Regeneration of Coked Catalysts Modelling and Verification of Coke Burn Off in Single Particles and Fixed Bed Reactors

Chemical Engineering Science 60 (2005) 4249–4264

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Regeneration of coked catalysts—modelling and verification of cokeburn-off in single particles and fixed bed reactors

Christoph Kern, Andreas Jess∗

Department of Chemical Engineering, University Bayreuth, Universitätsstr. 30, 95447 Bayreuth, Germany

Received 14 July 2004; received in revised form 20 December 2004; accepted 27 January 2005Available online 18 April 2005

Abstract

The regeneration of a coked naphtha reforming catalyst (Pt/Re–Al2O3) was studied by kinetic investigations on the effective rate ofcoke burn-off. For temperatures of industrial relevance for the catalyst, i.e., below 550◦C (deactivation), the coke burn-off within thecylindrical particles(dP ≈ 2 mm) is determined by the interplay of chemical reaction and pore diffusion; limitation by external masstransfer can be excluded forT <750◦C. Based on the parameters of the intrinsic kinetics and of the structure of the catalyst (porosity,tortuosity), the regeneration process is modelled and discussed both on the level of a single particle and in a technical fixed bed reactor.The results of modelling are compared with data from lab-scale investigations (coke profiles within the particles) and the performancedata of the regeneration in an industrial fixed bed reactor (moving reaction zone); the agreement of calculation and measurement is inboth cases complete.� 2005 Elsevier Ltd. All rights reserved.

Keywords:Regeneration; Coke burn-off; Moving reaction zone; Single particle; Fixed bed reactor

1. Introduction

In several refinery and petrochemical processes the cat-alyst deactivates by coke formation, e.g. during crackingof heavy oil, hydrodesulphurization and reforming of naph-tha into high octane gasoline. The catalyst must be regen-erated by continuous or periodic coke combustion. In caseof a fixed bed reactor, the regeneration procedure is con-ducted periodically after a certain time of operation, i.e., thereactor is shut down for burn-off. During this non-steady-state, process precautions have to be taken to avoid exces-sive high temperatures, e.g. in case of naphtha reforming thePt–Al2O3-catalyst, the latter loses surface and mechanicalresistance beyond temperatures of 550◦C (LePage, 1978).So the air is strongly diluted with nitrogen to avoid damageto the catalyst.

A mathematical model of the decoking process would bea helpful tool both with respect to a better understanding of

∗ Corresponding author. Tel.: +49 921 55 7431; fax: +49 921 55 7435.E-mail address:[email protected](A. Jess).

0009-2509/$ - see front matter� 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.ces.2005.01.024

the processes of coke burn-off and to determine how toperform the process both rapidly and safely. Such a modelshould be based on experimental data of the intrinsic kinet-ics. In addition, mass and heat transfer have to be consid-ered both on the level of a particle as well as of a fixed bedreactor.

Regeneration and deactivation were already extensivelystudied with respect to the nature of coke deposits, e.g. cokeformation and decoking on different catalytic sites (metallicor acidic) by means of temperature programmed oxidation orsimilar techniques (e.g.Beltramini et al., 1991; Parera, 1991;Zhang et al., 1991; Fung et al., 1991). Although these studiescontribute to a better understanding of the basic principlesof decoking, they are not adequate to describe the actualprocesses within a particle or a fixed bed.

Regeneration of a coked particle involves both chem-ical reaction and transport processes, since oxygen mustbe transported by external mass transfer and pore diffu-sion to the internal coked surface. As already outlined byWeisz (Weisz and Goodwin, 1963, 1966), pore diffusionstrongly influences the effective rate of burn-off, at least for

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4250 C. Kern, A. Jess / Chemical Engineering Science 60 (2005) 4249–4264

particle diameters and temperatures relevant for industrial(fixed bed) processes (>1 mm, >400◦C). So during theunsteady process, radial gradients of the O2-concentrationand with proceeding burn-off also of the carbon content in aparticle are established (Ishida and Wen, 1968; Wen, 1968;Froment and Bischoff, 1990).

Model calculations of decoking in a fixed bed (Westerterpet al., 1988) show that a moving reaction zone migratesthrough the reactor, which leads to an overheating of thecatalyst, if the velocity of the zone is too fast. In practice, theprocess is therefore often conducted too slowly, for fear ofdamage to the expensive catalyst. Up to now, models of cokeburn-off in a fixed bed reactor are often based on severalsimplifications, e.g. on the assumption that external masstransfer completely controls the burn-off rate (Westerterpet al., 1988).

In the present work, the regeneration of a commercialnaphtha reforming catalyst was taken as a representativemodel system and was studied by systematic experimentalas well as by theoretical investigations both on the scale ofa single particle and of a technical reactor (details inKern,2003; Tang et al., 2004; Tang, 2004). This approach has (tothe our best knowledge) not been taken before in such anintegrated form: (1) The intrinsic kinetics of coke burn-offas well as the role of external and internal mass transferwere studied by lab-scale experiments. (2) The coke burn-off within a single particle was modelled and compared withradial coke profiles measured after a certain stage of burn-off. (3) Thereafter, the regeneration process within a techni-cal reactor was modelled and studied for different boundaryconditions. (4) Finally, the results of reactor modelling werecompared with the performance data of a real technical re-forming fixed bed reactor, which were kindly provided bythe MIRO refinery (Karlsruhe, Germany).

Some experimental and theoretical results with respect tothe influence of chemical reaction rate, diffusion and porestructure on regeneration within single particles were alreadypresented in detail elsewhere, thereby taking mainly pureAl2O3 as a model catalyst (Tang et al., 2004; Tang, 2004).So the focus of this paper is the coke burn-off within afixed bed.

2. Experimental methods

Before coke burn-off, the catalyst was deactivated up to acoke content of 20 wt% by passing toluene orn-heptane (asmodel hydrocarbons for naphtha) in N2/H2 over the catalyst.

To determine the kinetic parameters of coke burn-off (re-action order of oxygen,EA, km,0; list of symbols and ab-breviations at the end of this paper) isothermal experimentswere performed in two lab-scale reactors, thereby varyingthe initial carbon load, temperature, and O2 content (detailsin Kern, 2003). A tubular reactor was used for an O2 con-tent of less than 2 vol% (2 bar, 350–550◦C, modified res-

idence time� with respect to the mass of fresh catalyst:0.02 kg h/m3). For higher concentrations (2–10 vol%), aBerty-type reactor (2 bar, 350–500◦C, � (related to feed):0.2 kg h/m3) with an internal recycle ratio of about 20 wasused to avoid a temperature runaway, i.e., to ensure isother-mal conditions.

Supplementary to the isothermal experiments, the kineticparameters were also determined from the ignition temper-atures at O2 contents up to 100 vol% (see Section 3.1).

