Autothermal oxidative coupling of methane with ambient feed temperature

Accepted Manuscript Autothermal Oxidative Coupling of Methane with Ambient Feed Temperature Sagar Sarsani, David West, Wugeng Liang, Vemuri Balakotaiah PII: DOI: Reference:

S1385-8947(17)31138-5 http://dx.doi.org/10.1016/j.cej.2017.07.002 CEJ 17267

To appear in:

Chemical Engineering Journal

Received Date: Revised Date: Accepted Date:

10 May 2017 27 June 2017 1 July 2017

Please cite this article as: S. Sarsani, D. West, W. Liang, V. Balakotaiah, Autothermal Oxidative Coupling of Methane with Ambient Feed Temperature, Chemical Engineering Journal (2017), doi: http://dx.doi.org/10.1016/ j.cej.2017.07.002

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Autothermal Oxidative Coupling of Methane with Ambient Feed Temperature Sagar Sarsani, David West*, Wugeng Liang SABIC, Sugarland, Texas-77478 and Vemuri Balakotaiah Department of Chemical and Biomolecular Engineering University of Houston, Houston, Texas-77204

Abstract We report the exploitation of thermal effects and bifurcation (ignition and extinction) behavior to enable steady-state operation of an Oxidative Coupling of Methane (OCM) reactor with ambient feed and furnace temperature. Using a simplified kinetic and reactor model and results from bifurcation theory, we explain the experimentally observed ignition-extinction behavior for catalysts of different activity and reactor tubes of varying diameter when the furnace temperature or the space time are varied. We apply the theory to analyze the impact of reactor tube diameter and heat loss on the feasible region of autothermal operation and present experimental evidence for the existence of isolated high temperature/conversion branches. The results indicate that when catalyst activity is high enough, it is possible to operate an OCM reactor autothermally using the reactor feed (at ambient temperature or lower) as coolant, which enables the maximum practical single-pass methane conversion. _____________________________________ *Corresponding author: [email protected] Key words: autothermal operation, ignition, extinction, bifurcation, hysteresis 1

Highlights: 

Oxidative coupling of methane with ambient feed temperature is demonstrated



Ignition and extinction behavior with varying CH4/O2 ratio is explained



Impact of reactor tube diameter on observed ignition-extinction behavior is analyzed



The feasible region of autothermal operation with ambient feed temperature is identified



Ignition-extinction behavior of catalysts with different activities are compared

Graphical Abstract:

Photograph of laboratory scale oxidative coupling of methane reactor operating with ambient feed temperature and without external heating. The catalyst (La-Ce oxide) powder is sandwiched between quartz particles.

2

1. Introduction The shale gas revolution has made low cost natural gas abundant, encouraging renewed interest in natural gas conversion to useful chemicals. Oxidative Coupling of Methane (OCM) is a potential route for direct conversion of methane to C2 and higher hydrocarbons (i.e., C2+ hydrocarbons). It has perhaps the highest carbon atom efficiency of any known route for methane conversion to chemicals. OCM has been extensively studied since first reported by Keller and Bhasin [1] in 1982, with more than 2700 papers and 140 patents published [2]. Many publications have focused on the development of catalysts with high C2+ yield. The search for high yield catalysts was likely motivated by an early economic analysis that suggested a minimum target of 35% per-pass methane conversion and 88% C2+ selectivity is needed for manufacturing cost competitiveness [3]. However, in addition to good economics a commercial process must first be feasible. Some basic practical engineering problems must be solved before the scale-up and commercialization of OCM is even feasible. The reactions between methane and oxygen leading to C2+ products are highly exothermic, while the complete oxidation reactions of methane or C 2+ products (to CO2 and H2O) are even more exothermic. It is also well known that there is an optimum catalyst temperature range in which C2+ product selectivity is maximized; this is in the range 10501200 K, depending on the catalyst [4, 5]. At suboptimal temperatures oxygenated products are formed, while at too high temperature gasification and deep oxidation of the C 2 products take over. Moreover, catalyst deactivation occurs at too high temperature. Maximizing the profit of an industrial OCM process requires operation at the optimal selectivity with as high methane conversion as possible. Consequently, the catalyst temperature must be controlled at some optimal and possibly narrow range. The high heat of reaction of OCM requires limiting the 3

methane conversion to a relatively low value in order to avoid a runaway reaction [6, 7]. Hoebink et al. [7] showed that a cooled multi-tubular reactor capable of avoiding runaway is not commercially feasible. Even with a methane to oxygen ratio of 10, it would require about 12 million tubes for a world scale ethylene plant (1000 kTA). Schweer et al. [4] determined the limits of stability and performance of a laboratory scale non-isothermal fixed bed reactor cooled or heated by a fluidized sand bath. They found that a temperature of 853 K was required to initiate the reaction and observed large axial temperature gradients, as high as 250 K. Controlling the maximum hot-spot temperature within their catalyst to less than 1273 K required limiting the inlet oxygen concentration to 20% (O2/CH4=0.25). In order to increase total oxygen concentration (to 30%), C2+ yield, and methane conversion, they used two reactors in series with interstage cooling and distributed oxygen feed. However, the maximum methane conversion obtained was about 31% for both co-feed and distributed feed operation. Similarly both modes of operation obtained the same maximum C2+ selectivity, showing no benefit of distributed feed operation. Even if this approach had been successful in increasing methane conversion and selectivity at the laboratory scale, it could not possibly be scaled up to industrial scale given the results of Hoebink et al. [7]. Similarly, an adiabatic reactor with feed temperature of 853 K and 20% O2 is not feasible either, because the adiabatic temperature rise is about 1000 1100 K for O2/CH4 = 0.25. Clearly no catalyst could withstand the adiabatic temperature (about 1900 K). The main focus of this paper is on demonstrating the feasibility of doing OCM in an adiabatic (or near-adiabatic) autothermal reactor and on defining the necessary conditions for this mode of operation. We use the term autothermal to describe intentional operation within the region of steady-state multiplicity in which most or all of the catalyst bed is in an ignited state. Once ignited no further input of heat is used. The maximum benefit of autothermal operation is 4

obtained when reactants are fed at the lowest possible temperature which enables the highest possible methane conversion. This basic concept was demonstrated by Tarasov and Kustov in a 10 mm i.d., vacuum jacketed, laboratory reactor using 15% La2O3 on MgO catalyst for short periods of time (about one hour) [8]. However, in their experiment the reaction extinguished within about 20 minutes after the vacuum insulation was released. We will show that autothermal operation requires understanding of the ignition and extinction behavior and external heat transfer characteristics of the catalyst/reactor system. In the remaining section of the introduction we will review previous work in which ignition and extinction have been observed. Several groups have measured hot spot temperatures within the catalyst bed in laboratory scale testing that exceed the feed or furnace temperature by 150300 °C [4, 9, 10]. Annapragada and Gulari [11] first reported ignition and hysteresis behavior in OCM. On increasing furnace temperature they observed ignition at 725 °C, with sustained activity on reducing furnace temperature to 575 °C. Using pelletized Mn-Na2WO4/SiO2 catalyst and a space time of 0.36 s, Lee et al. [12] observed ignition in a 25.4 mm diameter reactor tube at ~780 °C and hysteresis on cooling, with extinction at a furnace temperature of about 660 °C. However, in order to limit the maximum catalyst temperature the reactants were diluted with N 2 (60%). More recently, Noon et al. [13] reported a significantly lower ignition temperature of 520 °C and sustained activity down to 230 °C with a La-Ce oxide nano-fiber catalyst (with much lower space times, about 0.01 s). Comparing nano-fiber and powder catalysts under the same conditions, the observed ignition temperature was 90 degrees lower for the nano-fiber catalyst. The authors speculated that the lower ignition temperature may be due to differences in the crystal structure and porosity produced during the rapid electrospinning process used to synthesize the nano-fiber catalyst.

