Kinetics of Hydrogenation of Dimethyl Oxalate to Methyl Glycolate on an Activated Carbon-Supported Copper Catalyst

Abstract

A catalyst with the active component Cu loaded onto the carrier activated carbon was prepared, and metal Ca was introduced into the catalyst to modify it. This catalyst was used in the hydrogenation reaction of dimethyl oxalate, and the reaction kinetics was studied. The kinetic experiments were carried out in a fixed bed reactor with a reaction temperature varying from 483 K to 513 K, reaction pressure varying from 1.5 Mpa to 2.5 Mpa, and the weight hourly space velocity of dimethyl oxalate varying from 0.435 h⁻¹ to 0.726 h⁻¹. Eight possible dynamic models were proposed, the optimal model was selected, and the parameters of the optimal model were calculated using MATLAB. The results showed that dimethyl oxalate adsorbed on the active site by dissociation adsorption, and the dissociation adsorption of ester was the rate-controlling step. The parameters of the model were consistent with thermodynamics and statistical analysis, further proving that the model has good forecasting performance.

1. Introduction

Methyl glycolate (MG) has a unique molecular structure and can be used to produce organic chemicals such as pharmaceuticals and perfumes [1,2,3]. In recent years, it has received extensive attention because it can be used as an important raw material for the synthesis of biocompatible and biodegradable polyglycolic acid [4,5]. Traditional synthesis methods of MG, such as carboxylation of formaldehyde and condensation of methyl formate and formaldehyde, have some problems such as strict reaction conditions, high pollution, and low yield [6,7,8]. Compared with the traditional process, dimethyl oxalate (DMO) hydrogenation to produce MG is environmentally friendly and has warm reaction conditions and high yield [9,10]. DMO hydrogenation is a consecutive reaction which includes hydrogenation of one ester group of dimethyl oxalate to produce MG and hydrogenation of another ester group of the MG further to produce ethylene glycol (EG). Since the thermodynamic equilibrium constant of the second step is higher than that of the first step [9,11], MG is easy to further hydrogenate to EG, so it is important to develop an effective and stable catalyst with which to control the reaction and keep it in the first step.

Cu-based catalysts are widely used in ester hydrogenation due to their excellent performance and low cost. Abbas [12] developed a sonochemical approach, which can load a 50% Cu mass fraction on porous SiO₂, and the Cu is highly dispersed on the surface of porous SiO₂, forming Cu particles with small size. Compared with the traditional hydrothermal synthesis method, it has a higher Cu⁺/Cu⁰ ratio, which is conducive to increasing the MG selectivity; the conversion of DMO and the selectivity of MG can reach 90% and 94%, respectively. Wang [13] used ammonia evaporation to prepare a Cu/ZrO₂-SiO₂ catalyst. By adding a certain amount of ZrO₂ to the Cu/SiO₂ catalyst, the dispersion of copper was improved, and the grain size of the Cu particles was reduced. At the same time, strengthens the interaction between Cu and SiO₂, which is conducive to improving the ratio of Cu⁺ and significantly improving the catalytic activity and stability in this reaction. The conversion of DMO and the selectivity of MG can reach 93.32% and 88.17%, respectively. Cui [14] used the ammonia evaporation–impregnation method to load copper on activated carbon (AC). Activated carbon is an ideal support because it has a high specific surface area and abundant surface functional groups; the synthesized Cu/AC catalyst has high selectivity to MG. The conversion of DMO and the selectivity of MG can reach 83.31% and 92.04%, respectively. Zhang [15] used a one-pot hydrothermal method to load copper on N-doped carbon microspheres. Nitrogen atoms have an electronic effect that can enhance the interaction between Cu and carbon microspheres. The aforementioned group found that by changing the doping amount of nitrogen atoms, preventing the aggregation of Cu particles and adjusting the proportion of Cu⁺, the conversion of DMO and the selectivity of MG could reach 80.1% and 80.3%, respectively. The previous work of our group has found that an activated carbon-supported copper catalyst had high activity and MG selectivity for this reaction with the addition of Ca [16]; the conversion of DMO and the selectivity of MG reached 98% and 84%, respectively. For the hydrogenation reaction of dimethyl oxalate, Ye [17] proposed that the stability of the active sites of Cu-based catalysts was poor. Introducing metal additives such as Zn, Ni, Co, Pt, Pd, Au, and La was found to be beneficial in improving the stability of the catalyst. The conversion of DMO and the selectivity of EG could reach 100% and 90%, respectively. Li [18] modified Cu/SiO₂ with organic substances. The results showed that modifying the catalyst with organic substances was beneficial in reducing the agglomeration and sintering of metallic Cu particles, adjusting the ratio of Cu⁰/Cu⁺, and generating a new carbon layer to protect the Cu metal particles, thereby improving the hydrogenation performance of the catalyst. The conversion of DMO and the selectivity of EG could reach 100% and 99%, respectively. Strekalova [19] summarized the influence of secondary metals such as Ce, Fe, Zn, Pt, Pd, Ag, and Au on the performance of metal Cu-based catalysts; the second metal doped into the catalyst can form a strong interaction force with metal Cu, inhibit the sintering of Cu particles. It can be conducive to improving the stability of the catalyst and the selectivity of required alcohols; the conversion of DMO and the selectivity of EG could reach 100% and 95.3%, respectively.

