Coffee Pulp Gasification for Syngas Obtention and Methane Production Simulation Using Ni Catalysts Supported on Al2O3 and ZrO2 in a Packed Bed Reactor

1. Introduction

Nowadays, the methanation of CO₂, also known as the Sabatier reaction, is of great interest in power-to-gas systems since it produces a substitute natural gas (SNG) and enables the valorization of CO₂ [1]. Furthermore, the resulting methane is a combustible gas and does not present many difficulties in its storage [1,2]. As CO₂ is a cause and promoter of climate change, it is highly desirable to develop new processes that capture and/or reuse it [1,2,3], and thus avoid the use of fossil fuels, since their combustion generates more greenhouse gas (GHG) emissions [4,5]. Additionally, being a fuel that can result from the reuse of CO₂, in principle a zero or low carbon footprint can be established once it has been burned, as well as biofuels [6].

Moreover, synthesis gas (syngas) feeds, the raw material used for CO₂ methanation, can be obtained from the gasification of renewable sources, such us agro-industrial residues and municipal organic waste, among others [7,8]. This study investigates syngas obtained from coffee pulp, which is conventionally used as fertilizer, animal feed, and/or low-quality fuel and, if not properly treated, it may cause environmental damage [9,10]. Therefore, valorizing coffee pulp promotes green chemical synthesis and follows the principles of circular economy. It also contributes to obtaining high added-value products to base the economy and consumption patterns on more sustainable activities [11]. However, to incorporate the biorefinery concept, the coffee pulp considered is a byproduct after a phytochemical extraction process with solvents to take advantage of all its potential to generate high added value products [8].

Moreover, for the formation of methane from CO₂, there must be enough H₂ [3]. Therefore, this study aims to determine the composition of syngas from coffee pulp gasification using steam as gasifying agent, varying the ratio of steam-biomass ratio (S/B) and operation temperature. Then, it considers simulation of the catalytic conversion of syngas into methane in a packed bed reactor. Matlab^© software is used to solve the mathematical model. Nickel-based catalysts are extensively studied for this reaction and because their high performance/cost ratio [5,12,13,14], being the Ni catalyst supported on alumina the most widely used at industrial scale [1,12,13]. For this reason, in the present work selected catalysts are based on Ni supported in Al₂O_3, and comparing their performance on the process with ZrO₂ as a support, because this oxide shows higher [15]. Based on chemical kinetic models, a commercial Ni/Al₂O₃ and two Ni/ZrO₂ catalysts are compared in terms of CO₂ and H₂ conversion, CH₄ selectivity, and the molar fraction evolution of these chemical species along the catalyst bed. The evaluation of the reaction system with all compounds in a packed bed reactor simulation for CO₂ methanation allows for a more comprehensive understanding of the process, identification of potential interactions and by-products, and reactor design optimization.

1.1. Syngas from biomass as raw material for methanation catalytic process

Gasification is the thermo-chemical conversion of a carbonaceous fuel, and it is characterized by being endothermic process, meaning it requires a heat source [16]. Therefore, it is performed at high temperatures, typically ranging from 500 to 1400 °C, and can take place under atmospheric or elevated pressures, reaching up to 33 bar [17]. Gasifiers traditionally operate within distinct configurations, including fixed-bed, fluidized-bed, and moving-bed systems[18]. This process involves a partial fuel oxidation by using an oxidizing agent, which could be oxygen, air, steam or mixtures of them [19,20]. Despite using air as a gasifying agent is cheap, the syngas dilution by the N₂ presence can lead to a reduction in its high heating value, as well as a decrease in the overall efficiency of the gasification process [21]. Utilizing steam as the gasifying agent leads to the formation of a syngas characterized by its elevated calorific value, typically ranging from 10 to 15 MJ N/m3, and a hydrogen-rich composition [20]. Additionally, [22] highlights the outcomes of syngas generation through biomass gasification with steam. This work demonstrates a yield enhancing of both hydrogen and carbon dioxide, while also presenting a notably higher calorific value in comparison to gasification using oxygen or air as gasifying agents. Therefore, steam is selected as gasifying agent in the present study.