5

The ignition and extinction behavior of highly exothermic catalytic reactions in flow systems has been studied extensively both experimentally and theoretically in the past fifty years. A recent review [14] discussed thermal effects expected in catalytic partial oxidations and gave simple criteria for when they are expected. This article also presented some general results on the impact of adiabatic temperature rise, catalyst activity, feed temperature, space time, characteristic heat removal time, external mass transfer and intra-particle diffusional limitations on the ignition and extinction behavior of reactors in which partial oxidation reactions occur. Some of these results are extended and used in the interpretation of the experimental data presented in this work. While the basic theory is not new, this is the first time it has been presented in dimensional form and applied to oxidative coupling. In the remaining sections we present examples of experimental bifurcation diagrams using furnace temperature and space time as bifurcation variables. We interpret these behaviors using theory and analyze the effects of tube diameter and importance of catalytic activity on the bifurcation behavior and its impact on the feasible region for autothermal operation. Finally, we show two examples of stable autothermal operation in laboratory reactors without any external heating and with reactants fed at ambient temperature.

2. Material and methods 2.1 La-Ce oxide catalyst Except where noted, the inorganic materials were obtained from Sigma Aldrich Chemical Company with purity of 99.9%. La-Ce oxide powder catalyst with 15:1 La/Ce mass ratio was prepared by combining aqueous solutions of La(NO3)3∙6H2O (24.85 g dissolved in 40 ml of deionized water) and Ce(NO3)3∙6H2O (1.65 g in 10 ml of water) and heating at 85 oC for 2 hours 6

with stirring. The obtained mixture was dried overnight at 125 oC to yield a dry powder, which was then calcined at 625 oC for 5 hours prior to use. The final powder consisted of irregular particles with number average diameter of 11 µm (determined by SEM) and BET surface area of 15.7 m2/g, measured using a Quantachrome Autosorb®-6iSA. The sample was outgassed at 300 o

C for 4 hours before measurement. The XRD pattern of the catalyst is shown in Fig. 1a. XRD

measurements were performed with PANalytical X’Pert (Cu Kα1 X-ray source, wavelength=1.54 Å; scanned in the range 2θ = 1090° with step size of 0.02°). The XRD pattern indicates the main phase in the catalyst is La(OH)3. This suggests the solid, which is hygroscopic, absorbed moisture from the ambient air and formed hydroxide prior to analysis.

2.2 Mn-Na2WO4/SiO2 catalyst Mn-Na2WO4/SiO2 catalyst was prepared using the incipient wetness method. Silica gel (Davisil® Grade 646, 3560 mesh, W. R. Grace and Company) was used after drying overnight. Mn(NO3)2·4H2O was dissolved in deionized water then added dropwise onto the silica gel. The resulting manganese impregnated silica material was dried overnight. Similarly, Na2WO4·2H2O was dissolved in deionized water and added drop-wise onto the dried manganese silica material then dried overnight at 125 °C and calcined at 800 °C for 6 hours under airflow to obtain the final Mn-Na2WO4/SiO2 catalyst with particle size in the range 0.250.5 mm. The BET surface area was determined to be 2.0 m2/g and its XRD pattern is shown in Fig. 1b. Three different phases are identified in the diffraction pattern; Na2WO4, Mn2O3, and -cristobalite.

2.3

Catalytic experiments

7

Experiments were carried out in fixed bed reactors made of fused quartz tubing (Technical Lab Glass) of various dimensions as shown in Table 1. The tubes were loaded as shown in the schematic diagram in Fig. 2 with other details given in Table 1, by first inserting a short plug of quartz wool followed by a layer of quartz particles and a thin layer (0.5 mm) of quartz felt. The catalyst powder or particles were added to the tube and followed by another layer of quartz felt, quartz particles, and finally another plug of quartz wool. The quartz particles, felt, and wool were supplied by Technical Lab Glass. No attempt was made to measure the catalyst temperature. Throughout this paper, whenever temperature is reported we mean furnace setpoint temperature unless otherwise noted. Reactant gas flows were controlled using Bronkorhst Thermal Mass Flow Controllers. A small quantity of Neon gas was mixed with the CH4 and O2 for use as an internal standard (the combined feed typically contained 13% of Ne). No other diluents were used. The reactors were heated using a conventional tube furnace (ATS).

The

reactor effluent was analyzed directly (without water removal) using an Agilent 6890 gas chromatograph equipped with two columns and flame ionization and thermal conductivity detectors. In some cases for faster analysis, the effluent was air cooled and water removed by a small knock-out vessel, then passed through a Genie membrane filter and analyzed using an Agilent micro GC. As shown in Fig. 2 the reactor could be by-passed in order to analyze the feed mixture. In some cases temperature programmed experiments were performed using the following procedure. Starting from some low temperature the furnace temperature was increased in 25 degree steps at a rate of 5 degrees/min. Once the set point was reached three GC samples were analyzed; normally this required at least 30 min. at each set point. If consistent results were obtained then the temperature was increased to the next point (25 degrees higher) and the triplicate analysis repeated. On cooling down the temperature was reduced in smaller increments

8

(usually 10 or 15 degrees). Again three analyses were done at each setpoint. In this manner the temperature programmed experiment shown in Fig. 3 required 9 hours to perform. In most of the experiments reported here the catalyst was stable enough that the experiment could be replicated several times. In some experiments the Mn-Na2WO4/SiO2 catalyst deactivated after ignition as reported below.

3. Results 3.1

Ignition, extinction, and hysteresis (steady-state multiplicity) — experimental examples Figs. 3a and 3b show examples of ignition, extinction, and hysteresis for O2 conversion

and C2+ selectivity, respectively, using a La-Ce oxide in a 4 mm reactor with a space 0.014 s space time. Throughout this paper we will use the term space time to denote the ratio of total catalyst volume to volumetric flowrate at standard temperature and pressure (STP). (The actual contact time at the reactor or feed temperature is typically much smaller, by a factor 273.15/T.) At constant flow rate and feed ratio, the oxygen conversion (C2+ selectivity) remain near zero as furnace temperature is increased from about 300 °C until the ignition point is passed at about 460 °C. After ignition the oxygen conversion (C2+ selectivity) abruptly increases as shown in Fig. 3a (3b). Further increase in temperature beyond ignition yields little increase in selectivity or conversion which indicates the system is externally mass transfer limited after ignition. Once the catalyst is ignited, decreasing furnace temperature causes only minor changes in selectivity or conversion until the extinction point is reached (about 280 °C). This hysteresis behavior is similar to that reported by Noon et al. [13]; however, they observed this wide autothermal range only with nano-fiber catalysts, not powder.

9

Fig. 4 shows a temperature programmed experiment showing hysteresis in a 10.5 mm i.d. reactor with a space time of 0.058 s. Ignition occurred a little above 370 °C in this case, almost 100 degrees lower than in the previous example. Oxygen conversion remained fairly constant as the furnace temperature was decreased to 170 °C, the lowest temperature obtainable with the furnace power turned off. On opening the furnace to allow further cooling, the reactor tube was observed to be glowing yellow, but the reaction extinguished within a few minutes. Fig. 5 shows another temperature programmed experiment with a 4 mm reactor at conditions similar to those of Fig. 3, except much lower flowrate and longer bed length (3 mm) was used (giving a 58 ms space time vs. 14 ms in Fig. 3). In this case there is a more gradual light-off behavior and hysteresis was not observed. Our attempts to perform an ignition/extinction experiment like that shown in Fig. 3, using Mn-Na2 WO4/SiO2 catalyst, were unsuccessful. While we did observe ignition, the catalyst rapidly deactivated and it was not possible to observe hysteresis as reported by Lee et al. [12], who used diluted feed and catalyst pellets. Fig. 6 shows a temperature programmed experiment using Mn-Na2WO4/SiO2 catalyst in a 4 mm tube with 0.28 s space time. There is much more gradual increase in oxygen conversion and C2+ selectivity compared to Fig. 3 and no hysteresis was observed on cooling. Similar results were obtained using a 22 mm tube with CH4/O2=7.4 and 9.1 s space time, but the methane and oxygen conversion curves were shifted toward lower temperature; 100% O2 conversion was reached at a furnace temperature of 650 °C.

