Two-step TSAR process for biogas upgrading: computational study of CO 2 capture and catalytic methanation via reactive regeneration in a dual-function adsorber/reactor with conductive structured internals

1 Introduction

Biomethane is one of the possible solutions to reduce the carbon footprint of several hard-to-abate industries. In fact, it can be used as a replacement for fossil methane since the existing gas infrastructure is already biomethane-ready (European Biogas Association, 2025). Biomethane can also be used to further diversify EU’s gas suppliers, reducing dependency on foreign gas and improving energy security. For this reason, REPowerEu Plan (European Commission, 2022a) outlined as there is a clear need to scale-up biomethane by 2030, reaching a production of 35 billion cubic meters (bcm) per year and an estimated investment of €37 billion (European Commission, 2022b).

Biogas is obtained from biomass (such as agricultural waste, sewage sludge, etc.) throughout an anaerobic digestion process where the bio-waste is fermented at controlled temperature and in absence of oxygen. The fermentation is carried out in the digesters by bacteria that digest the organic fraction and transform it into biogas (AB Group, 2025). The biogas obtained is a mixture of mainly methane (CH₄, 50%–70%) and carbon dioxide (CO₂, 30%–50%), its composition varies depending on the type of organic waste used. The mixture may also contain small traces of nitrogen (N₂, 0%–3%), water vapor (H₂O, 5%–10%), hydrogen sulfide (H₂S, 0.005%–2%), ammonia (NH₃, <1%), oxygen (O₂, 0%–1%), halogenated hydrocarbons (VOC, <0.6%), siloxanes (0%–0.02%) and other impurities (Ryckebosch et al., 2011). This mixture must get through a purification process, called upgrading, where the contaminants and the CO₂ are removed from the mixture, obtaining almost pure biomethane. This step is essential to remove corrosive compounds such as hydrogen sulfide and to increase the Lower Calorific Value (LCV) of biogas by removing CO₂ (methane has an LCV of 50.4 MJ/kg-CH₄ while biogas LCV is approximately 20–25 MJ/m³-biogas (Angelidaki et al., 2018)). The final target is to obtain almost pure biomethane (95%–97%) which can be a substitute for fossil methane. The CO₂ separation process can be performed in different ways. The most common are chemical absorption in alkanolamines (MEA, DEA, MDEA), adsorption on a solid surface with a regeneration phase with increased temperature or reduced pressure, cryogenic separation and membrane separation (Angelidaki et al., 2019).

The upgrading process separates significant fractions of carbon dioxide from biogas usually in a 30%–50% range. This CO₂ can be either emitted to the atmosphere without increasing the net amount of greenhouse gases because of its biological origin or can be valorized and reused in other applications. Among the possible solutions the captured CO₂ can be sold to other industries as chemical feedstock, or it can be stored to reduce the carbon emissions in the atmosphere, or it can be converted into methane using power-to-gas technologies, increasing the total methane production by around 35% (Cordova et al., 2022). The conversion of carbon dioxide and hydrogen into methane is performed by the Sabatier reaction: CO₂ + 4H₂ → CH₄ + 2H₂O using a metal oxide catalyst (Muller et al., 2013).

The power-to-gas process can be performed in two main ways, as presented by Faria et al. (2025), in their study on the concepts for the intensification of carbon dioxide methanation processes. One option is to perform the Sabatier reaction with the CO₂ still mixed in the source gas. This approach can be limited by the high percentage of methane in the inlet gas mixture. In fact, due to the reversible nature of the Sabatier reaction, the presence of methane in the feed can inhibit the reaction and make the conversion less effective. To solve this issue, the methanation reaction can be coupled with a water removal process which shifts the equilibrium towards the products, allowing a higher CO₂ conversion. This methanation process enhanced by water removal was analyzed in Agirre et al. (2021) where the CO₂ present in the biogas is converted into methane using Zeolite 4A for water sorption and to enhance the reaction. The same approach has been proposed also by Gomez et al. (2022), where sorption enhanced methanation is used to produce high quality synthetic natural gas under mild conditions (275 °C and 1atm).

An alternative solution requires CO₂ to be first captured from the biogas and then converted into synthetic methane using green hydrogen as reactant. This option is versatile and can be used for different CO₂ sources, including direct capture from air. In this solution, the Sabatier reaction is performed in more favorable conditions due to the absence of biomethane from the starting mixture. However, the separation of CO₂, which must be performed before the methanation reaction, requires an additional reactor and thus a higher cost. To intensify the process a two-purpose reactor, with a mixed bed capable of both CO₂ capture and conversion, can be adopted. This reactor exploits the properties of Dual Functioning Materials (DFM) that can do both tasks at the same time. An exhaustive study of these materials has been done by Omodolor et al. (2020) where a review of several materials for carbon capture and conversion is reported. In a similar work, Park et al. (2021) studied how two materials: a catalyst for the methanation and an adsorber can work together in a bed where the two materials’ pellets are mechanically mixed.