In addition to these kinetic investigations the coked anddecoked catalyst was characterized with respect to structuralparameters, which are essential to evaluate the role of inter-nal mass transfer in the effective burn-off rate:

• The specific internal surface area, the porosity, and thepore diameter of the coked catalyst were measured by N2-adsorption (BET-method, Micromeritics Gemini 539),

• The tortuosity�P includes a variety of aspects such asaltered diffusion path length, variations in pore diameter,interconnecting pores, changing cross-sectional areas inconstrictions, and dead end pores. In this work the tor-tuosity was determined by the pulse field gradient (PFG)NMR technique withn-heptane as probe molecule (Kern,2003; Tang et al., 2004; Tang, 2004; Ren, 2003; Ren etal., 2000). Thereby also the change of the tortuosity dur-ing regeneration was determined.

• The radial carbon distribution within single (coked andpartly regenerated) particles was measured by SEM/EDX(JSM840A, Jeol/INCA, Oxford) at theDepartment ofMaterials Processing(University Bayreuth). Therefore, itmust be noted, that the initial radial carbon distributionwas proven to be always homogeneous, which is the re-sult of the very low reaction rate of deactivation by cok-ing (for details seeKern, 2003; Tang et al., 2004; Tang,2004).

Characteristic data of the reforming catalyst used for theexperiments are listed inTable 1.

3. Data evaluation

3.1. Intrinsic kinetics of coke burn-off

In this work, the coke was regarded as pure carbon, so thesmall hydrogen content of the coke (4.5 wt%; molar C/H-ratio of about 1.75, as determined by elementary analysis(EA 3000, HEKAtech)) was not considered in the data eval-uation, i.e., the kinetic data given in this paper are all re-lated to the carbon of the carbonaceous deposits. During theisothermal measurements, the initial and the actual amountof carbon was calculated by planimetry from the gas analysis(CO2, 0–5000 ppm) and the volume rate of the off-gas. (Re-mark: CO was not formed during coke burn-off(<5 ppm),which reflects the activity of Pt for oxidation of CO.) Thecarbon concentration within the catalyst is given here as the

C. Kern, A. Jess / Chemical Engineering Science 60 (2005) 4249–4264 4251

Table 1Characteristic data of the reforming catalyst

Designation (company) E-802 (Engelhard, USA)Composition in wt%: Pt/Re/Cl (rest Al2O3) 0.26/0.50/1Catalyst density,�cat (fresh catalyst) 1400 kg/m3

Catalyst bulk density,�B 770 kg/m3

Geometry: length/diameter of extrudates 2–8 mm/1.6 mmSpecific internal BET-surface areaABET (fresh catalyst) 200 m2/g

carbon loadLC , i.e., as the mass of carbon per mass of freshcatalyst.

The intrinsic rate of regeneration is given by

rm = km,CLCcqO2(1)

with

km,C = km,C,0 e−EA/RT . (2)

The experiments with varied oxygen content show, that thereaction order with respect to the oxygen concentration isabout one (Kern, 2003). For the tubular reactor used here, therate constant (assuming plug flow) can then be calculated by

km,C = − ln(1 −XO2)

�LC. (3)

The Berty-type reactor with a relative high internal recycleratio of about 20 can be regarded as an ideal stirred tankreactor, andkm,C is then given by

km,C = 1

LC

XO2

�(1 −XO2). (4)

For an oxygen content higher than 10 vol%, the isother-mal operation was hard to realize, and the reactivity of thecoke was determined by using the following non-isothermalmethod: The feed gas (N2/O2-mixture) is passed throughan electrically heated quartz reactor with a fixed bed of thecoked catalyst. Starting from room temperature, the sampleis heated with a rate of 10 K/min. At first, the temperaturein the bed rises according to the heating rate of the ovenuntil a sudden and pronounced increase in temperature oc-curs. This break in the temperature curve is considered to bethe ignition temperature. The rate constant is then deducedfrom the ignition temperatures at different O2-contents (here10–100 vol%) according to the theory of thermal explosion(heat generation equals dissipation). The underlying theoryand details of this so-called ignition point method are de-scribed elsewhere (Kern, 2003; Herbig and Jess, 2002; Heinand Jess, 2000; Herbig, 2002).

3.2. Determination of diffusional parameters

The influence of pore diffusion is considered by the effec-tiveness factor�pore, i.e., (in case of no influence of external

diffusion) by the ratio of the effective (measured) rate con-stant to the (maximum) intrinsic rate constant(dP → 0),and is given for a first-order reaction by (see e.g.Baernset al., 1987):

�pore= km,C,eff

km,C= tanh�

�≈ 1

�for ��2. (5)

The so-called Thiele modulus (for a coked particle with auniform carbon load) is given by

� = Vm/Am√km,CLC�P /DO2,eff , (6)

wherebyVm/Am is the ratio of the particle volume to theexternal particle surface area.

It should be noted that� depends on the carbon loadLC ,which changes during burn-off with time and in case of aresistance of pore diffusion also with the radial position inthe particle. The Thiele-approach as given by Eqs. (5) and(6) can then not be applied anymore, and numerical sim-ulations are needed. Nevertheless, the initial effectivenessfactor �pore,0 is used here (in addition to the results of nu-merical simulations, where�pore and� are not needed) asa descriptive measure for the pore diffusion resistance, sim-ply defined by Eqs. (5) and (6) forLC = LC,0. So strictlyspeaking,�0 and �pore,0 are only valid at the start of theregeneration.

To describe the effective oxygen diffusion within theporous catalyst—expressed by an effective diffusion coef-ficientDO2,eff—it has to be considered that only a portionof the particle is permeable, and that the path through theparticle is random and tortuous. Both aspects are taken intoaccount by the porosity�P and the tortuosity�P (Eq. (7)),whereby both factors change with the coke content duringregeneration:

DO2,eff = �P�PDO2,pore= �P /�P(

1DO2,mol

+ 1DO2,Knu

) . (7)

Depending on the pore diameter, the diffusivity in a poreis the combined diffusivity of the molecular and Knudsendiffusivity, the latter calculated by

DO2,Knu = dpore

3

√8RT

�MO2

. (8)

If also external diffusion has to be considered, Eq. (5) has tobe extended. The overall effectiveness factor�overall is then


given by

�overall =(km,CLC

�Am+ 1

�pore

)−1

. (9)

The external mass transfer coefficient� was calculated basedon the Sherwood-number(Sh= �dP /DO2,mol) as given bySchlünder (1986).

4. Modelling methodology

4.1. Coke burn-off within a single particle

The radial profiles of the oxygen and carbon load within asingle catalyst particle and the time needed to reach a certaindegree of coke burn-off were simulated by the commercialcomputer programPresto(solver for differential equations,CiT GmbH, Rastede, Germany, details inWulkow et al.,2001).