3.2

Theoretical interpretation The interpretation of the above laboratory data and scale-up assessment of the OCM

process requires both qualitative and quantitative understanding of the relationship between 10

catalyst activity (given by the density of catalytic sites or pre-exponential factor k0 based on unit reactor volume), feed inlet (Tin) and furnace temperature (Tf) adiabatic temperature rise (Tad or CH4/O2 ratio), space time () and activation energy (E/R) as well as other parameters (e.g. catalyst particle size, tube size, heat transfer at the wall, etc.) as these parameters determine the existence and location of the ignition and extinction points. Here, we explain these relationships qualitatively using the simplest possible models. Quantitative determination of the relationships requires more detailed models (e.g. partial differential equation models that account for spatial gradients in the reactor as well as inside the catalyst particles) along with physical property variations and more detailed kinetic models (for selectivity predictions). This is beyond the scope of this article and will be pursued in future work. Adiabatic Temperature Rise:

The adiabatic temperature rise (Tad) is an important factor in understanding the ignition/extinction behavior of both laboratory scale and full scale reactors in which highly exothermic reactions occur. When oxygen is the limiting reactant, it is the increase in the temperature of the reaction mixture when the system reaches complete oxygen conversion. For the case of a single step oxidation (in which the product composition is known in advance), this is a well-defined quantity and can be calculated from the feed composition and thermodynamic data. Obviously, for the case of multiple reactions, e.g. parallel oxidations or oxidations coupled with dehydrogenation and reforming reactions, the adiabatic temperature rise depends on the product distribution. But for the purpose of understanding ignition and extinction behavior, this detail is not important and thermal effects can be approximated based on moles of oxygen

11

consumed. For the case of OCM, the primary oxidation reactions are listed below (along with heat of reaction per mole of extent, as well as per mole of oxygen consumed):

(1) CH 4  2O2  CO2  2 H 2O

H R0  802 kJ / mole  401kJ / moleO2

1 (2) 2CH 4  O2  C2 H 6  H 2O H R0  177 kJ / mole  354kJ / moleO2 2 (3) CH 4  O2  CO  H 2  H 2O H R0  278 kJ / mole  278 kJ / moleO2 1 (4) CH 4  O2  CO  2 H 2 2 (5) 2CH 4  O2  C2 H 4  2 H 2O

H R0  36 kJ / mole  72 kJ / moleO2 H R0  282 kJ / mole  282 kJ / moleO2

For most catalysts we have examined, including the two discussed in this work, the primary products are CO/CO2 and C2H6 and hence reaction 5 can be ignored. That is, ethylene is not produced as a primary product by catalytic reactions but mostly by secondary reactions such as homogeneous dehydrogenation, or oxidative dehydrogenation, of ethane. Further, as the catalyst temperature increases, the selectivity to C2 products increases (see Fig. 6), reaching a maximum before deep oxidation, secondary and homogeneous reactions become important. Within the primary oxidations, the fact that C2 selectivity increases with increasing temperature implies that the apparent activation energy of the dimerization reaction is higher than that of CO/CO 2 forming reactions. Thus, the activation energy of the dimerization reaction is used in the qualitative bifurcation analysis presented below. Table 2 lists the adiabatic temperature rise for the first four oxidation reactions. The last column of Table 2 lists the Zeldovich number, B = γβ/(1+β), where the dimensionless activation energy γ = E/RTin and the dimensionless adiabatic temperature rise β = Tad/Tin. The Zeldovich number B is a measure of the nonlinearity introduced due to thermal effects; nonlinear effects increase exponentially with the magnitude of B. The value of B in Table 2 is calculated using

12

activation energy (E/R) of 10,500 K and Tad for the methane dimerization reaction. The actual temperature rise in laboratory experiments depends on the operating conditions, catalyst, and the product selectivity. For example, with CH4/O2=4 the actual temperature rise in an adiabatic reactor in which only reactions 1-4 (in Table 2) occur can be between 271 and 1305 K depending on the product distribution. As in the case of Tad, the value of B is highly dependent on the inlet temperature. As the inlet temperature increases, B decreases and the temperature sensitivity of the system reduces. For sufficiently high inlet temperatures, the ignition/extinction behavior may disappear. The activation energy (E/R=10500 K) used in Table 2 corresponds to the La-Ce catalyst in our experiments. Simplified Kinetics: To examine the ignition and extinction behavior of the two catalysts used in our experiments, we use simplified kinetics that approximates the temperature sensitivity of the heat generation rate of the dimerization reaction. The first-order rate constant for the La-Ce catalyst was approximated as k  4  107 exp  10500 / T  s 1 while the same for the Mn-Na2 WO4/SiO2 catalyst was estimated as k  3  1010 exp  23000 / T  s 1 .

In making these estimates, the

activation energies are determined by using C2H6 selectivity at different temperatures but with low oxygen conversion (typically below 20%). The pre-exponential factors were estimated based on oxygen conversion at a fixed temperature and space time, again at low conversions and near isothermal conditions. It should be stressed that these simplified kinetics is sufficient to explain only the ignition-extinction behavior and cannot be used to predict product distribution. Heat loss in Laboratory Reactors:

13

The interpretation of laboratory scale OCM data requires at least a qualitative understanding of how the ignition-extinction behavior changes with external heat transfer to the furnace. This has already been stated in the literature [14], but has to be interpreted in the context of OCM experiments. An important parameter that determines whether the reactor is close to adiabatic or isothermal operation is the characteristic heat exchange time  h . For a laboratory reactor (such as a quartz tube packed with powdered catalyst), this can be estimated from the equation [14]:

h 

VRC pv (T ) UAh



0.25d tC pv (T ) U

,

(1)

where d t is the tube (inside) diameter, VR is the reactor volume, Ah is the heat transfer area,

C pv (T ) is the volumetric specific heat of the reaction mixture and U is the overall heat transfer coefficient between the catalyst and the furnace. The latter may be expressed as  2t  1 1 d dt 1   t Ln  1  w   , U hi 2k w d t  (d t  2tw ) h0 

