1 Introduction

Steam reforming (SR) is the most widespread process for the generation of hydrogen-rich synthesis gas from light hydrocarbons [1]. In an endothermic reaction the feed stock such as natural gas is converted with water steam to synthesis gas in catalytic channel reactors. Process heat as well as fuel gas is usually used for the steam generation [2–4]. Recently, the reforming of hydrocarbons by catalytic partial oxidation (CPOx) to hydrogen or synthesis gas has been paid much attention to because of its potential of providing suitable fuels for mobile fuel cells using the existing infrastructure [5–10]. Unlike steam reforming, CPOx can exothermally or autothermally convert logistic fuels with oxygen to hydrogen and synthesis gas in catalytic channel reactors. For both reforming processes, temperature control is a dominant parameter in the design of a reactor [11, 12]. Improper temperature control will easily result in either hot spots or a very low degree of conversion. Modeling of such a reactor offers an efficient way to optimize the design of the process.

Directly coupling chemistry with mass and heat transport at this level, however, greatly exceeds the capability of conventional computational fluid dynamics (CFD) calculations [13, 14]. Computational fluid dynamics is able to predict very complex flow fields, even combined with heat transport, due to recently developed numerical algorithms and the availability of faster computer hardware also providing bigger memory. Taking into account detailed models for chemical reactions, particularly heterogeneous reactions, however, is still very challenging due to the large number of species mass conservation equations, their highly nonlinear coupling, and the wide range of time scales introduced by the complex reaction networks [15]. In the present work, an approach is proposed to model hydrocarbon reforming by coupling detailed chemical kinetics with complex 3D computational fluid dynamics. Catalytic chemistry is confined within the geometrically simple channels and modeled with the low-dimensional plug flow model [16] to which interactive thermal control of the multi-channel reforming reactor has been implemented recently as a tail-gas combustor surrounding the external surface of the catalytic channels. The geometrically complex flow of the tail gas combustor is simulated using FLUENT without involving any chemistry [17].

Coupling of chemistry with CFD is accomplished by the exchange of temperature and heat flux profiles at the channel walls based on the user-defined-function (UDF) interface in FLUENT. In the present work, methane and propane are used as model fuels of the reformer.

2 Modeling approach

2.1 Chemistry models within multi-channels

Since the detailed chemistry is confined within the geometrically simple channels of the reformer, the plug flow model is the most straightforward representation of the catalytic reforming process. The plug code was designed for the non-dispersive one dimensional flow of a chemically reacting ideal gas mixture, assuming that there is no variation in the transverse direction, and the axial diffusion of any quantity is negligible relative to the corresponding convective term. The model is based on solving the equations for total and species continuity, energy conservation and the equation of state

$$\frac{{{\text{d}}\left( {\rho uA_{\text{c}} } \right)}}{{{\text{d}}z}} = A_{\text{s}} \sum\limits_{k = 1}^{{k_{\text{g}} }} {\dot{s}_{k} M_{k} } ,$$
(1)
$$\rho uA_{\text{c}} \frac{{{\text{d}}\left( {Y_{k} } \right)}}{{{\text{d}}z}} + Y_{k} A_{\text{s}} \sum\limits_{k = 1}^{{k_{\text{g}} }} {\dot{s}_{k} M_{k} } = M_{k} \left( {A_{\text{s}} \dot{s}_{k} + A_{\text{c}} \dot{\omega }_{k} } \right) ,$$
(2)
$$\rho uA_{\text{c}} \frac{{{\text{d}}\left( {C_{\text{p}} T} \right)}}{{{\text{d}}z}} + \sum\limits_{k = 1}^{{k_{\text{g}} }} {\dot{\omega }_{k} h_{k} M_{k} } A_{\text{c}} + \sum\limits_{k = 1}^{{k_{\text{g}} }} {\dot{s}_{k} h_{k} M_{k} } A_{\text{s}} = UA_{\text{s}} \left( {T_{\text{w}} - T} \right) ,$$
(3)
$$pM = \rho RT.$$
(4)

