Modeling Catalytic Partial Oxidation of Methane to Syngas in Short

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Modeling Catalytic Partial Oxidation of Methane to Syngas in Short-Contact-Time Packed-Bed Reactors R. C. Ramaswamy, P. A. Ramachandran,* and M. P. Dudukovic Department of Chemical Engineering, Washington UniVersity in St. Louis, One Brookings DriVe, St. Louis, Missouri 63130

The catalytic partial oxidation of methane to syngas presents interesting challenges, because of the interaction of exothermic combustion and endothermic reforming reactions. The heterogeneous plug-flow and axialdispersion models are used to analyze the steady-state and dynamic behavior exhibited by this process in a short-contact-time packed-bed reactor. The effects of inlet mass velocity and feed quality on the product yield and hot spots are analyzed. The role of coupling exothermic and endothermic reactions on the magnitude of the temperature peak in the reactor has been studied for different methane-to-oxygen and the methaneto-steam ratios in the feed. The effects of film-transfer coefficients and axial-dispersion coefficients on the steady-state profiles are also discussed. The evidence of wrong-way behavior, because of the response to the perturbation of the inlet temperature and the feed quality, in this short-contact-time reactor is presented. 1. Introduction Syngas is an important feedstock for the production of synthetic automotive fuels (synfuels) and for a variety of chemicals, such as methanol and its derivatives. Syngas is produced from a wide range of hydrocarbons, such as natural gas (mostly methane), naphtha, and coal, by the following methods, depending on its end use:1-4 (i) steam reforming (SR), (ii) autothermal reforming, (iii) noncatalytic partial oxidation with oxygen or air, (iv) catalytic partial oxidation (CPO) with oxygen or air, and (v) combined reforming. Recently, there have been several research activities that have focused on generating synthesis gas via one or other forms of carbon dioxide reforming5-7 (as a way to treat greenhouse gases) (e.g., CO2 reforming (with methane; endothermic), combined CO2 and steam reforming (endothermic), or tri-reforming of methane (CO2 reforming, steam reforming, and partial oxidation of methane; autothermal/exothermic). One should note that the production of synfuels and the chemicals from natural gas and coal, through the syngas route, can reduce the consumption of crude oil and provides an opportunity to utilize stranded resources (stranded natural gas). The petroleum industry is also showing interest in such processes, and several oil companies (such as Shell) are building plants in Qatar, in the Middle East, to be commissioned in the second part of this decade, to convert natural gas to Fischer-Tropsch liquids (fuels).8 The research on the conversion of methane to synthesis gas by the catalytic partial oxidation has recently gained momentum (in the past 10-15 years), because of the availability of pollutant-free natural gas and the ability of this process to produce a CO/H2 ratio of 0.5, which is required for downstream processes such as methanol synthesis. Syngas production via the catalytic partial oxidation route proceeds through the coupled exothermic combustion reaction(s) and the endothermic reforming reactions, in the same catalyst bed. The simultaneous occurrence of combustion and reforming reactions makes this route more attractive, because it minimizes the energy requirement for the production of syngas, compared to the steam reforming route. A brief summary of this process is provided in the following paragraphs. * To whom correspondence should be addressed. Tel.: 314-9356531. Fax: 314-935-7211. E-mail address: [email protected].

Several experimental studies of the catalytic partial oxidation of methane to syngas, at atmospheric pressure, in fixed beds, honeycomb monoliths, and fluidized beds are available in the literature.1 The mean residence times in these reactors are generally on the order of seconds. Chaudhary et al.9 and Schmidt’s group10-14 have studied the production of syngas in a millisecond-contact-time packed-bed reactor and monolith reactor, respectively, under atmospheric conditions. The production of syngas at higher operating pressure is attractive to industry, because of the ease of integration with the downstream processes and larger volumetric reactor productivity. However, only limited experimental work is available at higher operating pressure in the open literature.15-17 However, note that, at higher pressure, the conversion of methane is limited by the thermodynamic equilibrium, and the homogeneous gas-phase reactions also occur with the heterogeneous reactions.18,19 The mechanism of methane conversion to syngas, via the partial oxidation process, is still debated in the literature. Although the possibility of performing the reaction via the direct route (in one step, from methane to syngas) has been reported by several researchers, there seems to be an increasing consensus that (for most of the catalysts and the operating conditions studied) the reaction occurs mainly via the indirect route (total combustion, followed by reforming reactions).6,20 Note that the hot spot could be eliminated if the reaction occurs via the direct route (low exothermicity). There is also a debate on the occurrence of carbon dioxide reforming (which also deposits carbon on the catalyst) in the partial oxidation process. Although there is evidence that such reactions may not be important for Rh systems, it is generally agreed that these reactions will become important at higher temperature (especially in the indirect route of syngas generation) and for other catalyst systems. It is the work of Schmidt’s group10-14 that recently renewed the interest in the partial oxidation process. They11 reported that, with highly active Rh-based catalysts, the entire process could be completed in a short contact time (on the order of milliseconds) with higher syngas selectivity and the reactors used for this process are called short-contact-time reactors. However, the interactions of exothermic and endothermic reactions coupled to shorter flow time in the reactor have made this process very complex and, hence, a suitable mathematical

10.1021/ie070084l CCC: $37.00 © 2007 American Chemical Society Published on Web 08/15/2007

Ind. Eng. Chem. Res., Vol. 46, No. 25, 2007 8639 Table 1. Pre-exponential Factors for Reaction Rates, Heats of Adsorption, and Activation Energies Pre-exponential factor constant

