Effect of Periodic Variation of the Inlet Concentration on the

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Effect of Periodic Variation of the Inlet Concentration on the Performance of Reverse Flow Reactors Geng Chen,†,‡ Yong Chi,*,†,‡ Jian-hua Yan,†,‡ and Ming-jiang Ni†,‡ † ‡

State Key Lab of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, China Institute for Thermal Power Engineering, Zhejiang University, Hangzhou 310027, China ABSTRACT: Reverse flow reactors are regarded as an appropriate tool for removing gaseous pollutants from industrial effluents. This paper presents the results of an experimental study on a particular reverse flow reactor with periodic variations in inlet concentration; these experimental results are compared with those obtained by numerical simulation studies. Catalytic oxidation of methane is chosen as model reaction. When the inlet concentration is low (i.e., close to extinction limits) and periodically varied, the interaction between the feeding cycle period and the flow-reversal cycle period may lead to reactor instability; adjusting the period of flow reversal is one way to maintain thermal stability in such situations. Results of numerical investigations reveal that if the flow-reversal cycle time is an odd multiple of the inlet variation cycle time, a harmonic response will occur, with sharply increased variation of the maximum temperature. Basically, it is the inequality of total methane input during the two half-cycles during flow-reversal operations that cause reactor instability. Adjusting the phase between the two cycle periods may ease the inequality of the inlet concentration values, which procures a second strategy to enhance reactor stability. The temperature maximum is very sensitive to the heat-transfer parameters, when periodic inlet variations are introduced.

1. INTRODUCTION The promulgation of increasingly stringent air emission standards has led to growing concerns about the emission of numerous gaseous pollutants, such as total organic compounds (TOC) and volatile organic compounds (VOCs), and thus requires their treatment during industrial processes. The advantages of catalytic oxidation in reverse flow fixed bed reactors for treating these pollutants over homogeneous combustion or other technologies have been demonstrated in recent research.1,2 Basically, such a reverse flow reactor (RFR) integrates a catalytic fixed bed with a regenerative heat exchanger, in which the feed flow direction is periodically reversed. When exothermic reactions take place in a fixed bed catalytic reactor featuring a central catalyst section, a temperature wave is generated that creeps along with the gas flow. With periodic feed flow reversal, the heat released by reaction is trapped in the reactor and the catalyst section acts as thermal flywheel, maintaining high temperature and thus sustaining catalytic reaction even with lean feed. After the pioneering work of Matros,3 consecutive investigations on RFR behavior were performed during the past decades, both by numerical simulation and experimental analysis. Matros and Bunimovich4 and Kolios et al.5 prepared detailed reviews. Due to its intrinsic nonstationary character, RFR behaves in a rather sophisticated manner. The study of reactor response to different factors of influence became a major topic in this field,68 addressing operating parameters (flow rate, cycle period, chemical character, and concentration), catalyst types and activities,9,10 wall effects,11 and control of the ignited steady state,12 etc. These studies were carried out with constant values of all inlet parameters, implying that no input variations were intentionally introduced during these studies. Due to the high thermal inertia of the solid catalyst a RFR is able to overcome sudden temporary decreases in inlet concentration. The temperature maximum drops as soon as combustible r 2011 American Chemical Society

feed is cut off. Yet temperatures promptly recover when this feed is restored, thus reaching a pseudo-steady-state after several flowreversal cycle periods. Van de Beld et al.7,13 and Salomons et al.14 carried out experimental investigations on catalytic hydrocarbon combustion. Snyder and Subramaniam15 mathematically treated SO2 oxidation in RFR and observed a similar reactor behavior as described before. However, in real industrial processes, the nature of the gas stream (such as hydrocarbon concentration and flow rate) may vary in time and in line with changes in the production process, e.g., changes in reactor load, operating conditions, and scheduled producing procedure, etc. Continuous variations in the inlet conditions will affect the reactor behavior or may even endanger the safety of operation, causing either reactor extinction or reactor runaway (with eventual thermal deactivation of the catalyst). So, possible ways to avoid, alleviate, or control such negative effects are of practical interest. Onlya few data can be found on this topic. Cittadini et al.16 carried out a numerical investigation on RFR behavior when either inlet concentration or flow rate is varying periodically. For particular ratios between feeding cycle and flow-reversal cycle the interaction of both cycles may cause serious problems of instability. Xiao et al.17 developed a control strategy and tested it on a commercial SO2 flow-reversal converter with continuous inlet concentration variations within a certain range. Because variations in input parameters are common during real processes, it is necessary to understand the reactor behavior under such conditions, for control, optimization, and safety purposes. The present work investigates the effects of periodic variations of the inlet concentration on RFR and possible ways to maintain steady Received: November 21, 2010 Accepted: March 2, 2011 Revised: January 30, 2011 Published: March 30, 2011 5448

dx.doi.org/10.1021/ie102342w | Ind. Eng. Chem. Res. 2011, 50, 5448–5458

Industrial & Engineering Chemistry Research

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operation under such varying conditions, even when operating close to extinction. The experimental study is performed on a bench-scale reactor, choosing methane as model reactant. A mathematical model is developed and then verified by comparison with experimental data. When carrying out numerical simulations various influencing factors, including different types of inlet variation wave (rectangular, sinus, ...), feeding cycle period, and initial phase difference between the two cycles are considered.

Before starting a test, it is necessary to preheat the reactor, to raise the bed temperature above the ignition temperature of catalysts. An electric preheater is used to heat both the inert beds and the central catalytic bed. Meanwhile, ambient air is fed from one, periodically switching end of the reactor. Once the reactor is preheated to 500 C and a uniform temperature distribution is attained, methane is fed into the reactor and the solenoid valves are activated in a programmed manner.

