Millisecond methane steam reforming for hydrogen production: A computational fluid dynamics study

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 8 ) 1 e2 2

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Millisecond methane steam reforming for hydrogen production: A computational fluid dynamics study Junjie Chen*, Xuhui Gao, Longfei Yan, Deguang Xu Department of Energy and Power Engineering, School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo, Henan, China

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abstract

Article history:

The potential of methane steam reforming to produce hydrogen in thermally integrated

Received 20 August 2017

micro-chemical systems at short contact times was theoretically explored. Methane steam

Received in revised form

reforming coupled with methane catalytic combustion in microchannel reactors for hydrogen

6 May 2018

production was studied numerically. A two-dimensional computational fluid dynamics model

Accepted 7 May 2018

with detailed chemistry and transport was developed. To provide guidelines for optimal

Available online xxx

design, reactor behavior was studied, and the effect of design parameters such as catalyst loading, channel height, and flow arrangement was evaluated. To understand how steam

Keywords:

reforming can happen at millisecond contact times, the relevant process time scales were

Microchannel reactors

analyzed, and a heat and mass transfer analysis was performed. The importance of energy

Steam reforming

management was also discussed in order to obtain a better understanding of the mechanism

Hydrogen production

responsible for efficient heat exchange between highly exothermic and endothermic re-

Process intensification

actions. The results demonstrated the feasibility of the design of millisecond reforming sys-

Micro-combustion

tems, but only under certain conditions. To achieve this goal, process intensification through

Computational fluid dynamics

miniaturization and the improvement in catalyst performance is very important, but not sufficient; very careful design and implementation of the system is also necessary to enable high thermal integration. The channel height plays an important role in determining the efficiency of heat exchange. A proper balance of the flow rates of the combustible and reforming streams is an important design criterion. Reactor performance is significantly affected by flow arrangement, and co-current operation is recommended to achieve a good energy balance within the system. The catalyst loading must be carefully designed to avoid insufficient reactant conversion or hot spots. Finally, operating windows were identified, and engineering maps for designing devices with desired power were constructed. © 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

Introduction The production of synthesis gas, primarily a mixture of hydrogen and carbon monoxide, from hydrocarbons has

received a great deal of interest in recent years due to the need to produce high-content hydrogen streams for fuel cell applications and internal combustion engines [1e4]. Industrially, syngas is produced by steam reforming of natural gas

* Corresponding author. Department of Energy and Power Engineering, School of Mechanical and Power Engineering, Henan Polytechnic University, 2000 Century Avenue, Jiaozuo, Henan, 454000, China. E-mail addresses: [email protected], [email protected] (J. Chen). https://doi.org/10.1016/j.ijhydene.2018.05.039 0360-3199/© 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Chen J, et al., Millisecond methane steam reforming for hydrogen production: A computational fluid dynamics study, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.05.039

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Nomenclature

S/V 2

Acatalyst catalytically active surface area, m , Eq. (12) Ageometric geometric surface area, m2, Eq. (12) feed concentration of the fuel, mol/m3, Eq. (25) Cfuel,in Ci,interface concentration of the i-th species at the gaswashcoat interface, mol/m2, Eq. (14) specific heat capacity at constant pressure, cp J/(kg$K), Eq. (8) d gap distance between the plates, i.e., channel height, m, Fig. 1 and Eq. (26) mean pore diameter of the catalyst, m, Eq. (17) dpore D diffusion coefficient, m2/s, Eq. (6) thermal diffusion coefficient, m2/s, Eq. (6) DT effective diffusion coefficient of the i-th species Di,eff inside the washcoat, m2/s, Eq. (14), as defined by Eq. (16) Di,Knudsen Knudsen diffusion coefficient of the i-th species inside the washcoat, m2/s, Eq. (16), as defined by Eq. (17) Di,molecular molecular diffusion coefficient of the i-th species inside the washcoat, m2/s, Eq. (16) mixture-averaged diffusion coefficient of the k-th Dk,m gaseous species, m2/s, Eq. (6) thermal diffusion coefficient of the k-th gaseous DTk species, m2/s, Eq. (6) € hler number, dimensionless, as transverse Damko Day defined by Eq. (30) catalyst/geometric surface area, m2/m2, as defined Fcat/geo by Eq. (12) Fo Fourier number, dimensionless, as defined by Eq. (32) view factor for solid-ambient, unity, Eq. (19) Fs-∞ h total specific enthalpy, J/kg, Eq. (8) specific enthalpy of the k-th gaseous species at hok reference temperature, J/kg, Eq. (8) external heat loss coefficient, W/(m2$K), Eq. (19) ho Q standard molar enthalpy of reaction, kJ/mol, D r Hm Eq. (20) adsorption rate constant of the k-th gaseous kad,k species, Eq. (24) K ratio of catalyst loadings, Fig. 6, as defined by Eq. (29) number of the species in the gas phase, Eq. (4) Kg number of the species on the surface of the Ks catalyst, Eq. (9) l reactor length, i.e., channel length, Fig. 1 and Eq. (28) m total number of gaseous and surface species, Eq. (9) p pressure, Pa, Eq. (2) clet number, dimensionless, as defined by Pe Pe Eq. (31) q heat flux, W/m2, Fig. 1 and Eq. (18) R ideal gas constant, J/(mol$K), Eq. (7) effectiveness surface molar production rate of the s_i;eff i-th species inside the washcoat, mol/(m2$s), Eq. (13) surface molar production rate of the m-th surface s_m species, mol/(m2$s), Eq. (9)

T Tamb To Tw,o u  u uin v Vk ! Vk Wk W x y Yk

surface-to-volume ratio, i.e., catalytically active surface area per unit volume, m2/m3, Eq. (25) absolute temperature, K, Eq. (4) ambient temperature, K, Eq. (19) reference temperature, K, Eq. (8) temperature at the external surface of the solid wall, K, Eq. (19) streamwise velocity component, m/s, Eq. (1) average flow velocity, m/s, Eq. (28) inlet velocity, m/s, Fig. 4 transverse velocity component, m/s, Eq. (1) diffusion velocity of the k-th gaseous species, m/s, Eq. (5) diffusion velocity vector of the k-th gaseous species, m/s, Eq. (6) relative molecular mass of the k-th gaseous species, dimensionless, Eq. (5) relative molecular mass of the gas mixture, dimensionless, Eq. (6) streamwise reactor coordinate, Fig. 1 and Eq. (1) transverse reactor coordinate, Fig. 1 and Eq. (1) mass fraction of the k-th gaseous species, Eq. (4)

Greek variables G site density for surface phase, mol/m2, Eq. (9) g catalytically active surface area per washcoat volume, m2/m3, Eq. (14), as defined by Eq. (15) sticking coefficient of the k-th gaseous species, gk Eq. (24) d wall thickness, m, Fig. 1 dcatalyst thickness of the washcoat, m, Eq. (14) ε emissivity, Eq. (19) catalyst porosity, dimensionless, Eq. (16) εp effective emissivity for solid-ambient, Eq. (19) εs-∞ h effectiveness factor, Eq. (11), as defined by Eq. (13) surface coverage of free sites, Eq. (24) qfree l thermal conductivity, W/(m$K), Eq. (4) gas thermal conductivity, W/(m$K), Eq. (4) lg thermal conductivity of the solid wall, W/(m$K), ls Eq. (10) m dynamic viscosity, kg/(m$s), Eq. (2) r density of the gas mixture, kg/m3, Eq. (1) s Stefan-Boltzmann constant, W/(m2$K4), Eq. (19) site occupancy of the m-th surface species, Eq. (9) sm t time scale, s, Eq. (25) catalyst tortuosity factor, dimensionless, Eq. (16) tp treaction intrinsic reaction time scale, as defined by Eq. (25) axial transfer time scale, as defined by Eq. (28) tx transverse transfer time scale, as defined by ty Eqs. (26) and (27) F Thiele modulus, dimensionless, Eq. (13), as defined by Eq. (14) gas-phase molar production rate of the k-th u_ k gaseous species, mol/(m3$s), Eq. (5) Subscripts amb ambient, Eq. (19) g gas, Eq. (4) i species index, Eq. (13)