A(kk)

k1a (kmol/(kgcat bar2 h)) k1b (kmol/(kgcat bar2 h)) k2 (kmol bar0.5/(kgcat h)) k3 (kmol bar0.5/(kgcat h)) k4 (kmol/(kgcat bar h))

2.92 × 106 2.46 × 106 4.225 × 1015 1.020 × 1015 1.955 × 106

KCO (bar-1) KCH4 (bar-1) KH2O KH2 (bar-1) ox KCH (bar-1) ox 4 KO2 (bar-1)

activation energy, Ek (kJ/mol)

A(Ki)

heat of adsorption, ∆Hk (kJ/mol)

86.0 86.0 240.1 243.9 67.13 8.23 × 10-5 6.65 × 10-4 1.77 × 105 6.12 × 10-9 1.26 × 10-1 7.87 × 10-7

70.65 38.28 -88.68 82.9 27.3 92.8

Ke,2 (bar2) ) exp[(-26830/T) + 30.114] Ke,3 (bar2) ) exp[(-22430/T) + 26.078] Ke,4 ) exp[(4400/T) - 4.036]

model is required for understanding the process and for the optimization and the reactor control. Syngas can also be produced in several novel reactor configurations by coupling suitable exothermic combustion reactions with endothermic methane steam (or CO2) reforming reactions such as those in regenerative and/or recuperative fashion. In the reactors with a regenerative mode of coupling, the combustion and reforming reactions occur in the same catalyst bed but at different times (e.g., reverse-flow reactor) as energy released by the exothermic reaction, in the first halfcycle, is stored by the bed for utilization during the endothermic process in the second half-cycle.21,22 Smit et al.23 recently demonstrated that catalytic partial oxidation can be performed in both the half cycles in the reverse-flow packed-bed reactor and with the distribution of oxygen through the membranes. The main concern in the reverse-flow reactor is that it must be operated in a dynamic fashion. In recuperative coupling, the two reactions are separated in space but coupled via heat transfer through the separating wall in either counter-current or cocurrent arrangement.24,25 The occurrence of hot spots is the major problem in the recuperative mode of coupling. More information on these types of coupling can be found in Kulkarni and Dudukovic´26 and Ramaswamy et al.27,28 and the references cited therein. BP has worked extensively to demonstrate the synthesis gas generation in a counter-current heat-exchanger reactor in their Alaskan facility.24 In the adiabatic packed-bed reactors that are being discussed in this paper, or in the monolith reactors, both the exothermic and endothermic reactions occur simultaneously in the same catalyst bed (for packed beds) or at the catalyst wall (for monoliths). Here, the conversion of the reactants and the temperature profiles are dependent on the interaction between these two classes of reactions. Several modeling studies of the catalytic partial oxidation of methane to syngas (in direct mode of coupling) are available in the literature. Some of these studies include the following: the one-dimensional steady-state pseudohomogeneous model of an adiabatic packed-bed reactor, using Ni/Pt catalyst kinetics, by de Groote and Froment,2 and steadystate one-dimensional heterogeneous models reported by de Smet et al.18 and Avci et al.29 Similarly, the modeling studies of the monolith reactor include a transient-state one-dimensional (1-D) two-phase dispersion model of a platinum monolithic reactor by Veser and Frauhammer,30 the steady-state twodimensional (2-D) detailed-flow model of a monolithic channel (using FLUENT) by Deutschmann and Schmidt.31,32 Detailed kinetics of partial oxidation on the rhodium catalyst was used in the work of Deutschmann and Schmidt.31,32 Recently, Bizzi et al.19,33,34 studied the partial oxidation of methane in short-

contact-time packed-bed reactors, using the rhodium catalyst with and without detailed chemistry. The detailed chemistry may be required to discriminate different reaction mechanisms/steps, whereas, the global kinetics is sufficient for the reactor studies, such as scaleup and design. The reported modeling studies in the literature primarily discuss the steady-state behavior of this process, in particular, the effects of feed temperature, the importance of gas-phase reactions at higher operating pressure, and the role of thermal conductivity of the catalyst bed and gas hourly space velocity (GHSV) on the methane conversion and on the product pattern. The interaction between exothermic and endothermic reactions becomes more significant during the transient operations and there is only limited information available in the literature on the dynamic behavior of these reactors.20-22, 25, 35,36 In this work, we investigate some of the transient aspects in more detail, using 1-D transient heterogeneous plug flow and axial dispersion models of the short-contact-time packed-bed reactors. Some of the key transient behavior, including the wrong-way phenomenon, such as temperature response to a sudden increase or decrease in the feed temperature (from a steady-state profile) is analyzed. The steady-state and dynamic behavior that results from the interaction of the exothermic and endothermic reactions due to the addition of steam in the feed is also investigated. The effects of the inlet mass velocity (hence, GHSV) on the temperature profile and on the product distribution are also discussed. Here, we attempt to resolve the debated issue of the causes for the increase in the conversion of methane with the increase in GHSV in the short-contact-time reactors. The effects of transport coefficients and dispersion coefficients on the hot spot, length of the reactor, and the time taken to reach the steady state are presented. The next section (Section 2) presents the heterogeneous plug flow and axial dispersion models and the solution procedure used in this work. The steady-state and dynamic behaviors exhibited by the partial oxidation process are discussed in Section 3. The summary and conclusions are provided at the end of the paper. 2. Model Development This section presents the transient heterogeneous plug flow and axial dispersion models for the packed-bed reactors. The rate of the reactions and other correlations for the transport properties used are also presented here. The solution procedure used in this work is provided is section 2.5