2. EXPERIMENTAL SETUP A schematic diagram of the reactor used in this work is presented in Figure 1. The reactor is a 1.4 m long, 60 mm internal diameter stainless steel tube with wall thickness of 3.0 mm. It consists of three sections: two inert sections at both ends and a catalytic section in the middle. The inert sections, each 0.5 m long, are filled with R-Al2O3 pellets with a diameter of 67 mm, whereas the catalytic section is 0.4 m long and filled with a Pd/γAl2O3 commercial catalyst (Hangzhou Kaiming Catalysts Co., Ltd.) consisting of 35 mm diameter spheres. The reactor is surrounded by an insulation blanket (0.45 m thick) to minimize heat losses. The whole system is operated with periodic flow reversal, triggered by means of two pairs of solenoid valves actuated jointly. Methane (99.9% purity) is supplied from cylinders; a mass flow controller controls its flow. An electronic timer, linked to the mass flow controller generates the periodic variation of the methane feed desired. Gas composition is determined continuously with a Gasmet DX4000 portable Fourier transform infrared spectroscopy (FTIR) gas analyzer. Temperature along the reactor centerline is measured at 17 points using type K thermocouples and recorded automatically with a time interval of 5 s.

3. MATHEMATICAL MODELING A heterogeneous one-dimensional dynamic model, derived from the conservation equations, is adopted. Plug flow is assumed. Such a model has been demonstrated to be sufficiently accurate for describing the behavior of a reverse flow reactor, as studied in this work.18 A heterogeneous model is used, since it is more accurate for highly exothermic reactions under unsteadystate conditions. For the same reason the transient terms (e.g., ∂Tg/∂t in eq 1) were taken into account in the gas equations and the energy equation for the solid phase. The reaction is assumed to be fast and accumulation of methane on the catalyst surface is ignored in the mass balance in the solid phase, while intraparticle mass transport is incorporated by means of the effectiveness factor (Thiele modulus). Radial dispersion of heat and mass are neglected, given the relatively small reactor diameter. Pressure loss along the reactor length is ignored. In a bench-scale reverse flow reactor, adiabatic conditions are hard to achieve, given the inevitable heat losses through the wall. Hence, heat transport between gas phase and reactor wall is included. The main physical properties used in the numerical simulation are listed in Table 1. energy balance for the gas phase: u0 Fg, 0 DTg keff , g D2 Tg DTg ¼ þ Dt εFg Dx cp, g Fg Dx2

4hw ðTg Tw Þ hav ðTg Ts Þ εcp, g Fg εcp, g Fg DR

ð1Þ

mass balance for the gas phase: u0 Fg, 0 DCg DCg D2 Cg av ¼ þ Deff kg ðCg Cs Þ Dt εFg Dx Dx2 ε

ð2Þ

energy balance for the solid phase: keff , s D2 Ts DTs hav ð RA Þhe V ΔH ¼ ðT T Þ þ s g cp, s Fs Dt cp, s Fs Dx2 ð1 εÞcp, s Fs ð3Þ

Figure 1. Schematic of the experimental setup: 1, air blower; 2, reactor; 3, pressure reducer; 4, mass flow controller; 5, timer; 67, solenoid valve; 8, thermocouple.

Table 1. Main Physical Properties Used in the Simulation inlet gas temperature

298 K

catalyst thermal conductivity

reactor bed length

1.4 m

activation energy

95244 J/mol

reactor wall thickness bed void fraction

3 mm 0.405

preexponential factor inert pellet diameter

2.0 108 s1 67 mm

catalyst pellet diameter

35 mm

inert pellet density

1765 kg/m3

inert pellet thermal conductivity

1.13 W/(m K)

catalyst density

3

1240 kg/m

5449

0.73 W/(m K)

dx.doi.org/10.1021/ie102342w |Ind. Eng. Chem. Res. 2011, 50, 5448–5458


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B ¼ Ea =ðRT0 Þ,

where

Ha0 ¼ ð1 εÞηk¥ =ðkg av Þ

ð4Þ

ð RA Þhe V ¼ ηk¥ expð Ea =ðRTs ÞÞCs

εkeff , g 1 ¼ , BoH Lu0 cp, g Fg, 0

mass balance for the solid phase: kg av ðCg Cs Þ ¼ ð1 εÞð RA Þhe V

in the catalyst section

St H, W ¼

ð5Þ kg av ðCg Cs Þ ¼ 0

1 εDeff ¼ , BoM Lu0

ð6Þ

in the inert sections

DTw kw D Tw hw ðTw Tg Þ ¼ Dt cp, w Fw Dx2 cp, w Fw dw 2

Deff

keff , g ε DTg ¼ T0 Tg u0 cp, g Fg, 0 Dx

DCg u0 ¼ ðCg Cg, 0 Þ Dx ε DTs DTw ¼ ¼0 Dx Dx

t > 0, Z ¼ L :

t ¼ 0:

ð8Þ

ð9Þ ð10Þ

DCg DTg DCs DTs DTw ¼ ¼ ¼ ¼ ¼0 Dx Dx Dx Dx Dx ð11Þ

Tg ¼ Ts ¼ Tw ¼ T0 ,

Cg ¼ Cs ¼ 0

ð12Þ

For computational purpose, these model equations are now rewritten under dimensionless form: Fg Dτg Dτg 1 D2 τg ¼ þ St H ðτg τs Þ St H, w ðτg τw Þ Fg, 0 Ds Dz BoH Dz2

ð13Þ Fg, 0 DYg DYg 1 D2 Y g ¼ þ St M ðYg Ys Þ Ds Fg Dz BoM Dz2

ð14Þ

Dτs 1 D2 τs St H St M ΔTad: 1 ¼ ðτs τg Þ þ Yg 1 BoH, s Dz2 CR 1 þ Ha Ds ðCRÞT0 ð15Þ Dτw 1 D2 τ w ¼ St w ðτw τg Þ BoH, w Dz2 Ds

