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lthough the reactor is the heart of most process plants, it usually
is treated as a black box or a proprietary item and is not cov-
ered by commercial simulators. Each technology developer or licensor
uses its own procedure to develop its reactor model. Such a procedure
often is lengthy and expensive, due to ill-defined steps, many trial-and-
error mistakes, and excessive pilot-plant campaigns. Finally, even if the
reactor is successfully scaled up to commercial size, the credibility of
the design and the optimum operating conditions of the reactor often is
questionable.
On the other hand, a plant owner may not have the know-how or con-
fidence to modify, revamp, or modernize the reactor or its operation. The
owner needs to build an in-house model for any such effort.
This article suggests a well developed and tested procedure for build-
ing a robust reactor model/model package, and details tips and traps. It
also recommends proven ways to substantially cut the cost and time for
the effort. This article primarily focuses on catalytic gas/solid reactions
and reactor systems.
ASubhash Dutta
and Ronald Gualy,
GTC Technology Corp.
Reactor Modeling
BuildRobustReac torModels
CEP October 2000 www.aiche.org/cep/ 37
Whether scalingup a new reactoror revamping anexisting one, use
this proven 14-stepapproach.
Discuss This Article!
To join an online discussion
about this article with theor authors and other
readers, go to the
ProcessCity Discussion
Room for CEParticles at
www.processcity.com/cep.
Photo credit. Applied ReactorTechnologies, Inc.
Copyright 2000
American Institute
of Chemical Engineers.
All rights reserved.
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38 www.aiche.org/cep/ October 2000 CEP
Reactor Modeling
MODELBUILDING STEPS
There are 14 basic steps in building arobust reactor model for either re-vamp or scale-up. The time and effortrequired for a revamp model for anexisting system is substantially lower,however, than that for a scale-upmodel for a new process due to ac-cumulated process know-how anddata from both operating plant andvarious bench/pilot-plant units used in
the early development of the process.
STEP 1 DEFINE REAC-
TION TYPE. This is the firstand most basic categorization. It isbased on the phases (gas, liquid, orsolid) involved in the reaction sys-tem, and whether the solid phase, ifinvolved, is catalytic or noncatalyticin nature. This definition of the reac-tion type for example, homoge-neous, gas/solid catalytic, gas/solidnoncatalytic, or gas/liquid imme-
diately establishes the nature ofthe effort and its relative degree ofdifficulty.
Provided the mechanism and ki-netics of the involved reaction systemare known, the degree of difficulty inbuilding a reactor model generally in-creases in the following, approximateorder:
homogeneous gas phase;homogeneous liquid phase;gas/solid catalytic or liquid/solid
catalytic;
gas/liquid;gas/solid noncatalytic or liquid/solid
noncatalytic;gas/liquid/solid catalytic; andgas/liquid/solid noncatalytic.
Systems involving the liquid phasemay be subdivided further into oneswithout phase transfer between gasand liquid, and those with it. The lat-ter category is perhaps the most diffi-cult, and is beyond the scope of thisarticle.
STEP 2 DESIGN, BU ILD,AND OPERATE A TESTUNIT. A proper laboratory or pro-cess development unit (PDU) is re-quired if the available data or knowl-edge on the reaction mechanism andkinetics, and the reactor hydrodynam-ics appear inadequate. Such a unit ismandatory for a new reaction system.
For reactions involving solids (cat-alytic or noncatalytic), a minimum oftwo stages of a PDU usually are need-ed for studying the reaction mecha-
nism and kinetics. In the first stage,the solids are used in the form of afine powder to allow generation oftrue or intrinsic kinetic data with min-imum pore-diffusion resistance. In thesecond stage, the PDU should mimicas closely as possible the design, hy-drodynamic conditions, and operation,including the solids particle size, ex-pected in the commercial unit.
Unfortunately, a close approach toa commercial system often is not pos-sible in a lab-scale PDU. Therefore,
an extensive pilot-plant campaignusually is undertaken. A robustmodel, however, can minimize, if not
eliminate, the cost and effort of suchpilot-plant campaigns.
Additional PDUs, called coldmodels, because no reactions occurin them, may be needed to assessthe hydrodynamics of a totally newreactor configuration, fluid/solid,fluid/fluid, or three-phase system. At-trition, adhesion (particle stickiness),fluidizability, and flow characteristicsof a new solid catalyst are some keyissues that must be studied in the coldmodels, as well as standard test units.
Again, a robust model can keepall test units as small as practicaland minimize the efforts in testcampaigns.
If, for the same catalytic activity, afluidized-bed system far outperformsa fixed-bed design, according to themodel analysis (to be described later),an additional and separate develop-ment and test campaign is requiredfor the development of the fluidized-bed catalyst.
Extensive cold-model testing and
demonstration may be necessary, par-ticularly for cases where the opera-tion, control, and performance of areactor or a reactor-regenerator dualsystem critically depends upon thesolids circulation system to estab-lish correlations/methodology for de-sign, operation, and control of suchunits. (The modeling and design ofdifficult solids circulation systems,such as ones with cross-flow and dou-ble loops, e.g., as in fluid catalyticcrackers, is outside the scope of this
article.)The key design criterion of a PDU
is to ensure that it can cover a widerange of conditions both higherand lower than those expected in thecommercial units for four key op-erating variables:
1. space velocity or throughput (ofboth fluids and solid in flow reactors);
2. temperature;3. pressure; and4. composition.Another key feature of the PDU
What is a robust model?
Such a model is a practical, reliable, and useful package for analyzing,
scaling up, designing, and optimizing a given reaction and reactor
system. It provides the best design for a new system, revamp, or
modernization, and the optimum operating conditions for an existingreactor. The model predicts the performance for a wide variety of designs
and operating conditions, including those used in the commercial reactor.
It also covers conditions beyond normal operations, to predict upset, off-
specification, turndown, and unsafe situations.
Such a model should be based primarily on fundamental principles of
reaction engineering and reactor hydrodynamics. It should use the
minimum number of adjustable/experimental parameters and be solved
by standard mathematical routines requiring minimum execution time.
And, it should be easy be integrate with other in-house or commercial
simulation packages.
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should be accurate monitoring of re-actor temperature profiles, if suchprofiles are significant. Temperature
often is the most dominant and criti-cal variable in reactor design andoperation.
In addition, the PDU must havethe flexibility to readily accommodatemodifications, such as injection ofmultiple feed points, insertion ofsolid/gas sampling, aeration, and tem-perature probes, change of tempera-ture profiles, installation or swappingof internals, and variation of feed anddischarge port/plenum designs. It alsoshould enable easy catalyst/solids
loading and discharge, and productrecycle.
STEP 3 COLLECT ANDANALYZE DATA. Alwayskeep scale-up, and commercial de-sign and operation in mind when de-signing the PDUs and planning theexperiments. A carefully planned testcampaign is needed to collect datathat adequately cover wide ranges ofthe four key operating variables,while minimizing the number of ex-
periments necessary.In the initial stage, change only
one variable at a time, while, if possi-ble, keeping all others constant. Nearthe final experimental campaign,study several possible and diversecombinations of these variables say, high temperature/low pressureand low temperature/high pressure,high throughput/high temperature andlow throughput/low temperature, etc.These data are useful for testing thereaction model for wide-ranging op-
erating conditions.Temperature usually plays the key
role in the reaction kinetics of mostsystems; so, dedicate the maximumnumber of experiments to this singlevariable. Study various combinationsof temperature with other variables.For reactions involving solids, cat-alytic or noncatalytic, vary both solidparticle size and temperature so thatthe data cover conditions rangingfrom negligible to significant pore-diffusion resistance. The effect, if
any, of pore diffusion on reaction rateand product selectivity then can beestablished from these data.
