Chemical Engineering Science 60 (2005) 7121–7130www.elsevier.com/locate/ces

The influence of distributed reactant injection along the height of afluidized bed reactor

Fahad Al-Sherehy, John R. Grace∗, Alaa-Eldin M. AdrisDepartment of Chemical and Biological Engineering, University of British Columbia, 2216 Main Mall, Vancouver, Canada V6T 1Z4

Received 30 January 2005; received in revised form 29 May 2005; accepted 27 June 2005Available online 15 August 2005

Abstract

A two-phase model is used to simulate spreading the introduction of reactant feed along the height of a fluidized bed reactor foroxidative dehydrogenation of ethane to ethylene. The reactor model is used to predict the reactor performance for different ethane-to-oxygen molar feed ratios, with premixed and non-premixed feed. The proposed model is used to simulate the premixed feed (withoutsecondary injection), and for distributed feed with secondary injection at one, three and five injection levels above the primary distributor.Predictions from the model are shown to compare favourably with experimental data from an industrial pilot reactor of diameter 97mm.A case study is then employed to explore a wider range of conditions than is possible experimentally. Oxidant distribution is shown tobe beneficial in expanding the range of reactant compositions beyond those normally allowed by safety constraints. Distributing the feedover a number of levels improves the reactor performance, especially in reducing the selectivities of undesired by-products. Feeding gasat several levels is generally more promising than introducing feed at a single secondary injection level.� 2005 Elsevier Ltd. All rights reserved.

Keywords:Fluidization; Jets; Hydrodynamics; Multiphase reactors; Dehydrogenation; Reaction engineering

1. Introduction

Many chemical processes involve consecutive reactionswith the intermediate being the desired product. One possi-bility to improve the selectivity is to separate the intermedi-ate product from the reaction mixture. Another is to alter theconcentration profile by distributed addition of one of thereactants. The latter is not always helpful in improving re-actor performance. The main factors justifying reactant dis-tribution depend on the type of reaction (e.g. parallel/series,reversible vs. irreversible, etc.) and the degree of mixingwithin the reactor.Several industrial processes have implemented reac-

tant distribution along the reactor height. For example, tolower NOx emissions, secondary air is usually added in

∗ Corresponding author. Tel.: +1 6048223121; fax: +16048226003.E-mail address:jgrace@chml.ubc.ca(J.R. Grace).

0009-2509/$ - see front matter� 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.ces.2005.06.031

circulating fluidized bed combustors, sometimes also withtertiary air. Staged addition has also been used in bubblingbed combustion (e.g.Bramer, 1995). A similar concept hasbeen implemented in the Sohio process for the produc-tion of acrylonitrile where air enters through the grid anda propylene–ammonia mixture is fed through a sparger lo-cated some distance above the grid (Yates et al., 1987). An-other example is in the partial oxidation of butane to maleicanhydride in a circulating fluidized bed in which catalystis oxidized in one chamber and reacted with butane in an-other to avoid direct contact of the hydrocarbon with oxygen(Contractor and Sleight, 1988).A second important motivation for distributed-addition

of reactant is to maintain the composition of the gaseousmixture outside the explosion limits. The ethane-to-ethylenereaction is typical of this type of reaction. In the oxidativedehydrogenation of ethane, the desired reaction for ethyleneproduction competes with reactions that produce acetic acidand carbon oxides. Stoichiometric relations for the four main

7122 F. Al-Sherehy et al. / Chemical Engineering Science 60 (2005) 7121–7130

reactions are (Thorsteinson et al., 1978)

C2H6 + 0.5O2 → C2H4 + H2O, (1)

C2H4 + O2 → CH3COOH, (2)

C2H4 + 2O2 → 2CO+ 2H2O, (3)

C2H4 + 3O2 → 2CO2 + 2H2O. (4)

