Introduction

The tri-reforming of methane (TRM) process is an advanced technology for producing syngas (a mixture of hydrogen (H2) and carbon monoxide (CO)) from methane (CH4)1. This process combines three main reforming reactions—steam methane reforming (SMR), dry methane reforming (DMR), and partial oxidation of methane (POX)—into a single integrated system. The intelligent integration of these three reactions in one reactor or system to overcome the challenges of each individually and achieve operational efficiency has made this process highly attractive2,3. One of the advantages of TRM is its ability to produce syngas with a desired H₂/CO ratio (typically between 1.5 and 2.5) for various applications4. Furthermore, the heat generated from POX supplies energy for the endothermic SMR and DMR reactions, significantly reducing the need for external heating and improving the overall energy efficiency of the process5. Additionally, coke formation and subsequent catalyst deactivation are greatly minimized in this process. The presence of steam (H2O) and carbon dioxide (CO2) helps prevent coke deposition on the catalyst. Moreover, the endothermic nature of SMR and DMR reactions reduces local temperatures, further suppressing coking6,7. Another advantage is the consumption of greenhouse gas CO2, which can be sourced from various outlets such as associated gas, flue gases, or even the atmosphere, as a useful feedstock. The process also allows the use of diverse CH4 sources, such as natural gas and biogas, and enables the adjustment of reactant ratios to achieve the desired product8,9.

In other words, the TRM has emerged as a promising and versatile technology for syngas production, primarily due to its unique ability to integrate three distinct reactions: SMR, DMR, and POX within a single catalytic reactor. The fundamental advantage of this process lies in its synergistic thermal management. While SMR and DMR are highly endothermic and require significant external energy, the exothermic nature of POX provides in-situ heat, potentially leading to an autothermal operation. This drastically reduces the energy intensity of the process and improves the overall thermal efficiency, making it more economically viable for large-scale applications10,11.

From a chemical perspective, TRM offers unparalleled flexibility in tuning the H2/CO molar ratio. For industrial processes such as Methanol synthesis and Fischer-Tropsch synthesis, a specific ratio (typically around 2.0) is required. Traditional SMR often yields a ratio higher than 3.0, while DMR results in a ratio close to 1.0. By carefully adjusting the feed composition (CH4, CO2, H2O, and O2), TRM can precisely target the desired syngas quality while simultaneously utilizing CO2, a major greenhouse gas, as a reactant12.

Regarding the catalytic systems, significant research has been dedicated to developing materials that can withstand the harsh, high-temperature environment of TRM. Nickel-based catalysts supported on metal oxides such as Al2O3, MgO, ZrO2, and CeO2 are widely used due to their low cost and high initial activity. However, they are prone to deactivation via carbon deposition (coking) and thermal sintering13,14. Recent literature has focused on enhancing these catalysts by adding promoters like alkaline earth metals or noble metals (e.g., Ru, Rh, Pt) to improve oxygen mobility and suppress carbon formation. For instance, the use of CeO2 as a support or promoter has shown remarkable results in oxygen storage capacity, which facilitates the gasification of carbonaceous species. Operating temperatures for these systems typically range between 700 °C and 950 °C at atmospheric or elevated pressures, depending on the downstream integration requirements15,16.

Thermodynamic evaluation of the TRM reactions provides the scientific basis for process design and is crucial for optimizing performance, predicting system behavior, and preventing operational issues. This assessment is used to predict reaction feasibility and chemical equilibrium, study the effects of temperature, pressure, and reactant ratios on conversion rates and syngas yield, optimize the H₂/CO ratio in syngas, reduce coke production, and predict thermal equilibrium conditions to achieve autothermal operation17,18,19,20. A few thermodynamic studies have been conducted on the TRM process. Zhang et al. conducted a thermodynamic analysis of the TRM process using the Gibbs free energy minimization method and then investigated the effect of operating variables on the product distribution17. Szczygieł et al.18 evaluated the TRM and DRM processes, and Chein and Hsu19 evaluated the TRM and carbon gasification (CG) processes from a thermodynamic perspective. Furthermore, in a similar study, Okonkwo et al. evaluated the thermodynamics of tri-reforming of oxyfuel combustion exhaust gas21.

Several studies have focused on the optimization of the Tri-Reforming of Methane (TRM) process using various techniques. Table 1 shows a detailed comparison of optimization Studies in TRM.

