CO 2 Conversion to Methanol over Novel Carbon Nanoﬁber-Based Cu / ZrO 2 Catalysts—A Kinetics Study

: Ongoing industrialization has deteriorated the global environment. Global warming is a human-induced issue a ﬀ ecting the environment. The alarming increase in CO 2 emissions is among the major contributors to global warming. The conversion of CO 2 to methanol is an economically viable and environmentally friendly solution to mitigate its concentration. Here, hydrogenation of CO 2 was studied over carbon nanoﬁber-based Cu / ZrO 2 catalysts. Kinetics investigations were carried out for the reaction. Overall, kinetics data indicated that CO 2 conversion follows a pseudo-ﬁrst-order reaction. The kinetics studies were further modeled by using an artiﬁcial neural network, which supported the experimental kinetics study.


Introduction
Rapid industrialization to cope with growing population demands has adversely affected the natural environment. The rise in CO 2 concentration as a result of industrialization is considered to be a major contributor to global warming [1]. CO 2 hydrogenation to methanol provides a win-win situation by diminishing CO 2 concentration on the one hand while producing fuel in the form of methanol on the other [2][3][4][5].
CO 2 hydrogenation to methanol is given by Reaction 1 [6].
To support methanol synthesis on an industrial scale, many kinetics models have been proposed in the literature for CO 2 conversion to methanol. Kinetic investigations of low-temperature CO 2 conversion have a potential impact on designing and controlling the reactor systems for such processes [7]. Several kinetic models with variant reaction mechanisms have been reported for methanol synthesis by CO 2 conversion. The Langmuir-Hinshelwood-Hougen-Watson model was applied over a CuO/ZnO/Al 2 O 3 catalyst by Skrzypek et al. [8]. Similarly, a dual-site mechanism-based kinetic model was developed [9]. Likewise, a kinetic model with three-site adsorption was applied over a copper-zinc catalyst [10].
Recently, Díez-Ramírez et al. [11] documented the application of a three-site mechanism-based model over a Pd-Cu-Zn/SiC catalyst.
The early-stage kinetics model assumes that methanol synthesis is only possible from CO, where CO 2 cannot be used in the synthesis of methanol [12][13][14][15]. More recently, complex kinetics models have been introduced based on experimental findings that indicate that methanol is not produced mainly from CO but in fact from CO 2 [8,[15][16][17].
An artificial neural network (ANN) model has been applied for CO 2 hydrogenation to methanol. The application of this model has been found to be very promising for describing the chemistry of complex reactions. Similarly, the model also helps understanding of the reaction mechanism where exact mechanisms of reactions are not well comprehended. The application of this model is therefore best suited in the case of complex CO 2 hydrogenation with non-univocal reaction mechanisms. Furthermore, an ANN model has been recorded as 120-5000 times faster when compared to phenomenological models, giving extra advantage to this model regarding computation time [18]. Therefore, the ANN model has found wide application in kinetics investigations in chemical and biological reactors [19,20]. The ANN model was applied to investigate kinetics study over the Al 2 O 3 catalyst for methanol dehydration by Alamolhoda et al. [21] in using a slurry reactor. The study found that the experimental kinetics data was significantly matched by ANN model estimations. In this approach, which is considered to be very effective due to the involvement of computer architecture, the ANN model uses the numerical input and output values obtained from experimental data.
Carbon nanofibers (CNFs), due to high surface area, are considered to be a good catalyst support [22,23]. The application of CNFs is further amplified in liquid-phase reactions due to the complete absence of bottle-like pores which ultimately mitigate mass transfer limitations [24,25]. Therefore, CNF-supported catalysts have been reported to have better catalytic profiles compared to traditional metal oxide-based catalysts [1]. In the current work, kinetics studies of CNF-supported Cu/ZrO 2 catalysts in terms of CO 2 conversion have been undertaken. The significance of the current study can be comprehended by the fact that it can potentially be applied for the understanding of a detailed reaction mechanism of CO 2 conversion to methanol over CNF-supported Cu/ZrO 2 catalysts, which is one of the hypotheses of the current work.
The goal of the current work is a kinetics study of CO 2 conversion. Based on our previous work, the catalyst with optimum activity (Cu.ZrO 2 /CNFs with 15 wt.% of Cu and ZrO 2 each) was used. The catalyst was characterized by X-ray diffraction (XRD) and scanning electron microscopy (SEM) techniques to assess the phase and morphology of the catalyst, respectively. Furthermore, the reported kinetics data was supported by the application of an ANN model in the current work.