Because of the relative high thermal conductivity of thesolid phase, the simulation of decoking in a particle is onlybased on the mass balances of O2 and carbon. Assumingthat axial gradients of the O2-content and carbon load canbe neglected in the cylindrical particles(Lp/dP ≈ 4), thefollowing mass balances for the gas and solid phase arise:

�P�cO2

�t= d

r dr

(DO2,eff r

�cO2

�r

)− rm�P , (10)

�LC�t

= −MC rm. (11)

The intrinsic rate of O2-conversion is

rm = �nO2

�mcat= km(T )LCcO2. (12)

These differential equations are solved numerically for theboundary conditions:

�cO2/�r = 0 for r = 0 (particle center) (13)

cO2 = cO2,G, for r = rp (particle surface) (14)

4.2. Modelling of regeneration in a fixed bed reactor

For the modelling of the coke burn-off in an adiabatictechnical fixed bed reactor a so-calledone-dimensional pseu-dohomogeneous reactor model with axial mixingwas used,which can be characterized as follows:

• Due to the high ratio of the reactor to particle diameterin case of a technical fixed bed( 100), radial gradientsof the O2-content and temperature are neglected.

• Axial dispersion of heat and mass transfer is taken intoaccount by the use of an effective dispersion and heatconduction coefficientDax,eff andax,eff (see Section 5.5).

• The temperature difference between the solid and gasphase can be estimated by

(TG − TS)= −RH�P rm,eff/�AV . (15)

The temperature difference calculated by Eq. (15) forthe maximum temperature technically relevant for reform-ing (550◦C), a high carbon load(10 gC/gcat and a superfi-cial velocity of 0.5 m/s (�=140 W/(m2 K); from Schlünder,1986) is then 10 K. So�T was neglected, i.e., no thermaldistinction was made between the gas and solid phase.

Based on the aforementioned assumptions the differentialequations for the mass and heat balance of the solid and thegas phase are

�BMC

�LC�t

= −�B rm,eff , (16)

�dcO2

dt= − uG�

dcO2

dz+Dax,eff

d2cO2

dz2− �Brm,eff , (17)

(�BcS + � �G cp,G)�T�t

= − uG��Gcp,G�TG�z

+ ax,eff�2TG

�z2+ RH �Brm,eff . (18)

The effective dispersion coefficients of heat and mass(ax,eff , Dax,eff ) in the fixed bed were calculated based onliterature correlations (Verein Deutscher Ingenieure, 2002):

Dax,eff =Dfb + ue dP

2, (19)

ax,eff = f b + ue �G cp,G dP2

. (20)

f b andDfb represent the minimal values ofax,eff andDax,eff without gas flow:

Dfb =DO2,mol(1 − √1 − �), (21)

f b = GK. (22)

Based on literature correlations (Verein DeutscherIngenieure, 2002), the factorK is given here for a voidageof the fixed bed of 0.4 by

K = 11kP + 4

2kP + 13. (23)

(Remark: Eq. (23) is only valid forK <20.)ThereforekP is the ratio of the thermal conductivity of

gas and solid phase. For a typical value of the thermal con-ductivity S of porous Pt/Al2O3 particles of 0.2W/(mK)(Baerns et al., 1987), kP can be estimated here by

kP = SG(500◦C)

= 0.2(W/mK)

0.05(W/mK)= 4. (24)

So for the given catalyst and reaction conditions, the valueof K (Eq. (23)) is here about 2.3.


The boundary conditions for the solution of differentialequations (16)–(18) by the above-mentioned computer pro-gramPrestoare:

For z= 0 (reactor inlet):

uG�(cO2,0 − cO2)= −�Dax,eff�cO2

�z, (25)

uG� �G cp,G(T0 − T )= −ax,eff�T�z

(26)

and forz= L (reactor outlet):

�cO2/�z= 0, (27)

�T/�z= 0. (28)

5. Results and discussion

5.1. Structural parameters of catalyst

As shown byKern (2003), the influence of the carbon loadon the porosity�P and tortuosity�P of the catalyst particleis approximately given by the following linear relationships:

�P = 0.65− 1.3LC , (29)

�P = 2.59− 5.4LC . (30)

So for a typical initial loadLC of 0.15 gC/gcat, the �P de-creases and�P increases by 30% compared to the fresh cat-alyst. (More details inKern, 2003; Tang, 2004; Tang et al.,2004.)

5.2. Intrinsic coke reactivity

Results on the intrinsic kinetics of deactivation and re-generation of the catalyst were already presented elsewhere(Kern, 2003; Jess and Kern, 2001; Jess et al., 1999; Ren etal., 2002). The main results are:

• Hydrogen strongly inhibits the rate of coke formation,but has no influence on the reactivity of the carbonaceousdeposits.

• Compared to toluene, the coke formation rate is muchlower in case of heptane.

• The reactivity of the coke does not depend on the condi-tions of coke formation (H2-pressure, feedstock for cokeformation), although the time needed to reach a certaincarbon load is quite different.

• Two sorts of coke are formed on the metal (Pt/Re) andthe acidic sites(Al2O3), respectively, whereby the latteris much less reactive. In the beginning of decoking, thesmall amount of metal coke (e.g. 2% of the total carbonfor LC,0 = 0.15 gC/gcat) is rapidly burned off; for themodelling of the decoking process, only the second dom-inating (with respect to the amount) and less reactive typeof coke on alumina was considered.

0.0011 0.0012 0.0013 0.0014 0.0015 0.0016 0.0017

1/T in 1/K

k m,C

in m

3/(

kg. s) Ignition point method

Tubular reactor

Berty type reactor

101

100

10-1

10-2

10-3

10-4

10-5

400 500 °C

Fig. 1. Intrinsic kinetics of coke-burn-off.

0.01

0.10

1.00

0.0006 0.0012 0.0018Reciprocal temperature in 1/K

Effe

ctiv

enes

s fa

ctor

LC,0 = 14.5 gC /100 gKat

Technically relevant temperature range

ηpore,0

ηoverall

°C550 750 300 1000

Fig. 2. Influence of temperature on the pore and overall effectivenessfactor: comparison of measurement and calculation (ue = 0.2 m/s (at500◦C), p= 1 bar,yO2 = 0.5 vol%, �P = 0.46, �P = 1.7, dpore= 10 nm,� = 5 (kg s)/m; line: calculation).

• The intrinsic rate of O2-conversion (of the less reactivecoke) is given in the whole range from 1% to 100% oxy-gen by (Fig. 1):

rm = − �nO2

�mcat= km,C(T )LCcO2 (31)

with

km,C(T )= 1.6 × 106 (m3/kg s)e−107,000/RT .

• The reactivity of the coke is practically independent ofthe carbon load (if the small amount on the metal sites isneglected).