Please cite this article in press as: Chen J, et al., Millisecond methane steam reforming for hydrogen production: A computational fluid dynamics study, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.05.039

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 8 ) 1 e2 2

in k m o rad

inlet, Fig. 4 and Eq. (25) gaseous species index, Eq. (4) surface species index, Eq. (9) outer, Eq. (19) radiation, Fig. 1 and Eq. (18)

[5,6]. This reaction is highly endothermic, and is a relatively slow process, with typical contact times exceeding 1 s [5]. Recently, considerable progress has been made in the catalytic partial oxidation of methane [7e9]. While millisecond contact times have been approached for this reaction, methane steam reforming has historically been considered a slow reaction [10,11]. Interestingly, there has been an increased emphasis on discovering new steam reforming ways to convert methane into syngas at short contact times [12e17]. Millisecond methane steam reforming is important in fuel cells [18,19] and engines [20,21], but, unfortunately, it is often difficult to implement in practice. This paper will describe modeling efforts to further intensify the methane steam reforming process to the millisecond level. How to ensure the effective implementation of methane steam reforming at millisecond contact times is a great challenge in reactor design. There is limited evidence that millisecond methane steam reforming is feasible. This technology, however, requires very careful design and implementation of the reaction system. Several methane steam reforming reactions at less than 10 ms have been described in the literature, but with the aid of tailored reactor design such as microchannel reactors loaded with highly active rhodiumbased catalysts [12e14,22]. Attempts to conduct this reforming process over other catalysts at millisecond contact times have not yet been successful, because their catalytic activities are much lower compared with rhodium-based catalysts. Additionally, millisecond reaction kinetics for the water-gas shift reaction have also been reported in the literature [23], but only under certain conditions. Furthermore, the mechanism between the fast reforming process and reactor design under these conditions has not yet been fully understood. Recent literature has suggested that microchannel reactors may reduce the contact time to a few or tens of milliseconds [12,22]. These reactors have long been offered as a route to scale-up or commercialize fast reactions due to their intrinsic ability to manage the rising challenges of heat and mass transport that accompany reductions in contact time. Microreaction technology offers process intensification in the form of enhanced transport [22,24], and thus facilitate exploiting fast intrinsic reaction kinetics. To take full advantage of process intensification, these systems have channels with dimensions in the range of 0.1e0.3 mm [12e14], which can significantly improve both heat and mass transfer rates [23,24]. Furthermore, microreaction technology can greatly improve the efficiency, effectiveness, and productivity of chemical and energy production facilities [25e29]. Short contact time reactors based on microreaction technology are attractive for high throughput, resulting in significant capital and operating cost savings for commercial

s w x y

3

solid, Eq. (10) wall, Eq. (19) streamwise component, Eq. (4) transverse component, Eq. (4)

applications [12,17,30,31]. Efficient heat exchange in such a reactor can be achieved by placing a heat source and a heat sink in close proximity to each other, permitting high heat flux operation [12,30,31]. This significantly reduces the resistances to heat and mass transfer, which results in residence times that can be as short as a few milliseconds, but raises questions about the design and operability of such a reactor. This is the concept behind the coupled short contact time catalytic plate reactors discussed in this study, which aim to understand and develop a thermally integrated micro-chemical system that transfers the heat released by an exothermic reaction efficiently to an endothermic reaction. Millisecond steam reformers hold great promise for the production of hydrogen for portable power applications [12e14]. However, many questions remain concerning the design principle of the millisecond reforming process. An efficient operation needs not only a high degree of heat integration, but also novel technologies for process intensification through miniaturization and the improvement in catalyst performance. This requires not only fast transport but also fast reforming chemistry. Consequently, the major challenge lies in how to achieve millisecond methane steam reforming for hydrogen production by process intensification. Even though methane steam reforming via microreaction technology has been intensively studied, both theoretically [32e38] and experimentally [39e44], the general principles for the design of fast reforming processes are not readily available, but are highly desirable for practical applications. It is therefore necessary to have a full understanding of the fast reforming process at a fundamental level, which is beneficial to optimization of the process. The main innovation of this paper is to understand how methane steam reforming can happen at millisecond contact times. Methane steam reforming coupled with methane catalytic combustion in microchannel reactors was presented, as an example for illustration. A catalytic plate reactor that enabled efficient heat exchange was developed. Twodimensional reacting flow simulations with detailed chemistry and transport were performed to understand the role of heat and mass transfer in the system. Four typical variables of interest were evaluated for their impact on the reactor design and performance toward the aim of further process intensification. An order of magnitude estimate of dimensionless groups was made, and design maps for efficient operation were constructed. The primary objective of this paper is to explore the potential of methane steam reforming to produce hydrogen at short contact times. Of particular interest is to develop the general design guidelines of thermally integrated micro-devices for hydrogen production via fast steam reforming.

Please cite this article in press as: Chen J, et al., Millisecond methane steam reforming for hydrogen production: A computational fluid dynamics study, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.05.039

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Reaction system and modeling approach Due to the small nature of short contact time reaction systems, it is extremely difficult to determine the heat and mass transfer characteristics internal to the reactors [45e47]. Numerical simulations are critical to understand heat and mass transfer phenomena occurring in these systems and can improve the design to achieve the desired performance [47,48]. Detailed modeling is necessary to understand the complex interplay between kinetics and transport in the performance of these systems [45e47]. More efficient modeling tools such as detailed chemistry can greatly expand the ability to evaluate critical design tradeoffs for optimizing short contact time reactors.

Geometric model The reaction system considered in this study is the exothermic methane catalytic combustion coupled with endothermic steam reforming of methane, taking place in alternate channels of a catalytic plate reactor. The reactor consists of closely spaced catalytically coated plates. The catalytic combustion provides heat to the fast steam reforming reaction on opposite sides of separating plates, and the plates serve as the primary means of thermal coupling between them. A schematic diagram of the reactor used in this study is given in Fig. 1, with horizontal arrows indicating directions of flow. The design is based on compact heat exchanger arrangement, making possible efficient heat exchange between highly exothermic and endothermic reactions [49], with the potential to enable high thermal integration and thus higher efficiencies [50,51]. A physical implementation of this design in the form of modular stackable plates has been recently suggested by Loffler et al. [52]. Recent studies have demonstrated that the internal heat exchange plays the most important role for the optimization of the process [40,50,51,53,54], and the management of heat in a compact format is the most crucial challenge [55]. Therefore, one of the aims in design is to understand the effect of thermal coupling between the endothermic and exothermic reactions on the reactor performance. The reaction system combines methane catalytic combustion over a supported platinum catalyst with methane steam reforming over a supported rhodium catalyst in adjacent channels. On the reforming side, the main chemical reactions involved in the process are steam reforming, watergas shift, and reverse methanation. Rhodium is chosen as the reforming catalyst due to its very high conversion and excellent selectivity to syngas at very short contact times [56,57], whereas nickel do not provide adequate activity and good conversion under the same conditions. Despite this fact, nickel is the industrial catalyst for methane steam reforming, and thus the question, whether steam reforming over nickel is feasible at millisecond contact times by intensifying the process through miniaturization, needs to be addressed. Detailed chemistry will be discussed in more detail later in this paper. In order to evaluate the effect of various design parameters, a reference point is established. A “base case”, for which typical operation is considered, is given in Table 1. The channel dimensions are nominally 0.2 mm high and 50.0 mm

long. For fast chemistry, narrow channels may be required to minimize heat and mass transfer resistances, offering a high degree of compactness [58,59]. Molar steam-to-carbon ratios in the feed is assumed to be 3.0, since ratios higher than 2.0 are typically used [60]. Flow rates, whenever reported, assume a reactor width, referring to the third dimension, of 10.0 mm. Due to inherent symmetry conditions at the centerline of the channels, only half of each channel and the connecting plate are modeled to minimize the computational intensity.

