kinetic for hts and lts

Applied Catalysis A: General 250 (2003) 161–175

Reaction kinetics and reactor modeling for fuel processing ofliquid hydrocarbons to produce hydrogen: isooctane reforming

Manuel Pachecoa,∗, Jorge Sirab, John Kopaszca Department of Refining and Petrochemicals, Center for Research and Development of the Venezuelan Oil Industry (PDVSA-Intevep),

Sector el Tambor, P.O. Box 76343, Los Teques, Edo Miranda, Venezuelab Department of Mechanical Engineering, Universidad de los Andes, Mérida, Venezuela

c US Department of Energy, Chemical Technology Division, Argonne National Laboratory, Argonne, IL 60439, USA

Received 22 October 2002; received in revised form 21 March 2003; accepted 28 March 2003

Abstract

A mathematical model was developed in the framework of the process simulator Aspen Plus® in order to describethe reaction kinetics and performance of a fuel processor used for autothermal reforming of liquid hydrocarbons. Ex-perimental results obtained in the facilities of Argonne National Laboratories (ANL) when reforming isooctane using aceria-oxide catalyst impregnated with platinum were used in order to validate the reactor model. The reaction kineticsand reaction schemes were taken from published literature and most of the chemical reactions were modeled using theLangmuir–Hinshelwood–Hougen–Watson (LHHW) formulation to account for the effect of adsorption of reactants and prod-ucts on the active sites of the catalyst. The water-gas-shift (WGS) reactor used to reduce the concentration of CO in thereformate was also modeled. Both reactor models use a simplified formulation for estimating the effectiveness factor of eachchemical reaction in order to account for the effect of intraparticle mass transfer limitations on the reactor performance.Since the data in the literature on kinetics of autothermal reforming of liquid hydrocarbons using CeO2-Pt catalyst is scarce,the proposed kinetic model for the reaction network was coupled to the sequential quadratic programming (SQP) algorithmimplemented in Aspen Plus® in order to regress the kinetic constants for the different reactions. The model describes thetrend of the experimental data in terms of hydrogen yield and distribution of products with a relative deviation of±15% forreforming temperatures between 600 and 800◦C and reactor space velocities between 15 000 and 150 000 h−1.© 2003 Elsevier Science B.V. All rights reserved.

Keywords: Kinetic modeling; Reactor modeling; Reforming; Gasoline; Hydrogen

1. Introduction

There is consensus in the scientific internationalcommunity representing both the energy and trans-portation sectors that hydrogen could find a more ex-tended use as a fuel or an energy carrier in the future.Hydrogen is the fuel for polymer electrolyte mem-

∗ Corresponding author.E-mail address: [email protected] (M. Pacheco).

brane fuel cells (PEMFC) which are considered as themost technologically mature of the different types offuel cells. In these fuel cells pure hydrogen or a refor-mate gas containing hydrogen can be fed to the anode,while oxygen is fed to the cathode and a electrochemi-cal reaction takes place producing electricity plus heatand water as byproducts. When analyzing the com-mercial viability of the fuel cell technology, the morerelevant issue is the fuel to feed the fuel cell ratherthan the fuel cell itself. Hydrogen can be produced

0926-860X/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved.doi:10.1016/S0926-860X(03)00291-6

162 M. Pacheco et al. / Applied Catalysis A: General 250 (2003) 161–175

Nomenclature

Cp gas-phase heat capacitydp diameter of catalyst particleDeff,j effective diffusivity of speciesjDm,j molecular diffusivity of speciesjF(y) objective function to be minimized

during the parameter regressionG mass velocity of the gas per unit

cross section of the reactorh heat transfer coefficient at the

boundary layer around the catalyst

jD dimensionless number(kcρN2/3Sc /G)

jH dimensionless number(hN2/3Pr /CpG)

k gas-phase thermal conductivitykc mass transfer coefficient at the

boundary later around the catalystkj reaction rate constant for reactionjKi adsorption constant for speciesi

(1/atm)KH2O dissociative adsorption constant for

water vaporL reactor length (cm)NPr Prandtl number(Cpµ/?)NRe Reynolds number(dpG/µ)

NSc Schmidt number(µ/ρDm)

Pi partial pressure of speciesirj reaction rate for reactionjr′j pseudo-first order

reaction rate expression for reactionj used for the effectiveness factorcalculation (r′j = rj)

rp catalyst particle radiusyi,cal calculated mole fraction for the

ith experimental measurementyi,m measured mole fraction for theith

experimental measurementz axial coordinate along the reactor

bed (cm)

Greek lettersβH parameter to quantify intraparticle

temperature gradients (defined inEq. (16))

βWGS reversibility factor for the water-gas-shift reaction (defined inEq. (11))

−�H heat of reaction

φ Thiele modulusκ gas-phase thermal conductivityλ catalyst thermal conductivityµ gas-phase viscosityρ gas-phase densityσi standard deviation for theith

experimental measurement

from fossil fuels through a process of fuel reformingusing natural gas, naphthas, gasolines or even heav-ier fuels like Diesel[1], gasoil, etc. Other pathways tohydrogen have been proposed based on water electrol-ysis and solar energy, reforming of biofuels or otherrenewable sources of fuels and energy.

