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Numerical Investigations of the Influencing Factors on a Rotary Regenerator-Type Catalytic Combustion Reactor Zhenkun Sang *, Zemin Bo, Xiaojing Lv and Yiwu Weng Key Laboratory for Power Machinery and Engineering of Ministry of Education, Shanghai Jiao Tong University, Shanghai 200240, China; [email protected] (Z.B.); [email protected] (X.L.); [email protected] (Y.W.) * Correspondence: [email protected]; Tel.: +86-021-3420-6342 Received: 13 March 2018; Accepted: 10 April 2018; Published: 24 April 2018

Abstract: Ultra-low calorific value gas (ULCVG) not only poses a problem for environmental pollution, but also createsa waste of energy resources if not utilized. A novel reactor, a rotary regenerator-type catalytic combustion reactor (RRCCR), which integrates the functions of a regenerator and combustor into one component, is proposed for the elimination and utilization of ULCVG. Compared to reversal-flow reactor, the operation of the RRCCR is achieved by incremental rotation rather than by valve control, and it has many outstanding characteristics, such as a compact structure, flexible application, and limited energy for circulation. Due to the effects of the variation of the gas flow and concentration on the performance of the reactor, different inlet velocities and concentrations are analyzed by numerical investigations. The results reveal that the two factors have a major impact on the performance of the reactor. The performance of the reactor is more sensitive to the increase of velocity and the decrease of methane concentration. When the inlet concentration (2%vol.) is reduced by 50%, to maintain the methane conversion over 90%, the inlet velocity can be reduced by more than three times. Finally, the highly-efficient and stable operating envelope of the reactor is drawn. Keywords: ultra-low calorific value gas; catalytic combustion; rotary regenerator; methane conversion; inlet velocity; inlet concentration

1. Introduction Methane is the second largest greenhouse gas after carbon dioxide, and has a global warming potential over 21 times higher than carbon dioxide [1]. Consequently, the effect of methane on climate change is almost equivalent to carbon dioxide. It is estimated that, by 2020, the world’s methane growth rate will be about 12–16% [2]. Ultra-low calorific value gas (ULCVG), gas calorific value of less than 3 MJ/Nm3 , is a low methane concentration and high volumetric flow case, thus, the utilization via flaring processes can be achieved merely under the conditions of supplemental fuel. Obviously, heat or electrical generation from the utilization of ULCVG can provide a significant economy, since ULCVG is often discharged directly into the environment without utilization. In addition, utilization of ULCVG will provide an opportunity to earn carbon credits, and a further benefit would be achieved. In 2015, China produced 63% of its energy from coal, and has about 11,000 coal mines, but the elimination and utilization technologies of coal mine methane are not applied by a majority of small coal mines. Consequently, the utilization rate is only 35.3%. According to the Chinese 13th Five-Year plan, the utilization rate above 50% and 2800 MW electricity from mine gas should be realized in 2020. Therefore, the utilization of ULCVG is a crucial and valuable mission.

Catalysts 2018, 8, 173; doi:10.3390/catal8050173

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Catalysts 2018, 8, 173

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Catalytic combustion can be adapted for a wide range of concentrations and low-temperature operation, achieving low or zero emissions of CO and NOx [3–5]. Therefore, catalytic combustion is recommended as the best option due to low and variable concentrations of ventilation air methane (VAM), as well as its high volumetric flow [6]. In the view of economy and feasibility, CFRR (catalytic flow reversal reactor), TFRR (thermal flow reversal reactor), lean burn gas turbines, and CMR (catalytic monolith reactor) can mitigate lower-heat value gas [7–9]. However, not all the VAM is used to provide energy production in the TFRR and CFRR system, because some of the energy is stored directly by the reactor to attain autothermal operation. For TFRR and CFRR, the necessary amount of methane to sustain a reaction is 0.12% and 0.45%, respectively, and providing additional fuel or electrical heating is necessary on the conditions of lower VAM concentrations [10]. Moreover, how to use TFRR and CFRR to produce electricity continuously is an intractable problem, as the methane concentration is mutative overtime. By virtue of the exceedingly low pressure drop, high geometrical area, high mechanical strength, and high resistance to dust, CMR is deemed to be more suitable for power generation applications than TFRR and CFRR [7]. However, prior to CMR a recuperator is required to preheat the incoming flow. Additionally, a CMR is more efficient and cost effective than CFRR for the elimination of volatile organic compounds (VOCs) [11]. In the past decade, the Commonwealth Scientific and Industrial Research Organization (CSIRO) had been developing a novel gas turbine system, which includes a CMR and regenerator [12]. Recently, a prototype unit had been successfully developed and commissioned by CSIRO. The experimental results demonstrated that this system can produce 19–20 kW of electricity output at very low methane concentrations (0.8 vol %) [13]. Nevertheless, the volume of the regenerator accounts for almost 40% of the entire system, and some methane should be discarded in order to avoid catalyst deactivation when the methane concentration is high. A system for the utilization and mitigation of VAM, named VamTurBurner©, was presented [10,14]. A gas turbine with natural gas as the fuel is used to produce electricity and preheat the incoming ventilation air directly to overcome the catalytic ignition temperature of methane. Hence, the high-temperature combustion product is a source of heat, which enters heat exchangers or steam turbines to generate thermal or electrical productions. However, the application of this system is limited, because a gas turbine is essential to preheat the incoming VAM for the operation of this system. A rotary regenerator was patented by Fredrik Ljungstrom as early as 97 years ago, which had a round disk or drum making for a large heat-transfer surface. Compared to traditional heat exchangers, a rotary regenerator with higher thermal efficiency is a possibility to achieve the autothermal operation [15]. As the matrix drum rotates, hot gas flows through and heats a portion of the disk, while cold incoming gas flows in the opposite direction through the remaining preheated portion. By virtue of the rotation of the matrix drum, heat is stored and rejected alternately by each matrix element [16]. Thus far, the rotary reactor is competitive to the other reversal flow reactors, such as CFRR and TFRR, with two similarities: treating lower-heat value gas and applying internal regeneration of the reaction heat to sustain the oxidation reaction. However, the rotary reactor has a unique advantage as the operation depends on the rotation of the reactor, not the control of a series of valves, which is helpful to minimize conversion losses during flow switching. Therefore, a rotary reactor can overcome the unavoidable reduction of the valve lifetime from the reversal reactor for the elimination of VOCs, and had a better performance than valve-operated reverse-flow. Moreover, a rotating reverse-flow reactor had a significantly more compact structure and flexible operation than the system including a rotary regenerator and a catalytic reactor [17,18]. When the rotary regenerator is used in a gas turbine system, due to the very large pressure difference between the inlet gas and outlet exhaust gas, during continuous rotation, the sealing system is difficult to keep from leaking gas. In order to prevent the radial leakage and develop efficient utilization technology of ULCVG, an incremental rotary reactor, a rotary regenerator-type catalytic combustion reactor (RRCCR), is proposed based on the principles of flameless combustion and rotary