For multiple reaction systems, se-ries or parallel, to establish the kinet-ics of the overall reaction with betterconfidence, you ideally should collectdata on each component reaction.Thus, for systems A B C orX Y, X Z, each reaction A B,B C, X Y, and X Z should bestudied separately, if possible, partic-ularly to see the temperature effect oneach and to determine the reaction ac-tivation energy.
Examination of the data from both
PDU and an existing commercialunit, if available, should reveal foreach variable both the trends of its ef-fect and its relative importance on thereaction system. The tabulated andgraphical representation of the dataalso provide a consistency check pointing to bad data points thatshould be eliminated and helpingidentify experiments that should berepeated. Data consistency and repro-ducibility, as well as a wide range ofcoverage of all key variables, are es-
sential for building a robust model.
STEP 4 ESTABLISHTHE PRELIMINARY RE-ACTION MECHANISM ANDKINETICS. This is perhaps themost critical and important task inbuilding a robust model. It also isusually the most-time-consuming ef-fort (excepting experimental or pilot-plant campaigns), particularly forcomplex reactions. Without a satis-factory reaction mechanism and ki-
netics, though, the model may be ap-plicable only to narrow ranges ofconditions and may be dangerous touse for reactor scale-up, control, andoperation, and in dynamic simula-tions.
Begin this step with a literaturesearch. For most reaction systems ofcommercial interest, there usually isan abundance of information in theopen literature. This information,however, may not exactly match youroperating conditions or catalyst for-
mulation. Nevertheless, it is goodenough, in most cases, to formulateor select reaction-mechanism and rate
expressions that best represent yoursystem. Carefully consider the repu-tation and reliability of the informa-tion source, quality of data, and ex-perimental and analytical details be-fore selection of the reaction mecha-nism. A model builders prior experi-ence can be particularly helpful atthis stage.
For a totally new reaction system,the mechanism and rate expressionsneed to be established by systematicand fundamental analysis of reaction
rate data, as described in the literature(14).
Establishing the reaction kineticsinvolves two steps selection ofrate expressions, and, then, determi-nation of rate parameters. These pa-rameters usually are found by usingthe selected rate expressions andmatching rate data obtained from asimple and close-to-ideal experimen-tal unit like a plug-flow reactor (PFR)or continuous stirred-tank reactor(CSTR). For a complex (multiple-re-
action) system, this often involves atrial-and-error procedure for the ini-tial estimates, followed by fine-tuningwith a suitable parameter-estimationroutine.
Rate expressions normally used inengineering kinetics involve fourtypes of parameters: (1) pre-exponen-tial factors; (2) activation energies;(3) reaction order with respect to eachcomponent involved in each rate ex-pression; and (4) adsorption con-stants. For reaction systems of com-
mercial interest, a literature searchoften can lead you to reasonable ini-tial estimates for the latter three pa-rameters. The pre-exponential factorsmust be determined from actual datafor the catalyst or reaction conditionsof interest.
For gas/solid reaction systems,Langmuir-Hinshelwood-type rate ex-pressions that involve adsorption con-stants in the denominators are prefer-able. This type of rate expressionclearly reflects the change of reaction
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order with the change in gas concen-tration or pressure in the system.Thus, for example (5), in the follow-
ing rate expression for the conversionof n-butane to maleic anhydride, theorder of the reaction with respect to
n-butane goes from unity to zero, asthe concentration ofn-butane increas-es in the reaction mixture from a verylow to a very high value:
R = k1b1CBCO0.3/(1+b1CB)
where CB and CO are molar concen-trations ofn-butane and oxygen in thereaction mixture, and k1 and b1 are therate and adsorption constants of thereaction.
With the advent of inexpensive,high-speed computers and easilyavailable, powerful numerical tech-niques, it no longer is necessary tosimplify rate expressions for in-stance, by treating them as zero-, first-,or second-order systems. A zero-orderrate expression is not desirable, any-way, because it normally is applicableonly to a limited, high concentrationrange of the particular component. Forexample, for many oxidation systems,rates are expressed either as a zero or
small fractional order with respect tooxygen concentration. Yet, such a rateexpression, which often indicates apseudo (false) order of oxygen in ex-cessive oxygen concentration, is inap-plicable near complete oxygen conver-sion. A zero order implies that the re-action can proceed in the absence ofoxygen, which is not possible.
Unless absolutely required, the re-action mechanism only should consistof a limited number of reactions in-volving just the significant reactants
and products. A complex reactionmechanism with a very large numberof reactions is both unnecessary andunacceptable for most practical appli-cations. Many commercially signifi-cant systems can be well representedby a maximum of 510 reactions.Similarly, unless essential (for in-stance, for polymerization reactions),mechanisms involving free radicalsor other difficult-to-measure interme-diates should be avoided wheneverpossible.
STEP 5 STUDY THESAFETY ASPECTS. For anew, exothermic reaction system, thisis a critical step to assure the safetyand proper control of the commercial
reactor. Lab-scale reactors and evenpilot-plant units usually are made ofrelatively small diameter tubes thatallow for heat loss to the surroundings.The diameter of a commercial reactor,on the other hand, is large enough toapproach adiabatic conditions andcause heat buildup. Explosion hazardsof a reaction mixture increase with thebuildup of reaction heat with or with-out associated pressure rise.
The reaction mixtures explosioncharacteristics, which depend primari-
ly upon heat source (hot spot, spark, orflame, for example), gas composition,temperature, and pressure, must be de-termined carefully through experimen-tal programs carried out in a special-ized laboratory. These programs usual-ly provide combustion or flammabilitydiagrams for the reaction system. Sucha diagram, usually triangular, showsthe unsafe or explosive envelope ofgas mixture compositions at the partic-ular temperature and pressure (seeFigure 1). A series of such diagrams
are generated for wide ranges of tem-perature, pressure, and compositionsof the gas mixture so that inlet andoutlet gas compositions and conditionsof the commercial reactor are covered
with adequate margins.In modeling and scale-up, the op-
erating conditions for most parts ofthe reactor, including its inlet andoutlet, are kept outside the explosionenvelopes.
The explosion characteristics,however, are also influenced by manysecondary factors. For instance, in thepresence of fine solids in intimatecontact with reacting gases, such asin a fluidized-bed reactor, it is possi-ble to design and operate the reactor
well within the envelopes with negli-gible risk of explosion. This is be-cause no hot spots are generated insuch a reactor, due to vigorous mix-ing taking place. Caution must be ex-ercised, though, in designing the free-board region of such a reactor, be-cause hot spots may be created there,due to the flow of a very dilutegas/solids mixture.
Explosion phenomena are dividedinto two broad types deflagrationand detonation. Most explosion dia-
Reactor Modeling
40 www.aiche.org/cep/ October 2000 CEP
100% Inert
Typical SafeCommercial Operationwith Inert as Diluent
Typical SafeCommercial
Operation withHC as Diluent
MOC (Minimum OxygenContent) f or Explosion
9% O228% HC63% Inert
100% HC100% O2
DeflagrationRegion
25% O265% HC10% Inert
28% O272% HC0% Inert
95% O25% HC0% Inert
65% O210% HC25% Inert
s Figure 1. Typical deflagration explosion diagram for hydrocarbon/oxygen/inert mixture at a giventemperature and pressure.
