of various parameters
(such as operating temperature, input steam flow rate, steam concentration) on hydrogen production. The coupled model is validated against the experimental results.
The coupled model simulation results show good agreement with the experimental results.
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154 BIOGRAPHICAL SKETCH
Abhishek Kumar Singh was born in Aligarh, India in 1984. He graduated with a
Bachelor of Technology degree in mechanical engineering from Aligarh Muslim
University in 2006. He worked as a software engineer in Accenture and JP Morgan
Chase. To pursue his aspiration of receiving higher education, he enrolled in the PhD program in mechanical engineering at University of Florida in 2009 and was subsequently accepted for research work by Dr. Jörg Petrasch. His research concentrated on multi-scale, multi-physics analysis of an iron/iron oxide looping cycle for hydrogen production. Parts of his research have been published in the International
Journal of hydrogen energy and proceedings of ASME conferences. He is awarded
Marshall Plan Foundation fellowship to work at FH Vorarlberg; Austria.
155