Transient Effects during Dynamic Operation of a Wall-Cooled Fixed-Bed Reactor for CO₂ Methanation

2.1 Stationary and Transient Isothermal Kinetic Measurements

The setup for the isothermal kinetic measurements (Fig. S1 in Supporting Information) consists of a gas dosing unit, a small fixed-bed reactor, and a gas analysis. The feed rates of the gases H₂, CO₂, N₂, and CH₄ were adjusted by mass flow controllers. Steam was added by a water saturator and the respective pipes were heated to prevent condensation. All experiments were conducted with a volumetric flow rate of 50 L h⁻¹ (STP) and at 1 bar.

The lab-scale reactor was externally heated and cooled by a thermo-oil thermostat to provide isothermal conditions. The reactor had a diameter of only 1.4 cm and was charged with 1.5 g (1.8 g for transient experiments) of catalyst particles (NiSat 310 RS from Clariant) diluted with 7.5 g of inert quartz sand to ensure isothermal conditions. The bed length was about 5 cm. Data of the catalyst are given in Tab. 1.

For temperature measurements to prove isothermal conditions, a guiding tube for a thermocouple with a diameter of 2 mm was placed in the center of the tubular reactor.

For the steady-state and isothermal kinetic experiments, the product gas passed through cooling traps at 0 °C and at –78 °C, respectively, and was then analyzed by a gas analyzer (Fisher-Rosemount MLT 2) for CO, CO₂, CH₄, and H₂. The experiments were conducted in a temperature range from 170 °C to 230 °C with syngas consisting of 4–20 % CO₂, 5–80 % H₂, 0–45 % H₂O, and 0–25 % CH₄. Nitrogen was only added to adjust the concentrations, e.g., to vary the concentration of only one reactant.

For the transient kinetic experiments the product gas was analyzed by a mass spectrometer (Pfeiffer MS Thermostar). By this, the response time of the gas analysis to a change of the adjustment of the mass flow controllers was lower than 10 s. In addition, a small amount of helium (1 L (STP) h⁻¹; typically 2 % of the total gas flow) was continuously added as an inert internal standard allowing the detection of volume flow fluctuations, e.g., an increasing signal of helium indicates a lower volume flow. Furthermore, the helium signal was used for the dead-time correction. The step change experiments between two concentrations were performed at 220 °C and the response signal was observed.

2.2 Transient Volume Flow Step Change Experiments with a Cooled Single-Tube Methanation Reactor

For the cooled single-tube methanation reactor (Fig. S2), a mass flow controller for a premixed syngas (63 % H₂, 15.3 % CO₂, and 21.7 % N₂) was applied. The reactor was a jacketed stainless-steel tube (inner diameter 2 cm, length 1 m). It was heated and cooled by an oil thermostat (LAUDA USH 400) and contains a 10-cm filling of glass spheres for consistent conditions at the inlet and subsequent 88-cm filling of catalyst. A guiding tube in the center of the reactor (3 mm diameter) over the total length was used to measure the axial temperature profile by means of a movable thermocouple.

Two cooling traps were placed downstream of the reactor to condense the product water, one at room temperature and the other one at 0 °C. The dry gas composition was analyzed by an infrared gas analyzer for CO, CO₂, as well as CH₄ and a thermal conductivity detector for H₂.

For axial temperature profile measurements, a sled driven by a stepper motor moved the thermocouple downwards the reactor. A computer controlled the mass flow controller in the same way as the stepper motor moved the thermocouple and recorded the measured temperature and gas concentration data from the gas analyzer. The experiment started with a volume flow of 60 L h⁻¹ for 45 min at a cooling temperature of 183 °C. Then, a step change of the flow to 7.5 L h⁻¹ was conducted for 45 min. This procedure was also done with a reverse step change (7.5 L h⁻¹ → 60 L h⁻¹).

To record the transient temperature profile with only one thermocouple (Fig. S3), both experiments were repeated 29 times at different positions of the thermocouple inside the reactor. Hence, the total experimental time of both step change experiments was 45 h. Within the first 10 cm of the reactor – the hotspot region – the temperature was measured in intervals of 1 cm. For the next 10 cm of the reactor length, the thermocouple was moved in intervals of 2 cm and from this part of the reactor onwards to the end of the catalyst bed in the reactor in intervals of 5 cm.

4.1 Steady-State Kinetics of Methanation

Various approaches for the kinetics of CO₂ methanation are given in the literature ^25-27. In this work, a Langmuir-Hinshelwood-Hougen-Watson (LHHW) approach was chosen as it allowed the best prediction of the reaction rate over a wide range of conditions. The rate equation is taken from Koschany's approach for a Ni/AlO_(x) catalyst ²⁵:

(5)

The constants k_m and K_1–3 depend on temperature and can be described by the Arrhenius (Eq. 6) and van't Hoff equation (Eq. 7), respectively.

(6)

(7)

The equilibrium constant K_p (in Pa⁻²) was calculated according to the equation developed by Aparicio ²⁸ (with T in K):

(8)

Due to low conversion of CO₂ (< 15 %), differential conditions are assumed. A high conversion of CO₂ and thus a high concentration of steam were simulated by addition of H₂O to the feed gas. All experimentally determined parameters are listed in Tab. 3.