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2.1. Transient Plug Flow Model. The species mass balance and energy balance equations for the gas phase and the solid phase are presented here: Species Mass Balance in the Gas Phase:

bF g

Sp ∂yig ∂yig + MT ) bRig - nifo ∂t ∂z V

Mass Balance for the Gas Phase:

bF*g

kgiap(Fig - Fis) ∂yig ∂yig + M*T ) bR*ig - (1 - b) ∂t* ∂z* Rref

(7)

(1) Mass Balance for the Solid Phase:

kgiap(Fig - Fis) ∂F*is ) R*is + ∂t* Rref

Continuity Equation:

∂Fg ∂MT + )0 b ∂t ∂z

(8)

(2) Energy Balance for the Gas Phase:

where MT (MT ) Fgug) is the mass flux (equal to the inlet mass flux at the steady state). Species Mass Balance in the Solid Phase:

∂Fis Sp ) (1 - b)Ris + nifo ∂t V

(1 - b)

∑

FgiCpgi

∂Tg ∂t

+

∑

FgiugCpgi

∂Tg ∂z

(4)

(-∆Hj)Rjg ∑ j)1

Energy Balance for the Solid Phase:

∂Ts ∂t

nrxs

) (1 - b)

(-∆Hj)Rjs + ∑ j)1 (1 - b)hap(Tg - Ts) (6)

The species densities/concentrations are calculated using the ideal gas law. The total density of mixture is given as

F)

∑

Fi )

∑ j)1

(-∆H*j )R*jg - (1 - b)

hap(Tg - Ts) (9)

(-∆HrefRref)


F*bedC*pcatβ

∂T*s ∂t*

nrxs

) (1 - b)

(-∆H*j )R*js + ∑ j)1 hap(Tg - Ts) (1 - b) (10) (-∆HrefRref)

nrxg

) b

(1 - b)hap(Tg - Ts) (5)

FbedCpcat

∂T*g

nrxg

b

where kgi is the mass-transfer coefficient of species i. The accumulation and reaction of the species in the gas film surrounding solid particles is neglected in this work. Energy Balance for the Gas Phase:

b

∂T*g

∑ ygiC*pgi ∂t* + M*Tβ ∑ ygiC*pgi ∂z* )

(3)

where Fis is the mass density of species i in the solid phase, and

nifo ) kgi(Fig - Fis)

bF*gβ

In this work, the Ergun equation is used to calculate the pressure drop at each and every axial position, which complements the aforementioned set of model equations. The inlet and initial conditions used are mentioned in the Results and Discussion section for every simulation study. 2.2. Dimensionless Transient Axial Dispersion Model. The species mass-balance and energy-balance equations for the gas phase and the solid phase are given as follows. Mass Balance for the Gas Phase:

bF*g

∑ piMwt,i

∂yig bF*g ∂2yig ∂yig + M*T ) bR*ig 2 ∂t* Pemg ∂z* ∂z* kgiap(Fig - Fis) (1 - b) (11) Rref

RgT

The aforementioned equations (eqs 3-6) are rendered dimensionless as follows:

Mass Balance for the Solid Phase:

kgiap(Fig - Fis) ∂F*is ) R*is + ∂t* Rref

tRref Fi zRref T , t* ) , yi ) , T* ) z* ) MTref Fref F Tref MT (-∆H) F R F* ) , M*T ) , R* ) , (-∆H*) ) Fref MTref Rref (-∆Href) Cpg TrefCpref , β) C*pg ) Cpref (-∆Href) The resulting dimensionless equations of the transient heterogeneous plug flow model are as follows.

(12)

Energy Balance for the Gas Phase:

∂T*g

b ∂2T*g

∑ ygiC*pgi ∂t* - Pe

bF*g

[

b

nrxg

Tg

∂z*2

∂T*g

1

∑ ygiugC*pgi ∂z* ) β

+ M*T

]

hap(Tg - Ts)

(-∆H*j )R* ∑ jg - (1 - b) (-∆H j)1

refRref)

(13)

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CH4 + 2O2 f CO2 + 2H2O


F*bedC*pcat

∂T*s

-

∂t*

1 - b ∂2T*s PeTc ∂z*2

)

1 β

(∆H773K ) -800 kJ/mol) (17a)

[

nrxs

(1 - b)

(-∆H*j )R* ∑ js + j)1

]

hap(Tg - Ts)

(14) (1 - b) (-∆HrefRref)

(∆H773K ) 222 kJ/mol) (17b) CH4 + 2H2O T CO2 + 4H2 (∆H773K ) 185 kJ/mol) (17c) CO + H2O T CO2 + H2

Here,

Pemg )

CH4 + H2O T CO + 3H2

(∆H773K ) -37 kJ/mol) (17d) MTref2 Daxi,mRrefFref

, PeTg )

MTref2Cpref , λegRref

The respective rate equations for the chemical reactions described in eqs 17a-17d are given as follows:

PeTc )

MTref2Cpref λecRref

r1 )

k1a pCH4 pO2 (1 +

ox KCH p 4 CH4

+ KOox2 pO2)2

k1b pCH4 pO2

The boundary conditions used to solve the aforementioned set of axial dispersion equations are given as follows. At z* ) 0:

dyi (ugFgi - ug0Fgi0) Pemg ) dz* MTref F*g dT*g (ugFgC*pgT*g - ug0Fg0C*pg0T*g0) PeTg ) dz* MTref dT*s )0 dz*

k2 (15a)

r2 )

pH22.5

(15b)

(15c)

k3 r3 )

pH23.5

At z* ) L*:

dy*i dT*g dT* s ) ) )0 dz* dz* dz*

r4 ) (16)