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grams usually cover deflagration,which is caused by sudden gas expan-sion by an accelerated reaction. The
maximum pressure buildup due to suchan explosion can be estimated from thepressure/volume relationship of thecomplete reaction/combustion process.The detonation process, on the otherhand, is more violent, generating shockwaves that travel at a speed several or-ders of magnitude higher than the pres-sure wave caused by deflagration. Thelocal pressure buildup from this phe-nomenon, thus, is substantially higher for most hydrocarbon/air mixtures,about 1520 times the initial pressure,
compared to a maximum of two timesin case of deflagration. See, for exam-ple, Ref. 6 for details on these explo-sion phenomena.
Therefore, the detonation charac-teristics of the reaction mixtureshould be studied, along with defla-gration, to address reactor safetymore thoroughly.
STEP 6 DEFINE REAC-TOR TYPE AND ITS HY-DRODYNAMICS. The reactor
type is defined by: (a) the physicalconfiguration of the volume occupiedby the reaction system; (b) the flowmode of various streams in and out ofthe reactor; and (c) the hydrodynamicrepresentation of the flows within thereactor volume. Thus, for example, aCSTR usually represents a stirredvessel with continuous flow of a ho-mogeneous fluid stream or continu-ous phase in and out of the vessel.The hydrodynamic representation ofa CSTR assumes the fluid stream is
completely mixed as soon as it entersthe vessel and attains the outlet com-position instantaneously. A PFR em-bodies the other extreme. It usually istubular (with a high ratio of length,L,to diameter, D) in configuration. Theflow in and out this reactor type is thesame as that in the CSTR. The repre-sentation of the PFR hydrodynamics,however, assumes a total absence ofaxial mixing of the flowing streamswithin the reactor.
A homogeneous reactor usually is
designed using the performance equa-tions of either the CSTR or PFR. Thisallows easier analysis, design, and
scale-up of such reactors. But, theseidealized reactors do not closelyenough mirror the behavior of a realreactor. Such a reactor is better repre-sented by a system with axial disper-sion or by an axially dispersed reactor(ADR), the performance of whichfalls between that of a CSTR and aPFR. For a simple first-order reac-tion, A B, the steady-state mass-balance equation of an ADR can bedescribed as:
(1)
where Da is the axial dispersioncoefficient.
The predicted behavior of theADR approaches that of a PFR for noaxial dispersion, i.e.,Da = 0, and thatof a CSTR for infinite dispersion(complete mixing), i.e.,Da = . For areal reactor, Da is a finite numbergreater than zero.
In developing a robust model, itmay be advisable to start with an
ADR equation, rather than a CSTR orPFR one. For initial model develop-ment, the ADR equation can beturned into simple CSTR or PFR onesby substituting the two limiting val-ues ofDa. But, including the Da termallows you to fine-tune the model at alater stage to predict the reactor per-formance more precisely. To use thisapproach, however, the value ofDaneeds to be determined by experi-ment or from one of the many corre-lations available in literature, for ex-
ample, in Refs. 14 and 710. Thesecorrelations usually are available inthe form of the dimensionless Pecletnumber, NPe (=Lu/Da, whereL and urepresent tube length and fluid veloci-ty, respectively). The Peclet numbertypically is expressed as a function ofReynolds number, NRe, which repre-sents the flow behavior within the re-actor.NPe > 100 normally indicates anapproach to the behavior of a PFR,while NPe < 1 to that of a CSTR.Qualitatively, a longer tube length or
higher fluid velocity means morePFR-like performance, and the re-verse more CSTR-like.
The above discussions are for con-tinuous flow reactors. For both homo-geneous and heterogeneous reactors,however, part of the reaction mixtureor one or more of the phases can becaptive or in nonflow condition,while the rest can be in continuous orintermittent flow mode. Reactants canbe injected along the reactor length orreactor path in the case of multiple-reactor systems. The reactor productcan be recycled with the reactor feedbefore or after separation stages.
These represent batch, semi-batch,multi-injection, and recycle reactortypes. For heterogeneous reactors, theflow of the phases can be co- orcounter-current.
For gas/solid reactors, the gas usu-ally is in a continuous flow mode.The solid, however, can remain fixedin position within the reactor throughwhich the gas percolates. Or, bothsolid and gas can flow continuouslyin co- or counter-current modethrough the reactor. With the solid re-
maining fixed within the reactor,there are again various reactor types for example, the nonadiabaticpacked-bed tubular reactor (NAPB-TR), adiabatic packed-bed multistagereactor (APBMSR), monolithic reac-tor, and radial flow reactor. AnAPBMSR can be operated with directquench (interstage cooling or heating)by feed or recycle-gas injection or in-direct quench by a heat exchanger.For continuous flow of both gas andsolid, the possible reactor types in-
clude moving bed (co- and counter-current), bubbling and turbulent flu-idized beds, circulating and fast flu-idized beds, and entrained beds.
For gas/liquid systems, the reactorgenerally used is either a stirred tankor a bubble column. The bubble col-umn can be vertically or horizontallysparged, vertical or horizontal flow,gas-lifted (internally or externally),and with or without a forced liquid-circulation loop. The bubble columnsalso can be categorized according to
Dad
2cA
dz 2 udcAdz kcA = 0
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mixing modes of the liquid and gasstream, which can be CSTR, PFR orADR, depending upon the design and
operating conditions. The mode ofeach phase, to be used in modelbuilding, is determined from observa-tions of the flow behavior in a reactorprototype or from previous knowl-edge of the behavior from similar andwell-defined systems.
For a liquid/solid or gas/liquid/solidreactor, the solid can be a slurry or flu-idized, or a stationary packed bed or amonolith. In the continuous-flowmode, it can enter and exit the reactorwith the continuous liquid-flow
stream. As indicated above, manyother designs and operating modes ofthe liquid/solid and three-phase reac-tors are possible.
A combination of the reactor typesalso can be employed for example,a CSTR followed by a PFR, or a cir-culating fluidized bed (CFB) fol-lowed by a bubbling fluidized bed(BFB). The latter typifies some flu-idized catalytic cracking (FCC) reac-tors, where the riser section can besimulated by a CFB and the disen-
gagement zone at the top of the riserby a BFB.
Reactors of very complex geome-try, unusual shape, or with internalsthat modify the flow patterns in anunpredictable manner cannot bemodeled according the procedure de-scribed in this article. Use of suit-able computational fluid dynamics(CFD) codes, together with good re-action kinetics, may be a viable op-tion for these difficult reactors. Dueto their high complexity and long
computation time, however, suchCFD-based models may not findeasy or routine applications in plantoperation and control.
S TEP 7 DETERMINEDETAILS TO BE IN-CLUDED IN THE MODELS.Model building should proceed insteps starting with a relatively simplepreliminary model. This approach isused for two important reasons. First,it enables you to easily obtain and
verify approximate values of manymodel parameters (for example, thekey rate parameters) needed as start-
ing or initial guesses in numerical so-lution of more complex models dur-ing the final stages. Second, it pro-vides a framework for relatively easi-ly developing and debugging thebasic structure and computer codefor the final model. Details to be in-cluded in both the initial and finalmodels need to be accounted for atthis step, however, to allow a smoothtransition.
As an example of this step-wiseprogression, a reactor that is expected
to behave close to a PFR first can bemodeled by simplifying Eq. 1 to:
(2)
where k= k0 exp (-E/RT).Equation 2 is obtained by drop-
ping the second-order derivative termcontaining the axial-dispersion-coef-ficient term,Da, from Eq. 1. Equation2 is much easier to solve and elimi-nates the need for the unknown pa-rameter, Da. Furthermore, the results
obtained can be verified by anothersimple, stepwise calculation proce-dure, for example, with a spreadsheet.Once a numerical solution procedurefor Eq. 2 is established and approxi-mate rate parameters are determined,Eq. 1 can be quickly solved by usingthe same procedure to obtain thevalue ofDa and refined rate parame-
ters. In both steps, the same experi-mental data are used for evaluation ofparameters.
