Accepted Manuscript

Kinetic Modeling of the Oxidative Dehydrogenation of Ethane to Ethylene overa MoVTeNbO Catalytic System

Gamaliel Che-Galicia, Roberto Quintana-Solórzano, Richard S. Ruiz-Martínez,Jaime S. Valente, Carlos O. Castillo-Araiza

PII: S1385-8947(14)00474-4DOI: http://dx.doi.org/10.1016/j.cej.2014.04.042Reference: CEJ 12021

To appear in: Chemical Engineering Journal

Received Date: 5 February 2014Revised Date: 7 April 2014Accepted Date: 11 April 2014

Please cite this article as: G. Che-Galicia, R. Quintana-Solórzano, R.S. Ruiz-Martínez, J.S. Valente, C.O. Castillo-Araiza, Kinetic Modeling of the Oxidative Dehydrogenation of Ethane to Ethylene over a MoVTeNbO CatalyticSystem, Chemical Engineering Journal (2014), doi: http://dx.doi.org/10.1016/j.cej.2014.04.042

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Kinetic Modeling of the Oxidative Dehydrogenation of Ethane to

Ethylene over a MoVTeNbO Catalytic System

Gamaliel Che-Galiciaa, Roberto Quintana-Solórzanob,*, Richard S. Ruiz-Martíneza, Jaime S.

Valenteb, Carlos O. Castillo-Araizaa,*

a Grupo de Procesos de Transporte y Reacción en Sistemas Multifásicos, Depto. de IPH, Universidad

Autónoma Metropolitana - Iztapalapa, Av. San Rafael Atlixco No. 186, C.P. 09340, México D.F.,

MÉXICO

b Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas Norte No. 152, C.P. 07730, México D.F.,

MÉXICO

*To whom correspondence should be addressed:

E-mail, corresponding author I: coca@xanum.uam.mx (C.O.C.A.)

E-mail, corresponding author II: rquintana@imp.mx (R.Q.S.)

Tels: + 52 55 5804 4648 (C.O.C.A), + 52 55 9175 8530 (R.Q.S.)

Abstract

The oxidative dehydrogenation of ethane to ethylene (ODH-Et) is investigated over a high

activity-selectivity MoVTeNb mixed oxide. Experiments are performed using a mixture of

ethane, oxygen and nitrogen as feedstock, at temperatures from 400 to 480 °C, inlet partial

pressures of oxygen and ethane from 5.0 to 24.2 kPa, and space-times from 10 to 140

gcat·h·molethane-1. Ethylene selectivity varies from 76 to 96 %, for an ethane conversion range 17 -

85 %. In a set of experiments at 440 °C feeding ethylene instead of ethane, ethylene conversion is

from 3 to 14 % and COx are the only reaction products, the CO being the dominant species with a

selectivity range 73 - 79 %. Kinetic models based on Langmuir-Hinshelwood-Hougen-Watson

(LHHW) and Mars-van Krevelen (MvK) formalisms, and combinations of them are developed to

describe the ODH-Et. Physicochemical and statistical criteria are employed to contrast the

performance of these kinetic approaches. The LHHW kinetics exhibits the best capacity to

represent the observations, being a potential model for the conceptual design of ODH-Et reactors

in future investigations. Kinetic parameters indicate: (i) ethylene formation is the reaction

demanding the lowest activation energy; (ii) total oxidations of ethane are the reactions

demanding the largest activation energies; (iii) reaction rates, including that of catalyst oxidation,

are weakly affected by changes in the oxygen partial pressure, explaining the high selectivity to

ethylene of MoVTeNbO; and (iv) water is the component with the highest affinity to be adsorbed

on active sites affecting negatively reaction rates.

Key words: Oxidative dehydrogenation reaction; MoVTeNbO catalyst; ethylene; kinetic

modeling; Langmuir-Hinshelwood-Hougen-Watson; Mars-van Krevelen.

