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Library of Congress Cataloging-in-Publication Data:
Names: Farrauto, Robert J., 1941- author. | Dorazio, Lucas, author. | Bartholomew, C. H., author.
Title: Introduction to catalysis and industrial catalytic processes / Robert J. Farrauto, Lucas Dorazio, C. H. Bartholomew.
Description: Hoboken : John Wiley & Sons, Inc., 2016. | Includes index. Identifiers: LCCN 2015042209 (print) | LCCN 2015044585 (ebook) | ISBN
9781118454602 (cloth) | ISBN 9781119089155 (pdf) | ISBN 9781119101673 (epub) Subjects: LCSH: Catalysis.
Classification: LCC QD505 .F37 2016 (print) | LCC QD505 (ebook) | DDC 660/.2995–dc23
LC record available at http://lccn.loc.gov/2015042209
To my wife Olga (Olechka) who has been a partner, friend, and critic over the precious years we have been together. She has provided love, understanding, focus, and a new vision to life. I thank my loving daughters, Jill Marie and Maryellen, and their husbands Glenn and Tom. I am fortunate to have inspiring grandchildren Nicky, Matt, Kevin, Jillian, Owen, and Brendan and stepdaughters Elena and Marina. I want to acknowledge my brother John (wife Noella) and sister Marianna (husband Ron) who have supported me emotionally through all of our years together. I am forever grateful to my parents who raised me as a proud Italian-American with a desire to help others.
To my wife Cara, whose encouragement and support helped complete this project, and to my young children Lauren and Zach for their support and genuine interest in my career.
To my loving wife, friend, and critic, Karen, of over 49 years, who has supported me in all good things and forgiven my faults and mistakes; my 5 children and 10 grandchildren who have brought me mostly joy, been a constant source of fun and entertainment, and have given me understanding, support, love, excitement, inspiration, and challenges that have led to my growth; my loving, supportive brothers and sisters (all 7); and my dad and mom who taught me to love learning, life, and the Christian way. I especially dedicate this work (an offspring of our earlier book) to my son Charles who died unexpectedly on September 25, 2014 and who greatly touched and brightened the lives of his family, friends, and coworkers.
“Simplicity is the ultimate sophistication.”
THESE WORDS of Leonardo da Vinci were recently quoted by Steve Jobs of Apple in the book by Walter Isaacson. Simplicity was the first guiding principle in the preparation of this introductory book. The second guiding principle was to share our considerable industrial and academic experience in working with and teaching about catalysis fundamentals and industrial catalytic processes.
All of us authors have worked in industry and academia, two of us as technical consultants. Dr. Farrauto was affiliated with BASF (formerly Engelhard), Iselin, New Jersey for 37 years having worked in environmental, chemical, petroleum, and alternative energy fields and is now Professor of Practice in the Earth and Environmental Engineering Department at Columbia University in the City of New York. Dr. Dorazio, a research engineer at BASF (New Jersey), has worked in catalysis research and in scale-up of catalysts for the chemical, petroleum, and environmental fields. He is also Adjunct Professor in the Chemical Engineering Department at New Jersey Institute of Technology (NJIT). Dr. Bartholomew, Professor Emeritus in the Chemical Engineering Department at Brigham Young University, Provo, Utah, worked for a year at Corning Glass (with Dr. Farrauto) in auto emissions control after which he taught and conducted research and consulting for 41 years in catalyst design/deactivation and reactor/process design for environmental cleanup and synthetic fuel production. He continues to be active in writing, teaching short courses, and consulting. All of us have been widely engaged in various degrees of teaching industrial catalysis at the undergraduate and graduate levels. Bartholomew and Farrauto have coauthored the widely used text and reference book entitled “Fundamentals of Industrial Catalytic Processes,” a more advanced, in-depth version of the topics in the current book and a likely sequel to this book.
Industrial catalytic applications are seldom taught in undergraduate chemistry and chemical engineering programs, a surprising fact, given the large number of commercial processes that utilize catalysis. Thus, we accepted the challenge of writing a book that would introduce senior level undergraduates and new graduate students to this exciting field of catalytic processes, which is fundamental to chemical engineering and chemistry as practiced in industry. The need for a thorough understanding of fundamental principles of chemistry and catalysis is given. The transition of this knowledge to their commercial applications is our objective, especially for the many chemistry and chemical engineering students who spend much of their careers working in industry with catalytic processes. We also include the many professionals of varying disciplines who suddenly find themselves with a new assignment of working on a catalytic process without previous training in the basics of catalysis and catalytic processes.