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technology. If the rotation angle is reasonable, there is no difference between incremental rotation and continuous rotation in terms of thermodynamic or heat transfer [19]. However, incremental rotation has outstanding advantages on controlling radial leakage than continuous rotation. The feasibility of RRCCR was proved in our previous research [20]. Therefore, based on the typical parameters of a 100 kW stage gas turbine, this research gives priority to explore the influence of the changes of the inlet velocity and concentration on the performance of the RRCCR. The results are beneficial to develop a more efficient and convenient technology. 2. Results and Discussion 2.1. Effect of Inlet Velocity Through the operation of 11 periods, the RRCCR is in the cyclic steady state (CSS), and only the parameters in CSS are important for scientific analysis. Then, the performance and parameters of the RRCCR have periodic characteristics. Consequently, only parameters in one period during the CSS are analyzed, and the time shown in this paper is in one period, using a relative expression. In fact, the ULCVG flow is fluctuating, which directly reflects the change of the inlet velocity. In order to simplify the calculation, three cases are simulated and analyzed assuming that the inlet methane concentration is fixed at 2%, and the inlet velocity is defined as three cases, 15 m/s, 20 m/s, and 25 m/s, respectively. In Figure 1 state I is between two adjacent dashed lines on the left side, and state II is between two adjacent dashed lines on the right side. The gas temperature is in areas above the solid line, while the exhaust gas temperature is in areas below the solid line. When the inlet velocity is raised from 20 m/s to 25 m/s, at the initial time the outlet gas temperature decreases by around 5%, from 1035 K to 981 K, and the outlet exhaust gas temperature increases by about 9%, while at the end time the outlet gas temperature decreases by about 6%, from 1198 K to 1125 K, and the outlet exhaust gas temperature increases by about 5.7%. Therefore, it is concluded that, as the inlet velocity increases, the outlet gas temperature decreases monotonically, and the outlet exhaust gas temperature increases gradually. Consequently, increasing inlet velocity lessens the performance of the reactor. Nevertheless, when the inlet velocity is reduced from 20 m/s to 15 m/s, at the initial time the outlet gas temperature increases by around 1%, from 1035 K to 1049 K while, at the end time, the outlet gas temperature increases by about 3%, from 1198 K to 1232 K. Based on the inlet velocity of 20 m/s, there is the same increment or decrement of velocity, but the different variations of temperature reveal that the outlet gas temperature is more sensitive to the increment of the inlet velocity, which should be paid more attention in the design process. Additionally, it can be seen that the variation of the outlet exhaust gas temperature is approximately linear due to the effect of thermal inertia of the reactor wall. Further, this rule can be used to roughly evaluate the outlet exhaust gas temperature. As implied in Figure 2, the inlet velocity exerts an important effect on the methane conversion rate. As the inlet velocity increases, the methane conversion rate decreases. When the inlet velocity increases from 20 m/s to 25 m/s, the maximum methane conversion rate is reduced by about 5%, from 95% to 90%, while the minimum value is greatly reduced by about 16%, from 90% to 75%. However, when the inlet velocity is reduced from 20 m/s to 15 m/s, the maximum methane conversion rate is only raised by about 4%, but up to 99%, while the minimum value is changed from 90% to 95%, an increment of 5%. The gas residence time in the channel becomes short due to the improving inlet velocity, resulting in the decrease of the density of the adsorption reaction. Therefore, there are less time and fewer species for reactions to take place, which can decrease the methane conversion rate. There is the same variation of the inlet velocity by 25%, but the outlet gas temperature and methane conversion rate have differences of about 2–6 times, meaning that the performance of the RRCCR is sensitive to the increase of the inlet velocity. Meanwhile, there is a critical value for the inlet velocity. If the inlet velocity is less than that value, it is difficult to improve the performance of the RRCRR. Therefore, there is a stable and narrow range for the inlet velocity to maintain the superior performance of the reactor.

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Figure1. 1. The The gas gas temperature temperatureat atdifferent differentinlet inletvelocities; velocities;CCin,ch4 in,ch4 ==2%. Figure 2%. Figure 1. The gas temperature at different inlet velocities; Cin,ch4 = 2%.

Figure 2. The effect of inlet velocities on the methane conversion rate; Cin,ch4 = 2%. Figure in,ch4 = 2%. Figure2.2.The Theeffect effectofofinlet inletvelocities velocitiesononthe themethane methaneconversion conversionrate; rate;CC in,ch4 = 2%.

In that the temperature of hot-spots gradually increase in the same location, just the profiles of Intemperature that the temperature oftime hot-spots gradually in to thebesame location, the profiles of3. wall at the end of each state areincrease required andjust shown Figure In that the temperature of hot-spots gradually increase in the analyzed same location, just theinprofiles of wall temperature at the endwall timetemperature of each state are arequired to beeven analyzed and shown in Figure The 3. Clearly, the profiles of the have similar trend at different inlet velocities. wall temperature at the end time of each state are required to be analyzed and shown in Figure 3. Clearly, the profiles increases of the wallslightly temperature a similar trend even at different inlet velocities. wall temperature at the have pre-combustion zone, and decreases rapidly at velocities. the The postClearly, the profiles of the wall temperature have a similar trend even at different inlet wall temperature increases slightly at the pre-combustion zone, and decreases rapidly at thethe postcombustion zone. Due to the low thermal conductivity, the upstream heat transfer through The wall temperature increases slightly at the pre-combustion zone, and decreases rapidly atwall the combustion zone. Due to the low thermal the location upstream heat transfer through the wall is choked. Consequently, it is easy formconductivity, hot-spots at the ignition zone. the post-combustion zone. Due to thetolow thermal conductivity, theofupstream heat Additionally, transfer through is temperature choked. Consequently, it is is over easy 1000 to form hot-spots at theoflocation of ignition zone. Additionally, the of hot-spots at the end state I/II, andthe it can be seen a successive the wall is choked. Consequently, itK is easy to time form hot-spots at location of as ignition zone. temperature of hot-spots is 1000 Kbeneficial at the end to time ofcatalytic state I/II,ignition and it can seen as aNonetheless, successive ignition source is over extremely the ofbe methane. Additionally, thewhich temperature of hot-spots is over 1000 K at the end time of state I/II, and it can ignition source which is extremely beneficial to the catalytic ignition of methane. Nonetheless, increasing inlet velocity can result in the decrease of the temperature andignition rotation of is be seen asthe a successive ignition source which is extremely beneficial of to hot-spots, the catalytic increasing the inlet velocity can accumulation result in the decrease of the the reactor. temperature of hot-spots, and rotation is favorable to avoid the further of heat in methane. Nonetheless, increasing the inlet velocity can result in the decrease of the temperature of favorable to avoid the further accumulation of heat in the reactor. hot-spots, and rotation is favorable to avoid the further accumulation of heat in the reactor.