For this example and in anotherexample to follow, the equations areshown for only one reaction and forup to two reactants. Most reactionsare more complex, involving multiplereactions and many more reactants. Asimilar equation, therefore, has to bewritten for material balance on eachreactant. Also, for each reaction, atleast two rate parameters, k0 and E,must be estimated by data simulation.Thus, a significant number of modelparameters need to be evaluated for
most reaction systems.For a bubble-column reactor in
which a flowing gas A reacts with liq-uid B, A + B Products, the cou-pled heat- and mass-balance equa-tions (adapted from Ref. 8) are shownin the box, and represent the targetequations of the final model:
Balance of A in gas phase: Eq. 3;Balance of A in liquid phase: Eq. 4;Balance of B in liquid phase: Eq. 5;Heat balance (liquid phase): Eq. 6.The recommended procedure is to
start with a preliminary model for thesystem at steady state to avoid thecomplexity of time-derivative terms.Assume that the system is isothermal(with an average temperature be-tween inlet and outlet values) and isPFR in performance. For the prelimi-nary model, the reactor equationsthen become:
udcAdz
+ kcA = 0
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42 www.aiche.org/cep/ October 2000 CEP
(3)
(4)
(5)
(6)
(8)a*uLdcALdz
+ KLa cAL* cAL Lk2cALcB = 0
Leff2Tz2
+ a*LcpLuLTz
kwaw T Tw + L HR k2cALcB =Tt
LDaL2cBz2
+ a*uLcBz
Lk2cALcB =cBt
LDaL2cALz2
+ a*uLcALz
+ KLa cAL* cAL Lk2cALcB =
cALt
GDaG2cAGz2
z
uG cAG KLa cAL* cAL =
cAGt
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(7)
see box for Eq. 8
(9)
Equations 79 do not require theparameters DaG, DaL, eff, L, cpL, kw,HR, or the heat-balance equation.Once Eqs. 79 are solved satisfactori-ly and the rate parameters of the reac-tion system are determined, introducethe second-order terms containing theaxial dispersion coefficients, DaG and
DaL, and then the steady-state heat-
balance equation (Eq. 6 minus thetime derivative term). After thesteady-state model is found to run
satisfactorily with all establishedmodel parameters, add the time-derivative terms of Eqs. 36 to devel-
op the final unsteady-state reactormodel.
Model complexity and the num-ber of required model parametersgrow with details that account forvarious phenomena that may be im-portant to the specific reactor typeand reaction system involved. Table1 provides a list of some of thesephenomena and their relevance tovarious reactor types. This table alsopoints out details that may or maynot be important for the various re-
actor types. Exclude the unimportantdetails to minimize model-buildingeffort.
S TEP 8 CHOOSE THERIGHT BALANCE EQUA-TIONS. You now should select the
governing mass-, heat-, and pressure-balance equations, including thosedescribing the solids circulation sys-tem design and control (if necessary),that adequately describe the reactorperformance and are consistent withSteps 6 and 7 (e.g., Eqs. 36 for ourexample). Such equations alreadyhave been developed for most reactortypes of commercial interest and areavailable in the open literature (forexample, Refs. 14 and 713). Expe-rience and judgment are required,
however, in choosing the equationsfor a specific need or reactor type,particularly when several alternatives
a*uLdcBdz
Lk2cALcB = 0
ddz
uGcAG KLa cAL* cAL = 0
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Table 1. Relative importance of major phenomena that may affect reactor models.
Phenomenon W here It Usua ll y I s Mo re Important W here It Usua ll y I s Less Important W here It Mu st Be Considered [Comment]
Pore-diffusion (a) Reactions involving solid partic le Catalytic bubbling fluidized-bed (BFB) Fixed- and moving-bed G/S reactorresistance size >1/16 in. and circulating fluidized-bed (CFB) models and fast reaction systems
(b) All fast, noncatalytic gas/solid reactors with partic le size
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are proposed in the literature. In somecases, the complete set of equationsneeds to be developed by combining
the best information from several lit-erature sources. The equations ideallyshould:
be based more on sound princi-ples of reaction engineering and reac-tor hydrodynamics than empiricism;
contain a minimum number ofadjustable parameters;
include hydrodynamic, circula-tion system, and other parameters viareliable correlations or values alreadyavailable in the open literature, forexample, KLa for a bubble-column re-
actor; have undergone successful test-
ing and validation; be free of unnecessary details or
complications; be readily solvable by standard
mathematical routines; and be easy to use, expand, and
modify.
STEP 9 SELECT EVAL-UATION PROCEDURES.Now, determine correlations, sources,
or methodologies for evaluating allnonkinetic model parameters, and hy-drodynamic and solids circulation phe-nomena involved in the reactor equa-tions of Step 8. The reliability of the ki-netic parameters and the success of thefinal model depend to a large extentupon the values of these parameters,which fall into the following categories:
thermophysical properties like density, heat capacity, thermalconductivity, viscosity, surface ten-sion, diffusivity, solubility, and heats
of formation of the componentsand the reaction mixture as a functionof reactor operating conditions;
effective diffusivities of gaseswithin solid pores;
effective thermal conductivitiesof solids;
axial and radial dispersioncoefficients;
interphase (or interzone) heat-and mass-transfer coefficients;
wall heat-transfer coefficients;
various hydrodynamic proper-
ties like bubble size, bubble veloc-ity, and bubble fraction in a BFB re-actor and bubble columns, phase
holdups in two- and three-phase reac-tors, voidage profiles in a CFB reac-tor; and
all parameters in the design andcontrol equations of the solids circu-lation systems.
Parameters of the first category nor-mally are readily available, except forsolid components, from many oftodays commercial simulation pack-ages. These parameters can be automat-ically retrieved from these packages orin-house simulators, once the model is
properly integrated. Correlations or ap-proximate values for most of the otherparameters are available in the open lit-erature. The reliability of the estimates,however, varies depending upon boththe parameter and the correlation used and, thus, demands careful evalua-tion. Also, once the final model is de-veloped, a parametric sensitivity analy-sis may be required to determine whichof the above parameters need reevalua-tion to improve the model.
STEP 10 DETERMINEMODEL STRUCTURE ANDSOLUTION PROCEDURES.This step involves: (a) planning themodel structure and required subrou-tines, and (b) selecting numerical pro-cedures to solve the model equationsand to estimate model parameters.
The model structure should pro-vide maximum flexibility for expan-sion and easy modification. It shouldaccommodate additional details orfeatures in successive stages as the
model grows. It should be built onseparate subroutines dedicated to oneor more key elements of the model.Such elements include effective dif-fusivity of gases, catalyst effective-ness factors, interphase mass transfer,phase holdups, bed voidage profile,axial and radial dispersions, bubbleproperties, wall heat transfer, etc. Asthe model grows, each of these sub-routines can be improved individuallyas needed without disturbing the rest.The structure also can be built on
subroutines that contain governingmass- and heat-balance (or perfor-mance equations) characterizing each
distinct reactor type. All these sepa-rate equation packages can share thesame numerical routines, as appropri-ate, to generate model solutions.