(2)

where hi ( h0 ) is the tube inside (outside) heat transfer coefficient, and tw ( k w ) is the tube wall thickness (thermal conductivity). The interior heat transfer coefficient is calculated using standard packed-bed correlations [15] while the external heat transfer coefficient h0 is approximated as the sum of convective and radiative contributions: ho  Num 0

k f (T ) dt

  (T 2  T f2 )(T  T f ),

(3)

where Num 0 is the mean Nusselt number for free convective heat transfer (for a vertically placed reactor tube in a furnace),  is the emissivity factor,  is the Stefan-Boltzmann constant, T is the reactor (catalyst) temperature and T f is the furnace temperature. Num 0 is calculated using 14

standard free convective heat transfer correlations [16] and length of the packed section of the reactor tube. Though we have included all contributions to heat transfer coefficient, radiation heat loss is the dominant mechanism in the range of temperatures we studied and the overall heat transfer coefficient can be approximated by the last term in Eq. (2). In order to estimate typical values of  h , we have the taken the properties of the gas mixture to be that of methane,   0.7 , furnace gas to be air, and listed in Table 3 the calculated characteristic heat loss times for different reactor tubes at some typical reactor and furnace temperatures. The values in the second column correspond to a typical lab scale operation with dilute feed close to isothermal conditions. The third column corresponds to conditions that may be found on the ignited branch, and the last column is at conditions that might be present on the extinguished branch below the ignition point. [Obviously, these values vary strongly with reactor and furnace temperature and Eqs. (1-3) can be used to approximate the temperature dependence for more accurate calculations.] As can be seen from this table, typical values of  h are in the range of few milliseconds to a hundred milliseconds, which is also the range of typical space times used in most laboratory scale OCM experiments. This observation is important in interpreting laboratory scale data. In contrast to the laboratory reactors,  h may be orders of magnitude higher in well insulated large scale industrial reactors, typically in the range 102-104 s, making their operation close to adiabatic. Thus, there is an enormous variation of the heat loss time (e.g. five to seven orders of magnitude) and the analysis of the impact of this variation on the ignition-extinction behavior (both experimentally and modeling) is not explored in the literature. To first approximation, the heat loss time is proportional to the reactor tube diameter, and for the same bed length, to the square root of the catalyst bed volume. Thus, the heat loss time may be considered to be proportional to the square root of the reactor scale-up factor. 15

Ignition & Extinction Behavior for a Single Oxidation Reaction: The bifurcation (ignition-extinction) behavior of various chemical reactor models has been discussed in the literature [6]. Here, we use it to explain our experimental results using the simplest reactor models and kinetics. Since oxygen is the limiting reactant, we assume the kinetic rate is zero-order in methane mole fraction and first-order in oxygen mole fraction and for the purpose of bifurcation analysis, approximate the chemistry by a single step reaction (AB). We also assume that catalyst particle size is small enough so that both inter and intra-particle gradients can be neglected. Further, we assume radial gradients are negligible. With these assumptions, the conversion () and reactor/catalyst temperature ( T ) along the tube as a function of feed/inlet and furnace temperatures ( Tin , T f ) can be described by the pseudohomogeneous model: 1 d 2 d    a ( z )k (T ) (1   )  0; 0  z  1 Pem dz 2 dz 1 d 2T dT    ( Tad )a ( z )k (T ) (1   )  (T  T f )  0 2 Peh dz dz h 1 d    0; Pem dz

(4)

1 dT  T  Tin  0 at z  0 Peh dz

d  dT   0 at z  1 dz dz

Here, a ( z ) is the activity profile (zero in the inert quartz region and unity in the catalyst region) and the Peclet numbers based on the total length of the packed-tube ( L  Lc  L f  La ; Lc = length of catalytic section, L f = length of fore-section, La = length of after-section,   L / u ) are defined by

Pem 

u LC pv u L ; Pem  , Dm,eff kb,eff

(5) 16

where u is the superficial gas velocity in the bed, Dm,eff ( kb,eff ) is the effective axial dispersion coefficient (effective conductivity) in the bed. These transport properties as well as the gas velocity and volumetric heat capacity vary with temperature as well as bed properties, but for the purpose of the present discussion we take average values. Analyzing the bifurcation features of the model even with these simplifications is non-trivial and we consider here only the limiting case in which both Peclet numbers (based on length of catalytic section) are small. In this limiting case of the CSTR behavior, integrating Eqs. (4) over the length of the catalytic section, the exit conversion () and reactor temperature as ( T ) can be described by the algebraic equations: T  Tin  ( Tad )



k0 exp   E / RT    (T  T f ) 1  k0 exp   E / RT   h

k0 exp   E / RT  1  k0 exp   E / RT 

(6a)

(6b)

It may be shown that the bifurcation behavior of the model described by Eqs. (4) is bounded by three limiting cases, one of which is the above CSTR model, the second is the PFR model corresponding to both Peclet numbers being infinity. The third limiting case is the lumped thermal reactor (LTR) model, corresponding to heat Peclet number of zero and mass Peclet number of infinity. The PFR model exhibits no ignition and extinction behavior while the LTR model has the largest separation between ignition and extinction points [6, 17]. Thus, except in the two ideal limits of isothermal and adiabatic plug flow operation, the same mass/volume of catalyst packed in tubes of different diameter can lead to different Peclet numbers and lead to different observed ignition-extinction behavior. Similarly, while the inert packing has little influence on the ignition-extinction behavior in the adiabatic limit, it influences the heat loss time on the ignited branches. In the above simplified model, this can be accounted by reducing 17

the heat loss time based on the length of the ignited part of the bed. [The space time in Eqs. (6) is based on the length of the catalytic section but flow rate or velocity at the inlet. When the flow rate changes with temperature, the value at the catalyst temperature should be used when comparing with experiments.] In most laboratory experiments, the incoming gas is pre-heated to the furnace temperature and reaches the furnace temperature before entering the catalyst bed. Thus, we can reduce the number of parameters by one by assuming that Tin  T f and simplify Eq. (6a) to

T  T f  ( Tad )*

k0 exp   E / RT  ( Tad ) ; ( Tad )* = 1  k0 exp   E / RT     1    h 

(7)

We now examine the dependence of conversion () and temperature ( T ) with furnace temperature as the bifurcation variable, with all other parameters fixed. As discussed above, the heat loss time depends on the tube diameter as well as on the furnace and reactor temperature. However, for simplicity of analysis we take an average value for each tube diameter as the qualitative bifurcation features are not impacted by this simplification. [The temperature dependency of  h is included in the calculations that compare the computed bifurcation diagrams with experiments. Also, note that the space time based on STP conditions differs from that at the catalyst temperature by a factor (273/ T).] Bifurcation features with varying furnace temperature ( T f ): First, we note that when both  and  h are fixed, the maximum temperature difference between the furnace and catalyst cannot exceed ( Tad )* . This simple criterion can be used to determine whether or not a reactor operates close to isothermal or adiabatic condition, and, obviously, there is no ignition or extinction when the operation is close to isothermal (h << ). 18

It is well known that for any fixed ( Tad )* , there is a critical value of the product k0 , beyond which a plot of  versus T f displays ignition and extinction [14]. For the above model, this boundary may be shown to be

k0 



 2 1    exp  ; 2   1      1





( Tad )* . E/R

(8)

Fig. 7 shows a plot of the locus defined by Eq. (8) for two different values of the activation energy (E/R) corresponding to the two catalysts used in the experiments. It may be observed from this figure and Eq. (8) that the critical value of the catalyst activity needed to eliminate (or generate) ignition/extinction varies exponentially with ( Tad )* . Though not shown in Fig. 7, it is also important to note that the reactor (catalyst) temperature and the inlet temperature at the hysteresis point increase along the locus. However, the Damköhler number at the hysteresis point, k(T) , is of order unity and decreases slightly along the locus. Some important practical implications follow from Fig. 7: (i) the ( Tad )* value has to exceed some critical value (or methane to oxygen ratio has to be below a critical value) in order to observe ignition and extinction in such systems; (ii) for catalysts with higher activation energy, the hysteresis (or ignition and extinction) occurs at higher feed and reactor temperatures; (iii) for any fixed ( Tad )* , the ignition and extinction temperatures are lowered as the value of k 0 is increased beyond that at the hysteresis point (i.e. well into the multiple solution region); (iv) if the heat loss time is an order of magnitude smaller than the space time, it is extremely difficult to observe ignition and extinction as the temperature rise is a small fraction of the true adiabatic temperature rise (closer to isothermal operation). Conversely, for the temperature rise to be close to theoretical adiabatic