The reaction conditions corresponding to the literature are shown in

Table 1. The reaction conditions corresponding to the literature.

Substrate	Product	Temperature /°C	Pressure /Mpa	Hydrogen Ester Ratio	LHSV of DMO /h	Reference
DMO	MG	220	2.5	200	0.257	[12]
DMO	MG	230	2.5	100	0.4	[13]
DMO	MG	220	2.5	120	0.18	[14]
DMO	MG	220	3	80	0.6	[15]
DMO	MG	240	2	80	0.9	[16]
DMO	MG	230	2.5	100	0.6	[17]
DMO	EG	190	3	100	0.6	[18]
DMO	EG	185	2	100	1.2	[19]

.

The study of the relevant mechanism and kinetics can provide theoretical support for developing catalysts and for industrial applications. Some scholars have conducted kinetic studies on the hydrogenation of dimethyl oxalate to produce ethylene glycol, and the results have shown that in the DMO hydrogenation reaction, DMO undergoes dissociation adsorption [20], and the rate-controlling step is the surface reaction or dissociation adsorption of ester [21,22].

Although some researchers have carried out kinetic studies on copper-based catalysts, catalyst studies have all been based on SiO₂, and reports carried out for the hydrogenation mechanism and kinetics studies with activated carbon as a support are rare. The support has a great impact on the catalytic performance of the catalyst. At the same time, for ester hydrogenation reactions on copper-based catalysts, the adsorption state of DMO on the catalyst and rate-controlling steps are still controversial.

Our research group prepared a catalyst with the active component metal Cu loaded onto activated carbon and introduced metal Ca to modify the catalyst (Cu-Ca/AC), which enabled the catalyst to have a high catalytic effect. In this work, the intrinsic kinetics of gas-phase hydrogenation of DMO on a self-made and optimized Cu-Ca/AC catalyst have been studied. Cu is the active component, Ca is the metal additive, and AC is the carrier, activated carbon. Based on the assumption of different ester adsorption types (dissociative adsorption or non-dissociative adsorption) and rate-controlling steps, eight different binary LHHW kinetic models were proposed. Using nonlinear least squares fitting method to solve the eight models in turn, select the optimal model, and calculate the kinetic parameters of the corresponding equation. The results showed that DMO adsorbed on the catalyst surface and dissociated to form methoxy group and acyl group. The rate-controlling steps of the two reactions were both ester dissociation adsorption. The model satisfies both thermodynamic criteria and statistical tests.

2. Results and Discussion

2.1. Elimination of Diffusion Effect

When studying the dynamics of gas–solid reaction systems, we should exclude the influence of internal and external diffusion to ensure that the reaction is in the intrinsic state. In order to investigate under which condition the effect of internal diffusion can be ignored, we use three different particle size catalysts (20–40 mesh, 40–60 mesh, and 60–80 mesh) to study the effect of particle size on the reaction under the same experimental conditions. As shown in Figure 1a, when the catalyst particle size is less than 20 mesh, the conversion rate of DMO is almost equal. In order to investigate the under which conditions the influence of external diffusion can be ignored, we keep the weight hourly space velocity (WHSV) of DMO constant, and the experiments are carried out with 1.6 g and 3.2 g catalysts, respectively, under the same other conditions. As shown in Figure 1b, when the WHSV of DMO is higher than 0.2813 h⁻¹, the conversion rate of DMO does not change with the change in catalyst mass, indicating that the influence of external diffusion has been eliminated. Therefore, during the experiment, it is necessary to ensure that the WHSV is higher than or equal to 0.2813 h⁻¹ to eliminate the influence of external diffusion.

2.2. Reaction Performance

In general, the DMO hydrogenation reaction consists of the following three reactions:

$$({\mathrm{COOCH}}_3{)}_2+2{\mathrm{H}}_2\to {\mathrm{HOCH}}_2{\mathrm{COOCH}}_3+{\mathrm{CH}}_3\mathrm{OH}$$

(1)

$${\mathrm{HOCH}}_2{\mathrm{COOCH}}_3+2{\mathrm{H}}_2\to {\mathrm{HOCH}}_2{\mathrm{CH}}_2\mathrm{OH}+{\mathrm{CH}}_3\mathrm{OH}$$

(2)

$${\mathrm{HOCH}}_2{\mathrm{CH}}_2\mathrm{OH}\to {\mathrm{CH}}_3{\mathrm{CH}}_2\mathrm{OH}+{\mathrm{H}}_2\mathrm{O}$$

(3)

Equation (1) represents the carbonyl hydrogenation of DMO to obtain MG, and Equation (2) represents the further hydrogenation of carbonyl group of MG to obtain EG. When the reaction temperature is increased, EG will be deeply hydrogenated to produce ethanol (EtOH). In this reaction, under the selected reaction conditions, Equation (3) can be ignored due to the small amount of EtOH that is generated.