The use of DFM allows both CO₂ adsorption and methanation in the same reactor, but to have a continuous biogas upgrading, it is necessary to have two reactors operating in alternate mode, such that while the first one is upgrading biogas the other can regenerate the bed by converting the adsorbed CO₂ and vice versa. This solution is efficient from an energy point of view since it exploits the energy produced from the exothermic methanation reaction for the endothermic desorption of carbon dioxide. It is, however, important to keep under control the possible formation of hotspots in the reactor bed. For this reason, this technology is mainly used for low CO₂ concentration flows such as flue gas (Miguel et al., 2017; Gharamaleki et al., 2026) and is less utilized for biogas flows where the carbon dioxide concentration can go up to 50%. Dolat et al. (2026) recently proposed a study focusing on the kinetic modelling of CO₂ capture and utilization on NiRu-Ca/Al, showing the trade-off between adsorption capacity and methanation rate with temperature. Moving to high CO₂ concentration flows, the work presented by Martins et al. (2022) developed a process for biogas upgrading and CO₂ valorization. The process uses a pair of packed bed reactors containing a mixture of k-promoted hydrotalcite (for CO₂ sorption) and Ru/Al₂O₃ (for methanation) working in alternate mode at constant temperature with a change in the feed flow according to the phase of the process (biogas for the upgrading phase and H₂ for the methanation). The results of the study indicate high methane productivity, with a reported 70.3% CH₄ purity in the product stream under optimal conditions achieved at 350 °C. However, the authors reported that during the adsorption phase, undesired steam reforming of methane was observed, making the process more efficient at 300 °C to limit this phenomenon.

In this kind of process, it is crucial to keep the temperature under control. Both the adsorption and the methanation are exothermic reactions, and the heat produced must be dissipated to keep the temperature within a certain range. Besides, to take advantage from different optimal temperature of the adsorption and the reactive regeneration step a Temperature Swing Adsorption (TSA) configuration is needed, where adsorption at a low temperature and high temperature regeneration are realized, exploiting the lower adsorption capacity of the material at higher temperatures.

TSA processes can be performed in several ways. Traditional processes may use a hot purge gas or an external heating jacket. More recent studies instead adopted an external electric heater (Kamlekar et al., 2026) or an internal heat exchanger (Chen et al., 2021). To intensify the process, internal conductive structures such as monoliths and foams are used to increase the overall heat transfer coefficient between the bed and the outer wall of the reactor. Another option is to electrify those structures, exploiting the Joule effect to supply heat to the reactor (Perez-Botella et al., 2025).

Among different internal structures, good thermal control can be achieved using Periodic Open Cellular structures (POCS). These are 3D printed periodic structures that, due to a high-engineered geometry, are capable of good heat and mass transfer properties. In particular, the POCS are printed with an outer skin layer that secures optimal contact with the inner wall of a tubular reactor and thus a high heat exchange coefficient (Panzeri et al., 2025). The use of these structures allows also to change dynamically the temperature of the reactor, allowing for low temperature adsorption and high temperature regeneration.

The goal of this work was to study with a 1D heterogeneous dynamic model the performance of a multi-tubular packed POCS reactor used for a two steps cyclic TSAR process. The cycle starts with the biogas upgrading phase where the CO₂ is captured into a solid sorbent, resulting in a high purity biomethane flow. Subsequently, the captured CO₂ is desorbed and reacts with a H₂ flow, producing synthetic methane. Finally, the reactor is cooled down to its initial conditions required for the biogas upgrading phase. The following sections provide a comprehensive overview of the process, explain the model’s governing equations, and present the results from multiple sensitivity analyses.

2 Materials and methods

2.1 Process description

The investigated process proposes an integrated solution for biogas upgrading and valorization of captured CO₂ through methanation. At the core of the process two multi-tubular fixed-bed reactors alternate between CO₂ sorption and methanation phases. Within the reactors’ tubes, a mechanical mixture of CO₂ sorbent and methanation catalyst is packed into aluminum-based POCS. External cooling and heating of the reactor tubes is achieved by high-pressure steam evaporation and condensation. The system operates in alternating cycles: (1) biogas upgrading through CO₂ sorption, and (2) Simultaneous sorbent regeneration and CO₂ methanation. During the second phase, green hydrogen is fed to the reactor, aligning the process with power-to-gas applications. Employing a TSA-like operational approach, where each reactor alternates between process steps, further improves CO₂ conversion from biogas and enhances the yield of pure CH₄.

2.1.1 Process layout

Given the cyclic nature of the process, necessitating a single reactor to alternate between the two main steps, a two parallel reactor solution is proposed. The proposed solution enables continuous biogas processing by alternating each of the two reactors between the adsorption and regeneration phases. Figure 1 presents the proposed process layout including all the connections between the gas storage and the two reactors. Figure 2 instead shows the cycle diagram with the time evolution of a single reactor. In the first step the biogas, after a preheating step, flows through the first reactor where CO₂ is captured. The preheat step is not included in the model and is used to bring the biogas to the reactor operating temperature. After the CO₂ is adsorbed, the biomethane leaves the reactor to reach the biomethane storage vessel, where the products are collected. This vessel can be connected to the grid and is used as temporary storage for methane. The reactor temperature is controlled through the use of saturated boiling water in the external shell of the reactor, removing the heat generated from CO₂ sorption. Subsequently, as the sorbent present inside the reactor is saturated, the flow of biogas is redirected to the second reactor. The first reactor, now completely saturated, undergoes the regeneration step where hydrogen feeding starts and the reactor temperature is increased through heating with saturated condensing steam on the external shell of the reactor. The combined effects of temperature increase and hydrogen feed facilitate the desorption of CO₂, which subsequently reacts with hydrogen over the catalyst pellets to produce methane and water. The resulting mixture, comprising reaction products and unconverted CO₂ with excess hydrogen, exits the reactor and is fed to a condenser, where water is removed. The resulting gas mixture is recycled to the incoming biogas feed and directed to the second reactor, which operates in the adsorption phase of the process. When the reactor’s bed is fully regenerated, the methanation phase ends and the reactor is cooled down to the adsorption temperature by feeding saturated water in the outer shell of the reactor. To purge the reactor during the cooling phase, a portion of previously upgraded biomethane is recirculated within the reactor effectively displacing any unconverted hydrogen from the reactor. During this phase, the first portion of the recirculated biomethane is used as purge gas, being contaminated by the residual products. To avoid losses such contaminated methane is recirculated to the adsorber together with all the methanation products, while in the final stage of the cooling phase biomethane is just used to maintain a proper atmosphere in the reactor and it is sent back to the biomethane storage vessel. Once the reactor’s bed temperature meets the required specifications for the upgrading phase, the cycle ends and is periodically repeated.

