Liquid-Phase Hydrogenation over a Cu/SiO₂ Catalyst of 5-hydroximethylfurfural to 2,5-bis(hydroxymethyl)furan Used in Sustainable Production of Biopolymers: Kinetic Modeling

Abstract

2,5-bis(hydroxymethy)lfuran (BHMF), a renewable compound with extensive industrial applications, can be obtained by selective hydrogenation of the C=O group of 5-hydroxymethylfurfural (HMF), a platform molecule derived from lignocellulosic biomass. In this work, we perform kinetic modeling of the selective liquid-phase hydrogenation of HMF to BHMF over a Cu/SiO₂ catalyst prepared by precipitation–deposition (PD) at a constant pH. Physicochemical characterization, using different techniques, confirms that the Cu/SiO₂–PD catalyst is formed by copper metallic nanoparticles of 3–5 nm in size highly dispersed on the SiO₂ surface. Before the kinetic study, the Cu/SiO₂-PD catalyst was evaluated in three solvents: tetrahydrofuran (THF), 2-propanol (2-POH), and water. The pattern of catalytic activity and BHMF yield for the different solvents was THF > 2-POH > H₂O. In addition, selectivity to BHF was the highest in THF. Thus, THF was chosen for further kinetic study. Several experiments were carried out by varying the initial HMF concentration (C⁰_HMF) between 0.02 and 0.26 M and the hydrogen pressure (P_H2) between 200 and 1500 kPa. In all experiments, BHMF selectivity was 97–99%. By pseudo-homogeneous modeling, an apparent reaction order with respect to HFM close to 1 was estimated for a C⁰_HMF between 0.02 M and 0.065 M, while when higher than 0.065 M, the apparent reaction order changed to 0. The apparent reaction order with respect to H₂ was nearly 0 when C⁰_HMF = 0.13 M, while for C⁰_HMF = 0.04 M, it was close to 1. The reaction orders estimated suggest that HMF is strongly absorbed on the catalyst surface, and thus total active site coverage is reached when the C⁰_HMF is higher than 0.065 M. Several Langmuir–Hinshelwood–Hougen–Watson (LHHW) kinetic models were proposed, tested against experimental data, and statistically compared. The best fitting of the experimental data was obtained with an LHHW model that considered non-competitive H₂ and HMF chemisorption and strong chemisorption of reactant and product molecules on copper metallic active sites. This model predicts both the catalytic performance of Cu/SiO₂-PD and its deactivation during liquid-phase HMF hydrogenation.

1. Introduction

Over the last century, the development of society has been largely driven by fossil resources, which have been used as raw materials in the production of fuels, chemicals, pharmaceuticals, and especially plastics [1]. Specifically, the use of plastics has grown exponentially, in line with improvements in quality of life. However, this growth has brought about a strong dependence on fossil resources [2]. Furthermore, it has generated increasing concern about its environmental impact, particularly in relation to climate change [3,4]. In this context, scientific and technological efforts have intensified toward processing biomass-derived compounds, such as sugars, to obtain platform molecules that are building blocks for producing bio-based plastics [5].

Currently, there is a consensus that platform molecules derived from lignocellulosic biomass should be explored as alternatives to fossil-derived molecules, as they are widely available, are low-cost, and do not compete with food [6]. Among them, 5-hydroxymethylfurfural (HMF) stands out for its great potential to replace petroleum-based molecules due to its high chemical reactivity, which allows it to be converted into a variety of valuable compounds [7,8,9,10]. One of the compounds to which HMF can be converted is 2,5-bis(hydroxymethyl)furan (BHMF). This compound could be used in the production of biopolymers, such as polyurethanes and polyesters, which are among the most widely used plastics in the world [9,10]. A reaction scheme showing the selective HMF hydrogenation to BHMF is shown in Scheme 1.

Processes based on heterogeneous catalysis satisfy green chemistry principles such as reducing pollution and dangerous chemicals and minimizing waste and by-products [11]. Moreover, to enable the industrial viability of such transformation routes, it is necessary to develop efficient production processes based on heterogeneous catalysis. These processes require catalysts that are not only active, selective, and stable under reaction conditions but also inexpensive and prepared through simple methods. Moreover, catalysts should be easily recoverable and reusable to ensure process sustainability. So, it is expected that heterogeneous catalysis will play a central role in the search for sustainable solutions to issues related to the production of biopolymers, such as polyurethanes and polyesters, from BHMF.

Several research works on liquid-phase heterogeneous catalytic conversion of HMF into BHMF have been published [12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29]. Among them, supported monometallic catalysts based on noble metals, such as Pt [12,13], Au [14], and Ir [15], have been used. However, the high cost of these metals compromises the economic viability of technologies that rely on them. Supported metal catalysts based on non-noble metals have also been employed with the aim of finding a possible solution to this issue. Ni-based catalysts have been shown to be active in the hydrogenation of both the carbonyl group and the aromatic ring of HMF [16,17]. In particular, under certain reaction conditions or combined with a specific support, Ni-based catalysts were active in the hydrogenolysis of C-OH bonds and, as a consequence, 2,5-dimethylfuran (DMF) was obtained [18,19]. NiGa and NiPt bimetallic systems supported on hydrotalcite and SBA-15 have also been used, reaching BHMF selectivities of 96% and 82%, respectively [20,21]. However, despite this high selectivity, a major drawback of this study lies in the complexity of the catalyst’s preparation methods, which may hinder its scalability and practical application. Co-based catalysts exhibited high activity in HMF hydrogenation, but low selectivities to BHMF were obtained due to the occurrence of hydrogenolysis reactions [22,23]. Srifa et al. added Pt to a Co/Al₂O₃ catalyst to increase selectivity to BHMF. Although the catalyst achieved a high BHMF yield (99%), it was not stable under the reaction conditions, exhibiting loss of activity and selectivity, and leaching of the metallic phase [23]. Cu-based catalysts are the non-noble metal catalysts most selective to BHMF, and under mild reaction conditions, they promote selective carbonyl hydrogenation, preventing the cleavage of C-O or C-C bonds [24,25,26,27,28,29]. HMF conversions greater than 95%, with selectivities to BHMF between 95 and 98%, were reached using supported Cu monometallic catalysts, such as Cu/ZnO [24], Cu/SiO₂ [25,26], and Cu/MgAlO_X [27]. A copper-based catalyst supported on CeO₂ modified with trace amounts of Pd showed high selectivity to BHMF (99.9%) at 80% conversion of HMF under the conditions used in the work [28]. However, its preparation involved intricate synthesis strategies aimed at achieving spatially controlled metal species on the support, which may pose challenges for large-scale implementation. Rezayan et al. reported the production of BHMF using a bimetallic CuCoAl catalyst, prepared via a co-precipitation method, which was cost-effective and scalable. Although the catalyst showed good stability, the BHMF selectivity (~91%) was lower than that of the monometallic Cu catalysts due to the presence of hydrogenolysis products [29]. So, bimetallic Cu-based catalysts showed better stability than monometallic ones, but HMF conversions and selectivities to BHMF were lower than those observed with monometallic Cu catalysts.

