reactors of Author Perry

There may be a need for appropriate mixing, control of flow dis-tribution and residence time, contacting between the reactants sometimes in the presence of a catalyst or biocatalyst, rem

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DOI: 10.1036/0071511423

REACTOR CONCEPTS

Reactor Types 19-4

Classification by Mode of Operation 19-4

Classification by End Use 19-7

Reactor Tracer Responses 19-15

Understanding Reactor Flow Patterns 19-16

Connecting RTD to Conversion 19-17

Segregated Flow 19-18

Early versus Late Mixing—Maximum Mixedness 19-18

Reaction and Mixing Times 19-20

SINGLE-PHASE REACTORS

Liquid Phase 19-20 Homogeneous Catalysis 19-20 Gas Phase 19-21 Supercritical Conditions 19-21 Polymerization Reactors 19-21

FLUID-SOLID REACTORS

Heterogeneous Catalysts 19-25 Catalytic Reactors 19-27 Wire Gauzes 19-27 Monolith Catalysts 19-27 Fixed Beds 19-30 Moving Beds 19-33 Fluidized Beds 19-33 Slurry Reactors 19-36 Transport Reactors 19-36 Multifunctional Reactors 19-36 Noncatalytic Reactors 19-36 Rotary Kilns 19-36 Vertical Kilns 19-36

19-1

Section 19 Reactors*

Carmo J Pereira, Ph.D., MBA DuPont Fellow, DuPont Engineering Research and

Technology, E I du Pont de Nemours and Company; Fellow, American Institute of Chemical

Engineers

Tiberiu M Leib, Ph.D Principal Consultant, DuPont Engineering Research and

Technol-ogy, E I du Pont de Nemours and Company; Fellow, American Institute of Chemical Engineers

*The contributions of Stanley M Walas, Ph.D., Professor Emeritus, Department of Chemical and Petroleum Engineering, University of Kansas (Fellow, American Institute of Chemical Engineers), author of this section in the seventh edition, are acknowledged.

The authors of the present section would like to thank Dennie T Mah, M.S.Ch.E., Senior Consultant, DuPont Engineering Research and Technology, E I du Pont

de Nemours and Company (Senior Member, American Institute of Chemical Engineers; Member, Industrial Electrolysis and Electrochemical Engineering; Member, The Electrochemical Society), for his contributions to the “Electrochemical Reactors” subsection; and John Villadsen, Ph.D., Senior Professor, Department of Chem- ical Engineering, Technical University of Denmark, for his contributions to the “Bioreactors” subsection We acknowledge comments from Peter Harriott, Ph.D., Fred

H Rhodes Professor of Chemical Engineering (retired), School of Chemical and Biomolecular Engineering, Cornell University, on our original outline and on the ject of heat transfer in packed-bed reactors The authors also are grateful to the following colleagues for reading the manuscript and for thoughtful comments: Thomas

sub-R Keane, DuPont Fellow (retired), DuPont Engineering Research and Technology, E I du Pont de Nemours and Company (Senior Member, American Institute of Chemical Engineers); Güray Tosun, Ph.D., Senior Consultant, DuPont Engineering Research and Technology, E I du Pont de Nemours and Company (Senior Mem- ber, American Institute of Chemical Engineers); and Nitin H Kolhapure, Ph.D., Senior Consulting Engineer, DuPont Engineering Research and Technology, E I.

du Pont de Nemours and Company (Senior Member, American Institute of Chemical Engineers).

Copyright © 2008, 1997, 1984, 1973, 1963, 1950, 1941, 1934 by The McGraw-Hill Companies, Inc Click here for terms of use

SOME CASE STUDIES

Nomenclature and Units

In this section, the concentration is represented by C Mass balance accounting in terms of the number of moles and the fractional conversion is discussed in Sec 7 and can be very useful The rate of reaction is r; the flow rate in moles is N a ; the volumetric flow rate is V′; reactor volume is V r Several equations are presented with- out specification of units Use of any consistent unit set is appropriate.

Following is a listing of typical nomenclature expressed in SI and U.S Customary System units Specific definitions and units are stated at the place of application

in this section.

U.S Customary

Deff Effective diffusion coefficient m 2 /s ft 2 /s

D e Effective dispersion coefficient m 2 /s ft 2 /s

E(t) Residence time distribution

E(t r) Normalized residence time

distribution

f a Fraction of A remaining

unconverted, C a /C a0 or n a/a0

F(t) Age function of tracer

h Heat-transfer coefficient kJ(s⋅m 2 ⋅°C) Btu(h⋅ft 2 ⋅°F)

first-order reaction

Pe Peclet number for dispersion

PFR Plug flow reactor

q Heat flux, reaction order,

or impeller-induced flow

r Rate of reaction per

unit volume, radius

u(t) Unit step input

U Overall heat-transfer coefficient kJ(s⋅m 2 ⋅°C) Btu(h⋅ft 2 ⋅°F)

v Volumetric flow rate

v ij Stoichiometric coefficients

U.S Customary

ε Void fraction in a packed bed, particle porosity

η Effectiveness factor of porous catalyst

A chemical reactor is a controlled volume in which a chemical reaction

can occur in a safe and controllable manner A reactor typically is a

piece of equipment; however, it can also be a product (such as a

coat-ing or a protective film) One or more reactants may react together at

a desired set of operating conditions, such as temperature and

pres-sure There may be a need for appropriate mixing, control of flow

dis-tribution and residence time, contacting between the reactants

(sometimes in the presence of a catalyst or biocatalyst), removal (or

addition) of heat, and integration of the reactor with the rest of the

downstream process Depending on the nature of the rate-limiting

step(s), a reactor may serve primarily as a holding tank, a heat

exchanger, or a mass-transfer device Chemical reactions generate

desired products and also by-products that have to be separated and

disposed A successful commercial unit is an economic balance of all

these factors A variety of reactor types are used in the chemical,

petrochemical, and pharmaceutical industries Some of these reactors

are listed in Table 19-1 They include gas, liquid, or multiphase batch

reactors, stirred tank reactors, and tubular rectors

There are a number of textbooks on chemical reaction engineering

Davis and Davis (Fundamentals of Chemical Reaction Engineering,

McGraw-Hill, 2003) provide a lucid discussion of kinetics and

princi-ples A more comprehensive treatment together with access to

Chemical Reaction Engineering, 3d ed., Prentice-Hall, 1999) A chemistry-oriented perspective is provided by Schmidt (The Engi- neering of Chemical Reactions, Oxford University Press, 1999) The

book by Froment and Bischoff provides a thorough discussion of tor analysis and design A practical manual on reactor design and

reac-scale-up is by Harriott (Chemical Reactor Design, Marcel Dekker, 2003) Levenspiel (Chemical Reaction Engineering, 3d ed., Wiley,

1999) was among the first to present a phenomenological discussion offundamentals The mathematical underpinnings of reactor modeling

are covered by Bird et al (Transport Phenomena, 2d ed., Wiley, 2002).

This section contains a number of illustrations and sketches from

books by Walas (Chemical Process Equipment Selection and Design, Butterworths, 1990) and Ullmann [Encyclopedia of Chemical Tech- nology (in German), vol 3, Verlag Chemie, 1973, pp 321–518].

Mathematical models may be used to design reactors and analyzetheir performance Detailed models have mainly been developed forlarge-scale commercial processes A number of software tools are nowavailable This chapter will discuss some of the reactors used commer-cially together with how mathematical models may be used For addi-tional details, a number of books on reactor analysis cited in this sectionare available The discussion will indicate that logical choices aimed atmaximizing reaction rate and selectivity for a given set of kinetics canlead to rational reactor selection While there has been progress inrecent years, reactor design and modeling are largely an art

REACTOR CONCEPTS

Since a primary purpose of a reactor is to provide desirable conditions

for reaction, the reaction rate per unit volume of reactor is important in

analyzing or sizing a reactor For a given production rate, it determines

the reactor volume required to effect the desired transformation The

residence time in a reactor is inversely related to the term space

veloc-ity (defined as volumetric feed rate/reactor volume) The fraction of

reactants converted to products and by-products is the conversion The

fraction of desired product in the material converted on a molar basis is

referred to as selectivity The product of conversion and the fractional

selectivity provides a measure of the fraction of reactants converted to

product, known as yield The product yield provides a direct measure of

the level of (atom) utilization of the raw materials and may be an

impor-tant component of operating cost A measure of reactor utilization

called space time yield (STY) is the ratio of product generation rate to

reactor volume When a catalyst is used, the reactor has to make

prod-uct without major process interruptions The catalyst may be

homoge-neous or heterogehomoge-neous, and the latter can be a living biological cell A

key aspect of catalyst performance is the durability of the active site.

Since a chemical or biochemical process has a number of unit

opera-tions around the reactor, it is often beneficial to minimize the variability

of reactant and product flows This typically means that the reactor is

operated at a steady state Interactions between kinetics, fluid flow,

transport resistances, and heat effects sometimes result in multiple

steady states and transient (dynamic) behavior Reactor dynamics can

also result in runaway behavior, where reactor temperature continues

to increase until the reactants are depleted, or wrong-way behavior,

where reducing inlet temperature (or reactant flow rate) can result in

temperature increases farther downstream and a possible runaway

Since such behavior can result in large perturbations in the process and

possibly safety issues, a reactor control strategy has to be implemented.

The need to operate safely under all conditions calls for a thorough

analysis to ensure that the reactor is inherently safe and that all possible

unsafe outcomes have been considered and addressed Since various

solvents may be used in chemical processes and reactors generate both

products and by-products, solvent and by-product emissions can cause

emission and environmental footprint issues that must be considered.

Reactor design is often discussed in terms of independent and

dependent variables Independent variables are choices such as

reac-tor type and internals, catalyst type, inlet temperature, pressure, and

fresh feed composition Dependent variables result from independent

variable selection They may be constrained or unconstrained

Con-strained dependent variables often include pressure drop (limited due

to compressor cost), feed composition (dictated by the composition ofthe recycle streams), temperature rise (or decline), and local andeffluent composition The reactor design problem is often aimed atoptimizing independent variables (within constraints) to maximize anobjective function (such as conversion and selectivity)

Since the reactor feed may contain inert species (e.g., nitrogen andsolvents) and since there may be unconverted feed and by-products inthe reactor effluent, a number of unit operations (distillation, filtration,etc.) may be required to produce the desired product(s) In practice,the flow of mass and energy through the process is captured by aprocess flow sheet The flow sheet may require recycle (of unconvertedfeed, solvents, etc.) and purging that may affect reaction chemistry.Reactor design and operation influence the process and vice versa

REACTOR TYPES

Reactors may be classified according to the mode of operation, theend-use application, the number of phases present, whether (or not) acatalyst is used, and whether some other function (e.g., heat transfer,separations, etc.) is conducted in addition to the reaction

Classification by Mode of Operation

Batch Reactors A “batch” of reactants is introduced into the

reactor operated at the desired conditions until the target conversion

is reached Batch reactors are typically tanks in which stirring of thereactants is achieved using internal impellers, gas bubbles, or a pump-around loop where a fraction of the reactants is removed and exter-nally recirculated back to the reactor Temperature is regulated viainternal cooling surfaces (such as coils or tubes), jackets, reflux con-densers, or pump-around loop that passes through an exchanger.Batch processes are suited to small production rates, to long reactiontimes, to achieve desired selectivity, and for flexibility in campaigningdifferent products

Continuous Reactors Reactants are added and products removed

continuously at a constant mass flow rate Large daily production ratesare mostly conducted in continuous equipment

A continuous stirred tank reactor (CSTR) is a vessel to which

reac-tants are added and products removed while the contents within thevessel are vigorously stirred using internal agitation or by internally (orexternally) recycling the contents CSTRs may be employed in series or

in parallel An approach to employing CSTRs in series is to have a large

19-4

TABLE 19-1 Residence Times and/or Space Velocities in Industrial Chemical Reactors*

Residence time or

(raw materials) Type phase Catalyst T,°C P, atm velocity page† Acetaldehyde (ethylene, air) FB L Cu and Pd chlorides 50–100 8 6–40 min [2] 1, [7] 3 Acetic anhydride (acetic acid) TO L Triethylphosphate 700–800 0.3 0.25–5 s [2]

Acrolein (formaldehyde, acetaldehyde) FL G MnO, silica gel 280–320 1 0.6 s [1] 1 384, [7] 33 Acrylonitrile (air, propylene, ammonia) FL G Bi phosphomolybdate 400 1 4.3 s [3] 684, [2] 47 Adipic acid (nitration of cyclohexanol) TO L Co naphthenate 125–160 4–20 2 h [2] 51, [7] 49 Adiponitrile (adipic acid) FB G H 3 BO 3 370–410 1 3.5–5 s [1] 2 152,

Alkylate (i-C4 , butenes) CST L H 2 SO 4 5–10 2–3 5–40 min [4] 223

Allyl chloride (propylene, Cl 2 ) TO G NA 500 3 0.3–1.5 s [1] 2 416, [7] 67

7,800 GHSV

10,000 GHSV

Aniline (nitrobenzene, H 2 ) B L FeCl 2 in H 2 O 95–100 1 8 h [1] 3 289

Aniline (nitrobenzene, H 2 ) FB G Cu on silica 250–300 1 0.5–100 s [7] 82

Aspirin (salicylic acid, acetic anhydride) B L None 90 1 >1 h [7] 89

815 GHSV [9] 109

Benzoic acid (toluene, air) SCST LG None 125–175 9–13 0.2–2 h [7] 101

34,000 GHSV Butadiene sulfone (butadiene, SO 2 ) CST L t-Butyl catechol 34 12 0.2 LHSV [1] 5 192

i-Butane (n-butane) FB L AlCl 3 on bauxite 40–120 18–36 0.5–1 LHSV [4] 239, [7] 683

