Periodic Operation of Asymmetric Bidirectional Fixed-Bed Reactors

770

Ind. Eng. Chem. Res. 1998, 37, 770-781

Periodic Operation of Asymmetric Bidirectional Fixed-Bed Reactors with Temperature Limitations Milind S. Kulkarni and Milorad P. Dudukovic´ * Chemical Reaction Engineering Laboratory, Department of Chemical Engineering, Washington University, Saint Louis, Missouri 63130-4889

Possible ways of coupling a solid-catalyzed endothermic reaction with an exothermic reaction in a bidirectionally fed fixed-bed reactor, operated in a periodic steady state, when the maximum allowable temperature is limited by either process, catalyst, or materials constraints, are discussed. Steam reforming of natural gas coupled with methane combustion is considered as an example. The catalyst bed is heated by the combustion reaction during the exothermic semicycle, while the endothermic reaction, with reactants fed from the opposite end, cools the bed during the endothermic semicycles. It is shown that two modes of periodic operation are possible. In the wrong-way process, reactants are fed at temperatures below the initial bed temperature, which results in maximum temperatures that can exceed the allowable limits. To suppress excessive temperature overshoots the fuel feed concentration must be very low, which leads, due to the creeping temperature hot zone, to only a small fraction of the heat produced during the exothermic semicycle being available for the endothermic reaction. Thermal efficiency and the reactor productivity are low. In the normal process, the inlet reactant temperature is above the ignition temperature, leading to a stationary spreadout temperature profile, high thermal efficiency, and high reactor productivity, as well as to controllable maximum temperature. Simulations for the wrong-way and normal processes are described as well as the possibilities of achieving very high thermal efficiencies in a process that integrates the reactor with heat recovery units. Introduction Coupling of an endothermic reaction with an exothermic reaction in the same packed-bed reactor has been discussed in detail by Kulkarni and Dudukovic´ (1996a,c, 1997). Typically, the exothermic reaction (e.g. methane combustion) takes place in the bed during an exothermic (odd) semicycle when a mixture of fuel (e.g., methane) and air is fed into the hot bed. The heat generated by this exothermic reaction is then utilized to drive the endothermic reaction, which occurs during the next endothermic (even) semicycle when the reactants are fed into the bed from the other end of the reactor. This process was renamed bidirectional, asymmetric fixedbed operation. It is well established that the maximum transient temperature rise in the bed is greater than the adiabatic temperature rise whenever the feed gas temperature is below the initial bed temperature (Kulkarni and Dudukovic´, 1996b; Il’in and Luss, 1992; Chen and Luss, 1989; Matros, 1989; Pinjala et al., 1988; Mehta et al., 1981; Sharma and Hughes, 1979; Van Doesburg and DeJong, 1976a,b; Crider and Foss, 1966) and a periodic process involving this wrong-way behavior was called the wrong-way process (Kulkarni and Dudukovic´, 1996c). Theoretically, the wrong-way behavior should be expected whenever in the inlet section of the reactor the rate of heat generation due to reaction is much lower than the rate of heat transfer between gases and solids (i.e., when the gases are heated by the solids before the exothermic reaction takes off). Hence, in practice, the wrong-way behavior should occur only when the inlet gas temperature for the exothermic semicycle is below the ignition temperature. Bidirectional symmetric operation of fixed-bed reactors, when

the same feed for an exothermic reaction is periodically switched from one end to the other, has been studied extensively and found industrial applications in sulfuric acid production (Matros, 1989) and volatile organic compound (VOC) abatement (Van de Beld and Westerterp, 1994, 1996; Van de Beld et al., 1994). The wrongway process is particularly useful for catalytic combustion of dilute VOC mixtures where maximum temperatures far in excess of adiabatic temperature rise are needed. However, this situation is more an exception than a rule as practically all processes in the chemical industry are subject to a variety of temperature limitations. The maximum allowable temperature often is limited by the onset of rapid catalyst deactivation, material of construction and potential for chemical degradation of reactants and products, to mention just a few reasons. The wrong-way process leads to very high temperatures that can deactivate the catalyst, destroy the reactor, or degrade the chemicals. Therefore, the utility of the wrong-way process becomes dubious for systems with strict maximum temperature limitations. Eigenberger and Nieken (1988) and Matros (1989) have suggested the removal of heat from the bed, by heat exchangers/recuperators, to control the temperature in symmetric fixed-bed reactors involving only exothermic reactions. However, when the reaction rates are very high, the rate of heat removal by an external medium is much lower than the rate of heat generation by the exothermic reaction, and this idea does not seem applicable in many instances. Only direct, cold-shot quenching may work, but this procedure dilutes the reactant stream. Therefore, it is necessary to approach this problem from another angle that does not involve the removal of heat from the reactor.

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Ind. Eng. Chem. Res., Vol. 37, No. 3, 1998 771