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Figure 3. 3. Profiles Profiles of of wall wall temperature temperature along along the the axis 10 s, s, C Cch4,in 2%. ch4,in= = Figure axis on on combustion combustion side. side. tt == 10 2%. Figure 3. Profiles of wall temperature along the axis on combustion side. t = 10 s, Cch4,in = 2%.

Since there Since thereisisaahigh highaspect aspectratio ratioof ofthe thechannel channel(about (about423), 423),the thecontour contourof ofpartial partialamplification amplification Since there is a high aspect ratio of the channel (about 423), the contour of partial amplification isisused to analyze the methane conversion in the channel. Figure 44shows the calculation model and used to analyze the methane conversion in the channel. Figure shows the calculation model is used to analyze the methane conversion in the channel. Figure 4 shows the calculation model and and the contour of partial amplification in zone A, B, and C. The contour at zone A demonstrates that the the amplificationininzone zoneA,A,B,B,and and The contour at zone A demonstrates thecontour contour of of partial partial amplification C.C. The contour at zone A demonstrates thatthat the the methane only heat transfer the pre-combustion zone. ItItapparent isisapparent methane not oxidized, asthere thereis onlyheat heattransfer transferatat at the pre-combustion zone. apparent at methaneisis isnot notoxidized, oxidized, as as there isisonly the pre-combustion zone. It is at at zone B that the catalytic combustion starts from the surface of the reactor, and quickly expands to the zone B that the catalytic combustion starts from the surface of the reactor, and quickly expands to the zone B that the catalytic combustion starts from the surface of the reactor, and quickly expands to the middle Through continued combustion post-combustion zone, middle area along theflow flowdirection. direction.Through Throughcontinued continued combustion atthe the post-combustion zone, middlearea areaalong alongthe flow direction. combustion atat the post-combustion zone, the atatzone zone C, and the distribution the outlet temperature the methane conversion isover over90% 90%at zoneC, C,and andthe the distribution of the outlet gas temperature themethane methaneconversion conversion is is over 90% distribution ofof the outlet gasgas temperature is isis relatively relatively uniform. relativelyuniform. uniform.

Figure4.4.Contour Contour of of methane methane conversion. t =t10 s, Cs,ch4,in = 2%.= 2%. Figure conversion.vv==2020m/s, m/s, = 10 Cch4,in Figure 4. Contour of methane conversion. v = 20 m/s, t = 10 s, Cch4,in = 2%.

2.2. Effect of Inlet Concentration 2.2. Effect of Inlet Concentration 2.2. Effect of Inlet Concentration If methane is completely converted, the estimated adiabatic flame temperature increase by 265 If methane is completely converted, the estimated adiabatic flame temperature increase by If methane is completely converted, estimated flame exerts temperature K per 1%vol. of methane [21], meaningthe that methaneadiabatic concentration a directincrease impact by on265 265 K per 1%vol. of methane [21], meaning that methane concentration exerts a direct impact on K performance per 1%vol. ofofthe methane [21],investigations meaning that methane exerts directtoimpact reactor. The on the effect ofconcentration inlet concentration areahelpful master on performance of the reactor. The investigations on the effect of inlet concentration are helpful to master performance of theofreactor. The because investigations onmethane the effect of inlet concentration arewith helpful master the performance the reactor, the inlet concentration is fluctuating the to actual the performance of the reactor, because the inlet methane concentration isthree fluctuating with the actual ULCVG flow. First, the inlet velocity fixed at methane 20 m/s, and the effects of different methane the performance of the reactor, becauseisthe inlet concentration is fluctuating with the actual ULCVG flow. First, the inlet velocity fixed at 20 m/s, and the effects ofrespectively, three different methane concentrations (1%,the 1.5%, and 2%) onisisthe performance thethe reactor studied. ULCVG flow. First, inlet velocity fixed at 20 m/s, of and effectsare, of three different methane concentrations (1%, 1.5%, and 2%) on the performance of the reactor are, respectively, studied. Finally, Finally, the inlet velocity also 2%) changed according to the low methane concentration to maintain a concentrations (1%, 1.5%,isand on the performance of the reactor are, respectively, studied. the inlet velocity is also changed according to the low methane concentration to maintain a high outlet high outlet gas temperature and methane conversion rate, so that high performance can be achieved. Finally, the inlet velocity is also changed according to the low methane concentration to maintain a gas temperature and conversion rate, so that high can be achieved. It cangas be seen in methane Figureand 5 that, duringconversion operation, as methane increases, outlet high outlet temperature methane rate, soperformance thatconcentration high performance can the be achieved. gasIttemperature also increases, but the outlet exhaust gas temperature is gradually reduced. can be seen in Figure 5 that, during operation, as methane concentration increases, theFor outlet

gas temperature also increases, but the outlet exhaust gas temperature is gradually reduced. For


