Optimization of nickel catalyst loading in Ni/γAl2O3 for producing carbon nanotubes through natural gas decomposition

Carbon nanotubes can be produced at high quality through hydrocarbon catalytic decomposition. In addition, hydrogen can be produced as a valuable byproduct at a competitive price. In this article, the loading of the active phase in the decomposition catalyst is optimized using natural gas as a widely available hydrocarbon. Natural gas decomposition was investigated using different nickel loadings. Natural gas decomposition, as a widely available hydrocarbon, is investigated by manipulating nickel loading to optimize the loading of the active phase in the decomposition catalyst. Optimizing the catalyst loading can achieve higher quality and yield of carbon nanotube. In addition, a higher carbon nanotube yield will maximize hydrogen production. Increasing the quality of produced carbon and the amount of hydrogen will improve the overall process economics. Nickel is a highly active catalyst for natural gas decomposition and has a higher carbon affinity compared to other metallic catalysts. Different nickel loadings were tested for natural gas decomposition. Optimization was used to calculate the optimum nickel loading based on the experimental results. The optimum nickel loading over alumina was 12.5%. The economic analysis of the process indicated that the optimum nickel loading is 30%.


Introduction
Hydrocarbon catalytic decomposition can be used to produce high-quality carbon nanotubes. Carbon nanotubes formed are an interesting product. Furthermore, hydrogen is created at a reasonable cost. Hydrogen is currently produced and employed to generate clean energy. Several publications discussed the development of electrolysis systems and new materials for producing and consuming hydrogen to reduce carbon emissions (Chinnakutti et al. 2022;Theerthagiri et al. 2022;Yu et al. 2022;Panda et al. 2022). Natural gas is an interesting feedstock for hydrogen production, which may result in significant carbon dioxide emissions (Nabgan et al. 2021). Natural gas decomposition can produce highquality carbon nanotubes over nickel and metallic-supported metallic catalysts (Pham-Huu et al. 2002;Louis et al. 2005;Shen et al. 2007). However, nickel is quite expensive and more suitable for hydrocarbon decomposition. Remarkably, the natural gas decomposition approach has not been 1 3 comprehensively investigated. While industrial processes exist that use hydrocarbons at extremely high temperatures for producing carbon black, the catalytic decomposition of natural gas and other hydrocarbons can be used to generate hydrogen at a reasonable price in addition to carbon nanotubes (Amin et al. 2011a;Chin et al 2006;Al-Fatesh et al. 2016).
Carbon nanotubes can be used in several applications, including adsorption and catalysis (Saleh 2016). The price of carbon nanotubes will determine the feasibility of applying this process in the industry (Amin et al. 2011a(Amin et al. , 2011bChin et al. 2006;Omoriyekomwan et al. 2021;Qin et al. 2021). Hydrogen production as a byproduct will improve the process economics (Amin et al.2011a(Amin et al. , 2011bChin et al. 2006;Al-Fatesh et al. 2016). Catalytic decomposition of hydrocarbons will produce carbon monoxide-free hydrogen, which can be used in many applications like fuel cells and ammonia production (Amin et al. 2011b). Developing an active and selective catalyst is the first step to commercializing natural gas decomposition. The developed catalyst should be designed considering a higher affinity for carbon and carbon nanotube quality. The carbon nanotubes could be single or multi-walled tubes (Amin et al. 2011b). Usually, the diameter of the produced carbon nanotubes is within the same range as the diameter of the metal active site (Pham-Huu et al. 2002;Louis et al. 2005;Shen et al. 2007).
The surface reaction steps include natural gas adsorption over the catalyst surface, a series of dehydrogenation steps, and lastly, hydrogen is desorbed. After the hydrogen desorption step, carbon segregates/dissolves into the active site (Nabgan et al. 2021). After segregation/dissolution, the formed carbon dissolved in the active site particle at the front end. Then, carbon diffuses to the rear end of the active site particle. The active site particle separates from the support (alumina), forming a carbon nanotube, while the active site is exposed at the carbon nanotube tip (Qin et al. 2021). The surplus formed carbon from natural gas decomposition is deposited on the available active site particle. Therefore, the free active site particle surface available for natural gas reaction/decomposition steadily diminishes as the formed carbon deposits and accumulates over the available active site (Pham-Huu et al. 2002;Louis et al. 2005;Shen et al. 2007).
The temperature profoundly affects the reaction duration and carbon nanotube properties. The reaction was suppressed after 5 min at 750 °C (Veziri et al. 2008). Using ethane as a carbon feedstock, the optimum loading was 10 wt% of the active phase over silica at a temperature range of 650-700 °C (Vanyorek et al. 2011). 10 wt% nickel loading over alumina was found to be the optimum loading for maximizing the carbon-nanotubes yield in several studies (Ping et al. 2016;Amin et al. 2012). The produced carbon nanotubes vary considerably as a function of temperature, and the diameter is usually within the same range as the active phase (Amin et al. 2011b;Sivakumar et al. 2011). So far, the previous work was focused on conducting experimental work with different loading and was not extended to employing mathematical methods to predict the optimum loading considering other process parameters and operating cost.
In this work, several nickel loadings over alumina were prepared to investigate the effect of metallic loading on carbon yield using the wet impregnation method. The prepared catalysts were tested in a thermal gravimetric analyzer. The experimental results were used to optimize nickel loading over alumina for natural gas decomposition to producing carbon nanotubes. Optimization techniques were used to predict the optimum nickel loading over alumina, considering process parameters and operating cost. This article investigates the optimization of the catalyst to maximize the carbon nanotubes yield to improve the process economics as a step towards the commercialization of the process.