The initial conditions may vary depending on the simulation study and are mentioned in section 3. In the simulation study presented in this work, instead of using the Danckwert’s boundary condition (eqs 15a and 15b), Dirichlet boundary conditions (Fgi|z*)0 ) Fgi0, Tgi|z*)0 ) Tgi0) are used, because of the large Pemg and PeTg values. The heat loss due to radiation is not included in our model, because we observed that the effect of radiation on the temperature profiles is not significant for the range of parameters that we investigated (this is consistent with the observation by other researchers37). The steady-state plug flow and axial dispersion models can be easily obtained by equating the terms corresponding to time derivatives in the respective transient models (eqs 7-14) to zero. 2.3. Reaction Rates. The following four reactions are considered to represent the partial oxidation of methane to syngas, and the corresponding rate expressions are obtained from the literature.18 These reactions are widely used in the literature to study this process, and they include total combustion (eq 17a), steam reforming (eq 17b), CO2 reforming (eqs 17c and 17d combined), and water-gas shift reaction (eq 17d). Other reaction schemes and the rate expressions to represent this process (for different catalyst systems studied) have been provided by Numaguchi and Kikuchi,18 Bizzi et al.,19 and Wolf et al.,37 and the rate expression for methane catalytic combustion is provided by Ma et al.38

+

(

ox (1 + KCH p + KOox2 pO2) 4 CH4

pCH4 pH2O -

(

pH23pCO Ke,2

(Den)2

pCH4 pH2O -

(

)

2

(Den)2

(18a)

(18b)

)

pH24pCO2 Ke,3

(18c)

)

pH2 pCO2 k4 pCO pH2O pH2 Ke,4

(18d)

(Den)2

Den ) 1 + KCO pCO + KH2 pH2 + KCH4 pCH4 +

KH2O pH2O pH2

The values of the pre-exponential factors, activation energies, heats of adsorption, and equilibrium constants are given in Table 1. We have used the aforementioned global kinetics to demonstrate the coupling and interactions of exothermic and endothermic reactions in packed-bed reactors. These rate expressions are developed for the Ni/Pt catalyst system, and it should be noted that the temperature and product profiles obtained with Ni/Pt and Rh catalyst systems are qualitatively similar. De Smet et al.18 used the aforementioned kinetics (eqs 18a-18d) with an effectiveness factor of ∼10-3 (for all reactions) to simulate the industrial reactor. The effectiveness factor has been used in their work because the catalyst is assumed to be porous. Studies with the rhodium catalyst,14,19 which is nonporous, shows that the catalyst is highly active for the partial oxidation process and the reaction is completed within a very short contact time (on the order of milliseconds). However, the global kinetic scheme for the partial oxidation processes with the rhodium catalyst is not well-established. In this work, we have used the aforementioned kinetics without any effectiveness factor to qualitatively simulate the steadystate and transient behavior in short-contact-time reactors and to analyze the coupling of exothermic and endothermic reactions in the partial oxidation process. The development of reactor models coupled to the particle-level mass- and heat-transport

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models will be very complex, and such an advanced model is subsequently needed, which could exhibit additional features like multiple steady states in these systems, coupling effects within the pellet etc. The future research in this area should focus on the development of a sound global kinetic model for the short-contact-time partial oxidation process and on the steady-state and dynamic analysis of the reactors with the developed kinetic model. 2.4. Transport Properties. The heterogeneous models require the particle-to-fluid heat- and mass-transfer coefficients. These film-transfer coefficients are calculated based on the correlations recommended by Wakao and Kaguei39 and are given below. Heat-Transfer Correlation:

Nu ) 2 + 1.1Re0.6Pr1/3

(19)

where

Re ) Pr )

lϑFmix µmix

Cpgmixµmix Kmix

Nu ) l)

hl Kmix

dpb 1 - b

ϑ)

MT Fmixb

Mass-Transfer Correlation:

Shi ) 2 + 1.1Re0.6Sci1/3

(20)

where

Sci )

µmix FmixDim

Shi )

kgil Dim

The viscosity, thermal conductivity, specific heat, and the diffusivity of the species used in this work are corrected for the temperature and/or pressure. The respective mixture properties at any point in the reactor are calculated based on the mixture rule for gases.40 2.5. Solution Procedure. The transient plug-flow and transient axial dispersion model equations (eqs 7-14) are solved by the method-of-lines (MOL) approach.41 In this approach, the partial differential equations (PDEs) are converted to a set of ordinary differential equations (ODEs) by suitable discretization of spatial derivatives and the resulting ODEs, in time, are then integrated using an explicit algorithm. We have used an automatic step-size adjustable FORTRAN routine, LSODE, that was obtained from Netlib libraries as an ODE integrator. It is observed that the explicit solver (corresponding to the feature MF ) 10, in the LSODE solver) is more robust and faster compared to the stiff solver (MF ) 22) for this problem. The second-order finite difference upwind discretization scheme is used to discretize the spatial derivatives. The discretization scheme has been made robust to spurious oscillations using total