Abbreviations: ER: Eley-Rideal; FID: flame ionization detector; GC: gas chromatograph;

LHHW: Langmuir-Hinshelwood-Hougen-Watson; MvK: Mars-van Krevelen; MvK-LHHW:

Mars-van Krevelen and Langmuir-Hinshelwood-Hougen-Watson; ODEs: ordinary differential

equations; ODH-Et: oxidative dehydrogenation of ethane to ethylene; RDS: rate-determining

steps; TCD: thermal conductivity detector.

1 Introduction

Ethylene is a basic material for the world's Petrochemical Industry. This olefin is the main

raw material for the production of polyethylene, ethylene oxide and ethylene dichloride, among

others important chemical products. In 2012, it is reported that the global ethylene demand nearly

reached 141 million tons and is expected to increase to more than 150 million tons in 2015 [1].

Presently, ethylene is mainly produced via the steam cracking of diverse hydrocarbon streams,

particularly gas oils, naphtha, LPG as well as natural gas and, in a minor grade, via the direct

(catalytic) dehydrogenation of ethane along with the fluid-catalytic-cracking of gas oils [2]. All

the current conventional processes to produce ethylene, however, exhibit a set of drawbacks

related to thermodynamics, energy requirements, catalyst deactivation by coke deposition, control

of conversion/selectivity and products separation [3-5]. By reason of all these limitations and

considering the continuous increase in the worldwide demand of ethylene, the design of new

processes to cope with these industrial deficiencies is clearly mandatory.

The catalytic oxidative dehydrogenation of ethane to ethylene (ODH-Et) appears as an

attractive alternative to complement and even gradually replace the current commercial processes

for ethylene production. Nevertheless, there are still some important issues to be dealt with by

academy and industry in order to extend the ODH-Et to a commercial scale, the development of a

highly active and selective catalyst being one of the most crucial matters. Even though several

catalytic systems have been reported in the literature to be active for the ODH-Et [6-12], a

multimetallic mixed oxide containing Mo, V, Te and Nb (MoVTeNbO) corresponds to one of the

most promising materials in view of its high of conversion of ethane and selectivity to ethylene,

attributed to the presence of two crystalline phases designated M1 and M2, the former having the

most important contribution to the catalytic performance [13-22]. Specifically, for MoVTeNbO

catalysts, it has been proposed that V species are the active sites in ethane activation, the presence

of Mo species enhance the catalytic activity of V atoms, the role of Te species is directly

associated with the formation of an active and selective crystalline phase M1 and the Nb species

seem to have a promoter effect enhancing the selectivity to ethylene [13,14,23-26]. It is also

noteworthy that the MoVTeNbO system starts to be active for the ODH-Et at temperatures below

400 ºC, a value substantially lower compared with the one required by the existing commercial

thermal processes. Evidently, decreasing the operating temperature not only leads to a substantial

energy saving but also decreases the number of side reactions. Also, during the ODH-Et,

advantageously, a limited number of reaction products (ethylene, carbon dioxide, carbon

monoxide and water) are observed, while the catalyst does not undergo deactivation by coke due

to the presence of molecular oxygen in the reaction mixture [27-29]. The aforementioned

MoVTeNbO catalytic system is a high efficiency novel material for the ODH-Et that presents

remarkably high values of selectivity to ethylene (>90 %) at levels of ethane conversion ca. 60 %,

as reported elsewhere [13,14,22]. Therefore, envisaging a possible future application of this

material formulation on the conceptual design of catalytic reactors, it is necessary to develop its

own kinetics.