2.1.2 Reactor description

This process utilizes multi-tubular reactors with 4 m long tubes having an internal diameter of 3 cm. These sizes are chosen to allow sufficient adsorption capacity while keeping the reactor as compact as possible to allow better heat transfer. For reference, considering a typical biogas plant as described by Nava et al. (2024), a total biogas flow of 500 kg/h is assumed, composed on average of 59%vol. CH₄, 40%vol. CO₂ and 1%vol N₂. To synchronize the two parallel reactors, the inlet flow rate to each tube during the adsorption step is chosen to equal the time required by the adsorption and the regeneration steps. A biogas storage vessel, as shown in Figure 1, is used to accommodate short term fluctuations in biogas composition and flowrate. Besides the reactor was designed at the maximum biogas flow rate. A strategy to cope with long-term decrease is explained in detail in the Supplementary Section S3.

As previously introduced, the catalyst and sorbent pellets are packed inside an aluminum-alloy (AlSi10Mg) periodic open cellular structure (POCS) for enhanced heat transfer capabilities as sketched in Figure 3. Zeolite 13X is considered as CO₂ sorbent and Ru/γ-Al₂O₃ as a catalyst for the CO₂ methanation reaction.

The diamond cell was selected as the POCS geometry for this application, as it is widely utilized and recognized for its high efficiency in heat transfer applications (Panzeri et al., 2025). To grant a high effective conductivity, a relative density 1 − ε P O C S = 0.22 was adopted. At the same time, to maintain good packing capabilities, the chosen cell diameter is 8 mm, which allows the 1 mm particles to densely pack inside the metallic structure. In fact, as reported in Ambrosetti et al. (2020a), the packing efficiency of an open cell depends on the ratio between the window and the pellet diameters (Equation 1).

R = d w i n d o w d p e l l e t (1)

Where the windows diameter (Equation 2) is the dimension of the aperture through which the particles pass and is computed from the cell and strut diameter d c e l l and d s.

d w i n d o w = 6 3 π 0.5 3 4 d c e l l − 3 3 d s (2)

Where d s is obtained from (Equation 3) Ferroni et al. (2021)

ε P O C S = 1 − V P O C S V T O T = 1 − π d s 3 d c 3 3 d c d s + 2 2 3 − 6 (3)

The ratio R should be between 3 and 5, in fact a lower ratio would result in a large ε B e d, higher than 0.45, while increasing the ratio would result in a similar ε B e d but in a worst heat transfer, because the POCS branches are less tight. In this application the ratio R is 4.57.

Two important parameters are the void fractions of the bed inside the void of the POCS, ε B e d and its specific surface S V, which are computed according to Ambrosetti et al. (2020a) (Equation 4) and Ferroni et al. (2021) (Equation 5). In Table 1 are reported the characteristics of the structure.

ε B e d = 1 − V B e d V T O T − V P O C S = 0.375 + 0.018 d p e l l e t d w i n d o w + 0.607 d p e l l e t d w i n d o w 2 (4)

S V = 4 π d s 2 d c 3 3 d c d s + 2 3 − 3 − 2 2 (5)

TABLE 1. POCS geometrical parameters.

2.2 Reactor model

A 1D heterogenous dynamic model of a single reactor tube was developed using gProms software platform. In a previous work, Zanco et al. (2022) modelled the CO₂ adsorption and desorption on zeolite 13X in an externally heated fixed bed reactor. The model here proposed combines the CO₂ sorption kinetics used therein with methanation kinetics reported by Falbo et al. (2018) for Ru-based catalysts. The enhanced heat transfer properties resulting from the presence of the metallic POCS in the reactor tube are modeled as reported by Ambrosetti et al. (2020a) for a packed POCS bed configuration. The model consists of two phases: a pseudo-homogenous phase and POCS phase. The pseudo-homogenous phase accounts for the catalyst pellets, the sorbent pellets, and the reacting gas mixture. On the other hand, the POCS phase accounts for the metallic POCS, which is considered inert to all the chemical reactions taking place in the reactor tube and affects only the heat transfer properties.

2.2.1 Governing equations

The overall mass balance equation for the pseudo-phase (Equation 6) consists of an advective transport term and the adsorption term which accounts for the mass loss caused by the CO₂ adsorption.

ε B e d u ∂ G ∂ t = − ∂ G ∂ z + 1 − φ C a t ε P O C S 1 − ε B e d M W C O 2 r a d s (6)

The i-species mass balance equation for the pseudo-phase (Equations 7a, 7b) consists of an advective transport term and two consumption/production term representative of both the methanation reaction and the CO₂ adsorption. φ C a t is the catalyst volumetric fraction with respect to the total bed volume (Equation 8).