variation diminishing (TVD) algorithms (using the van-leer splitter).42 The grid independence of the solution is verified, and the number of nodes used for the simulation in this work is 250, unless otherwise stated. In our model, the pressure drop at each point along the reactor length is updated at every time step using the Ergun equation, which is a steady-state equation. The discretization of the Ergun equation results in a set of algebraic equations, which are solved using a modified Newton-Powell hybrid solver (HYBRD) from the Netlib libraries. 3. Results and Discussions In this section, the computed steady-state behavior (section 3.1) and the dynamic behavior (section 3.2) exhibited by the catalytic partial oxidation of methane in the short-contact-time packed-bed reactor are presented. 3.1. Steady-State Behavior. Here, we analyze the effect of mass- and heat-transfer coefficients on the temperature and concentration profiles. The effects of feed quality (in particular, the addition of steam in the feed) and the mass flow rate on the methane conversion, the product pattern, and the hot spot are discussed (using a plug-flow heterogeneous model). The influence of the axial dispersion coefficients (within the limitation of Dirichlet boundary conditions) on the performance of the short-contact-time reactor is also presented. The sensitivity studies, with respect to the feed temperature and the operating pressure, are well-recorded2,18 and, hence, not reported in this paper. 3.1.1. Effect of Heat- and Mass-Transfer Coefficients. The steady-state temperature profiles predicted using the plug-flow model for two sets of heat- and mass-transfer coefficients are shown in Figure 1a. The input parameters used in the simulation are presented in Table 2. The heat- and mass-transfer coefficients are smaller for case 2, compared to case 1. For Case 2, the mass-transfer coefficients are ∼10% and the heat-transfer coefficients are 30% lower than those of Case 1 (multiply the heat- and mass-transfer correlations (eqs 19 and 20, respectively) by the respective factors). The temperature profiles corresponding to Case 1 qualitatively match some of the experimental and other modeling results published in the literature.19,43 In this process, the exothermic reaction is dominant initially and, hence, the temperature increases near the inlet of the reactor. The increase in the reactor temperature favors the endothermic reaction subsequently. After the concentration of one of the reactants (here, oxygen, which is the limiting reactant) participating in the exothermic reaction decreases (or is completely consumed), the endothermic reaction becomes predominant and, therefore, a drop in temperature in observed in the later section of the reactor. In the portion near the reactor inlet, where the exothermic reaction is dominant, the solid-phase temperature is higher than the gas-phase temperature. On the other hand, the gas-phase temperature is higher than the solid-phase temperature when the endothermic reaction is dominant (near the reactor exit). This also shows that there exists a point in the reactor where the gas and solid phase may have similar temperature and, at that point, the rate of heat generation by the exothermic reaction matches the rate of heat consumption by the endothermic reaction, in an adiabatic reactor (such a trend can be observed in the work by Wolf et al.37). For the cases discussed in Figure 1a, the temperature profiles reach the equilibrium value, for both sets of film coefficients, near the exit. However, Case 2 requires more reactor length to reach the equilibrium, compared to Case 1. Note that the magnitude of temperature peak is higher for the case with the higher transport coefficient. We also observed that the temperature peak


Figure 1. (a) Steady-state temperature profiles predicted by the heterogeneous plug-flow model for two sets of heat- and mass-transfer coefficients (parameters used are reported in Table 2). (b) Steady-state concentration profiles predicted by the heterogeneous plug-flow model for Case 1 (other parameters are reported in Table 2). Table 2. Model Input Parameters (Base Case) parameter

value

reactor length catalyst diameter inlet temperature inlet pressure reactant mass flow rate feed composition (mole fraction) CH4 O2 CO2 H2O CO H2 bed porosity heat capacity of catalyst

0.1 m 0.002 m 700 K 40 atm 20 kg/(m2 s) 0.6666 0.3333 0.0000 0.0000 0.0000 0.0001 0.43 750 J/(kg K)

is higher for the case simulated with the pseudo-homogeneous model (de Groote and Froment2 also showed sharp temperature peak), for the parameters reported in Table 2. This shows that the presence of heat- and mass-transfer resistances minimizes the hot spot in the reactor, for this process. The predicted concentration profiles (for film transfer coefficients corresponding to case 1) are shown in Figure 1b. The

methane and oxygen concentrations fall drastically near the reactor inlet with the production of CO and H2. The equilibrium conversion is achieved in these reactors at a short length of ∼0.02 m. The ratio of CO/H2 at the reactor exit is 0.52. Note that the nonequilibrium conditions can result when the reactor length is very small (for example, 0.015 m). For further simulations, the film coefficients corresponding to Case 1 were used. 3.1.2. Effect of Steam in the Feed. It is known, generally, that the addition of steam to the feed increases hydrogen generation and reduces the exit/equilibrium temperature. This is due to increase in the rate of reforming reactions (endothermic; steam reforming process produces a H2/CO ratio of 3 in the product). We observed that, for some cases, the magnitude of the temperature peak increases with the addition of steam (compared to the case without steam in the feed),44 and this is due to the steam-to-methane and methane-to-oxygen ratios in the feed. Hence, in this section, the effects of addition of steam at constant and varying methane-to-oxygen ratios are analyzed. 3.1.2.1. Varying Methane-to-Oxygen Ratio (Fixed Amount of Steam in the Feed). First, the amount of steam (molar percent) in the feed was kept constant and the methane-tooxygen ratio was varied. Figure 2a shows the resulting axial temperature profiles. As the methane-to-oxygen ratio increases, at a fixed molar percentage of steam, the temperature peak (as well as the exit temperature) decreases. This is due to the occurrence of reforming reactions preferentially over the combustion reaction, because of the availability of more methane and less oxygen. The temperature peak shifts to the right, with the addition of steam, away from the reactor inlet, because of the increased rate of endothermic reactions (in addition to the reduced rate of the exothermic combustion reaction) near the inlet. For the cases studied, the temperature peak is higher for the feed with the lower methane-to-oxygen ratio. The CO-to-H2 profiles for these cases are plotted in Figure 2b. The carbon monoxide-to-hydrogen ratio at the reactor exit decreases with the addition of steam, compared to the case without steam in the feed. Among the cases with steam in the feed, the CO-to-H2 ratio, at the reactor exit, decreases as the feed methane-to-oxygen ratio increases, because of the formation of more hydrogen. Note that CO can be produced in this process (as inferred from eqs 17b and 17c) by the reverse water-gas shift reaction (consuming CO2 and H2 and producing more CO; CO2 reforming reactions). This study shows that, for the fixed amount of water in the feed, the lower methane-to-oxygen ratio in the feed results in a higher-temperature peak, a higher CO-to-H2 ratio, and also less CO2 in the product. 3.1.2.2. Fixed Methane-to-Oxygen Ratio (with Varying Amount of Steam in the Feed). Here, the molar ratio of methane to oxygen in the feed is kept constant at 2 and the amount of steam in the feed is varied. Figure 3a shows the predicted temperature peak and the respective equilibrium temperature as a function of the molar percentage of steam in the feed. The equilibrium temperature is calculated at the constant inlet pressure (reported in Table 2) using CHEMKIN software. Here, the equilibrium temperature (and the temperature at the reactor exit) decreases with the addition of steam, whereas the temperature peak passes through a maximum at ∼20% steam in the feed. The CO-to-H2 ratios corresponding to the equilibrium conversion and at the position 0.025 m in the reactor are plotted in Figure 3b. The CO-to-H2 ratio decreases as the addition of steam decreases. In the absence of steam, or in the presence of a small percentage of steam in the feed, the