Butanols (propylene hydroformylation) FB L PH 3 -modified 150–200 1,000 100 g L⋅h [1] 5 373

Co carbonyls Butanols (propylene hydroformylation) FB L Fe pentacarbonyl 110 10 1 h [7] 125

Caprolactam (cyclohexane oxime) CST L Polyphosphoric 80–110 1 0.25–2 h [1] 6 73, [7] 139

acid Carbon disulfide (methane, sulfur) Furn G None 500–700 1 1.0 s [1] 6 322, [7] 144 Carbon monoxide oxidation (shift) TU G Cu-Zn or Fe 2 O 3 390–220 26 4.5 s [6] 44

7,000 GHSV

Coking, delayed (drum, 100 ft max height) B LG None 500–440 4 0.3–0.5 ft/s [1] 10 8

vapor Cracking, fluid catalytic Riser G Zeolite 520–540 2–3 2–4 s (14) 353

Cracking, hydro (gas oils) FB LG Ni, SiO 2 , Al 2 O 3 350–420 100–150 1–2 LHSV [11]

Cracking (visbreaking residual oils) TU LG None 470–495 10–30 450 s, 8 LHSV [11]

Cumene hydroperoxide (cumene, air) CST L Metal porphyrins 95–120 2–15 1–3 h [7] 191

Cyclohexane (benzene, H 2 ) FB G Ni on Al 2 O 3 150–250 25–55 0.75–2 LHSV [7] 201

Cyclohexanol (cyclohexane, air) SCST LG None 185–200 48 2–10 min [7] 203

Cyclohexanone (cyclohexanol) MT G Cu on pumice 250–350 1 4–12 s [8] (1963) Cyclopentadiene (dicyclopentadiene) TJ G None 220–300 1–2 0.1–0.5 LHSV [7] 212

Dibutylphthalate (phthalic anhydride, butanol) B L H 2 SO 4 150–200 1 1–3 h [7] 227

Diethylketone (ethylene, CO) TO L Co oleate 150–300 200–500 0.1–10 h [7] 243

Dimethylsulfide (methanol, CS 2 ) FB G Al 2 O 3 375–535 5 150 GHSV [7] 266

3.3 LHSV [8] (1938) Dodecylbenzene (benzene, propylene tetramer) CST L AlCl 3 15–20 1 1–30 min [7] 283

Ethanol (ethylene, H 2 O) FB G H 3 PO 4 300 82 1,800 GHSV [2] 356, [7] 297 Ethyl acetate (ethanol, acetic acid) TU, CST L H 2 SO 4 100 1 0.5–0.8 LHSV [10] 45, 52, 58 Ethyl chloride (ethylene, HCl) TO G ZnCl 2 150–250 6–20 2 s [7] 305

1,880 GHSV [6] 13

Ethylene, propylene chlorohydrins (Cl 2 , H 2 O) CST LG None 30–40 3–10 0.5–5 min [7] 310, 580 Ethylene glycol (ethylene oxide, H 2 O) TO LG 1% H 2 SO 4 50–70 1 30 min [2] 398

Ethylene glycol (ethylene oxide, H 2 O) TO LG None 195 13 1 h [2] 398

Formaldehyde (methanol, air) FB G Ag gauze 450–600 1 0.01 s [2] 423

Glycerol (allyl alcohol, H 2 O 2 ) CST L H 2 WO 4 40–60 1 3 h [7] 347

19-5

Residence time or

(raw materials) Type phase Catalyst T,°C P, atm velocity page†

3,000 GHSV Hydrodesulfurization of naphtha TO LG Co-MO 315–500 20–70 1.5–8 LHSV [4] 285,

125 WHSV [6] 179,

[9] 201

Isoprene (i-butene, formaldehyde) FB G HCl, silica gel 250–350 1 1 h [7] 389

Maleic anhydride (butenes, air) FL G V 2 O 5 300–450 2–10 0.1–5 s [7] 406

Methanol (CO, H 2 ) FB G ZnO, Cr 2 O 3 350–400 340 5,000 GHSV [7] 421

Methanol (CO, H 2 ) FB G ZnO, Cr 2 O 3 350–400 254 28,000 GHSV [3] 562

3.1 LHSV Methyl chloride (methanol, Cl 2 ) FB G Al 2 O 3 gel 340–350 1 275 GHSV [2] 533

Methyl ethyl ketone (2-butanol) FB G ZnO 425–475 2–4 0.5–10 min [7] 437

Methyl ethyl ketone (2-butanol) FB G Brass spheres 450 5 2.1 s [10] 284

13 LHSV Nitrobenzene (benzene, HNO 3 ) CST L H 2 SO 4 45–95 1 3–40 min [7] 468

Nitromethane (methane, HNO 3 ) TO G None 450–700 5–40 0.07–0.35 s [7] 474

Phenol (chlorobenzene, steam) FB G Cu, Ca phosphate 430–450 1–2 2 WHSV [7] 522

900 GHSV

Phthalic anhydride (o-xylene, air) MT G V 2 O 5 350 1 1.5 s [3] 482, 539, [7] 529 Phthalic anhydride (naphthalene, air) FL G V 2 O 5 350 1 5 s [9] 136, [10] 335 Polycarbonate resin (bisphenol-A, phosgene) B L Benzyltriethylammonium 30–40 1 0.25–4 h [7] 452

chloride Polyethylene TU L Organic peroxides 180–200 1,000–1,700 0.5–50 min [7] 547

Polyethylene TU L Cr 2 O 3 , Al 2 O 3 , SiO 2 70–200 20–50 0.1–1,000 s [7] 549

Propionitrile (propylene, NH 3 ) TU G CoO 350–425 70–200 0.3–2 LHSV [7] 578

Reforming of naphtha (H 2 /hydrocarbon = 6) FB G Pt 490 30–35 3 LHSV [6] 99

t-Butyl methacrylate (methacrylic acid, i-butene) CST L H 2 SO 4 25 3 0.3 LHSV [1] 5 328

Toluene diisocyanate (toluene diamine, phosgene) B LG None 200–210 1 7 h [7] 657

Tricresyl phosphate (cresyl, POCl 3 ) TO L MgCl 2 150–300 1 0.5–2.5 h [2] 850, [7] 673 Vinyl chloride (ethylene, Cl 2 ) FL G None 450–550 2–10 0.5–5 s [7] 699

Aldehydes (diisobutene, CO) CST LG Co Carbonyl 150 200 1.7 h [12] 173

Allyl alcohol (propylene oxide) FB G Li phosphate 250 1 1.0 LHSV [15] 23

NOxpollutant (with NH 3 ) FB G V 2 O 5 ⋅TiO 2 300–400 1–10 [14] 332

Automobile emission control M G Pt/Rh/Pd/Al 2 O 3 350–500 1 20,000 GHSV [16] 69

Nitrogen oxide emission control M G V 2 O 5 -WO 3 /TiO 2 300–400 1 4–10,000 [16] 306

GHSV Carbon monoxide and hydrocarbon emission M G Pt-Pd/Al 2 O 3 500–600 1 80–120,000 [16] 334

Ozone control from aircraft cabins M G Pd/Al 2 O 3 130–170 1 ~10 6 GHSV [16] 263

Vinyl acetate (ethylene + CO) MT LG Cu-Pd 130 30 1 h L, 10 s G [12] 140

*Abbreviations: reactors: batch (B), continuous stirred tank (CST), fixed bed of catalyst (FB), fluidized bed of catalyst (FL), furnace (Furn.), monolith (M), tubular (MT), semicontinuous stirred tank (SCST), tower (TO), tubular (TU) Phases: liquid (L), gas (G), both (LG) Space velocities (hourly): gas (GHSV), liquid (LHSV), weight (WHSV) Not available, NA To convert atm to kPa, multiply by 101.3.

multi-†1 J J McKetta, ed., Encyclopedia of Chemical Processing and Design, Marcel Dekker, 1976 to date (referenced by volume).

2 W L Faith, D B Keyes, and R L Clark, Industrial Chemicals, revised by F A Lowenstein and M K Moran, John Wiley & Sons, 1975.

3 G F Froment and K B Bischoff, Chemical Reactor Analysis and Design, John Wiley & Sons, 1979.

4 R J Hengstebeck, Petroleum Processing, McGraw-Hill, New York, 1959.

5 V G Jenson and G V Jeffreys, Mathematical Methods in Chemical Engineering, 2d ed., Academic Press, 1977.

6 H F Rase, Chemical Reactor Design for Process Plants, Vol 2: Case Studies, John Wiley & Sons, 1977.

7 M Sittig, Organic Chemical Process Encyclopedia, Noyes, 1969 (patent literature exclusively).

8 Student Contest Problems, published annually by AIChE, New York (referenced by year).

9 M O Tarhan, Catalytic Reactor Design, McGraw-Hill, 1983.

10 K R Westerterp, W P M van Swaaij, and A A C M Beenackers, Chemical Reactor Design and Operation, John Wiley & Sons, 1984.

11 Personal communication (Walas, 1985).

12 B C Gates, J R Katzer, and G C A Schuit, Chemistry of Catalytic Processes, McGraw-Hill, 1979.

13 B E Leach, ed., Applied Industrial Catalysts, 3 vols., Academic Press, 1983.

14 C N Satterfield, Heterogeneous Catalysis in Industrial Practice, McGraw-Hill, 1991.

15 C L Thomas, Catalytic Processes and Proven Catalysts, Academic Press, 1970.

16 Heck, Farrauto, and Gulati, Catalytic Air Pollution Control: Commercial Technology, Wiley-Interscience, 2002.

cylindrical tank with partitions: feed enters the first compartment and

over (or under) flows to the next compartment, and so on The

compo-sition is maintained as uniform as possible in each individual

compart-ment; however, a stepped concentration gradient exists from one

CSTR to the next When the reactants have limited solubility

(miscibil-ity) and a density difference, the vertical staged reactor with

counter-current operation may be used Alternatively, each CSTR in a series or

parallel configuration can be an independent vessel Examples of

stirred tank reactors with heat transfer are shown in Fig 19-1

A tubular flow reactor (TFR) is a tube (or pipe) through which

reac-tants flow and are converted to product The TFR may have a varying

diameter along the flow path In such a reactor, there is a continuous

gra-dient (in contrast to the stepped gragra-dient characteristic of a

CSTR-in-series battery) of concentration in the direction of flow Several tubular

reactors in series or in parallel may also be used Both horizontal and

ver-tical orientations are common When heat transfer is needed, individual

tubes are jacketed or a shell-and-tube construction is used The reaction

side may be filled with solid catalyst or internals such as static mixers (to

improve interphase contact in heterogeneous reactions or to improve

heat transfer by turbulence) Tubes that have 3- to 4-in diameter and are

several miles long may be used in polymerization service

Large-diame-ter vessels, with packing (or trays) used to regulate the residence time in

the reactor, may also be used Some of the configurations in use are axial

flow, radial flow, multishell with built-in heat exchangers, and so on

A reaction battery of CSTRs in series, although both mechanically

and operationally more complex and expensive than a tubular reactor,

provides flexibility Relatively slow reactions are best conducted in a

stirred tank reactor battery A tubular reactor is used when heat

trans-fer is needed, where high pressures and/or high (or low) temperatures

occur, and when relatively short reaction times suffice

Semibatch Reactors Some of the reactants are loaded into the

reactor, and the rest of the reactants are fed gradually Alternatively,

one reactant is loaded into the reactor, and the other reactant is fed

continuously Once the reactor is full, it may be operated in a batch

mode to complete the reaction Semibatch reactors are especially

favored when there are large heat effects and heat-transfer capability

is limited Exothermic reactions may be slowed down and

endother-mic reactions controlled by limiting reactant concentration In

biore-actors, the reactant concentration may be limited to minimize toxicity

Other situations that may call for semibatch reactors include control

of undesirable by-products or when one of the reactants is a gas of

lim-ited solubility that is fed continuously at the dissolution rate

Classification by End Use Chemical reactors are typically used for

the synthesis of chemical intermediates for a variety of specialty (e.g.,agricultural, pharmaceutical) or commodity (e.g., raw materials for poly-

mers) applications Polymerization reactors convert raw materials to

polymers having a specific molecular weight and functionality The ference between polymerization and chemical reactors is artificially

dif-based on the size of the molecule produced Bioreactors utilize (often

genetically manipulated) organisms to catalyze biotransformations eitheraerobically (in the presence of air) or anaerobically (without air present)

Electrochemical reactors use electricity to drive desired reactions

Exam-ples include synthesis of Na metal from NaCl and Al from bauxite ore Avariety of reactor types are employed for specialty materials synthesisapplications (e.g., electronic, defense, and other)

Classification by Phase Despite the generic classification by

oper-ating mode, reactors are designed to accommodate the reactant phasesand provide optimal conditions for reaction Reactants may be fluid(s) or

solid(s), and as such, several reactor types have been developed phase reactors are typically gas- (or plasma- ) or liquid-phase reactors Two-phase reactors may be gas-liquid, liquid-liquid, gas-solid, or liquid- solid reactors Multiphase reactors typically have more than two phases