ð16Þ

with the following dimensionless parameters and numbers: z ¼ x=L, s ¼ tu0 =εL, τ ¼ T=T0 , Y ¼ C=C0 , Cg, 0 ð ΔHÞ ð1 εÞFs cp, s , CR ¼ ΔTad: ¼ εFg, 0 cp, g cp, g Fg, 0

av hL , c p , g F g, 0 u 0

4hw L cp, g Fg, 0 DR u0 St M ¼

av kg Lu0

1 εkw ¼ , BoH, w Lu0 cp, w Fw εLhw St w ¼ u0 cp, w Fw dw

ð7Þ

boundary and initial conditions:

StH ¼

εkeff , s 1 ¼ , BoH, s Lu0 cp, s Fs

energy balance for the wall:

t > 0, Z ¼ 0:

Ha ¼ Ha0 expð B=τs Þ,

A FORTRAN code has been developed for the dynamic simulation of the reaction system under transient conditions. The above system of partial differential equations (PDEs) is transformed into a set of ordinary differential equations (ODEs) using the method of lines (MOL). The reactor length is subdivided into 281 equidistant points. The resulting ODE system is solved through the FORTRAN routine VODE developed by LLNL (Lawrence Livermore National Laboratory, University of California).

4. RESULTS AND DISCUSSION Obviously, when comparing different reactor behaviors in relation to periodic variations of their inlet concentration, a unified framework of consistent criteria should first be specified. In this work, a pseudo-steady-state (PSS) must be attained before introducing the inlet concentration variations. As reported by Salomons et al.14 the axial temperature profile of a reactor in the PSS may be affected by its initial thermal state (e.g., the presence of an electric preheater). Thus for a proper comparison on RFR behavior under different operating conditions, all systems must start at the same or at least a comparable thermal state (initial temperature distribution). But it is impossible to achieve exactly the same initial thermal states during experiments. To attain similar PSS temperate profiles in different tests that apply the same operating parameters, a prolonged preheating procedure with relatively low heat output of the electrical preheater is adopted. Moreover, a PSS is maintained for over 10 cycles of flow reversal, before introducing the inlet concentration variation. Figure 2 illustrates the interrelation between the flow-reversal cycle and feed variation cycle and describes at the same time how the periodic inlet concentration variation is introduced. A squarewave variation between a maximum molar fraction and zero is adopted, to simulate the periodic changes in inlet concentration during an industrial process with variable operating conditions. The initial phase difference between the two cycles is zero unless stated otherwise. As velocity is a vectorial quantity, its sign refers to the direction of gas flow. Positive values pertain to a forward flow half-cycle (e.g., gas flowing upward in the reactor, as shown in Figure 1) and negative values refer to a reversed flow half-cycle (e.g., gas flows downward in the reactor, as shown in Figure 1). The time-averaged concentration over a full cycle is defined as the average inlet concentration (Cav) and used as a criterion of gross energy input into the RFR, when comparing the reactor 5450


Industrial & Engineering Chemistry Research performance under various operating conditions. Net energy input depends on gross energy input and on catalytic conversion of methane. A square-wave variation is not necessarily typical for real processes, as inlet parameters usually fluctuate in a complex and seemingly stochastic temporal pattern. However, study of the effect of periodic variation in model cases can give insight into RFR behavior with unsteady feed conditions. Square-wave variations are the simplest to achieve experimentally. Moreover, such a wave variation features all major basic characteristics, namely, frequency (cycle time), amplitude, and initial phase difference. The effect of frequency is the major topic of this paper, and the effects deriving from any initial phase differences are included on the basis of the numerical simulation part of this work. As for the effect of amplitude, it is implicitly treated during numerical simulations when comparing the effect of different wave types (square wave and sine wave). Generally speaking, higher amplitude also means larger variation in inlet concentration between two semicycles, resulting in greater shock load to operations. Further evidence relating to this deduction can be established by numerical simulation of different wave types (square wave and sine wave). 4.1. Results of the Experimental Tests. Choosing the catalytic oxidation of methane as model reaction, the minimum concentration of methane needed to maintain autothermal

Figure 2. Periodic variation in inlet concentration. A positive value of gas flow velocity refers to forward flow half-cycles, and a negative value refers to reversed flow half-cycles.

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operation in this unit is established at 3630 ppmv (ΔTad. = 120.0 K, with a gas superficial velocity of 0.16 m/s, a gas hourly space velocity (GHSV) of 1440 h1 and a flow-reversal cycle time of 600 s). This value is determined experimentally through trial-and-error: in a test series the inlet methane concentration is gradually decreased until reactor extinction occurs several flowreversal cycles after startup. Standard conditions feature an average methane concentration of 3996 ppmv (ΔTad. = 130.0 K), a switching time of 600 s, and a superficial velocity of 0.16 m/s. The axial temperature distribution of the reactor is shown in Figure 3, with and without inlet concentration variation. Both temperature profiles are acquired at the end of a flow-reversal cycle, when the flow direction is about to switch. Cittadini et al.16 carried out a mathematical simulation of such conditions and showed that both maximum temperature and outlet concentration vary considerably when the inlet concentration is very low, close to the extinction limit. These reactor behaviors are also observed in our experiments. As shown in Figure 3, with inlet concentration variation, the temperature plateau tends to shrink, which means that the temperature level of the reactor is lower than in the PSS. Although in both situations the total methane input is equal, the average temperature decreases because of lower average methane conversion during periodic feeding. During the half-cycle without methane feed, temperature drops in the catalytic section. When methane is fed again, the reactor gradually heats up, but complete conversion can no longer be achieved, especially at the start of the cycle, when the methane feed just resumed (see Figure 4). In the case in which the cycle time of inlet variation, tfeed, is very long, the hot zone in the catalytic section is not long enough to ensure sufficient conversion of methane, after prolonged cooling. As a consequence, conversion is rather low, i.e., 79% for tfeed = 900 s, and reactor extinction eventually occurs. For a RFR with stable inlet, feed reactor extinction is very slow, taking several hours in a bench-scale reactor or even much longer in industrial reactors. But such procedure accelerates when variation is introduced in the inlet feed. Without sufficient heat supply, the reactor even extinguishes during the cooling part of the cycle. Figures 4 and 5 show the evolution of both maximum temperature and outlet concentration during a typical test, thus illustrating the effects of introducing periodic inlet variations on reactor behavior. A reverse flow reactor reaches a PSS several flow-reversal cycles after startup. A bell-shaped temperature profile first develops and then moves back and forth in the reactor, following