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Figure 2. (a) Effect of water in the feed on temperature profiles (gas phase), with varying methane-to-oxygen ratios. (b) Effect of water in the feed on CO/H2 profiles, with varying methane-to-oxygen ratios.

equilibrium composition is achieved at the shorter reactor length. For larger percentages of steam in the feed, more reactor length is needed to attain the equilibrium conversion. The initial increase in the temperature peak with water in the feed is due to the water-gas shift reaction. With further increases in the percentage of water in the feed, the partial pressures of methane and oxygen in the feed are reduced and, hence, the rate of the combustion reaction is reduced and the magnitude of temperature peak is decreased. The aforementioned two studies show that the addition of water in the feed may increase the maximum temperature in the reactor, depending on the methane-to-oxygen and/or methaneto-steam ratio, and, hence, a proper protocol must be established to control the temperature peak and the exit temperature. 3.1.3. Effect of Inlet Mass Velocity. The increase in the reactant mass velocity increases the productivity and decreases the contact time in the reactor. The effect of the mass velocity on the temperature profile, predicted by the heterogeneous plugflow model, is shown in Figure 4. The temperature peak increases as the inlet velocity increases, but is shifted toward the reactor exit. This shift is due to the decrease in Damko¨hler (Da) numbers of the exothermic and endothermic reactions. The increase in the temperature peak can be attributed to the reduced

Figure 3. (a) Effect of water in the feed on temperature peak and the equilibrium temperature, with constant methane-to-oxygen ratio. (b) Effect of water in the feed on CO/H2 ratio, with a constant methane-to-oxygen ratio.

rate of endothermic reforming reactions (and, thus, the temperature rise due to the exothermic combustion reaction is not curbed by the endothermic reaction). This increase in the temperature peak increases the methane conversion slightly. There is some experimental evidence for the increase in methane conversion with the increase in GHSV in the literature.14,19 The methane conversion and the selectivity to CO and H2 for the range of mass velocity investigated are shown in Table 3. There is another school of thought regarding the increase in methane conversion with GHSV, which needs some clarification and is discussed here. Bizzi and co-workers19,33,34 attributed such an increase in methane conversion with mass velocity to the increase in the mass-transfer rate. It is generally observed that the conversion decreases (for any isothermal homogeneous reaction system) with the increase in the mass velocity, because of the decrease in the residence time for the reactants. For the heterogeneous (fluid-solid) systems, velocity influences the mass and heat transport and, hence, affects the conversion (for example, for systems such as A f B or A T B, conversion is given as XA ) 1 - exp(-KmL/ug), where Km is the mass-transfer rate (given in units of 1/s) L the length of the reactor, and ug the inlet superficial velocity). The dependence of mass-transfer


Figure 4. Effect of inlet mass velocity on the temperature profiles (other parameters are reported in Table 2).

Figure 5. Temperature profiles predicted by axial dispersion model (parameters as reported in Table 2).

coefficients on the velocity scales as ReR, where R ranges from 1/3 to a maximum of ∼0.8. (This is true for the heat transfer rate also.) Therefore, the net conversion decreases as the velocity increases. The conversion can only increase initially or pass through a maximum if the dependence of the mass-transfer coefficient on velocity scales as a power greater than one (R > 1). This suggests that the increase in conversion due to the increase in the mass-transfer rate may not be the only reason for the experimentally observed behavior in short-contact-time reactors. In contrast to the aforementioned explanation, there are two different ways by which methane conversion could increase in this non-isothermal system. First, the increase in the masstransfer rate supplies more reactants (Fickian type diffusion) to the catalyst surface. The presence of more methane and oxygen increases the rate of exothermic reaction and, thus, increases the temperature at the catalyst surface. This higher temperature at the catalyst surface favors the endothermic reforming reactions (which also use methane) and thus contribute to increase in methane conversion. Often, the aforementioned phenomenon is offset by convection and the short residence time and thereby, the methane conversion increases, initially, only slightly. This

Figure 6. (a) Evolution of the maximum gas-phase temperature in the reactor predicted by the plug flow and axial dispersion models (feed compositions: 53% CH4, 27% O2, 20% H2O (with water); 67% CH4, 33% O2 (without water)). (b) Evolution of the reactor exit temperature predicted by the plug-flow and axial-dispersion models (feed compositions: 53% CH4, 27% O2, 20% H2O (with water); 67% CH4, 33% O2 (without water)).