Mathematical model Since the Knudsen number is of the order of 104, the standard hypotheses of thermofluids such as the continuum medium and the no-slip condition will still apply. The following assumptions are made: ideal gas behavior is assumed; steady state is considered for reactor operation; flow regimes in both channels are laminar, since the Reynolds numbers are less than 280 under all the conditions studied in this paper. The radiative heat exchange between surfaces is modeled on both sides of the reactor. Commercial computational fluid dynamics software ANSYS® Fluent® Release 16.0 [61] is applied. The model presented in this paper includes detailed chemistry and transport to provide an accurate description of the system, and to obtain a better understanding of the physical mechanism responsible for efficient heat exchange between highly exothermic and endothermic reactions. However, modeling of detailed chemistry in current versions is limited due to a great number of elementary reaction pathways and difficulties in handling stiff chemistry. Furthermore, the surface reaction model of Fluent software does not account for the surface coverage. Therefore, the Fluent software is coupled to external subroutines that model detailed chemistry. Furthermore, transport phenomena can be important and must be accounted for. Due to the potential contribution of gas-phase chemistry in catalytic combustion, numerical simulations are performed by taking into account the detailed gas-phase and surface chemistry simultaneously, which will be discussed later. The governing equations for the gas-phase reacting flow are solved together with user specified chemical kinetics. Note that the symbols used here and below are defined in the Nomenclature section at the beginning of the paper. Continuity equation: vðruÞ vðrvÞ þ ¼ 0: vx vy

(1)

Momentum equations:
 
  vðruuÞ vðrvuÞ vp v vu 2 vu vv v vu vv þ þ  2m  m þ  m þ vx vy vx vx vx 3 vx vy vy vy vx ¼ 0; (2)
 
 vðruvÞ vðrvvÞ vp v vv vu v vv 2 vu þ þ  m þ  2m  m vx vy vy vx vx vy vy vy 3 vx  vv þ vy ¼ 0:

(3)

Energy equation:

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Fig. 1 e Schematic diagram of the microchannel reactor in a parallel plate configuration modeled in this study. To minimize the computational intensity, only half of each channel and the separating plate are modeled by taking properly into account the inherent symmetry of the geometry. Dashed lines represent lines of symmetry in flow channels. For the “base case”, both combustion channel and reforming channels are 0.2 mm high, and the separating wall is 0.2 mm thick. The horizontal arrows indicate directions of reactant flow, with the dotted arrow denoting the counter-current operation. Note that the schematic diagram is not to scale. ! Kg X vðruhÞ vðrvhÞ v vT þ þ Yk hk Vk;x  lg r vx vy vx vx k¼1 ! Kg X v vT Yk hk Vk;y  lg r ¼ 0: þ vy vy k¼1

 vðruYk Þ vðrvYk Þ v v  þ þ ðrYk Vk;x Þ þ rYk Vk;y  u_ k Wk ¼ 0; k vx vy vx vy (4)

¼ 1; …; Kg :

(5)

The species diffusion velocities Vk,x and Vk,y in Eqs. (4) and (5) are computed by using mixture-averaged diffusion, including thermal diffusion for the light species such as gasphase atomic hydrogen and molecular hydrogen [62]:

Gas phase species equation:

Table 1 e Model parameters used for the base case computation. Combustion side Geometry Plate length Channel height Gas phase Inlet conditions Temperature Pressure Velocity Equivalence ratio Molar steam-to-carbon ratio Catalyst Thickness Catalyst/geometric surface area ean pore diameter Surface site density Porosity Tortuosity factor Kinetics Solid wall Thickness Thermal conductivity

Reforming side

50.0 mm 0.2 mm

300 K 0.1 MPa 6.0 m/s 0.8

400 K 2.0 m/s 3.0

0.08 mm 20 20 nm 2.72  109 mol/cm2 (platinum) 0.5 3 Refer to the chemical kinetics section

2.72  109 mol/cm2 (rhodium) 2.66  109 mol/cm2 (nickel) 0.6 3

0.2 mm 80.0 W/(m$K)

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T  Yk W Dk W ! V k ¼ Dk;m V ln þ Vðln TÞ: Wk rYk W

(6)

The ideal gas law and the caloric equation of state can be written as p¼

rRT W

(7) ZT

and hk ¼

hok ðTo Þ

þ

cp;k dT:

(8)

To

The coverage equations of the surface species are given by sm

s_m ¼ 0; m ¼ Kg þ 1; …; Kg þ Ks : G

(9)

Since the heat transfer within the wall can significantly influence the thermal coupling and reactor performance [53,54], the steady state energy equation in the solid phase is explicitly accounted for:     v vT v vT ls þ ls ¼ 0: vx vx vy vy

k ¼ 1; …; Kg :

(11)

Acatalyst : Ageometric

(12)

The catalyst/geometric surface area can also be used to describe the dependence of overall reaction rate on catalyst loading, which will be discussed in more detail later. Internal mass transport limitations inside the washcoat (i.e., catalyst layer) are accounted for by introducing the concept of effectiveness factor h. The effectiveness factor is determined by the Thiele modulus. In this approach, the effectiveness factor is defined as the ratio of the effective surface reaction rate inside the washcoat to the surface reaction rate with no mass transfer limitations: h¼

s_i;eff tanhðFÞ : ¼ F s_i

(14)

The term in the square root in the above equation represents the ratio of intrinsic surface reaction rate to diffusive mass transport in the washcoat. Large values of the Thiele modulus represent fast reactions with slow diffusion. In contrast, when the values of the Thiele modulus are small, the diffusion is fast while slow reactions limit the overall reaction rate. The effectiveness factor and the Thiele modulus are computed for the user-defined species, and methane is chosen in this study. The catalytically active surface area per washcoat volume, g, is given by g¼

Fcat=geo : dcatalyst

(15)

In Eq. (14), the effective diffusion coefficient of the i-th species inside the washcoat, Di,eff, can be written as   tp 1 1 1 ¼ þ : Di;eff εp Di;molecular Di;Knudsen

(16)

In the above equation, a parallel pore model is employed to describe the porous structure of the catalyst layer. The Knudsen diffusion coefficient of the i-th species, Di,Knudsen, can be expressed as Di;Knudsen

dpore ¼ 3

sffiffiffiffiffiffiffiffiffiffi 8RT : pWi

(17)

Conjugate heat transfer is taken into account by coupling the solid energy equation to the gas energy equation at each of the gas-washcoat interfaces. The energy boundary condition at the specified gas-washcoat interfaces is given by     Kg X vT vT þ ls þ ðs_k hk Wk Þinterface ¼ 0: q_rad  lg vy interface vy interfaceþ k¼1 (18)

The catalyst/geometric surface area, Fcat/geo, can be used as a scaling factor for the catalytically active surface area Acatalyst and the geometric surface area Ageometric of the channel wall [63]: Fcat=geo ¼

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s_i g : Di;eff Ci;interface

(10)

A high wall thermal conductivity of 80.0 W/(m$K) is used. It has been found that the operation window of thermally integrated micro-devices and their heat-exchange modes are highly dependent on the wall thermal conductivity [13,53]. For high wall thermal conductivities, the thermal coupling between the two processes is strong, making possible efficient heat exchange [53]; in contrast, for low wall thermal conductivities, the formation of hot spots can damage the catalyst and the reactor material, making the operation of the system impractical [13,53]. The gas-washcoat interfacial boundary condition for the gaseous species can be written as   rYk Vk;y interface þ hFcat=geo Wk ðs_k Þinterface ¼ 0;

F ¼ dcatalyst

(13)

The dimensionless Thiele modulus in the above equation can be expressed as

here, the subscripts () and (þ) refer to the properties just below and above the gas-washcoat interface, respectively. The net radiation method for diffuse-gray areas is employed to obtain expressions for the radiative heat exchange between the surfaces [64]. The emissivity of each element of the surfaces is assumed to be 0.8 [65]. The total heat loss from the left and right edges of the wall to the surroundings is accounted for, via the following expression:

q ¼ ho ðTw;o  Tamb Þ þ εs∞ Fs∞ s T4w;o  T4amb :

(19)

The external heat loss coefficient, ho, is assumed to be 20 W/(m2$K) [65]. The view factor for solid-ambient, Fs-∞, is assumed to be at unity. The effective emissivity, εs-∞, is assumed to be 0.8 [65].