XRD and TEM Investigations
The XRD spectrum and transmission electron microscopy (TEM) image of the CZC450 catalyst are displayed in Figure 1

Kinetics Study
A slurry reactor was employed to evaluate the kinetics study for CO2 hydrogenation to methanol.
To evaluate the rate of CO2 conversions, the concentrations of H2 and H2O were neglected.
For the concentration ratio = , the reaction rate is given as follows: Where , and is the initial concentration of CO2, initial concentration of CH3OH and CO2 conversion fraction, respectively.
, and and are equilibrium CO2 conversion, equilibrium CO2 concentration and equilibrium CH3OH concentration, respectively The equilibrium constant ( ) is given by Combining Equations (1)-(3) CO2 conversion at equilibrium is obtained as Integration of Equation (4) gives

Kinetics Study
A slurry reactor was employed to evaluate the kinetics study for CO 2 hydrogenation to methanol.
To evaluate the rate of CO 2 conversions, the concentrations of H 2 and H 2 O were neglected.
For the concentration ratio M = , the reaction rate is given as follows: where C CO 2 O , C CH 3 OH O and X CO 2 is the initial concentration of CO 2 , initial concentration of CH 3 OH and CO 2 conversion fraction, respectively.
X CO 2 e , C CO 2 e and C CH 3 OH e and are equilibrium CO 2 conversion, equilibrium CO 2 concentration and equilibrium CH 3 OH concentration, respectively. The equilibrium constant (k c ) is given by Combining Equations (1)-(3) CO 2 conversion at equilibrium is obtained as Integration of Equation (4) gives A graph plotted between −ln(1 − X CO 2 X CO 2 e ) against reaction time for the kinetics data obtained at different reaction temperatures resulted in a straight line as depicted in Figure 2, therefore supporting a pseudo-first-order kinetics hypothesis for CO 2 conversion. Catalysts 2020, 10, x FOR PEER REVIEW 4 of 10 The magnitudes of k1, obtained from slope are documented in Table 1.

Activation Energy
The Arrhenius equation was used to calculate activation energy as depicted in Equation (6).
where k1 shows rate constant, representing effective collisions between the reactants. R represents the universal gas constant, while Ea stands for activation energy.
Integrating Equation (6), we get the linearized Arrhenius Equation (7), lnk1 was plotted versus 1/T to measure the activation energy as shown in Figure 3. A value of 54 kJ/mole activation energy was found in the current case, very close to the reported data in Table 2. The magnitudes of k 1 , obtained from slope are documented in Table 1.

Activation Energy
The Arrhenius equation was used to calculate activation energy as depicted in Equation (6).
where k 1 shows rate constant, representing effective collisions between the reactants. R represents the universal gas constant, while Ea stands for activation energy.
Integrating Equation (6), we get the linearized Arrhenius Equation (7), lnk 1 was plotted versus 1/T to measure the activation energy as shown in Figure 3. A value of 54 kJ/mole activation energy was found in the current case, very close to the reported data in Table 2.

Application of Artificial Neural Networks
An ANN model with a feed-forward back-propagation network was employed in the current study. Four algorithms, namely trainbr, trainlm, traingdm, and traingda, were used to evaluate the experimental data. Figure 4 shows good agreement between the experimental and predicted data, indicating the accuracy of the kinetics data. Such agreement between the experimental data and ANN-predicted data was reported for Pt-Sn/c-Al2O3 catalyst-based propane dehydrogenation by Amini et al. [28].

Application of Artificial Neural Networks
An ANN model with a feed-forward back-propagation network was employed in the current study. Four algorithms, namely trainbr, trainlm, traingdm, and traingda, were used to evaluate the experimental data. Figure 4 shows good agreement between the experimental and predicted data, indicating the accuracy of the kinetics data. Such agreement between the experimental data and ANN-predicted data was reported for Pt-Sn/c-Al 2 O 3 catalyst-based propane dehydrogenation by Amini et al. [28].