Our goal is to explain the fundamental principles of catalysis and their applications of catalysis in a simple, introductory textbook that excites those contemplating an industrial career in chemical, petroleum, alternative energy, and environmental fields in which catalytic processes play a dominant role. The book focuses on non-proprietary, basic chemistries and descriptions of important, currently used catalysts and catalytic processes. Considerable practical examples, recommendations, and cautions located throughout the book are based on authors’ experience gleaned from teaching, research, commercial development, and consulting, including feedback from many students and associates. Suggested readings (reviews, books, and journal articles) are included at the end of each chapter to encourage interested readers to deepen their knowledge of these topics. Process diagrams have been simplified to provide an overview of principal process units (e.g., reactors and separation units) and important process steps, including reactant and product streams. Nevertheless, it should be recognized that commercial engineering process flow sheets include many other details and specifications, for example, piping, pumps, valves, heat exchangers, and other process equipment needed to operate and control the plant, including special equipment for plant start-up, catalyst pretreatment, purges, safety, regeneration, and so on.
Chapters 1–5 introduce the reader to basic principles of catalysis, including reaction kinetics, simple reactor design concepts, and catalyst preparation, characterization, and deactivation. Accompanying each chapter are questions and suggested readings. Chapters 6–15 describe by category applications and practice in the industry, including process chemistry, conditions, catalyst design, process design, and catalyst deactivation problems for each catalytic process. Chapter 6 describes hydrogen and syngas generation processes for different end applications. Processes for the synthesis of ammonia, methanol, and hydrocarbon liquids (Fischer–Tropsch process) are presented in Chapter 7. Processes for selective catalytic oxidation to (a) commodity chemicals, including nitric, cyanic, and sulfuric acids, formaldehyde, and ethylene oxide, and (b) specialized products such as acrylic acid, maleic anhydride, and acrylonitrile are presented in Chapter 8. Catalytic processes for hydrogenation of vegetable oils, olefins, and functional groups for highly specialized products are presented in Chapter 9. Catalytic processes in refining of petroleum to fuels are presented in Chapter 10. Selected commercial processes utilizing (a) homogeneous catalysts, (b) commercial enzymes, and (c) polymerization catalysts are described in Chapter 11. Chapters 12, 13, and 14 summarize features of important processes for catalysts used in environmental control of gaseous emissions from (a) stationary sources (e.g., power plants) and mobile sources, including (b) gasoline- and (c) diesel-fired vehicles. The final chapter 15 gives a brief summary of (1) catalytic processes for production of bio diesel and ethanol fuels from edible biomass which will ultimately find application to production of similar fuels from non-edible cellulosic biomass and (2) catalyst technology for the emerging hydrogen economy with emphasis on fuel cell technology.
New York, New York
Iselin, New Jersey
Provo, Utah
22 November 2015
Robert J. Farrauto
Lucas Dorazio
Calvin H. Bartholomew
Drs. Farrauto and Dorazio acknowledge BASF (and Engelhard) for their strong leadership in the field of catalysis. We also acknowledge our students at Columbia University and NJIT, respectively, who have provided course and teaching evaluations that have been invaluable in showing us the need for a simple approach to catalysis and industrial processes.
Dr. Bartholomew is grateful for the financial support of his research, teaching, and writing endeavors by Brigham Young University and of his research by DOE, NSF, GRI, and many companies. He wishes to acknowledge the opportunity to work with distinguished colleagues and friends on the Faculty (especially in the Chemical Engineering Department and Catalysis Laboratory) and some 200+ bright, creative, hardworking graduate and undergraduate students and postdoctoral fellows who worked with him under his direction at BYU. He has also enjoyed the stimulation of teaching more than 750 company professionals during dozens of short courses on catalysis, deactivation, and Fischer–Tropsch synthesis. He wishes to acknowledge the collaboration with and friendship of Dr. Robert Farrauto over the past 42 years, first at Corning Glass, then on a landmark paper, and now two books addressing industrial catalytic processes; he is especially grateful for Bob’s patience with him during the long process of preparing the first and second editions of Fundamentals of Industrial Catalytic Processes.