5.3. Influence of internal mass transfer

Fig. 2shows the result of an experiment with an initial car-bon load of 0.145 gC/gcat. The bed was heated from 300◦Cup to 600◦C with a small rate (0.5–1◦C/min), so stationaryconditions can be assumed. Because of the small O2-content


Table 2Parameters for the modelling of coke burn-off within a single catalystparticle

Frequency factor,km,C,0 1.6 × 106 m3/(s kg)Activation energy,EA 107,000 J/molDensity of the catalyst,�cat 1400 kg/m3

Porosity,�∗P

0.53Tortuosity,�∗

P3.10

Average pore diameter,dpore 10 nmEffective diffusion coefficient,DO2,eff

a 4 × 10−7 m2/s

aTypical values for a coke load of 10 gC/100 gcat and in case ofDO2,eff —for a temperature of 500◦C and 1 bar.

(0.5 vol%) the carbon load of the catalyst during the exper-iment was considered to be constant and equivalent to theinitial value.Fig. 2 indicates that the (overall) effectivenessfactor calculated by Eq. (9) (based on the Thiele modulus�0 for LC = LC,0) and the measured data are consistent. Itshould be noted here, that the pore diameter was used as the“fitting parameter” in the calculation. If the pore diameter isset to 10 nm, a good agreement with the experimental datais obtained (seeFig. 2), which is well in the pore diameterdistribution (2–25 nm; seeKern, 2003).

For temperatures below 750◦C, the overall effectivenessfactor almost equals the one with respect to pore diffusion,i.e.,�overall�0.9�pore, which clearly indicates that the influ-ence of external mass transport can be neglected, at least forthe particles used here and technically relevant temperatures(<550◦C with respect to deactivation).

5.4. Regeneration of a single coked particles

5.4.1. Numerical solutionsBased on Eqs. (10)–(14), the decoking process within

a single particle was numerically simulated. The essentialparameters of the modelling are given inTable 2.

The calculated profiles of the oxygen concentration andthe carbon load within a single particle during the regener-ation process are shown inFig. 3 for two typical burn-offtemperatures (450 and 550◦C). In addition, the initial effec-tiveness factor�0 (calculated with the initial Thiele modulus�0 for LC = LC,0) as a measure for the magnitude of thepore diffusion resistance is given.

As expected, the influence of pore diffusion on the rate ofcoke combustion increases with temperature, and gradientsof the oxygen concentration and the carbon load occur. Thiseffect is even more pronounced in case of a very high tem-perature of 650◦C (right side ofFig. 4). Therefore it mustbe noted that 650◦C is unrealistic for a technical regenera-tion (Tmax of reformer catalyst is about 550◦C), but is alsoshown here as an instructive comparison. A relative sharpreaction front within the particle is then formed, which mi-grates from the outer surface to the centre of the particle.In case of a very low temperature of 350◦C (Fig. 4, left),diffusion limitations disappear, but the regeneration time is

then very long (>4 days) compared to about 8 h in case ofa technically realistic temperature of 450◦C.

The strong influence of pore diffusion with increasingtemperature is also reflected by the (initial) effectivenessfactor �0: At 350◦C, �0 is 98%, whereas for 450, 550 and650◦C values of 79%, 39%, and 17% are reached.

Finally, the coked catalyst was regenerated at differenttemperatures up to a burn-off degree of about 50%. Theradial carbon profiles in the decoked particles were measuredby SEM/EDX. InFig. 5, two selected profiles and also theexperimental times to reach 50% burn-off are compared withthe numerically calculated data. For the simulation (550 and700◦C), the values of�P and �P of the entirely decokedcatalyst were used, as a pronounced practically carbon-freeshell was formed, which dominates the diffusion resistance.The calculated and measured values both of the C-profilesand the time needed for regeneration are in good agreement.The scattering of the experimental data is evoked from thefact that three C-profiles were measured for each sample.The pronounced development of a C-free outer shell for atemperature of 700◦C is also reflected by the photograph ofthe cross section of the particles. The “white” shell obviouslyindicates the outer C-free zone.

The thickness of the C-free zone (as determined bythe photographs) is about 0.15 mm (700◦C) and less than0.1 mm (550◦C, not shown, seeTang, 2004), which is alsoin good agreement with the modelled values of 0.15 mm(r/r0 =0.81 for 700◦C) and about zero for 550◦C ( Fig. 5).

Fig. 6 depicts that the burn-off time, defined here as thetime to reach 90% coke burn off, is constant up to a certaininitial carbon load (1 g per 100 g of (fresh) catalyst for thegiven example of a temperature of 450◦C), and then stronglyincreases, which reflects the increasing influence of porediffusion with increasing carbon load.

5.4.2. Analytical (closed) solutionA description of the coke burn-off process within a single

particle by well-known closed solutions like thehomoge-neous modelor theshrinking core modelis only reasonablefor the border cases of complete control by chemical reac-tion or by pore diffusion, respectively.

In order to describe quantitatively the burn-off processwithout the need of an elaborated numerical solution (seeSection 5.4.1), an advanced closed solution was developed.This model is slightly more complicated than the two afore-said border cases, and includes the influence of the porediffusion as well as the influence of the intrinsic kineticson the effective rate of coke burn-off. The objectives to de-rive such a closed solution in addition to the results of thenumerical calculations were as follows: (1) The numericalsolutions can be proved and verified, at least for selectedborder cases. (2) If the closed solution fits quite well thenumerical “correct” solution, the former can be taken as thebasis and input for the modelling of the regeneration of awhole fixed bed reactor. By this means, the closed solution


0

20

40

60

80

100

L C /

L C,0

in %

CO

2 / C

O2,

0 in %

relative particle radius r/r0

0

20

40

60

80

100

0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1


55 min

115min

200 min

325 min

440 min

55 min

115 min

200 min

325 min440 min

20 min

40 min

135 min

210 min

20 min

40 min

75 min 135 min

210 min

T = 550 °C; ηpore,0 = 39 %T = 450 °C; ηpore,0 = 79 %

75 min

Fig. 3. Radial profiles of O2-content (relative to the gas phase) and carbon content (relative to the initial value) in a single cylindrical particle at differenttimes (modelled results forLC,0 = 10 wt%, yO2 = 2 vol%, dP = 1.6 mm,p = 1 bar,dpore= 10 nm, �P and �P are calculated by Eqs. (29) and (30)).

0 0.2 0.4 0.6 0.8 1

10 min

30 min

65 min 125 min

200 min

125 min

200 min


0 0.2 0.4 0.6 0.8 1relative particle radius r/r0

T = 650 °C; ηpore,0= 17 %

0

20

40

60

80

100

,

0

20

40

60

80

100

500 min1100 min

2000 min6300 min 3400 min

500 min

1100 min

2000 min

3400 min

6300 min

T = 350 °C; ηpore,0 = 98 %

65 min 30 min

10 min

L C /

L C,0

in %

CO

2 / C

O2,

0 in %

Fig. 4. Radial profiles of O2-content (relative to the gas phase) and carbon content (relative to the initial value) in a single cylindrical particle at differenttimes (modelled results forLC,0 = 10 wt%, yO2 = 2 vol%, dP = 1.6 mm,p = 1 bar,dpore= 10 nm, �P and �P calculated by Eqs. (29) and (30)).