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It can be seen in Figure 5 that, during operation, as methane concentration increases, the outlet gas Catalysts 2018, 8, x FOR PEER REVIEW 6 of 14 temperature also increases, but the outlet exhaust gas temperature is gradually reduced. For different methane concentrations, the outlet gas temperature is very different. typical methane Catalysts 2018, 8, x FOR PEER REVIEW 6 of 14 different methane concentrations, the outlet gas temperature is veryAdifferent. A typicalconcentration methane (1.5%)concentration increases by(1.5%) approximately and the increase theincrease outlet of gas is about 6–8%. increases by33%, approximately 33%, andofthe thetemperature outlet gas temperature different methane concentrations, thebemethane outlet temperature is concentration very different. A typical methane is about 6–8%. However, should notedgas that the methane (1.5%) by However, it should be notedit that the concentration (1.5%) decreases bydecreases approximately concentration (1.5%) increases by approximately 33%, and the increase of the outlet gas temperature approximately 33%, and the outlet gas temperature drop is about 8–20%. Especially in the conditions 33%, and the outlet gas temperature drop is about 8–20%. Especially in the conditions of 1% vol. is 6–8%. However, should to be noted that the methane concentration (1.5%) decreases by of about 1% vol. 20 m/s, ittoisit difficult the CSS, because the outlet gas temperature becomes and 20 m/s, itand is difficult achieve theachieve CSS, because the outlet gas temperature becomes smaller approximately 33%, and the outlet gas temperature drop is about 8–20%. Especially in the conditions smaller and smaller. The reduction of the methane concentration reduces the density of the and smaller. The reduction of the methane concentration reduces the density of the adsorption of 1% vol. and 20 m/s,which it is difficult achieve the the outlet CSS, because the outlet Eventually, gas temperature becomes adsorption reaction, further to decreases gas temperature. it is unable to reaction, which further decreases the outlet gasmethane temperature. Eventually, it is the unable to establish smaller and smaller. The reduction of the concentration reduces density of that the the establish the self-sustaining operation of the reactor. As mentioned previously, it can be drawn self-sustaining operation of thefurther reactor. As mentioned it can be drawn that the adsorption reaction, which decreases the outletpreviously, gas temperature. it is when unable to inlet when the inlet velocity is fixed, there is a corresponding range of methaneEventually, concentrations to achieve velocity is fixed, there is a corresponding range methane concentrations achieve satisfactory establish the performance self-sustaining of the reactor. As mentioned previously, ittocan be drawn satisfactory ofoperation the reactor, but the of actual concentration will vary depending onthat the performance of the reactor, but the actual concentration will vary depending on the system of interest. when the inlet velocity is fixed, there is a corresponding range of methane concentrations to achieve system of interest. satisfactory performance of the reactor, but the actual concentration will vary depending on the system of interest.

Figure 5. The effect methaneconcentrations concentrations on v =v20= m/s. Figure 5. The effect of of methane on the thegas gastemperature; temperature; 20 m/s. 5. The effectthat of methane concentrations on the rate gas temperature; = 20the m/s.inlet methane Figure 6Figure demonstrates the methane conversion is reducedv as

Figure 6 demonstrates that the methane is reduced as the conversion inlet methane concentration decreases. For example, under theconversion condition of rate 2% methane, the methane Figure 6 demonstrates that the methane conversion rate is reduced as the inlet methane concentration decreases. For example, the condition of 2% methane, the methane conversion rate is higher than 91%. Under theunder condition of 1.5% methane, the methane conversion rate is rate concentration decreases. For example, under the condition of 2% methane, the methane conversion approximately However, with methane, during the operation of the reactor, is higher than 91%. 86–92%. Under the condition of1% 1.5% methane, the methane conversion rate is eventually approximately rate is higher than 91%. Under the condition of 1.5% of methane, the methane conversion rateand is the self-operation cannot be achieved, sincethe theoperation amount oxidized methane is getting smaller 86–92%. However, with 1% methane, during of the reactor, eventually the self-operation approximately 86–92%. However, with 1% methane, during the operation of the reactor, eventually smaller. Fortunately, to the thermal inertia of the reactor wall, the reactor with mediocre cannot be achieved, since due the amount of oxidized methane is getting smaller and smaller. Fortunately, the self-operation cannot be achieved, since time the amount of oxidized is getting smaller and performance can still maintain for a certain under the conditionmethane of high inlet velocity (20 m/s). due to the thermal inertia of the reactor wall, the reactor with mediocre performance can still maintain smaller. Fortunately, due to the thermal inertia of the reactor wall, the reactor with mediocre Therefore, the lower inlet methane concentration needs smaller inlet velocity so that methane has for a performance certain time can under the condition high inlet velocity m/s). Therefore, thevelocity lower inlet methane stilltime maintain for aof certain under the(20 condition of high inlet (20 m/s). sufficient residence to occupy the activetime vacancy. concentration smaller velocity so that methane has sufficient residence to occupy Therefore,needs the lower inlet inlet methane concentration needs smaller inlet velocity so thattime methane has the activesufficient vacancy. residence time to occupy the active vacancy.

Figure 6. The effect of concentrations on the methane conversion rate. v = 20 m/s. Figure 6. The effect of concentrations on the methane conversion rate. v = 20 m/s.

Figure 6. The effect of concentrations on the methane conversion rate. v = 20 m/s.

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In the conditions of high inlet velocity (20 m/s) and low concentration (1%vol.), the reactor thestable. conditions high velocity (20 m/s) low concentration cannot cannotInbe Basedofon theinlet previous results, theand reduction of the inlet(1%vol.), velocitythe is reactor beneficial to be stable. on the previousrate. results, thethe reduction the inlet inlet velocities velocity ison beneficial to improve improve theBased methane conversion Thus, effects ofoflow the combustion of the methane conversion rate. Thus, the effects(1.5% of lowand inlet velocities the combustion ofFigure methane methane are studied at low inlet concentration 1%vol.). Theon results presented in 7 are studied inlet concentration (1.5% andwhen 1%vol.). results presented in Figure 7 indicate indicate that,atatlow low concentration (1.5%vol.), theThe inlet velocity is 15 m/s, the methane that, at lowrate concentration (1.5%vol.), when thevelocity inlet velocity is 15 m/s, methane conversion rate is conversion is over 90%. When the inlet is reduced to 9 the m/s, the methane is almost over 90%. When the Additionally, inlet velocity is reduced 9 m/s, the methane is almost completely oxidized. completely oxidized. when the to inlet methane concentration is lower (1%vol.), the Additionally, when the inlet methane concentration is of lower (1%vol.), the methane conversion is above methane conversion is above 90% at the inlet velocity 7 m/s, and above 97% at the inlet velocity of 3 90% m/s.at the inlet velocity of 7 m/s, and above 97% at the inlet velocity of 3 m/s. Whenthe themethane methaneconcentration concentrationisislow, low,reducing reducingthe theinlet inletvelocity velocityisisthe themost mostdirect directmethod methodtoto When maintainthe the reactor at When thethe methane concentration is high, a highainlet maintain athigh highperformance. performance. When methane concentration is high, highvelocity inlet will decrease the reactor performance, and a low inlet will result in the wall temperature to be velocity will decrease the reactor performance, and velocity a low inlet velocity will result in the wall close to the to permissible of most materials. temperature be close tolimit the permissible limit of most materials.