Chemical kinetics The main chemical reactions involved in the reforming process are [66]:  methane steam reforming:

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CH4 þ H2 O4CO þ 3H2 ;

1

Dr HQm ð298:15 KÞ ¼ þ206:2 kJ,mol : (20)

 water gas-shift: CO þ H2 O 4CO2 þ H2 ;

1

Dr HQm ð298:15 KÞ ¼ 41:2 kJ,mol : (21)

 reverse methanation: CH4 þ 2H2 O4CO2 þ 4H2 ;

1

Dr HQm ð298:15 KÞ ¼ þ165 kJ,mol : (22)

The chemical reaction involved in the combustion process is: CH4 þ 2O2 /CO2 þ 2H2 O;

1

Dr HQm ð298:15 KÞ ¼ 802:3 kJ,mol : (23)

The oxidation reaction of methane can occur both on the surface of the catalyst and in the gas phase, depending on the operation conditions [67,68]. It is generally assumed that the contribution of gas-phase chemistry in small-scale combustion systems is negligible. This is due to the fact that the residence time is of the order of a few milliseconds, a time that is too short to ignite the mixture homogeneously, as well as surface chemistry can significantly inhibit the onset of gasphase ignition [67]. In practice, however, many small-scale combustion systems do not conform to this assumption, so that computations based on it may be inaccurate. For example, gas-phase chemistry can be fast enough to compete with surface chemistry [67], especially at high temperatures [68]; gas-phase chemistry can be sustained between parallel plates with the gap as low as 0.2 mm [67]. In this study, the reaction temperature is sufficiently high, and thus the initiation of gas-phase reactions is possible, providing another route for heat generation. Therefore, the gas-phase chemistry is not negligible, which greatly increases the complexity of the numerical model. In this study, detailed gas-phase and surface chemistry on the combustion side are included in the numerical model. The gas-phase chemistry on the reforming side is negligible, which will be discussed later. For the methane catalytic combustion over platinum, the gas-phase reaction scheme is based on the Leeds methane oxidation mechanism, initially developed by Hughes et al. [69]  nyi et al. [70]. The mechand subsequently improved by Tura anism consists of 105 reactions involving 25 species, and it has been tested successfully against a wide variety of experimental data reported in the literature [69,70]. A number of detailed surface reaction mechanisms for methane catalytic combustion over noble metal catalysts are available in the literature. The surface chemistry is modeled using the kinetic mechanism proposed by Deutschmann et al. [71], derived for supported platinum catalysts. The mechanism consists of 24 elementary reactions involving 9 gaseous and 11 surface species. The density of platinum surface sites, i.e. the number of adsorption sites per surface area of the platinum particle, is taken to be 2.72  109 mol/cm2 [71]. More details can be found in the literature [71]. An electronic version of the surface reaction mechanism is available on the DETCHEM website [72]. Methane steam reforming can take place both in the gas phase and especially on the surface of a ruthenium catalyst, depending on the operation conditions [73]. However, recent

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experiments have demonstrated that methane is not converted in the gas phase up to temperatures of 950  C [74]. Additionally, the small scale of the reaction system make it more prone to surface chemistry due to the high surface-areato-volume ratio, i.e., the enhanced mass transfer. Furthermore, it has been found that gas-phase reactions have a negligibly small contribution, less than 0.6%, to the overall methane conversion under all the conditions studied in this paper. Therefore, in order to minimize the computational intensity, the methane steam reforming reaction is assumed to take place only on the surface of the catalyst. The gas-phase chemistry on the reforming side is negligible for the sake of simplicity without affecting the accuracy of the solution. For the methane steam reforming over rhodium, the surface chemistry is modeled using the mechanism developed recently by Karakaya et al. [75]. The mechanism has been validated against a number of experiments within the temperature range of 298e1173 K [75]. It is worth noting that the mechanism is thermodynamically consistent within the temperature range of 273e1273 K, and it is easy to be implemented into standard kinetic software packages such as CHEMKIN [76] and Surface-CHEMKIN [77]. The mechanism consists of 48 elementary reactions involving 6 gaseous and 12 surface species. The density of rhodium surface sites is also taken to be 2.72  109 mol/cm2 [75]. The adsorption kinetics is given in the form of sticking coefficients. For the methane steam reforming over nickel, gas-phase chemistry is also negligible, and the surface chemistry is modeled using the mechanism presented recently by Delgado et al. [78]. The mechanism consists of 52 elementary reactions involving 6 gaseous and 14 surface species, and it has been validated against experiments within the temperature range of 373e1173 K [78]. Additionally, the mechanism is thermodynamically consistent within the temperature range of 273e1273 K. The density of nickel surface sites is taken to be 2.66  109 mol/cm2 [78]. The electronic versions of both the reforming mechanisms, over rhodium and nickel, are available on the DETCHEM website [72]. A mean pore diameter of 20 nm, together with a tortuosity factor of 3, is assumed for both catalysts. A nominal catalyst loading is used for both flow channels. This is expressed through the surface area factor (catalyst/geometric surface area, Fcat/geo) as described earlier. The area factor serves as model parameter to account for the catalyst loading, since a linear relationship between them can be found [63]. The nominal area factor for both channels is assumed to be 20. The catalytically active surface area is typically much higher than the geometric surface area. In general, higher values of the area factor make the process faster [63]. This means that high catalyst loadings are important in realizing high conversions at short residence times. Radical adsorption and desorption are accounted for in the numerical model. The adsorption rate constant kad,k of the kth gaseous species is computed by using a modified MotzWise correction [79].  kad;k ¼

2 2  gk qfree



gk Gm

sffiffiffiffiffiffiffiffiffiffiffiffiffi RT : 2pWk

(24)

Thermodynamic data are obtained from the provided kinetics schemes. The details of kinetics and its validation as

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well as properties of the catalyst can also be found from the provided kinetics schemes. Transport properties are obtained from the Sandia CHEMKIN transport database [62]. For both the combustion and the reforming mechanisms, the gas-phase and surface reaction rates are handled through the CHEMKIN [76] and Surface-CHEMKIN [77] interfaces, respectively.

Computation scheme The boundary conditions are given as follows. At the inlet, a uniform inlet velocity profile is employed, and Danckwerts boundary conditions are applied for the temperatures and species. The no-slip condition is applied for both velocity components at each of the gas-washcoat interfaces, as the Knudsen number remains small. Radiative properties and surface reaction mechanisms are specified at each of the gaswashcoat interfaces. Symmetry boundary conditions are imposed at the centerlines of the channels, which implies a zero transverse velocity and zero transverse gradients of all variables. At the exit, the pressure is specified, and the transverse gradients of temperature and species, with respect to the direction of the flow, are set to zero. The dependence of the physical properties of chemical species on temperature is accounted for. The fluid viscosity, thermal conductivity, and specific heat are computed as a mass-weighted average of the values for each constituent. The specific heat of each individual species is modeled as a polynomial function of local temperature. The viscosity, thermal conductivity, and diffusion coefficient of each individual species are dependent on the local composition and temperature. In order to compare the results with those obtained from an independent model, the NASA Computer program CEA (Chemical Equilibrium with Applications) developed by Gordon and McBride [80,81] is employed to compute chemical equilibrium compositions and properties of the gas mixture. An orthogonal staggered mesh is used, and the node spacing is kept relatively small within the catalyst structure and near the entrance to the reactor. Computational fluid dynamics simulations using detailed chemistry and transport for design and optimization are a CPU-intensive task. In order to achieve an adequate balance between accuracy and computational effort, numerical simulations are carried out using meshes with varying nodal densities to determine the optimal node density and spacing. A typical mesh consists of 200 nodes in the axial direction and 200 nodes in the transverse direction. Additionally, a mesh in excess of 80,000 nodes is utilized for the largest dimension. The mesh independency of the solution is verified by varying level of refinement. The conservation equations are solved implicitly through a steady-state segregated solver using an under-relaxation factor control method. The model is discretized using a second-order upwind approximation, and the pressurevelocity coupling is discretized using the “SIMPLE (semi-implicit method for pressure linked equations)” algorithm. The solution is deemed to be converged as the residuals of the conservation equations are less than 106. Parallel computation is adopted. The computation time of each simulation varies for the problems considered in this paper, depending on the initial guess as well as the parameter set, from several hours to two days.