Chapter 1
Figure 1.1 Catalyzed and uncatalyzed reaction energy paths illustrating the lower energy barrier (activation energy) associated with the catalytic reaction compared with the noncatalytic reaction
Figure 1.2 Illustration of catalyzed versus noncatalyzed reactions
Figure 1.3 Catalytic Fe–Ce redox reaction catalyzed by Mn
Figure 1.4 Activation energy diagram for (a) noncatalytic thermal reaction of CO and O2 and (b) the same reaction in the presence of Pt. Activation energy for the noncatalyzed reaction is Enc. The Pt-catalyzed reaction activation energy is designated Ec. Note that heat of reaction ΔH is the same for both reactions
Figure 1.5 Conversion of CO versus temperature for a noncatalyzed (homogeneous) and catalyzed reaction
Figure 1.6 Particulate catalysts for fixed bed reactors: spheres, extrudates, and tablets. Powdered catalysts for batch slurry phase processors. A cartoon of a fixed bed reactor loaded with catalyst tablets
Figure 1.7 Adsorption isotherm (θCO) for CO on Pt for large, moderate, and low partial pressures of CO. The slope at low partial pressures of CO equals the adsorption equilibrium constant KCO
Figure 1.8 Illustration of Langmuir–Hinshelwood reaction mechanism
Figure 1.9 Illustration of Mars–van Krevelen reaction mechanism
Figure 1.10 Illustration of Eley–Rideal reaction mechanism
Figure 1.11 L–H kinetics applied to increasing PCO at constant PO2. Maximum rate was achieved when an equal number of CO molecules and O atoms are adsorbed (θO = θCO) on adjacent Pt sites
Figure 1.12 Ideal dispersion of Pt atoms on a high surface area Al2O3 carrier
Figure 1.13 Illustration of the sequence of chemical and physical steps occurring in heterogeneous catalysis
Figure 1.14 Conversion versus temperature profile illustrating regions for chemical kinetics, pore diffusion, and bulk mass transfer control
Figure 1.15 Relative rates of bulk mass transfer, pore diffusion, and chemical kinetics as a function of temperature. Chemical kinetics controls the rate between temperatures A and B. Pore diffusion controls from B to C temperatures, while bulk mass transfer controls at temperatures greater than C
Figure 1.16 Reactant concentration gradients within a spherical structured catalyst for three regimes controlling the rate of reaction
Chapter 2
Figure 2.1 (a) SEM of γ-Al2O3 (80,000× magnification) and (b) SEM of α-Al2O3 (80,000× magnification)
Figure 2.2 Three zeolites: (a) mordenite, (b) ZSM-5, and (c) Beta
Figure 2.3 Ceramic and metallic (center image) monoliths of different shapes and cell geometries
Figure 2.4 Ceramic washcoated monoliths
Chapter 3
Figure 3.1 (a) Adsorption isotherm for nitrogen for BET surface area measurement. (b) Linear plot of the BET equation for surface area measurement. (c) Nitrogen adsorption/desorption isotherm for pore size measurement
Figure 3.2 Mercury penetration as a function of pore size of catalyst
Figure 3.3 Differential porosimetry for a porous catalyst
Figure 3.4 Particle size measurement using laser light scattering analysis
Figure 3.5 Thermal gravimetric analysis and differential thermal analysis of the decomposition of barium acetate on ceria
Figure 3.6 Electron microprobe showing a two-washcoat-layer monolith catalyst. The top layer is Rh on Al2O3 and the bottom layer is Pt on Al2O3
Figure 3.7 SEM of γ-Al2O3 with its highly porous network
Figure 3.8 X-ray diffraction patterns of γ- and α-Al2O3
Figure 3.9 (a) Chemisorption isotherm for determining surface area of the catalytic component. (b) Pulse chemisorption profiles for the dynamic chemisorption method
Figure 3.10 Transmission electron micrograph of Pt on TiO2
Figure 3.11 Transmission electron micrograph of Pt on CeO2
Figure 3.12 X-ray diffraction profile for different crystallite sizes of CeO2
Figure 3.13 An XPS spectrum of various oxidation states of palladium on Al2O3
Figure 3.14 NMR profile of a Y faujasite zeolite