19

value (and operation close to adiabatic), we need the heat loss time to be an order magnitude larger than the space time. We have shown in Fig. 7 (by the triangular markers) the estimated location of the conditions corresponding to the experimental results shown in Figs. 3, 4 and 5 for the La-Ce catalyst. Two of these clearly fall well above the hysteresis locus, while the third one (Fig. 5) is just on the boundary. The experimental conditions shown in Fig. 6 for the Mn-Na2WO4/SiO2 catalyst fall below the corresponding hysteresis locus but cannot be seen in Fig. 7 as it is outside the range of the graph; this experiment is closer to isothermal conditions. Fig. 8 shows computed bifurcation sets (ignition and extinction locus) in the plane of furnace temperature and adiabatic temperature rise for the La-Ce catalyst for tube diameters and space times corresponding to the experimental results shown in Figs. 3 and 4. In computing these loci we have taken into account the variation of the heat loss time with furnace and catalyst temperature but have not adjusted it for increased heat transfer area that could result due to inert packing. As shown in Fig. 8, the ignition and extinction points for the 10.4 mm reactor are shifted to lower furnace temperatures and the separation between them (width of the hysteresis region) increases. The experimental ignition and extinction points from Figs. 3 and 4 are shown by the markers in Fig. 8. For the larger tube diameter, the predicted extinction point extends to a furnace temperature of about 70 °C. As noted earlier, in that experiment (Fig. 4) the reactor quenched when the furnace door was opened. Thus, the simple model explains qualitatively (and also with reasonable quantitative accuracy) the observed ignition and extinction behavior. Our simple model can also explain the disappearance of the hysteresis observed in Fig. 5 with increase in space time and length of the catalyst bed. By increasing the space time from 14 to 58 ms and decreasing the heat loss time by a factor 0.4 (corresponding to about 3 times longer

20

bed compared to that in Fig. 3), we have found that hysteresis disappears. The model can also explain qualitatively the lack of ignition and extinction behavior for the Mn-Na2WO4/SiO2 catalyst shown in Fig. 6. The computed bifurcation diagram of catalyst temperature and oxygen conversion versus furnace temperature is shown in Fig. 9. These results show that the experiment is close to isothermal but there is still a predicted temperature difference of about 100 °C between the catalyst and furnace at high oxygen conversion. These results also show the limitations of our simplified kinetic model: it is only qualitative and cannot predict product composition. Also, the quantitative accuracy at high oxygen conversions is not so good. In order to further explain the deactivation of this catalyst soon after ignition, we have used the model to compute the bifurcation diagram for the same conditions shown in Fig. 6 but with a shorter space time of 14 ms. These results, shown in Fig. 10, clearly indicate that the catalyst temperature on the entire ignited branch is much higher than the deactivation temperature (about 1000 °C). [Remark: The bifurcation diagram shown in Fig. 10 is a plot of the steady state solution of the species and energy balance equations. Between the up and down arrows (the ignition and extinction points, respectively) there are three solution branches. Only the bottom (extinguished) and top (ignited) branches are stable (and can be observed experimentally, like in Fig. 3), the middle one is unstable and cannot be experimentally observed without special control.] Fig. 10 also shows the impact of catalyst activity on the ignition-extinction features. Here, the computed bifurcation diagrams are compared for the two catalysts under identical experimental conditions (4 mm tube and space time of 14ms). We note that an ignited steadystate exists for the more active La-Ce catalyst at a temperature that is about 400 °C lower than that for the less active Mn-Na2WO4/SiO2 catalyst. This comparison clearly indicates that in the

21

context of OCM, having a catalyst of higher activity is a necessary condition for obtaining an ignited steady-state at lower feed and catalyst temperatures.

3.3

Impact of heat loss with space time as bifurcation variable The effect of heat loss on O2 conversion at a fixed furnace temperature and varying space

time, in reactors of different diameters is shown in Figs. 11 and 12. These data were obtained by starting at high space time [105 ms for the 4 mm i.d. tube (Fig. 11), 70 ms for the 2.3 mm i.d. tube (Fig. 12)] and increasing reactant flow in steps. In both cases, O2 conversion first decreases, goes through a minimum and then either gradually (4 mm tube) or abruptly (2.3 mm tube) increases. As we show in the next section, this type of behavior is mainly due to thermal effects and heat loss, and to our knowledge, has never been reported in the OCM literature. The C2+ selectivity, and CH4 conversion are also shown in Figs. 11 and 12. It is interesting to note that in both figures C2+ selectivity is less than 5% for space times above those which correspond to the minimum in O2 conversion (about 70 ms in Fig. 11 and 10 ms in Fig. 12). The transition from low to high conversion and selectivity occurs as the space time is about three times the average heat loss time (see Table 3). An explanation of this behavior is provided by the theory presented in the next section. Fig. 13 shows bifurcation diagrams of oxygen conversion versus space time for three different furnace temperatures for the Mn-Na2 WO4/SiO2 catalyst. At low furnace temperature (600 and 650 °C), the conversion on the lower branch increases with space time, while at the higher temperature (700 °C) it is nearly 100% for the entire range of space times (flow rates) spanned in the experiment. At the intermediate furnace temperature (650 °C), in addition to the low conversion branch, we have also found a high conversion state at short space time, indicated by the green square and arrow in the upper left corner of the figure. In order to reach this steady22

state, the space time was fixed at the lowest possible value and the furnace temperature was slowly reduced from 700 to 650 °C. This experiment clearly confirms the existence of multiple steady-states and an isolated high conversion branch for the same operating conditions. This is the first report of operation on an isolated ignited branch in the OCM literature. This observation is explained in the theory presented below. Table 4 compares the product compositions of the ignited/isolated (green arrow in Fig. 13) and extinguished steady-states (circled point in Fig. 13). Although the furnace temperature and space-time is the same for both experiments (650 °C), the composition is completely different. The O2 conversion in the isolated, ignited state is nearly complete, CH4 conversion is 20%, and C2+ selectivity is 65%. In contrast, at the circled (extinguished) point the methane conversion is only 1% and the main product is CO2 (85%).

3.4 Bifurcation features with varying space time (  ) As discussed in the literature [18], the bifurcation behavior is more complex when the space time is taken as the bifurcation variable. It is known that in this case there can be isolated solutions branches that can only be reached through special start-up procedures. Instead of repeating the theory that is discussed in the literature, we show here the phase diagrams in the physical and operating parameter space and use them to explain the different types of experimentally observed behavior. Fig. 14 shows a phase diagram (consisting of the hysteresis and isola varieties) for the MnNa2WO4/SiO2 catalyst for a fixed furnace temperature of 873 K. In calculating this phase diagram, we have assumed the heat loss time to be constant at an average value. A more accurate calculation, which we do not pursue, can be done by replacing the heat loss time by tube diameter. The bifurcation diagrams of conversion (and/or temperature) versus space time that 23

exist in three of the large regions are detailed below. Two other regions exist that are very small and cannot be seen on the scale of Fig. 14 (a mushroom and an S plus isola). These regions are not important for the present discussion. In region (a), there is no ignition and extinction point as either the heat loss is too large or the adiabatic temperature rise is too small. The bifurcation diagram that exists in region (b) is shown in Fig. 15. There is an isolated high conversion steadystate branch (isola) with two extinction points. The extinction point at low space times is also known as the blow-out point as the extinction occurs due to space time being smaller than the characteristic heat generation time. The catalyst/reactor temperature at this left extinction point is very high. The extinction point at the higher space time occurs mainly due to heat loss through reactor wall. The temperature on the isolated branch begins to fall at the point where the heat loss time becomes close to the characteristic reaction time. The heat generation rate decreases with catalyst temperature until extinction occurs. [Remark: The two extinction points are marked by arrows. The bottom half of the loop between the extinction points is an unstable branch. In order to observe the upper, stable, ignited branch it is necessary to heat the reactor above the unstable branch.] The extinguished branch is also shown in Fig. 15. Conversion monotonically increases with increasing space time along this branch. Without knowing an isola exists this would be the only state likely to be observed in this region of parameter space. The bifurcation diagram that exists in region (d) is shown in Fig. 16. It can be separated into two regions. At short space times, the heat loss is small and the reactor behavior is close to adiabatic with the diagram being S-shaped. However, at higher space times (exceeding the heat loss time) the catalyst temperature drops rapidly and reaches the furnace temperature, while the conversion reaches a minimum and starts to increase again. Beyond the minimum in conversion, the curve approximates that of an isothermal reactor at furnace temperature. These observations explain (qualitatively) the