Regardless of the hydrocarbon feedstock being usedfor hydrogen production via fuel reforming, a tool isneeded in order to analyze the relationship betweenfuel formulation and fuel reformability, between fuelreformability and nature of the catalytic system, andto determine the reaction kinetics and assess the im-portance of heat and mass transfer issues on reactorperformance. This work is aimed at developing andvalidating a preliminary mathematical model to de-scribe these phenomena. This model was validatedusing experimental data collected in a fixed-bed mi-croreactor packed with a noble-metal based catalystproprietary to the US Department of Energy[2].

Since naphtha cuts are very complex mixtures ofhydrocarbons, this work was initiated with the studyof reformability of isooctane as a representative paraf-fin in a naphtha cut. The reaction scheme that hasbeen proposed in the literature for partial oxidationand steam reforming of hydrocarbons has been im-plemented and the unknown kinetic parameters weredetermined through a data regression algorithm. A de-tailed description of this reaction scheme will be givenin the present contribution. A simplified mathemati-cal model was implemented to account for the intra-particle diffusional limitations due to the high reactiontemperatures and high reaction rates. This intraparti-cle diffusional limitation was accounted for by esti-mating effectiveness factors for each of the reactionsconsidered in the kinetic mechanism. The low andhigh temperature water-gas-shift (WGS) reactors useddownstream of the fuel reformer were also modeled.The coupling of thermolysis reactions that heavier

M. Pacheco et al. / Applied Catalysis A: General 250 (2003) 161–175 163

hydrocarbons undergo to produce lighter hydrocarbonmolecules, which are also reformed to produce hydro-gen, will be the subject of following publications.

2. Reaction kinetics for partial oxidation andsteam reforming of liquid hydrocarbons

Reforming of liquid hydrocarbons in order to pro-duce hydrogen (or synthesis gas) has not been studiedas deeply as that for lighter hydrocarbons like methaneor natural gas. Published kinetic data for the partialoxidation or steam reforming reactions of hydrocar-bons C5 to C8 is scarce. In the present contribution anattempt is made to develop a kinetic and reactor modelto describe autothermal reforming of isooctane using aceria oxide catalyst impregnated with platinum. Isooc-tane is used as a model molecule for a C8 naphtha orparaffinic gasoline. Due to the fact that hydrocarbonsundergo a thermal cracking or thermolysis[3] whenin contact with a high temperature media, the hydro-carbon molecules that are actually reformed in the re-actor are a spectrum of lighter hydrocarbons formedafter the thermolysis process. In order to simplify theanalysis, in the present contribution, it is assumed thatthe molecule that is actually reformed is the actualfuel fed to the reactor, i.e. isooctane. Pant and Kun-zru [4,5] show that the conversion ofn-heptane andmethylcyclohexane due to the thermolysis reactions attemperatures from 680 to 800◦C and residence timefrom 0.1 to 0.6 s can be as low as 10% and as highas 80% for the most severe reaction conditions. Thereactor residence time for the hydrocarbon reformingreactions studied in the present contributions was be-tween 0.02 and 0.2 s. A detailed modeling of naphthapyrolysis coupled to the reforming reactions is under-way and will be the subject of a future publication.

Direct partial oxidation of isooctane can be repre-sented as

C8H18 + 4O2 ⇒ 8CO+ 9H2 (1)

Two reaction schemes have been proposed to explainthe partial oxidation of a hydrocarbon to CO and H2[6–8]. Some authors consider that the hydrocarbon un-dergoes combustion followed by both steam and car-bon dioxide reforming, the other mechanism is basedon the catalytic pyrolisis of the hydrocarbon followedby hydrogen desorption and carbon oxidation. Even

though these reaction schemes have been proposedprimarily for methane partial oxidation, the combus-tion route was assumed in the present contribution be-cause of the relatively high amount of CO2 present inthe reformate in the early stages of the reaction. Thisreaction scheme can be described as

C8H18 + 16O2 ⇒ 8CO2 + 9H2O (2)

C8H18 + 8H2O ⇒ 8CO+ 17H2 (3)

C8H18 + 8CO2 ⇒ 16CO+ 9H2 (4)

Reaction 2 corresponds to the catalytic combustion ofthe hydrocarbon, while reactions 3 and 4 correspond tothe steam and CO2 reforming reactions, respectively.

Xu and Froment[9,10] when modeling steam re-forming of methane on a Ni-Al2O3 catalyst indicatedthat the hydrocarbon can be steam reformed to CO2and H2 as well, that is

C8H18 + 16H2O ⇒ 8CO2 + 25H2 (5)

Besides the reactions described earlier, it is clear thatthe presence of CO and water in the system impliesthat the WGS reaction should play a role

CO+ H2O ⇒ CO2 + H2 (6)

In the present work reactions 2 through 6 were usedto describe the partial oxidation, steam reforming andCO2 reforming that take place in the fuel processingreactor for hydrogen production. Rostrup-Nielsen[11]proposed a reaction mechanism for steam reformingof hydrocarbons where it is assumed that hydrocar-bons are chemisorbed on a catalyst dual site followedby successive�-scissions of the carbon–carbon bonds.The resulting C1-species react with chemisorbedsteam. Using Langmuir equation for describing thesurface concentration of hydrocarbon (CnHm), steamand hydrogen, the following expression is obtainedfor the reaction rate

r = kAPCnHm

(1 + (kA/krKw)(PH2/PH2O)PCnHm

+KH2O(PH2O/PH2)+√KH2PH2)

2

(7)

wherePi is the partial pressure of speciesi, KH2O thedissociative adsorption constant of water,KH2 the ad-sorption constant for hydrogen,kA the reaction rateconstant for the hydrocarbon chemisorption, andkr


the reaction rate constant for the reaction between ad-sorbed C1-species and chemisorbed oxygen producedfrom water dissociation.

