2011 - Mogalicherla and Elbashir - Development of a Kinetic Model for Supercritical Fluids

Published: March 01, 2011

r 2011 American Chemical Society 878 dx.doi.org/10.1021/ef101341m | Energy Fuels 2011, 25, 878889

ARTICLE

pubs.acs.org/EF

Development of a Kinetic Model for Supercritical FluidsFischer-Tropsch SynthesisAswani K. Mogalicherla and Nimir O. Elbashir*

Chemical Engineering Program, Texas A&M University at Qatar, PO Box 23874, Doha, Qatar

ABSTRACT: Kinetic models for Fischer-Tropsch synthesis (FTS) were derived to express the reaction behavior in eitherconventional reaction media (gas-phase) or nonconventional media (near-critical and supercritical solvent media). These modelswe developed from experimental data generated from a commercial alumina supported cobalt catalyst (15% Co/Al2O3) in a xedbed reactor. Two models were developed: the rst one assumes ideal gas phase behavior for the gas phase reaction and uses partialpressures to express reactant and product concentrations in rate expressions while the second model accounts for the nonidealbehavior of the reaction mixture under elevated pressures via the utilization of fugacity parameters and fugacity coecients. Thefugacity coecients were estimated from a modied Redlich-Kwong-Soave equation of state. A comparison was conductedbetween the estimated kinetic parameters from the fugacity-based kinetic model and the partial pressure based kinetic model. Theheat of adsorption of carbonmonoxide and hydrogenwas calculated from the estimated kinetic parameters and an attempt wasmadefor qualitative analysis of mechanistic details of the reaction in both near critical and supercritical FTS and gas-phase FTS. It wasobserved that the fugacity-based models more accurately predict the carbon monoxide consumption rates in the gas phase as well asin near critical and supercritical FTS conditions. Similarly, the fugacity-based model was found to successfully predict the methaneformation rates for both gas phase FTS and the near critical and supercritical phase FTS.

1. INTRODUCTION

Fischer-Tropsch synthesis (FTS) holds great potential forthe production of ultraclean transportation fuels, chemicals, andother hydrocarbon products through the conversion of readilyavailable syngas (CO/H2) from abundant resources (coal,natural gas, and biomass). The conventional FTS reactors havedierent inherent limitations depending on the type of reactorand its congurations; such as controlling reaction selectivities,pore diusional resistance, hot spots formation, catalyst deacti-vation, catalyst separation, etc. Conducting FTS reactions insupercritical uid (SCF) media has been demonstrated to havecertain advantages over the traditional routes.1-12 The advan-tages can be attributed to the use of SCF solvents which oerhigh diusivities (relative to a liquid), high solubilities, andimproved heat transfer properties (relative to a gas). It wasclaimed that the enhancement in the production of heavyhydrocarbons in the supercritical phase FTS relative to theconventional media is a direct eect of the increased solubilityof hydrocarbons in the supercritical solvent media that alsoenhance the in situ extraction of products and secondaryreactions.13,14

The most common commercial FTS catalysts are either iron-based or cobalt-based catalysts, while other catalysts like ruthe-nium and nickel have also been considered but only in lab scalereactors. The industry is currently focusing on cobalt catalystsdue to their high FTS activity, better catalyst stability in hydrogenrich environments, and lower selectivity to oxygenatedcompounds.15,16 The FTS reaction is a surface-catalyzed polym-erization process, whereby adsorbed CO and H2 molecules reacton the surface of a catalyst with adsorbed hydrogen to formmonomers (e.g., CHx based on the widely accepted surfacereaction model) that further react to give a wide spectrum ofcarbon products (C1-C60). Several extensive studies reported

attempts to understand and model the kinetics of the FTSreaction over a number of cobalt-based catalysts. Nevertheless,most of these kinetic models have not covered high pressureoperation as the one required for the supercritical solvent FTSoperation.17-19 Under such high pressure operation, classicalchain-growth models, such as the standard Anderson SchultzFlory (ASF) model, cannot satisfactorily predict the productdistribution of FTS reaction. Similarly, high pressure operationsignicantly inuences the activation and deactivation of FTScatalytic systems.20 Few reports addressed the development ofkinetic models for the FTS reaction under near critical andsupercritical conditions. The power law models were developedby Bochniak and Subramaniam4 and Fan et al.21 to predict thereaction kinetics in near-critical and supercritical FTS conditionsover an iron-based catalyst. In their studies, the major objectivewas to estimate the catalyst eectiveness factor in supercriticalconditions and to compare it to conventional gas phase reactionunder equivalent conditions. Elbashir and Roberts10 reported amechanistic model using the Langmuir-Hinshelwood-Hougen-Watson approach for a cobalt based catalyst. Irankhah et al.22

extended this model to a Co-Ru/Al2O3 catalyst tested undersupercritical conditions. These mechanistic models were devel-oped assuming ideal gas-law behavior and were found to be inreasonable agreement with the experimental data obtainedfrom the conventional gas-phase FTS operation; however, theyfailed to predict the reaction kinetics under near critical andsupercritical operations.10 Despite the agreement on the non-ideality of FTS reaction behavior in near critical and super-critical conditions phase relative to conventional reaction

Received: October 3, 2010Revised: January 22, 2011

879 dx.doi.org/10.1021/ef101341m |Energy Fuels 2011, 25, 878889

Energy & Fuels ARTICLE

media, there is still a need for quantitative assessment of thekinetic model under such conditions. The objective of thepresent study is to investigate the possibility of accounting forthe nonideality of this reaction in supercritical phase viaextending the widely accepted kinetic model for cobalt catalystsin gas-phase FTS to supercritical FTS by accurately represent-ing reactant concentrations. The developed kinetic models forthe FTS reaction in this study have been represented in terms offugacity parameters and fugacity coecients, and they showgood credibility in predicting the reaction behavior over a widerange of operating conditions.