In this paper we report the results of a study of the asymmetric reactor involving coupling of an exothermic and endothermic reaction and demonstrate the advantages of the normal process over the wrong-way process for asymmetric fixed-bed reactors with temperature limitation. In the normal process, the feed gas temperature for the exothermic semicycle is maintained equal to or above the initial bed temperature (at the very beginning of the process) and is at a temperature at which the reaction is self sustaining. Reactants are mixed at the entrance of the fixed bed reactor to prevent the reaction before reactants enter the bed. During the first exothermic semicycle, the maximum temperature rise in the bed is equal to the adiabatic temperature rise. However, during the subsequent cycles the maximum temperature rise in the bed could increase beyond the adiabatic temperature rise because, during endothermic semicycles, the hot temperature zone is pushed toward the entrance for the exothermic semicycles (Kulkarni and Dudukovic´, 1996c) and, hence, the entering gas temperature is now below the bed temperature. However, the wrong-way behavior can now be effectively suppressed, and the maximum temperature is restricted around the adiabatic temperature rise because the inlet gas temperature for the exothermic semicycle is at or above the ignition temperature. Under such conditions the rate of heat generation by the reaction far exceeds the rate of heat transfer from solids to the gas, the wrong-way behavior is suppressed, and maximum bed temperature can be kept below the maximum allowable temperature. To illustrate these concepts, we consider the production of synthesis gas by the endothermic reaction between steam and methane coupled with the exothermic combustion reaction of methane and air. The steam reforming reaction is generally not carried out beyond 1500 K (Blanks et al., 1990; Ferriera et al., 1992; Wagner and Froment, 1992), although this is not necessarily the maximum temperature allowed by all catalysts. For our example we set 1500 K as the maximum allowable temperature. Steam Reforming. The popular methods of producing CO and H2 are (1) steam reforming (primary and secondary) of hydrocarbons, (2) partial oxidation of hydrocarbons, and (3) coal gasification. Reactions that produce CO and H2 are endothermic in nature and all of the aforementioned processes require external heat supply or autothermal operation in which part of the fuel is burned. Partial oxidation derives the heat from partial oxidation of the hydrocarbon fuel. Coal gasification also derives the required heat from the partial combustion of coal. The primary steam reforming involves the reaction between methane and steam to produce synthesis gas in a shell and tube configuration. The endothermic steam reforming takes place in the tubes, while a fossil fuel is combusted outside to supply heat (Wagner and Froment, 1992). However, this process is not very efficient because of low heat transfer rates. Also, there is the additional problem of coke deposition at high concentrations of the hydrocarbon feed. Steam reforming of hydrocarbon fuels has been studied extensively by Mond and Langer (1888), Twigg (1989), Rostrup-Nielsen (1975, 1984), Van Hook (1980), and, as mentioned, Wagner and Froment (1992). Blanks et al. (1990) used an autothermal reactor in the production of synthesis gas by partial oxidation of

Figure 1. A typical operation of an asymmetric fixed-bed reactor.

methane in which the endothermic steam reforming and exothermic partial oxidation of methane occurred simultaneously in the same reactor, which was operated periodically in the reverse flow mode. They first established an inverted ‘U’ shaped temperature profile by introducing and burning a methane + air mixture at the center of the initially cold reactor. Then, catalytic partial oxidation and synthesis gas production took place in the bed with the reactants fed from one end of the bed. The reactants got heated as they entered the bed, and the reaction occurred in the hot zone. The products were cooled before they left the reactor. After a certain time, the reactants were fed from the other end of the reactor to push the inverted ‘U’ shaped temperature profile back into the bed. This process is quite thermally efficient but encounters severe coke deposition problems. The RE-GAS Process. Levenspiel (1988) proposed the RE-GAS process to produce synthesis gas. The process involves coupling of the endothermic steam reforming reaction with exothermic combustion reaction using a fixed bed. During an exothermic semicycle the exothermic reaction heats the bed. During endothermic semicycles, the endothermic steam reforming takes place in the bed, with reactants, steam, and methane fed from the opposite end. Thus each cycle involves an exothermic and an endothermic semicycle (Figure 1). After repeated cycles, the bed operates in a periodic steady state. The coke that is deposited during the endothermic semicycle is completely burnt during the exothermic semicycle. Here, steam reforming and combustion are indirectly coupled in the sense that they do not occur simultaneously in the same space. There have been no cited studies in the literature to explore the possibilities of producing synthesis gas by the REGAS process. Because this process offers a unique possibility of autothermal coupling of the steam reforming reaction with hydrocarbon combustion, along with possible prevention of coke deposition, a preliminary evaluation of this process seems warranted. We use this RE-GAS process as an example to assess the wrong-way and normal processes and to demonstrate the temperature control (i.e., not exceeding the upper temperature bound) in an asymmetric fixed-bed reactor achievable by the normal process.

772 Ind. Eng. Chem. Res., Vol. 37, No. 3, 1998

Reactions and Kinetics. Methane is the major constituent of natural gas that is extensively employed in the production of synthesis gas by steam reforming. The main reactions are:

CH4 + H2O S CO + 3H2

5

∆H ) 2.06 × 10 J/mol ∆H ) -4.12 × 104 J/mol

CO + H2O S CO2 + H2

The process is globally endothermic because the endothermicity of the first reaction is larger than the exothermicity of the second reaction. The process involves many elementary steps, and the detailed kinetics is very elaborate. The focus of this study is to gain a physical insight in the RE-GAS process and, for this purpose, a simple global kinetics suggested by Bodrov et al. (1964, 1967; as reported in Ferreira et al., 1992) is used. The rate of methane reaction with steam is given by:

(-rs,CH4) ) Ψk0,s,CH4Tse-(Eas,CH4/RTs)CCH4 mol/m3‚s where Ψ is the global effectiveness factor. Methane combustion with air has been extensively studied in the literature. The combustion of methane also involves many elementary reactions. However, a global reaction scheme can be written as:

CH4 + 2O2 f 2H2O + CO2 ∆H ) -8.02703 × 105 J/mol As mentioned before, the focus of this study is to gain insight into the overall behavior of the RE-GAS type process and not to simulate the kinetics in great detail. A simple global kinetics that represents the kinetics of the combustion process fairly accurately suffices for our current study. For this purpose we have used the global kinetic expression for methane combustion given by Mulholland et al. (1993)

Table 1. Parameters Used in the Simulation of Methane Reforming and Combustion parameter

wrong-way process

normal process

Tg,in (K) Tg,0 (K) Ts,0 (K) yA,in,exo yA,in,endo k0,g,A (m3/mol‚s) k0,s,A (m3/mol‚s) Eag,A (J/mol) Eas,A (J/mol) ∆Hg,A (J/mol) ∆Hs,A (J/mol) h (J/m2‚K‚s) Cp,g,exo (J/kg‚K) Cp,g,endo (J/kg‚K) Fs (kg/m3) ap (m2/m3) uin (m/s) P (Pa) L (m) Mw,exo Mw,endo dp γs (J/m‚K‚s) De,g,pore (m2/s) De,h,ms (m2/s) De,h,g (J/m.K) De,h,s (J/m‚K)

400 1100-1300 1100-1300 0.008-0.01 0.008-0.01 1.7 × 108 11 396.5 200 928 129 704 -802 703.17 2.06 × 105 13.77 1150 2600 2704.28 600 1 2.026 × 105 10 0.5 28 17 0.005 4.67 7.5 × 10-7 0.0025 0.015 0.335

1100 1100 1100 0.005-0.01 0.5 1.7 × 108 11 396.5 200 928 129 704 -802 703.17 2.06 × 105 13.77 1150 2600 2704.28 600 1 2.026 × 105 10 0.5 28 17 0.005 4.67 7.5 × 10-7 0.0025 0.015 0.335