ε B e d ∂ C i ∂ t = − ∂ u C i ∂ z − 1 − φ C a t ε P O C S 1 − ε B e d r a d s + φ C a t ε P O C S 1 − ε B e d ν i r m e t f o r i = C O 2 (7a)

ε B e d ∂ C i ∂ t = − ∂ u C i ∂ z + φ C a t ε P O C S 1 − ε B e d ν i r m e t f o r i ≠ C O 2 (7b)

φ C a t = V C a t a l y s t V B e d (8)

The sorbent was considered totally selective and CO₂ adsorption rate in the mass balance uses a linear driving force as used by Karka et al. (2019) (Equation 9). The saturation condition (q C O 2 *) was computed according to local temperature and partial pressure as indicated in Hefti et al. (2015).

r a d s ρ s = d q C O 2 d t = K C O 2 q C O 2 * − q C O 2 (9)

The pseudo-phase energy balance equation (Equation 10) consists of an axial energy conduction term, axial advective energy transfer, heat exchange with the POCS and with the coolant, and energy production due to both methanation and adsorption exothermicity. The heat capacity term that considers the contribution of the bed (c p s), gas (c p g) and steel tube (c p T) as well. ε T is a fractional term computed as a ratio between the volumes of the steel tube and the pseudo phase used to account for the extra inertia provided by the tube.

ε P O C S 1 − ε B e d ρ s c p s + ε T ρ T c p T + ε B e d ρ g c p g ∂ T ∂ t = − u ρ g c p g ∂ T ∂ z − 1 − φ C a t ε P O C S 1 − ε B e d r a d s Δ H a d s + φ C a t ε P O C S 1 − ε B e d r m e t Δ H m e t + U P O C S − B e d S V T P O C S − T + k e f f , B e d ∂ 2 T ∂ z 2 + 4 D h B e d T E x t e r n a l − T (10)

The packed-bed effective axial thermal conductivity (k e f f , B e d) and the heat transfer coefficient between the POCS and the pseudo-phase (U P O C S − B e d) are calculated as reported by Balzarotti et al. (2020). The reaction enthalpy (Δ H m e t) is calculated as a function of the pseudo-phase temperature.

The POCS energy balance equation (Equation 11) considers the axial heat conduction term through the solid structure, and heat exchange with the pseudo-phase and with the external coolant.

1 − ε P O C S ρ P O C S c p P O C S ∂ T P O C S ∂ t = U P O C S − B e d S V T − T P O C S + k e f f , P O C S ∂ 2 T P O C S ∂ z 2 + 4 D h P O C S T E x t e r n a l − T P O C S (11)

Effective conductivity k e f f , P O C S was computed from the bulk phase conductivity, according to Bracconi et al. (2018); Bracconi et al. (2020).

The modified Ergun equation (Equation 12) for packed foam (Ambrosetti et al., 2020b) was used for pressure drop calculation. This equation was chosen to account for both laminar (viscous losses) and turbulent (inertial losses) flows.

d p d z = − 4.17 S V T O T 2 ε T O T 3 μ g u + 0.292 S V T O T ε T O T 3 ρ g u 2 (12)

Where ε T O T and S V T O T are the porosity and the surface area obtained by considering both the contribution of the POCS and of the packed bed pellets (Equation 13; Equation 14).

ε T O T = ε P O C S ε B e d (13)

S V T O T = S V + 6 ε P O C S − ε B e d d p e l l e t (14)

Last, the boundary conditions used in the model are reported in Table 2.

TABLE 2. Boundary conditions.

Rate equations and parameters of the adsorption, desorption and methanation kinetics, together with the heat transfer model are reported in the supplementary material, in Supplementary Sections S1.1–S1.3 respectively.

2.2.2 Model solver

Multiflash tool was used for the calculation of all the physical and chemical properties of the gas mixture, according to the Soave-Redlich-Kwong equations.

The DA Solver of gPROMS software platform was used to implement Back Differentiation Formula (BDF) with variable time step as a solver for the differential algebraic model equations. A first order Backward Finite Difference Method was used for the discretization of the axial reactor coordinate using 60 discretization points along the axial coordinate in an equal-spaced grid. Further increasing of the number of discretization points was checked to have negligible effect on the results.

2.2.3 Key performance indicators

To better evaluate the performance of the configurations investigated it is necessary to define a set of Key Performance Indicators (KPIs). The first indicator considered is the size of the reactor. In fact, given a target biogas flow that needs to be upgraded, it is possible to compute the number of tubes needed in the reactor, by calculating the inlet flow to the single tube which equals the adsorption and the regeneration time. For all the simulations the tube geometry was kept the same. The second KPI is the percentage of CO₂ converted each cycle. The last performance indicator selected is the purity of synthetic methane produced during the methanation step of the process. In fact, having a lower purity does not necessarily mean that the conversion of CO₂ is lower, but can be caused also by a large amount of unconverted H₂. The selected KPIs are summed up in Table 3 where n ˙ C O 2 I N and n ˙ C O 2 O U T are the carbon dioxide molar flow rates respectively at the inlet and at the outlet of the reactor, t 0 the cycle starting time, t A d s and t D e s the time at which respectively the adsorption and desorption phases end and last t f is the finishing time. As previously mentioned, the inlet flow rate to the single tube was changed to equal adsorption and regeneration times: Equation 15.

t A d s − t 0 = t f − t A d s (15)

TABLE 3. KPIs.

3 Results

3.1 Benchmark case

A benchmark condition was first established, involving a simple cycle where biogas upgrading continues until the bed reaches complete saturation. At this point, feeding biogas to the reactor stops, the reactor is heated, and hydrogen is introduced to begin the methanation step. Once all adsorbed CO₂ is released, indicated by a rise in the molar fraction of H₂ at the reactor outlet, the hydrogen feed ceases, and biomethane is supplied to purge any remaining hydrogen from the reactor. Simultaneously, the reactor is cooled to 200 °C to prepare it for the next cycle. The reactor’s operating conditions throughout the cycle are detailed in Table 4.

TABLE 4. Reactor operating conditions for the benchmark case.