Single-present The most common type of multiphase reactor is a solid reactor; however, liquid-liquid-solid reactors are also used The clas-sification by phases will be used to develop the contents of this section

gas-liquid-In addition, a reactor may perform a function other than reaction

alone Multifunctional reactors may provide both reaction and mass

transfer (e.g., reactive distillation, reactive crystallization, reactive branes, etc.), or reaction and heat transfer This coupling of functionswithin the reactor inevitably leads to additional operating constraints onone or the other function Multifunctional reactors are often discussed

mem-in the context of process mem-intensification The primary driver for functional reactors is functional synergy and equipment cost savings

multi-REACTOR MODELING

As discussed in Sec 7, chemical kinetics may be mathematicallydescribed by rate equations Reactor performance is also amenable toquantitative analysis The quantitative analysis of reaction systems isdealt with in the field of chemical reaction engineering

The level of mathematical detail that can be included in the analysisdepends on the level of understanding of the physical and chemicalprocesses that occur in a reactor As a practical matter, engineeringdata needed to build a detailed model for some new chemistry typicallyare unavailable early in the design phase Reactor designers may usesimilarity principles (e.g., dimensionless groups), rules of thumb, trendanalysis, design of experiments (DOE), and principal-componentanalysis (PCA) to scale up laboratory reactors For hazardous systems

in which compositional measurements are difficult, surrogate tors such as pressure or temperature may be used As more knowl-edge becomes available, however, a greater level of detail may beincluded in a mathematical model A detailed reactor model maycontain information on vessel configuration, stoichiometric relation-ships, kinetic rate equations, correlations for thermodynamic andtransport properties, contacting efficiency, residence time distribu-tion, and so on

indica-Models may be used for analyzing data, estimating performance,reactor scale-up, simulating start-up and shutdown behavior, and con-trol The level of detail in a model depends on the need, and this isoften a balance between value and cost Very elaborate models are jus-tifiable and have been developed for certain widely practiced andlarge-scale processes, or for processes where operating conditions areespecially critical

Modeling Considerations A useful reactor model allows the

user to predict performance or to explore uncertainties not easily orcost-effectively investigated through experimentation Uncertaintiesthat may be explored through modeling may include scale-up options,explosion hazards, runaway reactions, environmental emissions, reac-tor internals design, and so on As such, the model must contain an

optimal level of detail (principle of optimal sloppiness) required to

meet the desired objective(s) For example, if mixing is critical to formance, the model must include flow equations that reflect the role

per-of mixing If heat effects are small, an isothermal model may be used

(a)

FIG 19-1 Stirred tank reactors with heat transfer (a) Jacket (b) Internal coils.

(c) Internal tubes (d) External heat exchanger (e) External reflux condensor (f)

Fired heater (Walas, Reaction Kinetics for Chemical Engineers, McGraw-Hill,

1959.)

A key aspect of modeling is to derive the appropriate momentum,

mass, or energy conservation equations for the reactor These

bal-ances may be used in lumped systems or derived over a differential

volume within the reactor and then integrated over the reactor

vol-ume Mass conservation equations have the following general form:

(19-1)The general form for the energy balance equation is

(19-2)The model defines each of these terms Solving the set of equations

provides outputs that can be validated against experimental

observa-tions and then used for predictive purposes Mathematical models for

ideal reactors that are generally useful in estimating reactor

perfor-mance will be presented Additional information on these reactors is

available also in Sec 7

Batch Reactor Since there is no addition or removal of reactants,

the mass and energy conservation equations for a batch reactor with a

constant reactor volume are

V r r(C,T) + V r = 0 (19-3)

−qA k − V r(−∆Hr )r(C,T) + V r ρc p = 0 (19-4)

where qA kis the addition (or removal) of heat from the reactor Mean

values of physical properties are used in Eqs (19-3) and (19-4) For an

isothermal first-order reaction r(C,T) = kC, the mass and energy

equations can be combined and the solution is

Typically batch reactors may have complex kinetics, mixing, and

heat-transfer issues In such cases, detailed momentum, mass, and energy

balance equations will be required

Semibatch Reactor Feed is added for a fixed time, and the

reac-tion proceeds as the feed is added The reactor equareac-tions governing

the feed addition portion of the process are

in Eq (19-6) yields

After feed addition is completed, the reactor may be operated in a

batch mode In this case, Eqs (19-3) and (19-4) may be used with the

concen-Ideal Continuous Stirred Tank Reactor In an ideal CSTR,

reactants are fed into and removed from an ideally mixed tank As aresult, the concentration within the tank is uniform and identical tothe concentration of the effluent The mass and energy conservationequations for an ideal constant-volume or constant-density CSTR

with constant volumetric feed rate V′ may be written as

V ′C0= V′C + V r r(C,T) + V r (19-11)

V ′ρc p T0= −Q(T) + V′ρc p T − V r(−∆H)r(C,T) + Vr ρc p (19-12)

where Q(T) represents any addition or removal of heat from the

reac-tor and mean values of physical properties are used For example, if

heat is transferred through the reactor wall, Q(T) = A k U(T c −T), where

A k is the heat-transfer area, U is the overall heat-transfer coefficient, and T cis the temperature of the heat-transfer fluid

The above ordinary differential equations (ODEs), Eqs (19-11)

and (19-12), can be solved with an initial condition For an isothermal

first-order reaction and an initial condition, C(0)= 0, the linear ODEmay be solved analytically At steady state, the accumulation term iszero, and the solution for the effluent concentration becomes

Since the contents of an ideal CSTR are perfectly mixed, the sion within the reactor is infinite In practice, CSTRs may not be ide-ally mixed In such cases, the reactor may be modeled as having afraction of the feed α in bypass and a fraction β of the reactor volumestagnant The material balance is

disper-C = αC0+ (1 − α)C1 (19-14)(1− α)V′C0= (1 − α)V′C1+ (1 − β)kV r C1 (19-15)

where C1is the concentration leaving the active zone of the tank

Elimination of C1will relate the input and overall output tions For a first-order reaction,

The two parameters α and β may be expected to depend on reactorinternals and the amount of agitation

Plug Flow Reactor A plug flow reactor (PFR) is an idealized

tubular reactor in which each reactant molecule enters and travelsthrough the reactor as a “plug,” i.e., each molecule enters the reactor

at the same velocity and has exactly the same residence time As aresult, the concentration of every molecule at a given distance down-stream of the inlet is the same The mass and energy balance for a dif-

ferential volume between position V r and V r + dV rfrom the inlet may

be written as partial differential equations (PDEs) for a

constant-density system:

+ V′c pρ − (−∆H)r(C,T) + c pρ = 0 (19-18)

where Q(T) represents any addition of heat to (or removal from) the

reactor wall and mean values of physical properties are used The

above PDEs can be solved with an initial condition, e.g., C(x,0)=

C t=0(x), and a boundary condition, e.g., C(0,t) = C0(t), which is the

concentration at the inlet At steady state, the accumulation termabove is zero, and the solution for an isothermal first-order reaction isthe same as that for a batch reactor, Eq (19-5):

per unit time

Energy generated per unit time

Accumulation

of energy per unit time[

Amount of A

accumulated per unit time[

C = C0exp−k = C0e −kt (19-19)

A tubular reactor will likely deviate from plug flow in most practical

cases, e.g., due to backmixing in the direction of flow, reactor

inter-nals, etc A way of simulating axial backmixing is to represent the

reac-tor volume as a series of n stirred tanks in series The steady-state

solution for a single ideal CSTR may be extended to find the effluent

concentration after two ideal CSTRs and then to n ideal stages as

In this case, V ris the volume of each individual reactor in the battery

In modeling a reactor, n is empirically determined based on the extent

of reactor backmixing obtained from tracer studies or other

experi-mental data In general, the number of stages n required to approach

an ideal PFR depends on the rate of reaction (e.g., the magnitude of

the specific rate constant k for the first-order reaction above) As a

practical matter, the conversion for a series of stirred tanks approaches

a PFR for n> 6

An alternate way of generating backmixing is to recycle a fraction of

the product from a PFR back to the inlet This reactor, known as a

recy-cle reactor, has been described in Sec 7 of the Handbook As the recyrecy-cle

ratio (i.e., recycle flow to product flow) is increased, the effective

disper-sion is increased and the recycle reactor approaches an ideal CSTR

Tubular Reactor with Dispersion An alternative approach to

describe deviation from ideal plug flow due to backmixing is to

include a term that allows for axial dispersion D ein the plug flow

reac-tor equations The reacreac-tor mass balance equation now becomes

V′ − D e + r(C, T) + = 0 (19-21)

The model is referred to as a dispersion model, and the value of the

dispersion coefficient D eis determined empirically based on

correla-tions or experimental data In a case where Eq (19-21) is converted to

dimensionless variables, the coefficient of the second derivative is

referred to as the Peclet number (Pe = uL/D e ), where L is the reactor

length and u is the linear velocity For plug flow, D e= 0 (Pe 1 ∞) while

for a CSTR, D e= ∞ (Pe = 0) To solve Eq (19-21), one initial condition

and two boundary conditions are needed The “closed-ends” boundary

conditions are uC0= (uC − D e ∂C/∂L) L= 0and (∂C/∂L) L = L= 0 (e.g., see

Wen and Fan, Models for Flow Systems in Chemical Reactors, Marcel

Dekker, 1975) Figure 19-2 shows the performance of a tubular reactor

with dispersion compared to that of a plug flow reactor

Ideal chemical reactors typically may be modeled using a

combina-tion of ideal CSTR, PFR, and dispersion model equacombina-tions In the case

of a single phase, the approach is relatively straightforward In the case

of two-phase flow, a bubble column (fluidized-bed) reactor may be

modeled as containing an ideal CSTR liquid (emulsion) phase and a

plug flow (with dispersion) gas phase containing bubbles Given inlet

gas conditions, the concentration in the liquid (emulsion) may be

cal-culated using mass-transfer correlations from the bubbles to the liquid

(emulsion) along with reaction in the liquid (emulsion) phase along the

length of the reactor In flooded gas-liquid reactors where the gas and

liquid are countercurrent to each other, a plug flow (with dispersion)

model may be used for both phases The concentration of reactant in a

phase at each end of the reactor is known The concentration of the

other phase is assumed at one end, and mass-transfer correlations and

reaction kinetics are used together with a plug flow (with dispersion)

model to get to the other exit The iterative process continues until the

concentrations at each end match the feed conditions

Reactor Selection Ideal CSTR and PFR models are extreme cases

of complete axial dispersion (D e = ∞) and no axial dispersion (D e= 0),

respectively As discussed earlier, staged ideal CSTRs may be used to

represent intermediate axial dispersion Alternatively, within the context

of a PFR, the dispersion (or a PFR with recycle) model may be used to

represent increased dispersion Real reactors inevitably have a level of

dispersion in between that for a PFR or an ideal CSTR The level of

dis-persion may depend on fluid properties (e.g., is the fluid newtonian),

V′ fluid flow (e.g., the level of mixing), transport properties (e.g., the diffu-sivity of reactants in the fluid), and reactor geometry The effect of

dis-persion in a real reactor is discussed within the context of an ideal CSTRand PFR model in Fig 19-2

Figure 19-2a shows the effect of dispersion on the reactor volume

required to achieve a certain exit concentration (or conversion) As Penumber increases (i.e., dispersion decreases), the reactor begins toapproach plug flow and the reactor volume required to achieve a cer-tain conversion approaches the volume for a PFR At lower Pe num-bers, reactor performance approaches that of an ideal CSTR and thereactor volume required to achieve a certain concentration is much

higher than that of a PFR This behavior can be observed in Fig 19-2b

that shows the effect of exit concentration on reaction rate At a givenrate, an ideal CSTR has the highest exit concentration (lowest conver-sion) and a PFR has the lowest exit concentration (highest conver-

sion) As Fig 19-2c shows, since the concentration in an ideal CSTR is

the same as the exit concentration, there is a sharp drop in tion from the inlet to the bulk concentration In contrast, the concen-tration in the reactor drops continuously from the inlet to the outletfor a PFR At intermediate values of Pe, the “closed-ends” boundarycondition in the dispersion model causes a drop in concentration tolevels lower than for an ideal CSTR

concentra-As discussed in Fig 19-2, for a given conversion, the reactor dence time (or reactor volume required) for a positive order reactionwith dispersion will be greater than that of a PFR This need for alonger residence time is illustrated for a first-order isothermal reac-tion in a PFR versus an ideal CSTR using Eqs (19-13) and (19-19)

Equation (19-22) indicates that, for a nominal 90 percent conversion,

an ideal CSTR will need nearly 4 times the residence time (or volume)

of a PFR This result is also worth bearing in mind when batch reactorexperiments are converted to a battery of ideal CSTRs in series in thefield The performance of a completely mixed batch reactor and asteady-state PFR having the same residence time is the same [Eqs.(19-5) and (19-19)] At a given residence time, if a batch reactor pro-vides a nominal 90 percent conversion for a first-order reaction, a sin-gle ideal CSTR will only provide a conversion of 70 percent Theabove discussion addresses conversion Product selectivity in complexreaction networks may be profoundly affected by dispersion Thisaspect has been addressed from the standpoint of parallel and consec-utive reaction networks in Sec 7

Reactors may contain one or more fluid phases The level of sion in each phase may be represented mathematically by using some

disper-of the above thinking

In industrial practice, the laboratory equipment used in chemicalsynthesis can influence reaction selection As issues relating to kinet-ics, mass transfer, heat transfer, and thermodynamics are addressed,reactor design evolves to commercially viable equipment Often,more than one type of reactor may be suitable for a given reaction Forexample, in the partial oxidation of butane to maleic anhydride over avanadium pyrophosphate catalyst, heat-transfer considerations dictatereactor selection and choices may include fluidized beds or multi-tubular reactors Both types of reactors have been commercialized.Often, experience with a particular type of reactor within the organi-zation can play an important part in selection

There are several books on reactor analysis and modeling including

those by Froment and Bischoff (Chemical Reactor Analysis and Design, Wiley, 1990), Fogler (Elements of Chemical Reaction Engineering, Prentice-Hall International Series, 2005), Levenspeil (Chemical Reac- tion Engineering, Wiley, 1999), and Walas (Modeling with Differential Equations in Chemical Engineering, Butterworth-Heineman, 1991).

