Chemical Reaction Engineering Module User’s Guide Chemical Reaction Engineering Module User’s Guide © 1998–2018 COMSOL Protected by patents listed on www.comsol.com/patents, and U.S. Patents 7,519,518; 7,596,474; 7,623,991; 8,219,373; 8,457,932; 8,954,302; 9,098,106; 9,146,652; 9,323,503; 9,372,673; and 9,454,625. Patents pending. This Documentation and the Programs described herein are furnished under the COMSOL Software License Agreement (www.comsol.com/comsol-license-agreement) and may be used or copied only under the terms of the license agreement. COMSOL, the COMSOL logo, COMSOL Multiphysics, COMSOL Desktop, COMSOL Server, and LiveLink are either registered trademarks or trademarks of COMSOL AB. All other trademarks are the property of their respective owners, and COMSOL AB and its subsidiaries and products are not affiliated with, endorsed by, sponsored by, or supported by those trademark owners. For a list of such trademark owners, see www.comsol.com/trademarks. 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Other useful links include: • Support Center: www.comsol.com/support • Product Download: www.comsol.com/product-download • Product Updates: www.comsol.com/support/updates • COMSOL Blog: www.comsol.com/blogs • Discussion Forum: www.comsol.com/community • Events: www.comsol.com/events • COMSOL Video Gallery: www.comsol.com/video • Support Knowledge Base: www.comsol.com/support/knowledgebase Part number: CM021601 Contents Chapter 1: User’s Guide Introduction About the Chemical Reaction Engineering Module 14 The Scope of the Chemical Reaction Engineering Module . 14 The Chemical Reaction Engineering Module Physics Interface Guide . 15 The Material Database. 19 Common Physics Interface and Feature Settings and Nodes . 19 Where Do I Access the Documentation and Application Libraries? . 19 Overview of the User’s Guide 23 Chapter 2: The Chemistry and Reaction Engineering Interfaces Overview of the Reaction Engineering and Chemistry interfaces 26 Using the Reaction Node. 27 Using the Species Node . 30 Using the Equation View Node - Reactions and Species . 32 Theory for the Reaction Engineering and Chemistry Interfaces 34 Reaction Kinetics and Rate Expressions . 34 The Equilibrium Constant . 35 Handling of Equilibrium Reactions . 39 Reactor Types in the Reaction Engineering Interface . 42 Transport Properties . 49 CHEMKIN Data and NASA Polynomials . 53 Working with Predefined Expressions . 54 References for the Reaction Engineering Interface . 56 CONTENTS | 3 The Reaction Engineering Interface 58 Features Nodes Available for the Reaction Engineering Interface . 66 Initial Values . 66 Reaction . 67 Species . 71 Reversible Reaction Group . 75 Equilibrium Reaction Group. 77 Species Group . 78 Additional Source . 79 Reaction Thermodynamics . 80 Species Activity . 80 Species Thermodynamics. 80 Feed Inlet. 81 Generate Space-Dependent Model . 82 Parameter Estimation . 90 Experiment . 91 The Chemistry Interface 94 Feature Nodes Available for the Chemistry Interface . 97 Reaction . 98 Species . 102 Reversible Reaction Group . 105 Equilibrium Reaction Group. 106 Species Group . 108 Reaction Thermodynamics . 108 Species Activity . 109 Species Thermodynamics. 109 Study Steps for the Reaction Engineering Interface 110 Reactor Types and Solver Study Steps . 110 Solver Study Steps for Parameter Estimation . 110 Chapter 3: Chemical Species Transport Interfaces Overview of Chemical Species Transport Interfaces 115 Available Physics Interfaces . 115 4 | CONTENTS Coupling to Other Physics Interfaces . 117 Adding a Chemical Species Transport Interface and Specifying the Number of Species. 