Figures 4a,b presents the i-species flow rates temporal evolution at the outlet of the reactor during the different stages of the process, As shown in Figure 4a, at time zero, a biogas stream of 20 NL/min, containing 60%vol. CH₄ and 40%vol. CO₂ at 200 °C, is fed to the reactor, resulting in 342 tubes needed to process a total of 500 kg/h of biogas. The fed biogas purges the excess hydrogen together with residual synthetic methane present in the reactor from the prior cycle, as demonstrated by the stream composition at the reactor outlet shown in Figure 4b. As the process progresses, a continuous flow of purified biomethane exits the reactor, facilitated by the sorbent within the reactor that efficiently captures CO₂. It is worth mentioning that the exothermic CO₂ adsorption results in local temperature increase that identifies the sorbent saturation front along the reactor axis. As the sorbent progressively become saturated, the adsorption front resulting in the local temperature raise moves towards the reactor outlet, as evident in Figure 4c showing the temperature evolution for several axial points along the reactor length. As soon as the sorbent becomes completely saturated, CO₂ concentration in the outlet flow increases. When the molar fraction of CO₂ at the outlet of the reactor exceeds 2%, the biogas feed is stopped. Then a steady stream of green hydrogen is fed in parallel to the biogas flow to the reactor with a flow rate of 40 NL/min at 350 °C. Simulations were performed also with a H₂ feed temperature of 100 °C, showing a small influence of the flow temperature on the process performance, resulting in a 0.1% reduction in CO₂ conversion. Simultaneously, the reactor is heated externally to 350 °C by condensing steam in the outer shell of the multi-tubular reactor. Nevertheless, for the initial part of the methanation step of the process, CO₂ slip continues and no H₂O exits the reactor indicating a delay between hydrogen feeding and the outcome of methanation products at the outlet of the reactor. Successively, a mixture of CO₂, CH₄, H₂O, and H₂ exits the reactor. The complex nature of the methanation phase of the process, combining the two chemical steps, CO₂ desorption and catalytic methanation reaction, with the typical heat and mass transport phenomena in an externally heated reactor tube explains the presence of the different species in the outlet of the reactor. The concentration of CO₂ in the gas phase is governed by the dynamic balance between desorption and methanation reaction kinetics. Gradual heating of the reactor, governed by heat transfer rate and thermal capacity, facilitates CO₂ desorption, which is further supported by a decrease in the partial pressure of CO₂ due to H₂ feed. At lower reactor temperatures, methanation rate is limited, resulting in the slip of considerable quantities of desorbed CO₂ and unreacted H₂. As the reactor temperature rises, the formation of synthetic methane becomes apparent, accompanied by increased H₂O production and a corresponding decrease in H₂ flow rate at the reactor outlet. CO₂ desorption and methanation progress until the complete regeneration of the sorbent made evident by an increase in the H₂ flow rate exiting the reactor and a drop in the methane and H₂O flow rates. In particular, the methanation phase ends when the CH₄ flow rate is less than 2 mmol/s. The final step of the cycle is reactor cooling, where biomethane is fed to the reactor with a flowrate of 12 NL/min at 200 °C and, at the same time, the reactor is externally cooled to 200 °C. Biogas feeding and the cycle restarts as soon as the temperature at the reactor outlet reaches 205 °C. Since the benchmark case does not operate under optimized conditions and the operating conditions are chosen to analyze the reactor’s behavior during complex adsorption and reactive regeneration cycles, the calculated performance results are far from optimal. In this scenario, the amount of CO₂ adsorbed is 2.32 mol/cycle, the CO₂ conversion is 43.7%, and the synthetic methane purity is 26.4%vol.

A better understanding of the complex nature of the methanation step can be obtained by examining the axial evolution of the reactor temperature and the molar composition of the reacting species along the reactor axial coordinate. Figure 5 illustrates the evolution of axial profiles during the initial 60 s of the methanation step. At t = 0 s, as the process transitions from the adsorption to the methanation step, the sorbent within the reactor is nearing full saturation, with only the final segment of the reactor bed remaining partially available. Although high-purity biomethane is obtained at the reactor outlet during the adsorption step, the reactor gets filled with biogas with an elevated CO₂ concentration as the sorbent gets converted. Upon feeding of H₂ at 350 °C as inlet temperature and gradual heating of the reactor, CO₂ desorption occurs, followed by the CO₂ methanation reaction, which is evidenced by H₂O formation. Both processes accelerate on increasing the reactor temperature until the sorbent is fully regenerated. Noteworthy, a significant proportion of CO₂ desorbs upon H₂ introduction, reducing the CO₂ partial pressure, even before the catalyst reaches its activation temperature resulting in the calculated low CO₂ conversion.

3.2 Effect of operating parameters

The performances of the proposed process were assessed through a sensitivity analysis that simulates the impact of four operating variables. Specifically, the variables considered are the cycle pressure, the temperatures during both adsorption and desorption phases, and the hydrogen flow rate in the methanation step. The study was conducted considering a single pass configuration without recycling the outlet stream of the methanation step to the feed biogas in the adsorption step. The other parameters that were not explicitly varied during the optimization process will remain consistent with the benchmark case values.

3.2.1 Operating pressure

Firstly, the sensitivity of the results on the pressure was evaluated by varying the operating pressure between 15 and 35 bar Figure 6 shows that increasing the operating pressure positively affects the CO₂ conversion and the amount of biogas processed in a single tube, reducing the overall reactor size. On increasing the operating pressure from 15 to 25 bar the reactor size decreases from 415 to 342 tubes, thanks to the increase in CO₂ adsorption capacity of the sorbent, and CO₂ conversion improves from 39.4% to 43.7% due to a kinetic effect. On increasing the operating pressure to 35 bar, a further improvement in the process performance was computed, where the reactor size reaches 309 tubes and the calculated CO₂ conversion is 47.0%.

