![C. Reactor/process
design perspective
Hardware
and
Software
Scientific &
Engineering
Tasks
Scientific &
Engineering
Disciplines
Discover
Reaction
Laboratory
Reactor
Kinetic Model
Development
Chemical Kinetics
and Catalysis
Rate/Selectivity &
Rate Equation
Reactor Model
Reactor Model
Development
Reaction
Engineering &
Mathematics
Reactor /Process
Design
Catalytic Reactor
Design
Pilot Plant
Reactor
Finl. Plant Design
& Economic
Studies
Large Scale
Plant
Process Design
Economics
Intrinsic
Kinetics
Catalyst Prop.
Diff., Mass Trans
Fig. 12.1 Structure of Catalytic Process
Development [adapted from J. M. Smith,
Chem. Eng. Prog., 64, 78 (1968)].](https://image.slidesharecdn.com/catalyticreactors-250418015217-fe9c663a/85/Catalytic-Reactors-in-which-all-types-of-reactor-7-320.jpg)
![Fig. 12.2 Features of
representative laboratory
reactors [Levenspiel, 1979].](https://image.slidesharecdn.com/catalyticreactors-250418015217-fe9c663a/85/Catalytic-Reactors-in-which-all-types-of-reactor-11-320.jpg)
![Table 12.7 Proposed Guidelines for Choosing Catalyst Form, Pretreatment, and
Reaction Conditions and for Reporting of Data [Ribiero et al., 1996].
1. Catalyst Properties and Characterization
a. Catalysts/surfaces should be carefully prepared and pretreated so as to be free of solid
contaminants such as sulfur, chlorides, and carbon that might affect activity.
b. Support effects should be avoided by studying reactions on single crystals of the
active catalytic phase, e.g., metal, metal films, and/or relatively highly-concentrated,
poorly-dispersed supported metals. Preparation methods should be used which
minimize decoration of the metal surface, e.g., decomposition of metal carbonyls on
supports. Supported base metal catalysts need to be well-reduced to avoid
complications due to unreduced metal oxides.
c. In the case of structure-sensitive reactions, effects of surface structure and/or
dispersion need to be taken into account.
d. Metal dispersion/surface area should be measured using proven and/or standard
(ASTM) methods, e.g., hydrogen chemisorption or titration rather than CO
chemisorption for metals.
e. Methods of preparation and characterization should be reported in detail. Methods for
calculating surface area and dispersion should also be carefully reported. Reporting
these methods and the surface area or dispersion of catalyst samples should be a
requirement for publication of specific activity data.](https://image.slidesharecdn.com/catalyticreactors-250418015217-fe9c663a/85/Catalytic-Reactors-in-which-all-types-of-reactor-35-320.jpg)
![Differential Analysis
of Rate Data
X
slope =
ln C
A
b
ln (-r
A)
W/FA0
XA
1.0
0.5 X
X X
X
X
X
X
X
X
0
slope = -rA'
a
X
X
X
Fig. 12.16
(a) Differential analysis to obtain
reaction rates. (b) Plot to obtain
reaction orders.
Differential analysis of rate data involves the following steps:
1. The identical series of runs (as in integral analysis) are made in a packed bed at a fixed initial
concentration CAo and fixed temperature while varying the catalyst mass W and/or the initial molar flow
rate FAo to generate a range of W/FAo values at different conversions (XA).
2. A plot of conversion XA versus W/FAo data is made for each set of runs at a fixed temperature. A best fit
of the data is made using a simple quadratic or cubic equation, and the corresponding curve is plotted on
the same figure, as illustrated in Figure 4.20(a).
3. Tangents to the curve are drawn at regular intervals along the curve corresponding to the best fit, and the
slopes of these tangents are evaluated (Figure 12.16a); the slopes on this plot correspond to the reaction
rate, i.e. dXA = ( rA)[d(W/F)]. Tangents can be evaluated more accurately by differentiating the equation
for the best fit of the data and evaluating the derivative at various intervals over the data set.