A variety of highly effective nu-merical-solution packages, which canbe easily integrated into the model,are available today. For example,Refs. 1416 describe specific mathe-matical routines in detail, along withtheir theory and areas of application.Selected routines from these andmany other available software pack-
ages can be tried with the variousequation sets of the model; the bestselections then can be included in themodel as subroutines. (For more in-formation on software available, seethe on-line CEP Software Directoryat www.aiche.org/CEP/software/.)
Versatility, ease of use, fast con-vergence time, and freedom from so-lution errors are among the key selec-tion criteria. These routines, however,only can provide local solutions. Aglobal solution of highly nonlinear
equations as encountered in reactionkinetics (an integral part of most re-actor-performance equations) cannotbe achieved through any of the avail-able routines. A good initial guess orinitialization of each of the model pa-rameters, therefore, is always neces-sary for these applications.
S TEP 11 DEVELOP APRELIMINARY MODEL.Now, using the design and operatingconditions from Step 3 and the pre-
liminary reaction mechanism and rateexpressions obtained from Step 4, de-velop a model based on the proce-dures and equations established inSteps 810. After satisfactory com-puter code is generated, the majortask of this step is to determine a pre-liminary set of rate parameters. Thisis accomplished by first consideringonly the major reactions and productsand using an initial set of representa-tive data. Preliminary values of acti-vation energies, reaction orders, and
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adsorption constants from a literaturesearch or approximations are used atthis stage. Keeping these values con-
stant, the pre-exponential factors ofthe reaction rates are found, usuallyvia trial-and-error by comparing keyobservations like conversions ofmajor reactants and selectivities ofmajor products with model projec-tions. The data should be taken at ap-proximately the same temperature, sothat the effects of other variables arenot masked by that of temperature.
Next, using additional data reflect-ing the effect of temperature, get thebest values of both pre-exponential
factors and reaction activation ener-gies with a parameter-estimation rou-tine. These parameters, along with thereaction orders and adsorption con-stants, are fine-tuned in Step 13 to bediscussed later.
STEP 12 INCLUDE AD-DITIONAL DETAILS FORTHE FINAL MODEL. These de-tails, as determined in Step 7, shouldbe introduced preferably in stages, sothat eachs impact on the results and
relative importance are established.This stagewise approach also helps ina smoother model development, dueto easier debugging of modified orextended program codes.
Only major reactions, reactants,and products were considered in thedevelopment of the preliminarymodel. At this step, therefore, all nec-essary minor reactions, reactants, andproducts need to be incorporated, andthe preliminary reaction mechanismand rate expressions expanded, as
necessary.
STEP 13 DEVELOP THEFINAL MODEL BY TUN-ING PARAMETERS. Once allthe necessary details are incorporat-ed, you must tune the model parame-ters, primarily, the kinetic ones, be-cause the preliminary model relied ononly a few sets of representative data.In this step, use all available data ideally, these should represent a widevariation in design and operating con-
ditions. Screen the entire data set for"bad" data, both qualitatively, viatrend analyses by graphs and tabula-tions, and quantitatively, through pa-rameter-estimation procedures. Elimi-nate data points that cannot be repro-duced satisfactorily by these data rec-onciliation procedures.
It may be necessary at this step tocarry out additional tests or experi-ments to fill gaps in the data and to ver-ify observations that cannot be matched
satisfactorily by a model. Additionaldata at this step also may be required toimprove the reaction-mechanism andrate expressions. For complex systemsinvolving many reactions, the effects ofthe concentration of each component ofthe reaction mixture on each reactionrate may need to be studied for a betterestimation of the reaction orders or forbetter rate expressions. For a solid-cat-alyzed heterogeneous reaction, the im-pact of the concentration of each com-ponent or of pressure may have to be
studied in more detail or over a widerrange to satisfactorily determine the ad-sorption constants. Additional experi-ments, particularly on temperature ef-fect, on one or more of the componentreactions often are required to confirmreaction activation energies.
Now, use the parameter-estimationroutine again to obtain the best possi-ble estimates of all the rate parame-ters by comparing the model projec-tions with key observations for theentire data set.
S TEP 14 MAKE SCALE-UP PROJECTIONS ANDESTABLISH THE OPTIMUMDESIGN. At this stage, consider avariety of possible combinations ofdesign and operating variables withinranges deemed feasible from prelimi-
nary safety and mechanical consider-ations. Narrow down the ranges insuccessive projections by taking intoaccount various other limitations,such as pressure drop, heat-transferrate, and throughputs and holdups ofvarious phases (gas, solid, and liquid)within the reactor. Then, evaluate thebest design and operating conditionsbased on yield, productivity, andproduct quality on additional factorssuch as control and operational flexi-bilities, detailed safety and mechani-
cal checks, and compatibility withupstream and downstream sectionsfor an existing plant and use eco-nomics to make the final selection.
Figure 2 shows a flow chart for themodel-building steps and indicatesthe relative effort and importance ofeach of these steps. Bold solid lineshighlight the major flow path, whiledotted lines show the interactions be-tween the steps. The relative efforttypical of each step is depicted quali-tatively by the size of each rectangle.
CEP October 2000 www.aiche.org/cep/ 45
s Photo credit.Applied Reactor Technologies, Inc.
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Deeper tints indicate the most criticalsteps. Step 2 is broken into three sep-arate and parallel steps 2A, 2B,
and 2C, the latter two for hydrody-namic tests and solids circulation-system tests and demonstration, if re-quired. Step 2A and Steps 35 areunique to a new reaction system andare grouped as a reaction modelblock. All the remaining steps belongto a common block called a reactormodel or model package and, oncedeveloped for multiple-reactor con-figurations, can be shared by any newreaction system or for system revampand modernization.
Building multiple-reactormodels
A package must contain a multi-
plicity of reactor models if it is to de-termine the best configuration forplant revamp or modernization. Sucha multiple-reactor model packagealso is necessary for developing anew reaction or catalyst system be-fore launching major pilot-plant ornew process-development campaigns.For any known reaction system orcatalyst activity, the package shouldpredict the performance of a given re-actor configuration, as well as of avariety of alternative configurations.
The model must be applicable to anycombination of reactions and reactorsystems included in the package. It
should identify optimum operatingconditions to best meet a given de-mand from an existing reactor, andevaluate various possible new designoptions or modifications of an exist-ing reactor.
For example, assuming the samecatalyst activity for a catalytic gas/solidreaction system, a user can immediatelydetermine the possible advantages ofswitching from an existing fixed-bedreactor to a fluidized-bed one as part ofa revamp or modernization, or quickly
Reactor Modeling
46 www.aiche.org/cep/ October 2000 CEP
PDU Tests forReaction Kinetics
Cold Model Testsfor Reactor
Hydrodynamics
(if Necessary)
DefineReaction Type
Collect andAnalyze PDU
and/or CommercialPlant Data
Establish PreliminaryReaction Mechanism
and Kinetics
DevelopPreliminary Model
DevelopFinal M odel
Cold Model Tests andDemonstrations of
Novel Solids'Circulation System
Study Safety Aspectsof Reaction System
Step 2A
Step 2B
Step 2C
Step 3 Step 4
Step 5
Step 6
Step 1
Step 7
Step 8
FinalPreliminary
Step 9
Step 10
Step 11
Step 12Step 13Step 14
Scale-upProjections andOptimum Design
Add AdditionalDetails for
Final M odel
Determine ModelStructure and
Numerical
Solution Procedure
Determine NonkineticParameters and
Hydrodynamic/Solids'Circulat ion Design
Equations
Choose GoverningMass, Heat and
Pressure Balance
Equations
Determine Detailsfor Preliminary
and Final M odels
Define Reactor
Type and itsHydrodynamics
ReactionModel
ReactorModel/Model
Package
s Figure 2. Relative effort,importance, and flow chart ofmodel-building steps forgas/solid reactors.