Regarding kinetic studies of liquid-phase HMF hydrogenation using heterogeneous catalysts, very few works have been reported to date. In this sense, it is worth mentioning the work of Jain and Vaidya, since these authors used a commercial Ru(5%)/C catalyst to perform kinetic modeling of the catalytic hydrogenation of HMF to BHMF in the liquid phase, applying power law and LHHW models [30]. They used water as a solvent and H₂ gas as the hydrogenating agent, analyzing the effect of initial HMF concentration, H₂ pressure, catalyst concentration, and reaction temperature on the rate of reaction. In general, the reaction conditions were similar but not identical to the ones used in the present work. In addition to how the catalysts used in each work are different, it is very important to highlight that Jain and Vaidya performed an analysis considering only the initial HMF conversion rates. This partial analysis is very useful, especially for determining the intrinsic activity of the catalyst, but it is insufficient for establishing a complete kinetic expression that allows the prediction or modeling of the actual behavior of the catalyst throughout a complete run. This becomes important when the catalyst is used in a production reactor.

In our previous work, we found that a monometallic Cu/SiO₂ catalyst prepared by the precipitation–deposition method showed the best performance, with high HMF final conversion (~91%) and BHMF selectivity (~99%) at 393 K and 1500 kPa of H₂ pressure [31]. This catalyst, prepared by a simple synthesis method, can be easily recovered and reused in reaction. This makes it highly attractive for use in the development of green processes, such as the production of BHMF. Now, in this work, we focus on a detailed kinetic study for the selective production of BHMF from HMF using this Cu/SiO₂ catalyst (Scheme 1). Therefore, this study allows us to deepen the knowledge on HMF hydrogenation over metallic copper silica-supported catalysts, directly contributing to the design of efficient and environmentally friendly processes, in accordance with the principles of sustainable chemistry.

2. Materials and Methods

2.1. Catalyst Preparation and Characterization

A Cu/SiO₂-PD catalyst precursor was prepared by the precipitation–deposition method at a controlled pH and temperature, as detailed in Zelin et al. [31]. Summarizing, aqueous solutions of Cu(NO₃)₂.₃H₂O and K₂CO₃ were simultaneously added to a stirred suspension of SiO₂ (Sigma-Aldrich) in milli-Q^® water. The temperature was adjusted and controlled at 338 K, while the pH of the solution was maintained at 7.2 ± 0.2. The slurry obtained was separated by filtration, dried at 358 K overnight, and finally calcined in air flow at 673 K for 4 h.

The metallic load of the oxide precursor achieved in the calcined sample was determined by atomic absorption spectroscopy (AAS) using a Perkin-Elmer 3110 spectrometer. The specific surface area (Sg), pore volume (Vg), and pore diameter (dm) were measured using a N₂ physisorption at 77 K in a Quantachrome Autosorb I sorptometer.

The crystalline structure of the hydrated precursor, the oxide precursor, and a reduced sample in hydrogen flow at 523 K and passivated in O₂ (1%)/N₂ flow at room temperature were studied via X-ray diffraction (XRD), employing an Empyrean Serie 2 X-ray system (Panalytical) with Ni-filtered Cu-Kα radiation (λ = 0.1540 nm) and a 2°/min speed scan.

The temperature-programmed reduction (TPR) profiles of the Cu/SiO₂-PD oxide precursors were obtained in H₂(5%)/Ar flow (60 cm³/min) using a Hiden Analytical QGA system equipped with a quadrupole mass analyzer.

2.2. Catalytic Tests

The liquid-phase catalytic hydrogenation of HMF (AVA Biochem, purity ≥ 99%) was carried out in a 500 cm³ stainless steel autoclave at 200–1500 kPa of H₂ pressure, 393 K, using 150 cm³ of solvent: tetrahydrofuran (THF) (Cicarelli, pro-analysis + 99.0%), 2-propanol (2-POH) (Cicarelli, pro-analysis +99.0%), and water (H₂O). The initial HMF concentration (C⁰_HMF) was between 0.02 M and 0.26 M and the mass of the catalyst was adequate to obtain a relationship of W/n⁰_HMF = 25 g/mol. Prior to the catalytic tests, the samples were activated ex situ in H₂ (100%) flow (60 cm³/min) for 2 h at 523 K, then were cooled down in H₂ flow and transferred to a high-pressure reactor under an inert atmosphere (N₂). Next, a predetermined amount of HMF and 1 cm³ of hexadecane, used as an internal standard, were added to the solvent. Afterwards, the system was purged and pressurized with 100 kPa of N₂. Then, the reaction mixture was stirred at 760 rpm and heated up to the reaction temperature at 5 K/min. Once the reaction temperature was reached, H₂ was added to the reactor in order to set the previously established partial pressure of H₂.

