Kinetic modeling of levulinic acid hydrogenation to γ-valerolactone in water using a carbon supported Ru catalyst

Article abstract of DOI:10.1016/j.apcata.2016.06.033

γ-Valerolactone (GVL) is considered a very interesting green, bio-based platform chemical with high application potential for the production of both biofuels and biobased chemicals. In this contribution, we report a kinetic study on the hydrogenation of levulinic acid (LA) to 4-hydroxypentanoic acid (4-HPA) and the subsequent intramolecular esterification to GVL in water using Ru/C (3?wt.% Ru) as the catalyst in a batch set-up. A large number of experiments was performed in a temperature range of 343–403?K, a hydrogen pressure range from 30 to 60?bar and initial LA concentrations between 300 and 2500?mol?m^?3. Experimental data, supported by calculation, indicate that intra-particle diffusion of LA and hydrogen affect the overall reaction rate and as such a heterogeneous model with both reaction and diffusion was used to model the data. The hydrogenation reaction of LA to 4-HPA was modelled using a Langmuir-Hinshelwood type expression whereas the reaction of 4-HPA to GVL was modelled as an equilibrium reaction occurring in the bulk of the liquid, catalyzed by a Br?nsted acid, in this case LA and 4-HPA. A good fit between experiments and model was observed. The results were compared to a kinetic model without considering mass transfer and diffusion limitations.

Full text of DOI:10.1016/j.apcata.2016.06.033

Accepted Manuscript
Title: Kinetic modeling of levulinic acid hydrogenation to
␥-valerolactone in water using a carbon supported Ru catalyst
Author: A.S. Piskun H.H. van de Bovenkamp C.B. Rasrendra
J.G.M. Winkelman H.J. Heeres
PII:
S0926-860X(16)30347-7
DOI:
Reference:
http://dx.doi.org/doi:10.1016/j.apcata.2016.06.033
APCATA 15929
To appear in:
Applied Catalysis A: General
Received date:
Revised date:
Accepted date:
20-10-2015
20-6-2016
22-6-2016
Please cite this article as: A.S.Piskun, H.H.van de Bovenkamp, C.B.Rasrendra,
J.G.M.Winkelman, H.J.Heeres, Kinetic modeling of levulinic acid hydrogenation to
␥-valerolactone in water using a carbon supported Ru catalyst, Applied Catalysis A,
General http://dx.doi.org/10.1016/j.apcata.2016.06.033
This is a PDF file of an unedited manuscript that has been accepted for publication.
As a service to our customers we are providing this early version of the manuscript.
The manuscript will undergo copyediting, typesetting, and review of the resulting proof
before it is published in its final form. Please note that during the production process
errors may be discovered which could affect the content, and all legal disclaimers that
apply to the journal pertain.

Kinetic Modeling of Levulinic Acid Hydrogenation to
γ-Valerolactone in Water Using a Carbon Supported Ru Catalyst
A.S. Piskun1, H.H. van de Bovenkamp1, C.B. Rasrendra2 J.G.M. Winkelman1 and H. J. Heeres1*
1 – Department of Chemical Engineering, ENTEG, University of Groningen, Groningen, The Netherlands
2 – Department of Chemical Engineering, Institut Teknologi Bandung, Bandung, Indonesia
* corresponding author h.j.heeres@rug.nl
1

Graphical abstract
2000
1800
1600
1400
1200
1000
800
LA
HPA
GVL
600
400
200
0
0
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
time (s)
2

Highlights





The hydrogenation of levulinic acid to γ-valerolactone was studied
Reactions were performed using Ru/C in water in a batch set-up
Mass transfer limitations play an important role
4-hydroxypropionic acid is a clear intermediate
Hydrogenation reaction was modelled using a LHHW mechanism
3

Abstract
γ-Valerolactone (GVL) is considered a very interesting green, bio-based platform chemical with
high application potential for the production of both biofuels and biobased chemicals. In this
contribution, we report a kinetic study on the hydrogenation of levulinic acid (LA) to 4-
hydroxypentanoic acid (4-HPA) and the subsequent intramolecular esterification to GVL in
water using Ru/C (3 wt.% Ru) as the catalyst in a batch set-up. A large number of experiments
was performed in a temperature range of 343-403 K, a hydrogen pressure range from 30-60 bar
and initial LA concentrations between 300 and 2500 mol/m3. Experimental data, supported by
calculation, indicate that intra-particle diffusion of LA and hydrogen affect the overall reaction
rate and as such a heterogeneous model with both reaction and diffusion was used to model
the data. The hydrogenation reaction of LA to 4-HPA was modelled using a Langmuir-
Hinshelwood type expression whereas the reaction of 4-HPA to GVL was modelled as an
equilibrium reaction occurring in the bulk of the liquid, catalyzed by a Brönsted acid, in this case
LA and 4-HPA. A good fit between experiments and model was observed. The results were
compared to a kinetic model without considering mass transfer and diffusion limitations.
Keywords: levulinic acid, hydrogenation,
ruthenium catalyst, kinetic modelling, batch
set up
4