The result of gasification is a fuel gas known as syngas. The main components of syngas are carbon monoxide (CO), hydrogen (H₂), carbon dioxide (CO₂), steam (H₂O_(g)), methane (CH₄), nitrogen (N₂) if the oxidation agent is air or a mixture of it with other agents, some hydrocarbons in very low quantity and contaminants, such as carbon particles, tar, and ash [16,23]. In the existing literature, the typical syngas composition derived from agro-industrial waste exhibits a hydrogen content falling within the range of 40% to 50%, carbon monoxide at 9.97% to 12.38%, carbon dioxide levels ranging between 25.04% and 26.50%, and consistently maintains methane levels below 0.5%. [24]. However, the final syngas composition depends of operational parameters, the type of biomass and gasifier configuration [23].

Syngas can be used as raw material to heat, generate electricity, or to synthesize high added-value chemical and fuel products through several conversion routes, such as a methanol or synthetic fuels production [8,11]. Therefore, biomass gasification has been considered a viable option for the conversion/utilization of a variety of feedstocks such as vegetable waste, agro-waste, industrial waste, kitchen waste, food waste, and agricultural waste, and even the key to a successful substitution of petroleum derivatives [25,26]. The conditions for this obtention are described in materials and method section.

1.2. Catalytic methane production

In CO₂ methanation, catalysts are needed to achieve high reaction rates, high conversions during CO₂ hydrogenation, and high selectivity towards methane formation [1,14]. The more reported active metal phases used in this reaction are Ni, Ru, Rh, and Co, [1,5,12]. Nickel-based catalysts have been subjected to comprehensive investigation across diverse conditions, owing to their economic advantage and comparatively heightened catalytic activity [5]. In addition, CO₂ methanation performance is affected by the nature of the catalyst support because it plays an important role in the dispersion of active-metallic sites and metal-support interaction [27], being the more used various metal oxides (e.g., Al₂O₃, TiO₂, SiO₂, ZrO₂, and CeO₂) [5]. Figure 1 is a schematic of the catalytic reaction system that was applied here in a packed bed reactor operating on the gas phase.

Figure 1. Schematic of the catalytic reaction system for a CO₂ methanation process. Source: Own work.

Figure 1. Schematic of the catalytic reaction system for a CO₂ methanation process. Source: Own work.

In Figure 1, (A) indicates the chemical reaction of CO₂ methanation; (B) the Reverse Water Gas Shift (RWGS) reaction; and (C) CO methanation. The carbon dioxide methanation reaction is exothermic and favored at high pressures and low temperatures [1]. The RWS reaction interferes with the selectivity towards methane production. In theory, CO₂ methanation is more favorable an H₂/CO₂ ratio equal to or greater than the stoichiometric ratio (4:1) [14].

The catalysts employed in the methanation process are highly susceptible to the presence of impurities in the stream. These impurities can lead to catalyst poisoning and deactivation, thereby diminishing the catalytic performance and overall efficiency [4,28]. The impurities including chlorine and sulfur compounds, ammonia, tars, and particulate matter [28]. The formation of carbon deposits on nickel-based catalysts during the CO methanation reaction has been extensively investigated, and can be a significant problem, but it does not pose a concern during the CO₂ methanation reaction [4]. Therefore, it is better to use a syngas with higher CO₂ content than CO as a carbon source. Furthermore, the H₂S presence in the syngas should be analyzed if a real operation is considered.

1.3. Ni/ZrO₂ catalyst

In the present work, the kinetic information was taken from [29]. In the latter, the two Ni/ZrO₂ catalysts were tested for methane production by carbon dioxide hydrogenation. Catalysts were prepared using the incipient wetness impregnation method. According to [29], the impregnated sample was calcinated to obtain NiO/ZrO₂-C at 500°C for 3 hours, while NiO/ZrO₂-P was synthesized using dielectric barrier discharge (DBD) plasma for 1 hour. Subsequently, the oxidized metal catalysts were subjected to hydrogen reduction at elevated temperatures to form Ni/ZrO₂-C and Ni/ZrO₂-P.