slight increase in the methane conversion with the mass velocity is reported in Table 3. Second, there is a possibility that an increase in the temperature peak increases the temperature upstream of the peak in the reactor (due to the dispersion) and at the inlet to the catalyst bed, and, hence, results in higher methane conversion. This is explained in the next section. As discussed previously, when convection dominates over dispersion, methane conversion decreases as the mass velocity increases, which is normally the case at larger velocities. From Table 3, it is clear that, for much-larger inlet mass velocity (or GHSV) values, the exit methane conversion is reduced. For this case, the temperature peak occurs very near the reactor exit (and for even larger velocities, the temperature peak can be pushed out of the reactor), as shown in Figure 4. When the temperature peak occurs near the exit of the reactor, the residence time for the predominant endothermic reactions (between the position of the temperature peak and the reactor exit) decreases and thereby contribute to a decrease in methane conversion, and product selectivity. This is true for the mass velocity of 150 kg/(m2 s), shown in Table 3 (this value is chosen for the sake

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Table 3. Effect of Inlet Mass Velocity on the Reactor Performance mass flow rate (kg/(m2 s))

inlet linear velocity (m/s)

methane conversion at the exit (%)

H2 selectivity at the exit

CO selectivity at the exit

pressure drop at the reactor exit (atm)

20 40 80 150

1.36 2.73 5.46 10.22

84.9 85.0 85.6 80.7

1.856 1.857 1.864 1.877

0.967 0.967 0.968 0.917

0.58 2.17 7.77 18.00

of illustration). The increase in conversion due to the increase in the inlet linear or mass velocity is counterbalanced by the increase in the pressure drop across the packed-bed reactor. The pressure drop calculated using the Ergun equation for different mass flow rates is reported in Table 3. This increase in the pressure drop may limit the commercial application of these reactors at higher GHSV values. 3.1.4. Effect of Axial Dispersion Coefficients. Bizzi and coworkers33,34 have shown that the mass and gas-phase thermal dispersion coefficients can often be neglected in the modeling of the short-contact-time packed-bed reactors, because of large Pemg and PeTg values. On the other hand, the axial dispersion has a significant role in the transient profiles and, in some cases, it could displace the temperature peak to the upstream of the reactor during the wrong-way operation.45 Hence, in this work, we have analyzed the effect of these dispersion coefficients on the temperature profiles. The mass and thermal dispersion coefficients can be calculated from the literature,46 and, in this work, an average value of Daxi,m ) 1.4 × 10-3 m2/s and λe,g ) 0.07 W/(m K) is used. The effective thermal conductivity for the solid can be obtained from Wakao and Smith,39 and, here, λe,c ) 1 W/(m K) is used.33 The effect of the dispersion coefficients on the temperature profiles for the base case parameters reported in Table 2 are presented in Figure 5. The temperature profiles are qualitatively similar for the cases with and without dispersion coefficients. The presence of thermal dispersion coefficients (gas) did not have much effect on the temperature profile, whereas the mass dispersion coefficient affects the profile somewhat. In the presence of the mass dispersion coefficient, the temperature peak and the exit temperature decrease. It is to be noted that the dispersion effects can play a large role in these reactors, if the reaction zone is sandwiched between two conducting inert packing, as observed in some of the experiments.14,19 In such a reactor arrangement, as the mass velocity increases, the temperature peak increases. This, in turn, increases the temperature at upstream points of the reactor (due to dispersion) and at the inlet to the catalyst bed resulting in higher methane conversion. In this work, for further simulation (transient) studies, values of Daxi,m ) 0.0 and λe,g ) 0.07 W/(m K) (predominantly focusing on the thermal dispersions) were used. 3.2. Dynamic Behavior. The transient characteristics are important for the design and control of the partial oxidation reactors. Phenomena such as wrong-way behavior are commonly observed in packed-bed reactors (where, for example, exothermic reaction is conducted), because of the perturbation in the feed temperature and flow rates, and are important in realizing the steady-state and stable operation of the reactor. Suitable control and operation protocols are developed based on the temperature excursion observed during this transient behavior. Similarly, the evolution of the temperature profiles (from initial conditions) is important for the safe startup of the partial oxidation reactor where the exothermic and endothermic reactions occur simultaneously. In this section, we analyze the evolution of the temperature and concentration profiles during the startup of these short-contact-time packed-bed reactors. Some

wrong-way behavior that is observed in these reactors due to changes in feed temperature and due to the addition of steam in the feed is also presented. 3.2.1. Evolution Profile. Figure 6a shows the time series of the maximum gas-phase temperature in the reactor predicted by the heterogeneous plug flow and the axial dispersion models for two cases: one with steam in the feed and the other without steam in the feed. The feed compositions of these two cases are 53% CH4, 27% O2, 20% H2O for the feed with steam and 67% CH4, 33% O2 for the feed without steam. In this simulation, the initial conditions along the reactor are kept the same as the inlet conditions. Here, the complete ignition of exothermic reaction occurs at ∼0.3 s (for the type of kinetics used), and, hence, the magnitude of the maximum temperature in the reactor increases sharply. The time at which this sharp increase in temperature occurs is predicted to be the same by both the plug-flow and the axialdispersion models. The maximum temperature for the case with steam in the feed is higher than that for the case without steam and is consistent with the steady-state results discussed previously (for the feed composition used). Also, for the case with steam, the time taken for the exothermic reactions to begin is slightly longer than that for the case without steam. This may be due to the reduced combustion rate (because of decreases in the partial pressures of oxygen and methane in the feed) and increased reforming rate (because of water in the feed). Note that, for these cases, the temperature profile evolves smoothly and finally reaches the steady state. This trend may not be expected for the processes with a very high exothermic reaction rate and/or heat of reaction or for the case with the lower heat capacity of the catalyst bed (one such extreme case will be the coupling of homogeneous exothermic and endothermic reactions). In such situations, the maximum temperature in the reactor may overshoot the steady-state temperature peak due to the short exothermic reaction time scale, compared to other time scales involved in the process (endothermic reaction time scale, the time scale of dissipation of heat by the solids, etc.). Figure 6b shows the evolution of the gas-phase temperature at the reactor exit. Here, the exit temperature for the case with water in the feed is lower than that without water, which is consistent with the equilibrium limitations and our earlier discussions. The time taken to reach the steady state is slightly longer for the axial-dispersion model, compared to the plugflow model, which is due to the presence of the dispersion time scale in the problem. This study shows, for the parameters and initial conditions used in this work, that the time required to reach the steady state is ∼2 s. Although this time seems very short, it is several orders of magnitude greater than the residence time of the reactants (based on the inlet conditions) in the reactor. This type of transient behavior, with shorter time to reach the steady state, should be anticipated in the system with very active catalysts. 3.2.2. Wrong-Way Behavior. Wrong-way behavior in the packed-bed reactors is well-recorded for exothermic reactions.45,47,48 The wrong-way phenomenon is caused by a sudden drop in the feed temperature, which results in a temperature excursion in the bed, because of the different propagation speeds