Liquid samples were periodically collected during the reaction, at intervals of 15–30 min. Off-line analysis of these samples was conducted employing gas chromatography in a Shimadzu 2014 GC (Jenck S.A., Buenos Aires, Argentina) chromatograph equipped with an ALPHA DEXTM 120 column (30 m × 0.25 mm × 0.25 μm film thickness) and a flame ionization detector. Mass spectroscopy analyses were also performed, employing a Thermo Scientific Trace 13000 (Thermo Fisher Scientific, Buenos Aires, Argentina) spectrometer coupled with a Thermo Scientific Trace 1300 gas chromatograph equipped with a TR 5MS column (30 m × 0.25 mm × 0.25 μm film thickness) to identify unknown products.

The HMF conversion was calculated as X_HMF = ($n_{\mathit{HMF}}^0$ − n_HMF)/n⁰_HMF, where n⁰_HMF is the initial number of HMF moles and n_HMF is the number of HMF moles at a given reaction time. The product yields (y_j) were calculated as y_j = (n_j/υ_j)/(n⁰_HMF/υ_HMF), where n_j is the number of moles of product j and υ_HMF and υ_j are the stoichiometric factors of HMF and product j, respectively. Selectivity to product j (S_j) was obtained as S_j = y_j/ X_HMF.

The initial rates of HMF hydrogenation (r⁰_HMF, mol/h·g) are determined from the slope at the zero time of the HMF conversion vs. W·t/n⁰_HMF curves, where W is the total catalyst weight (g) and t is time of reaction (h).

The carbon balance (CB) is defined as follows:

$$CB=({\alpha }_{HMF}·n_{HMF}+{\alpha }_{BHMF}·n_{BHMF})/{(\alpha }_{HMF}·n_{HMF}^0)$$

where ${\alpha }_{HMF}$ and ${\alpha }_{BHMF}$ are the number of carbon atoms in HMF and BHMF, which is 6 for both molecules. Thus, the CB expression simplifies to the following:

$$CB=(n_{HMF}+n_{BHMF})/n_{HMF}^0$$

2.3. Procedure for Numerical Calculus and Fittings

The differential HMF mass balance is presented in Equation (A1) and was resolved by numerical integration using an algorithm based on the fourth-order Runge–Kutta method. This numerical resolution is performed simultaneously with the optimization of the parameters to be adjusted using the General Reduced Gradient (GRG) algorithm for non-linear optimization problems (Solver) that minimizes the sum of the squared errors (SSE). Finally, the confidence intervals of the optimized estimators, obtained as a result of fitting and numerical integration, are obtained using macro Excel^R, developed by Robert de Levie [32].

3. Results

3.1. Textural and Physicochemical Properties of Cu/SiO₂-PD Catalyst

The results obtained from the physicochemical characterization of the Cu/SiO₂-PD catalyst and SiO₂ used in this work are summarized in

Table 1. Physicochemical characterization of the Cu/SiO₂-PD catalyst and support [31].

Samples	Cu(a) (%w/t)	Sg (m2/g)	Vp (cm3/g)	dp (nm)	TPR(b) (K)	${\mathbf{D}}_{{\mathbf{N}}_2\mathbf{O}}$(c) (%)	${\mathbf{D}}_{{\mathbf{N}}_2\mathbf{O}}$(d) (nm)	dTEM(e) (nm)
SiO2	-	296	1.06	14.3	-	-	-	-
Cu/SiO2-PD	8.0	270	0.94	12.7	566	21	3.6	4.7

^(a) Copper content determined by atomic absorption spectroscopy. ^(b) Temperature at maximum hydrogen consumptions in temperature programed reduction experiments. ^(c) Metallic copper dispersion determined by titration with nitrous oxide at 363 K. ^(d) Copper metal particle size estimated from metallic dispersion assuming cubic geometry. ^(e) Copper metal particle size estimated from transmission electron microscopy.

. The Cu load, determined by AAS, was 8 wt%. The BET surface area (Sg), pore volume (Vp), and pore diameter (dp) of the catalyst were approximately 10% lower than those of the support. This indicates that the textural properties of the support did not change significantly following Cu precipitation–deposition on it.

The X-ray powder diffractograms for Cu/SiO₂-PD are shown in Figure 1. For the hydrated, calcined, and reduced–passivated samples of Cu/SiO₂-PD (Figure 1, diffractograms (1), (2), and (3)), only the amorphous halo in the 2θ range 20–30°, attributed to the SiO₂ support, was observed. This indicates that the Cu phase is supported on the internal surface of silica pores forming crystalline domains smaller than 4 nm, as previously reported [31].

The TPR of the calcined sample (Figure S1) showed a peak at 566 K with a small shoulder at 590 K, which may be due to reduction of Cu species with different support interactions, i.e., to silica species of different natures. In previous works, we assigned the peak at 566 K to the reduction of CuO, and the signal at 590 to the reduction of copper phyllosilicates [31].

In previous studies, we verified by TEM and N₂O chemisorption that Cu/SiO₂-PD is composed of nanoparticles between 3 and 5 nm in size, which are highly dispersed on the silica surface [31,33]. N₂O chemisorption measurements showed that metal dispersion (D_N2O) on Cu/SiO₂-PD is about 21%, with the mean metallic copper particles size (d_N2O) of 3.6 nm. On the other hand, the estimated mean size found by TEM was d_TEM = 4.7 nm, very similar to that obtained by N₂O chemisorption.

3.2. Catalytic Test

3.2.1. Solvent Influence on Catalytic Performance

The influence of the solvent on the catalytic activity and selectivity of BHMF during HMF hydrogenation was investigated at 393 K and 1500 kPa of H₂ pressure. Three different solvents were tested: tetrahydrofuran (THF), 2-propanol (2-POH), and water (H₂O).

Figure 2 shows the conversion of HMF as a function of time for these three solvents, while

Table 2. Liquid-phase HMF hydrogenation over Cu/SiO₂-PD catalysts at 393 K and 1500 kPa of H₂ pressure (W = 0.5 g; V_Solv = 150 cm³).