The reaction conditions have a great influence on the performance of the catalyst. Figure 2a,b show the effect of temperature on the reaction. With the increase in reaction temperature, the conversion of DMO increases, and the selectivity of MG decreases. For example, under the conditions of WHSV = 0.563 h⁻¹ and P = 2 MPa, when the reaction temperature raised from 483 K to 513 K, the conversion of DMO increased from 65.22% to 97.09%, while the selectivity of MG decreased from 95.64% to 80.46%. This is because the reaction rate of both steps increased as the reaction temperature increased. Both reactions are sensitive to temperature. Figure 2c,d reflect the influence of pressure on catalyst performance. As can be seen from Figure 2c,d, the influence of pressure on the reaction is relatively low compared with that of temperature. Under the conditions that the temperature was 503 K and the WHSV of DMO was 0.563 h⁻¹, when the pressure increased from 1.5 MPa to 2.5 MPa, the conversion of DMO only increased by 5.6%, and the selectivity of MG only changed by 3.65%. In addition, it can be seen from the figure that a low WHSV (representing the contact time between reactants and catalysts) will lead to excessive hydrogenation of MG and reduce the yield of MG.

2.3. Reaction Mechanism and Kinetic Modeling

In the kinetics of ester hydrogenation, the LHHW model is often used [23,24,25,26]. Based on the LHHW model, the reaction process consists of the following steps. Step 1: the reactants are adsorbed on the surface of the catalyst in a non-ionized or ionized state; Step 2: surface reactions occur between the adsorbed reactants at the active site; Step 3: the product of the reaction is desorbed from the surface. There is a slow reaction (RDS) in the above steps, which controls the rate of the overall reaction, and the other steps are considered to be approximately in thermodynamic equilibrium.

At present, a large number of copper-based catalysts are used for ester hydrogenation reactions, but there is still controversy about what the active site is. Early studies on the kinetics of ester hydrogenation mainly focused on the LHHW model, which has a single active site [23,27,28]. Ai [29] synthesized a mesoporous silica-supported copper catalyst for DMO hydrogenation of EG. The results showed that Cu⁺ was responsible for the adsorption and activation of intermediates (methoxy and acyl) and reactants, and Cu⁰ was responsible for the dissociation of hydrogen during DMO hydrogenation. The formation of Si-O-Cu increased the ratio of Cu⁺/(Cu⁰ + Cu⁺) and enhanced the catalytic performance. Ye [30] prepared a Cu/SiO₂ catalyst and pointed out that the efficiency of the catalyst can be attributed to the synergistic effect of Cu⁰ and Cu⁺, which are conducive to the dissociation of hydrogen and the activation of C-O bonds in DMO molecules, respectively. Wang [10] designed experiments to confirm that two kinds of Cu active sites have a balancing effect on catalyst performance, among which the Cu⁰ site is responsible for hydrogen dissociation and the Cu⁺ active site adsorbs methoxyl and acyl groups produced during ester group dissociation. In addition, Cu⁺ can be used as an electrophilic group or Lewis acid site to polarize the C-O bond.

According to the reaction mechanism and reaction path, we made the following hypotheses:

• The adsorption of ester and hydrogen occurs at two different active sites (double active sites).
• The adsorption type of ester is dissociative adsorption or non-dissociative adsorption.
• All the active sites are equal, and the change in catalyst surface coverage does not affect the adsorption activation energy and desorption activation energy.
• The adsorption or surface reaction of reactants is the rate-controlling step of the reaction.

Based on the above assumptions, eight competing dynamic models are proposed in

Table 2. Eight rival kinetic models with each assumption.

No.	Adsorption Type of Ester	RDS
		R1	R2
1	non-dissociation	adsorption	adsorption
2	non-dissociation	adsorption	surface reaction
3	non-dissociation	surface reaction	adsorption
4	non-dissociation	surface reaction	surface reaction
5	dissociation	adsorption	adsorption
6	dissociation	adsorption	surface reaction
7	dissociation	surface reaction	adsorption
8	dissociation	surface reaction	surface reaction

.