117 Theory for the Transport of Diluted Species Interface 120 Mass Balance Equation . 121 Equilibrium Reaction Theory . 122 Convective Term Formulation. 124 Solving a Diffusion Equation Only . 124 Mass Sources for Species Transport . 125 Adding Transport Through Migration . 127 Supporting Electrolytes . 128 Crosswind Diffusion . 129 Danckwerts Inflow Boundary Condition . 130 Mass Balance Equation for Transport of Diluted Species in Porous Media . 131 Convection in Porous Media . 132 Diffusion in Porous Media . 134 Dispersion . 135 Adsorption . 137 Reactions. 138 Mass Transport in Fractures . 139 Theory for the Reactive Pellet Bed . 140 References . 148 Theory for the Transport of Concentrated Species Interface 150 Multicomponent Mass Transport . 150 Multicomponent Gas Diffusion: Maxwell-Stefan Description . 151 Multicomponent Diffusivities . 153 Multicomponent Diffusion: Mixture-Averaged Approximation . 155 Multispecies Diffusion: Fick’s Law Approximation . 157 Multicomponent Thermal Diffusion . 158 Regularization of Reaction Rate Expression . 158 References for the Transport of Concentrated Species Interface. 159 CONTENTS | 5 Theory for the Electrophoretic Transport Interface 160 Theory for the Surface Reactions Interface 166 Governing Equations for the Surface Concentrations . 166 Governing Equations for the Bulk Concentrations . 167 ODE Formulations for Surface Concentrations . 169 Surface Reaction Equations on Deforming Geometries . 170 Reference for the Surface Reactions Interface . 171 Theory for the Nernst-Planck Equations Interface 172 Governing Equations for the Nernst-Planck Formulation . 172 Convective Term Formulation. 174 Theory for the Reacting Laminar Flow Interface 175 Pseudo Time Stepping for Mass Transport . 175 The Stefan Velocity . 175 The Chemical Reaction Rate . 177 The Transport of Diluted Species Interface 179 The Transport of Diluted Species in Porous Media Interface . 183 Domain, Boundary, and Pair Nodes for the Transport of Diluted Species Interface. 184 Transport Properties . 186 Turbulent Mixing . 188 Initial Values . 189 Mass-Based Concentrations. 189 Reactions. 189 No Flux . 191 Inflow . 191 Outflow . 192 Concentration . 192 Flux . 192 Symmetry . 193 Flux Discontinuity . 193 Partition Condition . 194 Periodic Condition . 195 Line Mass Source. 195 Point Mass Source . 196 6 | CONTENTS Open Boundary . 197 Thin Diffusion Barrier . 197 Thin Impermeable Barrier . 197 Equilibrium Reaction . 198 Surface Reactions . 199 Surface Equilibrium Reaction . 199 Fast Irreversible Surface Reaction . 200 Porous Electrode Coupling . 200 Reaction Coefficients . 201 Electrode Surface Coupling . 201 Porous Media Transport Properties. 202 Adsorption . 204 Partially Saturated Porous Media . 205 Volatilization . 207 Reactive Pellet Bed . 208 Reactions. 211 Species Source. 212 Hygroscopic Swelling . 213 Fracture . 213 The Transport of Diluted Species in Fractures Interface 215 Boundary, Edge, Point, and Pair Nodes for the Transport of Diluted Species in Fractures Interface . 217 Adsorption . 218 Concentration . 219 Flux . 219 Fracture . 219 Inflow . 220 No Flux . 221 Outflow . 221 Reactions. 221 Species Source. 222 The Transport of Concentrated Species Interface 223 Domain, Boundary, and Pair Nodes for the Transport of Concentrated Species Interface . 229 Transport Properties . 230 Porous Media Transport Properties. 234 CONTENTS | 7 Electrode Surface Coupling . 237 Turbulent Mixing . 238 Reaction . 239 Reaction Sources. 240 Initial Values . 241 Mass Fraction . 242 Flux . 242 Inflow . 243 No Flux . 244 Outflow . ..