Catalysts Synthesis
CNF GNF-100 type, acquired from Carbon Nano-material Technology Co. Ltd., Korea was used as the catalyst support. Deposition precipitation method was used for catalyst synthesis [25,29,30]. Copper nitrate tri-hydrate (R&M Chemicals, London, UK) and zirconyl nitrate hydrate (Sigma-Aldrich, Louis, MO, USA) were used as starting materials for Cu and ZrO2, respectively. In a typical experiment, the required quantities of copper nitrate triydrate and zirconyl nitrate hydrate were dissolved in distilled water. Upon total dissolution of the nitrate salts, the required amount of pH was adjusted to 8 by urea solution. The slurry was stirred for 18 h at 85-90 °C.
Catalyst Cu.ZrO2/CNFs with 15 wt.% each (Cu and ZrO2) with CNFs as a support was synthesized. The synthesized catalyst was cooled to avoid leaching of active catalyst components, filtered, washed, and dried overnight at 100 °C. The dried catalyst was calcined at N2 flow at 450 °C for 3 h and labeled as CZC450 catalyst. The catalyst underwent reduced H2 flow with rate of 2000 cm 3 h −1 for 6 h at 380 °C before kinetics investigations.

Characterization
The PANalytical X-ray diffractometer model Empyrean (Malvern Panalytical Ltd, Malvern, UK) was employed to investigate phase studies of catalyst. Room-temperature XRD studies were conducted from 20 to 80 at 2θ Bragg angle.
Zeiss LIBRA 200TEM TEM (A Carl Zeiss SMT AG Company, Oberkochen, Germany) was employed to investigate catalyst morphology in the current work.

Catalysts Synthesis
CNF GNF-100 type, acquired from Carbon Nano-material Technology Co. Ltd., Korea was used as the catalyst support. Deposition precipitation method was used for catalyst synthesis [25,29,30]. Copper nitrate tri-hydrate (R&M Chemicals, London, UK) and zirconyl nitrate hydrate (Sigma-Aldrich, St. Louis, MO, USA) were used as starting materials for Cu and ZrO 2 , respectively. In a typical experiment, the required quantities of copper nitrate triydrate and zirconyl nitrate hydrate were dissolved in distilled water. Upon total dissolution of the nitrate salts, the required amount of pH was adjusted to 8 by urea solution. The slurry was stirred for 18 h at 85-90 • C.
Catalyst Cu.ZrO 2 /CNFs with 15 wt.% each (Cu and ZrO 2 ) with CNFs as a support was synthesized. The synthesized catalyst was cooled to avoid leaching of active catalyst components, filtered, washed, and dried overnight at 100 • C. The dried catalyst was calcined at N 2 flow at 450 • C for 3 h and labeled as CZC450 catalyst. The catalyst underwent reduced H 2 flow with rate of 2000 cm 3 h −1 for 6 h at 380 • C before kinetics investigations.

Characterization
The PANalytical X-ray diffractometer model Empyrean (Malvern Panalytical Ltd., Malvern, UK) was employed to investigate phase studies of catalyst. Room-temperature XRD studies were conducted from 20 to 80 at 2θ Bragg angle.
Zeiss LIBRA 200TEM TEM (A Carl Zeiss SMT AG Company, Oberkochen, Germany) was employed to investigate catalyst morphology in the current work.

Kinetics Study
Slurry reactor model Parr 4593 was used in the current study. A kinetics investigation for CO 2 conversion was conducted at 453, 473, 493, and 513 K reaction temperature with constant 40 bar pressure. 0.5 g of catalyst was placed in a reactor vessel containing 25 mL ethanol, used as the reaction solvent [31]. The reaction was stirred at 1300 rpm to avoid mass transfer limitations [32,33]. The kinetics of the process was investigated in a dynamic mode by taking the sample at different time intervals. The samples were analyzed at reaction times of 20, 40, 60, 80, 100, 120, 140, 160, and 180 min and gas samples were studied by GC TCD for CO 2 conversion. The experiment lasted for 3 h.