Table 1 Detailed Comparison of Optimization Studies in TRM.
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Problem statement and innovations of this study

The present study consists of two parts. In the first part, a thermodynamic analysis of the TRM is conducted. The equilibrium composition of components is calculated under various operating conditions and feed ratios. Using these results, the effects of temperature, pressure, and the ratios of steam to methane (H2O/CH4), carbon dioxide to methane (CO2/CH4), and oxygen to methane (O2/CH4) in the feed on the CH4, CO2, and H2O conversion, as well as the H2 and CO yield and their ratio in the produced syngas, are investigated.

Another key advantage of the TRM process is its ability to adjust the H₂/CO ratio in the syngas produced. Different H₂/CO ratios are crucial for various chemical and industrial processes. Theoretically, syngas with an H₂/CO ratio of 2:1 is suitable for methanol production. Methanol production from syngas is one of the most fundamental and important processes in the petrochemical and chemical industries, holding significant economic, industrial, and environmental importance22,23. Therefore, this study calculates the optimal operating conditions for producing syngas suitable for methanol production using a genetic algorithm (GA) optimization approach.

The novelty of the present study is twofold:

Methodological novelty (stoichiometric vs. non-stoichiometric)

Most existing studies rely on the Gibbs Free Energy Minimization (GFEM), which is a non-stoichiometric approach. In this work, a direct system of nonlinear equilibrium constant equations (stoichiometric) is utilized. When integrated into a GA requiring thousands of iterations, this stoichiometric approach ensures higher computational stability and transparency. It guarantees that the optimization path strictly follows the specific reaction network (SMR, DMR, WGS), avoiding potential convergence issues or “black-box” numerical errors often encountered in GFEM-based iterative loops. Unlike GFEM, the stoichiometric approach allows for a direct coupling of specific reaction extents, providing deeper mechanistic insights into how individual reactions like RWGS or DMR respond to perturbations in feed composition.

Optimization constraint novelty

Unlike previous studies that often optimize for a “general maximum yield,” the GA used in this study specifically designed to hit an exact industrial target (H2/CO = 2) while simultaneously satisfying strict inequality constraints (> 90% conversion) for both methane and carbon dioxide. This makes the results more applicable to the specific requirements of a downstream methanol synthesis unit.

Reaction network

The TRM process is based on three simultaneous main reactions, which are24,25:

  • SMR:

$$C{H}_{4}+{H}_{2}O\rightleftharpoons CO+3{H}_{2}{\varDelta H}_{{r}_{298}}^{o}=206kJ.{mol}^{-1}$$
(1)

  • DMR:

$$C{H}_{4}+{CO}_{2}\rightleftharpoons2CO+2{H}_{2}{\varDelta H}_{{r}_{298}}^{o}=247kJ.{mol}^{-1}$$
(2)

  • POX:

$$C{H}_{4}+{0.5O}_{2}\rightleftharpoons CO+2{H}_{2}{\varDelta H}_{{r}_{298}}^{o}=-36kJ.{mol}^{-1}$$
(3)

In addition to the three main reactions, the following reactions also occur in the process reactor24,25:

  • CH4 full combustion:

$$C{H}_{4}+{2O}_{2}\rightleftharpoons C{O}_{2}+2{H}_{2}O{\varDelta H}_{{r}_{298}}^{o}=-802kJ.{mol}^{-1}$$
(4)

  • Water-gas shift reaction (WGSR):

$$CO+{H}_{2}O\rightleftharpoons C{O}_{2}+{H}_{2}{\varDelta H}_{{r}_{298}}^{o}=-41kJ.{mol}^{-1}$$
(5)

Furthermore, reactions such as CH4 decomposition, Boudouard reaction, and Boggs reaction may occur, leading to coke deposition on the catalyst surface and subsequently reducing its activity. These reactions are considered in calculations related to catalyst activity coefficients in the simulation of TRM reactors. The thermodynamic evaluation in this study was performed using the Equilibrium Constant Method (a stoichiometric approach). In a stoichiometric framework, incorporating heterogeneous phases (solid carbon) introduces significant mathematical challenges, such as phase-boundary discontinuities. This often leads to numerical instability or convergence issues when solving the non-linear system of equations across a wide temperature range. Also, by focusing on the 700–1000 °C range in this study and in the presence of H2O and O2, the thermodynamic driving force for the Boudouard reaction and methane decomposition is effectively suppressed. So, the gas-phase equilibrium assumption becomes physically sound and highly reliable and the Boudouard reaction and other carbon deposition reactions are not included in the thermodynamic analysis26,27.