1. Introduction
A substantial amount of research activities is currently undertaken worldwide to identify
attractive routes to produce biofuels and biobased chemicals from lignocellulosic biomass [1-3].
A very promising and versatile option is the conversion of the carbohydrate fractions in
lignocellulosic biomass to levulinic acid (LA, 4-oxo-pentanoic acid) [4-6]. LA is an interesting
building block that can be converted to a variety of useful compounds with high application
potential such as, 1,4-pentanediol, methyltetrahydrofuran (MTHF) [4,5], mixtures of alkanes,
butenes, 5-nonanone, adipic acid and γ-valerolactone (GVL) [7-9]. Among the derivatives of LA,
GVL is identified as a promising platform chemical for the synthesis of biofuels and biobased
chemicals. Examples are the use as an oxygenate in transportation fuels, as a co-monomer for
the preparation of polymers like polyhydroxyalkanoates [7], as a precursor for long chain
alkanes, to be used as a hydrocarbon fuels [8,9], and as a starting material for the synthesis of
adipic acid and derivatives.
GVL can be obtained by the hydrogenation of LA using either heterogeneous or homogeneous
catalysts in the liquid or gas phase. Palkovits and co-workers recently published a detailed
review on LA hydrogenations using heterogeneous catalysts [10]. A wide range of catalysts has
been used, the most common being supported noble metals. Particularly Ru based catalysts
have shown to be very efficient and close to quantitative GVL yields have been reported at high
LA conversions. A number of studies have been reported on bimetallic Ru catalysts and the use
of co-catalysts. Bimetallic catalysts like RuSn/C are in general less active but lead to enhanced
catalyst stability [11]. Co-catalysts and particularly heterogeneous acids have been reported to
significantly increase the reaction rate [12-14]. For instance, the LA conversion for
hydrogenations with Ru/C and Ru/Al2O3 as catalysts in the presence of Amberlyst A70 was twice
as high as a reaction in the absence of the solid acid co-catalyst at otherwise similar conditions.
Solvent effects have been investigated in detail and have shown to play an important role. It
appears that supported Ru catalysts are particularly active in water. For instance Al-Shaal et al.
investigated the hydrogenation of LA and alkyl-levulinates using ruthenium-based catalysts
(Ru/C, Ru/Al2O3 and Ru/SiO2) in alcohol and alcohol/water mixtures [15]. A significant increase
in the LA conversion and GVL selectivity was observed when part of the alcohol was replaced by
5

water. Similar positive effects of water on catalyst activity and selectivity were reported by
Sautet et al. using Ru-supported catalysts in water and THF. DFT calculations [16] revealed that
the increase in activity of Ru catalysts in water compared to organic solvents lies in a hydrogen
bonding effect of a chemisorbed water molecule on the surface with a ketone group. Thus, the
use of water as a solvent is not only cheap and environmental friendly, but also results in higher
catalytic activity for Ru-based catalysts for ketone hydrogenations.
Two possible pathways have been proposed for the liquid phase hydrogenation of LA to GVL.
The first involves dehydration of LA to α-angelicalactone (α-AL) [17] followed by a subsequent
hydrogenation of the C-C double bond to form GVL (Scheme 1). The alternative route involves
hydrogenation of the carbonyl group of LA to form 4-hydroxypentanoic acid (4-HPA). In the
next step, an intramolecular esterification leads to the formation of GVL. Experimental studies
reveal that the second route is dominant when using Ru catalysts, though the first cannot be
excluded a priori.
Scheme 1: Catalytic hydrogenation of LA to GVL and subsequent products
6