The chemical kinetics proposed in that study did not include a model such as the Langmuir – Hinshelwood – Hougen –Watson kinetics, which explicitly considers mass transfer in the chemical kinetics. However, simple power-law kinetics for direct reactions can be used for technical applications [30]. Although, CO selectivity for this kinetic does not allow due to it only considers reaction (1). Then, the kinetic model of Ni/ZrO₂ catalysts follows a power-law model, as shown in Equation (1).

$${-r’}_{CO2}=\frac{A}{{\left(R’\ast T\right)}^{\propto +\beta }}{e}^{\frac{-Ea}{R\ast T}}\ast P_{CO2}^{\propto }\ast P_{H2}^{\beta }$$

(1)

Where ${-r’}_{CO2}$ is the kinetic rate for CO₂; A, is a pre-exponential factor related with chemical kinetics in (L/g*h); R, the ideal constant of gases (8.314*10^-3 kJ/mol); R’, the ideal constant of gases (0.082 atm*L/K*mol); Ea, the activation energy in kJ/mol; T, the reaction temperature in K, and P_CO2, and P_H2, the partial pressure of the CO₂ and H₂ in atm, respectively. Table 1 shows the values of the chemical kinetic model of the two Ni/ZrO₂ catalysts.

Table 1. Kinetic parameters of Ni/ZrO₂ catalysts [29].

Catalyst	Ea (kJ mol-1)	α	β	A (L g-1 h-1)
Ni/ZrO2-P	93.61	0.65	0.29	2.48×1010
Ni/ZrO2-C	93.12	0.44	0.54	6.93×109

Table 1. Kinetic parameters of Ni/ZrO₂ catalysts [29].

Catalyst	Ea (kJ mol-1)	α	β	A (L g-1 h-1)
Ni/ZrO2-P	93.61	0.65	0.29	2.48×1010
Ni/ZrO2-C	93.12	0.44	0.54	6.93×109

1.4. Commercial Ni/Al₂O₃ catalyst

CO₂ methanation reaction with a 14–17 wt.% Ni/Al₂O₃ commercial catalyst is studied in the present work, based on the kinetic model established in [1]. The main rate expressions for CO₂ methanation, CO methanation, and RWGS used in the present study are detailed in Equations (2)–(4), respectively.

$${r’}_{CO2meth}=\frac{k_{CO2meth}\ast K_{H2}\ast K_{CO2}\ast P_{H2}\ast P_{CO2}\ast (1-\frac{P_{CH4}\ast P_{H2O}^2}{P_{H2}^2\ast P_{CO2}\ast K_{eq,CO2meth}})}{{(1+K_{CO2}\ast P_{CO2}+K_{H2}\ast P_{H2}+K_{H2O}\ast P_{H2O}+K_{CO}\ast P_{CO})}^2}$$

(2)

$$r_{’RWGS}=\frac{k_{RWGS}\ast K_{CO2}\ast P_{CO2}\ast (1-\frac{P_{CO}\ast P_{H2O}}{P_{H2}\ast P_{CO2}\ast K_{eq,RWGS}})}{(1+K_{CO2}\ast P_{CO2}+K_{H2}\ast P_{H2}+K_{H2O}\ast P_{H2O}+K_{CO}\ast P_{CO})}$$

(3)

$${r’}_{COmeth}=\frac{k_{COmeth}\ast K_{H2}\ast K_{CO}\ast P_{H2}\ast P_{CO}\ast (1-\frac{P_{CH4}\ast P_{H2O}}{P_{H2}^3\ast P_{CO}\ast K_{eq,COmeth}})}{{(1+K_{CO2}\ast P_{CO2}+K_{H2}\ast P_{H2}+K_{H2O}\ast P_{H2O}+K_{CO}\ast P_{CO})}^2}$$

(4)

Where ${-r’}_i$ is the kinetic rate for each reaction; Ea, the activation energy in kJ/mol; Pi is the partial pressure of component i in bar; Ki is the adsorption constant of component i; Keq,i is the chemical equilibrium constant for reaction i. Table 2 and Table 3 show the adsorption and kinetic parameters, respectively, of this catalyst model.

Table 2. Adsorption parameters of Ni/Al₂O₃ catalyst. [1].

Parameter	KCO	KH2O	KCO2	KH2
Q (KJ/mol)	40.6	14.5	9.72	52.0
Ko (bar-1)	2.39x10-3	6.09x10-1	1.07	5.2x10-5

Table 2. Adsorption parameters of Ni/Al₂O₃ catalyst. [1].