Figure Figure7.7.Effect Effectofofinlet inletvelocities velocitiesand andconcentrations concentrationson onthe themethane methaneconversion conversionrate. rate.

2.3. 2.3.OperationalDiagram OperationalDiagram According Accordingtotothe theprevious previousresults, results,the theinlet inletvelocity velocityand andconcentration concentrationhave havea amajor majorimpact impacton on the stability and performance of the reactor. To determine the highly-stable and efficient the stability and performance of the reactor. To determine the highly-stable and efficientworking working envelops, such as as methane methaneconversion conversionover over90%, 90%,and and outlet exhaust envelops,some somerestrictions restrictions are are given, given, such anan outlet exhaust gas gas temperature below 750 K. temperature below 750 K. The Theoperating operatingmap mapofofthe theRRCCR RRCCRcan canbebefound foundininFigure Figure8.8.The Thehigh-velocity high-velocitylimit limitisisdetermined determined by the upper curve. The velocity is above this curve, leading to a reduction of the methane conversion by the upper curve. The velocity is above this curve, leading to a reduction of the methane conversion rate, determined by by the the lower lowercurve, curve,which whichis rate,and andeven evencombustion combustionblowout. blowout. The The low-velocity low-velocity limit limit is is determined isdetermined determinedby bythe the nearly nearly complete complete methane methane conversion. conversion. Between Between the the two twocurves, curves,the thereactor reactorhas has superior performance which is desired to be maintained in actual operation. Even if superior performance which is desired to be maintained in actual operation. Even ifthe theinlet inlet concentration concentrationisisvariable, variable,there thereisisa areasonable reasonableinlet inletvelocity velocitytotoenable enablethe thereactor reactortotoachieve achieveefficient efficient and stable operation. Hence, this finding is very helpful for design, but actual values should and stable operation. Hence, this finding is very helpful for design, but actual values shouldvary vary according accordingtotothe thesystem systemofofinterest. interest.


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Figure 5 W/m/K. Figure8.8.Operational Operationalmap mapfor formethane methanecatalytic catalyticcombustion combustionon onPt. Pt.λλw = = 5 W/m/K. Figure 8. Operational map for methane catalytic combustion on Pt. λww = 5 W/m/K.

3. 3. Rotary Regenerator Type Rotary Regenerator TypeCatalytic CatalyticCombustion CombustionReactor Reactor 3. Rotary Regenerator Type Catalytic Combustion Reactor AA schematic Figure 9,9,and it can be seen that the main main part is schematicdiagram diagramofof ofthe theRRCCR RRCCRisis isshown showninin A schematic diagram the RRCCR shown in Figure Figure 9, and and ititcan canbe beseen seenthat thatthe the mainpart part is aa ceramic ceramic monolith monolith reactor reactor with walls coated by a porous material including catalytically-active with walls coated by a porous material including catalytically-active is a ceramic monolith reactor with walls coated by a porous material including catalytically-active particles. particles.Monolith Monolithstructures structuresplay playaaasignificant significantrole roleinin inenergy energyapplications applicationsand andenvironmental environmental particles. Monolith structures play significant role energy applications and environmental protection, which includes integration of various process operations, such as chemical reactions, protection,which whichincludes includesintegration integrationofofvarious variousprocess processoperations, operations,such suchasaschemical chemical reactions, protection, reactions, separation, and heat exchange [22]. The concept of the RRCCR is proposed based on the principles of separation, and heat exchange [22]. The concept of the RRCCR is proposed based on the principles separation, and heat exchange [22]. The concept of the RRCCR is proposed based on the principles ofof catalytic forlean lean concentration and low-temperature The of principle of catalyticcombustion combustion concentration and low-temperature ignition.ignition. The principle autothermal catalytic combustionfor for lean concentration and low-temperature ignition. The principle of autothermal operation is that sufficient preheating can be achieved by heat storage and be released operation is that sufficient preheating can be achieved by heat storage and be released alternately in the autothermal operation is that sufficient preheating can be achieved by heat storage and be released alternately in the incremental rotary reactor. Inmetal contrast to the metal ceramic core allow can incremental reactor. In contrast to the regenerator, theregenerator, ceramic corethe can effectively alternately in rotary the incremental rotary reactor. In contrast to the metal regenerator, the ceramic core can effectively heat to be recovered andconvenience reused [19].ofFor convenience of description, the more heatallow to be more recovered reused [19]. For description, the RRCCR is artificially effectively allow more heatand to be recovered and reused [19]. For convenience of description, the RRCCR is artificially divided into combustion and heat sides, eliminating ULCVG mainly at the divided into combustion and heat sides, eliminating ULCVG mainly at the combustion side and RRCCR is artificially divided into combustion and heat sides, eliminating ULCVG mainly at the combustion side andgas achieving exhaust gas heat at recovery primarily at the heat side. achieving exhaust heat recovery primarily the heat side. combustion side and achieving exhaust gas heat recovery primarily at the heat side.

1–ULCVG inlet, 2–gas outlet, 3–exhaust gas inlet, 4–exhaust gas outlet 1–ULCVG inlet, 2–gas outlet, 3–exhaust gas inlet, 4–exhaust gas outlet Figure 9. Schematic illustration of a rotary regenerator-type catalytic combustion reactor. Figure 9. Schematic illustration of a rotary regenerator-type catalytic combustion reactor. Figure 9. Schematic illustration of a rotary regenerator-type catalytic combustion reactor.