Solvent	${\mathit{r}}_{\mathit{H}\mathit{M}\mathit{F}}^0$ 102 a (mol/h.g)	XHMF b (%)	${\mathit{y}}_{\mathit{B}\mathit{H}\mathit{M}\mathit{F}}$c (%)	SBHMF d (%)	CB e (%)
THF	1.44	91	90	98	99
2-POH	0.94	59	58	98	98
H2O	0.35	20	9	45	98

^a Initial conversion rate of HMF hydrogenation. ^b HMF conversion after 5.5 h reaction. ^c Yield in BHMF after 5.5 h reaction. ^d Selectivity to BHMF at 20% of HMF conversion. ^e Carbon balance.

summarizes the obtained values of the initial HMF hydrogenation rate (r⁰_HMF), HMF conversion (X_HMF), and BHMF selectivity (S_BHMF) at a 20% conversion level. The Cu/SiO₂-PD catalyst was active for the hydrogenation of HMF in all solvents, presenting the following activity order: THF > IPA > H₂O. The HMF conversion achieved at the end of the reaction for the different solvents followed the same pattern as that observed for the initial catalytic activity. X_HMF was higher than 90% when THF was used as the solvent, and with 2-POH, the conversion recorded was close to 60%, while with water, it did not exceed 20%. The balance of carbon (CB) with Cu/SiO₂-PD in the liquid-phase HMF hydrogenation was higher than 97% for all experiments.

Regarding product distribution, BHMF was the only product detected when THF and 2-POH were used as solvents, achieving selectivities of 98%, respectively. However, BHMF selectivity was only 45% when H₂O was used as a solvent, with 1-hydroxy-2,5-hexanedione and 2,5-hexanedione as by-products coming from the ring-opening reaction of the HMF molecules with water. These two compounds were identified by GC-MS of samples taken from the reactor during the run (Figures S2 and S3). These results are in agreement with those obtained by other authors, who report that the catalytic hydrogenation of HMF in water produces a ring-opening reaction [34,35,36].

These results confirm that solvent selection is extremely important to achieve high hydrogenation rates and BHMF selectivity in the liquid phase when molecular H₂ is used as a reducing agent. On the other hand, the application of BHMF in the field of polymers to obtain polyurethane foams, self-healing materials, and resins is usually carried out using THF as a solvent [9,36,37]. The use of the same solvent in both steps allow the potential implementation of a “one-pot” process involving the sequential hydrogenation and polymerization reactions in a single reactor. The efficiency of these “one-pot” processes lies in their ability to reduce auxiliary and intermediate stages, such as the separation and purification of intermediate products. This saves time and resources in production leading to the implementation of a more sustainable process.

3.2.2. Kinetic Modeling of HMF Hydrogenation with the Cu/SiO₂-PD Catalyst

Hypothesis and Principal Model Rate Equations Used

A summary of the set of experimental conditions, number of runs,${ r}_{HMF }^0$ values determined from the slope of the curves $X_{HMF} vsW·t/n_{HMF }^0$, and turnover frequency (TOF) is given in

Table 3. Number of independent catalytic runs performed with $W/n_{HMF}^0$ = 25 g/mol. Initial HMF hydrogenation rate are estimated from the slope of the curve $X_{HMF} vs W·t/n_{HMF }^0$a t = 0 and the corresponding TOF values.

Run	${\mathit{C}}_{\mathit{H}\mathit{M}\mathit{F}}^0$(M)	PH2 (kPa)	T (K)	${\mathit{r}}_{\mathit{H}\mathit{M}\mathit{F}}^0$·102 (mol/h.g)	TOF (1/h)
1	0.020	1500	393	0.48	227
2	0.040	1500	393	0.70	333
3	0.065	1500	393	1.32	624
4	0.130	1500	393	1.44	680
5	0.260	1500	393	1.50	707
6	0.040	700	393	0.39	185
7	0.040	400	393	0.23	110
8	0.040	200	393	0.14	64
9	0.130	1000	393	1.27	601
10	0.130	500	393	1.31	620
11	0.130	200	393	1.24	586

.

Based on the complete set of experimental data obtained in this work, primarily the concentration of HMF and BHMF in solution at varying reaction times and under different experimental conditions, we performed several analyses of HMF hydrogenation kinetics in the liquid phase over a Cu/SiO₂-PD catalyst. We began with an analysis of the initial rates, r⁰_HMF, estimated from the slope of the curves ${ X}_{HMF} vsW·t/n_{HMF }^0$ at time zero, to determine the effects of H₂ pressure and the initial concentration of HMF on the reaction rate, i.e., to estimate the apparent orders with respect to both reactants. Then, based on a pseudo-homogeneous power law-like model (Equation (1)), we fitted and estimated the apparent reaction orders now considering a subset of data obtained along the whole run, i.e., not only from the initial data ($r_{HMF}^0$). Next, we fitted the experimental data using distinct heterogeneous LHHW-like models to finally select the model that gave the best fitting with kinetic parameters significantly different from zero. It is essential to know the mathematical expression that fully describes the model and the estimates obtained by fitting with the corresponding confidence intervals to express the uncertainty associated with the estimation.

The power law model for the HMF hydrogenation rate is given in Equation (1).

$$\left(r_{HMF}\right)=k_{ph}·{\left(C_{HMF}\right)}^n·{\left(C_{H_2}\right)}^m$$

(1)

where k_ph is the pseudo-homogeneous kinetic constant of the reaction, n is the kinetic order with respect to HMF, and m is the kinetic order with respect to H₂. ${ C}_{HMF }$ and $C_{H_2}$ are the H₂ and HMF liquid concentrations, respectively. The orders are empirical or apparent, taking virtually all possible values: integer, fractional, positive, negative, or zero. These apparent kinetic orders, as a pseudo-homogeneous model, will generally assume positive fractional values that are only valid within the narrow range of conditions where they are estimated. This model is named model 1.

To analyze and determine insights into the results obtained with the heterogeneous catalytic reaction system under study, we propose a classical Langmuir–Hinshelwood–Hougen–Watson (LHHW)-type approach. From this analysis, two heterogeneous models were proposed. The first heterogeneous model considered that all adsorption sites are identical for the adsorption of H₂, HMF, and BHMF, i.e., competitive chemisorption (model 2). The second heterogeneous model considered two different types of chemisorption sites: an S1 type for H₂ adsorption and S2 for adsorption of HMF and BHMF (model 3), i.e., non-competitive chemisorption.