Figure 3.15 DRIFT spectra of CO chemisorbed on different precious metal particles of catalysts prepared in different ways. The CO chemisorption followed by FT-IR measurements was performed at room temperature after the catalysts were treated at 400 °C for 1 h with 7% H2 in Ar gas
Chapter 4
Figure 4.1 Illustration of the three processes that can limit the reaction rate during heterogeneous catalysis
Figure 4.2 Illustration showing how experimental rate measurements can be plotted in order to determine the concentration dependence used in the power rate law
Figure 4.3 Illustration showing how experimental rate measurements can be plotted in order to determine the activation energy and pre-exponential factor used in the Arrhenius expression
Figure 4.4 Conversion versus temperature at different space velocities. Experiment is performed to determine the rate constant at various temperatures
Figure 4.5 Arrhenius plot for determining activation energies
Chapter 5
Figure 5.1 Idealized cartoon of perfectly dispersed Pt on a high-surface γ-Al2O3
Figure 5.2 Conceptual diagram of sintering of the catalytic component on a carrier
Figure 5.3 TEM of fresh and sintered Pt on Al2O3 in an automobile catalytic converter application. “Black dots” are platinum crystallites. The size difference in crystallites between the two pictures is the result of sintering
Figure 5.4 Idealized conversion versus temperature for various aging phenomena
Figure 5.5 Illustration of the sintering of the catalyst carrier occluding the catalytic component
Figure 5.6 Microscopy images of low surface area rutile (a) and high surface area anatase (b). Each set of four photos show the structure at increasing magnification
Figure 5.7 (a) NMR profile of a thermally aged zeolite showing the loss of the Si–O–Al bridges. Si(3Al), Si(2Al), and Si(Al) are seen to decrease in intensity with the progressively more severe thermal aging. (b) Growth of penta- and octahedral coordination sites in a thermally deactivated zeolite
Figure 5.8 Conceptual cartoon showing selective poisoning of the catalytic sites
Figure 5.9 Conceptual cartoon showing masking or fouling of a catalyst washcoat
Figure 5.10 XPS spectrum of the surface of a contaminated Pt on Al2O3 catalyst
Figure 5.11 Electron microprobe showing the deposition location of the poisons within the washcoat of a monolith catalyst used in an automobile catalytic converter. The X-ray beam is scanned perpendicular to the axial direction through thickness of the washcoat
Figure 5.12 TGA/DTA in air of coke burn-off from a catalyst
Figure 5.13 TGA/DTA profile for desulfation of Pd on Al2O3 catalyst
Chapter 6
Figure 6.1 Illustration of industrial hydrogen generation process
Figure 6.2 A series of metallic tubes filled with particulate catalysts bathed in a furnace of burning natural gas providing the required heat of reaction. The rate of reaction and temperature are highest near the heat source
Figure 6.3 Reduction or activation of Ni SR catalyst: H2O (steam)/H2 as a function of temperature for redox of NiO/Ni
Figure 6.4 H2O/C versus temperature: a high H2O/CH4 ratio allows higher temperatures for coke-free operation. To the right of the line is the coke forming regime
Figure 6.5 WGS equilibrium: free energy and equilibrium constant for WGS as a function of temperature
Figure 6.6 Typical performance of a HTS WGS catalyst with respect to exit CO
Figure 6.7 Reformer schematic for pure H2
Figure 6.8 Overall process flow diagram for preformed natural gas to H2 and N2 for NH3 production
Figure 6.9 Monolith catalysts for H2 generation using PSA or PROX
Figure 6.10 Illustration of a highly simplified catalyzed double pipe heat exchanger where a combustion catalyst is applied to the inside surface and a steam reforming catalyst is applied to the outside surface of the inner tube
Figure 6.11 Preferential oxidation of 0.5% CO using a (Pt, Fe, Cu)/Al2O3 monolith catalyst