2. KINETIC MODELING

In the present work, a kinetic model was derived based onexperimental data obtained from a commercial cobalt catalyst(15 wt % Co/Al2O3) where testing was conducted in gas phase,near-critical, and supercritical media composed of hexanes in axed-bed reactor. The experimental data on which this model isbased were reported in the work of Elbashir and Roberts11 andElbashir et al.12 The reactor was allowed to run continuouslyuntil steady state performance was achieved, with respect toconversion and selectivity, as determined by product analysisfrom the GC data. For the gas phase FTS, the steady stateperformance has been achieved after approximately 24 h time-on-stream (TOS), while for the supercritical hexanes FTS itrequires around 48 h TOS to reach steady state performance.The average carbon number calculated from experimentallydetermined hydrocarbon product distribution was in the rangeof 9.5-11 for SCF-FTS and 5.0-6.6 for gas phase FTS.According to their report,12 the optimal reactor performancefor FTS reaction under near critical and supercritical solventconditions (will later be referred to as SCF-FTS) was obtainedfor an H2/CO ratio (V) of 2 and hexanes (solvent)/syngas ratio(S) of 3/1. The following experimental conditions have beenselected to develop these kinetic models: temperature range230-250 C (503-523 K), pressure range 35-79 bar, H2/COfeed ratio of 2-1, with supercritical solvent (hexanes)/syngasmolar ratio of 3/1 (i.e., S = 3), and CO ow rate varied from8.1 10-4 to 16.2 10-4 mol/s. For the gas phase reaction, thepartial pressure of syngas was kept constant and argon was usedas inert media to maintain the desired space velocity. Under suchreaction conditions, carbon monoxide conversion was found tovary between 30 and 85%, corresponding to an integral reactorperformance. Few experimental data (four data points) at other

hexane to syngas ratios and H2/CO ratios has also beenconsidered. A total of 14 experimental points were used inestimating parameters for SCF-FTS kinetics, and 9 data pointswere used in estimating parameters for gas phase FTS kinetics.The product distribution obtained at typical operating condi-tions of supercritical phase FTS and gas phase FTS is shown inFigure 1. In order for us to simplify the prediction of the kineticparameters under such nonideal reaction conditions, we devel-oped an approach outlined in Figure 2 that provides a simulta-neous assessment of the inuence of the reaction conditions(temperature, pressure, solvent/syngas ratio, etc.) on the reac-tion kinetics as well as on the phase behavior and the thermo-physical characteristics of the reaction mixture. At the rst stageof the model development, the thermodynamic analysis toaccount for the phase behavior of the SCF-FTS reaction mixturewas carried out separately from the kinetic model. However,during the parameter estimation stages the two models wereintegrated.2.1. Rate Equations and Mathematical Expression for

Reactor Models. Subramaniam and McHugh23 reported thatin supercritical conditions, pressure effects on rate constants aredominant only for pressures more than 99 bar and solute(reactants and products) mole fractions in reaction media lessthan 0.15. In the present work, the maximum operating pressureis 80 bar and the solute mole fraction (syngas mole fraction) isaround 0.25. Elbashir et al.11 have conducted experiments bykeeping the partial pressure of syngas constant and varying thesystem pressure using Argon to maintain constant space velocity.The difference between the two experiments was too small, and itconforms that there was no pressure effect on the observedreaction kinetics in gas phase FTS. In supercritical conditions, thepseudo first-order rate constant obtained from experimentalrates (observed rate of reaction/operating pressure) was invar-iant with the density of the supercritical solvent, indicating thatkinetic constants reported in the present analysis are free ofpressure effects.24 Thus, the pressure effects on rate constantswere neglected and only the effect of thermodynamic nonideal-ities on reaction rates were considered in the proposed kineticmodel. One of the most common assumptions of the kineticmodels for the FTS reaction over cobalt based catalysts is toconsider the hydrogenation of surface carbon as the rate-deter-mining step. Similar assumptions have been used in developingkinetic models for the reaction in near critical and supercriticalconditions, expressing reaction rates in terms of partialpressures.10 Even though the high pressure supercritical reactionmedia is likely to result in thermodynamic nonidealities, most ofthe previous kinetic models for near critical and supercritical FTSmodels have utilized the partial pressure of reactants in their rateexpressions.23 Elbashir and Roberts10 suggested using activitiesrather than partial pressures to more accurately predict kineticsunder supercritical conditions. In the case of insignificant pres-sure effects on reaction rate constants, the rate expression derivedfor gas-phase reactions can directly be extended to supercriticalconditions simply by replacing the partial pressure of reactantsand products with fugacities. This approach was adopted byErmakova et al.25 in kinetic modeling of supercritical FTSreaction on an iron-based catalyst.The model adopted in the present study is based on previous

kinetic models for cobalt-based FTS catalysts.10,17,26 The rateexpressions are derived utilizing the Langmuir-Hinshelwood-Hougen-Watson (LHHW) approach. Considering our experi-mental data that show very low selectivity toward CO2, the rate of

Figure 1. Product distribution at 523 K for dierent pressures in SCF-FTS and gas phase FTS.