Artificial Neural Networks for Kinetics Estimations
An ANN model with back-propagation method was used as a supporting tool in the current work ( Figure 5). Hence, as predicted, the kinetics data performed at 40 bar constant reaction pressure. The role of pressure in the reaction helps in the kinetics of the reaction, but higher pressure is usually not recommended in industry. Therefore, optimum pressure value is adopted in this study and, while keeping it constant, temperature varies, to find the rate of the reaction. The adopted ANN procedure replicated our experimental finding and, in comparison with the experimental data, the predicted results show a reasonable estimate.
Catalysts 2020, 10, x FOR PEER REVIEW 7 of 10 Slurry reactor model Parr 4593 was used in the current study. A kinetics investigation for CO2 conversion was conducted at 453, 473, 493, and 513 K reaction temperature with constant 40 bar pressure. 0.5 g of catalyst was placed in a reactor vessel containing 25 mL ethanol, used as the reaction solvent [31]. The reaction was stirred at 1300 rpm to avoid mass transfer limitations [32,33]. The kinetics of the process was investigated in a dynamic mode by taking the sample at different time intervals. The samples were analyzed at reaction times of 20, 40, 60, 80, 100, 120, 140, 160, and 180 min and gas samples were studied by GC TCD for CO2 conversion. The experiment lasted for 3 h.

Artificial Neural Networks for Kinetics Estimations
An ANN model with back-propagation method was used as a supporting tool in the current work ( Figure 5). Hence, as predicted, the kinetics data performed at 40 bar constant reaction pressure. The role of pressure in the reaction helps in the kinetics of the reaction, but higher pressure is usually not recommended in industry. Therefore, optimum pressure value is adopted in this study and, while keeping it constant, temperature varies, to find the rate of the reaction. The adopted ANN procedure replicated our experimental finding and, in comparison with the experimental data, the predicted results show a reasonable estimate. In addition, four algorithms were used in a MATLAB platform for CO2 conversion. The "trainlm" and "trainbr" types are the network training updates bias and weight value of your input and target data, based on the Levenberg-Marquardt optimization procedure. The algorithm type "trainlm" is considered to be the fastest back-propagation algorithm and recommended to be the first-choice supervised algorithm that does not require memory as compared to other algorithms. The algorithm type "trainbr" curtails the combination of both weights and squared errors; by doing that, it determines the correct combination so that the network can produce a correct generalization of the input and output data. This process is known as Bayesian regularization. The type "traingda" is the network training function, which operates by updating the weight and bias based on output and input data according to gradient descent with adaptive learning rate procedure. The performance of this algorithm is sensitive to the proper setting of the learning rate. Setting learning to high creates unstable and oscillated algorithms, whereas setting the learning rate to low can take the algorithm too long to converge. The type "traingdm" is the network training function, which updates weight and bias values using gradient decent with momentum procedure. In addition, four algorithms were used in a MATLAB platform for CO 2 conversion. The "trainlm" and "trainbr" types are the network training updates bias and weight value of your input and target data, based on the Levenberg-Marquardt optimization procedure. The algorithm type "trainlm" is considered to be the fastest back-propagation algorithm and recommended to be the first-choice supervised algorithm that does not require memory as compared to other algorithms. The algorithm type "trainbr" curtails the combination of both weights and squared errors; by doing that, it determines the correct combination so that the network can produce a correct generalization of the input and output data. This process is known as Bayesian regularization. The type "traingda" is the network training function, which operates by updating the weight and bias based on output and input data according to gradient descent with adaptive learning rate procedure. The performance of this algorithm is sensitive to the proper setting of the learning rate. Setting learning to high creates unstable and oscillated algorithms, whereas setting the learning rate to low can take the algorithm too long to converge. The type "traingdm" is the network training function, which updates weight and bias values using gradient decent with momentum procedure.

Conclusions
In the current work, CO 2 conversion has been reported using a CNF-supported Cu/ZrO 2 catalyst. Kinetics investigations were carried out for the title reaction. The overall kinetics studies revealed that CO 2 conversion follows pseudo-first-order kinetics. Similarly, the Arrhenius model was used to calculate the activation energy of the reaction. The kinetics data were supported using an ANN model.