While reaction (1) is of potential industrial importance, ithas not yet been commercialized, in large part because it isconstrained by a major safety issue in that the ethane/oxygenreactor feed mixture may well be combustible. An explosionmay occur if the feed composition falls inside the explosionenvelope. To avoid explosions, the feed composition mayneed to be sub-optimal from a reactor yield viewpoint. Theminimum oxygen concentration needed to bring the feedmixture below the lower explosion limit of ethane–oxygenmixture at 265◦C and 202.6 kPa is estimated (Al-Sherehy,1997) based on the correlation proposed byCrowl andLouvar (1990)to be 8.8% by volume. In the present study,as a safety precaution, the oxygen maximum concentrationin the premixed feed introduced through the windbox wasmaintained below 7% by volume.Another factor of importance is that the oxidation of

paraffins is highly exothermic, and the situation can becomehighly hazardous and difficult to control if deep oxidationof the paraffins or intermediate olefins into carbon oxidesshould occur (Cavani and Trifirò, 1995). The fluidized bedis the reactor of choice for highly exothermic gas-phase re-actions, where there is a danger of a temperature runaway orexplosion. Also, because of the thermal inertia and the largeparticle surface area, one can have higher concentrations offeed in fluidized beds, well within the usual flammabilityregion, resulting in significant cost savings, due to higherper-pass conversion and yield (Kunii and Levenspiel, 1991;Leib et al., 1996).In oxidative dehydrogenation reactions, the oxygen-to-

hydrocarbon molar ratio has a strong impact on the reactionperformance and on the likelihood of falling inside the ex-plosion limits. Oxygen-rich feeds result in low product se-lectivities and high hydrocarbon conversions. Oxygen-leanfeeds lead to high product selectivities, but low per passconversion. Distributing the oxygen along the height of thereactor lowers the in situ oxygen partial pressure, thus pro-moting the desired reaction, while at the same time main-taining higher conversion (Tonkovich et al., 1996).Most previous research work on oxidative dehydro-

genation reactors focused on developing and comparingcatalysts. Few investigations have used reactors other thanconventional fixed bed reactors. Among these are fluidizedbed reactors, membrane reactors, and fixed beds with dis-tributed oxygen feed (Choudhary et al., 1989; Santamariaet al., 1992; Schmidt et al., 1994; Tonkovich et al., 1996;Al-Sherehy, 1997, 2002). Several studies have treated de-layed addition of reactants (Aris, 1961; Van de Vusse andVoetter, 1961; Jackson and Senior, 1968; Sheintuch et al.,

1986; El-Halwagi, 1990), focusing on the advantages ofdelayed addition, modeling and optimization for tubularreactors and bubble-column slurry reactors.In the present work a two-phase diffusion model (May,

1959; Van Deemter, 1961) is extended to simulate the effectof secondary gas injection into a bubbling fluidized bed. Theproposed model accounts for changes in the overall gas flowat each injection level, adapted from a model previouslyshown (Al-Sherehy et al., 2004) to give good predictions forgasmixing in a distributed-feed fluidized bed laboratory unit.Model predictions are tested against data from industrialpilot plant oxidative dehydrogenation experiments.

2. Base model: limiting case with primary gas only

The model equations are similar to those successfullyused (Al-Sherehy et al., 2004) to model gas mixing in a flu-idized bed with gas jet injection, except that we now con-sider a steady-state situation, meaning that time-derivativeterms can be dropped, whereas reaction termsmust be added.Model equations for a steady-state reactive system are de-rived by writing mole balances for the bubble and densephases for a slice of the bed of height�z and unit cross-sectional area. A steady-state mole balance on componenti(wherei = 1 for ethane, 2 for oxygen, 3 for ethylene, 4 foracetic acid, 5 for carbon monoxide, 6 for carbon dioxide, 7for water and 8 for nitrogen) in the bubble phase gives

Qb

A

dCbi

dz− �bDab

d2Cbi

dz2+ kbdiab(Cbi − Cdi)

− �P �b�bRbi = 0. (5)

Similarly, a mole balance on componenti in the dense phasegives

Qd

A

dCdi

dz− �dDad

d2Cdi

dz2+ kbdiab(Cdi − Cbi)

− �P �d�dRdi = 0. (6)

Boundary conditions are

@z = 0, Cbi = Dab�bA

Qb

dCbi

dz+ C0i ,

Cdi = Dad(1− �b)A

Qd

dCdi

dz+ C0i , (7)