0.0 0.2 0.4 0.6 0.8 1.00

20

40

60

80

100

Relative particle radius r /ri 0

T = 550 °CB

C,0 = 0.21 g

C/g

cat

yO2

= 1 vol.-%P = 1.1 barBurn-off degree: 50 %tExp

= 2.2 hr

Model (dpore

= 20 nm, tmodel

= 2.2 h)

0

20

40

60

80

100

0.15 mm

T = 700 °CB

0 = 0.21 g

C/g

cat

yO2

= 1 vol.-%P = 1.2 barBurn-off degree: 50 %tExp

= 1.7 h

Model (dpore = 20 nm, tmodel = 1.6 h)

10 32 54 76 8

mm

The thickness of the carbon -free outershell is about 0.15 mm

T = 700 °C

LC,0

Rel

ativ

e co

nten

t of c

oke

L C /

L C,0

[%]

LC,0

Fig. 5. Comparison of measured and calculated radial coke profiles in a partly regenerated Pt–Al2O3 particle (regeneration conditions: fixed bed,yO2 = 1 vol%, p = 1–1.2 bar, Pt–Al2O3-cylinders:dP = 1.6 mm,Lp = 2–8 mm;�P = 0.5, �P = 3.5).

0

200

400

600

800

1000

0.1 1 10 100

Initial carbon load LC,0 in gC /100gKat

Bur

n-of

f tim

e in

min

(X

C =

90

%)

T = 450 °C

no influence of pore diffusion

Fig. 6. Influence of initial carbon load on the regeneration time (upto a burn-off degree of 90%) for a temperature of 450◦C (conditions:yO2 = 2 vol%, dP = 1.6 mm, p = 1 bar, dpore= 10 nm, �P and �P arecalculated by Eqs. (29) and (30)).

for the level of a particle simplifies the numerical solutionof the coke burn-off in a technical fixed bed reactor (see be-low Section 5.5), and thus bridges the coke burn-off withina particle and the regeneration on the macroscopic scale ofa technical reactor.

The closed solution, which was finally selected (for detailsseeKern, 2003) is the so-called “shrinking core model withinfluence of the chemical reaction” (subsequently denotedas the “combined model”) and is based on the assumptionof two consecutive steps (Fig. 7):

1. O2-diffusion through an entirely regenerated shell of theparticle ranging from the outer surface up to a definedreaction front atr = rRF :

−nO2 = 2�rRFLpDO2,eff

(�cO2

�r

)r=rRF

. (32)


r

rRF

P

LC = LC,0LC = 0 Reaction-

front (RF)

cO2,G cO2

cO2, RF

r

L

Fig. 7. Combined model (shrinking core with influence of chemicalreaction).

2. Chemical reaction without pore diffusion resistance inthe remaining core(0<r < rRF ) with a constant carbonload ofLC,0:

nO2 = �r2RFLpkm,CLC,0cO2,RF�cat. (33)

So according to this model, the influence of pore diffusionis restricted to a carbon-free shell (Eq. (32)), whereas inreality (at least for medium temperatures and not too lowdegrees of burn-off) carbon is present in this outer zone. Thisleads to an underestimation of the carbon conversion by themodel. To the contrary, the assumption thatLC in the core(Eq. (33)) is still equivalent to the initial value overestimatesthe burn-off rate compared to reality, where bothLC andcO2 decrease in the core of the particle. As shown below,these two effects compensate each other quite well.

The concentration gradient atr = rRF can be calculatedbased on the stationary mass balance for the carbon freeshell:

0 = �2cO2

�r+ 1

r

�cO2

dr. (34)

The boundary conditions are

cO2 = cO2,RF for 0<r�rRF , (35)

cO2 = cO2,G for r = rp. (36)

(The latter condition implies that the external mass transferresistance can be neglected.)

Eq. (34) then yields:(�cO2

�r

)r=rRF

= − (cO2,G − cO2,RF )

ln(rRF )− ln(rp)

1

rRF. (37)

Based on Eqs. (35), (32) and (33), the oxygen concentrationat r = rRF (relative to the one in the gas phase) is given by

cO2,RF

cO2,G

={

1 − r2RF km,CLC,0�cat

2DO2,effln

(rRF

rp

)}−1

. (38)

The correlation between the amount of coke converted perunit time and the position of the reaction frontrRF can be de-duced from the following considerations: (1) The convertedamount of coke corresponds to the oxygen diffusing into theparticle. (2)VC represents the volume of the core, wherecoke is still present at the initial levelLC,0. This leads to

�nC

�t= − nO2 = �catLC,0

MC

�VC�t

= 2�rRF Lp�catLC,0

MC

�rRF�t

. (39)

Based on Eqs. (38) and (39), the velocity of the reactionfront and the change of the average coke load are then givenby

�rRF�t

= −0.5MCcO2,G

1km,CrRF

− rRFLC,0�catDO2,eff

ln(rRFrp

) , (40)

�LC�t

= 2LC,0rZG

r2p

�rZG�t

. (41)

Integration of Eq. (41) leads to:

LC = LC,0r2RF /r

2p, (42)

rRF = r2p

√LC/LC,0. (43)

Finally, Eqs. (42), (43), and (40) lead to the rate of changeof the average carbon load:

�LC�t

= − MCcO2,G

1km,CLC

− r2p�cat4DO2,eff

ln(LCLC,0

) . (44)

Integration of Eq. (44) leads to

t = 1

C1(−C2LC ln(LC/LC,0)

+ ln(LC/LC,0)+ C2 ln(LC/LC,0)) (45)

with

C1 = −MCkm,CcO2,G, (46)

C2 = r2pkm,C�P4DO2,eff

. (47)

So Eq. (45) can be used to calculate the burn-off degreeXC(=1 − LC/LC,0).

It should be mentioned that two classical border cases canbe derived from Eq. (44):


0

20

40

60

80

100

0 200 400 600 800

Regeneration time in min

Bur

n-of

f deg

ree

XC

in %

numerical solutioncombined model

650 °C

450 °C

400 °C

350 °C

500 °C

Fig. 8. Comparison of the numerical solution and the closed solution(combined model) (conditions:LC,0 = 10 gC/100 gcat; �P /�P = 0,17;p = 1 bar; yO2 = 2 vol%).

1. At low temperatures(r2pkm,C�P /DO2,eff � 1), Eq. (44)

reduces to thehomogeneous model:

�LC�t

= −MCkm,CcO2,GLC . (48)

In this case, the effective reaction rate of the coke combus-tion is only determined by the chemical reaction without anyinfluence of pore diffusion.2. At high temperatures(r2

pkm,C�cat/DO2,eff 1), Eq. (44)is reduced to

�LC�t

= 4DO2,effMCcO2,G

r2p�cat ln(LC/LC,0)

. (49)

In this case, the effective reaction rate is entirely controlledby the O2-diffusion through the carbon-free shell of the par-ticle. This classical so-calledshrinking core model(withoutinfluence of chemical reaction) represents the case that thereaction is confined to a front. In contrast to theshrinkingcore model with influence of chemical reaction(combinedmodel) used here, the O2-content gets zero on that front, sothat no reaction occurs within the coked core of the particle.

