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Modeling and simulation of a novel internal circulating fluidized bed reactor for selective catalytic… Cheng, Xingxing 2013

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  MODELING AND SIMULATION OF A NOVEL INTERNAL CIRCULATING FLUIDIZED BED REACTOR FOR SELECTIVE CATALYTIC REDUCTION OF NITROGEN OXIDES by Xingxing Cheng M. Sc., Southeast University, Nanjing, 2008 B. Eng., Southeast University, Nanjing, 2006  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF  THE REQUIREMENT FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (CHEMICAL AND BIOLOGICAL ENGINEERING)  The University of British Columbia (Vancouver) October 2013 ?Xingxing Cheng, 2013 ii  Abstract The internal circulating fluidized bed (i-CFB) reactor exhibits an ability to overcome the negative impact of excessive O2 present in the flue gas on selective catalytic reduction of NOx with hydrocarbons as the reductant (HC-SCR) by decoupling NOx adsorption and reaction into two separate zones. A mathematical model has been developed in this study, which includes three sub-models: hydrodynamics, adsorption and reaction kinetics. Each sub-model was developed separately and validated by experimental data before they were integrated into the i-CFB model. For the hydrodynamics of i-CFB, solids circulation rates, which were later used for model parameter fitting, were measured using optical fibre probe. The hydrodynamics model was then developed based mass and pressure balance. Adsorption isotherm and deNOx reaction kinetics were developed based on a series of fixed bed experimental data: O2 adsorption, NOx adsorption and NOx reaction. The kinetic model was further evaluated by fluidized bed adsorption and reaction experiments. The simulation results of the integrated i-CFB model showed good agreement with the experimental data. It is observed from the model that the performance of the current laboratory scale i-CFB reactor was dominated by the catalyst reactivity, rather than the catalyst adsorption rate, because of too short a solids residence time in the reduction zone for the deNOx reaction. Simulation results for i-CFBs with different cross sectional areas of the adsorption and reduction zones showed that a large reduction zone could significantly enhance the overall deNOx efficiency, and there existed an optimal reduction zone to adsorption zone area ratio at which NOx conversion is maximized at a given operating condition. It was also observed that the performance of i-CFB reactors with a larger reduction zone is less sensitive to gas bypass from reduction zone to adsorption zone. Overall, the i-CFB model developed in this study can be used as a tool to assist reactor design and scale up, and to provide guidance on how to further improve the NOx reduction efficiency. The simulation iii  results showed that it is possible to achieve a higher deNOx efficiency higher while avoiding the negative effects of flue gas O2.   iv  Preface  Chapter 2 is based on a literature review which was submitted for publication: Xingxing Cheng and Xiaotao T. Bi, ?A review of recent advances in selective catalytic NOx reduction reactor technologies?. Xingxing Cheng was responsible for all the literature review and the manuscript preparation. Dr. Bi provided feedback and insight throughout this process and edited the manuscript. Chapter 3 is based on the experimental and modeling work conducted in a hot model i-CFB reactor. Xingxing Cheng was responsible for the experimental design, data collection and analysis, model development and manuscript preparation. Dr. Zhiwei Chen (postdoctor fellow in UBC), Dr. Jun Xu (a former visiting student from China), and Dr. Chuigang Fan (a former postdoctor fellow in UBC), kindly helped with the experimental work on solids circulation rate measurement. A manuscript based on Chapter 3 will be published: Xingxing Cheng and Xiaotao T. Bi, ?Hydrodynamics of an i-CFB deNOx reactor?, Powder Technology. Dr. Bi provided feedback throughout this process and edited the manuscript. Similar but different to the work in Chapter 3, another hydrodynamic model was developed for coarse bed materials and the performance of different distributors was compared. The work was presented in the Conference of Fluidization 2013 and has been published in the conference proceeding: Xingxing Cheng and Xiaotao Bi, (2013), ?Gas bypass and solids circulation rate of an i-CFB reactor with coarse particles?, Fluidization 2013. Xingxing Cheng was responsible for the model development and manuscript preparation. Dr. Bi provided feedback and insight throughout this process, edited the manuscript and presented the work in the conference.  Chapter 4 is based on the modeling work conducted by Xingxing Cheng, who carried out all the model development, program coding, data analysis and manuscript preparation. The part of adsorption modeling in fixed bed has been published: Xingxing Cheng and Xiaotao T. Bi, ?Modeling NOx adsorption onto Fe/ZSM-5 catalysts in a fixed bed reactor?, International Journal of Chemical Reactor v  Engineering, Volume 11, Issue 1, Pages 1-12. For this part, Xingxing Cheng carried out all the model development, program coding, data analysis and paper preparation. Dr. Xiaotao T. Bi provided feedback throughout this process and edited the manuscripts. An earlier version of the kinetic modeling part has been published: Xingxing Cheng and Xiaotao T. Bi, (2012), ?Reaction Kinetics of selective catalytic reduction of NOx by propylene over Fe/ZSM-5?, Chemical Engineering Journal, Volume 211-212, Pages 453-462. In this part, Xingxing Cheng carried out all the model development, program coding, data analysis and paper preparation. Dr. Xiaotao T. Bi provided feedback throughout this process and edited the manuscripts. Most of the experimental data used for the modeling was obtained by Terris Tianxue Yang, who conducted the experiment in a fixed bed unit. A paper has also been published: Terris T. Yang, Hsiaotao T. Bi, Xingxing Cheng, (2011), ?Effects of O2, CO2 and H2O on NOx adsorption and selective catalytic reduction over Fe/ZSM-5?, Applied catalysis B: Environmental. Volume 102, Issue 1-2, Pages 163-171. For this paper, Terris T. Yang carried out all the experimental design, data collection and analysis and paper preparation. Dr. Xiaotao T. Bi provided feedback and insight throughout this process and edited the manuscripts. Xingxing Cheng helped with the revision of the paper, conducted part of the literature review and data analysis. Chapter 5 is based on experimental and modeling work in a fixed bed unit and a fluidized bed unit. Xingxing Cheng was responsible for the experimental design, data collection and analysis, model development, program coding and manuscript preparation. Dr. Zhiwei Chen and a former visiting student from China, Dr. Luning Tian, kindly helped with the experimental setup and running. A paper based on Chapter 5 has been published: Xingxing Cheng and Xiaotao T. Bi, (2013), ?Modeling and simulation of nitrogen oxides adsorption in fluidized bed reactors?, Chemical Engineering Science, Volume 96, Pages 42-54. Dr. Xiaotao T. Bi provided feedback and insight throughout this process and edited the manuscript. Chapter 6 is based on the modeling work conducted by Xingxing Cheng, who was responsible for the model development, program coding and manuscript preparation. The work will be submitted to a journal for publication: Xingxing Cheng, Xiaotao T. Bi, ?Modeling catalytic reduction of NOx in the vi  reaction zone of an i-CFB reactor?. Dr. Xiaotao T. Bi provided feedback and insight throughout this process and edited the manuscript. An earlier version of the fluidized bed model, together with a different kinetic model was published in a conference proceeding:  Xingxing Cheng, Xiaotao Bi, (2010), ?Modeling of fluidized bed hydrocarbon catalytic deNOx reactors?, Proceedings of 10th China-Japan Symposium on Fluidization. Xingxing Cheng carried out all the model development, program coding, data analysis and manuscript preparation. Dr. Bi provided feedback and insight throughout this process, edited the manuscript and presented the work in the conference. Chapter 7 is based on the modeling work conducted by Xingxing Cheng, who was responsible for the model development, program coding and manuscript preparation. The work will be submitted to a journal for publication: Xingxing Cheng, Xiaotao T. Bi, ?Modeling catalytic reduction of NOx in a novel i-CFB reactor?. Dr. Xiaotao T. Bi provided feedback and insight throughout this process and edited the manuscript.vii   Table of contents  Abstract ......................................................................................................................................................... ii Preface ......................................................................................................................................................... iv Table of contents ......................................................................................................................................... vii List of tables ............................................................................................................................................... xiii List of figures ............................................................................................................................................. xiv List of abbreviations .................................................................................................................................. xix Nomenclature ............................................................................................................................................. xxi Acknowledgements ................................................................................................................................ xxxvi Chapter 1 Introduction .................................................................................................................................. 1 1.1 Background ......................................................................................................................................... 1 1.2 Previous research results summary on i-CFB ..................................................................................... 4 1.3 A review on fluidized bed reactor models .......................................................................................... 6 1.4 Research objective of this study ......................................................................................................... 8 1.5 Thesis layout ....................................................................................................................................... 9 Chapter 2 Literature review: SCR reactors ................................................................................................. 10 2.1  SCR technologies: reaction mechanisms and catalysts ................................................................... 10 2.1.1 NH3-SCR ................................................................................................................................... 10 2.1.2 HC-SCR .................................................................................................................................... 12 viii  2.1.3 NOx storage reduction (NSR) .................................................................................................... 14 2.2 SCR reactors ..................................................................................................................................... 15 2.2.1 Structured reactors ..................................................................................................................... 15 2.2.2 Fluidized bed reactors ............................................................................................................... 20 2.2.3 Moving bed reactors .................................................................................................................. 22 2.3 Multifunctional SCR reactors ........................................................................................................... 24 2.3.1  Decoupled adsorption-reaction................................................................................................. 24 2.3.2 Combined SCRs ........................................................................................................................ 35 2.4 Summary ........................................................................................................................................... 36 Chapter 3 Hydrodynamics in i-CFB: experiments & modeling .................................................................. 38 3.1 Introduction ...................................................................................................................................... 38 3.2 Experiment details ............................................................................................................................ 38 3.2.1 Experimental setup .................................................................................................................... 38 3.2.1 Bed expansion ........................................................................................................................... 42 3.2.2 Gas bypass ................................................................................................................................. 42 3.2.3 Solids circulation rate ................................................................................................................ 43 3.3 Hydrodynamics model of i-CFB ...................................................................................................... 46 3.3.1 Mass and pressure balance equations ........................................................................................ 46 3.3.2 Pressure drop calculation .......................................................................................................... 47 3.3.3 Effective bed height .................................................................................................................. 48 3.4 Results and discussion ...................................................................................................................... 52 ix  3.4.1 Bed expansion characteristics ................................................................................................... 52 3.4.2 Gas bypass ................................................................................................................................. 54 3.4.3 Measured solids circulation rates .............................................................................................. 56 3.4.4 Prediction of solids circulation rate ........................................................................................... 62 3.5 Summary ........................................................................................................................................... 66 Chapter 4 Development of deNOx reaction kinetics ................................................................................... 67 4.1 Introduction ...................................................................................................................................... 67 4.2 Experiments ...................................................................................................................................... 69 4.2.1 Experimental setup .................................................................................................................... 69 4.2.2 Adsorption performance of Fe/ZSM-5 ...................................................................................... 72 4.3 Adsorption and reaction modeling in fixed bed................................................................................ 74 4.3.1 Kinetics of adsorption ............................................................................................................... 74 4.3.2 NOx reduction kinetics model ................................................................................................... 76 4.3.3 Governing equations of the fixed bed reactor model ................................................................ 77 4.4 Modeling results and discussion ....................................................................................................... 80 4.4.1 Fitting of adsorption isotherm curves ........................................................................................ 80 4.4.2 Model parameters for the fixed bed adsorption model .............................................................. 82 4.4.3 Simulations of NOx adsorption in fixed bed.............................................................................. 86 4.4.4 deNOx reaction kinetics for Fe/ZSM-5 catalyst ........................................................................ 88 4.5 Summary ........................................................................................................................................... 90 Chapter 5 Modeling NOx adsorption in fluidized bed reactors ................................................................... 92 x  5.1 Introduction ...................................................................................................................................... 92 5.2 Experiment........................................................................................................................................ 93 5.3 Fluidized bed adsorption model........................................................................................................ 94 5.3.1 Adsorption isotherm .................................................................................................................. 94 5.3.2 Governing equations for fluidized bed ...................................................................................... 94 5.3.3 Hydrodynamics ......................................................................................................................... 96 5.3.4 Mass transfer ............................................................................................................................. 97 5.3.5 Gas and solids mixing ............................................................................................................... 97 5.4 Experimental results ......................................................................................................................... 98 5.4.1 Fixed bed ................................................................................................................................... 98 5.4.2 Fluidized bed ............................................................................................................................. 99 5.5 Modeling results ............................................................................................................................. 100 5.5.1 Parameter fitting ...................................................................................................................... 100 5.5.2 Simulation of fluidized bed NOx adsorption ........................................................................... 104 5.5.3 Simulation of adsorption zone in an i-CFB deNOx reactor ..................................................... 109 5.6 Summary ......................................................................................................................................... 115 Chapter 6 Modeling NOx reduction in fluidized bed reactors ................................................................... 117 6.1 Introduction .................................................................................................................................... 117 6.2 Fluidized bed reactor model ........................................................................................................... 117 6.2.1 Model governing equations ..................................................................................................... 117 6.2.2 Model parameters .................................................................................................................... 119 xi  6.3 Fluidized bed modeling results ....................................................................................................... 119 6.3.1 Model verification ................................................................................................................... 119 6.3.2 Fluidized bed simulation ......................................................................................................... 122 6.3.3 Simulation of reduction zone of an i-CFB .............................................................................. 126 6.4 Summary ......................................................................................................................................... 135 Chapter 7 Modeling catalytic NOx reduction in i-CFB reactors ............................................................... 136 7.1 Introduction .................................................................................................................................... 136 7.2  i-CFB experiment .......................................................................................................................... 136 7.3 i-CFB model ................................................................................................................................... 138 7. 3.1 Reaction zones........................................................................................................................ 139 7.3.2 Governing equations ............................................................................................................... 141 7.3.3 Hydrodynamics ....................................................................................................................... 144 7.4  Modeling results and comparison with experimental data ............................................................ 145 7.4.1 Model verification ................................................................................................................... 145 7.4.2 Sensitivity analysis .................................................................................................................. 150 7.5 Simulation of i-CFB: design and optimization ............................................................................... 153 7.5.1 Solids back-mixing .................................................................................................................. 153 7.5.2 Solids circulation rate .............................................................................................................. 156 7.5.3 i-CFB configurations ............................................................................................................... 158 7.6 Summary ......................................................................................................................................... 166 Chapter 8 Conclusions and recommendations for future work ................................................................. 168 xii  8.1 Conclusions .................................................................................................................................... 168 8.1.1 Hydrodynamics model ............................................................................................................ 168 8.1.2 Adsorption model .................................................................................................................... 169 8.1.3 Reaction model ........................................................................................................................ 170 8.1.4 i-CFB model ............................................................................................................................ 171 8.2 Recommendations for future work ................................................................................................. 172 References ................................................................................................................................................. 174 Appendix A More discussions on solids circulation rate .......................................................................... 186 Appendix B Derivation of adsorption isotherm ........................................................................................ 188 Appendix C Detailed discussion on kf ...................................................................................................... 192 Appendix D Details of adsorption experiments ........................................................................................ 195 D.1 Experimental procedure of fixed bed adsorption ........................................................................... 195 D.2 Experimental details of fluidized bed adsorption .......................................................................... 196 D.3 Experimental results of fixed bed adsorption ................................................................................ 197 D.4 Experimental results of fluidized bed adsorption .......................................................................... 198 Appendix E Sensitivity analysis of fluidized bed adsorption model ........................................................ 200 Appendix F MATLAB codes for i-CFB model ........................................................................................ 201     xiii  List of tables   Table 1.1  Inlet conditions of experiments conducted by Yang [11] ............................................................ 5 Table 1.2 Submodels and data sources used for the modeling of the i-CFB reactor .................................... 9 Table 3.1  Dimensions of the cold model i- CFB unit ................................................................................ 40 Table 3.2 Fine Fe/ZSM-5 particle properties .............................................................................................. 42 Table 3.3 Calculation procedures for effective bed heights ........................................................................ 51 Table 4.1 Inlet conditions of fixed bed adsorption experiments ................................................................. 72 Table 4.2 Fitted parameters for adsorption model ...................................................................................... 81 Table 4.3 Comparison of fitted and estimated mass transfer parameters .................................................... 85 Table 4.4 Fitted kinetic model parameters (T=350 ?) ............................................................................... 89 Table 5.1 Experimental conditions of NOx adsorption ............................................................................... 94 Table 5.2 Parameters used in the fluidized bed adsorption model ............................................................ 103 Table 6.1 Inlet conditions for different fluidized bed used for simulation ............................................... 129 Table 7.1 i-CFB equations and boundary conditions ................................................................................ 142    xiv  List of figures  Figure 1.1 Schematic of the integrated NOx adsorption-reduction process .................................................. 3 Figure 2.1 Schematics of wire gauze structured reactor [50] ...................................................................... 17 Figure 2.2 Wire-mesh honey comb reactor [50] ......................................................................................... 18 Figure 2.3 Schematics of ceramic foam [51] .............................................................................................. 19 Figure 2.4 Schematics of MOC?s low-pressure-drop deNOx fluidized bed reactor [5] .............................. 21 Figure 2.5 Fluidized bed reactor for simultaneous SO2/NOx removal [57] ................................................ 22 Figure 2.6 Moving bed SCR reactors, (a), MMC design [58], (b), BWPGG design [59] .......................... 23 Figure 2.7 Mechanism of decoupled deNOx process, (a), HC-SCR; (b), direct NO decomposition .......... 25 Figure 2.8 Schematic of NOXSO?s IFB reactor [64] .................................................................................. 27 Figure 2.9 Schematics of a temperature swing adsorption (TSA) process [69] .......................................... 30 Figure 2.10 Working principle of loop reactor [73] .................................................................................... 32 Figure 2.11 Reverse flow reactor ................................................................................................................ 33 Figure 2.12 Countercurrent internal recirculation reactor [75] ................................................................... 33 Figure 2.13 Schematics of the rotating reactor ........................................................................................... 34 Figure 3.1 Schematics of the i-CFB reactor ................................................................................................ 39 Figure 3.2 Schematics of the i-CFB system ................................................................................................ 41 Figure 3.3 Schematics of the gas bypss between the draft tube and the annulus ........................................ 43 Figure 3.4 Details of the tip of the optical fibre probe for particle velocity measurement ......................... 44 Figure 3.5 Voidage calibration of the optical probe (Symbols: experimental data, line: correlation) ........ 45 Figure 3.6 Schematic of four i-CFB flow modes and the effective bed height ........................................... 51 Figure 3.7 Measured voidage data for ZSM-5 powders and comparison with the Cai correlation (Symbols: experimental data, line: correlation) ........................................................................................................... 53 xv  Figure 3.8 Gas bypass ratios at different Ud0. (a), from draft tube to annulus, Rd-a; (b), from annulus to draft tube, Ra-d (Symbols: experimental data, lines: correlation) ................................................................ 55 Figure 3.9 Measured radial profiles of (a) voidage and (b) particle velocity at different Ua0, (Ud0=1 m/s, bed loading=2.275 kg. Symbols: experimental data, lines: connection of symbols) .................................. 58 Figure 3.10 Measured radial profiles of (a) particle velocity and (b) voidage at different Ua0, (Ud0=1 m/s, bed loading=3.3 kg. Symbols: experimental data, lines: connection of symbols) ...................................... 59 Figure 3.11 Measured radial profiles of (a) axial particle velocity and (b) voidage at Ua0=0.1 m/s (Symbols: experimental data, lines: connection of symbols) ...................................................................... 60 Figure 3.12 Net solids circulation rate at different Ud0, with bed solids loadings of (a), 2.275 kg, and (b), 3.3 kg. Symbols: experimental data, lines: connection of symbols) ........................................................... 61 Figure 3.13 Calculated (a) voidage and (b) effective bed height at a bed solids loading of 3.3 kg (Symbols: calculated data points, lines: connection of symbols) ............................................................... 63 Figure 3.14 Fitted CD values as a function of Rep (Symbols: experimental data, lines: connection of symbols) ...................................................................................................................................................... 64 Figure 3.15 Predicted (a) CO2,d and (b) Gs as a function of Ua0 ................................................................... 65 Figure 4.1 Fixed bed reaction system ......................................................................................................... 70 Figure 4.2 Adsorption capacity of (a) O2 at different temperatures and (b) NOx at different O2 concentrations (Symbols: experimental data, lines: connection of symbols) ............................................. 73 Figure 4.3 Schematics of NOx adsorption mechanism onto the catalyst surface ........................................ 78 Figure 4.4 Adsorption capacities as a function of the feed concentration at different temperatures (Symbols: experimental data; lines: isotherm model) ................................................................................. 81 Figure 4.5 Comparison of fitted and experimental adsorption curves in the fixed bed reactor at 325? with NO=600 ppm .............................................................................................................................................. 82 Figure 4.6 Comparison of model fitted and experimental adsorption curves at different (a) NOx concentrations and  (b) temperatures. (Symbols: experimental data; lines: model fitting) ......................... 86 xvi  Figure 4.7 (a): gas phase concentration along the reactor length; (b): effluent concentration as a function of time at different temperatures ................................................................................................................. 87 Figure 4.8 Effluent NOx concentration as a function of time at different GHSV ....................................... 88 Figure 4.9  Modeled and simulated conversions at different HC:NO ratios in fixed bed, (a), NOx conversion; (b), HC conversion. (Symbols: experimental data; lines: model fitting) ................................. 90 Figure 5.1 Schematic of mass transfer (a) in the fluidized bed and (b) around particles ............................ 95 Figure 5.2  Adsorption capacity at different feed NOx concentrations. (Symbols: experimental data; lines: fitted isotherm model) ................................................................................................................................. 99 Figure 5.3 Breakthrough curves at (a) different NOx inlet concentrations at 250 ?; and (b) different gas velocities at 300 ? .................................................................................................................................... 100 Figure 5.4 Comparison of model-fitted and experimental breakthrough curves at different (a) velocities and (b) temperatures (Symbols: experimental data; lines: model fitting) ................................................. 102 Figure 5.5 Model evaluation at different temperatures (Symbols: experimental data; lines: model fitting) .................................................................................................................................................................. 104 Figure 5.6 (a) Outlet NOx concentrations in different phases as a function of time; (b), dimensionless NOx concentration as a function of dimensionless bed height, (t=170 s) ......................................................... 106 Figure 5.7 Influence of particle size on outlet NOx concentrations .......................................................... 107 Figure 5.8 Influence of superficial gas velocity on outlet NOx concentration .......................................... 109 Figure 5.9 Gas and solids flow in (a) conventional fluidized bed and (b) continuous fluidized bed decoupled from the i-CFB reactor ............................................................................................................ 110 Figure 5.10 NOx adsorption performance as a function of Gs* ................................................................. 113 Figure 5.11 NOx adsorption performance as a function of Cs,feed/Cs* ........................................................ 115 Figure 6.1 Modeled NOx and HC conversion as a function of superficial gas velocity in the fluidized bed (Symbols: experimental data; lines: model fitting) ................................................................................... 122 Figure 6.2 NOx conversion at different Ug in fixed and fluidized bed reactors ........................................ 123 Figure 6.3 Dimensionless axial profiles of NOx concentration in different phases .................................. 124 xvii  Figure 6.4 NOx conversion at different gas dispersion and interphase mass transfer coefficient as a function of Ug ............................................................................................................................................ 125 Figure 6.5 Dimensionless solids phase NOx concentration along the reactor at different settings ........... 126 Figure 6.6 Flow diagram of fluidized bed and decoupled i-CFB ............................................................. 127 Figure 6.7 Dimensionless NOx concentration as a function of Ug for different reactors .......................... 131 Figure 6.8 Xr as a function of Ug in different reactors .............................................................................. 132 Figure 6.9 Overall efficiency, Xr, and slip ratio, Sl, as a function of Gs/Gs0 ............................................ 133 Figure 6.10 Xr and Sl values at different solids circulation rate ............................................................... 135 Figure 7.1 Schematics of i-CFB model ..................................................................................................... 139 Figure 7.2 Schematics of the flow regions of i-CFB studied .................................................................... 140 Figure 7.3 (a) NOx and (b) HC conversion as a function of Ua0 (O2=4%, Ud0=0.6 m/s. Symbols: experimental data; lines: model fitting) .................................................................................................... 147 Figure 7.4 NOx conversion as a function of Ua0 at O2=4%, a), Ud0=0.75 m/s, b), Ud0=0.9 m/s (Symbols: experimental data; lines: model fitting) .................................................................................................... 148 Figure 7.5 NOx conversion as a function of Ua0 at a), Ud0=0.6 m/s , b), Ud0=0.75 m/s (Symbols: experimental data; lines: model fitting) .................................................................................................... 149 Figure 7.6 Comparison of NOx conversion in an i-CFB and a regular fluidized bed (Symbols: experimental data; lines: model fitting) .................................................................................................... 150 Figure 7.7 Sensitive of NOx conversion in i-CFB to gas bypasses ........................................................... 152 Figure 7.8 Sensitivity of NOx conversion to variations in NOx adsorption capacity and reduction rate constant ..................................................................................................................................................... 153 Figure 7.9 Profile of dimensionless NOx concentration along bed height ................................................ 155 Figure 7.10 Axial profiles of dimensionless solids phase NOx concentrations at different Gs ................. 157 Figure 7.11 NOx conversion as a function of solids circulation rate Gs .................................................... 158 Figure 7.12 Schematics of the simulated i-CFB ....................................................................................... 160 Figure 7.13 NOx conversion as a function of AR/Atotal .............................................................................. 162 xviii  Figure 7.14 NOx concentration change as a function of AR/Atotal at different zones ................................. 163 Figure 7.15 Sensitivity of NOx conversion to NOx adsorption capacity for i-CFBs with different configurations ........................................................................................................................................... 165 Figure 7.16 Sensitivity of NOx concentration change to catalyst NOx adsorption capacity ..................... 165 Figure A.1 Experimental and modeled solids circulation rates at a bed solids loading of 2.275 kg. (Symbols: experimental data; lines: modeling results.) ............................................................................ 187 Figure D.1 Schematics of fluidized bed set-up ......................................................................................... 196 Figure D.2 Fixed bed NOx adsorption breakthrough curves at 250 ? ..................................................... 198 Figure D.3 Repeated breakthrough curves in the fluidized bed (T=300 ?, NO=900 ppm) ..................... 198 Figure D.4  Breakthrough curve of different NOx inlet concentrations at (a) 300 ? and (b) 350 ?. ...... 199 Figure E.1 Model sensitive analysis ......................................................................................................... 200      xix   List of abbreviations  BWPGG Babcock & Wilcox Power Generation Group CSTR Continuously stirred tank reactors  deNOx NOx reduction ESP Electrostatic precipitator  FCC Fluidized catalytic cracking Fe(AA)3 Iron(III) acetylacetonate GHSV Gas hourly space velocity, h-1 HC Hydrocarbon HC-SCR Selective catalytic reduction with hydrocarbon I.D.  