In the mechanism proposed by Rostrup-Nielsen[11]it is implicit that the catalyst support and the promotersenhance adsorption of steam, which is then transportedor “spilled over” to the active metal surface

H2O + support⇒ H2O–support (8)

H2O–support+∗ ⇒ O–∗ + H2 (9)

Due to the possible strong support-metal interactionand/or to the direct activation of steam by the activemetal (H2O+∗ ⇒ O–∗ + H2), the surface of the ac-tive metal may be covered by water. In order to de-velop Eq. (7), it was assumed that activated oxygen(O–∗) was the most abundant reaction intermediateand that the surface concentration of heavier hydrocar-bons chemisorbed on dual sites (CnHz–∗

2) was negli-gible.

The basic assumption proposed by Rostrup-Nielsen[11], regarding successive�-scissions of the carbon-carbon bonds in the heavier hydrocarbon resultingonly in C1-species, is perhaps an important simplifi-cation of the actual mechanism because, as Savage[3]describes, there is a family of hydrocarbon pyrolysisreactions that includes homolytic dissociation of theC–C bonds, radical recombination (reverse reaction),β-scission, radical disproportionation, isomerization,hydrogen abstraction, among others. The magnitudeof the C–H and C–C bond dissociation energies of thedifferent bonds present in the hydrocarbon moleculeis what determines the kinetics and product distribu-tion in the hydrocarbon pyrolysis reactions. Anotherassumption implicit inEq. (7) is that chemical re-versibility is negligible. Despite these simplificationsin the Rostrup-Nielsen mechanism for steam reform-ing of higher hydrocarbons,Eq. (7)has been the basisfor building reaction kinetic models for steam reform-ing of hydrocarbons.

Using a combination of mass spectrometry and gascromatography, Kopasz et al.[12] have shown thatduring autothermal reforming of isooctane and otherliquid hydrocarbons using a Pt-CeO2 catalyst, C1 toC4 hydrocarbons are the dominant species that resultfrom the cleavage of the original fuel molecules dur-ing the process of thermolysis. This indicates that aspectrum of lighter hydrocarbons are produced and

then reformed. However, the introduction of all theselighter hydrocarbons in the kinetic model would makeit much harder to handle especially when modelingreforming of a complex hydrocarbon blend like gaso-line or naphtha. Simplifications are needed for com-putational calculations.

Most published work on steam reforming of lightand heavier hydrocarbons use rate expressions similarto Eq. (7) to explain the experimental observations.Avci et al. [13] used rate expressions similar toEq. (7)to model steam reforming of methane, propane andoctane; however, they did not consider reversibility inthe kinetic expressions used for steam reforming ofhydrocarbons.

Only recently[14] experimental measurements onsteam reforming and autothermal reforming of liquidhydrocarbon fuels using a proprietary Pt-Rh-Al2O3catalyst have been published; however, no kinetic orreactor modeling was presented in this publication.Due to the lack of published kinetic data specificallyfor the Pt-CeO2 catalyst under study in the presentcontribution, it was necessary to use the general formof the rate expressions developed for other catalyticsystems and regress the kinetic parameters in order toadjust the model predictions to the experimental data.Table 1shows the rate expressions used in the presentwork for the kinetic modeling of the reforming reac-tions, the catalyst used and the respective reference.

It has to be emphasized that the kinetic expres-sions described inTable 1have been developed dur-ing studies of partial oxidation and steam reforming ofmethane and the general functionality of these expres-sions has been adopted in this work for the equivalentreactions involving isooctane. As it was mentionedabove, Rostrup-Nielsen[11] showed that the experi-mental data for light and heavy hydrocarbons can beexplained by using a Langmuir-type mechanism todescribe the adsorption and reaction of reactants andproduct on the catalyst active sites. The kinetics modelused by Xu and Froment[9] implemented in this con-tribution is consistent with this mechanism.

3. Reaction kinetics for low and hightemperature water-gas-shift

Since the goal of this work was to develop a math-ematical model for a fuel processor for hydrogen


Table 1Rate expressions and references used in the reformer modeling

Reaction Expression forri T (◦C) Catalyst Reference

C8H18 + 16O2 ⇒8CO2 + 9H2O

r1 = k1PiC8PO2 800–900 Ni/Al2O3 [6]

C8H18 + 8H2O ⇒8CO + 17H2

r2 = k2

P2.5H2

(PiC8PH2O − P3

H2PCO/K1

(1 +KCOPCO +KH2PH2 +KiC8PiC8 +KH2OPH2O/PH2)2

)500–750 Ni/Mg Al2O3 [9,10]

C8H18 + 8CO2 ⇒16CO+ 9H2

r3 = k3PiC8PCO2

(1 − P2

COP2H2

K3PiC8PCO2

)800–900 Ni/Al2O3 [6]