Natural gas as the primary fuel is used to launch the reactor and achieve the cyclic steady state. Natural gas as the primary fuel is used to launch the reactor and achieve the cyclic steady state. Then the fuel isgas transformed to ULCVG. ULCVG pours into reactorthe from 1 and is as the primary fuel isCompressed used to launch the reactor andthe achieve cyclic steady Then Natural the fuel is transformed to ULCVG. Compressed ULCVG pours into the reactor from 1 and is heated to the catalytic ignition temperature of methane. Subsequently, high-temperature gas is state. Then fuel is transformed to ULCVG. Compressed ULCVG pours into the reactor from heated to thethe catalytic ignition temperature of methane. Subsequently, high-temperature gas is generated due totothe exothermic reaction. The high-temperature gas releases heat in the heat 1 and is heated the catalytic ignition temperature of methane. Subsequently, high-temperature generated due to the exothermic reaction. The high-temperature gas releases heat in the heat consumption unit (HCU) enters the reactor in the opposite direction again. Then the exhaust gas is generated to and the reaction. high-temperature gas releases heat in thegas heat consumption unitdue (HCU) andexothermic enters the reactor in The the opposite direction again. Then the exhaust gas releases heat which is trapped inside the reactor bed onopposite the heat direction side. Finally, theThen exhaust gas is consumption unit (HCU) and enters the reactor in the again. the exhaust releases heat which is trapped inside the reactor bed on the heat side. Finally, the exhaust gas is discharged into thewhich environment from 4. the reactor bed on the heat side. Finally, the exhaust gas is gas releases heat is trapped inside discharged into the environment from 4. Owing to the limited heat storage cold gas flow, after a period of time the reactor discharged into environment fromand 4. incoming Owing to thethe limited heat storage and incoming cold gas flow, after a period of time the reactor wall cannot preheat the ULCVG to undergo flameless combustion. However, the incremental rotation wall cannot preheat the ULCVG to undergo flameless combustion. However, the incremental rotation through a certain number of degrees, such as 90 or 180 degrees, can realize the combustion again, through a certain number of degrees, such as 90 or 180 degrees, can realize the combustion again, because in the reactor a part of the heat side with sufficient heat is changed to a part of the combustion because in the reactor a part of the heat side with sufficient heat is changed to a part of the combustion


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Owing to the limited heat storage and incoming cold gas flow, after a period of time the reactor wall cannot preheat the ULCVG to undergo flameless combustion. However, the incremental rotation through a certain number of degrees, such as 90 or 180 degrees, can realize the combustion again, because in the reactor a part of the heat side with sufficient heat is changed to a part of the combustion side. After the spinning motion, the reactor will be suspended for a semi-cycle, approximately from 5 to 20 s. Here the rotation plays the role of a flow reversal valve. Finally, the operational stability is realized through this circulation. Catalysts 2018, 8, x FOR PEER REVIEW 14 The RRCCR with ULCVG as the primary fuel can provide energy products with9 ofultra-low pollution and has a compact structure and flexible operation. Additionally, side.emission After the spinning motion, the reactor will be suspended for a semi-cycle, approximately fromall the high-temperature gas production is used directly to produce electricity or other energy, and exhaust 5 to 20 s. Here the rotation plays the role of a flow reversal valve. Finally, the operational stability is realizedapplied through to thispreheat circulation. gas is merely the incoming mixture airflow. Moreover, the RRCCR can be used in RRCCR with ULCVG as theThe primary fuel canwould providebeenergy products withand ultra-low distributed The energy generation systems. production a source of heat, can be used emission and haselectricity, a compact structure flexible Additionally, all the highto drivepollution a turbine to provide or can beand used in aoperation. heat exchanger to produce hot water temperature gas production is used directly to produce electricity or other energy, and exhaust gas for local inhabitants. Furthermore, residual heat can be used by an organic Rankine cycle system to is merely applied to preheat the incoming mixture airflow. Moreover, the RRCCR can be used in generate electricity. distributed energy generation systems. The production would be a source of heat, and can be used to drive a turbine to provide electricity, or can be used in a heat exchanger to produce hot water for

4. Numerical Models and Simulation Approach local inhabitants. Furthermore, residual heat can be used by an organic Rankine cycle system to generate electricity.

4.1. Model Geometry and Mesh 4. Numerical Models and Simulation Approach

For a monolith reactor model, usually only one channel is required to be analyzed due to assuming that all 4.1.Model channelsGeometry behaveand essentially alike. However, during the operation of the RRCCR, the catalytic Mesh combustion and heat recovery occur on different sides, and only one channel cannot reflect the For a monolith reactor model, usually only one channel is required to be analyzed due to characteristic of the RRCCR. Since the reactor rotates 180 degrees each time, a reduced 2D model assuming that all channels behave essentially alike. However, during the operation of the RRCCR, shown the in Figure with fourand parallel channels is presented, the effects catalytic10 combustion heat recovery occur on different enabling sides, and the onlyassessment one channel of cannot of different and concentrations on the performance of degrees the RRCCR. Thea geometry reflectvelocities the characteristic of the RRCCR. Since the reactor rotates 180 each time, reduced 2D model model shown in Figure 10 with four parallel channels is presented, enabling the assessment the described herein is reasonably simplified in order to save simulation resources and cost,ofwhich can of different ontransfer, the performance of the combustion. RRCCR. The geometry simulateeffects the coupling of velocities the fluid and flow,concentrations rotation, heat and catalytic For this model, model described herein is reasonably simplified in order to save simulation resources and cost, which the combustion occurs in the two adjacent channels, while the heat recovery occurs in the other two can simulate the coupling of the fluid flow, rotation, heat transfer, and catalytic combustion. For this adjacentmodel, channels. The related parameters can be found in Table 1. the combustion occurs in the two adjacent channels, while the heat recovery occurs in the other two adjacent channels. The related parameters can be found in Table 1. Table 1. Parameters of a reactor channel. Table 1. Parameters of a reactor channel. Single Channel

Catalyst

Single Channel

Catalyst

Hd mm

Wt mm

L mm

1.2

0.4 0.4

508 508

Hd mm 1.2

Wt mm

L mm

Catalyst

Catalyst Pt Pt

The Properties of Cordierite The Properties of Cordierite Thermal Conductivity Thermal−Conductivity Wm 1 K−1 kg mol m−2 kg−1 K−1 Wm−1 K−1 2.7063 × −910−9 970 970 2.7063 × 10 5 5

Load Density Specific Heat J Load Density Specific Heat J kg mol m−2 kg−1 K−1

State I (solid line): 1–ULCVG inlet, 2–gas outlet, 3–exhaust gas inlet, 4–exhaust gas outlet. State II (dotted line): 1–exhaust gas outlet, 2–exhaust gas inlet, 3–gas outlet, 4–ULCVG inlet. Figure 10. Schematic of the computational model.