The number of papers addressing kinetic aspects related to the ODH-Et is not large

[6,22,30-40]. Some reported kinetics are based on macroscopic mechanisms such as Langmuir-

Hinshelwood-Hougen-Watson (LHHW) [30-35], Eley-Rideal (ER) [36,37], Mars-van Krevelen

(MvK) [38,39] or a combination of MvK and LHHW (MvK-LHHW) [40]. Other models based

on Power Law (PL) empiricisms have been also reported [22,38]. Even though all these models

are specific for each catalyst formulation and do not take into consideration elementary steps,

some aspects about the macro mechanism can be deduced from them. In fact, concerning

mechanistic issues, there is no unanimity yet about the macroscopic mechanisms involved in the

ODH-Et [6,30-40]. The discussion has been mainly focused on defining the “type of oxygen”,

i.e., lattice oxygen or superficial oxygen adsorbed from the gas phase on the active site is

responsible for the ODH-Et leading to ethylene and total oxidation products. Additionally, it is

still on debate whether the fed ethane reacts in the gas phase or as an adsorbed species on the

catalyst surface, and whether the reaction products have an influence on the catalyst performance

or not. On the basis of a LHHW kinetics over a V2O5/SiO2 reported elsewhere [30], it was

concluded that water has a strong influence on the rate of ethylene formation and that

intermediate oxygenated species contribute substantially to the formation of carbon oxides.

Another LHHW kinetics obtained over a VOx/c-Al2O3 catalyst in the absence of gas phase

oxygen [35], demonstrated that the competitive adsorption of ethane, ethylene and carbon oxides

occurred and had a positive effect on the formation of active sites selective to ethylene

production. Besides, an ER formalism, which considers that gas phase ethane reacts with

adsorbed oxygen over a (K-doped) V2O5/SiO2 [36], suggested that water adsorbed on the catalyst

surface impacted negatively on both ethane conversion and ethylene selectivity. Likewise, MvK

kinetics on a mixed Ni-Nb oxide [38] suggested that oxygen in the catalyst lattice produced two

types of active sites, one responsible for the ethylene formation and ethylene total oxidation, and

the other involved in the ethane total oxidation. Finally, a combination of MvK-LHHW

formalisms over a VOx/γ-Al2O3 catalyst [40] indicated that the MvK mechanism governs

ethylene formation, whereas ethane and ethylene total oxidations occur in accordance with a

LHHW mechanism.

The purpose of this work is, thus, to develop a series of kinetic models based upon LHHW

and MvK formalisms, and combinations of them, to describe the catalytic ODH-Et. The kinetics

are novel as they characterize the performance of a high activity-selectivity MoVTeNb mixed

oxide on the aforementioned reaction. The parameters associated to the kinetics models are

obtained via a nonisothermal regression of steady-state catalytic experimental data obtained in a

laboratory scale fixed-bed reactor. Both physicochemical and statistical criteria are used to

contrast the developed models and then select the most suitable one. Apart from obtaining rate

equations that can be readily used for the reactor design and scale-up, the combination of

experimental issues with kinetic information can contribute to a better understanding of the

macroscopic mechanism involved in the ODH-Et.

2 Experimental procedures

2.1 Catalyst preparation

A multimetallic mixed oxide with a nominal atomic ratio of Mo:V:Te:Nb equal to

1:0.24:0.24:0.18 was synthesized. The preparation procedure comprised a set of steps which are

briefly described herein; (i) preparing at 80 °C and continuous stirring an aqueous solution

containing tetra-hydrated ammonium hepta-molybdate (Merck, 99 %), telluric acid (Aldrich, 98

%), and ammonium meta-vanadate (Sigma-Aldrich, 99.5 %); (ii) separately preparing at 80 °C a

second aqueous solution containing niobium oxalate (ABCR Lab. 99 %) and oxalic acid

(Aldrich, 98 %). Solution of step (ii) was added to the solution of stage (i) keeping a vigorous and

continuous stirring to yield a slurry, which was then cooled to room temperature. Next, the pH of

the aforementioned slurry was adjusted to 2.5 with the addition of 1 M nitric acid. The acidified

slurry was later placed in a rotary evaporator operated at 50 °C and 27 kPa to gradually eliminate

the water. The resultant powder was dried overnight at 100 °C and finally activated by means of a

thermal treatment at 600 °C for 2 h under nitrogen flow. Some additional details about the

catalyst preparation procedure along with a set of important physicochemical properties of the

resulting solid were reported previously [22].