C8H18 + 16H2O ⇒8CO2 + 25H2

r4 = k4

P3.5H2

(PiC8P

2H2O − P4

H2PCO2/K4


)500–750 Ni/Mg Al2O3 [9,10]

CO + H2O ⇒CO2 + H2

r5 = k5

PH2

(PCOPH2O − PH2PCO2/K5


)500–750 Ni/Mg Al2O3 [9,10]

production with emphasis on fuel cell applications,water-gas-shift (WGS) reactors have to be useddownstream of the fuel reformer in order to increasethe overall efficiency of hydrogen production and tolower the CO content in the reformate which could ir-reversibly deactivate the catalyst used in the anode ofpolymer electrolyte membrane (PEM) fuel cells if theCO concentration is higher than about 100 ppm[15].

In this contribution two water-gas-shift reactors(also called shifters), a high temperature shift (HTS)and a low temperature shift reactor (LTS) were mod-eled downstream from the reformer. The reactionkinetics for the WGS reaction under high and lowtemperature conditions and for a wide variety of cata-lyst has been studied by Keiski and coworkers[16,17].A commercial iron-oxide/chromium-oxide catalyst aswell as a copper-based catalyst were studied by theseresearchers. By varying the reaction temperature,H2O-to-dry gas ratio, space velocity, and CO, CO2,and/or H2 concentration in the gas fed to the shifters,the following power-law type of rate expression wasdeveloped by Keiski and coworkers:

rWGS = kWGSCnCOC

mH2OC

p

CO2CqH2(1 − βWGS) (10)

whereCi is the molar concentration of speciesi, βWGSis the reversibility factor that accounts for the approachto chemical equilibrium.

βWGS = CCO2CH2

KTCCOCH2O(11)

andKT is the equilibrium constant.

Depending on the temperature range and catalystused the kinetic parameters and reaction orders of reac-tants and products used inEq. (10)change. These pa-rameters and orders were implemented in the presentwork for the modeling of the high temperature andlow temperature shifters. This kinetic model was ini-tially coupled through a user-supplied subroutine tothe Aspen Plus® plug-flow reactor model in order tosimulate the high and low temperature water-gas-shiftreactors and validate the models using the experimen-tal data[16,17].

4. Mass and heat transfer issues

Due to the high temperature at which the reform-ing and WGS reactions take place, the important heateffects, and large reaction rates; it is expected thatdiffusional limitations and heat transfer resistance in-side the catalyst and at the boundary layer aroundthe catalyst play important roles in the reactor per-formance.

The relationship between the importance of masstransfer resistance through the boundary layer at thesurface of the catalyst and temperature difference be-tween catalyst surface and bulk fluid may be easilyderived for steady-state conditions[18].

kc(Co − Cs)(−�Hr) = h(Ts− To) (12)

wherekc is the mass transfer coefficient at the bound-ary layer,Co andCs are the reactant concentrations at


the bulk fluid and catalyst surface; respectively,−�Hris the heat of reaction,h is the heat transfer coefficientat the boundary layer around the catalyst, andTs andTo are the temperature at the catalyst surface and bulkfluid, respectively. Using the correlations commonlyaccepted for estimating the heat and mass transfer co-efficients in packed beds,Eq. (12)can be written interms of the Schmidt and Prandtl numbers as follows:

(Ts − To) =(jD

jH

)(NPr

NSc

)2/3

(Co − Cs)−�Hr

ρCp

(13)

From Eq. (13)it can be seen that the maximum tem-perature difference between the catalyst surface andthe bulk fluid can be estimated by considering a com-pletely mass-transfer controlled reaction (Co Cs)due to the external mass transfer resistance. Therefore,the extent of the heat transfer resistance at the bound-ary layer around the catalyst can be estimated by theterm

(Ts − To)max =(jD

jH

)(NPr

NSc

)2/3 −�Hr Co

ρCp(14)

Table 2shows the range of values of thermophysicalproperties like gas-phase (reformate) density, viscos-ity, heat capacity, and estimated values for heat andmass transfer coefficients at the boundary layer. Thisrange of values is for temperatures between 600 and800◦C and for a reactor pressure of 6 psig. Consid-

Table 2Thermophysical and transport properties of the reformate and es-timated heat and mass transfer coefficients at the boundary layer

600◦C 800◦C

Gas density (kmol/m3) 0.01434 0.01167Gas viscosity (g/cm2 s) 3.56E−4 4.09E−4Gas heat capacity (cal/gmol K) 7.647 7.312Gas thermal conductivity

(cal cm/(s cm2 K))5.63E−4 7.07E−4

Schmidt number (usingisoctane diffusivity)

∼1.7–2.1

Prandtl number ∼0.45Reynolds number ∼0.75–1.5Nusselt number for heat transfer ∼2.5Gas–solid heat transfer

coefficient (cal/(cm2 s K))∼2.5E−2

Mass transfer coefficient usingisooctane diffusivity (cm/s)

∼120

ering that the key component to make these calcu-lations is isooctane and considering that the overallheat of reaction for autothermal reforming is of theorder of 5% of the heat of reaction for partial oxida-tion (∼40 kcal/mol); the maximum temperature gra-dient through the boundary layer is about 19◦C atthe entrance of the reformer. This maximum temper-ature gradient at the boundary layer rapidly drops toabout 6◦C at half the bed length and 3◦C at the bedexit. This indicates that under the conditions of fuelreforming studied in this work, temperature gradients(and therefore heat transfer resistance) could becomeimportant only close to the region where the fuel isfed to the reformer. Also, it is important to mentionthatEq. (13)emphasizes that if the heat of reaction islarge, mass transfer limitations at the boundary layeron the catalyst surface may be small, yet heat trans-fer can still be important. This leads to the conclusionthat for most of the reactor bed, both heat and masstransfer resistance at the boundary layer could be ne-glected for modeling purposes under the conditionsanalyzed in the present study. This assumption maynot be correct close to the reactor inlet.

