Enhancing Hydrogen Production in a Porous Reactor for the Steam Methane Reforming: Optimizing Operating Parameters and Radiation Heat Transfer Mechanism Open Access

In order to move toward a low-carbon and sustainable energy system, hydrogen production is essential. Hydrogen is a flexible energy basis with a widespread variety of uses in manufacturing, power production, and transportation. Hydrogen is receiving more and more attention as a possible decarbonization selection due to the increased mandate for sustainable energy sources [1]. Notwithstanding, the industrial production of hydrogen poses several obstacles concerning expenses, effectiveness, and ecological consequences. Hydrogen exhibits considerable promise as an environmentally friendly energy source, rendering it appropriate for a range of uses such as the generation of clean electricity through gas turbines [2], internal combustion engines powered by hydrogen [3], and fuel cells for the electrification of diverse industries [4]. These uses highlight how hydrogen has the potential to be a key component in producing power that is cleaner and more efficient, which will aid in the shift to a sustainable energy future. Gray hydrogen is produced by reforming fossil fuels without capturing CO₂ [5,6], blue hydrogen is produced by reforming fossil fuels while capturing CO₂ [7], and green hydrogen is shaped by water electrolysis through renewable energy foundations like wind, solar, nuclear, biomass, and hydropower. These three basic approaches to hydrogen production are categorized by color. Technologies for producing hydrogen can be divided into four groups: photocatalytic [8], thermochemical [9], electrochemical [10], and biological [11]. Gray and blue hydrogens are produced in thermochemical hydrogen generation systems by high-temperature reactions with feedstocks. These methods include steam reforming of hydrocarbons [12], partial oxidation [13], auto-thermal reforming [14], and biomass gasification [15].

Studying energy shifts and the equilibrium conditions that control the reaction is referred to as thermodynamics and kinetics in the solid-state redox (SMR). Examining reaction's energy change and figuring out reaction mixture's equilibrium composition at various pressure and temperature levels are two aspects of the thermodynamic analysis. It is well-established that factors such as temperature, pressure, and steam-to-carbon (S/C) ratio have a similar effect on the production of hydrogen by SMR approaches [12]. Temperature is the primary factor that affects efficiency, hydrogen output, and purity, according to Hanak et al. [25]. At high temperatures, the exothermic carbonation reaction limits the amount of CO₂ that can be removed, whereas the endothermic reaction of the steam reforming promotes fuel conversion. Since the catalyst conformation marks the calculated constraints and instruments, various kinetic models are developed. An earlier kinetic study for the SMR over nickel indicated that steam and methane react in first order with respect to methane, with methane breakdown being the rate-determining phase [26]. A kinetic model for the SMR that takes into account the side WGS reaction was developed by Xu and Froment [27]. The explicit emphasis of this model is a Ni-impregnated MgAlO₄ catalyst. The authors conducted over 120 separate theoretical simulations using strict model discrimination and parameter estimation methodologies. In their study on SMR at 640 °C, Rout et al. [28] employed CaO-C12Al14O33 as a catalyst to examine the impact of CO₂ capture kinetics using the TGA and a fixed bed reactor. They determined that the fixed bed reactor is healthier for kinetic lessons because of its improved gas–solid contact and lack of bypass problems.

For the purpose of investigating the impact of catalyst composition on the performance, Zhao et al. [29] used Ni-CaO-CaZrO3 as bi-functional materials in their SMR at 600 °C. They found that the catalyst containing 15 wt% Ni, 60 wt% CaO, and 25 wt% CaZrO3 performed best but deactivated slowly and could be recovered through additional carbonation steps in the extended cyclic operation. The process of thermochemical energy storage was studied using a variety of numerical models for reaction and transport in porous media, considering local heat and mass transfer and reaction inside the reactor. Guo and Dai’s [30] replication of heat and flow transport in a randomly packed bed took into account the bed non-uniform pore distribution and inhomogeneity. A finite volume method based on the Chimera grid was used, and this method produced a detailed local flow field and temperature field. With an increase in the input of the Reynold number, flow inhomogeneity rises. It appears that wall effects have a different impact on heat transport. Higher temperature gradients are produced by low vacancies, which suggest enhanced heat transmission. By using a 1D numerical model under isothermal conditions, Diglio et al. [31] studied sorption-enhanced SMR in fixed beds. A thermodynamic analysis was conducted, and the results showed that it is possible to meet process's heat and power requirements by using a small amount of the produced H₂$(approximately0.4molH2/molCH4)$⁠, making the process energy self-sufficient. Heat transport in a thermochemical apparatus in a solar volumetric absorbent headset was examined by Villafán-Vidales et al. [32]. The results showed that the foam temperature decreases as the rate of gas flow increases. The study conducted by Valdés-Parada et al. [33] for a gas phase reaction is another illustration of how the reactor size can be optimized using this kind of method. Developing volumetric solar receivers, or catalytic monoliths, which are employed in the SMR, has two primary goals: transferring heat to the reactor volume and maintaining temperature homogeneity [34–41]. However, there hasn’t been much research done on the topic of thermochemical schemes and the impact of chemical responses [42,43]. A honeycomb monolithic reactor subject to the incursion of solar light on its obverse face was described using a mathematical model to describe the recurring water-splitting/renewal procedure at the measure of a sole station (one-dimensional delinquent) [42]. Other models [34,35] concentrated on simulating heat transmission in catalytic monoliths.