LHHW approaches contain different mechanistic assumptions, but there is still no agreement about the reaction steps actually occurring ²⁹. The reaction orders of H₂ and CO₂ (both 0.5) were determined by experiments with varied concentration of both components (for CO₂ see also Fig. 1). The order for CO₂ indicates a dissociative adsorption of CO₂ into CO and atomic O on the surface followed by CO methanation ¹⁸, ³⁰; the reaction order of H₂ can be explained by dissociative adsorption. Thus, CO₂ and H₂ each occupy two active sites. For SNG production, a high conversion of CO₂ is demanded. This yields significant amounts of CH₄ and H₂O, and product inhibition may occur. Thus, the influence of both product compounds on the methanation kinetics was also investigated. The experimental data gave no evidence for an influence of methane, but steam (water) is an inhibiting agent (Fig. 1).

Fig. 1 shows a decreasing reaction rate for constant H₂ and CO₂ partial pressures caused by an increasing partial pressure of water; this was also observed by Marwood et al. ¹⁹, who reported a decreasing CO coverage on the catalyst when water was added, and thus a reduction of adsorbed C-species. In the literature ²⁵, ³¹, ³², the reaction order of water in the respective adsorption term is assumed to be unity.

Inhibition effects are represented by the adsorption terms for CO₂, H₂, and H₂O in the denominator of the LHHW approach. The strength of each inhibition is indicated in Tab. 4 by the comparison of the respective adsorption terms at a typical reaction temperature of 220 °C and different degrees of CO₂ conversion. Inhibition by H₂ and CO₂ declines with increasing conversion; for steam this is reverse.

The inhibiting effect of steam on the rate and conversion of CO₂, respectively, is also demonstrated in Fig. 2; just for comparison, the hypothetical case without H₂O inhibition is also depicted. Up to 20 % CO₂ conversion, the formed steam has almost no influence on the rate, but at higher conversion, inhibition becomes more and more relevant. Note that for the conditions given in Fig. 2 (220 °C, 1 bar, 20 % CO₂, 80 % H₂), the thermodynamic equilibrium conversion of CO₂ is 98.4 %. Almost full conversion can only be reached for lower temperatures (e.g., X_CO2,eq = 99.3 % at 180 °C), and higher temperatures are unfavorable with regard to CO₂ methanation (e.g., X_CO2,eq = 94.9 % for 300 °C).

Finally, a parity plot of the experimental results is presented in Fig. 3. The agreement of measured and calculated values is mainly in a range of ± 10 %.

4.2 Transient Response on the Kinetics on Partial Pressure Step Changes

In Sect. 4.1 the intrinsic steady-state kinetics were discussed. However, for dynamic operation it is necessary to know how fast the catalyst responds to changes of the reaction conditions such as the inlet gas composition, and whether and how fast steady-state conditions are again reached. Therefore, step change experiments were conducted. For example, if the time delay is very short, the kinetics determined at steady-state kinetics can be assumed to be valid also for a transient operation of a reactor, which simplifies the respective modeling.

The transient kinetic experiments were conducted under isothermal conditions. A mass spectrometer was used to analyze the feed and product gas. With helium as internal standard, changes of the volume flow during the initial phase of the step change and the dead time, respectively, could be identified and separated from real catalyst effects. The focus of the transient experiments was to investigate the influence of a stoichiometric change of the partial pressures of H₂ and CO₂ (Figs. 4 and 5) as well as of H₂O (Fig. 6).

Figure 4 reveals that the catalyst responds fast to a partial pressure step change of the feed gases CO₂ and H₂ from initially low to high values. The H₂-to-CO₂ ratio was thereby kept constant at a value of 4. While the contents of CO₂, H₂, and CH₄ are already constant after about 25 s, the water content exhibits a certain delay before a stable value is achieved. Obviously, water, which is formed to a higher extent after the step change compared to before, adsorbs on the surface until the corresponding new adsorption equilibrium is reached. This corresponds to an initially slightly higher conversion (lower content) of CO₂ compared to the finally reached stationary value as water adsorption inhibits the reaction rate.

This behavior is similar but now in the reverse direction, if the step change is done from high to low partial pressures of CO₂ and H₂ (Fig. 5). Again, the new adsorption equilibrium for water is established with a certain delay as compared to H₂ and CO₂, which now leads to an initially slightly lower conversion of CO₂ (more pronounced visible by lower methane content). Now, the amount of water formed after the step change is lower compared to before the change, and the inhibition by a water adsorbed on the surface, until the new adsorption equilibrium is established by desorption after about 1 min, leads to a decrease of the reaction rate.

So, ad- and desorption of steam is obviously the main effect prolonging the time required to reach steady-state conditions. In order to study this more explicit, only the steam content was now changed stepwise from 20 % to a feed gas free of steam (Fig. 6). As expected, the content, i.e., the production rate, of methane is lower before the step change due to the higher (surface) concentration of water and the corresponding inhibiting effect by steam adsorption. After the step change from a rather high steam content of 20 % to a feed gas free of steam, methane production increases until after about 7 min the expected values (and accurately calculated by the kinetic model) for steady state are reached. The influence of the “delayed” steam ad- and desorption is also important to a certain extent for the transient operation of a wall-cooled fixed-bed reactor, as inspected is in the next Sect. 4.3.