2.4. Parameter Estimation

The reaction rate equations and differential equations of reactants and products involved in this study are as follows:

$${\mathrm{r}}_{\mathrm{DMO}}=-{\mathrm{r}}_1$$

(4)

$${\mathrm{r}}_{\mathrm{MG}}={\mathrm{r}}_1-{\mathrm{r}}_2$$

(5)

$${\mathrm{r}}_{\mathrm{EG}}={\mathrm{r}}_2$$

(6)

$${\mathrm{r}}_{\mathrm{MeOH}}={\mathrm{r}}_1-{\mathrm{r}}_2$$

(7)

$${\mathrm{r}}_{\mathrm{H}2}=-2{\mathrm{r}}_1-2{\mathrm{r}}_2$$

(8)

$${\mathrm{r}}_{\mathrm{i}}={\displaystyle \frac{\mathrm{d}{\mathrm{F}}_{\mathrm{i}}}{\mathrm{dm}}}(\mathrm{i}=\mathrm{DMO},\mathrm{MG},\mathrm{EG},\mathrm{MeOH},{\mathrm{H}}_2)$$

(9)

r₁ and r₂ represent the reaction rates of Equation (1) and Equation (2) respectively. Given the inlet molar flow rate of reactants, the molar flow F_i of various products in the reaction process was solved by simultaneous differential equations, and then the conversion of DMO and the selectivity of MG were calculated.

The dynamics parameters were calculated using MATLAB (R2022a). Firstly, the parameters were estimated by using the GA (genetic algorithm) function, setting the residual sum of squares (RSS) as the objective function and using the lsqnonlin function to search the values near the parameters before finally obtaining a minimum RSS value. Differential equations were solved by using the ode23 function.

$$\mathrm{RSS}={\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{N}}{[({\mathrm{X}}_{\exp ,\mathrm{i}}-{\mathrm{X}}_{\mathrm{cal},\mathrm{i}})}^2{+({\mathrm{Y}}_{\exp ,\mathrm{i}}-{\mathrm{X}}_{\mathrm{cal},\mathrm{i}})}^2]}$$

(10)

The proposed models were solved in turn. The determination coefficients, R² and RSS, of each model were obtained and are shown in

Table 3. The fitting effect of each model.

Model	1	2	3	4	5	6	7	8
RSS	0.1376	0.1835	0.1549	0.1372	0.0385	0.1446	0.1458	0.1714
R2 (for X)	0.9893	0.9817	0.9827	0.9876	0.9990	0.9804	0.9897	0.9642
R2 (for Y)	0.9689	0.9538	0.9589	0.9682	0.9751	0.9523	0.9685	0.9589

. The results show that Model 5 and Model 1 have better fitting effects.

Both Model 5 and Model 1 were able to reflect the experimental results well, and in order to further determine which model was more accurate, additional experiments were conducted under different conditions. As shown in

Table 4. Results of extra experiments of DMO hydrogenation at 2 MPa.

No.	Temp. [K]	n(H2)/n(DMO)	WHSV of DMO	Con. exp [%]	Con. cal of Model 1/5 [%]	Con. Relative Error of Model 1/5 [%]	Sel. exp [%]	Sel. cal of Model 1/5 [%]	Sel. Relative Error of Model 1/5 [%]
1	503	80	0.375	99.88	95.38/98.18	4.51/1.70	82.38	84.32/80.77	2.35/1.95
2	493	80	0.375	91.18	93.99/89.49	3.08/1.85	89.43	90.41/87.69	1.95/1.10
3	483	80	0.375	72.64	75.94/74.56	4.54/2.64	92.42	94.42/93.79	2.16/1.48

, Model 1 did not predict the conversion of DMO as well as Model 5. Therefore, Model 5 had a better prediction effect and was more suitable for the kinetic model.

The reaction rate equation of Model 5 is shown as follows:

$$\begin{array}{l}{\mathrm{r}}_1={\displaystyle \frac{{\mathrm{k}}_1({\mathrm{P}}_{\mathrm{DMO}}-\frac{{\mathrm{P}}_{\mathrm{MeOH}}{\mathrm{P}}_{\mathrm{MG}}}{{{\mathrm{K}}_{\mathrm{P}1}{\mathrm{P}}_{\mathrm{H}2}}^2})}{{({\mathrm{K}}_{\mathrm{EG}}{\mathrm{P}}_{\mathrm{EG}}+{\mathrm{K}}_{\mathrm{MeOH}}{\mathrm{P}}_{\mathrm{MeOH}}+\frac{{\mathrm{K}}_{\mathrm{MG}}{\mathrm{P}}_{\mathrm{EG}}{\mathrm{P}}_{\mathrm{MeOH}}}{{\mathrm{K}}_{\mathrm{P}2}{\mathrm{P}}_{\mathrm{H}2}}+\frac{{\mathrm{K}}_{\mathrm{DMO}}{\mathrm{P}}_{\mathrm{MeOH}}{\mathrm{P}}_{\mathrm{MG}}}{{\mathrm{K}}_{\mathrm{P}1}{\mathrm{P}}_{\mathrm{H}2}}+1)}^2}}\\ {\mathrm{r}}_2={\displaystyle \frac{{\mathrm{k}}_2({\mathrm{P}}_{\mathrm{MG}}-\frac{{\mathrm{P}}_{\mathrm{MeOH}}{\mathrm{P}}_{\mathrm{EG}}}{{{\mathrm{K}}_{\mathrm{P}2}{\mathrm{P}}_{\mathrm{H}2}}^2})}{{({\mathrm{K}}_{\mathrm{EG}}{\mathrm{P}}_{\mathrm{EG}}+{\mathrm{K}}_{\mathrm{MeOH}}{\mathrm{P}}_{\mathrm{MeOH}}+\frac{{\mathrm{K}}_{\mathrm{MG}}{\mathrm{P}}_{\mathrm{EG}}{\mathrm{P}}_{\mathrm{MeOH}}}{{\mathrm{K}}_{\mathrm{P}2}{\mathrm{P}}_{\mathrm{H}2}}+\frac{{\mathrm{K}}_{\mathrm{DMO}}{\mathrm{P}}_{\mathrm{MeOH}}{\mathrm{P}}_{\mathrm{MG}}}{{\mathrm{K}}_{\mathrm{P}1}{\mathrm{P}}_{\mathrm{H}2}}+1)}^2}}\end{array}$$