oxygen removal by water formation has been equated to the rateof carbon hydrogenation (both are the slowest steps in thereaction). To account for the nonideality of the FTS reaction inthe near-critical and supercritical phase operation (SCF-FTS),the partial pressures in the reaction rate expressions as in thework of Elbashir and Roberts10 have been replaced by thefugacities. The temperature dierence in the catalyst particlewas estimated to be 0.34 K, and by using the Damkohlerequation, we found that the catalyst particles are isothermal,which indicates the absence of hot spot formation.27 Theexternal temperature rise in the bulk reaction phase has beendetermined from (T)bulk = [dP rateobserved (-H)]/(6CPfGjHNPr

-0.67) and was 2.3 K in supercritical phase FTSand 5.2 K for gas-phase FTS.27 These numbers are nearlymatching with the temperature rise reported in the middle ofthe reaction bed on the same experimental set up in anindependent study.28 For this range of temperature gradients,the increase in reaction rate due to temperature rise of the bulkgas phase will be compensated by decrease in concentration atthe catalyst surface, and as a result, we consider our assumptionof isothermal reaction to be appropriate. The presence of theexternal mass transfer from the bulk gas phase to the catalystsurface has also been veried utilizing Mears criterion forexternal diusion. For all the experiments, the dimensionlessnumber (rateobserved Fb dp)/(2kC Cbulk) was found tobe less than 0.1 indicating that the reaction is away from externalmass transfer limitations at the specied conditions. The phy-sical properties of the uids required for above analysis wereadopted from ASPEN Plus2006 and the correlations for heatand mass transfer were taken from standard chemical reactionengineering textbooks.27 Finally, the following assumptionshave been made to develop this kinetic model:(1) At any location inside the reactor cross section, the

product distribution, average carbon number, and hy-drogen usage ratio are assumed to be similar to that atthe reactor outlet.

(2) The reactor is operating under isothermal conditions.(3) Internal and external mass transfer limitations inside the

catalyst bed have been neglected under the speciedreaction conditions.

The mathematical expressions of the rate equations used inthis study are listed in Table 1. The active length of the reactorbed was estimated to be around 2 cm based on a catalyst loadingof 1 g (screened to 100-150 m of particle size) in an HIP high-pressure reactor bed of a conventional downow xed-bedstainless steel reactor (1.27 cm 25.4 cm; eective volume:32 cm3). The bed porosity was calculated from the availablecorrelations to be around 0.32 based on catalyst particle size andreactor diameter, assuming that the catalyst particles haveirregular shapes.2.2. Estimation of the Fugacity of Carbon Monoxide

and Hydrogen under Typical Fischer-Tropsch SynthesisOperation. In the present study, the fugacity of the FTS reactionmixture has been evaluated using the modified Soave-Redlich-Kwong EOS and the mixing rules proposed by Yermakova andAnikeev.29 The primary reason for choosing the SRK EOS in thisanalysis is the ability of SRK EOS in predicting the phasebehavior of FTS reaction mixture which has been well-demon-strated in the literature.25,29,30 Water is one of the major FTSproducts; the amount of water present in the reaction mixture isrelatively small compared to amounts of hydrocarbon solventpresent in the system. The advantages of the Peng-RobinsonEOS over SRK EOS have been demonstrated only for CO2- orwater-rich supercritical reaction systems.31,32 However in nearcritical and supercritical FTS, the reaction mixture is rich inhydrocarbon solvent(hexane) where the SRK EOS accuratelyrepresents phase behavior. The fugacity parameters and fugacitycoefficients for this model represent all components in the FTSreaction mixture including reactants (CO and H2) and typicalproducts (olefins (C2-C22), paraffins (C1-C25), water) inaddition to the solvent in SCF-FTS that has been representedby hexanes (C6 mixture). Figure 3 shows the outline and theequations used to estimate the fugacities of the aforementionedcompounds.29 The constants Kij and Cij in the above procedureare binary interaction parameters, which are normally estimatedfrom thermodynamic experimental data. In general, these inter-action parameter values are too small having an order ofmagnitude 10-2 and are considered as zero in the vapor-liquidequilibrium (VLE) estimation, except in few cases such as for thehydrogen-hydrocarbon mixtures. Nevertheless, in the present

Figure 2. Schematic of the approach to develop a kinetic model for FTS in near critical and supercritical reaction media.



work binary interaction parameters were set to zero due to a lackof experimental VLE data under the specified reactionconditions.2.3. Parameter Estimation. The equation for CO conversion

was integrated with respect to reactor length using an ordinarydifferential equation solver in MATLAB (ODE45). The fugacitycoefficients were determined in terms of CO conversion, hex-ane/syngas ratio, H2/CO ratio, temperature, and pressure sepa-rately and then incorporated to be part of ODE45. The kineticparameters were optimized by least-squares regression analysis.The Maltlab function called lsqnonlin which uses the Leven-berg-Marquardt algorithmwas used for the optimization of theobjective function. For getting an initial guess of the parametersduring isothermal parameter estimation, an objective function(showed below) was minimized using the genetic algorithmfunction in MATLAB (minimization and fitness function of