Hydrogenation of LA at elevated temperatures can lead to over-hydrogenation and the
formation of 1,4-pentanediol (1,4-PDO) [18,19], 2-methyltetrahydrofuran (2-MTHF) [18,19],
pentanoic acid (PA) [20,21] and 5-nonanone [22] (Scheme 1). Though not desired when
targeting GVL, some of these products have also potential for commercialization.
Despite high academic and industrial interest on the catalytic hydrogenation of LA to GVL, a
very limited number of kinetic studies on the reaction have been reported yet. These studies
are of pivotal importance i) to gain insights in the reaction pathways and catalytic steps and ii)
for scale up purposes and the development of optimum reactor configurations for the
hydrogenation of LA to GVL. In 2012, we reported a detailed experimental study on LA
hydrogenation to GVL in water using Ru/C as the catalyst (5 wt.% Ru) [23]. In this research, the
effect of reaction temperature and catalyst intake on LA conversion and product selectivity was
determined. This research was the first step to obtain a kinetic model for the hydrogenation of
LA to GVL. While performing this research, Bond et al. published a kinetic model for the
hydrogenation of aqueous LA solution to GVL over Ru/C catalyst (5 wt.% Ru) in a packed bed
reactor [24]. It was assumed that the reaction proceeds via the 4-HPA route (Scheme 1). The
hydrogenation reaction was modelled using a simplified Langmuir-Hinshelwood expression (eq
1). As such, the reaction was proposed to be zero order in LA and half order in hydrogen. The
apparent activation energy the hydrogenation reaction was calculated to be 48 ± 5 kJ/mol.
(1)
The esterification of 4-HPA to GVL was modelled as homogeneous acid-catalyzed reaction
which occurs in the liquid phase. Reversibility was not taken into account in the model. The
activation energy for the esterification reaction was calculated to be 70 ± 4 kJ/mol.
Another relevant kinetic study is from Zhang et al. [25]. They studied the hydrogenation of LA to
GVL using Pd/C as the catalyst in a batch set-up. The experimental data were successfully
modelled using a Langmuir type equation with dissociative adsorption of hydrogen. The
activation energy for the hydrogenation reaction was calculated to be 33 KJ/mol.
7

We here report a detailed kinetic study on the conversion of LA to GVL using a Ru/C catalyst.
The hydrogenation reaction was carried out in water, an environmentally benign solvent, and in
a batch set-up. Reaction conditions like temperature (343-403 K), hydrogen pressure (30-60
bar) and initial LA concentration (300-2500 mol/m3) were varied in a systematic manner. The
experimental data for the hydrogenation of LA to 4-HPA were modelled using a Langmuir-
Hinshelwood model, the ring-closure of 4-HPA to GVL as an acid catalyzed equilibrium reaction.
2. Experimental Section
2.1 Materials
The Ru/C catalyst (3 wt.% Ru) was obtained from Evonik. The d10 was 5 x 10-6 m, d50 25 x 10-6 m
and d90 75x 10-6 m and an average of 60 x 10-6 m was taken for calculations. Ruthenium is well
dispersed on the catalyst support and the average Ru particle size is between 1-3 nm (TEM,
Supplementary information, Figure S5). Levulinic acid (purity > 98%); γ-valerolactone (purity
98%); deuterium oxide, D2O (purity > 99%); 1,4-dioxane (purity 99.5%) were purchased from
Acros Organics Hydrogen (purity > 99.999 vol.%). and nitrogen gas (purity > 99.9 vol.%) were
from Linde. Milli-Q water was used for all experiments. All chemicals were used without
purification.
2.2 Experimental procedure for hydrogenation of levulinic acid
The hydrogenation reactions were performed in a 300 ml stainless steel batch autoclave (Buchi
GmbH). The mantle of the autoclave was equipped with (electrically operated) heating rods and
a cooling coil (using water) to allow for good temperature control. The reactor content was well
mixed using a magnetically induced overhead stirrer equipped with a Rushton type impeller.
The temperature and pressure were measured online. The reactor was equipped with a dip-
tube to allow for liquid sampling during reaction. An overview of relevant reactor and catalyst
properties is given in Table 1.
8

Table 1. Reactor and catalyst properties
Reactor volume (L-phase)
Catalyst intake
1 x 10-4
1.47 x 10-4
30 x 10-6
m3
kg
m
Average catalyst particle
radius
Catalyst particle density
Catalyst hold-up
7.50 x 102
1.97 x 10-3
1.97 x 102
kg/m3
m3cat/m3
m2/m3
L
Liquid-solid area
Water (100 ml) with the appropriate amount of LA and catalyst was introduced into the
autoclave. At a stirring rate of 2000 rpm, the system was flushed with nitrogen for 5 minutes.
The mixture was heated to the desired temperature and subsequently hydrogen was admitted
until the target pressure was reached. This moment is set as t = 0 min. During the reaction, the
pressure was maintained constant by the supply of hydrogen. Samples were collected at
different time intervals and analysed for their composition by 1H-NMR.
2.3. Concentration calculations from 1H-NMR analysis
1
The composition of a reaction mixture (LA, HPA and GVL) was determined quantitatively by H-
NMR. A sample (approximately 200 µL) was weighed, dissolved in D2O and 1,4-dioxane (internal
standard, IS, 10 µL) was added. All spectra were integrated using MestReNova software. The
number of moles of A in a sample was calculated using Equation 2.
where NA is the number of moles of A in the sample, NIS the known amount of moles of the
internal standard in the sample, IA is the peak area of the methyl group of component A (δ 2.1
ppm for LA, δ 1.03 ppm for 4-HPA and δ 1.3 ppm for GVL, IIS the peak area of the CH2 groups in
9