To assess the feasibility of the aforementioned reactions and determine whether they are spontaneous or non-spontaneous at different temperatures, the Gibbs free energy of the reactions must be calculated. The Gibbs free energy of a reaction is a criterion that determines the spontaneity and direction of a chemical reaction under varying temperature conditions and constant pressure. It depends on both the enthalpy change and entropy change of the reaction and is calculated using the Gibbs-Helmholtz equation21:

$$\varDelta G\left(T\right)={\varDelta H}_{r}\left(T\right)-T\varDelta S\left(T\right)$$
(6)

The changes in enthalpy and entropy of reactions at different temperatures are obtained using the following relationships21:

$${\varDelta H}_{r}\left(T\right)={\varDelta H}_{{r}_{298}}^{o}+{\int}_{298}^{T}\varDelta{C}_{p}dT$$
(7)
$$\varDelta S\left(T\right)={\varDelta S}_{298}^{o}+{\int}_{298}^{T}\frac{\varDelta{C}_{p}}{T}dT$$
(8)
$$\varDelta{C}_{p}=\sum{C}_{{p}_{Products}}-\sum{C}_{{p}_{Reactants}}$$
(9)

Figure 1 shows the changes in the Gibbs free energy of TRM reactions as a function of temperature in the range of 0 to 1500 °C. As observed, within the studied temperature range, the POX and CH4 full combustion reactions exhibit negative Gibbs free energy values, indicating that they are spontaneous.

The SMR and DMR reactions become spontaneous at temperatures above 622 °C and 646 °C, respectively. Below these temperatures, they are non-spontaneous and proceed in the reverse direction. However, the WGS reaction shows an opposite trend. This reaction is spontaneous at temperatures below 868 °C, while at higher temperatures, the reverse water-gas shift (RWGS) reaction becomes spontaneous. These findings are highly valuable for analyzing the effect of temperature on the equilibrium composition of various components17,28.

Fig. 1
Fig. 1The alternative text for this image may have been generated using AI.
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Plot of Gibbs free energy changes as a function of temperature for TRM reactions.

The equilibrium constants of the TRM reactions can be calculated using the following relation:

$${K}_{a}={e}^{\left(\frac{-\varDelta G\left(T\right)}{RT}\right)}$$
(10)

In the above relation, the equilibrium constant is expressed in terms of the activity (a) of the reaction components. Assuming the reaction components behave as ideal gases and partial pressures are measured in bar, the activity-based equilibrium constant can be considered equivalent to the equilibrium constant expressed in terms of partial pressures (KP​)29. Figure 2 shows the variations of the equilibrium constants for the reactions under study as a function of temperature. The values of the equilibrium constants are used to calculate the equilibrium composition of various components in the process.

Fig. 2
Fig. 2The alternative text for this image may have been generated using AI.
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Plot of equilibrium constant variations as a function of temperature for TRM reactions.

The equilibrium constant in terms of mole fractions of the reaction components (Ky​) is calculated according to the following relation29:

$${K}_{y}={K}_{p}{{P}_{tot}}^{-\varDelta n}$$
(11)

Thermodynamic evaluation of the process

Two methods are commonly used to calculate the equilibrium mole fractions of components in a set of reversible reactions: the reaction equilibrium constant and the Gibbs free energy minimization methods30. The Gibbs free energy minimization method is a powerful tool for calculating chemical equilibrium and is preferred for multi-reaction systems with numerous reaction components. However, this method has limitations, including computational complexity, a strong dependence on thermodynamic data, the need to define atomic constraints, and convergence issues in minimization (e.g., divergence due to poor initial guesses or convergence to incorrect local minima)31.

In the reaction equilibrium constant method used in this study, equilibrium concentrations are determined using the reaction equilibrium constant relation. This method is preferred for single and simple reactions or multiple reactions when the reaction network is known, and the number of unknowns (equilibrium mole fractions of reaction components) equals the number of equations32.

As observed in Figs. 1 and 2, the POX and CH4 full combustion reactions exhibit negative Gibbs free energy and very large equilibrium constants within the operational temperature range. Therefore, these reactions can be considered irreversible, and the equilibrium constant relation need not be written for them. Additionally, Under the conditions studied, where the oxygen-to-methane ratio (O2/CH4) is kept significantly below the stoichiometric requirement for complete combustion, oxygen acts as the limiting reactant. Therefore, at the thermodynamic equilibrium of the TRM process, it can be concluded that oxygen is virtually entirely consumed, and its equilibrium concentration is assumed to be zero for the purpose of the stoichiometric calculations.

Among the three remaining reactions—SMR, DMR, and WGS —only two are independent. This is because the DMR reaction can be derived from the combination of SMR and the RWGS reactions. Thus, the equilibrium constant equation needs to be written for two of these three reactions.