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discriminate between a BFB and aCFB, if models for these reactor config-urations are available. The package
speeds quantitative comparisons of theperformance and the advantages anddisadvantages of various possiblefixed-bed configurations, such as multi-tubular, multistage adiabatic quench,radial flow, or double-wall annulartubular, if such models also are includ-ed. Multistage feed injection, partial ortotal products recycle, and programmedtemperature profiles are among themany options for minor design modifi-cations that can be easily included inthis model package, as well.
Figure 3 schematically shows howa multiple-reactor model package canhelp discriminate between alternativereactor concepts and decide on thebest option(s) for any reaction system.This discrimination process, if carriedout early in the scale-up or revamp ef-forts, leads you to the most competi-tive design promptly and avoids wast-ed efforts from trial and error in longexperimental or pilot-plant campaigns.
To develop such a package for anygiven reaction system, repeat Steps
614, excluding Step 13, for all reac-tor types of possible interest. Use thekinetic parameters of the first reactortype determined in Step 13. Select thebest reactor configurations for a newreaction or catalyst system by com-paring the optimum designs and oper-ating conditions determined in Step14 for all the reactor types studied.
One of the biggest advantages ofbuilding such a model package isthat, once developed, it is applicableto any other reaction or catalyst sys-
tem involving the covered reactortypes. At plants that include a varietyof reaction systems and reactor con-figurations, the package can be an im-portant asset for meeting the constantdemands for reactor revamps andmodernization. It also can be a valu-able tool in utilizing existing reactorsfor new products and catalyst sys-tems, when the demands for old prod-ucts decline or an advanced catalystformulation must be used for eco-nomic benefits.
Tips and traps
Collect adequate data on each ofthe four major variables. You must
have a sufficient number of observa-tions on the effect of each of the fourmajor variables, namely, through-put(s), temperature, pressure, andfeed composition. Insufficient obser-vations on any one of these may leadto bias in the parameter estimationthat will cause greater errors inmodel predictions.
Cover various combinations ofvariables. The test or experimentalprograms should be planned, if possi-ble, in such a way as to provide data
on a variety of variable combina-tions, including some extreme condi-tions, such as high temperature/lowpressure, low temperature/high pres-sure, high temperature/high pressure,and low temperature/low pressure.More robust model parameters canbe obtained through validation withsuch data.
Ensure ranges are adequate. Amodel is strictly applicable only tothe ranges covered by the data uponwhich it is built. The wider the data
coverage, therefore, the wider theapplicability of the model. Thus, thedata should cover an adequate rangeof each of the four major operatingvariables. The coverage should ex-tend both below and above the ex-pected operating conditions of thecommercial reactor, so that themodel, when needed, can satisfacto-rily predict off-specification andtransient conditions.
Pay particular attention to the im- pact of temperature. Because of its
exponential effect, temperature oftenis the most dominant variable forchemical reactions. Therefore, studythe effect of temperature most thor-oughly and systematically. It also isadvisable to evaluate the impact ofother variables at various tempera-ture levels so as to gain an under-standing of the entire possible oper-ating domain of the reaction system.This also provides more data on tem-perature effect that are useful for abetter estimation of the reaction acti-
vation energies and, thus, increasedreliability of the model.
For most reactions, a good
knowledge of reaction activation en-ergies is essential to accurately pre-dict reactor yields and product quali-ty. This also is critical for the designand control of reactors with sharptemperature peaks, such as steam-cooled tubular fixed-bed reactors forexothermic reactions. These reac-tors, which normally have a verynarrow operating window, are proneto temperature runaways withoutproper design and control.
Assess the effect of residence time.
This is important because, for manycomplex reactions, the final productsare generated through intermediatesformed early in the reaction.
An example is the liquid-phaseoxidation of p-xylene to p-toluicacid in the commercial productionof dimethyl terephthalate (DMT).The p-toluic acid is generated viatwo intermediates, p-tolul alcoholand p-toluol aldehyde, which areformed very early in the reactions.As time progresses, these intermedi-
ates get oxidized to the final prod-uct. Concentrations of these prod-ucts in the reaction mixture, there-fore, are very high early in the pro-cess, and negligible at the end. Datacovering a wide range of reactiontimes starting from a very lowvalue, thus, are necessary to revealthis fact and the true reaction mech-anism for the process. Only a care-ful evaluation of the residence-timeeffect on this reaction system woulddisclose that the reaction products
p-toluic acid and p-toluic ester ac-celerate thep-xylene oxidation. Thisrate-acceleration effect must be ac-counted for by the rate expressionsof this reaction system.
Get rate data on each componentreaction. As indicated earlier, suchrate data should be collected, if pos-sible, particularly to confirm the ac-tivation energy of that reaction.
Perfect the reaction model first.Reaction mechanism and kineticsgenerally are the most dominant fac-
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Reactor Modeling
48 www.aiche.org/cep/ October 2000 CEP
MixedGases
HCGases
Air
Air
HT FluidIn
Adiabatic
QuenchReactor
Multi-Tubular FixedBed w ith Varying
Catalyst Concentration M ulti-TubularFixed Bed
Adiabatic Quench Reactorwith Split Air Flow
Radial FlowReactor
Double-Wall HeatExchanger Reactor
Bubbling FluidBed (BFB)
BFB/BFB Combow ith Catalyst asOxygen Carrier
CFB/BFB Combo w ithCatalyst as Oxygen Carrier
M ultistage BFB
M ultistage BFBwith Split Air Flowand Temperature
Programming
Circulating FluidBed (CFB)
HCGases
OutletGas
Gas/SolidMultiple-
Reactor ModelPackage
OutletGas
OutletGas
BFW
Economics
OutletGas
InletGas
Inlet Gas
SolidsIn
Solids Out
HC GasesGas Out
Products
?BFB/CFB Catalyst
Development Feasible?
BestTechnicalDesigns
Air
HT FluidIn
Steam
?? ?
?
?
?
?
?
?
??
?
?
?
Control, Operational Flexibilities, Detailed Safety,Mechanical Checks, and Compatibility with
Upstream and Downstr eam Sections
TheFinal
Design
FluidizedBed
Design
Solids Out
Air
HC Gases
Product
HC Gases
HC Vapor
Stripping Gas
Flue Gas
FlueGas
Regenerator(BFB)
Regenerator(BFB)
Reactor(CFB)
Reactor (BFB)
StrippingGas
StrippingGas
Products
Air
Air
StrippingGas
Fixed-BedDesign
Solids In
s Figure 3.Decision-makingwith multiple-reactormodel package.
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tors in determining reactor perfor-mance and design. (Exceptions,however, include systems involving
novel or difficult solids circulationsystems, and some very fast reac-tions like combustion and gasifica-tion or instantaneous absorption withreaction in a liquid phase, where thechemical conversion rates essentiallyare diffusion controlled.) The fol-lowing words of caution, therefore,are in order for building a robustmodel for most chemical reactors.
Dont attempt to model a reac-tor before perfecting the reactionmodel. Otherwise, the reliability of
the overall model invariably isquestionable. Efforts spent on a re-liable reaction model are always justified, because they save effortand trial-and-error downstream dur-ing design, scale-up, and operationof the reactor.
Dont concentrate on reactorhydrodynamics. A great deal of ef-fort often is focused on the study ofreactor hydrodynamics like bubbleproperties in a BFB reactor, or clus-ter behaviors in a CFB reactor,
while ignoring the importance of areliable reaction model. A reactormodel combines the reaction andhydrodynamic models of the reactor.We cannot overemphasize that, inmost cases, an inadequate reactionmodel affects the reliability of thereactor model far more than an inad-equate hydrodynamic model.