4. Values of rA versus XA are plotted on linear or log-log plots to determine reaction orders. For example,
for an irreversible reaction in which data are fitted by a simple power rate law, rA = k CA
α
, a plot of
ln( rA) versus ln(CA) is linear with a slope
(Figure 12.16b).
5. Differential analysis is a useful scoping tool to explore forms of the rate expression; however, in the end
a nonlinear regression and rigorous statistical analysis is required to obtain kinetic parameters with
acceptable accuracy.](https://image.slidesharecdn.com/catalyticreactors-250418015217-fe9c663a/85/Catalytic-Reactors-in-which-all-types-of-reactor-39-320.jpg)
Catalytic Reactors in which all types of reactor
- 1. "An ounce of careful plant design is worth ten pounds of reconstruction." LECTURE 12: LABORATORY AND INDUSTRIAL CATALYTIC REACTORS: SELECTION, APPLICATIONS, AND DATA ANALYSIS I. Introduction A. Why study reactors? B. Definition and classification of reactors C. Reactor/process design perspective: from the laboratory to the full-scale plant D. Selection of reactors in the laboratory and plant II. Laboratory and Bench Scale Reactors A. Kinds B. Criteria for selection of lab/bench scale reactors; applications III. Plant Reactors A. Common types B. Fixed catalyst bed reactors: characteristics, advantages, limitations C. Fluidized beds: characteristics, advantages, limitations D. Criteria for selection IV. Collecting, Analyzing and Reporting Data from Laboratory Reactors A. General approach and guidelines B. Criteria for choosing catalyst form and pretreatment, reaction conditions C. Choosing mode of reactor operation; differential and integral reactors D. Analyzing and reporting data from laboratory reactors 1. Analysis of rate data: objectives and approach 2. Integral analysis 3. Differential analysis V. Examples
- 2. New HDS Unit, ARCO Carson, CA Refinery
- 4. I. Introduction A. Why study reactors? 1. The design of catalyst and reactor are closely interrelated. 2. Design of catalytic processes requires a knowledge reactor design, operation optimization and selection 3. Progress in improving our standard of living depends on our ability to design reactors 4. Our personal existence depends on controlling cellular reactions in our body while that of the human race hangs on the outcome of enormous global reactions.
- 5. B. Definition and Classification of Reactors 1. What is a Reactor? a. A device that encloses the reaction space, and which houses the catalyst and reacting media. b. A container to which reactants are fed and products removed, that provides for the control of reaction conditions. 2. Classification of Reactors a. Size b. Methods of charging/discharging: batch or steady-state flow c. Motion of particles with respect to each other d. Fluid flow type: tubular or mixed-fluid
- 6. Table 12.1 Classification of Catalytic Reactors Basis for Classification Classes Examples Size Laboratory Bench scale Pilot scale Plant scale 0.5 cm diam. tubular microreactor (0.1-1 g catalyst) 2.5 cm diam. x 30-50 cm long tubular reactor (50-200 g catalyst) 7.5 cm diam x 6-10 m long tubular reactor (20-100 kg catalyst) 1-6 m diam x 20-50 m long tubular reactor (20-100 metric tons cat.) Methods of charging and discharging Batch Flow, steady state Stirred liquid and solids a. tubular, fixed catalyst bed b. slurry, mixed fluid, mixed solids Motion of catalyst particles relative to each other Fixed Relative motion Tubular fixed solids (fixed bed) a. fluidized bed b. slurry bubble column Fluid flow Tubular, plug flow Mixed fluid flow Turbulent gas in tubular fixed bed Slurry reactor with mechanical stirring
- 7. C. Reactor/process design perspective Hardware and Software Scientific & Engineering Tasks Scientific & Engineering Disciplines Discover Reaction Laboratory Reactor Kinetic Model Development Chemical Kinetics and Catalysis Rate/Selectivity & Rate Equation Reactor Model Reactor Model Development Reaction Engineering & Mathematics Reactor /Process Design Catalytic Reactor Design Pilot Plant Reactor Finl. Plant Design & Economic Studies Large Scale Plant Process Design Economics Intrinsic Kinetics Catalyst Prop. Diff., Mass Trans Fig. 12.1 Structure of Catalytic Process Development [adapted from J. M. Smith, Chem. Eng. Prog., 64, 78 (1968)].