@z = H,dCbi

dz= 0,

dCdi

dz= 0. (8)

Reactor outlet concentrations are then

CHi = QbCbi + QdCdi

QT

. (9)

Assuming ideal gas behaviour, we can write the concentra-tions of componenti in the bubble and dense phases as

Ci = niP

RgT∑

ni

. (10)

F. Al-Sherehy et al. / Chemical Engineering Science 60 (2005) 7121–7130 7123

Analogous equations for unsteady state, one-dimensionalaxial dispersion without reaction were previously shown(Al-Sherehy et al., 2004) to provide a good basis for mod-elling axial gas mixing in a fluidized bed with and withoutdistributed introduction of gas.To simplify the model, the following additional assump-

tions are adopted:

1. Gas is distributed between the two phases according tothe two-phase model.

2. The catalyst bed is assumed to be isothermal, consistentwith observations (Al-Sherehy, 2002) showing that tem-perature gradients along the bed were insignificant. Heatlosses are also neglected.

3. Changes in the number of moles due to reaction areneglected as the conversion is too small to affect themole balance significantly.

4. The volume fraction,�b, of bed occupied by solids dis-persed in the bubble phase is expected to be in the inter-val 0.001�b < �b <0.01�b (Kunii and Levenspiel, 1991).A mean value (0.0055�b) is assumed for�b.

5. Gas is assumed to be in plug flow in the bubble phase. Avery small value ofDab (1×10−6m2/s) is used to sim-plify solving the bubble phase and dense phase equationssimultaneously using the available Fortran subroutine.

6. Gas is axially dispersed in the dense phase with (Leeand Kim, 1989)

Pea = UT D

Dad

= 0.02566

(UT

Umf

)−0.54(

�p

�g

)0.067

×(

dp

D

)−0.588

. (11)

7. The dense phase bed voidage is taken to be�mf through-out the bed.

8. Since the temperature in the experimental work waslower in the freeboard than in the bed and the gas ve-locities were small enough that entrainment was mod-est, the modeling is carried out only for the dense bed(0�z�H), excluding the freeboard.

Changes in diffusivities of each component are accountedfor as the gas composition varies along the reactor height.The inter-phase mass exchange for componenti, kbdi , iscalculated using the equation ofSit and Grace (1981)

kbdab = 6�bdb

[Umf

3+ 2

√Dmi�mf Ub

�db

], (12)

whereDmi is the effective diffusivity of componenti in thegas mixture, which can be estimated based on relationshipsgiven byWilke and Lee (1955)andReid et al. (1977).The bubble diameter and velocity (db and ub) increase

with height, butdb is constrained not to exceed themaximumstable bubble sizedbmax (Grace, 1982). The mean bubblediameter as a function of height,z, and operating conditions

is estimated by theMori and Wen (1975)semi-empiricalcorrelation, with initial bubble diameter at the distributorplate calculated from theMiwa et al. (1972)correlation.The reaction rate terms,Rbi and Rdi , in Eqs. (5) and

(6) are the rates of reaction of componenti in the bubbleand dense phases, respectively. These terms were obtained(Al-Sherehy, 2002) based on kinetic expressions given orig-inally by Thorsteinson et al. (1978). The rate of ethane con-sumption and the rates of CH3COOH, CO and CO2 produc-tion (see Eqs. (1)–(4)) are given by

RC2H6 = −1.038× 103e−5625/T PC2H6PO2

(1+ 2.286PC2H4 + 14.63PO2)2, (13)

RC2H4O2 = 9.377× 104e−5632/T PC2H4PO2PH2O

(1+ 1.843PC2H4 + 4.215PO2 + 1.465PH2O)3,

(14)

RCO = 1.755× 1010e−15 270/T PC2H4PO2

(1+ 0.3119PC2H6 + 6.83PC2H4)2, (15)

RCO2 = 8.626× 105e−9318/T PC2H4P1/2O2

(1+ 3.787PC2H4)2

. (16)

The rate of ethylene production,RC2H4, can be written

RC2H4 = −RC2H6 − RC2H4O2 − 0.5RCO − 0.5RCO2. (17)

The rate of oxygen consumption,RO2, can be written

RO2 = 0.5RC2H6 − RC2H4O2 − RCO − 1.5RCO2, (18)

whereas the rate of water production,RH2O, is given by

RH2O = −RC2H6 + RCO + RCO2. (19)

Isothermal operation is assumed so that no energy balanceis required.

