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In this work a one-dimensional mathematical model was developed to simulate methane conversion and hydrogen yield in a fixed-bed reactor filled with catalyst particles. For the reason that reforming reactions are sorely endothermic process, the heat is supplied to the reactor through electrical heating. The reforming reactions have been investigated from a modelling view point considering the effect of different temperatures ranging from 500 ℃ and 977 ℃ on the conversion of methane and hydrogen yield. Simulation results show that the steam reforming of methane in a fixed-bed reactor can efficiently store high temperature end thermal energy. When the operating temperature is increased to 977 ℃, the conversion of methane is 97.48% and the hydrogen yield is 2.2408. As a conclusion, the maximum thermochemical efficiency will be obtained under optimal operating temperature (977 ℃) and the steam/methane (3.86) ratio.

Nowadays there are worldwide increasing interests concerning climate change and greenhouse gas emissions. Environmental problems derived from different energy generation sources and the fossil fuels prices have enhanced the development of new technologies for energy production. The significant reduction of carbon dioxide (CO_{2}) emissions in energy production and fuels is demanded to ensure sustainable developments. Therefore, future energy supply system features electricity and hydrogen as the dominant energy carriers. Steam Reforming of Methane (SRM) is still the predominant method for producing a hydrogen-rich synthesis gas (H_{2} + CO). Hydrogen is conventionally produced on a large-scale by the SRM. In conventional technology, SRM is carried out using multi-tubular fixed-bed reactors [_{4}), water (H_{2}O), hydrogen (H_{2}), carbon monoxide (CO) and dioxide carbon (CO_{2}).

The world consumption is about 50 million ton of hydrogen per year (137 million kg of hydrogen per day) and the request for hydrogen is increasing rapidly [

-Steam Reforming of Methane (SRM);

-Water Gas-Shift (WGS);

-Reverse Methanation (RM).

Steam reforming of methane is a quite complex process. It not only involves the transfer and diffusion of reactants and products, between the bulk phase and catalyst surface, as well as within the catalyst, but also involves several reactions simultaneously in parallel or in series. The most of the researches have been experimentally and numerically investigated to produce H_{2} at high temperature [

The objective of this paper is to evaluate the performance of the conventional FBR used to simulate the SRM. Based on the energy and mass balances of chemical species, a system of Partial Differential Equation (PDE) was formulated for describing governing equations of the energy and mass balances. Simulations presented from the model equations provide the evaluation of the SRM process in FBR reactor with a nickel catalyst. The performance of above reactor was studied in terms of temperature profiles, methane conversion at different temperatures and hydrogen production at different temperatures.

The reaction rates were formulated by Xu and Froment [

With,

where R_{i} is reaction rates i (i = 1, 2 and 3), respectively; k_{i} is reaction rate constants i (i = 1, 2 and 3), respectively; K_{i}_{ }is adsorption constant of chemical species i (i = CH_{4}, H_{2} and CO), respectively; K_{eq}_{.,i} is equilibrium constants i (i = 1, 2 and 3), respectively; P_{i} is partial pressures of chemical species i (reaction zone) (i = CH_{4}, H_{2}O, H_{2}, CO and CO_{2}), respectively; _{2}O, H_{2} and CH_{4}).

The feeding partial pressures (

With,

The net rates of chemical species (consumption and formation) for reactions (1), (2) and (3) have been obtained by using the Equation as follows [

where r_{i} is the net rates of chemical species (i) in the reactions (1), (2) and (3), s_{ij} is the stoichiometric coefficients of chemical species and R_{j} is the overall rates of the reactions (1), (2) and (3).

Effectiveness factors (h_{i}) are used to account for the intraparticle transport limitation. Thus, Equation (8) was modified using h_{i} as follows.

Equation (9) has been used to obtain the net rates of chemical species (

A schematic configuration of the proposed system used in the development of the mathematical model is shown in

operation, fixed-bed FBR is continuously fed with a gas mixture (H_{2}O/CH_{4} = 3.86) inlet. The base data used for the geometric conditions, catalyst properties and inlet operating conditions are illustrated in

・ Energy balance of the gas phase;

where

・ Initial and boundary for the Equation (12)

・ Energy balance of the solid phase;

In Equation (14), _{j}, h_{j}, R_{j} are density of the catalyst, enthalpy of reaction j, effectiveness factor of reaction j, rate of reaction j, respectively.

・ Initial and boundary for the Equation (14)

Based on these simplifications, the differential molar balances to all chemical species (CH_{4}, H_{2}O, H_{2}, CO and CO_{2}) in the shell side are given as follows.

・ Mass balance of methane:

・ Initial and boundary conditions for the Equation (16):

・ Mass balance of water:

・ Initial and boundary conditions for the Equation (18):

・ Mass balance of hydrogen:

Sizes | |
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Geometric conditions | FBR |

Catalyst properties | |

0.48 | |

2850 | |

0.07 | |

0.07 | |

0.57 | |

Inlet operating conditions | |

500 | |

973 | |

650 kPa | |

20.89 | |

0.0034 | |

10.45 | |

11.08 | |

9.812 | |

48.16 |

・ Initial and boundary conditions for the Equation (20):

・ Mass balance of carbon monoxide:

・ Initial and boundary conditions for the Equation (22):

・ Mass balance of carbon monoxide:

・ Initial and boundary conditions for the Equation (24):

In Equations (12)-(25), ^{2}), spatial time (s), gas flow rate (m^{3}/s^{1}), diameter of the reactor (m), respectively; ^{3}), particle radius (m), reactor length (m), void fraction of bed (-), respectively;

Parabolic partial differential equations (PDEs) are frequently used to model one verity of engineering phenomena such as the steady-state conduction in a solid and the reaction-diffusion type problems. In order to solve the governing equations the engineering problems, several numerical methods have been developed to solve EDPs. The choice of method depends on the desired accuracy, as well as, concerns about the stability and robustness of the system while maintaining computational efficiency. Furthermore, these characteristics depend on the form of the PDE will be solved.

