Sylvain Rodat
email: sylvain.rodat@promes.cnrs.fr.

Stéphane Abanades

Gilles Flamant

High-Temperature Solar Methane Dissociation in a Multitubular Cavity-Type Reactor

Keywords: Hydrogen production, Concentrated solar energy, Methane dissociation, Solar reactor, Natural gas, Carbon black

come

1-Introduction

In order to counter the rising CO 2 emissions, the decarbonisation of energy is required and hydrogen appears as the most promising energy carrier. Natural gas (mainly composed of methane) may play a major role on the way toward a carbon free energy [START_REF]A multi-year plan for the hydrogen R&D program[END_REF] . It is the cleanest hydrocarbon fuel and it can benefit from transportation infrastructures. Nowadays, hydrogen is mainly produced from steam methane reforming [START_REF] Dahl | [END_REF] , while carbon black is principally produced from the furnace process [START_REF] Donnet | Carbon Black, Second Edition[END_REF] . Both processes release large amounts of CO 2 in the atmosphere. Solar thermal methane cracking could be a solution for the clean co-production of hydrogen and carbon black. About 92% of the pollution associated with the two conventional processes is eliminated [START_REF] Wyss | [END_REF] . The overall reaction can be written as:

CH 4 2H 2 +C (1)
∆H° = 75 kJ mol -1 (216 kJ mol -1 for CH 4 at 298 K and products at 2000 K).

The reaction is endothermal and solar thermal energy is used as power input, which results in the absence of CO 2 release in the process. At thermodynamic equilibrium, the dissociation is complete for temperatures beyond 1500 K 5 . Nevertheless, Holmen et al. 6 point out the presence of products such as C 2 H 6 , C 2 H 4 , and C 2 H 2 depending on the residence time. These species are the ones involved in the commonly accepted dehydrogenation of methane [START_REF] Back | Pyrolysis: theory and industrial practice[END_REF] . Thermodynamic equilibrium is not reached due to kinetic limitations. The overall decomposition of methane has been studied by investigating either a catalytic or a non-catalytic reaction. For non-catalytic reaction, activation energies range between 312 kJ/mol [START_REF] Jr | [END_REF] and 451 kJ/mol 9 , whereas activation energies are lower (143 kJ/mol 10 -236 kJ/mol 11 ) for the catalytic decomposition reaction.

In previous works on methane cracking, Lédé et al. 12 mentioned in 1978 the use of a solar reactor to apply thermal shocks to methane. A complete bibliographic survey on methane pyrolysis after 1960 was published by Billaud et al. 13 . Solar thermal cracking of methane also enabled the production of nanotubes 14 . Special interest was given to solar methane cracking for the co-production of hydrogen and carbon black during the last five years. Two possible reactor designs were investigated, the direct [15][16][17][18][19] and the indirect heating concepts [START_REF] Dahl | [END_REF][START_REF] Wyss | [END_REF]20 . In the latter configuration, the solar irradiated zone is separated from the reacting flow whereas in the former, no separation is used, and particles seeding is required for efficient gas heating.

This work reports on the results obtained with a novel prototype-scale solar reactor (mean power: 20 kW) featuring a cubic graphite cavity (behaving as a black-body cavity) with four vertical inside tubular reaction zones. This design enables the control of the reactor tube temperature and is also suitable for scaling-up. Previous results on low temperature runs (in the range 1670-1770 K) have already been reported and have permitted to validate the Dsmoke kinetic code for the chemical reaction modelling applied to methane decomposition 21 . It also showed that increasing the temperature favour the methane conversion. Therefore, a second series of experiments at higher temperatures was performed in the range 1823-2073 K and the noteworthy results are discussed in the following sections.

2-Experimental Section

2.1-Design of the reactor

The reactor is presented in Fig. 1. It is composed of a graphite cavity receiver of cubic shape. Its side is 20 cm long and the aperture diameter is 9 cm. The reactor was designed for a nominal power in the range 15-25 kW. Inside the cavity, four independent and identical tubular reaction zones are positioned vertically and work in parallel. Each reaction zone is composed of two concentric tubes (Fig. 2). This design warrants a pre-heating of the feed gas by the hot products. The innermost tube is 4 mm i.