Experimental
The catalysts used in the research were prepared using the wet impregnation method by employing an aqueous solution of Ni(NO 3 ) 2 .6H 2 O (from Alfa Aesar) over alumina (Al 2 O 3 nano-powder from Alfa Aesar). The catalyst was prepared by dissolving nickel nitrate precursor in methanol; alumina was added to the prepared solution at different ratios according to the desired loadings. The mixture is stirred at 90 °C for 2 h in a closed vessel. Then, the solution is dried at 90 °C in an open atmosphere. The prepared catalyst samples were prepared with different catalyst loadings, including 5, 10, and 15 wt% Ni/Al 2 O 3 .
The prepared catalyst is calcined before using the catalyst for the catalytic decomposition of natural gas. The calcination step takes place within the thermal gravimetric analyzer. The calcination temperature was 650 °C and was carried out under an air atmosphere for 1 h. The reduction step was conducted in situ inside the thermal gravimetric analyzer at the same reaction temperature for 90 min using a 5% H 2 and 95% N 2 mixture. The rate of natural gas decomposition is investigated using the TGA by recording the weight change of a catalyst sample, as shown in Fig. 1.
The rate calculated from the experimental raw data ( r A(TGA) ) is calculated by the weight change of the catalyst and has a unit of mg carbon deposited/mg catalyst/min. Figure 1 shows an example of the typical result generated using the TGA. The reacting gas was natural gas in the range of 84-240 ml/min. Methane was used to express the natural gas conversion in the equations below since methane is the dominant constituent in natural gas. The natural gas conversion was defined as follows: The specific rate of carbon formation, r C , relative to the initial amount of nickel in the catalyst can be defined as follows: The thermal gravimetric analyzer (TGA) used for conducting this research is Thermax 500, manufactured by Thermo Cahn. The thermal gravimetric analyzer was used to monitor the catalyst weight in micrograms. By monitoring the catalyst weight, we can study the natural gas decomposition since any increase in weight reported while natural gas is flowing is assumed to be the weight resulting from carbon deposition on the catalyst. Initially, the catalyst is weighed and placed in a flat bottom sample holder made of quartz inside the TGA. The TEM was accomplished using the FEI-Philips CM300 microscope operating at an accelerating voltage of 200 kV from FEI Company, USA. The SEM was performed using the Phenom Pro X SEM analyzer from Thermo Scientific.