2.2 Kinetic experiments

2.2.1 Experimental Setup

Measurements of the catalytic performance were carried out in a tubular fixed-bed reactor

made of quartz with an internal diameter of 1.0×10-2 m and length of 4.0×10-2 m, which was

operated isothermally and at atmospheric pressure (ca. 80 kPa). All tests were performed over a

bed consisting of 0.60 g of catalyst, sieved for an average particle size equal to 150 µm prior to

be loaded into the reactor. The reaction feedstock was composed of a mixture of ethane (or

ethylene), oxygen and nitrogen with a varying composition depending on the experiment. In

order to obtain the data required to calibrate the aforementioned kinetic models, three sets of

experiments were effectuated. In the first set both temperature and space-time (Wcat·Fethane,o-1)

were varied within the ranges 400 - 480 ºC for the former, and 23 - 70 gcat·h·molethane-1, keeping

constant the inlet partial pressure of ethane, oxygen, and nitrogen at 7.0, 5.5, and 65.5 kPa,

respectively. The second set of experiments was performed at 440 ºC varying the inlet partial

pressure of ethane (2 6

oC Hp ) at constant inlet partial pressure of oxygen (

2

oOp ), and vice versa; thus,

the inlet partial pressure of each reactant was spanned from 5.1 to 22.3 kPa resulting in a

Wcat·Fethane,o-1 range from 10 to 140 gcat·h·molethane

-1. The third set of experiments was carried out

feeding into the reactor ethylene instead of ethane at the operating conditions used in the second

set of experiments. In the absence of catalyst, no reaction between ethane and oxygen occurred in

a test performed at 480 °C.

An assessment of the mass and heat disguises at pellet scale was performed in accordance

with the procedure and criteria outlined elsewhere [41]. Deviations to the ideal flow pattern of the

reactor were also evaluated. Some of the basic parameters used to assess the referred criteria were

the following: catalyst bed length of 8.5×10-3 m, bed porosity of 0.3 m3·m-3; effective diffusion

coefficient of 2.75 × 10-5 m2·s-1; catalysts tortuosity of 5.0 m·m-1, specific reaction rate of ethane

of 3.44 × 10-6 mol·(gcat·s)-1, reaction temperature of 480 ºC, ethane conversion of 0.85 mol·mol-1;

and activation energy for ethane oxidative dehydrogenation equal to 90.0 kJ·mol-1. Table 1

displays a summary of the assessed kinetic criteria for an experiment performed at the most

severe conditions, i.e., those leading to the maximum specific reaction rate of ethane, which

indicate that experimental observations were obtained under plug flow conditions and in absence

of internal and external, heat and mass transfer resistances.

Table 1 is shown here.

2.2.2 Analysis of reaction products

The compositions of the reactor by-pass and the reactor effluent were analyzed online in an

Agilent 7890A Gas Chromatograph (GC). GC’s configuration includes two detectors, a flame

ionization detector (FID) and a thermal conductivity detector (TCD), as well as an array of three

columns, namely, a 30 m × 0.53 mm × 40 µm HP Plot Q, a 30 m × 0.25 mm × 5 µm HP Plot

Al2O3/S and a 30 m × 0.53 mm × 50 µm molecular sieve. Hydrocarbons were quantified in the

FID whereas non hydrocarbons (COx, nitrogen, oxygen, etc.) in the TCD. By applying Eq. (1),

the molar outlet flow rate of any component n was calculated by means of the internal standard

method employing chromatographic information:

i.s. i.s n nn

i.s. i.s. n

F M A dF

A d M= × (1)

Fn is outlet molar flow rate, Mn corresponds to the molecular mass An denotes the

chromatographic surface area, and dn is the chromatographic calibration factor. The subscript i.s.

is used to denote the internal standard, nitrogen being utilized.