Fig. 8shows the influence of the time on the burn-off de-gree at different temperatures. The agreement of the “exact”numerical solution and the approximation by the closed so-lution (Eq. (44), (combined model)) is very good.

The effective reaction raterm,eff according to the com-bined model is given by

rm,eff = − �LCMC�t

= km,C,effLCcO2,G. (50)

Insertion of Eq. (44) into Eq. (50) yields

rm,eff = cO2,G

1km,CLC

− r2p�cat4DO2,eff

ln(LCLC,0

) . (51)

This expression for the effective reaction rate was used forthe modelling of the coke burn-off in a fixed bed reactor (see

Table 3Parameters of the modelling of coke burn-off in a fixed bed reactor(assumed to be constant)

Particle diameter,dP 1.6 mmBulk density of fixed bed,�B 770 kg/m3

Porosity of fixed bed,� 0.4Heat capacity of solid phase, 1000 J/(kg K)cS (500◦C)Heat capacity of gas phase, 30 J/(mol K)cp,G (500◦C, 1 bar)Density of gas phase, 16 mol/m3

�G (480◦C, 1 bar)Effective axial heat conductivity 0.54W/(m K)of fixed bed,ax,eff

a

Effective axial diffusion coefficient 7.7 × 105 m2/sof fixed bed,Dax,eff

a

aThe effective axial heat conductivity and the effective axial diffusioncoefficient of the fixed bed are calculated by correlations published inVerein Deutscher Ingenieure (2002)(see also Section 4.2).

Section 5.5) and builds the link between the microscopicand the macroscopic scale of the regeneration process. (Notethat if also the external diffusion would play a role, Eq. (51)could be extended by simply adding the term 1/(�Am) inthe denominator of Eq. (51).)

5.5. Regeneration of a coked fixed bed

5.5.1. Numerical solutionsBased on the numerical solution of the Eqs. (15)–(28) and

(51) (parameters inTable 3), the regeneration of a cokedfixed bed was modelled. A typical result within a technicalfixed bed reactor of industrial scale (8 m length) is shown inFigs. 9and10(for details of the first 6 h). After an inductionperiod of about one day, a reaction front with a constantvelocity is developed. This velocity can also be deduced bya mass balance:

Within a time interval�t , the reaction front moves in axialdirection by�z. The amount of oxygen, which enters thevolume element with the length�z within the time interval�t is converted by reaction with coke and thereafter neededto “fill up” the void of the bed:

(uG� cO2,in

)�t =

(�BLC,0M̃C

+ � cO2,in

)�z. (52)

The velocity of the reaction frontuRF (=�z/�t) is thengiven by

uRF = uG� cO2,in

�BLC,0MC

+ � cO2,in

≈ uG� cO2,inMC

�B LC,0. (53)

(uG� represents the superficial velocityue.)Within the initial period of regeneration, also a heat front

moves through the bed, which heats up the reactor zoneahead of the moving reaction front from the initial temper-atureT0 to the maximum temperatureTmax. The velocity of


0

0.02

0.04

0.06

0.08

0.1

Cok

e lo

ad o

f the

cat

alys

t in

kg C

/kg c

at

0

0.04

0.08

0.12

0.16

Oxy

gen

conc

entr

atio

n in

mol

/m3

400

450

500

550

0 2 4 6 8Length of reactor in m

Tem

pera

ture

in °

C

Regeneration time:

1 1.3 h 2 6 h 3 14 h 4 30 h 5 56 h 6 111 h 7 167 h 8 195 h

End of the regeneration after approx. 200 h

Oxygen breakthrough after approx. 170 h

1

7

2 3

4 5 6

7

8

1

2

3

4

5

67 8

6

3 4

5

8

uRF

uRF

uRF = 4.7 cm/h

Fig. 9. Modelled profiles of carbon load, oxygen-concentration and temperature in a fixed bed reactor at different stages of regeneration (conditions: seeTables 2 and 3; LC,0 = 10 gC/100 gcat; p = 1 bar; yO2 = 1 vol%; ue = 0.5 m/s).

the heat front (here about 1.1 m/h) is much higher than theone of the reaction front (0.05 m/h), and can be calculatedanalogous to the reaction front based on a respective heatbalance by

uHF = uG� �G cp,G�G cp,G + �BcS

≈ uG� �G cp,G�BcS

. (54)

The influence of the effective axial heat dispersionax,effon the spread of the heat front is shown inFig. 11. Thewidth of the heat zone is only clearly increased in case of an(unrealistic) increase of the heat dispersion coefficientax,effby a factor of 10 compared to the “correct” value of about0.43W/(m K) as calculated by Eq. (20). If the axial heatdispersion is completely neglected in the model(ax,eff =0),the width of the reaction zone gets slightly smaller. In otherwords, the accuracy of the value of the axial heat dispersioncoefficient calculated by Eq. (20) does not play a role, as it

can certainly be assumed, that the error of the calculation ofax,eff by Eq. (20) is much smaller than a factor of 10. Notethat even in case of no axial heat dispersion(ax,eff = 0),the temperature decrease in the heat exchange zone is not astep function, above all in the rear part (Fig. 11). The reasonis that the input signal (T -increase in the reaction front) isnot an ideal step function.

The influence of the axial dispersion coefficient of massDax,eff on the spread of the reaction zone is even smaller, asshown inFig. 12(see alsoKern, 2003)). Even a modellingwith an unrealistic high value of the effective dispersioncoefficient (factor 1000 higher compared to the “correct”value as calculated by Eq. (20)) does not lead to a signifi-cant enlargement of the reaction zone. (Remark: If the ax-ial dispersion of mass is completely neglected in the model(Dax,eff = 0), the width of the reaction zone is the sameas in the case of modelling with the correct value, and


Regeneration time:

1 6 min 2 17 min 3 80 min 4 213 min 5 360 min

400

450

500

550

0 2 4 6 8

Length of reactor in m

Tem

pera

ture

in °

C

1 2

5

Heat front past 213 min

Temperature rise

34

uHF = 112 cm/h

Fig. 10. Modelled temperature profiles in a fixed bed reactor at the beginning of regeneration (conditions: seeTables 2 and 3; LC,0 = 10 gC/100 gcat;p = 1 bar; yO2 = 1 vol%; ue = 0.5 m/s).

400

450

500

550

0 2 4 6 8Length of reactor in m

Tem

pera

ture

in °

C

uHF = 112 cm/h

)Km(W0eff,ax =λ

)Km(W3.4eff,ax =λ

)Km(W43.0eff,ax =λ(correct value according to Eq. (20))

Fig. 11. Influence ofax,eff on the modelled temperature profiles of the heat and reaction front (conditions: seeTables 2 and 3; LC,0 = 10 gC/100 gcat;p = 1 bar; yO2 = 1 vol%; ue = 0.5 m/s).