MATLAB, uses genetic algorithm). This objective function wasdefined as (all_points_i(Xexpt,i-Xmodel,i)2) where Xexp representsthe experimentally determinedCO conversion or CH4 selectivityand Xmodel represents the corresponding values determined bythe model. A similar optimization technique was applied toestimate the kinetic parameters for CO conversion rates andCH4 formation rates. In the earlier studies on the same kineticmodel, the temperature sensitivity of kinetic parameters was notaccounted and they were assumed as constants.10,22 As outlinedin Figure 2, the parameter estimation was conducted for reactionconditions at two temperatures 513 and 523 K and at specifiedreaction conditions (e.g., pressure, hexane (SCF) to syngas ratio(S), H2/CO ratio (V), and CO flow rate). The physicalsignificance and the temperature sensitivity of the estimatedparameters were examined. It has been widely accepted that thekinetic parameters are sensitive to the reaction temperature andfollow the Arrhenius law in temperature dependence. As de-scribed in Figure 2, parameter estimation has been conducted attwo levels. At the initial level, parameters were estimated for eachtemperature. At that stage, the total number of parametersestimated was four in CO conversion kinetics and the totalnumber of parameters in CH4 yield models was three. In the nextlevel, Arrhenius law was incorporated into the parameters toevaluate the temperature sensitivity model. The pre-exponentialfactor and activation energy for each kinetic parameter wasevaluated in the second level. Therefore, the number of para-meters estimated in the second level of the CO conversion modelis eight (4 2). Similarly, the total number of parameters in themethane yield model is six (3 2). The nonlinearity of the rateexpression drastically increased after incorporating Arrheniusexpressions in the reaction rates equation. As a result, theparameter estimation process becomes less accurate and moredifficult due to the strong correlation between the pre-exponen-tial factor and activation energy. Froment33 suggested incorpor-ating the reparameterization at mean temperatures in kineticmodeling to resolve this issue. In the present case, 513 K wasconsidered as the average temperature to estimate the para-meters for the CO consumption rate while 523 K has been

Table 1. Rate Equations, Fugacity Coecients, and Reactor Model Equationsa

CO consumption rate (mol/gcat 3min) rCO KfCO1=2 fH2

1=2

1 K1 fH2 1=2 K2 fCO1=2 K3 fCO 2

CH4 formation rate (mol/gcat 3min) rCH4 1 fH221 3 fCO1=2 fH2 - 1=21=2 - 1 - 1 1

fugacity coecient () and fugacity of CO and H2 H2 fH2YH2 P; CO fCOYCOP

fCO 1 - XCODNMNA PCO; fH2 V -

2N M2N

XCO

DNMNA PH2

whereDNMNA : 1 V S SV - 2N M=2NXCO XCO=N

where DNMA refers to the denominator of the fugacity term of CO

isothermal plug ow reactor models for CO conversion and CH4 yielddXCOdH rCOFcat1 - bAcrFCOdXCH4dH

rCH4Fcat1- bAcrFCO

aWhere V is H2 to CO feed ratio; S is the hexane to syngas feed ratio; XCO is conversion of carbon monoxide at any catalyst bed cross section; XCH4 ismethane yield;H is the catalyst bed height; FCO is inlet molar ow rate (mol/min) of CO;Acr is the reactor cross section; b is the bed porosity; Fcat is thecatalyst particle density; P is the total pressure;i is the fugacity coecient; Yi is the mole fraction of the ith compound in the reaction mixture; k,K1,K2,K3, 1, 2, 3 are the kinetic parameters; at H = 0, XCO = 0 and XCH4 = 0.

Figure 3. Equations used for fugacity estimation.



chosen for the CH4 formation rate expression, i.e.

KT K@513=K@513KT K@513 exp- E=R1=T- 1=51313

KiT Ki@513=Ki@513KiT Ki@513 exp-Hi=R1=T - 1=513 14

similarly iT i@513 exp- ei=R1=T - 1=523 and i 1- 3 15where E is the activation energy of FTS, Hi is the heat ofadsorption, and ei the activation energy for parameters in themethane yield model.

3. RESULTS AND DISCUSSIONS

3.1. Fugacity of H2 and CO. As shown in Figure 3, there arethree roots for the compressibility factor Z while solving thefugacity using the modified RKS EOS. A similar approach hasbeen adopted by Masuku et al.34 for estimating the chain growthprobability in FTS. In reality, phase splitting or condensationinside catalyst pores takes place whenever a sufficient amount oflong chain hydrocarbons are present. The reaction conditionsused for this study are supposed to yield a single phase for theSCF-FTS according experimental measurements of the phasebehavior and the visualization of the critical properties for atypical reactionmixture in a variable-volume-view-cell in previous

Figure 4. Partial pressures vs fugacity along the reactor length at 523 K and 79 bar (a) for carbon monoxide and (b) hydrogen.



reports.11 On the other hand, our findings showed a maximumchain growth probability of 0.70 for the gas-phase FTS and 0.85 forthe SCF-FTS (which is in agreement with the data of Biquizaet al.35). In a typical integral reactor both the conversion and thechain growth probability increase axially from the inlet to the outletof the reactor bed resulting in a great possibility of single phaseoperation over a large fraction of the reaction bed. As a result, wesimplified our calculations by assuming a single phase for thereaction mixture under the specified conditions. Thus, the largestreal root for Z has been selected. It was observed that Z is sensitiveto CO conversion as well as to the hydrocarbon product distribu-tion from the synthesis reaction. The calculated values of Z werefound to vary from0.9 to 1.7 as a function of the reaction conditions.Our ndings show that under typical SCF-FTS operating

conditions (e.g., 250 C and 79 bar for hexane/syngas ratio of3 and H2/CO feed ratio of 2), the partial pressure of CO and H2dropped from 6.6 to 1.1 bar and 13.2 to 1.8 bar, respectively. Thefugacity estimated in the present work is not only sensitive toreactants concentrations but also to the product distribution.The variation of partial pressure and fugacity along the reactorlength is shown in Figure 4. It can be observed from Figure 4 thatthere is a dierence between the partial pressure of carbonmonoxide and hydrogen and the respective calculated fugacityparameters. The variation of fugacity coecients with reactantpartial pressures in the reactor is shown in Figure 5. As shown inFigure 4, the dierence between the partial pressure and thecalculated fugacity parameters is more signicant at the reactorinlet (high CO and H2 partial pressures); however, Figure 5shows lower fugacity coecients at the reactor outlet (low COand H2 concentrations). The decrease in the fugacity coecientindicates an increase in the nonideal behavior of the FTS reactionmixture as CO and H2 conversion increases. These ndings alsoshow that the products forming during the FTS reaction havegreat impact on the concentration of reactants on the catalystsurface. For a similar process, Zimmerman and Bukur36 lumpedthe whole product distribution prole into propylene andcalculated the fugacity coecients as 1( 0.05. A similar attemptwas made in this study to investigate the eect of lumpinghydrocarbon products from FTS into single compound (e.g., C5paran). In that case, a marginal decrease in fugacity coecientwas observed. As a result, a typical hydrocarbon product dis-tribution was used to estimate the fugacities and the fugacitycoecients in the supercritical FTS media. The sensitivityanalysis of estimated fugacities has been conducted by using