(11)

In Equation (11), the reaction rate constant k_i is based on the Arrhenius equation, and the adsorption equilibrium constant K_i is based on the Van’t Hoff equation.

$${\mathrm{k}}_{\mathrm{i}}={\mathrm{k}}_{\mathrm{i},0}\exp \left({\displaystyle \frac{{-\mathrm{Ea}}_{\mathrm{i}}}{\mathrm{RT}}}\right) \hspace{1em}(\mathrm{i}=1,2)$$

(12)

$${\mathrm{K}}_{\mathrm{i}}={\mathrm{K}}_{\mathrm{i},0}\exp \left({\displaystyle \frac{-\Delta {\mathrm{H}}_{\mathrm{i}}}{\mathrm{RT}}}\right){\hspace{1em}(\mathrm{i}=\mathrm{DMCD}, \mathrm{MHMCC}, \mathrm{CHDM}, \mathrm{MeOH}, \mathrm{H}}_2)$$

(13)

In the formula, K_p1 represents the reaction equilibrium constant of R1, and K_p2 represents the reaction equilibrium constant of R2. The values of K_p1 and K_p2 were estimated using the Benson [31] group’s contribution method. The values of K_p1 and K_p2 at different conditions are shown in

Table 5. Reaction equilibrium constants at different temperatures.

T [K]	Kp1	Kp2
493	27.1	2.27
503	20.3	2.10
513	15.1	1.96
523	9.9	1.82

below [32].

The values of reaction rate constant k_i and adsorption equilibrium constant K_i obtained by fitting Model 5 are shown in

Table 6. Estimated parameters of Model 5.

Parameters	Pre-Exponential Factor	Activation Energy/Heat of Adsorption
	ki,0 [mol gcat−1h−1)]	Eai [kJ·mol−1]
k1	3.59 × 109	127.29
k2	4.95 × 108	130.51
	Ki,0 [MPa−1]	ΔHi [kJ·mol−1]
KDMO	5.72 × 10−3	−50.02
KMG	3.08 × 10−3	−54.62
KEG	1.02 × 10−3	−40.35
KMeOH	1.80 × 10−3	−18.93
KH2	6.0 × 10−4	−12.14

.

Table 7. Activation energy and adsorption heat of dimethyl oxalate hydrogenate reactions in our references.

Substrate	Catalyst	Ea1 /kJ·mol−1	Ea2 /kJ·mol−1	ΔHDMO /kJ·mol−1	ΔHMG /kJ·mol−1	ΔHEG /kJ·mol−1	ΔHMeOH /kJ·mol−1	Reference
DMO	Cu/SiO2	51.2	73.2	−32.38	−69.26	−75.07	−27.04	[20]
DMO	Cu/SiO2	36.38	44.84	−56.28	−48.09	−34.09	−74.42	[25]
DMO	Cu-Ca/AC	127.29	130.51	−50.02	−54.62	−40.35	−18.93	our study

lists the numerical values of the activation energy and adsorption heat of the dimethyl oxalate hydrogenate reactions in the studies referenced herein. As can be seen from the table, the activation energy value of dimethyl oxalate hydrogenation ranges from 30 to 140 kJ·mol⁻¹, depending on the type of catalyst. The activation energy calculated in this study was within this range, and the activation energy value was large, indicating that the reaction is very sensitive to temperature. The adsorption heat of DMO ranges from −60 to −30 kJ·mol⁻¹, and the adsorption heat of DMO calculated in this study fell within this range. The adsorption heat of MG in our references ranges from −80 to −40 kJ·mol⁻¹; our calculated adsorption heat of MG was −54 kJ·mol⁻¹, which is relatively reasonable. The adsorption heat values of EG range from −80 to −30 kJ·mol⁻¹, and the value calculated in this study was −40.35 kJ·mol⁻¹, which also fell within a reasonable range. The adsorption heat range of methanol (MeOH) is large, and the value calculated in this study was −19 kJ·mol⁻¹, which is similar to −27 kJ·mol⁻¹ (the value calculated by Gu [20]).