3. Extended model: model with distributed gas injection

The above assumptions are sufficient for cases where nosecondary gas is injected horizontally into a bubbling bedabove the distributor plate. In the base-model, radial disper-sion is assumed to be rapid so that all radial concentrationprofiles at any height above the distributor are assumed tobe uniform. Experiments reported elsewhere (Al-Sherehy,2002; Al-Sherehy et al., 2004) indicate that uniform radialdistributions were achieved within a short distance (220mm)above each injection level for the column of relatively smalldiameter (152mm) investigated. Therefore, using the sameassumptions to simulate the regions above and below the in-jection level, with the total flow given a step change at theinjection level, should provide a reasonable first approxima-tion for the conditions explored in this work.When there is distributed gas injection, the secondary gas

is assumed to be immediately distributed in a uniform man-ner across the entire injection level, with all of the gas en-tering with the secondary jet added to the bubble phase,

7124 F. Al-Sherehy et al. / Chemical Engineering Science 60 (2005) 7121–7130

Fig. 1. Schematic diagram of phase flows, dispersion and hold-ups formodel with distributed gas injection.

consistent with the usual two-phase approach widely usedfor bubbling fluidized beds. The base-model equations aresolved up to the lowest injection level. At this level, the pa-rameters in Eqs. (5) and (6) are recalculated, after adjustingthe volumetric flow of the bubble phase to include the addi-tional gas from the jets introduced at that level. At the samelevel, the bubble diameter is adjusted using the correlation ofMori and Wen (1975), assuming that the initial bubble sizedb0 equalsdb calculated just below the injection level. Ax-ial dispersion and total exchange rate are also re-evaluatedusing the same relationships as for the base-model.Fig. 1shows a schematic representation of the secondary feed in-jection for the model with distributed gas injection, corre-sponding to Model I in the gas tracer study ofAl-Sherehyet al. (2004).

4. Solution algorithm

When Eqs. (5) and (6) are written for each component,there are 16 second-order ordinary differential equationswith two-boundary values. These equations were solved nu-merically using Visual FORTRAN 5.0 using the BVPFDsubroutine. This subroutine solves a (parameterized) systemof differential equations with boundary conditions at twopoints, using a variable order, variable-step-size finite dif-ference method with deferred corrections. The bed height isdivided into a number of grid points, and the complete set ofsimultaneous ordinary differential equations is integrated inthe forward direction, starting with the initial conditions. Ateach grid point, model parameters are calculated. Gas prop-erties and hydrodynamic parameters are calculated at eachheight.

In the model with distributed gas injection, secondary gasis assumed to be added to the bubble phase and to be uni-formly distributed across the injection level. The equationsare solved by dividing the reactor into(N + 1) sections inseries, whereN is the number of injection levels. For eachsection, the equations were solved by the BVPFD subrou-tine, and the outlet gas from the section was then used as thefeed to the next section. The bubble size calculated at thetop of each section also served as the initial bubble size forthe next section, with the bubble phase volumetric flow rateaugmented by the addition of the secondary injected gas atthe appropriate secondary levels. Note that the model withdistributed gas injection reduces to the base model for thespecial case where all of the gas enters the bed through theprimary distributor. Hence the model with distributed gasinjection is general enough to be used for all cases below,i.e., with and without secondary gas injection.