Parameter	KCO	KH2O	KCO2	KH2
Q (KJ/mol)	40.6	14.5	9.72	52.0
Ko (bar-1)	2.39x10-3	6.09x10-1	1.07	5.2x10-5

Table 3. Kinetic parameters of Ni/Al₂O₃ catalyst. [1].

Parameter	kCO2,meth	kRWGS	kCO,meth
Ea (KJ/mol)	110	97.1	97.3
ko (mol/min*g)	1.14x108	1.78x106	2.23x108

Table 3. Kinetic parameters of Ni/Al₂O₃ catalyst. [1].

Parameter	kCO2,meth	kRWGS	kCO,meth
Ea (KJ/mol)	110	97.1	97.3
ko (mol/min*g)	1.14x108	1.78x106	2.23x108

2. Results and Discussion

2.1. Syngas description

We performed the gasification of the coffee pulp at two temperatures and two steam/biomass (S/B) ratios. The compositions of the obtained syngas in %V/V are shown in Table 4. S/B ratios were used because steam was the gasifying agent selected in this work. Assuming an ideal gas behavior for syngas, the composition in %V/V is equivalent to molar fraction.

Table 4. Composition of syngas (%V/V) obtained from coffee pulp waste at different temperatures and steam/biomass (S/B) ratios.

Steam/biomass (S/B) ratio	S/B 0.5		S/B 1.0
Temperature (oC)	700	800	700	800
Hydrogen (%)	48.46	46.51	54.41	50.19
Methane (%)	0.27	0.23	0.25	0.09
Carbon monoxide (%)	24.21	44.06	18.87	37.81
Carbon dioxide (%)	25.05	7.68	24.81	11.39
Ethane (%)	0.14	0.02	0.07	0.03
Ethylene (%)	1.03	0.80	0.59	0.09
Propane (%)	0.74	0.39	0.82	0.37
H2S (%)	0.1	0.31	0.18	0.03
H2/CO2 ratio	1.93	6.06	2.19	4.41

Table 4. Composition of syngas (%V/V) obtained from coffee pulp waste at different temperatures and steam/biomass (S/B) ratios.

Steam/biomass (S/B) ratio	S/B 0.5		S/B 1.0
Temperature (oC)	700	800	700	800
Hydrogen (%)	48.46	46.51	54.41	50.19
Methane (%)	0.27	0.23	0.25	0.09
Carbon monoxide (%)	24.21	44.06	18.87	37.81
Carbon dioxide (%)	25.05	7.68	24.81	11.39
Ethane (%)	0.14	0.02	0.07	0.03
Ethylene (%)	1.03	0.80	0.59	0.09
Propane (%)	0.74	0.39	0.82	0.37
H2S (%)	0.1	0.31	0.18	0.03
H2/CO2 ratio	1.93	6.06	2.19	4.41

According to the results described in Table 4, the formation of CO₂ is favored under conditions where the S/B ratio is 0.5 and 1.0 at 700 °C. However, there is no significant variation in temperature that allows establishing a better operating condition for this gasification parameter. Although, at a gasification temperature of 700°C, a slightly higher amount of CO₂ is achieved for an S/B ratio of 0.5. On the other hand, higher amounts of H₂ are achieved, like CO₂, for both S/B ratios at 700 °C. Additionally, upon analyzing the considered reactions, CO can contribute to methane formation according to reaction B. Therefore, according to the data in Table 4, better production is achieved for both S/B ratios and temperatures of 800°C. Although, at this temperature, the production of CO₂ is not high as at 700°C. H₂/CO₂ ratios are greater than stochiometric ratio for reaction 1 (4:1), when gasification temperature of 800^oC for both S/B ratios is implemented. Furthermore, with S/B of 0.5 better value for this relation is achieved.

According to [20] and [26], as raising the gasification temperature leads to a reduction of chemical species that can poison and enhance catalyst deactivation. However, it is true for the own gasification results when a S/B of 1.0 is used, because in an S/B ratio of 0.5, the behavior is contrary to what is established by these references. Therefore, The S/B ratio could affect the formation of H₂S since there is a clear variation in the formation of this poison agent when comparing both gasification temperatures. To obtain synthesis gases from coffee pulp with the most adequate composition to avoid the possible acceleration of catalyst poisoning and deactivation, the temperature of 800 ^oC and S/B of 1.0 should be selected, due to it presents the lowest value for H₂S formation in the syngas.