Figure 3. Axial temperature profile in the reactor with and without variation of the inlet concentration (continuous line for model predictions, symbols for experimental) with u0 = 0.16 m/s, tc = 600 s, and Cav = 3996 ppmv. 5451



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Figure 4. Evolution of reactor outlet concentration, with and without periodic variation of the inlet concentration. For both cases, u0 = 0.16 m/ s, tc = 600 s, and Cav = 3996 ppmv: upper, constant inlet concentration; lower, inlet concentration varies periodically, tfeed = 360 s.

Figure 5. Evolution of maximum temperature in the reactor, with and without periodic variation of the inlet concentration. For both cases, u0 = 0.16 m/s, tc = 600 s, and Cav = 3996 ppmv: upper, constant inlet concentration; lower, inlet concentration varies periodically, tfeed = 360 s.

flow-reversal successions. In a PSS, the axial temperature profiles are almost the same during successive flow reversal cycles. So, during one cycle, the temperature of every single point in the reactor goes up during the first half-cycle and again goes down in the second half-cycle, or vice versa. Also, the maximum temperature varies with steady feed, as shown in Figure 5. In the meantime, the outlet concentration remains almost the same during successive flow cycles, with a relative high and adequate methane conversion rate. The sudden initial increase in outlet concentration is attributed to the short-circuiting of gas flow when the solenoid valves are simultaneously operated to switch the gas flow direction. Unreacted methane situated in the pipes between the valves is then directly emitted, without passing over catalyst, the so-called washout. Unburned methane, released by this washout, constitutes about 0.61.0% of the total feed during one full flow-reversal cycle in this reactor setup. When a periodic inlet concentration variation is introduced, both the maximum temperature and the outlet methane

Figure 6. Interaction between flow-reversal cycle and inlet concentration variation cycle: effect on the average temperature of the catalytic section: (a) tc = 600 s; (b) tfeed = 720 s. For both cases, u0 = 0.16 m/s and Cav = 3996 ppmv.

concentration vary stochastically (see Figures 4 and 5). Compared to that in the PSS, the range of the maximum temperature variation slightly increases (about 10 K), whereas the cycle time approaches tfeed. However, the temperature measured in the inert section varies as in the PSS, with a cycle time of tc. This reactor behavior is always observed, while applying different tfeed values. Because the reactor is relatively unstable, it is very sensitive to varying operating conditions. Even a small change in operating parameters will lead to large fluctuations in temperature. Nevertheless it is possible to maintain autothermal operation while using very lean methane feed, even quite close to extinction limit concentration. According to Cittadini et al.16 interaction between tfeed and tc in such situations will cause reactor instability or even extinction when tfeed comes close to tc. Such reactor behavior is also observed during our experimental study, as shown in Figure 6a. The reactor extinguishes in two distinct cases: when tfeed comes too close to tc and when tfeed becomes sufficient long. When tfeed comes close to tc, reactor extinction cannot be attributed to the too long time of cooling without thermal supply (methane feed), since autothermal operation is still maintained when tfeed/tc = 1.2. Accordingly, it is postulated 5452



Figure 7. Evolution of maximum temperature by different means to avoid reactor extinction. For both cases, u0 = 0.16 m/s, Cav = 3996 ppmv, tc = 600 s, tfeed = 900 s, and adjustments are made at t = 30 min: upper, Cav is increased to 5000 ppmv; lower, tc is shortened to 300 s.

that tc is a characteristic response time of a RFR system. If periodic variation in the inlet parameters (methane concentration variation in this case) is introduced and its cycle time is close to the characteristic response time of the reactor system, then a transition of the reactor state from PSS to an unstable state will take place. To prove such hypothesis, a series of tests is performed. As shown in Figure 6, reactor extinction indeed occurs when tc is close to tfeed, regardless of the values assumed by tc and tfeed. For example, in Figure 6b, when tfeed is fixed at 720 s, different reactor behavior is observed when changing tc. The reactor extinguishes when tfeed is close to tc, regardless of tc. Quantitative analysis of such reactor behavior is rather complicated and postponed for future work. It can also be seen from Figure 6b that when tfeed is comparatively long, adjusting tc may improve reactor stability. For a specific periodic inlet concentration variation, a shorter tc leads to a smaller creeping range of the hot zone and to more heat trapped in the catalytic section. The temperature plateau remains wide enough to ensure an adequately high methane conversion. So when tc is reduced from 720 to 600 s, or even to 342 s, the reactor remains comparatively stable (tc is reduced to 342 s in Figure 6b so that tfeed/tc = 2.1, corresponding with the values listed in Figure 6a). On the other hand, lengthening tc also favors stable operation, because the higher frequency of the inlet variation affects less reactor stability. Still, when the reactor is close to its extinction limit, too long tc will also lead to extinction. Another way to raise reactor temperature and thus maintain stable operation is by increasing the heat supply (e.g., adding auxiliary fuel or using an electric heater). Experiments are performed comparing the effect of adding auxiliary fuel and of shortening tc on maintaining the ignition state of the reactor. Results are shown in Figure 7. At the start the reactor is operated at PSS with u0 = 0.16 m/s, Cav = 3996 ppmv, and tc = 600 s. Then a periodic concentration variation (with tfeed = 900 s and Cav = 3996 ppmv) is introduced, and this moment is marked as starting point (t = 0). As in such conditions reactor extinction occurs within 120 min, too late a change in operating conditions will lead to failure of the test. So at t = 30 min (after a full concentration variation cycle), the following changes are made: an auxiliary methane stream with constant concentration is