It is important to mention that these calculations ofheat transfer resistance were performed consideringthe worst case where there is a complete mass transferresistance at the boundary layer. It is likely that theactual mass transfer resistance will be shared betweenthe external boundary layer and the intraparticle masstransfer; therefore the external temperature gradientwill be lower than that estimated earlier.

The other important working hypothesis in this as-sessment of the heat/mass transfer effect is the overallheat of reaction. A fraction of the heat of reaction forthe partial oxidation is considered because this workis concerned with the autothermal reforming of isooc-tane where the heat released by the partial oxidationreactions is used for the endothermic steam reformingreactions. Only a slightly higher O2/C ratio is used tomaintain the system just slightly exothermic.

With respect to the intraparticle heat transfer resis-tance it can be shown that under steady-state condi-tions the diffusion flux of reactants across a boundarylayer surrounding some fraction of the catalyst porousstructure equals the rate of reaction within the surface.Also, the heat released or consumed by the reactionmust all be transferred across the same boundary. Sat-terfield[18] mathematically represents these transport


phenomena in the following form

(T − Ts) = Deff(Cs − C)−�Hr

λ(15)

where T is the temperature at any point within thecatalyst particle,C the molar concentration of the re-acting species at the same point,−�Hr the enthalpychange on reaction, andλ the thermal conductivity ofthe porous catalyst.Ts andCs are the boundary valuesat the outer surface of the catalyst.

From Eq. (15) a dimensionless parameter can bederived that quantifies the effect of intraparticle heattransfer resistance and the maximum temperature gra-dient within the catalyst. Satterfield[18] representsthis parameter as

βH = −�Hr CsDeff

λTs(16)

Satterfield[18] summarizes data of thermal conduc-tivity of a wide variety of catalysts in powder form

and shows that it varies between 3E−4 and 1E−3cal/(s cm◦C). If a thermal conductivity for the porouscatalyst of 5E−4 cal/(s cm◦C) is used, the value ofparameterβH is of the order of 10−4 to 10−3 for thissystem and under the conditions studied in the presentcontribution. This corresponds to a maximum temper-ature gradient within the catalyst of the order of 0.5◦Cat the reformer entrance and about 0.04◦C at the endof the catalyst bed. For these calculations the effec-tive diffusivity of isooctane was calculated consider-ing both molecular and Knudsen diffusion. A tortu-osity factor of 2 was assumed[18], a mean pore ra-dius of 6.3E−10 m was calculated given the measuredpore size distribution and a catalyst void fraction of0.05–0.19 was estimated based on the measured to-tal pore volume (0.01–0.05 cm3/g). This assessmentindicates that intraparticle heat transfer resistance isunimportant under the conditions studied in the presentwork; and therefore the intrinsic reaction rates can beevaluated at the bulk fluid temperature and correctedfor the effect of intraparticle mass transfer resistanceby using the effectiveness factor of each reaction.

5. Effectiveness factor model

Due to the complexity of the kinetic expressions de-scribed inTable 1the integration of the mass transferequations that describe the intraparticle mass transferresistance represents a challenge especially becausethe solution of the intraparticle problem has to becoupled with the interparticle description in order tomodel the reactor. In this work a simplified approachwas used for estimating the effectiveness factor foreach reaction throughout the reactor bed. This ap-proach is based on the use of reversible pseudo-firstorder expressions for the reaction rates instead of theLangmuir–Hinshelwood–Hougen–Watson (LHHW)formulation only for the purpose of estimating theeffectiveness factor. In this approach the LHHW ex-pressions are rewritten in a more simplified form thathas an analytical solution for the effectiveness factor.This approach can be explained with an example. Theexpression for describing the reaction rate for steamreforming of isooctane to produce CO and hydrogen(Eq. (3)) described inTable 1is

r2 = k2

P2.5H2

(PiC8PH2O − P3

H2PCO/K1

(1 +KCOPCO +KH2PH2 +KiC8PiC8 + (KH2OPH2O/PH2))2

)(17)

This expression can be rewritten in reversiblepseudo-first order form:

r′2 = r2 = k′2

(PiC8 − PCO

Keq2

)(18)

where k′2 is the pseudo-first order reaction constant

andKeq2 is a parameter that includes the original equi-librium constant.

k′2 = k2PH2O

P2.5H2(1 +KCOPCO +KH2PH2

+KiC8PiC8 + (KH2OPH2O/PH2))2

(19)

and

Keq2 = K1PH2O

P3H2

(20)