binary interaction parameters reported by Biquiza et al.35 wherethe interaction parameters for CO, H2, and hexane with hydro-carbon compounds were expressed in terms of carbon number.As shown in Figure 5, the fugacities of CO and H2 weremarginally inuenced with the binary interaction parameters.Therefore, further studies were conducted without binary inter-action parameters.3.2. Parameter Estimation for Rate of CO Consumption.

Even though the kinetic model used in the present study has beenwidely accepted in literature, the temperature sensitivity of thekinetic parameters has not been taken into consideration.17,22 Toinvestigate the significance of temperature sensitivity, our modelparameter estimation was conducted at two different tempera-tures (513, 523 K). These temperatures have been selected basedon the previous assessment of the optimum operating conditionsfor the SCF-FTS.11,12 The estimated kinetic parameters of theisothermal conditions are shown in Table 2 for two temperaturesunder typical experimental conditions within the near critical andsupercritical region .11

As shown in Table 2, the model parameters are sensitive totemperature, since the kinetic constant K increases with tem-perature while the adsorption constants K1 and K3 decrease withtemperature. Nevertheless, the term K2 was found to increasewith the temperature. K2 is a function of the rate constants ofOH* radical formation (kO1) and CH* radical formation (kC1).

10

The parameter K2 can also expressed as follows17,10

K2 KCkcf

p 1=

kcf

p

where KC is the dissociative adsorption equilibrium constant forCO and kcf is (kO1/kC1).The parameter K2 is sensitive to the temperature and it

depends on the heat of dissociative adsorption of CO andactivation energies of the reactions that form OH* and CH*.For nonisothermal conditions, the initial guess values for activa-tion energy for the parameters were calculated from parametersestimated at 513 and 523 K.

Figure 5. Partial pressure vs fugacity coecient along the reactor lengthat 523 K and 79 bar for carbon monoxide and hydrogen.

Table 2. Isothermal Parameter Estimation for near Criticaland Supercritical Conditions

temperature, K

K 104 (mol/gcat 3min 3 bar)

K1 102(1/bar0.5)

K2 102(1/bar0.5)

K3 104(1/bar)

523 6( 0.5 12( 2 50( 4 1( 0.3513 3.5( 0.65 17( 3 27( 3 2( 0.8

Table 3. Final Estimates of the Kinetic Parameters forSupercritical FTS

parameter

fugacity based

model

partial pressure

based model

K@513 (mol/gcat 3min 3 bar) (4 ( 0.5) 10-4 (3.5 ( 0.7) 10-4K1@513 (1/bar

0.5) (16.9 ( 1.1) 10-2 (15.0 ( 1.6) 10-2K2@513 (1/bar

0.5) (20.0 ( 1.2) 10-2 (17.1 ( 1.1) 10-2K3@513 (1/bar) (2 ( 0.4) 10-4 (1.5 ( 0.2) 10-4E (kJ/mol) 103.9 ( 2.6 91 ( 4.4H1 (kJ/mol) -50.1 ( 3 -74 ( 11.1H2 (kJ/mol) 149.5 ( 5.5 151 ( 7.1H3 (kJ/mol) -99.7 ( 11.1 -107 ( 6.2R2 (SSreg) 0.92 0.80



A similar approach was applied in the estimation of the kineticparameters using the reactants partial pressures instead offugacities in developing the kinetic model. The nal estimatesfor the values of the parameters for both fugacity based andpartial pressure based kinetic models and parameter 95% con-dence intervals are shown in Table 3. All condence limit valuesare much smaller than the parameter mean values indicating thatregression analysis is meaningful. The estimated CO conversionsand experimentally determined CO conversion at dierentpressures and temperatures are plotted together in Figure 6.Under testing conditions in SCF-FTS, our ndings show that thefugacity-based kinetic model has better represented the reactionperformance. A common approach to check the sensitivity of thedetermined parameters is to conduct an F-test to discriminate thekinetic model. In the present work, the F-test was conducted onboth the fugacity-based model and partial pressure-based modeland both passed that test. The F-value of the fugacity-basedmodel was found to be 1.6 while that of the partial pressure-basedmodel was found to be 2.9, both are less than the critical F-valueof 4.6. This nding is a positive sign indicating that the regressionis statistically meaningful.37 For given experimental conditions,the maximum variation in these experimental conversions waswithin 3% of the mean values reported; however the fugacitymodel and partial pressure model dier by a minimum of 2% to a

maximum of 14% indicating that the dierence between partialpressure model and fugacity model is not due to experimentaluncertainties. The goodness of t was also examined in terms ofthe linear regression coecient R2 to compare experimental dataand model predicted values of CO conversion. The data listed inTable 3 prove that the fugacity-based model statistically betterrepresents SCF-FTS with a higher R2 value and lower F-valuethan the partial pressure model. We conducted a simple analysisthat a 20% change the in initial guess value showed a maximum5% change in the estimated value for both the gas phase FTS andSCF-FTS, which will not have much impact on the nalcomparisons made in this study.Also, as shown in Table 3, there is an appreciated dierence

between the parameters estimated from the fugacity based modeland those from the partial pressure based model. The activa-tion energy from the fugacity based model was found to be 103.9kJ/mol whereas that from the partial pressure model was foundto be 91 kJ/mol. These values agree well with previously reportedvalues.38 The apparent activation energy calculated from experi-mental data collected at dierent temperatures from -R[(dln(rate))/(d(1/T))] was found to be 110 kJ/mol, which is nearlymatching the activation energy obtained from the fugacity-basedmodel. The heat of adsorption of H2 and CO over the cobaltbased catalyst was calculated from the kinetic parameters