Apart from the equilibrium mole fraction of oxygen, which is known (zero), the equilibrium mole fractions of the other five components (CH4, H2O, CO2, CO, and H2) are unknown. Solving for these requires the simultaneous solution of five equations:

  • Elemental mass balance for carbon (C):

$${{n}_{{C}_{total}}=n}_{{CH}_{4}}^{0}+{n}_{{CO}_{2}}^{0}={{n}_{{CH}_{4}}}^{eq}+{{n}_{{CO}_{2}}}^{eq}+{{n}_{CO}}^{eq}$$
(12)

  • Elemental mass balance for oxygen (O):

$${n}_{{O}_{total}}={n}_{{H}_{2}O}^{0}+2{n}_{{CO}_{2}}^{0}+2{n}_{{O}_{2}}^{0}={{n}_{{H}_{2}O}}^{eq}+2{{n}_{{CO}_{2}}}^{eq}+{{n}_{CO}}^{eq}$$
(13)

  • Elemental mass balance for hydrogen (H):

$${n}_{{H}_{total}}=4{n}_{{CH}_{4}}^{0}+2{n}_{{H}_{2}O}^{0}=4{{n}_{{CH}_{4}}}^{eq}+2{{n}_{{H}_{2}O}}^{eq}+2{{n}_{{H}_{2}}}^{eq}$$
(14)

The above elemental balance equations illustrate the conservation of Carbon (C), Hydrogen (H), and Oxygen (O) atoms between the feed and the equilibrium products.

  • Equilibrium constant equation for SMR:

$${K}_{{y}_{SMR}}=\frac{{n}_{CO}{{n}_{{H}_{2}}}^{3}}{{n}_{{CH}_{4}}{n}_{{H}_{2}O}}\times{\left(\frac{1}{{n}_{tot}}\right)}^{2}$$
(15)

  • Equilibrium constant equation for DMR:

$${K}_{{y}_{DR}}=\frac{{{n}_{CO}}^{2}{{n}_{{H}_{2}}}^{2}}{{n}_{{CH}_{4}}{n}_{{CO}_{2}}}\times{\left(\frac{1}{{n}_{tot}}\right)}^{2}$$
(16)

The system of nonlinear equations described above is solved using coding in MATLAB R2024b software with the fsolve command. This numerical method is used to find roots of the nonlinear equations by iteratively optimizing initial guesses until convergence is achieved.

Optimization using a GA

A GA is an intelligent optimization and search technique inspired by the principles of natural evolution and genetics. This algorithm is employed to identify optimal or near-optimal solutions for complex, multi-faceted problems33,34.

In this method, an initial population is first generated randomly. Each individual within the population consists of chromosomes representing the key process variables: temperature, pressure, and the molar ratios of H2O/CH4, CO2/CH4, and O2/CH4 in the feed stream. The fitness function of all individuals in the population is evaluated using the thermodynamic assessment code described in the previous section. In this study, the fitness function is defined as the absolute difference between the hydrogen-to-carbon monoxide (H₂/CO) ratio in the produced syngas and the target value of 2. The objective of the optimization is to minimize this fitness function.

Subsequently, a select percentage of the population is chosen as parents via the Tournament selection method. The crossover operator is then applied to these parents to generate offspring. This study utilizes an Arithmetic crossover technique. Following this, the mutation operator is applied to a subset of the population. For this purpose, the Gaussian method was selected as the mutation operator.

The entire population, comprising the initial individuals, their offspring, and the mutated individuals, is then ranked based on their fitness values. A lower fitness value corresponds to a higher rank. The top-ranked individuals, equal in number to the initial population size (100 individuals in this study), are selected to form the next generation.

This iterative cycle continues until the termination criterion, which is a maximum of 200 generations in this study, is met. Figure 3 illustrates the flowchart of the GA implemented in this work. The optimization was conducted using the GA, with code developed in MATLAB R2024b11,35,36.

Fig. 3
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Flowchart of the GA implemented in the present study.

Table 2 summarizes the parameters employed in the GA for the optimization process37.

Table 2 Parameters of the GA employed in the present study.
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Thermodynamic evaluation results

Effect of temperature investigation

Figure 4 illustrates the effect of temperature on the equilibrium conversion of reactants (CH4, H2O, and CO2), the molar yield of products (H2 and CO), and the equilibrium H2/CO molar ratio.

