INTRODUCTION TO CATALYTIC COMBUSTION R.E. Hayes Professor of Chemical Engineering Department of Chemical and Materials Engineering University of Alberta, Canada and S.T. Kolaczkowski Professor of Chemical Engineering Department of Chemical Engineering University of Bath, United Kingdom GORDON AND BREACH SCIENCE PUBLISHERS Australia Canada China France Germany India Japan Luxembourg Malaysia The Netherlands Russia Singapore Switzerland Thailand United Kingdom
Table of Contents Preface Acknowledgements Nomenclature xvii xix xxi CHAPTER 1. Introduction 1 1.1 The basics: Terminology and conservation equations 4 1.1.1 Commonly used terms 4 1.1.2 Classification of reactors 12 1.1.3 Momentum balances 14 1.1.4 Energy balances 15 1.1.5 Material balances 16 1.1.6 The coupling of material, energy and momentum balances 16 1.2 Catalytic combustion and transport processes 17 1.3 Catalytic combustion chemistry 20 1.4 Formation of NO x 23 1.5 Catalyst support systems 25 1.5.1 Pellets in a packed or fluidized bed 26 1.5.2 Multichannel monoliths 30 1.5.3 Parallel plates 38 1.5.4 Fibre pads and gauzes 38 1.5.5 Sintered metals 39 1.6 Palladium based catalysts for methane combustion 40 1.6.1 Influence of temperature on chemical composition of the catalyst 41 1.6.2 Catalyst dispersion 44 1.6.3 Catalyst poisoning and fouling 44 1.6.4 Catalyst/support interactions 45 1.6.5 Catalyst promoters 46 1.6.6 Additives to the catalyst support 46 1.6.7 Preparation of palladium catalyst 46 1.7 Example applications of catalytic combustion 47 1.7.1 Examples of primary combustion processes 48 1.7.1.1 Stationary gas turbines 50 1.7.1.2 Radiant heaters 58 1.7.1.3 Process heating 62 1.7.2 Examples of secondary combustion processes 65 1.7.2.1 Catalytic converters for gasoline (petrol) engines 67
X CONTENTS 1.7.2.2 Catalytic converters/traps for diesel engines 75 1.7.2.3 Catalytic incineration of organic emissions 78 1.8 Catalytic monoliths in NOx reduction reactors 82 1.9 System design 85 1.10 Summary 87 Introductory Note to Chapters 2 to 6 89 Additional Reading on Catalytic Combustion 89 Additional Reading on Catalytic Converters 90 References 90 CHAPTER 2. Thermodynamics, Kinetics and Transport Phenomena 97 2.1 Thermodynamics 99 2.1.1 Open and closed systems 99 2.1.2 The thermodynamic state 100 2.1.3 Equations of state 100 2.1.3.1 The ideal gas law 101 2.1.3.2 Non-ideal behaviour 101 2.1.4 Multicomponent mixtures 102 2.1.5 Energy balances in open and closed systems 106 2.1.6 Enthalpy changes in systems 112 2.1.6.1 Enthalpy change resulting from temperature change the heat capacity 112 2.1.6.2 Enthalpy change with pressure 115 2.1.6.3 Enthalpy change due to composition change the heat of reaction 116 2.1.6.4 The first law for an open steady state reacting system 121 2.1.6.5 Heat of combustion 125 2.1.7 Chemical reaction equilibrium the equilibrium constant 126 2.1.8 Catalyst decomposition pressure 132 2.2 Kinetics 134 2.2.1 Rate expressions and mechanisms 135 2.2.2 Homogeneous combustion kinetics 138 2.2.2.1 Homogeneous combustion of carbon monoxide 139 2.2.2.2 Homogeneous combustion of hydrocarbons 140 2.2.3 Catalytic combustion kinetics 143 2.2.3.1 Adsorption 146 2.2.3.2 Langmuir Hinshelwood Hougen Watson reaction models 152 2.2.3.3 Rate models for catalytic oxidation reactions 165 2.2.3.4 Comments on the use of rate equations 176 2.2.3.5 Final word on catalytic rate models 177