A full-scale reactor design may include a much larger number of parallel flow channels, usually ranging from a few hundreds to many thousands or even more [22]. Numerical simulations for a two-channel model and a one-hundredchannel model considering edge heat losses are performed. Fig. 2 shows contour plots of the methane conversion in the reforming channel for the base case. The results indicate that the difference in methane conversion between the two models is usually within 6.7%. The results obtained for the onehundred-channel model indicate that all combustion channels behave essentially alike except those in the vicinity of the reactor's edge, and the same is true for all reforming channels (data not shown). Consequently, to understand how methane steam reforming can happen at millisecond contact times, only two representative channels are considered in this paper to reduce computational effort. This approach can be applied to gain more detailed insight into the transport phenomena and chemical reactions occurring within the reaction system [58,59].

Numerical validation The model developed above is validated by comparing the numerical results with the experimental data available in the literature [82,83]. In order to verify the combustion scheme implemented in the present investigation, the experimental results reported by Dogwiler et al. [82] are utilized. The combustor length and gap size are 250.0 and 7.0 mm, respectively. The catalyst temperature distribution measured by thermocouple serves as the energy boundary condition at the gas-wall interfaces. Fig. 3(a) shows the streamwise centerline OH concentration profiles compared to the experimental results. The OH concentration profiles predicted in the present work is shifted axially to match the measured peak OH locations. There is a sharp rise in the concentration of OH radicals along the centerline, indicating the onset of ignition in the gas phase, which is accurately predicted by the present work. The locations of homogeneous ignition is predicted within 16% in all the cases examined. It is shown that the numerical predictions are in good agreement with the experimental data. In order to verify the steam reforming scheme implemented in the present investigation, the experimental results reported by Zhai et al. [83] are utilized. The channel length and gap size are 30.0 mm and 0.5 mm, respectively. The catalytic performance of steam reforming of methane over rhodium has been investigated, and the details of the experimental case is available in the literature [83]. The methane conversion and the selectivity to carbon dioxide are compared to the experimental data available in the literature in Fig. 3(b). It is also shown that the numerical predictions are in good agreement with the experimental data.

Results and discussion Time-scale analysis One of the first issues to examine is time-scale analysis of the relevant processes. Industrially, steam reforming of methane over nickel is a relatively slow process, with a typical residence time of a few seconds [5]. In contrast, the process can be

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Fig. 2 e Contour plots of the methane conversion in the reforming channel for the base case.

operated at millisecond contact times over rhodium in microchannel reactors due to fast chemistry and transport [13,14]. In order to explore whether fast transport, i.e., miniaturization alone, is sufficient for process intensification, the relevant reaction and transport time scales are quantified, and the feasibility of the steam reforming over nickel at millisecond contact times by intensifying the process through miniaturization is also analyzed. The relevant process time scales in both channels are plotted in Fig. 4(a) and (b), respectively. The intrinsic reaction time scale (the effects of transport phenomena are absent) represents as the time needed for the fuel to reach a concentration that is equal to 50% of its initial value [84]: 0:5Cfuel;in : treaction ¼  s_fuel ðS=VÞ þ u_ fuel

(25)

The gas-phase chemistry on the reforming side is negligible, i.e., u_ fuel ¼ 0, as discussed earlier. The reaction time scales are computed at the three temperatures specified, 900, 1200, and 1500 K. While the reaction rate is a function of local composition, the results reported herein are representative order of magnitude. Note that at a temperature of 1500 K, the reforming time scales are extrapolations, as the surface reaction mechanisms are not applicable to this case. The transverse mass transfer time scale between the bulk and the surface represents the time needed for the reactant to reach the surface of the catalyst, from the channel center by diffusion ty;diffusion of species ¼

d2 : 4Dfuel

(26)

The transverse heat transfer time scale can be expressed as ty;diffusion of heat ¼

lg d2 with DT ¼ : 4DT rcp

(27)

The axial mass and heat transfer is determined by the average residence time, and its time scale can be written as l tx z : u

(28)

The time scale is computed based on the reactor length and the average flow velocity, using an inlet velocity corrected to the three average temperature of 900, 1200, and 1500 K.

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In Fig. 4(a), typical reaction and gas-phase transport time scales on the reforming side are indicated. As the reaction temperature increases from 900 to 1500 K, the corresponding time scale decreases from approximately 800 to 0.2 ms for rhodium, which is in agreement with the experimental data available in the literature [12], and from approximately 700 to 3 ms for nickel. While the intrinsic reaction rate over both catalysts is similar at low temperatures such as 900 K, the difference between them is significant at high temperatures such as 1500 K. Computations are performed at various feed compositions, and the results indicate that the ratio of reforming time scale over rhodium to that over nickel can be up to 20 in the temperature range from 900 to 1500 K. Under typical operating conditions, a temperature of 1200 K and 50% conversion, methane steam reforming over rhodium appears approximately an order of magnitude faster than over nickel. For the reaction system considered in this study, the transverse transfer time scales are of the order of tens of microseconds, which are typically much smaller than the reaction time scales. On the other hand, the axial transfer time scales are of the order of a few milliseconds. For highly active rhodium-based catalysts, the reforming reaction time is shorter than the residence time at high temperatures such as 1500 K. However, the reaction time, especially over nickelbased catalysts, can become comparable to or longer than the residence time at low and moderate temperatures such as 900 and 1200 K. In this case, it is difficult to achieve the complete conversion of fuel. Overall, process intensification, in terms of external mass and heat transfer on the reforming side, has been achieved. The improvement in catalytic activity or catalyst loading, with the reforming reaction rate increased by approximately an order of magnitude, will be beneficial. Fig. 4(b) shows the results obtained for the relevant process time scales on the combustion side. The combustion time scales range from approximately 0.005 to 0.5 ms, depending on the temperature. They are much smaller than the reforming time scales within the range of the temperature examined here (900e1500 K), and the difference between them becomes more pronounced at low temperatures. On the other hand, there is considerable overlap between the reaction and transverse transfer time scales. This behavior is quite different from that observed on the reforming side, suggesting that the combustion process is limited by a mixed-control regime involving chemical kinetics and gas phase mass transport. Therefore, the process can be further intensified by reducing the physical dimension of the combustion channel. The improvement in catalytic activity or catalyst loading will not be as beneficial, as the process will become transport controlled. There is no overlap between the residence time scale and the other time scales. This indicates that the combustion process is less sensitive to incomplete conversion than the reforming process.

Heat exchange characteristics Next issue to examine is the effect of thermal coupling of highly endothermic and exothermic reactions, since thermal management is very important for the design of system [54,55]. For this purpose, the changes in reactor performance in terms of both temperature and conversion profiles are

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Fig. 3 e Panel (a) shows a comparison of streamwise centerline OH concentrations after the homogeneous ignition with experimental and numerical results available in the literature [82]. Panel (b) shows a comparison of the methane conversion and the selectivity to carbon dioxide with experimental results available in the literature [83].

shown in Fig. 5(a). Hereafter, the conversion of methane on the combustion side and on the reforming side will be referred to as “combustion conversion” and “reforming conversion”, respectively; where appropriate, the exothermic (combustion) and the endothermic (reforming) reaction chambers (or channels) are referred to as “combustor” and “reformer”, respectively. The results shown in Fig. 5(a) indicate that the wall temperature, as well as the temperature in both the reaction chambers, first increases in the direction of flow, and then decreases very slowly. There are no significant axial

temperature gradients within the wall in all the cases studied due to the high wall thermal conductivity used. Fig. 5(a) shows that the maximum temperature difference along the wall is approximately 150 K. The latter part of the wall is essentially isothermal in the axial direction, since a high wall thermal conductivity can significantly reduce the axial temperature gradients and can spread the energy. There is a slight decrease in the axial wall temperature near the exit of the reactor. This can be attributed to the heat loss from the right edge of the wall to the surroundings, as defined by Eq. (19). Complete