This study conducts a detailed numerical study based on the computational fluid dynamics (CFD) to investigate the procedure of SMR for manufacturing hydrogen. For the purpose of creating a CFD model, a mesh of a representative section of a reformer reactor will be created and connected to the ansys fluent modeling program. The study considers process modeling and optimization of the SMR process, investigating the effects of all operational parameters that affect the reactor performance for hydrogen production, including temperature, S/C ratio, and gas hourly space velocity (GHSV). For this, detailed user-defined functions (UDFs) written in c++ were developed for modeling the reaction kinetics of the SMR process, assembled, and bowed to the ansys fluent software. A better understanding of heat transfer mechanisms within the reformer should result in better optimization of the required total input heat and better efficiency of the system. For this, special emphasis is made to investigate the belongings of radiation heat transfer mechanism on the reformer reactor performance for hydrogen production. The current study considers the development and concurrent testing of various model combinations of radiation heat transfer schemes and reaction kinetics mechanisms inside a reformer tube of an SMR reactor.

In this study, a single reformer tube was considered to perform numerical simulations. The tube is axisymmetric, and the domain was solved for the governing equations and reaction kinetics in the 2D domain as indicated in Fig. 1. Methane and steam are fed into the reactor tube via the supply inlet section. They react over the catalyst to create CO₂, hydrogen, and a small amount of intermediate CO. The specifications [44] of the reactor and catalyst are shown in Table 1.

This model is quicker than the P-1 model and necessitates less memory, and this model can be cast only for optically thick media.

In this study, the three models were studied to get the best model in SMR applications as shown in Sec. 4.

Tables 2 and 3 list the pre-exponential coefficients and activation energies for the SMR reactions and species.

To streamline the model and cut down the computation time, a number of assumptions were taken into account; a list of them is provided as follows:

• Laminar flow in a steady-state, isothermal situation has been examined

• The feed inlet of the reactor consists of pure methane and steam, and the gas mixtures are assumed to be in an ideal gas state.

• The inertial and viscous resistances are the same in all directions, and the reformer catalytic bed has been described as pseudo-homogeneous.

• The mass, heat, and velocity gradients are considered in axial and radial directions.

In the reforming process, a velocity inlet boundary condition was applied at the reforming inlet and pressure outlet condition at its outlet. The reactants were believed to enter the reactor at the reforming zone inlet at the same steady temperature as applied to reactor's fixed outer wall. Table 4 shows the cases studied in this study.

The mesh independence analysis was carried out to evaluate the mesh sensitivity to the numerical results. Various mesh sizes with 2404, 4026, 6660, 7500, and 8528 cells were investigated, as listed in Table 5. Each mesh scheme has a minimum orthogonal quality of 1 and maximum aspect ratios of 8.12, 5.27, 3.66, 3.25, and 3.05, respectively. All meshes are compared in terms of the methane conversion ratio at an S/C ratio of 3 and GHSV of 1000 h⁻¹. The variation in the methane conversion is negligible for meshes of more than 7500 cells. Maximum variations in methane conversion have been noted, approximately 0.78%. As a result, the output can be produced regardless of the various mesh configurations. Considering this, the mesh containing 7500 cells has been chosen for additional research and model validation.