2.2. Catalytic simulation of methanation

Once obtained the syngas compositions after gasification, we analyzed the CO₂ conversion rate, CH₄ selectivity and H₂ conversion throughout the weight catalytic bed (w) of each one of the syngas compositions and catalysts considering the kinetics described above. The results are shown in Figure 2, Figure 3 and Figure 4.

Figure 2. CO₂ conversion Ni based catalysts for all syngas composition: (a) Ni/ZrO₂-P, (b) Ni/ZrO₂-C and (c) Commercial Al₂O₃.

Figure 2. CO₂ conversion Ni based catalysts for all syngas composition: (a) Ni/ZrO₂-P, (b) Ni/ZrO₂-C and (c) Commercial Al₂O₃.

Figure 3. CH₄ selectivity for Ni based catalysts for all syngas composition: (a) Ni/ZrO₂-P, (b) Ni/ZrO₂-C and (c) Commercial Al₂O₃.

Figure 3. CH₄ selectivity for Ni based catalysts for all syngas composition: (a) Ni/ZrO₂-P, (b) Ni/ZrO₂-C and (c) Commercial Al₂O₃.

Figure 4. H₂ conversion Ni based catalysts for all syngas composition: (a) Ni/ZrO₂-P, (b) Ni/ZrO₂-C and (c) Commercial Al₂O₃.

Figure 4. H₂ conversion Ni based catalysts for all syngas composition: (a) Ni/ZrO₂-P, (b) Ni/ZrO₂-C and (c) Commercial Al₂O₃.

At 800 ^oC of gasification for both S/B ratios, the feed syngas streams contain a lower concentration of CO₂, resulting in a decreased reactant-to-catalyst ratio, in other words, it has a lower space velocity. This condition leads to higher conversion rates for these gasification process parameters. To obtain an accurate comparison, it is necessary to evaluate the results obtained at 700 ^oC and those obtained at 800 ºC, separately for all simulated catalysts. In Figure 2, Figure 3 and Figure 4, Ni/ZrO₂-P obtained better results than Ni/ZrO₂-C in terms of CO₂ conversion, H₂ conversion and CH₄ selectivity. In accordance with [29], this behavior is due to a greater number of active sites, which can be provided by highly dispersed Ni particles on Ni/ZrO₂-P, leading to a higher reaction rate for CO₂ methanation. The surface Ni concentration of Ni/ZrO₂-P, estimated at Ni/Zr = 0.18, is higher than Ni/ZrO₂-C catalyst (Ni/Zr = 0.13). Therefore, this indicates a better Ni dispersion on the support induced by plasma decomposition. In addition, it has been proposed that this method of preparation facilitates the partial reduction of ZrO₂ to create more oxygen vacancies, this improving CO₂ activation [29]. For these ZrO₂ supported catalysts, at 700^oC is better to use S/B ratio of 1.0 to obtain high conversions for CO₂ and CH₄ selectivity. However, for same temperature, the H₂ conversion is best when Ni/ZrO₂-C catalyst uses a syngas from S/B of 1.0 and for Ni/ZrO₂-P, S/B of 0.5. The highest CH₄ selectivity and H₂ conversion were produced for 800 ^oC with S/B ratio of 1.0 and CO₂ conversion at S/B of 0.5.

Regarding the results of the commercial Ni/Al₂O₃ catalyst in Figure 1 (c) and Figure 2 (c), it achieved the highest values of CO₂ conversion and CH₄ selectivity with a syngas obtained using an S/B ratio of 1.0 for both temperatures in the gasification process. According to Figure 4 (c), the H₂ conversion behavior of this support is opposite to that of the two other parameters for the mentioned S/B gasification condition.

Figure 5 shows the quantitative percentage comparisons of catalysts and their improvement for CO₂ conversion (a), CH₄ selectivity (b) and H₂ conversion (c) at the reactor outlet, using all the syngas compositions. The results are expressed in percentages (%).

Figure 5. Comparison in percentage (%) of CO₂ conversion (a), CH₄ selectivity (b) and H₂ conversion (c) of the catalysts under study.

Figure 5. Comparison in percentage (%) of CO₂ conversion (a), CH₄ selectivity (b) and H₂ conversion (c) of the catalysts under study.