Inner diameter i-CFB Internal circulating fluidized bed IFB Interconnected fluidized bed  IMPO Impregnation in organic solution LNP Lean NOx traps  MMC Mitsui Mining Company  MOC Mobile Oil Company  NH3-SCR Selective catalytic reduction with ammonia NSR NOx storage-reduction NTP Non-thermal plasma  O.D. Outer diameter PUC China University of Petroleum (Beijing, China) xx  SCR Selective catalytic reduction SNCR Selective non-catalytic reduction VOC Volatile organic compound ZSM-5 One type of zeolite   xxi  Nomenclature  A Reactor cross area, m2 Aa Cross sectional area of the annulus, m2 AA Cross sectional area of the adsorption zone, m2 ab Contacting area of bubbles in unit volume, m-1 Ad Cross sectional area of the draft tube, m2 Ai Arrhenius pre-exponential coefficient of reaction i, mol/s.m3 Aor Area of orifice, m2 AR Cross sectional area of the reduction zone, m2 Atotal Total cross sectional area, m2 b Adsorption coefficient in Langmuir isotherm, - B Lumped coefficient for site coverage on the catalyst, - b0 Adsorption coefficient in Langmuir isotherm, - bNO2 Adsorption coefficient in Langmuir isotherm of NO2, - C0 Initial concentration, mol/m3 Ca,H Concentration in the dense (high) phase of the annulus, mol/m3 Ca,in Inlet concentration of the annulus, mol/s xxii  Ca,L Concentration in the bubble (low) phase of the annulus, mol/m3 Ca,out Concentration at the outlet of the annulus, mol/m3 CD Discharging coefficient of the orifice, - Cd,H Concentration in the dense (high) phase of the draft tube, mol/m3 Cd,in Inlet concentration of the draft tube, mol/s Cd,L Concentration in the bubble (low) phase of the draft tube, mol/m3 Cd,out Concentration at the outlet of the draft tube, mol/m3 Cfeeding Feeding concentration, mol/m3 Cg Concentration in gas phase, mol/m3 Cg* Gas phase concentration in equilibrium with solids phase, mol/m3 Cg,in Inlet concentration in gas phase, mol/m3 Cg,out* Outlet gas phase NOx concentration in equilibrium with solids phase inlet NOx concentration, mol/m3.cat Cgi Concentration in gas phase of species i, mol/m3 CH Concentration in high (dense) phase, mol/m3. cat CHC,a Hydrocarbon concentration in the annulus, mol/m3 CHC,a0 Hydrocarbon concentration in the flue gas fed into the annulus, mol/m3 CHC,d Hydrocarbon concentration in the draft tube, mol/m3 xxiii  CHC,d0 Hydrocarbon concentration in the reductant gas fed into the draft tube, mol/m3 Ci Concentration of species i, mol/m3 Cin,NOx-A NOx concentration at the inlet of the adsorption zone, mol/m3 Cin,NOx-R NOx concentration at the inlet of the reduction zone, mol/m3 CL Concentration in low (bubble) phase, mol/m3. cat cm Total number of active on the catalyst, mol/kg cat CNO NO concentration, mol/m3 CNO,a NO concentration in the annulus, mol/m3 CNO,a0 NO concentration in the flue gas fed into the annulus, mol/m3 CNO,d NO concentration in the draft tube, mol/m3 CNO,d0 NO concentration in the reductant gas fed into the draft tube, mol/m3 CO2 O2 concentration, mol/m3 CO2,a Oxygen concentration in the annulus, mol/m3 CO2,a0 Oxygen concentration in the flue gas fed into the annulus, mol/m3 CO2,d Oxygen concentration in the draft tube, mol/m3 CO2,d0 Oxygen concentration in the reductant gas fed into the draft tube, mol/m3 Cout Outlet concentration, mol/m3 Cout,NOx-A NOx concentration at the outlet of the adsorption zone, mol/m3 xxiv  Cout,NOx-R NOx concentration at the outlet of the reduction zone, mol/m3 Cs Concentration in solids phase, mol/m3. cat Cs* Solids phase NOx concentration in equilibrium with gas phase inlet NOx concentration, mol/m3.cat Cs,feeding Concentration in feeding solids, mol/m3. cat Cs,in Inlet concentration in solids phase, mol/m3 Cs,out* Outlet solids phase NOx concentration in equilibrium with gas phase inlet NOx concentration, mol/m3.cat CXNOx-A NOx concentration change in the adsorption zone, % CXNOx-R NOx concentration change in the reduction zone, % D Diameter, m Da Diameter of the annulus zone, m Db Bubble diameter, m Dd Diameter of the draft tube, m De Effective diffusivity, m2/s Dg Gas axial dispersion coefficient, m2/s DH Axial dispersion coefficient of high (dense) phase, m2/s DL Axial dispersion coefficient of low (bubble) phase, m2/s xxv  Dm Molecular diffusivity, m2/s dp Particle diameter, m Ds Axial dispersion coefficient of solids phase, m2/s E Overall efficiency, - Eai Activation energy of reaction i, J/mol Er Reduction efficiency, % F Gas flow rate at room temperature, m3/s FA Flow rate in the adsorption zone, m3/s Fa0 Flow rate of feeding gas in the annulus, m3/s Fa-d Flow rate of gas bypass from the annulus to the draft tube, m3/s Fb Gas flow rate in bubble phase, m3/s Fd Gas flow rate in the draft tube, m3/s Fd0 Flow rate of feeding gas in the draft tube, m3/s Fd-a Flow rate of gas bypass from the draft tube to the annulus, m3/s Fflue-gas Flow rate of flue gas, m3/s Ffw Gas-wall friction force per unit volume of the column, N/m3 Fpw Particle-wall friction force per unit volume of the column, N/m3 Fr Froude number,- xxvi  FR Flow rate in the reduction zone, m3/s g Acceleration due to gravity, 9.8 m/s2 Gs Solids circulation rate, kg/m2.s Gs* Dimensionless solids circulation rate Gs,0 Minimum solids circulation rate, kg/m2.s H Bed height, m Ha Bed height in the annulus, m HCA Hydrocarbon molar flow rate in the adsorption zone, mol/s HCR Hydrocarbon molar flow rate in the reduction zone, mol/s HCt Total hydrocarbon molar flow rate, mol/s Hd Bed height in the draft tube, m Hdraft-tube Height of the draft tube, m Hf Expanded bed height, m HG Gap distance in the distributor, mm Hmf Bed height at minimum fluidization, m Hs Bed height, m k Overall mass transfer coefficient, s-1 K Adsorption equilibrium in linear adsorption isotherm, - xxvii  k1 Reaction rate coefficient of reaction 1 (forward), - k'1 Intraphase mass transfer coefficient, s-1 k-1 Reaction rate coefficient of reaction 1 (reversed), - k2 Reaction rate coefficient of reaction 2 (forward), - k'2 Intraphase mass transfer coefficient, s-1 k-2 Reaction rate coefficient of reaction 2 (reversed), - k3 Reaction rate coefficient of reaction 3, - k4 Reaction rate coefficient of reaction 4, - kc External mass transfer coefficient, m/s kf Intraphase mass transfer coefficient, s-1 kF Freundlich adsorption constant related to sorption capacity, - k'f Modified intraphase mass transfer coefficient, s-1 kf0 Intraphase mass transfer coefficient, s-1 kFi Freundlich adsorption constant related to sorption capacity of species i, - kFNO2 Freundlich adsorption constant related to sorption capacity of NO2, - kFO2 Freundlich adsorption constant related to sorption capacity of O2, - kHL Interphase mass transfer coefficient, m/s ki Reaction rate coefficient of reaction i, - xxviii  Ki Adsorption equilibrium of species i, - ki0 Reaction rate coefficient of reaction i, - Ki0 Adsorption equilibrium of species i, - KNO2 Adsorption equilibrium of NO2, - k'NO2 Lumped Freundlich adsorption constant related to sorption capacity of NO2, - k''NO2 Freundlich adsorption constant related to sorption capacity of NO2 lumped with O2, -  KO2 Adsorption equilibrium of O2, - L Reactor length, m  La Effective bed length in the annulus, m La0 Initial effective bed length in the annulus, m Ld Effective bed length in the draft tube, m Ld0 Initial effective bed length in the draft tube, m Le Effective distance of optical fibre, m Lj Jet penetration depth, m m1 Reaction order, - m2 Reaction order, - m3 Reaction order, - m4 Reaction order, - xxix  m5 Reaction order, - Ma Catalyst weight in the annulus, kg Md Catalyst weight in the draft tube, kg Mloading Catalyst loading in i-CFB, kg MNO Molecular weight if NO, 30 g/mol n Freundlich adsorption constant related to sorption intensity, - N(Q) Number of sites having adsorption energy Q, - ni Constant in Freundlich adsorption equations of species i, - nNO2 Constant in Freundlich adsorption equations of NO2, - nNOx Constant in Freundlich adsorption equations of NOx, - nO2 Constant in Freundlich adsorption equations of O2, - P Operation pressure, Pa Pec Correlated P?clet number, - Pef Fitted P?clet number, - PeH P?clet number of high (dense) phase, - Pes P?clet number of solids phase, - Q Adsorption energy, J/mol q Adsorbate loading, mol/m3 cat xxx  q- Average adsorbate loading, mol/m3 cat q* Adsorbate loading in equilibrium, mol/m3 cat Qb Volumetric gas flow rate in bubble phase, (m3/s) qe Adsorption capacity, mol/m3. cat qe,i Adsorption capacity of species i, mol/m3. cat qeNOx Adsorption capacity of NOx, mol/m3. cat qeO2 Adsorption capacity of O2, mol/m3. cat QNOx,d-a  Molar flow rate of NOx returned from the annulus to the draft tube, mol/s QNOx,feeding Molar flow rate of NOx in the feeding flue gas, mol/s QNOx,slip  Molar flow rate of NOx slipping out of the reduction zone, mol/s R Ideal gas constant, 8.314 J/Pa.K r Radius, m R0 Radius of fluidized bed, m  r1 Reaction rate of reaction 1, mol/s.m3 r2 Reaction rate of reaction 2, mol/s.m3 r3 Reaction rate of reaction 3, mol/s.m3 r4 Reaction rate of reaction 4, mol/s.m3 Ra Radius of the annulus, m xxxi  Ra-d Gas bypass ratio from the annulus to the draft tube, % Rd Radius of the draft tube, m Rd-a Gas bypass ratio from the draft tube to the annulus, % Re Reynolds number,  - Rec Reynolds number at transition velocity, -  Rep Reynolds number around particles, - rHC Reaction rate of HC, mol/s.m3 RHC:NO Molar ratio of HC:NO, - Ri Reaction rate of species i, mol/s.m3 rNOx Reaction rate of NOx, mol/s.m3 rO2 Reaction rate of O2, mol/s.m3 Rp Radius of particles, m S Integrated area of the adsorption curve, s Sc Schmidt number, - Sh Sherwood number, - Sl NOx slip ratio from reduction zone, % t Time, s T Temperature, K xxxii  T0 Ambient temperature, ? t1/2 Breakthrough time, s U Superficial gas velocity, m/s Ua Real gas velocity in the annulus, m/s Ua,H Gas velocity of the dense (high) phase in the annulus, m/s  Ua,L Gas velocity of the bubble (low) phase in the annulus, m/s  Ua0 Feeding gas velocity in the annulus, m/s Ub Bubble rise velocity, m/s Uc Transition velocity at which standard deviation of pressure fluctuation reaches a maximum, m/s Ud Gas velocity in the draft tube, m/s Ud,H Gas velocity of the dense (high) phase in the draft tube, m/s  Ud,L Gas velocity of the bubble (low) phase in the draft tube, m/s  Ud0 Feeding gas velocity in the draft tube, m/s Ug Gas velocity, m/s UH Gas velocity in high (dense) phase, m/s UL Gas velocity in low (bubble) phase, m/s Umf Minimum fluidization velocity, m/s xxxiii  Uout Gas velocity at the outlet, m/s Up Particle velocity, m/s Up,a Particle velocity in the annulus, m/s Up,d Particle velocity in the draft tube, m/s Us Solids velocity, m/s Ut Terminal velocity, m/s Vcatalyst Volume of catalyst, m3 Vg Gas volumetric flow rate, m3/s Vs Solids volumetric flow rate, m3/s Wcat Catalyst loading, g X Conversion, % x Fraction, - Xr NOx conversion in reduction zone, % Y Dimensionless coefficient, - z Axial position in the reactor, m ?P Pressure drop, Pa ?Pa Pressure drop in the annulus, Pa ?Pa0 Initial pressure drop in the annulus, Pa xxxiv  ?Pd Pressure drop in the draft tube, Pa ?Pd0 Initial pressure drop in the draft tube, Pa ?Por Pressure drop through the orifice, Pa ? Pre-exponential coverage coefficient, - ? Voidage, - ?a Voidage in the annulus, - ?b Bubble fraction, - ?d Voidage in the draft tube, - ?mf Voidage at minimum fluidization, - ?s Solids fraction, - ? Coverage on the catalyst, - ?T Total coverage on the catalyst, - ? Coefficient for Freundlich constant related to temperature, - ? Dynamic viscosity, Pa.s ?g Gas density, kg/m3 ?p Density of catalyst particles, kg/m3 ? Time lag, s ?a,H Fraction of high (dense) phase in the annulus, - xxxv  ?a,L Fraction of low (bubble) phase in the annulus, - ?d,H Fraction of high (dense) phase in the draft tube, - ?d,L Fraction of low (bubble) phase in the draft tube, - ?H Fraction of high (dense) phase, - ?L Fraction of low (bubble) phase, - ? Slip factor, -    Spherical coefficient, -  s?xxxvi   Acknowledgements  I would like to take this opportunity to express my sincere gratitude to my supervisor, Dr. Xiaotao Bi, for his immense guidance and financial assistance during my research. I give utmost appreciation to my research committee members, Dr. Jim Lim and Dr. W. Kendal Bushe, for their valuable suggestions at the start of this work. Many individuals who contribute to this research would be greatly acknowledged. Dr. Terris Tianxue Yang, a former PhD student in our group, who carried out the preliminary research work on i-CFB catalytic reduction of NOx by hydrocarbon in our group, provided very used suggestions on the experimental work. Dr. Chuigang Fan, a former postdoctor fellow in our group, contributed a lot to the setup of the fixed bed and i-CFB units. Dr. Zhiwei Chen, a postdoctor fellow from Dr. Bi?s group, helped a lot with the model development, program coding, solids circulation rate measurement and fluidized bed setup. Dr. Jun Xu, a former visiting student from China, provided help with the i-CFB reactor setup and solids circulation rate measurement. Dr. Luning Tian, a former visiting student from China, helped with the experimental work of fluidized bed adsorption investigation. I also appreciate the hard work of the technical and administrative staff in the department stores, offices and workshop. This research was financially supported by the Canada Foundation for Innovation (CFI) and the Natural Science and Engineering Research Council of Canada (NSERC). I?m also grateful to a CSC Scholarship from China.  Last but not least, I am sincerely grateful to my family for their endless support and encourage throughout my whole life. 1  Chapter 1  Introduction  1.1 Background Growing environmental awareness in recent years has resulted in the introduction of more rigorous and stringent environmental laws and regulations. The term ?air pollutant? covers all substances which may harm humans, animals, vegetation and material [1, 2]. The main sources of air pollution are the combustion processes of fuels used in power plants, vehicles and other incineration processes. Key combustion-generated air contaminants are sulfur oxides (principally SO2), particulate matter, carbon monoxide, hydrocarbons and nitrogen oxides (NOx). NOx are considered as the primary pollutants of the atmosphere, since they are responsible for the formation of photochemical smog, acid rain and ground level ozone, the destruction of stratosphere ozone layer and even global warming (mainly associated with N2O) [1-3].  There are two major sources of NOx: mobile combustion engines and stationary sources, such as power plants [1-4]. The abatement of NOx emission can be generally classified into three categories:  pre-combustion control, combustion modification and post-combustion control [2]. Pre-combustion control can be achieved by fuel purification to reduce the nitrogen content in the fuel. Combustion modification alters operational conditions to reduce the NOx formation. Both pre-combustion and combustion controls are helpful, but can only achieve a modest reduction in NOx emissions, usually less than 50% [3, 5]. For applications required to achieve high NOx reduction, post combustion control is needed. Post-combustion control, as the term suggests, deals with nitrogen oxides in exhaust gases from combustion or incineration processes. The most commonly used technologies are selective non-catalytic reduction (SNCR) and selective catalytic reduction (SCR) of NOx [3, 4]. 2  SNCR reactors are typically operated at 870-980 ?, with urea or ammonia as the reductant to reduce NOx to N2 [3, 4]. Capital costs are moderately low because no catalyst is required. A drawback of this approach is that the maximum level of NOx reduction achievable is only about 50% [5]. The SCR process is a proven technology for NOx emission control [4, 5]. It operates at moderate temperatures, with a higher capital and operating costs than SNCR. It adds reducing agent to a NOx containing flue gas stream and relies on a catalyst, usually honeycomb monoliths, to promote the reduction of NOx by reducing agent. It is the only single method which can achieve more than 75% NOx control efficiency for the flue gases emitted from stationary combustion sources with a high selectivity toward N2 [6]. A well-designed SCR reactor could reach an efficiency of 94% and tolerable ash contents up to a maximum of 50 g/m3 [6]. The NH3-SCR offers a practical approach for NOx abatement, and has been commercialized [6, 7]. However, it has the following drawbacks: the handling of large quantities of NH3 is a concern because NH3 is toxic and corrosive. Furthermore, un-reacted NH3 may potentially be discharged to the environment (ammonia slippage) [3, 4]. It could also react with SO3 and H2O to form ammonium sulphate, causing the fouling of downstream equipment. Vanadium emissions and high operating costs are also obstacles for this technology [3, 8]. Taking the drawbacks of the NH3-SCR process into account, hydrocarbons instead of NH3 have been considered as the most promising alternate reducing agents for the SCR process. As a technology under development, most studies have focused on the development of catalysts, the selection of reducing agents, or the understanding of the reaction mechanisms of the process [9]. In order for such a technology to be used in industrial processes, engineering aspects still need to be considered to address technical challenges in the reactor design and scale-up for the HC-SCR process. To avoid the negative impact of the poisoning components and excess O2 in the flue gas, Yang and Bi [10] proposed a new concept of an integrated NOx adsorption-reduction process, where the NOx 3  adsorption and reduction are carried out in two separate zones of the reactor, as shown in Fig. 1.1. The flue gas is passed into the adsorption zone where NOx is adsorbed by the catalyst. The NOx-adsorbed catalyst particles then move into the reaction zone where NOx is reduced by injected hydrocarbons at controlled oxygen concentrations, and at the same time, other adsorbed flue gas contaminants are also stripped from the catalyst. The regenerated catalyst particles are then recirculated back to the adsorption zone to establish a continuous operation. The hypothesis has then been validated in a novel internal circulating fluidized bed (i-CFB) reactor and the work was presented in Yang?s PhD thesis [11]. Reduction zoneAdsorption zoneCatalystCatalystFlue gasReductant gas Figure 1.1 Schematic of the integrated NOx adsorption-reduction process  4  1.2 Previous research results summary on i-CFB The main objective of Yang?s work [11] was to evaluate the potential application of the integrated adsorption-reduction process for the selective catalytic reduction of NOx with hydrocarbons in the internal circulating fluidized bed (i-CFB) reactor.  The catalyst used by Yang [11] was Fe/ZSM-5, which showed a good performance. The catalyst support was H/ZSM-5 (BET surface area of 171 m2/g), which was obtained as a free sample from Albemarle Corporation. The fine Fe/ZSM-5 catalyst was prepared by wet impregnation in organic solution (IMPO) of toluene. The prepared fine Fe/ZSM-5 catalyst has an iron content of 5% and a BET surface area of 163 m2/g, which is slightly lower than the original ZSM-5 catalyst support. The reducing agent used for the HC-SCR process was propylene, which also showed good NOx reduction activity over ZSM-5 catalysts in other researches [12, 13]. Three experiment units were built by Yang [11]: a fixed bed unit to test the adsorption performance and reaction kinetics of the catalyst; a cold model i-CFB unit to investigate the hydrodynamics, mainly gas bypass; and a hot model i-CFB, with the same dimension of cold model i-CFB, to study the deNOx performance. The hypothesis of i-CFB was validated by Yang [11] by a series of experiments. In the fixed bed reactor, the catalyst was tested at different inlet conditions for its adsorption and reaction performances. The hydrodynamics of i-CFB, mainly gas bypass between the annulus and draft tube, was investigated in the cold model i-CFB unit. Then the deNOx reaction was studied in the hot model i-CFB reactor. The results showed that the catalyst exhibited promising NOx reduction performance and a strong ability to inhibit the negative impact of excess O2 in the i-CFB reactor, proving that adsorption-reduction two-zone reactor is effective for the NOx removal from oxygen-rich combustion flue gases. For different experiments, the different reaction conditions and parameters investigated are summarized in Table 1.1. Details of the data could be found in [11]. It should be noted that another catalyst Fe/ZSM-5 (PUC), 5  which was prepared from a different ZSM-5 support, was also tried by Yang [11]. But its performance for deNOx is much worse. Similarly, some other i-CFB configurations with different distributors were also tested, but finally dropped due to the unsatisfactory hydrodynamic characteristics. These results won?t be used for the modeling. In this thesis, only the selected results are discussed. Table 1.1  Inlet conditions of experiments conducted by Yang [11] Unit Experiment Inlet condition Parameters investigated Fixed bed NO adsorption O2=4% NO=200, 400, 600, 800, 1000 ppm GHSV=5000 h-1 NOx adsorption breakthrough curves NOx adsorption capacity NOx reaction O2=0.5, 1, 2, 4, 8 % NO=600 ppm HC:NO= 0.5, 1, 2, 4 GHSV=5000 h-1 NOx conversion HC conversion Cold model i-CFB Hydrodynamics Ua0=0.2~0.45 m/s Ud0=0.4~0.9 m/s Gas bypass ratios: Ra-d, Rd-a Hot model i-CFB NOx reaction NO=600 ppm HC:NO=1, 2 O2=1, 4, 8, 12 % Ua0=0.2~0.5 m/s Ud0=0.6~0.9 m/s NOx conversion HC conversion Regular fluidized bed NOx reaction NO=600 ppm HC:NO=1, 2 O2=1, 4, 8 % Ug=0.2~0.6 m/s NOx conversion HC conversion   6  1.3 A review on fluidized bed reactor models For the modeling of fluidized bed reactors, two types of models have been proposed: mechanistic models and computational fluid dynamic (CFD) models.  Mechanistic modeling is an interactive process of representing a system found in nature by an abstract mathematical description based on physical and chemical principles in order to make prediction and gain insights about the system?s underlying phenomena. This process attempts to match observations with a set of equations describing and explaining what is observed and/or measured in nature, and predicting the behaviour of a system [14]. Mechanistic models are the most traditional method used for fluidized bed modeling since 1950s [15]. They incorporate the key factors, such as dispersion, convection, mass transfer, mass and molar balance equations, leaving out factors of lesser importance. These models could provide rational approaches for predicting key features of fluidized beds while keeping the calculation simple.  The other type is the computational fluid dynamic (CFD) model, which is established based on fundamental continuity, momentum and energy equations (Navier-Stokes equations). CFD codes have had great success in recent decades in simulating single-phase flows. Similar approaches have been attempted by a number of research groups for multiphase flows. With the fast development of high speed computers, CFD models have become an expanding subject and are playing an important role in fluidization applications. There are two categories of CFD models for gas-solids flows: Lagrangian-Eulerian models and Eulerian-Eulerian models. While multiphase CFD models will no doubt make valuable future contributions to predicting the performance of fluidized bed reactors, they are currently unable to make reliable predictions [16]. Comparing to CFD models, mechanistic models are currently more reliable, while also being much easier to be used [16]. In the current study, the mechanistic model is selected.  7  The conversion in gas-solids fluidized bed reactors has been observed to be lower than those with the gas flow being assumed as in plug flow or  well-mixed flow [17]. Historically, two classes of mechanistic models have been proposed to describe the performance of fluidized bed reactors: one is based on a pseudo-homogeneous approach and the other on a two-phase approach [18]. The pseudo-homogeneous approach, where the existence of more than one phase is not taken into account, applies the conventional single phase flow models, such as dispersion models, CSTR-in-series models, to fluidized bed reactors.  The two-phase approach, however, considers the fluidized reactor to consist of at least two phases, a bubble phase and an emulsion/dense phase, and proposes separate governing equations for each phase with a term describing mass interchange between the two phases. The concept of two-phase fluidization [15] and the first two-phase fluidized-bed reactor model [19] dated back to the 1950s. Since then, various two-phase reactor models have been developed for different fluidization regimes. Those models, which incorporate solid fractions, mixing and interphase exchange, have been used for modeling and scale-up of fluidized bed reactors. Such models include the Grace [20] two-phase model, the Kunii and Levenspiel [21] three-phase model, the Kato and Wen [22] bubble assemblage model and the Partridge and Rowe [23] cloud model, just to list a few. These models have either been derived or comprehensively summarized by Grace [20, 24], Kunii and Levenspiel [25] and more recently by Marmo et al. [26] for bubbling bed. Bi et al. [27] summarized models developed for turbulent fluidized bed reactors, accounting for interchange of gas between low- and high-density phases, axial dispersion, gas convection and reaction. Recently, generalized comprehensive models were further developed by Abba [28] and Mahecha-Betero [14], which are applicable across the flow regimes most commonly encountered in industrial scale fluidized bed reactors.  8  1.4 Research objective of this study The possible application of the integrated adsorption-reduction process for the selective catalytic reduction of NOx with hydrocarbons was identified and demonstrated by Yang [11] in an internal circulating fluidized bed. The i-CFB reactor exhibited the ability to overcome the negative impact of excessive O2 in the flue gas using Fe/ZSM-5 as the deNOx catalyst. In order to scale up this process and to understand the underlying fundamental mechanism of this novel i-CFB reactor system, a mathematical reactor model is needed. Furthermore, the NOx conversion in the current i-CFB design was less than 80%, which needs to be further optimized in order to improve the deNOx efficiency. Modeling is an effective and efficient approach to systematically examine the i-CFB reactor at low-cost. The objective of this research is to develop a mathematical model for the i-CFB reactor to predict, simulate and ultimately improve the performance of the i-CFB reactor, assisting the design and scale up of pilot and commercial i-CFB deNOx reactors.  Before developing the i-CFB model, three different parts will be studied first: hydrodynamic, adsorption kinetics and reaction kinetics. Key hydrodynamic parameters of an i-CFB include gas bypass and solids circulation rate. An adsorption isotherm of the investigated catalyst will be developed based on fixed bed adsorption experimental data and then evaluated by fluidized bed adsorption experimental data. Similarly, reaction kinetics of the catalyst will be developed from fixed bed reaction experiment data and then evaluated by the fluidized bed performance data. Finally, the hydrodynamic, adsorption and reaction kinetics models are integrated to simulate the performance of i-CFB reactors. Data in Yang?s thesis [11] will be used to fit model parameters and evaluate the model predictions. Additional experiments are also carried out to measure the model parameters not investigated in the previous studies. Different parts of the i-CFB model, together with the experimental data sources, are listed in Table 1.4.    9  Table 1.2 Submodels and data sources used for the modeling of the i-CFB reactor Models Sub-models Experimental data source Hydrodynamics Gas bypass rate Yang [11] Solids circulation rate This study Adsorption  Fixed bed adsorption: adsorption isotherm Yang [11] and this study Fluidized bed adsorption performance This study Reduction  Fixed bed reaction: kinetics Yang [11] Fluidized bed reaction performance Yang [11] i-CFB model i-CFB reaction performance Yang [11]  1.5 Thesis layout Chapter 1 provides the background of the project, a summary of previous work conducted in our group and the objectives of this study. A literature review is then presented in Chapter 2 to summarize the development of SCR technologies and novel reactors. Hydrodynamics of i-CFB, including gas bypass and solids circulation rate, is studied by both experiment and modeling in Chapter 3. Adsorption breakthrough curves and reaction kinetics are developed based on fixed bed test data in Chapter 4. Then adsorption isotherms and kinetics are used to model adsorption performance in fluidized beds, together with the performance of the adsorption zone in an i-CFB, in Chapter 5. NOx reaction kinetics is applied to investigate the NOx reduction performance in a fluidized bed reactor in Chapter 6. Finally, the NOx reaction in the i-CFB is modeled and simulated in Chapter 7 by integrating the hydrodynamic, adsorption and reaction kinetics models in Chapters 3 to 6. Recommendations are also made on how to improve the design and performance of the i-CFB for catalytic NOx reduction. Conclusions drawn from this study and recommendations for future studies are given in Chapter 8. 10  Chapter 2  Literature review: SCR reactors1   To date, SCR technology has been reviewed extensively [2, 8, 9, 29, 30], with a special focus on the reaction mechanism and catalyst development. Only limited efforts have been made to address the knowledge and advancement of reactor design and process optimization. The main focus of this chapter is to review and examine the recent development of SCR reactors and processes. First, SCR mechanism and catalyst development will be briefly reviewed for different reducing agents: NH3/urea, hydrocarbons and hydrogen. Then the SCR reactors developed for different purposes will be discussed. Some non-SCR reactors, such as non-selective reduction (NSR) and direct NO decomposition, will also be examined, since they show either a high similarity with the SCR technology or have been used in combination with SCR for NOx removal.  2.1  SCR technologies: reaction mechanisms and catalysts 2.1.1 NH3-SCR Currently, NH3-SCR is the most widely used technology for its high efficiency and wide operating temperature window [3]. This method involves the reaction of NOx with NH3 within a catalytic bed at appropriate temperature ranges (200-400 ?). NOx species react with NH3 according to several reactions, with the dominant ones being [3]:                                                      1 A version of this chapter has been submitted for publication: Xingxing Cheng and Xiaotao T. Bi, A review of recent advances in selective catalytic NOx reduction reactor technologies. 11  OHNONHNO 2223 6444 ????        (2.1) OHNNHNO 2232 12786 ???        (2.2) Ammonia is first chemisorbed onto the active sites of the catalyst surface, where it reacts with adsorbed NOx from the flue gases. Depending on applications there are different possible ammonia sources, e.g. liquefied ammonia, ammonium carbamate, urea dissolved in water and solid urea. The catalyst is of primary importance for the process, and much of the on-going research has been focused on improving the catalyst performance. The catalysts for NH3-SCR processes are normally metal or metal oxides supported on SiO2, TiO2, carbon-based materials or zeolites [9]. The selection of catalyst depends on the efficiency of NOx removal, operating temperatures and catalyst regeneration. Almost all metals and their combinations have been tested in SCRs of NOx reduction by NH3. Among metal oxides studied, pure vanadium and oxidized vanadium on oxide supports such as alumina, silica, zirconia and titania have been extensively investigated. Additionally, catalysts based on pure, supported and/or mixed metal oxides of iron, copper, chromium and manganese were also extensively tested. Particular interest has been placed on V2O5 mixed with WO3 and/or MoO3 supported on TiO2 because of their robustness to SO2 poisoning and their high reactivity at temperatures around 300 ? [31]. However, vanadium is a pollutant to the environment and is difficult to dispose of.  Catalysts with metals supported on zeolites have become popular for their comparable efficiencies and lower prices than TiO2. The most studied catalysts are Cu/ZSM-5 and Fe/ZSM-5. Cu/ZSM-5 is well known as the best low temperature SCR catalyst [32]. It is favored for configurations where the exhaust gas temperature is below 450 ?. Fe/ZSM-5 has also been studied extensively for NH3-SCR [33-37]. Fe/ZSM-5 SCR catalysts are preferred at higher temperatures, from 450 ? to 600 ? [37, 38]. To expand the temperature window, combinations of Cu-zeolite and Fe-zeolite have been tested, and it was reported that the temperature range could be widened for this combined catalyst system [38]. Other metals have 12  also been added to the zeolite to widen the temperature window. Kim [9] added Mn to Fe/ZSM5 catalyst and demonstrated excellent low-temperature SCR activity.  2.1.2 HC-SCR  NH3-SCR offers a practical approach for NOx abatement, and has been commercialized [7]. However, it has the following drawbacks: the handling of large quantities of NH3 is a concern because NH3 is toxic and corrosive. Furthermore, un-reacted NH3 may potentially be discharged to the environment (ammonia slippage). It could also react with SO3 and H2O to form ammonium sulphate, causing the fouling of downstream equipment. Vanadium emissions and high operating costs are also obstacles for this technology [8]. Taking the drawbacks of NH3-SCR process into account, hydrocarbons instead of NH3 have been considered as the most promising alternate reducing agents for the SCR process. The first study on SCR of NOx with hydrocarbons was reported by Iwamoto et al. [39]. Thereafter, SCR of NOx by hydrocarbons (HC-SCR) has attracted considerable attention as an alternative to ammonia or urea process for the treatment of oxygen-rich flue gases, and various types of catalysts and reducing agents have been widely investigated [40].  Three types of catalyst have been studied for HC-SCR reaction: metal oxides (represented by Ag/Al2O3), ion-exchanged zeolites (Cu/ZSM-5) and noble metal catalysts (Pt). The metal oxide catalysts for the reduction of NOx by hydrocarbons have attracted attention due to its high activity and hydrothermal stability [9, 41]. Zeolite based catalysts have received much attention due to its high activity and relatively wide temperature window. So far, the most extensively studied catalysts are Cu and Fe supported on zeolite, especially ZSM-5 [9]. Cu/ZSM-5 might be the most studied catalyst for its high NO conversion over a wide temperature window (300-550 ?) using various reducing agents. However, deactivation of zeolite catalyst by H2O and SO2 in the flue gas is still an obstacle in the practical applications. Comparing to Cu/ZSM-5, Fe/ZSM-5 shows better resistance against water vapour at lower 13  reaction temperatures 250-400 ? [11]. Compared to metal oxides and ion exchanged zeolites, noble metal catalysts are active at low temperature regions. Moreover, they show relatively better resistance against SO2 [9]. The major issue with Fe/ZSM-5 is its low selectivity toward N2 (typically 30%).  There are two main mechanisms for selective catalytic reduction of NOx by hydrocarbons. One is the adsorption/dissociation mechanism [9], which involves the adsorption of NO on the active metal sites and then dissociation into N(ads) and O(ads). The O(ads) reacts with hydrocarbon to form CO2, and two N(ads) combine to produce N2. The reactions on noble metal are usually regarded as following the adsorption /dissociation mechanism. The other one is the oxidation-reduction mechanism [9]. NO first reacts with oxygen to produce some initial reactive intermediates such as NO2, NO3(ads). At the same time, hydrocarbon is activated to hydrocarbon oxygenates. The intermediates can differ for different catalysts and reducing agents. In recent years evidence has been generated to support the adsorption/reduction mechanism, at least in principle, although full details at the elementary reaction level on the catalyst surface remain to be established [42]. More about the catalysts and mechanism of HC-SCR can be found in earlier review papers [9, 41]. One of the obstacles for HC-SCR is its lower NOx conversion than that in NH3-SCR at a given reductant to NOx stoichiometric ratio, because of the poor selectivity of HC toward NOx. The utilization efficiency of hydrocarbons is quite poor with less than one-tenth of injected hydrocarbon being used for NOx reduction, if the oxidant is taken as NO, and less than one in five if it is NO2. The remainder is wasted through combustion. The overall removal of NOx under practical conditions in vehicles tests is low, less than 30%, due to many factors including inhibition by the high steam content, the interactions within hydrocarbon mixtures and a poor temperature match [42].  Recently, selective catalytic reduction of NOx by H2 (H2-SCR) has attracted more and more attention for the NOx removal [8]. When H2 is used as the reducing agent, NOx can be effectively reduced at low temperatures (T<200 ?). Moreover, that the combustion of H2 in air produces water without any 14  CO2 formation makes it environmentally benign. Nobel metals, and particularly supported Pt and Pd catalysts, exhibited higher NOx conversion.  But the cost is very high compared to the catalysts used for NH3- and HC-SCR. Moreover, only a few catalysts have been tested on their water and SO2 resistance for the H2-SCR reaction. More information on the mechanism and factors controlling the performance of H2-SCR catalyst can be found in [8].  2.1.3 NOx storage reduction (NSR) NOx storage reduction (NSR), also known as lean NOx traps (LNP), was first developed by Toyota and is generally regarded as a leading deNOx technology for lean burn vehicle engines. NSR catalysts usually consist of a NOx storage component (typically BaO) and a precious metal (Pt and Rh) supported on gamma-alumina. Under the lean-conditions NO was adsorbed onto the BaO surface and oxidized to NO2 over the catalyst which was then stored in a form of nitrate at the BaO surface. After changing periodically to short cycles of fuel-rich conditions the stored NOx was released from the BaO surface and reduced to N2 by HC, CO, and H2 generated from incomplete combustion of fuels over the noble metal catalyst, resulting in the regeneration of the BaO catalyst. The NOx reduction efficiency could reach essentially up to 100%.  Generally speaking, NSR is not classified as an SCR technology, but an independent NOx control technology. However, all aspects of this technology, no matter its application, catalysts or reaction kinetics, show a high similarity with SCR technology, especially HC-SCR. To some extent, it can be considered as an SCR process with NOx adsorption and reduction decoupled. There is also a trend to combine the NSR and SCR technologies for deNOx of lean burn engines.   15  2.2 SCR reactors 2.2.1 Structured reactors   2.2.1.1 Monolith reactors The conventional configuration of SCR reactors is the catalytic monolith reactor, with the catalysts pre-formed into two shapes, plate-type and honeycomb-type [6]. The catalytic monolith reactor has been widely used as a pollution abatement device because of its structural integrity and unique advantages such as high heat and mass transfer rates per unit of pressure drop, high specific interfacial area, and ease of scale-up compared to packed bed or ceramic foam reactors [43]. It consists of a matrix of a large number of parallel channels of about 1 mm in hydraulic diameter. The catalyst is deposited in the form of a washcoat (of typical average thickness of 10-50 ?m) on the inner walls of the channels. As the reacting fluid flows along the channel, the reactants diffuse transverse to the flow direction from the bulk gas phase into the washcoat where they diffuse and react on the active catalyst sites. There are also some disadvantages of this reactor, such as the absence of radial mixing, low interphase mass and heat transfer rates and low contact areas. In a typical monolith reactor, only 10% of the volume is occupied by the catalytically active ?washcoat?, with the rest being the monolith itself and the empty channels [44]. Moreover, the NOx removal efficiency may gradually decrease due to the plugging by fly-ash in the straight channels of the monolith honeycomb catalyst. The conventional monolithic catalyst works the best with flue gases from furnaces and engines, which contain moderate amounts of NOx and other gaseous pollutants, but are relatively free of particulates. It could not work well for flue gases with a high dust load. Several modified configurations were proposed for SCRs to be operated with high dust loadings. Kraftanlagen [45] proposed the use of a rotating basket or rotating honeycomb element. Exhaust gases containing NOx would flow over a segment in rotation, so that incoming air, flowing in the opposite direction, could dislodge some of the particulates 16  from the catalyst. Kittrell and Herman [46] tested the reduction of nitric oxide in a dust laden gas with ammonia in a reactor with the gas passing near, but not through, the catalyst bed. The only way for NOx to reach the catalyst bed was via diffusion from a plurality of centrally located tubes containing fine perforations. Dust laden gas passed through the tubes, but never impinged directly on the catalyst bed.  2.2.1.2 Metal wire reactors As an alternative to monolith reactors, metal wire gauzes as catalyst supports and structured reactor internals were recently studied by Od?owski [47] for NH3-SCR as schematically shown in Fig. 2.1. This new structure was also investigated by the same group on its hydrodynamics [48] and other applications, such as for the combustion of VOCs [49].  It was reported that this new type of structured catalytic reactors possesses high mass transfer rates and moderate flow resistances [48]. When used for NH3-SCR, wire gauze internals decreased reactor length by 10 times comparing to monolith [47] because of the enhanced heat and mass transfer rates. Furthermore, even for a moderately fast reaction such as NH3-SCR of NOx, the catalyst loading and activity play less important roles than the catalyst distribution inside the reactor. The support structure determines the external and the internal diffusional resistances, and thus, reactor yield as well as the overall flow resistance. Although proven to be highly efficient for NOx reduction, problems could arise during operation since the layers of weaved metal wires could be plugged by fly ash more easily than the monolith reactor. Cleaning the plugged ash could also be more difficult than the monolith because of the lack of straight channels inside the reactor.  17  Flue gas Figure 2.1 Schematics of wire gauze structured reactor [50]  In a further study of Sun [50], a wire-mesh honeycomb was manufactured by stacking alternatively corrugated and plain wire-mesh sheets, as shown in Fig. 2.2, which combined the characteristics of wire-mesh and monolith catalysts. This structure was found to not only enhance the external mass-transfer rate but also provide a more uniform fluid flow distribution across the entire cross section of the bed, which offered better efficiencies of gas-solid contact. Since gas could pass through the straight channels, dust tolerance of this reactor could also be better than the wire gauze structured reactor. The wire-mesh honeycomb, compared to the ceramic monolith with a similar cell density, had a higher geometric surface area, larger open frontal area, lower pressure-drop and also a higher NOx conversion efficiency, as evidenced from HC-SCR experiments [50].  18   Figure 2.2 Wire-mesh honey comb reactor [50]  Conventional packed bed reactors were also investigated as a comparison to the gauze reactor and monolith reactor by Jod?owski [47]. The catalyst loading and the flow resistance of the three types of reactors followed such an order: packed bed reactor>gauze reactor>monolith. Based on the results, the conventional packed bed reactor appears to be ineffective for high-efficiency exhaust gas cleaning applications because of its high flow resistance and the high diffusional resistance (especially internal diffusion) that gives a very low effectiveness factor of the catalyst pellet.   2.2.1.3 Ceramic or metal foam reactors Another packed structure, monolith ceramic or metal foam, as shown in Fig. 2.3, has attracted increasing attention because of its unique structure and morphology which offers the potential for having a low pressure drop and high heat and mass transfer rates, which is different from other packed bed reactors [51]. Foam monoliths can be made of ceramic or metal. The open cell foams consist of a network of interconnected solid struts building cavities (=cells) that communicate through windows. Ceramic foams and metallic foams have open porosities of about 75-85% and 95%, respectively. The open structure of foams allows the fluid to pass through with low-pressure drops while maintaining good radial mixing and 19  enhanced turbulence in the tortuous flow paths. The heat transport to the walls occurs not only by conduction, as in honeycombs, but also by convection and radiation. Patcas [51] showed that catalytic foam packings combine a high permeability to gas flow with good mass and heat transfer characteristics. The pressure drop and mass transfer coefficient are between those of packed bed and honeycomb monoliths. Compared to honeycomb monoliths, foams offer the advantage of radial mixing and more efficient heat transfer. Although never tested for SCR application, the feasibility of its application should be investigated in the future by coating SCR catalysts onto the foam support. The foam reactor could be a potential alternative to a monolith reactor, especially in the applications where heat transfer and mass transfer are of greater importance. Due to the tortuous flow paths, the dust load is expected to be more problematic than both monolith and metal wire structure reactors.      Figure 2.3 Schematics of ceramic foam [51]  2.2.1.4 Combined NOx and PM capture Unlike the above reactors, an integrated SCR-ESP reactor with the catalyst coated on collector plates of the electrostatic precipitator (ESP), was constructed to capture particulate and reduce NOx [52]. Ammonia injected either directly into the ESP or upstream catalytically reduces NOx to N2. An excess amount of ammonia also helps the capture of particulates in the ESP because of the increased particle surface 20  conductivity. This could also prevent problems of ammonia slippage. In another study [53], high-temperature fabric filters were coated with a layer of a proprietary vanadium/titanium (V/Ti) catalyst. The catalyst-coated fabric filters are targeted for simultaneous NOx and particulate control in power plants or industrial facilities installed with high temperature baghouses. Issues pertaining to the successful development and marketing of this technology, such as catalyst and filter durability, NOx and particulate control efficiencies, ammonia slip levels, and catalyst deactivation have also been addressed [52].   2.2.2 Fluidized bed reactors  Fluidized beds have been extensively explored for NOx removal. Small Fe particles supported on silica sand (139-400 ?m) were fluidized in a bubbling bed for NO reduction with CO as a reducing agent at high temperatures, i.e., 700-900 ? [54]. Alumina particles or CuOx/Al2O3 were also used as catalysts for the reduction of NO in bubbling fluidized bed reactors [55, 56]. Irfan et al. [56] evaluated NO removal over CuO/?-Al2O3 catalyst in a bubbling fluidized bed and investigated the effects of fluidizing gas velocity, NH3 to NO molar ratio, and the static bed height on the reduction of NO at various reactor temperatures. It was observed that bubble size increase with increasing gas velocity led to a decrease in NO conversion. Therefore, there is a need to decrease the bubble size and solids back-mixing in the fluidized bed in order to improve the reactor performance. Another major issue concerning fluidized beds is excessive sorbent attrition, requiring mechanically strong catalysts to minimize attrition losses. However, the mechanical strength of SCR catalysts has seldom been investigated. CuO/?-Al2O3 prepared by Rahmaninejad [31] was reported to have a high attrition resistance based on the durability test. After 25 regeneration cycles, the catalytic activity for NOx reduction did not decrease noticeably. Fluidized beds also show advantages over fixed beds for treating flue gases with high dust loadings. The fluidized bed reactor was applied by Mobile Oil Company [5] (MOC)  for high dust flue gas treatment from the FCC process. Gas containing NOx and entrained catalyst fines pass up through a bed 21  of catalyst at a sufficient velocity to expand and fluidize the catalyst bed. Particulates deposited on the catalyst are dislodged or elutriated by fluidizing gases, preventing fouling of the deNOx catalyst. A reduction efficiency of up to 90% could be reached, while the pressure drop through such a bed was reasonably low although higher than that through a honeycomb. An improved reactor design was developed to lower the pressure drop by allowing side entry of gases into the fluidized bed to lower the superficial gas velocity, as presented in Fig. 2.4. NOx, NH3 Figure 2.4 Schematics of MOC?s low-pressure-drop deNOx fluidized bed reactor [5]  Gao [57] used a fluidized bed for simultaneous removal of NOx and SO2, in which NOx was reduced by NH3 over coarse WO3/TiO2 particles and SO2 was adsorbed onto fine particles consisting of CuO, ZnO and dust. Both fine and coarse particles were fluidized, with only fine particles being entrained from the bed continuously for regeneration. The schematic of the unit is shown in Fig. 2.5. The reaction temperature was tested from 300 ? to 600 ? and it was found that at 600 ? the highest efficiency was achieved with 100% NOx reduction and 80% SO2 capture. 