It is worth mentioning that setting 25bar as the upper operating pressure limit is recommended in order to avoid an additional hydrogen compression stage downstream the electrolyser. In fact, a recent study about high pressure fuel cells, (Hancke et al., 2024), indicated that operating the electrolyser at pressures up to 30 bar increases the cell efficiency, whereas higher pressures showed negative effect on the performance. Thus, an operating pressure of 25 bar was selected for all simulations presented in this work, in order to account for hydrogen transportation losses.

Being that increasing the pressure allows the reactor to store more CO₂, resulting in higher rate of CO₂ released during the methanation step, the hydrogen flow rate during the methanation step was varied to maintain excess of hydrogen during the methanation step. For the simulation at 15 bar, the H₂ flow rate per single tube was set to 30 NL/min raising to 48 NL/min on increasing the pressure to 35 bar.

3.2.2 Adsorption step temperature

Moving on to the second parameter subject to the sensitivity analysis, Figure 7 presents the impact of the coolant temperature during the adsorption step of the process.

Operating the adsorption step at a higher temperature (i.e., closer to the temperature of the subsequent methanation step) improves overall process performance by reducing the reactor heating time. A higher initial temperature for methanation allows the catalyst to reach its activation temperature more quickly, thereby enhancing CO₂ conversion. However, operating the adsorption step at higher temperature leads to a notable reduction in the CO₂ sorbent’s capacity, requiring more adsorber to be packed into the reactor, thus a bigger number of tubes. As a trade-off, the adsorption step reactor temperature chosen for the following simulations is 200 °C.

3.2.3 Hydrogen flow rate

Regarding the amount of H₂ that needs to be fed into the reactor during the regeneration step, it is important to strike a balance between having high CO₂ conversion and having a low amount of unconverted hydrogen in the products. A higher hydrogen rate can shift the reaction equilibrium towards methane production, but a high hydrogen excess will result in lower methane purity in the reaction products. Additionally, green hydrogen is highly valuable; therefore, its use should be minimized.

Figure 8 presents the impact of the H₂ feed flowrate in the methanation step. As evident from the results, an increased hydrogen flow rate positively affects CO₂ conversion, rising from 40.3% H₂ feed of 30 NL/min to 45.6% with H₂ feed of 50 NL/min. The CO₂ conversion grows moderately to 46.7% upon increasing the H₂ feed to 60 NL/min. On the contrary, the methane purity is constantly decreasing from 28.9% to 21.5%, passing from 30 NL/min to 60 NL/min, with a 26.4% purity at 40 NL/min.

3.2.4 Regeneration step temperature

The proposed process involves using aluminum-based POCS as conductive internals inside the reactor tubes. Since additive manufacturing is commonly used to produce POCS, the AlSi10Mg alloy was chosen for its strong mechanical properties and excellent compatibility with 3D printing (Aboulkhair et al., 2019; Fulcher et al., 2014). Since the thermal expansion of the POCS is expected to be higher than that of the reactor steel tube, compressive stress will develop in the POCS. Combined with fatigue stress from repeated heating and cooling cycles, this could result in mechanical failure of the POCS. Accordingly, to prevent premature damage to the internal structure, the upper limit of the reactor temperature is set to be 350 °C. According to Uzan et al., 2018, at 350 °C the ultimate tensile strength of AlSi10Mg drops to just one-tenth of its strength at room temperature.

Figure 9 shows the effect of the reactor temperature during the methanation step of the process KPIs. As a general trend, increasing the reactor temperature has a favorable effect on the performance of the reactor. CO₂ conversion increases from 40% to 44% on increasing the outer wall temperature of the methanation step from 310 °C to 330 °C. Upon further increase in the methanation temperature the conversion remains almost the same with very small variation. Similarly, CH₄ purity increases with temperature, rising from 22% at 310 °C to 25% at 330 °C. Even though the maximum CO₂ conversion was calculated at 330 °C, the CH₄ purity further increases with the reactor temperature. This behavior can be explained by the fact that, despite regeneration temperatures closer to the adsorption one may facilitate the heating/cooling transients, the methanation reaction kinetics is not fast enough to cope with the CO₂ desorption one at lower temperature.

High temperatures in this application are needed to fully activate the catalyst, but having saturated steam as heating fluid at 350 °C is close to the technical limit. A more active catalyst would help to solve this issue taking advantage of the smaller gap between adsorption and reaction temperature. This is shown in Figure 10, where CO₂ conversion and CH₄ purity performances are plotted as a function of a multiplying activity factor, assuming a heating temperature of 300 °C. Results in Figure 10 show that the methane purity is already higher than in the benchmark conditions with twice the activity, while, to achieve CO₂ conversion of the benchmark, a 3 times more active catalyst is necessary.

3.3 Process optimization strategies

To improve the performance of the proposed process, three different strategies were evaluated. Firstly, the impact of the partial utilization of the reactor adsorber will be presented. Then simulations performed applying reactor bed layering will be shown, where a non-uniform sorbent to catalyst ratio was used along the reactor axial coordinate. Finally, the impact of recycling the regeneration step products to the feed biogas will be discussed.

3.3.1 Partial adsorber utilization

As stated previously, CO₂ desorption at low reactor temperature, hence with low slow methanation kinetics, results in high CO₂ slip and significant reduction in the overall conversion. To reduce this phenomenon, partial bed utilization strategies could be implemented. In fact, by using only a portion of the bed in the upgrading step, leaves unsaturated sorbent at the tail end of the reactor where the prematurely desorbed CO₂ can be trapped for successive conversion when the conditions are more favorable to the methanation reaction. Practically, being that the adsorption front travels along the reactor like a wave, local temperature increase can indicate the front of sorbent saturation. Utilizing several temperature indicators along the reactor axial coordinate would facilitate the detection of the local hot spot which identifies the local CO₂ adsorption as presented in (Figure 4c).