Figure 6. Comparison between experimental values of CO conversions and the estimated values by the fugacity based model and the partial pressurebased model in SCF-FTS as function of (a) temperature at P = 65 bar, S = 3, and V = 2 and (b) pressure at T = 523 K, S = 3, and V = 2.



obtained from the fugacity based model. The heat of adsorptionof hydrogen on the cobalt catalyst is calculated as 2(-H1) 116.2 kJ/mol using the basic mechanism of the reaction wherebyK1=

KH. Zowtiak and Bartholomew

39 have reported that theadsorption of hydrogen on the cobalt catalyst is an activatedadsorption process whereby the extent of adsorption is a functionof the type of catalyst support and metal loading. The heat ofadsorption of hydrogen calculated in the present work agreedwith the reported values of Zowtiak and Bartholomew39 for a 10wt % Co/Al2O3 (105 kJ/mol) and Vannice

40 for the 2 wt % Co/Al2O3 (80 KJ/mol). Other important kinetic parameters areK3 =KCO whereby KCO is the equilibrium adsorption coecient forcarbon monoxide and H3 which represents the heat of adsorp-tion of carbon monoxide. In the present work, H3 wascalculated as 99.7 kJ/mol. Vannice40 reported the heat of adsorp-tion of CO on 2 wt % Co/Al2O3 to be around 185 kJ/mol. Theheat of adsorption of CO calculated from kinetic parametersreported by Yates and Sattereld41 was found to be around70 kJ/mol. van Der Laan and Beenackers42 reviewed the heat ofadsorption of CO and H2 on VIII metal catalysts during the FTSreaction. They concluded that the variations in the reported valuesof the heat of adsorption of CO during FTS may be attributed tothe dierence in the reaction conditions or metal loading of thecatalyst.Similarly, the kinetic parameters for the gas phase FTS

conditions and parameter 95% condence intervals have beenestimated following the same aforementioned process as shownin Table 4. The comparison between the estimated CO

conversions and the experimentally determined values for thegas phase FTS at 20 bar and dierent reaction temperatures areplotted in Figure 7. Both the fugacity and partial pressure basedmodels predicted fairly well the gas-phase FTS reaction perfor-mance. The F-value of the fugacity based model was found to bearound 1.05 while for the partial pressure based model it wasfound to be around 1.1, both being less than the critical F-valueof 3.6. The regression coecients R2 between experimentaland model predictions of CO conversions for both the fugacityand partial pressure based models were also found to beidentical.The parameters for gas-phase FTS kinetics dier from those

under SCF-FTS conditions. The apparent activation energyestimated from the kinetic parameters of the gas-phase reactionwas found to be 75 kJ/mol; however, for SCF-FTS, the activationenergy was found to be around 103.9 kJ/mol. The loweractivation energy in the gas-phase reaction could be attributedto the diusion limitations inside the catalyst pores. Uner26 andKellner and Bell43 mentioned that the decrease in hydrogenadsorption equilibrium constant results in a decrease of themethane formation rates and increase of the chain growthprobability. Our ndings show that the hydrogen adsorptioncoecient (K1) value obtained from gas-phase FTS data is higherthan the value obtained from the near critical and supercriticalphase FTS data. These results could also explain the highmethane selectivity and low chain growth probability obtainedfor gas-phase FTS compared to SCF-FTS. On the other hand,the adsorption equilibrium constant and heat of adsorption ofCO in gas-phase conditions are lower than the values obtainedfrom near critical and supercritical reaction generated dataindicating strong CO adsorption on active sites in near criticaland supercritical conditions compared to gas-phase conditions.As shown in Table 4, the magnitude of kinetic parameter K2@513is less in the gas-phase reaction conditions compared to SCF-FTS. As reported earlier a smaller value of K2 can be due to thelower magnitude of either kcf or KC. The lower kcf in gas-phaseFTS can occur when the rate constants for OH* radical formationis smaller than the rate constant for CH* radical formation. Thisnormally results in lower water formation rates in gas-phase FTScompared to SCF-FTS, and it is in agreement with previousreports in this eld.6 For the case of high KC, the dissociativeadsorption of CO is more rapid and produces more surfacecarbon and the strong carbon-metal bond leads to productionof heavier hydrocarbons. Therefore, the smaller value of K2 ingas-phase conditions can also be due to the smaller KC i.e. theslow rate of dissociative adsorption of CO in gas-phase FTSconditions compared to that in SCF-FTS. The aforementionedndings of the kinetic models are in excellent agreement with

Table 4. Final Estimates of the Kinetic Parameters of Gas-Phase FTS

parameter

fugacity based

model

partial pressure

based model

K@513 (mol/gcat 3min 3 bar) (3 ( 1.1) 10-4 (2.9 ( 1.2) 10-4K1@513 (1/bar

0.5) (24 ( 3.1) 10-2 (23.3 ( 2.6) 10-2K2@513 (1/bar

0.5) (16 ( 2.1) 10-2 (16.5 ( 2.6) 10-2K3@513 (1/bar) (1 ( 0.25) 10-4 (1.1 ( 0.1) 10-4E (kJ/mol) 74.5 ( 11.1 81 ( 5.6H1 (kJ/mol) -58.8 ( 4.3 -52 ( 7.1H2 (kJ/mol) 141.4 ( 9.3 155.1 ( 5.8H3 (kJ/mol) -74.8 ( 5.7 -80.1 ( 3.2R2 (SSreg) 0.85 0.84

Figure 7. Comparison of experimental and estimated CO conversionsin gas-phase FTS at P = 20 bar, S = 0, V = 2.