2.2-Experimental procedure

Each experiment starts with a heating period (about 30 min) with an argon flow in the tubes in order to reach the targeted temperature. Temperature is controlled thanks to a solar-blind optical pyrometer (wavelength: 5.14 µm) pointing toward a tube wall through a CaF 2 window. A type B thermocouple (Pt-Rh) is placed in contact with the graphite cavity but has to be removed for temperatures above 1973 K (maximal working temperature for this device). Once the desired temperature is reached, a controlled mixture of argon and methane can be injected. This is enabled thanks to 8 mass-flow controllers (4 for methane and 4 for argon). Two mass-flow controllers are dedicated to each tube (Brooks Instruments model 5850 S, precision 0.7% of the measurement +/-0.2% of the full scale, range 0-10 NL/min (0-1.67x10 -4 Nm 3 s -1 ) for methane and 0-20 NL/min (0-3.33x10 -4 Nm 3 s -1 ) for argon, where NL means Normal Liter that corresponds to one liter at normal conditions (101,325 Pa, 273.15 K)). There is no gas pre-heating before entering the reactor tubes since the gases are fed through a water-cooled copper component at the top of the reactor (Fig. 1). When leaving the reactor tubes, the gas products are collected in this same water-cooled copper component that allows the cooling of products below 373 K.

Then, the gases flow in a water-cooled pipe before entering a solid-gas separation unit. Accordingly, the products flow through a filter bag (diameter: 127 mm, length: 800 mm) to separate carbon particles. It is made of Ryton with a Mikrotex membrane (type 3601-57, 500 g/m²). Then, a bypass stream to be analyzed is aspired through a set including a primary sampling pump that feeds a continuous analyzer and a secondary sampler (peristaltic pump) that feeds a gas chromatograph (GC, Varian CP 4900). The GC is equipped with 2 channels (the retention times are reported after each relevant species): channel 1 enabled thanks to the use of a venturi vacuum pump (P6010 SI32-3X4, feed pressure 400 kPa, maximum vacuum flow of 3.2 NL/s (5.33x10 -5 Nm 3 s -1 ) at -40 kPa). In order to monitor the pressure in each tube, absolute pressure transmitters with ceramic cells equip each tube entrance. The measurement scale is 0-400 kPa and the precision is +/-0.30% of the full scale.

2.3-Experimental conditions

The investigated temperature range is 1823-2073 K. Temperature was proved to be homogeneous in the graphite cavity according to numerical simulations 22 . They also confirmed that the gas temperature has reached the wall temperature at the pyrometer position (Fig. 2). The methane mole fraction varies between 10% and 100% with a total methane flow-rate ranging between 0.8 NL/min and 12 NL/min (1.33x10 -5 and 2x10 -4 Nm 3 s -1 ). The absolute pressure is about 40 kPa inside the tubes. The flow is laminar (Reynolds number < 2000). The typical mean duration of an experimental run at a given temperature is 45 min before tube blocking (due to carbon accumulation), and it depends strongly on the experimental conditions (dilution ratio, methane flow-rate and conversion). The pre-heating period is about half an hour.

3-Results and Discussion

For each experimental condition, various parameters are calculated:

• The residence time τ of the gas species is calculated by dividing the volume of the isothermal part of the tube (part inserted in the graphite cavity, Fig. 2) by the volumetric inlet flow-rate of argon and methane at the real tube temperature and pressure. It is often referred as "space time" 23 . It permits to give a characteristic reaction time even if chemical expansion is not included. In the following discussion, "residence time" will always refer to this definition.

0 r Q V τ= (2)
• The CH 4 conversion gives the proportion of methane that has been transformed and it is defined as:

4 4 4 4 CH 0, CH CH 0, CH F F.y F X - = (3)
• The H 2 yield is the proportion of methane that has been converted into hydrogen and it is calculated from:

4 2 2 CH 0, H H 2.F F.y Y = (4)
• The C yield is the proportion of methane that has been converted into solid carbon and it is expressed as:

4 6 2 4 2 2 2 4 4 CH 0, H C H C H C CH CH 0, C F ) F.y . 2 F.y . 2 F.y . 2 -(F.y F Y + + + = (5)
where CH4 0, F is the inlet molar flow-rate of CH 4 , y i is the mole fraction of species i, and F is the total outlet flow-rate (including argon as buffer gas) obtained from:

6 2 4 2 2 2 2 4 H C H C H C H CH Ar F.y F.y F.y F.y F.y F F + + + + + = (6)
F Ar is the molar flow-rate of Ar.