22   Figure 2.5 Fluidized bed reactor for simultaneous SO2/NOx removal [57]  The fluidized bed configuration offers a number of advantages over the honeycomb structure, including a better gas solid contact, less chance for dust clogging, and a more compact reactor size, as well as facilitation of in-situ regeneration of the catalyst. Further effort is still needed to investigate catalyst attrition in the fluidized bed. Careful design is also required to improve the reaction performance by decreasing bubble size and solids back-mixing.   2.2.3 Moving bed reactors  Moving beds, which can prevent dust clogging and has low solids back-mixing, has also been applied for NOx control. A moving bed technology invented by Mitsui Mining Company (MMC) in the 1980s [58] 23  and shown in Fig. 2.6 (a) could be used for either NOx adsorption or reaction. The catalyst particles move from the top to the bottom and are then regenerated and recirculated to the top feeding chamber. Flue gases flow horizontally through the reactor to have the NOx reduced by the catalysts. Various baffles with different shapes are installed in the reactor to control the gas distribution and solid movement. Another configuration of moving beds, which also permits continuous introduction of refreshed catalysts, was applied for NOx reduction recently by Babcock & Wilcox Power Generation Group (BWPGG) [59], as shown in Fig. 2.6(b). Similar to the configuration in Fig. 2.6(a), solids move downward in the reactor while the flue gas flows horizontally through the catalysts. The configurations of baffles installed in the reactor could ensure a good distribution of gas and solids and also a good contact between gas and solids. The continuous operation mode of a moving bed makes the regeneration of catalysts more convenient, which is particularly important for the low sulfur-resistance catalysts, such as Cu and Fe on zeolite. But the continuous recirculation of solids may increase the operation cost of the reactor.  (a)     (b) Figure 2.6 Moving bed SCR reactors, (a), MMC design [58], (b), BWPGG design [59] 24   2.3 Multifunctional SCR reactors 2.3.1  Decoupled adsorption-reaction 2.3.1.1 Mechanism For a heterogeneous catalytic reaction, reactants are first adsorbed onto the surface of the catalyst and then reaction takes place. DeNOx reactor performance could be improved if the adsorption and reaction can take place in different regions of the reactor in order to avoid the negative effects of other gas species on the catalyst performance or to concentrate the NOx for high-efficiency destruction. This may also offer an opportunity for the adsorption and reaction to be optimized independently. This constitutes the basic principle of the decoupled SCR process, with a single reactor serving multiple functions.  For HC-SCR, as discussed in section 2.1.2, one of the major problems is the low selectivity of hydrocarbon toward NOx, especially with flue gases of a high O2 concentration. There has been strong experimental evidence [60-63] that NOx conversion could be seriously suppressed by the high O2 concentration in the flue gas because of its competitive oxidation reaction with the reducing agent. Therefore, the deNOx performance can be potentially improved if the direct contact of HC and O2 can be avoided, see Fig. 2.7(a). In the direct NO decomposition process, NOx in the flue gas could be first adsorbed onto the catalyst. The adsorbed NOx is then desorbed from the catalyst by a separate inert gas stream, usually N2 or Ar. The inert gas stream, which now contains concentrated NOx, could then be treated to decompose NOx into N2 at a high efficiency, often assisted by plasma, as illustrated in Fig. 2.7(b). Usually, the flue gas temperature is controlled to be low during NOx adsorption and high during desorption. Many different reactor configurations have been designed to facilitate these decoupling processes, which will be reviewed next. 25  CatalystCatalystNOO2HCNO, O2NO2HCN2, H2O, etcStep 2: NO2 reduction by HCStep 1: NO oxidation and adsorptionO2 favorableO2 inhibitedHC-SCRNO2 (a) CatalystCatalystNOON2NOxNOxStep 2: NO decompositionStep 1: NO adsorptionO2 favorable,Lower temperatureO2 inhibited,Higher temperatureNO decompositionNOxPlasmaN2  (b) Figure 2.7 Mechanism of decoupled deNOx process, (a), HC-SCR; (b), direct NO decomposition  26   2.3.1.2 SCRs with catalyst swing In order to separate adsorption and reaction in a bi-functional reactor, catalysts saturated with one reactant in the adsorption zone could move to another zone to react with reducing agent or other reactants. The circulating fluidized bed is the most widely used reactor to continuously move particles between different zones of the reactor. An internal circulating fluidized bed, i-CFB (UBC) was proposed by Yang and Bi [10] for an integrated NOx adsorption-reduction process of HC-SCR. The aim was to avoid the negative impact of the excess O2 and poisoning components in the flue gas. The NOx adsorption and reduction are carried out in two separate zones of the reactor, as illustrated in Chapter 1. The flue gas passes through the adsorption zone where NOx is absorbed by the catalyst. The NOx-adsorbed catalyst particles then move into the reaction zone where NOx is reduced by injected hydrocarbons at controlled oxygen concentrations, and, at the same time, other adsorbed flue gas contaminants can also be stripped from the catalyst. The regenerated catalyst particles are then circulated back to the adsorption zone to establish a continuous operation. The feasibility of this design was validated by experiments on an i-CFB. The catalyst used was Fe/ZSM-5 and reducing agent is C3H6. The goal of avoiding negative impact of O2 was further demonstrated by comparing the performance of the i-CFB and a regular fluidized bed loaded with the same amount of catalysts [10].  With the catalyst particles circulating between a reduction zone and an oxidizing zone, it is also expected that the flue gas contaminants such as dusts could be stripped from the catalyst, minimizing fouling and catalyst deactivation caused by the deposit of carbon and other contaminants. Those features can potentially prolong the catalyst life in treating flue gases of high dust loading, although experimental validation is still needed. An interconnected fluidized bed (IFB) was also proposed for simultaneous removal of SO2 and NOx by NOXSO corporation [64] in 1990s, as shown schematically in Fig. 2.8. The IFB consists of multiple 27  compartments, with the flow of solids between compartments being induced and controlled by means of the difference in gas aeration rates. The solids flow from one compartment to the other over a weir or through an orifice which connect the respective compartments. The compartments with upflowing solids act as the adsorber and regenerator and the solids downflow compartments serve as stripper and cooler between two reactors. NOx and SO2 were first adsorbed onto the adsorbents in the adsorber at about 120 ?. Then NOx was removed from the adsorbent in the stripper and SO2 was removed in the regenerator at 680 ?. Hot sorbent was then cooled down to 130 ? and returned to the adsorber. The adsorption-regeneration concept was investigated extensively by the NOXSO corporation in the 1990s in a series of regular fluidized beds. It was reported that the system could remove 70-90% NOx and 90% SO2 [64]. However, the NOx control efficiency in the integrated IFB unit was never reported. The IFB reactor was further investigated in Delft University of Technology [65, 66], with a focus on the hydrodynamics and its potential applications for biomass combustion [66]. Flue gas Air Air Air AirSteam SteamMethane/SteamAdsorber Heater Regenerator CoolerClean gas to stackNOx-rich gas to burnerSlfur-rich gas to ClausWarm air to air heaterR1 R2 R3 R4 R5 R6 R7 R8R1 Figure 2.8 Schematic of NOXSO?s IFB reactor [64] 28  This adsorption-reduction process in a circulating fluidized bed could be further extended to NH3-SCR. V2O5-based catalyst could only adsorb NH3 on the surface and the SCR reaction takes place between adsorbed NH3 species and gaseous NO [67]. In the application of CFB, NH3 could be adsorbed onto the catalysts and then used to reduce NO, avoiding the direct contact of NH3 with SO2 to decrease sulfur poisoning. This method is similar to the rotary bed reactor proposed by Riekert et al. [45], in which it was proven that ammonia bisulfate could be prevented when NH3 was first adsorbed on to the catalyst before contacting flue gas. This feature is especially important for NH3-SCR with zeolite as the catalysts, which have a lower sulfur tolerance. Moreover, zeolite could adsorb both NO and NH3 [67]. The adsorption zone could be designed to adsorb either NO or NH3, depending on the specific requirement of the system.   2.3.1.3 SCRs with gas switching In fluidized beds, catalysts can move from one zone to another to decouple the adsorption and reaction. Such a decoupling could also be realized by switching different gas streams from one zone to another, with one zone operated in the adsorption mode while the other operated in the NOx reduction mode. A combined adsorption-discharge plasma catalytic process for removing low-concentration NOx from flue gases was proposed by Yu [68]. NOx in an oxygen-rich gas stream is first adsorbed by the catalyst in the reactor operated in the adsorption mode (plasma off). Then in the plasma discharge mode, flue gases are switched off while Ar or N2 is turned on to the reactor as the plasma carrier gas to decompose NOx adsorbed on the catalysts by plasma, with  the negative effect of flue gas O2 being avoided. To improve the decomposition of adsorbed NOx in N2 plasma, solid carbon as a scavenger for oxygen species was mixed to the catalyst. The decomposition efficiency of adsorbed NOx was observed, and the carbon was progressively burned off, providing a possibility for the simultaneous removal of NOx and unburned carbon particles at a low energy consumption. 29  A continuous NOx reduction process, which combines non-thermal plasma (NTP) and temperature swing adsorption (TSA), was proposed and tested by Yoshida [69-71] for diesel engine exhaust gas NOx treatment. As shown in Fig. 2.9, the system comprises of two adsorption chambers, 1 and 2, which operate in series. Hot exhaust gas from an engine first indirectly heats up adsorption chamber 1, in which the adsorbent is regenerated by thermal desorption, and the exhaust gas subsequently enters adsorption chamber 2, where NOx is removed by adsorption. A small amount of N2 or low-O2 gas (containing less than a few percent O2) is supplied to chamber 1 to elute desorbed NOx from the chamber. This concentrated NOx stream passes to an NTP reactor and is subsequently reduced. The gas exiting the NTP reactor still contains NOx, and is injected to the air intake of the engine. The adsorbent used is a mixture of CuO and MnOx. It was claimed that both high energy efficiency and high NOx-removal efficiency could be achieved with this system, but the compact design of the adsorption chambers to fit diesel engines will be a challenge. The advantage of this system is that no additional fuel injection (for CO/H2 generation) or urea injection is needed. However, an additional system to produce low O2 gas stream is required. One possible way to produce the low O2 gas is to pass a small amount of air through a particulate-matters (PM) collection unit where the unburned hydrocarbons or carbon particles are reacted with O2 in the air. 30   Figure 2.9 Schematics of a temperature swing adsorption (TSA) process [69]  The above configuration consists of two reactors, one for adsorption and the other one for reaction. Adsorption and reaction take place alternately between these two reactors, which thus requires the two reactors to be exactly identical in order to maintain a stable operation. However, usually the reaction rates of adsorption and reaction are not the same, requiring different reaction time and reactor size. For example, Yoshida [69] pointed out that a bigger adsorption chamber is needed, but not the desorption chamber. Although this unsymmetrical requirement could be balanced by adjusting flow rates in the two reactors, the system could be much simpler for design and operation if identical reactors are adopted.  Another problem associated with the swing-reactor system is the discontinuous alternation between the reactors. Taking the adsorption-reduction system as an example, flue gases and reducing agent are switched alternately between the two reactors. The adsorption time is determined by the breakthrough characteristics of the catalyst. In order to ensure the high capture efficiency, adsorbate concentration must be controlled at a low level. Therefore, most of the catalysts along the reactor are far away from being 31  saturated with NOx. This leads to a very low utilization efficiency of the total adsorption capacity. Comparing to the gas swing reactor, internal circulating bed (i-CFB) offers a higher utilization efficiency of the catalyst adsorption capacity. In i-CFB, highly saturated catalysts are continuously recirculated into the reduction zone and the size of the adsorption and reduction zones can be optimized independently. A more advanced gas switching system, loop reactors, has been proposed for the NH3-SCR process [72-74]. Loop reactors use a network of reactors with periodical switching of the feeding position from one reactor to the next one in sequence. In the reactor, a set of valves allows for the change of the feeding position, thus achieving a sustained dynamic behavior. The working principle is illustrated in Fig. 2.10. The proposed loop reactors take the advantage of the catalysts that could strongly adsorb NH3 in the NH3-SCR process to avoid the ammonia slip while fulfilling the required high NOx conversion. It should be noted that in the loop reactor of Fissore [72], adsorption and reaction are not completely separated although the main purpose of the reactor is to use the high capacity of NH3 adsorption. NH3 and the flue gas were fed to the reactor together. A network of three reactors was built to simulate the behavior of a moving bed [72], which contains commercial zeolite catalysts supported on a monolith. Five three-way valves are required to change the feed position along the sequence of the three reactors: from initial 1-2-3 to 2-3-1 and finally to 3-1-2. The feasibility of  the reactor was demonstrated by both numerical simulations and experiments [72], where NOx reduction efficiency was maintained at more than 90% and ammonia emission was decreased to about 1/10 of the emission from a regular reactor. It was also evidenced that the adsorption capacity can play a role even more important than the catalytic activity [74]. Recent research in Barresi?s group [73] showed the possibility of using an industrial-scale loop reactor to carry out NH3-SCR. The advantages have been highlighted in a case study, where a substantial reduction in energy consumption (65kW vs.130 kW) and the complete avoidance of NH3 slip were achieved.  The main drawback of loop reactors is represented by the reactor configuration, whose piping is much more ?complex? than in the conventional system. Loop reactors were also extensively studied in 32  Sheintuch?s group [75-79], with a main focus on improving the thermal efficiency of the reactor, as well as the design and control technology.  Figure 2.10 Working principle of loop reactor [73]  Another alternative design, which serves a similar function as the loop reactor, is the reverse flow reactor, where sustained dynamic behaviour is obtained by periodically reversing the flow direction, as shown in Fig. 2.11. The reverse flow reactor was first applied for NH3-SCR by Agar [80] in the 1980s. Similar to the loop reactor proposed in Barresi?s group, this reactor also takes advantage of the high NH3 adsorption capacity of catalysts by trapping NH3 in the catalyst. The feasibility of the process was demonstrated by experiments and detailed kinetic modeling. It was reported that this type of reactor design offered high NOx removal efficiency without ammonia slip and ameliorated problems associated with the fluctuations and distribution of the flue gas. However, the reverse flow reactor has a serious drawback, namely the wash-out, i.e. the emission of unconverted reactants when the flow direction is reversed [73]. 33   Figure 2.11 Reverse flow reactor  Countercurrent internal recirculation reactor, as shown in Fig. 2.12, is another design that performs similar to the reverse flow reactor and loop reactor. The main feature of countercurrent internal recirculation reactor is good heat exchanging. In the reactor, the feed gas enters through one (say, inner) tube and then turns around and flows out through (the outer) another. Attaching two such mirror-imaged reactors will form an arrangement similar to the heat-exchanging reactor with countercurrent flow. This reactor is attractive for the NOx-SCR application only when heat released from the reaction is of great significance. Sheintuch [75] compared the performance of a loop reactor, a reverse flow reactor and an internal recirculation reactor in terms of temperature distribution for ethylene oxidation. The results showed that the simpler inner?outer internal-recycle reactor may perform better at low flow rates than that with a flow reversal, but the conclusion is reversed at high flow rates. The performance of loop reactor depends on the switching frequency, reaction/adsorption/desorption kinetics and the reactor length, while the performance of the other two reactors mainly depends on the thermal conductivity of the catalyst bed.  Figure 2.12 Countercurrent internal recirculation reactor [75]  34  Rotating reactors have also been used for NOx-SCR, which behave between a swing reactor and a loop reactor. As shown in Fig. 2.13, the reactor is divided into an adsorption zone and a reduction zone. The catalyst is rotating between the two zones. The rotation of catalyst could also be achieved by switching the feeding gas. Every sector along the axial direction (say, a fan-shaped sector) could be considered as a swing reactor, swinging between the adsorption zone and the reduction zone. However, from the viewpoint of cross section, the reactor could be considered as a loop reactor. Kraftanlagen [45] used a rotary basket reactor where reducing agent NH3 and flue gas pass through the catalyst bed alternately. For catalysts with a higher NH3 storage capacity, NH3 could be first stored onto the catalyst surface before reacts with NOx. The advantage of the NH3 storage-reduction process is the avoided undesired secondary reactions, which form ammonium bisulfate before flue gas and ammonia are introduced onto the catalysts. It was found that the formation of ammonium bisulfate was almost completely prevented. The process could effectively exclude the undesirable deposits onto the catalyst surfaces and the downstream equipment.  Figure 2.13 Schematics of the rotating reactor  35  2.3.2 Combined SCRs 2.3.2.1 Combined NSR-SCR NH3-SCR and NOx storage and reduction (NSR) technologies have been commonly used for controlling NOx in exhaust gases from lean-burn engines. Studies have also been conducted on the combined NSR and SCR system [81-86]. The coupling between a NOx-trap catalyst and a NH3-SCR catalyst located downstream or as a second layer in  a monolith was first patented by Ford in 2004 [86]. The emission control system is used for the treatment of exhaust streams from diesel engines and lean burn gasoline engines to enhance the NOx removal efficiency [81-84].  A typical NSR-SCR system has an NSR catalyst and an SCR catalyst located downstream of the NSR catalyst [85]. While the reduction of NO and NO2 to N2 occurs in the presence of NSR catalyst during the fuel-rich periods, ammonia can also form as a by-product from the NSR catalyst, e.g.: 232 CONHOHCONO ????        (2.3) The generated NH3, a regulated air pollutant, must also now be controlled before the exhaust is vented to the atmosphere, which is accomplished in the SCR catalyst bed where NH3 is used as the NOx reducing agent. This method combines the advantages of NSR and SCR catalysts. Nitrogen oxides are intermediately stored during lean operation, and released during rich operation to form NH3 and stored on either the adsorbent or the SCR catalyst. The stored NH3 can be released to reduce nitrogen oxides during a subsequent fuel-lean operation. The combined system showed a superior NOx removal efficiency (as high as 99.5% at 300 ?) and a lower ammonia slip compared to the single NSR catalyst at all temperatures examined [81]. The highest activity could be obtained during the rich pulse with both CO and H2 as reductants [84]. Cu-ZSM-5 [84, 87] and Fe-ZSM-5 [88-90] are usually used as the SCR catalyst for this combined SNR/SCR process. It was also reported that a mixture of NSR and SCR catalysts gives 36  better performances than the dual bed system [91]. More details on the development and mechanism of such a combined NSR-SCR system could be found in a recent review [91].  2.3.2.2 Combined HC-SCR and NH3-SCR Beside combined NSR and NH3-SCR systems, combined HC-SCR and NH3-SCR systems have also been proposed recently in a dual bed system [92]. The first bed is a single layer (layer A) catalyst bed and the second bed is a double layer (layers A and B) catalyst bed including a first layer catalyst and a second layer catalyst to reduce the nitrogen oxides to N2. The layer A catalyst is selected from the group consisting of Ag/Al2O3, Ag/Y, Ag/ZSM-5, Ag/Ba/Y, or a combination thereof; and the layer B catalyst comes from the group of Pt/Al2O3, Pt/Ba/Al2O3, Cu/ZSM-5, CuCo/Y, Pd/Al2O3, or a combination thereof. The first bed reduces NOx initially through the (HC+OHC)/SCR process to N2, meanwhile also producing NH3 as a byproduct over layer A in the first bed. The NH3 subsequently reduces NOx over layer A and layer B through the NH3/SCR process, producing more N2 and thereby enhancing the NOx reduction efficiency of the hybrid catalyst system.   2.4 Summary  SCR technology has been extensively studied in recent decades. Most of the research mainly focuses on reaction mechanisms and catalyst development. To date, the most widely used SCR technologies include NH3-SCR, HC-SCR and NSR. Among these technologies, NH3-SCR offers the highest NOx reduction efficiency, the best sulfur tolerance and moderate catalyst and operation cost. Ammonia slip is the main obstacle of this technology. As an ammonia-free process, HC-SCR also has high NOx reduction efficiencies. The catalyst cost could be even lower than NH3-SCR. But most of the HC-SCR catalysts tend to be easily poisoned by sulfur in the flue gas. Another problem of this process is hydrocarbon combustion by oxygen presented in the flue gas. NSRs are been developed for lean-burn engines.  37  Although the deNOx efficiency of current SCR technologies is generally high enough to meet the stringent requirements, there still exist drawbacks such as the high cost of the noble metal catalyst. It is expected that proper selection and design of the SCR reactor could alleviate these problems and accelerate the wide application of these technologies. Moreover, catalyst regeneration, which could keep the catalyst activity and prolong the life of catalyst, also impose special requirements for the reactor design. Monolith reactors are simple and the most widely used reactor for its low pressure drop, relatively high interfacial area and ease of scale-up. Other structural reactors, e.g., metal wire reactors and foam reactors, show some advantages over monolith reactors with better mass transfer and heat transfer properties. The major concern for their applications is ash plugging. Comparing to fixed bed reactors, fluidized bed reactors offer a better gas-solid contact and smaller reactor size, as well as easier catalyst regeneration. But further investigation is required to improve the attrition resistance of catalysts and decrease solids back-mixing. Moving bed reactors, which have less solids back-mixing than fluidized beds, were also applied for SCR process. Besides the basic reactors, various multifunctional reactors were also developed for SCR process based on the specific reaction mechanism. These reactors allow for coupling several operations (chemical reaction, separation, and/or heat exchange process) into a single equipment, thus improving yield and selectivity, and reducing investment and operation costs, in comparison to traditional reactor configurations. In these reactors, SCR reactions could be either decoupled or coupled. Adsorption and reaction could be decoupled in the reactor by either catalyst circulation or gas switching to provide better reaction conditions for each step. Different SCR technologies could also be combined to take advantage of each other. Multifunctional reactors should be further investigated since they could potentially enhance the deNOx performance significantly. 38   Chapter 3  Hydrodynamics in i-CFB: experiments & modeling2  3.1 Introduction  The performance of the i-CFB reactor is expected to be impacted significantly by the hydrodynamics in the i-CFB, including both the gas bypass between the draft tube and the annulus regions and the internal solids circulation, which should be well studied in order to properly design the reactor and select suitable operating conditions as well as to provide data for modeling such a reactor. Several studies have been reported on the hydrodynamics of i-CFB reactors, mainly focused on the measurement of solids circulation rates [93, 94] and the development of correlations for predicting the solids circulation rate [95, 96]. These empirical or semi-empirical models could not be applied directly to i-CFBs with different configurations. In this chapter, the performance of the reactor is investigated both experimentally and analytically. Gas bypassing, bed expansion and solids circulation rate in a deNOx i-CFB reactor are tested in a cold model unit. The solids circulation rate is then predicted based on pressure and mass balance equations.   3.2 Experiment details 3.2.1 Experimental setup The i-CFB reactor was constructed by Yang [11], with the configuration shown in Fig. 3.1. The dimensions of the model unit are listed in Table 3.1. There was a draft tube in the reactor. The distance of                                                      2 A version of this chapter will be pubished:  Xingxing Cheng and Xiaotao T. Bi, Hydrodynamics of an i-CFB deNOx reactor, Powder technology. 39  the opening gap between the draft tube and distributor was selected as 10 mm by Yang [11] through a series of experiments. Gas was fed to both the draft tube and annulus at different flow rates and the bed particles circulated between the draft tube and annulus. If the draft tube is taken out, the i-CFB could be operated as a regular fluidized bed. Bed expansion was tested in such a regular fluidized bed.  12345677777    Gas flow    Solid flow1 ? Draft tube gas intlet2 ? Annulus gas inlet3 ? Distributor4 ? Draft tube5 ? Freeboard6 ? Exhaust gas outlet7 ? Measurement points  Figure 3.1 Schematics of the i-CFB reactor     40  Table 3.1  Dimensions of the cold model i- CFB unit Item Dimension Draft tube diameter, mm 50.8 (I.D.), 63.5 (O.D.) Draft tube length, mm 1016 Column diameter, mm 101.6 (I.D.), 114.3 (O.D.) Column height, mm 1092 Freeboard diameter, mm 254.0 (I.D.), 266.7 (O.D.) Freeboard height, mm 508 Annulus gas distributor opening ratio 2.1% Holes on the distributor 52 holes of 1.6mm diameter Gas nozzle diameter, mm 34.9 (I.D.), 38.1 (O.D.)   The i-CFB system is shown schematically in Fig. 3.2. For the experiments of solids circulation rate, building air was fed to both the annulus and draft tube as the fluidizing gas. For the measurment gas bypass ratio, CO2 was also fed into the draft tube or annulus as a tracer. The bed material used in the experiment was zeolite particles which were the same as the catalyst tested by Yang [11] in the i-CFB reaction experiment.  Some properties of the particles are given in Table 3.2. In the table, Uc is transition velocity from bubbling to turbulent fluidization and was determined based on the maximum standard deviation of pressure fluctuations as described in [97].  41  GasAnalyzerComputerCycloneVentVentCO2Building airBuilding airSampling, outlet of draft tubeSampling, gas mixtureD5D4D3D2D1Bag houseSampling, outlet of annulusSampling, inlet of draft tubeSampling, inlet of annulusi-CFBreactor Figure 3.2 Schematics of the i-CFB system       42  Table 3.2 Fine Fe/ZSM-5 particle properties Material Bulk density (kg/m3) Average particle diameter (mm) Umf*a (m/s) Uc*b (m/s) Ut*c (m/s) Fe/ZSM-5  968 0.155 0.01 0.38 0.90  Note: *a: measured; *b: measured. *c: calculated from correlation: ? ? ? ?15.0*2** 591.018???????????pptddU , ? ? 3/12* ?????? ?? ???? gdd gpgpp , ? ?3/12*?????????? gUU gpgt t ???? [25]  3.2.1 Bed expansion Bed voidage is an important flow structure parameter which determines the pressure drop in i-CFB. Here, bed expansion was investigated in a fluidized bed with the same dimension of the i-CFB reactor as shown in Fig. 3.1 but with a flat perforated plate as the distributor and the absence of the draft tube. Building air was used as the fluidizing gas, and zeolite powders were used as the bed material. Pressure drop was measured between points D1 and D3 at different gas inlet velocities and voidage was calculated according to Eq. (3.1) by neglecting frictional losses between gas/particle mixture and wall surfaces.  ? ?HgP p ?? ??? 1          (3.1) where, ?P is the pressure drop between the two points, ?p is the density of tested particles, ? is the voidage in the bed, and H is height of the bed between the two measurement points.  3.2.2 Gas bypass The gas bypass between the draft tube and annulus was studied by Yang [11] using CO2 tracer method with the bed loaded with 3.3 kg zeolite powders. At a given steady state operating condition, continuous 43  CO2 tracer was injected into the inlet gas flow of the annulus, with CO2 concentrations at the outlet of the draft tube and the annulus, and the inlet of the draft tube and the annulus being monitored. The schematics of gas bypass is shown in Fig. 3.3. Gas bypass ratios, Rd-a and Ra-d, which are defined in Eq. (3.2), were then calculated based on the mass balance of CO2 tracer. 0dadad FFR ?? ?,  0adada FFR ?? ?        (3.2) where Fd0, Fa0, Fd-a and Fa-d are the flow rates of the gas fed to the draft tube, fed to the annulus, bypassing from the draft tube to the annulus and bypassing from the annulus to the draft tube, respectively. Draft tubeAnnulusFa0Fd0FdaFadFaFd Figure 3.3 Schematics of the gas bypss between the draft tube and the annulus     3.2.3 Solids circulation rate Experimentally, solids circulation rate can be determined from the vertical flux of particles passing through one or more of the regions using a number of methods [98] such as multi-fiber optical probes, radioactive tracer particles, and hot solids tracer techniques. In the current study, optical fiber probes were used to measure solids flux for fine catalyst particles. A particle velocity analyzer (PV-4A) manufactured by the Institute of Process Engineering, Chinese Academy of Sciences, was used for the measurement, 44  which included an optical fibre probe, a light conversion box, a data acquisition board and a program for sampling and recording data into the computer for analysis. This technique has been widely applied to determine particle velocity and voidage in fluidized beds [99, 100].  The optical fibre probe used in the current work is shown in Fig. 3.4. There are three bundles of fibres of 15 microns in diameter. Each bundle has a diameter of about 0.8 mm. The measurement volume of the probe employed in this work is less than 2 mm3, and is very small compared to the size of bubbles. Thus, this probe is sensitive to the local flow pattern but does not impose significant inteference on the passing bubbles. The central bundle of fibres is for light projection, whereas the other two act as light receivers, corresponding to two sampling channels A and B. The basic mechanism to measure the velocity is to calculate the time lag, ?, between the moments when the particles pass the two light receivers by cross-correlation method. The particle velocity, Up, can then be calculated by: Up= Le /?.  Figure 3.4 Details of the tip of the optical fibre probe for particle velocity measurement  The probe was calibrated employing the zeolite particles used in this study. A rotating plate with glued particles was driven by a motor. Particles rotated together with the rotating plate, at a preset particle velocity, Up, and the time lag, ?, between the two channels of the probe was measured by the cross-correlation of the signals from the two channels. The effective distance was then calculated by multiplying the particle rotating velocity and the time lag. In a typical measurement, two series of signals were recorded from the system, which represent the intensity of the reflected light through the two 45  channels. These data series were divided into several groups, with cross-correlation being carried out on each group to find the time lag between the two channels.  For the measurement of local bed voidage, the optical fibre probe was calibrated in a packed bed. It is practically very challenge to create homogeneous gas-solid suspensions over a sufficiently wide range of solids concentrations. Black coke particles can absorb light and give no reflection back to the receicing tip of the probe. Therefore, these particles can not be ?seen? by the probe. Here, a mixture of bed particles and coke particles at different volume fractions of coke was used to simulate packed bed with different voidages, represented by black coke particles. However, one should note that the property of coke particles is not exactly the same as the ?void? between particles since these particles could affect light penetration throgh the bed, leading to inaccuracy of the calibration, especially when there is a large light penetration depth of the probe. The calibration curve is shown in Fig. 3.5. The local voidage was then correlated with the probe reading by an exponential equation (see Fig. 3.5). Details on the optical fibre probe calibration by the mixture of two particle components can be found in [99, 101].  40 80 120 160 2000.40.50.60.70.80.9Voidage, ?Voltage, V (mV)??0.775*e(-0.0157*V)+0.428R2=0.99 Figure 3.5 Voidage calibration of the optical probe (Symbols: experimental data, line: correlation)  46  The measurement was conducted at point D4 in the annulus, 950 mm above the bottom. Both solids velocity and local voidage were measured along the radial direction at an interval of 2.5 mm. The average solids flux in the annulus Gs could be calculated by the integration of local solids flux along the radial direction:   ? ?? ??? adRR pps rdrUG 21 ???        (3.3) The particle back-mixing in fluidized beds can affect the particle velocity measurement, and also its influence is difficult to be determined. In this work, the instantaneous particle velocity signals were obtained over a period of time, which then were averaged to give the average solids velocity, avoiding the effect of the particle back-mixing on the particle velocity measurement [102].   3.3 Hydrodynamics model of i-CFB 3.3.1 Mass and pressure balance equations In an i-CFB, the internal circulation of solids is created by the pressure difference between the draft tube and the annulus operating at different superficial gas velocities. The solids circulation rate dictates both the gas and solids residence time in each region and hence the extent of NOx adsorption and catalytic NOx reduction. There are several correlations in the literature, which link the bed hydrodynamics to the solids circulation rate [93, 95, 103]. Because the solids circulation rate is influenced by the bed geometry in addition to fluid and particle properties and gas velocity, those correlations from the literature could not be used directly when the geometry of the reactor is changed. In this research, the solids circulation rate is estimated based on the mass and momentum balances in the i-CFB reactor. Solids mass balance equations include the conservation of total solids inventory in the system and solids circulation rate balance between the draft tube and the annulus: 47  ? ? ? ? dddpaaapdaloading HAHAMMM ???? ?????? 11     (3.4) ? ? ? ?daddppaapps AAUUG ????????? ???? 11 ,,       (3.5) where Mloading, Ma and Md are total bed loading, mass of bed material in the annulus and mass of bed material in the draft tube, respectively. Ha, Hd, ?a, ?d, Aa, Ad, Up,a and Up,d are the bed heights, voidage, cross-sectional area and particle velocity in the annulus and the draft tube, respectively. The driving force of the solids circulation is the pressure difference between the annulus and the draft tube, subtracting the pressure drop across the orifice connecting them. The pressure balance in the whole system is orda PPP ?????          (3.6) where ?Pa, ?Pd and ?Por are the pressure drop in the annulus, in the draft tube and through the orifice, respectively.  3.3.2 Pressure drop calculation In a fluidized state, the pressure drop could be expressed by Eqs. (3.7) and (3.8), which consist of the pressure drops due to gravity, solids acceleration, fluid-wall friction and particle-wall friction. ? ? ? ? pwtubedraftgwtubedraftappapaaa FHFHUgLP ?? ??????? 2,15.01 ????    (3.7) ? ? ? ? pwtubedraftgwtubedraftdppdpddd FHFHUgLP ?? ??????? 2,15.01 ????    (3.8) where La and Ld are the effective bed heights in the annulus and draft tube, respectively. Fgw and Fpw are the gas-wall and the particle-wall frictional force per unit volume of the column, respectively. In the case of gas velocities lower than 6 m/s, and straight column with diameter in excess of 4 cm, the contribution 48  of gas-wall friction Fgw could be neglected [104]. Konno and Saito?s equation [105], which was developed for relatively low concentration of solids in vertical column, was used to calculate the solid-wall friction.  ? ? 5.0/057.0 dspw DgGF ??         (3.9) The pressure drop across the orifice between the bottoms of annulus and draft tube could be correlated with solids circulation rate Gs. For mechanical valves like slide valves where the solids flow is controlled by changing the opening area, the pressure drop across the control valve and solids flux can be related by [106]: ? ?2112????????????aororapaorDsAAPAACG??        (3.10) The discharge coefficient CD in Eq. (3.10) has values typically between 0.2 and 0.6 with an average value of 0.4, although it depends on the geometrical configuration, orifice edge parameters and the Dor/dp ratio. So CD needs to be fitted from the experimental data for specific configurations.   3.3.3 Effective bed height To obtain the effective bed height for Eqs. (3.7) and (3.8), the flow in the i-CFB was categorized into four different operating modes as shown in Fig. 3.6. It should be noted that the flow mode is classified here in such a way to facilitate the calculation of effective bed height and is different from the flow patterns reported in the literature [107]. ? If there is not sufficient bed solids loading and the gas velocity inside the draft tube is lower than the particle transport velocity, the draft tube could not be fully filled with particles and a flow pattern in 49  Fig. 3.6(a) will be created without internal solids circulation. The initial pressure drops in the two zones could be obtained by tubedraftd HL ??0           (3.11) ? ?? ? aapdddploadinga AALML ???????? 11 00        (3.12) ? ? 00 1 aapa gLP ?? ???          (3.13) ? ? 00 1 ddpd gLP ?? ???          (3.14) If 00 da PP ??? , there is no solids circulation. This regime is of little interest in the operation of i-CFB. But this procedure could be used to identify whether there is solids circulation or not. It should be noted that if the gas velocity in the annulus is bigger than that in draft tube, particles could be entrained to the annulus, forming solids circulation reversely. This case is not considered for the i-CFB yet and will not be discussed here. ? When the solids loading and/or the gas velocity in the draft tube are increased, particles fill up the draft tube and start to circulate to the annulus region. This corresponds to flow pattern (b) in Fig. 3.6. In this mode, the effective bed height in the draft tube is the same as the draft tube height, and the effective annulus bed height could be calculated by overall mass balance.  ? If the particle loading and/or gas velocity are further increased, the annulus bed height could exceed the height of the draft tube and flow pattern (c) is established. In this case, the effective annulus bed height can still be calculated by mass balance and the effective draft tube bed height is equal to the effective annulus bed height. An initial guessed value of effective draft tube height should be taken to start the mass balance calculation, and the mass balance equations are then iterated to obtain the final bed height values. 50  0ad LL ?                (3.15) ? ?? ? aapdddploadinga AALML ???????? 11        (3.16) ? When the bed loading or gas velocity is further increased, the annulus dense bed becomes too high and the gas jet on top of the draft tube becomes unstable or can no longer penetrate through. As a result, flow pattern (d) is formed. The vertical jet penetrate length Lj could be estimated in the same way as jet penetration depth in spout-fluid bed [108].   1966.0252.11 ?????????? ddgpgajgDUDL???       (3.17) The effective draft tube bed height, Ld, is the sum of draft tube length and jet height, and the effective annulus bed height La equals Ld. The detailed criteria and calculation procedures for each of the four flow patterns are given in Table 3.3. 51  (a) (b) (c) (d) Figure 3.6 Schematic of four i-CFB flow modes and the effective bed height  Table 3.3 Calculation procedures for effective bed heights Flow patter ?00 da PP ??? ?00 da LL ? ?00 daj LLL ?? La Ld (a) N -- -- Calculated from mass and pressure balance Calculated from mass and pressure balance (b) Y Y -- Calculated from mass balance tubedraftd HL ?? (c) Y N Y Calculated from mass balance ad LL ?  (d) Y N N da LL ?  jtubetdrafd LHL ?? ?   52  3.4 Results and discussion 3.4.1 Bed expansion characteristics The bed voidage at different inlet gas velocities was measured in a cylindrical fluidized bed and plotted in Fig. 3.7. The experimental data were fitted to obtain correlations for the modeling of bed voidage in the i-CFB reactor.  Cai [109] modified Babu?s correlation [110] to fit their bed expansion data obtained in both bubbling and turbulent fluidization regimes. The bubble size and bubble rise velocity are estimated, respectively, by, ? ? ? ? ? ?? ?mfmfmffb UUPUUPUUPHD ???????? ? 1.025.0104.1exp21.0 22442.006.08.0    (3.18) ? ? 5.071.0 bmfb gDUUU ???         (3.19) Gas flow rate in the bubble phase is calculated as ? ?AUUYAUF mfbbb ??? ?         (3.20) with Y being correlated to ? ? 19.048.009.026.0108.0 ???? ppmfs dUUHY ?       (3.21) where ? ?mfmfs HH ??? 1/ . By assuming no particles inside the bubble phase, the bubble phase fraction (?b) and the bed voidage in the fluidized bed could then be calculated by 53  ? ?bmfb UUUY ???         (3.22) ? ? mfbb ???? ??? 1          (3.23) When the Cai correlation was compared with our experimental data, it was found that the correlation gave a good agreement with experimental data with an error within 3.24%. To further improve the bed expansion prediction, the correlation of Y in Cai?s correlation is slightly modified to ? ? 19.048.009.026.0116.0 ???? ppmfs dUUHY ?       (3.24) The calculated values from modified Cai correlation was plotted in Fig. 3.7, which has an error less than 2.44%. This correlation will be applied to both the annulus and draft tube zones of the i-CFB reactor. 0.0 0.2 0.4 0.6 0.80.50.60.70.80.9 Experiment Cai's correlationVoidage, ?Inlet gas velocity, U, m/sR2=0.953 Figure 3.7 Measured voidage data for ZSM-5 powders and comparison with the Cai correlation (Symbols: experimental data, line: correlation)  54  It should be noted that the Cai correlation can only be used for bubbling and turbulent regimes. If the gas velocity exceeds Ut, the draft tube is operated as a transport riser. The Pugsley correlation [111], which was developed for transport risers with diameters of 0.05 to 1 m and for particles with diameters of 50 to 350 ?m, could be used for the estimation of voidage:  pspUGU???? ??           (3.25) where Gs is the solids circulation rate and U is the superficial gas velocity inside the draft tube. The slip factor was defined as the ratio of gas interstitial velocity to the average particle velocity and correlated to the Froude number. 41.047.06.51 tpFrFrUU ???? ??         (3.26) where Fr and Frt are Froude number and particle Froude number, respectively. ? ? 5.0dgDUFr ? , ? ? 5.0dtt gDUFr ?        (3.27)  3.4.2 Gas bypass Gas bypass is very important for the design and operation of i-CFB, which determines both the gas velocities and actual reactant concentrations in the annulus and draft tube. The measured gas bypass data from Yang [11] were shown in Fig. 3.8, where Rd-a is the gas bypass ratio from draft tube to the annulus and Ra-d is from the annulus to draft tube. It can be seen from Fig. 3.8(a) that Rd-a increases with increasing Ud0, gas feed rate to the draft tube. It is seen that more gas leaks to the annulus as the gas velocity in the draft tube increases. However, when 55  the gas velocity in the annulus is higher, less gas leaks from draft tube to the annulus, leading to a lower Rd-a. Also, the effect of feed gas velocity in the annulus is less significant at lower Ud0, as evidenced from the slopes of Rd-a at different Ud0. At Ud0=0.45 m/s, Rd-a is almost unaffected by Ud0. Comparing to Rd-a, Ra-d data are much more scattered and show no obvious trend. The change in both Ua0 and Ud0 has almost no effect on Ra-d, which fluctuates in the range of 5~9%, as shown in Fig. 3.8(b).  