5. Comparison of model with experimental data

Model predictions were tested against experimental datafrom an industrial pilot scale reactor (Al-Sherehy, 2002)of inside diameter 97mm and height 1800mm operat-ing at 265◦C and 202.6 kPa in an industrial pilot plantof catalyst particles. The primary distributor contained 25holes of diameter 6.4mm on a triangular pitch. The free-board section had an inside diameter of 146mm and was600mm tall. Four gas injection nozzles each at heightsof 50,160,250,500,650 and 750mm above the primarydistributor could be used to inject secondary feed gashorizontally and radially into the reactor. Oxidative dehy-drogenation experiments were carried out: (a) without sec-ondary oxygen/air injection; (b) with secondary oxygen/airinjection; (c) with non-premixed feed (i.e., ethane was theprimary gas, while enriched air was fed as secondary gasabove the main distributor).The catalyst was a proprietary industrial catalyst of mean

particle diameter 97�m and density 2450 kg/m3 containingmixed oxides of molybdenum and vanadium. Since this cat-alyst was broadly similar to that employed byThorsteinsonet al. (1978)and our experiments were conducted in a sim-ilar range of conditions, the kinetics were assumed to be ofthe same form, with the constants adjusted to fit microreac-tor experimental results as explained byAl-Sherehy (2002).The experiments were conducted over a brief enough timeperiod that catalyst deactivation could be neglected. In ad-dition, the particles were small enough that internal masstransfer limitations could be ignored.Fig. 2 shows that the predictions of the base model, es-

pecially those for the ethane and oxygen conversions, arein good agreement with the experimental data for runs inwhich there was no secondary gas injection, i.e., all the gasentered the bed through the primary distributor.Fig. 3 shows predictions of the model with distributed

gas injection plotted against relevant experimental data on a

F. Al-Sherehy et al. / Chemical Engineering Science 60 (2005) 7121–7130 7125

Fig. 2. Model predictions compared with experimental conversionsand selectivities without secondary injection.T =265◦C; P =202.6 kPa;UP = 0.09–0.17m/s; H0 = 350–740mm; ethane-to-oxygen molar feedratio= 9.1; O2 feed concentration=6.5%mol.

Fig. 3. Model predictions compared to experimental conversions andselectivities for pilot plant reactor with secondary addition of feed gas.For experimental details seeAl-Sherehy (2002).

parity plot. The model is seen to have given mostlyfavourable agreement with the experimental data.Fig. 4 shows the predicted and experimental variation of

key conversion and selectivity parameters with the superfi-

Fig. 4. Model predictions compared to experimental conversions andselectivities for secondary gas addition atz = 160mm with dif-ferent secondary gas injection velocities and a constant primarygas superficial velocity ofUP = 0.09m/s. Qj /A = 0.02,0.03 and0.06m/s; T = 265◦C; P = 202.6 kPa; H0 = 740mm.

cial gas velocity increment provided by secondary gas in-jection 10mm above the primary distributor for a static beddepth of 740mm. Except for a few points, the predicted andactual trends and values are in good agreement.Fig. 5 indicates that the trends and values also show good

agreement when conversions and selectivities are plottedagainst the total superficial gas velocity above the jet injec-tion level. InFig. 6, the independent variable on the abscissaaxis is the static bed depth. Except for the CO selectivity,the model is again seen to do an excellent job of predictingthe conversions and selectivities.

6. Case study

Given the success of the distributed flowmodel, the modelis next used to predict the reactor performance for differ-ent ethane-to-oxygen molar feed ratios (2.9–20.3) with pre-mixed and non-premixed feed. The Base Model is used tosimulate the premixed feed (without secondary injection),while the model with distributed gas injection is used tosimulate non-premixed feed (with secondary injection). Thenon-premixed feed cases are simulated for one, three and fiveinjection levels (in addition to the primary gas fed throughthe distributor plate at the bottom). The case study allowsexploration of a wider range of operating conditions thanwas possible experimentally for safety and practical reasons.

7126 F. Al-Sherehy et al. / Chemical Engineering Science 60 (2005) 7121–7130

Fig. 5. Model predictions compared to experimental conversions and se-lectivities for secondary air addition atz = 160mm with different pri-mary gas superficial gas velocities and constant a secondary air injectionvelocity of 1.8m/s(Qj /A = 0.03m/s). Overall oxygen molar feed com-position: 8.6% forUP = 0.09m/s, or 8.2% forUP = 0.14 and 0.17m/s.T = 265◦C; P = 202.6 kPa; H0 = 740mm.