The equilibrium conversion of reactants and the molar yield of products are obtained through the following relationships:

$${X}_{i}\left(\%\right)=\frac{{{n}_{i}}^{0}-{n}_{i}}{{{n}_{i}}^{0}}\times100$$
(17)
$${Y}_{{H}_{2}}\left(\%\right)=\frac{{{n}_{{H}_{2}}}^{eq}}{2{n}_{{CH}_{4}}^{0}+{n}_{{H}_{2}O}^{0}}\times100$$
(18)
$${Y}_{CO}\left(\%\right)=\frac{{{n}_{CO}}^{eq}}{{n}_{{CH}_{4}}^{0}+{n}_{C{O}_{2}}^{0}}\times100$$
(19)
Fig. 4
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Plots of (a) variations in the equilibrium conversion of reactants, (b) molar yield of products, and (c) H2/CO equilibrium molar ratio as a function of temperature at a pressure of 1 bar and a molar feed ratio of CH₄:H₂O: CO₂:O₂ = 1:0.54:0.48:0.1.

As observed in Fig. 4a, the equilibrium CH4 conversion increases from 78% at 700 °C to 100% at 1000 °C. This behavior can be attributed to the reaction pathways illustrated in Fig. 1. At temperatures above 700 °C, CH4 is consumed in the CH4 full combustion, POX, SMR, and DMR reactions, and its consumption rate increases with increasing temperature. CO2 also shows a similar trend to CH4, with the conversion increasing from 55% at 700 °C to 86% at 1000 °C. In the temperature range of 700 to 868 °C, CO2 is produced in two reactions: WGS and CH4 full combustion, and consumed in the DMR reaction. Given the positive conversion, it can be concluded that the consumption rate is higher. However, at temperatures above 868 °C, the WGS reaction proceeds in the reverse direction, and CO2 is consumed in two reactions: DMR and RWGS.

For H2O, the conversion with respect to temperature reaches a maximum at 868 °C. This is because at temperatures lower than 868 °C, H2O is consumed in the WGS and SMR reactions, and conversion increases with increasing temperature. However, at temperatures higher than that, H2O is produced in the RWGS reaction, and conversion decreases with temperature.

As illustrated in Fig. 4b, the yield of H2 and CO increases with temperature. This is attributed to the fact that, syngas (H2 and CO) is generated via all three main processes: POX, SMR, and DMR. However, it is observed that the yield of CO at temperatures above 868 °C exceeds the yield of H2. This is because at temperatures below 868 °C, part of the CO produced is converted to H2 in the WGS reaction. Still, at temperatures above that, the process is reversed.

Furthermore, as shown in Fig. 4c, the H₂/CO ratio decreases from 1.80 at 700 °C to 1.69 at 1000 °C. This decline occurs because, at lower temperatures, a fraction of the CO produced is converted to H2 via the WGS reaction, thereby increasing the H₂/CO ratio. At higher temperatures, the WGS reaction equilibrium shifts toward reactants, reducing its influence and resulting in a lower ratio.

Investigation of pressure effect

In this study, the pressure was investigated in the range of 1 to 10 bar. While atmospheric pressure (1 bar) is thermodynamically optimal for methane conversion, the range was extended to 10 bar to assess the process under industrially relevant conditions where downstream integration and reactor volume minimization are critical27. Figure 5 illustrates the influence of pressure within the temperature range of 700 to 1000 °C on the conversion of reactants, the yield of products, and the H2/CO ratio in the produced syngas. As observed, increasing the pressure leads to a decrease in the conversion of CH4, H2O, and CO2, as well as a reduction in the yields of H2 and CO.

This phenomenon can be explained by Le Chatelier’s principle. An increase in system pressure shifts the reaction equilibrium in the direction that counteracts this change by reducing the pressure. Since the SMR and DMR reactions involve an increase in the total number of gaseous moles (Δng > 0), the reverse reaction pathway is favored at higher pressures to reduce the number of moles and, consequently, the pressure. Therefore, elevated pressure promotes the reverse reforming reactions, resulting in lower reactant conversion and a decrease in syngas yield.

However, the results indicate that the conversion of oxygen remains unchanged with varying pressure; oxygen is completely consumed across all pressure levels. This is because, within the studied temperature range, the CH4 full combustion and POX reactions can be considered irreversible.