By comparing the catalysts, it is possible to observe in Figure 5, with respect to CO₂ conversion and CH₄ selectivity, the highest values were achieved with ZrO₂ and Al₂O₃ supported catalysts, respectively. This trend is constant for all the syngas compositions examined in this study. This result is in accordance with [15], which reports that the catalytic system exhibited a higher activity with ZrO₂ supports than with their Al₂O₃ counterparts. The CH₄ selectivity produced with Al₂O₃ corroborates what was reported in [27], that this support presents superior methane selectivity. For H₂ conversion, it is better Al₂O₃ support than ZrO₂ supports. However, when synthesis gases from 700^oC and both S/B ratios are used with Ni/ZrO₂p catalyst, the H₂ conversions are better than the obtained for Ni/Al₂O₃ commercial catalyst. Additionally, ZrO₂p shows better conversions and selectivity than ZrO₂c. Therefore, the loss of CH₄ selectivity of ZrO₂ catalysts are more significant for the calcination preparation than for the plasma preparation, when compared to the commercial Ni catalyst supported on Al₂O₃.

Since the power-law kinetic model for Ni/ZrO₂ catalysts only include Reaction (A) for CO₂ methanation, it is not possible to stablish the CO selectivity. However, chemical kinetic model for commercial Ni/Al₂O₃ catalyst consider all reactions. Therefore, this catalyst allows to calculate the selectivity for CO, to determine the performance of gasification conditions in Sabatier process to increase CH₄ yield and to minimize the by-products generation. Figure 6 illustrates the CH₄, CO and H₂O selectivity for commercial Ni/Al₂O₃ catalyst considering all the gasification conditions.

Figure 6. CH₄, CO and H₂O selectivity comparison for commercial Ni/Al₂O₃ catalyst considering all the gasification conditions.

Figure 6. CH₄, CO and H₂O selectivity comparison for commercial Ni/Al₂O₃ catalyst considering all the gasification conditions.

Figure 6 shows a better behavior over Ni/Al₂O₃ catalyst for CO selectivity at 800 ^oC when S/B of 0.5 is applied. At 700 ^oC the same effect is shown for S/B of 1.0. Furthermore, with these gasifying conditions CH₄ selectivity are lower. This can be explained by the fact that with these S/B conditions for gasification at the respective temperatures, they have a higher amount of CO and a lower amount of CO₂ in their composition. The selectivity towards H₂O is more marked when S/B is 1.0 for both gasification temperatures. It can be explained because with an S/B ratio at this value, a higher amount of steam is feed.

3. Materials and Methods

This section starts with a detailed description of the biomass gasification procedure for syngas production from coffee pulp after a solvent phytochemical extraction to obtain chlorogenic acid. Then, a theorical kinetic study is considered for methane production using Ni based catalysts on ZrO₂ and Al₂O₃ supports on a packed bed reactor. It presents a mathematical model that includes the assumptions and all the equations that are necessary to simulate a packed bed reactor considering a heterogenous catalyst for the reactive system. Finally, it details the CO₂ conversion, H₂ conversion and CH₄ selectivity of the model constructed here when it was simulated with each catalyst, using its respective chemical kinetic parameters found in the cited references.

3.1. Gasification experimental system

These residual coffee pulps are taken as a solid filtered after a solvent phytochemical extraction process using ethanol/H₂O (70/30 %V/V) at ambient temperature, atmospheric pressure and coffee pulp-to-solvent ratio of 1 to 4. They were subjected to gasification using a horizontal furnace reactor. The reactor comprises a quartz tube with an external diameter of 3.5 cm (internal diameter of 3.0 cm) and a length of 50 cm. The quartz tube is inserted into the annular space of the 40 cm long horizontal furnace. The furnace is heated by electric resistances and its temperature is controlled through a proportional-integral-derivative (PID) loop, enabling continuous monitoring of the reactor temperature. To facilitate the gasification process, the sample was loaded into a 2.0 cm diameter and 13.5 cm length quartz sample holder within the reactor. Inside the sample holder, a K-type thermocouple was inserted to accurately measure the temperature of the sample bed.

The gasification experiments were conducted at two different temperatures: 700 ^oC and 800 ^oC. Additionally, two steam-to-biomass ratios (S/B) were tested, namely 0.5 and 1.0, to evaluate their effects on the gasification process.