Figure 11 illustrates the axial profiles of temperature and composition for the methanation step utilizing only 75% of the sorbent in the reactor. During the first stage of the regeneration step, part of the CO₂ filling the reactor along with the desorbed CO₂ from the reactor inlet part, gets adsorbed in the initially unconverted sorbent at the final portion of the reactor. Figure 12 compares the i-species flow rates exiting the reactor in the benchmark case (dashed lines) with those of the partial adsorber utilization case herein discussed (solid lines), showing that lower flow rates of unconverted CO₂ are calculated for the partial sorbent utilization case. It is possible to notice how the amount of CH₄ produced is about the same for the two cases, while the amount of unconverted CO₂ is sensibly lower. This happens because there is no substantial difference regarding the methanation reaction, the main advantage here is the recapture of previously desorbed CO₂ that can be converted into CH₄ in the last portion of the bed. The drawback of adopting this strategy is the reduction of the flow rate of biogas entering the tube during the adsorption phase. In fact, by utilizing 75% of the sorbent, it is necessary to reduce the feed by 25% to achieve the same duration of the adsorption and the regeneration phases, resulting in an increase in the number of tubes required for the reactor (456 instead of 342).

The effect of partial bed utilization on the key performance indicators is illustrated in Figure 13. A significant increase in the CO₂ conversion was calculated, rising from 44% for the benchmark case to 61% on utilizing 62.5% of the sorbent. A slight increase in methane purity is calculated as well, reaching 32% on utilizing 62.5% of the sorbent.

3.3.2 Bed layering

The second optimization strategy evaluated is the bed layering where a non-uniform sorbent to catalyst ratio is utilized along the reactor length. As detailed in Section 3.1, the observed low CO₂ conversion is primarily attributed to high CO₂ slip, which results from the slower kinetics of the methanation reaction compared to CO₂ desorption. The reduction in CO₂ partial pressure upon feeding H₂ into the reactor shifts the equilibrium towards CO₂ desorption and limited methanation catalyst activity at low reactor temperatures results in the high CO₂ slip and low computed CO₂ conversion.

The reactor is divided into two sections: an initial zone containing only CO₂ sorbent without methanation catalyst, and a final section with a mixture of the catalyst and the sorbent. Two cases were analyzed, each utilizing the same total amount of catalyst but differing in the distribution of the catalyst’s volumetric fraction along the final section of the reactor. Case A considers all the catalysts stock to be distributed homogenously in the last meter of the reactor bed (0.8/0.2 catalyst/sorbent ratio), dividing the reactor into two different homogeneous sections. The second simulated case, Case B, accounts for a gradual increase of the catalyst fraction from 0 to 1 of the reactor bed in the second section of the reactor starting from 2.4 m.

Also in these simulations, 75% of the sorbent was used during the CO₂ adsorption step. In particular, for both Case A and B, 75% of the sorbent is used when a temperature increase is noticed at z = 2.4 m. A difference with respect to the previous simulations is that the steam temperature during the regeneration step was reduced from 350 °C to 340 °C to compensate for the hotspot caused by the concentration of the catalyst in the last portion of the bed.

Table 5 highlights the results of the simulations performed for each bed layering configuration in comparison with the benchmark case and the partial bed utilization case. Evidently, the highest CO₂ conversion was calculated for layering Case A, however, this arrangement results in a hot spot with a temperature reaching up do 462 °C (Figure 14a) exceeding the limitations set for the structural integrity of the POCS. Case B provides an acceptable compromise resulting in a slightly lower CO₂ conversion with a marked reduction of the maximum hot spot temperature of the reactor, keeping within the required design range (Figure 14b). A comparison between Layering case B with 75% bed utilization without layering is presented in S.I. Supplementary Figure S1.

TABLE 5. Comparison between different bed configurations.

3.3.3 Recycle of the regeneration step products

As previously discussed, even on applying different reactor optimization strategies, it is not possible to reach a complete conversion of CO₂, hence a sufficiently high CH₄ purity during the methanation step. Given that the mixture obtained from the regeneration step has similar concentrations of CO₂ and CH₄ to the feed biogas, although with a significant H₂ concentration, one possible processes optimization strategy is recycling, upon water removal, the outlet stream from the regeneration step to biogas feed to the adsorption step, as already indicated in Figure 1. A simplified scheme representing the proposed process is reported in Figure 15 showing the main streams. The average flow rates of each of these streams, reported in Table 6, were computed considering two parallel reactors, cycling between the steps of the process to treat a constant stream of biogas. The composition of the streams reported in Table 6 was calculated at dry conditions, considering an average flow rate of removed water of 4.9 NL/min. For simplicity a complete removal of water from the products was considered, based on the fact that at 25 °C and 25 bar the residual water fraction would be just 0.13%.

TABLE 6. Flow rates and volume composition of the main cycle streams in the recycle configuration.

During the cooling step, the recirculated biomethane corresponds to approximately 60% of the upgraded methane stream. In addition, about 10% of the total methane becomes contaminated with methanation products during the purge phase. This contaminated methane is recirculated together with the methanation products (Flux D in Figure 15), to avoid losses.