• The reactor thermo-chemical efficiency represents the fraction of solar energy that is converted and stored in a chemical form as hydrogen 18 :

solar ) Treactor ( Products ) T ( Reactant CH CH 0, ch 0 4 4 . X . F P H s → ∆ = η (7)
• The reactor thermal efficiency also takes into account the heating enthalpy of both the nonconverted reactants and the inert gas, it is expressed as:

∫ ∫ + ∆ + - = → η (8)
where ∆H (J.mol -1 ) is the enthalpy change of the reaction (1) when the reactants are fed at T 0 =298 K and the products are obtained at T reactor , P solar is the solar power input (W), Cp i is the specific heat of species i (J.mol -1 .K -1 , function of temperature).

This set of indicators is the foundation of the discussion below.

3.1-Steady state, stability, reproducibility

CH 4 and H 2 off-gas mole fractions given by the on-line analyzer are plotted in Fig. 3, along with the temperature measured by the pyrometer. Four consecutive experimental conditions are represented: the first run is carried out with 36 NL/min (6x10 -4 Nm 3 s -1 ) of Ar and 8 NL/min (1.33x10 -4 Nm 3 s -1 ) of CH 4 , the second run with 36 NL/min (6x10 -4 Nm 3 s -1 ) of Ar and 12 NL/min (2x10 -4 Nm 3 s -1 ) of CH 4 , the third run is identical to the first in order to test reproducibility, the last run is carried out with 28 NL/min (4.67x10 -4 Nm 3 s -1 ) of Ar and 8 NL/min (1.33x10 -4 Nm 3 s -1 ) of CH 4. First, a plateau on the H 2 off-gas mole fraction is obtained for the first three experimental conditions after about 1 to 2 minutes. It shows that steady state is rapidly reached. For the last experimental condition, this plateau is not observed even after 6 min. and the H 2 mole fraction increases with time. This is due to a pressure increase in the reactor tubes as a result of tube blocking by carbon deposition.

Consequently, the residence time increases and so does the H 2 yield. The pressure can increase from 40 kPa to 100 kPa in a few minutes, consequently the experiment is stopped.

Then, the first and third experimental runs prove that the same results are achieved for the same experimental conditions, both for H 2 and CH 4 off-gas concentrations (less than 1% difference on the CH 4 conversion and H 2 yield); and that there is no influence of the previous experimental conditions.

Finally, the temperature measurement shows fluctuations depending on the presence or absence of methane in the flow. As soon as methane is injected, the temperature decreases whereas it increases when stopping the methane flow (argon flow-rate is maintained). The variation is about 20-30 K. The decrease of temperature when CH 4 is injected stems from the endothermic dissociation reaction. Thus, a slight reactor over-heating was set under argon flow before CH 4 injection to anticipate the temperature decrease and to reach the given reaction temperature during experiments.

3.2-Temperature influence

A maximum working temperature of 2073 K has been achieved. In Fig. 4, CH 4 conversion and C 2 H 2 mole fraction are plotted versus residence time for different temperatures (1823 K, 1973 K, and 2073 K). The methane mole fraction in the inlet gas is kept constant at 20%. The total gas flow-rate is changed, which thereby determines the gas residence time. The influence of temperature is clear: the higher the temperature, the higher the conversion for a given residence time. For a 11 ms residence time, CH 4 conversion is 79%, 93%, and 100% at 1823 K, 1973 K, and 2073 K, respectively. The methane conversion is total for temperatures higher than 1823 K and residence times longer than 25 ms.