Mass transfer limitation
The instantaneous reaction rate for the fresh catalyst before deactivation began was used as the initial rate. The rate based on the catalyst weight ( r A(w) ) is expressed by the following Equation (Perkins 2022): where, C w : Catalyst weight in mg. MW : Molecular weight of carbon = 12 gC∕moleC Figure 2 shows the effect of the reaction gas flow rate at 550 °C using 10 wt.% Ni/Al 2 O 3 . Figure 2 shows that the flow rate does not affect the total active time of the catalyst. However, the results indicate that the flow rate clearly affects the reaction rate (Amin et al. 2011b;Maqbool et al. 2021). Figure 2 shows an initial spike in the rate followed by a plateau and a steady decrease in the rate. It was assumed that the initial spike considers the mass of hydrogen before it desorbs from the catalyst. The rate at the spike was used as the carbon formation rate. The time zero was assigned to the time the natural gas started to flow to the TGA.
A CFD simulation for the sample holder inside the TGA was developed to estimate the velocity around the particle. The effect of natural gas velocity on the rate is shown in Fig. 2. It was important to investigate the controlling step in the reaction, either the reaction kinetics or the external mass transfer, which can be achieved by varying the flow rate of the catalyst particle size (Amin et al. 2011b;Al-Fatesh et al. 2016; Banu and Bicer 2021; Amin and Abedi 2018). The particle size throughout this study was 500 µm. The natural gas flow rate varied between 84-240 ml/min. The results for 240 ml/min were not shown in Fig. 2 since the results showed a similar trend to the results observed with other flow rates. The rate observed at different flow rates will be analyzed further to detect the controlling regime. Table 1 shows the raw data extracted from the experimental work and the velocity around the particle, calculated through CFD simulation using the Advanced simulation library (Banu and Bicer 2021). Initial experiments in our lab have shown that the maximum conversion can be achieved within the temperature range of 500-600 °C. The effect of flow rate was investigated using 10 wt% Ni/Al 2 O 3 at 550 °C.
The reaction rate was measured at different catalyst particle sizes using a variable natural gas flow rate at 550 °C. The results indicate that the optimum particle size was 725 μm. As shown in Table 2, the maximum carbon deposition rate was achieved using a particle size of 725 μm. This particle size was chosen for further experimental work. The rate of reaction based on the external surface area per catalyst volume can be calculated from the following equations (Fogler 1999). The results are shown in Table 3: where r A(w) : the reaction rate in mol∕ .gcat as calculated using Eq. 3. C : Catalyst density in kg/m 3 , a C : External surface area of catalyst per volume of catalytic bed, m 2 ∕m 3 , d p : Catalyst particles average diameter; m, : Bed porosity. Figure 3 shows the relationship between the rate based on external surface area vs. the square root of velocity divided by particle diameter. Further investigation and analysis are needed to understand the nature of the controlling regime.
By studying the effect of velocity on reaction rate, it was clear that for flow rates 84-240 ml/min, the experimental results indicate that the reaction is controlled by external mass diffusion (Doraiswamy and Uner 2013). Experimental data suggest that velocity influences the rate, which implies that the external mass diffusion still controls the rate (Fogler 1999;Perkins 2022). For a reaction controlled by external mass diffusion, the effective rate constant can be expressed as follows (Fogler 1999):

For a first-order reaction
For a second-order reaction

For half-order reaction
where, k r : Intrinsic reaction rate constant. k c Is the mass transfer coefficient and is a function of the operating conditions and the equipment used (Fogler 1999): U : The velocity around the particle (from the CFD simulation). d p : Particle diameter.
To calculate the effective order of the reaction, the external effectiveness factor (ηx) will be plotted as a function of the Damkohler number (Da), Assuming isothermal operation as follows (Doraiswamy and Uner 2013): If ηx is plotted against Da on a double logarithmic chart, the curve accurately determines reaction order, as shown in Fig. 4.   Fig. 3 The variation of reaction rate with particle size and velocity past the particle The square root of the velocity over particle size, s -1/2 The reaction rate, Figure 4 shows the relation between the external effectiveness factor and the Damkohler number, assuming a firstorder reaction. Figure 4 indicates that the reaction is a firstorder reaction (Fogler 1999;Perkins 2022). Figure 5 shows the relation between the external effectiveness factor and the Damkohler number, assuming a secondorder reaction. Figure 5 shows that natural gas decomposition is not a second-order reaction (Fogler 1999;Perkins 2022). Figure 6 shows the relation between the external effectiveness factor and the Damkohler number, assuming a halforder reaction. Figure 5 indicates that natural gas decomposition is not a half-order reaction (Fogler 1999;Perkins 2022).

For half-order reaction
The data analysis indicates that the natural gas decomposition over Ni/Al 2 O 3 is a first-order reaction. The intrinsic specific reaction rate is calculated assuming a first-order reaction. Table 4 shows an increase in the effective specific rate with increasing velocity. Using Eqs. 6 and 9, the intrinsic specific reaction rate and the mass transfer constant were calculated and shown in Table 4.
The kr values in Table 4 justify our conclusions that the external mass diffusion controls the reaction since kr is four orders of magnitude higher than kc.

Effect of natural gas concentration
Nitrogen is used as a make-up gas to vary the natural gas concentration to study the effect of natural gas concentration on the reaction rate. After studying different natural gas flow rates, we concluded that the reaction is a first-order reaction, as discussed in the previous section (Amin et al. 2012(Amin et al. , 2011bFogler 1999). However, using an inert gas is important to check the reaction order at different concentrations of natural gas. Several concentrations of natural gas and nitrogen were used to study the catalyst performance using 10 wt% Ni/Al 2 O 3 at 550 °C and 120 ml/min. The mass transfer coefficient is calculated from Eq. 9.