Chemical Kinetics Reactor models include chemical kinetics in

the mass and energy conservation equations The two basic laws of

kinetics are the law of mass action for the rate of a reaction and the Arrhenius equation for its dependence on temperature Both of these

strictly apply to elementary reactions More often, laboratory data are

used to develop mathematical relationships that describe reaction

rates that are then used These relationships require analysis of the

laboratory reactor data, as discussed in Sec 7 Reactor models will

require that kinetic rate information be expressed on a unit reactor

volume basis Two-phase or multiphase reactors will require a level of

detail (e.g., heat and mass transport between phases) to capture the

relevant physical and chemical processes that affect rate

Pressure Drop, Mass and Heat Transfer Pressure drop is

more important in reactor design than in analysis or simulation The

size of the compressor is dictated by pressure drop across the reactor,

especially in the case of gas recycle Compressor costs can be

signifi-cant and can influence the aspect ratio of a packed or trickle bed

reac-tor Pressure drop correlations often may depend on the geometry, the

scale, and the fluids used in data generation Prior to using literature

correlations, it often is advisable to validate the correlation with

mea-surements on a similar system at a relevant scale

Depending on the type of reactor, appropriate mass-transfer

corre-lations may have to be used to connect intrinsic chemical kinetics to

the reaction rate per unit reactor volume A number of these tions have already been discussed in Sec 5 of the Handbook, “Heatand Mass Transfer.” The determination of intrinsic kinetics hasalready been discussed in Sec 7 of the Handbook In the absence of acorrelation validated for a specific use, the analogy between momen-tum, heat and mass transfer may often be invoked

correla-The local reactor temperature affects the rates of reaction, rium conversion, and catalyst deactivation As such, the local temper-ature has to be controlled to maximize reaction rate and to minimizedeactivation In the case of an exothermic (endothermic) reaction,higher (lower) local temperatures can cause suboptimal local concen-trations Heat will have to be removed (added) to maintain more uni-form temperature conditions The mode of heat removal (addition)will depend on the application and on the required heat-transfer rate.Examples of stirred tank reactors with heat transfer are shown inFig 19-1 If the heat of reaction is not significant, an adiabatic reactormay be used For modest heat addition (removal), a jacketed stirred

equilib-tank is adequate (Fig 19-1a) As the heat exchange requirements

(a)

(b)

FIG 19-2 Chemical conversion by the dispersion model (a) Volume relative to plug flow against residual concentration ratio for a first-order reaction (b) Residual concentration ratio against kC0t for a second-order reaction (c) Concentration profile at the inlet of a closed-ends vessel with disper- sion for a second-order reaction with kC0t= 5.

increase, internal coils or internal tubes that contain a heat-transfer

fluid may be required (Fig 19-1b and c) In special cases, where the

peak temperature has to be tightly controlled (e.g., in bioreactors) or

where fouling may be an issue, the liquid may be withdrawn,

circu-lated through an external heat exchanger, and returned to the reactor

(Fig 19-1d) In some cases, the vapor above the liquid may be passed

through an external reflux condenser and returned to the reactor (Fig

19-1e) In highly endothermic reactors, the entire reactor may be

placed inside a fired heater (Fig 19-1f), or the reactor shell may be

heated to high temperatures by using induction heat

Several of the heat-transfer options for packed beds are illustrated

in Fig 19-3 Again, if heat requirements are modest, an adiabatic

reactor is adequate (Fig 19-3a) If pressure drop through the reactor

is an issue, a radial flow reactor may be used (Fig 19-3b) There are

few examples of radial flow reactors in industry Potential problems

include gas distribution in the case of catalyst attrition or settling A

common way of dealing with more exothermic (endothermic)

reac-tions is to split the reactor into several beds and then provide interbed

heat exchange (Fig 19-3c) For highly exothermic (endothermic)

reactors, a shell-and-tube multitubular reactor concept may be

uti-lized (Fig 19-3d) The reactor now begins to look more like a heat

exchanger If multiple beds are needed, rather than using interbed

heat exchangers, cold feed may be injected (also called cold shot) in

between beds (Fig 19-3e) In some cases, the heat exchanger may be

outside the reactor (Fig 19-3f) The concept of a reactor as a heat

exchanger may be extended to an autothermal multitubular reactor in

which, for example, the reactants are preheated on the shell side with

reaction occurring in the tubes (Fig 19-3g) Such reactors can have

control issues and are not widely used A common approach is to have

multiple adiabatic reactors with cooling in between reactors (Fig 19-3h).

If the reaction is endothermic, heat may be added by passing the

effluents from each reactor through tubes placed inside a common

process heater (as is the case for a petroleum reforming reactor shown

in Fig 19-3i) For highly endothermic reactions, a fuel-air mixture or

raw combustion gases may be introduced into the reactor In an

extreme situation, the entire reactor may be housed within a furnace

(as in the case of steam reforming for hydrogen synthesis or ethane

cracking for ethylene production)

At times, the reaction may be exothermic with conversion being

limited by thermodynamic equilibrium In such cases, packed beds in

series with interstage cooling may be used as well The performance

enhancement associated with this approach is shown for two cases in

Table 19-2 Such units can take advantage of initial high rates at high

temperatures and higher equilibrium conversions at lower

tempera-tures For SO2oxidation, the conversion attained in the fourth bed is97.5 percent, compared with an adiabatic single-bed value of 74.8 per-cent With the three-bed ammonia reactor, final ammonia concentra-tion is 18.0 percent, compared with the one-stage adiabatic value of15.4 percent

Since reactors come in a variety of configurations, use a variety ofoperating modes, and may handle mixed phases, design provisions fortemperature control may draw on a large body of heat-transfer theoryand data These extensive topics are treated in other sections of thisHandbook and in other references Some of the high points pertinent to

reactors are covered by Rase (Chemical Reactor Design for Process Plants, Wiley, 1977) Two encyclopedic references, Heat Exchanger Design Handbook (5 vols., Begell House, 1983–1998) and Cheremisi- noff (ed.) (Handbook of Heat and Mass Transfer, 4 vols., Gulf,

1986–1990), have several articles addressed specifically to reactors

Reactor Dynamics Continuous reactors are designed to operate

at or near a steady state by controlling the operating conditions Inaddition, process control systems are designed to minimize fluctua-tions from the target conditions and for safety Batch and semibatchreactors are designed to operate under predefined protocols based onthe best understanding of the process However, the potential forlarge and unexpected deviations from steady state as a result ofprocess variable fluctuations is significant due to the complexity andnonlinearity of reaction kinetics and of the relevant mass- and heat-transfer processes For a set of operating conditions (pressure, tem-perature, composition, and phases present), more than one steadystate can exist Which steady state is actually reached depends on theinitial condition Not all steady states are stable states, and only thosethat are stable can be reached without special control schemes Morecomplex behavior such as self-sustained oscillations and chaoticbehavior has also been observed with reacting systems Further, dur-ing start-up, shutdown, and abrupt changes in process conditions, thereactor dynamics may result in conditions that exceed reactor designlimits (e.g., of temperature, pressure, materials of construction, etc.)and can result in a temperature runaway, reactor blowout, and even anexplosion (or detonation) Parametric sensitivity deals with the analy-sis of reactor dynamics in response to abrupt changes

Steady-State Multiplicity and Stability A simple example of

steady-state multiplicity is due to the interaction between kinetics and

heat transport in an adiabatic CSTR For a first-order reaction atsteady state, Eq (19-13) gives

Criteria for Chemically Reacting Systems,” in Dynamics and Modeling of Reactive Systems, Stewart et al (eds.), Academic Press, 1980], Schmitz

[Adv Chem Ser., 148: 156, ACS (1975)], and Razon and Schmitz [Chem Eng Sci., 42 (1987)] However, many of these criteria for specific reac-

tion and reactor systems have not been validated experimentally

Linearized or asymptotic stability analysis examines the stability of a

steady state to small perturbations from that state For example, when

heat generation is greater than heat removal (as at points A− and B+ in

Fig 19-4), the temperature will rise until the next stable steady-state

temperature is reached (for A − it is A, for B+ it is C) In contrast, when

heat generation is less than heat removal (as at points A+ and B− inFig 19-4), the temperature will fall to the next-lower stable steady-state

temperature (for A + and B− it is A) A similar analysis can be done around steady-state C, and the result indicates that A and C are stable

steady states since small perturbations from the vicinity of these return

the system to the corresponding stable points Point B is an unstable

steady state, since a small perturbation moves the system away to either

A or C, depending on the direction of the perturbation Similarly, at

conditions where a unique steady state exists, this steady state is alwaysstable for the adiabatic CSTR Hence, for the adiabatic CSTR consid-

ered in Fig 19-4, the slope condition dQ H /dT > dQ G /dT is a necessary

and sufficient condition for asymptotic stability of a steady state In eral (e.g., for an externally cooled CSTR), however, the slope condition

gen-is a necessary but not a sufficient condition for stability; i.e., violation ofthis condition leads to asymptotic instability, but its satisfaction does notensure asymptotic stability For example, in select reactor systems even

tures 502 ⇒ 433, 502 ⇒ 471, 502 ⇒ 496°C To convert feet to meters, multiply by 0.3048; BPSD to m 3 /h, multiply by 0.00662.

where C f is the feed concentration and a and b are constants related

to Arrhenius rate expression The energy balance equation at steady

state is given by

Q G (T) = −∆H r V r r(C,T) = V′ρC p (T − T f)= Q H (T) (19-24)

where Q G is the heat generation by reaction, Q H is the heat removal by

flow, T is the reactor temperature at steady state, and T fis the feed

temperature Plotting the heat generation and heat removal terms

ver-sus temperature gives the result shown in Fig 19-4 As shown, as many

as three steady states are possible at the intersection of Q G and Q H

Another example of multiplicity is shown in Fig 19-15 for an adiabatic

catalyst pellet, indicating that three effectiveness factor values can be

obtained for a given Thiele modulus for a range of Prater numbers and

Thiele modulus values, leading to three potential steady states Multiple

steady states can occur in different reactor types, including isothermal

systems with complex nonlinear kinetics and systems with interphase

transfer, the main requirement being the existence of a feedback

mech-anism—hence, a homogeneous PFR (without backmixing) will not

exhibit multiplicity Depending on the various physical and chemical

interactions in a reactor, oscillatory and chaotic behavior can also occur

There is a voluminous literature on steady-state multiplicity,

oscilla-tions (and chaos), and derivation of bifurcation points that define the

con-ditions that lead to onset of these phenomena For example, see

Morbidelli et al [“Reactor Steady-State Multiplicity and Stability,” in

Chemical Reaction and Reactor Engineering, Carberry and Varma (eds),

Marcel Dekker, 1987], Luss [“Steady State Multiplicity and Uniqueness

a unique steady state can become unstable, leading to oscillatory or

chaotic behavior

Local asymptotic stability criteria may be obtained by first solving

the steady-state equations to obtain steady states and then linearizing

the transient mass and energy balance equations in terms of deviations

of variables around each steady state The determinant (or slope) and

trace conditions derived from the matrix A in the set of equations

obtained are necessary and sufficient for asymptotic stability

q r= Aq r x = C − Css y = T − Tss

∆ = det(A) > 0 σ = trace(A) < 0 (19-25)

where x and y are the deviation variables around the steady state (Css,

Tss) The approach may be extended to systems with multiple

concen-trations and complex nonlinear kinetics For additional references on

asymptotic stability analysis, see Denn (Process Modeling, Longman,

1986) and Morbidelli et al [“Reactor Steady-State Multiplicity and

Stability,” in Chemical Reaction and Reactor Engineering, Carberry

and Varma (eds.), Marcel Dekker, 1987]

Parametric Sensitivity and Dynamics The global stability and

sensitivity to abrupt changes in parameters cannot be determined

from an asymptotic analysis For instance, for the simple CSTR, a key

question is whether the temperature can run away from a lower stable

where T is the reactor temperature, T jis the cooling jacket

tempera-ture, E is the activation energy, and R is the universal gas constant.