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added and Cav is increased to 5000 ppmv in test A, while tc is shortened to 300 s in test B. Although the average methane concentration is increased in test A, the maximum temperature gradually drops between neighboring cycles and reactor extinction gradually occurs. When auxiliary methane is added, the maximum methane concentration increases as well. If even more methane is added, a hot spot may form in the catalyst section. During the actual experiment, soon after the methane concentration is increased, the temperature near the ends of a catalytic section increases sharply, resulting in an M-shaped axial temperature distribution. But the temperature peak gradually moves out of the catalytic section in the half-cycle of feed variation with lean methane concentration. So auxiliary fuel must be added with caution, or hot spots may form in the reactor, causing thermal deactivation of the catalyst. In test B a relatively stable state is maintained after shortening tc. However, the reactor is still very sensitive to variations in operating conditions. The superficial velocity suddenly increased to 0.18 m/s at t = 135 min and drops to 0.14 m/s at t = 150 min. A dramatic variation in the maximum temperature is observed; see Figure 7. To validate the mathematical model used in this work, the simulation results are compared with the experimental data, acquired from operating the bench-scale reactor described above. Due to the relatively small diameter of the unit, radial heat loss and axial heat conduction through the metallic reactor wall cannot be neglected. Good correspondence between simulated and observed axial temperature profile in typical tests is attained, as shown in Figure 3. The value and position of the maximum temperature in the catalytic section can be well-predicted by the model adopted when the inlet methane concentration is constant. But when periodic feed is introduced, simulation sometimes yields a relatively poor prediction of the experimental results: when conducting experiments, the reactor is in an unstable state and very sensitive to fluctuations in operating conditions. During experiments the maximum temperature then varies stochastically. 4.2. Numerical Simulations. Significant heat losses will always occur, as adiabatic conditions can hardly be achieved in a small, bench-scale reactor. Hence, its behavior may differ from that of industrial units. To eliminate the effects of heat loss, a mathematical simulation using a modified model is carried out in this part of the work for analyzing reactor behavior. The modified model is derived from the previously validated model, while the heat transfer between the gas phase and the reactor wall is not taken into consideration. Meanwhile, to eliminate the effect of the inert section on reactor behavior, the inert sections in the following simulation studies are replaced by catalytic sections, while keeping all other model equations, parameters, and the calculation procedure unchanged. Thus, the modified model describes an idealized flow reversal catalytic reactor under adiabatic conditions without inert sections at the ends, as originally proposed by Matros.3 The program codes are rebuilt accordingly. In the following comparison an average methane concentration of 1000 ppmv (ΔTad. = 32.5 K) is selected. The extinction limit is about 620 ppmv (ΔTad. = 20.6 K), as determined by both trial-and-error tests and simplified model calculations.19 This value ensures a relative high thermal level of the reactor, so that a wider range of the parameter tfeed/tc can be applied in the simulation. Various operating conditions are considered, including superficial gas velocity, flow-reversal cycle period, catalyst activity (kinetic data from ref 10; Ea = 1.22 105 J/mol and 5453



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Figure 8. Maximum temperature variation in various operating conditions, when a periodic variation in inlet feed is introduced with a succession of tfeed to tc ratios (Ea = 122 kJ/mol; k¥ = 2.71 109 1/s): (a) u0 = 0.1 m/s and tc = 1800 s; (b) u0 = 0.1 m/s and tc = 600 s; (c) u0 = 0.3 m/s and tc = 600 s; (d) u0 = 0.1 m/s and tc = 1800 s; For all cases, Cav = 1000 ppmv (ΔTad. = 32.5 K).

k¥ = 2.71 109 1/s) and types of variation wave (square wave and sine wave). The range of maximum temperature variation is shown in Figure 8 as a function of the tfeed/tc in these operating conditions. Generally speaking, when the average inlet concentration is relatively high, the temperature level is high enough to ensure total conversion of the methane fed. The only important concern is catalyst deactivation, following hot spot formation in the catalytic bed. Interestingly, the shapes of all the curves shown in Figure 8 are almost the same, regardless of either the operating conditions or catalyst activities. The variation of the maximum temperature increases with rising tfeed/tc. When tfeed/tc is about 1/7, 1/5, 1/3, and close to 1.0, several peaks of these curves are detected. The amplitude of the maximum temperature variation reaches a maximum when tfeed/tc = 1. In analogy with electrical networks or structural systems, the term resonance behavior can be applied to describe such an effect. Here, the reverse flow reactor is further regarded as a dynamic system, into which a variation in gas-phase composition introduces a periodic disturbance. This also implies that the flowreversal tc is a characteristic response time of this system and that the flow-reversal cycle wave can be taken as base wave of the dynamic reactor system. Rewriting the (square) base wave equation as a Fourier series gives 4A 1 1 sinðωtÞ þ sinð3ωtÞ þ sinð5ωtÞ uðtÞ ¼ π 3 5 1 þ sinð7ωtÞ þ ::: ð17Þ 7 where ω = (2π)/tc.