Table 5. Estimated Kinetic Parameters for CH4 Formation innear Critical and Supercritical FTS and in Gas-Phase FTSReaction

parameter supercritical phase reaction gas-phase reaction

1@523 0.105 ( 0.06 0.145 ( 0.092@523 139.86 ( 11.1 96.5 ( 16.23@523 0.073 ( 0.012 0.048 ( 0.021e1 (kJ/mol) 16.27 ( 2.1 10.3 ( 1.1e2 (kJ/mol) 129.2 ( 12.4 110.24 ( 7.8e3 (kJ/mol) -12.05 ( 1.6 2.58 ( 0.87R2 0.94 0.98



the experimental data in SCF-FTS (e.g., as discussed in refs 11and 12).In general, our ndings suggest that the fugacity-based kinetic

model resolves conceptual hurdles in kinetic parameter estima-tions for nonideal conditions such as these in SCF-FTS or highpressure gas-phase FTS. As a result, this concept has beenextended to develop a fugacity-based kinetic model for theestimation of the kinetics parameters for the methaneformation rate.3.3. Parameter Estimation for Methane Formation Rates.

Methane formation is the most anomalous reaction in the set ofreactions that take place during FTS. In several studies aremarkable decrease in CH4 selectivity was found under SCF-FTS conditions compared to that under gas-phase conditionsunder a wide range of reaction conditions and on differentcatalsysts13 (and references therein). These results have been

attributed to the improved heat transfer in the reaction zone ofSCF-FTS, resulting from the higher density facilitated by thepresence of the supercritical solvent. The parameters for thefugacity-based model and parameter 95% confidence intervalswere evaluated from the experimental data obtained from bothgas-phase and SCF-FTS conditions as listed in Table 5. As shownin Figures 8 and 9, the fugacity-based model predicts fairly wellthe rate of CH4 formation in both SCF-FTS and gas-phase FTS.The activation energies and kinetic parameters in gas phase FTSwere found to be different from those of the SCF-FTS. Also, theactivation energy ofmethane formationwas found to be significantlylower than the activation energy of carbon monoxide consumption,which indicates that methane formation rate is much faster than theCHX radical formation under the reaction conditions.As shown in the Table 5, the higher activation energy for

methane formation (e1) and the lower value of kinetic constant

Figure 8. Comparing experimental and estimated CH4 yield in SCF-FTS as a function of (a) temperature at P = 65 bar, S = 3, andV = 2 and (b) pressureat T = 523 K, S = 3, and V = 2.



1@523 for SCF-FTS indicates that the reactants need moreenergy for methane formation compared to that required for thegas-phase FTS conditions. As reported in an earlier study,102 isdirectly proportional to 1/Kt where Kt is the rate constant for thechain termination reaction. The high value of 2 indicates lowchain termination rate in near SCF-FTS relative to gas-phaseFTS. Therefore, the chain growth probability in the SCF-FTS isfound to be higher than that of gas-phase FTS under relativelyidentical conditions.One of the major advantages of using supercritical uids in

FTS is to enhance the in situ extraction of heavy hydrocarbonsfrom the catalyst pores to free the active sites as well as to providemore vacant sites for the readsorption of primary products.13 Thefraction of vacant active sties during FTS is equivalent to(1/[1 K1(fH2)1/2 K2(fCO)1/2 K3fCO]2) as stated in thedeveloped kinetic model.10 Our ndings showed that at 513 Kand 20 bar syngas partial pressure, the fraction of vacant sites inSCF-FTS is around 0.22; whereas for gas-phase FTS, it is around0.19. This dierence in the number of vacant sites could also beattributed to the nonidealities as accounted for by the fugacitycoecient as well as to the transport properties in the SCFmedia.The active site occupancy by any oligmer (building block)strongly depends on the concentration of the respective com-pounds at the active metal surface at the micro level. Thesupercritical uid reduces the concentration of heavy hydrocar-bon at micro levels due to its superior extraction capability. Itincreases the desorption rate of heavy compounds from theactive site which is a molecular level phenomena. The primaryhydrocarbons desorbed from the active site can either readsorbon the same active site or another vacant site (such a scenario hasbeen assumed in several kinetics model to describe nonideal ASFproduct distribution).13 Our qualitative conclusion is that pri-mary products have more chances to readsorb in SCF-FTScompared to gas phase FTS.11 It has to be mentioned here thatthe advantages of SCF-FTS arise from several reasons such asimproved heat and mass transfer. Along with them, having morevacant sites is also another favored condition for obtainingheavier hydrocarbons in SCF-FTS.In the present work, both the partial pressure based kinetic

model and the fugacity based kinetic model assume that the FTSreaction mixture exists as a single phase in the reactor; however,in actual conditions the reaction mixture exists as vapor/liquid,

and as a result, there is a great possibility for phase splitting after acertain conversion inside the reactor bed.29 Despite the useful-ness of thermodynamics simulation models, which have beenutilized in this study, there is still a need for the experimentalmeasurements of the SCF-FTS phase behavior for better under-standing and prediction of the reaction behavior in near criticaland supercritical conditions.