(1973) is used to estimate the mass dispersion coefficient in the gas phase. Thermal diffusivity is estimated with the expression developed for the heat regenerators by Babcock et al. (1966). The list of estimated physical parameters is given in Table 1. Finally, the effectiveness factor (Ψ) for the endothermic steam reforming reaction is estimated by the method given by Smith (1981). The effectiveness factor for the first-order reaction is given as a function of Thiele-type modulus (Φ), the Arrhenius number (R), and a heat of reaction parameter (β):

(-rg,CH4) ) k0,g,CH4e-(Eag,CH4/RTg)CCH4CO2 mol/m3‚s Physical Parameters. Simulation of the RE-GAS process requires estimation of several physical parameters. Heat transfer coefficients, thermal conductivities, viscosity, mass and heat dispersion coefficients for the gas and the solid phases, and effectiveness factors are required. Considering the nature of the simulation most of the properties are estimated at a representative temperature. The parameters Cp,g and Cp,s are estimated according to the work of Perry and Green (1984). The gas density is calculated with the ideal gas law. Thermal conductivity of the gas is estimated with the Euken’s Correlation (Perry and Green, 1984). Physical properties of the alumina support are used as the representative properties of the catalyst. The semiempirical correlation for heat transfer coefficient proposed by Kunii and Levenspiel (Levenspiel, 1983) is used to estimate the heat transfer coefficient between the gas and solids. Viscosity is calculated with the ChapmanEnskog theory of gases (Reid et al., 1987). Effective thermal conductivity and the solid heat dispersion coefficient is estimated with the correlation given by Kunii and Smith (1960) and Yakae and Kunii (1960). Edwards and Richardson (1968) developed a correlation for the mass dispersion coefficient. For the particle diameter and Reynolds number beyond the range of their correlation, the chart given by Levenspiel

Ψ)

1 -Rβ/5 for Φ > 2.5 e Φ

where

3Φ )

x

dp 2

Eas (-∆Hs)De,poreCp,s ks/Fs ; R) ; β) De,pore RTs λsTs

The reaction essentially occurs when Φ > 2.5, so the effectiveness factor is quite accurately estimated with the aforementioned equations. The effectiveness factor is calculated as a function of temperature. The Model Equations The model used for the simulation of the RE-GAS process is essentially similar to the model introduced by Kulkarni and Dudukovic´ (1996c, 1997). Only exothermic methane combustion takes place in the bed during the exothermic semicycle and only endothermic steam reforming reaction takes place during the endothermic semicycle. Combustion reaction occurs only in the gas phase and not in the solid phase because concentration of the fuel used is very low. Steam reforming occurs in the solid phase. Global kinetics for both reactions are employed. The mass and heat dispersion in both gas and solid phase is accounted for


by the model. The effect of heat and mass transfer in the catalyst is approximated by an effectiveness factor. Because there is negligible external mass transfer resistance at the high velocities employed, external mass transfer resistance is neglected, which is supported by the data in the literature (Ferreira et al., 1992). The model at first assumes gas to be incompressible when gas dispersion terms in eqs 1, 3, and 4 are incorporated as shown later. However, dispersion in the gas phase is negligible and, hence, second-order terms are dropped from eqs 1, 3, and 4. In the case of negligible dispersion in the gas phase, when the secondorder derivatives terms are dropped, eqs 1-5 describe the process for a compressible gas with a constant total gas mass flux (Kulkarni, 1992) as shown in Appendix 1. Methane is represented as component A in the model equations for convenience. The model equations consist of the energy balance for the gas and solid phase, (eqs 1 and 2, respectively); reactant A (methane) mass balance in the gas phase (exothermic semicycle) and in the solid phase (endothermic semicycle) (eqs 3 and 4, respectively); and the overall continuity (eq 5). All equations are written in dimensionless form: 2 ∂θg ∂θg 1 ∂ θg ) + -U ∂τ Peh,g ∂z2 ∂z

1 g)/(θg-θg,d)) τs/r,g,ATRg,Aγ((1-θ ΩgyAyB - Stg (θg - θs) (1) g,A Ωg 2 ∂θs 1 ∂ θs s)/(θg-θg,d)) + τs/r,s,ATRs,Aγ((1-θ yA + ) s,A ∂τ Peh,s ∂z2 Sts(θg - θs) (2) 2 ∂yA ∂yA 1 ∂ yA -U ) 2 ∂τ Pems,g ∂z ∂z g)/(θg-θg,d)) ΩgyAyB τs/r,g,Aγ((1-θ g,A

2 ∂yA ∂yA 1 ∂ yA s)/(θg-θg,d)) ) - τs/r,s,Aγ((1-θ -U yA s,A 2 ∂τ Pems,g ∂z ∂z

∂Ωg ∂(ΩgU) ))0 ∂τ ∂z

(3)

θg ) θg,0

θs ) θs,0

Effect of Dispersion Although, in general, hyperbolic differential equations are numerically more challenging to solve than the elliptic equations, the former can be faster to solve than the elliptic ones by applying the numerical approximations suggested by Kulkarni (1996). The implicitexplicit scheme that results in the explicit simultaneous equations is described in detail by Kulkarni (1996). A brief description of the applied discretization is given in Appendix 2. The system of equations generated by the applied discretization appears to be more stable for the hyperbolic system of equations. Therefore, before simulating the RE-GAS process using the reactionconvection-dispersion model (eqs 1-5), it was advisable to study the effect of heat and mass dispersion in the gas phase on the system. Using the parameters listed in Table 1, the first exothermic semicycle of a typical periodic operation was simulated using both the reaction-convection-dispersion model and the model without dispersion terms in the gas phase. Simulation results showed negligible effect of dispersion in the gas phase because the convection terms dominate. Therefore, the gas heat and mass dispersion terms are dropped from the model eqs 1, 3, and 4. The difference between the gas temperature and the catalyst temperature is negligible because of high heat transfer rates between the gas and solids. Thus, both gas and catalyst temperature can be used as representative bed temperature for the discussion of results. Attainability of Periodic Operation. Kulkarni and Dudukovic´ (1997) developed the necessary conditions for a periodic operation of an asymmetric fixedbed reactor. The criteria to be satisfied were given as:

[uinFgm,inyA,inXA(-∆Hg,A)t*odd]exo (4) (5)

@z)0

[uinFgm,inyA,inXA(∆Hs,A)t*even]endo

)

Qexo g 1 (7a) Qendo

and

t*even ωr,odd e ωr,even t*odd

(7b)

where the front velocity is given by:

1 ∂θg ) θg,in - θg Peh,g ∂z ∂θs 1 ∂yA )0 ) yA,in - yA (6a) ∂z Pems,g ∂z and no gradient at the exit:

@z)1 ∂θs )0 ∂z

Ωg ) Ωg,0 (6c)

The physical significance of the dimensionless parameters is explained by Kulkarni and Dudukovic´ (1996a-c, 1997).