4.3 Effects of Changing Volume Flow in a Wall-Cooled Fixed-Bed Reactor

Subsequent to the studies on the isothermal steady-state kinetics and on transient effects on the kinetics, experiments were conducted in a non-isothermal wall-cooled fixed-bed reactor. The transient behavior of the reactor was studied by a step change of the total volume rate. The reactor was also modeled as described in Sect. 3. For calculation of the conversion and heat production, the steady-state kinetics (see Sect. 4.1) were used. The experiment focused on biogas upgrading.

Biogas typically contains 60 % CH₄ and 40 % CO₂. Hence, at least 4 mol H₂ has to be admixed per mol CO₂ to achieve 100 % conversion of CO₂ to CH₄. Here, a slightly higher ratio of 4.2 was applied for adjusting a small H₂ excess to ensure full conversion. Methane was not added to the feed gas; instead, the respective amount of N₂ was added. Before presenting the dynamic measurements, the steady-state temperature profiles are illustrated in Fig. 7. The model describes the measured temperature profile and the location of the hotspot temperature satisfactorily. For the shorter residence time (higher volume rate), the model predicts a slightly higher CO₂ conversion, i.e., 69 % compared to 60 % measured, which may be explained by inaccuracies at high H₂O-to-H₂ ratios.

The transient experiments with the wall-cooled fixed-bed reactor were of interest as the hotspot behavior during a load change is important for safe operation. In order to achieve the strongest effect, a step change was chosen, while in industrial practice the load change would be realized by a ramp. Note that the equilibrium conversion of CO² to methane is 100 % for the given low reaction temperature of around 190 °C. The transient temperature profiles were measured as described in Sect. 2.2.

In Fig. 8, the temperature profile at different times after the step change and in Fig. 9 only the measured and modeled hotspot temperatures (i.e., maximum axial temperatures as depicted as filled marks in Fig. 8) are displayed.

The model predicts a faster adjustment of the steady-state hotspot temperature after about 2 min, whereas 5 min are needed experimentally (Fig. 9). Furthermore, the model fails to describe the change of the hotspot in this interval. The model shows an immediate increase of the hotspot temperature, whereas in the experiment the temperature of the hotspot decreases initially and then rises subsequently. This is observed over the whole length of the reactor (see Fig. 8). The measured temperature rise at the rear end of the reactor at t = 60 s is probably due to the exothermic adsorption of CO₂ and H₂, which is not present before in the rear section prior to the step change because of almost complete conversion of these components.

The reason for this unexpected measured “wrong-way behavior” of the reactor is the delay of the establishment of the new adsorption equilibrium of steam being not considered by the model, which assumes that the steady-state reaction rate at a given temperature is instantaneously reached. Hence, the model only accounts for transient thermal effects, and the desorption kinetics and the adsorption capacity of the catalyst are not considered. So, the overall response time of the reactor of in total 5 min is in about equal amounts the result of the “delayed” ad-/desorption of steam and of the “thermal” behavior. The former effect is not reflected by the model that only considers the steady-state kinetics (only depending on temperature and the gas-phase concentrations of CO, H₂, and H₂O) and the general transient mass and heat balance.

The transient kinetic experiments presented in Sect. 4.2 clearly show that the reaction rate and the adsorption equilibrium, respectively, require some time to reach steady state, if the steam content in the syngas changes (Fig. 6). The hotspot position at the higher volumetric flow of 60 L h⁻¹ (STP) is located at a reactor length of 5 cm. At this position, the (modeled) CO₂ conversion and, therefore, the content of steam in the syngas is lower (2.4 %) compared to 16 % steam for the lower flow rate (7.5 L h⁻¹) adjusted before the step change from a low to a high volumetric rate was conducted (subfigure of Fig. 9). Thus, the reaction rate and in turn the level of the hotspot temperature are diminished until the respective surplus of adsorbed steam has desorbed into the gas phase.

Fig. 10 illustrates the result of an experiment conducted in reverse direction, i.e., step change from high to low volumetric flow. Again, the model predicts that the steady state is reached earlier. Now the hotspot temperature slightly moves towards the entrance of the reactor (from l = 5 cm to 4 cm according to the experiment), and a clear but small temperature rise is observed before the new steady state is reached. This is a consequence of the pseudo-homogeneous model used in this work.

At the initially high volume flow, the content of steam at the hotspot position is only 2 %, while at the same reactor position 13 % of steam is present (at steady state). This again leads to the “wrong-way behavior”, but now with a higher rate and hotspot temperature, respectively, in the transitional period (0 < t < 120 s). Now a certain additional amount of steam adsorbs in the front region located near the hotspot, which at first has to be produced through the reaction. This takes about 120 s to a higher rate and hotspot temperature in that period compared to the model (not considering this effect).