- 8. D. Choosing reactors in the lab and plant Reactors are used for many different purposes: 1. to study the mechanisms and kinetics of chemical reactions to provide data for validation of process simulations 2. to investigate process performance over a range of process variables 3. to obtain design data 4. to produce energy, materials and products. Choosing the right reactor is critical to the engineering process and is dictated by many different variables such as • reaction type • rate of deactivation • economics • other process requirements
- 9. II. Common Lab and Bench Scale Reactors 1. fixed bed tubular 2. stirred gas, fixed bed 3. stirred liquid/gas, stirred catalyst 4. fluid bed 5. fixed bed, transient gas flow Laboratory and bench-scale reactors vary greatly in size, complexity, cost, and application.
- 10. Table 12.2 Laboratory and Bench-Scale Catalytic Reactors Classes Class Examples Features Fixed bed tubular Laboratory differential/integral Bench-scale integral 0.5 cm diam tubular microreactor (0.1-1 g catalyst, solid catalyst, gas fluid; glass or metal 2.5 cm diam. x 30-50 cm long tubular reactor (50-200 g catalyst); solid catalyst, gas or liquid fluid; metal Stirred gas, fixed bed Stirred batch Batch recycle Berty Carberry microreactor, 1 g catalyst, glass or met. microreactor, 1 g catalyst, glass or met. bench-scale, 2-200 g cat., 10-100 atm, stainless steel, circulating gas bench-scale, 2-200 g cat., 10-100 atm, stainless steel, spinning catalyst basket Stirred liquid/gas, stirred catalyst Stirred batch Bubble slurry bench-scale, 2-50 g cat., 1-200 atm, glass or metal heterogeneous or homogeneous catalyst Fluid bed Laboratory Bench-scale transport Recirculating transport microreactor, 1-5 g cat, 1 atm, glass bench-scale, 50- 200 g catal, 1-10 atm, metal Fixed bed, transient gas flow Pulse flow TPD/TPSR Radio tracer exchange MS/Transient response Frequency response microreactor, 0.1-1 g catalyst, glass or metal, 1 atm
- 11. Fig. 12.2 Features of representative laboratory reactors [Levenspiel, 1979].
- 12. 10/30 female joint 10/30 male joint 9 mm O-ring joint 4 ft. preheater coil of 2 mm capillary tubing Thermocouple guide of 2mm capillary tubing 7" Fritted disc Catalyst space Figure 12.3 Laboratory Pyrex FBR reactor (courtesy of the BYU Catalysis Laboratory).
- 13. Figure 12.4 Berty internal recycle reactor.
- 14. Gas-Liquid CSTR (UCSB) Batch Reactor (UCSB)
- 15. Bench scale reactor (courtesy of Shell Corp.)