In these equations ρ (kg/m3) indicates the mass density of the mixture, u (m/s) the axial velocity, \(A_{\text{c}}\) (m2) the area of the cross section of flow channels, z (m) the axial coordinate, \(A_{\text{s}}\)(m) the surface area per unit length, \(k_{\text{g}}\) the number of gas-phase species, \({\dot{s}}_{k}\) (mol/(m2·s)) the molar production rate of species k as a result of surface reactions, M k (kg/mol) molecular weight of species k, Y k the mass fraction of species k, \({{\dot{\omega }_{k}}}\) (mol/(m3·s)) the molar production rate of species k as a result of gas-phase reactions, C p (J/(kg·K)) the specific heat capacity of the mixture, T (K) the gas temperature, h k (J·kg-1) the specific enthalpy of species k, U (J/(m2 K s)) the heat transfer coefficient of the mixture, p (Pa) the pressure, and M (kg/mol) the average molecular weight of the mixture, \(T_{\text{w}}\)(K) the stationary wall temperature and R (8.314 J/(K·mol)) the ideal gas constant. However, since the present work accounts for heat exchange between the reformer channels and the tail gas combustor, all the wall temperatures of the channels are interactively introduced from the CFD calculations described in the following section. The system of differential equations is solved using the differential algebraic equation solver LIMEX.

2.2 Computational fluid dynamics within the tail gas combustor

In the present work, three-dimensional Navier-Stokes equations and the equation of state are used to solve the transient problem of a laminar flow taking into account heat transfer, representing the most adequate description of a flow with arbitrary geometries. They form a set of elliptic equations for the conservation of total mass, momentum in x, y, and z direction, and energy, providing solution for the velocity, pressure, and temperature inside the flow domain. The system of equations is solved using FLUENT. Figure 1a shows the geometrical model of the multi-channel reformer proposed in the present work. The five channels are 0.005 m in diameter and the outer vessel is 0.05 m in diameter. Since in the present work no reactions are considered within the tail gas combustor hot air is used as the inlet gas. The reforming process is confined within the five tubes in order to investigate the effect of the spatial distribution of the tubes on the efficiency of the reforming processes. Figure 1b shows an example of the stationary velocity field within the outer vessel predicted by FLUENT. It is clear that the cooling and heating effect of hot air on the tubes is very different, especially for the above and below tubes.

Fig. 1
figure 1

Geometrical model of the multi-channel reformer proposed in this paper a and an example of the stationary velocity field within the reformer predicted by FLUENT b

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2.3 Coupling algorithm

Since direct coupling of detailed chemistry with heat exchange greatly exceeds the capability of CFD simulations, we propose to couple FLUENT with plug code in order to consider complex reaction mechanisms. Figure 2 schematically illustrates the communication between plug code and FLUENT. The differential Eqs. (1) to (4) are solved for the five tubes using the axial wall temperature profiles specified by FLUENT, while heat fluxes through the channel walls are treated as a result of the reacting flow within the tubes; the flux profiles are introduced into FLUENT as boundary conditions using the UDF interface. The outer flow solution obtained from FLUENT provides new temperature profiles of the channel-walls and are used to update the solution of the chemical reactions occurring inside the tubes. The iterative process continues until convergence between the inner and outer problems is achieved. In a sense, this method is quite general because there are no restrictions concerning the external geometry or the chemistry and transport within the tubes.

Fig. 2
figure 2

Schematic description of heat exchange between the tube and the external environment a and scheme of the communication between PLUG code and FLUENT b

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For adapting the 3D FLUENT mesh to plug code sections, the entire tube is subdivided into a number of bands/sections. Subsequently, the projections of all grids on the axis of the tube are calculated. Grids are then classified into corresponding bands/sections in order to obtain a mean temperature of each section as shown in Fig. 3. The heat flux change of each section is defined as a result of the enthalpy difference between the starting position and the ending position of the section:

$$q = \rho uA_{\text{c}} \frac{{h_{{^{\text{in}} }} - h_{{^{\text{out}} }} }}{{A_{s} (z_{{^{\text{in}} }} - z_{{^{\text{out}} }} )}} ,$$
(5)

where q (J/(m2·s)) indicates the heat flux and h (J/kg) is the enthalpy of the mixture.