As shown in Figure 3, the data predicted using kinetic Model 5 are close to our experimental values, indicating that the Model 5 is effective.

In addition, as shown in Figure 4, the relative errors between the experimental values of DMO conversion and MG selectivity and the calculated values were calculated. As can be seen from Figure 4, Model 5 has a good fitting effect.

2.5. Model Testing

In general, the model also needs to satisfy the F-test:

$$\mathrm{F}={\displaystyle \frac{{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{N}}{{( \hat{\mathrm{y}}}_{\mathrm{i}}- \overline{\mathrm{y}} )}^2{/(\mathrm{N}}_{\mathrm{p}}-1)}}{{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{N}}{{( \hat{\mathrm{y}}}_{\mathrm{i}}{-\mathrm{y}}_{\mathrm{i}})}^2{/(\mathrm{N}-\mathrm{N}}_{\mathrm{p}})}}} > 10 \times { \mathrm{F}}_{0.99}{(\mathrm{N}}_{\mathrm{p}}{-1,\mathrm{N}-\mathrm{N}}_{\mathrm{p}})$$

(14)

The calculated F value of X_DMO is 126.6, and that of Y_MG is 50.59; both of them are higher than 10 × F_0.99 (=21.98), indicating the accuracy of the kinetic mode.

In addition to statistical verification, the kinetic parameters of the reaction should also abide by the laws of physics and chemistry; for example, the adsorption enthalpy ($\Delta \mathrm{H}$) of the reaction and the adsorption entropy ($\Delta \mathrm{S}$) of each substance must abide by the corresponding thermodynamic laws [33]. At the same time, the adsorption equilibrium constant K_i, calculated using the Boundart [34] criterion, should be thermodynamically consistent. Their values should meet the following requirements:

$${\mathrm{K}}_{\mathrm{i}}=\exp ({\displaystyle \frac{\Delta \mathrm{S}}{\mathrm{R}}})$$

(15)

$${0<-\Delta \mathrm{S}<\mathrm{S}}_{\mathrm{g}}$$

(16)

$$41.8\le -\Delta \mathrm{S}\le 51-0.0014\Delta \mathrm{H}$$

(17)

where S_g represents the entropy of the gas [35], and R is the ideal gas constant. As shown in

Table 8. Validation of model parameters by physicochemical laws.

Substance	ΔS	Sg [J mol−1 K−1]	51 − 0.0014ΔH
DMO	−42.09	364.84	−121.03
MG	−43.18	345.12	−127.47
EG	−93.05	323.55	−107.49
MeOH	−73.12	239.7	−77.485
H2	−46.00	130.6	−51.84

, the adsorption equilibrium constants all conform to thermodynamic criteria.

2.6. Discussion of Reaction Mechanism

In the literature, there are some controversies about the adsorption state of ester in the ester hydrogenation reaction.

Table 9. Adsorption states of esters obtained by different scholars.

Substrate	Catalyst	Adsorption Type of Ester	Reference
furfural	Cu/SiO2	non-dissociation	[36]
diethyl maleate	copper chromite	non-dissociation	[37]
ethyl acetate	Cu/SiO2	dissociation	[38]
butyl butyrate	Cu/ZnO/Al2O3	dissociation	[39]
formate/acetate	Cu/SiO2	dissociation	[40]
dimethyl oxalate	Cu/SiO2	dissociation	[21]
dimethyl oxalate	Cu/SiO2	dissociation	[23]
dimethyl oxalate	Cu/SiO2	dissociation	[25]
dimethyl oxalate	Cu/SiO2	dissociation	[41]
dimethyl oxalate	Cu-Ca/AC	dissociation	our study

lists the adsorption states of esters obtained by different scholars. According to studies of ester group hydrogenation kinetics, the dissociation adsorption mechanism seems to be more reliable in DMO hydrogenation reactions.

In this study, the dissociative adsorption mechanism was also applicable to the hydrogenation of DMO. It can be found from the analysis that after the Cu-Ca/AC catalyst was reduced, Cu²⁺ was completely reduced to Cu⁰ and Cu⁺. These two Cu species with different valence states served as the active sites of the catalyst and coexisted on the surface of the catalyst. At the Cu⁺ active site, the DMO molecule formed methoxy and acyl groups by breaking the C-O bond. The resulting acyl species were hydrogenated at the Cu⁺ active site to form MG. The resulting MG dissociated at the Cu⁺ active site into methoxy and acyl groups, which continued to hydrogenate to form EG. Within DMO hydrogenation preparing an MG reaction, the surface reaction or adsorption of reactants may all have been RDS. In this work, the rate-controlling steps of R1 and R2 were the dissociation adsorption of ester. Based on the discussion of the above mechanism, the reaction path is shown in

Table 10. Reaction pathway of DMO hydrogenation.