Satterfield[18], Froment and Bischoff[19] indicatethat the Thiele modulus for a first order reversibleithreaction taking place in a spheric catalyst of radiusrp and using thejth species as the key component is


defined as

φi = rp

3

√k′i(Keqi + 1)

Deff,jKeqi(21)

and that the effectiveness factor can be estimated by

ηi = 1

φi

(3φi)coth(3φi)− 1

3φi(22)

In this formulation the effective diffusivity ofjthspecies is estimated considering both Knudsen andmolecular diffusion

1

Deff,j= t

θ

(1

Dk,j

+ 1

Dm,j

)(23)

whereτ is the tortuosity factor andθ is the void frac-tion of the catalyst, respectively. Based on the rangeof values for the tortuosity factor in different catalyticsystems given by Satterfield[18], τ is assumed to beequal to 2. Using the pore size distribution of the cat-alyst θ was estimated to be equal to 0.19.

It is important to notice that the intrinsic reactionrates calculated by the reversible pseudo-first orderexpressions (r′j) are identical to the intrinsic reactionrates calculated using the original formulation (rj)taken from the reaction mechanism for the partial oxi-dation and steam reforming reactions described earlierin the present contribution. The functionality of the in-trinsic reaction rate expressions is modified only to beable to estimate the effectiveness factor from an ana-lytical solution of the mass transfer equations that de-scribe the intraparticle mass transfer-reaction process.

6. Model validation and data regression:autothermal reforming of isooctane

Autothermal reforming of isooctane performed atthe facilities of Argonne National Laboratory (ANL)was chosen as the system used for the regression ofthe kinetic parameters and model validation. The ANLproprietary Pt-CeO2 catalyst was used for fuel reform-ing in a micro-reactor of 0.42 cm of internal diameterand 5 cm long which is placed inside a furnace fortemperature control. About 2 g of catalyst is crushedand packed in the micro-reactor for each experimentalrun. A detailed description of the experimental setupis given by Kopasz et al.[12]. Table 3shows the re-action conditions for these experiments.

Table 3Reaction conditions for autothermal reforming of isooctane

Reactor temperature (◦C) 600, 700 and 800Reactor pressure (psig) 5–7Space velocity (h−1) 15000–150000Catalyst size (mm) 0.51–0.76Catalyst pore radius (m) 5.8E−10–2.8E−9H2O/C (mol/mol in the feed) 1.43O2/C (mol/mol in the feed) 0.42

Performing an energy balance calculation that con-siders the exothermic heat of reaction of the partialoxidation reactions and the endothermic effect of thesteam reforming reactions, it can be shown that a molarsteam-to-carbon ratio of 1.43 and oxygen-to-carbonratio of 0.42 can be used to make the system almostautothermal allowing only for a slightly higher O2/Cratio to allow for some exothermicity in the system.

The kinetic models described inTable 1 for thesteam reforming, partial oxidation and CO2 reform-ing were implemented in a user-supplied FORTRANsubroutine of the process simulator Aspen Plus®. Thissubroutine coupled to the rigorous plug-flow reactormodel of Aspen Plus® (RPLUG) was also designedto perform mass transfer calculations involving es-timation of the effective diffusivity of the differentspecies at the catalyst side, Thiele modulus and effec-tiveness factor for the different reactions. This kineticsubroutine was also coupled to a data-fit algorithmbuilt-in Aspen Plus® which uses a version of the se-quential quadratic programming (SQP) formulation inorder to regress the kinetic parameters needed to ad-just the model predictions to the experimental data.This regression was performed by minimizing a ob-jective function,F(x), that quantifies the difference be-tween predicted and measured reformate compositionsweighted by the inverse of the standard deviation ofthe measured composition.

F(y) = MinN∑i=1

(yi,m − yi,calc

σiyi,m

)2

(24)

whereyi,m andyi,calc are the measured and calculatedvalues of the ith data point; respectively, andσi is thestandard deviation for the experimental measurement.

After performing a sensitivity analysis on the effectof kinetic parameters, six parameters were chosen forthe regression. These parameters were the five preex-ponential factors of the Arrhenius-type expressions for


the reaction rate constantsk1 throughk5 described inTable 2, and the pre-exponential factor for the disso-ciative adsorption constant for water vapor at the cata-lyst active sites (KH2O).KH2O was the only adsorptionconstant regressed because the sensitivity analysis per-formed on the model indicated that the major contri-bution to the adsorption term in the kinetic expressionswas due to the dissociative adsorption of water. Asan example, the dissociative adsorption term for wa-ter (PH2OKH2O/PH2) in the reaction rate expressionsdescribed inTable 2accounts for about 92–98% ofthe denominator at 800◦C and GHSV= 15 000 h−1.Since only the pre-exponential factors are regressed,with this approach it is assumed that the activation en-ergies for the different reactions and the enthalpy ofadsorption of water vapor are the same in this catalyticsystem with respect to the values reported in the liter-ature. It is important to mention that despite the hightemperature, the inhibition effect of reactant and prod-uct adsorption on the catalyst active sites is significant.This inhibition effect due to reactants and products ad-sorption is illustrated by a denominator in the reactionrate expressions that varies along the reactor bed from12 to 150 at 800◦C and 15 000 h−1. The regressionof these kinetic parameters was performed simultane-ously for three different temperatures and four differ-ent space velocities studied experimentally involvingmore than 50 experimental measurements. Reactionrate coefficients and a water adsorption dissociativecoefficient greater than zero were considered as phys-ical constraint during the data regression process.