Fig. 3
figure 3

Illustration of adapting the 3D FLUENT mesh to a PLUG band/section leading to a mean wall temperature of the section

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3 Results and discussion

3.1 Chemistry of methane CPOx

In the CPOx process methane is exothermically reacted with oxygen over a catalyst bed with a high conversion and selectivity for the formation of syngas, the overall reaction is given by

$${\text{ CH}}_{ 4} { + }\frac{ 1}{ 2}{\text{O}}_{ 2} \to {\text{CO + 2H}}_{ 2} , \quad \Delta {\text{H = }} - 3 8 {\text{ kJ/mol.}}$$
(6)

Since the emergence of short contact time reactors, catalytic partial oxidation of methane on noble metal catalysts is extensively being explored. Nonetheless, thermal control of the reformer and fundamental understanding of the underlying chemistry is urgently needed for widely spread commercial use of CPOx. In the present work, the multi-channel reformer is modeled using a surface reaction mechanism of methane CPOx proposed by Schädel [14].

The inner walls of the five inner channels illustrated in Fig. 1a are coated with rhodium (Rh) catalyst. The feed gas to the inner catalytic channels is a mixture of 29.52% CH4 and 14.72% O2 resulting in a carbon-to-oxygen ratio of unity. N2 is used as a diluting gas, the inlet temperature is 100 °C and the inlet velocity is 0.2 m/s. The tail gas combustor is fed by hot air at 600 °C with a velocity of 1 m/s. Heat is removed from the outer walls of the outer vessel to an ambient environment at 25 °C with a heat transfer coefficient of 1 W/(m2·K). Figure 4 illustrates a coupled temperature solution for the methane CPOx reformer. The temperature profiles of the reacting gas (T gas) within the channels are predicted using PLUG code, while those of all channel walls (T wall) as well as the inset of the 2D temperature distribution are calculated using FLUENT. One can recognize that the CH4/O2 mixture within the channels is heated gradually by the hot air of the outer vessel till the reaction is ignited and the temperature increases rapidly due to the exothermal character of methane CPOx.

Fig. 4
figure 4

Temperature solution of the proposed reformer for the methane CPOx process obtained by coupling FLUENT with PLUG (DETCHEM) (The temperature profiles of the reacting gas T gas within channels are predicted by DETCHEM while those of all channel walls, and T wall are calculated using FLUENT. The color of the 2D inset represents the wall temperature.)

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Hot spots do occur for all of the five channels, corresponding to the maximum mole fraction of H2O within the channels as shown in Fig. 5. Figure 5 also shows that hydrogen is indeed formed by the reaction of residual methane with water formed upstream, i.e., by the steam reforming process. Further calculations demonstrate that an increasing temperature at the inlet of the catalytic tubes leads to an increasing methane conversion as shown in Fig. 6. Moreover, it is also found from the Figs. 5 and 6 that methane conversion increases with decreasing inlet velocity of the reacting gas.

Fig. 5
figure 5

Molar fraction of dominant species formed by the methane CPOx process as a function of the axial position for tube 1 (Calculations are performed with a tube inlet velocity of 0.2 m/s, and an inlet temperature of 100 °C.)

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Fig. 6
figure 6

Conversion of methane as a function of the temperature at the inlet of the catalytically active tubes (Calculations are performed with a tube inlet velocity of 0.6 m/s and an inlet temperature of 100 °C.)

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3.2 Chemistry of propane SR

Currently most of the syngas is produced by steam reforming (SR) of hydrocarbons on noble metal catalysts and it is the best-established process for the production H2 on a technical scale. Propane steam reforming (SR) process described by the reaction

$${\text{C}}_{ 3} {\text{H}}_{ 8} + {\text{ 3H}}_{ 2} {\text{O}} \to 3 {\text{CO }} + {\text{ 7H}}_{ 2}, \quad\Delta {\text{H }} = \, + 4 9 8 {\text{ kJ}}/{\text{mol}},$$
(7)

which is strongly endothermic.

Therefore, the thermal balance of SR requires large heat exchange reactors, resulting in an extreme difficulty in scaling down reactors to small sizes required for most mobile applications. In the present work, the proposed multi-channel reformer is modeled using a surface reaction mechanism of propane SR on the Rh catalyst as shown in Table 1.