Elementary Reaction Steps
${\mathrm{H}}_2+2^{\ast } \leftrightarrow 2{\mathrm{H}}^{\ast }$ ${\mathrm{CH}}_3{\mathrm{OOCCOOCH}}_3+2^{\ast }\to {\mathrm{CH}}_3{\mathrm{OOCC}}^{\ast }\mathrm{OH}+\#$
${\mathrm{CH}}_3{\mathrm{OOCC}}^{\ast }\mathrm{OH}+\mathrm{H}\# \leftrightarrow { \mathrm{CH}}_3{\mathrm{OOCC}}^{\ast }\mathrm{HOH}+\#$
${\mathrm{CH}}_3{\mathrm{OOCC}}^{\ast }\mathrm{HOH}+\mathrm{H}\# \leftrightarrow {\mathrm{CH}}_3{\mathrm{OOCC}}^{\ast }{\mathrm{H}}_2\mathrm{OH}+\#$
${\mathrm{CH}}_3{\mathrm{OOCC}}^{\ast }\mathrm{HOH}+\mathrm{H}\# \leftrightarrow { \mathrm{CH}}_3{\mathrm{OOCC}}^{\ast }{\mathrm{H}}_2\mathrm{OH}+\#$
${\mathrm{CH}}_3{\mathrm{OOC}}^{\ast }{\mathrm{H}}_2\mathrm{OH} \leftrightarrow { \mathrm{HOCH}}_2{{\mathrm{CH}}_3\mathrm{OOC}+ }^{\ast }$
${\mathrm{HOCH}}_2{\mathrm{COOCH}}_3+2^{\ast } \to { \mathrm{HOCH}}_2{\mathrm{C}}^{\ast }\mathrm{O}+{\mathrm{CH}}_3{\mathrm{O}}^{\ast }$
$\mathrm{HOCH}{\mathrm{C}}^{\ast }\mathrm{OH}+\mathrm{H}\# \leftrightarrow { \mathrm{HOCH}}_2{\mathrm{C}}^{\ast }\mathrm{OH}+\#$
${\mathrm{HOCH}}_2{\mathrm{C}}^{\ast }\mathrm{OH}+\mathrm{H}\# \leftrightarrow { \mathrm{HOCH}}_2{\mathrm{C}}^{\ast }\mathrm{HOH}+\#$
${\mathrm{HOCH}}_2{\mathrm{CH}}^{\ast }\mathrm{OH}+\mathrm{H}\# \leftrightarrow { {\mathrm{HOCH}}_2\mathrm{C}}^{\ast }{\mathrm{H}}_2\mathrm{OH}+\#$ ${\mathrm{HOCH}}_2{\mathrm{C}}^{\ast }{\mathrm{H}}_2\mathrm{OH}\leftrightarrow {\mathrm{HOCH}}_2{\mathrm{CH}}_2\mathrm{OH}{+ }^{\ast }$ ${\mathrm{CH}}_3{\mathrm{O}}^{\ast }+\mathrm{H}\#\leftrightarrow {\mathrm{CH}}_3{\mathrm{OH}}^{\ast }+\#$
${\mathrm{CH}}_3\mathrm{OH}\#\leftrightarrow { \mathrm{CH}}_3\mathrm{OH}+\#$

# represents the Cu⁺ active site that adsorbs ester molecules, * represents the Cu0 active site that adsorbs hydrogen.

.

The reaction process for the mechanism of DMO is shown in Figure 5.

3. Experiment

3.1. Materials

Cu(NO₃)₂·3H₂O (≥99%) and Ca(NO₃)₃·4H₂O (≥99%) were purchased from Shanghai Titan Technology Co., LTD. (Shanghai, China). CH₃OH (≥99.8%) was purchased from Shanghai Wohua Chemical Co., LTD. (Shanghai, China); NH₃·H₂O (25–28 wt%) was purchased from Shanghai Lingfeng Chemical Reagent Co., LTD., (Shanghai, China); (COOCH₃)₂ (≥99%) was purchased from Shanghai Meryl Biochemical Technology Co., LTD., (Shanghai, China); NH₂CONH₂ (≥99%) was purchased from Shanghai Chuangsai Technology Co., LTD. (Shanghai, China); activated carbon (AC) (≥99%) was purchased from Jiangsu Zhuxi Activated Carbon Co., LTD. (Liyang, Jiangsu, China); H₂ (99.99%) was purchased from Shanghai Pujiang Special Gas Co., LTD. (Shanghai, China); and N₂ (99.99%) was purchased from Air Liquide (Shanghai) Compressed Gas Co., LTD. (Shanghai, China).