Table 4shows the results of the data regression pro-cess when the pre-exponential factors of the reactionrate coefficientsk1 throughk5 described inTable 2,

Table 4Results of the kinetic parameter regression

Parameter Pre-exponentialfactor

Activation energyand heat ofadsorption ofwater (kJ/mol)

k1 (mol/(gcats bar2)) 2.58E+08 166k2 (mol bar0.5/(gcats)) 2.61E+09 240.1k3 (mol/(gcats bar2)) 2.78E−05 23.7k4 (mol bar0.5/(gcats)) 1.52E+07 243.9k5 (mol/(gcats bar)) 1.55E+01 67.1KH2O (dimensionless) 1.57E+04 �HH2O = 88.7

The parameters and their respective use are defined inTable 1.

as well as, the pre-exponential factor of the waterdissociate adsorption coefficient were regressed. AnArrhenius-type of expression was considered for thedependency of these parameters with temperature.The activation energies of these reactions and the heatof adsorption of water were taken from references[6] through [10] and are reported onTable 4. Theminimum converged value of the objective function(Eq. (24)) was 1.27 which is equivalent to an averagerelative error between the measured and calculatedvalues of about 15%, considering a standard deviationof 10% for the reformate composition measurements.The adsorption coefficients for hydrogen, CO and iso-octane were considered to be the same as those report-ed in the cited references ([6] through[10]) because,as it was indicated before, the competitive adsorptioneffect of these three species accounts for a minorfraction to the whole inhibition effect with respect tothe contribution of water dissociative adsorption.

Figs. 1 and 2compare the product distribution mea-sured experimentally in the reformate stream and themodel predictions for a space velocity of 15 000 and150 000 h−1, respectively. Since in the model devel-oped in the present work, the thermolysis reactions ofheavier hydrocarbons to produce lighter hydrocarbonsis not accounted for, the comparison of hydrocarbonsin the reformate is based on the lumped hydrocarbonsmeasured experimentally (C1 through C4) and uncon-verted isooctane predicted by the model.

Figs. 1 and 2show that the model is capable ofquantifying the distribution of products in the refor-mate stream under a wide range of conditions; al-though the relative error in the prediction of hydrogenconcentration increased from about 13% for a spacevelocity of 15 000 h−1 to 23% at 150 000 h−1. Fig. 3depicts a parity plot that indicates the quality of thefit for the whole set of experimental data. From thiscomparison it was determined that the average relativeerror in the model prediction was 15.5% if only H2,CO and CO2 are considered in the calculation of thedeviation between model prediction and experimentaldata. When unconverted hydrocarbons are included,the average relative deviation between experimentaldata and model predictions increased to 21.9%. Thisshows the importance of incorporating the thermoly-sis reactions in order to quantify the effect of thermalcracking of the heavier hydrocarbons on the overallproduct distribution in the reformate.


Fig. 1. Comparison between experimentally measured reformate composition and model predictions. GHSV= 15 000 h−1 and 700◦C.

In order to illustrate the model performance and ca-pabilities,Fig. 4 shows the concentration profile pre-dicted by the reactor model at 15 000 h−1 and 800◦C.This figure indicates that water vapor concentrationpeaks early in the reactor because of the competitivecontribution of consumption and production as shownin the proposed mechanism. Also, oxygen is quicklyconsumed in the partial oxidation reactions, and bothCO and CO2 reach a concentration plateau also due to

Fig. 2. Comparison between experimentally measured reformate composition and model predictions. GHSV= 150 000 h−1 and 800◦C.

the relative contribution of the reactions where thesespecies are consumed and produced. At this low spacevelocity the model indicates that the concentration ofhydrogen along the bed increases steadily.

Fig. 5 describes the typical order of magnitude forthe effectiveness factors of the reaction network usedto describe the reformer. Close to the section wherethe fuel is fed to the reactor effectiveness factors con-verge to values of the order of 10−4 to 10−3. However,


Fig. 3. Parity plot of reformate composition. GHSV= 15 000–150 000 h−1 and 600 to 800◦C.

as oxygen, water and fuel get depleted along the bed,the order of magnitude of the reaction rates is signif-icantly reduced and the effectiveness factor increase.Particularly for the partial oxidation reaction the maxi-

Fig. 4. Predicted composition profile along the reformer bed at 15 000 h−1 and 800◦C.

mum value of the effectiveness factor of∼1 is reachedonly at about 0.1% of the catalyst bed starting from∼5 × 10−4 because of the rapid depletion of oxy-gen. The increase in the order of magnitude ofη is


Fig. 5. Predicted effectiveness factors for the different reactions taking place in the reformer.

more gradual for the other reactions considered in thepresent work. It is important to notice that the dimen-sionless axial coordinate inFig. 5 had to be repre-sented in logarithmic scale to be able to capture thedetails and rapid change of the effectiveness factorscalculated near the feed point of the reactor wherethe concentration of reactants is highest. The order ofmagnitude of the estimated effectiveness factors indi-cates that significant improvement in the reactor effi-ciency could be gained by reducing the diffusion pathto the catalyst active sites.