0

0.04

0.08

0.12

0.16

3 4 5 6


Oxy

gen

conc

entr

atio

nin

mol

/m3

sm1073.7D

22eff,ax

−.=

tmod = 111 h

(correct value according to Eq. (19)) s

m1073.7D25

eff,ax−.=

Fig. 12. Influence of effective axial dispersion on the spread of the reactionzone in a fixed bed reactor during regeneration (conditions: seeTables 2and 3; LC,0 = 10 gC/100 gcat; p = 1 bar; yO2 = 1 vol%; ue = 0.5 m/s).

therefore not shown inFig. 12). So the influence of the axialdispersion of mass can be neglected here, because the width

and velocity of the reaction zone, which determine the re-generation time, are practically independent of the value ofDax,eff . Nevertheless, the modelling was always done withthe correct values forDax,eff (Eq. (19)) and also ofax,eff(Eq. (20)).

In contrast to the small influence of axial dispersion, thepronounced influence of the resistance of pore diffusion onthe width of the reaction front is shown inFig. 13. In caseof an (unrealistic) small pore diameter of only 1 nm, whichis 10 times lower than the real mean value of the catalystused here, the diffusion coefficient is much lower (strong in-fluence of Knudsen diffusion), and the width of the reactionzone is about 4 m.

With respect to determine the total time needed for cokeburn-off, it should be noted, that about 200 h are neededcompared to the minimum time in case for ideal step func-tions of carbon load and O2-content (infinite high reactionrate). In the latter hypothetical case only 170 h(LR/uRF =8 m/4.7 cm/h) are needed. In other words, the regenerationtime is 15% longer than theoretically needed in the absence


0

0.02

0.04

0.06

0.08

0.1

0 2 4 6 8


Cok

e lo

ad in

kg C

/kg

cat

nm100dpore =

nm1dpore =

nm10dpore =

tmod = 85 h

(Low influence of pore diffusion)

(High influence of pore diffusion)

Fig. 13. Influence of pore diffusion on the spread of the reaction zone ina fixed bed reactor during regeneration (conditions: seeTables 2 and 3;LC,0 = 10 gC/100 gcat; p = 1 bar; yO2 = 1 vol%; ue = 0.5 m/s).

400

450

500

550

600

650

0 2 4 6 8


Tem

pera

ture

in °

C

9 cm/h

3.6 cm/h

0.9 cm/h

tmod= 25 h

∆Tad

LC,0 = 0.01 kgC /kgcat



Fig. 14. Influence of the initial carbon load on the temperature profilesof the heat and reaction front (conditions: seeTables 2 and 3; p= 1 bar;yO2 = 1 vol%; ue = 0.1 m/s).

of kinetic limitations, which underlines the need and advan-tage of accurate modelling.

5.5.2. Temperature effects of regenerationThe adiabatic temperature increase (for a steady-state pro-

cess) is given by

�Tad = cO2,inRH/�G cp,G. (55)

In case of the unsteady regeneration process, an unexpectedoverheating above this adiabatic end temperature can oc-cur (Fig. 14). The higher the velocity of the reaction front,i.e., the lower the carbon load of the bed (see Eq. (53)), thehigher is this unwanted overheating effect (wrong way of be-haviour). This effect is already described in literature (Wickeand Vortmeyer, 1959; Emig et al., 1980; Eigenberger, 1983).To quantify this wrong way of behaviour, the heat balanceof the reaction zone is instructive, whereby the originator ofthe balance moves forward with the velocity of the reactionzone:

QR =QG −QS . (56)

The heat flux produced by the coke burn-off is

QR = (uG − uRF )�cO2,in |RH |= (uG − uRF )��Tad�Gcp,G. (57)

The heat flux needed to heat up the gas phase from the inlettemperatureT0 up to the final end temperatureTmax is givenby

QG = (uG − uRF )��Gcp,G(Tmax − T0). (58)

The heat flux, which “enters” the reaction zone (from theviewpoint of the moving observer) by the already heatedsolid is given by

QS = uRF ��BcS(Tmax − T0). (59)

The Eqs. (53), (55)–(59) then lead to

�Tmax

�Tad=uHF − uRF ��Gcp,G

(��Gcp,G−�BcS)

uHF − uRF . (60)

So the higher the velocity of the reaction front (the smallerthe difference betweenuHF and uRF ), the higher is theoverheating of the bed, as it is clearly shown inFig. 14.

Such a wrong way of behaviour may be also inducedby a non-uniform initial axial carbon load (Fig. 15), heredeliberately calculated for a strong decrease of the carbonload within the second third of the bed. At first, i.e., inthe region with a high load of 0.1 g per g catalyst, the adi-abatic “stationary” temperature increase is almost reached(Tmax − T0 = 1.015�Tad). As soon as the carbon load de-creases, an overheating of the bed (wrong way behaviour) isinduced, and the temperature increases above the maximumallowable value of 550◦C (catalyst deactivation). Thus, itmust be noted that this scenario is unrealistic in case of naph-tha reforming, where carbon formation—if at all—increasesin axial direction due to the formation of coke precursors.Nevertheless,Fig. 15 is of theoretical interest and may beinstructive for other decoking processes.

5.5.3. Coke burn-off in a technical reactorPerformance data of the regeneration process of a tech-

nical naphtha reformer were kindly provided by the MIRO-refinery (Karlsruhe, Germany). So the burn-off model couldbe finally tested and compared with the regeneration in atechnical fixed bed reactor. The respective results are givenin Fig. 16, indicating that the agreement is complete. It mustbe noted that this agreement was reached although (1) notthe same, but a similar catalyst with the same geometry isused in the MIRO refinery. (2) The technical coke burn-offis done at 20 bar, whereas the kinetic parameters were de-duced from experiments at about 2 bar. (3) The C/H-ratio ofthe catalyst of the technical unit is unknown, so the valueobtained in this work was used (1.75 mol/mol) to account forthe fact that hydrogen also contributes about 28% to the heatgeneration (for simplification neglected in the modelling re-sults shown before).


0

0.02

0.04

0.06

0.08

0.1

Cok

e lo

adin

kg C

/kg c

at

400

450

500

550

600

650

0 2 4 6 8


Tem

pera

ture

in °

C Regeneration time:

1 0.4 min 2 12 min 3 70 min 4 110 min 5 118 min 6 125 min 7 140 min

1

2

3

4

56

7

1

2 3 4 5 6

7

∆Tad

Fig. 15. Modelled profiles of carbon load and temperature in a fixed bed reactor with non-uniform initial axial carbon distribution (conditions: seeTables2 and 3; p = 1 bar; yO2 = 1 vol%; ue = 0.25 m/s).