The appropriate boundary conditions are those of flux continuity at the entrance:

∂θg )0 ∂z

yA ) yA,0

∂yA )0 ∂z

Initial conditions are

@ t ) 0 and 0 e z e 1

(6b)

ωr )

uFgCp,g

(

(1 - )FsCp,s

1-

) (

)

∆Tad ∆Tad )ω 1∆Tmx ∆Tmx

(7c)

The first criterion (eq 7a) assures that the first law of thermodynamics is not violated and the second criterion (eq 7b) assures that the hot zone does not escape from the bed during the periodic operation. In addition, Kulkarni and Dudukovic´ (1997) showed that for a periodic operation to be possible the heat of the exothermic reaction must be greater than the heat of the endothermic reaction. For the temperature front and the hot zone to stay well inside the bed, the differential creep velocity should be equal to zero (Kulkarni and Dudukovic´, 1996c):


ωr,diff )

ωr,oddt*odd - ωr,event*even )0 t*odd + t*even

(8)

The heat of methane combustion is much greater than the heat of the steam reforming reaction. For the same inlet conditions for both exothermic and endothermic semicycles, it can be shown from eqs 7 and 8 that the period of the exothermic semicycle must be greater than the period of the endothermic semicycle. From the equations just presented and parameters listed in Table 1 it is evident that methane combustion and steam reforming reaction can be coupled in an asymmetric fixed-bed reactor operating in a periodic steady state. Simulation Results for the Wrong-Way Process The steam reforming operation is typically carried out at temperatures around 1500 K (Blanks et al., 1990; Ferreira, et al., 1992; Wagner and Froment, 1992). The catalyst used for steam reforming is usually nickel supported on alumina. Therefore, we set the maximum allowable temperature in the bed equal to 1500 K. The ignition temperature for the combustion reaction is reported to be 990 K (Mullholand et al., 1993), which implies that for low fuel concentrations the initial bed temperatures must be higher than 990 K. However, because of the wrong-way behavior, the maximum temperature in the bed can then exceed 1500 K. Hence, to maintain the maximum temperature rise in the bed below 1500 K, the inlet concentration of fuel (methane) must be very low, which poses an additional problem. If the concentration of the fuel coming in is quite low, the total heat released by the combustion reaction during the exothermic semicycle is also very low. Because the temperature front creeps continuously forward in the axial direction towards the reactor exit, the period of the exothermic semicycle cannot be very long. At the same time, the energy (‘heat’) stored in the bed does not increase proportionally with the duration of the exothermic semicycle because of the front movement. Therefore, the heat available for the endothermic semicycle is very low as well, which demands that the concentration of methane (the reactant) in the endothermic semicycle also be low, that the period of the endothermic semicycle be very short, or both. Both of these requirements decrease the production rate of synthesis gas. Also, as the inlet concentration of methane increases during the endothermic semicycles, the front velocity for the endothermic semicycle (ωr,even) decreases (eq 7c). This relationship implies that to satisfy the zero differential creep velocity criterion of eq 8, the endothermic semicycle must last for a longer period of time, whereas the amount of heat generated during the exothermic semicycle remains the same! Thus, the energy criterion (eq 7) is not satisfied unless the concentration of the fuel for the exothermic semicycle is increased, which allows longer exothermic semicycle periods (eqs 7 and 8). However, at higher concentrations of fuel, the maximum transient temperature rise is greater than the maximum allowable temperature. Thus, the regenerative production of the synthesis gas by the wrong-way process can be accomplished only in the limited region where concentrations of reactants are very low in both semicycles. The existence of the temperature front during an endothermic semicycle is an approximation that is valid only when the maximum temperature in the bed does not decrease considerably.

Figure 2. (a) Temperature profiles at periodic steady state for the wrong-way RE-GAS process (yA,in ) 0.008; Tmx < 1500 K). (b) Methane mole fraction profiles at periodic steady state for the wrong-way RE-GAS process (yA,in ) 0.008; Tmx < 1500 K).

Figure 2a shows the periodic steady-state temperature profiles at the end of an exothermic and an endothermic semicycle. To maintain the maximum temperature in the bed below 1500 K, the inlet mole fraction of the fuel was maintained at 0.008. Because this mole fraction does not allow very high inlet concentrations of methane during the endothermic semicycles, the inlet methane mole fraction was also maintained at 0.008 for the endothermic semicycles. For high concentrations of methane during the endothermic semicycle, the bed cools down and no reaction can occur. As can be seen from Figure 2b, methane conversion for both semicycles is nearly complete. For complete conversions, as is the case here, the efficiency of the process is given by Kulkarni and Dudukovic´ (1997) as:

ηcycle )

[∆Hs,AFgm,inuinyA,int*even]endo [(-∆Hg,A)Fgm,inuinyA,int*odd]exo

(9)

It is evident from eq 9 that when the heat of reaction and the semicycle period for the exothermic semicycle are higher than the those for the endothermic semicycle, the energy efficiency per cycle is very low. This obviously is the case here, especially because when the heat


produced during the exothermic semicycle is high, the front velocity is low (eq 7) and the period of the exothermic semicycle is required to be greater than that for the endothermic semicycle (eqs 6 and 7). All this indicates that the simulated process is working at an energy efficiency as low as 16%. Therefore, this method is not a very efficient way to couple these two reactions. The excess heat that leaves the bed should then be used to produce steam. Because the outlet temperature of the gases for the exothermic semicycle is always greater than the gas inlet temperature for the endothermic semicycle, some of the heat leaving the bed can be used in the production of steam and/or to heat methane. Thus, the overall efficiency of the process, defined as the ratio of the rate of total heat requirement to the rate of total heat supply, i.e.