The hypotheses made for the formulation of both LHHW mechanisms used in this work are the following:

• The reactants, namely H₂ and HMF, can be adsorbed on the adsorption sites (S, or S1 and S2) with 1:1 stoichiometry;
• The H₂ chemisorption is non-dissociative;
• The reaction product, BHMF, can be adsorbed on the adsorption sites (S, or S1 and S2) with 1:1 stoichiometry;
• The surface irreversible reaction between adsorbed H₂ and HMF is the controlling step of the reaction;
• The adsorptions of H₂, HMF, and BHMF on the catalyst sites are reversible steps in equilibrium;
• According to the experimental conditions, for each catalytic run, the H₂ concentration in the liquid phase is constant and determined by the H₂ pressure and the Henry constant in THF.

Considering the first hypothesis, the main elementary reaction steps for the proposed LHHW reaction mechanism are the following:

H2(g) ⇌ H2(l)	⋯	H = PH2(g)/CH2(l)
H2(l) + S1 ⇌ H2S1	⋯	KH = CH2S1/(CH2(l)·CS1)
HMF + S2 ⇌ HMFS2	⋯	KA = CHMFS2/(CHMF·CS2)
HMFS2 + H2S1 ⇀ BHMFS2 + S1	⋯	rHMF = ksr·CHMFS2·CH2S1
BHMFS2 ⇌ BHMF + S2	⋯	KB = CBHMFS2/(CBHMF·CS2)

For the particular case corresponding to model 2, where both catalytic sites are identical (S1 = S2 = S), only one total site balance needs to be performed, leading to Equation (2):

$$C_{TS}=C_S+C_{H2S}+C_{HMFS}+C_{HMFS}$$

(2)

In the case of model 3, two total active balance sites should be considered for the catalyst, $C_{TS1}$ and $C_{TS2}$, given by Equations (3) and (4).

$$C_{TS1}=C_{S1}+C_{H2S1}$$

(3)

$$C_{TS2}=C_{S2}+C_{HMFS2}+C_{HMFS2}$$

(4)

Appendix A presents the mathematical development necessary to deduce the final rate of reaction expressions of each model. The catalytic reaction rate expression for model 2 is given in Equation (5).

$$\left(r_{HMF}\right)={\displaystyle \frac{\left(\raisebox{1ex}{$k_{sr}·K_A·K_H·{C_{TS}}^2$}\!\left/ \!\raisebox{-1ex}{$H$}\right.\right)·C_{HMF}^0·P_{H2}·C*}{{\left[1+\raisebox{1ex}{$K_H·P_{H2}$}\!\left/ \!\raisebox{-1ex}{$H$}\right.+K_A·C_{HMF}^0·C*+K_B·C_{HMF}^0·\left(1-C*\right)\right]}^2}}$$

(5)

For model 3, the corresponding catalytic reaction rate expression is given in Equation (6).

$$\left(r_{HMF}\right)={\displaystyle \frac{\left(\raisebox{1ex}{$k_{sr}·K_A·K_H·C_{TS1}·C_{TS2}$}\!\left/ \!\raisebox{-1ex}{$H$}\right.\right)·C_{HMF}^0·P_{H2}·C*}{\left[1+\raisebox{1ex}{$K_H·P_{H2}$}\!\left/ \!\raisebox{-1ex}{$H$}\right.\right]·\left[1+K_A·C_{HMF}^0·C*+K_B·C_{HMF}^0·\left(1-C*\right)\right]}}$$

(6)

In both equations, the HMF concentration is expressed in a dimensionless way (C* = $C_{HMF}/C_{HMF}^0$) to make explicit the presence of the initial HMF concentration ($C_{HMF}^0$) as a parameter for consideration.

Influence of Hydrogen Pressure

The influence of hydrogen pressure ($P_{H_2}$) was investigated at 393 K and varying $P_{H_2}$ between 200 and 1500 kPa at two different initial HMF concentrations ($C_{HMF}^0$ = 0.13 M and $C_{HMF}^0$ = 0.04 M). Figure 3a,b show the HMF conversion as a function of $W·t/n_{HMF }^0$ for different $P_{H_2 }$ and two different $C_{HMF}^0$. For $C_{HMF}^0$ = 0.13 M (Figure 3a), the conversion profiles did not show significant differences between them, especially at HMF conversion levels below 30%. The $r_{HMF }^0$ calculated for these runs showed approximately the same values (run 4,9–11; Table 3). In contrast, when the initial HMF concentration was 0.04 M (Figure 3b), the $r_{HMF }^0$ increased as $P_{H_2 }$ increased (run 2,6–8; Table 3). The apparent reaction order of H₂ (m) at the two $C_{HMF }^0$ concentrations was estimated by applying a linear regression over the plot of $\mathit{ln}{r}_{HMF}^{0}vs \mathit{ln}{P}_{H_2}$, as shown in Figure 3c. The estimated m was (0.06 ± 0.08) at a 0.13 M initial HMF concentration, explaining the lack of influence of H₂ pressure on the initial rate of the HMF hydrogenation. However, the estimated m for an initial HMF concentration of 0.04 M was (0.81 ± 0.07), in agreement with the positive effect of H₂ pressure on the HMF hydrogenation rate (Figure 3c) at this level of HMF concentration.