Dont rush to extensive PDUand pilot-plant campaigns. With theexception of some systems as indi-cated above, place more emphasis
on careful data collection and analy-sis to build a solid reaction modelrather than on extensive PDU orpilot-plant campaigns.
Dont downplay the regenerationmodel in reactor-regenerator dualsystem. In such systems, such as aFCC, a solid catalyst typically is incontinuous circulation between thereactor and the regenerator. The de-sign and performance of each ofthese units, as well as the solids cir-culation loop design and control, in-
timately depend upon both reactionand regeneration kinetics. So, the re-action model for each system must
be developed with equal care. This isparticularly true for some processesinvolving partial oxidation reactions,where the catalyst itself acts as thecarrier for oxygen. Oxygen is fed inthe regenerator to oxidize the cata-lyst, which then moves to the reactorto be reduced.
Adequately address the solids cir-culation system. For reactor-regener-ator dual systems, the inability toproperly scale up and design thesolids circulation loop could be the
worst bottleneck. The circulationlines connecting these two units mustbe sized and equipped with solidsflow control devices in such a waythat the operational flexibility or lim-itations of solids flow rate do notcompromise the optimum operationof either the reactor or the regenera-tor. This may be particularly criticalfor a system, as cited above, wherethe catalyst itself has to act as anoxygen carrier for the reactor, and,thus, which demands an unusually
high solids circulation rate.Dont use a too complex or too
simple reaction model. An overlycomplex model is undesirable, be-cause of the extra effort of handlingsuch a system and the difficulty ofparameter estimation. It also is un-necessary, as, for most practical ap-plications, it wont improve perfor-mance much, if at all. An over-sim-plified model (such as one withpseudo-first order or zero-order ki-netics or without some important in-
termediate reactions) also is unac-ceptable, as it is applicable to a lim-ited range of operating conditions.For example, it does not apply atvery low contact times, when prima-ry intermediates may be at very highconcentrations, or at very high con-tact times, when some componentsattain near-complete conversion.
Use alternative methods to checkresults. During model building and,particularly, during expansion fromsimpler to more advanced models, it
is advisable to check the models re-sults against those from alternativemethods. Such methods may include
spreadsheet calculations or analyti-cal solutions of simplified kinetics.For example, the conversions pre-dicted by an advanced model for asingle reaction of first- or second-order kinetics of a fixed- or flu-idized-bed reactor should be thesame as those obtained from analyti-cal solutions available in the litera-ture for these systems. Such checksassure that, in spite of continued ex-pansion and increasing complexity,the model can reproduce results for
known simple systems.Take extra care in defining reac-
tor hydrodynamics. A model shouldbe based as closely as possible onthe actual hydrodynamics of the sys-tem. For example, a tubular reactorwith high aspect (length to diameter,L/D) ratio, operating with a highfluid velocity, should be representedby a close-to-PFR model. An ADRmodel should represent the same re-actor with internal baffles that cre-ate local turbulence and mixing.
Misrepresentation of hydrodynamicsleads to false models of limited ap-plication.
Dont make the hydrodynamicmodel too complex or too simple.The hydrodynamic model should notinclude, for example, local or micro-phenomenon that likely have negligi-ble impact on the overall reactor be-havior. For most practical applica-tions, a very detailed hydrodynamicmodel may not contribute to an over-all improvement of reactor model
predictions. On the other hand,though, the hydrodynamic modelshould not ignore major phenomenaoccurring within the reactor volume.Thus, if there are distinct zones of to-tally different hydrodynamic behav-iors (for example, PFR, mixed, deadzones, etc.), each occupying a signif-icant reactor volume, the impact ofeach zone on the reactor performanceneeds to be evaluated.
Examine entrance and exit effects.Many reactor-design models are fo-
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cused only on the main body of the re-action zone, for example, the packed-bed section of a fixed-bed reactor or
the dense bed of a BFB reactor. Reac-tions may continue, however, beyondsuch sections into the plenums or free-board regions of these reactors, due to
gas-phase or dilute-phase reactions.For exothermic reactions, this maylead to temperature buildup in these
regions, causing product degradationand, in extreme cases, possible explo-sion by temperature runaway. Be par-ticularly careful about the mixing zone
and injection procedure for hydrocar-bons and oxidants in the entrance sec-tion of partial oxidation reactors, due
to explosion possibilities of the reac-tion mixture. Attention to entrance andexit effects also is very important in aCFB reactor, because the design ofthese sections may significantly affectthe hydrodynamic behavior of the en-tire reactor.
In many cases, a significant frac-tion of the total conversion occursvery close to the reactor entrance.This conversion may depend to alarge extent upon the design of theentrance region or fluid- or
fluid/solid-distributor device at theentrance. The model, therefore,
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Literature Cit ed
1. Levenspiel, O., Chemical Reaction
Engineering, Wiley, New York
(1972).
2. Froment, G. F., and K. B. Bischoff,
Chemical Reactor Analysis and De-
sign, Wiley, New York (1979).
3. Satterfield, C. N., HeterogeneousCatalysis in Practice, McGraw-Hill,
New York (1980).
4. Butt, J. B., Reaction Kinetics and Re-
actor Design, 2nd Ed., Marcel Dekker,
New York (1999).
5. Dutta, S., and G. D. Suciu, Unified
Model Applied to the Scale-up of Cat-
alytic Fluid Bed Reactors of Commer-
cial Importance in Fluidization VI,
J. R. Grace et al., eds., Engineering
Foundation, New York, pp. 311318
(1989).
6. Nettleton, M. A., Gaseous Detonations
Their Nature, Effects and Control,
Chapman & Hall, London (1987).7. Fan, L. S., Gas-Liquid-Solid Fluidiza-
tion Engineering, Butterworths, Boston
(1989).
8. Deckwer, W.-D., Bubble Column Reac-
tors, Wiley, New York (1992).
9. Kastanek, F. J., J. Zahradnik, J. Kra-
tochvil, and J. Cermak, Chemical Re-
actors for Gas Liquid Systems, Ellis
Horwood, New York (1993).
10. Kunii, D., and O. Levenspiel, Flu-
idization Engineering, Butterworth-
Heinemann, Boston (1991).
11. Kwauk, M., Fluidization Idealized
and Bubbleless with Applications, Sci-
ence Press, Beijing (1992).
12. Cheremisinoff, N. P., and P. N.
Cheremisinoff, Hydrodynamics of
Gas-Solids Fluidization, Gulf, Houston
(1984).
13. Zenz, F. A., Fluidization and Fluid-Par-
ticle Systems, Reinhold, New York
(1960).
14. Press, W. H., S. A. Peakolsky, W. T.
Vetterling, and B. P. Flannery, Nu-
merical Recipes in Fortran 77: The Art
of Scientific Computing, Cambridge
Univ. Press, New York (1995).
15. Riggs, J. B., An Introduction to Nu-
merical Methods for Chemical Engi-
neers, Texas Tech Univ. Press, Lub-
bock, TX (1994).
16. Cutlip, M. B., and M. Shacham, Prob-
lem Solving in Chemical Engineering
with Numerical Methods, Prentice Hall,
Upper Saddle River, NJ (1999).
17. Dutta, S., and R. Gualy, General Re-actor Model Improves HPI Applica-
tions,Hydroc. Proc., pp. 4553 (July
(1999).