Similarly, for a jacketed PFR, a conservative criterion for stability is

Tmax− T j < ∆T c , where Tmaxis the temperature of the hot spot

Another example of sensitivity to abrupt changes is the wrong-way effect, exhibited, for instance, in packed-bed reactors, where an abrupt

reduction in feed rate or in feed temperature results in a dramaticincrease in reactor peak temperature for exothermic reactions Eitherthe reactor may eventually return to the original steady state or, if ahigher-temperature steady state exists, the reactor may establish a tem-perature profile corresponding to the new high steady state Such adynamic excursion can result in an increase of undesirable by-productsconcentration, catalyst deactivation, permanent reactor damage, andsafety issues; e.g., see work by Luss and coworkers [“Wrong-WayBehavior of Packed-Bed Reactors: I The Pseudo-homogeneous

Model,” AIChE J 27: 234–246 (1981)] For more complex systems, the

transient model equations are solved numerically A more detailed

dis-cussion of parametric sensitivity is provided by Varma et al (Parametric Sensitivity in Chemical Systems, Cambridge University Press, 1999).

Reactor Models As discussed earlier, reactor models attempt to

strike a balance between the level of detail included and the ness of the model Too many details in the model may require a largernumber of adjustable model parameters, increase computationalrequirements, and limit how widely the model may be used Too fewdetails, on the other hand, increase ease of implementation but maycompromise the predictive or design capabilities of the model Figure19-5 is a schematic of the inherent tradeoff between ease of imple-mentation and the insight that may be obtained from the model.Increases in computational power are allowing a more cost-effectiveinclusion of a greater number of details Computational fluid dynamics(CFD) models provide detailed flow information by solving theNavier-Stokes transport equations for mass, momentum, and heat bal-ances The user will, however, need to be familiar with the basic ele-ments of the software and may need a license A typical numericalsolution of the governing transport equations is obtained within theeulerian framework, using a large number of computational cells (orfinite volumes that represent reactor geometry) Current capabilities incommercial CFD software can be used to resolve the flow, concentra-tion, and temperature patterns in a single phase with sufficient detailand reasonable accuracy for all length and time scales The ability tovisualize flow, concentration, and temperature inside a reactor is useful

useful-in understanduseful-ing performance and useful-in designuseful-ing reactor useful-internals

RT2



E

TABLE 19-2 Multibed Reactors, Adiabatic Temperature Rises

and Approaches to Equilibrium*

Oxidation of SO 2 at atmospheric pressure in a four-bed reactor Feed 6.26%

*To convert atm to kPa multiply by 101.3.

SOURCE: Plant data and calculated design values from Rase, Chemical

Reac-tor Design for Process Plants, Wiley, 1977.

FIG 19-4 Multiple steady states of CSTRs, stable and unstable, adiabatic (a) First-order reaction, A and C stable, B unstable, the dashed line is for a reversible reaction (b) One, two, or three steady states depending on the combination (C , T).

Addition of transport properties and more than one phase (as is thecase with solid catalysts) within a CFD framework complicates theproblem in that the other phase(s) also may have to be included in thecalculations This may require additional transport equations toaddress a range of complexities associated with the dynamics andphysics of each phase, the interaction between and within phases, sub-grid-scale heterogeneities (such as size distributions within eachphase), and coupling with kinetics at the molecular level For exam-ple, one needs the bubble size distribution in a bubble column reactor

to correctly model interfacial area and local mass-transfer coefficients,which can further affect the chemical kinetics Although phenomeno-logical models describing such physical effects have greatly improvedover the years, this area still lacks reliable multiphase turbulence clo-sures, or experimentally validated intraphase and interphase transportmodels Mathematical modeling in industrial practice will continue toinvolve compromises between computational complexity, experimen-tal data needs, ability to validate the model, cost, and the time frame

in which the work may be useful to the organization

FIG 19-5 Hierarchy of reactor models.

RESIDENCE TIME DISTRIBUTION AND MIXING

The time spent by reactants and intermediates at reaction conditions

determines conversion (and perhaps selectivity) It is therefore often

important to understand the residence time distribution (RTD) of

reaction species in the reactor This RTD could be considerably

dif-ferent from what is expected Reasons for the deviation could be

channeling of fluid, recycling of fluid, or creation of stagnant regions

in the reactor, as illustrated in Fig 19-6

This section introduces how tracers are used to establish the RTD

in a reactor and to contrast against RTDs of ideal reactors The section

ends with a discussion of how reactor performance may be connected

to RTD information

TRACERS

Tracers are typically nonreactive substances used in small concentrationthat can be easily detected The tracer is injected at the inlet of the reac-tor along with the feed or by using a carrier fluid, according to some def-inite time sequence The inlet and outlet concentrations of the tracer

Short-circuiting

Stagnant regions

Packed bed

Extreme short-circuitingand bypassChanneling, especially

serious in countercurrenttwo-phase operations

FIG 19-6 Some examples of nonideal flow in reactors (Fig 11.1 in Levenspiel, Chemical tion Engineering, John Wiley & Sons, 1999.)

Reac-are recorded as a function of time These data Reac-are converted to a

resi-dence time distribution of feed in the reactor vessel Tracer studies may

be used to detect and define regions of nonideal behavior, develop

phe-nomenological zone models, calculate reactor performance

(conver-sion, selectivity), and synthesize optimal reactor configurations for a

given process The RTD does not represent the mixing behavior in a

vessel uniquely Several arrangements of reactors or internals within a

vessel may provide the same tracer response For example, any series

arrangement of the same number of CSTR and plug flow reactor

ele-ments will provide the same RTD This lack of uniqueness may limit

direct application of tracer studies to first-order reactions with constant

specific rates For other reactions, the tracer curve may determine the

upper and lower limits of reactor performance When this range is not

too broad, or when the purpose of the tracer test is to diagnose

maldis-tribution or bypassing in the reactor, the result can be useful Tracer

data also may be taken at several representative positions in the vessel in

order to develop a better understanding for the flow behavior

Inputs Although some arbitrary variation of input concentration

with time may be employed, five mathematically simple tracer input

signals meet most needs These are impulse, step, square pulse (started

at time a, kept constant for an interval, then reduced to the original

value), ramp (increased at a constant rate for a period of interest), and

sinusoidal Sinusoidal inputs are difficult to generate experimentally.

Types of Responses The key relationships associated with

trac-ers are provided in Table 19-3 Effluent concentrations resulting from

impulse and step inputs are designated Cδand C u, respectively The

mean concentration resulting from an impulse of magnitude m into a

vessel of volume V r is C0= m/V r The mean residence time is the ratio

of the vessel volume to the volumetric flow rate:

t

⎯=

or t⎯=

(19-27)

The reduced time is t r = tt⎯ Residence time distributions are

used in two forms: normalized, E(t r)= CδC0; or plain, E(t)=

E(t)dt = 1, and the relation between them is E(t r)= t⎯E(t) The area

between the ordinates at t1and t2is the fraction of the total effluent

that has spent the period between those times in the vessel The age

function is defined in terms of the step input as

F(t)= =t

0

Reactor Tracer Responses

Continuous Stirred Tank Reactor (CSTR) With a step input of

magnitude C f, the unsteady material balance of tracer

can be integrated to yield

= F(t r)= 1 − exp (−t r) (19-30)

With an impulse input of magnitude m or an initial mean

concentra-tion C0= m/V r, the material balance is

+ C = 0 with C = C0, t= 0 (19-31)And integration gives

= E(t r)= exp(−t r) (19-32)These results show that

t Cδdt



∞ 0

Cδdt

V r



V′

Multistage CSTR Since tubular reactor performance can be

simulated by a series of CSTRs, multistage CSTR tracer models areuseful in analyzing data from empty tubular and packed-bed reactors

The solution for a tracer through n CSTRs in series is found by

induc-tion from the soluinduc-tion of one stage, two stages, and so on

TABLE 19-3 Tracer Response Functions

Mean residence time:

Variance:

σ 2(t)=∞ 0

(t − t)2E(t) dt = −t2 +

Variance, normalized:

σ 2(t r) = = −1 +

=1 0

(t r− 1) 2dF(tr) Skewness, third moment:

γ 3(t r) =∞

0 (t r− 1) 3E(tr ) dt r

∞ 0

t2Cδdt



∞ 0

t2Cδdt



∞ 0

Cδdt

E(t)



I(t) E(t)

tCδdt



∞ 0

Cδdt

The solution for a step response can be obtained by integration

where E(t r ) and F(t r ) for various values of n are shown in Fig 19-7.

The theoretical RTD responses in Fig 19-7a are similar in shape to

the experimental responses from pilot and commercial reactors shown

in Fig 19-8 The value of n in Fig 19-8 represents the number of

CSTRs in series that provide a similar RTD to that observed

commer-cially Although not shown in the figure, a commercial reactor having

a similar space velocity as a pilot reactor and a longer length typically

has a higher n value than a pilot reactor due to greater linear velocity.

The variance of the RTD of a series of CSTRs, σ2, is the inverse of n.

σ2=∞ 0

(t r− 1)2E(t r ) dt r= (19-36)

Plug Flow Reactor The tracer material balance over a

differen-tial reactor volume dV ris

by t r = 1, or t = t⎯

Tubular Reactor with Dispersion As discussed earlier, a

multi-stage CSTR model can be used to simulate the RTD in pilot and

com-mercial reactors The dispersion model, similar to Fick’s molecular

diffusion law with an empirical dispersion coefficient D ereplacing the

diffusion coefficient, may also be used

the literature [Otake and Kunigata, Kagaku Kogaku, 22: 144 (1958)].

The plots of E(t r ) versus t rare bell-shaped, similar to the response for

a series of n CSTRs model (Fig 19-7) A relation between σ2(t r ), n,

and Pe (for the closed-ends condition) is

Examples of values of Pe are provided in Fig 19-8 When Pe is

large, n1 Pe2 and the dispersion model reduces to the PFRmodel For small values of Pe, the above equation breaks down

since the lower limit on n is n= 1 for a single CSTR To better resent dispersion behavior, a series of CSTRs with backmixing may

rep-be used; e.g., see Froment and Bischoff (Chemical Reactor sis and Design, Wiley, 1990) A model analogous to the dispersion

Analy-model may be used when there are velocity profiles across the tor cross-section (e.g., for laminar flow) In this case, the equationabove will contain terms associated with the radial position in thereactor

reac-Understanding Reactor Flow Patterns As discussed above, a

RTD obtained using a nonreactive tracer may not uniquely representthe flow behavior within a reactor For diagnostic and simulation pur-poses, however, tracer results may be explained by combining theexpected tracer responses of ideal reactors combined in series, in par-allel, or both, to provide an RTD that matches the observed reactorresponse The most commonly used ideal models for matching anactual RTD are PRF and CSTR models Figure 19-9 illustrates theresponses of CSTRs and PFRs to impulse or step inputs of tracers.Since the tracer equations are linear differential equations, a

Laplace transform L{f(t)}= 

0

∞

f(t)e −st dt may be used to relate tracer

inputs to responses The concept of a transfer function facilitates thecombination of linear elements

C

⎯

output(s) = (transfer function) C⎯input(s) = G(s)C⎯input(s) (19-43)Some common Laplace transfer functions are listed in Table 19-4.The Laplace transform may be inverted to provide a tracerresponse in the time domain In many cases, the overall transferfunction cannot be analytically inverted Even in this case,moments of the RTD may be derived from the overall transfer

function For instance, if G′and G″are the limits of the first and

second derivatives of the transfer function G(s) as s1 0, the mean

residence time and variance are

t

⎯= G′

0 and σ2(t) = G″0− (G′0)2 (19-44)

In addition to understanding the flow distribution, tracer

experi-ments may be conducted to predict or explain reactor performance

based on a particular RTD To do this, a mathematical expression for

the RTD is needed A PFR, or a dispersion model with a small value

of the dispersion coefficient, may be used to simulate an empty

tubu-lar reactor Stirred tank performance often is nearly completely mixed

(CSTR) In some cases, to fit the measured RTD, the model may have

to be modified by taking account of bypass zones, stagnant zones, or

other parameters associated with the geometry and operation of the

reactor Sometimes the vessel can be visualized as a zone of complete

mixing in the vicinity of impellers followed by plug flow zones

else-where, e.g., CSTRs followed by PFRs Packed beds usually deviate

substantially from plug flow The dispersion model and some

combi-nation of PFRs and CSTRs or multiple CSTRs in series may

approxi-mate their behavior Fluidized beds in small sizes approxiapproxi-mate CSTR

behavior, but large ones exhibit bypassing, stagnancy,

nonhomoge-neous regions, and several varieties of contact between particles and

fluid The additional parameters required to simulate such mixing

behavior can increase the mathematical complexity of the model

The characteristic bell shape of many RTDs can be fit to

well-known statistical distributions Hahn and Shapiro (Statistical Models

in Engineering, Wiley, 1967) discuss many of the standard

distribu-tions and condidistribu-tions for their use The most useful distribudistribu-tions arethe gamma (or Erlang) and the gaussian together with its Gram-Charlier extension These distributions are represented by only a fewparameters that can be used to determine, for instance, the mean andthe variance

Qualitative inspection of the tracer response can go a long waytoward identifying flow distribution problems Additional references

on tracers are Wen and Fan (Models for Flow Systems in Chemical Reactors, Marcel Dekker, 1975) and Levenspiel (Chemical Reaction Engineering, 3d ed., Wiley, 1999).