The influence of operating pressure on the H2/CO ratio exhibits a dual and temperature-dependent behavior, as illustrated in Fig. 5f. At lower temperature regimes, an increase in pressure tends to slightly enhance or stabilize the H2/CO ratio, as the system’s equilibrium is heavily influenced by the WGS reactor and methanol-precursor kinetics. However, as the temperature increases, a reversal in this trend occurs. At elevated temperatures, increasing the pressure leads to a reduction in the H2/CO ratio. This phenomenon can be explained by the Le Chatelier’s principle acting on the reforming reactions (SMR and DMR), which involve an increase in the total number of moles. High pressure suppresses these reactions, but its inhibitory effect is more pronounced on the SMR pathway compared to the DMR and RWGS reactions at specific thermal conditions. This conflict between pressure-driven mole reduction and temperature-driven reaction kinetics results in an ‘inversion point’ where the pressure’s impact on syngas quality reverses. Consequently, selecting an optimal pressure is vital, as it must balance the kinetic requirement for high pressure with the thermodynamic necessity of maintaining a H2/CO ratio near 2.0.

In addition, the very high pressures typically accelerate coke formation, but elevated pressures are often preferred to reduce the sizing of downstream compression stages for methanol or Fischer-Tropsch synthesis. So, it is necessary to maintain a careful balance between conversion, efficiency, and catalyst longevity27.

Fig. 5
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Variations of the (a) CH4, (b) H2O, (c) CO2 equilibrium conversion; (d) H2, (e) CO molar yield; and (f) H2/CO equilibrium molar ratio as a function of temperature and pressure at a fixed molar feed ratio of CH₄:H₂O: CO₂:O₂ = 1:0.54:0.48:0.1.

Investigation of the effect of H2O/CH4 ratio in the feed

Figure 6 illustrates the influence of the H₂O/CH4 ratio in the feed on reactant conversion, product yields, and the H₂/CO ratio in the outlet syngas.

As observed in Fig. 6a, the CH4 conversion increases with a higher H₂O/CH4 ratio. According to Le Chatelier’s principle, increasing the H2O concentration shifts the equilibrium of the SMR reaction toward the products (to the right), thereby enhancing the equilibrium conversion of CH4. Furthermore, the additional H2O inhibits carbon formation (coking) via CH4 decomposition, which helps maintain catalyst activity for a longer duration and consequently improves CH4 conversion.

Figure 6b illustrates that at lower temperatures, an increase in H2O results in higher H2O conversion. This is due to the shift in equilibrium of both the SMR and WGS reactions toward the products as the H2O concentration increases. Conversely, at higher temperatures, the H2O equilibrium conversion decreases as the concentration of H2O increases. This occurs because, at elevated temperatures, the rate of CH4-consuming reactions is high, making CH4 the limiting reactant. H2O consumption is thus constrained by its reaction capacity with the available CH4, resulting in a significant portion of the H2O leaving the reactor unreacted. It is important to note that this decrease in H2O conversion does not imply lower energy efficiency, as the excess H2O prevents coking and promotes H2 production.

According to Fig. 6c, the CO2 equilibrium conversion decreases with an increasing H₂O/CH₄ ratio. This is attributed to two factors: firstly, increased H2O concentration enhances the WGS reaction (according to Le Chatelier’s principle), leading to greater CO₂ production and thus a lower net conversion of CO₂. Secondly, in the context of combined reforming, CH4 has a higher tendency to react with H2O than with CO₂. Therefore, as the H2O/CH4 ratio increases, the SMR reaction is favored, leaving less CH4 available for the DMR reaction, which further contributes to the reduced conversion of CO₂.

Figure 6d shows that increasing the H2O/CH4 ratio increases H2 yield. As previously explained, this enhances both the SMR and WGS reactions, thereby increasing H2 production. For CO, there are two competing effects: on the one hand, promoting SMR increases CO production, while on the other hand, enhancing the WGS reaction consumes CO, reducing the CO yield, as depicted in Fig. 6e.

Finally, Fig. 6f confirms that the H₂/CO ratio increases with the H2O/CH4 ratio, which is consistent with the discussed phenomena.

Fig. 6
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Variations of the (a) CH4, (b) H2O, (c) CO2 equilibrium conversion; (d) H2, (e) CO molar yield; and (f) H2/CO equilibrium molar ratio as a function of temperature and H2O/CH4 feed ratio at a fixed molar ratio of CH₄:CO₂:O₂ = 1:0.48:0.1 (with H₂O variable).

Investigation of the effect of CO2/CH4 ratio in the feed

The effect of the CO₂/CH4 ratio in the feed on the CH4, CO2, and H2O conversion, as well as on the H2 and CO yield, and the H₂/CO ratio at various temperatures is presented in Fig. 7.