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Fig. 4 e Intrinsic reaction and transport time scales in (a) the reforming channel and (b) the combustion channel. The rightmost, middle, and leftmost points correspond to time scales at temperatures of 900, 1200, and 1500 K, respectively.

combustion conversion is achieved due to fast chemistry. An outlet reforming average conversion of 98.8%, which is close to the equilibrium value, is achieved. The variation of absolute values of the heat flux consumed from the reforming reaction and generated from the combustion reaction, respectively, along the length of the reactor is shown Fig. 5(b). There is a small (second) peak appeared in the generated heat flux profile, indicating that the initiation of gas-phase reactions is possible. Catalytic combustion provides the necessary heat flux to heat up both the process streams, and part of this heat flux is used to drive the endothermic reaction at the same time. Since the system is in a steady state, the overall energy balance within the wall indicates that the net heat generated, as represented by the shaded region shown in Fig. 5(b), from the exothermic and endothermic reactions is absorbed as sensible heat of the two process streams. The maxima in the heat fluxes consumed and generated are almost located at the same axial position, i.e., approximately 18 mm. The exothermic reaction proceeds much faster than the endothermic reaction, and thus more heat is generated by combustion than consumed by reforming. The excess heat raises the reaction temperature at the front of the reactor, as illustrated in Fig. 5(a). At the end of the

reactor, i.e., axial position 50 mm, the difference between the heat fluxes generated and consumed becomes smaller, and thus both fluid and wall temperatures stabilize at approximately 1060 K. While the transverse difference in temperature is negligible in the solid phase, there exist steep gradients of the species and temperatures in the gas phase near the reaction region (data not shown for brevity). Since axial diffusion of energy and species is not negligible, it is necessary to use a two-dimensional model in order to provide an accurate description of the system. Overall, the operating and design parameters chosen for the base case can provide an efficient thermal coupling between the two process streams.

Effect of catalyst loading The relation between energy consumption and generation is important to ensure the efficient operation of system [53,54]. In order to gain further insight into the reactor behavior, the effect of catalyst loading is evaluated in terms of the catalyst/ geometric surface area. The catalyst/geometric surface area is a direct measure of catalyst loading [63], which in turn affects surface reaction rates and thus the rate of energy consumption or generation. The ratio of catalyst loadings, K, is defined as

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Fig. 5 e (a) Wall temperature and conversions in both channels, and (b) consumed and generated heat fluxes along the length of the reactor for the base case. The net heat generated, as represented by the shaded region shown in Panel (b), from the exothermic and endothermic reactions is absorbed as sensible heat in both channels.

K¼

Fcat=geo  : Fcat=geo base case

(29)

The ratio is used to evaluate the effect of catalyst loading as compared to the base case. Fig. 6 shows the effect of catalyst loading on the reactor behavior in terms of axial wall temperature profiles and outlet conversions. Fig. 6(a) and (b) show the results obtained for the case of catalyst loading variation in the combustion channel. As the catalyst loading decreases from the base case, Kcombustion ¼ 1.0, to a lower value, Kcombustion ¼ 0.5, the rate of the combustion reaction decreases gradually and thus lower

conversion is obtained at the outlet (Fig. 6(b)). Therefore, compared to the base case, there is a smaller amount of heat generated, thus decreasing the temperature (Fig. 6(a)). On the reforming side, both reaction rate and equilibrium conversion decrease, thus decreasing the outlet conversion (Fig. 6(b)). If the catalyst loading decreases to a minimum value, Kcombustion ¼ 0.5, the amount of heat generated by combustion is so small that steam reforming makes use of sensible heat available in the gas mixture, resulting in the formation of a cold spot (the blue line in Fig. 6(a)). The wall cools down until the axial position of approximately 8 mm is reached, and then the situation reverses. The amount of heat generated becomes

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larger than that of heat consumed, and thus the temperature starts to increase slowly. On the other hand, as the catalyst loading increases from the base case, Kcombustion ¼ 1.0, to a higher value, Kcombustion ¼ 2.0, there is a larger amount of heat generated, thus increasing the outlet conversions on both sides (Fig. 6(b)). However, a hot spot develops because the combustion reaction is faster than the reforming reaction (as discussed previously in Fig. 4), the heat generation overcomes the heat consumption, and both the process streams are heated up. The increase in temperature can enhance the rate of the reforming reaction, which in turn leads to an increase in heat consumed so that the temperature eventually decreases (Fig. 6(a)). The situation may not be desirable, as hot spots could result in rapid catalyst deactivation. Fig. 6(c) and (d) show the results obtained for the case of catalyst loading variation in the reforming channel. It is shown that higher values of catalyst loading do not improve reactor performance. As the catalyst loading increases from the base case, Kreforming ¼ 1.0, to a higher value, Kreforming ¼ 2.0, the rate of the reforming reaction initially increases and the rate of heat consumption also increases. Therefore, the temperature decreases (Fig. 6(c)) and this, in turn, constrains the rate of the combustion reaction. In certain cases (Kreforming greater than or equal to 2.0), this cooling effect is so strong that a cold spot develops (the red line in Fig. 6(c)). Overall, as the catalyst loading increases from the base case, Kreforming ¼ 1.0, to a higher value, Kreforming ¼ 2.0, lower temperatures (Fig. 6(c)) and concomitant lower conversions (Fig. 6(d)) are obtained on both sides of the reactor. On the other hand, as the catalyst loading decreases from the base case, Kreforming ¼ 1.0, to a lower

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value, Kreforming ¼ 0.5, complete conversion is achieved on the combustion side, whereas the conversion on the reforming side decreases due to a lack of catalytic activity (Fig. 6(d)). As discussed above, the ratio of heat generated to heat consumed is important in design, as it can directly affect the reactor thermal behavior. To illustrate this, the heat fluxes generated and consumed along the length of the reactor are depicted in Fig. 7 for two representative cases. Fig. 7(a) shows the results obtained for the case of Kreforming ¼ 2.0, when a cold spot develops, and Fig. 7(b) shows the results obtained for the case of Kreforming ¼ 0.5, when a hot spot is formed. If the heat flux consumed exceeds the heat flux generated, both process streams are cooled down, thus decreasing the temperatures and the reaction rates on both sides. However, the decrease in the rate of the reforming reaction is more significant. At a certain position along the length of the reactor, an axial distance of approximately 8 mm in Fig. 7(a), the heat flux generated becomes larger than the heat flux consumed, and thus both process streams are heated up. As a result, a minimum in temperature (approximately 848 K) is obtained along the length of the reactor, and thus a cold spot is formed as shown in Fig. 6(c) for the case of Kreforming ¼ 2.0 (the red line). In this case, the initiation of gas-phase reactions is impossible due to the low temperatures. In another situation, the opposite occurs (Fig. 7(b)). At the reactor entrance, the heat flux generated is higher than the heat flux consumed. In this case, both process streams are heated up, thus increasing the reaction rates on both sides. At the front of the reactor, most of the heat available is released, and thus a peak in both heat flux profiles is obtained. Afterwards, the heat flux generated

Fig. 6 e Wall temperature profiles and conversions in both channels as a function of catalyst loading (a, b) on the combustion side and (c, d) on the reforming side. The ratio of catalyst loadings, K, is used to express the influence of catalyst loading as compared to the base case. Please cite this article in press as: Chen J, et al., Millisecond methane steam reforming for hydrogen production: A computational fluid dynamics study, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.05.039

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decreases rapidly due primarily to fuel depletion, thus decreasing the reaction rate on the reforming side and the heat consumed. After a certain location along the length of the reactor, an axial distance of approximately 15.6 mm in Fig. 7(b), the heat flux generated becomes lower than the heat flux consumed, which is in consistence with the formation of a hot spot shown in Fig. 6(c) for the case of Kreforming ¼ 0.5 (the blue line). These results indicate that a good thermal balance within the system is required to avoid steep temperature gradients, i.e., hot spots.