It should be noted that the net gas exchange is mostly from draft tube to the annulus based on calculated gas flow rate both from the annulus to draft tube and from draft tube to annulus (results are not shown here), which is in opposite to the net solids flow from the annulus to the draft tube. The low gas bypass from annulus to draft tube can limit the oxygen concentration buildup in the NOx reduction zone in an i-CFB, leading to potential improvement of the overall deNOx efficiency. 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50101520253035404550556065 Ud0=0.45 m/s Ud0=0.6  m/s Ud0=0.75 m/s Ud0=0.9  m/sRd-a (%)Annulus inlet velocity, Ua0 (m/s)Bed loading=3.3 kg0.15 0.20 0.25 .30 0.35 0.40 0.45 0.5056789 Ud0=0.45 m/s Ud0=0.6  m/s Ud0=0.75 m/s Ud0=0.9  m/sRa-d (%)Annulus inlet velocity Ua0 (m/s)Bed loading=3.3 kg                                            (a)                                                                                   (b) Figure 3.8 Gas bypass ratios at different Ud0. (a), from draft tube to annulus, Rd-a; (b), from annulus to draft tube, Ra-d (Symbols: experimental data, lines: correlation)  For modeling the hydrodynamics of the i-CFB, the gas bypass Rd-a data are correlated to Ua0 and Ud0 by  56  300.10616.00039.1 ???????????????????mfdmfaad UUUUR   (R2=0.865)      (3.28) Since Ra-d is much scattered across a narrow range, an average value of 7% was used. Ra-d=7%          (3.29) It should be noted that the equations are only valid within the experimental range, 0.45 m/s<Ud0<0.9 m/s and 0.2 m/s<Ua0<0.475 m/s. If Ud0>0.9 m/s, Rd-a is predicted to be more than 100% and is unrealistic. The same problem also happens when Ua0 is smaller than 0.2 m/s.  It is observed that at a higher Ud0, the increase in Rd-a slows down with increasing Ud0. The difference between the values of Rd-a at Ud0=0.75 m/s and Ud0=0.9 m/s is very small. So, when Ud0 is higher than 0.9 m/s, the values of Rd-a at Ud0=0.9 m/s is taken in the modeling. Also, when Ua0 is smaller than 0.2 m/s, the Rd-a values at Ua0=0.2 m/s is used. It should be warned that this assumption could potentially lead to errors in the modeling, since these values have not been confirmed experimentally. The real gas velocities in the annulus and draft tube can now be calculated as: ? ?addadadaaa AAURURUU /000 ?????? ??       (3.30) ? ?daadadaddd AAURURUU /000 ?????? ??       (3.31)  3.4.3 Measured solids circulation rates The solids circulation rate in the i-CFB reactor was measured at two different particle loadings, 2.275 kg and 3.3 kg. The packed bed heights are 0.29 m and 0.42 m, respectively. The particle velocity and voidage in the annulus were measured at different radial positions by the optical fibre probe. Fig. 3.9(a) shows the particle velocity as a function of dimensionless radial positions at different annulus gas velocity 57  Ua0 with a particle bed loading of 2.275 kg. The value of r is referred to the distance from the axis of the i-CFB to the measurement point and R0 is the column radius. The annulus zone is from r/R0=0.5 to r/R0=1. The positive values of the particle velocity indicate a downflow of particles while negative values indicate an upflow of particles. It can be seen that the particle velocity increases with decreasing Ua0. However, this does not necessarily mean that the solids circulation rate is higher, since the solids circulation is determined by both particle velocity and the local voidage. For most of the curves in Fig. 3.9(a), especially at lower Ua0, local particle velocity is higher at the outer side of the annulus than at the inner side. For a particle loading of 2.275 kg at a low annulus gas velocity, the flow pattern (b) in Fig. 3.6 is expected, in which solids falls down fast near the outer wall of the annulus. At a higher Ua0, particle velocities in the middle of the annulus are very small, and sometimes the solids even move upward there. Most of the solids flow down the annulus along both the inner and outer walls of the annulus. The reactor may be operated at the flow pattern (c) in Fig. 3.6 at a higher annulus gas velocity, in which some solids from the jet above the draft tube fall down along the outer side wall, and some solids penetrate through the jet to the dense annulus zone and then fall down along the inner wall.   The measured radial voidage profile is shown in Fig. 3.9(a). The voidage is seen to be very low near both inner and outer walls of the annulus, and reaches a peak around the middle of the annulus, indicating the presence of fewer particles in the middle region of the annulus. The voidage decreases with increasing the annulus gas velocity, which is contradictory to that commonly observed in the fluidized bed which increases with increasing the inlet gas velocity. One likely explanation is that the optical probe at point D4 in Fig. 3.3 is located in the dilute region well above the upper surface of the dense fluidized bed. In the freeboard region of a fluidized bed or in the downcomer with countercurrent gas-solids flow, the voidage decreases with increasing the inlet gas velocity.  58  0.6 0.7 0.8 0.9 1.00.700.750.800.85Mloading=2.275 kgUd0=1 m/sVoidage, ?r/R0 Ua0=0.1 m/s Ua0=0.2 m/s Ua0=0.4 m/s Ua0=0.6 m/s0.6 0.7 0.8 0.9 1.0-0.050.000.050.100.150.200.25Particle velocity, Up (m/s)r/R0 Ua0=0.1 m/s Ua0=0.2 m/s Ua0=0.4 m/s Ua0=0.6 m/sMloading=2.275 kgUd0=1 m/s  (a)                                                                                   (b) Figure 3.9 Measured radial profiles of (a) voidage and (b) particle velocity at different Ua0, (Ud0=1 m/s, bed loading=2.275 kg. Symbols: experimental data, lines: connection of symbols)  When particle loading is increased to 3.3 kg, the radial distribution of axial particle velocity in the annulus varies only slightly in the middle section, as shown in Fig. 3.10(a). The particle velocity increases slowly from the inner wall toward the middle of the annulus. Close to the column wall, the velocity increases substantially. The particle velocity decreases first when Ua0 increases from 0 to 0.4 m/s and then increases a lot when Ua0 is further increased to 0.6 m/s.  The radial voidage profile at a solids loading of 3.3 kg, as shown in Fig. 3.10(b), is also different from that at a solids loading of 2.275 kg. At a low Ua0, the voidage is almost flat along the radial direction, especially near the draft tube, indicating a uniform solids distribution in the annulus. At a high Ua0, voidage begins to decrease along the radial direction, leading to a denser region near the outer wall of the annulus. A valley appears on all profiles near the column wall. Combining with the radial particle velocity distribution, it can be concluded that more particles move downward near the column wall. Similar to Fig. 3.9(a) at the solids loading of 2.275 kg, the overall voidage decreases with increasing gas velocity. However, the voidage increases when Ua0 further increases to 0.6 m/s. This can be explained by the bed expansion at different Ua0. It is likely that the optical probe is already immersed in the dense 59  section of the fluidized bed at Ua0=0.4 m/s. So if Ua0 further increases, the measured voidage increases in the same way as the overall bed voidage. 0.5 0.6 0.7 0.8 0.9 1.00.000.050.100.150.200.25Mloading=3.3 kgUd0=1 m/sParticle velocity, Up (m/s)r/R0 Ua0=0.1 m/s Ua0=0.2 m/s Ua0=0.4 m/s Ua0=0.6 m/s 0.5 0.6 0.7 0.8 0.9 1.00.750.800.850.90Mloading=3.3 kgUd0=1 m/sVoidage, ?r/R0 Ua0=0.1 m/s Ua0=0.2 m/s Ua0=0.4 m/s Ua0=0.6 m/s (a)                                                                                   (b) Figure 3.10 Measured radial profiles of (a) particle velocity and (b) voidage at different Ua0, (Ud0=1 m/s, bed loading=3.3 kg. Symbols: experimental data, lines: connection of symbols)  Fig. 3.11 shows the measured radial profiles of particle velocity and voidage at different Ud0. The particle velocities show a similar trend at different Ud0, but the effect of Ud0 is not very clear. Comparing to particle velocity, the voidage in Fig. 3.11(b) is greatly influenced by Ud0, decreasing with increasing Ud0. Combining the solids velocity and voidage in the annulus, it can be inferred that the solids circulation rate increases with increasing Ud0.  60  0.5 0.6 0.7 0.8 0.9 1.00.000.050.100.150.200.25Mloading=2.275 kgUa0=0.1 m/sParticle velocity, Up (m/s)r/R0 Ud0=0.75 m/s Ud0=1 m/s Ud0=1.25 m/s0.5 0.6 0.7 0.8 0.9 1.00.60.70.80.91.0Mloading=2.275 kgUa0=0.1 m/sVoidage, ?r/R0 Ud0=0.75 m/s Ud0=1 m/s Ud0=1.25 m/s (a)                                                                                   (b) Figure 3.11 Measured radial profiles of (a) axial particle velocity and (b) voidage at Ua0=0.1 m/s (Symbols: experimental data, lines: connection of symbols)  The overall net solids flux in the annulus, Gs, is calculated from the integration of the local solids flux across the cross section of the annulus. Fig. 3.12(a) shows Gs as a function of Ua0 at different draft tube velocities with a solids loading of 2.275 kg. As discussed above, the solids circulation rate mostly increases with increasing the draft tube gas velocity Ud0, but decreases with increasing Ua0. This can be explained by the pressure balance over the i-CFB reactor. When the draft velocity increases at a constant annulus velocity, solids circulation is increased because of the increased pressure difference between the draft tube and the annulus. On the other hand, at a constant draft tube gas velocity, the increase of annulus gas velocity increases the bed expansion in the annulus, which lowers the pressure buildup in the annulus and the pressure difference between the draft tube and the annulus, leading to the reduced solids circulation rate.  Gs at a high bed solids loading of 3.3 kg is not sensitive to the annulus gas velocity at high draft tube gas velocities. At a low draft tube velocity, Ud0=0.5 m/s, Gs increases from Ua0=0 to Ua0=0.1 m/s  but decreases to less than 15 kg/m2.s when Ua0 is increased from 0.1 to 0.4 m/s. This is likely caused by the small gas velocity difference between the draft tube and annulus, which can lead to loss of 61  pressure difference between these two zones. Also, Gs is less sensitive to Ud0 at 3.3 kg solids loading than at a bed solids loading of 2.275 kg. It is seen from those two figures that Gs is a strong function of bed solids loading and inlet gas velocities. At low bed solids loadings and low Ud0, Gs decreases as the annulus gas velocity increases. However, the trend changes and tends to be reversed at high bed solids loadings and high Ud0. Many factors may influence the solids circulation rate of the i-CFB at different solids loadings. The trends of these curves cannot be simply explained by the differences of the inlet gas velocities. Gas bypass at different bed solids loading and inlet gas velocities could directly influence the actual gas velocity in both the annulus and draft tube, which determines the voidage in each zone. Effective bed heights in both zones are also influenced by operating conditions. These influencing factors will be further discussed in the modeling section. 0.1 0.2 0.3 0.4 0.5 0.6102030405060Solid circulation rate, Gs (kg/m2.s)Annulus inlet velocity, Ua0, m/s Ud0=0.75 m/s Ud0=1 m/s Ud0=1.25 m/sMloading=2.275 kg 0 0.1 0.2 0.3 0.4 0.5 0.6101520253035Solid circulation rate, Gs (kg/m2.s)Annul  i l t locity, Ua0, m/s Ud0=0.5 m/s Ud0=1 m/s Ud0=1.4 m/sMloading=3.3 kg (a)                                                                                   (b) Figure 3.12 Net solids circulation rate at different Ud0, with bed solids loadings of (a), 2.275 kg, and (b), 3.3 kg. Symbols: experimental data, lines: connection of symbols)  62  3.4.4 Prediction of solids circulation rate The solids circulation rate at a bed solids loading of 3.3 kg is modeled by mass and pressure balance equations. The real gas velocities in the annulus and draft tube are adjusted by the gas bypass ratios. Then voidage in both zones is calculated using Cai?s correlation. Fig. 3.13(a) shows the estimated voidage, with the closed symbols corresponding to the voidage in the annulus and the open symbols for the voidage in the draft tube. It can be seen that the voidage in the draft tube is always higher than the voidage in the annulus, since the velocity in the draft tube is always higher than in the annulus. From the bed expansion characteristics shown in Fig. 3.7, voidage is expected to increase from 0.6 to 0.85 when the gas velocity increases from 0.1 m/s to 0.6 m/s. The curves of annulus voidage ?a seem to be quite different from expected without gas bypass. The voidage in the annulus increases with increasing the draft tube inlet gas velocity because more gas passes from the draft tube through the orifice to the annulus zone at higher Ud0. At the same Ud0, the slopes of most ?a vs. Ua curves are lower than the slope in Fig. 3.7, due to smaller Rd-a values at higher Ua0. It can be concluded that the voidage in both zones of the i-CFB reactor is substantially changed by gas bypass. Following the procedure given in Table 3.3, effective bed heights in the two zones are estimated through mass balance and plotted in Fig. 3.13(b). In the figures, ?a? is annulus and ?d? denotes draft tube. At low Ua0 and Ud0, type (b) flow pattern is expected with Ld=Hd and La < Hd. But at higher Ua0 and Ud0, the flow patterns are expected to be either type (c) or type (d), with the effective heights of annulus and draft tube being the same and larger than the length of draft tube. It can be seen that the effective bed height increases with increasing both Ud0 and Ua0. At low Ud0, the slope of the curves is steep, because increasing inlet gas velocity can significantly increase the expansion of the fluidized bed. But at higher Ud0 and Ua0, the top of the annulus dense bed exceeds the height of the jet above the draft tube and flow patterns (c) or (d) are formed. Further increasing the inlet gas velocity has little effect on the effective bed height. 63  0.1 0.2 0.3 0.4 0.5 0.60.50.60.70.80.91.0Voidage, ?Annulus inlet velocity, Ua0, m/s Annulus:Ud0=0.5 m/s Draft tube:Ud0=0.5 m/s Annulus:Ud0=1  m/s Draft tube:Ud0=1  m/s Annulus:Ud0=1.5 m/s Draft tube:Ud0=1.5 m/sBed loading=3.3 kg0.1 0.2 0.3 0.4 0.5 0.60.50.60.70.80.91.01.11.21.3Bed loading=3.3 kgEffective bed height (m)Ann lus inlet velocity, Ua0, m/s A n lus, Ud0=0.5 m/s Draft tube, Ud0=0.5 m/s A n lus, Ud0=1 m/s Draft tube, Ud0=1 m/s A n lus, Ud0=1.5 m/s Draft tube, Ud0=1.5 m/s (a)                                                                                   (b) Figure 3.13 Calculated (a) voidage and (b) effective bed height at a bed solids loading of 3.3 kg (Symbols: calculated data points, lines: connection of symbols)  Pressure drop across the annulus and draft tube is estimated based on the estimated voidage and effective bed height, and the pressure drop across the orifice ?Por is obtained based on the pressure difference between the annulus and the draft tube. The values of ?Por are further fitted into Eq. (3.10) to obtain the discharge coefficient CD at each operating condition. The calculated CD data are shown in Fig. 3.14 as a function of Reynolds number of the particles passing through the orifice, Rep, defined as:  ?? appgpUd ,Re ?         (3.32) The fitted CD  values are quite scattered and varied from 0.13 to 0.21, which falls reasonably into the range as reported in the literature [106]. Since no obvious trend with Rep was observed, an average CD value of 0.167 is taken for further simulation. 64  0.2 0.4 0.6 0.8 1.00.000.050.100.150.200.250.300.35CDRep Figure 3.14 Fitted CD values as a function of Rep (Symbols: experimental data, lines: connection of symbols)  Using the current model, hydrodynamics at a bed solids loading of 3.3 kg is further investigated for the design of an i-CFB reactor. In an i-CFB deNOx reactor, flue gas is fed into the annulus and NOx in the flue gas will be adsorbed onto the catalyst surface. The oxygen concentration in the flue gas is always high in lean combustion of fuels, and the presence of high level oxygen favours the NOx adsorption. In the draft tube, NOx adsorbed on the catalyst surface is reduced by hydrocarbons. The reduction reaction is inhibited by O2 because hydrocarbon reductant is consumed by oxygen. Therefore, careful control of the oxygen concentration inside the draft tube is of great importance to achieve the high deNOx efficiency of the deNOx reactor. Here, the actual O2 concentration in the draft tube is estimated based on the gas bypass ratios and the gas flow rate into the draft tube using 3. (33). It is assumed that O2 only exists in the gas fed into the annulus with a concentration of 8%. dadaaOddaaOdO URCFFCC 00,0,, 222 ????? ??      (3.33) 65  Fig. 3.15(a) shows the predicted O2 concentration in the draft tube, CO2,d, at various inlet gas velocities. All the values of CO2,d are very low, ranging from 0.25% to 0.5%. This is due to the low gas bypass ratios from annulus to draft tube. The predicted low oxygen concentration in the draft tube can thus achieve a high NOx reduction efficiency.  The overall NOx abatement efficiency is determined by both the adsorption in the annulus, which directly removes NOx from the flue gas, and the reduction in the draft tube. The NOx adsorption efficiency in the annulus is strongly affected by the solids circulation rate, which represents how the NOx can be efficiently transferred to the reduction zone and also determines the contact time between gas and catalyst. Fig. 3.15(b) shows the predicted solids circulation rate at different inlet gas velocities. It is seen that Gs is smaller at lower Ud0, e.g. 0.6 m/s. But further increasing Ud0 from 0.75 m/s to 0.9 m/s has little effect on Gs and even leads to lower values of Gs. The broad width of the peak also indicates that the i-CFB can be well operated over a wide range of Ua0, with the optimal annulus velocities between 0.25 to 0.45 m/s. 0.20 0.25 0.30 0.35 0.40 0.45 0.500.250.300.350.400.450.50Bed loading = 3.3 kgCO2,d, %Annulus inlet velocity, Ua0, m/s Ud0=0.6 m/s Ud0=0.75 m/s Ud0=0.9 m/s0.20 0.25 0.30 0.35 0.40 0.45 0.505101520253035 Ud0=0.6   m/s Ud0=0.75 m/s Ud0=0.9   m/sGs, kg/m2.sAnnulus inlet velocity, Ua0,Bed loading = 3.3 kg                                            (a)                                                               (b) Figure 3.15 Predicted (a) CO2,d and (b) Gs as a function of Ua0  66  3.5 Summary The hydrodynamics of an i-CFB deNOx reactor have been studied by both experiment and modeling. Gas bypass was investigated by a CO2 tracer method, and the solids circulation rate was measured using an optical fibre probe at bed solids loadings of 3.3 kg and 2.275 kg. It was found that the solids circulation rate was a strong function of bed loading and feeding gas velocities. At low bed loading and low draft tube velocity, the solids circulation rate decreased as the annulus gas velocity increased. However, this trend could be be reversed at high bed loading and high draft tube velocity. A hydrodynamic model was then developed based on mass and pressure balances. The discharging coefficient CD was extracted from fitting the experimental data and an average value of 0.167 was taken for model simulation. The model captures the characteristics of the solids flow and gas flow distribution, and could serve as a useful tool for the design and simulation of the i-CFB deNOx reactor system. However, modeling at different bed solids loadings requires the gas bypass characteristics being measured. With data on both the gas bypass and solids circulation rate, the hydrodynamic behavior could be coupled with the reaction kinetics to simulate the i-CFB performance for NOx reduction.   67   Chapter 4  Development of deNOx reaction kinetics3  4.1 Introduction  In order to model the i-CFB deNOx reactor, the NOx reduction kinetics of the selected catalyst needs to be developed first. Different from the conventional catalytic reactor where adsorption and reaction take place at the same time and at the same zone, adsorption and reduction take place in two different zones of the i-CFB reactor. Adsorption and reaction kinetics therefore should be decoupled and modeled separately for the adsorption zone and reduction zone and the performance of the adsorption and reduction zones is then linked by the solids circulation between the two zones. Although there are several kinetic models that separate adsorption and reduction for NSR catalyst [112], most of them are developed for Pt/Ba/Al catalyst and are based on intricate element reactions. These models are not applicable for the i-CFB reactor, in which both hydrodynamics and kinetics are very complex. In this chapter, a kinetic model will be proposed, consisting of two simplified sub-models, one adsorption model and one reduction model. The adsorption isotherm and kinetic parameters are fitted by the corresponding fixed bed experimental data. For governing equations of kinetic model, surface reaction and surface adsorption are usually embedded into the gas phase mass balance equation, even with NOx storage being considered [113, 114]. For the modeling of NSR (non-selective reduction) reaction, NOx adsorption onto the catalyst surface in                                                      3 A version of the adsorption modeling in this chapter has been published: Xingxing Cheng and Xiaotao T. Bi, Modeling NOx adsorption onto Fe/ZSM-5 catalysts in a fixed bed reactor, International Journal of Chemical Reactor Engineering, 11(1): 1-12. An earlier version of the kinetics development part in this chapter has been published: Xingxing Cheng, Xiaotao Bi, (2012), Reaction kinetics of selective catalytic reduction of NOx by propylene over Fe/ZSM-5. Chemical Engineering Journal, 211-212: 453-462. 68  the fuel-lean cycle and then be reduced in the fuel-rich cycle were modeled separately. For example, Lindholm [112] modeled NOx storage and reduction with hydrogen as the reducing agent over Pt/Ba/Al catalyst in a monolith reactor. The reactor was treated as a series of continuously stirred tank reactors (CSTR). Reaction takes place on the catalyst surface between adsorbed NOx and reduction agent during the fuel-rich cycle. The mass transport to the catalyst is modeled for adsorption, desorption, and reaction on the catalyst surface stages, separately, over a lean and rich cycle. The same model was also used for the modeling of NOx adsorption and NO oxidation over Cu/ZSM-5 monolith catalyst [115], and a similar model was used [116, 117] for NOx storage/reduction on Pt/Ba/Al monolith catalysts. Instead of CSTR, axial dispersion was considered in the gas phase mass balance equation. At the same time, less sophisticated reactions have also been proposed. Metkar et al. [118] recently developed a kinetic model for NH3-SCR over Fe- and Cu-zeolite monolith catalyst in which gas diffusion in the washcoat was considered. It was also reported by [118] that diffusion is very important in the SCR reactor and should be included in the reactor model. These models could work well with the monolith reactors where there is a distinct boundary between the gas phase and washcoat and reactants diffuse through the layer of the washcoat. However, gas flow and mass transfer in the packed bed could be different, where the gas species diffuses into the pores of each particle. Also, model developed for monolith reactor could not be extended to fluidized bed reactors, where both diffusion inside the particles and the mixing of the solids need to be considered.  To model the adsorption-reduction process, solids phase mass balance should be considered in the adsorption model in which the reaction term should be incorporated into the solids phase to account for catalytic reaction of adsorbed NOx on the solids surface. In this chapter, kinetic model will be developed by fitting into the data obtained from a fixed bed reactor. Mass transfer between solids and gas phase is incorporated into the model, with the mass transfer coefficients being obtained from fitting fixed bed adsorption breakthrough curves. Both solids and gas phase mass balance equations were considered with the reaction term embedded into the solids phase mass balance equation. 69   4.2 Experiments  4.2.1 Experimental setup Fixed bed experimental data of O2 adsorption, NOx adsorption and NOx reaction are needed for the development of reaction and adsorption kinetics. Data for reaction kinetics are taken from the fixed bed reaction experiments of Yang [11]. NOx adsorption was also tested by Yang [11] at different inlet NO concentrations and temperatures, with the inlet O2 concentration being kept at 4%. NOx adsorption at different inlet O2 concentrations, as well as O2 adsorption, is thus studied here in the same experimental setup as shown in Fig. 4.1, which consists of a tubular reactor, a gas supply and flow rate control unit, a gas preheating unit, a gas heating unit (furnace), a gas analysis unit and a data acquisition system. A stainless steel tubular reactor with an inner diameter of 13.5 mm was used in this experiment, and the catalyst packing height was maintained at 50.8 mm throughout all the tests.  70  PressureTransducer HeatingRegulatorO2 CO2NO N2 HCH2O   WaterEvaporator    GasPreheater  Temp.ControllerThermocouplePressureTransducerVent  Gas AnalyzerComputerTubularReactorFurnaceThermocouples     (3 lines)SO2 Figure 4.1 Fixed bed reaction system  Fe/ZSM-5 catalyst, which shows good performance in the previous i-CFB study of Yang [11], was tested in the adsorption experiment. The catalyst support is H/ZSM-5 (average particle size of 155 ?m, apparent bulk density of 968 kg/m3, and BET surface area of 171 m2/g), which was obtained as a free sample from Albemarle Corporation. The method to prepare the fine Fe/ZSM-5 catalyst was described in [63]. The prepared fine Fe/ZSM-5 catalyst has an iron content of 5% and a BET surface area of 163 m2/g, which is slightly lower than the original ZSM-5 catalyst support. The model flue gas used in the experiment was a mixture prepared from several gas cylinders: 50% O2 balanced with N2, 0.6% NO balanced with N2 and pure N2 gas cylinders from Praxair Products Inc. 71  The compositions (NOx and O2) of the effluent gases were analyzed by a Horiba PG-250 flue gas analyzer. Before the start up of the experiment, the reactor was first heated to the desired temperature with pure N2 gas passing through the catalyst bed. After the reactor temperature was stabilized, the flow of a gas mixture at a preset composition was turned on to start the experiment, with the gas mixture inlet composition determined by the same gas analyzer. In the NOx adsorption experiment, the model flue gas was pre-mixed with pure N2 as the balancing gas according to the preset flow rate and concentrations of NO and O2. The mixed flue gas was then preheated to 150 oC by the preheating system, with the composition being measured by the gas analyzer. After stable readings of the analyzer were reached, which corresponded to the inlet model flue gas concentrations, the three-way valves switched the flow to the reactor inlet and the time was recorded as the starting point of the adsorption. During the adsorption process, the gas composition at the reactor?s outlet was continuously monitored until the NOx concentration became stable, with the final NOx concentration defined as the equilibrium NOx concentration. Thereafter, the NO flow from the gas cylinder was turned off and, at the same time, HC (i.e. propylene) at the same flow rate of NO was added into the O2 + N2 flow to start the catalytic reduction process by reacting propylene with the adsorbed NOx on the catalyst. After 45 minutes, the HC flow was turned off and the gas composition passing through the catalyst bed was adjusted to 10% O2 + balanced N2 at a flow rate of 500 ml/min to further remove the adsorbed HC or other intermediate species produced in the reduction process. This stripping process took 30~45 minutes or even longer to lower the outlet CO concentration to below 5 ppm. Afterward, pure N2 was used to purge the catalyst bed for another 45 minutes to remove all adsorbed COx and O2 from the catalyst.  To investigate the O2 adsorption performance, which would be later used for the modeling of NOx reduction kinetics, the O2 adsorption experiment was also conducted.  Similar procedures as the NOx 72  adsorption were followed for the O2 adsorption experiment. The only difference is that the reactor was purged with pure N2 after adsorption. Inlet O2 concentrations were set to be 0.4% and 1%, which is lower than most of the inlet O2 concentrations in the NOx adsorption test. This is because O2 adsorption capacity is much lower than NOx. When inlet O2 concentration is higher than 1%, adsorption breakthrough time will become shorter than the measurement system response time, leading to significant experimental errors. Four to eight repeated runs were used to obtain the standard deviation, with two times of standard deviations corresponding to 95% of confidence level. Different experiments and experimental conditions are summarized in Table 4.1. The gas hourly space velocity (GHSV) was set to 5000 h-1. It should be noted that only experimental data at 350 ? are used for the kinetic development. This is because 350 ? was found to be the optimum reaction temperature for Fe/ZSM-5 catalyst, and deNOx reaction in the i-CFB was only tested at 350 ? by Yang [11]. Table 4.1 Inlet conditions of fixed bed adsorption experiments Experiment NO inlet, ppm Inlet HC:NO Inlet O2, % Gas velocity Fixed bed O2 adsorption N/A N/A 0.4, 1 GHSV=5000 h-1 Fixed bed NOx adsorption 200, 400, 600, 800, 1000 N/A 4 GHSV=5000 h-1 Fixed bed reduction 600 0.5, 1, 2, 4 0.5, 1, 2, 4, 8 GHSV=5000 h-1  4.2.2 Adsorption performance of Fe/ZSM-5 The NOx adsorption curves at different NO concentrations are given in [11]. The adsorption capacity could be calculated by 73  ? ? catNOfeedinge WSTRMFCPq ?????????2731003      (4.1) where S is the area under the adsorption curve, calculated from integration of the adsorption curve: ? ???????? ?? tfeedingout dtCCS01          (4.2) The adsorption capacities at different temperatures and 4% O2 were reported in [11]. The adsorption of NOx at different O2 concentration and O2 adsorption were tested following the same procedure, with the obtained adsorption capacities being shown in Fig. 4.2. As expected, O2 adsorption capacities are much smaller than the NOx adsorption capacity in Fig. 4.2(b) and decrease with increasing temperature. The NOx adsorption was significantly promoted by the presence of O2, which increased about 7 times when O2 concentration increased from 1% to 8%. This is because NO is first oxidized to NO2 before adsorbed onto the catalyst surface. At higher O2 concentrations, more NO is oxidized to NO2, leading to a higher adsorption capacity of NOx. 0.4 0.5 0.6 0.7 0.8 0.9 1.00.00.51.01.52.02.53.03.54.0qeO2 (mol/m3 cat)O2 (%) T=200 oC T=250 oC T=350 oC0 1 2 3 4 5 6 7 8 91020304050607080qeNOx, (mol/m3 cat)O2, (%)T=350 oCNO=600 ppm  (a)      (b) Figure 4.2 Adsorption capacity of (a) O2 at different temperatures and (b) NOx at different O2 concentrations (Symbols: experimental data, lines: connection of symbols)  74  4.3 Adsorption and reaction modeling in fixed bed The detailed kinetic model was divided into two sub-models, i), NOx oxidation and adsorption, ii), NOx reduction. These two sub-models describe the steps occurring over Fe/ZSM-5 catalyst during the NOx adsorption and reduction, which could be used for the modeling of the i-CFB deNOx reaction.  4.3.1 Kinetics of adsorption The Fe-zeolite includes a number of different sites and it has been reported that the Fe/ZSM-5 catalysts contain three different Fe species: aggregated ?-Fe2O3, FexOy, oligomer in the extra-framework, and oxo-Fe3+ at ion-exchanged sites [36]. It was further suggested that the ion-exchanged oxo-Fe3+ are the active sites for the SCR reaction, and that these sites only represent a small fraction of the total Fe content. However, due to the uncertainty in the actual nature of these active sites, and in order to keep the model as simple as possible, only a single type of sites was considered in this study for the NOx adsorption, denoted as *.  Detailed Langmuir-Hinshelwood and Eley-Rideal models have been reported in the literature [115]. In this work, we emphasize on global kinetics that is simple enough to be integrated into the NOx adsorption-reduction model. NO adsorption experiments at zero O2 concentration showed that only a small amount of NO was adsorbed on the catalyst surface. Therefore, NO adsorption was ignored. Furthermore, NOx adsorption is highly promoted by O2 concentration, which was confirmed in Fig. 4.2(b), leading to the assumption that the main component of NOx adsorbed on the catalyst surface is NO2. Since the adsorption of NO2 on the Fe/ZSM-5 catalyst is more favorable than that of NO, it is assumed that NO is first oxidized by adsorbed O2 and then adsorbed onto the catalyst surface as NO2. The kinetics of NOx adsorption is proposed here as *2*2 11 ,2 OO kk ?? ??? ?          (4.R1) 75  ** 2, 22 NOONO kk ?? ??? ?               (4.R2) The equilibrium constants of adsorption are  11 /2 ?? kkKO,  22 /2 ?? kkKNO         (4.3) The net adsorption rates for oxygen and NOx could be expressed as  ???????????????? ? 22121211 *][1[*]*][[*]222OKCkOkCkr OOO     (4.4) ???????????????? ? *][1*][*][*][ 2222222NOKOCkNOkOCkr NONONO    (4.5) At equilibrium, 01 ?r , 02 ?r , so, [*]*][ 2/12/1 22 ??? OO CKO         (4.6) *][*][ 22 OCKNO NONO ???         (4.7) where, [*] represents the number of vacant sites on the surface of the catalyst, [NO2*] is the number of sites occupied by NO2, since NO2 is the only form of NOx adsorbed on the catalyst surface, which represents the adsorbed NOx. At equilibrium, [O*] and [NO2*] are the adsorbed oxygen and NO2 concentrations on the surface of the catalyst and, therefore, represent the adsorption capacity of these species.  catmmolqO Oe 3/2*][ 2??         (4.8) catmmolqNO NOxe 32 /*][ ?         (4.9) 76  The adsorbed O2 and NO2 could be expressed into Freundlich equations with the derivations shown in Appendix B: 2222OOnFOOe Ckq ??          (4.10) 22222NONOOOnFNOnFONOxe CkCkq ????           (4.11)  4.3.2 NOx reduction kinetics model The NOx reduction kinetics model consists of two simplified reactions, hydrocarbon combustion (4.R3) and NOx reduction (4.R4). Here, both oxygen and NO2 are assumed to be adsorbed on the catalyst surface already, with their molar concentration being obtained from the adsorption model above. Adsorption was assumed to be at equilibrium, so [O*] and [NO2*] were the saturated concentrations on the catalyst surface, calculated from Eqs. (4.10) and (4.11). OHCOOHC 2263 33*9 ???                                               (4.R3) OHCONOHCNO 222632 33*5*2 ?????                       (4.R4) The power law kinetic model is applied for reactions (4.R3) and (4.R4). 21 *][33 mmHC OCkr ???          (4.12) 543 *][*][ 244 mmHCm OCNOkr ????         (4.13) The reaction rates of NOx, hydrocarbon and oxygen are then expressed as 77  42rrNOx ??           (4.14) 43 rrrHC ???           (4.15) 43 5.25.42 rrrO ???            (4.16)  4.3.3 Governing equations of the fixed bed reactor model  Besides adsorption capacity, breakthrough behaviour is also very important for the design of NOx adsorbers. Based on the gas dispersion, the dynamic adsorption has been modeled with the gas phase being assumed as in plug flow [119, 120], continuously stirred tanks in series with each tank perfectly mixed [115, 121], or axial dispersion [122-124].  Olsson et al. [115] considered the HC-SCR monolith reactor as a series of continuously stirred tank reactors. This approach is suitable for models with intricate adsorption kinetics, because only reaction and mass transfer between the gas and solids phase were considered in each tank. Also, the number of tanks could be easily adjusted. In this study where the simple adsorption kinetics is considered, an axial dispersion model is developed to fit the breakthrough curve in the fixed bed reactor. The differential mass balance equations provide the starting point for the development of a mathematical model to describe the dynamic adsorption behavior of the system.  A general approach to model the adsorption in the fixed bed needs to consider the following steps: 1, the external diffusion; 2, the diffusion inside the catalyst pores; 3, the adsorption at the surface of the catalyst. Although rigorous this approach is often over-sophisticated, because it involves too many adjustable parameters. Also the effect of these processes on the shape of the breakthrough curves is almost identical and can?t be determined independently from the macroscopic experiments [121]. Thus simplified models are required for application purposes. The simplest  and most frequently used model for 78  the external transport is the film model, introduced by Whitman [125]. Here it is considered that NOx is adsorbed onto the catalyst surface and the pores of the catalyst after it diffuses through a thin film, with the porous solids being seen as a pseudo-homogeneous medium. All mass transfer resistances are located across the film adjacent to the particle surface as shown in Fig. 4.3. The NOx concentration in the film is in equilibrium with the NOx concentration in the gas phase. The same method is applied for O2 adsorption and hydrocarbon transferring into the solids phase. For hydrocarbon, the concentration in the film is assumed to be the same as in the bulk, because hydrocarbon is only transferred to the solids. Mass transfer constant of the film, kf, represents both inter-phase and intra-phase mass transfer resistances of the particle. The reaction term is embedded in the solids phase mass balance equation, representing the catalytic surface reaction.   CSCS*kfCgUg Figure 4.3 Schematics of NOx adsorption mechanism onto the catalyst surface  General assumptions for the system include: 1. Since the NOx concentrations were at ppm levels, the exothermic heat of adsorption was negligible and isothermal condition was assumed.  79  2. The pressure drop through the bed is negligible, and thus the gas velocity is considered constant. 3. Thermal equilibrium exists between the bulk gas phase and the solids surface. 4. All mass transfer resistances are limited to the film around the particle. 5. The radial concentration gradients in the reactor are negligible in both gas and solids phases. The following governing equations are derived for each species: Solids phase:   ? ? issfsssss RCCkzCUzCDtC ????????????? *22    (4.17) Gas phase:   ? ?*221 ssfssggggg CCkzCUzCDtC ?????????????????  (4.18) Since in the fixed bed particles are in stationary, the particle velocity and dispersion coefficients are zero. The solids phase equation becomes: ? ? issfs RCCktC ?????? *        (4.19) Initial and boundary conditions are: 0,,0 , ????? zCCCz singg  0,0, ??????? zCzCLz sg 0,0 CCt ??  where, Cs* is the equilibrium concentration of the catalyst, determined by the solids phase concentration and the adsorption equilibrium of each species. For the reduction in fixed bed, only steady state is considered.   80  4.4 Modeling results and discussion 4.4.1 Fitting of adsorption isotherm curves In order to fit Eq. (4.11) into experimental adsorption capacity, it is assumed that  222' FNOFONO kkk ??              (4.20) So,  2222' NONOOONOnnNOxe CCkq ???         (4.21) If O2 concentration is set to be constant, 222' OONOnCk ?could be lumped to k??NO2.  2222''' OONONOnCkk ??          (4.22) And Eq. (4.11) becomes  22'' NONONO nNOxe Ckq ??          (4.23)  So, nNO2 could be obtained by first fitting the data at a constant O2 concentration by taking natural logarithm (ln) of Eq. (4.23). ? ? ? ? ? ?NOCnkq NONONOxe ln''lnln 22 ???          (4.24) Then kNO2 was calculated for each data point at different oxygen concentrations. 22 /'' NONOnNOxeNO Cqk ?          (4.25) k?NO2 and nO2 were then fitted by taking ln of Eq. (4.22). 81  ? ? ? ? ? ?2222 lnln''ln ' ONO Cnkk ONO ???        (4.26) Finally, kFO2 could be obtained from the O2 adsorption experiment. The derived isotherm was fitted into the experimental capacities at different inlet NO concentrations and temperatures, as shown in Fig. 4.4. It could be seen that the fitting values, plotted as lines, agree well with experimental data, which are presented as symbols in the figure. The fitted isotherm parameters were given in Table 4.2. 0.000 0.005 0.010 0.015 0.020 0.025010203040506070T=350 oCT=325 oCT=375 oCT=300 oCT=275 oCR2=0.97 T=275 oC T=300 oC T=325 oC T=350 oC T=375 oCqe (mol/m3 cat)C0 (mol/m3) Figure 4.4 Adsorption capacities as a function of the feed concentration at different temperatures (Symbols: experimental data; lines: isotherm model)  Table 4.2 Fitted parameters for adsorption model O2 adsorption NO2 adsorption Parameter Value Parameter Value nO2 0.7356 nNO2 0.5539 kO2 -0.0206T+19.712 k?NO2 -0.0314?T2+36.107?T-9876  82  4.4.2 Model parameters for the fixed bed adsorption model Gas mixing coefficient Dg and mass transfer coefficient kf were obtained by fitting the fixed bed model to the adsorption curve at 325? with NO=600 ppm.  The fitted values for Dg and kf are 1.2?10-4 m2/s and 1.776?10-3 s-1, respectively, with the fitted adsorption curve and the experimental data shown in Fig. 4.5. 0 1000 2000 3000 4000 50000.00.20.40.60.81.0C/C0t (s) Experiment Model A Model B-k1' Model B-k2' Figure 4.5 Comparison of fitted and experimental adsorption curves in the fixed bed reactor at 325? with NO=600 ppm  The fitted mass transfer coefficient kf and gas mixing coefficient Dg are compared with those estimated from correlations in the literature. The Pe number fitted in this model, Pef, is calculated as 02.20???ggf DULPe         (4.27) The Pe is estimated by  the Wen and Fan [126] correlation 14.124.11Re5.1775.0 ???cPe        (4.28) 83  The fitted value is seen to be in reasonable agreement with the literature value. The classic linear driving force model for mass transfer [127] is  ? ? ? ?** gg CCkKqqktq ??????       (4.29) where q* is the adsorbate loading in equilibrium with the solute concentration, Cg, in the bulk fluid; Cg* is the concentration in equilibrium with the average loading q ; k is the overall mass transfer coefficient, which includes both external and internal transport resistances; and K is the adsorption equilibrium constant for a linear adsorption isotherm of the form q=KCg. The factor kK is related to internal and external diffusions by, epcpDRkRkK 1531 2??         (4.30) where the second term on the right side represents the internal resistance and the first term represents the external mass transfer resistance. For the estimation of the external mass transfer coefficient kc in fixed beds, the correlation of [128] could be used: 2/13/1 Re1.10.2 ScDdkShmpc ???                410Re3 ??     (4.31) For the term ? ?*gg CCkK ?  in Eq.(4.25), it is assumed that the adsorption follows a linear isotherm, q=KCg [127]. However, the adsorption of NOx on Fe/ZSM-5 follows the Freundlich type isotherm. The model with mass transfer treated as kK(Cg-Cg*) could not well capture the adsorption characteristics of Fe/ZSM-5. So the mass transfer term was modified to capture the Freundlich type adsorption performance. In our model, the mass transfer term ? ?*ssf CCk ?  is comparable to the term ? ?qqk ?*  in Eq. 84  (4.29). Similar modification of the model was also adopted by Dasgupta [123] to enable the Langmuir form of isotherm to be used. But in Dasgupta?s model, only intra-phase mass transfer resistance was considered. Since there is no correlation available in the literature for k, Eqs. (4.17) and (4.19) were slightly modified to equations (4.32) and (4.33) in order to evaluate kf. ? ?*22 '11 ggfgsggsgg CCkzCUzCDtC ?????????????????      (4.32) ? ?*' ggfs CCktC ????          (4.33) where Cg* is the concentration in the gas phase in equilibrium with local solids phase NOx concentration, which could be calculated by 2222/1'*NOOONOnnsg CkCC??????????          (4.34) Denoting this model as Model B and the model in section 4.3.3 as Model A, it is noted that the difference between these two models is that Model B is based on the gas phase concentration while Model A is based on the solids phase concentration. Following equations (4.30) and (4.31), kf? (=kK) was calculated to be 9.49 s-1 with an effective diffusivity De of 3.97?10-9 m2/s. Model B was then fitted to the same experimental data with the same Dg value as Model A and the best-fit value of kf? is 3.55 s-1 (named as k1?). The model-fitted results were also plotted in Fig. 4.5. However, Model B did not fit the experiment very well, since it over-estimated the outlet concentration at the beginning when kf?=k1?. When kf? was increased to k2?=11.84 s-1, the model, as shown in Fig. 4.5, under-estimated the experiment at the beginning and over-estimated outlet concentration at the end. It could thus be concluded that the best fitted value of kf? is in the range of 3 s-1 to 12 s-1, which is 85  reasonable since the kf? value estimated from literature correlation is 9.49 s-1 as shown above. This result suggests that the fitted value of kf in Model A is reasonable. Table 4.3 summarizes the Pe number and kf? at different temperatures obtained from data fitting and correlations. It is seen that both parameters do not vary significantly in the range of the tested temperatures, which are from 275 ? to 375 ?, and can be assumed to be constants in the simulation.  