The established model was validated against both theoretical and experimental data from Ben-Mansour et al. [44] and Hoang et al. [50] at an S/C ratio of 3 and pressure of 5 bar. Hoang et al. [50] experimentally investigated the optimal conditions of temperature and the S/C ratio to achieve high hydrogen production, efficient reforming, and low CO concentration. Ben-Mansour et al. [44] conducted a numerical study to analyze the effects of various parameters such as temperature and S/C ratio on the methane conversion.

To validate the model, a comparison was made between the numerical results and the experimental data as shown in Fig. 2. The validation case was conducted at temperatures ranging from 773 K to 1073 K in increments of 50 K, with a GHSV of 5000 h⁻¹, a pressure of 5 bar, and an S/C ratio of 3. Three radiation models were evaluated and the DO model was selected as it provided the closest agreement with the experimental data.

This trend is consistent with the findings of both experimental and theoretical studies, further validating the model accuracy. To simulate the experimental work, a steel reactor was generated and meshed with fined mesh sizes where nickel catalyst was used in this numerical study with specifications mentioned earlier. Figure 2 demonstrates the relationship between methane conversion and reforming temperature. As the temperature increases, the methane conversion rate also increases, indicating a higher degree of methane being converted into products. This trend is consistent with the findings of both experimental and theoretical studies, further validating the model accuracy.

In the modeling of SMR, the choice of a radiation model plays a crucial role in predicting the process accurately. Considering the significance of thermal energy transfer via radiation, particularly in high-temperature operations like SMR, selecting an appropriate radiation model becomes essential. The three commonly employed radiation models for SMR simulations are the P-1 model, the Rosseland model, and the DO model. These three radiation models were used for validation, as previously mentioned, and to investigate their impact on the methane conversion ratio. Figure 3 illustrates the utilization of different radiation models in this study: P-1 model, Rosseland model, and DO model, at constant reforming situations of 873 K temperature, 10 bar pressure, S/C ratio of 3, and GHSV of 5000 h⁻¹.

The study analysis reveals that the DO radiation model performs better than other radiation models in terms of the methane conversion ratio. When comparing other radiation models, the DO model produces the highest methane conversion ratio under identical parameters of temperature, pressure, GHSV, and S/C as agreed with Amini et al. [48]. The methane conversion in the DO model is remarkably improved by 4.44% over the P-1 model. Moreover, the DO model exhibits a noteworthy enhancement of 18.65% in the methane conversion ratio compared to the Rosseland model.

The reforming temperature affects reaction kinetics, equilibrium conversion, and the SMR process performance. Figures 4 and 5 illustrate the contours of H₂O and CH₄ mass fractions throughout the SMR reactor tube at various wall temperatures using the DO radiation model with constant reforming pressure of 10 bar, S/C ratio of 3, and GHSV of 1000 h⁻¹. The simulations were conducted under a constant pressure of 10 bars, a fixed GHSV of 1000 h⁻¹, and an S/C ratio of 3 (with an inlet mass fraction of H₂O of 0.75 and an inlet mass fraction of CH₄ of 0.25). As temperature rises, there is a corresponding increase in the thermal energy available for molecular collisions, resulting in elevated reaction rates. This trend is consistent with the Arrhenius relationship, which governs reaction kinetics stating that reaction rates exponentially increase with temperature. Initially, at the inlet of the reactor, the concentration of H₂O and CH₄ are at the highest (0.75 and 0.25 respectively). As the reactants progress through the reactor and interact with the catalyst, the steam reforming reaction takes place, resulting in the production of products. Consequently, the concentrations of water and methane gradually reduced lengthwise of the reactor until they reached their minimum values of 0.314 and 0.026 for H₂O and CH₄, respectively at the reactor outlet with steam and methane conversion of 58.13% and 89.6%.

Figure 6 demonstrates that as the temperature increases, the conversion of reactants into products also increases. This observation further supports the notion that higher temperatures facilitate more efficient conversion in the SMR process.

The catalyst and reactant gases often have shorter contact periods when the GHSV ratio is higher. This can impact on the equilibrium conversion of the reforming processes and the reaction rates. Conversely, extended contact times due to a lower GHSV ratio improve the conversion and reaction rates but also raise the risk of adverse reactions. Figure 7 shows the outcome of reforming temperature on the methane conversion ratio at different GHSVs. It shows the positive influence of increasing temperature of reforming on the methane conversion ratio at a constant pressure of 10 bar using the DO radiation model and an S/C ratio of 3. It is clear from Fig. 7 that the effect of temperature on the CH₄ conversion has an almost linear increase because raising the temperature during reformation usually quickens the reaction rate, enabling methane to be converted to H₂ and CO more quickly. Reaction kinetics, equilibrium shifting, activation energy, and other variables are some of the ways that the temperature in reforming reactions influences the rate of reaction. As previously documented [51], increasing the temperature releases more thermal energy, which enables reactant molecules to cross the activation energy barrier and promotes quicker reaction rates.