Figure 6.12 Various catalytic processes for generating H2 and synthesis gas from desulfurized natural gas (methane) and methanol
Chapter 7
Figure 7.1 Simplified flow sheet for NH3 synthesis illustrating a “quench”-type ammonia converter and two-stage feed gas compression
Figure 7.2 Simplified illustration of a single-stage radial flow ammonia converter
Figure 7.3 Illustration of methanol quench reactor design
Figure 7.4 Illustration of staged cooling design
Figure 7.5 Illustration of cooled tube reactor design
Figure 7.6 Illustration of shell-cooled reactor design
Figure 7.7 Flow sheet for methanol synthesis
Figure 7.8 Bubble slurry reactor for Fischer–Tropsch
Figure 7.9 Loop reactor for Fischer–Tropsch
Chapter 8
Figure 8.1 Surface roughening (sprouting of PtRh gauze)
Figure 8.2 High-pressure NH3 oxidation/HNO3 plant with Pd getter gauze
Figure 8.3 An expanded view of the reactor containing the stacks of oxidation and getter gauzes
Figure 8.4 HCN process flow diagram
Figure 8.5 The Claus process with staged reaction and liquid sulfur removal
Figure 8.6 Elemental sulfur is reacted with dry air at 900 °C producing SO2. Staged air injection into the second and third stages for cooling is shown in Figure 8.8
Figure 8.7 SO2/SO3 equilibrium as a function of temperature
Figure 8.8 Quench reactor for SO3 production with staged air injection for cooling for stages 2 and 3
Figure 8.9 The O2 process for ethylene oxide production
Figure 8.10 Process for low methanol concentration process to formaldehyde over a (Fe, Mo)/SiO2 catalyst
Figure 8.11 Process using Ag catalyst
Figure 8.12 Propylene to acrolein to acrylic acid process flow diagram. Tubular reactor with a diameter of about 2.5 cm and a length of about 4 m cooled by a molten carbonate
Figure 8.13 Process for converting propylene to acrylonitrile
Chapter 9
Figure 9.1 Illustration comparing difference between a semibatch stirred tank reactor and a continuous stirred tank reactor
Figure 9.2 Illustration of a semibatch stirred tank reactor (STR). The sparger (or also called dip tube) is used for continuous addition of a reactant, which is hydrogen for hydrogenation reactions. Not shown is the removal of unreacted hydrogen from the headspace, which must occur to maintain the desired reactor pressure
Figure 9.3 Illustration showing hydrogen consumption versus time during typical hydrogenation reaction
Figure 9.4 Illustration of the mass transfer path taken by hydrogen as it diffuses from the gas bubble, through the bulk liquid, and ultimately to the catalyst particle. In most hydrogenation reactions, the rate of this diffusion process limits the overall rate of reaction
Figure 9.5 Kinetic rate for a catalytic slurry-phase batch reaction
Figure 9.6 Linolenic oil shown as an example of an unsaturated fat molecule
Figure 9.7 Sequential reactions at 140 and 200 °C
Figure 9.8 CATOFIN propane dehydrogenation to propylene using Cr2O3/Al2O3 catalyst
Figure 9.9 Flow diagram for dehydrogenation of ethyl benzene to styrene
Chapter 10
Figure 10.1 Simplified illustration of the crude oil refining process. The desalting process (removal of inorganic components in the crude using a water wash) is not shown
Figure 10.2 Examples of metal-containing (nickel porphyrin) and sulfur-containing (thiophene) species typically found in crude oil
Figure 10.3 The HDM/HDS process flow diagram. Inset shows presulfided catalyst and its positive effect on decreasing excessive gas make and hydrogen consumption
Figure 10.4 Catalyst deactivation by HDM metal deposition (masking) and coking
Figure 10.5 Controlled O2 addition in coked catalyst regeneration
Figure 10.6 Faujasite zeolite
Figure 10.7 Schematic of FCC reactor with catalyst regenerator
Figure 10.8 Process flow diagram for naphtha reforming
Figure 10.9 Regeneration and rejuvenation of (Pt, Re)/γ-Al2O3 + Cl- reforming catalyst
Chapter 11
Figure 11.1 Hydroformylation process using a cobalt homogeneous catalyst