The model and the selected parameters are further evaluated with other experimental data at different temperatures and inlet concentrations. The model prediction and experimental data at different inlet NO concentrations at 325? are compared in Fig. 4.6(a). It can be concluded that the model can well predict the experiment at different NO concentrations. Fig. 4.6(b) compares model and experiment at different temperatures at inlet NO=400 ppm. Again, the model can well capture the trend that the breakthrough time is longer at a lower temperature, although the modeling curves do not exactly match the experimental data. The experimental curve is not as smooth as the model because of temperature fluctuations (?2?) during the adsorption experiment. The mass transfer and dispersion coefficients could change with temperature. In this model, however, they were assumed to be independent of temperature. The comparison of the model and experimental data at different temperatures shows that this assumption works reasonable for the NO adsorption process in our research. So it could be concluded that the model could well capture the adsorption process at different conditions. It also confirms that the fitted values of kf and Dg, which are assumed to be constants and independent of temperature, work well over this tested temperature range. Table 4.3 Comparison of fitted and estimated mass transfer parameters T (?) Fitted Pe Pe from correlation Fitted kf?, s-1 kf? from correlation, s-1 275 20.02 12.07 3.55 9.49 325 20.02 12.14 3.55 9.91 375 20.02 12.22 3.55 10.32  86  0 1000 2000 3000 4000 50000.00.20.40.60.81.0 O2=4%T=325oC 200ppm 400ppm 600ppm 800ppm 1200ppmC/C0t, (s)200ppm1000ppm400ppm800ppm600ppm0 1000 2000 3000 4000 50000.00.20.40.60.81.0375 oC350 oC325 oC300 oCNO=400ppm O2=4% 275 oC 300 oC 325 oC 350 oC 375 oCC/C0t, (s)275 oC (a)     (b) Figure 4.6 Comparison of model fitted and experimental adsorption curves at different (a) NOx concentrations and  (b) temperatures. (Symbols: experimental data; lines: model fitting)  4.4.3 Simulations of NOx adsorption in fixed bed The model was used to simulate the NOx adsorption at other conditions. Fig. 4.7(a) presents the gas phase NOx concentration along the reactor length. The curves show the concentrations at different time, ranging from 500 s to 3000 s. The NO gas adsorbs onto the catalyst surface along the reactor and the concentration decreases along the reactor. The axial profile of NOx concentration is almost linear, suggesting that mass transfer between solid and gas phase might be the rate-limiting step in overall NOx adsorption process. At the early stage of adsorption, t=300 s, most of the catalysts are unsaturated and the NOx was adsorbed onto the surface of the catalyst all along the reactor. As time passes more catalysts are saturated and the gas phase NO concentration increases with time all along the reactor. At t=3000 s, most of the catalyst in the reactor is saturated and the NO concentration is close to the inlet concentration even at the outlet of the reactor. Breakthrough time t1/2, which represents the time when effluent concentration reaches half of the initial (feed) concentration, was calculated from the simulated adsorption curves. For t=500 s, L1=26.5 mm when C/C0=0.5, which means that the minimum catalyst bed length is 26.5 mm in order to achieve a breakthrough time t1/2=500 s. Also, if t1/2=700 s, the minimum catalyst bed length 87  increases to L2=34 mm. The required catalyst bed length is larger when longer breakthrough time t1/2 is desired. One advantage of modeling is that the model can simulate the process at the conditions which are not measured in the experiment. Fig. 4.7(b) shows the effluent NOx concentration as a function of time at different temperatures. For T=500?, the breakthrough time is reached soon after the start of the adsorption process. When the temperature is lowered, the breakthrough time becomes longer. The breakthrough time increases about 400 s when the temperatures decrease from 300? to 200?. 0 1 2 3 4 50.00.20.40.60.81.0t=3000 sT=300oCNO=500ppmC/C0L (cm)t=500 st= 700 st=1000 st=2000 sL1 L2 L30 1000 2000 3000 4000 50000.00.20.40.60.81.0C/C0t, (s) T=200 oC T=300 oC T=500 oCNO=600ppmO2=4%t1 t2 t3 (a)     (b) Figure 4.7 (a): gas phase concentration along the reactor length; (b): effluent concentration as a function of time at different temperatures  The adsorption performance was also simulated at different inlet gas velocities. The feed gas velocity is represented by the gas hourly space velocity (GHSV). Fig. 4.8 shows the effluent concentrations as a function of time at different GHSVs. It is quite obvious that the outlet concentration is higher when GHSV is higher, which means that there is a shorter residence time for the gas to be adsorbed onto the catalyst surface, leaving more NO gas escaped. At a lower gas velocity, e.g., GHSV=1000 h-1, the effluent concentration increases slowly. There is no NOx shown at the outlet until 88  after 2700 s. But at GHSV>6000 h-1, NOx could be detected at the outlet immediately and the concentration increases very fast. Intercepting the curves at C/C0=0.5, breakthrough time t1/2 can be obtained at different GHSV. From Fig. 4.8, for GHSV=2000, 3000, 4000, 5000 and 6000, 7000 h-1, the corresponding t1/2s are 3000, 2000, 1500, 1200, 950 and 750 s, respectively. Breakthrough time decreases very fast at higher GHSV. There is nearly a linear relationship between 1/GHSV and breakthrough time, with the deviation most likely related to the gas axial dispersion. 0 1000 2000 3000 4000 50000.00.20.40.60.81.0GHSV=7000 h-1GHSV=6000 h-1GHSV=5000 h-1GHSV=4000 h-1GHSV=3000 h-1GHSV=2000 h-1C/C0t (s)GHSV=1000 h-1NO=500 ppmT=300 0C Figure 4.8 Effluent NOx concentration as a function of time at different GHSV  4.4.4 deNOx reaction kinetics for Fe/ZSM-5 catalyst To develop the deNOx reaction, the same gas mixing coefficient Dg and mass transfer coefficient kf were used as the ones obtained by fitting the adsorption model to fixed bed adsorption breakthrough curves. It should be noted that kf was fitted from fixed bed NOx adsorption breakthrough curves at inlet O2=4%, NO=600 ppm. However, values of kf are dependent on the adsorption capacity of each reactant. Here the fitted kf value is denoted as kf0. kf will be adjusted in the model for different reactants and different 89  reaction condition by Eq. (4.35) using adsorption equilibrium constant K, in which i denotes different reactants and 0 represents the reaction condition at the fitting condition. Detailed discussion of kf is shown in Appendix C. iiff KKkk /00?          (4.35) deNOx reaction kinetic model was coded into Matlab and fitted with experimental data. The best-fitting parameters were found by using the function of ?fminsearch? (unconstrained nonlinear optimization) in Matlab and shown in Table 4.4. Table 4.4 Fitted kinetic model parameters (T=350 ?) Sub-model  Model and Parameter  Fitted experiment (fixed bed)  Adsorption  736.022 88.6*][5.0 OCqeO O ?? O2 adsorption 505.0736.02 2350*][ NOO CCqeNO NOx ?? NOx adsorption Reduction 7.08.03 *][5.2 OCr HC?  NOx reduction 01.0012.024 *][*][0155.0 OCNOr HC?  NOx reduction  Figs. 4.9(a) and (b) present the NOx and HC conversion at different O2 and hydrocarbon concentrations, with the symbols representing the experimental data and lines for the modeled values. Experimental data at O2=0.5%, 4%, and 8% were used for the fitting of kinetic parameters and data at O2=1% and 2% were used for verification. The model shows a good fitting to the experiment for most of the data points with an average error of about 7% for NOx conversion and about 5% for HC conversion. But poor agreement was observed for HC conversion at inlet HC:NO=4. It is interpreted to be due to the catalyst deactivation at higher HC concentrations since unreacted HC tends to deposit on the catalyst surface. At a given O2 concentration, NOx conversion is seen to increase with increasing the inlet hydrocarbon concentration or inlet HC to NOx molar ratio. NOx reduction increased as O2 increased from 90  0.5 to 1%, but then decreased with further increase in O2 concentration. This is because that small amount of O2 is required to oxidize NO to NO2, but higher O2 concentration in the flue gas leads to the hydrocarbon oxidation, leaving less HC reductant for NOx reduction and thus decreasing the NOx conversion. The i-CFB is designed to solve this negative effect of excess O2 in the flue gas. 0 1 2 3 4020406080100 O2=0.5% O2=1% O2=2% O2=4% O2=8%O2=8%O2=4%O2=2%O2=1%NOx conversion (%)HC:NOT=350oCO2=0.5%0 1 2 3 430405060708090100 O2=0.5% O2=1% O2=2% O2=4% O2=8%O2=8%O2=4%O2=2%O2=1%T=350oCHC conversion (%)HC:NOO2=0.5% (a)                                                                                   (b) Figure 4.9  Modeled and simulated conversions at different HC:NO ratios in fixed bed, (a), NOx conversion; (b), HC conversion. (Symbols: experimental data; lines: model fitting)  4.5 Summary A simplified deNOx reaction kinetic model was proposed, consisting of an adsorption sub-model and a reduction sub-model. To develop the adsorption model, the kinetics of NO oxidation and adsorption was considered, following the Freundlich type isotherm. The isotherm parameters were then obtained by fitting equations to the adsorption capacities experimental data obtained from a fixed bed unit. The deNOx reaction kinetics includes NOx reduction and hydrocarbon oxidation. Kinetic parameters were successfully extracted by fitting the model equations to NOx reduction experimental data.  In applying the model to a fixed bed reactor, mass transfer between solids and gas phase was also considered in the governing equations. The mass transfer and axial dispersion coefficients are fitted from 91  the measured NOx breakthrough curve. The reaction term was embedded into the solids phase mass balance equation. The model could be further extended for the modeling of deNOx reactions in fluidized bed reactors. 92   Chapter 5  Modeling NOx adsorption in fluidized bed reactors4  5.1 Introduction NOx adsorption kinetics was derived from experimental data obtained in a fixed bed reactor in Chapter 4. However, NOx adsorption takes place in the fluidized bed in an i-CFB reactor, which behaves quite differently from the fixed bed reactor. There is thus a need to investigate the NOx adsorption characteristics in fluidized beds in order to develop a reactor model for the novel i-CFB reactor.  In this chapter, NOx adsorption is first tested experimentally in a fluidized bed reactor using Fe/ZSM-5 catalyst, prepared by the same method as described in Chapter 1. One should note that minor difference in the preparation procedure could lead to significant variation of the catalyst performance. In Chapter 4, the adsorption isotherm was developed for the catalyst prepared by Yang [11], which showed some difference in the adsorption performance from the catalyst prepared in this study. To keep consistency, adsorption characteristics is also investigated in the fixed bed to develop new adsorption isotherms for this newly prepared catalyst.  A number of fluidized bed models have been reported in the literature [129, 130]. Water vapor adsorption was modeled and simulated in a fluidized bed reactor for thermo-chemical energy conversion by Darkwa [131]. The gas phase moisture concentration was investigated. Voidage in the column was assumed to be constant without consideration of the presence of gas bubbles. A simple model derived from mass balance was used by Hamed [132] for the adsorption and desorption of water vapor in a fluidized bed loaded with silica gel particles. The voidage in the bed was assumed to be constant and the                                                      4 A version of this chapter has been published: Xingxing Cheng and Xiaotao T. Bi, (2013), Modeling and simulation of nitrogen oxides adsorption in fluidized bed reactors, Chemical Engineering Science, 96: 42-54. 93  adsorbent in the reactor was treated as a CSTR, with outlet gas phase concentrations being investigated for the designing purpose. Axial dispersion models were also developed to investigate both liquid and solids phase concentrations [133, 134]. In all of these models, bubbles, which are quite important for the mass transfer, were not considered. On the other hand, the two phase model, consisting of bubble phase and dense phase, was used widely for the modeling of chemical reactions in fluidized beds [20, 28]. Few studies have examined the solids phase concentration of adsorbed gases in fluidized bed catalytic reactors. To our knowledge, there has been no model developed specifically for NOx adsorption in fluidized bed reactors. In this study, NOx concentration profiles in both gas phase and solids phase are investigated, since solids saturated with NOx in the adsorption zone would be circulated to the reduction zone for catalytic reduction in the i-CFB reactor. Bubbles are also an important factor in determining the mass transfer rate from the bubble phase to the dense phase. Different from other adsorption models in the literature, the current model considers the existence of adsorbing gas in three phases: solids phase with adsorbed species, gas in the bubble phase and gas in the dense phase. NOx adsorption isotherms were obtained from a fixed bed reactor for Fe/ZSM-5 catalyst, and then used in the fluidized bed adsorption model to assess and evaluate the NOx adsorption performance in a fluidized bed reactor using the same catalyst.   5.2 Experiment The adsorption characteristics of Fe/ZSM-5, prepared by the method described in [11], is investigated in both fixed and fluidized bed (hot model unit) reactors. The configuration of the fixed bed reactor has already been given in detail in Chapter 4 and will not be repeated here. The details of the experiments are given in Appendix D. Other experimental conditions are summarized in Table 5.1.  94  Table 5.1 Experimental conditions of NOx adsorption  Fixed bed experiment Fluidized bed experiment Temperature, ? 250, 300, 350 250, 300, 350 NO inlet concentration, ppm 200, 400, 600, 800, 1000 300, 600, 900 Gas velocity, m/s 0.07 0.04, 0.06, 0.08   5.3 Fluidized bed adsorption model 5.3.1 Adsorption isotherm The Freundlich equation, which was found to give a good fit to our experimental data, is also used to model the adsorption isotherm of NOx on Fe/ZSM-5. NOxnFe Ckq 0??            (5.1)  5.3.2 Governing equations for fluidized bed A bubbling fluidized bed consists of two phases, bubble phase and dense phase. The mass transfer of NOx not only takes place between the bubble phase and dense phase, but also between gas and particles in the dense phase, as shown in Fig. 5.1(a). Three phases were thus considered in the current study, particles in the dense phase, gas in the dense phase and the bubble phase. It is assumed that there are no solids particles in the bubble phase and adsorption takes place only in particles of the dense phase. The gas film model was used to describe the mass transfer between particles and the gas in the dense phase, which assumes that a film in equilibrium exists at the surface of the particles as shown in Fig. 5.1(b). Here it is considered that NOx is first adsorbed onto the external surface of the catalyst particle and then diffuses into the catalyst, with the porous particles being treated as a pseudo-95  homogeneous medium. Mass transfer constant of the film, kf, represents both inter-phase and intra-phase mass transfer resistances of the particle. Other general assumptions for the modeled system include: 1. The pressure drop throughout the bed is negligible, and thus the gas velocity is considered constant. 2. Thermal equilibrium exists between the bulk gas phase and the solids surface. 3. All mass transfer resistances are limited to the film around the particle. 4. The concentration gradients are negligible in both gas and solids phases.  CSCS*kfCgUgSDense phaseBubble phaseSSS   (a)        (b) Figure 5.1 Schematic of mass transfer (a) in the fluidized bed and (b) around particles  Differential mass balance equations for an element of the adsorption column provide the starting point for the development of a mathematical model to describe the dynamic adsorption behavior of the system.  Governing equations are: ? ? tCCCkzCUzCD ssssfssssssss ???????????? ????? *221      (5.2) for particles in the dense phase, ? ? ? ? ? ? ? ? ? ? tCCCakCCkzCUzCD HsHHLbHLssfHsHHHsHH ??????????????????? ??? 111 *22 96  (5.3) for the dense phase, and ? ? tCCCakzCUzCD LLHLbHLLLLLLL ????????????? 22     (5.4) for the bubble phase. Initial and boundary conditions are: ingLsingH CCzCCCz ,, ,0,,0 ?????? 0,0,0, ?????????? zCzCzCHz LsH 0,0,0,0 ???? LsH CCCt  where CH, CL and Cs* are the NOx gas concentrations in the dense phase, the bubble phase, and the equilibrium concentration in the dense phase, respectively, with the same unit, mole/m3 gas. Cs is the average concentration in the particles per unit catalyst volume with a unit of mole/m3 cat. Cs* could be calculated from the adsorption isotherm fitted from fixed bed experiments. ?H and ?L are the fractions of dense phase and bubble phase, respectively, with ?L equal to bubble fraction ?b and ?H=1-?L. Parameter ab is the specific dense-bubble phases contacting surface area, defined as  bbb da?6?          (5.5)  5.3.3 Hydrodynamics The total voidage consists of two parts, voidage in the dense phase and the bubble fraction. The voidage in the dense phase is assumed to equal the voidage at minimum fluidization, ?mf, and the gas velocity is assumed to remain at the minimum fluidization velocity umf.  The estimation of other parameters, such as bed height and bubble velocity, are calculated in the same way as shown in Chapter 3.  97   5.3.4 Mass transfer  Interphase mass transfer coefficient is estimated by Sit and Grace?s equation [135] for three-dimensional freely bubbling beds: 5.023 ???????????bbmfmmfHL DUDUk ??       (5.6) Intra-phase mass transfer coefficient between the solids phase and gas phase kf consists of external mass transfer and internal mass transfer and was correlated to be Eqs. (4.29) to (4.31) as shown in Chapter 4.  In fitting the models to the experimental breakthrough curves, interphase mass transfer coefficient kHL was estimated from the correlation shown above, while intra-phase mass transfer coefficient kf was fitted by the experimental data and checked against the literature.  5.3.5 Gas and solids mixing For axial solids dispersion in bubbling beds, there are several correlations in the literature [136, 137]. The correlation of Morooka [138] was selected in this study due to its similar experimental settings, with Ug?0.02 m/s, D=32 ?195 mm, Hbed=1?3m with FCC particles as the bed material, dp=80 ?m. ? ? ????????????????????????8.05.61/23.019DgUDgUDDDUPe ggsgs    (5.7) There are several correlations in the literature for gas dispersion, either vertical or radial, in fluidized beds [27]. However, the dispersion coefficients correlated in the literature are the overall 98  dispersion, different from DL and DH in Eqs. (5.3) and (5.4) for dense and dilute phases, separately. Therefore, the literature correlations are not directly applied in the model.  Dispersion in the bubble phase was assumed to be 0, DL=0, according to the two-phase model of [20]. Gas mixing coefficient in the dense phase DH was obtained by fitting the adsorption breakthrough curves at different gas velocities and temperatures. Since gas dispersion in the dense phase is caused mainly by the movement of solids, DH is expected to be similar to the solids dispersion coefficient Ds. This assumption was also confirmed by the study of [28], who measured both the solids dispersion and dense phase gas dispersion and found the values were similar. However, no correlation was reported by Abba [28] due to the scarcity of data points. So the fitted DH from the current study was compared with Ds calculated from Eq. (5.7).  5.4 Experimental results 5.4.1 Fixed bed Adsorption breakthrough performances on Fe/ZSM-5 were tested at different temperatures and inlet NOx concentrations. A series of adsorption breakthrough curves were obtained, as shown in Appendix D, and used to calculate the adsorption capacities.  The calculated adsorption capacities are plotted in Fig. 5.2 and fitted to the Freundlich isotherm equation, giving: ? ? 989.0555119.1701345.0 24786.02 ??????? RCTTqe     (5.8) This equation will later be used in the simulation of fluidized bed adsorption. 99  0.000 0.005 0.010 0.015 0.020 0.02501020304050T=350 oCT=300 oCqe, mol/m3 catC0, mol/m3 T=250 oC T=300 oC T=350 oCT=250 oC Figure 5.2  Adsorption capacity at different feed NOx concentrations. (Symbols: experimental data; lines: fitted isotherm model)  5.4.2 Fluidized bed Some typical breakthrough curves at different inlet NOx concentration and gas velocities are presented in Fig. 5.3, with more results given in Appendix D. Unlike the breakthrough curves in the fixed bed where an initial period with almost zero NOx concentration exists, there is no time delay in the fluidized bed breakthrough curves. This is caused by the gas bypassing from the bubble phase and will be further discussed in the modeling section. Although fluctuations also exist and the curves are not very smooth, it is quite clear that the slopes are bigger at higher inlet NOx concentrations, which is consistent with the fixed bed adsorption results. The outlet NOx concentration also increases slower at lower superficial gas velocities, as shown in Fig. 5.3(b), due to longer contacting time with the catalyst.  100  0 500 1000 1500 2000 2500 3000 35000.00.20.40.60.81.0C/C0t, s 300ppm 600ppm 900ppmT=250 0CU=0.08 m/s0 5 0 1 0 15 0 2000 2500 3000 35000.00.20.40.60.81.0C/C0t, s U=0.04 m/s U=0.06 m/s U=0.08 m/sT=3 00CInlet NO=600 ppm (a)      (b) Figure 5.3 Breakthrough curves at (a) different NOx inlet concentrations at 250 ?; and (b) different gas velocities at 300 ?  5.5 Modeling results 5.5.1 Parameter fitting The model was coded into MATLAB with the partial differential equations differentiated with Crank-Nicolson method. The fluidized bed model was first fitted to the measured adsorption breakthrough curves of the fluidized bed with both gas dispersion coefficient in the gas phase, DH, and gas-particle mass transfer coefficient, kf, as the fitting parameters. The outlet gas concentration was calculated from both the predicted dense phase and bubble phase gas concentrations as:  LLHHLLLHHHout UUCUCUC ???????        (5.9) The best-fitted parameters at different temperatures and superficial gas velocities are shown in Table 5.2, and Fig. 5.4 shows a good agreement between measured and fitted adsorption breakthrough curves. 101  The fitted parameters were further compared to the values from literature data and correlations. The kf values calculated from literature correlations were also shown in Table 5.2. It should be noted that the literature correlation is based on the linear driving force model for mass transfer as indicated by Eq. (4.29) in Chapter 4. The kf? from correlation and shown in Table 5.2 is equivalent to kK in Eq. (4.29). However, the fitted kf value in this study is based on the equivalent term of ? ?qqk ?*  according to the mass balance equation, Eq. (5.2). To make the fitted value comparable with that estimated from the correlation, further treatment is required. In Table 5.2, fitted kf values are multiplied by K, the adsorption equilibrium constant for a linear adsorption isotherm in the form of q=Kc, with each K being calculated for the given specific condition. It can be seen from the table that the values of the fitted kf? are in the same order as the values estimated from correlations, implying that the fitted values are quite reasonable. The difference between these values could be caused by the inaccurate calculation of NOx diffusivity. Only diffusivity of NO was considered in the calculation. But in fact, NO2, from the oxidation of NO, is also very important for the NOx adsorption. This factor was not considered for the calculation of literature value, leading to the inaccuracy of the calculation. Different adsorption isotherm could also contributor to the variation between literature and fitted values. The estimated values of the first and second terms of Eq. (4.30), which represent the external and internal mass transfer respectively, are also shown in Table 5.2. The internal mass transfer resistance is seen to be much higher than the external one, suggesting that the internal mass transfer is the rate-limiting step. Both fitted and calculated kf? values show a similar trend, increasing with increasing reactor temperature, likely associated with the increased gas diffusivity at higher temperatures. However, fitted kf? increases with increasing the gas velocity while calculated kf? remains at a constant. It is anticipated that the external mass transfer rate will increase with increasing the gas velocity but its contribution to the overall intra-phase mass transfer coefficient is almost negligible.  102  The fitted PeH values are very close to the literature values of Pes calculated from Eq. (5.7), confirming that solids dispersion is well correlated with gas dispersion in the dense phase. Fitted PeH decreases with increasing temperature while Pes from correlation remains at a constant at different temperatures. It is noticed [138] that the correlation was developed based on data obtained at constant temperatures without temperature effect being considered. In lack of reliable correlations, the fitted values will be used in the simulation of adsorption in the fluidized bed reactors in this study. The sensitivities of the model to these parameters are shown in Appendix D. 0 500 1000 1500 20000.00.20.40.60.81.0U=0.08 m/sU=0.06 m/sC/C0t (s) U=0.04 m/s U=0.06 m/s U=0.08 m/sU=0.04 m/s0 10 1500 2000.00.20.40.60.81.0T=350 oCT=300 oCC/C0t (m) T=250 oC T=300 oC T=350 oCT=250 oC (a)       (b) Figure 5.4 Comparison of model-fitted and experimental breakthrough curves at different (a) velocities and (b) temperatures (Symbols: experimental data; lines: model fitting)       103  Table 5.2 Parameters used in the fluidized bed adsorption model T, (?) 300 300 300 250 300 350 Gas velocity, (m/s)  0.04 0.06 0.08 0.08 0.08 0.08 DH, fitted, (m2/s)  0.0107 0.0133 0.0173 0.013 0.0173 0.019 PeH, fitted 0.4037 0.4872 0.4994 0.6646 0.4997 0.4547 Pes, literature 0.3704 0.6252 0.9201 0.9201 0.9201 0.9201 kf fitted, (s-1) 0.0019 0.0023 0.0031 0.0021 0.0031 0.0036 K, (linear) 1112.7 1112.7 1112.7 1954.5 1112.7 605.9 kf?= kf*K,  (s-1) 2.11 2.56 3.45 4.1 3.45 2.18 kf? literature, (s-1) 9.70 9.70 9.70 9.27 9.70 10.12 Rp/(3kc) (?105), (s) 2.65 2.56 2.49 2.89 2.49 2.17 Rp2/(15De), (s) 0.103 0.103 0.103 0.108 0.103 0.0988  The current model was evaluated using the breakthrough curves that were not used for the parameter fitting. As shown in Fig. 5.5, the model-predicted adsorption curves could well represent the experimental adsorption performance at different temperatures and inlet gas conditions, indicating that the current model could be used for the simulation of bubbling fluidized bed adsorption. The sensitive analysis of the model is shown in Appendix E. 104  0 500 1000 1500 20000.00.20.40.60.81.0T=350 oC NO=900 ppmT=350 oC NO=300 ppmT=300 oC NO=600 ppmC/C0t (s) T=250 oC NO=300 ppm T=300 oC NO=600 ppm T=350 oC NO=300 ppm T=350 oC NO=900 ppmU=0.08 m/sT=250 oC NO=300 ppm Figure 5.5 Model evaluation at different temperatures (Symbols: experimental data; lines: model fitting)  5.5.2 Simulation of fluidized bed NOx adsorption  To further examine the adsorption performance of fluidized beds, the current adsorption model is applied to study those parameters not measured in the experiment. The outlet NOx concentrations of the three phases are plotted as a function of time in Fig. 5.6(a) for a typical adsorption condition with T=300 ?, U=0.08 m/s and 4% inlet oxygen concentration. The concentrations are normalized by the corresponding saturation values in each phase. It is seen that the concentration in the solids phase increases steadily from 0 at the start of adsorption. The concentrations in the dense phase and bubble phase are generally higher than zero because of the gas bypass from the bubble phase. Due to high interphase mass transfer between the bubble phase and the dense phase, the difference in the gas phase NOx concentration between the dense phase and the bubble phase is quite small. Comparing with interphase mass transfer, the mass transfer between the particles and gas in the dense phase is much smaller and rate limiting, reflected by the large difference between the solids phase NOx concentration curve and the other two curves. As time 105  passes, NOx concentration on the particle surface builds up gradually. The three curves converge after about 300 s, indicating the approach to saturation.  Fig. 5.6(b) shows the axial concentration profiles under the same operating conditions at t=170 s which corresponds to the breakthrough time, t1/2, when effluent concentration reaches half of the initial (feed) concentration. It is seen again that the dense phase and bubble phase NOx gas concentrations are very close to each other due to the fast interphase mass transfer, but they are quite different from the solids phase concentration. The concentration difference between the particles and gas in the dense phase decreases along the reactor height due to the transfer of NOx from the gas to the particles. It should also be noted that the NOx concentration in the particles is almost constant along the reactor, indicating strong solids mixing in the fluidized bed.  Solids mixing is not desirable for gas-solids reactions in a fluidized bed reactor, since too much back-mixing could lower the reaction rate. The effect of solids mixing on the adsorption performance was further examined by treating solids as plug flow (PFR) as in a moving or fixed bed, where the axial dispersion of particles is neglected. The simulated results were shown in Fig. 5.6(b) as dash lines. Comparing with the normal fluidized bed with strong solids mixing, NOx concentration in solids phase decreases along the bed height in plug flow reactors. The gas phase NOx concentration also confirms that less solids mixing could give a better NOx capture efficiency, as reflected by the low outlet NOx concentration. The i-CFB deNOx reactor is expected to perform better if the solids back-mixing is reduced because of the higher deNOx capture efficiency and higher NOx concentration on solids at the bottom of the adsorption zone which will be circulated to the reduction zone to be reduced by hydrocarbon reductant. A higher adsorbed NOx concentration on catalyst surfaces passed to the reduction zone will likely improve the NOx reduction and thus the overall performance of the whole i-CFB reactor. To reduce solids back-106  mixing in the i-CFB reactor, one can consider the use of internals/baffles or division of the adsorption zone into multiple stages. 0 50 100 150 200 250 300 3500.00.20.40.6T=300 oCC0=600 ppmU=0.08 m/sDimensionless concentrationt, s CH/C0 CL/C0Cs/Cs*0.0 0.2 0.4 0.6 0.8 1.00.00.20.40.60.81.0T=300 0CC0=600 ppmU=0.08 m/st=170 sDimensionless concentrationDimensionless bed heightPFR-Cs/Cs*Cs/Cs*CH/C0CL/C0PFR-CH/C0PFR-CL/C0 (a)      (b) Figure 5.6 (a) Outlet NOx concentrations in different phases as a function of time; (b), dimensionless NOx concentration as a function of dimensionless bed height, (t=170 s)  The performance of fluidized bed deNOx reactors can also be improved by the use of small particles. Since the rate-limiting step is the mass transfer between the solids phase and the gas phase (which lumps external and internal mass transfer), not between the dense phase and the bubble phase, effort should be made to improve the mass transfer coefficient or to increase the gas-solids contact area. As revealed in the previous section, internal mass transfer is the rate-limiting step. So it can be approximated that epf DRk 151 2?. Decreasing the particle size is expected to increase the mass transfer coefficient kf. On the other hand, smaller particles can also increase the gas-solids contact area. Simulated curves of outlet NOx concentrations for different particle sizes are shown in Fig. 5.7.  It is seen that there is a clear difference between the solids phase NOx concentrations for different particle sizes. When dp decreases by 20%, solids phase NOx concentration increased by 12% at 170 s, greatly enhancing the adsorption performance. Correspondingly, the outlet gas phase NOx concentration 107  decreases with decreasing dp, leading to improved total NOx abatement efficiency. The maximum NOx capture efficiency at the start of the adsorption, which mostly corresponds to the continuous adsorption process in the i-CFB reactor with fresh catalyst, increases from 85.6% to 91.7% and 96.5% when dp decreases to 0.8 and 0.9 times of the original size, respectively. What can be learned from this analysis is that small particles should be used in i-CFB reactors so that there are large particle surface areas for adsorption. However, one should also note that too small a particle size may create other operational problems, such as stickiness of particles, in the fluidized bed reactor.  It should be noted in the figure that the dimensionless Cs sometimes exceeds corresponding Cg. At a local point, this should not occur because NOx cannot be transferred from the gas phase to the solids phase beyond the equilibrium. However, the results presented here are averaged values over the whole reactor. The saturation concentration given by Eq. (5.1) is not linear to the gas phase concentration. So the driving force is not linear to the gas concentration. However, all the concentrations are normalized by the feed concentration. Therefore, the higher value of dimensionless Cs than Cg is possible and does not necessarily reflect the reversal in local mass transfer. 0 40 80 120 1600.00.10.20.30.40.50.6Cg/C0, 0.8*dpCg/C0, 0.9*dpT=300 oCInlet NO=600 ppmU=0.08 m/sDimentionless concentrationt (s)Cg/C0, dpCs/Cs*, dpCs/Cs*, 0.9*dpCs/Cs*, 0.8*dp Figure 5.7 Influence of particle size on outlet NOx concentrations 108   In the reactor design, gas flow rate is a very important operating parameter. So the influence of superficial gas velocity on the fluidized bed reactor NOx adsorption is investigated by simulation with the results plotted in Fig. 5.8. Since kf was fitted at different velocities previously, it was correlated to gas velocity Ug by Eq. (5.10). Pes correlation from the literature, Eq. (5.7), was used for the calculation of DH. For the current column diameter and particles, Eq. (5.7) is corrected by the fitted Pes data to Eq. (5.11). It should be noted that this correlation is only applicable to the current fluidized bed reactor and the current catalyst particles. 964.00006.003.0 2 ???? RUk gf       (5.10) ? ? 994.06247.1678.13 2, ?????? RPeUPe literaturesgH     (5.11) Fig. 5.8 illustrates that the outlet solids phase NOx concentration increases with increasing the superficial gas velocity, because more NOx is supplied to the reactor. However, due to the shortened contact time, the outlet gas NOx concentration also increases, lowering the total NOx abatement efficiency. Therefore, low gas velocity is desirable to achieve higher NOx capture efficiency for a given reactor catalyst loading or height.  109  0 40 80 120 1600.00.10.20.30.40.50.6Cg/C0U=0.04 m/sT=300 oCInlet NO=600 ppmDimentionless concentrationt (s)Cg/C0U=0.06 m/sCg/C0U=0.08 m/sCg/C0U=0.10 m/sCs/Cs*U=0.04 m/sCs/Cs*U=0.06 m/sCs/Cs*U=0.08 m/sCs/Cs*U=0.10 m/s Figure 5.8 Influence of superficial gas velocity on outlet NOx concentration  5.5.3 Simulation of adsorption zone in an i-CFB deNOx reactor As an important element in the i-CFB reactor, the adsorption in fluidized bed was modeled as part of a continuously operated adsorption column decoupled from the i-CFB.  As shown in Fig. 5.9, different from the batch operated fluidized bed in which solids stay in the bed all the time, solids are fed to the adsorption reactor from the top and discharged from the bottom into the reduction reactor with NOx being reduced there by reduction agent.  Two more parameters should be considered in modeling the decoupled i-CFB, solids circulation rate, Gs, and NOx concentration on the fed solids surfaces, Cs,feeding. The solids circulation rate, Gs, represents how effectively the adsorption zone can be replaced by refreshed solids. In most cases, NOx is not completely reduced and the NOx concentration remaining on the solids surface leaving the reduction zone is not zero, depending on the design and operation of the reactor. This concentration will correspond 110  to the NOx concentration in the feeding solids into the adsorption zone, Cs,feeding. The reduction efficiency in the reduction zone can be expressed as *,1sCCE feedingsr ??             (5.12) where Cs* is the saturated solids phase concentration at Cg,in. Cg,outCg,inUgCs,feedingCs,outUsCg,outCg,inUgConventional fluidized bed Decoupled i-CFB Cg,outCg,inUgCs,outCs,inUs(Adsorption zone) (Reduction zone) (a)      (b) Figure 5.9 Gas and solids flow in (a) conventional fluidized bed and (b) continuous fluidized bed decoupled from the i-CFB reactor  The governing equations are still Eqs. (5.2) to (5.4) but the initial and boundary conditions become: ginLsginH CCzCCCz ?????? ,0,,0 111  0,,0, , ???????? zCCCzCHz LfeedingssH 0,0,0,0 ???? LsH CCCt  Different from the dynamic breakthrough curve of the conventional fluidized bed, only the final steady state was investigated for i-CFB unit. The final stable concentration of the outlet NOx, denoted as Cg here, also determines the overall deNOx efficiency of i-CFB, E, by  01 CCE g??              (5.13) The adsorption performance of the continuous adsorption reactor representing the decoupled adsorption zone of the i-CFB reactor was then simulated at different solids flow rate, gas velocity, Cs,feeding and catalyst loading M. It should be noted that the catalyst loading M represents the weight of the catalyst in the adsorption reactor, different from the total catalyst loading of the i-CFB system. Solids circulation rate was taken as a dimensionless value. 0,*sss GGG ?           (5.14) Here, Gs,0 is the minimum solids circulation rate calculated from *,,*,,outgoutsCCCCVVingfeedingssg???          (5.15) Where Cs,out* and Cg,out* are in equilibrium with Cg,in and Cs,feeding, respectively. Vs and Vg are the volume flow rate of gas and solids, respectively. Gs0 could then be calculated from Vs. AVG sss /0, ??          (5.16) 112   The effect of solids circulated rate Gs on the NOx capture efficiency was investigated and the outlet concentrations of both the solids phase and gas phase were plotted in Fig. 5.10. The feeding NOx concentration in the solids phase was set to be 20% of the saturated concentration, which corresponds to an 80% NOx reduction efficiency in the reduction zone of an i-CFB reactor.  It could be anticipated that both solids and gas phases will be saturated if there is no refreshed solids feeding to the reactor. So the values of both Cs/Cs* and Cg/C0* are equal to 1 at Gs=0. If the solids are refreshed effectively enough, the adsorption bed could be filled with regenerated catalysts, with the solids phase NOx concentration equal to the feeding NOx concentration. With the current setting, the lowest value of Cs/Cs* is found to be 0.2. The simulated results of Cs/Cs* agree well with what are expected, with all the curves start from 1 at Gs=0 and then decrease to 0.2 when Gs increases. Similar trends are also observed for the gas phase NOx concentration, which also starts at 1 and then stabilizes at a fixed value when Gs is high enough.  But the lowest gas phase concentration is different for different values of Cs/Cs*since it is determined by many factors such as mass transfer and contacting time.  It is noted that slopes of all the curves are very sharp when Gs is very small, usually between 0 and 2 kg/m2.s. After that, further increase of Gs has little effect on both solids and gas phase concentrations. The reactor is almost filled with refreshed catalysts since Cs/Cs* values are very close to 0.2. So, for the current fluidized bed, the catalysts could be effectively refreshed when Gs is higher than 2 kg/m2.s. Further increasing Gs could not improve the NOx capture efficiency substantially. In order to increase the overall NOx abatement efficiency, other methods should be explored, such as changing the bed solids loading to increase the contacting time or NOx reduction efficiency in the reduction zone to lower the NOx concentration on the particles fed to the adsorption zone. Fig. 5.10 also illustrates how the bed loading affects the solids and gas phase NOx concentrations. Although the solids concentration curves at different bed loading are very similar, it can still be seen that the solids phase NOx concentration is slightly higher at higher solids loadings. At a fixed Gs, there is a 113  larger fraction of newly refreshed solids in the adsorption zone when there is a lower solids holdup in the bed, leading to a lower overall solids phase NOx concentration. Contacting time between the gas and solids phases is critical for NOx adsorption. Comparing with the solids phase NOx concentration, gas phase NOx concentration is more influenced by the bed loading. At a higher bed loading, the outlet gas phase NOx concentration is much lower due to longer contacting time between the gas and solids phases. It is also found that Cg/C0* decreases significantly when bed loading increases from 0.5 kg to 1 kg. But further increasing the bed loading from 2 kg to 4 kg does not give such a significant improvement. The lowest value of gas phase NOx concentration is determined by the equilibrium to the solids phase NOx concentration. Therefore, a higher NOx capture efficiency could be achieved by improving the reduction zone efficiency and lowering feeding solids phase NOx concentration. 0 10 20 300.00.20.40.60.81.0M=4 kgCs/Cs*M=2 kgCs/Cs*M=1 kgCs/Cs*M=0.5 kg, Cs/Cs*M=4 kg, Cg/C0M=2 kg, Cg/C0Dimensionless concentrationGs*, dimensionlessCs, feeding/Cs*=0.2T=300 0CC0=600 ppmUg=0.08 m/sM=0.5 kg, Cg/C0M=1 kg, Cg/C0 Figure 5.10 NOx adsorption performance as a function of Gs*  114  The effect of Cs,feeding on the NOx capture efficiency was investigated with the results plotted in Fig. 5.11.  Here the X-axis is a dimensionless parameter, Cs,feed/Cs*,  where Cs* is the corresponding saturation concentration of inlet NOx concentration C0. And Y-axis is the dimensionless Cg/C0. It can be seen that the outlet gas NOx concentration increases with increasing feed solids phase NOx concentration, since less NOx can be adsorbed onto the catalyst surface. So a good performance of the NOx reduction zone in an i-CFB is very important to keep Cs,feed at a low level.  Catalyst loading M also has a significant effect on the NOx adsorption as can be seen in the figure. The NOx adsorption performance is significantly improved at higher catalyst loadings. At Cs/Cs*=0.4, the NOx abatement efficiency can be increased from 20% to 60% when M increases from 0.5 kg to 1 kg. Further increasing M from 1 kg to 2 kg could still improve the NOx capture efficiency. So for an i-CFB reactor, it is very important to keep sufficient catalyst in the adsorption zone to ensure the full abatement of NOx from the gas stream. In order to evaluate the NOx adsorption performance, parameter Cg* is introduced, with its definition given in Eq. (5.17). It can be considered as the limit of NOx abatement at a given Cs,feed. Coefficient kF is the equilibrium constant in Eq. (5.1). ? ? NOxnFsg kCC /1* /?          (5.17) Dimensionless Cg*/C0 is also plotted in Fig. 5.10. It can be seen that the curve at M=2 kg is very close to the curve of Cg*/C0, which is the limit of the NOx capture efficiency. Thus it is not surprising that further increasing M to 4 kg has little effect on improving the NOx abatement as shown in Fig. 5.10. In fact, a key parameter affecting the amount of catalyst staying in the adsorption zone is the overall solids circulation rate in the i-CFB. The solids feed rate is determined by the gas velocities in both the adsorption zone and the reduction zone. However, the influence of Ug could not be fully investigated here because the hydrodynamics of an i-CFB reactor was not included in the current continuous adsorption 115  model. Further modeling is required to couple the hydrodynamics of i-CFB with the NOx adsorption and reduction kinetics. 0.0 0.2 0.4 0.6 0.8 1.00.00.20.40.60.81.0M=1kgGs=6 kg/m2.sT=300 oCUg=0.08m/sCg/C0Cs,feeding/Cs*Cg/C0 at equilibiumM=2kgM=0.5kg Figure 5.11 NOx adsorption performance as a function of Cs,feed/Cs*  5.6 Summary A two-phase adsorption model was proposed for the NOx adsorption in a fluidized bed reactor. The model parameters were obtained by fitting the experimental breakthrough curves. With the fitted mass transfer and gas dispersion coefficients, the model agrees well with the experimental results.  Further simulation of NOx adsorption performance suggested that small size particles and low gas velocity should be used to improve the fluidized bed performance. Simulation of the adsorption zone in a decoupled i-CFB showed that the NOx concentration on the surface of feed catalysts could affect the NOx abatement efficiency. At the same time, it is essential to maintain a large amount of catalyst in the adsorption zone to achieve a 116  high deNOx efficiency. Since hydrodynamics of i-CFB was not included in the current model, the influence of solids feed rate and superficial gas velocity could not be fully investigated.  