From CO₂ to Methane: A Thermodynamic Study of the Sabatier Reaction for Clean Energy Applications ^†

Abstract

This work presents a numerical analysis of the steady-state thermodynamic equilibrium of the CO₂ methanation reaction, based on solving mass balance equations using equilibrium constants. It evaluates how temperature, pressure, and the H₂/CO₂ ratio affect methane yield and by-product formation. The results show that temperatures below 450 °C, high pressures, and a stoichiometric H₂/CO₂ ratio maximize methane production and CO₂ conversion. For instance, at 400 °C and 10 bar, the equilibrium molar fractions are approximately 0.30 for CH₄, 0.00021 for CO, and 0.020 for CO₂. The process is particularly promising when renewable hydrogen is used, offering a viable pathway for CO₂ valorization. The methane produced can be integrated into existing natural gas networks, supporting the energy transition and helping reduce greenhouse gas emissions.

1. Introduction

The world’s heavy reliance on the combustion of fossil fuels to meet energy demands has led to a sharp increase in atmospheric carbon dioxide (CO₂) levels. Fossil fuel consumption is projected to reach 56% by 2040 [1]. As CO₂ is a major contributor to the greenhouse effect, concerns about reducing its emissions have grown significantly. One of the most explored solutions in recent years is carbon capture and storage (CCS), which involves trapping CO₂ emissions from industrial sources, transporting them, and storing in underground geological formations [2]. However, due to high costs and potential long-term environmental risks, global attention is shifting toward a more promising alternative: carbon capture and utilization (CCU) [1]. Within this context, CO₂ methanation has emerged as an increasingly attractive approach. The exothermic Sabatier reaction, Equation (1), is accompanied by the endothermic reverse water gas shift reaction (RWGS), Equation (2) [3].

$$\mathrm{CO}+3{\mathrm{H}}_2\leftrightarrow {\mathrm{CH}}_4+{\mathrm{H}}_2\mathrm{O} \left(\mathrm{g}\right) -206 {\mathrm{KJ} \mathrm{mol}}^{-1} \left(298 \mathrm{K}\right)$$

(1)

$${\mathrm{CO}}_2+{\mathrm{H}}_2\leftrightarrow \mathrm{CO}+{\mathrm{H}}_2\mathrm{O} \left(\mathrm{g}\right) +41 {\mathrm{KJ} \mathrm{mol}}^{-1} \left(298 \mathrm{K}\right)$$

(2)

Using the Sabatier reaction, synthetic natural gas (SNG), primarily methane (CH₄), can be produced from CO₂ and hydrogen (H₂). When hydrogen is sourced renewably via electrolysis, this pathway offers a compelling route to combat global warming [4]. SNG stands out for its high energy content and lower CO₂ emissions compared to traditional fossil fuels [5]. Moreover, it benefits from compatibility with the existing extensive natural gas infrastructure, enabling seamless integration into current energy systems [4].

This study focused on the influence of temperature, pressure, and the H₂/CO₂ molar ratio on reaction yield, the formation of by-products such as carbon oxides, and the overall energy balance. The objective is to identify the operating conditions that maximize methane production and minimize the formation of undesired compounds, thereby contributing to the optimization of the methanation process.

2. Materials and Methods

Considering the methanation reaction of CO₂, assuming a perfect gas mixture, the equilibrium constant is expressed as follows in Equation (3) [6]:

$${\mathrm{K}}_{\mathrm{eq}}={\displaystyle \frac{{\mathrm{X}}_{{\mathrm{CH}}_4}\times {\left({\mathrm{X}}_{{\mathrm{H}}_2\mathrm{O}}\right)}^2}{{\mathrm{X}}_{{\mathrm{CO}}_2}\times {\left({\mathrm{X}}_{{\mathrm{H}}_2}\right)}^4}}\times {\left({\displaystyle \frac{{\mathrm{P}}_{\mathrm{T}}}{{\mathrm{P}}_0}}\right)}^{-2}$$

(3)

where ${\mathrm{X}}_{\mathrm{i}}$ are the molar fractions of the compounds. P_T is the total pressure and P₀ the reference pressure (1 bar).