Figure 10. Schematic of the computational model. Both solid and fluid fields are generated by a quadrilateral mesh. However, different mesh generation strategies in fluid and solid domains are adopted due to the difference between the anisotropy of the fluid near the wall and the isotropy of the solid. As the fluid field, the mesh node


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Both solid and fluid fields are generated by a quadrilateral mesh. However, different mesh generation strategies in fluid and solid domains are adopted due to the difference between the anisotropy of the fluid near the wall and the isotropy of the solid. As the fluid field, the mesh node spacing (0.01 mm) is refined close to the wall in the radial direction. As the solid field, the grid node spacing (0.3 mm) is uniform in the radial direction. The mesh independent verification is studied by 30,000, 60,000, and 120,000 mesh cells, respectively. Finally, the 60,000 mesh cells case is adopted regarding the accuracy and calculation cost. 4.2. Reaction Mechanism and Mathematical Model Since the gas calorific value is less than 3 MJ/Nm3 and the height size is smaller than the quenching diameter (less than 2.25 mm) of the gas phase reaction with low thermal conductivity, the gas phase reaction is ignored [23]. Additionally, as the aspect ratio of a channel is very high (about 423), the radiation transport is neglected as it has scarcely any effect on the temperature distribution within the monolith channels for the ceramic support materials [24]. Computational Fluid Dynamics (CFD) models are able to predict a very complex flow field, even combined with catalytic combustion, which is used for the management, design, and operation of catalytic reactors [25,26]. Hence Ansys Fluent 15.0 (ANSYS, Pittsburgh, PA, USA), combining multi-step methane reactions on Pt, is used to perform this simulation. This mechanism contains seven adsorption reactions, 11 surface reactions, and five desorption reactions involving 11 surface species, i.e., Pt(s), CH3 (s), CH2 (s), CH(s), C(s), CO2 (s), CO(s), H2 O(s), OH(s), H(s), and O(s) [27]. The calculated models are 2D unsteady, all the mathematical models are described as follows, and the model equations are discretized by a finite volume formulation based on quadrilateral mesh. Continuity equation: ∂(ρ) ∂(ρui ) = 0 i = 1, 2 (1) + ∂t ∂xi Momentum equation: ∂(ρui ) ∂ ρui uj ∂p ∂ 2 ui 1 ∂2 uj + =− +µ + µ ∂t ∂xi ∂xi ∂xj xj 3 ∂xi xj

(2)

Energy equation: ∂(ρh) ∂(ρuj h) + = ∂t ∂xj

! ∂ ∂Ys ∂ ∂T ∑[ ∂xj (ρhs Ds ∂xj ) + ∂xj λs ∂xj ] + Sh s

(3)

Component equation: ∂(ρYs ) ∂(ρuj Ys ) ∂ ∂Ys + = (ρDs ) + Rcs ∂t ∂xj ∂xj ∂xj

(4)

Solid wall heat conduction equation: ∂(ρh) ∂ ∂T + (λw ) = Sh ∂t ∂xj ∂xj

(5)

Ideal gas equation: p = ρRT ∑

Ys Ms

(6)

4.3. Simulation Methods and Boundary Conditions The period of the RRCCR, including state I and state II, is 20 s. The stationary time is 10 s in each state. At the end time of each state, the reactor is rotated rapidly by 180 degrees. Therefore, the rotation


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time is neglected. The numerical calculation is carried out by modifying the position of the inlet and outlet according to Figure 10 and Table 2. For example, in state I, the ULCVG comes into the reactor from inlet 1, and leaves the reactor from outlet 2. In state II, however, the inlet and outlet location of the ULCVG is changed: the ULCVG enters the reactor from inlet 4 and leaves the reactor from outlet 3. Table 2. Switch order and boundary conditions. State

Gas Name

No. Inlet

Boundary Condition

Value/m/s, K

Gas Name

No. Outlet

Boundary Condition

Values/bar

ULCVG

1

Velocity inlet

u, 427

Gas

2

Pressure outlet

3

Exhaust gas

3

Mass flow inlet

UDF

Exhaust gas

4

Pressure outlet

1.15

ULCVG

4

Velocity inlet

u, 427

Gas

3

Pressure outlet

3

Exhaust gas

2

Mass flow inlet

UDF

Exhaust gas

1

Pressure outlet

1.15

State I

State II

In a typical 100 kW stage microturbine, the pressure ratio is about 3 and the temperature drop in the turbine is about 220 K. Through the compressor, the ULCVG with a temperature of 427 K is admitted into the reactor. Hence, the temperature drop in the HCU is assumed to be 220 K. A user-defined function (UDF) is adopted to decrease the outlet gas temperature by 220 K as the inlet condition of exhaust gas temperature after each time step. The mathematical specification of the boundary conditions is drawn up as below. State I: T3(t) = T2(t) − 220 (7) State II: T2(t) = T3(t) − 220

(8)

Coupled thermal conditions are used between the reactor wall and fluid, because both of them are in the transient case. The reaction mechanism is assigned to the interface of the fluid and reactor wall from 74.2 to 100% L. In addition, at the fluid/wall interface, no-slip and no normal species diffusive flux boundary conditions are used. The incoming flow is laminar due to the low Reynolds number, and the fluid density is assumed to be that of an ideal gas. The transport coefficients, such as viscosity and thermal conductivity, are calculated by the ideal gas mixing law, and mass diffusion coefficients are calculated by the kinetic theory. These coefficients depend on temperature and composition.The time step is set as 0.002 s, which is smaller than the residence time of gas traveling through the reactor (~0.02 s). The material of the reactor is selected by cordierite and, therefore, an-isotropic thermal conductivity is assigned to the solid field. At the entrance of the RRCCR, fixed flat profiles are assumed for velocity, species concentration, and temperature. The inlet and outlet boundary conditions are also listed in Table 2. Additionally, a linear temperature distribution from 420 K to 950 K is assigned to the initial wall by UDF. Parallel functions are used by means of the segregated solver of ANSYS Fluent 15.0 and the cyclic steady state (CSS) is obtained after 11 periods. ϕ is the methane conversion rate, defined as: ϕ=

Cch4,in − Cch4,out × 100% Cch4,in

(9)

where Cch4,in is the inlet methane concentration (by volume). Cch4 ,out is the outlet methane concentration (by volume).