CONNECTING RTD TO CONVERSION

When the flow pattern is known, the conversion for a given reactionmechanism may be evaluated from the appropriate material andenergy balances When only the RTD is known (or can be calculatedfrom tracer response data), however, different networks of reactorelements can match the observed RTD In reality, reactor perfor-mance for a given reactor network will be unique The conversionobtained by matching the RTD is, however, unique only for linearkinetics For nonlinear kinetics, two additional factors have to be

FIG 19-8 Residence time distributions of pilot and commercial reactors σ 2 = variance of

the residence time distribution, n= number of stirred tanks with the same variance, Pe =

Peclet number (Walas, Chemical Process Equipment, Butterworths, 1990.)

1 䊊 Aldolization of butyraldehyde 0.050 20.0 39.0

2 䊉 Olefin oxonation pilot plant 0.663 1.5 1.4

3 ⵧ Hydrodesulfurization pilot plant 0.181 5.5 9.9

accounted for to fully describe the contacting or flow pattern: the

degree of segregation of the fluid and the earliness of mixing of the

reactants

Segregated Flow The degree of segregation relates to the

tendency of fluid particles to move together as aggregates or

clumps (e.g., bubbles in gas-liquid reactors, particle clumps in

flu-idized beds, polymer striations in high-viscosity polymerization

reactors) rather than each molecule behaving independently (e.g.,

homogeneous gas, low-viscosity liquid) A system with no

aggre-gates may be called a microfluid, and the system with aggreaggre-gates a

macrofluid (e.g., see Levenspiel, Chemical Reaction Engineering,

3d ed., Wiley, 1999) In an ideal plug flow or in an ideal batch

reac-tor, the segregated particles in each clump spend an equal time in

the reactor and therefore the behavior is no different from that of a

microfluid that has individual molecules acting independently The

reactor performance is therefore unaffected by the degree of

segre-gation, and the PFR or ideal batch model equations may be used to

estimate performance As shown below, however, this is not the

case for a CSTR where the performance equation for a microfluid

is the same as that of an ideal CSTR, while that of a CSTR with

seg-regated flow is not

In segregated flow the molecules travel as distinct groups All

mol-ecules that enter the vessel together leave together The groups are

small enough that the RTD of the whole system is represented by a

smooth curve Each group of molecules reacts independently of anyother group, that is, as a batch reactor For a batch reactor with apower law kinetics,

When a conversion and an RTD are known, a value of k may be

esti-mated by trial and error so the segregated integral is equal to theknown value If a series of conversions are known at several residencetimes, the order of the reaction that matches the data may be esti-mated by trial and error One has to realize, however, that the RTDmay change with residence time Alternatively, for known intrinsickinetics, a combination of ideal reactors that reasonably match bothRTD and performance may be considered

Early versus Late Mixing—Maximum Mixedness The

con-cept of early versus late mixing may be illustrated using a plug flowreactor and an ideal CSTR in series In one case, the ideal CSTR pre-cedes the plug flow reactor, a case of early mixing In the other case,the plug flow reactor precedes the CSTR, and this is a case of late mix-ing Each of the two arrangements has the same RTD

In maximum mixedness (or earliest possible mixing), the feed is mately mixed with elements of fluid of different ages, for instance, using

inti-multiple side inlets at various points along a plug flow reactor The

TABLE 19-4 Some Common Laplace Transform Functions

Element Transfer function G(s)

amount and location of the inlet flows match the RTD This means that

each portion of fresh material is mixed with all the material that has the

same life expectation, regardless of the actual residence time in the

ves-sel up to the time of mixing The life expectation under plug flow

con-ditions is related to the distance remaining to be traveled before leaving

the vessel The concept of maximum mixedness and completely

segre-gated flow is illustrated in Fig 19-10 Segresegre-gated flow is represented as

a plug flow reactor with multiple side outlets and has the same RTD.

In contrast to segregated flow, in which the mixing occurs only after

each side stream leaves the vessel, under maximum mixedness flow,

mixing of all molecules having a certain life expectancy occurs at the

time of introduction of fresh material These two mixing extremes—as

late as possible and as soon as possible, both having the same RTD—

correspond to extremes of reactor performance

The mathematical model for maximum mixedness has been

pro-vided by Zwietering [Chem Eng Sci 11: 1 (1959)].

= r c− (C0− C) (19-47)

where r c is the chemical reaction rate; e.g., for an order q, r c = kC q

The above differential equation in dimensionless variable form

(where f = C/C0and t r = t/t⎯) becomes

= kt⎯ C0q−1 f q− (1− f) (19-48)with boundary condition

which makes

kt⎯

C0q−1 f q∞− (1− f∞)= 0 (19-50)The conversion achieved in the vessel is obtained by the solution of the

differential equation at the exit of the vessel where the life expectation

is t = 0 The starting point for the integration is (f∞,t∞) When

integrat-ing numerically, however, the RTD becomes essentially 0 by the time t r

approaches 3 or 4 Accordingly, the integration interval is from (f∞, t r≤ 3

or 4) to (feffluent,t r = 0) with f∞obtained from Eq (19-50)

The conversion is a maximum in segregated flow and a minimum

under maximum mixedness conditions, for a given RTD and reaction

orders>1 A few comparisons are made in Fig 19-11 In some ranges

of the parameters n or r c, the differences in reactor volume for a given

conversion, when segregated or maximum mixedness flow is assumed,

< segregated flow (and the opposite is the case for orders <1).Increased deviation from ideal plug flow increases the effect of segre-gation on conversion At low conversion, the conversion is insensitive

to the RTD and to the extent of segregation

Novosad and Thyn [Coll Czech Chem Comm 31: 3,710–3,720

(1966)] solved the maximum mixedness and segregated flow tions (fit with the Erlang model) numerically There are few experi-mental confirmations of these mixing extremes One study with a

FIG 19-10 Two limiting flow patterns with the same RTD (a) Segregated flow (b) Maximum mixedness flow.

FIG 19-11 Ratio of reactor volume for maximum mixedness and segregated

flow models as a function of the variance (or n), for several reaction orders.

(a)

(b)

50-gal stirred tank reactor found segregation at low agitation and was

able to correlate complete mixing and maximum mixedness in terms

of the power input and recirculation within the vessel [Worrell and

Eagleton, Can J Chem Eng pp 254–258 (Dec 1964)].

REACTION AND MIXING TIMES

Reactants may be premixed or fed directly into the reactor To the

extent that the kinetics are limiting (i.e., reaction rate is slow), the rate

of mixing plays a minor role in determining conversion or selectivity

If the time to mix reactants is comparable to the reaction rate,

how-ever, mixing can have a significant impact

The characteristic chemical reaction time t ror characteristic time

scale of the chemistry may be calculated from the reaction rate

expression For a single reaction,

where C0is a reference concentration of the limiting reactant and T0

is a reference temperature For a first-order reaction, t r=1⁄k , where k

(s−1) is the rate constant

Mixing may occur on several scales: on the reactor scale (macro), on

the scale of dispersion from a feed nozzle or pipe (meso), and on a

molecular level (micro) Examples of reactions where mixing is

impor-tant include fast consecutive-parallel reactions where reacimpor-tant

con-centrations at the boundaries between zones rich in one or the other

reactant being mixed can determine selectivity

Much of the literature around mixing times has been developed

around the mixing of two liquids in agitated stirred tanks The

macromix-ing time t macan be defined as the time for the concentration to settle

within, say,±2 percent of its final value (98 percent homogeneity) With

a standard turbine in a baffled tank and Re (= nD2aρ/µ) > 5000,

t ma≅  2

where n is the stirrer speed, D t is the tank diameter, D ais the agitator

diameter, and H is the height of the tank; t mavaries inversely with the

stirrer speed In a case of a tank with an aspect ratio of unity and

D a /D t=13, nt ma≅ 36 For a stirrer speed of 120 rpm, the

where q is the flow induced by the impeller The induced flow is about

2 times the direct discharge from the turbine, creating uncertainty in

estimating q; tciris roughly one-fourth of the macromixing time

The micromixing time t miis the time required for equilibration ofthe smallest eddies by molecular diffusion, engulfment, and stretch-ing For liquid-liquid mixing, stretching and engulfment are limiting

factors and t midepends on the kinematic viscosity (µ/ρ) and the localrate of energy dissipation φε⎯:

t mi= 17 1/2

(19-54)For a kinematic viscosity of 10−6m2/s and an energy dissipation of 1.0

W/kg, t mi= 0.017 s The local energy dissipation will vary greatly withposition in the tank with its greatest value near the tip of theimpeller Injection of reactant at the point of greatest turbulence

minimizes t mi

The mesomixing time t meis the time for “significant mixing” of anincoming jet of feed liquid with the surrounding fluid A formula for

estimating t meis the time for turbulent diffusion to transport liquid

over a distance equal to the feed pipe diameter d0

If the diameter of the pipe is proportional to the agitator diameter, t me

increases as d0

2/3

Since t medepends on the local energy dissipation, it is

sensitive to location Typically, t me(> t mi) is a fraction of a second or so

A parameter used to diagnose mixing issues for reactive systems is

the Damköhler number Da which is the ratio of the mixing time to the

reaction time, Da= tmixing/t r Small Da numbers (Da<< 1) indicate atively rapid mixing compared to the reaction, so mixing is less impor-tant In contrast, large Da numbers (Da>>1) indicate a need toconsider mixing issues A more complete discussion of the topic is pro-vided in the appropriate section of the Handbook, in Baldyga and

rel-Bourne (Turbulent Mixing and Chemical Reactions, Wiley, 1998), and

in Harriott (Chemical Reactor Design, Marcel Dekker, 2003).

V r



q

SINGLE-PHASE REACTORS

Section 7 of this Handbook presents the theory of reaction kinetics

that deals with homogeneous reactions in batch and continuous

equipment Single-phase reactors typically contain a liquid or a gas

with (or without) a homogeneous catalyst that is processed in a

reac-tor at conditions required to complete the desired chemical

transfor-mation

LIQUID PHASE

Batch reactions of single or miscible liquids are often done in stirred

or pump-around tanks The agitation is needed to mix multiple feeds

and to enhance heat exchange with cooling (or heating media) during

the process Topics that acquire special importance on an industrial

scale are the quality of mixing in tanks and the residence time

distrib-ution in vessels where plug flow may be the goal A special case is that

of laminar and related flow distributions characteristic of

nonnewton-ian fluids, which often occurs in polymerization reactors The

infor-mation about agitation and heat transfer in tanks is described in the

relevant Handbook section

Homogeneous Catalysis A catalyst is a substance, usually used

in small amounts relative to the reactants, that increases the rate of

a reaction without being consumed in the process Liquid-phase

reactions are often conducted in the presence of homogeneous

cat-alysts Typically, homogeneous catalysts are ions or metal coordination

complexes or enzymes in aqueous solution The specific action of aparticular metal complex can be altered by varying the ligands (orcoordination number) of the complex or the oxidation state of thecentral metal atom Some examples of homogeneous catalysts inindustrial practice include hydrolysis of esters by hydronium(H3O+) or hydroxyl (OH−) ions, hydroformylation of olefins using

Rh or Co carbonyls, decomposition of hydrogen peroxide by ferrousions, decomposition of nitramides catalyzed by acetate ion, inver-sion of sucrose by HCl, halogenation of acetone by H+and OH−,and hydration of isobutene by acids A characteristic of homoge-neous catalysis is that, compared to solid catalysis, the reaction(s)proceeds under relatively mild conditions A key issue associatedwith homogeneous catalysis is the difficulty of separating productand catalyst

In stirred tanks, the power input to agitate the tank will depend onthe physical properties of the liquid In tubular reactors, the axial dis-persion in empty tubes may be estimated [e.g., Wen in Petho and

Noble (eds.), Residence Time Distribution Theory in Chemical neering, Verlag Chemie, 1982] as

Engi-= + 1≤ Re ≤ 2000 and 0.2 ≤ Sc ≤ 1000

(19-56)

(Re)(Sc)

192

1

(Re)(Sc)

1

Pe

= + Re≥ 2000

In a general case, the velocity may also be a function of radius One

such case is that of laminar flow which is characterized by a parabolic

velocity profile The velocity at the wall is zero while that at the

cen-terline is twice the average velocity In such cases, a momentum

bal-ance equation is solved along with the equations for heat and mass

transfer, and each equation contains terms for the radial

contribu-tion Laminar flow can be avoided by mixing over the cross-seccontribu-tion

For this purpose, in-line static mixers can be provided For very

vis-cous materials and pastes, screws of the type used for pumping and

extrusion are used as reactors When the temperature of the

reac-tants changes during the course of the reaction (due to either the

heat of reaction or the work required to keep the contents well

mixed), material and energy balance equations have to be solved

simultaneously

Examples

• Crude oil is heated to temperatures at which it thermally cracks into

gasoline and distillate products and lower-molecular-weight gases

This liquid cracking process is referred to as visbreaking A

schematic of the process and the effect of operating variables on

performance is shown in Fig 19-12

• The Wacker process for the oxidation of ethylene to acetaldehyde

with PdCl2/CuCl2at 100°C (212°F) with 95 percent yield and 95 to

99 percent conversion per pass

• The OXO process for higher alcohols: CO+ H2+ C3H6 1

n-butanal1 further processing The catalyst is a rhodium

triph-enylphosphine coordination compound at 100°C (212°F), 30 atm

(441 psi)

• Acetic acid from methanol by the Monsanto process, CH3OH+

CO1 CH3COOH, rhodium iodide catalyst, 3 atm (44 psi), 150°C

(302°F), 99 percent selectivity

See a review of industrial processes that employ homogeneous

cata-lysts by Jennings (ed.), Selected Developments in Catalysis, Blackwell

Scientific, 1985

GAS PHASE

There are few examples of industrial processes with pure gas-phase

reactions The most common and oldest example is combustion

Although termed homogeneous, most gas-phase reactions take place

in contact with solids, either the vessel wall or particles as heat

carri-ers With inert solids, the only complication is with heat transfer

Sev-eral of these reactions are listed in Table 19-1 Whenever possible,

liquefaction of gas-phase systems is considered to take advantage of

the higher rates of liquid reactions, to utilize liquid homogeneous

cat-alysts, or to keep equipment size down

The specific type of equipment used for gas-phase reactions

depends on the conditions required for undertaking the reaction

Examples of noncatalytic gas-phase reactions are shown in Fig 19-13

In general, mixing of feed gases and temperature control are major

process requirements Gases are usually mixed by injecting one of the

streams into the rest of the gases using a high-speed nozzle, as in the

flame reactor (Fig 19-13d).