1.4-dioxane at δ 3.6 ppm and HIS and HA are the number of H atoms corresponding with the
relevant NMR peak (3 for HA and 8 for HIS). The concentrations of LA, GVL and 4-HPA in the
samples were calculated using Equation 3.
Where Vt is the liquid volume in the NMR tube and Df the dilution factor, which was calculated
using Equation 4.
2.4 Definitions
The conversion of LA, the yield and the selectivity of 4-HPA and GVL were calculated according
to Equation 5-8.
(7)
(8)
Where XLA is the conversion of LA (mol.%); CLA,0 the initial concentration of LA (mol/L); CLA the
concentration of LA at a certain time t (mol/L); YGVL the yield of GVL (mol.%); Y4-HPA the yield of
4-HPA (mol.%) and Si the selectivity to GVL or 4-HPA (mol.%).
10

3. Results and discussion
3.1 Screening experiments
All experiments were carried out in a batch reactor with Ru/C (3 wt.% Ru) as the catalyst
(powder). A total of 29 experiments was performed within the experimental window of
operation (Table 2, see Table S6 in the supplementary information for the conditions for the
individual experiments).
Table 2. Range of conditions of the hydrogenation runs.
property
range
T(K)
343-403
30-60
PH2 (bar)
(CLA)initial (mol/m3)
300-2500
An experimental set of data was obtained, consisting of the concentration profiles of LA, HPA
and GVL. Two typical concentration versus time profiles are given in Figure 1.
1400
LA
GVL
HPA
1200
1000
800
600
400
200
0
0
1000
2000
3000
4000
5000
time (s)
11

300
250
200
150
100
50
LA
GVL
HPA
0
0
500
1000
1500 2000 2500
time (s)
3000
Figure 1. Experimental and model data for two selected experiments (top: run 7, 363 K, 45 bar;
bottom: run 11, 363 K, 45 bar).
Only 4-HPA was observed as an intermediate in all experiments. Even at higher temperatures,
neither α-angelicalactone nor subsequent hydrogenation products of GVL like 1,4-pentanediol
1
or MTHF were observed at the prevailing reaction conditions (HPLC, supported by H-NMR). In
some of the cases, particularly at low temperatures and low initial LA concentrations, the
amount of 4-HPA shows a clear optimum, see Figure 1 (right) for details. The selectivity to 4-
HPA can be as high as 40-50%. These observations indicate that the conversion of LA to GVL
involves two consecutive reactions: the hydrogenation of LA to 4-HPA followed by
intramolecular esterification of 4-HPA to GVL. All reaction mixtures contained significant
amounts of 4-HPA after reaction, even after prolonged reaction times, indicating that the
conversion of 4-HPA to GVL is an equilibrium reaction in water (Scheme 2). Extended
equilibrium studies for the 4-HPA/GVL equilibrium reaction, supplemented by DFT calculations
have been carried and will be published in due course [26].
Based on the concentration time profiles in the batch reactor set-up, a reaction network for the
hydrogenation of LA in water using Ru/C catalysts is proposed and given in Scheme 2.
12

Scheme 2: Proposed and modelled reaction network for the hydrogenation of LA to GVL
3.2 Mass transfer limitations
The catalytic hydrogenation of LA in water using a Ru/C catalyst is an example of a three phase
gas-liquid-solid reaction. As such, the conversion rate and product selectivity may be affected
by mass-transfer limitations of the reactants. To gain insights in possible mass transfer effects
of hydrogen from the gas to liquid phase, the effect of the stirring rate on the LA conversion
was determined and the results are presented in Figure 2. It shows that the LA conversion does
not depend on the stirring rate provided that the stirring rate exceeds 1200 rpm. Thus, to avoid
gas-liquid transfer limitation, all reactions for the kinetic modeling were performed at a stirring
rate of 2000 rpm.
Figure 2. Effect of the agitation rate on the LA conversion (initial LA concentration: 600 mol/m3,
45 bar, 363 K, Ru/C, 40 min batch time)
13