7. Model validation and data regression: highand low temperature water-gas-shift (WGS)

A similar methodology used for validating thekinetic model for the autothermal reformer (ATR)was also used for validating the kinetic model forwater-gas-shift at low and high temperatures.Eqs. (10)and (11) for describing the low and high tempera-ture WGS reaction kinetics were implemented in aFORTRAN-based kinetic subroutine that was cou-pled to the rigorous plug-flow reactor model of AspenPlus®. The approximate methodology described above

for estimating the Thiele modulus and effectivenessfactor was also implemented in this subroutine toaccount for intraparticle mass transfer resistance. Thekinetic model implemented has 3 parameters (kWGS,n andm with p = q = 0 in Eq. (10)), because Keiskiet al. [16,17] show that it gives better accuracy.

Fig. 6 compares the experimental data of CO con-version reported by Keiski et al. at high and low tem-peratures with the CO conversions predicted by themodel implemented in the present work. This figureshows that for the minimum and maximum reactiontemperatures studied by these researchers the kineticmodel agrees fairly well with the experimental data.However, for the intermediate temperature studied thedeviation of the model predictions are larger. Keiskishowed a similar trend with respect to the performanceof his model.

8. Case study: autothermal reformer andshifter integration

Once the autothermal reformer model for process-ing isooctane as a model molecule and the kineticmodel for the water-gas-shift reaction kinetics were


Fig. 6. CO conversion along the shifter reactor used by Keiski and coworkers. CO/H2O = 6.1, GHSV= 3260 h−1. Indicated temperaturescorrespond to the reactor inlet. Symbols correspond to experimental data and lines to model predictions.

validated against experimental data, an integratedmodel of the two types of reactors was implemented.A reformer, a high temperature shifter and low tem-perature shifter were integrated in a single model. AH2O/CO molar ratio of 4 was used at the feed of thehigh temperature shift and no aditional water was su-plied at the inlet of the LTS reactor.Table 5describesthe condition of the different reactors in this case studyusing conditions for the high and low temperatureshifters similar to those reported by Myers et al.[20].

Table 5Conditions used for simulating the integrated reformer and water-gas-shift reactors

ATRSpace velocity (GHSV) h−1 15000Temperature (◦C) 700Molar H2O/C in the feed 1.43Molar O2/C in the feed 0.42Reactor volume (cm3) 0.7

HTSTemperature (◦C) 400Molar H2O/CO in the feed 4

LTSTemperature (◦C) 200Molar H2O/CO in the feed Outlet concentration

from the HTS

Fig. 7 depicts the concentration of CO along thereformer and CO conversion reactors. It can be seenthat using this configuration and operating conditions,the model predicts a reduction in the CO concentra-tion from about 5.5% molar in the reformate to 0.17%molar in the product of the low temperature shifter. Itis important to notice also the chemical equilibriumreached in the second half of the high temperature

Fig. 7. CO profile along autothermal reformer (ATR), high tem-perature shift (HTS) and low temperature shift (LTS) reactorspredicted by the model.


shifter responsible for the plateau in the CO concen-tration. Only the change in operating temperature fromthe HTS to the LTS can reduce the CO concentrationfurther.

9. Conclusions

A pseudo-homogeneous model that includes de-scription of the reaction kinetics and intraparticle masstransfer resistance was developed and validated forautothermal reforming of a liquid hydrocarbon andthe water-gas-shift reaction to be used in the pro-cess of hydrogen production via catalytic reformingof a hydrocarbon-base fuel. For the description of thereformer, the model uses the Langmuir–Hinshelwood–Hougen–Watson formulation as described in the liter-ature for representing most of the reaction network,while for the CO converters the kinetic model is basedin a semi-empirical formulation also previously pub-lished. Kinetic parameters for the reformer reactionnetwork were regressed using experimental data undera wide range of conditions for isooctane autothermalreforming using a Pt-CeO2 catalyst. Kinetic parame-ters for the water-gas-shift model were used as pub-lished in the literature.

The model implemented for describing the perfor-mance of the reformer is able to predict the availableexperimental data for the distribution of H2, CO andCO2 in the reformate with a deviation of about 15%.The effectiveness factors for the different reactions,estimated using a reversible pseudo-first order approx-imation for the more complex kinetics, was of the or-der of 10−4 to 10−3 in the first stages of the reformeradjacent to the reactor feed point. Larger effectivenessfactors were estimated closer to the reactor exit due tothe decrease of the reaction rates when the hydrocar-bon and other reactants are depleted along the cata-lyst bed. These low effectiveness factors encounteredalong the reformer bed despite the small size of thecatalyst used in the present work indicates that signif-icant improvements in the reactor efficiency could beachieved by using structured catalyst like monolithsor other structures with a suitable and sufficiently thincatalytic coating.

The model for describing the water-gas-shift reac-tion was also coupled to an intraparticle mass transferresistance model and validated against published ex-

perimental data. Both the autothermal reforming andwater-gas-shift reactor models were coupled to studyan integrated case including the high and low temper-ature water-gas-shift reactors.

Acknowledgements

The authors thanks PDVSA-Intevep and the US De-partment of Energy for allowing the publication of thepresent contribution.

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kinetic for hts and lts

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