- 16. II. Laboratory and Bench Scale Reactors B. Criteria for selection of lab and bench-scale reactors; applications 1. Satisfying intended application 2. Avoiding deactivation 3. Avoiding inter- and intra- particle heat and mass transport limitations 4. Minimizing temperature and concentration gradients 5. Maintaining ideal flow patterns 6. Maximizing the accuracy of concentration and temperature measurements 7. Minimizing construction and operating costs
- 17. Table 12.3 Seven Criteria for Selection of Laboratory and Bench-Scale Catalytic Reactors Criterion Issues Involved/Measures of/Methods to Meet Criterion 1. Satisfy purpose of measurement (i.e., application) Measure: (1) intrinsic activity/selectivity, (2) kinetics of reaction and deactivation Obtain mechanistic understanding Simulate process 2. Avoid catalyst deactivation where possible; where not, decide if fast or slow See Chap. 5 (B&F) on avoiding different kinds of catalyst deactivation Fast decay causes activity and selectivity disguises and requires use of transient or transport reactor Slow decay best studied using CSTR or differential reactor 3. Avoid inter- and intra-particle heat and mass transport limitations Thiele modulus less than 0.5; small particles or thin catalyst layer Minimize film thickness with high flow rates, turbulence Operate at low conversions Use CSTR or differential reactor 4. Minimize temperature and concentration gradients Gradients cause activity and selectivity disguises Maximize mixing in batch reactor and CSTR; use inerts Use CSTR or differential reactor where possible 5. Maintain ideal flow patterns Minimize mixing and laminar flow in tubular reactors; Maximize mixing and minimize gradients in CSTR Avoid gas or liquid holdup in multi-phase reaction systems 6. Maximize accuracy of concentration and temperature measurements Sensitive analytical methods and well-placed, sensitive probes Sufficiently high product concentrations 7. Minimize construction and operating costs Select the least expensive reactor that will satisfy the other criteria Consider ways of minimizing size of catalyst and volume of reactant gas
- 18. Table 12.4 Applications of Lab/Bench Test Reactors Reactor Type Catalyst Selection Activity/Selectivity Reactor/Design Fundamental Mechanism Process Simulation Life Kinetics Integral Adiabatic X (overall avg. conv.) X X Isothermal X (overall conv. at T) X X Differential Single Pass X (intrinsic) X (intrinsic) X (eliminate) Recycle X (intrinsic) X (intrinsic) X (eliminate) Stirred gas X (intrinsic) X (kinetics) X (intrinsic) X (eliminate) X (model) Fluid bed/ Transport X (fast deact.) X (fast deact.) X (fast deact.) X Micro-pulse X (comparative, initial) X Transient X (elem. steps) X X (model)
- 19. Common Types of Catalytic Plant Reactors 1.Fixed-bed Reactors a. Packed beds of pellet or monoliths b. Multi-tubular reactors with cooling c. Slow-moving pellet beds d. Three-phase trickle bed reactors 2.Fluid-bed and Slurry Reactors a. “Stationary” gas-phase b. Gas-phase c. Liquid-phase i. Slurry ii. Bubble Column iii. Ebulating bed
- 20. Table 12.5 Characteristics of Plant-Scale Fixed Bed Reactors Advantages 1. Ideal plug (or mixed) flow 2. Simple analysis 3. Low cost, low maintenance 4. Little loss or attrition 5. Greater variation in operating conditions and contact times is possible 6. Usually a high ratio of catalyst to reactants long residence time complete reaction 7 Little wear on catalyst and equipment 8. Only practical, economical reactor at very high pressures Disadvantages 1. Poor heat transfer in a large fixed bed. a. Temp. control and measurement difficult b. Thermal catalyst degradation c. Non uniform rates. 2. Non uniform flow patterns e.g. channeling 3. Swelling of the catalyst; deformation of the reactor 4. Regeneration or replacement of the catalyst is difficult - shut down is required. 5. Plugging, high pressure drop for small beads or pellets - ∆P is very expensive. 6. Pore diffusional problems intrude in large pellets Overcoming the Disadvantages 1. Monolithic supports overcome disadvantages 2, 5 & 6 2. Temperature control problems are overcome with: a. Recycle b. Internal and external heat exchanges c. Staged reactors d. Cold shot cooling e. Multiple tray reactor - fluid redistributed & cooled between stages. Catalyst is easily removed - varied from tray to tray. f. Use of diluents g. Temperature self regulation with competing reactions, one endo and one exothermic. h. Temp control by selectivity and temporarily poisoning the catalyst
- 21. B. Fixed-bed reactors: characteristics, advantages, limitations Advantages: • Flexible- large variation in operating conditions and contact times is possible • Efficient- long residence time enables a near complete reaction • Generally low-cost, low-maintenance reactors Disadvantages: • Poor heat transfer with attendant poor temperature control • Difficulty in regenerating or replacing spent catalyst
- 22. Product Feed Inert balls Catalyst Reactants Inlet Liquid Or Gaseous Bath Reactor Tube Gas Or Liquid Flow Outlet Product Reactor Tube a.. I II III IV 1 2 3 4 Fresh feed Recycle gas b. Fig. 12.6 Commercial fixed-bed reactor designs for controlling temperature: (a) multi-tubular heat-exchange reactor, (b) series of fixed-bed, adiabatic reactors with interstage heating or cooling. Figure 12.5 Commercial fixed-bed, adiabatic catalytic reactor.