The operating conditions and design values for the casestudy areP =202.6 kPa; T =265◦C; UT =0.14m/s; H0=1000mm; D = 97mm. Ethane is always the primary gas,while air is the oxidant and secondary gas when there is dis-tributed feed. Secondary gas is distributed equally amongall injection levels when there is more than one such level.Secondary gas is injected at:zj = 50mm for single-levelinjection; 50,250,500mm for three injection levels; and50,250,500,650 and 750mm for five injection levels. Forthe premixed feed casesUP = 0.14m/s, while for non-premixed feed,UP = 0.05–0.11m/s.Reactor performance predictions are shown inFigs. 7–10.

Fig. 7c provides different safety zones in operating such areactor system:(1) For premixed feed (solid points) the operation is only

safe when: (a) the ethane-to-oxygen molar feed ratio>9.4;and (b) the exit oxygen concentration<7%mol, i.e., it fallsin the bottom right quadrant ofFig. 7c.(2) Non-premixed feed (open points). In this case the feed

is inherently safe since oxygen and ethane enter separately.Hence the operation meets the safety criterion if the exitoxygen concentration<7%mol, i.e., it corresponds to thelower half ofFig. 7c.

Fig. 6. Model predictions compared to experimental conversionsand selectivities for secondary air addition atz = 160mm, Qj /A =0.03m/s with different static bed heights. Overall oxygen molarfeed composition= 8.6%; ethane-to-oxygen molar feed ratio= 5.8;T = 265◦C; P = 202.6 kPa; UP = 0.09m/s.

Fig. 7 shows the ability of oxidant distribution to expandthe range of reactant compositions beyond those normally al-lowed by the safety constraints with, as above, 7%mol takenas the maximum safe concentration for O2 in a premixedfeed (ethane+ air), beyond which an explosive mixturemight form. This concentration corresponds to 9.4 ethane-to-oxygen molar feed ratio, as represented by the verticallines inFig. 7 when the oxygen is derived from air. To theleft of the vertical lines, operating the reactor with premixedfeed is unsafe, while when gas is distributed over three orfive levels, the oxygen concentration is low enough through-out this region that the reactor itself is safe to operate. Thereactor with distributed oxidant is constrained by the oxygenconcentration at the reactor outlet as shown inFig. 7c. Ap-plying the same safety constraint as for the premixed feed,beyond a molar feed ratio of 4.2, distributed feed is unsafebecause the O2 concentration at the reactor outlet exceeds7%mol (as shown by the horizontal line inFig. 7c).In Fig. 7a, the ethane conversion increases with increasing

ethane-to-oxygen molar feed ratio up to 7.0 (for premixedfeed and non-premixed feed with a single injection level)and 4.2 (for non-premixed feed with three injection levels).This initial increase occurs due to the non-linear kinetics

F. Al-Sherehy et al. / Chemical Engineering Science 60 (2005) 7121–7130 7127

Fig. 7. Predicted conversions and oxygen concentrations at reactor out-let vs. ethane-to-oxygen molar feed ratio.P = 202.6 kPa; T = 265◦C;constantUT = 0.14m/s; H0 = 1000mm; D = 97mm; secondary gasinjected at z = 50mm (single level), at 50,250,500mm (three lev-els) or at 50,250,500,650,750mm (five levels); primary gas is al-ways ethane; oxidant and secondary gas is air, equally distributed amongupper injection levels. For premixed feedUP = UT ; otherwise totalQj /A = 0.03–0.09m/s, UP = 0.05–0.11m/s.

(Eqs. (13)–(16)). Then the ethane conversion decreasessignificantly, while for the five-injection-level case, theconversion break-point is below 2.9 molar feed ratio (notshown). These trends are consistent with other predictions(e.g. Tonkovich et al., 1996; Cavani and Trifirò, 1995;Moghaddam et al., 1994), where the ethane conversion in-creases with increasing ethane-to-oxygen molar feed ratiountil the amount of oxygen becomes insufficient to reactwith the extra ethane. On the other hand, oxygen conversionincreases rapidly with increasing ethane-to-oxygen molarfeed ratio, then almost levels off.