Examples

• In the cracking of light hydrocarbons and naphtha to olefins, heat is

supplied from combustion gases through tubes in fired heaters at

800°C (1472°F) and sufficiently above atmospheric pressure to

overcome pressure drop Superheated steam is injected to bring the

temperature up quickly and retard coke deposition The reaction

time is 0.5 to 3.0 s, followed by rapid quenching The total tube

length of an industrial furnace may be more than 1000 m Some

other important gas-phase cracking processes include conversion of

toluene to benzene, diphenyl to benzene, dicyclopentadiene to

cyclopentadiene, and 1-butene to butadiene Figure 19-13a shows a

cracking furnace

• The Wulf process for acetylene by pyrolysis of natural gas utilizes a

heated brick checkerwork on a 4-min cycle of heating and reacting

Heat is transferred by direct contact with solids that have been

pre-1.35

(Re)0.125

which 0.03 s is near the peak (Faith, Keyes, and Clark, Industrial Chemicals, vol 27, Wiley, 1975).

• The Wisconsin process for the fixation of nitrogen from air operates

at 2200°C (3992°F), followed by extremely rapid quenching tofreeze the small equilibrium content of nitrogen oxide that is made

[Ermenc, Chem Eng Prog 52: 149 (1956)] A pebble heater

recir-culates refractory pebbles continuously through heating and tion zones Such moving-bed units have been proposed for cracking

reac-to olefins but have been obsolesced like most moving-bed reacreac-tors

• Acetylene may be produced from light hydrocarbons and thas by injecting inert combustion gases directly into the reacting

naph-stream in a flame reactor Figure 19-13a and d shows two such devices; Fig 19-13e shows a temperature profile (with reaction

times in milliseconds)

• Oxidative pyrolysis of light hydrocarbons to acetylene is conducted

in a special burner, at 0.001- to 0.01-s reaction time, peak at 1400°C(2552°F), followed by rapid quenching with oil or water A portion

of a combustible reactant is burned by adding a small amount of air

or oxygen to generate the reaction temperatures needed

• Chlorination reactions of methane and other hydrocarbons cally result in a mixture of products whose relative amounts can becontrolled by varying the Cl/hydrocarbon ratio and recyclingunwanted derivatives For example, one can recycle the mono and

typi-di derivatives when only the tri and tetra derivatives are of value

or keep the chlorine ratio low when emphasizing the lower atives Temperatures are normally kept in the range of 230 to

deriv-400°C (446 to 752°F) to limit carbon formation but may be raised

to 500°C (932°F) when favoring CCl4 Exothermic processes lize cooling through heat-transfer surfaces or cold shots Shell-and-tube reactors with small-diameter tubes, towers with internalrecirculation of gases, or multiple stages with intercooling may beused for these reactions

uti-SUPERCRITICAL CONDITIONS

At near-critical or supercritical conditions, a heterogeneous reactionmixture (e.g., of water, organic compounds, and oxygen) becomeshomogeneous and has some liquid and gaseous properties The rate ofreaction may be considerably accelerated because of (1) the highergas-phase diffusivity, (2) increase of concentration due to liquidlikedensity, (3) enhanced solubility, and (4) increase of the specific rate ofreaction by pressure The mole fraction solubility of naphthalene inethylene at 35°C (95°F) goes from 0.004 at 20 atm (294 psi) to 0.02 at

100 atm (1470 psi) and 0.05 at 300 atm (4410 psi) High destructiveefficiencies (above 99.99 percent) of complex organic pollutant com-pounds in water can be achieved with residence times of under 5 min

at near-critical conditions The critical properties of water are 374°C(705°F) and 218 atm (3205 psi)

We are not aware of any industrial implementation of supercriticalconditions in reactors Two areas of potential interest are wastewatertreatment (for instance, removal of phenol or organic compounds)and reduction of coke on refining catalysts by keeping heavy oildecomposition products in solution A pertinent reference is by Kohn-

stam (“The Kinetic Effects of Pressure,” in Progress in Reaction Kinetics, Pergamon, 1970) More recent reviews of research progress are by Bruno and Ely (eds.), Supercritical Fluid Technology, CRC Press, 1991; Kiran and Brennecke (eds.), Supercritical Engineering Science, ACS, 1992.

POLYMERIZATION REACTORS

Polymerization reactors contain one or more phases There areexamples using solvents in which the reactants and products are inthe liquid phase, the reactants are fed as a liquid (gas) but the prod-ucts are solid, or the reactants are a slurry and the products are sol-uble Phase transformations can occur, and polymers that formfrom the liquid phase may remain dissolved in the remainingmonomer or solvent, or they may precipitate Sometimes beads are

FIG 19-12 (a) Visbreaking flow sketch, feed 160,000 lbm/h, k800= 0.000248/s, tubes 5.05-in ID by 40 ft (b) Q/A = 10,000 Btu(ft2⋅h), Pout= 250 psig (c) Q/A = 10,000

Btu(ft 2⋅h), Pout= 150 or 250 psig (d) Three different heat fluxes, Pout= 250 psig (e) Variation of heat flux, average 10,000 Btu(ft2⋅h), Pout= 250 psig ( f ) Halving the specific rate T in°F To convert psi to kPa, multiply by 6.895; ft to m, multiply by 0.3048; in to cm, multiply by 2.54.

formed and remain in suspension; sometimes emulsions form In

some processes, solid polymers precipitate from a gas phase into a

fluidized bed containing product solids Polymers are thought of as

organic materials; however, inorganic polymers may be also

synthe-sized (e.g., using crystallization and precipitation) Examples of

inorganic polymers are zeolites

The structure of the polymer determines its physical properties,

e.g., crystallinity, refractive index, tensile strength, glass transition

temperature (at which the specific volume changes slope), and

processability The average molecular weight can cover a wide range

between 104to 107 Given the change in molecular weight, the

vis-cosity can change dramatically as conversion increases For example,

in styrene polymerization, the viscosity increases by a factor of 106asconversion increases from 0 to 60 percent Initiators of chain poly-merization reactions have concentration as low as 10−8g⋅mol/L sothey are highly sensitive to small concentrations of poisons and impu-rities The reaction time can also vary Reaction times for butadiene-styrene rubbers are 8 to 12 h; polyethylene molecules continue togrow for 30 min, whereas ethyl acrylate in 20 percent emulsion reacts

in less than 1 min, so monomer must be added gradually to keep thetemperature within limits In some cases, the adiabatic temperaturerise may be very high For example, in polymerization of ethylene, ahigh adiabatic temperature rise may lead to reactor safety issues byinitiating runaway ethylene decomposition reactions The reactor

FIG 19-13 Noncatalytic gas-phase reactions (a) Steam cracking of light hydrocarbons in a tubular fired heater (b) Pebble heater for the fixation of nitrogen from

air (c) Flame reactor for the production of acetylene from hydrocarbon gases or naphthas [Patton, Grubb, and Stephenson, Pet Ref 37(11): 180 (1958).] (d) Flame

reactor for acetylene from light hydrocarbons (BASF) (e) Temperature profiles in a flame reactor for acetylene (Ullmann Encyclopadie der Technischen Chemie, vol.

3, Verlag Chemie, 1973, p 335).

operating conditions have to be controlled such that the possibility of

ethylene decomposition is eliminated.

Since it is impractical to fractionate the products and reformulate

them into desirable ranges of molecular weights, immediate

attain-ment of desired properties must be achieved through the correct

choice of reactor type and operating conditions, notably of

distribu-tions of residence time and temperature Reactor selection may be

made on rational grounds, for historical reasons, or to obtain a

propri-etary position

Each reactor is designed based on the need for mass transfer, heattransfer, and reaction Stirred batch (autoclave) and continuous tubularreactors are widely used because of their flexibility In stirred tanks, idealmixing is typically not achieved, wide variations in temperatures mayresult, and stagnant zones and bypassing may exist Devices that coun-teract these unfavorable characteristics include inserts that cause radialmixing, scraping impellers, screw feeders, hollow-shaft impellers (withcoolant flow through them), recirculation using internal and externaldraft tubes, and so on The high viscosity of bulk and melt polymerization

reactions is avoided with solution, bead, or emulsion polymerization, and

more favorable RTDs are obtained In tubular reactors, such as for

low-density polyethylene production, there are strong temperature gradients

in the radial direction and cooling may become an issue These reactors

are operated in a single phase, often with multiple catalyst injection

points, and the reactor can be several miles in length Examples of

poly-merization reactors are illustrated in Fig 19-14

A number of terms unique to polymerization are discussed in Sec 7

of this Handbook A general reference on polymerization is Rodriguez

(Principles of Polymer Systems, McGraw-Hill, 1989) and a reference guide on polymerization reactors is available by Gerrens [German

Chem Eng 4: 1–13 (1981); ChemTech, pp 380–383, 434–443

(1982)] and Meyer and Keurentjes (Handbook of Polymer Reaction Engineering, Wiley VCH, 2005).

FLUID-SOLID REACTORS

A number of industrial reactors involve contact between a fluid (either

a gas or a liquid) and solids In these reactors, the fluid phase contacts

the solid catalyst which may be either stationary (in a fixed bed) or in

motion (particles in a fluidized bed, moving bed, or a slurry) The

solids may be a catalyst or a reactant (product) Catalyst and reactor

selection and design largely depend upon issues related to heat

trans-fer, pressure drop and contacting of the phases In many cases,

con-tinuous regeneration or periodic replacement of deteriorated or

deactivated catalyst may be needed

HETEROGENEOUS CATALYSTS

Solid catalysts may have a homogeneous catalyst (or enzyme) or

cat-alytic ingredients dispersed on a support The support may be

organic or inorganic in nature For example, a catalyst metal atom

may be anchored to the polymer (e.g., polystyrene) through a group

that is chemically bound to the polymer with a coordinating site such

as −P(C6H5)2 or −C5H4 (cyclopentadienyl) Immobilized catalysts

have applications in hydrogenation, hydroformylation, and

polymer-ization reactions [Lieto and Gates, ChemTech, pp 46–53 (Jan.

1983)] Metal or mixed metal oxides may be dispersed on amorphous

materials (such as carbon, silica, or alumina) or exchanged into the

cages of a zeolite Expensive catalytic metal ingredients, such as Pt or

Pd, may be < 1 percent of catalyst weight Catalysts may be shaped as

monoliths, shaped pellets, spheres, or powders Some exceptions are

bulk catalysts such as platinum gauzes for the oxidation of ammonia

and synthesis of hydrogen cyanide, which are in the form of several

layers of fine-mesh catalyst gauze

The catalyst support may either be inert or play a role in catalysis

Supports typically have a high internal surface area Special shapes

(e.g., trilobed particles) are often used to maximize the geometric

sur-face area of the catalyst per reactor volume (and thereby increase the

reaction rate per unit volume for diffusion-limited reactions) or to

min-imize pressure drop Smaller particles may be used instead of shaped

catalysts; however, the pressure drop increases and compressor costs

become an issue For fixed beds, the catalyst size range is 1 to 5 mm

(0.04 to 0.197 in) In reactors where pressure drop is not an issue, such

as fluidized and transport reactors, particle diameters can average less

than 0.1 mm (0.0039 in) Smaller particles improve fluidization;

how-ever, they are entrained and have to be recovered In slurry beds the

diameters can be from about 1.0 mm (0.039 in) down to 10 µm or less

The support has an internal pore structure (i.e., pore volume and

pore size distribution) that facilitates transport of reactants (products)

into (out of) the particle Low pore volume and small pores limit the

accessibility of the internal surface because of increased diffusion

resistance Diffusion of products outward also is decreased, and this

may cause product degradation or catalyst fouling within the catalyst

particle As discussed in Sec 7, the effectiveness factor η is the ratio

of the actual reaction rate to the rate in the absence of any diffusion

limitations When the rate of reaction greatly exceeds the rate of

dif-fusion, the effectiveness factor is low and the internal volume of the

catalyst pellet is not utilized for catalysis In such cases, expensive

cat-alytic metals are best placed as a shell around the pellet The rate of

diffusion may be increased by optimizing the pore structure to

pro-vide larger pores (or macropores) that transport the reactants

(prod-ucts) into (out of) the pellet and smaller pores (micropores) that

provide the internal surface area needed for effective catalyst

disper-sion Micropores typically have volume-averaged diameters of 50 to

200 Å with macropore diameters of 1000 to 5000 Å The pore volumeand the pore size distribution within a porous support determine itssurface area The surface area of supports can range from 0.06 m2/mL(18,300 ft2/ft3) to 600 m2/mL (1.83 × 108ft2/ft3) and above Higherpore volume catalysts have higher diffusion rate at the expense ofreduced crush strength and increased particle attrition

The effective diffusion coefficient Deffdetermines the rate of sion and therefore the volume of the catalyst utilized The coefficient

diffu-is determined by the nature of the diffusing species and the porestructure of the catalyst It has been found to be directly proportional

to the product of diffusivity and porosity ε and inversely proportional

to the tortuosity τ (that is empirically determined) In large pores of

>1000 Å, where molecules collide with one another and the tion with the pore walls is minimal, molecular (or bulk) diffusion isimportant For pore diameters in the range of 50 to 200 Å, collisionwith the pore walls becomes more important, and this regime is calledthe Knudsen diffusion regime In an extreme case where the size ofthe molecule is comparable to the size of the pore, the size and con-figuration of the pores themselves affect diffusivity This happenswhen the diffusing molecule is very large (as in transporting largeorganometallitic molecules through catalyst pores in heavy oilhydrotreating) or the pore is very small (as in diffusion in zeolites), orboth (e.g., see Sec 7 for diffusion regimes) ε ranges from 0.1 to 0.5andτ ranges from 1 to 7 In the absence of other information, a τ value

interac-of 3 to 4 may be used; however, it is best measured for the catalyst interac-ofinterest Expressions for estimating the effective diffusion coefficient

are available in textbooks such as Satterfield (Heterogeneous Catalysis

in Practice, McGraw-Hill, 1991).