With the same operating conditions used for the simulated case “Layering B”, except for a slight increase in the H₂ flow rate from 40 NL/min to 50 NL/min, the process can treat a biogas stream of 500 kg/h having the composition presented in Table 6, to produce a stream of methane and hydrogen with very low concentration of CO₂. This configuration allows a conversion of 64.7% per passage. Overall CO₂ conversion increases up to 99.4%. Additional inlet flow rate to the adsorber associated with the recycle results in a marked increase of the number of tubes (1092) needed to keep the adsorption phase equal to the regeneration one.

The outlet stream of this process (Strem B) has potential to be used in most of the common applications as the product mixture has a lower heating value of about 48 MJ/kg or to be injected into the future natural gas grid that is expected to accommodate significant quantities of hydrogen (European Clean Hydrogen Alliance, 2025).

4 Conclusion

A two-step Temperature Swing Adsorption/Reaction (TSAR) process was investigated by model simulation for simultaneous biogas upgrading and CO₂ valorization through catalytic methanation. The proposed dual-function adsorber/reactor employs a mixed bed of Zeolite 13X and Ru/γ-Al₂O₃ packed within aluminum-based Periodic Open Cellular Structures (POCS), which provide superior heat transfer rates enabling an effective heat management during cyclic operation.

Simulation results show the performance of the single pass cycle. Under benchmark conditions (25 bar, 200 °C–350 °C), the process achieved 43.7% CO₂ conversion and 26.4%vol CH₄ purity during the methanation phase, with 2.32 mol CO₂ adsorbed per cycle. Sensitivity analyses showed that higher operating pressure and optimized H₂ feed enhance CO₂ conversion up to 47%, while excessive hydrogen leads to a reduction in CH₄ purity due to unreacted H₂ slip. The reactor temperature was identified as a critical parameter, with optimal methanation performance achieved at 330 °C–350 °C, consistent with the thermal stability limits of AlSi10Mg-based POCS. Further reduce in temperature can be achieved with a more active catalyst.

Implementation of process optimization strategies significantly improved performance. Partial bed utilization (75%) increased CO₂ conversion to 58% A further improvement is obtained layered bed configurations combining sorbent and catalyst yielding CO₂ conversions up to 62.4% with a maximum temperature increase of around 10 °C. Finally, recycling of methanation products to the adsorption step allows an overall CO₂ conversion up to 99.4% with an enhanced CH₄ purity of 83 %vol. Such an improvement would require to increase the reactor size from ∼500 to ∼1100 tubes.

These results demonstrate that the TSAR process effectively couples CO₂ capture and utilization within a compact cyclic system, enabling the simultaneous production of biomethane and synthetic methane with reduced carbon emissions. The combination of reactive regeneration and conductive structured internals represents a promising intensification pathway for sustainable biogas upgrading and Power-to-Gas applications.

Overall, this computational study shows a promising potential of the TSAR process for biogas upgrading to biomethane. However, future experimental validation will be needed to demonstrate the feasibility in real life operation (e.g., in the presence of contaminants).

Generative AI statement

The author(s) declared that generative AI was not used in the creation of this manuscript.

Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fceng.2026.1800980/full#supplementary-material

Supplementary material Supplementary material at the source

Glossary

Δ H a d s Adsorption enthalpy (k J / k m o l) Δ H m e t Reaction enthalpy (k J / k m o l) ε B e d void fraction of the bed packed in POCS ε P O C S POCS void fraction ε T O T Total reactor void fraction μ g Gas viscosity (P a s) ν i Stochiometric coefficient ρ g Gas density (k g / m 3) ρ P O C S POCS density (k g / m 3) ρ s Bed density (k g / m 3) ρ T Steel tube density (k g / m 3) φ C a t Catalyst to bed ratio χ C O 2 CO₂ conversion C i Gas concentration (m o l / m 3) c p g Gas heat capacity (k J / k g K) c p P O C S POCS heat capacity (k J / k g K) c p s Bed heat capacity (k J / k g K) c p T Steel tube heat capacity (k J / k g K) D Tube inner diameter (m) d c POCS cell diameter (m) d p e l l e t Pellet diameter (m) d s POCS strut diameter (m) d w i n d o w POCS window diameter (m) G Mass flux density (k g / m 2 s) h B e d Bed overall heat transfer coefficient (k W / m 2 K) h P O C S POCS overall heat transfer coefficient (k W / m 2 K) K C O 2 Adsorption mass transfer constant (1 / s) k e f f B e d Bed effective thermal conductivity (k W / m K) k e f f P O C S POCS effective thermal conductivity (k W / m K) M W Molar weight (k g / k m o l) n i ˙ Species molar flow rate (N L / ⁡ min) n I N − S i n g l e T u b e Total flow rate entering a single tube (N L / ⁡ min) n T O T − R e a c t o r I n l e t Total flow rate at the reactor inlet (N L / ⁡ min) p Pressure (b a r) q C O 2 Adsorption capacity (m o l / k g) q C O 2 * Adsorption capacity at equilibrium R POCS aspect ratio r a d s Adsorption rate (m o l / m 3 s) r m e t Reaction rate (m o l / m 3 s) S V POCS surface to volume ratio (1 / m) t Time coordinate (s) t 0 Cycle starting time (min) t a d s Adsorption step finish time (min) t d e s Desorption step finish time (min) t f Cycle finish time (min) T Pseudo-phase temperature (K) T E x t e r n a l External fluid temperature (K) T P O C S POCS temperature (K) u Gas velocity (m / s) U P O C S − B e d POCS to bed heat transfer coefficient (k W / m 2 K) z Axial coordinate (m)

Footnotes

Edited by: Yongliang Yan, Newcastle University, United Kingdom

Reviewed by: Michael Short, University of Surrey, United Kingdom

Jackline Mwende Mutunga, Kenyatta University School of Engineering, Kenya