To further assess intra-particle mass transfer limitation of hydrogen and LA, the Weisz-Prater
criterion [27] was determined for a number of experiments; see Supplementary information for
calculation details. The values of Weisz-Prater criterion for the selected experiments are
between 0.2 and 6.1 for LA and 0.7 and 6.9 for H2. This implies that the reaction does not solely
take place in the kinetic regime and that at least intra-particle pore diffusion limitations of
hydrogen and LA play a role in these experiments, even with the small catalyst particles used in
this study (90% of the particles is smaller than 75 x 10-6 m).
3.3 Reactor model development
The hydrogenation experiments have been conducted in a batch reactor with the catalyst
suspended in the liquid phase. A constant pressure of hydrogen gas is maintained in the
headspace. The data obtained from an experiment consists of a set of transient concentrations
of the components LA, 4-HPA and GVL. To extract kinetic information from the experimental
data, a series of mass transfer and reaction steps has to be taken into account, see also Figure
3:




hydrogen transfer from the constant pressure head space to the liquid phase
transport of hydrogen and LA from the liquid phase to the catalyst particles
diffusional transport of the components in the catalyst to the ruthenium active sites
hydrogenation of LA to 4-HPA catalyzed by ruthenium in the porous particles


transport of 4-HPA from the catalyst to the liquid phase
conversion of 4-HPA to GVL via a homogeneous liquid phase equilibrium reaction
14

Figure 3. Scheme of component transfer and reaction steps.
Based on experimental findings (Figure 2), it is assumed that mass transfer of hydrogen from
the gas to liquid phase is faster than the mass transfer and reaction in the liquid-solid phase
and as such has not been incorporated into the model.
The experimental results can be modeled using a mathematical model comprising a series of
balances and rate equations. The liquid phase component balances for the variation of the
concentrations in time are:
(9)
(10)
(11)
15

with the initial conditions
(12)
(13)
(14)
Liquid to solid transport of hydrogen, H2, LA and HPA can be represented by:
(15)
(16)
(
)
The balance for diffusion and reaction in the catalyst particles reads:
(
)
where Ri(S) denotes the production rate of i in the catalyst (Ri(S)=Ri(S)(r)). The boundary
conditions to Eq. (16) are
(17)
(18)
The catalyst particle reaction/transfer steps, Eqs (16-18), are formulated here using the pseudo-
steady-state approximation. This is justified because the diffusion times that are characteristic
for the particle dynamics are several orders of magnitude smaller than the reaction times that
determine the reactor dynamics as described by Eqs (9)-(11).
16

3.4 Model development for the catalytic hydrogenation reaction
Kinetic studies on the hydrogenation of ketone and aldehyde groups using support Ru/C
catalysts have been reported in the literature. Examples include the hydrogenation of 2-
butanone [28], cinnamaldehyde [29], D-glucose [30] and D-lactose [31]. Typically, Langmuir-
Hinshelwood type of mechanisms are proposed. The exact form is depending on whether
adsorption, reaction or desorption is assumed to be rate determining and on competitive or
non-competitive adsorption of the reactants. In the literature on Ru/C catalyzed
hydrogenations of carbonyl groups ample arguments can be found for both competitive and
non-competitive adsorption. For simplicity, but also in the absence of any contradicting
indications, we have applied a Langmuir-Hinshelwood-Hougen-Watson (LHHW) model with
competitive adsorption of hydrogen and organic molecules on the metal sites ( ). Depending
s
on the type of hydrogen adsorption, two mechanisms are considered here. In mechanism A
molecular hydrogen adsorption is assumed, while in mechanism B adsorption of hydrogen is
dissociative, see Tables 3 and 4.
Table 3: Mechanism A with molecular H2 adsorption.
A1
A2
A3
A4
Table 4: Mechanism B with dissociative H2 adsorption.
B1
B2
B3
B4
B5
The adsorption and desorption steps are assumed to be rapid. Therefore the hydrogenation
rate is determined by the rate of a surface reaction, step A3 in mechanism A, and steps B3 or B4
in mechanism B. Reaction rate equations can be derived, following the LHHW methodology, as
17

(19)
(20)
√
√
(21)
√
The production rates of the components, as mentioned in Eq. (16) can be identified as
(22)
where R1,(S) is given by Eq (19), (20) or (21).
The possible involvement of GVL in the denominator term was also assessed experimentally by
performing a hydrogenation reaction at standard conditions in the presence of GVL. The results
are given in Figure 4. Clearly, the presence of GVL retards the reaction rate and suggests that
GVL adsorption to active catalysts sites affects the reaction rate and justifies the introduction of
an additional GVL denominator term.
18