For parabolic equations, several numerical methods can be used to obtain a solution [

The one-dimensional model presented for this work provides the temperature profiles (as shown in the gas and solid phases) and the molar flow rates of each chemical species. As a result, SRM was tested in a conventional FBR for the simulations of this work; a hot inert initial state has been used where a steady flow of N_{2} at 500˚C and 650 kPa is fed under adiabatic conditions (no heat gain or loss through the reactor walls).The modelling for SRM in the FBR, sketched in _{4}, H_{2}O, H_{2}, CO and CO_{2}), as well as, the energy balances of the gaseous and solid phases at this reactor type.

The dynamics modelling bases on energy and species balances with the intrinsic kinetic equations reported by Xu and Froment [

The conventional FBR technology is still applied on industrial scale to steam reforming of methane [

The steam reforming of methane in a FBR, filled with catalyst particles, is still applied at industrial scale. Due the endothermic nature of the reforming reactions, heat is supplied through electrical heating. Therefore, the reactor and catalyst particles are exposed to significant temperature gradients. As a result, we show in this section the temperature profiles (temperatures of the gaseous and solid phases) for this reactor mode.

Parameters | Values | Parameters | Values |
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4.473 × 10^{-6} | 2.367 × 10^{3} | ||

3.34 × 10^{-2 } | 5.617 × 10^{-11 } | ||

1.271 × 10^{8 } | 4.765 × 10^{-7 } | ||

8.314 | 1.871 × 10^{6 } | ||

0.012 | 11.069 | ||

8.141 × 10^{14} | 2.172 × 10^{5 } | ||

3.757 × 10^{3} | 2400 | ||

4.129 × 10^{14} | 0.989 | ||

3.247 × 10^{-5 } | 0.876 | ||

336 | 1.735 | ||

150.2 | 0.43 | ||

0.459 | 291.83 | ||

−37.67 | 219.51 | ||

0.2259 | 0.0076 | ||

0.8724 | 0.0061 | ||

0.0123 | 0.0016 |

The performance of SRM process under the operating time of 45 sec, spatial time (τ) of

The _{2}, CO and CO_{2} increase continuously in the direction of the relative reactor length, while the molar flow rates of CH_{4} and H_{2}O decrease. The wet basis products at z/L = 1.0 contain about 3.27% of CH_{4}, 44.30% of H_{2}O, 32.59% of H_{2}, 12.87% of CO and 6.87% of CO_{2}.

The efficiency of SRM process by the exit of the reactor (z/L = 1.0), spatial time (τ) of

The _{4}, 44.89% of H_{2}O, 32.97% of H_{2}, 13.07% of CO and 6.21% of CO_{2}.

Based on results from the dynamics modelling after that all curves describing the temperatures and molar flow rates reach to steady levels, the following definitions (the conversion of methane and the yield of hydrogen) of chemical species (

where

The

The

Concerning the context of steam reforming of methane in presence of a nickel catalyst (N_{i}(6.7%wt.)/γ-A_{2}O_{3}), a numerical methodology (method of lines) was applied to establish forecasts over the operation in a FBR reactor. A computer code to process and analyze the performance of the operating variables led to the following conclusions:

1) SRM reactions have great effects on temperature distribution of FBR. The WGS reaction happens in reverse, absorbing heat and reducing the temperature of the catalyst. As a result, we can report that there are negative gradients between the phases.

2) The methane conversion is enhanced in FBR with higher temperature. Simulation results showed that a conversion from 97.48% could be achieved in a FBR at reaction temperature of 977˚C.

3) The H_{2} yield achieved level from 2.2408 in FBR at reaction temperature of 977˚C while the H_{2} yield reached level from 1.6513 at reaction temperature of 500˚C.

The authors of this paper would like to thank CNPq (National Council of Scientific and Technological Development) for the financial support given (Process 48354/2012).

Fernando Antôniode Araújo Silva,Kenia Carvalho Mendes,Jornandes Dias da Silva, (2016) A Simulation Study of the Steam Reforming of Methaneina Fixed-Bed Reactor. Engineering,08,245-256. doi: 10.4236/eng.2016.84021

^{2}/m^{3}

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_{1}) rate constants, kmol kPa^{0.5}/kgcat h

_{2}) rate constants, kmol kPa^{−1}/kgcat h

_{3}) rate constants, kmol kPa^{0.5}/kgcat h

_{4}, H_{2} and CO), kPa^{−1}

_{2}O, (-)

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_{4}, H_{2}O, H_{2}, CO and CO_{2}), kPa

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_{cat.}h

_{cat.}h

_{4}, H_{2}O, H_{2}, CO and CO_{2}), (-)

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