Qtotal Qr,exo + Qutility can be made considerably higher. However, in this study we do not concern ourselves with the design of the whole plant; but we would like to point out that although the overall energy efficiency of the plant can be higher, the efficiency of the auto thermal fixed-bed reactor itself is very low. An additional problem for the wrong-way process is posed by the limit on the maximum temperature in the bed. A change in the feed concentration can result in a large and undesirable increase in the catalyst temperature. Figure 3a shows how the maximum temperature in the bed increases beyond 1500 K for a 25% increase in the inlet fuel in the fraction from 0.008 to 0.01. Figure 3b displays the methane mole fraction profiles. Therefore, the wrong-way process would have to be operated with extreme caution, if at all. A Final Note on the Wrong-Way Process. It is important to note that under practically all conditions, the wrong-way operation of a fixed-bed reactor involving combustion of a fuel during the exothermic semicycles poses problems resulting from the high temperature rise. Because the temperature front creeps toward the exit of the bed, which involves taking the heat from the bed as the front traverses through it, the heat stored in the bed during the exothermic semicycle does not increase proportionally with the period of the exothermic semicycle. Thus, the heat available for the endothermic reaction in the subsequent endothermic semicycle is not sufficient for the feed having high reactant concentration. Hence, to increase the heat input during the exothermic semicycle, the inlet concentration of the fuel must be raised, which is not practical because the temperature rise in the bed can be excessively high for high fuel concentration. For example, the adiabatic temperature rise for a methane + air mixture, with a methane concentration as low as 10%, is ≈3300 K. It is impractical to operate a process that requires equipment that can withstand repeated temperature swings from 400K to 3700 K. In the case of the wrong-way processes, the maximum temperature rise is more than two times the adiabatic temperature rise and, hence, the range of the temperature swing is much greater. Thus, from the practical point of view, taking into consideration the refractive high temperature materials available today and those that appear likely to be available in the near future, any type of the wrong-way process involving pure combustion during the exother-

Figure 3. (a) Temperature profiles at periodic steady state for the wrong-way RE-GAS process (yA,in ) 0.01; Tmx > 1500 K). (b) Methane mole fraction profiles at periodic steady state for the wrong-way RE-GAS process (yA,in ) 0.01; Tmx > 1500 K).

mic semicycles may not be feasible. Also, as already mentioned, when the heat of the exothermic reaction is very high compared with the heat of the endothermic reaction, the efficiency of the wrong-way process is very low. Therefore, it is advisable to couple only exothermic and endothermic reactions of comparable heats of reaction. The Normal Process The wrong-way process was found unattractive to couple exothermic and endothermic reactions in the REGAS process for synthesis gas production when an upper temperature limit of operation is imposed because of low energy efficiency and very high temperatures reached in the fixed-bed reactor. Thus, for strict temperature control, the fixed-bed should be operated in the thermodynamic regime where the maximum temperature rise in the bed is closer to the adiabatic temperature rise. Simulation of the Normal Process. Some features of the normal process and the wrong-way process were compared by Kulkarni and Dudukovic´ (1996c). In the normal process, the inlet temperature of the feed gas for the exothermic semicycle is equal to the initial bed temperature, which is above the extinction temperature.


Figure 5. Effect of increasing inlet gas temperatures on the maximum temperature rise (∆Tmax) for the same difference between the initial bed temperature and the inlet gas temperature.

Figure 4. A schematic to explain the wrong-way behavior of a normal process.

For the first exothermic semicycle, the maximum temperature rise in the bed is equal to the adiabatic temperature rise and, hence, the front velocity is equal to zero (eq 7). There is a monotonic temperature rise from the entrance of the bed during the first exothermic semicycle. However, during the endothermic semicycle that follows, the front exhibits a finite velocity in the negative direction, which results in the finite displacement of the front towards the entrance for the exothermic semicycle (Figure 4). Because there was a monotonic increase in temperature from the entrance for the exothermic semicycle, the movement of the front toward the entrance for the exothermic semicycle (in the negative direction) increases the bed temperature at the entrance for the exothermic semicycle (Figure 4). Kulkarni and Dudukovic´ (1996c) showed that under these conditions the bed essentially exhibits the wrong-way behavior in subsequent exothermic semicycles, and the maximum temperature rise in the bed is again greater than the adiabatic temperature rise. However, this subsequent wrong-way behavior of the fixed bed can be repressed in the normal process by manipulating the duration of the semicycle periods and heat transfer rates. When the heat generation rate by the exothermic reaction is higher compared with the heat transfer rate between gas and solids, the magnitude of the wrong-way behavior is greatly decreased. This situation can be accomplished by setting the inlet gas temperature such that the exothermic reaction occurs very quickly compared with the heat transfer rates, which implies mixing the preheated reactants for the exothermic reaction only at the entrance of the bed. Thus, even when the temperature of the bed at the entrance for the exothermic semicycle is higher than the inlet gas temperature, the bed exhibits negligible wrongway behavior at higher reaction rates. Figure 5 shows the effect of increasing the inlet gas temperatures on

the maximum temperature rise in the bed for the same difference between the initial bed temperature and the inlet gas temperature of 200 K. It is evident that at higher temperatures, the reaction rates dominate the heat transfer rates and the maximum temperature rise in the bed decreases with increasing inlet gas temperature for a constant difference between the inlet gas temperature and the initial bed temperature. The ignition temperature for the gas phase combustion reaction is reported as 990 K (Mulholland, 1993). Because the concentration of the fuel required to maintain the maximum temperature below 1500 K is very low for lower bed temperatures and higher inlet gas temperatures are required to minimize the wrongway behavior, the inlet fuel + air temperature is set at 1100 K. Fuel and air can be heated separately in heat regenerators and mixed at the entrance of the fixed bed. The combustion reaction heats the bed. During the endothermic semicycle, a mixture of steam + methane at 400 K is introduced into the bed from the opposite direction. The mixture is heated in the fixed bed by the transfer of energy from the solids before the endothermic reaction occurs. There is a finite movement of the temperature front in the negative direction, which as explained before, increases the bed temperature at the entrance for the exothermic semicycle (Figure 6a). However, as can be observed from the figure, the maximum temperature rise in the bed stays well below 1500 K because the reaction rates are too high for a significant wrong-way behavior to occur. Figure 6b displays the methane mole fraction profiles at a periodic steady state. The results were obtained using feed values of yA,exo ) 0.01 and yA,endo ) 0.5, and semicycle periods of t* odd ) 500 s and t* even ) 30 s. Because the inlet gas temperature for the endothermic semicycle is nearly three times lower than that for the exothermic semicycle, the inlet gas density for the endothermic semicycle is nearly three times greater than that for the exothermic semicycle. Hence, even for shorter endothermic semicycle periods, the output of the process is still high. The normal process has another advantage over the wrong-way process. The temperature front forms a broad plateau instead of a sharp peak (compare Figures 6a and 2a), and this plateau does not creep during an