24

selectivity trends observed in Fig. 6 and 7 for the La-Ce catalyst as well as the isolated steadystate observed in Fig. 8 for the Mn-Na2 WO4/SiO2 catalyst. Phase and bifurcation diagrams that are similar to those shown in Figs. 14-16 can be constructed for the La-Ce catalyst but we do not show this calculation. Finally, it should be pointed out that as the furnace temperature is reduced, the loci shown in Fig. 14 move to higher values of space times. With ambient furnace temperature, the left extinction point of the isola is outside the practical range of interest for the Mn-Na2 WO4/SiO2 catalyst, while it stays within the feasible region for the more active La-Ce catalyst.

3.5

Feasible regions for autothermal operation As discussed above, with sufficient catalyst activity and proper combination of CH4/O2

and residence time it is possible to operate an adiabatic OCM reactor autothermally using low feed gas temperature to remove the heat of reaction. The maximum benefit is obtained if the extinction point is at or below ambient temperature; this enables operation with CH 4/O2=4, which corresponds to ~10001100 K adiabatic temperature rise. In order to determine the region of autothermal operation for the La-Ce catalyst, we calculated the left extinction point for the case in which both furnace and feed are at ambient temperature (300 K). In this calculation, we fix the tube diameters corresponding to experimental values and also consider the heat loss time as a function of catalyst/reactor temperature. This boundary of autothermal operation is shown in Fig. 17. The adiabatic case (having the largest region of autothermal operation) corresponds to a reactor with large diameter (e.g., industrial scale). For smaller values of reactor diameter, the extinction locus has a minimum with respect to space time. For Tad* values below this minimum, an ignited (isolated) steady-state does not exist and autothermal operation is not feasible (this corresponds to CH4/O2~5.5 for the 34 mm 25

tube) with 300 K feed temperature. However, for Tad* above this minimum, there is a range of space times in which an ignited (high conversion) state exists and autothermal operation is feasible. As can be expected intuitively, this boundary is closer to the adiabatic limit for shorter space times and larger tube diameters. In Fig. 17, we also show the approximate location of the two experimental points in which we were able to demonstrate autothermal operation as discussed below.

3.6

Experimental examples of operation with ambient feed temperature

As explained in the previous section, an ignited state can exist when inlet temperature is close to ambient provided the adiabatic temperature rise is sufficiently high and the catalyst is active enough; this was possible with the La-Ce catalyst. In order to exploit this bifurcation behavior, the reactor was started differently than a typical method. First, the temperature of the furnace was set to about 600 °C then CH4 and O2 were fed at a molar ratio of 20 and flow rate corresponding to space time of 45 ms (based on flow rate at STP and catalyst volume). The feed composition and feed (furnace) temperature were then changed in small steps simultaneously to final values of CH4/O2=4 and furnace and feed temperature at ambient (~25 °C) while maintaining constant total reactant flow rate. In order to achieve feed temperatures below about 100 °C it was necessary to turn the furnace completely off and open the furnace to enable it to cool down. Fig. 18 shows the methane conversion and C2+ selectivity over an extended period of time in this mode of operation. This result has important implications for operation of an adiabatic reactor at larger scales. As far as we know, this is the first report of stable operation of OCM with ambient feed and furnace temperature for an extended period of time. For larger tube diameter it becomes easier to operate in the autothermal state. Fig. 19 shows a photograph of a 34 mm i.d. laboratory packed bed reactor operating in an ignited state with ambient feed 26

temperature and without external heating. This photograph was taken with the furnace turned off and open to the lab. As predicted by the theory, it was not possible to operate autothermally with feed at ambient temperature with Mn-Na2WO4/SiO2 catalyst. The results shown in Fig. 6 are similar to other data published in the literature. As stated in the introduction, this catalyst has been studied extensively and has high selectivity to C2 products (it is capable of producing 80% C2+ selectivity at about 20% methane conversion). However, it is much less active compared to the La-Ce catalyst. We were able to achieve ignition and reduce the feed and furnace temperature to 110 °C without extinction. The results are summarized in Table 5. The selectivity is poor compared to typical published results, probably because the catalyst temperature is too high in the ignited state, owing to the low CH4/O2 ratio (3.5) needed to maintain ignition. The low activity of this catalyst requires much higher temperature for ignition compared to La-Ce oxide, as shown in Figs. 46. In addition Mn-Na2WO4/SiO2 is very sensitive to high temperatures and can be easily deactivated after ignition. This is why we were not able to obtain data of the type shown in Fig. 3. Mn-Na2WO4/SiO2 deactivates during the long period of time needed to obtain the data. Hysteresis has been reported for this catalyst [12], but the feed was diluted with N2 (60%); this limited the maximum catalyst temperature to a little over 1000 °C.

4. Summary and conclusions The main goal of this article is to show by experiments that it is possible to carry out oxidative coupling of methane with reactants fed at ambient temperature. We were able to do this for the active La-Ce catalyst but not for the less active Mn-Na2 WO4/SiO2 catalyst. We have also demonstrated experimentally the impact of tube diameter on the observed ignition-extinction behavior when the furnace temperature or the space time is taken as the bifurcation variable. 27

Further, evidence for the existence of isolated high conversion (temperature) states in OCM experiments at short space times is presented. Using a simple reactor model that includes the impact of heat loss time on tube diameter, catalyst (reactor) and furnace temperatures, we have explained qualitatively all the experimentally observed ignition-extinction behavior. The theory based on the simple model also guided us to experimental conditions for autothermal operation of the reactor with ambient feed. While much more detailed kinetic models have been published [7, 1922], the heat loss effect turns out to be an essential element of physics that has not been adequately described in literature. This aspect of the problem is shown to be necessary for explaining the results from different diameter reactors and otherwise surprising trends with regard to varying space time (for example the rapid decrease in conversion and selectivity shown in Figs. 11, 12, and 16; and the isolated states of Figs. 13 and 15). The results presented in this work demonstrate that both catalyst activity and selectivity are important factors in assessing the scale-up feasibility of any OCM catalyst. While the La- Ce catalyst is active enough to enable autothermal operation with ambient feed and furnace temperatures, it is not selective enough for the C2+ products. In contrast, the Mn-Na2 WO4/SiO2 catalyst is highly selective to C2+ products (under near isothermal lab conditions) but not active enough to enable autothermal operation with ambient feed temperature. The commercialization of the OCM process using an autothermal adiabatic reactor requires both an active and selective catalyst. We hope this paper will motivate the search for such catalysts. We have made various simplifications and assumptions to arrive at a simple model that explained the various experimental observations. We now discuss briefly the validity of these assumptions and the impact of relaxing them on the model predictions (Space limitations prevent us from going into a detailed discussion.) Using the kinetic parameters and catalyst properties, 28

and a typical operating temperature of 900 °C for the OCM catalysts, it may be shown that intraparticle gradients can be neglected if the particle size is smaller than about 0.1mm for the La-Ce catalyst and 1 mm for the Mn-Na2 WO4/SiO2 catalyst (which is the case in our experiments). Similarly, using standard heat and mass transfer correlations for packed-beds, it may be shown that there is no particle level ignition or extinction in our experiments; this is certainly not true if larger size particles or pellets are used, especially for the La-Ce catalyst. We also note that since the extinction point is always determined by the kinetics, external mass transfer is not important near extinction but becomes important on the ignited branch (far to the right of the extinction point) at much higher temperatures, but this region of operation is not of practical interest. For simplicity of bifurcation calculations, we have assumed the reaction to be first order in oxygen concentration. This assumption does not impact the predicted ignition locus but as is well known, the extinction point is very sensitive to the reaction order. In the case of OCM, the true order of the deep oxidation and dimerization reactions with respect to oxygen may be half instead of first order (based on the mechanisms proposed in the literature). If this is the case, the separation between ignition and extinction points increases compared to our predictions (and the region of autothermal operation expands). However, the qualitative predictions of the model remain valid. The simple model used in this work neglects both homogeneous reactions as well as deep oxidation reactions that may become important at higher temperatures. As shown in the literature, inclusion of deep oxidation reactions and/or the coupling between homogeneous and catalytic chemistry can induce additional bifurcations [18, 23] and this needs to be investigated further in the OCM context. 29