Figure 4: Effect of the presence of GVL on the LA conversion. □: only LA (0.6 M), ■: LA + GVL
(LA 0.6 M, GVL 0.6 M, 45 bar, 90 °C, Ru/C intake: 2 wt.% on LA).
Hydrogenation reactions with pure 4-HPA could not be performed as it is well known that the
intramolecular esterification of 4-HPA to GVL is a relatively fast reaction at 90°C (vide infra) and
as such GVL formation interferes with the rate data analysis.
The possibility of considerable catalyst deactivation of the Ru/C on the timescale of the
experiments (typically less the 3h) is not likely on the basis of extensive studies in a continuous
set-up for runtimes of over 100 h with this particular catalyst [32]. As such, it was not
considered in this kinetic study.
3.5 Modeling of the intermolecular esterification of 4-HPA to GVL
Regarding the intramolecular esterification reaction of 4-HPA to GVL, it is assumed that the
reaction is an equilibrium reaction which occurs in the bulk water phase and is catalyzed by a
Brönsted acid [24, 27]. The latter assumption is justified by individual studies using Brönsted
acids and is in line with recent data from Bond [24].
(23)
Two acids, LA and 4-HPA, are present in the reaction mixture and it is assumed that both
catalyse the esterification reaction. The proton concentration for a mixture of two acids in
different concentrations can be approximated by:
(24)
√
Where Ka,LA and Ka,HPA are dissociation constants of levulinic acid (10-4.6) and 4-
hydroxypentanoic acid (10-5.7), respectively [33]. A more detailed explanation regarding the
derivation and validity of eq. 24 is given in the supplementary information.
3.6 Modeling of the mass transfer coefficients
19

In stirred slurry and gas slurry reactors the mass transfer coefficient for transport from the
liquid to the solid phase is usually correlated via dimensionless numbers with an equation of
the form
(25)
where the Sherwood number is obtained as a function of the Reynolds and Schmidt numbers
[27]. With the small particle diameters used here, the second part of the relation for Sherwood
is negligible, and the liquid solid mass transfer coefficients, kl,i, can be calculated from
(26)
3.7 Model solution and parameter optimization
The mathematical model for calculating the liquid phase concentration profiles over time was
programmed in MATLAB. The set of ordinary differential equations (ODE’s) for the
concentrations, Eqs (9)-(15), was solved numerically using the ode23s routine. The right-hand-
sides of the ODE’s needed for the integration were obtained from solving the catalyst particle
problem Eqs (16)-(18) with the bvp4c routine.
The solution algorithm of the mathematical model is incorporated as a subroutine of the
parameter optimization process. For a specific kinetic model as given by Eq. (19), (20) or (21)
the unknown parameters comprise reaction rate constants and adsorption equilibrium
constants. The optimization was achieved by minimization of the differences between the
calculated and measured concentration data:
(27)
∑
∑
∑
20

For each experiment the weight factor, wi, was taken as the initial LA concentration. This way,
all concentrations are scaled between 0 and 1, and the experiments each contribute with
approximately the same weight to the solution. The parameters were optimization using the
fminsearch function where initial values were generated from a limited number of iterations
with the lsqnonlin function.
3.8 Model results
An experimental set of data was obtained, consisting of the concentration profiles of LA, HPA
and GVL, as described in the experimental section. The challenge of finding optimum
parameters of LHHW type of kinetic models is notorious due to local minima of the objective
function and strong correlations among the parameters. This is especially true if the
temperature dependency is taken into account via an Arrhenius type of dependency for the
reaction rate constants or a Van ‘t Hoff dependency for the adsorption equilibrium constants.
Therefore we applied a two-step strategy where each model was first optimized taking into
account only the experiments performed at 363 K. This temperature is the intermediate of the
experimental range of temperatures applied here. An initial optimization revealed that for each
model the adsorption equilibrium constants of hydrogen and HPA were statistically not
significant; their 95% confidence intervals encompassed zero. Apparently, the surface
coverages of hydrogen and HPA were very small as compared to the other components.
Consequently, the terms pertaining to the adsorption equilibria of hydrogen and HPA in the
denominator of the LHHW reaction rate models were dropped, and the model equations
reduce to
(28)
(29)
√
(30)
21