Figure 11.2 Dow (Davy McKee) LP Oxo Selector process using the Rh catalyst
Figure 11.3 Monsanto acetic acid process
Figure 11.4 Phillips loop reactor
Figure 11.5 TiCl3/MgCl2 process for polyethylene
Chapter 12
Figure 12.1 (a) VOC abatement process with heat integration. (b) VOC abatement with supplemental heating
Figure 12.2 Slipstream reactor concept used for VOC abatement design
Figure 12.3 Catalyst abatement of food processing fumes
Figure 12.4 SCR with V2O5 and a metal-exchanged zeolite: 1.1 NH3/NO and zeolite
Figure 12.5 SCR reactor schematic. It would be worth mentioning that the widening, that is, lower velocity, increases contact time
Figure 12.6 Ozone abatement reactor design
Chapter 13
Figure 13.1 Gasoline-relative engine emissions and temperature as a function of air/fuel ratio
Figure 13.2 Monolith catalyst housed in a metal canister secured in the exhaust
Figure 13.3 Optical micrographs of double-layered washcoated ceramic monoliths
Figure 13.4 Conversion proceeding axially down the channel of a monolith with poisoning. Units of time are arbitrary units
Figure 13.5 Temperature profiles (ΔT/ΔL) for an exothermic reaction down the axial length of a catalyzed monolith channel caused by sintering
Figure 13.6 Simultaneous conversion of HC, CO, and NOx for TWC as a function of air/ fuel ratio
Figure 13.7 Oxygen sensor response output as a function of air/fuel ratio
Figure 13.8 Electron microprobe scan of an automotive catalyst contaminated with P and S from lubricating oil
Figure 13.9 Close-coupled TWC catalyst, under-floor TWC, and oxygen sensors connected to electronic feedback to control air/fuel ratio close to stoichiometric (λ = 1)
Chapter 14
Figure 14.1 NOx–particulate trade-off with emission regulations
Figure 14.2 Electron microprobe scans of the washcoat of an aged diesel oxidation catalyst. (a) Zn and Ca. (b) P and S
Figure 14.3 Wall flow filter. Soot particulates deposit on the porous wall, while the gaseous components (CO2,H2O, NO, and NO2) and air pass through. The soot is combusted periodically by raising the inlet temperature to >500 °C when a small amount of diesel fuel is injected into the DOC
Figure 14.4 SCR with Cu and Fe zeolites
Figure 14.5 Schematic of simplified diesel exhaust aftertreatment system. A diesel oxidation catalyst and wall flow filter (or diesel particulate filter) are contained in one canister, a dosing system for injecting urea to the SCR catalyst. An ammonia decomposition catalyst (Pt/γ-Al2O3//ceramic monolith) is installed at the outlet of SCR. The DOC catalyzes the oxidation of CO, HC, and some of the NO to NO2 and generates sufficient heat (∼500 °C) by oxidizing injected diesel fuel to initiate combustion of the soot collected on the wall flow filter. The NO and NO2 exiting the filter are mixed with inject urea, which hydrolyzes to NH3 and enters the SCR catalyst. EGR may be used to further reduce the engine out NO. Not shown is a turbocharger than compresses the air as it enters the combustion chamber. This further enhances the power of the engine to move heavy loads
Figure 14.6 Chemistry of NOx reduction in using BaO to capture NO2 during lean operation
Figure 14.7 Deactivation of the NOx trap by sulfur oxide poisoning
Figure 14.8 Driving profile for a LNT. During lean mode (fuel economy), NO is converted to NO2 over a Pt catalyst, which is adsorbed in the alkaline trap. Regeneration (solid area) occurs when the engine is commanded to a stoichiometric mode where the NOx is desorbed from the BaO and the Rh in the TWC reduces it to N2
Chapter 15
Figure 15.1 Biodiesel production process
Figure 15.2 A comparison of power generation for a coal-fired power plant, gasoline/ diesel internal combustion engine, and a H2–O2 low-temperature fuel cell
Figure 15.3 A single cell of the PEM fuel cell
Figure 15.4 Voltage–current profile for the PEM fuel cell. The curve with the maxima represents the power profile