Concerning C 2 H 2 mole fraction in the off-gas, it seems to be more affected by residence time than by temperature. The lowest C 2 H 2 concentrations are reached for the highest residence times. Assuming a first order kinetic expression 16 and an ideal plug-flow reactor model, the residence time τ can be calculated from 19

: 4 4 ) 1 ln( ) 1 ( CH CH X X k αβ β α τ - - + - = ( 9
)
where α is the chemical expansion factor, β is the physical dilatation factor, and k is the kinetic rate constant, following an Arrhenius law:

) / .exp(-E k k a 0 RT = ( 10
)
where E a denotes the activation energy (J/mol), k 0 the pre-exponential factor (s -1 ), R the universal gas constant (8.314 J/mol K), and T the absolute temperature (K).

Thus, it is possible to determine the kinetic rate k for different experimental temperatures. Data from previous reported results at lower temperatures 21 are also included. Then, from the plot ln(k)=f(1/T), a linear regression (determination factor = 0.9982) allows estimating a pre-exponential factor of 1.42x10 7

s -1 and an activation energy of 172 kJ/mol. These values are consistent with previously reported activation energy for heterogeneous (catalytic) methane decomposition. The produced carbon black can play the role of catalyst 11 . This simplified model permits to estimate that the incertitude (for T=1823 K)

on CH 4 conversion is +/-1% for a temperature incertitude of +/-10 K (that corresponds to the incertitude of experimental temperature measurements). Similarly, the incertitude on CH 4 conversion is less than +/-2% if the residence time is estimated at +/-10%. A variation of +/-6% of the activation energy (estimated incertitude of the slope) also affects the CH 4 conversion by +/-17%. Thus, uncertainties on the temperature or the residence time have a weak influence on the CH 4 conversion, whereas the value of the activation energy is more critical and it just provides an order of magnitude of the kinetic parameters.

3.3-Residence time influence

The influence of residence time was studied at a given temperature for a constant CH 4 mole fraction in the feed gas mixture (10%). Residence times between 15 ms and 70 ms were tested at 1823 K (Fig. 5).

For clarity reasons, C 2 H 4 mole fraction is not represented because it was always below 400 ppm. C 2 H 6 was not detected. In order to change the residence time, flow rates were modified. The first conclusion is that the CH 4 conversion and the H 2 yield are improved when increasing the residence time. A more in-depth analysis of the results also gives a scheme of the methane decomposition sequence. For residence times between 25 .

Instead of speaking in terms of space time based on the inlet gas flow-rate (τ = V r /Q 0 ), it would be possible to calculate the mean residence time that takes into account the flow-rate at the exit of the reactor:

) 1 ( 4 0 α β τ CH r m X Q V + = (11)
If the reference is taken at the entrance of the isothermal part of the reactor where the reaction occurs, then β=1. Thus, τ = 1.10.τ m for a 10% CH 4 mole fraction in the feed (α = 0.1) and X CH4 =1. The "real" residence time (time required for an inert tracer to cross the reactor volume) is thus between the space time and the mean residence time. For sufficient dilution with argon, simulation results 21 confirm that there is no significant difference between the "real" residence time and the space time. Obviously, the space time must be twice the mean residence time when complete dissociation is reached for pure methane. For this study on the influence of the residence time, a CH 4 mole fraction of 10% is low enough to assimilate the space time to the real residence time.

3.4-Influence of the CH 4 mole fraction in the feed

The influence of the methane concentration was investigated with a constant flow-rate of argon ( 18NL/min, 3x10 -4 Nm 3 s -1 ) and a methane flow-rate varying from 2 NL/min to 10 NL/min (3.33x10 -5 -1.67x10 -4 Nm 3 s -1 ), that is to say, a methane mole fraction in the feed varying from 10% to 36% (Fig. 6).

The corresponding residence times, calculated at the actual tube temperature (1923 K) and pressure of each experimental condition, varies from 20 ms to 17 ms. Thus, the residence is almost constant. Both CH 4 conversion and H 2 yield are plotted. The CH 4 conversion is actually declining when increasing CH 4 mole fraction in the feed. This may be due to the endothermic reaction. The H 2 yield seems to dwindle sooner. Then, the higher the CH 4 mole fraction in the feed gas, the higher the amount of H flow-rate. The residence time was 62 ms for 4 NL/min (6.67x10 -5 Nm 3 s -1 ) of CH 4 (mean residence time from Eq. 11 of 31 ms). The quantity of by-products was negligible. Therefore, this run shows that reaction completion can be achieved with pure methane in the feed for a residence time much longer than the one used in Fig. 6. Nevertheless, one must point out that the long residence time due to the low gas velocity caused a substantial carbon deposit in the tubes. Even if increasing the mole fraction improves the efficiency of the reactor, high methane concentrations along with high residence times favor carbon deposition.