Influence of HMF Concentration

The effect of initial HMF concentration ($C_{HMF}^0$ = 0.02 M − 0.26 M) on the catalytic activity and HMF conversion was studied at T = 393 K and $P_{H_2}$ = 1500 kPa, while keeping the $W/n_{HMF }^0$ ratio constant. Figure 4a shows the influence of $C_{HMF}^0$ on the HMF conversion rate (runs 1–5). Precisely, the $r_{HMF}^0$ increased with rising initial HMF concentration, as can be seen in Table 3. This increase in the initial hydrogenation rate diminishes in importance for concentrations above 0.065 M. From the plot representing $\mathit{ln}{r}_{HMF}^0$ as a function of $\mathit{ln}{C}_{HMF}^0$ and applying lineal regression, the apparent reaction order with respect to HMF (n) was estimated (Figure 4b). In agreement with the above, the value of n depended on the range of initial concentrations analyzed. In the 0.02 M-to-0.065 M range (run 1 to 3; Table 3), the estimate for n was (0.86 ± 0.07), a positive apparent order with respect to HMF. For initial concentrations above 0.065 M (run 3 to 5; Table 3), the estimate for n was (0.09 ± 0.9), indicating that the reaction became independent of HMF concentration. These findings suggest that HMF molecules can be strongly chemisorbed on a Cu/SiO₂-PD catalyst and total coverage of the metallic active sites occurs at a high HMF concentration.

Pseudo-Homogeneous Modeling

First of all, we estimate the apparent order in H₂ (m) by fitting dimensionless concentration data $C* vs W·t/n_{HMF }^0$ with Equation (1) (model 1). This fit was performed on a subset of data corresponding to a maximum conversion level of 30% from runs 2, 4 and 6 to 11. These calculations allowed the estimation of the reaction order in H₂ when the initial HMF concentrations were 0.04 and 0.13, respectively. The parameter estimates and the 95% confidence intervals are presented in

Table 4. Estimates for the apparent reaction orders (n and m) from model 1 by fitting the experimental data and the initial rates ($r_{HMF}^0$) from Table 3, with 95% confidence intervals.

Runs	$\mathbf{From} {\mathit{r}}_{\mathit{H}\mathit{M}\mathit{F}}^0$		From Model 1
	m  a	n  a	m  a	n  a	DC b
2, 6–8	0.81 ± 0.07	n.a.	0.66 ± 0.04	−0.09 ± 0.90	0.9916
4, 9–11	0.06 ± 0.08	n.a.	0.10 ± 0.03	0.80 ± 0.93	0.9803
1–3 (4–5)	n.a.	0.86 ± 0.07	n.a.	0.78 ± 0.11	0.9782

^a m and n are the apparent orders with respect to H₂ and HMF, respectively (model 1). ^b DC: Determination coefficient, n.a.: not applicable.

. Figure 5a shows both the experimental data using the dimensionless concentration and the regression curve obtained with model 1. Table 4 also presents the determination coefficient (DC) of each regression, indicating the quality of the fitting.

An acceptable agreement between estimates for the apparent order with respect to H₂ (m) with model 1 (Figure 5) and from the plots of $\mathit{ln}{r}_{HMF}^0$ (Figure 3c) was obtained (Table 4). Indeed, with both fittings, a positive effect of H₂ pressure on the hydrogenation rate for an initial HMF concentration of 0.04 M (runs 2, 6–8) was found. In contrast, the linear regression of $\mathit{ln}{r}_{HMF }^0$ (Figure 3c) when the HMF concentration was 0.13 M (runs 4, 9–11) gave a 95% confidence interval greater than the estimate of m, while the fitting with model 1 produced an apparent order in H₂ that was significantly different from zero. However, this estimate was considerably smaller than the one found for an initial HMF concentration of 0.04 M, indicating a lower influence of H₂ pressure on the HMF hydrogenation rate as the HMF concentration increases.

These first outcomes indicate that the apparent reaction order in H₂ on the HMF rate of reaction depends to some extent on the initial HMF concentration. Moreover, the estimates of m lower than 1 indicate a possible strong interaction of HMF with the catalyst surface. In other words, the HMF molecules may be strongly adsorbed on the surface of the Cu/SiO₂-PD catalyst. Consequently, the higher the initial HMF concentration, the less accessible the metallic sites will be for H₂. This will influence the catalytic activity and the apparent order with respect to H₂.

Table 4 also presents the apparent orders of reaction with respect to HMF obtained from the non-linear regression of $C* vs W·t/n_{HMF}^0$ data for conversions below 30% (Figure 5b) and using Equation (1) (model 1). The estimate for n obtained from this fitting was (0.78 ± 0.11), which is in good agreement with that obtained from the linear regression of $ln r_{HMF}^0 vs ln C_{HMF }^0$ (0.86 ± 0.07).

LHHW Heterogeneous Modeling

The results obtained when the regression of the experimental data was carried out using LHHW models (model 2 and model 3) are presented in Figure 6 and

Table 5. Parameter estimates and their 95% confidence intervals from model 2 and 3 obtained by fitting experimental data from runs 1 to 8 considering HMF conversions less than 45%.

Parameter	Model 2		Model 3
	Estimate	CI a	Estimate	CI a
k	0.036	0.006	0.040	0.008
KH	0.018	0.007	0.031	0.019
KA	5.93	0.94	16.8	5.2
KB	7.01	2.29	26.5	11.7
DC b	0.9920		0.9849

^a Confidence interval of the estimator for a 95% confidence level. ^b DC: Determination coefficient.

. It is worth clarifying that in this case, runs 1 through 8 were fitted using the entire data set simultaneously, but for conversions lower than 45%. This allowed for individual, uncorrelated estimates of the kinetic parameters (not as lumped parameters). The estimates and their confidence intervals are presented in Table 5, as well as the determination coefficient (DC) obtained after fitting the data with both models.

Both LHHW models yielded similar fits, which did not show major discrepancies graphically. However, for the data subset under analysis, model 2 showed a slightly better fit (0.9920 vs. 0.9849) than model 3. It is worth noting that both models yielded positive parameter estimates, which were significantly different from zero with a 95% CI. Nevertheless, it is evident that both models deviated from the experimental results at high HMF concentrations (Figure 6).

If we use the estimates obtained from the data set of runs 1 to 8 (Table 5) as initial values to fit the full data set, i.e., runs 1 to 11 and for the entire time range analyzed, the estimates remain positive but their 95% CIs as well as DCs worsen (Table S2). This is because for high conversions or high reaction times, the considered models deviate from the experimental data (Figures S4 and S5). One of the possible causes could be the loss of catalytic activity of Cu/SiO₂-PD due to the blockage of active sites by strong adsorption of HMF or BHMF [31].