The produced syngas was analyzed using an Agilent Micro GC model 3000. This analytical instrument is equipped with two thermal conductivity detectors (TCD). One TCD utilizes a 10 m x 0.32 mm 5A molecular sieve column with argon as the carrier gas, while the other TCD employs an 8 m x 0.32 mm column with helium as the carrier gas.

3.2. Mathematical model for the methanation catalytic packed bed reactor simulation

This subsection discusses the simulation of a packed bed reactor operating in steady-state conditions. The conditions of the reactor were a total inlet molar flux of 0.1 mol/min, ambient pressure, and 400 °C as in [26]. Although this temperature does not achieve the highest conversion of CO₂, it offers the best CH₄ selectivity. In the simulation, the reactor considers a catalyst weight of 100 mg in a packed bed configuration at 1 atm. These conditions were maintained constant in all the simulations to be able to compare the behavior of the catalysts using the syngas compositions described above. The following considerations and simplifications proposed by [31] and [32] were implemented for this type of operation and reactor:

• Negligible radial diffusion: concentration and temperature profiles are assumed to be constants, which leads to a one-dimensional model.
• Constant radial speed.
• Temperature and pressure profiles in the catalyst are assumed to be constants (homogeneous catalytic particle).
• As in [13], the mechanisms related to catalyst deactivation, such as sulfur poisoning or carbon formation via the Boudouard reaction, are not taken into consideration or disregarded in the present study.

As the process is carried out in a packed bed reactor, the resulting model must be adjusted to the design equation of this type of reactor, which can be consulted in [13]. Equations (4)–(8) are the system of ordinary differential equations (ODEs) used here for the mass balance and reactor design. They express each reactive species involved in the Sabatier process.

$$\frac{{dF}_{CO}}{dW}={r’}_{CO}$$

(4)

$$\frac{{dF}_{CO2}}{dW}={r’}_{CO2}$$

(5)

$$\frac{{dF}_{H2}}{dW}={r’}_{H2}$$

(6)

$$\frac{{dF}_{CH4}}{dW}={r’}_{CH4}$$

(7)

$$\frac{{dF}_{H2O}}{dW}={r’}_{H2O}$$

(8)

Where Fi denotes the molar flux of species i; r’i, the chemical kinetics of species i; and W, the catalyst weight inside the heterogeneous reactor in grams.

Since the system has three chemical reactions in parallel: (1) CO₂ methanation, (2) RWGS, and (3) CO methanation, it should consider the species that appear in more than one of these reactions because the chemical kinetics of each of said reactions are coupled and given in parallel as well. Equations (16)–(20) show the global or total reactions for each species involved in the process described above, where each r_i is expressed in mol/min.g_cat.

$${r’}_{CO2}={-(r’}_{CO2-met}+{r’}_{RWGS})$$

(16)

$${r’}_{H2}=-(4.{r’}_{CO2-met}+{r’}_{RWGS}+3.{’r}_{CO-met})$$

(17)

$${r’}_{CH4}={r’}_{CO2-met}+{r’}_{CO-met}$$

(18)

$${r’}_{H2O}=2.{r’}_{CO2-met}+{r’}_{RWGS}+{r’}_{CO-met}$$

(19)

$${r’}_{CO}={r’}_{RWGS}-{r’}_{CO-met}$$

(20)

Catalyst performance is analyzed here by measuring CO₂ conversion and the selectivity of CH₄, CO and H₂O production. CO₂ conversion and the selectivity of CO₂ to CH₄ and by-products are described in Equation (21) and Equation (22).

$$X_{CO2}=\frac{F_{{CO2}_{in}}-F_{{CO2}_{out}}}{F_{{CO2}_{in}}}$$

(21)

$$S_{CO2/CH4}=\frac{F_{{CH4}_{out}}}{F_{{CO}_{out}}+F_{{CH4}_{out}}+F_{{H2O}_{out}}}$$

(22)

$$S_{CO2/CO}=\frac{F_{{CO}_{out}}}{F_{{CO}_{out}}+F_{{CH4}_{out}}+F_{{H2O}_{out}}}$$

(23)

$$S_{CO2/H2O}=\frac{F_{{H2O}_{out}}}{F_{{CO}_{out}}+F_{{CH4}_{out}}+F_{{H2O}_{out}}}$$

(24)

Where X_CO2 is the CO₂ conversion inside the reactor and S_CO2/CH4, S_CO2/CO and S_CO2/H2O are the selectivity of CO₂ to transform it into CH₄, CO and H₂O, respectively. F_{i_in} and F_{i_out} are the molar flux of components according to the subindex in mol/min.

