Buld Robust Reactor Models

8/3/2019 Buld Robust Reactor Models

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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.

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Photo credit. Applied ReactorTechnologies, Inc.

Copyright 2000

American Institute

of Chemical Engineers.

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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


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

Reactor Modeling


(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


7/16

(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


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

Reactor Modeling



9/16

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.


s Photo credit.Applied Reactor Technologies, Inc.


10/16

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


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.


11/16

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 impact 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-



12/16

Reactor Modeling


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.


13/16

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-



14/16

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,

Reactor Modeling


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).

23. Wen, C. Y., and S. Dutta, Research

Needs for Analysis, Design and Scale-up

of Fluidized Bed Reactors,AIChE

Symp. Ser., 73 (161), pp. 18 (1977).

24. Dutta, S., and R. Gualy, Overhaul

Process Reactors,Hydroc. Proc., 79 (9),

pp. 4350, (Sept 1999).

25. Dutta, S., and R. Gualy, Modernize

Process Reactors,Hydroc. Proc., 79

(11), pp. 91100, Nov (1999).

26. Dutta, S., and R. Gualy, Supermodel-

ing Reactors for Profitability,Chem.

Eng., 107 (6), pp. 7279 (June 2000).

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


15/16

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


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.


16/16

This article had been downloaded from www.aiche.org with permission.

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