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4.4. Model Validation According to our previous study [28], a CFD simulation is carried out based on the reaction mechanism to validate the accuracy. In the experiment, the premixed fuel is adjusted to the desired pressure by a pressure reducer then passes through a 15 kW electric heater, and finally enters the catalytic combustion chamber for the catalytic reaction. There are two water-cooled probes before and after the catalytic combustion chamber to collect the sample. Finally the content of each component in the sample gas is measured by a gas chromatograph. length of the ceramic monolith reactor is 127 mm. The diameter is12 90ofmm. Catalysts 2018, 8, x FOR PEER The REVIEW 14 The wall thickness is 0.18 mm, and the diameter of each channel is 1.27 mm. Theexperimental experimentaland andnumerical numericaldata data are are given given in the Figure 11 The 11 under under the theboundary boundaryconditions conditionsof an inlet concentration of 1.96%, an inlet velocity of 6 m/s, and an inlet pressure of 2.04 kPa. relative of an inlet concentration of 1.96%, an inlet velocity of 6 m/s, and an inlet pressure of 2.04The kPa. The error between computations and experimental data data is less thanthan 7%,7%, thethe main reason is isthat relative error between computations and experimental is less main reason thatititis guarantee the the operation of the at the adiabatic condition. Figure 11Figure illustrates isdifficult difficulttoto guarantee operation ofexperiment the experiment at the adiabatic condition. 11 that the methane conversion has a satisfactory agreement between them. The methane conversion illustrates that the methane conversion has a satisfactory agreement between them. The methane increases with the temperature increase of increase the incoming Therefore, is believeditthat conversion increases with the temperature of thepremixed incomingfuel. premixed fuel.itTherefore, is the numerical adopted in this studyin are reasonably believed that themodels numerical models adopted this study areaccurate. reasonably accurate.

Figure Figure11. 11.Verification Verificationofofthe themodel: model:methane methaneconversion. conversion.

5.5.Conclusions Conclusions RRCCR RRCCRisisa apromising promisingand andfeasible feasibletechnology, technology,which whichisisworthy worthytotobebepopularized popularizedfor forthe the utilization of ULCVG. It not only diminishes the effect of methane on the greenhouse effect, but utilization of ULCVG. It not only diminishes the effect of methane on the greenhouse effect, butalso also expands expandsthe thesupplement supplementofofenergy. energy.The Theinfluences influencesofofinlet inletvelocity velocityand andconcentration concentrationononthe thereactor reactor are analyzed by CFD technology. In general, inlet velocity and methane concentration affect not only are analyzed by CFD technology. In general, inlet velocity and methane concentration affect not the gas temperature, exhaust gas outlet temperature, and methane conversion rate, but also only the gas temperature, exhaust gas outlet temperature, and methane conversion rate, but the also temperature of hot-spots in the in reactor wall, which can becan seenbeasseen a continuous ignitionignition source. source. Thus the temperature of hot-spots the reactor wall, which as a continuous the occurrence of catalytic combustion is not only due only to sufficient preheating, but also the presence Thus the occurrence of catalytic combustion is not due to sufficient preheating, but also the ofpresence hot spots. of hot spots. First, First,asasthe theinlet inletvelocity velocityincreases, increases,the theoutlet outletgas gastemperature temperatureand andmethane methaneconversion conversionrate rate decrease. However, the performance of RRCCR is more sensitive to the increase of velocity, which decrease. However, the performance of RRCCR is more sensitive to the increase of velocity, which needs needs attention the design process. For example, when thevelocity inlet velocity (20increases m/s) increases moremore attention in thein design process. For example, when the inlet (20 m/s) by 25%, bythe 25%, the outlet gas temperature decreases by 5~6%, and the methane conversion decreases outlet gas temperature decreases by 5~6%, and the methane conversion decreases by 6–17%. by On6– the 17%. On the contrary, when the inlet velocity (20 m/s) is reduced by 25%, the outlet gas temperature contrary, when the inlet velocity (20 m/s) is reduced by 25%, the outlet gas temperature increases increases 1–3%, and the methane conversion by 3%. lessAs than 3%. As result, order to by 1–3%,by and the methane conversion increases increases by less than a result, inaorder to in improve the improve the performance of the reactor, there is only a narrow range of inlet velocities to be used. performance of the reactor, there is only a narrow range of inlet velocities to be used. Finally, with the increase of methane concentration, the outlet gas temperature, methane conversion rate, and peak temperature of the reactor wall have a similar trend. Relatively speaking, the performance of the RRCCR is more sensitive to the decrease of methane concentration, which should be paid more attention in the design process. When the inlet concentration is low, reducing the inlet velocity is an effective method to increase the methane conversion rate and achieve the selfsustained operation of the reactor. Moreover, when the inlet concentration (2%vol.) is reduced by


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Finally, with the increase of methane concentration, the outlet gas temperature, methane conversion rate, and peak temperature of the reactor wall have a similar trend. Relatively speaking, the performance of the RRCCR is more sensitive to the decrease of methane concentration, which should be paid more attention in the design process. When the inlet concentration is low, reducing the inlet velocity is an effective method to increase the methane conversion rate and achieve the self-sustained operation of the reactor. Moreover, when the inlet concentration (2%vol.) is reduced by 50%, the inlet velocity should be reduced by about three times to maintain methane conversion rate above 90%. Author Contributions: Y.W. and Z.S. conceived and designed the numerical experiments; Z.S. and Z.B. performed the numerical experiments; Z.S. and X.L. analyzed the data; Z.S. and Y.W. wrote the paper. Acknowledgments: This work was supported by the National Technology Research and Development Program of China (2014AA052803) and the National Natural Science Fund (51376123). Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature CMR CSS HCU ULCVG VAM Ds Wt Hd h hs L Ms p Rc s R Sh t T ui xi y Ys Greek letters ρ µ λs λw Subscripts s i, j

Catalytic monolith combustor Cyclic steady state Heat consumption unit Ultra low calorific value gas Ventilation air methane Diffusioncoefficient (m2 s−1 ) Reactor wall thickness (m) Hydraulic diameter (m) Mixture or solid enthalpy (J kg−1 ) Enthalpy of specie s (J kg−1 ) Reactor length (m) Molar mass of specie s (kg mol−1 ) Pressure (Pa) Generation or consumption rate (kg m−3 s−1 ) The universal gas constant, R = 8.314 (J mol−1 K−1 ) Heat sources due to chemical reactions (J m−3 s−1 ) Time (s) Solid or gas temperature (K) Velocity components (m s−1 ) x or y direction in Cartesian coordinates Vertical coordinates Mass fraction of species s Gas or solid density (kg m−3 ) Mixture viscosity coefficient (N s−1 m−2 ) Thermal conductivity of specie s (W m−1 K−1 ) Solid thermal conductivity (W m−1 K−1 ) s-th species x or ydirection

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