- 23. Advantages 1. Frequent regeneration of the catalyst possible. 2. Rapid mixing of solids in fluid beds means uniform gas composition. 3. Isothermal operation and efficient temperature control is practical. 4. Small-diameter particles in fluid minimize pore diffusional resistance. 5. Improved thermal efficiency because of high heat transfer rates. 6. In the case of highly exothermic, liquid phase reactions, slurry reactors are less complex and less expensive than heat- exchange-tubular systems. Disadvantages 1. Fluidized beds are complicated systems involving multiple reactors, heat exchangers, extensive valving and piping to provide continuous system. 2. $$ Extensive investment. Maintenance is high. 3. Fluid flow is complex in fluidized and slurry bubble columns - less than ideal contacting. Product distribution is changed - less intermediate formed in a series reaction. 4. Only a small variation in residence time possible. Low residence times. Conversion may be limited. 5. Attrition & loss of Catalyst. Table 12.6 Characteristics of Plant-Scale Fluidized and Slurry Bed Reactors
- 24. Deentrained vapor Product Spent catalyst Hydro- clone Fresh catalyst Feed a. Continuous phase Product Dispersed phase b. Figure 12.7 Liquid-phase slurry reactors: (a) forced-circulation, slurry-bed reactor, (b) bubble-column, slurry-bed reactor.
- 25. H2 reactants + H2 products shaft heater liquid P product withdrawal suspended catalyst particles rotor pressure vessel to heat source H2 from reservoir (consumption measured) Figure 12.8 Batch-slurry reactor for hydrogenation of specialty chemicals.
- 26. Product Steam stripping Flue gas Fluid-bed regenerator Air Transfer line Feed Transfer- line reactor Fig. 12.9 Design of typical FCC transfer-line (riser) reactor with fluidized-bed regenerator.
- 27. Products Riser reactor Catalyst stripper Steam Reactor feed Steam Air Overflow well Regenerator Flue gas Cyclone a. Products Cyclone Reactor Catalyst stripper Steam Air Reactor Regenerator Flue gas feed b. Figure 12.10 Commercial FCC riser reaction designs (a) Exxon, (b) UOP.
- 28. Fluid Cat Cracker (Chevron) Stacked Fluid Cat Cracker (UOP)
- 29. Shell Cat-Cracker All-riser Cracking FCC Unit
- 30. Criteria for Selection of Plant Reactors 1. General Criteria. a.deactivation rate and regeneration policy b.reaction conditions c.catalyst strength and attrition resistance d.process economics 2. Role of Cp/(-Hr) slope = T XA Cp -HR 1 rA XA 1 100 10 1000 T XA 1 rA XA c d a b Fig. 12.11 (a) Operating line for a highly exothermic reaction in an ideal tubular reactor with pure reactant and (b) corresponding reciprocal rate versus conversion curve and area V/FAo for a CSTR. (c) Operating line for a highly exothermic reaction in an ideal tubular reactor with dilute reactant and (d) corresponding reciprocal rate versus conversion curve and area V/FAo for a PFR.