ω ) FgCp,gu/[FsCp,s(1 - )] This spreading of the temperature plateau, as opposed to the complete displacement, increases the energy stored in the bed proportionately to the duration of the odd semicycle period. Hence, the front does not move in the positive direction (from the entrance of the exothermic semicycle to the entrance of the endothermic semicycle), but spreads in the positive direction. During the endothermic semicycles, however, the temperature profile shows a finite movement in the negative direction which is compensated by the “front spreading” during the exothermic semicycle. As the duration of the exothermic semicycle increases, larger sections of the bed are heated with the position of the front stagnant at the entrance for the exothermic semicycle. As the duration of the endothermic semicycle increases, more energy stored in the bed is utilized. At long endothermic semicycle periods, when the heat provided by the exothermic semicycle is less than the heat requirement of the endothermic semicycle, the bed cools down and no reaction can occur at periodic steady state. Because the front does not physically move during the exothermic semicycle, it cannot escape from the exit for the exothermic semicycle. Thus, a necessary condition for periodic operation of the normal process is the trivial energy balance; that is, the total (reactive + sensible) energy provided by the exothermic semicycle must be equal to the total energy utilized (reactive + sensible) of the endothermic semicycle and the conversion for the endothermic reaction must be finite. Thus, the necessary condition to reach periodic steady state is given by:

Qsn,exo + Qr,exo ) Qsn,endo + Qr,endo and Qr,exo > 0 Figure 6. (a) Periodic steady-state temperature profiles for the normal RE-GAS process (yA,in,exo ) 0.01; yA,in,endo ) 0.5; Tmx < 1500 K). (b) Periodic steady-state methane mole fraction profiles for the normal RE-GAS process (yA,in,exo ) 0.01; yA,in,endo ) 0.5; Tmx < 1500 K).

exothermic semicycle. Hence, as the duration of the exothermic semicycle increases, more heat is stored in the bed and is available for the endothermic semicycle, unlike in the wrong-way process where because of the front movement, less heat is stored in the bed. For longer exothermic semicycle periods, this temperature profile spreads in the bed without creeping; that is, more heat is stored in the bed, which allows longer endothermic semicycle periods. Because the temperatures in the bed are always high and more heat is available for the endothermic semicycle, the conversion for the endothermic reaction during the endothermic semicycle is nearly complete (Figure 6b). Criterion for Periodic Operation. In the normal process, the front velocity for the exothermic semicycle is equal to zero because ∆Tmx ≈ ∆Tad (see eq 7c) and the front cannot escape from the bed. The temperature of the bed increases until it reaches the adiabatic temperature rise, and then the heat of the gas is transferred (because no reaction occurs after this point) to the cooler solids (Figure 6a). Thus, the bed accumulates more heat with the passing of time, and the high temperature plateau spreads with the speed of the front velocity of a heat regenerator without reaction

|Qr,endo| > 0

i.e.

[Fg,inuinCp,gt*odd(Tg,in - Tg,out) + Fgm,inuinyA,inXAt*odd(-∆Hg,A)]exo ) [Fg,inuinCp,gt*even(Tg,in - Tg,out) + Fgm,inuinyA,inXAt*even(∆Hs,A)]endo w

t*odd ) t*even

[Fg,inuinCp,g(Tg,in - Tg,out) + Fgm,inuinyA,inXA(∆Hs,A)]endo [Fg,inuinCp,g(Tg,in - Tg,out) + Fgm,inuinyA,inXA(-∆Hg,A)]exo and XA,exo > 0 and XA,endo > 0 (10) Energy Efficiency. The purpose of the asymmetric operation of a fixed-bed reactor is to utilize the energy provided by the gases during the exothermic semicycles to drive the endothermic reaction without allowing the temperature of the exit gases to increase. The energy contained in the hot exit gases, either during the exothermic semicycles or during the endothermic semicycles, indicates the energy that was not utilized to drive the endothermic reaction during the endothermic semicycles. This energy that is lost by the hot exit gases decreases the efficiency of an asymmetric fixed-bed reactor, which is defined as follows:


Figure 7. Temperature profiles for the normal process with energy recycle.

η)

Qendo [Qexo + Qsn,odd,in]Tref)Tg,in,even

(11a)

The normal process involves heating of the fuel and air mixture from the reference temperature to the inlet temperature and a cycle of exothermic and endothermic reactions in the fixed-bed. Since the gases bring the sensible heat into the bed which is also used to drive the endothermic semicycle the energy efficiency of the normal process is defined as,

ηcycle )