3.5-Methane cracking versus natural gas cracking

Natural gas was introduced instead of methane to examine the effect of feedstock composition. A chromatography analysis of this natural gas highlights the presence of about 9.5 % ethane and trace amounts of CO 2 and N 2 . Fig. 7 plots the mole fractions of H 2 , C 2 H 2 , and CH 4 as a function of residence time for methane cracking and natural gas cracking experiments at 1873 K. The comparison shows a small discrepancy limited to a few percents, which is in the range of experimental uncertainties. As predicted by the Dsmoke kinetic software 21 , there is no difference between natural gas cracking and pure methane cracking for a residence time higher than 1 ms. The only difference is expected for shorter residence times due to the presence of ethane (C 2 H 6 ) that is easier to decompose than CH 4 . The reactor tubes and the filter were weighted before and after experiments. The mass of carbon accumulated in the tubes was 26.4 g, while 1.5 g of carbon was recovered in the filter. A total of 146.5 NL (0.1465 Nm 3 ) of methane was introduced in the reactor. Then, a mass balance between the recovered solid carbon and the amounts of gaseous species in the off-gas shows that 93% of the initial carbon mass and 92% of the initial hydrogen mass are retrieved at the exit according to the following calculations Fig. 9 shows the H mass balance. 75% of H atoms is found as H 2 gas, 14% is in the form of C 2 H 2 , 3% is contained in the unconverted CH 4 , and the remaining 8% is thus attributed to other hydrocarbons. A fraction of the missing H-content may also be found in the carbon black although the H-content in the channel black (that presents the largest amount of hydrogen) is less than 1% (molar) [START_REF] Donnet | Carbon Black, Second Edition[END_REF] .According to this balance, CH 4 is efficiently converted into H 2 (75% H 2 yield). 10 shows the C mass balance. 54 % of the carbon is contained in C 2 H 2 . Only 36% of the carbon is recovered as solid carbon either in the reactor tubes (34%) or in the filter (2%). 3% of carbon stays in the unconverted CH 4 . The remaining part (7%) may be contained in other hydrocarbons or may correspond to un-removed solid carbon. Methane is not as well converted into solid carbon as it is in H 2 due to the substantial presence of C 2 H 2 .

3.7-Efficiency of the reactor

Owing to the production of by-products, the thermo-chemical efficiency as defined previously in Eq. ( 7) is not perfectly suitable. Indeed, it only gives the real efficiency of the reactor if the dissociation was complete, otherwise it is under-estimated. According to previous kinetic analyses of the reaction with a detailed chemical mechanism model, C 2 H 6 and C 2 H 4 are rapidly decomposed, and C 2 H 2 is the only byproduct present in appreciable amount at the exit of the reactor 21 , which is consistent with the gas analysis results. Thus, a two-step dissociation scheme is proposed according to the experimental results:

CH 4 3/2 H 2 +½ C 2 H 2 endothermal, ∆H 1 ° = 188 kJ mol -1 (14) C 2 H 2 H 2 +2C exothermal, ∆H 2 ° = -227 kJ mol -1 (15)
The standard enthalpy of methane-to-acetylene formation (Eq. 14) is more than twice the standard enthalpy of single-step methane dissociation (Eq. 1). In addition, a part of acetylene formed from methane is not dissociated into hydrogen, as shown by the analysis of the exhaust gas stream. This intermediate step involving acetylene must be taken into account in the calculation of the reactor efficiency. The fractional conversions of the successive reactions ( 14) and ( 15) are the solutions of the following system:

4 , 0 ). . 2 / 3 . . 2 / 1 ( 2 CH H F X Y X F + = (16) 4 , 0 . . 2 / 1 ) 1 ( 2 2 CH H C F X Y F - = ( 17
)
where Y is the fractional conversion of reaction (15) defined as Y=F H2 /F 0,C2H2 where F 0,C2H2 is the molar flow-rate of acetylene issued from reaction (14). The fractional conversion X of reaction (14) should be equal to the CH 4 conversion X CH4 defined in Eq. ( 3) if the real chemical mechanism was only composed of reactions ( 14) and (15). Nevertheless, this assumption is not exactly satisfied since X is always smaller (about 6%) than X CH4 . This proves that the chemical mechanism includes additional steps and intermediates [26][27][28]

∫ ∫ + ∆ + ∆ + = η (19)
For each run, the solar power is calculated from calorimetric measurements at the center of the reactor aperture. As a first approximation, the solar flux density is assumed homogeneous at the aperture, which may lead to a slightly over-estimated solar power. The net solar power absorbed varies between 16.9 kW and 25.8 kW depending on the working temperature between 1823 K and 2073 K. Fig. 11 illustrates the evolution of the above defined efficiencies at 1823 K, 1873 K, 1973 K, and 2073 K. For each temperature, the CH 4 mole fraction in the feed was 20%. Obviously, the thermo-chemical efficiency (Eq. 18) is always lower than the thermal efficiency (Eq. 19). The calculated reactor thermo-chemical efficiencies are improved when accounting for the presence of acetylene as a high energy value by-product. In contrast, C 2 H 2 formation lowers the power available for methane dissociation. Indeed, the amount of energy consumed per mole of converted methane is higher in the two-step endothermal and exothermal reaction scheme (∆H 1 +½.Y.∆H 2 ) than in the single-step CH 4 dissociation (∆H 1 +½.∆H 2 ). Thus, the fraction of solar energy devoted to reaction enthalpy is strengthened when C 2 H 2 intermediate is considered in the calculation. For a given temperature, an increase in CH 4 flow-rate results in significant efficiencies improvement (both thermo-chemical and thermal), but in counterpart it affects the CH 4 conversion, especially at low temperature. At 1823 K, CH 4 conversion is only 79% for 6 NL/min (1x10 -4 Nm 3 s -1 ) of fed CH 4 , whereas CH 4 conversion is almost complete at higher temperatures. On the basis of the reported reactor efficiencies, an optimum temperature for reactor operation may exist. Indeed, CH 4 conversion exceeds 95% for temperatures higher than 1873 K, while thermal efficiencies tend to decrease when increasing the temperature (9.3% at 1823 K and 7.4% at 2073 K for 6 NL/min (1x10 -4 Nm 3 s -1 ) of CH 4 ). This is due to the increased solar power input when raising the temperature, and to more induced radiation losses. In order to maximize both the CH 4 conversion and the thermal efficiency of the reactor, a temperature between 1873 K and 1973 K is advised, the smallest being preferable for coupling the process with existing solar concentrating technologies. The optimum temperature range has been identified on the basis of optimized reaction efficiencies. Further work is required to optimize as well the solar concentrating systems and the carbon black properties that are both key issues for the process economics. A 50 kW pilot-scale solar reactor is under construction to produce larger quantities of carbon black and to determine its properties. The main heat losses in the current solar reactor were identified to be infrared radiation emission through the window and conduction through the watercooled front face. For increasing reactor efficiencies, the front face insulation should be improved and a higher solar concentration ratio is required to minimize IR-radiation losses.

4-Conclusion

Solar thermal dissociation of methane was investigated in a multi-tubular solar reactor prototype operating in the high temperature range 1823 K -2073 K. A wide range of experimental conditions was tested: methane flow rate up to 12 NL/min (2x10 -4 Nm 3 s -1 ), CH 4 mole fraction in the feed up to 100%, and residence time from 10 ms and beyond 100 ms. CH 4 conversion chiefly increased with temperature and residence time, whereas C 2 H 2 content in the off-gas was more lowered when raising the residence time than the temperature. C and H mass balances showed that C 2 H 2 formation strongly alleviates the C yield. Moreover, a two-step reaction mechanism was proposed involving C 2 H 2 intermediate. The highly endothermic C 2 H 2 formation lowers the power available for methane dissociation. Both thermal and thermo-chemical efficiencies are improved when increasing the methane flow-rate in the feed. The lower the temperature, the longer the required residence time for reducing C 2 H 2 formation. A temperature of about 1873 K is advised to optimize both the methane conversion and the reactor thermal efficiency. A test with a different feedstock composition (natural gas instead of methane) did not modify the reactor performances.