117   Chapter 6  Modeling NOx reduction in fluidized bed reactors5  6.1 Introduction In Chapter 5, NOx adsorption in a fluidized bed reactor was modeled and simulation was conducted on the performance of adsorption zone of the i-CFB reactor. NOx reduction zone, which is also an important part of the i-CFB reactor, is modeled in this Chapter based on the reaction kinetics developed in Chapter 4 and the fluidized bed adsorption kinetics developed in Chapter 5. The fluidized bed model is further applied to simulate NOx reduction in the reduction zone of the i-CFB reactor.  6.2 Fluidized bed reactor model 6.2.1 Model governing equations Similar to the fluidized bed adsorption model developed in Chapter 5, the fluidized bed reactor model consists of two phases, bubble phase and dense phase. Different from fixed beds, mass transfer of NOx, HC and O2 in the fluidized bed not only exists between the bubble phase and dense phase, but also between the gas phase and particle phase, as shown in Fig. 5.1. It is assumed that there are no solid particles in the bubble phase. Adsorption and reaction take places only on the particles of the dense phase. Model governing equations for the different phases are: ? ? tCRCCkzCUzCD ssissfssssssss ????????????? ????? *221     (6.1) for particles in the dense phase.                                                      5 A version of this chapter will be submitted for publication: Xingxing Cheng and Xiaotao T. Bi, Modeling catalytic reduction of NOx in the reaction zone of an i-CFB reactor. 118  ? ? ? ? ? ? ? ? ? ? tCCCakCCkzCUzCD HsHHLbHLssfHsHHHsHH ??????????????????? ??? 111 *22 (6.2) for the dense phase, and ? ? tCCCakzCUzCD LLHLbHLLLLLLL ????????????? 22     (6.3) for the bubble phase. Initial and boundary conditions are: ingLsingH CCzCCCz ,, ,0,,0 ??????     (6.4) 0,0,0, ?????????? zCzCzCHz LsH     (6.5) 0,0,0,0 ???? LsH CCCt       (6.6) Freeboard is also included in the model. The gas in the freeboard region is considered to be in plug flow with dispersed solid particles and no bubbles in the freeboard region. Two phases are considered in the model: gas phase and solids phase, with the reaction term embedded in the solids phase. The governing equations are: ? ? issfsssss RCCkzCUzCDtC ????????????? *22        (6.7) for solids phase, and ? ?*221 ssfssggggg CCkzCUzCDtC ?????????????????      (6.8) for gas phase. 119  The inlet concentrations are obtained from the outlet concentrations of the dense fluidized bed region. Solid fraction in the freeboard is calculated by Chen and Wen?s freeboard model [139], which incorporates elutriation and entrainment rates to calculate the solids hold up and solid velocity profiles in the freeboard region of a fluidized bed. For the reduction in fluidized bed, only steady state is considered, which is assumed to be reached until 6101 ?????tC , the same as used in the fixed bed model.   6.2.2 Model parameters  The hydrodynamic parameters, dispersion coefficients and interphase mass transfer coefficient kHL, are obtained in the same way as in Chapter 5. The intraphase mass transfer coefficient kf is determined by the properties of the catalyst. The catalyst used in the fluidized bed reaction experiment was prepared by Yang [11], which was also used for the kinetics development in Chapter 4. So the same kf value as used in Chapter 4 is used.  6.3 Fluidized bed modeling results 6.3.1 Model verification The model is coded in MATLAB and the differential equations are solved with a Crank-Nicolson method. The outlet concentration of the fluidized bed is calculated by Eq. (5.9). Fluidized bed reaction data, from Yang?s research [11], are used to evaluate the fluidized bed reaction model. Fig. 6.1(a) presents the modeled and experimental NOx conversions as a function of superficial gas velocity at different inlet O2 concentrations and HC:NO ratios. It could be seen that the model could well capture the effect of inlet O2 and HC concentration. Experimental data show that increasing HC:NO ratio has a positive effect on NOx conversion, while increasing O2 concentration has a negative impact on the NOx conversion. This observation is consistent with the modeling data. At O2=1%, NOx conversion in the fluidized bed is 120  predicted to increase from about 52% to 62% when HC:NO ratio increases from 1 to 2. As a comparison, NOx conversion at O2=1% in the fixed bed, as shown in Fig. 4.9(a), increases from 50% to 60% when HC:NO ratio increases from 1 to 2. Therefore, it could be concluded that HC shows similar effect on NOx conversion in both the fluidized bed and fixed bed.  For O2 effect, the model could well predict NOx concentration at lower inlet O2 concentration with an average error of about 4% at O2=1%. But when inlet O2 concentration is higher, the model tends to overestimate the NOx conversion, especially at lower Ug. The reason may be that catalysts used in the fixed bed and fluidized bed reaction were prepared separately and slight difference in the preparation could lead to some variation in the reaction kinetics. In modeling the fluidized bed, kinetics, which was developed from the fixed bed catalyst, may lead to the under-prediction of negative O2 effect. To further verify this assumption, experiment NOx conversions between the fluidized bed and fixed bed were compared at HC:NO=2. In the fluidized bed experiment, NOx conversion decreases from about 62% to 20% when O2 concentration is increased from 1% to 8%. However, in the fixed bed experiment, as shown in Fig. 4.9(a), NOx conversion decreases from about 60% to 40% when O2 concentration is increased from 1% to 8%. Although the data could not be directly compared due to different catalyst loading and gas velocity, the trend clearly shows that O2 concentration imposed a more serious negative effect in the fluidized bed than in the fixed bed, which may be attributed to the difference of the catalysts.  In terms of gas velocity, NOx conversion is not affected noticeably by superficial gas velocity for most data points, illustrated by experimental data. This is explained by better mass-solid transfer at higher Ug. However, the modeling results couldn?t well capture this trend. NOx conversion of the modeling results clearly decreases with Ug. But overall, the modeled NOx conversion is not very sensitive to gas superficial velocity. The differences between the experiment and modeling could be caused by the variation of reactor temperature in the fluidized bed, which fluctuated between 340? and 360? during the experiment.  121  Comparing to NOx conversion, the model shows a very poor agreement on HC conversion, as shown in Fig. 6.1(b). Most of the measured HC conversion data ranges from 30% to 60%, while corresponding modeling data range from 65% to 100%. The difference between the experimental data and modeling results could be caused partly by experimental errors. The HC conversion was estimated based on measured CO and CO2 concentrations by assuming that all converted HC goes to CO/CO2, ignoring other possible reaction intermediates. However, in our experiment some unidentified byproducts were detected by gas chromatography, which was believed to be HCN or cyanogens [140]. This will likely cause the underestimation of HC conversion. On the other hand, the reaction kinetics fitted from fixed bed data, as shown in Fig. 4.9(b), tends to overpredict fixed bed HC conversion data. This over-prediction is then likely carried over to the fluidized bed, contributing to the overprediction of HC conversion in the fluidized bed. Although the model overpredicts the experimental data significantly, it captures the right trends of the effect of O2, HC:NO ratio on HC conversion. HC conversion is predicted to decrease with HC:NO ratio and increase with O2 concentration. However, the experimental HC conversion decreases with Ug, while modeled conversion increases with Ug. The contradictory trends could also be attributed to experiment error.  But overall speaking, both experimental and modeling curves are not very sensitive to Ug.   122  0.25 0.30 0.35 0.40 0.45 0.50 0.550102030405060708090100HC:NO=2, O2=8%HC:NO=2, O2=8%HC:NO=1, O2=4%HC:NO=2, O2=4%HC:NO=1, O2=1%HC:NO=2, O2=1%Exp T=340-360 oCModel T=350 oCCatalyst loading=3.3 kg HC:NO=1, O2=1% HC:NO=2, O2=1% HC:NO=1, O2=4% HC:NO=2, O2=4% HC:NO=1, O2=8% HC:NO=2, O2=8%NO Conversion (%)Inlet gas velocity Ug, (m/s)0.25 0.30 0.35 0.40 0.45 0.50 0.550102030405060708090100HC:NO=2, O2=8%HC:NO=1, O2=8%HC:NO=2, O2=4%HC:NO=1, O2=4%HC:NO=1, O2=1%HC:NO=2, O2=1%Exp T=340-360 oCModel T=350 oCCatalyst loading=3.3 kg HC:NO=1, O2=1% HC:NO=2, O2=1% HC:NO=1, O2=4% HC:NO=2, O2=4% HC:NO=1, O2=8% HC:NO=2, O2=8%HC Conversion (%)Inlet gas velocity Ug, (m/s) (a)                                                                                   (b) Figure 6.1 Modeled NOx and HC conversion as a function of superficial gas velocity in the fluidized bed (Symbols: experimental data; lines: model fitting)  6.3.2 Fluidized bed simulation To further investigate the effect of superficial gas velocity, the NOx conversions in the fluidize bed were simulated and then compared to a fixed bed reactor, which has the same dimensions and is loaded with the same amount of catalyst. The results are shown in Fig. 6.2. NOx conversion in the fixed bed is predicted to be higher than the conversion in the fluidized bed. This is because there is a bubble phase in the fluidized bed, where there is little catalyst inside for reaction to take place. Comparing to the fluidized bed, the absence of gas bypass in the fixed bed leads to a higher NOx conversion. The superficial gas velocity Ug is seen to have a significant impact on NOx conversion in the fixed bed, decreasing from 68% to 54% when Ug increases from 0.25 m/s to 0.45 m/s, due to the shortened residence time at higher superficial gas velocities. Comparing to fixed beds, NOx conversion in fluidized beds is much less sensitive to Ug, decreasing less than 5% when Ug increases from 0.25 m/s to 0.45 m/s. The reaction taking place in the freeboard region, where there is a better mass transfer between gas and entrained particles, may also have contributed to the higher-than-expected NOx conversions at higher Ug. This is confirmed by simulating NOx conversion in a fluidized bed without considering the reactions taking place in the 123  freeboard region. As shown in Fig. 6.2, in the absence of reactions in the freeboard, the NOx conversion in the fluidized bed is significantly affected by Ug, decreasing from 56% to 45% as Ug increases from 0.25 m/s to 0.45 m/s, which is similar to the fixed bed. Therefore, it is essential to include the freeboard region in modeling deNOx reaction in the fluidized bed. 0.25 0.30 0.35 0.40 0.4540455055606570Fluidized bedwith freeboardNOx conversion (%)Inlet gas velocity Ug, (m/s)Fixed bedFluidized bedwithout freeboardT=350 0CHC:NO=1O2=1% Figure 6.2 NOx conversion at different Ug in fixed and fluidized bed reactors  Since NOx conversion in the fluidized bed is much lower than that in the fixed bed, it is necessary to explore how to increase the NOx conversion in fluidized beds. Simulated NOx concentrations in different phases along the reactor length are plotted in Fig. 6.3, expressed in a dimensionless form: CH/Cg0, CL/Cg0, and Cs/Cs0, where Cg0 is the inlet NOx concentration and Cs0 is the concentration in equilibrium with Cg0. It can be seen that NOx concentration is almost constant in the solids phase along the bed height due to a strong back-mixing. Thus solids phase could be considered as perfectly mixed. The dimensionless NOx concentration in the bubble phase decreases steadily from 1 to about 0.55 along the reactor since the bubble phase is modeled as in plug flow. For gas in the dense phase, the NOx concentration profile falls between the profiles of solids phase and bubble phase. This is because NOx in the dense phase (gas) is exchanged between both solids phase and bubble phase.  124  0.0 0.2 0.4 0.6 0.8 1.00.20.30.40.50.60.70.80.91.0Ug=0.3 m/sT=350 0CHC:NO=1O2=1%Dimensionless concentrationDimentionless bed height CH/Cg0 CL/Cg0 Cs/Cs0 Figure 6.3 Dimensionless axial profiles of NOx concentration in different phases  Since solids phase behaves like a CSTR in the freely bubbling fluidized bed, reducing axial solids dispersion is expected to improve the deNOx efficiency. This is evidenced by the simulation results presented in Fig. 6.4, where the fluidized bed with Ds and DH assumed to be 0 was simulated and compared with the normal fluidized bed. It is seen that NOx conversion increases as the solids dispersion is reduced, especially at lower Ug. At higher Ug, the improvement is marginal since the conversion of the fluidized bed is similar to the conversion in fixed bed as indicated in Fig. 6.2. Another possible way to improve the NOx conversion is to increase the mass transfer between bubble phase and dense phase. As shown in Fig. 6.4 which compares the performance of fluidized bed with different interphase mass transfer coefficient, kHL. NOx conversion increases as kHL increases. The conversion can be further increased if dispersion coefficients Ds and DH are zero and kHL is doubled. Installing baffles in a fluidized bed can decrease solids back-mixing and reduce the bubble size which in turn can increase the interphase mass transfer between the bubble and dense phases, as suggested by equation Eq. (5.6).   125  0.25 0.30 0.35 0.40 0.4550525456586062T=350 0CHC:NO=1O2=1%NOx conversion, %Inlet gas veloctiy Ug, m/s Current fluidized bed Fluidized bed, D=0 Fluidized bed, kHL*2 Figure 6.4 NOx conversion at different gas dispersion and interphase mass transfer coefficient as a function of Ug  In the i-CFB deNOx reactor, refreshed catalysts in the reduction zone will flow to the adsorption zone to adsorb NOx in the flue gas. The NOx concentration in the solids phase thus plays an important role in the capture efficiency of the adsorption zone because a lower NOx concentration on the catalyst surface is desired in order to increase the NOx adsorption to the catalyst. Although decreasing solids mixing and enhancing bubble-dense phase mass transfer could potentially improve the NOx reduction efficiency, it is also important to understand how these improvements could affect the NOx capture efficiency in the adsorption zone. Therefore, NOx concentration in the solids phase is further investigated under these conditions with the simulation results plotted in Fig. 6.5.  As expected, there exists significant axial gradient of NOx concentration on the solids surface at low or zero axial solids back-mixing (i.e. solids dispersion coefficient is 0). The dimensionless NOx concentration in the solids phase is much lower at the outlet, which is favorable for the NOx capture in the adsorption zone of the i-CFB.  126  As the interphase mass transfer increases, the figure shows that solids phase still behaves as a CSTR, with almost uniform solids phase NOx concentration along the reactor which is also higher than that of the fluidized bed at lower kHL. This is because more NOx is transferred from the bubble phase to gas in the dense phase, increasing NOx concentrations in the dense phase which in turn increases NOx concentration in the solids phase.  Overall, both increasing kHL and decreasing Ds could improve deNOx efficiency in the fluidized bed. Decreasing axial dispersion could further decrease solids phase NOx concentration at the outlet, which is favorable for NOx capture in the adsorption zone of i-CFB. Increasing kHL could lead to increased solids phase NOx concentration at the reactor outlet, which, however, is undesired for the NOx adsorption in the adsorption zone.  0.0 0.2 0.4 0.6 0.8 1.00.200.250.300.350.400.450.500.550.60Ug=0.3 m/sT=350 0CHC:NO=1O2=1%Cs/Cs0Dimentionless bed height Current fluidized bed Fluidized bed, D=0 Fluidized bed, kHL*2 Figure 6.5 Dimensionless solids phase NOx concentration along the reactor at different settings  6.3.3 Simulation of reduction zone of an i-CFB As shown in Fig. 6.6, different from the fluidized bed operated with solids in the batch mode, solids move into the reduction zone of the i-CFB reactor from the bottom and overflow from the top into the 127  adsorption zone. The solids fed to the reduction zone are saturated with NOx which is adsorbed from the flue gas in the adsorption zone. NOx on the catalyst surface is then reduced by reducing agent in the reduction zone.  Cg,outCg,inUgCs,feedingCs,outUsCg,outCg,inUgConventional fluidized bed Decoupled i-CFB Cg,outCg,inUgCs,outCs,inUs(Adsorption zone) (Reduction zone) Figure 6.6 Flow diagram of fluidized bed and decoupled i-CFB  Different from conventional fluidized bed, gas fed into the reduction zone of the  i-CFB contains only hydrocarbon and a small amount of O2, while NOx is carried into the bottom by solids from the adsorption zone. Two more parameters should be considered in modeling the reduction zone of the i-CFB, solids circulation rate, Gs, and NOx concentration on the fed particle surfaces, Cs,feeding. The solids circulation rate, Gs, determines how much solids are fed into the reduction zone and how long the solids could stay to have the NOx on the surface reduced by hydrocarbon. In most cases, the catalyst is not completely saturated by NOx in the flue gas and the NOx concentration on the solids surface leaving the adsorption zone, defined as Cs,feeding, depends on the design and operation of the reactor.  128  In a conventional fluidized bed, NOx in the flue gas is adsorbed onto the surface of the catalyst and then reduced by hydrocarbon reductant. But in the reduction zone of the i-CFB, NOx on the surface of catalysts is directly reduced by hydrocarbon reductant. At the same time, NOx could also desorb into the gas phase and slips out of the reactor. Therefore, different from the conventional fluidized bed, the catalytic NOx reduction efficiency in the reduction zone of the i-CFB is given by %1001,,, ????????? ??? ?feedingNOxadNOxslipNOxQQQXr        (6.9) where QNOx,feeding, QNOx,slip and QNOx,d-a are the amounts of NOx fed into the reduction zone by the catalysts, escaped from the reactor with the exhaust gases, and returned to the adsorption zone with the circulating catalysts, respectively, in unit of mole/s. Another parameter used to evaluate the performance of decoupled i-CFB is the slip ratio, defined as %100,, ??feedingNOxslipNOxQQSl        (6.10) where QNOx,feeding is the total amount of NOx fed to the i-CFB and the unit is also mole/s. The slip ratio, Sl, which represents the percentage of NOx escaped from the reduction zone, is an important parameter determining the overall deNOx efficiency in the i-CFB. When simulating the reduction zone in the i-CFB, the governing equations are still Eqs. (6.1) to (6.3). It should be noted that the adsorption term in the governing equations accounts for NOx desorption from the catalyst when NOx is fed through the solids. The initial and boundary conditions now become: ingLfeedingssingH CCCCCCz ,,, ,,,0 ????      (6.11) 0,0,0, ?????????? zCzCzCHz LsH     (6.12) 129  0,0,0,0 ???? LsH CCCt       (6.13) In order to evaluate the performance of the i-CFB, NOx reduction in conventional fluidized bed (A) and reduction zone of i-CFB fed with solids saturated by NOx (B) is directly compared. Bed catalyst loading is set to be 3 kg and the bed temperature is set as 350 ?. Inlet conditions for both gas and solids are shown in Table 6.1. The total amounts of NOx in the feed are the same for the two reactors, although the gas carriers are different. In reactor A, NOx is carried into the reactor by the gas feed (flue gas), while in reactor B, NOx is supplied by the solids feed. The NOx concentration in the fed solids of reactor B is set to be in equilibrium with the flue gas, calculated by the equilibrium of NOx: 2 222 ,0,0,*,,0 ONO xxx n Ogn NOgNOFNOsNOs CCkCC ??        (6.14) The total amount of NOx fed into the two reactors is the same. So, the solids circulation rate in reactor B could be calculated by NOx mass balance: smkgCCUGxxNOspNOggs ?? 2,0,0 /?        (6.15) Table 6.1 Inlet conditions for different fluidized bed used for simulation  Reactor A: Conventional fluidized bed Reactor B: Decoupled i-CFB fed with NOx saturated solids Feeding gas concentration Cg0,NOx=600 ppm Cg0,HC=600 ppm Cg0,O2=1% Cg0,NOx=0 ppm Cg0,HC=600 ppm Cg0,O2=1% Superficial gas velocity Ug=0.25 m/s ~ 0.45 m/s Same as Reactor A Feeding solids concentration N/A Cs0,NOx=Cs,NOx* Solids circulation rate 0 Determined by NOx feeding rate  130   NOx reduction in the two reactors is then simulated at different superficial gas velocities. Outlet concentrations of NOx in both the solids and gas phase are plotted in Fig. 6.7. The concentrations investigated are dimensionless values, divided by Cg0 or Cs0. Reactor A shows the highest gas and solids phase NOx concentrations. In reactor A, NOx is transferred from gas phase to the solids phase. So, the dimensionless concentration in the gas phase is higher than the concentration in the solids phase. The superficial gas velocity, Ug, shows little influence on the outlet NOx concentration.  When NOx is fed through the solids phase in reactor B, outlet NOx concentration of the gas phase is very low, because NOx in the gas phase comes from NOx desorption from the solids surface. A low gas phase concentration in reactor B could guarantee a low NOx slip ratio, improving the overall performance of i-CFB. A high solids phase NOx concentration at the outlet of reduction zone, however, implies a high NOx concentration on the catalyst returning to the adsorption zone, imposing a negative impact on NOx capture in the adsorption zone of i-CFB. Different from reactor A, the outlet NOx concentration in reactor B increases substantially with increasing Ug, especially in the solids phase. Based on the equation for estimating solids circulation rate in Eq. (6.15), Gs is expected to be higher at higher Ug. Therefore, a shorter residence time of the solids at a higher Ug lead to a lower NOx reduction and NOx desorption, which can further lead to a higher solids phase NOx concentration at the reactor outlet. 131  0.25 0.30 0.35 0.40 0.450.00.10.20.30.40.50.6Reactor BT=350 oCBed loading=3 kgInlet NOx=600 ppmHC:NO=1O2=1%Reactor BReactor ADimensionless NOx concentrationInlet gas veloctiy Ug, (m/s) Cg/Cg0 Cs/Cs0Reactor A Figure 6.7 Dimensionless NOx concentration as a function of Ug for different reactors  Fig. 6.8 shows the overall NOx reduction efficiency, Xr, in the two reactors. NOx conversion in reactor A is determined by the gas phase outlet concentration only since there are no solids leaving the reactor. The values are around 50%, slightly lower than the conversion simulated in the previous section due to a smaller bed catalyst loading. NOx conversion in reactor B is determined by both gas and solids phase NOx concentrations. The overall conversion in reactor B is much higher than the conversions in reactor A. This is anticipated since one important step in the deNOx reaction, adsorption, is already completed before the solids enter the reactor. NOx reduction decreases very quickly with increasing Ug, due to the shorter solids residence time at a higher solids circulation rate. 132  0.25 0.30 0.35 0.40 0.4530405060708090100T=350 oCBed loading=3 kgInlet NOx=600 ppmHC:NO=1O2=1%Reactor AXr (%)Inlet gas velocity Ug, (m/s)Reactor B Figure 6.8 Xr as a function of Ug in different reactors  Solids circulation rate, Gs, in i-CFB is a very important operating parameter for determining both the NOx capture efficiency in the adsorption zone and reduction efficiency in the reduction zone. It is anticipated that at a higher Gs, more solids will be re-circulated to the adsorption zone to capture NOx, leading to a lower NOx concentration on catalyst particles leaving the adsorption zone to the reduction zone. It is thus worth to investigate how Gs can affect the overall NOx reduction efficiency and NOx slip ratio in the reduction zone. The performance of an i-CFB is simulated at Ug=0.35 m/s with Gs changing. Other conditions remain the same as the settings for reactor B in Table 6.3. To investigate the effect of Gs on the performance of the reduction zone of the i-CFB, NOx molar flow rate is set to be constant by decreasing the solids phase NOx concentration at higher solids circulation rate, as shown in Eq. (6.16).  ssssCCGG 00?          (6.16) This is based on the assumption that the total NOx feeding rate and capture efficiency in the adsorption zone of the i-CFB reactor remain the same. The simulated Xr and Sl values are plotted in Fig. 133  6.9. It can be seen that the overall NOx reduction efficiency is slightly higher at higher Gs but decreases at lower Gs, indicating that Xr is hardly influenced by Gs if inlet NOx molar flow rate is maintained at a constant value. On the other hand, the change in NOx slip ratio is more significant, increasing by about 10% when Gs is decreased from 2*Gs0 to 0.5*Gs0. This could be explained by the difference in the solids phase NOx concentration Cs at different solids circulation rate Gs. A higher Cs at a lower Gs increases NOx mass transfer between solids and gas phases, which leads to a higher slip ratio. Therefore, a higher solids circulation rate is preferred for the i-CFB if the total feed NOx molar flow rate is kept constant. It should be noted that the solids phase NOx concentration at the outlet of the reduction zone will become higher as the slip ratio is lowered, for a given overall reduction efficiency.  0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2010203040506070T=350 oCUg=0.35 m/sBed loading=3 kgInlet HC=600 ppmO2=1%Percentage, (%)Gs/Gs0Overall reduction efficiency, XrSlip ratio, Sl Figure 6.9 Overall efficiency, Xr, and slip ratio, Sl, as a function of Gs/Gs0  Another important issue for i-CFB operation is how to set the hydrocarbon concentration in the reduction zone. In the conventional fluidized bed or fixed bed reactor, hydrocarbon concentration is determined based on the given NOx:HC ratio, since the superficial gas velocity is determined by the flow 134  rate of flue gas. However, gas streams of reducing agent and flue gases are fed into different zones of the i-CFB, making HC concentration and gas flow rate adjustable independently in the reduction zone.  To investigate the influence of HC concentration on the performance of the reduction zone of i-CFB, NOx reduction at Ug=0.35 m/s is simulated with other conditions kept the same as those for reactor B given in Table 6.3. Solids circulation rate Gs is increased from an initial value Gs0, to twice of Gs0, 2*Gs0, while solids phase NOx concentration is kept at a constant, Cs0. Here both Gs0 and Cs0 are the same as the values used in Fig. 6.10. To keep feed HC:NOx=1, either superficial gas velocity Ug or HC concentration CHC is increased proportionally. The two cases are simulated with the results of Xr and Sl plotted as a function of dimensionless Gs, Gs/Gs0, in Fig. 6.10. Xr for either case illustrates that the overall NOx reduction efficiency decreases when Gs increases, due to shorter residence time of solids in the reactor. NOx slip ratio, Sl, increases at the same time. Both Xr and Sl seem to be more sensitive to the change in gas velocity, Ug, than to the change in hydrocarbon concentration, CHC. It is seen that increasing Ug could lead to a lower overall NOx reduction and more NOx slippage, comparing to increasing the HC concentration. This is likely caused by the shorter contacting time between catalyst and gases at the higher Ug. Therefore, a reducing agent gas stream with higher HC concentrations is preferred in an i-CFB to improve the overall deNOx performance. It should be also noted that this conclusion is valid only when other operating parameters of the i-CFB are kept at constants. In a real i-CFB, when HC concentration is higher, gas velocity in the reduction zone becomes lower, which could further change the solids circulation rate in the i-CFB and affect NOx capture in the adsorption zone. An integral model is thus developed in next chapter to explore the performance of the i-CFB. 135  1.0 1.2 1.4 1.6 1.8 2.01020304050607010203040506070T=350 oCBed loading=3 kgO2=1%Ug0=0.35 m/sHC:NO=1 Slip ratio Sl, (%)Overall reduction efficiency Xr, (%)Gs/Gs0 Changing CHC Changing Ug Figure 6.10 Xr and Sl values at different solids circulation rate  6.4 Summary A model, which includes a bubble phase, gas in the dense phase and solids in the dense phase, was developed for the selective catalytic reduction of NOx in a fluidized bed reactor and was validated by the NOx conversion data measured in a fluidized bed reactor. The fluidized bed deNOx model was then applied to simulate NOx reduction in the reduction zone of the i-CFB reactor. Comparing with conventional fluidized beds, NOx conversion could be improved if NOx is fed through the solids phase, such as what happens in the reduction zone of an i-CFB. Also for the reduction zone of the i-CFB, a higher solids circulation rate is preferred if NOx feed rate is kept at a constant. This is because NOx slip ratio is lower at higher Gs, which could improve the overall NOx reduction efficiency of the i-CFB. If NOx feed rate is increased, HC feed rate should be increased proportionally. In this case, changing HC concentration and keeping gas velocity at a constant is preferred than changing gas velocity and keeping HC concentration at a constant. The overall NOx conversion becomes higher and NOx slip ratio is lower when the HC concentration is increased. 136   Chapter 7  Modeling catalytic NOx reduction in i-CFB reactors6  7.1 Introduction Combining the hydrodynamics model in Chapter 3, adsorption and reaction kinetics models in Chapters 4, and the fluidized bed reactor model in Chapters 5 and 6, an integrated i-CFB reactor model is developed in this chapter. Adsorption and reaction over the Fe/ZSM-5 catalyst are modeled in both the adsorption zone (annulus) and reduction zone (draft tube) of the i-CFB. The interaction of the adsorption and reduction zones is connected by the circulating catalysts between the annulus and draft tube. After being validated by the experimental data, the i-CFB reactor model is further used for optimizing the adsorption-reduction deNOx reactor performance based on simulations.  7.2  i-CFB experiment The deNOx performance in an i-CFB reactor was tested by Yang [11]. The experimental set up was already described in Chapter 3. In the proposed configuration, the flue gas is passed into the adsorption zone (annulus) where NOx is adsorbed by the catalyst particles. The NOx-rich catalyst particles then move downward and into the reduction zone (draft tube) where NOx adsorbed on the catalyst surface is reduced by injected hydrocarbons. The NOx-depleted catalyst particles are then recirculated back to the adsorption zone to maintain a continuous operation. By adjusting the gas flow rates in the annulus and the draft tube,                                                      6 A version of this chapter will be submitted for publication: Xingxing Cheng and Xiaotao T. Bi, Modeling catalytic reduction of NOx in a novel i-CFB reactor. 137  the bypassing of the flue gas from the adsorption zone to the reduction zone can be controlled to have the O2 concentration in the reduction zone maintained at desired levels. In the experiment of Yang [11], 3.3 kg Fe/ZSM-5 particles were loaded into the i-CFB reactor. The reactor was first preheated by passing the preheated building air through both the annulus and the draft tube. NO from the gas cylinder was blended with preheated building air and pure N2 to prepare the simulated model flue gas at desired NO and O2 concentrations. At the same time, propylene was injected into the preheated N2 to prepare the reductant gas mixture. The model flue gas was injected into the adsorption zone (annulus) through a conical distributor plate. The reductant gas mixture was injected into the reduction zone (draft tube) via a gas nozzle. The NOx reduction performance was monitored by measuring the gas composition at the inlet and outlet of the reactor. The model flue gas used in the experiment was a mixture prepared from a gas cylinder containing 20% NO balanced with N2 and a liquid N2 Dewar, with both supplied from Praxair Products Inc. Building air was used as the source of O2. NOx concentration in the model flue gas was controlled at 600 ppm with O2 concentration ranging from 4 to 12%. The reducing agent used in the experiment was propylene. The gas cylinder containing 40% propylene balanced with N2 was supplied by Praxair Products Inc. The reducing agent stream consisted of propylene + N2, with propylene-to-NOx molar flow ratio varied from 1 to 4. It should be noted that NO and HC were in different gas streams in the i-CFB reactor, i.e., the flue gas stream in the adsorption zone and the reductant gas stream in the reduction zone. To investigate the effect of gas velocities and other factors on the performance of the catalyst without changing HC:NO ratio, the ratio of HC:NO was defined as the molar flow rate of propylene to the reduction zone divided by the molar flow rate of NO to the adsorption zone. 00,00,:aaNOddHCNOHC FCFCR ?            (7.1) 138  The overall NOx conversion (XNOx) was calculated by Eq. (7.2) based on the initial concentration of NO in the total gas flow of the annulus and the draft tube, and the concentration of NOx in the gas mixture at the exit of the reactor. ? ? %1000,0,0,0 ???????aNOaoutNOdaaNOaNO CFCFFCFX x      (7.2)  7.3 i-CFB model The i-CFB reactor includes two reaction zones, an adsorption zone in the annulus and a reduction zone in the draft tube. Flue gas is fed into the annulus and reducing agent is fed into the draft tube. Gas bypass is considered  to obtain the actual gas velocities and concentrations at the entrance of each zone. The solids flow in the annulus and the draft tube is connected by the solids circulation between them. In the modeling of i-CFB reactor, both adsorption and reaction are considered in each zone. Same as the fluidized bed deNOx reaction model, three phases are considered for the governing equations of each zone, solids in dense phase, gas in dense phase and gas in bubble phase. Reactions take place on the surface of the catalyst. Gas leaving the annulus and draft tube enters the freeboard region, where it may continue the reaction before exits the i-CFB reactor. The schematics of the i-CFB reactor model is given in Fig. 7.1. 139  Reducing agentFlue gasGas bypassOutletFreeboardAnnulus(adsorption zone)Draft tube(reduction zone)Solids circulationSolids circulationDense phaseBubble phaseBubble phaseDense phaseBubble & dense phase mass transferBubble & dense phase mass transferMass transfer between solids & gasReaction Figure 7.1 Schematics of i-CFB model  7. 3.1 Reaction zones As discussed in Chapter 3, there are four possible flow patterns in the operation of an i-CFB: (a) no solids circulation, (b) annulus solids height lower than draft tube, (c) draft tube with a fully penetrating jet, and draft tube with an internal jet. The experimental conditions investigated in this study only covered flow patterns (b) and (c), as shown in Fig. 7.2, and thus studied in detail. For both flow patterns, the effective 140  bed heights in the annulus and draft tube are obtained from mass and pressure balances of the entire i-CFB, with the detailed calculation protocol being presented in Chapter 3. As confirmed in Chapter 6, the freeboard region plays an important role for the deNOx reaction in fluidized beds. So a freeboard region above the annulus and draft tube is considered in the model. Solids and gas flow above the dense bed reaction zone of the annulus and draft tube are very complex. For a first approximation, it is assumed for flow pattern (b) that gases in the annulus and draft tube are well mixed right above the dense bed region, which is located beneath the draft tube top. It is further assumed that the freeboard region starts right from the draft tube top as indicated by the dash red line in Fig. 7.2. For flow pattern (c), it is assumed that gases from the annulus and draft tube are well mixed above the effective bed height and the freeboard region starts from the top of the effective bed height. The solids fraction in the freeboard is treated in the same way as a regular fluidized bed, as described in Chapter 6. Patten (b) Pattern (c)FreeboardFreeboardAnnulusAnnulusDraft tubeDraft tube Figure 7.2 Schematics of the flow regions of i-CFB studied 141   7.3.2 Governing equations As the fluidized bed reactor model developed in Chapter 6, fluidized bed consists of two phases, bubble phase and dense phase. Mass transfer of NOx in the fluidized bed not only occurs between the bubble phase and dense phase, but also between the gas phase and particles. Adsorption and reaction take places only in the solids phase of the dense phase. In the i-CFB, the same fluidized bed reactor model is applied for both the adsorption zone (annulus) and reduction zone (draft tube). For each reaction zone, governing equations for the reactant in different phases are: ? ? tCRCCkzCUzCD ssissfssssssss ????????????? ????? *221     (7.3) for particles in the dense phase. ? ? ? ? ? ? ? ? ? ? tCCCakCCkzCUzCD HsHHLbHLssfHsHHHsHH ??????????????????? ??? 111 *22            (7.4) for gas in the dense phase. ? ? tCCCakzCUzCD LLHLbHLLLLLLL ????????????? 22     (7.5) for gas in the bubble phase. Initial conditions are: 0,0,0,0 ???? LsH CCCt       (7.6) 142  Total number of equations and boundary conditions for each equation are listed in Table  7.1. The linkage between the adsorption and reduction zones is represented by the boundary conditions. Table 7.1 i-CFB equations and boundary conditions Annulus Gas  Equation number Phase  Boundary condition: z=0 Boundary condition: z=H NO A1 Solids phase 01 ???zCA  11 DA CC ?  A2 High density phase aNOA CC ,2 ?  02 ???zCA  A3 Low density phase aNOA CC ,3 ?  03 ???zCA  HC A4 Solids phase 04 ???zCA  44 DA CC ?  A5 High density phase aHCA CC ,5 ?  05 ???zCA  A6 Low density phase aHCA CC ,6 ?  06 ???zCA  O2 A7 Solids phase 07 ???zCA  77 DA CC ?  A8 High density phase aOA CC ,8 2?  08 ???zCA  A9 Low density phase aOA CC ,9 2?  09 ???zCA  Draft tube Gas  Equation number Phase  Boundary condition: z=0 Boundary condition: z=H NO D1 Solids phase 11 AD CC ?  01 ???zCD  D2 High density phase dNOD CC ,2 ?  02 ???zCD  D3 Low density phase dNOD CC ,3 ?  03 ???zCD  143  Gas  Equation number Phase  Boundary condition: z=0 Boundary condition: z=H HC D4 Solids phase 44 AD CC ?  04 ???zCD  D5 High density phase dHCD CC ,5 ?  05 ???zCD  D6 Low density phase dHCD CC ,6 ?  06 ???zCD  O2 D7 Solids phase 77 AD CC ?  07 ???zCD  D8 High density phase dOD CC ,8 2?  08 ???zCD  D9 Low density phase dOD CC ,9 2?  09 ???zCD  Freeboard Gas  Equation number Phase  Boundary condition: z=H Boundary condition: z= freeboard outlet NO F1 Solids phase ? ?HZDHZAF CCfC ??? 111 , 01 ??? zCF  F2 Gas phase ? ?HZDHZDHZAHZAF CCCCfC ????? 32322 ,,, 02 ??? zCF  HC F3 Solids phase ? ?HZDHZAF CCfC ??? 443 , 03 ??? zCF  F4 Gas phase ? ?HZDHZDHZAHZAF CCCCfC ????? 65654 ,,, 04 ??? zCF  O2  F5 Solids phase ? ?HZDHZAF CCfC ??? 775 , 05 ??? zCF  F6 Gas phase ? ?HZDHZDHZAHZAF CCCCfC ????? 98986 ,,, 06 ??? zCF   The kinetic model equations developed in Chapter 4 are embedded in Eq. (7.3) as the reaction term and used for the modeling of both annulus and draft tube. Coefficients of mass transfer and dispersion are calculated in the same way in Chapter 4. 144   7.3.3 Hydrodynamics  In the i-CFB reactor, flue gas and reducing agent bypass between the annulus and draft tube. The gas bypass ratios, Ra-d and Rd-a, are calculated using the correlations fitted in Chapter 3, Eqs. (3.28) and (3.29).The actual gas velocities in the annulus and draft tube of i-CFB with gas bypassing could then be calculated from mass balance: ? ?addadadaaa AAURURUU /000 ?????? ??       (7.7) ? ?daadadaddd AAURURUU /000 ?????? ??       (7.8) Real inlet gas concentrations in annulus and draft tube could also be calculated from mass balance by Eqs. (7.9) to (7.14), assuming that there are only NO, O2 and N2 in the annulus inlet and only HC and N2 in the draft tube inlet. ? ? ? ?aadaaNOadaaaNOaNO URCFFFCC 00,00,, 1 ??????? ??     (7.9) dadaaNOddaaNOdNO UURCFFCC 00,0,, ????? ??      (7.10) ? ? ? ?aadaaOadaaaOaO URCFFFCC 00,00,, 1222 ??????? ??     (7.11) dadaaOddaaOdO UURCFFCC 00,0,, 222 ????? ??       (7.12) ? ? ? ?ddaddHCdadddHCdHC URCFFFCC 00,00,, 1 ??????? ??     (7.13) 145  adaddHCaaddHCaHC URCFFCC 00,0,, ????? ??      (7.14) Following the same procedure as described in Chapter 3 using Eqs. (3.4) to (3.10), solids circulation rate could be calculated based on mass and pressure balance of solids in the i-CFB. The bed expansions in both annulus and draft tube of i-CFB, as well as voidage, bubble size and bubble velocities, etc., are calculated in the same way as described in Chapter 3 using Eqs. (3.18) to (3.24), which are also used for the modeling of fluidized bed adsorption (in Chapter 5) and reaction (in Chapter 6).   7.4  Modeling results and comparison with experimental data 7.4.1 Model verification Catalytic NOx reduction in i-CFB reactor is simulated with the model described above. The model is coded into MATLAB with the codes shown in Appendix F. Outlet concentrations are calculated from the concentrations in both the bubble and dense phases of each reaction zone. The outlet concentration in the adsorption zone is given by:  LaLaHaHaLaLaLaHaHaHaouta UUCUCUC,,,,,,,,,,, ???????       (7.15) and the outlet concentration in the reduction zone is given by:  LdLdHdHdLdLdLdHdHdHdoutd UUCUCUC,,,,,,,,,,, ???????       (7.16) Then the total outlet concentration of the whole i-CFB is obtained from:  aaaaddoutdaaoutaout AUAUAUCAUCC ??? ,,        (7.17) 146  The overall conversion could now be calculated by:  ? ? %1001,,?????????????ddindaainadaoutoutAUCAUCAAUCX       (7.18) NOx and hydrocarbon conversions in the i-CFB were then modeled and compared with the experimental data at different operating conditions. Reaction in the i-CFB at O2=4% (in the flue gas) was first modeled at different Ua0, Ud0 and HC:NO ratios. The modeled results, together with the experimental data, are plotted as a function of the annulus gas velocity in Figs. 7.3 and 7.4. Fig. 7.3(a) shows the NOx conversion at Ud0=0.6 m/s. The model predicts the experimental data points with an average error of about 10%. NOx conversion decreases at higher Ua0 due to more flue gas being fed into the reactor. But the slopes of these curves are very small. At HC:NO=2, NOx conversion decreases from about 55% at Ua0=0.225 m/s to 43% at Ua0=0.425 m/s. So, the overall NOx removal efficiency is not very sensitive to inlet flue gas velocities. This could be caused by the enhanced freeboard region and bubble-dense phase mass transfer at higher gas velocities, as suggested by Eq. (5.6). In terms of HC:NO ratio, NOx conversion increases with increasing HC:NO ratio, as expected. When Ua0 is around 0.35 m/s, NOx conversion increases from less than 40% to more than 60% when HC:NO ratio increases from 1 to 4. Measured and model predicted HC conversions are plotted in Fig. 7.3(b). The prediction shows an average error of about 9% with experimental data. The error for some data points is more than 15%. This is likely caused by the kinetics used in the model, which gives a poorer agreement on HC conversion for some data points than on NOx conversion, as shown in Chapter 4. This inaccuracy is now carried on to the i-CFB model. Another possible cause is the uncertainties in the measured HC conversion. In the experiment, propylene was not directly measured but calculated from carbon balance based on the measured concentrations of CO and CO2 in the product stream. Other possible unmeasured intermediates from incomplete oxidation of propylene could lead to the underestimation of HC conversion. Overall, HC 147  conversions of both modeled and experimental data fall into the same range, between 100% and 60%, and the model could well capture the effect of Ua0 and HC:NO ratio on NOx conversion and HC conversion. 0.20 0.25 0.30 0.35 0.400102030405060708090100HC:NO=4HC:NO=2 HC:NO=1 HC:NO=2 HC:NO=4NOx conversion, %Ua0 (m/s)O2=4%Ud0=0.6 m/sCatalyst loading=3.3 kgModel T=350 oCExperiment T=340~360 oCHC:NO=10.20 0.25 . 0.35 0.40 0.450102030405060708090100HC:NO=4HC:NO=2 HC:NO=1 HC:NO=2 HC:NO=4HC conversion, %Ua0 (m/s)O2=4%Ud0=0.6 m/sCatalyst loading=3.3 kgModel T=350 oCExperiment T=340~360 oCHC:NO=1 (a)                                                                         (b) Figure 7.3 (a) NOx and (b) HC conversion as a function of Ua0 (O2=4%, Ud0=0.6 m/s. Symbols: experimental data; lines: model fitting)  NOx conversion was also modeled and compared with experimental data at Ud0=0.75 m/s with the results shown in Fig. 7.4(a). Similar to Fig. 7.3(a), NOx conversion is well predicted by the model with an average error of about 5%. NOx conversion decreases with increasing Ua0 and increases with increasing HC:NO ratio. A similar trend is also observed in Fig. 7.4(b)at a higher draft tube velocity of Ud0=0.9 m/s. From Figs. 7.3 and 7.4, it can be further observed that NOx conversion increases with increasing the draft tube velocity, Ud0, at a given overall HC:NO molar ratio. At Ua0=0.22 m/s and HC:NO=4, NOx conversions are 65%, 70%,  and 75%, for Ud0=0.6 m/s, 0.75 m/s and 0.9 m/s, respectively. Therefore, a higher draft tube velocity is preferred for achieving a high NOx conversion in the i-CFB.  At a higher Ud0, HC is more diluted in the reduction zone. deNOx efficiency increases with increasing Ud0, which suggests that NOx conversion is higher at lower HC concentration. This is contradictory to the conclusion obtained from the fluidized bed modeling, which showed that concentrated HC is preferred.  Here, the higher deNOx efficiency at a higher Ud0 can be attributed to the 148  increased gas exchange from the draft tube to the annulus, Rd-a, as indicated by Eq. (3.28), which will be investigated in detail in the sensitivity analysis to be presented in the next section.  