Higher temperatures can also facilitate the breakdown of bonds. Furthermore, raising the temperature can shift the equilibrium toward the desired products, such as CO and hydrogen, in certain reforming reactions, including steam methane reforming. Figure 7 shows that the methane conversion ratio increased by 379% when the reforming temperature was raised from 773 K to 1073 K. Excessive heat, however, should be avoided since this can result in catalyst deactivation and reduced reaction efficiency.

In assessing the impact of the GHSV, it was observed that the GHSV exerts minimal influence on the methane conversion ratio. This is due to the fact that the methane reaction rate with steam typically surpasses the mass transfer rate between the catalyst surface and the gas. In other words, the reaction proceeds rapidly, rendering alterations in the GHSV relatively inconsequential to the conversion ratio. Notably, the maximum change observed was 7.6% for low GHSV values (∼1000), where a reduction in GHSV from 30,000 to 5000 resulted in an increase in the methane conversion ratio from 57.75% to 61.06% (a 5.2% increment). The low effects of GHSVs also explain the high reaction rate in order to make the reaction quick or the conversion of methane and steam faster in the first part of the reactor as Ben-Mansour et al. [44] reported.

The S/C ratio is a crucial parameter in the SMR process that establishes the proportion of steam delivered to methane; it has significant effects on the reaction kinetics, product composition, and overall performance of the reforming process [44]. Higher S/C ratios usually result in less CO creation because of the water–gas shift reaction, which transforms CO into CO₂ and H₂, as shown in Figs. 8 and 9 at the input part of the reactor at a constant reforming temperature of 873 K, reforming pressure of 10 bar, and GHSV of 5000 h⁻¹ using the DO radiation model. We can note that the conversion happens in the first part of the reactor (high reaction rate). Thus, controlling the S/C ratio is essential to limiting the CO level in the reformated gas. Increasing the S/C ratio (2, 3, 4, and 5—case 37, case 43, case 49, and case 55, respectively) in reforming processes generally enhances the methane conversion due to the water–gas shift reaction and thermodynamic favorability.

More steam is produced by a larger S/C ratio, which encourages the water–gas shift reaction, in which water combines with CO to produce more H₂ and CO₂. The conversion of methane is aided by the increased availability of hydrogen. Hanak et al. [25] observed that the thermodynamic favorability at a larger S/C ratio keeps a higher water concentration, changing the equilibrium toward the desired products and increasing the methane conversion into H₂ and CO. Figure 10 illustrates the effect of S/C on the methane conversion ratio at a fixed reforming pressure of 10 bar, and a GHSV of 5000 h⁻¹. It illustrates that increasing the S/C ratio from 2 to 5 increases the methane conversion ratios by 86.7%, 81%, 75.5%, 80.3%, 58.6%, 44.6%, and 29.3% at reforming temperatures of 773, 823, 873, 923, 973, 1023, and 1073 K respectively.

Pressure significantly impacts SMR process's overall performance as well as the kinetics of the reaction, equilibrium conversion, and energy requirements. Figure 11 shows the effect of the reforming pressure on the methane conversion ratio, confirming that the less reforming pressure, the more methane conversion. Figure 11 indicates that the methane conversion increases with decreasing reforming pressure. According to equilibrium law, a decrease in pressure shifts the equilibrium of a reaction toward the side with a higher number of moles of gas. In SMR, the overall reaction involves the conversion of CH₄ and H₂O into CO and H₂. Since there are fewer moles of gas on the product side in Eq. (3) (1 mole of CO and 3 moles of H₂) compared to the reactant side (1 mole of CH₄ and 1 mole of H₂O), decreasing the pressure favors the forward reaction to increase the number of gas molecules and achieve a higher conversion ratio of methane. At lower reforming pressures, the reduced gas density leads to a decrease in the collision frequency between the reactant molecules, concluding methane and water. This lower collision frequency slows down the reaction kinetics, allowing more time for the equilibrium to shift toward the product side [14]. As a result, a higher methane conversion ratio can be achieved.