The most limiting assumption of our model is related to the Peclet numbers and the neglect of axial gradients. Based on the operating conditions of our experiments and catalyst bed lengths used, we have estimated that the effective heat Peclet number in most of our experiments is indeed less than unity but this is not always the case with the effective mass Peclet number. As stated in the model development section, a one-dimensional model with heat Peclet number smaller than unity (good thermal backmixing) and mass Peclet number much greater than unity (small mass backmixing) expands the region of multiplicity. As shown in the literature [17], the region of multiplicity/autothermal operation shrinks and disappears with increasing heat Peclet number. It should be pointed out that in some of our experiments with larger length of the catalyst bed, the heat Peclet number is greater than unity and could be the reason for the disappearance of hysteresis (along with increased heat loss due to larger heat transfer area). Our model also does not give any information on the temperature profile on the ignited branch of the bifurcation diagram. A more detailed investigation of the ignition-extinction behavior of laboratory or large scale reactors with catalyst and inert packing will be useful for more accurate quantitative comparison with experiments. Finally, the neglect of radial gradients in the reactor may be justified only for small diameter tubes and/or quenched branches, and the ignitionextinction features with strong radial as well as axial gradients may be substantially different quantitatively. A complete bifurcation analysis of detailed mathematical models with axial, radial (and particle level) gradients along with detailed kinetic models is a challenging task for future investigations. Finally, we hope that the experimental and modeling results presented here will motivate further investigation of bifurcations and thermal effects in oxidative coupling of methane. Acknowledgements 30

We would like to thank Jonathan Banke, Hector Perez, and James Lowery for their careful work in constructing the apparatus and performing the experiments. The work at the University of Houston was supported by SABIC.

5. References [1] G.E. Keller, M.M. Bhasin, Synthesis of ethylene via oxidative coupling of methane. 1. Determination of active catalysts, J. of Catal. 73 (1982) 919. [2] U. Zavyalova, M. Holena, R. Schlögl, M. Baerns, Statistical analysis of past catalytic data on oxidative methane coupling for new insights into the composition of high-performance catalysts, ChemCatChem 3 (2011) 1935–1947. [3] J.C.W. Kuo, C.T. Kresge, R.E. Palermo, Evaluation of direct methane conversion to higher hydrocarbons and oxygenates, Catal. Today 4 (1989) 463-470. [4] D. Schweer, L. Mleczko, M. Baerns, OCM in a fixed-bed reactor: limits and perspectives, Catal. Today 21 (1994) 357369. [5] V.I. Lomonosov, M.Yu. Sinev, Oxidative coupling of methane: mechanism and kinetics, Kinet. and Catal. 57 (2016) 647676. [6] V. Balakotaiah, D. Kodra, D. Nguyen, Runaway limits for homogeneous and catalytic reactors, Chem. Eng. Sci. 50 (1995) 11491171. [7] J.H.B.J. Hoebink, P.M. Couwenberg, G.B. Marin, Fixed bed reactor design for gas phase chain reactions catalyzed by solids: the oxidative coupling of methane, Chem. Eng. Sci. 49 (1994) 54535463. 31

[8] A.L. Tarasov, L.M. Kustov, Autothermal methane oxidative coupling process over La2O3/MgO catalysts, Chem. Eng. Technol. 38 (2015) 22432252. [9] S. Pak, J.H. Lunsford, Thermal effects during the oxidative coupling of methane over Mn/Na2WO4/SiO2 and Mn/Na2 WO4/MgO catalysts, Appl. Catal. A: Gen. 168 (1998) 131137. [10] B. Zohour, D. Noon, S. Senkan, New insights into the oxidative coupling of methane from spatially resolved concentration and temperature profiles, ChemCatChem 5 (2013) 2809−2812. [11] A.V. Annapragada, E. Gulari, Fe-P-O Catalysts for methane utilization—catalyst development and identification, J. of Catal. 123 (1990) 130146. [12] J.Y. Lee, W. Jeon, J. Choi, Y. Suh, J. Ha, D. J. Suh, Y. Park, Scaled-up production of C2 hydrocarbons by the oxidative coupling of methane over pelletized Na2 WO4/Mn/SiO2 catalysts: observing hot spots for the selective process, Fuel 106 (2013) 851857. [13] D. Noon, A. Seubsai, S. Senkan, Oxidative coupling of methane by nanofiber catalysts, ChemCatChem 5 (2013) 146–149. [14] V. Balakotaiah, D.H. West, Thermal effects and bifurcations in gas phase catalytic partial oxidations, Curr. Opin. Chem. Eng. 5 (2014) 6877. [15] S. Yagi, D. Kunni, Studies on heat transfer near wall surface in packed beds, AIChE J. 6, (1960) 97-104. [16] R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, second ed., J. Wiley & Sons, New York, 2002. [17] S. R. Gundlapally, V. Balakotaiah, Analysis of the effect of substrate material on the steadystate and transient performance of monolith reactors, Chem. Eng. Sci. 92 (2013) 198-210.

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[18] V. Balakotaiah, D. Luss, Multiplicity features of reacting systems. Dependence of the steady-states of a CSTR on the residence time, Chem. Eng. Sci. 38 (1983) 17091721. [19] Z. Stansch, L. Mleczko, M. Baerns, Comprehensive kinetics of oxidative coupling of methane over the La2O3/CaO catalyst, Ind. Eng. Chem. Res. 36 (1997) 25682579. [20] Y.S. Su, J.Y. Ying, W.H. Green Jr., Upper bound on the yield for oxidative coupling of methane, J. Catal. 218 (2003) 321333. [21] M.Yu. Sinev, Z.T. Fattakhova, V.I. Lomonosov, Yu.A. Gordienko, Kinetics of oxidative coupling of methane: Bridging the gap between comprehension and description, J. Nat. Gas Chem. 18 (2009) 273287. [22] P. N. Kechagiopoulos, J.W. Thybaut, G.B. Marin, Oxidative coupling of methane: A microkinetic model accounting for intraparticle surface-intermediates concentration profiles, Ind. Eng. Chem. Res. 53 (2014) 18251840. [23]. V. Balakotaiah, I. Alam, D. H. West, Heat and mass transfer coefficients and bifurcation analysis of coupled homogeneous-catalytic reactions, Chem. Eng. J. 321 (2017) 207-221.

33

i.d. (mm) 2.3 4.0 10.5 22 34

o.d. (mm) 6.3 6.35 12.75 25 38

quartz particle mesh size 5080 5080 2040 2040 2040

length of foresection (mm) 63.5 63.5 12 25 25

length of aftersection (mm) 63.5 63.5 12 25 25

Table 1. Description of reactor dimensions and support packings.