Assuming half order
After calculating the values of intrinsic specific reaction and mass transfer coefficient, as shown in Tables 5 and 6, the  effective specific reaction rate is calculated based on the presumed reaction order. By dividing the rate by the effective specific reaction rate, the result equals the bulk concentration of natural gas (Doraiswamy and Uner 2013;Fogler 1999). To investigate the reaction order, the bulk concentration of natural gas is compared to the true bulk concentration of natural gas. As shown in Table 5, the reaction is a firstorder reaction (Fogler 1999;Perkins 2022).

Effect of hydrogen concentration
The reaction gas in this set of experiments is a mixture of natural gas and hydrogen; two mixtures are used: 10% hydrogen (90% natural gas) and 5% hydrogen (95% natural gas) using 5 wt% Ni/Al 2 O 3 . The flow rate is kept at 120 ml/ min and the temperature at 550 ℃.
Increasing the hydrogen concentration decreases the reaction and deactivation rates, as shown in Table 7, as indicated by the time needed for deactivation. In the case of 90% natural gas, the reaction is suppressed after 20 min. In the case of 95% natural gas, hydrogen positively affects the deactivation rate. The hydrogen effect was reported in several articles (Amin et al. 2012(Amin et al. , 2011b.
The catalyst remained active for an experiment duration time of 300 min.
The results indicate that a maximum peak for the positive effect of hydrogen on the reaction rate (activity) and deactivation rate occurs when hydrogen is 5 vol% in the reacting gas. The hydrogen effect depends on the catalyst's nature and operating conditions. Hydrogen presence in feed reduces both carbon formation rate and deactivation rate by reducing encapsulating carbon formation, and carbon nanotubes formed are dependent on catalyst nature and feeding gas (Al-Fatesh et al. 2016;Amin et al. 2011b).

Optimization of catalyst performance
Several nickel catalysts supported over alumina were prepared using wet impregnation at different loadings. The prepared catalysts were tested for natural gas decomposition inside the TGA at 550 °C using 120 ml/min of natural gas as a reacting gas. The results obtained can be briefed in Table 8 below: A mathematical equation was developed to optimize the catalyst performance to model the nickel/alumina catalyst performance for natural gas decomposition at 550 °C (Veziri et al. 2008). The least-square method was used to   where, x: Nickel loading in mg. y: Carbon deposition rate mgC /min.mgNi. The model proposed indicates a carbon deposition rate even if the nickel loading reaches zero, which is not practical. However, researchers reported limited catalytic activity for alumina (Qin et al. 2021).
To predict the highest value of carbon deposition on the catalyst, Eq. 12 is differentiated to generate the following Equation (Vassiliadis et al. 2021): Equation 13 can be solved to find the maximum carbon yield. Using Eq. 13, the maximum carbon that can be generated over the Ni/Alumina is achieved at a nickel loading of 12.5%. The loading is a critical value for the catalyst performance/activity. However, increasing nickel loading over alumina may lead to low dispersion of nickel over alumina resulting in poor performance.
The most critical parameter to be optimized is the total cost of the process, which can be influenced by the following (Amin et al. 2011b;Doraiswamy and Uner 2013;Veziri et al. 2008;Vanyorek et al. 2011): • Cost of hydrogen produced as a byproduct • Nickel and aluminum cost • Nickel cost • Nitrogen cost • Power used The market value of hydrogen produced Using Eq. 13, an equation can be developed to calculate the market value of hydrogen produced (Chin et al. 2006), assuming a hydrogen price of $2.2/kg as shown in Eq. (14):

Nickel and alumina cost
The cost of nickel and alumina used can be calculated using the following Eq. (15): The market value of hydrogen produced = (y × 0.0000022 × 4) 12 Ni(NO 3 ) 2 : $128/kg. Al 2 O 3 : $80/kg. The experimental results indicated that the reaction time might vary considerably due to catalyst deactivation according to reaction conditions, as shown in Fig. 2. It is essential to consider the reaction time as one of the optimization parameters (Vanyorek et al. 2011;Amin et al. 2011b). A new function will be created to account for the utilization of the catalyst over time. The cost of the nickel/ alumina can be distributed over the reaction time. The new function is called a utilization function, and the value of the proposed function will be the ratio of the used catalyst per minute. Figure 7 shows the optimization toolbox fitting for the function developed for the utilization of the catalyst. The utilization function can predict the catalyst operating cost in $/min as a function of the nickel loading, as shown in Fig. 7. The data demonstrated in Fig. 7 indicate that utilization cost decrease as the loading increases, which means that the utilization cost inversely proportional to the nickel loading. So, higher nickel loading is more economical for large-scale production (Suelves et al. 2005). The utilization function was developed using the least square method (Vassiliadis et al. 2021): The catalyst utilization in $/min can be calculated using Eq. 16 as a function of the catalyst's initial amount in g. The cost of the raw materials and power required to operate the TGA is discussed below in detail: Natural gas cost 120 ml/min. m = 0.0043 $/min.