As observed, increasing the CO₂/CH₄ ratio enhances the equilibrium CH4 conversion (Fig. 7a). This is attributed to the promotion of the DMR reaction with higher CO2 concentrations. Conversely, increasing the CO₂ ratio has an inverse effect on H2O conversion (Fig. 7b), as it promotes the RWGS reaction, which consumes H2 and produces H2O. Furthermore, and as expected, increasing the CO2 concentration has a direct positive effect on its own conversion (Fig. 7c). According to Le Chatelier’s principle, this increase shifts the equilibrium of the DMR reaction toward the products (right) and the WGS reaction toward the reactants (left), thereby increasing the equilibrium conversion of CO₂. It is important to note, however, that excessive CO₂—unlike H2O—can lead to catalyst deactivation in the process.

Additionally, an increase in the CO₂/CH₄ ratio results in a higher CO molar yield (Fig. 7e). This occurs because the elevated CO₂ concentration further promotes the DMR and RWGS reactions, resulting in increased CO production.

Regarding the H2 yield (Fig. 7d), it exhibits a temperature-dependent response to the CO2/CH4 ratio. At lower temperatures, increasing the CO2/CH4 ratio leads to a slight increase in H2 yield. This is because the additional CO2 promotes the DMR, which serves as a source of H2 production. At these thermal conditions, the hydrogen generation from DMR outweighs its consumption via the RWGS reaction. However, as the temperature increases, the trend reverses, and the H2 yield decreases with a higher CO2/CH4 ratio. In this high-temperature regime, the RWGS reaction becomes thermodynamically much more favorable and faster. Consequently, a significant portion of the H2 produced by the reforming reactions is consumed by the excess CO2 to form CO and H2O.

As shown in Fig. 7e, the CO molar yield exhibits a monotonic increase with the CO2/CH4 ratio across all temperatures, driven by the synergistic promotion of both DMR and RWGS reactions. These combined effects explain the significant reduction in the equilibrium H2/CO ratio as the feed becomes richer in CO2 (Fig. 7f), highlighting the necessity of balancing CO2 levels to maintain the desired syngas quality for downstream synthesis.

Fig. 7
Fig. 7The alternative text for this image may have been generated using AI.
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Variations of the (a) CH4, (b) H2O, (c) CO2 equilibrium conversion; (d) H2, (e) CO molar yield; and (f) H2/CO equilibrium molar ratio as a function of temperature and CO2/CH4 feed ratio at a fixed molar ratio of CH₄:H2O: O₂ = 1:0.54:0.1 (with CO₂ variable).

Investigation of the effect of O2/CH4 ratio in the feed

Figure 8 illustrates the influence of the O₂/CH4 ratio in the feed on reactant conversion, product yields, and the H₂/CO ratio in the produced syngas.

As shown in Fig. 8a and c, increasing the oxygen concentration leads to an increase in the equilibrium CH4 conversion, while the H2O and CO2 equilibrium conversions decrease. This behavior occurs because a higher oxygen concentration promotes CH4 consumption via both POX and full combustion reactions, thereby reducing the extent of CH4 reforming (dry and steam). Additionally, the complete combustion of CH4 produces CO2 and H2O, thereby lowering the net equilibrium conversion of these components. Also, as discussed, increasing the oxygen concentration decreases the molar yields of H2 and CO, as demonstrated in Fig. 8d and e.

The H2/CO molar ratio exhibits a complex temperature-dependent behavior with respect to oxygen concentration, as depicted in Fig. 8f. At lower temperatures (typically below 800 °C), increasing the O2/CH4 ratio leads to a higher H2/CO ratio. This is primarily due to the dominance of full combustion and the subsequent WGS reaction, where the generated H2O promotes H2 production. However, a significant reversal in this trend is observed at higher temperatures (above 900 °C). In this elevated thermal regime, increasing oxygen concentration causes a decline in the H2/CO ratio. This reversal occurs because high temperatures favor the POX of methane and the endothermic RWGS reaction, both of which significantly enhance the thermodynamic stability and production rate of CO relative to H2. Therefore, the impact of oxygen on syngas quality is not uniform; it acts as a promoter for the H2/CO ratio at low temperatures but shifts toward CO enrichment at high temperatures, necessitating careful thermal management to achieve the stoichiometric requirements for methanol synthesis.

Fig. 8
Fig. 8The alternative text for this image may have been generated using AI.
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Variations of the (a) CH4, (b) H2O, (c) CO2 equilibrium conversion; (d) H2, (e) CO molar yield; and (f) H2/CO equilibrium molar ratio as a function of temperature and O2/CH4 feed ratio at a fixed molar ratio of CH₄:CO₂:O₂ = 1:0.54:0.48 (with O₂ variable).