3.2. Catalyst Preparation

The Cu-Ca/AC catalyst was prepared by urea-assisted ammonia evaporation and precipitation. Mixture A was formed of 5 g AC and an aqueous solution of 4 g NH₂CONH₂ in 50 mL deionized water. For solution B, 3.04 g Cu(NO₃)₂·3H₂O was dissolved in 50 mL deionized water, and then 28 wt% NH₃·H₂O was added drop by drop to it until the solution was clarified and transparent with a PH of 10–11. The final state of copper in solution B was Cu(NH3)₄²⁺ [16]. Solution C was formed of 0.591 g Ca(NO₃)₃ 4H₂O dissolved in 10 mL deionized water. After stirring mixture A for 30 min, solution B was added, and the mixture was stirred for 1 h. Then, the above mixture was put into a water bath at 353 K and stirred. Then, solution C was added to it drop by drop. The mixture was continuously stirred at 353 K until the PH of the solution was 6–7. During this process, the urea was hydrolyzed and the ammonia was evaporated; the copper and calcium were precipitated and supported on AC. The solid product was filtrated, washed three times with deionized water, and dried overnight in an oven at 353 K. Then, the solid was heated at 623 K for 3 h, pressed, crushed, and sieved through 40–60 mesh to prepare the catalyst. The catalyst was named Cu-Ca/AC; Cu was the active component, Ca was the metal additive, and AC, i.e., activated carbon, was the carrier.

3.3. Kinetic Experiment

The hydrogenation reaction of DMO was carried out in a fixed-bed reactor equipped with an 8 mm (internal diameter) and 50 cm (length) stainless steel tube. In typical fashion, the catalyst was loaded in the middle of the reactor, and the upper and lower sides of the catalyst were filled with quartz sand to distribute the gas feed and support the catalyst particles. Before the reaction, the catalyst was reduced in 50 mL/min of 10% H₂/N₂ at 573 K for 4 h. After the reaction bed was cooled down to the reaction temperature and the H₂ pressure was increased to a set value, DMO (15 wt%) dissolved in methanol was continuously pumped into the reactor at a constant flow rate. The solution was preheated, vaporized, and fully mixed with H₂; the n(H₂)/n(DMO) was 80. The vapor phase product was cooled to a liquid in a condensing tank, and the liquid product was collected in the gas–liquid separation tank. The reaction conditions were a temperature of 483–513 K, a reaction pressure of 1.5–2.5 Mpa, and a weight hourly space velocity (WHSV) of DMO varying from 0.435 h⁻¹ to 0.726 h⁻¹. The gas-phase products were trapped in liquid using a cooling condenser at 278 K.

The products were analyzed by using a GC2060 gas chromatograph equipped with an Agilent capillary column (specification: 30 m × 0.53 mm × 0.5 μm) and a hydrogen ion flame ionization (FID) detector.

The conversion of dimethyl oxalate and selectivity of products were calculated based on the following equations:

$$\mathrm{Conversion} (\%)={\displaystyle \frac{\mathrm{n}{\left(\mathrm{D}\mathrm{M}\mathrm{O}\right)}_{\mathrm{i}\mathrm{n}}-\mathrm{n}({\mathrm{D}\mathrm{M}\mathrm{O})}_{\mathrm{o}\mathrm{u}\mathrm{t}}}{\mathrm{n}{\left(\mathrm{D}\mathrm{M}\mathrm{O}\right)}_{\mathrm{i}\mathrm{n}}}} \times 100\%$$

(18)

$$\mathrm{Selectivity} (\%)={\displaystyle \frac{\mathrm{n}\left(\mathrm{M}\mathrm{G}\right) \mathrm{o}\mathrm{r} \mathrm{n}\left(\mathrm{E}\mathrm{G}\right)}{\mathrm{n}{\left(\mathrm{D}\mathrm{M}\mathrm{O}\right)}_{\mathrm{i}\mathrm{n}}-\mathrm{n}({\mathrm{D}\mathrm{M}\mathrm{O})}_{\mathrm{o}\mathrm{u}\mathrm{t}}}} \times 100\%$$

(19)

4. Conclusions

The intrinsic kinetics of gas-phase hydrogenation of DMO on a Cu-Ca/AC catalyst was studied in a fixed-bed reactor. The reaction process involved initial hydrogenation of DMO to produce the main product MG and excessive hydrogenation of MG to produce the byproduct EG. Based on the binary LHHW mechanism, eight different competitive dynamics models were proposed to describe the reaction process. The nonlinear least squares estimation method was used to fit the experimental data using eight models, and the parameters were calculated using MATLAB. Model 5 was in good agreement with the experimental results, and Model 5 also satisfied the thermodynamic criteria and statistical tests. Therefore, the mechanism of DMO hydrogenation reaction was revealed. DMO adsorbed on the catalyst surface dissociated to form a methoxy group and acyl group, and the acyl group hydrogenated to MG. MG generated EG through a similar step. The rate-controlling steps of R1 and R2 were both the dissociation adsorption of ester. The activation energies of DMO hydrogenation and MG hydrogenation were both relatively high (127.29 and 130.51 kJ·mol⁻¹, respectively), indicating that both reactions are sensitive to temperature.