18. Dutta, S., and B. Jazayeri, Alternate Re-
actor Concepts for Oxidative Coupling of
Methane, in Fluidization VII, C. Potter
and D. Nicklin, eds., Engineering Founda-
tion, New York, pp. 445453 (1992).
19. Dutta, S., Fluidized and Moving Bed
Desulfurization by Zinc Titanate,
AIChE Symp. Ser., 90 (301), pp.
157169 (1994).
20. Dutta, S., B. R. Christin, and M. F.
Raterman, Circulating Fluid Bed Re-
actor Model Developed for FCC/Art Re-generator, in Fluidization VI, J. R.
Grace et al., eds., Engineering Founda-
tion, New York, pp. 916 (1989).
21. Dutta, S., A Unified Approach to the
Modelling of Catalytic Fluidized Bed Re-
actors,Proceedings, 3rd World Congress
of Chem. Eng., Tokyo, Asian Pacific Con-
federation of Chemical Engineering, Bar-
ton, Australia, pp. 287290 (1986).
22. Dutta, S., S. C. Arnold, G. D. Sucio,
and L. Verde, Scale-up of a Catalytic
Fluid-bed Reactor Involving Complex
Kinetics,IChemE Symp. Ser., 87, pp.
517526 (1984).
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Needs for Analysis, Design and Scale-up
of Fluidized Bed Reactors,AIChE
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Process Reactors,Hydroc. Proc., 79 (9),
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Nomenclature
a = specific interfacial area based on
dispersion volume
a* = constant = +1 for counter-current,
-1 for co-current flow
aw = specific heat-transfer area
cA, cAG, = molar concentration of A, in gas,
cAL and in liquid, respectively
c*AL = molar concentration of A in
liquid in equilibrium with gas at
gas/liquid interface
cB = molar concentration of B in
liquid phase
cpL = specific heat capacity of liquid
Da, DaG, = axial dispersion coefficient of
DaL A, in gas, and liquid, respectively
E = reaction activation energy
HR = heat of reactionk, k2 = reaction rate constants
kw = wall heat-transfer coefficient
k0 = reaction pre-exponential factor
KL = liquid-side mass-transfer coefficient
R = gas constant
t = reaction time
T = reaction temperatureTw = wall temperature of heat-transfer
surface
u, uG, = linear velocity, of gas, and of
uL liquid, respectively
z = axial coordinate
Greek letters
G, L = gas- and liquid-phase holdups
eff = effective thermal conductivity of
liquid
L = liquid density
= reaction stoichiometric coefficient
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should account for this phenomenon.
Include sufficientflexibility in thetest unit. The design of the PDU or
the final model-validation or demon-stration unit should allow test runs tobe carried out over a wide range ofoperating conditions, as discussedearlier.
Consider alternative designs earlyon. In developing new technology ormodernizing a plant, use the packageto assess alternative reactor conceptsbefore a particular reactor type is se-lected. Typically, industry has chosena reactor type or design option with-out a quantitative evaluation of alter-
native concepts. This often leads toan inferior choice or wasted efforts infollowing a wrong development path.
Dont attempt a dynamic modelbefore perfecting the steady-statemodel. The availability of variouscommercial process simulators andcontrol and optimization tools has ledto a tendency in industry to rush tobuild dynamic reactor models. Itoften is not realized, however, that adynamic model is of little value untila robust steady-state model for the
same system has been perfected. Adynamic reactor model is meant topredict the transient behavior duringstartups, shutdowns, or emergencies,when operating conditions may be farfrom those of the normal operation atsteady state. But, before such predic-tions can be realistically attempted,the model first must successfullyforecast the behavior at steady state atvarious operating conditions. Manycommercial reactor models built onlyto apply around the steady-state oper-
ations in the plant, therefore, are to-tally inappropriate for dynamic modeldevelopment. These dynamic modelswould fail to predict reactor behaviorat startups, shutdowns, and in emer-gencies, when the reactors operate farfrom design or normal conditions.
A proven approachWe know these steps and our rec-
ommendations work, because wehave used them to develop a generalmodeling package that has proven it-
self for reaction and reactor systemsof various kinds in the real world.The currently available package ap-
plies to both catalytic and noncatalyt-ic gas/solid reactions of just aboutany complexity and kinetics, and re-actor systems of virtually any type,including those with a fixed bed, flu-idized bed (bubbling, turbulent, circu-lating, or entrained), or moving bed,singly or in combination. The modelcurrently is being extended to includeliquid-phase reactions.
The package handles many designmodifications like product recycle,multiple-feed injections, multistag-
ing, and temperature programming,as well as various design options foreach reactor type. It includes all nec-essary correlations and methodolo-gies for heat- and mass-transfer, andhydrodynamic calculations, perfor-mance equations for each reactorconfiguration, and a parameter-esti-mation routine. Customizing and in-corporating additional correlations,design features, and phenomena iseasy.
Details on the development and
application of this package are pro-vided elsewhere (5, 1726). The fourmost-recent publications (17, 24-26),in particular, provide background onthe use of the package, and a summa-ry of its features and applications.
With this package, it is possible toextract kinetic and other parametersfrom data obtained from virtually anytype of reactor and scale of operation
given a suitably wide range of op-erating conditions. It is not necessarythat such data be generated exclusive-
ly in idealized reactors, like integralor differential as in conventionalpractice. Such reactors, however, maybe needed to provide supplementarydata for improved parameters.
An early version was a key to thesuccessful scale-up of worlds firstfluidized-bed catalytic process (theALMA process) for production ofmaleic anhydride from n-butane directly from bench to commercialscale without going through a pilotplant. The model has been the basis
for successful development of anoth-er fixed-bed catalytic process plannedfor commercialization next year.
The package also has been used toscreen alternative reactor-design con-cepts for a variety of other commer-cial reaction systems, includingpropylene to acrylonitrile, naphtha-lene to phthalic anhydride, oxidativecoupling or methane, hot-gas desulfu-rization by zinc titanate, and partialoxidation of paraffins. It has served tosimulate lab, pilot-plant, and com-mercial data for a wide range of otherreaction and reactor systems, such asFCC catalyst regeneration in a CFB
reactor, FCC riser, methanol synthe-sis, ammonia synthesis in multistageadiabatic quench reactor, and hydroc-racking/isomerization of naphtha (anexample of an application for nonstoi-chiometric reactions of refineries).
Use of such a model packageshould substantially reduce themodel/model-package building effortfor most new and existing reactionand reactor systems. C EP
CEP October 2000 www.aiche.org/cep/ 51
S. DUTTAis senior staff consultant for GTC
Technology Corp., Houston ((281) 5974800;
Fax: (281) 5970932; E-mail: sdutta@
gtchouston.com), where he specializes in
reactor design and scale-up, and
implementation of reactor models. He has
more than 20 years of industrial experience,
including with Simulation Sciences, SABIC,
Englehard, Fluor Daniel, and Lummus Crest.
The author of more than 35 papers, a book
chapter, and a patent, he holds a PhD in
chemical engineering from the Indian
Institute of Technology, and is a member of
AIChE.
R. GUALYis general manager of the Chemicals
Group of GTC Technology Corp., Houston
(E-mail: [email protected]). Hisresponsibilities include business unit
marketing, sales and licensing of the
technologies. He also manages business
development and strategy, coordination and
negotiation of strategic alliances, definition
of research activities, and growth of the
business. He has been with the company
since its inception in 1994. He is the holder
of four patents, with others pending. He
received a BS in chemical engineering from
Texas A&M University, and is a registered
Professional Engineer. He is a member of
AIChE, and the American Management Assn.
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This article had been downloaded from www.aiche.org with permission.