Figure 7. Axial temperature profiles as a function of time (the feed temperature is reduced from 700 K to 650 K, and the feed composition is 67% CH4, 33% O2).

of the concentration and temperature profiles within the reactor. In this work, we have studied the wrong-way behavior in the packed-bed reactor where both exothermic and endothermic reactions happen. The occurrence of wrong-way phenomena due to sudden decrease and increase in the feed temperature is analyzed. Similarly, the transient temperature profiles that are observed in this reactor due to the introduction of steam in the feed are also investigated. 3.2.2.1. Decrease in the Feed Temperature. Here, the reactor is assumed to be operating at the steady state corresponding to the base case parameters reported in Table 2. The feed temperature is then decreased from 700 K to 650 K and the temperature profiles and concentration profiles during this transient period are monitored. Figure 7 shows the axial temperature profiles within the reactor during this transient period. These profiles reveal that, as the feed temperature is reduced, the reaction rates are reduced and, hence, the reactants with higher concentration meet the catalyst at a higher temperature in the downstream portion of the reactor. This results in wrong-way behavior with the temperature peak increasing beyond the steady-state value. The maximum increase in the magnitude of the temperature peak is not greater than 2% of the temperature peak corresponding to the initial temperature profile (steady-state profile corresponding to the feed temperature of 700 K). The temperature excursion due to wrong-way behavior is reduced or controlled, in this process (compared to pure exothermic process, where it can easily overshoot the adiabatic temperature rise), because of the presence of endothermic reactions. During this transient period, the reaction front moves to the right, away from the reactor inlet. This phenomenon continues until the steady state is achieved. The magnitude of the temperature peak at the steady state corresponding to the feed temperature of 650 K is lower than that of 700 K and is shifted to the right of the reactor inlet. 3.2.2.2. Increase in the Feed Temperature. The sudden increase in the feed temperature also results in the wrong-way behavior in this process and is investigated in this section. The initial conditions for the temperature and concentration of the species within the reactor correspond to those of the base case steady state. Now, the feed temperature is increased from 700 K to 750 K. The maximum gas-phase temperature and the temperature at the reactor exit during the transient period are

plotted in Figure 8a. There is a decrease in the maximum temperature observed, initially, followed by the temperature increase to the steady state. This is observed due to the different traveling speeds of the concentration and thermal waves and, thereby, the resulting interaction between the exothermic and endothermic reactions. The axial temperature profiles at the different instants of time are shown in Figure 8b. Because of the increase in the feed temperature, the rate of the exothermic reaction is increased near the reactor inlet. This, in turn, increases the rate of endothermic reaction, and, thereby, the temperature peak is reduced. With further increases in time, both the exothermic and endothermic reactions balance and finally settle at the steady state with a temperature peak greater than that for 700 K. In some of the transient temperature profiles, as shown in Figure 8b, two temperature peaks are observed. The first temperature peak occurs near the reactor inlet and is due to the increased exothermic rate, because of the increase in the feed temperature. This temperature peak occurs around the location where the final (steady-state) temperature peak corresponding to the imposed feed temperature is expected. The increase in the exothermic reaction rate increases the temperature, which, in turn, favors the endothermic reaction and, hence, the decrease in temperature is observed (after the temperature peak). The gaseous stream at this position in the reactor still has some unreacted methane and oxygen. When this gas stream (at lower temperature, compared to the previous instant or the initial condition) contacts the high-temperature bed (from the previous instant of time), the exothermic combustion reaction occurs, due to the presence of oxygen, resulting in the second peak in the temperature profile. However, during this transient period, the magnitudes of both these peaks are less than that of the initial profile and with increasing time, the second peak disappears. Note that the temperature peak that corresponds to 750 K is greater than that for 700 K and is moved toward the reactor inlet, because of the accelerated exothermic rate near the reactor inlet. The axial concentration profiles for methane and CO in the reactor are shown in Figures 8c and 8d, respectively. The methane conversion clearly increases (near the reactor inlet) as the feed temperature increases. The increase in CO concentration in the region near the inlet confirms the simultaneous occurrence of endothermic reactions along with the exothermic reactions. During the initial transients, methane conversion decreases at the exit, with the production of less CO, and, with increasing time, the methane conversion and CO production increases. The methane conversion and CO selectivity are higher at 750 K, compared to 700 K. The total duration of the transient lasts for

Modeling Catalytic Partial Oxidation of Methane to Syngas in Short

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