- 31. 3. Optimal Temperature Progression Figure 12.12 Optimum temperature progression (and locus of maximum rates) of (a) reversible endothermic reaction and (b) reversible exothermic reactions.
- 32. Exothermic reversible Exothermic irreversible Endothermic Qin Q Optimum Tmax T T T Tmax Cold feed Furnace Adiabatic reactors Cold product A B C D E F G Q Q Q XA a b Fig. 12.13 (a) Use of staged adiabatic tubular fixed-bed reactors with interstage cooling to achieve optimum temperature progression in the cases of exothermic reversible, exothermic irreversible and endothermic reactions. (b) Design schematic for staged adiabatic fixed-bed reactors with interstage furnace heating for a strongly endothermic reaction such as reforming of methane.
- 33. Collecting, Analyzing and Reporting Data from Laboratory Reactors Different purposes: 1. activity/selectivity and life data for catalyst selection 2. chemical reaction mechanistic and kinetic data for understanding the reaction at a fundamental level, modeling the reaction process, and/or designing reactors 3. process variable data over a wide range of conditions for purposes of designing large-scale reactors, experimentally validating models and optimizing the catalytic process. Data collection typically involves three major steps (Fig. 12.14): 1. selection of a reaction and catalyst 2. selection of a reactor type 3. analysis of the data
- 34. Select Reaction and Catalyst Criteria Data Select reactor and conditions Data Analysis Integral Differential Initial Rates Batch Flow CSTR Plug - integral or differential mechanism rate expression process optimization new experiments Figure 12.14 Process of obtaining rate and kinetic data; note that statistical methods are used in Steps 2 and 3 and in the recycle process.
- 35. Table 12.7 Proposed Guidelines for Choosing Catalyst Form, Pretreatment, and Reaction Conditions and for Reporting of Data [Ribiero et al., 1996]. 1. Catalyst Properties and Characterization a. Catalysts/surfaces should be carefully prepared and pretreated so as to be free of solid contaminants such as sulfur, chlorides, and carbon that might affect activity. b. Support effects should be avoided by studying reactions on single crystals of the active catalytic phase, e.g., metal, metal films, and/or relatively highly-concentrated, poorly-dispersed supported metals. Preparation methods should be used which minimize decoration of the metal surface, e.g., decomposition of metal carbonyls on supports. Supported base metal catalysts need to be well-reduced to avoid complications due to unreduced metal oxides. c. In the case of structure-sensitive reactions, effects of surface structure and/or dispersion need to be taken into account. d. Metal dispersion/surface area should be measured using proven and/or standard (ASTM) methods, e.g., hydrogen chemisorption or titration rather than CO chemisorption for metals. e. Methods of preparation and characterization should be reported in detail. Methods for calculating surface area and dispersion should also be carefully reported. Reporting these methods and the surface area or dispersion of catalyst samples should be a requirement for publication of specific activity data.
- 36. Table 12.7 Continued 2. Reaction Conditions a. TOF and kinetic data must be measured in the absence of pore diffusional restrictions, film mass transfer limitations, and heat transfer limitations (generally at low temperature and low conversion). Experimental evidence and calculations based on well-known criteria (e.g., the Thiele modulus for pore diffusional resistance) should be provided in publications to demonstrate that the data were obtained in the absence of these effects. b. TOF and kinetic data must be measured in the absence of deactivation effects, e.g., poisoning, coking, and sintering. The burden of proof that such effects are absent should be on the authors of a publication. c. TOF data should be collected over wide ranges of temperature and reactant concentrations to facilitate valid comparison with data from other laboratories and to provide meaningful data for determining temperature and concentration dependencies. d. TOF data should be reported at specified conditions of temperature, reactant concentrations, and conversion. These specifications should be used by reviewers and editors as a minimum reporting requirement for publication in a journal.