CONTENTS XI 2.3 Transport phenomena 178 2.3.1 Newton's law of viscosity 178 2.3.2 Flow regimes 180 2.3.3 Flow in ducts 181 2.3.3.1 The equation of continuity 182 2.3.3.2 The friction factor for flow in a duct 184 2.3.3.3 Flow in circular ducts 185 2.3.3.4 Flow in rectangular ducts 195 2.3.3.5 Flow in triangular ducts 196 2.3.3.6 Other shapes 197 2.3.4 Flow in porous media 197 2.3.5 Fourier's law of conduction and the energy equation 204 2.3.5.1 Conduction in one dimensional systems 204 2.3.5.2 Multidimensional systems 212 2.3.5.3 Conduction and convection in fluid systems with and without reaction 213 2.3.5.4 Conduction in porous media 216 2.3.6 Boundary layers and the heat transfer coefficient 216 2.3.6.1 Boundary layer development over a heated flat plate 217 2.3.6.2 Boundary layer development in the entrance of a circular duct 220 2.3.7 Fick's law of diffusion and the species balance equation 226 2.3.8 Boundary layer development and the mass transfer coefficient 236 2.3.9 The mass and heat transfer analogy 239 2.3.10 External heat and mass transfer resistance in catalysis 239 2.3.11 Diffusion and reaction in porous catalysts 244 2.3.11.1 The effective diffusivity 244 2.3.11.2 The effectiveness factor 250 2.3.11.3 Non-isothermal effectiveness factors 260 2.3.11.4 Effectiveness factors with complex kinetics 262 2.3.11.5 Diffusion and reaction in complex catalyst geometries 263 2.3.12 Combined internal and external mass transfer resistance 263 2.3.13 Heat transfer by radiation 269 Further Reading 275 References 276 CHAPTER 3. Modelling of Catalytic Combustion Reactors 281 3.1 Basic modelling concepts 282 3.1.1 Types of equations 282
хп CONTENTS 3.1.1.1 Constants and variables 282 3.1.1.2 Linear algebraic equations 282 3.1.1.3 Non4inear algebraic equations 283 3.1.1.4 Differential equations 283 3.1.2 Types of models 284 3.1.3 Choosing the model 285 3.1.4 Model validation 286 3.1.5 Overview/summary of the modelling process 287 3.2 Commercial software packages 288 3.3 Modelling of a single monolith channel 289 3.3.1 Basic model selection criteria 289 3.3.2 Model dimensionality 291 3.3.3 One dimensional steady state plug flow model laminar/turbulent flow 294 3.3.3.1 ID pseudo4iomogeneous plug flow model steady state 295 3.3.3.2 ID heterogeneous plug flow model steady state 300 3.3.3.3 Heat and mass transfer coefficients 313 3.3.4 One dimensional steady state dispersion model laminar/turbulent flow 331 3.3.5 Transient one dimensional models laminar/turbulent flow 338 3.3.6 Two dimensional model in cylindrical coordinates laminar flow 342 3.3.6.1 Momentum balance equations 342 3.3.6.2 Mass balance equation 343 3.3.6.3 The energy balance equation 346 3.3.7 Radiation modelling in a monolith channel 348 3.3.7.1 Integral approach to internal radiation transfer 353 3.3.7.2 Network of finite surfaces method for modelling internal radiation exchange 357 3.3.7.3 Estimating radiation loss from a monolith reactor 368 3.4 Modelling diffusion in the washcoat steady state 370 3.4.1 ID approximation steady state 372 3.4.2 Equations for solution in 2D steady state 375 3.4.3 Evaluating the effectiveness factor in a monolith reactor simulation 376 3.4.4 Effectiveness factors for washcoats with multiple reactions steady state 382 3.4.5 Transient diffusion reaction problems 382 3.5 Multiple channel honeycomb reactor models 383
CONTENTS хш 3.5.1 Continuum model 383 3.5.2 Discrete method with honeycomb reconfiguration 388 Packed bed reactor models 389 3.6.1 One dimensional plug flow model of a packed bed reactor 391 3.6.1.1 ID pseudo-homogeneous PFR model for an adiabatic packed bed steady state 391 3.6.1.2 ID heterogeneous PFR model for an adiabatic packed bed steady state 394 3.6.1.3 ID PFR models for a non-adiabatic packed bed steady state 399 3.6.2 One dimensional dispersion model for a packed bed reactor 402 3.6.2.1 Pseudo-homogeneous ID axial dispersion model for a packed bed steady state 403 3.6.2.2 Heterogeneous ID axial dispersion model for a packed bed steady state 404 3.6.3 Two dimensional model of a packed bed reactor 406 3.6.3.1 Pseudo-homogeneous 2D model for a packed bed steady state 406 3.6.3.2 Heterogeneous 2D model for a packed bed steady state 410 3.6.4 Transport properties in packed beds 413 3.6.4.1 Fluid/solid mass and heat transfer coefficients in packed beds 413 3.6.4.2 Dispersion coefficients in packed beds 415 3.6.4.3 Thermal conductivities in packed beds 417 3.6.4.4 Bed to wall heat transfer coefficients in packed beds 420 3.6.5 Effectiveness factors in packed beds 422 Consolidated porous media models 423 Numerical methods 423 3.8.1 Methods for initial value problems 424 3.8.2 Introduction to boundary value problems 427 3.8.3 The basis of the finite difference method 428 3.8.4 Finite difference solution of a one dimensional dispersion model 433 3.8.5 The basis of the finite element method 437 3.8.5.1 Finite element discretization 437 3.8.5.2 2D discretization of a monolith reactor channel 438 3.8.5.3 2D discretization of the washcoat 440 3.8.5.4 Discretization error 441 3.8.5.5 Interpolation polynomials 442