Qendo Qexo + Qpreheat

w ηcycle ) [Fgm,inuinyA,inXAt*even(∆Hs,A)]endo/ {[Fgm,inuinyA,inXAt*odd(-∆Hg,A)]exo + [Fg,inuinCp,gt*odd(Tg,in - Tg,out)]exo} (11b) For simplicity, it is assumed that both gas streams (for exothermic as well endothermic semicycles) are available at 400 K because at the operating pressure (2 atm), steam condenses at lower temperatures. For the case presented in Figure 6, the energy efficiency is 46%, which is nearly three times higher than that for the wrong-way process. The normal process involves preheating the reactants for the combustion reaction from available temperature of 400 K to the inlet temperature of 1100 K. Hence, the sensible heat that is carried out of the bed during both semicycles can be recycled to heat the fuel and air to further increase the overall efficiency. If it is possible to recycle all the heat, theoretically the efficiency of this process can rise to 100%. The temperature profiles for such a process using the reference temperature of 400 K are shown in Figure 7. The energy carried out of the bed by the hot exit gases during the endothermic semicycle (Qeven,recycle) and by the exit gases during the exothermic semicycle (Qodd,recycle) is used to preheat the inlet gas stream for the exothermic semicycle. The additional preheat, if needed, is provided by Qutility. As Qutility tends to zero the energy efficiency tends to 100%. The results shown in Figure 6 for the normal process are obtained using the inlet fuel mole fraction equal to 0.01, and semicycle periods of t*odd ) 500 s, and t*even ) 30 s. Even for this low concentration of fuel, the maximum transient temperature was greater than 1500 K for the wrong-way process (Figure 3a). Thus, the normal process offers accurate temperature control and higher energy efficiency. Also, the normal process can be operated at lower concentrations of fuel by propor-

Figure 8. (a) Periodic steady-state temperature profiles for the normal RE-GAS process (yA,in,exo ) 0.005; yA,in,endo ) 0.5; Tmx < 1500 K). (b) Periodic steady-state methane mole fractions profiles for the normal RE-GAS process (yA,in,exo ) 0.005; yA,in,endo ) 0.5; Tmx < 1500 K)

tionately increasing the period of the exothermic semicycle, or decreasing the period of the endothermic semicycle, without having to worry about satisfying the zero differential velocity criterion. For example, Figures 8a and 8b display the periodic steady-state temperature and concentration profiles, respectively, for the normal operation for the inlet fuel mole fraction of 0.005, methane feed of 50% for the steam reforming, and semicycle periods of t*odd ) 500 s and t*even ) 15 s. The complete conversion of methane in the steam reforming reaction is achieved under controlled temperature conditions. Productivity. The volumetric as well as molar productivity of synthesis gas is higher for the normal process than for the wrong-way process. In the case of the wrong-way process, a ratio of t* even/t* odd ratio of 0.623 is maintained to meet the needed dynamic and thermodynamic criteria for steady-state operation. The inlet conditions for both endothermic and exothermic semicycles were identical. Hence, in a cycle, 0.623 mol of methane react to produce synthesis gas for 1 mol of methane combusted. Because the inlet molar concen-


tration of methane is very low (0.008), the productivity is very low. In the case of the normal process, the period for the endothermic semicycle is much lower than the period for the exothermic semicycle (t*even/t*odd ) 0.06). However, the inlet temperature for the exothermic semicycle was nearly three times higher than that for the endothermic semicycle. The inlet molar concentration of methane during the endothermic semicycle is 50 times higher than it is in the case of the exothermic semicycle. Hence, in a cycle that involves an exothermic and an endothermic semicycle, 8.25 mol of methane react to produce synthesis gas during the endothermic semicycle for 1 mol of methane combusted during the exothermic semicycle. For example, for the parameters given in Table 1, 110 mol/m3s methane are combusted during the exothermic semicycle compared with 908 mol/m3s methane reacted to produce synthesis gas. The energy efficiency can be increased considerably by recycling the energy contained in the exit gases. The productivity can be increased by operating many reactors in parallel, so future research should focus on improving the energy efficiency. A Note on Thermodynamic Limitations. In this study we used the kinetic expression for the steam reforming reaction based on the assumption that the reaction is irreversible. To verify the validity of this assumption, the equilibrium conversions were calculated and compared with the simulated conversions for both the wrong-way and the normal processes. The assumption that the steam reforming reaction is irreversible is reasonably valid in the range of the temperatures encountered in the simulated fixed-bed reactor. However, thermodynamic limitations can be violated for lower gas velocities; that is, at higher residence times. Hence, care must be exercised when the the steam reforming of methane is assumed to be irreversible. The goal of this research was to gain physical insight into new processes and to explore the feasibility of their operation and not a detailed design of the plant. Hence, a simplified global kinetics for steam reforming reaction was adequate. However, for a more detailed simulation for design of a plant that can operate under a wide range of feed rates, the thermodynamic equilibrium limitations must be incorporated. Conclusions Coupling of the catalyzed endothermic steam reforming reaction to produce synthesis gas with methane combustion in an asymmetric a fixed-bed reactor operating in a periodic steady state is theoretically feasible. A cycle of operation involves first heating the bed by combustion reaction in the exothermic semicycle and then driving the endothermic steam reforming reaction with reactants fed from the opposite end during an endothermic semicycle. The wrong-way process involves feeding the reactants at a temperature below the bed temperature, which leads to the maximum transient temperature rise that can exceed the maximum allowable temperature. Hence, in the wrong-way process, the fuel concentration must be maintained extremely low to avoid unrealistic temperature overshoots. Only a small fraction of the heat produced during the exothermic semicycle is stored in the bed because of the finite movement of the temperature fronts. Under these conditions, achieving a stable periodic operation de-