Since the proposed LHHW models fail to provide an adequate fit when considering the high HMF conversion, i.e., low HMF concentrations, we decided to incorporate a term into the model that involves the observed activity diminution. With this aim in mind, we considered the decrease in active sites available due to the strong adsorption of BHMF (HMF) through an additional adsorption term. Considering this hypothesis, and following the same procedure as with LHHW, two new rate expressions were derived. Modified model 2 (Equation (7)) and modified model 3 (Equation (8)) are now used to solve the mass balance and perform the regression analysis.

$$\left(r_{HMF}\right)={\displaystyle \frac{\left(\raisebox{1ex}{$k_{sr}·K_A·K_H·{C_{TS}}^2$}\!\left/ \!\raisebox{-1ex}{$H$}\right.\right)·C_{HMF}^0·P_{H2}·C*·{\left(1-K_{BS}·C_{HMF}^0·\left(1-C*\right)\right)}^2}{{\left[1+\raisebox{1ex}{$K_H·P_{H2}$}\!\left/ \!\raisebox{-1ex}{$H$}\right.+K_A·C_{HMF}^0·C*+K_B·C_{HMF}^0·\left(1-C*\right)\right]}^2}}$$

(7)

$$\left(r_{HMF}\right)={\displaystyle \frac{\left(\raisebox{1ex}{$k_{sr}·K_A·K_H·C_{TS1}·C_{TS2}$}\!\left/ \!\raisebox{-1ex}{$H$}\right.\right)·C_{HMF}^0·P_{H2}·C*·\left(1-K_{BS}·C_{HMF}^0·\left(1-C*\right)\right)}{\left[1+\raisebox{1ex}{$K_H·P_{H2}$}\!\left/ \!\raisebox{-1ex}{$H$}\right.\right]·\left[1+K_A·C_{HMF}^0·C*+K_B·C_{HMF}^0·\left(1-C*\right)\right]}}$$

(8)

These two modified models incorporate a new parameter K_BS that considers the irreversible adsorption of BHMF on the S or S2 sites, i.e., sites remaining unavailable for the surface reaction because they are covered by BHMF.

The figures showing the results of the fittings using modified models 2 and 3, which consider the loss of active sites due to BHMF adsorption, are presented in Figure 7. The parameter estimates and their 95% CIs are summarized in

Table 6. Parameter estimates and their 95% CI for modified models 2 and 3 obtained after the fitting of the complete experimental data from runs 1 to 8 considering the loss of active sites. DC: Determination coefficient.

Parameter	Modified Model 2		Modified Model 3
	Estimate	CI a	Estimate	CI a
k	0.039	0.010	0.032	0.003
KH	0.031	0.012	0.015	0.008
KA	3.77	1.57	18.8	3.0
KB	0.022	7.91	6.24	5.44
KBS	2.46	2.57	1.90	1.08
CD	0.9744		0.9936

^a Confidence interval of the estimator for a 95% confidence level.

. It was found for modified model 2 that the estimates of two parameters (K_B and K_BS) are non-significantly different from zero with 95% confidence. In addition, the DC for the modified model 3 is higher than the one for the modified model 2. In addition, all the parameter estimates with modified model 3 are significantly different from zero with 95% confidence. It is worth noting that for this model, the estimates for the adsorption constants of HMF and BHMF (parameters K_A and K_B) reflect an important level of interaction of these molecules with the catalyst surface. Thus, it can be concluded that modified model 3 fits the experimental data better in its whole range than modified model 2.

Figure 7 presents the complete experimental data and the fits achieved when fitting was carried out considering modified models 2 and 3. The good quality of the fit for model 3 can be seen, which is consistent with the DC value obtained (Table 6).

As a measure of the goodness of fit from modified models 2 and 3, Figure 8 presents a parity plot showing the relation between the experimental and model data. It can be seen from the parity plot, on the one hand, that the data predicted by modified model 3 (red circles) fit the experimental data better than modified model 2 (blue circles). On the other hand, it can also be seen how the discrepancy between the experimental data and the data fitted by the models increases for higher HMF conversions or reaction times.

4. Discussion

Characterization by XRD, TPR, TEM, and N₂O chemisorption revealed that the Cu/SiO₂-PD catalyst is composed of a highly dispersed metallic copper phase on the large specific surface area of silica. The high selectivity to BHMF observed in the liquid-phase hydrogenation of HMF using this Cu/SiO₂-PD catalyst was attributed to a combined effect of the highly dispersed metallic copper phase and low surface acidity. However, partial catalyst deactivation, caused by a blockage of the active phase with strongly chemisorbed surface carbonaceous compounds, was observed [31].

In this work, it was found that the highest activity for the liquid-phase HMF hydrogenation over the Cu/SiO₂-PD catalyst was reached when THF was used as a solvent. The activity pattern obtained was THF > 2-POH > H₂O. In order to explain this pattern, the solvent–copper surface, solvent–H₂, and solvent–HMF interactions must be taken into account. In a previous paper, it was found that solvent–copper surface interactions with polar and non-polar solvents are, in general, very low [38]. Thus, they were not considered in this analysis. The higher activity ($r_{HMF}^0$) observed with organic solvents compared to H₂O may be strongly influenced by the more elevated solubility of H₂ in organic solvents, which is approximately five times that in water (Table S1, [39,40]). However, the difference in $r_{HMF }^0$ when comparing THF and 2-POH cannot be attributed to H₂ solubility, as it is very similar in both solvents. Therefore, the possible influencing factor on catalytic activity would be the solvation of HMF molecules by the solvent. One way to describe the reactant–solvent interaction is through solvatochromic scales of polarity, as already developed in previous works [40,41,42]. Kamlet et al. [43] introduced the solvatochromic parameters α and β, which measure the ability of a solvent to donate or accept hydrogen bonds. The values of α and β for 2-POH are higher than those for THF (Table S1), suggesting that the interaction between 2-POH and HMF is stronger than the interaction between THF and HMF. In other words, hydrogen bonds between HMF and 2-POH are stronger than those of HMF with THF. As a consequence, the HMF dissolved into 2-POH would be more stabilized in the liquid phase and less available to interact with the metal copper surface, influencing the reaction kinetics. Finally, it is likely that strong water–HMF interactions hinder HMF chemisorption on the metal copper surface, thus contributing to the very low activity during HMF hydrogenation on Cu/SiO₂-PD when water is used as the solvent. On the other hand, HMF and BHMF can interact with water molecules, forming intermediates that finally lead to ring opening, according to that proposed in previous works [34,35,36]. The last would explain the low selectivity to BHMF when water is used as a solvent.