XIV CONTENTS 3.8.5.6 The mathematical basis of the Galerkin finite element method 443 3.8.5.7 Integrating the weak form of the differential equation: The reference element 445 3.8.5.8 The matrix form of the elementary equations, assembling the global matrix 450 3.8.6 Finite element solution of a diffusion/reaction problem 450 3.9 Solution algorithms 459 Further Reading 464 References 464 CHAPTER 4. Homogeneous Gas Phase Reactions 469 4.1 General combustion characteristics 470 4.1.1 Combustion chemistry 471 4.1.2 Auto-ignition 479 4.1.3 Burning velocity 481 4.2 Combustion models 482 4.2.1 Diffusion flame (laminar/turbulent) model 482 4.2.2 Premixed flame model 484 4.2.3 Shock tube model 484 4.2.4 Well stirred reactor model 485 4.2.5 Plug flow model 492 4.3 Structure of rigorous schemes 495 4.4 Inclusion of catalytic/surface terms 498 4.5 Flame stabilization 499 4.6 Summary 501 References 502 CHAPTER 5. Experimental Studies 505 5.1 Pre-ageing of combustion catalysts 507 5.2 Acquisition and analysis of catalytic rate data 507 5.2.1 Laboratory reactors 508 5.2.1.1 Tubular reactor 509 5.2.1.2 Temperature measurement 515 5.2.1.3 Stirred tank/spinning basket/carberry reactor 517 5.2.1.4 Internal recycle stirred tank/berty reactor 518 5.2.1.5 Recycle tubular reactor 518 5.2.2 Error estimation 521 5.2.2.1 Errors evaluated using mathematical analysis 521 5.2.2.2 Errors evaluated using sensitivity analysis 525 5.2.3 Finding the kinetic expression 525
CONTENTS xv 5.2.4 Inter- and intraphase mass and heat transfer 536 5.3 Performance of pilot-scale reactor experiments 546 5.3.1 Supply of air 546 5.3.2 Preheating of inlet stream 547 5.3.3 Fuel and air mixing 548 5.3.4 Temperature measurement 549 5.3.5 Flow measurement 550 5.3.6 Gas analysis 550 5.3.7 Data acquisition 553 5.3.8 Pressure drop measurement 553 5.3.8.1 Monoliths 553 5.3.8.2 Packed beds 559 5.4 Acquisition of transport property data 559 5.5 Measurements to characterize the catalyst system 561 5.5.1 The recipe 561 5.5.2 The support system 561 5.5.3 The catalyst coated/impregnated system 562 5.5.3.1 Pore size, volume and distribution 563 5.5.3.2 Hydraulic diameter of monolith 565 5.5.3.3 Transport distance in catalyst phase 565 5.5.3.4 Measurement of effective diffusion coefficients 568 5.5.3.5 Gravimetric analysis 580 5.5.3.6 Catalyst distribution in the support 584 5.5.4 Catalyst loss from the reactor 584 Further Reading on Catalyst Preparation 586 References 586 CHAPTER 6. Combustion Applications: Examples of Modelling Studies 589 6.1 Modelling a single monolith channel in 2D 590 6.1.1 Investigating the Nusselt and Sherwood numbers 590 6.1.2 Mass transfer limitation and the 'light-off point 597 6.1.3 Oxidation of CO with LHHW kinetics Multiple steady states 605 6.2 Radiation losses from a monolith channel 609 6.3 Diffusion in a monolith washcoat use of diffusion barrier to reduce entrance temperature gradients 613 6.4 Understanding and interpreting literature results 617 6.5 Influence of intrusive measuring devices 628 6.6 Catalytic radiant heaters 633 6.7 Catalytic incineration of organic emissions 643 6.8 Summary 647 References 648
XVI CONTENTS Appendix A Appendix В Appendix С Appendix D Appendix E Appendix F Useful conversions Physical properties of ceramic and metal supports Physical properties of gases Summary of dimensionless groups Useful mathematical transformations A note on symbols 651 654 660 661 670 671 INDEX 675