According to the above-mentioned results, the optimal conditions for SMR involve lower reforming pressures, higher reforming temperatures, and higher S/C ratios. For instance, the highest methane conversion ratio of 98.15% was achieved at 5 bar pressure, 1073 K temperature, S/C ratio of 5, and 5000 h⁻¹ GHSV. Figure 12 shows the methane conversion ratio and the rapid decrease in CH₄ and H₂O concentrations within the reformer due to the high reaction rate of reactants. These trends are observed under the specified operating conditions (P = 5 bar, T = 1073 K, GHSV = 5000 h⁻¹, and S/C = 5) using the DO radiation model.

The study investigates the simulation of the SMR process for producing blue hydrogen. It analyzes the impact of the comprehensive parameters of the SMR process, such as reforming temperature, reforming pressure, S/C, GHSV, and radiation model. A 2D axisymmetric SMR model using UDF-ansys fluent was developed. The UDF is developed in c program for reforming reaction rates and coupled with fluent. The results designate that increasing the temperature of reforming accelerates the reaction rate, leading to faster conversion of methane to H₂ and CO. Increasing the reforming temperature from 773 K to 1073 K raised the methane conversion ratio by 379% because higher temperatures provide more thermal energy, enabling reactant molecules to overcome the activation energy barrier and facilitating faster reaction rates. The study also found that increasing the S/C ratio in reforming processes enhanced methane conversion. For instance, raising the ratio of S/C from 2 to 5 increases the methane conversion ratio by 86.7%, 81%, 75.5%, 80.3%, 58.6%, 44.6%, and 29.3% at 773, 823, 873, 923, 973, 1023, and 1073 K reforming temperature, respectively, because higher S/C ratio promotes the reaction of the water–gas shift, where water reacts with CO to yield additional H₂ and CO₂. This increases the availability of hydrogen-facilitated methane conversion. Raising the GHSV has no discernible effect on the conversion ratio, with a maximum change of 7.6%. The DO radiation model showed better alignment with the experimental data, in terms of methane conversion ratio, than the P-1 and Rosseland models. The maximum achieved methane conversion ratio in this study is 98.15% at 1073 K, 5 S/C, 2 bar, and 5000 h⁻¹ GHSV.

The authors wish to acknowledge the support established by King Fahd University of Petroleum & Minerals (KFUPM) done by the KFUPM Consortium for Hydrogen Future on Project No. H2FC2315.

There are no conflicts of interest. This article does not include research in which human participants were involved. Informed consent is not applicable. This article does not include any research in which animal participants were involved.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

$a$ =

absorption coefficient

$h$ =

convection coefficient

n =

refractive index

s =

path length

t =

time

u =

velocity

A =

area (m²)

C =

linear-anisotropic phase function coefficient

G =

incident radiation

I =

radiation intensity

P =

pressure

T =

temperature

X =

mass fraction

$Y$ =

specie

$r$ =

position vector

$s′$ =

scattering direction vector

$s$ =

direction vector

$u$ =

velocity vector

d_p =

diameter of the catalyst

A_i =

pre-exponential coefficient of reaction

E_a =

activation energy

E_{a, i} =

activation energy of reaction

F_j =

activation energy of adsorption

G_j =

pre-exponential coefficient for specie

K_eq =

equilibrium reaction rate constant

K_j =

species adsorption rate constant

CO =

carbon monoxide

CO₂ =

carbon dioxide

H₂ =

hydrogen

H₂O =

steam

Ni =

nickel

$∇$ =

nabla or gradient

$α$ =

reverse of viscous resistance

$β$ =

frictional pressure drop factor

ε =

porosity

$μ$ =

viscosity

$ρ$ =

density

$σ$ =

Stefan–Boltzmann constant

$σS$ =

scattering coefficient

$ϕ$ =

phase function

$Ω′$ =

solid angle

a =

activation

g =

gas

j =

specie

p =

particle

r =

rate

eq =

equilibrium

2D =

two-dimensional

DO =

discrete ordinates

GHSV =

gas hourly space velocity

in =

inlet

out =

outlet

PSA =

pressure swing adsorption

S/C =

steam-to-methane or steam-to-carbon ratio

SMR =

steam methane reforming

TGA =

thermogravimetric analysis

UDF =

user-defined function