34

CH4/O2

Tad1 (K)

Tad2 (K)

Tad3 (K)

Tad4 (K)

B

2.0

2075

1077

1565

403

27.4

2.5

1790

1110

1347

357

27.5

3.0

1585

1132

1191

322

27.7

3.5

1428

1148

1072

295

28.8

4.0

1305

1152

978

271

28.8

5.0

1120

1012

838

236

27.0

6.0

988

892

737

209

26.2

8.0

808

729

600

171

24.8

10.0

689

621

509

145

23.6

12.0

604

544

444

126

22.6

16.0

488

439

355

100

20.8

20.0

411

370

298

83

19.3

Table 2. Calculated adiabatic temperature rise for selected oxidation reactions as a function of methane to oxygen ratio with Tin=300 K. The last column gives the Zeldovich number for reaction 2, methane dimerization.

Tube i.d. (mm)

 h at

 h at

 h at 35

T = T f =900 K

T =1200 K, T f =300 K

T = T f =600 K

2.3

(ms) 2.3

(ms) 2.3

(ms) 7.2

4.0

5.8

6.0

20.6

10.5

19.5

20.4

70.4

22.0

45.6

47.2

157

34.0

74.8

77.0

254

Table 3. Estimated characteristic heat loss times for reactor tubes used in the experiments at some selected furnace and catalyst temperatures.

36

extinguished state CH4 conversion, mole % 0.96 O2 conversion, mole % 14.79 product selectivities, mole % ethylene 1.05 ethane 13.67 propylene 0.0 C2+ 14.72 CO 0.0 CO2 85.28

isolated/ignited state 20.19 99.47 45.27 15.17 4.71 65.16 0.0 34.84

Table 4. Comparison of product compositions on the extinguished and isolated branches of Fig. 13 (the points denoted by the green arrow and the circle).

37

CH4 conversion, mole %

27.16

product selectivities, mole % ethylene 25.43 ethane 9.33 propylene 2.62 C2+ 37.68 CO 32.92 CO2 29.39 H2/CO 0.82

Table 5. Results from Mn-Na2WO4/SiO2 catalyst (3.408 g) operated in the ignited state with feed and furnace temperature at 110 °C, CH4/O2 feed ratio = 3.5, 22 mm i.d. reactor, 15 mm catalyst bed height, space time = 275 ms.

38

Figure 1: (a) XRD pattern for La-Ce oxide powder catalyst; (b) XRD pattern for Mn-Na2 WO4 / SiO2 catalyst powder; (●) Na2WO4, (■) Mn2O3, (▲) α-cristobalite.

39

Figure 2: Schematic diagram of experimental system and schematic of reactor tube packed with catalyst powder.

40

(a)

(b)

Figure 3: Ignition and extinction behavior of La-Ce oxide powder catalyst (10 mg) in a 4 mm i.d. reactor; with 1 mm catalyst bed height, 14 ms space time, CH4/O2=4. (a) Oxygen conversion (b) C2+ product selectivity.

41

Figure 4: Temperature programmed experiment showing hysteresis in a 10.5 mm i.d. reactor; La-Ce oxide catalyst (0.25 g), 5 mm catalyst bed height, 58 ms space time, CH4/O2 = 4. Solid (dashed) line denotes increasing (decreasing) temperature.

42

Figure 5: Temperature programmed experiment without hysteresis. La-Ce oxide catalyst (20 mg) in a 4 mm i.d. reactor; 3 mm catalyst bed height, 58 ms space time, CH4/O2 = 4. Solid (dashed) line denotes increasing (decreasing) temperature.

43

Figure 6: Temperature programmed experiment with Mn-Na2WO4/SiO2 catalyst (0.999 g) in a 4 mm tube; 16 mm catalyst bed height, 0.28 s space time, CH4/O2 = 7.4.

44

Figure 7: Computed hysteresis boundary for La-Ce and Mn-Na2WO4/SiO2 catalysts with furnace (feed) temperature as the bifurcation variable. The experimental conditions corresponding to Figs. 3-5 are indicated by the triangle markers.

45

Figure 8: Computed bifurcation set for the La-Ce catalyst in 4 mm ( = 14 ms) and 10.5 mm ( = 58 ms) tubes in the furnace temperature-adiabatic temperature rise plane. The experimental ignition-extinction points shown in Figs. 3 and 4 are identified by markers.

46

Figure 9: Computed bifurcation bifurcation diagram of catalyst temperature and oxygen conversion versus furnace temperature for the Mn-Na2WO4/SiO2 catalyst corresponding to experimental conditions shown in Fig. 6. The dashed line is the isothermal line.

47

Figure 10: Comparison of computed bifurcation bifurcation diagrams of catalyst temperature and oxygen conversion versus furnace temperature for La-Ce and Mn-Na2WO4/SiO2 catalysts in a 4 mm tube with space time of 14 ms. The up and down arrows indicate ignition and extinction, respectively.

48

Figure 11: Experimental data showing dependence of conversion and selectivity on space time. La-Ce oxide powder catalyst (20 mg) in a 4 mm i.d. reactor, with 2.5 mm catalyst bed height, CH4/O2 = 4, furnace T = 500 °C.

49

Figure 12: Experimental results showing heat loss effect on conversion and selectivity. The space time axis is a log-scale. La-Ce oxide catalyst (10 mg) in 2.3 mm i.d. reactor with 5.5 mm catalyst bed height, CH4/O2 = 4. Furnace temperature = 500 °C.

50

Figure 13: Oxygen conversion vs. space time in the isola region. 1.0 g Mn-Na2WO4/SiO2 catalyst particles (1-2 mm size) in a 10.5 mm i.d. reactor; 13.3 mm catalyst bed height, CH4/O2 = 4. The red and green points are on the extinguished branch at furnace temperatures of 600 and 650 °C, respectively. The black triangles are on the ignited branch with furnace temperature of 700 °C. The green square (see arrow in upper left of figure) is on the isolated branch at 650 °C furnace temperature.

51

Figure 14: Computed phase diagram for Mn-Na2WO4/SiO2 catalyst in the plane of adiabatic temperature rise and heat loss time for a fixed furnace temperature of 873 K. The insets show the type of conversion versus space time diagram existing in each region.

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Figure 15: Computed bifurcation diagrams of catalyst temperature and oxygen conversion versus space time (on a logarithmic scale) for the Mn-Na2WO4/SiO2 catalyst in (the isola) region (b) of Fig. 14. The approximate location of the isolated state found in experimental results shown in Fig. 13 is indicated by the triangles. The arrows indicate the two extinction points.

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Figure 16: Computed bifurcation diagrams of catalyst temperature and oxygen conversion versus space time for the Mn-Na2WO4/SiO2 catalyst for parameters in region (d) of Fig. 14. The arrows indicate the ignition and extinction points.

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Figure 17: Computed region of autothermal operation with feed at ambient temperature (300 K) for the La-Ce catalyst in the space time-adiabatic temperature rise plane for tubes of different diameters. The approximate location of the operating conditions for experiments shown in Figs. 18 and 19 are identified by markers.

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Figure 18: Measured CH4 conversion and C2+ selectivity demonstrating stable autothermal operation of La2O3/CeO2 catalyst (494 mg) with 25 °C feed temperature; La/Ce = 15 (wt/wt), CH4/O2 = 4 (mol/mol), 10.5 mm i.d. reactor, 9 mm catalyst bed length, space time = 45 ms.

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Figure 19: Photograph of laboratory scale oxidative coupling of methane reactor with ambient feed. The catalyst (La-Ce oxide) powder (2.18 g) is sandwiched between quartz particles; 34 mm i.d. reactor, 5 mm bed height, CH4/O2 feed ratio = 4, space time = 45 ms. White lines indicate the approximate location of the catalytic section.

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