- 37. Analyzing and reporting data from laboratory reactors 1. Analysis of rate data: objectives a. finding a rate equation b. determining catalyst activity, selectivity and activity stability c. determining the effects of important process variables such as temperature, pressure, reactant concentrations, and space velocity on activity, selectivity and stability 2. Extracting rate constants and concentration dependencies a. Integral analysis b. Differential analysis
- 38. W F dx (-rA) x x x x x x o Figure 12.15 Test for integral analysis of rate data involving plot of W/FAo versus integrated reciprocal rate. Integral analysis of rate data involves the following steps: 1. A series of runs are made in a packed bed at a fixed initial concentration CAo and a fixed temperature while varying the catalyst mass W and/or the initial molar flow rate FAo to generate a range of W/FAo values at different conversions (XA). 2. A candidate rate equation is selected for testing using the design equation for plug flow. First try simpler rate equations, e.g. zero-, first- and second-order irreversible and use differential analysis to scope out possible reaction orders. 3. The left-hand side (W/FAo) and right-hand side (the integral of 1/ rA) of the design equation are each evaluated numerically and plotted against each other, as shown in Figure 4.19 to test for linearity. 4. Linearity of the plot (e.g. Figure 12.15) is used as the criterion for judging if the candidate rate equation is a useful model of the data, i.e. consistent with the data. 5. This should be followed by a nonlinear regression with statistical analysis to determine kinetic parameters. Integral Analysis of Rate Data
- 39. Differential Analysis of Rate Data X slope = ln C A b ln (-r A) W/FA0 XA 1.0 0.5 X X X X X X X X X 0 slope = -rA' a X X X Fig. 12.16 (a) Differential analysis to obtain reaction rates. (b) Plot to obtain reaction orders. Differential analysis of rate data involves the following steps: 1. The identical series of runs (as in integral analysis) are made in a packed bed at a fixed initial concentration CAo and fixed temperature while varying the catalyst mass W and/or the initial molar flow rate FAo to generate a range of W/FAo values at different conversions (XA). 2. A plot of conversion XA versus W/FAo data is made for each set of runs at a fixed temperature. A best fit of the data is made using a simple quadratic or cubic equation, and the corresponding curve is plotted on the same figure, as illustrated in Figure 4.20(a). 3. Tangents to the curve are drawn at regular intervals along the curve corresponding to the best fit, and the slopes of these tangents are evaluated (Figure 12.16a); the slopes on this plot correspond to the reaction rate, i.e. dXA = ( rA)[d(W/F)]. Tangents can be evaluated more accurately by differentiating the equation for the best fit of the data and evaluating the derivative at various intervals over the data set. 4. Values of rA versus XA are plotted on linear or log-log plots to determine reaction orders. For example, for an irreversible reaction in which data are fitted by a simple power rate law, rA = k CA α , a plot of ln( rA) versus ln(CA) is linear with a slope (Figure 12.16b). 5. Differential analysis is a useful scoping tool to explore forms of the rate expression; however, in the end a nonlinear regression and rigorous statistical analysis is required to obtain kinetic parameters with acceptable accuracy.
- 40. References 1. O. Levenspiel, Chemical Reaction Engineering, 2nd and 3rd Eds., John Wiley and Sons, 1972, 1999. 2. O. Levenspiel, The Chemical Reactor Minibook, OSU Bookstores, 1979. 3. J.M. Smith, Chemical Engineering Kinetics, 3rd Ed., McGraw Hill, 1981. 4. "Reactor Technology," Kirk-Othmer: Encyclopedia of Chemical Technology, Vol. 19, 3rd Ed, John Wiley, 1982, pp. 880-914. 5. G.F. Froment and K.B. Bischoff, Chemical Reactor Analysis and Design, John Wiley, 1990. 6. O. Levenspiel, The Chemical Reactor Omnibook, 1993, OSU Bookstores, 1993. 7. C. H. Bartholomew and R. J. Farrauto, Fundamentals of Industrial Catalytic Processes, Chapman and Hall, 2005, Chap. 4.