A 50 kW pilot solar reactor is currently under construction to investigate the process at a larger scale, and to characterize the properties of the solar-produced carbon black with respect to the commercial standards.

Acknowledgements:

This work was financially supported by the European Project Solhycarb (2006-2010, Contract SES-CT2006-19770). Authors thank Jean-Louis Sans, Olivier Prévost, Marc Garrabos and Emmanuel Guillot for their technical support during the solar reactor manufacturing and the experimental campaigns at the 1 MW solar furnace of CNRS-PROMES (France).

Nomenclature:

C pi specific heat of species i (J/mol.K, function of temperature)

  d. and 12 mm o.d., while the outer tube is 18 mm i.d. and 24 mm o.d.. A mixture of methane and argon is fed in the innermost tube and the products flow out through the annular space between the two tubes. The total tube length is 380 mm: 178 mm are heated in the graphite cavity directly exposed to solar irradiation, while the remaining length goes through the insulating layers. Three different insulating layers surround the graphite cavity in order to limit conduction losses. They form an insulation layer of 0.15 m thickness (0.05 m for each insulating material). The 3 insulating materials are a graphite felt in contact with the cavity (λ=0.53 W.m -1 .K -1 at 1873 K), an intermediate refractory ceramic fiber operating up to 1873 K (62% Al 2 O 3 , 30% SiO 2 , λ= 0.35 W.m -1 .K -1 at 1673 K), and an outer microporous insulator operating up to 1273 K (20% ZrO 2 , 77.5% SiO 2 , 2.5% CaO, λ=0.044 W.m -1 .K -1 at 1073 K). The reactor shell (535x535x373 mm) is made of stainless steel. As far as the front face is concerned, it is aluminummade with water-cooling channels. A water-cooled copper-made component enables to hold the hemispherical quartz window. This transparent window closes the cavity, which helps to create an inert atmosphere. It prevents the graphite from oxidizing since the graphite cavity is swept by a nitrogen flow.Both the direct concentrated solar radiations from the sun and the IR radiations from the cavity walls contribute to the tubes heating. The solar concentrating system used is the 1 MW solar furnace of the CNRS-PROMES laboratory. It is composed of a field of 63 sun-tracking heliostats (45 m² each) and a parabolic concentrator (1830 m²) delivering up to 9000 suns at the focal point. For the experiments at 15-25 kW scale, only a limited number of heliostats(25) was used along with a shutter to control the incoming flux density in the range 2-4 MW/m². Then, the reactor aperture (9 cm-diameter) determined the absorbed solar power.

Figure 1 .Figure 2 .

 12 Figure 1. Scheme of the prototype-scale solar reactor and filter

Figure 3 .

 3 Figure 3. On-line H 2 and CH 4 off-gas mole fractions and temperature versus time for four consecutive

Figure 4 .

 4 Figure 4. Temperature dependence of CH 4 conversion and C 2 H 2 off-gas mole fraction versus residence

Figure 5 .

 5 Figure 5. CH 4 conversion, H 2 yield, C yield, CH 4 and C 2 H 2 off-gas mole fractions versus residence time

Figure 6 .

 6 Figure 6. CH 4 conversion and H 2 yield versus CH 4 mole fraction in the feed at 1923 K

Figure 7 . 3 . 6 -

 736 Figure 7. Off-gas H 2 , C 2 H 2 , and CH 4 mole fractions for methane cracking (M) and natural gas cracking

Figure 8 .

 8 Figure 8. H 2 , CH 4 , and C 2 H 2 mole fractions in the off-gas versus time (T = 1923 K, Ar flow-rate: 18

(only H 2 ,

 2 C, CH 4 , and C 2 H 2 are taken into account, the other hydrocarbons are neglected):

Figure 9 .

 9 Figure 9. Typical H balance (T = 1923 K, Ar flow-rate: 18 NL/min)

Figure 10 .