Fig. 8. Predicted selectivities vs. ethane-to-oxygen molar feed ratio.H0 = 1000mm; D = 97mm; T = 265◦C; P = 202.6 kPa; constantUT = 0.14m/s; secondary gas injected at:z = 50mm (single level), at50,250,500mm (three levels) or at 50,250,500,650,750mm (five lev-els); primary gas is always ethane; oxidant and secondary gas and isair, equally distributed among upper injection levels. For premixed feedUP = UT ; otherwiseQj /A = 0.03–0.09m/s, UP = 0.05–0.11m/s.

Ethane conversion for the premixed feed is predicted tobe better than for the non-premixed feed with distributedoxidant in the non-explosive region for premixed feed (tothe right of the vertical line inFig. 7a). However, the oppo-site is observed at low ethane-to-oxygen molar feed ratios(<5.4) in the explosive premixed feed region. The sametrend is applicable to oxygen conversion. These results in-dicate that the fluidized bed hydrodynamics are responsiblefor the predicted lower ethane conversion for oxidant distri-bution cases in the non-explosive premixed feed region. Inparticular, the portion of the incoming gas entering higherin the bed has less opportunity for efficient contact with thecatalyst. Consistent with experimental results (Al-Sherehy,2002), the injection velocity, primary gas superficial veloc-ity and height of secondary injection determine whether ornot distributing the gas is beneficial.Fig. 8shows the selectivities for the target product(C2H4)

and the desirable by-product(CH3COOH) as functionsof the ethane-to-oxygen molar feed ratio. These selectivi-ties provide measures of the relative performance for the

7128 F. Al-Sherehy et al. / Chemical Engineering Science 60 (2005) 7121–7130

Fig. 9. Predicted ethylene and acetic acid yields vs ethane-to-oxygenmolar feed ratio. P = 202.6 kPa; T = 265◦C; constantUT = 0.14m/s; H0 = 1000mm; D = 97mm; secondary gas in-jected at z = 50mm (single level), at 50,250,500mm (three levels)or at 50,250,500,650,750mm (five levels); primary gas is alwaysethane; oxidant and secondary gas is air, equally distributed amongupper injection levels. For premixed feedUP = UT ; otherwise totalQj /A = 0.03–0.09m/s, UP = 0.05–0.11m/s.

different distribution modes. Ethylene selectivity is pre-dicted to increase with increasing ethane-to-oxygen molarfeed ratio due to a decrease in the oxygen feed concentra-tion. A lower oxygen concentration leads to less ethyleneover-oxidation to by-products. Hence, all cases with dis-tributed oxidant give better ethylene selectivity than forpremixed feed. In terms of yield, cases with premixed feedgive higher yields of ethylene and acetic acid for ethane-to-oxygen molar feed ratios>5.4, as shown inFig. 9.

Note that all of the predictions are for cases where thecolumn radius is small enough and the number of secondaryjets large enough that rapid radial mixing can be assumedimmediately above the secondary injection level. For largerreactors or fewer jets, more advanced models which includeradial mixing will be required.With distributed oxidant, the local oxygen concentration

is predicted to be lower. The trend for acetic acid selectivity,as shown inFig. 8b, differs from the trends for the other by-products (CO and CO2) shown inFig. 10. The former nearlyfollows the trend of the ethane conversion, with its selectiv-ity increasing with increasing ethane-to-oxygen molar feedratio, next reaching a maximum corresponding to the maxi-

Fig. 10. Predicted CO and CO2 selectivities vs. ethane-to-oxygenmolar feed ratio. P = 202.6 kPa; T = 265◦C; constantUT = 0.14m/s; H0 = 1000mm; D = 97mm; secondary gas in-jected at z = 50mm (single level), at 50,250,500mm (three levels)or at 50,250,500,650,750mm (five levels); primary gas is alwaysethane; oxidant and secondary gas is air, equally distributed amongupper injection levels. For premixed feedUP = UT ; otherwise totalQj /A = 0.03–0.09m/s, UP = 0.05–0.11m/s.

mum ethane conversion, then dropping significantly, due tolower ethane conversion and lower oxygen concentration.Hence, acetic acid selectivity in the non-explosive premixedfeed region (>9.4 ethane-to-oxygen molar feed ratio) is pre-dicted to be better for premixed feed than for non-premixedfeed with distributed oxidant, whereas the opposite is pre-dicted when the ethane-to-oxygen molar feed ratio<9.4.On the other hand, the selectivities of CO and CO2, two un-desirable products, are predicted to decrease with increas-ing ethane-to-oxygen molar feed ratio due to the decreasingoxygen concentration. Both of the latter two selectivities arealways lower with oxidant distribution than for the premixedfeed.