mands that the period of the exothermic semicycle be greater than the period of the endothermic semicycle, which requires that the concentration of the reactants for the endothermic semicycles be low. Although the efficiency for the wrong-way process is very low, the overall efficiency can be improved by recycling the heat. In the normal process, the inlet gas temperature is maintained above a temperature at which the rate of heat generation by reaction dominates the heat transfer rate to decrease the wrong-way behavior. The maximum temperature rise is then always around the adiabatic temperature rise and accurate temperature control is possible. Because the temperature front does not creep but only spreads during the exothermic semicycle, most of the heat produced by combustion is stored in the bed and is available for the next endothermic semicycle. Because more heat is available, the period of the endothermic semicycle can be increased or the concentration of the reactants for the endothermic reaction can be increased to improve the production rate of the process. Process efficiency per cycle is 46%, but with efficient heat regeneration with the inlet streams, 100% efficiency can be set as a theoretically achievable goal. Nomenclature Symbols A ) component A ap ) surface area/bed volume (m2/m3) B ) component B Cp ) heat capacity (J/kg‚K) D ) dispersion coefficient; thermal (J/m‚K‚s), mass (m2/s) dp ) particle diameter (m) Ea ) activation energy (J/mol) H ) enthalpy (J/kg) h ) heat transfer coefficient (J/m2‚K‚s) k ) reaction constant (s-1) for first-order reactions (m3/ mol‚s) for second-order reactions k0 ) frequency factor (s-1) L ) total bed length (m) Mw ) molecular weight of the gas Nu ) Nusselt number hdp/γg P ) total pressure (N/m2) Pe ) Peclet number: (1) heat, gas FguinCp,gL/De,g,h (2) heat, solids (1 - )FsuinCp,sL/De,h,s (3) mass, gas suinL/De,g,ms Pr ) Prandtl number Cp,gµ/λg p ) partial pressure (N/m2) Q ) total amount of heat produced/semicycle (J) R ) universal gas constant (J/mol‚K) Re ) Reynolds number dpuF/µ r ) rate of production (mol/m3 of bed‚s) St ) Stanton number (1) gases hapL/FguinCp,g (2) solids hapL/(1 - )FsuinCp,s T ) local temperature (K) TD ) thermal diffusivity (m2/s) t ) time (s) TR ) dimensionless group: (1) gases 1000(-∆H)/MwCp,s∆Tad (2) solids P(-∆Hs,B)/RTgFsCp,s∆Tad U ) dimensionless gas velocity u/uin u ) local gas velocity (m/s) X ) average convesion x ) local bed length (m) y ) mole fraction in gas phase; dependent variable z ) dimensionless axial x/L; independent variable

780 Ind. Eng. Chem. Res., Vol. 37, No. 3, 1998 Greek Symbols R ) Arrhenius number Eas/RTs β ) heat transfer parameter (-∆Hs)De,poreCp,s/λsTs ∆H ) enthalpy of reaction (J/mol) ∆T ) change in the temperature (K) ∆t ) time step (s) ∆y ) change in variable y ) void fraction Φ ) Thiele-type modulus (dp/6)x(ks/Fs)/De,pore γ ) dimensionless group Ea/RTg,ad η ) thermal efficiency λ ) thermal conductivity (J/m‚s) µ ) viscosity (kg/m‚s) θ ) dimensionless temperature: 1) fixed-bed reactor (T - Tin)/∆Tad 2) regenerator (T - T0)/(Tin - T0) θg,d ) dimensionless group (2Tg,in - Tg,in)/∆Tad F ) density (kg/m3) τ ) dimensionless time t/(L/uin) τs ) space time L/uin τs/r ) dimensionless group τs/τr τr ) characteristic reaction time 1/(k0Fgm,inNr-1/)eEa/RTg,ad ω ) front velocity in a heat regenerator ωr ) front velocity in a fixed-bed reactor Ω ) dimensionless density F/Fin Ψ ) overall effectiveness factor Subscripts and Superscripts A ) species A ad ) adiabatic B ) species B CH4 ) CH4, methane cycle ) cycle diff ) differential e ) effective, corrected eddy ) related to turbulent eddies endo ) endothermic reaction eq ) equilibrium even ) even or endothermic semicycle exo ) exothermic reaction g ) gas gm ) molar h ) heat transfer coefficient m ) molar ms ) mass transfer mx ) maximum min ) minimum new ) new O 2 ) O2 odd ) odd or exothermic semicycle out ) outlet conditions overall ) overall pore ) related to pores r ) with reaction recycle ) recycle s ) solid sn ) sensitive total ) total t ) time utility ) utility 0 ) initial conditions

Appendix 1 Kulkarni (1992) showed that for heat regenerators, the rate of change of density as well as spatial variation of the gas mass flux are negligible. Hence, the equation of continuity is written as

∂(σgu) ∂Fg )) 0 w Fgu ) Fg,inuin ) constant ∂t ∂z (A1.1)

However, Fg and u vary as functions of gas temperature (Tg) and time (t). Equation A1.1 is also realized by the order of magnitude analysis. For example, for a 5-m long fixed-bed having properties listed in Table 1, the average rate of change of density of the gas is of the order of 10-4 kg/m3s. Using numerical examples, Kulkarni (1992) showed that the rate of change in the gas density is negligible because of higher volumetric thermal capacity of the solids. Applying eq A1.1, the rate of change of enthalpy per unit volume of the bed with compressible gas is written as:

∂(Hg) ∂Hg ∂Tg ∂Tg ∂(FgHg) ) Fg ) Fg ) FgCp,g ∂t ∂t ∂Tg ∂t ∂t (A1.2)

Again, using eq A1.1, change in enthalpy per unit length of bed is given by:

-

∂(uFgHg) ∂(Hg) ∂Hg ∂Tg ) -uFg ) -uFg ) ∂x ∂x ∂Tg ∂x ∂Tg -uFgCp,g (A1.3) ∂x

Equation 1 is derived by applying eqs A1.2 and A1.3. Equations 3 and 4 are obtained by extending eq A1.1 for the average molar density. Equations 3 and 4 can be applied for gas-solid systems where the rate of change of molar density is generally negligible because of higher volumetric heat capacity of the solids. However, these equations are more accurate for negligible difference between average molecular weight of reactants and products. Appendix 2 Consider the following nonlinear equation:

∂2y ∂y ∂y ) κ2 2 + κ1 + F(y) ∂t ∂z ∂z

(A2.1)

with given boundary and initial conditions, where F(y) is a nonlinear function. Explicit discretization of the second-order terms and implicit discretization of firstorder terms lead to a system of explicit equations as shown in eqs A2.2 and A2.3. n n n+1 - yni yi+1 - 2yni + yi-1 yi-1 - yn+1 yn+1 i i + κ ) κ2 + 1 2 ∆t ∆x ∆x n+1 ) (A2.2) F(yi-1

w yn+1 ) i ∆t ∆t n n n+1 n+1 n ) + F(yi-1 )∆t + κ2 2(yi+1 - 2yni + yi-1 ) yi + (κ1yi-1 ∆x ∆x ∆t 1 + κ1 ∆x n n n+1 w yn+1 ) f(yi-1 ,yni ,yi+1 ,yi-1 ) i

(A2.3)

Thus, algebraic equations resulting from the implicitexplicit discretization are explicit in nature. The result-


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Received for review May 22, 1997 Revised manuscript received September 25, 1997 Accepted September 26, 1997 IE970368D

Periodic Operation of Asymmetric Bidirectional Fixed-Bed Reactors

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