The models A3 and B4 are not distinguishable any more, compare Eqs (28) and (30), due to the
low hydrogen coverage. The optimized parameters for the models of Eqs (28)-(30) are shown in
Table 5.
Table 5. Optimized parameters at 363 K with 95% confidence intervals.
model
A3,B4
B3
(63.3±2.9) 10-3
(343±15) 10-3
)
(1.32±0.06) 10-3
(0.84±0.12) 10-3
(0.41±0.03) 10-3
(1.61±0.07) 10-3
(0.89±0.13) 10-3
(0.40±0.03) 10-3
)
(0.042±0.013) 10-3 (0.039±0.01) 10-3
0.988 1.170
error sum
The confidence intervals are calculated from comparing χ2 -values where one of the parameters
is varied until the χ2-value has increased to the value given by
(31)
where F(m,N-m,0.95) denotes the 95% value of the Fisher distribution with (m,N-m) degrees of
freedom. Because model A3,B4 results in a smaller sum of errors, as compared to model B3, it
is selected as the preferred model henceforth. Some typical results are shown in Figure 1.
In the second step of the optimization strategy, the temperature dependency of the preferred
model A3,B4 was optimized. The kinetic parameters were expressed as
(32)
(
)
22

(33)
(34)
(
)
(
)
For simplicity, the variation of the adsorption equilibrium constants with the temperature was
not taking in to account here. Using the data from kinetic experiments at temperatures of 343-
403 K the optimized activation energy data were obtained as shown in Table 6. Some typical
results are shown in Figure 5.
Table 6. Activation energies and 95% confidence intervals.
parameter
EA (J/mol)
kr
(54.9±2.7) 103
(66.9±3.3) 103
(70.6±5.6) 103
k2
k-2
23

Figure 5. Experimental and model data for two selected experiments (top: run 26, 403 K, 45
bar; bottom: run 30, 343 K, 45 bar).
Agreement between experimental and modeled data for the dataset is good, see the parity plot
in Figure 6 for details.
Figure 6. Modeled versus experimental LA, HPA and GVL concentrations
24

4. Discussion
The modeling activities indicate that the hydrogenation of LA is best described by a LHMW
mechanism with a dual site surface reaction as the rate determining step. The mechanism is
characterized by dissociative hydrogen adsorption and competitive adsorption of LA and GVL at
the active sites of the catalyst surface. The competitive adsorption of the GVL is rationalized by
the observed reduction in initial reaction rate when performing a hydrogenation reaction in the
presence of GVL (Figure 4). The values for the adsorption constants (Kx with x = LA and GVL) are
1.32 x 10-3 and 0.84 x 10-3 m3/mol, respectively.
The apparent activation energy for the hydrogenation reaction is 54.9 ± 2.7 kJ/mol, which is
slightly higher than reported by Bond et al. (48 ± 5 kJ/mol) [24]. The small differences may be
related to the experimental set-ups used for the experiments (batch here versus a continuous
packed bed reactor) and differences in catalyst supplier. It is well known that the activity of
Ru/C catalysts is a function of, among others, the preparation method and the type of carbon
support used and major activity differences have been reported [34]. In addition, our studies
were performed with a different Ru loading (3%) than Bond (5%). The activation energy for
Ru/C as found in our study is much higher than for Pt/C by Zhang et al. (33 kJ/mol) [25].
Whether this relatively low value is indeed an intrinsic feature of the Pt/C catalyst or that the
kinetic analysis did not include proper attention to diffusional issues, is not clear.
The intramolecular esterification reaction was modeled as an acid catalyzed equilibrium
reaction with a first order dependency in reactants and products. The kinetic constants for the
forward reaction (k2) was 0.41±0.03 x 10-3 (m3/mol.s) at the reference temperature (363 K),
versus 0.042±0.013 x 10-3 (m3/mol.s) for the backward reaction (k-2). As such the forward
reaction is much faster and the equilibrium is far on the side of the product GVL. These findings
are in line with the experimental observations (see e.g. Figure 1). The value for the equilibrium
constant (k2/k-2) is about 10 at 363 K. This value is lower than that observed for the
independently experimentally determined equilibrium constant for the reaction at 293 K (16.5),
due to the temperature dependence of the equilibrium constant. The activation energy for the
forward reaction was 66.9 ± 3.3 kJ/mol, which is very close to the 70 kJ/mol reported by Bond
et al. [24].
25