Optimization results

This section presents the optimal operating conditions for achieving syngas with an H₂/CO ratio of 2, which is suitable for methanol production. The investigated operating parameters included temperature (700–1000 °C), pressure (1–10 bar), H2O/CH4 ratio (0.3–1), CO2/CH4 ratio (0.3–0.8), and O2/CH4 ratio (0.1–0.5).

The objective function for the optimization was defined by Eq. (20), which was minimized during the process:

$$FitnessFunction=\left|2-\frac{molesofH_2produced}{molesofCOproduced}\right|$$
(20)

In addition to the H₂/CO ratio in the produced syngas, the conversion percentages of CH4 and CO2 were also considered critical. Therefore, the optimization problem was subject to two constraints: CH4 and CO2 conversion must both exceed 90%. Thus, the problem was formulated as a single-objective optimization with inequality constraints.

Table 3 summarizes the optimal operating conditions derived from the optimization. The optimization results demonstrate that to satisfy the dual requirement of high CO2 conversion (90%) and a precise H2/CO ratio of 1.99, the system converges toward a low-pressure and high-temperature regime. Operating at 1.0 bar is essential to maximize the conversion of CO2, as the DMR is a mole-increasing process. Furthermore, the identified temperature of 989 °C provides the necessary thermal energy to drive the endothermic reactions, compensating for the lower O2/CH4 and CO2/CH4 ratios required to meet the conversion constraints. While the current optimization focuses on syngas quality and conversion, the global energy balance is considered outside the scope of this study.

Table 3 Optimal operating conditions for producing syngas suitable for methanol synthesis.
Full size table

Conclusion

This study was conducted in two main parts. In the first part, a thermodynamic analysis of the TRM process was performed using MATLAB R2024b, which simultaneously solves a system of nonlinear equations that includes reaction equilibrium constants and mass balance equations. Accordingly, the equilibrium composition of various components was calculated under different operating conditions and feed ratios. Subsequently, the effects of parameters such as temperature, pressure, and the ratios of H2O/CH4, CO2/CH4, and O2/CH4 on the CH4, CO2, and H2O conversion, as well as the H2 and CO yields and their ratio in the produced syngas, were investigated.

The results indicate that increasing temperature significantly promotes CH4 and CO2 conversions and H2 and CO yield; however, H2O conversion exhibits a non-monotonic trend, characterized by an initial increase followed by a decline at elevated temperatures. The H2/CO ratio decreases with increasing temperature because CO is more thermodynamically stable. Operating pressure has a dual impact. While it generally decreases reactants conversion, its effect on the H2/CO ratio is strictly temperature-dependent, exhibiting an inversion behavior in which the pressure’s influence reverses across different thermal regimes. Regarding feed ratios, H2O/CH4 increases H2 yield and the H2/CO ratio, whereas CO2/CH4 favors CO production and reduces the H2/CO ratio. The O2/CH4 ratio acts as a temperature-sensitive regulator, increasing the H2/CO ratio below 800 °C but promoting CO enrichment above 900 °C.

The second part of this study focused on optimizing the operating conditions to produce syngas suitable for methanol production using a GA. A single-objective optimization problem with constraints was defined, aiming to minimize the absolute difference between the H₂/CO ratio and the target value of 2. The constraints required that the CH4 and CO2 conversion exceed 90% under optimal conditions.

The optimization results revealed that a high-temperature and low-pressure environment is essential to overcome thermodynamic limitations and achieve the stringent constraint of 90% CO2 conversion. The optimal point was identified at a temperature of 989 °C and a pressure of 1.0 bar, with a feed composition of CH4:H2O: CO2:O2 = 1:0.61:0.30:0.10. Under these verified conditions, the CH4 conversion exceeds 99% and the CO2 conversion reaches the 90% threshold, yielding a syngas ratio of 1.99, which is ideal for industrial methanol synthesis.

These findings demonstrate that while tri-reforming of methane is a complex process influenced by competing reactions, a precise balance of feed ratios—particularly maintaining a lower O2/CH4 and CO2/CH4 ratio at atmospheric pressure—can maximize the conversion of greenhouse gases. The optimization data are fully consistent with the parametric sensitivity analysis, providing a reliable thermodynamic framework for the design and operation of TRM reactors. This study offers a clear roadmap for achieving high-purity syngas while optimizing the environmental benefits of CO2 utilization in the petrochemical industry.

It should be noted that the optimization performed in this study is focused primarily on the thermodynamic equilibrium and the target syngas quality. While the identified optimal temperature (989 °C) ensures high CO2 conversion, the optimization of the overall energy balance and thermal efficiency of the reactor is outside the scope of the present paper.