Furthermore, several dimensionless numbers are also evaluated in order to quantify the relevant time scales. The effect of clet, Fourier, channel height can be discussed invoking the Pe € hler numbers. and transverse Damko Fig. 8(a) shows the above dimensionless numbers for different reforming channel heights at constant inlet velocities. The variation range for the channel height is from 0.2 to 0.8 mm. The shaded region represents a kinetically-controlled € hler number (Day) is defined as regime. The transverse Damko the ratio between the transverse mass transfer time scale and the intrinsic reaction time scale

Effect of channel height Day ¼ The channel height is a very important parameter in the design of the system, as large channels increase the resistance to gas diffusion, whereas small channels reduce the resistance. In this section, the effect of channel height is investigated and reactor performance is evaluated for constant inlet flow velocities, modifying accordingly the inlet flow rates and keeping all other parameters at their base case values. The same alterations are made for both channels, respectively.

ty;diffusion of species d2 s_fuel ðS=VÞ ¼ : treaction 2Dfuel Cfuel;in

(30)

clet and Fourier numbers relate the transverse to the The Pe clet number axial mass and heat transfer time scales. The Pe (Pe), which can be used to evaluate whether the reactant molecules from the channel center have enough time to reach the surface of the catalyst before they exit the reactor, is defined as the ratio between the transverse mass transfer time scale and the residence time scale

Fig. 7 e Generated and consumed heat fluxes along the length of the reactor for two representative cases. A cold spot is formed, as shown in Panel (a), and a hot spot occurs, as shown in Panel (b). Please cite this article in press as: Chen J, et al., Millisecond methane steam reforming for hydrogen production: A computational fluid dynamics study, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.05.039

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 8 ) 1 e2 2

Pe ¼

ty;diffusion of species d2 u : ¼ 4Dfuel l tx

(31)

The Fourier number (Fo) is defined as the ratio between the residence time scale and the transverse heat transfer time scale Fo ¼

4lg l tx ¼ : ty;diffusion of heat d2 urcp

(32)

These dimensionless numbers are a function of the reactor axial co-ordinate, and they are computed at 10.0 mm downstream of the entrance for the sake of simplicity. Fig. 8(a) shows that the reforming channel height has little effect on € hler number. This is because higher the transverse Damko reforming channel heights not only result in larger transverse diffusion time scale, but also cause larger reaction time scale. Higher reforming channel heights increase reforming stream flow rates, thus decreasing the wall temperature, which in turn increases the reaction time scale. Overall, for the system considered, the reforming process is kinetically-controlled, as discussed previously in Fig. 4(a). Fig. 8(a) also quantifies the relative importance of transverse and axial transfer time scales (red and blue lines). The time scales for both mass and heat transfer in the transverse direction are always more than 10 times smaller than those in the axial direction (refer to Fig. 4(a) for more details). The maximum wall temperature and conversion are plotted for various values of channel height, in Fig. 8(b) for the reforming and combustion processes, respectively, at constant inlet velocities. The variation range for the channel height is from 0.2 to 0.8 mm. The solid and dashed lines refer to changes in the height of the reforming and combustion channel, respectively. It is found that the system is particularly sensitive to the channel height change. The channel height can significantly affect both conversion and temperature. As the reforming channel height increases from its base case value 0.2 mm, there is a decrease in the conversion on the reforming side due to the effects given as follows: (a) the resistance to the transverse mass transfer becomes more significant, (b) there are insufficient catalysts to drive the endothermic reforming reaction, and (c) there are larger quantities of reactants that need to be heated by a certain amount of sensible heat. Despite this decrease in conversion, there is a significant drop in temperature due to the increased quantities of reactants. On the other hand, as the combustion channel height increases from its base case value 0.2 mm, complete conversion is achieved on the reforming side in all the cases studied here, as shown in Fig. 8(b). This is due primarily to the increased energy input from the combustion side, although this effect is reduced by a significant drop in combustion conversion. There is a trade-off between the fuel input and the resistance to the transverse mass transfer, thus affecting the reactor performance. As the combustion channel height increases, combustion conversion decreases due to the increased resistance to the transverse mass transfer, despite the increased energy input; the decrease in conversion becomes more pronounced at higher combustion channel heights such as 0.8 mm. Interestingly, the temperature increases first and then decreases with increasing combustion channel height, exhibiting a parabola relationship (the red dashed line in Fig. 8(b)). On

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the left arm of the curve, conversion is nearly complete, and the temperature increases with increasing combustion channel height due to the increased energy input. In contrast, on the right arm of the curve, the resistance to the transverse mass transfer plays a more important role than the energy input, thus decreasing the temperature. Overall, the channel height plays an important role in reactor performance, when the inlet velocity is kept constant. A short distance between heat sink and heat source can improve the efficiency of heat exchange. While the use of larger reforming channels at constant inlet flow rates might be considered [13], this will conflict with the short contact time since the residence time will increase.

Effect of flow arrangement It has been found that the flow arrangement can greatly affect reactor performance [50,51,85]. While flow arrangements can also be counter-current or co-current in nature, systems operating under counter-current conditions for the exothermic and endothermic reaction streams offers several significant advantages over those operating under co-current conditions [50], making them more attractive, especially for heat-exchanger applications [86]. However, not only a high degree of thermal coupling, but also high controllability and reliability are required in order to achieve efficient operation of the system. In order to gain further insight into the reactor behavior, the effect of flow arrangement is evaluated under the same inlet conditions. Comparisons are made between the results obtained from the two flow arrangements in order to analyze their respective advantages and disadvantages. The rate of hydrogen flow is the most important performance measure of a thermally integrated device [13,14]. Therefore, high reforming stream flow rates, which decrease the conversions on both sides of the reactor, are employed here, making the system suitable for a direct comparison between the results obtained from the two flow arrangements. Both flow arrangements have been shown in Fig. 1, with the horizontal dotted arrow indicating the counter-flow of exothermic and reaction endothermic streams. Comparisons between the two flow arrangements are made in terms of the evolution of the heat flux (Fig. 9(a)) and conversion (Fig. 9(b)) along the length of the reactor. Fig. 9(a) shows the generated and consumed heat fluxes along the length of the reactor for both flow arrangements. For the co-flow system (solid lines), both reaction heat fluxes are more uniformly distributed along the length of the reactor. In contrast, for the counter-flow system (dashed lines), the generated and consumed heat fluxes are more concentrated towards the outlet of the reformer. The ratio of the local heat generated to heat consumed at the entrance to the reformer is 0.6 for the counter-flow system and 1.6 for the co-flow system. As a result, the more pronounced cooling of the reforming stream can be found near the entrance to the reformer for the counter-flow system. The same ratio at the outlet of the reformer is 4.8 for the counter-flow system, which leads to local overheating, whereas it is 2.8 for the co-flow system. Fig. 9(b) shows the conversion profiles along the length of the reactor for both systems. For the co-flow system (solid lines), the conversion on the combustion side increases

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 clet, Fourier, and transverse Damko € hler numbers, maximum wall temperature, and conversion versus channel Fig. 8 e Pe height. The solid and dashed lines refer to changes in the height of the reforming and combustion channel, respectively. The shaded region shown in Panel (a) represents a kinetically controlled regime. The combustible and reforming stream inlet velocities are kept constant at 6.0 and 2.0 m/s, respectively. The dimensionless numbers are computed at 10.0 mm downstream of the entrance.

gradually along the length of the reactor, reaching a maximum value of 75.6% at the outlet. In contrast, a higher conversion, 79.0%, is achieved on the combustion side for the counter-flow system (dashed lines); in this flow arrangement, however, most of the methane is converted in a relatively small region, near the outlet of the reformer. Therefore, the heat flux generated is concentrated towards the outlet of the reformer. The depletion of reactants on the reforming side, along the length of the reactor, can decrease the rate of the endothermic reaction and thus the capability of the reforming stream to consume the heat flux generated on the combustion side. Consequently, there exists a high thermal imbalance within the counter-flow system; additionally, the excess heat generated on the exothermic side overheats both process streams in their respective channels, thus increasing the contribution of gas-phase combustion to the overall fuel conversion. For the co-flow system, higher conversion is achieved on the reforming side except at the outlet. This is

because there is a significant increase in the temperature near the outlet of the reformer for the counter-flow system. Several characteristics are summarized for both systems in Table 2. Comparisons between them are made based on multiple performance criteria, such as outlet conversions on both sides, temperature, extremes of the temperature difference observed in the reactor, and ratio between local, and overall, generated and consumed heat fluxes in the combustion and reforming processes. The transverse difference in fluid temperature is defined as the difference between the temperatures at the wall and at the channel center. For the coflow system, a good balance between the heat generated and consumed can be achieved, which may eliminate hot spots and could provide a potential performance advantage. For the counter-flow system, a good utilization of the overall heat generated is achieved within the reaction system, and higher conversions are also achieved on both sides of the reactor. However, the temperature extremes becomes more

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Fig. 9 e Reaction heat fluxes and conversions along the length of the reactor. The solid and dashed lines represent the results obtained for the co-flow system and for the counter-flow system, respectively. Heat generation and consumption are better balanced during co-current operation.

pronounced in the reactor, and the differences in the fluid temperature in the transverse direction also become more significant. These situations are usually not desirable for practical operation, as they will greatly increase the possibility of either runaway or extinction of the system. Hot spots may further damage the catalysts on both sides of the reactor and impose more severe constraints on materials of construction;

additionally, cold spots may also result in poor performance or even reactor extinguishing.