In the case in which the cycle time of the base wave is an odd multiple of the disturbance cycle time, a harmonic response will occur. The reactor tends to be less thermally stable, and the variation of the maximum temperature increases. It even reaches a peak value when the cycle time of the base wave and the disturbance cycle become equal, because the amplitude of the first harmonic component is at its maximum. In Figure 8, there was supposed to be a peak at tfeed/tc = 1/11, but the variation is too small already and overlapped by the nearby peak at tfeed/tc = 1/7. Moreover, the maximum temperature variation is attenuated in amplitude, when the periodic inlet variation is introduced as a sine wave rather than as a square wave. According to eq 17, for a sine wave and a square wave with the same amplitude and cycle time, the amplitude of the first harmonic component of a square wave is 4/π times greater than for the sine wave. Thus, introducing an inlet variation in a square wave leads to a greater disturbance of the reactor thermal stability than would be the case for a sine wave. Yet, among all these cases, methane conversion never drops below 97% and ignition is maintained. Nevertheless, if the average methane concentration is sufficiently low, close to the extinction limit, reactor extinction can be expected in all these cases when tfeed/tc is close to 1. Numerical simulation shows that the minimum methane concentration required to maintain reactor ignition increases from 712 to 928 ppmv, when steady feed is converted to periodic feed (tfeed = tc), with superficial velocity of 0.3 m/s and switch time of 600 s (the same operating condition as shown in Figure 8c). So, resonance in a RFR is independent of reactor properties or operating parameters. This work thus supports the hypothesis that tc is the characteristic response time of a reverse flow reactor. Reaction extinction occurs when coming close to 5454



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Figure 9. Evolution of the axial temperature distribution in the reactor with periodic inlet concentration variation, with u0 = 0.1 m/s, Cav = 1000 ppmv, and tfeed = tc = 1800 s.

extinction limits and can be regarded as a limiting case of the harmonic response of a reverse flow reactor. Figure 9 shows the evolution of the axial temperature distribution when tfeed = tc. The inlet methane concentration remains zero during the first half switching cycle (the flow direction is from left to right in Figure 9) and attains twice the average concentration during the second half-cycle (from right to left in Figure 9). The temperature plateau gradually shifts toward the side with double methane feed (right side in Figure 9). It takes about 20 full flow-reversal cycles to reach a new pseudosteady-state. During this process, the temperature plateau shrinks and the maximum temperature increases from 705 to about 740 K. This maximum temperature almost equals the value when methane is fed steadily with the concentration of 2000 ppmv. Because the hot zone is more close to one end of the reactor, the outlet temperature increases in one half-cycle. That may cause problems to downstream pipes and control valves. On the other hand, if the average concentration decreases, close to the extinction limit, the temperature plateau will not be wide enough to ensure adequate residual time for the methane stream, and reactor extinction will finally occur. As shown in Figure 10a, when tfeed/tc = 1/3, the total methane input of the two half-cycles are not equal, within each full flow reversal cycle, and it is denoted as asymmetrical input. Obviously, when tfeed/tc = 1/5 or 1/7, it is an asymmetrical input just as well. When tfeed/tc = 1/2, the total methane input of the two halfcycles within every full cycle are equal, and it is denoted as symmetrical input. If tfeed/ttc is close to 1.0, e.g., tfeed/tc = 0.9, the input in every single flow reversal cycle is asymmetrical. If the methane input of nine successive first half flow cycles is added up, the value equals that of nine successive second half flow cycles. Thus, when taking several full flow-reversal cycles as a whole, it can be regarded as a symmetrical input. Possibly, this is the reason why a low-frequency variation appears when 0.9 < tfeed/tc < 1.1, as reported by Cittadini et al.16 Moreover, the more full cycles it takes to count as a symmetrical input, the greater the variation of the reactor thermal level will be. From this point of view, tfeed/tc = 1.0 is an extreme situation featuring a totally asymmetrical input. Therefore it is the most thermally unstable state. In fact, tfeed/tc is not decisive when defining whether a particular inlet feed is asymmetric, or not. Rather, it is the total

Figure 10. Concept of feed asymmetry, in all cases: tfeed/tc = 1/3. (a) For the asymmetric feed, the total methane inputs within the two halfcycles are not equal; (b) for the symmetric feed, the total methane inputs within the two half-cycles are equal.

methane input within each half flow-reversal cycle that matters. As illustrated in Figure 10b, with the same tfeed/tc, an asymmetric feed can be transformed into a symmetric feed, merely by changing the initial phase difference between tfeed and tc. As shown in Figure 8, when feed periodicity is introduced, reactor stability is affected much more with asymmetric feed and thus the amplitude of the maximum temperature variation is greater. A harmonic response occurs when tfeed/tc is about 1/7, 1/5, 1/3, and close to 1.0. That also implies that changing an asymmetrical feed to a symmetrical feed could be a way to ease such effects. Thus, adjusting the initial phase difference between the flow-reversal cycle and inlet variation cycle could be a reasonable means to restore stability. The results of such simulations are shown in Figure 11: with tfeed/tc = 1.0, when the initial phase difference is increased from 0 to 900 s, the totally asymmetrical feed is gradually changed to symmetrical feed and the maximum temperature variation is suppressed, implying that reactor stability is reinforced (Figure 11a). Similar phenomena are observed when tfeed/tc = 1/3 or 3.0. Figure 12 shows the minimum average inlet concentration required for autothermal operation when tfeed = tc for different initial phase differences. To determine these values, a PSS closing to extinction limit is reached first; then periodic feed with various average inlet concentrations, and different initial phase differences are introduced. For RFR operation, a higher inlet concentration results in a higher reactor temperature, which improves reactor stability. Conversely, if the reactor is more likely to be extinct (or a stable operation is harder to maintain), more fuel is 5455



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Figure 12. Minimum average inlet concentration needed for maintaining autothermal operating as a function of the initial phase difference, with u0 = 0.1 m/s and tfeed = tc = 1800 s.