Power used for operating the TGA
The TGA and its auxiliaries consume a power rate of (120 Volt*20 amp). 5.5 $/kWh*0.04 = 0.0022 $/min

The market value of natural gas decomposition and hydrogen
Without considering the market value of the carbon nanotubes, Eq. 17 can be used to optimize the catalyst performance and the feasibility of the natural gas catalytic decomposition over Ni/Al 2 O 3 (Vassiliadis et al. 2021). The previous equation is an objective equation, which is subjected to the inequality constraints: 1 ≤ x ≥ 30. Thirty percent is the suitable maximum loading for wet impregnation; a higher nickel percentage may produce a low-strength catalyst. By solving Eq. 17 using optimization tools, the optimum nickel loading is 30%. The dispersion measurements should limit the loading to ensure suitable utilization of nickel supported over alumina. The maximum profit per minute is $0.0021 without considering the profits generated through carbon nanotubes. So, an optimum loading of 12.5% is predicted using interpolation of the experimental data. The optimum active phase loading was 10% in several published articles (Ping et al. 2016;Amin et al. 2012;(17)

Carbon nanotubes characterization
The TEM graph for the produced carbon nanotubes is shown in Fig. 8 and Fig. 9 using 5 wt% Ni/Al 2 O 3 . The diameter of the carbon nanotubes is around 15-30 nm, which is within the same range as the nickel particle diameter. The TEM graphs show several types of carbon nanotubes, including hollow and solid carbon nanotubes, which can be used in several industrial applications. Figure 10 shows the SEM graph of the produced carbon nanotubes over 5 wt% Ni/ Al 2 O 3 . The SEM shows that the carbon nanotubes are produced in several diameters (within the range of 15-30 nm) and have a dense structure. Several articles reported similar observations (Amin et al. 2011b;Sivakumar et al. 2011). The carbon nanotubes diameter is usually within the same range as the active phase (Amin et al. 2011b;Sivakumar et al. 2011). Several experiments were conducted at 550 °C using 12.5 wt% Ni/Al 2 O 3 to investigate the catalyst performance using the optimized catalyst loading at 120 ml/min of natural gas. The carbon deposition rate observed was 0.125 mg C / min.mg Ni . The results indicate that 12.5% Ni/Al 2 O 3 showed a higher affinity for carbon deposition compared to the other examined catalyst. The carbon deposition rate was similar to that of 15 wt% Ni/Al 2 O 3 . However, 12.5 wt% is more costsaving than 15 wt% Ni/Al 2 O 3 .

Conclusions
A higher-quality carbon nanotube can be generated by optimizing the catalyst loading, maximizing hydrogen generation. The overall process economics can be improved by increasing the quality of produced carbon and the amount of hydrogen produced. Nickel is very active as a natural gas decomposition catalyst with a stronger carbon affinity than other metallic catalysts.
Natural gas decomposition to produce carbon nanotubes is studied in a thermal gravimetric analyzer. Several experiments were conducted at different flow rates to investigate the nature of the reaction-controlling regime. The experimental results indicate that the reaction is controlled by external mass diffusion. By analyzing the experimental results, it was clear that the reaction order is a first-order reaction. The produced carbon nanotubes were studied using the TEM technique. The diameter of the produced carbon nanotubes was 15-30 nm.
Several mathematical equations were developed to model the catalyst performance. Optimization techniques were used to optimize the nickel loading based on the experimental results. Using interpolation of the experimental data, a nickel loading of 12.5% was found to be the optimum nickel loading. A nickel loading of 12.5% showed similar activity and carbon deposition rate to 15% nickel loading. Considering the process's economics, an optimum nickel loading over alumina of 30% is predicted. The process is not commercial yet; more work is needed, including building a pilot-scale unit. The developed catalyst can be tested using the pilotscale reactor to collect data to optimize the process further and study the techno-economics of the process.

Declarations
Conflict of interest Conflict of interest there were no potential conflicts of interest revealed by the authors. The authors confirm that there are no relevant financial or non-financial competing interests to report.
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