Figure 15.5 A PEM single cell and arranged in a “stack.” Each cell is separated by an electrically conductive impermeable bipolar plate that serves as a gas manifold for the cells connected in series
Figure 15.6 Ideal H2 economy with the sun providing energy for a photovoltaic device generating sufficient voltage to electrolyze water to H2 and O2
| A | Frontal area (m2) |
| as | Geometric surface area = ratio of surface area to volume (m –1) |
| aSh | Fitted parameter used for mass transfer coefficient |
| B | Integral breadth (Scherrer’s formula) (°) |
| C | Concentration (mol/m3) |
| CBET | BET constant |
| CWP | Weisz–Prater criterion |
| D | Diffusivity (m2/s) |
| De | Effective diffusivity (m2/s) |
| Dk | Knudsen diffusivity (m2/s) |
| dp | Particle diameter (dh) = monolith channel diameter (m) |
| dpore | Pore diameter (m) |
| EA | Activation energy (J/mol) |
| Ecell | Net voltage of fuel cell (V) |
| E°cell | Standard state cell voltage (V) |
| Eo | Standard state voltage in the Nernst equation (V) |
| f | Friction factor |
| F | Molar flow (mol/s) |
| Fc | Faraday constant (C/V) |
| gc | Gravitational constant (m/s2) |
| GHSV | Gas hourly space velocity (h–1) |
| ΔGrxn | Free energy change during reaction (J/mol) |
| H | Henry’s law constant |
| ΔHrxn | Enthalpy change during reaction (J/mol) |
| J | Molar flux (mol/(m2 s)) |
| k | Reaction rate constant (mol/(s l)) |
| Keq | Equilibrium constant |
| kf, kd | Rate constants for absorption and desorption (mol/(s l)) |
| kMT | Mass transfer coefficient (m/s) |
| ko | Pre-exponential factor (g) |
| Mflow | Mass flow rate (kg/h) |
| MW | Molecular weight (mol/g) |
| n | Number of electrons transferred |
| NA | Avogadro’s number (mol–1) |
| P | Pressure (atm) |
| Pi | Partial pressure of species i (atm) |
| Po | Saturation pressure (atm) |
| r | Reaction rate per unit volume (mol/(s l)) |
| r´ | Reaction rate per unit mass (mol/(s g)) |
| R | Ideal gas constant (J/(mol K)) |
| Re | Reynolds number |
| rk | Rate of reaction on catalyst surface (mol/(s l)) |
| rMT | Rate of bulk diffusion (mol/(s l)) |
| rMT,g | Rate of bulk diffusion through gas phase (mol/(s l)) |
| rMT,g–l | Rate of diffusion through gas–liquid interface (mol/(s l)) |
| rMT,l–s | Rate of diffusion through liquid–solid interface (mol/(s l) |
| rp | Pore radius (m) |
| Rpellet | Radius of catalyst pellet (m) |
| rpore | Rate of pore diffusion (mol/(s g)) |
| Sc | Schmidt number |
| Sh | Sherwood number |
| ΔSrxn | Entropy change during reaction (J/K) |
| SV | Space velocity (h–1) |
| t | Residence time (min or h) |
| T | Temperature (°C or K) |
| tcrys | Thickness of crystallite (Scherrer’s formula) (nm) |
| u | Bulk stream velocity (m/s) |
| V | Reactor volume (m3) |
| Vad | Volume adsorbed at P (m3) |
| Vflow | Volumetric flow (m3/s) |
| Vm | Molar volume (mol/m3) |
| Vmono | Adsorbed volume at monolayer coverage (m3) |
| vo | Volumetric flow rate (m3/h) |
| Vrxtr | Reactor volume (m3) |
| Wcat | Catalyst mass (g) |
| WHSV | Weight hourly space velocity (h–1) |
| X | Fractional conversion |
| xSh | Fitted parameter used for mass transfer coefficient |
| Z | Reactor length (m) |
| β | Approach to equilibrium |
| γ | Surface tension (N/m) |
| δM | Thickness of mass transfer boundary layer (m) |
| ε | Binary interaction energy (K) |
| ε | Void fraction in the bed |
| εp | Particle porosity |
| θ | Contact angle (°) |
| θd | Bragg angle (°) |
| θi | Surface coverage of species i |
| λ | Molecule mean free path (m) |
| λ | X-ray wavelength (Å) |
| ρ | Catalyst bulk density (kg/m3) |
| ρg | Gas density (kg/m3) |
| σ | Interaction length (m) |
| σ | Surface tension of liquid nitrogen (N/m) |
| σp | Pore constriction |
| τ | Space time (h) |
| τp | Pore tortuosity |
| υ | Kinematic viscosity (m2/s) |
| Ω | Diffusion collision integral |
| A | Generic species “A” |
| B | Generic species “B” |
| i | Species |
| i | Inlet position |
| o | Outlet position |
| o | Denotes saturation pressure |