Table 2. Typical Parameter Values Adopted for a Sensitivity Analysis 1/BoH,s StM

Figure 11. Maximum temperature variation in the case of changing initial phase difference between the flow-reversal cycle and the inlet variation cycle: (a) tfeed = 1800 s, with inlet variation square wave and sine wave; (b) tfeed = 5400 s, with inlet variation square wave; (c) tfeed = 600 s, with inlet variation square wave. For all cases, u0 = 0.1 m/s, Cav = 1000 ppmv, and tc = 1800 s.

needed. So, the amount of combustibles needed to maintain ignition can be considered a suitable criterion for comparing reactor stability in a range of different operating conditions. As shown in Figure 12, when coming close to the extinction limit and setting tfeed = tc, the minimum methane concentration needed to maintain autothermal operation gradually decreases when the initial phase difference varies from 0 to 900 s. Note that the inlet feed is symmetrical when the initial phase difference is 900 s, which means the reactor stability is less likely to be at stake. Such a result corresponds well with those represented in

6.1 107 667.7

T0 u0

298 K 0.3 m/s

StH

591.5

tc

600 s

CR

1509.3

tfeed

600 s

ΔTad.

32.5 K

Figure 11a. Compared with adding auxiliary fuel, a more efficient and economic means to maintain RFR ignition is adjusting the flow-reversal cycle to avoid synchronization between flow-reversal cycle and inlet variation cycle. 4.3. Sensitivity Analysis. The influence of transport phenomena, such as convective heat transfer, is essential in optimizing the operating strategy when inlet conditions are varied. For this reason, a sensitivity analysis is performed and the effect of several transport parameters on the temperature maximum is investigated. The relevant operating parameters and typical values of the transport parameters at a temperature of 500 K are listed in Table 2. These values are calculated using the operating parameters listed in Table 1. The variation of maximum temperature is acquired after 150 full flow switch cycles when periodic inlet interruption is introduced. Results are shown in Figures 1315. The variation of maximum temperature of corresponding PSS is also shown for comparison. Because the steepness of the temperature front is determined by the axial dispersion of heat in the solid phase, lower effective heat conductivity leads to higher maximum temperature. On the other hand, a flat temperature profile and lower temperature plateau can be expected with rising heat dispersion. As discussed above, the temperature plateau shrinks under the interaction of tfeed and tc, the reactor tends to be more unstable with high axial heat dispersion rate and periodical inlet variation, which finally leads to light-off of the reaction, as shown in Figure 13. A rapid increase of the maximum temperature with periodic feed is observed when increasing the heat convection rate, while such effect is not so pronounced with steady feed. Improved heat exchange between gas and solid phase results in a higher temperature plateau and more heat storage in the central part of the reactor. When a periodic inlet variation is introduced, such effect occurs in a thinner part of the reactor; especially when 5456



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Figure 13. Dependence of the maximum temperature on heat dispersion in the solid phase.

Figure 15. Dependence of maximum temperature on interphase masstransfer rates.

Figure 14. Dependence of the maximum temperature on convection.

Figure 16. Dependence of maximum temperature on superficial gas velocity, tfeed = tc.

tfeed = tc, a dramatic increase in maximum temperature occurs, as shown in Figure 14. If ΔTad.,av is increased when heat convection is high, thermal deactivation of catalyst will occur and endanger safety operation of the reactor even if ΔTad.,av is relatively low. The effect of interphase mass transfer on maximum temperature is of utmost importance. For the reaction kinetics and operating parameters considered, the maximum temperature remains almost constant with changing StM (as shown in Figure 15). When mass transfer is slow, the conversion rate of methane decreases and the hot zone shrinks. Though the maximum temperature remains unchanged with periodic inlet variation, then the variation of maximum temperature is increasing. Figure 16 shows the effect of superficial gas velocity on maximum temperature with inlet concentration variation. A corresponding change of cycle time is made; thus, u0tc = constant. As the velocity of thermal front is linearly correlated with superficial gas velocity, so the displacement of the thermal front is the same during a half-cycle. A monotonous increase of the maximum temperature is observed when the gas velocity increases, whether the periodic inlet variation is introduced, or not. The temperature plateau evolves with gas velocity is in the same way. However, due to the strong dependence on the axial dispersion rate, the steepness of each temperature front on the side with double methane feed is almost the same with periodic

inlet variation. Thus, amplitude of maximum temperature variation remains almost constant in these conditions, as shown in Figure 16.

5. CONCLUSIONS The effects of periodic inlet concentration variation on RFR behavior are discussed. Both experimental investigation and numerical simulation are carried out. The interaction of inlet variation cycle period and flow-reversal cycle period will cause severe damage to reactor stability, which means reactor extinction if the average inlet concentration is very low. Experimental results show that, on the bench-scale flow-reversal reactor studied in this work, reaction extinction occurs when periodic inlet feed is introduced with an average methane concentration of 3996 ppmv, though the minimum methane concentration required to maintain autothermal operation is about 3630 ppmv. A mathematical model is built, and good correspondence between experimental results and numerical simulations is acquired. A modified model, which is derived from a previously verified model, is adopted for further numerical research. Applying harmonic analysis, it reveals that if the flow-reversal cycle time is an odd multiple of the inlet variation cycle time, a harmonic response will occur. The resonance behavior is in the maximum 5457


Industrial & Engineering Chemistry Research range when the inlet variation cycle period and flow-reversal cycle period are equal. Results of numerical simulation show that such reactor behavior is attributed to the asymmetry of the inlet parameters. Means to maintain steady operation are discussed and verified, namely, adjusting the flow-reversal cycle period or cycle phase between the two cycles. In short, adjusting the symmetry of the inlet parameters is beneficial to reactor stability. A sensitivity analysis is performed, and the effect of several transport parameters is discussed. The maximum temperature is very sensitive to heat-transfer parameters when periodic inlet variation is introduced.

’ AUTHOR INFORMATION Corresponding Author

*Tel.: þ86 0571 87952687. Fax: þ86 0571 87952438. E-mail: [email protected]. Funding Sources

Financial support for this work is provided by the National Basic Research Program of China (973 Program, 2011CB201500).