7. Conclusions

A simple two-phase model is used to predict axial con-centration profiles of reactants and products in a fluidizedbed reactor for the oxidative dehydrogenation of ethane. Themodel predictions are in reasonably good agreement with

F. Al-Sherehy et al. / Chemical Engineering Science 60 (2005) 7121–7130 7129

industrial pilot plant experimental results with and withoutdistributed feed of reactants, as well as being consistent withearlier gas mixing results. The model provides a good ba-sis for more comprehensive models to be developed in thefuture.The model shows that distributing oxidant can expand

the safe range of operation and improve reactor perfor-mance, in particular reducing the selectivities of undesiredby-products. Increasing the number of distribution levels isgenerally helpful. An optimization study is needed to op-timize the performance of this type of reactor over a widerange of parameters (e.g. premixed feed coupled with oxi-dant distribution, number of injection levels, flow distribu-tion, location of secondary injection points, etc.).

Notation

ab specific surface area of gas bubble, m2/m3

A column cross-sectional area, m2

C gas concentration, mol/m3

db bubble diameter, mdbmax maximum stable bubble diameter, mdp mean particle diameter, mD column diameter, mDab axial dispersion coefficient in bubble phase,

m2/sDad axial dispersion coefficient in dense phase,

m2/sDmi molecular diffusivity of componenti in gas

mixture, m2/sH expanded bed height, mH0 static bed height, mkbd interphase mass exchange coefficient be-

tween bubble and dense phases, m s−1

ni number of moles of componenti, dimension-less

N number of injection levels, dimensionlessP pressure, kPaPi partial pressure of componenti, kPaPea Peclet number for axial dispersion in dense

phase defined in Eq. (11), dimensionlessQ volumetric flow rate, m3/sR column radius, mRg gas constant, J/mol KRi rate of production of componenti by reaction

kmol/kg sT temperature,◦CUb bubble velocity, m/sUinj secondary feed injection velocity, m/sUmf superficial gas velocity at minimum fluidiza-

tion, m/sUP primary feed superficial gas velocity, m/sUT total superficial gas velocity, m/sz vertical coordinate measured from top of pri-

mary distributor plate, m

Greek letters

�b,�d fraction of bubble, dense phase volumes oc-cupied by solids, dimensionless

�b volume fraction of bed occupied by bubbles,dimensionless

�d dense phase voidage, dimensionless�mb bed voidage at minimum bubbling, dimen-

sionless�mf bed voidage at minimum fluidization, dimen-

sionless�g gas density, kg/m3

�p particle density, kg/m3

� fraction of bed volume occupied by phase,dimensionless

Subscripts

b bubble phase

d dense phase0 feedH at heightHi componentij jetP primary feedT total

Glossary

Reactor performance measures are defined as follows:Ethane conversion: (moles ethane in− moles ethane out)/moles ethane in

Oxygen conversion: (moles oxygen in− moles oxygenout)/moles oxygen in

Ethylene selectivity: total moles of carbon in ethyleneproduced/total moles of carbon in all products

Acetic acid selectivity: total moles of carbon in acetic acidproduced/total moles of carbon in all products

CO2 selectivity: total moles of carbon in CO2 produced/total moles of carbon in all products

CO selectivity: total moles of carbon in CO produced/total moles of carbon in all products

Ethylene yield: total moles of carbon in ethylene produced/total moles of carbon in ethane fed

Acetic acid yield: total moles of carbon in acetic acidproduced/total moles of carbon in ethane fed

Acknowledgements

The authors are grateful to SABIC Basic Industries Cor-poration and the Natural Sciences and Engineering ResearchCouncil of Canada (NSERC) for their support of the workpresented in this paper.

7130 F. Al-Sherehy et al. / Chemical Engineering Science 60 (2005) 7121–7130

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