350

400

450

500

550

0 2000 4000 6000 8000 10000

Length of reactor in mm

Tem

pera

ture

in °

C

Regeneration time:

1 7.5 h 2 19 h 3 27 h

1 2 3

∆Tad

= 137 K

Length of fixed bed (6700 mm)

modelled profil

measured profil

Fig. 16. Comparison of measured and modelled temperature profiles in a technical fixed bed reactor (MIRO-refinery, Karlsruhe, Germany) duringregeneration (conditions: seeTables 2 and 3; p = 20 bar;yO2 = 0,9 vol%; ue = 0.26 m/s; LC,0 = 21 gC/100 gcat).

Obviously the reactivity of carbonaceous deposits in tech-nical refinery processes and in lab-scale experiments is quitesimilar, which is also approved by experiments with pureAl2O3 (Tang, 2004; Tang et al., 2004).

In order to show the possible deviation of the reactionrate parameters in this work and the “real” kinetic param-eters of the coke under technical conditions,Fig. 17finallyshows the calculated temperature profiles in the case, thatthe “real” values of the intrinsic rate constant (MIRO re-

finery) would deviate from the calculation (based on ourlab-scale experiments with a different catalyst) by a factorof two and 0.5, respectively. According to this sensitivityanalysis, the “real” intrinsic reactivity seems to be slightlylower (better agreement in case of a factor of 0.5) thanthe one measured here by lab-scale experiments. It mustbe finally noted that the uncertainty of the intrinsic rateconstant experimentally determined is also relatively large(seeFig. 1).


350

390

430

470

510

550

4000 4500 5000 5500 6000 6500 7000

Length of reactor in mm

Tem

pera

ture

in °

C

Regeneration time:19 h

modelled profil

measured profil C,mk

C,mk5.0

C,mk2

Fig. 17. Influence of the intrinsic reaction rate constant on the modelledtemperature profile of the reaction front and comparison with the mea-sured profile in the technical reactor of the (MIRO-refinery in Karlsruhe,Germany) (conditions: seeTables 2 and 3; p = 20 bar;yO2 = 0,9 vol%;uL = 0.26 m/s; LC,0 = 21 gC/100 gcat).

6. Conclusions

The kinetics of coke burn-off were determined by sys-tematic lab-scale experiments. The experiments and theoret-ical considerations clearly indicate that for carbon loads of10 gC/100 gcat and temperatures above 400◦C the effectiverate of carbon burn-off is strongly influenced by pore diffu-sion. The external gas–solid mass transfer can be neglectedfor temperatures below 750◦C, i.e., for temperatures of in-dustrial relevance(T <550 ◦C). Based on the kinetic dataand the structural parameters of the catalyst (porosity, tor-tuosity), the regeneration process was modelled both on thelevel of a single particle and in a technical fixed bed reactor.The results of modelling were compared with coke profileswithin the particles and the performance data of regenera-tion of an industrial reactor. The agreement of calculationand measurement is in both cases complete.

Notation

Am external surface area per mass of catalyst, m2

ABET internal surface area per mass of catalyst,m2/kg

AV external surface area per volume of catalystm2/m3

cO2 concentration of O2, mol/m3

cO2,G concentration of O2 in the gas phase, mol/m3

cp,G heat capacity of gas phase, J/(mol K)cS heat capacity of solid phase, J/(kg K)dP diameter of particle, mDax,eff effective axial dispersion coefficient, m2/sDfb dispersion coefficientDax,eff without gas

flow, m2/sDO2,Knu Knudsen diffusion coefficient, m2/s

DO2,mol molecular diffusion coefficient, m2/s

DO2,pore pore diffusion coefficient, m2/sDO2,eff effective diffusion coefficient, m2/sEA activation energy, J/molEDX energy dispersive X-ray spectrometerkm,C reaction rate constant, m3/(kg s)km,C,0 frequency factor, m3/(kg s)kP ratio of thermal conductivities(=S/G)LC carbon load of catalyst (=mC/mcat),

kgC/kgcatLC,0 initial coke content of catalyst, kgC/kgcatLp length of a cylindrical particle, mmcat mass of catalyst, kgMC molecular weight of carbon, kg/molMO2 molecular weight of oxygen, kg/molNMR Nuclear magnetic resonancenC amount of carbon, molnO2 rate of oxygen, mol/sp pressurePFG Pulsed field gradient (NMR)PFR Plug-flow reactorq order of reactionQ heat flux, J/srm reaction rate per unit of mass of catalyst,

mol/(kg s)rm,eff effective rate per mass of catalyst, mol/(kg s)rp particle radius, mR ideal gas law constant (8.314), J/(mol K)SEM Scanning electron microscopySh Sherwood number,�dP /Dmolt time, sT temperature,◦C, KTG temperature of the gas phase,◦C, KTS temperature of the surface of particle,◦C, KT0 initial temperature,◦C, KTmax maximum temperature,◦C, Kue superficial gas velocity, m/suG interstitial gas velocity, m/suRF velocity of the reaction front, m/suHF velocity of the heat front, m/sVC core volume, m3

Vm volume of particle, m3/kgXO2 conversion of oxygeny gas volume fractionz axial coordinate in reactor, m

Greek letters

� heat transfer coefficient, W/(m2 K)� mass transfer coefficient, m/sRH heat of reaction, J/mol�t time interval�Tad adiabatic temperature increase,◦C, K�Tmax maximum adiabatic temperature increase,

◦C, K


�z interval in axial direction

� voidage of reactor bed�P porosity of particle�pore pore effectiveness factor�pore,0 initial pore effectiveness factor�overall overall particle effectiveness factorax,eff effective dispersion coefficient of heat,

W/(m K)f b effective dispersion coefficient of heatax,eff

without gas flow, W/(m K)S thermal conductivity of porous solid phase,

W/(m K)G thermal conductivity of gas phase, W/(m K)�P density of catalyst, kg/m3

�G density of gas phase, kg/m3

�B density of reactor bed�P particle tortuosity� modified resicence time, kg s/m3

� Thiele modulus�0 initial Thiele modulus

Acknowledgements

Financial support by the Max-Buchner-Forschungsstiftung(1970) and by the Deutsche Forschungsgemeinschaft (BL231/25) is gratefully acknowledged. The authors also wishto thank Engelhard for supplying the catalyst, theDe-partment of Materials Processing(University Bayreuth,Prof. M. Willert-Porada) for the helpful investigations onthe carbon distribution within the catalyst (SEM/EDX-measurements), Prof. B. Blümich and his co-workers (In-stitute of Technical Chemistry and Macromolecular Chem-istry, University of Aachen) for the fruitful cooperation andthe NMR-measurements of the tortuosity, and finally theMIRO-refinery(Karlsruhe, Germany) for the provision ofperformance data of the regeneration of the coked reformingcatalyst in a real technical fixed bed reactor.

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Documents

Regeneration of Coked Catalysts Modelling and Verification of Coke Burn Off in Single Particles and Fixed Bed Reactors