0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.500102030405060708090100HC:NO=4HC:NO=2HC:NO=1NOx conversion, % HC:NO=1 HC:NO=2 HC:NO=4Ua0 (m/s)O2=4%Ud0=0.75 m/sCatalyst loading=3.3 kgModel T=350 oCExperiment T=340~360 oC0.20 0.25 0.30 0.35 0.40 0.450102030405060708090100HC:NO=4HC:NO=2HC:NO=1NOx conversion, % HC:NO=1 HC:NO=2 HC:NO=4Ua0 (m/s)2=4%d0=0.9 m/sCatalyst loading=3.3 kgModel T=350 oCExperiment T=340~360 oC (a)                                                                         (b) Figure 7.4 NOx conversion as a function of Ua0 at O2=4%, a), Ud0=0.75 m/s, b), Ud0=0.9 m/s (Symbols: experimental data; lines: model fitting)  NOx conversion was further modeled at different inlet O2 concentrations. Fig. 7.5(a) shows the NOx conversion as a function of Ua0 at Ud0=0.9 m/s, HC:NO=2, and different O2 concentrations of  4%, 8% and 12%. The average error between the modeling results experimental data is 8%. Both model and experiment show a decrease of NOx conversion with increasing Ua0 and flue gas O2 concentration. The negative effect of O2 is caused by more HC being oxidized at higher O2 concentrations. However, this negative effect is very small in i-CFB. Modeled NOx conversions at O2=4%, 8% and 12% are very close to each other, confirming that i-CFB could be applied for the treatment of the flue gas containing high O2 concentrations. For HC conversion, both experimental and predicted results fall into the same range, between 100% and 70%, as shown in Fig. 7.5(b). Although there is a slight variation, the model could well predict the trend of i-CFB performance with an average error of 10%. Same as NOx conversion, HC conversion 149  decreases at higher inlet flue gas velocities. When O2 concentration in the flue gas increases, more HC trends to be oxidized by O2, leading to higher HC conversions. 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55020406080100O2=12%O2=8%O2=4%Ud0=0.9HC:NO=2Catalyst loading=3.3 kgModel T=350 oCExperiment T=340~360 oC O2=4% O2=8% O2=12%NOx conversion (%)Ua0 (m/s)0.20 0.25 0.30 0.35 0.40 0.45 0.50020406080100O2=12%O2=8%O2=4% O2=4% O2=8%HC conversion, %Ua0 (m/s)Ud0=0.9 m/sCatalyst loading=3.3 kgModel T=350 oCExperiment T 40~360 oC (a)                                                                         (b) Figure 7.5 NOx conversion as a function of Ua0 at a), Ud0=0.6 m/s , b), Ud0=0.75 m/s (Symbols: experimental data; lines: model fitting)  The performance of i-CFB is also compared with a regular fluidized bed by modeling the deNOx efficiency in both configurations. The same flue gas velocity, 0.4 m/s, is used, with the same HC:NO molar ratio, HC:NO=2. For i-CFB, the draft tube gas velocity is set at 0.9 m/s, because a high Ud0 can enhance the overall deNOx efficiency. The performance of these two configurations is compared at different inlet O2 concentrations, ranging from 1% to 12%, with the results plotted in Fig. 7.6. It is seen that NOx conversion in an i-CFB is higher than the conversion in a regular fluidized bed, confirming the better deNOx performance of i-CFB. For O2 effect, NOx conversion in the regular fluidized bed is strongly affected by the inlet O2 concentration, decreasing from 57% to about 33% when O2 concentration increases from 1% to 8%. NOx conversion in i-CFB also decreases as the O2 concentration in the flue gas increases, but the slope of the curve is very small, especially at high O2 concentrations, decreasing by less than 5% when the inlet O2 concentration increases from 4% to 12%. Further increasing O2 concentration 150  has little negative effect on the NOx reduction in i-CFB, proving that the i-CFB can effectively eliminate the negative O2 effect at high O2 concentrations. 0 2 4 6 8 10 1220304050607080Model T=350 oCExp T=340~360 oCCatalyst loading=3.3 kgHC:NO=2Fluidized bed: Ug=0.4 m/si-CFB: Ua0=0.4 m/s           Ud0=0.9 m/s Model: fluidized bed Exp: fluidized bed Model: i-CFB Exp: i-CFBNOx conversion (%)O2 concentratin (%) Figure 7.6 Comparison of NOx conversion in an i-CFB and a regular fluidized bed (Symbols: experimental data; lines: model fitting)  7.4.2 Sensitivity analysis  7.4.2.1 Gas bypass The sensitivity of the model prediction to gas bypass ratio is first examined, with predicted NOx conversions shown in Fig. 7.7. It is seen that the model is not sensitive to gas bypass from the annulus to the draft tube, Ra-d, at Ua0<0.3 m/s. However, at higher Ua0, NOx conversion becomes sensitive to Ra-d. This is because little gas is bypassed from the annulus to the draft tube at low flue gas feed rate to the annulus. At high flow rate of flue gas in the annulus, small changes in Ra-d can result in significant changes of the flow condition in the draft tube, making the overall NOx conversion more sensitive to Ra-d. At Ua0=0.4 m/s, NOx conversion decreases by about 10% when Ra-d is doubled, and increases by about 10% when Ra-d is halved. When Ra-d is bigger, more flue gas is bypassed from annulus to the draft tube. 151  O2 concentration in the draft tube is expected to increase correspondingly. A higher O2 concentration can lead to a lower NOx reduction efficiency in the draft tube, and further decreases the overall deNOx efficiency. For the same reason, deNOx efficiency will be improved if Ra-d is decreased. Therefore, gas bypass from the annulus to draft tube should be well controlled during the operation of an i-CFB deNOx reactor.  NOx conversion is much more sensitive to gas bypass from draft tube to annulus, Rd-a. When Rd-a is halved, NOx conversion is dramatically lowered, decreasing by more than 30%. It is expected that the deNOx performance of i-CFB will be quite poor if there is no hydrocarbon bypassing from the draft tube to the annulus. The case with Rd-a doubled is not calculated because too much gas bypass from the draft tube to annulus could cause too low a gas velocity in the annulus to establish solids circulation. Instead, NOx conversion is calculated with 10% increase in Rd-a. The simulated results in Fig. 7.7 show that NOx conversion is significantly improved with only a light increase in Rd-a. If less gas is bypassed from the draft tube to annulus, HC concentration in the draft tube will be higher and a higher NOx reduction is expected from the draft tube, leading to a higher overall deNOx efficiency of the i-CFB system. However, the i-CFB modeling results tell a different story, which may be attributed to the additional deNOx reactions in the annulus between NOx and bypassed HC. As more HC-containing gas bypasses to the annulus, hydrocarbon concentration in the annulus is increased, which enhances the catalytic reduction of NOx in the annulus. Correspondingly, the NOx concentration on the catalyst surface in the annulus will be lowered, which could further improve the NOx capture efficiency in the annulus and increase the overall deNOx efficiency of the i-CFB. 152  0.20 0.25 0.30 0.35 0.40 0.450102030405060708090100Rd-a/2Rd-a*1.1Ra-d/2Ra-d*2NOx conversion (%)Ua0 (m/s)Catalyst loading=3.3 kgUd0=0.7 m/sO2=5%HC:NO=2T=350 oCBase line Figure 7.7 Sensitive of NOx conversion in i-CFB to gas bypasses  7.4.2.2. Adsorption capacity and reaction rate The sensitivity of i-CFB performance to catalyst adsorption capacity and reaction rate is investigated by model simulation. For the base line, NOx conversion is calculated as a function of inlet flue gas velocity Ua0, and other conditions are set to be Ud0=0.7 m/s, O2=5%, HC:NO=2. As a comparison, NOx conversions are also obtained when NOx adsorption capacity, qeNOx, and NOx reaction rate, RNOx, are either halved or doubled. Results in Fig. 7.8 show that NOx conversion is not very sensitive to NOx adsorption capacity at low flue gas velocities. This can be explained by that the NOx adsorption capacity for the current catalyst is big enough to capture sufficient NOx onto the catalyst surface from the annulus and carry them to the draft tube. However, when Ua0 increases, NOx conversion becomes more sensitive to qeNOx, with higher qeNOx leading to a higher deNOx efficiency. Compared to NOx adsorption capacity, the performance of i-CFB is much more sensitive to the deNOx reaction rate. When the reaction rate constant is doubled, the overall deNOx efficiency could reach as high as 100%. When the reaction rate is halved, NOx conversions decrease to less than 20%. Therefore, in i-CFB, it is very important to use 153  catalysts of high catalytic reactivity, although NOx adsorption capacity is also very important at high flue gas flow rate in the annulus. 0.20 0.25 0.30 0.35 0.40 0.450102030405060708090100qeNOx/2RNOx/2NOx conversion (%)Ua0 (m/s)Ud0=0.7 m/sO2=5%HC:NO=2Catalyst loading=3.3 kgT=350 oCBase lineRNOx*2qeNOx*2 Figure 7.8 Sensitivity of NOx conversion to variations in NOx adsorption capacity and reduction rate constant  7.5 Simulation of i-CFB: design and optimization 7.5.1 Solids back-mixing  Solids mixing affects distributions of adsorbed NOx in the reactor system. Fig. 7.9 presents the dimensionless NOx concentration profile along the dimensionless bed height. For inlet condition in Fig. 7.9, i-CFB operates in the type (c) regime as shown in Fig. 7.2. So the effective bed heights of the annulus and draft tube are identical. The gas phase concentrations are calculated from NOx concentrations in both the bubble phase and the dense phase, as indicated by Eqs. (7.15) and (7.16). These concentrations are further divided by NOx concentration in the flue gas, Cg0, and plotted as dimensionless values. The NOx concentrations in the solids phase are divided by Cs0*, the equilibrium concentration of Cg0.  154  It is seen in Fig. 7.9 that the NOx concentration in solids phase is almost uniform along the bed height. This result is consistent with the results obtained in Chapter 6 for the fluidized bed reactor, which indicates that NOx concentration in solids phase is uniform due to strong solids back-mixing. Another interesting finding is that solids phase NOx concentration is almost identical in the annulus and draft tube, which indicates that NOx is sufficiently adsorbed in the annulus and circulated to the draft tube, so that the overall NOx reduction is limited and controlled by the NOx reduction rate in the draft tube at the simulated conditions.  The axial profiles of gas phase NOx concentrations are quite different from the profiles of the solids phase. Gas phase NOx concentration in the annulus decreases along the bed height since NOx is adsorbed onto the catalyst. In the draft tube, gas phase NOx concentration increases along the bed height because of NOx desorption. At H/H0>0.3, dimensionless NOx concentration in the solids phase is higher than the gas phase dimensionless NOx concentration in the annulus but still lower than the gas phase NOx concentration in the draft tube. Since solids phase NOx concentrations in the annulus and draft tube are almost the same, one may wonder how NOx could be adsorbed from the gas phase of a lower NOx concentration in the annulus and then desorbed to the gas with a high NOx concentration in the draft tube. This could be interpreted by the different equilibrium concentrations in the two zones. As shown in Table 4.4, NOx equilibrium concentration is a strong function of O2 concentration. In the annulus with fed flue gases, O2 concentration is higher which gives rise to a higher NOx adsorption capacity. Gas phase NOx concentration in equilibrium with Cs-A will be lower there. The dimensionless concentrations in equilibrium with Cs-A/Cs0* and Cs-D/Cs0* are calculated to be Cg-A*/Cg0=0.2 and Cg-D*/Cg0=2.05. Both equilibrium concentrations are plotted in Fig. 7.9. Cg-D*/Cg0 is not plotted proportionally to the axis since 2.05 exceeds the range. Now the driving forces of NOx mass transfer in both adsorption and reduction zones are clear. It could also be observed from the figure that Cg-A/Cg0 is very close to Cg-A*/Cg0 at the top of the reactor. It means that the solids are almost fully saturated with NOx at the outlet of the adsorption 155  zone. The NOx capture efficiency in the adsorption zone is already very high, to further improve the performance of adsorption zone the equilibrium adsorption capacity needs to be increased.  0.0 0.2 0.4 0.6 0.8 1.00.20.30.40.50.60.7HC:NO=2O2=4%Ua0=0.4 m/sUd0=0.9 m/sCatalyst loading=3.3 kgT=350 oCCg-D*/Cg0=2.05Cg-A*/Cg0Cg-A/Cg0Cs-A/Cs0* & Cs-D/Cs0*Dimensionless NOx concentrationDimentionless bed height H/H0Cg-D/Cg0 Figure 7.9 Profile of dimensionless NOx concentration along bed height  In the Chapter 6, it was observed that decreasing solids back-mixing could significantly enhance NOx reduction in the fluidized bed. To investigate the effect of solids back-mixing on the performance of i-CFB, both gas and solids dispersions are neglected, with both the annulus and draft tube being assumed to be operated in plug flows. With all other conditions remaining the same as the i-CFB shown in Fig. 7.9, the simulated results are found to be almost the same with those results given in Fig. 7.9. Although both zones are assumed to be in plug flow, solids phase NOx concentrations remain constant along the bed height. This could also be explained by the fast solids circulation in the i-CFB which makes the solids phase NOx concentration uniform along the reactor. Therefore, different from regular fluidized beds, decreasing solids back-mixing could not improve the performance of the i-CFB under the conditions simulated. 156   7.5.2 Solids circulation rate The i-CFB is simulated at different solids circulation rates. Here, Gs is calculated base on the cross-sectional area in the annulus. Fig. 7.10 presents the dimensionless NOx concentration of solids phase in both annulus and draft tube. It is observed that the concentration profile is strongly affected by solids circulation rate. Although strong back-mixing exists in fluidized beds, slopes of the concentration curves are quite big at lower solids circulation rates. The NOx concentration is lower at the top of annulus where catalysts are returned to the annulus from the draft tube. Similarly, NOx concentration is higher at the bottom of draft tube due to the feeding of catalyst adsorbed with NOx from the annulus. The NOx concentration decreases along the reactor height as NOx is either reduced or desorbed from the catalyst surface. When the solids circulation rate increases, catalyst residence in the draft tube becomes shorter. NOx could not be efficiently removed from the catalyst, leading to little change of NOx concentration on the catalyst surface along the reactor. Solids phase NOx concentrations in the annulus and draft tube also get closer at a higher Gs due to fast catalyst exchange between the two zones. At Gs>10 kg/m2.s, there is little difference in solids phase NOx concentration between the annulus and draft tube. Based on the discussion in the solids mixing section, it could be concluded that the axial profile of solids phase NOx concentrations depends on solids circulation rate in i-CFBs instead of solids back-mixing. It is also confirmed that it is not useful to decrease solids back-mixing in the i-CFB. 157  0.0 0.2 0.4 0.6 0.8 1.0 1.20.150.200.250.300.35HC:NO=2O2=4%Ua0=0.35 m/sUd0=0.9 m/sCatalyst loading=3.3 kgT=350 oCGs=30Gs=15Gs=10Gs=0.2Gs=4Gs=0.5Cs/Cs*H/H0 Cs,a/Cs* Cs,d/Cs* Figure 7.10 Axial profiles of dimensionless solids phase NOx concentrations at different Gs  The overall NOx conversion is also calculated at different solids circulation rates with the results presented in Fig. 7.10. Solids are exchanged more rapidly between the annulus and the draft tube at higher Gs, leading to effective NOx transfer between adsorption and reduction zones. NOx conversion in i-CFB is thus anticipated to increase with increasing solids circulation rate. The modeling result show that the conversion increases by about 5% when Gs is increased from less than 0.5 kg/m2.s to 5 kg/m2.s. Further increasing Gs has little effect on the improvement of conversion. Although the enhancing effect of Gs is confirmed, the increase in NOx conversion is lower than expected.  The net NOx conversion in annulus and draft tube is plotted in Fig. 7.11 to further explore the possible reason. It is seen that among the destroyed NOx, most is reduced in the annulus. Although draft tube is designed as the reduction zone, the converted NOx in draft tube is only about half of the converted NOx in the annulus. It is quite obvious that the potential of NOx reduction in the draft tube is not fully utilized in the current i-CFB design due to the low catalyst reactivity and short contact time in the draft tube. Together with Fig. 7.10, the NOx concentration profile shows that solids phase NOx concentration is 158  higher at higher Gs. This means that sufficient amount of NOx is passed by the catalyst from annulus to the draft tube. Instead of being efficiently consumed in the draft tube, majority of NOx is simply returned to the adsorption zone for the next adsorption-reduction cycle. Therefore, it is suggested that longer solids residence time in the draft tube is required to further reduce NOx in the reduction zone to fully utilize the potential of i-CFB. 0 5 10 15 2001020304050NOx conversion in draft tubeNOx conversion in annulusCatalyst loading=3.3 kgT=350 oCHC:NO=2O2=4%Ua0=0.35 m/sUd0=0.9  m/sNOx conversion (%)Gs (kg/m2.s)Total NOx conversion Figure 7.11 NOx conversion as a function of solids circulation rate Gs  7.5.3 i-CFB configurations In order to investigate the effect of solids residence time, NOx conversion is simulated for i-CFBs with different cross sectional areas of the adsorption and reduction zones with the schematics shown in Fig. 7.12. Areas of adsorption and reduction zones are denoted as AA and AR, respectively. One should note that the configuration of the i-CFB may not necessarily be the same one as tested experimentally which has a draft tube and an annulus zone. Other configurations could be applied, as long as the solids could be circulated between the two zones. The total cross sectional area of the i-CFB is denoted as Atotal, which is the sum of AA and AR. In the simulation, Atotal is kept constant, the same as the total cross sectional area 159  of the i-CFB tested in the experiment. The fraction of the reduction zone cross area, AR/Atotal, is changed from 0.2 to 0.8. To simplify the simulation and focus on the effect of AA to AR ratio, some other parameters are treated as simple as possible. Bed heights of the adsorption and reduction zones are assumed to be the same, determined by mass balance only. For a real i-CFB, bed height is determined by both mass and pressure balances, as well as the height of partition plate as shown in Chapter 3. Gas bypasses between the adsorption and reduction zones are not considered. The catalyst loading is set to be 3 kg. The net solids circulation flux in both annulus and draft tube is set to be constant, 0.15 kg/s, which is equivalent to about Gs=20 kg/m2.s in the experimental i-CFB. For all the cases investigated, solids are assumed to be flowing downward in the adsorption zone and upward in the reduction zone. In a real i-CFB, the direction of the solids flow depends on the pressure balance between the two zones. However, the assumption is reasonable and does not affect the simulation result. A simulation is also performed by changing the direction of solids flow manually. The results (not given here) showed that deNOx efficiencies are the same for different solids flow directions. This is because in both zones of the i-CFB, solids back-mixing is very strong, and solids in both zones could be considered to behave like CSTR reactors. The same conclusion was also obtained in the fluidized bed adsorption (Chapter 5) and reaction (Chapter 6) modeling.  O2 concentration in the adsorption zone is set at 8%, and O2 is also assumed to exist in the reduction zone with a concentration of 1%. In a real i-CFB, O2 in the reduction zone could come from the gas bypass from the adsorption zone. It could also come from the gas containing the reducing agent. However, a small portion of O2 in the reduction zone is essential for NOx reduction, since both Reactions (4.R3) and (4.R4) need O2. HCt:NOx molar ratio is set at 2, where HCt is the total molar flow rate of HC, which is fed into the reduction zone. Due to gas bypass, HC may also be present in the adsorption zone of the i-CFB. In Fig. 7.12, the fraction of HC passing through the reduction zone is denoted as x, and the HC fractional flow into the adsorption zone is (1-x). 160  To evaluate the performance of i-CFB, GHSV of the reactor is set to be 5000 h-1, same as the GHSV used in the fixed bed experiments. Here, GHSV of i-CFB is calculated by the flow rate of flue gas (gas in the adsorption zone) and the volume of catalyst in the whole reactor: catalystgasflueVFGHSV ?? 3600         (7.19) The volumetric flow rate of reducing agent is assumed to be half of the volumetric flow rate of flue gas. So when the cross sectional areas of both reaction and reduction zones change, the superficial gas velocity also changes.  Adsorption zoneReduction zoneAAARFlue gas Reducing agentHCR=xHCtHCA=(1-x)HCt Figure 7.12 Schematics of the simulated i-CFB  The simulated NOx conversions are plotted in Fig. 7.13 as a function of AR/Atotal. As expected, higher a solids residence time in the reduction zone leads to improved performance of i-CFB. When the cross-sectional area of reduction zone AR is increased, solids velocity in this zone will be decreased, increasing the solids residence time. The curve labeled as ?HCR=100%HCt, HCA=0? corresponds to the condition with all the hydrocarbon being fed into the reduction zone. The curve clearly shows that deNOx 161  efficiency in i-CFB could be significantly improved at higher AR/Atotal, with NOx conversion being increased from about 5% at AR/Atotal=0.2 to about 73% at AR/Atotal=0.7. Further increasing AR will decrease the overall deNOx efficiency. For the catalyst tested in this study, the optimum AR/Atotal ratio is around 0.7. It was shown in Chapter 6 that deNOx efficiency in the fluidized bed is lower than that in the fixed bed. This is due to gas bypassing in the bubble phase, which leads to poor contact between gas and catalyst particles. Here, the performance of deNOx reaction is compared between the i-CFB and the fixed bed reactor. The NOx conversion of fixed bed reactor with the same GHSV is 41%, as plotted in the figure. The performance of i-CFB is seen to be poorer than the fixed bed reactor if the cross sectional area of reduction ozone is not large enough. The advantage of i-CFB could be fully explored only when the solids residence time in the reduction zone is sufficiently long. If the reactor is well designed, the i-CFB reactor could perform much better than the fixed bed reactor. The sensitivity analysis shows that the overall deNOx efficiency is quite sensitive to gas bypass from draft tube to annulus Rd-a. A possible explanation is that a higher HC concentration in the annulus lowers the NOx concentration on the catalyst surface in the adsorption zone, which further improves the overall performance of i-CFB. Here, it is also investigated how HC distribution could affect the performance at different AR/Atotal ratios. NOx conversions at different HC distributions are also plotted in Fig. 7.13. At a lower AR/Atotal, NOx conversion increases when more HC goes through the adsorption zone. At AR/Atotal =0.3, NOx conversion increases by 5% when HCA/HCt increases from 0 to 10%. However, further increasing HCA has little effect on the improvement of deNOx efficiency. The NOx conversion is almost the same at HCA=30%HCt and HCA=50%HCt. Another interesting finding is that the positive effect of HCA is diminishing at high AR/Atotal, and the trend is even reversed at AR/Atotal > 0.65. This is because HC in the reduction zone could effectively be used for NOx reduction when AR/Atotal is higher and solids residence time is longer. It can also be concluded that the performance of i-CFB is less 162  sensitive to HC bypass at higher AR/Atotal ratios. Therefore, a larger cross sectional area of reduction zone is preferred for the i-CFB reactor. 0.2 0.3 0.4 0.5 0.6 0.7 0.801020304050607080NOx conversion (%)AR/Atotal HCR=100% HCt, HCA=0 HCR= 90% HCt,  HCA=10% HCt HCR= 70% HCt,  HCA=30% HCt HCR= 50% HCt, HCA=50% HCtCatalyst loading=3 kgT=350 oCGHSV=5000 h-1HC:NO=2Adsorption zone O2=8%Reduction zone O2=1%Fixed bed NOx conversionCurrent i-CFBconfiguration Figure 7.13 NOx conversion as a function of AR/Atotal  In order to explain how AR/Atotal affects NOx efficiency, NOx concentration changes in both adsorption and reduction zones are investigated. NOx concentration change is normalized by feeding NOx molar flow rate, as defined by:  %100,,, ??????????AANOinAANOoutAANOinANO FCFCFCCXxxxx     (7.20) %100,,, ??????????AANOinRRNOoutRRNOinRNO FCFCFCCXxxxx     (7.21) Positive CX values show lower NOx concentrations at the outlet, meaning that NOx reduction or adsorption dominates. Negative CX values indicate that NOx concentration increases along the reactor, meaning that NOx desorption dominates. The calculated CXs are plotted in Fig. 7.14. When AR/Atotal 163  increases, CX value in the reduction zone increases due to a longer residence time. Values of CXNOx-R increase from about -50% to about 0 when AR/Atotal increases from 0.2 to 0.7, which suggests more NOx is converted by HC instead of being desorbed from the catalyst and slipping out of the reactor. CXNOx-d values close to 0 indicate that almost all NOx on the catalyst surface is destroyed by HC and leaves little NOx desorbed into the gas phase. At the same time, NOx capture efficiency in the adsorption zone is increased, because NOx concentration on catalysts returning from the reduction ozone is lowered. CXNOx-a increases from 35% to 70% when AR/Atotal is increased from 0.2 to 0.65. Further increasing AR can decrease NOx capture efficiency due to shorter solids residence time in the adsorption zone. When the improvement of NOx reduction rate in the reduction zone cannot match the NOx capture rate in the adsorption zone, overall deNOx efficiency in the i-CFB will get worse. This is why the optimal performance of i-CFB is around AR/Atotal =0.7 in the simulated configuration, when the adsorption and reduction performances of the catalysts are matched. 0.2 0.3 0.4 0.5 0.6 0.7 0.8-40-20020406080Catalyst loading=3.3 kgT=350 oCGHSV=5000 h-1HCt:NO=2HCR=90% HCt, HCA=10% HCtAdsorption zone O2=8%Reduction zone O2=1%CXNOx-RNOx conversion (%)AR/AtotalCXNOx-A Figure 7.14 NOx concentration change as a function of AR/Atotal at different zones  164  As discussed previously, deNOx performance of i-CFB is not very sensitive to the catalyst adsorption capacity, qeNOx due to the insufficient solids residence time in the reduction zone, which makes NOx reduction reaction a rate-limiting step. With the cross sectional area of reduction zone increased, NOx reduction is no longer a rate-limiting step. Thus, there is a need to check the sensitivity to the adsorption capacity again. NOx conversions at HCR=90%HCt are calculated with NOx adsorption capacities either doubled or halved. The results are plotted in Fig. 7.15 together with the baseline. At a lower AR, NOx conversion is seen to be insensitive to qeNOx. qeNOx even has a negative effect on the overall deNOx efficiency. This is explained in Fig. 7.16 based on the concentration change in the adsorption and reduction zones. At a higher NOx adsorption capacity, NOx capture efficiency in the adsorption zone is improved, as indicated by higher CXNOx-a values. The NOx concentration on the catalyst surface is also expected to be higher in the adsorption zone. The NOx concentration on the catalyst surface in the reduction zone will increase at the same time, which could lead to higher desorption of NOx in the reduction zone. This phenomenon is indicated by the smaller CXNOx-R values in the figure. When NOx desorption in the reduction zone exceeds adsorption in the adsorption zone, overall deNOx efficiency decreases. At a lower AR, little NOx is converted catalytically in the reduction zone due to a short solids residence time, leading to serious NOx desorption. However, with a larger Ad, more NOx on the catalyst surface is reduced by HC, leaving less NOx desorbed from the catalyst. More NOx reaction in the reduction zone could also decrease the NOx concentration on the catalyst surface and further enhance NOx capture efficiency in the adsorption zone. Therefore, less NOx desorption in the reduction zone and more NOx adsorption in the adsorption zone make the overall deNOx efficiency significantly improved at a higher AR. In Fig. 7.15, the i-CFB performance is much more sensitive to NOx adsorption capacity at higher AR. NOx conversion increases by about 25% when qeNOx is doubled at AR/Atotal =0.8. At the same time, it is observed that the optimum value of AR/Atotal is higher when NOx adsorption capacity is higher. This means that a bigger reduction zone is preferred when the catalyst has a high NOx adsorption capacity. In terms of fixed bed reactor, NOx adsorption capacity has very little effect on the NOx conversion, as plotted in Fig. 7.15. The positive effect of qeNOx on NOx conversion is a unique feature of 165  the i-CFB reactor. It can also be concluded that a properly designed i-CFB with catalysts of sufficiently high adsorption capacity and reactivity can achieve a deNOx efficiency of more than twice in a fixed bed reactor. 0.2 0.3 0.4 0.5 0.6 0.7 0.8020406080100Current i-CFBconfigurationFixed bed NOx conversionsCatalyst loading=3.3 kgT=350 oCGHSV=5000 h-1HCt:NO=2HCR=90% HCt, HCA=10% HCtAdsorption zone O2=8%Reduction zone O2=1%NOx conversion (%)AR/Atotal Baseline qeNOx/2 qeNOx*2 Figure 7.15 Sensitivity of NOx conversion to NOx adsorption capacity for i-CFBs with different configurations  0.2 0.3 0.4 0.5 0.6 0.7 0.8-60-40-20020406080qeNOx/2-CXNOx-RqeNOx*2-CXNOx-RqeNOx/2-CXNOx-AqeNOx*2-CXNOx-ABaseline-CXNOx-RCatalyst loading=3.3 kgT=350 oCAdsorption zone O2=8%Reduction zone O2=1%HCR=90% HCt, HCA=10% HCtHCt:NO=2GHSV=5000 h-1NOx conversion (%)AR/AtotalBaseline-CXNOx-A Figure 7.16 Sensitivity of NOx concentration change to catalyst NOx adsorption capacity 166   7.6 Summary A mathematical model has been developed in this chapter to simulate the performance of the i-CFB deNOx reactor with the intention to assist the design and optimization of the reactor. The model consists of several sub-models, including the i-CFB hydrodynamics, NOx adsorption and reaction kinetics which were fitted and validated in previous chapters. The modeling results show a good agreement with the experimental data.  The simulation shows that deNOx efficiency of i-CFB reactor decreases slightly with increasing the inlet flue gas velocity Ua0, but the negative effect of Ua0 is expected to be much smaller than fixed bed reactor due to a better mass transfer at higher gas velocities and the contribution of the reactions in the freeboard region in the fluidized bed. For the reduction zone, deNOx efficiency increases with increasing the inlet gas velocity Ud0. This is attributed to the higher Rd-a at a higher Ud0, which could significantly increase NOx conversion as confirmed in the sensitivity analysis. In the sensitivity analysis, it is observed that the performance of i-CFB is very sensitive to gas bypass from draft tube to the annulus, Rd-a, but is less sensitive to Ra-d. For the catalyst properties, reaction kinetics rate of the catalyst is very critical in determining the i-CFB performance, but the catalyst adsorption capacity has only marginal impact on the performance of the simulated i-CFB reactor. Solids circulation rate Gs has little effect on the overall deNOx efficiency. The analysis of NOx adsorption and reaction at both the annulus and the draft tube zones revealed that solids residence time in the reduction zone is too short for the NOx reduction reaction for the current design of i-CFB reactor. Therefore, i-CFB reactors with different cross sectional areas for adsorption and reduction zones are investigated. The simulated results showed that a large reduction zone could significantly enhance the overall deNOx efficiency. The optimum reduction zone area fraction AR/Atotal should be around 0.65~0.7. 167  Further increases in the AR/Atotal ratio will decrease NOx conversion. It is also observed that the performance of the i-CFB at higher AR/Atotal ratios is less sensitive to gas bypass from the reduction zone to the adsorption zone. The deNOx efficiency of i-CFB reactor becomes more sensitive to NOx adsorption capacity at higher AR/Atotal. 168   Chapter 8  Conclusions and recommendations for future work   8.1 Conclusions The possible application of the integrated adsorption-reduction process was explored experimentally by Yang [11] for the selective catalytic reduction of NOx with hydrocarbons (HC-SCR) over selected catalysts in an internal circulating fluidized bed (i-CFB). The i-CFB exhibited an ability to overcome the negative impact of excessive O2 in the flue gas using Fe/ZSM-5(Albemarle) as the deNOx catalyst.  The objective of this research is to model the deNOx reaction in the i-CFB reactor in order to further optimizing the reactor design and improving its performance. The i-CFB model includes three sub-models: hydrodynamics, adsorption and reaction. Each sub-model was developed separately and validated by experimental data. An i-CFB model was then developed by integrating these sub-models and compared with i-CFB experimental data. The following conclusions can be drawn.  8.1.1 Hydrodynamics model Hydrodynamics of the i-CFB reactor was first studied experimentally. Gas bypass was investigated by CO2 tracer method by Yang [11], and solids circulation rate was measured in this research using an optical fibre probe at bed solids loadings of 3.3 kg and 2.275 kg. It was found that solids circulation rate was a strong function of bed loading and feeding gas velocities. At low bed loading and low draft tube gas velocity, solids circulation rate decreased as the annulus gas velocity increased. However, this trend could be reversed at high bed loadings and high draft tube velocities.  A hydrodynamic model was then developed based on mass and pressure balances. Solids discharging coefficient CD was extracted from fitting the experimental data and an average value of 0.167 169  was taken for model simulation. The model could well capture the characteristics of the solids flow and gas flow distribution, and could serve as a useful tool for the design and simulation of the i-CFB deNOx reactor system. Effective bed height and bed voidage in the draft tube and annulus could also be calculated by this model.  8.1.2 Adsorption model The NOx adsorption isotherm over Fe/ZSM-5 was first developed from regression of fixed bed adsorption experimental data and then applied to model fluidized bed NOx adsorption. To develop the adsorption kinetics, the kinetics of NO oxidation and adsorption was first proposed, following the development of Freundlich type isotherm. The isotherm parameters were fitted by adsorption capacities data obtained from fixed bed experiments. Then an axial dispersion model, which consists of a gas phase and a solids phase, was developed to simulate the breakthrough curve of NOx adsorption. The model parameters include mass transfer coefficient and axial dispersion coefficient. The well-established mass transfer equations from literature were modified to capture the Freundlich type adsorption performance, which showed a better agreement with the experimental breakthrough curves. A three-phase adsorption model, which includes bubble phase, solids in the dense phase and gas in the dense phase, was then proposed for the NOx adsorption in a fluidized bed reactor. The model parameters were obtained by fitting the experimental breakthrough curves. With the fitted mass transfer and gas dispersion coefficients, the model agreed well with the experimental data. Simulations of the adsorption zone in a decoupled i-CFB showed that the NOx concentration on the surface of feed catalysts could affect the NOx abatement efficiency. At the same time, the large catalyst holdup in the adsorption zone is essential for achieving a high deNOx efficiency.   170  8.1.3 Reaction model Similar to the adsorption model, kinetics of deNOx reactions was first developed with the kinetic parameters fitted from fixed bed experimental data. The kinetics was then used to model the deNOx performance in a fluidized bed. The kinetic model was divided into two sub-models, i), NO oxidation and adsorption, ii), NOx reduction. The adsorption model was the same with the model developed in the adsorption section. The reduction model consists of two simplified reactions, hydrocarbon combustion and NOx reduction. Same as the fixed bed adsorption model, two phases are included in the governing equations: solids phase and gas phase. The reaction term was embedded into the solids phase mass balance equation. The kinetics was further applied for the fluidized bed model, which included the bubble phase, gas in the dense phase and solids in the dense phase. The model could well predict NOx conversion in the fluidized bed. The fluidized bed deNOx model was further applied to simulate NOx reduction in the reduction zone of the i-CFB reactor. Comparing with conventional fluidized bed, NOx conversion could be improved if NOx is fed through the solids phase, as in the reduction zone of the i-CFB. Also for the reduction zone of the i-CFB, high solids circulation rates are preferred if NOx feeding rate is set at a constant. This is because the NOx slip ratio is lower at higher Gs, which corresponds to a better overall performance of i-CFB. If NOx feeding rate is increased, HC feeding rate should be increased proportionally. In this case, changing HC concentration and keeping gas velocity at a constant is preferred than changing gas velocity and keeping HC concentration at a constant. The overall NOx conversion becomes higher with a lower NOx slip ratio when HC concentration is increased.   171  8.1.4 i-CFB model The i-CFB model was developed by integrating the hydrodynamics, NOx adsorption and reaction kinetics. The modeling results showed good agreement with the experimental data. It is observed that deNOx efficiency of i-CFB decreases slightly with increasing inlet flue gas velocity Ua0, although the negative effect of Ua0 is much smaller than fixed bed reactors due to better mass transfer at higher gas velocities and the additional reaction in the freeboard region of the fluidized bed. For the reduction zone, deNOx efficiency increases with increasing the inlet gas velocity of reducing agent Ud0. This is explained by a higher Rd-a at higher Ud0, which could significantly increase NOx conversion, as confirmed in a sensitivity analysis. In the sensitivity analysis, it is observed that the performance of i-CFB is very sensitive to gas bypass from draft tube to annulus Rd-a, while less sensitive to Ra-d and solids circulation rate Gs. For the catalyst properties, the reduction efficiency of NOx adsorbed on the catalyst surface is very critical for the improvement of i-CFB performance. The simulation results showed that catalyst adsorption performance is not important for the deNOx performance of the current i-CFB reactor configuration. In a further simulation of i-CFB performance at different solids circulation rates, it is found that Gs has little effect on the overall deNOx efficiency. NOx reaction at both zones is then analyzed and it is found that the solids residence time in the reduction zone is too short in the current reactor design for the NOx reaction. Therefore, i-CFBs with different cross sectional areas of adsorption and reduction zones are investigated. The simulated results show that a bigger reduction zone area ratio could significantly enhance the overall deNOx efficiency. The optimum reduction zone area ratio AR/Atotal is determined by matching the adsorption rate in the adsorption zone with the reduction rate in the reaction zone. It is also observed that the performance of i-CFB at a higher AR/Atotal is less sensitive to gas bypass from reduction zone to adsorption zone. 172  Overall, the i-CFB model developed in this study can be used as a tool for reactor design and optimization. Simulations of deNOx reaction in the i-CFB can provide suggestions on how to further improve its performance. For the deNOx reaction in i-CFBs, it is possible to achieve a deNOx efficiency higher than fixed bed reactors with the same GHSV, while maintaining a good resistance to negative O2 effect.  8.2 Recommendations for future work The i-CFB model developed in this study could provide some guidance for the reactor design and operation. Further research in the following aspects is still needed for the scaleup and commercialization of i-CFB deNOx reactors: 1. The NOx reduction efficiency of the catalyst should be tested at different temperatures. The temperature-dependent kinetics can be developed based on the experimental data, and then be used to evaluate the i-CFB performance at different temperatures.  2. As confirmed by the i-CFB model, deNOx efficiency could be significantly enhanced at high NOx reduction rate of the catalyst. Therefore, performance of catalyst needs to be improved, especially on the NOx reduction rate constant. This can be achieved by introducing other metal promoters to the current Fe/ZSM-5 catalyst. Other catalyst preparation method or catalyst support could also be explored. 3. Catalyst with a better resistance to SO2 should be developed. Catalyst deactivation due to SO2 is one of the biggest obstacles for the wide application of HC-SCR process. It was observed in Yang?s fixed bed experiment [11] that SO2 in the flue gas feed could irreversibly decrease both the reduction efficiency and adsorption capacity of the Fe/ZSM-5 catalyst. Although effect of SO2 was not tested in i-CFB reactor, it is anticipated that the performance of i-CFB would be negatively affected by SO2 in the flue gas. Catalyst with a good resistance to SO2 is strongly desired. 173  4. Hydrodynamics of i-CFBs with different configurations should be tested in the future. It was found from the i-CFB deNOx simulation that a bigger cross sectional area of reduction zone could greatly increase the overall deNOx efficiency. However, it is known that hydrodynamics of the i-CFB, either gas bypass or solids circulation rates, is quite sensitive to the reactor configuration. Hydrodynamics of other i-CFB reactor configurations should be first investigated for potential applications for deNOx.  5. One major problem in fluidized beds is the attrition of solids, which could impact both the reaction kinetic and mechanical properties of the catalyst. Catalyst elutriation could also be a serious problem if solids are too fine. Attrition and elutriation of the selected catalyst should be tested before its application for i-CFB deNOx reactors. 6. As discussed in Chapter 2, one benefit of fluidized beds is the convenience of catalyst regeneration. How to regenerate HC-SCR catalyst will be an important topic for investigation. 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Reaction intermediates in the selective catalytic reduction of NOx over Fe/ZSM-5. J. Catal., 186(1). 91-99. [141]. C. Sheindorf, M. Rebhun, M. Sheintuch. (1981). A Freundlich-type multicomponent isotherm. J. Colloid Interface Sci., 79(1). 136-142.  186   Appendix A More discussions on solids circulation rate   Why Gs decreases when Ua0 increases at bed loading=2.275 kg which is contradict with the observation in the literature? Since the characteristics of gas bypass is unknown, detailed and accurate analysis could not be obtained. So here it is assumed that there is no gas bypass and the pressure drop could be analyzed quantitatively.  Following the calculated procedure in Table 3.1, most of the flow patterns of the tested points are type (b) in Fig. 3.4. The effective bed height in the draft tube equals the height of draft tube and the annulus effective bed height changes with the voidage. Since the inlet gas velocity of the draft tube does not change, the pressure drop ?Pd is constant. For most of the data points, the annulus is operated as a fluidized bed. It can be assumed that the pressure drop in the annulus is determined by the weight of solids in the annulus. ? ? aaaapa AgMLgP /1 ???? ??         (A.1) If the draft tube gas velocity is constant, voidage in the draft tube is constant, so does the amount of solids in the draft tube. Solids weight in the annulus does not change at various Ua0, which gives rise to a constant pressure drop across the annulus. Thus the pressure drop through the orifice, ?Por, remains constant. According to Eq. (3.10), solids circulation rate is influenced by ?Por and ?a. At higher Ua0, ?a becomes bigger, leading to lower Gs. 187  An attempt was made to model the solids circulation rate at bed solids loading of 2.275 kg, with the results plotted in Fig. A.1 as lines. Gas bypass was not considered since there are no data available. Therefore, the modeling results are not reliable for reactor design purpose. But they could be used to observe the trend of solids circulation rate at different conditions. It could be seen that all the modeling results fall into reasonable range of the experimental data. All the solids circulation rates decrease with annulus gas velocity, confirming the reasonability of the experiments and the explanations shown above. 0.1 0.2 0.3 0.4 0.5 0.610203040506070Ud0=1.25 m/sUd0=1 m/sUd0=0.75 m/s Exp-Ud0=0.75 m/s Exp-Ud0=1 m/s Exp-Ud0=1.25 m/sGs, kg/m2.sUa0, m/sMloading=2.275 kg Figure A.1 Experimental and modeled solids circulation rates at a bed solids loading of 2.275 kg. (Symbols: experimental data; lines: modeling results.)  188   Appendix B Derivation of adsorption isotherm  The rate constants KO2 and KNO2 could be described with the Arrhenius expression: RTEii aieAk /??           (B.1) Olsson et al. [115] observed that the desorption peak for NO2 was broad in the NO2 TPD on Cu/ZSM-5 catalyst, suggesting that NO2 is adsorbed on the surface with different energy levels.  Similarly, one could speculate that NOx could also be adsorbed on the surface of Fe/ZSM-5 catalyst with different energy levels. Fitting the adsorption equilibrium to the Langmuir isotherm, which has been widely used for NOx adsorption, it was found that the NOx adsorption data for Fe/ZSM-5 used in this work did not fit well into the Langmuir isotherm with a single activation energy, suggesting that NOx was adsorbed onto the surface of Fe/ZSM-5 with different energy levels. Therefore, the Freundlich isotherm, which assumes the adsorption energies follow an exponential distribution [141], was applied in this study.  ? ?RTnQQN /exp)( ????         (B.2) where N(Q) is the number of sites having adsorption energy Q, and ? and n are constants. It is further assumed that for each energy level, the coverage ? follows the Langmuir isotherm. For O2 adsorption, the coverage ? is 221 OOCbCb?????            (B.3) The adsorption coefficient b depends on the adsorption energy in the form ? ?RTQbb /exp0 ??          (B.4) 189  The fraction of adsorption sites occupied by adsorbate having an energy of adsorption between Q and Q+dQ is dQQNQd T )()( ????            (B.5) The total coverage by the adsorbate is obtained by integration of equation (B.5) over the whole range of adsorption energies, i.e. between the limits -? and +?. The integral after substitution of ?(Q) and N(Q) from equations (B.3)-(B.5) becomes ? ???? ?????????? dQRTnQCRTQbCRTQbOOT )/exp()/exp(1)/exp(2200 ?     (B.6) which yields nOnOnT ACCnRTb220 ??? ?        (B.7) If the adsorption is expressed in terms of mole of adsorbate per unit volume of adsorbent qe, the Freundlich isotherm is written in the form nOFnOnme CkCnRTbcq 220 ??? ?         (B.8) For O2 adsorption in the experiment with kinetics represented by reactions (4.R1) and (4.R2), Eq. (B.8) could still be used to calculate the O2 adsorption. This is because the adsorbed O2 and NO2 contribute to only a small part of the total active sites (calculated previously as 216 mol/m3 cat), which further implies that the adsorption of O2 is not affected by the absorbed NOx. The adsorption of NO2 could now be expressed as 22222 *][*][ 2 OnOFONONONONO CkCKOCKNO ??????      (B.9) 190   An exponential distribution of adsorption energies is also assumed for KNO2. To keep consistent with equation (B.3), KNO2 is replaced by bNO2. The total coverage of NO2 could be integrated as  ?? ???????? ???????? dQQNCbCkdQQNCkCb NONOnOFOnOFONONOT OO )()( 22222222   (B.10) The integration term in equation (B.10) could be calculated as ? ??????????????????????????????????????????dQQNCbCbCbdQQNCbCbdQQNCbCbCbdQQNCbNONONONONONONONONONONONONONONONONONO)(1)(1)(11)(222222222                (B.11) Similar to the integration of O2 coverage, the first term of equation (B.11) gives nNOnNONONONO CnRTbdQQNCbCb 0)(1 22 ??????? ????      (B.12) The second term could be integrated with the activation energy nNOnNONONONONONONONOCnRTbCdQRTQbRTnQCRTQbCRTQbdQQNCbCbCb1)/exp()/exp()/exp(1)/exp()(10000222????????????????? ????????????             (B.13) The total NO2 coverage, ?TNO2, is nNOnNOnnNOnnNOnT BCCnnRTbCnRTbCnRTb ?????????????? 1111 000 ???   (B.14) The adsorption capacity is  222222222 1110 NOOOnNOFNOnOFOmnNOnnOFONOe CkCkcCnnRTbCkq ????????? ?????????? ?  (B.15) 191  The adsorbed O2 and NO2 could be expressed as: 2222OOnFOOe ckq ??          (B.16) 22222NONOOOnFNOnFONOxe ckckq ????           (B.17)  192   Appendix C Detailed discussion on kf  Mass transfer term ? ?*ssf CCk ?  used in Eqs. (4.17) and (4.19) is slightly different with classic term ? ?qqk ?*  for mass transfer [127] as shown in Eq. (C.1). ? ? ? ?** gg CCkKqqktq ??????         (C.1) where q* is the adsorbate loading in equilibrium with the solute concentration, Cg, in the bulk fluid; Cg* is the concentration in equilibrium with the average loading q ; k is the overall mass transfer coefficient, which includes both external and internal transport resistances; and K is the adsorption equilibrium constant for a linear adsorption isotherm of the form q=KCg. For the term ? ?*gg CCkK ?  in Eq. (C.1), it is assumed that the adsorption follows a linear isotherm. However, the adsorption of NOx on Fe/ZSM-5 follows the Freundlich type isotherm. The model with mass transfer treated as kK(Cg-Cg*) could not well capture the adsorption characteristics of Fe/ZSM-5. So the mass transfer term is modified to capture the Freundlich type adsorption performance. The modified model is investigated in Chapter 4 and then confirmed to fit better with the experiment than the classic model. Similar modification of the model is also adopted by Dasgupta [123] to enable the Langmuir form of isotherm to be used. But in Dasgupta?s model, only intra-phase mass transfer resistance is considered. In order to investigate the characteristics of kf, there is a need to quote Eq. (C.1) again. Since the modified term ? ?*ssf CCk ?  is comparable to the classic term ? ?qqk ?* , it is expected that characteristics of parameter kf is similar with k. However, there is correlation in literature to calculate k directly. Eq. (C.2) is the most often used equation to calculate kK as a lumped factor. 193  epcpDRkRkK 1531 2??         (C.2) where the second term on the right side represents the internal resistance and the first term represents the external mass transfer resistance, kcav, since for a sphere the surface area/unit volume, av, is given by ? ?? ? ppp RRR /33/4/4 32 ???         (C.3) For the estimation of the external mass transfer coefficient kc in fixed beds, the correlation of Wakao [128] could be used: 2/13/1 Re1.10.2 ScDdkShmpc ???    410Re3 ??       (C.4) From Eq .(C.2), kK, as a lumped factor, is determined by the external and internal mass transfer characteristics and is independent with adsorption equilibrium K. Therefore, Eq. (C.2) could be simplified to Eq. (C.5), in which ? is a constant calculated from kc, Rp and De.  ??kK           (C.5) And then it is obvious that k is linear to 1/K, as shown in Eq. (C.6).  Kk /??           (C.6) It could be further expected that there is a same relationship between kf and K. Kk f /??           (C.7)  If there is a kf value (kf0) fitted at one condition, other kf values could be calculated from Eq. (C.8). Here, kc, Rp and De remain unchanged. It should be noted that Ki is the adsorption equilibrium of linear isotherm.  194  iiff KKkk /00?           (C.8) The value of Ki should be obtained according to Eq. (C.9) at each condition since the adsorption of NOx on Fe/ZSM-5 follows Freundlich isotherm. gingiFigieii CCkCqK i // ??         (C.9) It is assumed that hydrocarbon is transferred from the gas phase to solids and then reacts with adsorbed NOx on the catalyst surface. Therefore, different kf value is used for HC mass balance equation:  epcpf DRkRk 1531 2??         (C.10)   195   Appendix D Details of adsorption experiments  D.1 Experimental procedure of fixed bed adsorption  The simulated flue gas used in the experiment was a mixture prepared from several gas cylinders: 21% O2 balanced with N2, 0.3% NO balanced with N2 and pure N2 gas cylinders from Praxair Products Inc. The compositions (NOx and O2) of the effluent gases were analyzed by a Horiba PG-250 flue gas analyzer. Before the start up of the experiment, the reactor was first heated to the desired temperature with pure N2 gas passing through the catalyst bed. After the reactor temperature was stabilized, the flow of a gas mixture at a preset composition was turned on to start the experiment, with the gas mixture inlet composition determined by the same gas analyzer. In the NOx adsorption experiment, the model flue gas was pre-mixed with pure N2 as the balance gas according to the preset flow rate and concentrations of NO and O2. The composition of flue gas mixture was then measured by the gas analyzer. After stable readings of the analyzer were reached, which corresponded to the inlet model flue gas concentrations, the three way valves switched the flow to the reactor inlet and the time was recorded as the starting point of adsorption. During the adsorption process, the gas composition at the reactor?s outlet was continuously monitored until the NOx concentration became stable, with the final NOx concentration defined as the equilibrium NOx concentration. Thereafter, the NO and O2 flow from the gas cylinder was turned off and, pure N2 was used to purge the catalyst bed at 400? for 1 hour to remove all adsorbed NOx and O2 from the catalyst. 196  Experiments on the adsorption performance of the Fe/ZSM-5 catalyst were conducted at different temperatures and NO concentrations. Each experimental condition was repeated 3 times to obtain the average adsorption capacities.  D.2 Experimental details of fluidized bed adsorption  The adsorption performance of Fe/ZSM-5 was also tested in a hot model fluidized bed. The column diameter is 108 mm (I.D.) and the height is 1092 mm. The freeboard height and diameter are 1016 mm and 260 mm (I.D.), respectively. The schematic of the fluidized bed set-up is shown in Fig. D.1. The bed catalyst loading is 0.975 kg. The adsorption performance was tested at different temperatures and inlet gas velocities. The experimental conditions are also given in Table 1.  Figure D.1 Schematics of fluidized bed set-up  197  The model flue gas used in the experiment was a mixture prepared from 20% NO balanced with N2 and liquid N2 Dewar from Praxair Products. Building air was also used to provide O2 in the feed gas. The compositions (NOx and O2) of the effluent gases were analyzed by a Horiba PG-250 flue gas analyzer. In the experiment, the fluidized bed was first preheated by passing the preheated building air. After the desired temperature was reached in the reactor, the bed was purged with nitrogen for 1 hour. After the purging, 20% NO balanced with nitrogen, building air, and pure nitrogen was blended and injected to the fluidized bed after preheating. The adsorption performance was evaluated by measuring the NOx concentration at the top freeboard region of the fluidized bed. Afterward, pure N2 was used to purge the catalyst bed for another 1 hour to remove all adsorbed NOx from the catalyst.  The adsorption performance was tested at different temperatures and inlet gas velocities. One experimental condition, at 300? with an inlet NOx concentration of 900 ppm and a superficial gas velocity of U=0.08 m/s, was tested three times to check the repeatability of the experiment.  D.3 Experimental results of fixed bed adsorption  Adsorption breakthrough curves were measured with three repeats at each experimental condition. A series of typical adsorption breakthrough curves at 250? are shown in Fig. D.2. The results at other temperatures are not shown here. 198  0 500 1000 1500 2000 2500 3000 3500 40000.00.20.40.60.81.0C/C0t (s) 200ppm 400ppm 600ppm 800ppm 1000ppmT=2500CGHSV=5000 Figure D.2 Fixed bed NOx adsorption breakthrough curves at 250 ?  D.4 Experimental results of fluidized bed adsorption  The breakthrough test of NOx adsorption in the fluidized bed was repeated 3 times at 300 ?, an inlet NOx concentration of 900 ppm and U=0.08 m/s. All the curves shown in Fig. D.3 are in close agreement, with small discrepancies.  0 500 1000 15000.00.20.40.60.81.0C/C0t, sT=300 0CNO=900 ppmU=0.08 m/s Figure D.3 Repeated breakthrough curves in the fluidized bed (T=300 ?, NO=900 ppm)  199  Fig. D.4 (a) and (b) are the breakthrough curves at 300? and 350?, respectively. Although the adsorption capacities are not calculated, it can easily be seen that the adsorption capacities are smaller at higher temperatures, with the breakthrough curves becoming steeper as the temperature increases from 300 ? to 350 ?.  0 500 1000 1500 20000.00.20.40.60.81.0T=300 0CU=0.08 m/sC/C0t, s 300 ppm 600 ppm 900 ppm0 500 1000 1500 20000.00.20.4...C/C0t, s 300ppm 600ppm 900ppmT=350 0CU=0.08 m/s (a)      (b) Figure D.4  Breakthrough curve of different NOx inlet concentrations at (a) 300 ? and (b) 350 ?.200   Appendix E Sensitivity analysis of fluidized bed adsorption model  The sensitivity of model to different parameters was tested with the results plotted in Fig. E.1. The breakthrough curves were modeled with parameters of mass transfer and gas dispersion either doubled or halved. These curves were then compared with original curve. It is seen that the model is most sensitive to gas-solid mass transfer coefficient, kf. However, the breakthrough curve is not sensitive to either dense-bubbles phase mass transfer coefficient, kHL, or gas dispersion coefficient DH. This is because these parameters are already big enough.  0 200 400 600 800 10000.00.20.40.60.81.0C/C0t, (s) Original kHL*2 kHL/2 kf*2 kf/2 DH*2 DH/2T=250 oCU=0.08 m/s Figure E.1 Model sensitive analysis  201   Appendix F MATLAB codes for i-CFB model  %-----------main function------------------------------------------------- function iCFB   % i-CFB model   %--------write file, title------------------------------------------------ fid = fopen ('i-CFB model.txt', 'at');    fprintf (fid, '%12s\n\n', ' '); fprintf (fid, '%10s','Number'); fprintf (fid, '%10s','Ua0'); fprintf (fid, '%10s','Ud0'); fprintf (fid, '%10s','HC:NO'); fprintf (fid, '%10s','O2'); fprintf (fid, '%10s','exp-XNO'); fprintf (fid, '%10s','exp-XHC') fprintf (fid, '%10s','m-XNO'); fprintf (fid, '%10s','m-XHC');; fprintf (fid, '%10s','f-XNO'); fprintf (fid, '%10s\n','f-XHC');   fclose all;   %---------------data------------------------------------------------------ %-------%O2=4%; HC:NO=2 -------------------------------------------------- %Uga =[ 0.22 0.28 0.34 0.42 ];   %Ugd =[ 0.6  0.6  0.6  0.6  ];   %ExpXNO=[ 54.50 47.34 43.12 40.73];   %ExpXHC=[ 100   96.70 83.30 71.56 ];   %O2  = ones(4)*4;  %HCNO= ones(4)*2;   %--------O2=4%------------------------------------------------------------  %Uga=[ 0.22 0.35 0.22 0.35 ];   %Ugd=[ 0.6  0.6  0.6  0.6  ];   %ExpXNO=[51.93 35.41 64.04 58.53 ];   %ExpXHC=[100   100   91.19 65.69 ];   %HCNO=[ 1  1  4  4]; %O2  = ones(4)*4;    %--------O2=4%------------------------------------------------------------  Uga=[ 0.21 0.33 0.19 0.28 0.35 0.40 0.47 0.23 0.34  ];   Ugd=[ 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75  ];   202  ExpXNO=[ 53.45 39.47 59.12 52.04 46.55 41.59 41.59 70.44 62.65 ];   ExpXHC=[ 93.98 80    88.50 81.42 78.58 74.51 66.73 76.64 57.88 ];   HCNO=[1 1 2 2 2 2 2 4 4  ]; O2= ones(9)*4;    %--------O2=4%------------------------------------------------------------ %Uga=[ 0.21 0.34 0.28 0.35 0.40 0.46 0.21 0.32 ];   %Ugd=[ 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9  ];   %ExpXNO=[ 62.37 51.94 63.07 59.01 51.94 47.70 73.50 66.60 ];   %ExpXHC=[ 87.63 75.80 71.20 69.26 69.61 62.72 50.88 36.40 ];   %HCNO=[1 1 2 2 2 2 4 4 ]; %O2  = ones(8)*4;    %--------O2=12%-----------------------------------------------------------  %Uga=[ 0.3 0.3 0.3 0.4 0.4 0.4 ];   %Ugd=[ 0.6 0.75 0.9 0.6 0.75 0.9  ];   %ExpXNO=[31.01 36.76 56.49 28.20 34.75 49.35];   %ExpXHC=[ 0 0 0 0 0 0 ];   %HCNO=[ 2 2 2 2 2 2 ]; %O2  = ones(6)*12;    %------------calculating-------------------------------------------------- for number=1:9,      %---------basic setting--------------------------------------------------- T=350+273;         %temperature, K  P=1.013e5;         %pressure, Pa rou=1.29*293/T;    %gas density, kg/m3    nu=(7e-5*T^2+0.0579*T-7.2566)*1e-6;  %gas property, viscocity mu=(1e-9*T^3-4e-6*T^2+0.0067*T+0.1177)*1e-5; %gas property, viscocity   Hd=1.016; %m, i-CFB configuration, draft tube height Da=0.10;  %m, i-CFB configuration, annulus diameter Dd=0.05;  %m, i-CFB configuration, draft tube diameter Ad=3.14*Dd*Dd/4;    %m2, draft tube cross area Aa=3.14*Da*Da/4-Ad; %m2, annulus cross area   dp=150e-6;   %m catalyst diameter roubulk=979; %kg/m3, catalyst bulk density rous=roubulk/0.55; %kg/m3, catalyst density   epss=0.45;    %solids fraction at umf epsmf=1-epss; %voidage at umf Umf=0.01;     %m/s, minimum fluidization velocity G=3.3;        %kg, bed loading   %---------------feeding gas setting--------------------------------------- NOa0=600e-6;            %NO concentration in flue gas, partial pressure, ppm*e-6 O2a0=1e-2*O2(number);   203  %O2 concentration in flue gas, partical pressure, %*e-2 HCratio=HCNO(number);  %HC:NO ratio   Ua0=Uga(number); %m/s; annulus gas operation velocity Ud0=Ugd(number); %m/s, draft tube velocity   %----------------Ra-d, Rd-a----------------------------------------------- RAD=0.07;                                         %Ra-d RDA=0.01*1.039*(Ua0/Umf)^(-0.616)*(Ud0/Umf)^1.3;  %Rd-a   %----------actually inlet velocities considering gas bypassing------------ Ua=Ua0-RAD*Ua0+RDA*Ud0*(Ad/Aa);   %m/s, acturall inlet velocity in the annulus  Ud=Ud0-RDA*Ud0+RAD*Ua0*(Aa/Ad);   %m/s, acturall inlet velocity in the draft tube   %----------actually inlet concentrations considering gas bypassing-------- mNO=NOa0*P/8.314/T;    %mol/m3, NO concentration in feeding flue gas mO2=O2a0*P/8.314/T;    %mol/m3, O2 concentration in feeding flue gas mHC=mNO*HCratio*(Ua0*Aa)/(Ud0*Ad);  %mol/m3, HC concentration in feeding reducing agent   mNOa=mNO*(1-RAD)*(Ua0/Ua);        %mol/m3, acturall inlet concentraion of NO in the annulus mNOd=mNO*RAD*(Ua0*Aa)/(Ud*Ad);    %mol/m3, acturall inlet concentraion of NO in the draft tube mO2a=mO2*(1-RAD)*(Ua0/Ua);        %mol/m3, acturall inlet concentraion of O2 in the annulus mO2d=mO2*RAD*(Ua0*Aa)/(Ud*Ad);    %mol/m3, acturall inlet concentraion of O2 in the draft tube mHCd=mHC*(1-RDA)*(Ud0/Ud);        %mol/m3, acturall inlet concentraion of HC in the draft tube mHCa=mHC*RDA*(Ud0*Ad)/(Ua*Aa) ;   %mol/m3, acturall inlet concentraion of HC in the annulus   %-----------bubble and voidage parameter in draft tube--------------------------- Hf=Hd; Hs=Hf/(1-epsmf);  %m, parameter to calculate bubble property Dbd=0.21*Hf^0.8*(Ud-Umf)^0.42*exp(-1.4e-4-0.25*(Ud-Umf)^2-0.1*(Ud-Umf)); if Dbd>Dd,    Dbd=Dd; end     %m, bubble diameter in draft tube   Ubd=Ud-Umf+0.71*(9.8*Dbd)^0.5;  %m/s, bubble velocity in draft tube Y=0.108*Hs^0.26*(Ud-Umf)^0.09*dp^(-0.48)*rous^(-0.19);   if Ud<0.37,     epsd=0.5056*Ud+0.4538; else 204      epsd=0.481 *Ud+0.5604; end      epsbd=1-(1-epsd)/(1-epsmf);   Gd=rous*Ad*Hd*(1-epsd);      %kg, catalyst weight in draft tube Hsd=Hd;                      %m, initial effective bed height of draft tube   %-------------bubble and voidage parameter in annulus--------------------- Ga=G-Gd;               %kg, catalyst weight in annulus Hmf=Ga/Aa/roubulk;     %m, Hmf in annulus, for bubble parameter calculation Hs=Hmf/(1-epsmf);      %m, Hs in annulus Hf=Hmf;                %m, Hf in annulus   Dba=0.21*Hf^0.8*(Ua-Umf)^0.42*exp(-1.4e-4-0.25*(Ua-Umf)^2-0.1*(Ua-Umf)); if Dba>Da/2-Dd/2,    Dba=Da/2-Dd/2; end   %m, bubble diameter in annulus   Uba=Ua-Umf+0.71*(9.8*Dba)^0.5; %m/s, bubble velocity in annulus   if Ua<0.37,     epsa=0.5056*Ua+0.4538; else     epsa=0.481 *Ua+0.5604; end       epsba=1-(1-epsa)/(1-epsmf);      Ha=Ga/rous/(1-epsa)/Aa;        %m, initial bed height of annulus Hsa=Ha;                        %m, initial effective bed height of annulus   %------------calculating effecitive bed heights--------------------------- if Ha>Hd,       Lj=0.1*11.52*(1.206/(968/0.55)*Ud^2/9.8/0.05)^0.1966;     %m, jet height of draft tube     for i=1:2,    %iterating for effective bed heights         if Ha<=Hd+Lj,             Hsd=Ha;         else              Hsa=Ha+Lj;             Hsd=Hsa;         end         Gd=rous*Ad*Hsd*(1-epsd);         Ga=G-Gd;         Ha=Ga/rous/(1-epsa)/Aa;     end     end   %------------calculating solids circulation rate--------------------------- Pa=9.8*Hsa*rous*(1-epsa);   %Pa, initial pressure drop in annulus Pd=9.8*Hsd*rous*(1-epsd);   %Pa, initial pressure drop in draft tube 205    Gs=0;   %give an initial value   for i=1:2,   %iterating for solids circulation rate Por=Pa-Pd;   %Pa, initial pressure drop in orifice   fa=0.057*Gs*(9.8/0.1)^0.5;      %friction coefficient in annulus fd=0.057*Gs*3*(9.8/0.05)^0.5;   %friction coefficient in draft tube Fa=fa*Hsa-0.5*Gs^2/(968/0.55);  %Pa, pressure drop due to friction in annulus Fd=fd*Hd+0.5*9*Gs^2/(968/0.55); %Pa, pressure drop due to friction in draft tube   if Hsa>Hd,     Fa=fa*Hd-0.5*Gs^2/(968/0.55); end Por=Pa-Pd-Fa-Fd; Gs=0.17*0.146667*(2*968/0.55*(1-epsa)*Por/(1-0.021511))^0.5;   %kg/m2.s, solids circulation rate end   Usa=Gs/roubulk/(1-epsba);        %m/s, solids velocity in annulus Usd=Gs*Aa/Ad/roubulk/(1-epsbd);  %m/s, solids velocity in draft tube   %--------high-low phase mass transfer coefficient, kHL-------------------- Dm=zeros(3);   %m2/s, molecular diffusivity Dm=Di(T,P, 600e-6, 0, 1e-2); DmNO=Dm(1);    %m2/s, molecular diffusivity for NO kHLa=Umf/3+2*(DmNO*epsmf*Uba/3.14/Dba)^0.5;  %m/s, kHL in annulus kHLd=Umf/3+2*(DmNO*epsmf*Ubd/3.14/Dbd)^0.5;  %m/s, kHL in draft tube   %-----dispersion coefficients of solids & high phase, Ds & DH-------------- gDta=(9.8*(Da/2-Dd/2))^0.5; Pesa=19*((Da/2-Dd/2)+0.23)*Ua/gDta*(1+6.5*(Ua/gDta)^0.8);  %P?clet number of solids phase in annulus Dsa=Ua*(Da/2-Dd/2)/Pesa;  %m2/s, dispersion coefficients of solids phase in annulus DHa=Dsa;                  %m2/s, dispersion coefficients of high phase  in annulus   gDtd=(9.8*Dd)^0.5; Pesd=19*(Dd+0.23)*Ud/gDtd*(1+6.5*(Ud/gDtd)^0.8);  %P?clet number of solids phase in draft tube Dsd=Ud*Dd/Pesd;  %m2/s, dispersion coefficients of solids phase in draft tube DHd=Dsd;         %m2/s, dispersion coefficients of high  phase in draft tube   %----------other coeffiecients for governing equations-------------------- faHa=1-epsba;   %high phase fraction in annulus faLa=epsba;     %low  phase fraction in annulus faHd=1-epsbd;   %high phase fraction in draft tube faLd=epsbd;     %low  phase fraction in draft tube   206  UHa=Umf;        %m/s; high phase gas velocity in annlus ULa=Uba;        %m/s; low  phase gas velocity in annlus UHd=Umf;        %m/s; high phase gas velocity in draft tube ULd=Ubd;        %m/s; low  phase gas velocity in draft tube   aba=6*faLa/Dba;  %1/m, surface area of interphase boundary per unit bed volume in annulus abd=6*faLd/Dbd;  %1/m, surface area of interphase boundary per unit bed volume in % draft   tube as=6*epss/dp;    %1/m, surface area of catalyst particle per unit bed volume in annulus   kf=0.0148*3e-6/(1-epss); %1/s, intraphase mass transfer coefficient   %------summary of coefficients for calculating governing equations-------- %-----governing euqation numbers:  %----annulus:    1,  NO-Solids phase; 2,  NO-High phase;  %                3,  HC-Solids phase; 4,  HC-High phase;  %                5,  O2-Solids phase; 6,  O2-High phase;  %                7,  NO-Low   phase; 8,  HC-Low  phase; 9,  O2-Low phase; %----draft tube: 11, NO-Solids phase; 12, NO-High phase;  %                13, HC-Solids phase; 14, HC-High phase;  %                15, O2-Solids phase; 16, O2-High phase;  %                17, NO-Low   phase; 18, HC-Low  phase; 19, O2-Low phase;   %----annulus:   f1c=kf*as; f3c=f1c;   f5c=f1c;   f7c=kHLa*aba; f8c=f7c; f9c=f7c;   a1=Dsa; a2=DHa; a3=a1; a5=a1; a4=a2; a6=a2;   a7=0; a8=a7; a9=a7;   b1= -Usa; b2=UHa; b3=b1; b5=b1; 207  b4=b2; b6=b2;   b7=ULa; b8=b7; b9=b7;   %----draft tube:   f11c=kf*as; f13c=f11c;   f15c=f11c;   f17c=kHLd*abd; f18c=f17c; f19c=f17c;   a11=Dsd; a12=DHd; a13=a11; a15=a11; a14=a12; a16=a12;   a17=0; a18=a17; a19=a17;   b11=Usd; b12=UHd; b13=b11; b15=b11; b14=b12; b16=b12;   b17=ULd; b18=b17; b19=b17;   %-------interval set for differential equation calculation---------------- t=0.01;    %s,time interval M=20;      %number of length points ha=Hsa/M;  %m, length interval in annulus hd=Hsd/M;  %m, length interval in draft tube   %~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ %-------matrix for differential equation calculation----------------------   %----annulus: %-------matrix r1--------------------------------------------------------- r1=zeros(M,M);  208    for i=1:M-1;     r1(i,i)=1+2*a1*t/ha/ha;     r1(i+1,i)=-a1*t/ha/ha-b1*t/ha/2;         r1(i,i+1)=-a1*t/ha/ha+b1*t/ha/2; end   r1(M,M)=1+2*a1*t/ha/ha; r1(M,M)=r1(M,M)+(-a1*t/ha/ha+b1*t/ha/2);   %-------matrix r3, r5----------------------------------------------------- r3=r1; r5=r1;   %-------matrix r2--------------------------------------------------------- r2=zeros(M,M);    for i=1:M-1;     r2(i,i)=1+2*a2*t/ha/ha;     r2(i+1,i)=-a2*t/ha/ha-b2*t/ha/2;         r2(i,i+1)=-a2*t/ha/ha+b2*t/ha/2; end   r2(M,M)=1+2*a2*t/ha/ha; r2(M,M)=r2(M,M)+(-a2*t/ha/ha+b2*t/ha/2);   %-------matrix r4, r6----------------------------------------------------- r4=r2;    r6=r2;      %-------matrix r7--------------------------------------------------------- r7=zeros(M,M);     for i=1:M-1;     r7(i,i)=1+2*a7*t/ha/ha;     r7(i+1,i)=-a7*t/ha/ha-b7*t/ha/2;         r7(i,i+1)=-a7*t/ha/ha+b7*t/ha/2; end   r7(M,M)=1+2*a7*t/ha/ha; r7(M,M)=r7(M,M)+(-a7*t/ha/ha+b7*t/ha/2);   %-------matrix r8, r9----------------------------------------------------- r8=r7; r9=r7;   %----draft tube: %-------matrix r11-------------------------------------------------------- r11=zeros(M,M);     for i=1:M-1; 209      r11(i,i)=1+2*a11*t/hd/hd;     r11(i+1,i)=-a11*t/hd/hd-b11*t/hd/2;         r11(i,i+1)=-a11*t/hd/hd+b11*t/hd/2; end   r11(M,M)=1+2*a11*t/hd/hd; r11(M,M)=r11(M,M)+(-a11*t/hd/hd+b11*t/hd/2);   %-------matrix r13, r15--------------------------------------------------- r13=r11; r15=r11;   %-------matrix r12-------------------------------------------------------- r12=zeros(M,M);     for i=1:M-1;     r12(i,i)=1+2*a12*t/hd/hd;     r12(i+1,i)=-a12*t/hd/hd-b12*t/hd/2;         r12(i,i+1)=-a12*t/hd/hd+b12*t/hd/2; end   r12(M,M)=1+2*a12*t/hd/hd; r12(M,M)=r12(M,M)+(-a12*t/hd/hd+b12*t/hd/2);   %-------matrix r14, r16--------------------------------------------------- r14=r12;    r16=r12;      %-------matrix r17-------------------------------------------------------- r17=zeros(M,M);     for i=1:M-1;     r17(i,i)=1+2*a17*t/hd/hd;     r17(i+1,i)=-a17*t/hd/hd-b17*t/hd/2;         r17(i,i+1)=-a17*t/hd/hd+b17*t/hd/2; end   r17(M,M)=1+2*a17*t/hd/hd; r17(M,M)=r17(M,M)+(-a17*t/hd/hd+b17*t/hd/2);   %-------matrix r18, r19--------------------------------------------------- r18=r17; r19=r17;   %~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ %---------main calculation of differential equations---------------------- %---annulus u1=zeros(M,1);  %NO, solids phase u2=zeros(M,1);  %NO, gas   phase u3=zeros(M,1);  %HC, solids phase  u4=zeros(M,1);  %HC, gas   phase  210  u5=zeros(M,1);  %O2, solids phase  u6=zeros(M,1);  %O2, gas   phase  u7=zeros(M,1);  %NO, bubble phase  u8=zeros(M,1);  %HC, bubble phase  u9=zeros(M,1);  %O2, bubble phase   uu1=zeros(M,1);  %NO, solids phase uu2=zeros(M,1);  %NO, gas   phase uu3=zeros(M,1);  %HC, solids phase  uu4=zeros(M,1);  %HC, gas   phase  uu5=zeros(M,1);  %O2, solids phase  uu6=zeros(M,1);  %O2, gas   phase  uu7=zeros(M,1);  %NO, bubble phase  uu8=zeros(M,1);  %HC, bubble phase  uu9=zeros(M,1);  %O2, bubble phase   ff1=zeros(M,1);  %boundary, NO, solids phase ff2=zeros(M,1);  %boundary, NO, gas phase ff3=zeros(M,1);  %boundary, HC, solids phase ff4=zeros(M,1);  %boundary, HC, gas phase ff5=zeros(M,1);  %boundary, O2, solids phase ff6=zeros(M,1);  %boundary, O2, gas phase ff7=zeros(M,1);  %boundary, NO, bubble phase ff8=zeros(M,1);  %boundary, HC, bubble phase ff9=zeros(M,1);  %boundary, O2, bubble phase   %---draft tube u11=zeros(M,1);  %NO, solids phase u12=zeros(M,1);  %NO, gas phase u13=zeros(M,1);  %HC, solids phase  u14=zeros(M,1);  %HC, gas phase  u15=zeros(M,1);  %O2, solids phase  u16=zeros(M,1);  %O2, gas phase  u17=zeros(M,1);  %NO, bubble phase  u18=zeros(M,1);  %HC, bubble phase  u19=zeros(M,1);  %O2, bubble phase   uu11=zeros(M,1);  %NO, solids phase uu12=zeros(M,1);  %NO, gas phase uu13=zeros(M,1);  %HC, solids phase  uu14=zeros(M,1);  %HC, gas phase  uu15=zeros(M,1);  %O2, solids phase  uu16=zeros(M,1);  %O2, gas phase  uu17=zeros(M,1);  %NO, bubble phase  uu18=zeros(M,1);  %HC, bubble phase  uu19=zeros(M,1);  %O2, bubble phase   ff11=zeros(M,1);  %boundary, NO, solids phase ff12=zeros(M,1);  %boundary, NO, gas phase ff13=zeros(M,1);  %boundary, HC, solids phase ff14=zeros(M,1);  %boundary, HC, gas phase 211  ff15=zeros(M,1);  %boundary, O2, solids phase ff16=zeros(M,1);  %boundary, O2, gas phase ff17=zeros(M,1);  %boundary, NO, bubble phase ff18=zeros(M,1);  %boundary, HC, bubble phase ff19=zeros(M,1);  %boundary, O2, bubble phase   %---parameters CsNO=0;       %mol/m3, equilibrium concentration of NOx, initial CsO=0;        %mol/m3, equilibrium concentration of O2 , initial R=[0 0 0];    %mol/s , reaction rate, initial RSNO2=0;      %mol/s , reaction rate of NO2, initial RHC=0;        %mol/s , reaction rate of HC , initial RO2=0;        %mol/s , reaction rate of O2 , initial   KNOe=CssNO (mNO, mO2, T)/mNO; KNOa=CssNO(mNOa, mO2a,T)/mNOa; KNOd=CssNO(mNOd, mO2d,T)/mNOd; KO2a=CssO(mO2a,T)/mO2a; KO2d=CssO(mO2d,T)/mO2d;      KNOKNOea=KNOe/KNOa; KNOKNOed=KNOe/KNOd; KNOKO2a= KNOe/KO2a; KNOKO2d= KNOe/KO2d; KNOKHC= KNOe*10.12/2.18;   k=1; XNOa=0;    %initial conversion values XNOd=0; XHCa=0; XNOea=0; XNOed=0; XHCea=0;   ERROR=3e2;  %inital error value   %---------calculation----------------------------------------------------- while ERROR>1e-6,   %--------adsorption & reaction-----------         for i=1:M,          %---annulus         CsNO=CssNO(u2(i,1), u6(i,1),T);         CsO =CssO(u6(i,1),T);         R   =Reaction(u1(i,1), u3(i,1), u5(i,1), T)* (1-epsa);         RSNO2=Ra(1);         RHC  =Ra(2);         RSO  =Ra(3);                      ff1(i,1)= -f1c*KNOKNOea*(u1(i,1)-CsNO)  +RSNO2;        %NO, solids phase 212          ff3(i,1)= -f3c*KNOKHC*(u3(i,1)-u4(i,1)) +RHC;          %HC, solids phase         ff5(i,1)= -f5c*KNOKO2a*(2*u5(i,1)-CsO)  +RSO;          %O2, solids phase              ff2(i,1)=  f1c*KNOKNOea*(u1(i,1)-CsNO) - f7c*(u2(i,1)-u7(i,1)); %NO, gas phase         ff4(i,1)=  f3c*KNOKHC*(u3(i,1)-u4(i,1))- f8c*(u4(i,1)-u8(i,1)); %HC gas phase              ff6(i,1)=  f5c*KNOKO2a*(u5(i,1)-CsO/2) - f9c*(u6(i,1)-u9(i,1)); %O2, gas phase              ff7(i,1)= f7c*(u2(i,1)-u7(i,1));  %NO, bubble phase          ff8(i,1)= f8c*(u4(i,1)-u8(i,1));  %HC, bubble phase          ff9(i,1)= f9c*(u6(i,1)-u9(i,1));  %O2, bubble phase    %---draft tube         CsNO=CssNO(u12(i,1), u16(i,1),T);         CsO =CssO(u16(i,1),T);         R   =Reaction(u11(i,1), u13(i,1), u15(i,1), T)* (1-epsd);         RSNO2=Rd(1);         RHC  =Rd(2);         RSO  =Rd(3);                      ff11(i,1)= -f11c*KNOKNOed*(u11(i,1)-CsNO)  +RSNO2;%NO, solids phase         ff13(i,1)= -f13c*KNOKHC*(u13(i,1)-u14(i,1))+RHC;  %HC, solids phase         ff15(i,1)= -f15c*KNOKO2d*(2*u15(i,1)-CsO)  +RSO;  %O2, solids phase              ff12(i,1)=  f11c*KNOKNOed*(u11(i,1)-CsNO)  - f17c*(u12(i,1)-u17(i,1)); %NO, gas phase             ff14(i,1)=  f13c*KNOKHC*(u13(i,1)-u14(i,1))- f8c*(u14(i,1)-u18(i,1));  %HC gas phase              ff16(i,1)=  f15c*KNOKO2d*(u15(i,1)-CsO/2)  - f19c*(u16(i,1)-u19(i,1)); %O2, gas phase              ff17(i,1)= f17c*(u12(i,1)-u17(i,1));  %NO, bubble phase          ff18(i,1)= f18c*(u14(i,1)-u18(i,1));  %HC, bubble phase          ff19(i,1)= f19c*(u16(i,1)-u19(i,1));  %O2, bubble phase        end   %---solids recirculation     u1(M,1)=(u1(M,1)*(ha-t*Usa)+t*Usa*u11(M,1))/ha;     u3(M,1)=(u3(M,1)*(ha-t*Usa)+t*Usa*u13(M,1))/ha;     u5(M,1)=(u5(M,1)*(ha-t*Usa)+t*Usa*u15(M,1))/ha;       u11(1,1)=(u11(1,1)*(hd-t*Usd)+t*Usd*u1(1,1))/hd;     u13(1,1)=(u13(1,1)*(hd-t*Usd)+t*Usd*u3(1,1))/hd;     u15(1,1)=(u15(1,1)*(hd-t*Usd)+t*Usd*u5(1,1))/hd;   %-------------------------------------- %---annulus     ff1(1,1)=ff1(1,1)+(a1/ha/ha+b1/ha/2)*u1(1,1);      ff3(1,1)=ff3(1,1)+(a3/ha/ha+b3/ha/2)*u3(1,1);      ff5(1,1)=ff5(1,1)+(a5/ha/ha+b5/ha/2)*u5(1,1);          ff2(1,1)=ff2(1,1)+(a2/ha/ha+b2/ha/2)*mNOa;     ff4(1,1)=ff4(1,1)+(a4/ha/ha+b4/ha/2)*mHCa;     ff6(1,1)=ff6(1,1)+(a6/ha/ha+b6/ha/2)*mO2a; 213        ff7(1,1)=ff7(1,1)+(a7/ha/ha+b7/ha/2)*mNOa;     ff8(1,1)=ff8(1,1)+(a8/ha/ha+b8/ha/2)*mHCa;     ff9(1,1)=ff9(1,1)+(a9/ha/ha+b9/ha/2)*mO2a;   %---draft tube     ff11(1,1)=ff11(1,1)+(a11/hd/hd+b11/hd/2)*u11(1,1);      ff13(1,1)=ff13(1,1)+(a13/hd/hd+b13/hd/2)*u13(1,1);      ff15(1,1)=ff15(1,1)+(a15/hd/hd+b15/hd/2)*u15(1,1);          ff12(1,1)=ff12(1,1)+(a12/hd/hd+b12/hd/2)*mNOd;     ff14(1,1)=ff14(1,1)+(a14/hd/hd+b14/hd/2)*mHCd;     ff16(1,1)=ff16(1,1)+(a16/hd/hd+b16/hd/2)*mO2d;       ff17(1,1)=ff17(1,1)+(a17/hd/hd+b17/hd/2)*mNOd;     ff18(1,1)=ff18(1,1)+(a18/hd/hd+b18/hd/2)*mHCd;     ff19(1,1)=ff19(1,1)+(a19/hd/hd+b19/hd/2)*mO2d;   %-------------------------------------- %---annulus     ff1 = u1+t*ff1;     ff2 = u2+t*ff2;     ff3 = u3+t*ff3;     ff4 = u4+t*ff4;     ff5 = u5+t*ff5;      ff6 = u6+t*ff6;     ff7 = u7+t*ff7;     ff8 = u8+t*ff8;     ff9 = u9+t*ff9;   %---draft tube     ff11 = u11+t*ff11;     ff12 = u12+t*ff12;     ff13 = u13+t*ff13;     ff14 = u14+t*ff14;     ff15 = u15+t*ff15;      ff16 = u16+t*ff16;     ff17 = u17+t*ff17;     ff18 = u18+t*ff18;     ff19 = u19+t*ff19;   %-------------------------------------- %---annulus     uu1=chase(r1, ff1);     uu2=chase(r2, ff2);     uu3=chase(r3, ff3);     uu4=chase(r4, ff4);     uu5=chase(r5, ff5);     uu6=chase(r6, ff6);     uu7=chase(r7, ff7);     uu8=chase(r8, ff8); 214      uu9=chase(r9, ff9);   %---draft tube     uu11=chase(r11, ff11);     uu12=chase(r12, ff12);     uu13=chase(r13, ff13);     uu14=chase(r14, ff14);     uu15=chase(r15, ff15);     uu16=chase(r16, ff16);     uu17=chase(r17, ff17);     uu18=chase(r18, ff18);     uu19=chase(r19, ff19);   %-----------------------------     for i=1:M;                if uu1(i,1)<0,            uu1(i,1)=0;         end         if uu2(i,1)<0,            uu2(i,1)=0;         end         if uu3(i,1)<0,            uu3(i,1)=0;         end         if uu4(i,1)<0,            uu4(i,1)=0;         end         if uu5(i,1)<0,            uu5(i,1)=0;         end         if uu6(i,1)<0,            uu6(i,1)=0;         end         if uu7(i,1)<0,            uu7(i,1)=0;         end         if uu8(i,1)<0,            uu8(i,1)=0;         end         if uu9(i,1)<0,            uu9(i,1)=0;         end                  if uu11(i,1)<0,            uu11(i,1)=0;         end         if uu12(i,1)<0,            uu12(i,1)=0;         end         if uu13(i,1)<0,            uu13(i,1)=0; 215          end         if uu14(i,1)<0,            uu14(i,1)=0;         end         if uu15(i,1)<0,            uu15(i,1)=0;         end         if uu16(i,1)<0,            uu16(i,1)=0;         end         if uu17(i,1)<0,            uu17(i,1)=0;         end         if uu18(i,1)<0,            uu18(i,1)=0;         end         if uu19(i,1)<0,            uu19(i,1)=0;         end     end   %--------------------------------------     u1=uu1;     u2=uu2;     u3=uu3;     u4=uu4;     u5=uu5;     u6=uu6;     u7=uu7;     u8=uu8;     u9=uu9;       u11=uu11;     u12=uu12;     u13=uu13;     u14=uu14;     u15=uu15;     u16=uu16;     u17=uu17;     u18=uu18;     u19=uu19;       k=k+1;   %------------calculation monitor------------------------------------------     if rem(k,30000)==0,              number=number     CNOa=(u2(M,1)*faHa*UHa+u7(M,1)*faLa*ULa)/(faHa*UHa+faLa*ULa);     CHCa=(u4(M,1)*faHa*UHa+u8(M,1)*faLa*ULa)/(faHa*UHa+faLa*ULa);     CNOd=(u12(M,1)*faHd*UHd+u17(M,1)*faLd*ULd)/(faHd*UHd+faLd*ULd); 216      CHCd=(u14(M,1)*faHd*UHd+u18(M,1)*faLd*ULd)/(faHd*UHd+faLd*ULd);         CO2a=(u6(M,1)*faHa*UHa+u8(M,1)*faLa*ULa)/(faHa*UHa+faLa*ULa);       CO2d=(u16(M,1)*faHd*UHd+u18(M,1)*faLd*ULd)/(faHd*UHd+faLd*ULd);       XNOa=100*(mNOa*Ua*Aa-CNOa*Ua*Aa)/(mNO*Ua0*Aa);       XNOd=100*(mNOd*Ud*Ad-CNOd*Ud*Ad)/(mNO*Ua0*Aa);          ERROR=abs(XNOea-XNOa)/t+abs(XNOed-XNOd)/t     XNOea=XNOa;     XNOed=XNOd;          XNO=100*(mNOa*Ua*Aa-CNOa*Ua*Aa+mNOd*Ud*Ad-CNOd*Ud*Ad)/(mNO*Ua0*Aa);     XHC=100*(mHCa*Ua*Aa-CHCa*Ua*Aa+mHCd*Ud*Ad-CHCd*Ud*Ad)/(mHC*Ud0*Ad);     Xout=[XNO XHC]       end end   %------------write data file---------------------------------------------- fid = fopen ('complete.txt', 'at');   fprintf (fid, '%10.4f', number); fprintf (fid, '%10.2f', Ua0); fprintf (fid, '%10.2f', Ud0); fprintf (fid, '%10.2f', HCNO(number)); fprintf (fid, '%10.2f', O2(number)); fprintf (fid, '%10.2f', ExpXNO(number)); fprintf (fid, '%10.2f', ExpXHC(number)); fprintf (fid, '%10.2f', Xout); fclose all;       %------------------------------------------------------------------------- %------freeboard---------------------------------------------------------- %----------inet of freeboard----------------------------------------------     A=3.14*Da*Da/4;    % cross sectional area   Ugf = (Ua*Aa+Ud*Ad)/(Aa+Ad);   CNOf= (CNOa*Ua*Aa+CNOd*Ud*Ad)/(Ua*Aa+Ud*Ad); CHCf= (CHCa*Ua*Aa+CHCd*Ud*Ad)/(Ua*Aa+Ud*Ad); CO2f= (CO2a*Ua*Aa+CO2d*Ud*Ad)/(Ua*Aa+Ud*Ad);   SNOf= (u1(M,1)*Aa*(1-epsa)+u11(M,1)*Ad*(1-epsd))/(Aa*(1-epsa)+Ad*(1-epsd)); SHCf= (u3(M,1)*Aa*(1-epsa)+u13(M,1)*Ad*(1-epsd))/(Aa*(1-epsa)+Ad*(1-epsd)); SO2f= (u5(M,1)*Aa*(1-epsa)+u15(M,1)*Ad*(1-epsd))/(Aa*(1-epsa)+Ad*(1-epsd));   %-----------------freeboard interval-------------------------------------- N=20;    %number of length points LF=0.8;  %height of freeboard     hf=LF/N; %m, freeboard interval   %----------freeboard voidage---------------------------------------------- 217  Hs=Hd; Dbf=0.21*Hs^0.8*(Ugf-Umf)^0.42*exp(-1.4e-4-0.25*(Ugf-Umf)^2-0.1*(Ugf-Umf));     if Dbf>Da,         Dbf=Da;     end   F0=A*Dbf*3.07e-6*rou^3.5*9.8^0.5/mu^2.5*(Ugf-Umf)^2.5;  %kg/m2.s epsF=freeb(F0, Ugf);  % (20,2), (position, eps)   if Hsa<Hd,     for i=1:N,         if (Hsa+i*hf)<Hd,             epsF(i,2)=1;         end     end end   %---------freeboard calculation------------------------------------------- %--number: 21: NO-solids phase; 22: HC-solids phase; 23: O2-solids phase; %--------- 24: NO-gas   phase; 25: HC-gas   phase; 26: O2-gas   phase; a21=0;   a22=a21; a23=a21; b21=0; b22=b21; b23=b21;   b24=Ugf;  b25=b24; b26=b24;   %-------------matrix------------------------------------------------------ %-------matrix 21, r22, r23----------------------------------------------- r21=zeros(N,N);    for i=1:N-1;     r21(i,i)=1+2*a21*t/hf/hf;     r21(i+1,i)=-a21*t/hf/hf-b21*t/hf/2;         r21(i,i+1)=-a21*t/hf/hf+b21*t/hf/2; end   r21(N,N)=1+2*a21*t/hf/hf; r21(N,N)=r21(N,N)+(-a21*t/hf/hf+b21*t/hf/2);   r22=r21; r23=r21;   %------matrix r24,25,26--------------------------------------------------- r24=zeros(N,N); for i=1:N-1,        r24(i,i)=1+b24*t/hf;    218      r24(i+1,i)=-b24*t/hf;       r24(i,i+1)=0;   end     r24(N,N)=1+b24*t/hf;     r25=r24;   r26=r24;     %------------------------------------------------------------------------- u21=ones(N,1)*SNOf;   %NO, freeboard, solids phase u22=ones(N,1)*SHCf;   %HC, freeboard, solids phase u23=ones(N,1)*SO2f;   %O2, freeboard, solids phase u24=ones(N,1)*CNOf;   %NO, freeboard, gas phase u25=ones(N,1)*CHCf;   %HC, freeboard, gas phase u26=ones(N,1)*CO2f;   %O2, freeboard, gas phase   uu21=zeros(N,1);      %NO, freeboard, solids phase uu22=zeros(N,1);      %HC, freeboard, solids phase uu23=zeros(N,1);      %O2, freeboard, solids phase uu24=zeros(N,1);      %NO, freeboard, gas phase uu25=zeros(N,1);      %HC, freeboard, gas phase uu26=zeros(N,1);      %O2, freeboard,gas phase   ff21=zeros(N,1);      %NO, freeboard, solids phase ff22=zeros(N,1);      %HC, freeboard, solids phase ff23=zeros(N,1);      %O2, freeboard, solids phase ff24=zeros(N,1);      %NO, freeboard, gas phase ff25=zeros(N,1);      %HC, freeboard, gas phase ff26=zeros(N,1);      %O2, freeboard,gas phase   %-------------calculation------------------------------------------------- XNOe=0; ERROR=3e4;  % error, inital      while ERROR>1e-6,          for i=1:N,                   CsNO=CssNO(u24(i,1), u26(i,1),T);          CsO =CssO (u26(i,1),T);           Reac=Reaction(u21(i,1), u22(i,1), u23(i,1), T)*(1-epsF(i,2));           RSNO2=Reac(1);          RHC=Reac(2);          RSO=Reac(3);            ff21(i,1)= -f1c*KNOKNOea*(u21(i,1)-CsNO)  +RSNO2; %NO, solids phase         ff22(i,1)= -f3c*KNOKHC*(u22(i,1)-u25(i,1))+RHC;   %HC, solids phase         ff23(i,1)= -f5c*KNOKO2a*(2*u23(i,1)-CsO)  +RSO;   %O2, solids phase         ff24(i,1)=  f1c*KNOKNOea*(u21(i,1)-CsNO);         %NO, gas phase         ff25(i,1)=  f3c*KNOKHC*(u22(i,1)-u25(i,1));       %HC gas phase        219          ff26(i,1)=  f5c*KNOKO2a*(u23(i,1)-CsO/2);         %O2, gas phase       end        ff21(1,1)=ff21(1,1)+(a21/hf/hf+b21/hf/2)*SNOf;      ff22(1,1)=ff22(1,1)+(a22/hf/hf+b22/hf/2)*SHCf;      ff23(1,1)=ff23(1,1)+(a23/hf/hf+b23/hf/2)*SO2f;        ff24(1,1)=ff24(1,1)+(b24/hf)*CNOf;       ff25(1,1)=ff25(1,1)+(b25/hf)*CHCf;       ff26(1,1)=ff26(1,1)+(b26/hf)*CO2f;                 ff21  = u21+t*ff21;       ff22  = u22+t*ff22;        ff23  = u23+t*ff23;       ff24  = u24+t*ff24;       ff25  = u25+t*ff25;        ff26  = u26+t*ff26;            uu21=chase(r21, ff21);      uu22=chase(r22, ff22);      uu23=chase(r23, ff23);      uu24=chase(r24, ff24);      uu25=chase(r25, ff25);      uu26=chase(r26, ff26);        u21=uu21;      u22=uu22;      u23=uu23;       u24=uu24;       u25=uu25;       u26=uu26;         for i=1:N;                if u21(i,1)<0,            u21(i,1)=0;         end         if u22(i,1)<0,            u22(i,1)=0;         end         if u23(i,1)<0,            u23(i,1)=0;         end         if u24(i,1)<0,            u24(i,1)=0;         end        if u25(i,1)<0,            u25(i,1)=0;         end        if u26(i,1)<0,            u26(i,1)=0; 220         end       end   %---------------calculation monitor---------------------------------------     k=k+1;          if rem(k,20000)==0,         XNO=100*(mNOa*Ua*Aa+mNOd*Ud*Ad-u24(N,1)*A*Ugf)/(mNO*Aa*Ua0);         XHC=100*(mHCa*Ua*Aa+mHCd*Ud*Ad-u25(N,1)*A*Ugf)/(mHC*Ad*Ud0);         number=number         ERROR=abs(XNOe-XNO)/t         XNOe=XNO;         Xoutf=[XNO XHC]     end   end   %--------------write data file-------------------------------------------- fid = fopen ('complete.txt', 'at'); fprintf (fid, '%10.2f', Xoutf); fprintf (fid, '%10s\n','  '); fclose all;       %------------------------------------------------------------------------- end   %number   %-----------end of main function------------------------------------------   %------------------------------------------------------------------------- %--------------functions-------------------------------------------------- %------------function: equation calculation------------------------------- function x = chase (a,b) M=length(b); x=zeros(M,1); for i=2:M;     l=a(i,i-1)/a(i-1,i-1);     b(i,1)=b(i,1)-l*b(i-1,1);     a(i,i-1)=0;     a(i,i)=a(i,i)-l*a(i-1,i); end x(M,1)=b(M,1)/a(M,M); for i=1:M-1;     x(M-i,1)=(b(M-i,1)-a(M-i,M-i+1)*x(M-i+1,1))/a(M-i,M-i); end %-------------------------------------------------------------------------    %--------------diffusivity calculation------------------------------------  function y = Di(T,P, CNOin, CHCin, CO2in) MNO=30; vNO=30.419; 221  MO2=32; vO2=16.6; MHC=44; vHC=65.34; MN2=14; vN2=17.9; DNOHC=Dij(T,P,MNO,MHC,vNO,vHC); DNON2=Dij(T,P,MNO,MN2,vNO,vN2); DNOO2=Dij(T,P,MNO,MN2,vNO,vO2); DHCN2=Dij(T,P,MHC,MN2,vHC,vN2); DHCO2=Dij(T,P,MHC,MO2,vHC,vO2); DO2N2=Dij(T,P,MO2,MN2,vO2,vN2); CN2in=1-CNOin-CHCin-CO2in; y=zeros(3); y(1)=(1-CNOin)/(CHCin/DNOHC+CN2in/DNON2+CO2in/DNOO2); y(2)=(1-CHCin)/(CNOin/DNOHC+CN2in/DHCN2+CO2in/DHCO2); y(3)=(1-CO2in)/(CNOin/DNOO2+CHCin/DHCO2+CN2in/DO2N2); %-------------------------------------------------------------------------   %------------for diffusivity calculation---------------------------------- function y = Dij(T,P,Mi,Mj,vi,vj) y=0.1013*T^1.75*(1/Mi+1/Mj)^0.5/P/(vi^(1/3)+vj^(1/3))^2; %-------------------------------------------------------------------------   %----------NOx adsorption capacity---------------------------------------- function y = CssNO (CNO, CO2, Te) kNO2=-2.198*Te+1796.3; nNO2=0.5539; nO2=0.7356;   CSNO2=kNO2*(CO2^nO2)*(CNO^nNO2); y=CSNO2; %-------------------------------------------------------------------------   %-----------O2 adsorption capacity---------------------------------------- function y = CssO (CO2, Te) kO2=-0.0206*Te+19.712; nO2=0.7356;   CSO=kO2*(CO2^nO2); y=2*CSO; %-------------------------------------------------------------------------   %--------------reaction rate---------------------------------------------- function y = Reaction(CSNO2, CHC, CSO, Te)   %T=350 K=[  0.80     0.7     0.012     0.1     0.0    2.50     0.0155];   m1=K(1); m2=K(2); m3=K(3); m4=K(4); 222  m5=K(5); k3=K(6); k4=K(7);   r3=k3*CHC^m1*CSO^m2;    r4=k4*(CSNO2^m3)*(CHC^m4)*(CSO^m5);   rNO=-2*r4; rHC=-r3-r4;  rSO=-9*r3-5*r4;   y=zeros(3,1); y(1)= rNO; y(2)= rHC; y(3)= rSO; %-------------------------------------------------------------------------   %-------freeboard--------------------------------------------------------- function Feps = freeb (F0, U)  %F0=5;   assumed, kg/m2.s epsfree=1; Ug=U/epsfree; rou=0.8; dp=155e-6; mu=3.1e-5; roup=1700;   Us0=20*Ug; Hf=0.8; NH=500; NU=500; h=Hf/NH; Fi=zeros(NH,4); %1, height; 2, Fi0; 3,velocity; 4, solids hold up,kg/m3   Fi(:,1)=linspace(0,Hf,NH); Fi(:,2)=F0*exp(-6.4*Fi(:,1));   Ne=1; for nU=2:NU,     y=Us0*nU/NU;       dy=0;     i=1;       while y>0,         if y==Ug;             y=y+0.01;         end         NRe=rou*dp*abs(y-Ug)/mu;         CDs=24/NRe*(1+0.15*NRe^0.687)+0.42/(1+4.25e4*NRe^1.16);         CD=CDs*epsfree^(-4.7); 223          dy=-(roup-rou)*9.8/roup/y-0.75*CD*rou*(y-Ug)*abs(y-Ug)/roup/dp/y;         if dy>0,             dy=-0.001;         end         y=y+dy*h;              if y>0.00001,             Fi(i,3)=y;         end     end          i=i+1;     Fi0=Fi(Ne,2)-Fi(i-1,2);  % current flux          for j=1:i-2,         if Fi(j,3)>0,             Fi(j,4)=Fi(j,4)+Fi0/Fi(j,3);         end     end          Ne=i-1;   %number of ex point      end   for i=1:NH,     Fi(i,4)=Fi(i,4)+Fi(i,2)/(0.8-Ug);  %downflow particles end   Feps=zeros(20,2); for i=0:19;     Feps(i+1,1)=mean(Fi(i*25+1:i*25+25,1));     Feps(i+1,2)=1-mean(Fi(i*25+1:i*25+25,4))/roup; end %-------------------------------------------------------------------------   

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