4. CONCLUSION

The focus of this study is to develop a kinetic model to predictthe reaction behavior of FTS under nonideal conditions repre-sented by elevated pressures in conventional gas-phase FTS orcoupled with the presence of a solvent in near critical andsupercritical phase FTS conditions. In a previous study,10 wesuggested considering thermodynamic nonideality to betterrepresent the concentration of molecules of interest at the highpressure operating conditions as well as to include solvent eectson individual rate constants in the critical region and particularlyfor the initiation steps. At that stage, we were able to provide aqualitative description to the enhanced behavior of the reaction(both on activity and selectivity) in the near critical and super-critical FTS relative to the gas-phase FTS under comparableoperating conditions (described in ref 11). The ndings of thedeveloped fugacity based kinetic model correlate well with thepreviously proposed reaction pathway that assumes an increasedavailability of active sites in the supercritical medium thatpromote both the adsorption of the reactant molecules (COand H2) and possible incorporation of primary products (e.g., R-olens) into the chain growth process.11 In other words, operat-ing the FTS reaction in the near critical and supercritical FTSconditions provides more active sites on the catalyst surface withhigher coverage of active carbon than the regular ones; these siteswere assumed to suppress methane formation.

Our rst attempt to account for the nonideality of FTSreaction at high pressure gas-phase operation and in near criticaland supercritical conditions started with the development of afugacity based kinetic model. The calculated kinetic parametersfor this model and its ability to predict the reaction behavior inthe near critical and supercritical FTS have been compared tothose obtained from conventional partial pressure based kineticmodel. Activation energies for a few elementary steps and heat ofadsorption for hydrogen and carbon monoxide were calculatedfrom the estimated kinetic parameters. Our ndings showed thatthe fugacity-based models more accurately predict CO consump-tion rates under a variety of conditions compared to the predic-tions from the gas-phase FTS. On the other hand, the calculatedvalues of the hydrogen surface coverage, CHx monomer termi-nation rate, and methane formation rates in the gas-phase FTSwere found to be higher than those obtained in SCF-FTS underequivalent reaction conditions. The fugacity-based model alsoallows us to calculate the fraction of vacant sites and the rate ofCO dissociative adsorption in both cases and showed highervalues in SCF-FTS. Unlike the partial pressure model,10 thefugacity based model also successfully predicts methane forma-tion rates in both gas-phase and near critical and SCF-FTS in avariety of reaction conditions. Currently, the fugacity basedkinetic model is being extended to predict the hydrocar-bon product distribution in the nonideal reaction mixture ofSCF-FTS.44

Figure 9. Comparison of experimental and estimated CH4 yield in gas-phase FTS at P = 20 bar, S = 0, V = 2.



AUTHOR INFORMATION

Corresponding Author*E-mail: [email protected].

ACKNOWLEDGMENT

The authors would like to acknowledge the nancial supportof this work by Qatar National Research Funding under grant(NPRP 08-261-2-082). The authors would also like to acknowl-edge the invaluable discussion with Professor Dragomir Bukurabout this study.

NOMENCLATUREAcr = reactor cross section (cm

2)aii = mixing parameteram = mixing parameterbii = mixing parameterbm = mixing parameterCPf = specic heat capacity of uid (cal/mol 3K)dp = catalyst particle diameter (cm)E = activation energy (kJ/mol)ei = enthalpy (kJ/mol)fCO = fugacity of CO (bar)fH2 = fugacity of hydrogen (bar)FCO = CO feed rate (mol/min)G = mass ow rate (g/cm2 3 s)H = catalyst bed height (cm)jH = j factor for heat transferK = rate constant in LHHW model for rate of CO conversion

(mol/gcat 3min 3 bar)K1, K2, K3 = constants in LHHW model for rate of CO

conversion (1/bar0.5, 1/bar0.5, 1/bar)kC = external mass transfer coecient (cm/s)KC = CO dissociative adsorption constant (1/bar)kC1 = rate constants of CH* radical formation (1/s)Kcf = adsorption equilibrium constant for carbonKi@513 = constant in LHHWmodel for rate of CO conversion at

513 K (1/bar0.5)kO1 = rate constants of OH* radical formation (1/s)Kt = rate constant for chain termination reaction (1/s)M = average hydrogen atoms in the Fischer-Tropsch productsmi = mixing parameterN = average carbon numberNPr = Prandtl numberP = total pressure (bar)PCi = critical pressure of the ith component of the reaction

mixtureR = universal gas constant (J/mol)S = hexane to syngas feed ratioT = reactor temperature (K)TCi = critical temperature of the ith component of the reaction

mixtureV = H2 to CO feed ratioVm = molar volume (cc)XCH4 = methane yieldXCO = conversion of carbon monoxidexi = mole fractionYCO = mole fraction of COYH2 = mole fraction of H2Z = compressibility factor-H = heat of reaction (cal/mol of CO)

H1 = heat of adsorption (kJ/mol)H2 = heat of adsorption (kJ/mol)H3 = heat of adsorption (kJ/mol)Ri = mixing parameteri = mixing parameteri = mixing parameterb = bed porosityFcat = catalyst density (g/cm3)i = fugacity coecient for the ith compound1 = constant in model for rate methane formation2 = constant in model for rate methane formation3 = constant in model for rate methane formation, (mol/

gcat 3min 3 bar)i = acentric factor for the ith component of the reaction

mixture

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2011 - Mogalicherla and Elbashir - Development of a Kinetic Model for Supercritical Fluids

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