The activation energy for the intramolecular esterification reaction is larger than for the
hydrogenation reaction. As such, the esterification reaction is favored at higher temperatures
and the amounts of GVL and 4-HPA are expected to be at equilibrium values when performing
the reaction at the high end of the temperature range (403 K). This is indeed experimentally
observed, see Figure 1 for details. Thus, when aiming for high amounts of 4-HPA, the reaction
should be carried out at low temperatures whereas GVL formation is favored at higher
temperatures. However, it should be stressed that 100% selectivity to GVL is not possible in
water in the temperature range studies (333-403K) due to equilibrium considerations. As such,
reported literature studies with quantitative GVL selectivity in water are highly doubtful and
likely related to analytical issues.
In the development of this study, the experimental data were first fitted to a homogeneous
model, i.e. without taking any mass transfer or diffusion limitations into account, see
supplementary information for details. With the homogeneous model also a good fit was
obtained. However, calculation of the Weisz-Prater numbers from experimentally observed
rates indicated that diffusion limitation in the catalyst particles occurred. A comparison of the
kinetic parameters for both the homogeneous and heterogeneous model is given in Table 7.
Table 7. Comparison of kinetic data for the homogeneous and heterogeneous model
Heterogeneous
model
Homogeneous
(A3, B4)
(63.3±2.9) 10-3
(53.3±5.4) 10-3
)
(1.32±0.06) 10-3
(1.51±0.4) 10-3
(0.45±0.06) 10-3
(0.79±0.08) 10-3
(0.4±0.02) 10-3
)
) (0.84±0.12) 10-3
-
(0.41±0.03) 10-3
(0.042±0.013) 10-3 (0.04±0.01) 10-3
EA (J/mol) for kr (54.9±2.7) 103
(34.1±0.1) 103
26

EA (J/mol) for k2 (66.9±3.3) 103
EA (J/mol) for k-2 (70.6±5.6) 103
(62.5±3.6) 103
(65.7±6.8) 103
The majority of the kinetic parameters are about similar, particularly when considering the
confidence intervals. The two main exceptions are the values for kr and the corresponding
activation energy for this reaction. The activation energy for the homogeneous model is much
lower than for the heterogeneous model. This is in line with the known fact that the apparent
activation energies for mass transfer limited reactions are always lower than that of the
intrinsic kinetics of the reaction, and in the limit approaches a value of half of the intrinsic one
[27].
A comparison of the experimental data and the heterogeneous model with and without any
mass transfer limitation is given in Figure 7. Indeed clear differences are observed. For instance,
the model without diffusional components predicts that the drop in LA concentration versus
time is much more profound than for the heterogeneous model with diffusional limitations, as
expected.
Figure 7. Comparison of the experimental data and the heterogeneous model with and without
any mass transfer limitation. Symbols: measured concentrations run 7, 363 K, 45 bar; solid
lines: calculated with the final kinetic model; dotted lines: calculated with the same kinetic
model but without any mass transfer or diffusion limitation.
27

To further illustrate that the full heterogeneous model needs to be employed at the conditions
used here, the concentration profiles inside the catalyst particles were extracted from the
software. Some typical results are shown in Figure 8.
1
0.8
0.6
0.4
0
0.2
0.4
0.6
0.8
1
1
0.8
0.6
0.4
0
0.2
0.4
0.6
0.8
1
Figure 8. Calculated relative hydrogen concentration profiles in the catalyst (top) and the
relative LA concentration profiles in the catalyst (bottem, run 11, 363 K, 45 bar)
28

The figures nicely illustrate a pattern that is generally observed with the experiments;
significant concentration variations occur within the catalyst particles. Initially, at t=0, it is
especially the hydrogen concentration that decreases at the interior of the particle. At the
center however the concentration is still more than 40% of the liquid bulk value. Therefore,
even initially, all catalyst volume does participate in catalyzing the reaction and there is no
inactive part of the catalyst as would have been the case with more severe diffusion limitation.
As time progresses the hydrogen concentration inside the particle increases until near the end
when most of the LA is converted the concentration is equal to the liquid bulk value throughout
the particles.
An opposite trend is seen with the LA concentration profiles, see Figure 8 (right). Initially the LA
concentration decreases in the catalyst particle, but at the center the value still is some 75% of
the liquid bulk value. But now, with increasing time, the concentration in the catalyst
decreases. The observations are reflected in the catalyst effectiveness, see Figure 9. At the start
of the experiment the effectiveness is close to 75%, mainly due to the decreased availability of
hydrogen. Hydrogen is limiting here, despite its much higher diffusion coefficient, because of its
low concentration. During the experiment, gradually the limitation is shifted from the hydrogen
availability towards the LA availability. This is also illustrated by the Weisz-Prater numbers, NWP,
for hydrogen and LA that are also shown in Figure 9. The initially high NWP of hydrogen
gradually drops to very low values and on itself would lead to the erroneous conclusion that
after t=2000 the situation is free of diffusion limitation. Here the high NWP of LA is determining
the system behavior and still causes some diffusion limitation. For all experiments the catalyst
effectiveness factors were found to be in the range of 70 to 95%, varying from initially lower
values to higher values near the end at high conversion.
29