Following the same reasoning, for the RWGS reaction, the equilibrium constant can be given by Equation (4):

$${\mathrm{K}}_{\mathrm{eq}}={\displaystyle \frac{{\mathrm{X}}_{\mathrm{CO}}\times {\mathrm{X}}_{{\mathrm{H}}_2\mathrm{O}}}{{\mathrm{X}}_{{\mathrm{CO}}_2}\times {\mathrm{X}}_{{\mathrm{H}}_2}}}$$

(4)

The equilibrium constant can also be determined using the Gibbs free energy method, by Equations (5) and (6):

$${\mathrm{K}}_{\mathrm{eq}}=\exp \left(-{\displaystyle \frac{\Delta \mathrm{G}°}{\mathrm{RT}}}\right)$$

(5)

$$\Delta \mathrm{G}°=\Delta {\mathrm{H}}_0-\mathrm{T}\Delta {\mathrm{S}}_0$$

(6)

This method allows the molar fraction of each component present in the reaction products to be calculated from the state of thermodynamic equilibrium.

3. Results

3.1. Effect of Pressure and Temperature

As shown in Figure 1a, CH₄ formation is favored at low temperatures, below 450 °C, due to the exothermic nature of the CO₂ methanation reaction. Additionally, high pressures also promote CH₄ formation and, consequently, improve CO₂ conversion efficiency, since the methanation reaction involves a decrease in the total number of moles from reactants to products. Figure 1b illustrates the negative effect of the RWGS reaction, which, being endothermic, is favored by increasing reaction temperatures. This leads to the formation of CO and contributes to catalyst deactivation through carbon deposition [3]. At 1 bar and 400 °C, the molar fraction of CH₄ reaches 0.26, increasing to 0.30 at 10 bar. Conversely, at 550 °C and 1 bar, methane decreases to 0.13, while CO increases to 0.035 due to the dominance of the RWGS reaction.

3.2. Effect of H₂/CO₂ Ratio

Since H₂ is an expensive component, the highest H₂/CO₂ ratio studied was 4, which corresponds to the stoichiometry of the CO₂ methanation reaction [7].

Figure 2a shows that the molar fraction of CH₄ is unfavorable for H₂/CO₂ ratios below the stoichiometric value, with a corresponding increase in the molar fraction of CO₂ in the reaction products at equilibrium (Figure 2b). A lower H₂/CO₂ ratio also intensifies CO formation (Figure 2c). However, when optimal temperature and pressure conditions for maximum CH₄ selectivity are considered, the H₂/CO₂ ratio does not significantly affect the molar fraction of CO in the reaction products. When the H₂/CO₂ ratio decreases from 4 to 2 at 400 °C and 10 bar, the molar fraction of CH₄ drops from 0.30 to 0.24, with a corresponding increase in the molar fractions of CO₂ and CO.

4. Discussion

The results confirm that the CO₂ methanation reaction is highly dependent on operating conditions, particularly temperature and pressure. Temperatures above 450 °C significantly reduce CO₂ conversion efficiency, consistent with the exothermic nature of the reaction. Under these conditions, the RWGS reaction becomes more favorable, leading to increased CO formation.

Additionally, the H₂/CO₂ ratio plays an important role in chemical equilibrium. Ratios lower than the stoichiometric value (4/1) result in lower methane production and higher concentrations of residual CO₂ and CO in the products.

These results are in good agreement with previous studies. Fan and Tahir [1] reported that CO₂ methanation is most efficient at low temperatures (150–450 °C), high pressures, and an H₂/CO₂ ratio of 4, which favor CH₄ formation and suppress CO production. Miguel et al. [7] reached similar conclusions in their thermodynamic analysis. Overall, our findings confirm that methane yield is maximized under comparable operating conditions.

5. Conclusions

This study confirmed that CO₂ methanation is most efficient at temperatures below 450 °C and high-pressure conditions, using an H₂/CO₂ ratio close to the stoichiometric value. The reaction shows great potential as a solution for CO₂ valorization, particularly when hydrogen is produced from renewable sources such as water electrolysis powered by solar or wind energy. Moreover, the methane produced can be readily injected into existing natural gas networks without the need for major infrastructure modifications, representing a significant advantage in terms of integration and cost. These findings highlight the potential of the methanation process as a key technology for the energy transition and the reduction in greenhouse gas emissions.