 10 Figure 10. Typical C balance (T = 1923 K, Ar flow-rate: 18 NL/min)

Figure 11 .

 11 Figure 11. CH 4 conversion and reactor efficiencies (for a single-step reaction model or a two-step

  E a activation energy (J/mol) F total molar flow-rate (mol/s) F i molar flow-rate of species i (mol/s) F 0,i inlet molar flow-rate of species i (mol/s) ∆H° standard reaction enthalpy (J/mol) k 0 pre-exponential factor (s -1 ) m i mass of species i (kg) M i molecular weight of species i (kg/mol) NL Normal Liter (at normal conditions: 101.325 kPa and 273.15 K) P absolute pressure (Pa) P solar solar power input (W) Q 0 volumetric inlet flow-rate of argon and methane at the actual tube temperature and pressure (m 3 /s) R universal gas constant (8.314 J/mol K) T absolute temperature (K) T 0 reference temperature (298 K) r V volume of the isothermal part of the tubes where the reaction occurs (residence time (s)

  24 . Carbon yield is also represented and it can be observed that the decrease in the C 2 H 2 off-gas concentration corresponds to an increase in carbon yield. C 2 H 2 is thus converted into carbon black and H 2 . A residence time of 70 ms is needed in order to reach an off-gas C 2 H 2 mole

	fraction lower than 0.5%. A methane mole fraction of 50% in the feed gas mixture was also
	experimented at 1923 K for a residence time of 79 ms, and the resulting off-gas C 2 H 2 mole fraction was
	less than 300 ppm. With pure methane in the feed (without any argon flow), a residence time of 124 ms
	at 1923 K was reached and the off-gas C 2 H 2 mole fraction was below 400 ppm. To increase hydrogen
	yield and avoid acetylene formation, long contact times are required, whereas very high temperatures are
	not favourable
	15 ms and 18 ms, the H 2 yield increases due to a better CH 4 decomposition rate (off-gas concentration of
	CH 4 decreases), while the off-gas concentration of C 2 H 2 slightly increases. It means that methane is first
	converted into acetylene (2CH 4 → C 2 H 2 + 3H 2 ), thus releasing 1.5 mole of H 2 per mole of CH 4
	converted. For longer residence times, the H 2 yield is enhanced due to acetylene decomposition. Similar
	trends are observed in Fig. 4. For the lowest temperature (1823 K), C 2 H 2 off-gas concentration presents
	a maximum whereas it decreases quite monotonically for higher temperatures because the maximum

may occur at shorter residence times. This suggests that the rate of C 2 H 2 formation becomes lower than the rate of C 2 H 2 decomposition at any temperatures. Acetylene constitutes a reaction intermediate as reported previously

  2 produced, but the lower the CH 4 conversion. Nevertheless, 93% CH 4 conversion and 74% H 2 yield are still reached for a CH 4 mole fraction of 36% in the feed. Consequently, increasing the CH 4 mole fraction in the feed gas up to 36% allows enhancing the thermo-chemical efficiency, because a fairly good chemical conversion is maintained. An additional experimental run was also carried out at 1923 K for 100% methane in the feed. The dissociation was complete: the outlet H 2 flow-rate was twice the inlet CH 4

  . However, this two-step reaction model can fairly describe the production of the three major species (C, C 2 H 2 , and H 2 ) in a simple realistic way. Then, a more accurate expression of the thermo-chemical efficiency can be written as:

	, ch η	new	=	CH 0, F	4	. X	T .	T reactor 0 ∫	Cp CH	4	.dT	+	0, F	CH	4	. X	solar 1 T reactor ( P H ∆ .	)	/ 1 +	2	CH 0, F .	4	. Y . X . ∆ H	2	reactor T (	)	(18)
	and the thermal efficiency becomes:
										T	reactor																T	reactor
				0, F	CH	4	.		Cp CH	4	.dT	0, F	CH	4	.	X	.	reactor T ( 1 H	)	/ 1	. 2	0, F	CH	4	. Y . X .	H	reactor T ( 2	)	F Ar	Cp	. dT Ar
	, th	new								T 0																	solar P	T 0