The effectiveness factor η is the ratio of the rate of reaction in aporous catalyst to the rate in the absence of diffusion (i.e., under bulkconditions) The theoretical basis for η in a porous catalyst has beendiscussed in Sec 7 For example, for an isothermal first-order reaction

where C iis the bulk concentration of the reactant As discussed ously, η is a function of the ratio of the rate of reaction to diffusion,also called the Thiele modulus φ As the rate constant increases, ηdecreases and eventually reaches an asymptotic value (that depends

previ-onφ) Under these conditions, kη increases as k1 >2 The role of sion and reaction in porous catalysts, however, is more complicated in

diffu-a cdiffu-ase where hediffu-at effects diffu-are present In diffu-addition to the mdiffu-ass vation equation around the pellet, an energy balance equation isrequired Two additional dimensionless parameters are needed forestimating an effectiveness factor:

where∆H ris the heat of reaction, λ is the thermal conductivity of the

catalyst, E is the activation energy, and R is the universal gas constant.

The dimensionless parameter β, known as the Prater number, is theratio of the heat generation to heat conduction within the pellet and is

a measure of the intra-particle temperature increase; γ is the sionless activation energy for the reaction For an exothermic reac-tion, the temperature inside the catalyst pellet is greater than or equal

dimen-to the surface temperature The maximum steady-state temperature

inside the pellet is T s(1+ β) Figure 19-15 is one of several cases ined by Weisz and Hicks for a first-order reaction in an adiabatic

catalyst pellet [Chem Eng Sci 17: 263 (1962)] Although this

pre-dicts some very large values of η in some ranges of the parameters,

these values are often not realized in commercial reactors (see Table

19-5) The modified Lewis number defined as Lw′= λs/ρs C ps Deffcan

determine the transient temperature inside the pellet, which can be

much larger than the steady-state temperature

The concept of an effectiveness factor is useful in estimating the tion rate per catalyst pellet (volume or mass) It is, however, mainly use-ful for simple reactions and simple kinetics When there are complexreaction pathways, the concept of effectiveness factor is no longer easilyapplicable, and species and energy balance equations inside the particlemay have to be solved to obtain the reaction rates per unit volume of

reac-FIG 19-15 Effectiveness factors versus Thiele modulus for a first-order reaction in spheres

under adiabatic conditions [Weisz and Hicks, Chem Eng Sci., 17: 265 (1962).]

TABLE 19-5 Parameters of Some Exothermic Catalytic Reactions

catalyst Dumesic et al (The Microkinetics of Heterogeneous Catalysis,

American Chemical Society, 1993) use microkinetic analysis to

eluci-date reaction pathways of several commercial catalysts

Another complication is the fact that Fig 19-15 was developed for

the constant-concentration boundary condition, C⏐ r =R = C0 In a more

general case, external mass-transfer limitations will need to be

included

k m a(C0− C i)= r c (C i)= kηC i (19-59)

where k mis the external mass-transfer coefficient obtained from

litera-ture correlations and a is the external surface area per unit pellet

vol-ume The above equation will have to be solved for C i, the

concentration of the reactant on the external surface of the catalyst, so

that the rate per pellet can be obtained The reaction rate per unit

reac-tor volume then becomes r c(1− εb), where εbis the bed void fraction

A further complication is that catalyst activity declines with time

Catalysts may deactivate chemically (via poisons and masking agents),

thermally (via support sintering), or mechanically (through attrition)

Commercial catalyst life can range from a second to several years For

example, in refinery fluid catalytic cracking, the catalyst may lose most

of its activity in less than 10 s, and a transport bed reactor coupled with

a fluidized-bed regenerator is used to circulate catalyst In contrast, a

refinery hydroprocessing catalyst deactivates very slowly and a

fixed-bed reactor may be used without catalyst replacement for one or more

years The deactivation rate expression may often be inferred from

aging experiments undertaken under pilot-plant conditions of constant

temperature or conversion Since accelerated-aging experiments are

often difficult (especially when the concentration of reactant or

prod-ucts affects the deactivation rate), reactor designs where the catalyst

charge provides the required performance between regeneration

cycles is typically based on good basic data and experience The

litera-ture describes approaches aimed at managing deactivation In the case

of platinum reforming with fixed beds, a large recycle of hydrogen

pre-vents coke deposition while a high temperature compensates for the

retarding effect of hydrogen on this essentially dehydrogenating

process Fluidized beds are largely isothermal and can be designed for

continuous regeneration; however, they are more difficult to operate,

require provisions for dust recovery, suffer from backmixing, and are

more expensive Catalyst deactivation mechanisms and kinetics are

dis-cussed in detail in Sec 7 of the Handbook

A catalyst for a particular chemical transformation is selected using

knowledge of similar chemistry and some level on empirical

experi-mentation Solid catalysts are widely used due to lower cost and ease

of separation from the reaction medium Their drawbacks include a

possible lack of specificity and deactivation that can require reactor

shutdown for catalyst regeneration or replacement

There are number of useful books on catalysis Information on

cata-lysts and processes is presented by Thomas (Catalytic Processes and

Proven Catalysts, Academic Press, 1970), Pines (Chemistry of

Cat-alytic Conversions of Hydrocarbons, Academic Press, 1981), Gates

et al (Chemistry of Catalytic Processes, McGraw-Hill, 1979), Matar et

al (Catalysis in Petrochemical Processes, Kluwer Academic Publishers,

1989), and Satterfield (Heterogeneous Catalysis in IndustrialPractice,

McGraw-Hill, 1991) The books by Thomas (Catalytic Processes and

Proven Catalysts, Academic Press, 1970), Butt and Petersen

(Activa-tion, Deactivation and Poisoning of Catalyst, Academic Press, 1988),

and Delmon and Froment (Catalyst Deactivation, Elsevier, 1980)

pro-vide several examples of catalyst deactivation Catalyst design is

dis-cussed by Trimm (Design of Industrial Catalysts, Elsevier, 1980),

Hegedus et al (Catalyst Design Progress and Perspectives, Wiley,

1987), and Becker and Pereira (Catalyst Design, Marcel Dekker,

1993) A thorough review of catalytic reactions and catalysts arranged

according to the periodic table is in a series by Roiter (ed.) (Handbook

of Catalytic Properties of Substances, in Russian, 1968) Stiles

(Cata-lyst Manufacture, Dekker, 1983) discusses cata(Cata-lyst manufacture.

CATALYTIC REACTORS

Due to the considerations noted above, reactor selection will depend

on the type of catalyst chosen and its activity, selectivity, and

deactiva-tion behavior Some reactors with solid catalysts are represented inFig 19-16

Wire Gauzes Wire screens are used for very fast catalytic

reac-tions or reacreac-tions that require a bulk noble metal surface for reactionand must be quenched rapidly The nature and morphology of thegauze or the finely divided catalyst are important in reactor design.Reaction temperatures are typically high, and the residence times are

on the order of milliseconds

Since noble metals are expensive, the catalyst cost is typically high.The physical properties of the gauze pack are important to determineperformance, selectivity, and catalyst replacement strategy The gauze

is typically mounted over the top of a heat exchanger tube sheet orover porous ceramic bricks that are laid over the tube sheet Thegauze pack may be covered with a ceramic blanket to minimize radia-tion losses From a modeling standpoint, the external surface area pergauze volume and the external mass-transfer coefficient for each com-ponent are important parameters, and the reaction rate per unit vol-ume of catalyst may be limited by the rate of external mass transfer.The reaction rate can then be included into a corresponding PFR ordispersion model to obtain estimates of conversion and selectivity

• In hydrogen cyanide synthesis using the Andrussow process, air,methane, and ammonia are fed over 15 to 50 layers of noble metalgauze at 1050 to 1150°C at near atmospheric pressure

Monolith Catalysts For fast reactions that may require a slightly

higher residence time than gauzes or that do not benefit from the bulknoble metal gauze structure, monoliths may be used Most often, themonolith catalyst is an extruded ceramic honeycomb structure thathas discrete channels that traverse its length The catalytic ingredientsmay be dispersed on a high surface area support and coated on aninert honeycomb In some cases, the catalyst paste itself may beextruded into a monolith catalyst Monoliths may also be made ofmetallic supports Stainless steel plates (or wire mesh) with ridges may

be coated with catalysts and stacked one against the other in a reactor.Corrugated stainless steel layers may alternate in between flat sheets

to form the structure A variant is a stainless steel sheet that is gated in a herringbone pattern, coated with catalyst and then rolled(or folded back and forth onto itself) into a reactor module Examples

corru-of cross-sections corru-of the types corru-of monoliths used in industry are shown

in Fig 19-17

The thickness of monolith walls is adjusted according to the als of construction (ceramic honeycombs have thicker walls to providemechanical strength) The size of the channels is selected according tothe application For example, for particulate-laden gases, a largerchannel size ceramic monolith and a higher linear velocity allow theparticles to pass through the catalyst without plugging the channel Incontrast, for feed that does not contain particles, smaller channelmonoliths may be used The cell density of the monolith may varybetween 9 and 600 cells per square inch

materi-A monolith catalyst has a much higher void fraction (between 65and 91 percent) than does a packed bed (which is between 36 and

45 percent) In the case of small channels, monoliths have a highgeometric surface area per unit volume and may be preferred formass-transfer-limited reactions The higher void fraction providesthe monolith catalyst with a pressure drop advantage compared tofixed beds

A schematic of a monolith catalyst is shown in Fig 19-18a In cases

where pressure drop is limiting, such as for CO oxidation in cogenerationpower plant exhausts, monolith catalyst panels may be stacked to form athin (3- to 4-in-thick) wall The other dimensions of the wall can be onthe order of 35× 40 ft CO conversion is over 90 percent with a pressuredrop across the catalyst of 1.5 in of water Alternatively, the monolith may

be used as a catalyst and filter, as is the case for a diesel particulate filter

In this case, monolith channels are blocked and the exhaust gases from a

diesel truck are forced through the walls (Fig 19-18b) The filter is a

crit-ical component in a continuous regenerable trap NO in the exhaust

19-28

gases is oxidized into NO2that reacts with the soot trapped in the walls of

the filter to regenerate it in situ

Modeling considerations for monoliths are similar to those of gauze

catalysts; however, since the flow and temperature in each channel

may be assumed to be identical to those in the next channel, the

solu-tion for a single channel may reflect the performance of the reactor

For an application in which the reaction rate is mass-transfer-limited,

the reactant concentration at the wall of the catalyst is much lower

than in the bulk and may be neglected In such a case, the fractional

conversionξ is

ξ = 1 − e −k m at= 1 − exp−Sh aL (19-60)

Sc Re

where Sh (= k m d ch /D) is the Sherwood number, Sc ( = µ/ρD) is the

Schmidt number, and Re (= ud chρ/µ) is the channel Reynolds

num-ber; a is the geometric surface area per unit volume of monolith A

number of correlations for Sh are available for various types of liths For example, in the case of extruded ceramic monoliths, a corre-lation for estimating the external mass-transfer coefficient is provided

mono-by Uberoi and Pereira (Ind Eng Chem Res 35: 113–116 (1996)]:

Sh= 2.6961+ 0.139 ScRe 0.81

(19-61)Since typical monolith catalysts have a thin coating of catalyticingredients on the channel walls, they can be susceptible to poisoning

FIG 19-18 Monolith catalysts (a) Schematic of an automobile catalytic converter for the three-way removal of CO, hydrocarbons, and NO x (b) Schematic

of a diesel trap (Figs 7.10 and 9.6 in Heck, Farrauto, and Gulati, Catalytic Air Pollution Control: Commercial Technology, Wiley-Interscience, 2002.)