Most kinetic expressions studied and analyzed here depend on the partial pressures of the chemical species involved, and, since the system of differential equations is based on molar balance. Therefore, Equation (25) must be used to relate the partial pressures to the molar fluxes of each species.

$$P_i=\frac{F_i}{\sum _{i=1}^n{F}_i}\ast P_T$$

(25)

Where P_i is the partial pressure of species i inside the reactor; F_i, the molar flux of component i (mol/min); $\sum _{i=1}^n{F}_i$, the summation of all molar fluxes of the species involved (mol/min); and P_T, the total system pressure.

4. Conclusions

This paper presented a coffee pulp gasification after phytochemical extraction process, varying S/B ratios (0.5 and 1.0) and temperatures (700^oC and 800 ^oC). The resulting syngas is considered as raw material from methane production through Sabatier process. The adequate syngas according to H₂/CO₂ ratio is achieved with 800^oC and both S/B ratios because these conditions exceed the stoichiometric ratio (4:1) for the CO₂ methanation reaction. Additionally, the temperature of 800^oC reduces the formation of H₂S, what favors to avoid the acceleration of catalyst poisoning. However, in the present study is not considered in the catalyst simulation this effect.

Then, a comparative analysis of three Ni catalysts in terms of CO₂ methanation performance and behavior is considered. Such analysis was based on a mathematical model that simulated their chemical kinetics reported in their respective references, using MATLAB^©. The chemical kinetics of the two simulated Ni/ZrO₂ catalysts were taken from [29], where they were prepared adopting two different methods: one was obtained using dielectric barrier discharge (DBD) plasma; and the other, by calcination. In turn, the kinetics of the Ni/Al₂O₃ commercial catalyst, were taken from [1]. This study established CO₂ conversion, CH₄ selectivity and H₂ conversion in CO₂ methanation depending on catalyst preparation method, catalyst support, raw material composition, and gasification process conditions.

According to the results, Ni/ZrO₂-P has a better catalytic behavior than Ni/ZrO₂-C, which corroborates that the catalyst preparation method influences catalyst activity. Also, the catalyst support affects CO₂ conversion, H₂ conversion and CH₄ selectivity. ZrO₂-supported catalysts show better CO₂ conversion, but the Ni/Al₂O₃ commercial catalyst has higher CH₄ selectivity and H₂ conversion. Although, Ni/ZrO₂p catalyst presents better H₂ consumption than commercial Ni/Al₂O₃ for 700^oC and both S/B ratios.

Regarding the syngas composition, Ni/Al₂O₃ was more active for CO₂ conversion and selective for CH₄ when an S/B ratio of 1.0 for both temperatures was employed. In contrast, the H₂ conversion is better for S/B of 0.5. Furthermore, ZrO₂-c catalysts had better CO₂ conversion, H₂ conversion and CH₄ selectivity at 700^oC using S/B ratio of 1.0 and for 800^oC, it favors the CO₂ conversion with S/B of 0.5 and CH₄ selectivity and H₂ conversion at S/B ratio of 1.0. ZrO₂-p the gasification S/B of 1.0 present the best CO₂ conversion and CH₄ selectivity values for 700^oC. For 800^oC, a S/B of 1.0 improves CH₄ selectivity and H₂ conversion and S/B of 0.5 the CO₂ conversion.

Finally, the model presented in this study has the potential to be applied to evaluate the CO₂ methanation process using different types of syngas derived from various biomass sources and operating conditions during the gasification process. By utilizing the same catalysts studied in this paper, researchers can conduct theoretical exploratory research to quickly estimate the impact of different variables on CO₂ conversion, H₂ conversion and CH₄ selectivity. This approach offers the advantage of saving both time and resources by providing a valuable method to identify the variables at the gasification process that promote favorable CO₂ conversion, CH₄ selectivity and H₂ conversion.