It was determined that the HMF conversion rate increases with H₂ pressure when the HMF initial concentration is 0.04 M, and a reaction order with respect to H₂ near unity was estimated (0.81 ± 0.07) by linear regression. Instead, for an HMF initial concentration of 0.13 M, the estimate for the reaction order with respect to H₂ was not significantly different from zero (0.06 ± 0.08), confirming that the changes in the HMF hydrogenation rate with H₂ pressure depend in turn on the initial concentration of HMF. These results indicate that it is very likely that interactions between HMF molecules and metallic copper sites are important because they remain chemisorbed on them, hindering H₂ chemisorption. Therefore, no effect on the catalytic HMF hydrogenation can be observed as the H₂ pressure is raised when HMF concentration is high enough.

Experiments performed by varying the initial concentration of HMF, while keeping the H₂ pressure constant, showed that the estimate for the reaction order in HMF changes from a value close to unity (0.86 ± 0.07), for initial concentrations between 0.02 and 0.065 M, to a value close to zero (0.09 ± 0.90) in the concentration range of 0.065 to 0.26 M. Since this estimated reaction order varies according to the initial concentration range of HMF, the hypothesis of high HMF–active metal copper site interaction is proven. As a consequence of this high HMF–metallic copper interaction, at initial reagent concentrations greater than 0.065 M, the metallic copper surface is almost completely covered with HMF molecules. This hinders the chemisorption of new HMF molecules, and consequently, the hydrogenation rate is not influenced by increasing the HMF concentration in the liquid phase.

The fit with pseudo-homogeneous model 1 (Equation (1)) of the experimental data, up to a HMF conversion of 30% for different H₂ pressures, confirms what was observed in the linear regression for the initial HMF concentrations 0.04 M and 0.13 M. A positive order with respect to H₂ was estimated for an initial HMF concentration of 0.04 M, while in the case where initial HMF concentration was 0.13 M, an order of H₂ near zero was estimated. In addition, in all of the cases, the reaction order with respect to H₂ was less than one, which reinforces the proposal of high interactions between HMF and the active metal surface, leading to high metal surface coverage when the HMF concentration in the liquid phase is high enough. There was also a good agreement between the estimates for the reaction order in HMF at a given pressure, applying linear regression and pseudo-homogeneous modeling for data up to 30% HMF conversion.

In order to obtain better insight into the kinetics of liquid-phase HMF hydrogenation, a fitting of the experimental data up to 45% reactant conversion using heterogeneous LHHW models was carried out. Initially, two heterogeneous models were employed: one model considered the same type of metallic active sites for the chemisorption of H₂, HMF, and BHMF, and the other model assumed one type of active site for H₂ adsorption and another type for HMF and BHMF chemisorption. A good fitting of the experimental data was attained by applying both models, with all estimates significantly different from zero in both cases and with similar DCs. However, both models failed to fit data for conversions higher than 45%. This may be attributed to the loss of catalytic activity, probably caused by the blockage of metallic active sites by the strong adsorption of the reactant (HMF) or main product (BHMF), which becomes more important at higher HMF conversions. Therefore, two modified LHHW models that considered the strong adsorption of BHMF were proposed to fit the whole range of the experimental data. Modified model 3 gave a better fitting than modified model 2. In addition, all the estimates for the parameters with modified model 3 were significantly different from zero with 95% confidence. Moreover, the estimates for the two adsorption parameters, KA and KB, reflected the strong interactions of HMF and BHMF with active sites. Instead, two parameters that were not significantly different from zero were estimated with modified model 2. In this way, modified model 3 not only gave a better fitting than model 3 and modified model 2 but also may explain the catalyst deactivation due to blockage of active sites S2 by the strong adsorption of HMF and BHMF on them. These compounds can be desorbed by thermal treatment under air flow and catalyst activity can be recovered after subsequent reduction under H₂ flow [31].

5. Conclusions

It was found that Cu/SiO₂-PD catalytic performance for the liquid-phase hydrogenation of 5-hydroxymethylfurfural (HMF) is higher when tetrahydrofuran (THF), an aprotic molecule with moderate polarity, is used as a solvent instead of 2-propanol or water, both protic molecules of high polarity. This is attributed to both a lower H₂ solubility and interactions between the HMF and solvent, which favor HMF adsorption on surface metal copper sites.

Pseudo-homogeneous modeling, by linear and non-linear regression, indicates that there is an important interaction of the reactant and main product molecules with active metallic copper sites. This leads to a change in the reaction orders with respect to HMF and H₂, from positive orders to practically order zero, with increasing initial reactant concentrations. The latter means that total coverage of metallic active sites by the reactant and/or product molecules occurs.

Heterogeneous LHHW modeling is in agreement with the above, since the model that best fit the data considered the interaction of both HMF and 2,5-bis(hydroxymethyl)furan (BHMF) with metal copper sites. The estimates for the adsorption parameters are in agreement with the hypothesis of a high interaction of HMF and BHMF with metallic copper sites. The latter would explain the reversible deactivation of Cu/SiO₂-PD in the liquid-phase HMF hydrogenation previously found. Thus, this kinetic study allows us to predict not only the Cu/SiO₂-PD catalyst’s performance but also its deactivation during liquid-phase HMF hydrogenation.