’ NOTATION av = surface-gas volume ratio, m2/m3 C = molar concentration, mol/m3 cp = heat capacity, J/(kg K) Deff = axial mass dispersion coefficient, m2/s DR = reactor diameter, m dp = solid particle diameter, m dw = reactor wall thickness, m Ea = activation energy, J/mol ΔH = combustion enthalpy, J/mol h = gassolid heat transmission coefficient, W/(m2 K) k¥ = preexponential factor, 1/s kg = gassolid mass transmission coefficient, m/s keff = axial heat dispersion coefficient W/(m K) hw = gaswall heat transmission coefficient, W/(m2 K) L = reactor length, m R = ideal gas constant, J/mol K (RA)Vhe = heterogeneous reaction rate per catalyst volume, mol/m3 s s = normalized time coordinate T = temperature, K ΔTad. = adiabatic temperature rise, K t = time, s tc = switch time, s tfeed = feed variation cycle time, s u = gas velocity, m/s x = axial position along the reactor, m Y = normalized molar fraction z = normalized axial coordinate Greek Letters

ε = bed void fraction η = internal mass-transfer effectiveness factor F = density, kg/m3

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’ REFERENCES (1) Matros, Y. S.; Bunimovich, G. A.; Patterson, S. E.; Meyer, S. F. Is It Economically Feasible to Use Heterogeneous Catalysts for VOC Control in Regenerative Oxidizers? Catal. Today. 1996, 27 (12), 307. (2) Hayes, R. E. Catalytic Solutions for Fugitive Methane Emissions in the Oil and Gas Sector. Chem. Eng. Sci. 2004, 59 (19), 4073. (3) Matros, Y. S. Catalytic Processes under Unsteady-State Conditions. Studies in Surface Science and Catalysis, Vol. 43; Elsevier: Amsterdam, 1989. (4) Matros, Y. S.; Bunimovich, G. A. Reverse-Flow Operation in Fixed Bed Catalytic Reactors. Catal. Rev.Sci. Eng. 1996, 38 (1), 1. (5) Kolios, G.; Frauhammer, J.; Eigenberger, G. Autothermal FixedBed Reactor Concepts. Chem. Eng. Sci. 2000, 55 (24), 5945. (6) Matros, Y. S.; Bunimovich, G. A. Control of Volatile Organic Compounds by the Catalytic Reverse Process. Ind. Eng. Chem. Res. 1995, 34, 1630. (7) van de Beld, B.; Borman, R. A.; Derkx, O. R.; van Woezik, B. A. A.; Westerterp, K. R. Removal of Volatile Organic Compounds from Polluted Air in a Reverse Flow Reactor: An Experimental Study. Ind. Eng. Chem. Res. 1994, 33, 2946. (8) Ben-Tullilah, M.; Alajem, E.; Gal, R.; Sheintuch, M. Flow-Rate Effects in Flow-Reversal Reactors: Experiments, Simulations and Approximations. Chem. Eng. Sci. 2003, 58 (7), 1135. (9) Kushwaha, A.; Poirier, M.; Sapoundjiev, H.; Hayes, R. E. Effect of Reactor Internal Properties on the Performance of a Flow Reversal Catalytic Reactor for Methane Combustion. Chem. Eng. Sci. 2004, 59, 4081. (10) Hevia, M. A. G.; Ordo~ nez, S.; Díez, F. V. Effect of The Catalyst Properties on the Performance of a Reverse Flow Reactor for Methane Combustion in Lean Mixtures. Chem. Eng. J. 2007, 129 (13), 1. (11) Hevia, M. A. G.; Ordo~ nez, S.; Díez, F. V. Effect of Wall Properties on the Behavior of Bench-Scale Reverse Flow Reactors. AIChE J. 2006, 52 (9), 3203. (12) Nieken, U.; Kolios, G.; Eigenberger, G. Control of the Ignited Steady State in Autothermal Fixed-Bed Reactors for Catalytic Combustion. Chem. Eng. Sci. 1994, 49 (24, Part 2), 5507. (13) van de Beld, B.; Westerterp, K. R. Air Purification by Catalytic Oxidation in a Reactor with Periodic Flow Reversal. Chem. Eng. Technol. 1994, 17 (4), 217. (14) Salomons, S.; Hayes, R. E.; Poirier, M.; Sapoundjiev, H. Flow Reversal Reactor fFor the Catalytic Combustion of Lean Methane Mixtures. Catal. Today 2003, 83 (14), 59. (15) Snyder, J. D.; Subramaniam, B. Numerical Simulation of a Periodic Flow Reversal Reactor for Sulfur Dioxide Oxidation. Chem. Eng. Sci. 1993, 48 (24), 4051. (16) Cittadini, M.; Vanni, M.; Barresi, A. A.; Baldi, G. Reverse-Flow Catalytic Burners: Response to Periodical Variations in the Feed. Chem. Eng. Sci. 2001, 56 (4), 1443. (17) Xiao, W. D.; Wang, H.; Yuan, W. K. An SO2 Converter with Flow Reversal and Interstage Heat Removal: From Laboratory to Industry. Chem. Eng. Sci. 1999, 54 (10), 1307. (18) Fissore, D.; Barresi, A. A.; Baldi, G.; Hevia, M. A. G.; Ord o~ nez, S.; Díez, F. V. Design and Testing of Small-Scale Unsteady-State Afterburners and Reactors. AIChE J. 2005, 51 (6), 1654. (19) Cittadini, M.; Vanni, M.; Barresi, A. A.; Baldi, G. Simplified Procedure for Design of Catalytic Combustors with Periodic Flow Reversal. Chem. Eng. Process. 2001, 40 (3), 255.

Subscripts

0 = inlet conditions g = gas phase out = outlet conditions s = solid phase w = reactor wall 5458


Effect of Periodic Variation of the Inlet Concentration on the

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