Engineering maps In order to guide the reactor design based on a projected power requirement, operation diagrams are presented in this

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Table 2 e Comparison between co-current and countercurrent operation for the reactor. CoCountercurrent current Inlet velocity on the combustion side 6.0 m/s Inlet velocity on the reforming side 3.0 m/s Combustion conversion 75.6 79.0 Reforming conversion 48.6 58.7 Minimum wall temperature 870 K 848 K Maximum wall temperature 1047 K 1160 K Transverse difference in fluid temperature Minimum 66 K 180 K Maximum 570 K 687 K Ratio between overall generated and 3.78 3.26 consumed heat fluxes Ratio between local generated and consumed heat fluxes At the entrance to reformer 1.6 0.6 At the outlet of the reformer 2.8 4.8

section. While these diagrams clearly pertain to the specific fuel and a fixed geometry, the approach described here is general in nature, and similar findings can be expected for other thermally coupled reactors. Fig. 10(a) depicts the operation diagram indicating the power generated from hydrogen as a function of combustible stream residence time. The shaded region between the two curves indicates the possible operation diagram. The power generated is based on 100% utilization of the hydrogen produced in order to obtain insight into the operational limits of the system. It is worth noting that a lower efficiency would scale the results exactly proportionally. A balance between the two flow rates is found to be crucial in enabling efficient operation. For a fixed combustible stream flow rate, only a narrow range of powers can be obtained. The minimum power, i.e., the lower bound for the power generation, is determined by the stability limit of materials, because low reforming stream flow rates cause unacceptably high reactor temperatures. The stability of materials in terms of the maximum allowable wall temperature is the first important operability criterion [13,14]. An arbitrary temperature threshold of 1500 K is set as an upper materials stability limit typically employed in short contact time hightemperature reactors [13,14]. The melting points of common catalysts and typical fabrication materials are generally higher than this threshold. The combustor must remove heat at a rate sufficient to keep local wall temperatures below this level to avoid rapid catalyst deactivation. The maximum power, i.e., the upper bound for the power generation, is determined by the maximum hydrogen produced before extinction occurs. For example, a device of 10.0 mm width with a methane-air residence time of 8 ms can produce 27.0e39.8 W. When the reforming stream flow rate is too high, extinction of the combustion chemistry can occur. Powers outside this regime are impossible for a fixed combustible stream flow rate. Microreactor units are “numbered-up” or “scaled-out” to achieve higher powers through implementing a strategy for multiple units in parallel, or device dimensions are altered to enable lower powers, while keeping the residence times constant. To a great extent, the predicted powers depend on the choice of fuel. However, given a single reactor, consisting of

two channels only with fixed reactor length, operation outside this power regime without changing the fuel implies varying the combustible stream flow rate. There also exists a limit on allowable combustible stream flow rate, determined by both blowout and extinction. Recent experiments have demonstrated that the combustible stream residence-time is restricted to a rather narrow regime for self-sustained operation [87]. For fast flows, blowout may occur due to insufficient residence time, whereas for slow flows, extinction may occur due to insufficient heat generation. The resulting prohibited diagrams, based on the critical flow velocities of a stand-alone micro-combustor, are illustrated in Fig. 10(a) as the vertical shaded regions to provide insight into the nature of the combustible stream residence time limits. A two-parameter continuation is implemented to track the power generation as a function of the reforming stream flow rate for various combustible stream residence-times. Numerical simulations are performed for four different reforming stream residence-times. Fig. 10(b) shows the power generation based on the hydrogen produced for a reactor width of 10.0 mm as a function of reforming stream residencetime. The dashed line represents complete reforming conversion, and the pentagrams and circles represent the extinction and materials stability limits, respectively, for each of the combustible stream residence-times indicated. The high reforming conversions rationalize the proximity of the complete conversion curve and the operation (solid) lines in Fig. 10(b). The power generation plots can be used as a guide in designing thermally coupled reactors. In order to achieve the desired power, the required combustible stream residencetime can be estimated on the basis of the operation regime shown in Fig. 10(a). From the plot of power generated, shown in Fig. 10(b), the reforming stream residence-time can finally be estimated. For each of the selected power, a rather narrow regime of flow rates is allowed. Selecting a combustible stream residence-time in the middle of the allowable range (Fig. 10(a)) and a reforming stream residence-time near the minimum allowed (Fig. 10(b)) will ensure nearly complete reforming conversion and higher fuel utilization. This situation is highly desirable for the practical application of fuel cells.

Conclusions Methane steam reforming coupled with methane catalytic combustion in microchannel reactors by means of indirect heat transfer was studied numerically in order to provide practical guidance for the implementation of such design. A two-dimensional numerical model with detailed chemistry and transport was developed to optimize the thermally integrated system, and the effect of typical design parameters on the reactor behavior was evaluated. The main points can be summarized as follows:  Steam reforming of methane can be operated at millisecond contact times, provided that dimensions, catalysts, and flows are properly designed.  Process intensification through miniaturization is insufficient for efficient operation. Highly efficient reforming

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Fig. 10 e Panel (a) depicts the operation diagram indicating the power generated, based on 100% utilization of the hydrogen produced, as a function of combustible stream residence time. The vertical shaded regions indicate limits for a stand-alone micro-combustor; the external heat loss coefficient is assumed to be 20 W/(m2·K). Panel (b) shows the power generated from a 10.0 mm wide device as a function of reforming stream residence time for the combustible stream residence times indicated. The dashed line depicts complete reforming conversion. The pentagrams and circles depict the extinction and materials stability limits, respectively, for each combustible stream residence time.

catalysts are also required. Overall, miniaturization and the improvement in catalyst performance must be symbiotic in order to intensify the process.  The distance between the plates plays an important role in reactor performance.  The catalyst loading is a key variable, and must be carefully designed in order to avoid insufficient reactant conversion or hot spots.  Counter-current operation shows a slightly better performance, but exhibits significant temperature extremes. Co-

current operation is recommended, and a good balance between the heat generated and consumed can be achieved.  The balance between the combustible and reforming stream flow rates plays an important role in designing thermally integrated systems. However, there exists a relatively narrow range of balanced flow rates in order to meet material temperature constraints and avoid reactor extinction.  Finally, the costs of rhodium and platinum might be tolerable for small-scale systems. However, the

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development of lower-cost, high-activity catalysts is highly desirable, yet challenging. While short contact time reactors can bring many important advantages, several topics need to be further investigated in order to build confidence for their practical implementation. A particularly interesting topic in the context of short contact time reactors is catalyst deactivation, which causes overall or local thermal imbalance within the reaction system. Potential solutions for catalyst deactivation require further exploration. Furthermore, the success of short contact time reactors depends highly on robust catalysts suitable for the reactor operating conditions.

Acknowledgement This work was supported by the National Natural Science Foundation of China (No. 51506048).

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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 8 ) 1 e2 2

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Please cite this article in press as: Chen J, et al., Millisecond methane steam reforming for hydrogen production: A computational fluid dynamics study, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.05.039