Table 1 Detailed surface reaction mechanism of propane steam reforming
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The feed gas to the inner catalytic channels is a mixture of 7.90% C3H8 and 35.60% H2O resulting in a steam-to-carbon ratio of 1.5. N2 is used as diluting gas, and the temperature at the inlet is 100 °C leading to an inlet velocity of 0.2 m/s. Like the setup of methane CPOx, hot air is injected into the tail gas combustor at 600 °C with a velocity of 1 m/s and heat release from the outer walls of the outer vessel is set with a heat transfer coefficient of 1 W/(m2·K). The coupled temperature solution of this setup is shown in Fig. 7.

Fig. 7
figure 7

Temperature solution of the proposed reformer for the propane SR process obtained by coupling FLUENT with DETCHEM (The temperature profiles of the reacting gas T gas within the channels are predicted by DETCHEM while those of all channel walls, and T wall are calculated using FLUENT. The color of the 2D inset represents the wall temperature.)

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The temperature of the reacting gas is always lower than that of the catalytically active walls. Figure 8 illustrates the conversion of the reacting gas within the catalytically active channels and a propane conversion of 53.5% is achieved by the present setup. Results of thermodynamic calculations demonstrate that propane SR takes place at temperatures exceeding 600 K, while total propane conversion is reached at about 800 K [14]. Thus, higher temperatures are necessary to activate C3H8 molecule within a limited contact time.

Fig. 8
figure 8

Mole fraction of dominant species formed by propane SR process as a function of the axial position of tube 3 (Calculations are performed with a tube inlet velocity of 0.2 m/s, and an inlet temperature of 100 °C.)

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3.3 Combining propane SR with methane CPOx

Since the methane CPOx process is exothermic, while the propane SR is strongly endothermic, combining them in one reformer may be energetically favorable. In this paper, tube 3 was used for propane SR while methane CPOx carried out with an inlet temperature of 300 °C was performed in the remaining four tubes. All other boundary conditions of the reformer are the same as those reported in the sections 3.1 and 3.2.

Figure 9 shows the coupled temperature solution of this combined setup. For the methane CPOx process occurring in the tubes 1, 2, 4 and 5, the higher temperature of the reacting gas at the inlet results in shifting the hot spots to a position closer to the inlet than that shown in Fig. 4 but the maximum temperature at the hot spots decreases from about 1 800 K to about 1 600 K due to the endothermic propane SR process occurring in tube 3. On the other hand, the conversion of propane in tube 3 shown in Fig. 10 increases from 53.5% (see Fig. 8) to 63% implying that this design of the proposed reformer offers a way to exchange energy between the endothermic SR process and the exothermic CPOx process.

Fig. 9
figure 9

Temperature solution of the proposed reformer for the combined propane SR and methane CPOx process obtained by coupling FLUENT with DETCHEM (The temperature profiles of the reacting gas T gas within the channels are predicted by DETCHEM while those of all channel walls T wall are calculated using FLUENT. Calculations are performed with a CH4 CPOx tube inlet temperature of 300 °C and a C3H8 propane SR tube inlet temperature of 100 °C. The color of the 2D inset represents the wall temperature.)

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Fig. 10
figure 10

Mole fraction of dominant species formed by the propane SR process as a function of the axial position of tube 3 in the combined propane SR and methane CPOx reformer; calculations are performed with a CH4 CPOx tube inlet temperature of 300 °C and a C3H8 propane SR tube inlet temperature of 100 °C.)

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4 Conclusions

In the present work, a novel setup of catalytic reformers and an adequate modeling approach to simulate the hydrocarbon reforming processes by coupling a low-dimensional chemical kinetic model with the complex 3D computational fluid dynamics are proposed. Thermal control of the catalytically active tubes is achieved by heat exchange with the tail gas combustor. Simulation results of methane CPOx show that hydrogen is indeed formed by a steam reforming process of the residual methane with water formed upstream. Further simulations show that performing CPOx and the SR processes in a combined reformer should have beneficial effects.