The conversion of hydrocarbons (ethane or ethylene) denoted by XHC (Eq. (2)) as well as

the selectivity to a n product referred to as Sn (Eq. (3)) were based on a carbon mass balance

and computed as follows:

HC,in HC,outHC

HC,in

F FX 100

F

−= × (2)

nn

HC,in HC,out

F CS 100

2 (F F )= ×

−

(3)

where FHC is molar flow rate of the hydrocarbon used as reactant, Fn is outlet molar flow rate of

the product n and C is the carbon number of species n.

3 Kinetic Modeling

As a first step in the construction of a kinetic model, a global reaction network based on the

experimental observations is proposed, vide Fig. 1. This reaction network includes the species

detected by gases chromatography, namely, ethane, ethylene, carbon monoxide and carbon

dioxide. As also indicated in Fig. 1, oxygen is present as a second reagent while water is

invariably a reaction product in all reactions. Both parallel and consecutive reactions are

accounted for in which ethylene is produced from ethane (r1), carbon oxides (COx) are formed

out of the combustion of ethane corresponding to r2 and r3, and from the secondary combustion of

ethylene, vide r4 and r5.

Figure 1 is shown here.

Four kinetic models based on different macroscopic mechanistic approaches are developed

to characterize the ODH-Et over MoVTeNbO catalyst. Specifically, the first model is based on a

LHHW formalism, the second model is supported on a MvK formalism, while the third and

fourth models are constructed on a combination of MvK and LHHW, as will be discussed in

detail in Sections 3.1 to 3.3. It is important to point out that in the development of all these

models, the effect of the products on catalysts is captured indirectly by the estimated effective

parameters since for all studied operating conditions products accumulation (ethylene, COx and

water) was observed at different levels and, hence, the parameter estimation made use of total

products that were collected at the outlet of the steady-state reactor.

3.1 Langmuir-Hinshelwood-Hougen-Watson model

The kinetic model based on the LHHW formalism is constructed taking into consideration

the next assumptions: (i) there is a single type of active sites over the whole catalyst surface, (ii)

there is competitive adsorption of reactants (ethane and oxygen) and products (ethylene, carbon

oxides and water) for the active sites, (iii) oxygen adsorption is dissociative while that of the

other species is associative, (iv) surface reaction steps are considered fast taking place over a

finite number of active sites, (v) surface reactions are rate-determining steps (RDS), (v) all

products are susceptible to be re-adsorbed over the active sites, (vi) adsorption and desorption

steps are quasi-equilibrated. In a previous publication [22], apparent reaction orders for both

hydrocarbons and oxygen were found to be positive out of experiments over the MoVTeNbO

catalyst and, therefore, the adsorption of reagents is discarded as RDS.

Table 2 includes the reaction steps considered for building the kinetics (S represents the

active sites); namely, steps A and B denotes the adsorption of main reagents (oxygen and ethane),

steps 1 to 5 corresponds to the surface reactions, and steps C to F represent the desorption of

products. In Table 2, σj is the so-called Horiuti stoichiometric number used for describing the

times that each adsorption, desorption and reaction steps has to occur in order to complete a

single catalytic cycle comprising the overall reactions, the latter represented by steps I to V.

Notice that the adsorption of molecular O2 (step A) is a crucial stage for the surface reactions to

take place (steps 1-5).

Table 2 is shown here.

The rate of the five reactions (ri), accounted for in the reaction network of Fig. 1, are

expressed by eqs. (4) to (8). Notice that the calculation of ri involves a rate coefficient denoted by

ki, an adsorption equilibrium coefficient for the n-th component represented by Kn, the fraction

coverage of active sites designated *θ , the partial pressure of the reactant n represented by pn, and

the reaction order related to the partial pressure of the gas phase denoted by mi:

2 2 2 6 2 6

1 2 21 1 O O C H C H *r k (K p ) K p= θ (4)

2 2

2 2 2 6 2 6

m 2 m 12 2 O O C H C H *r k (K p ) K p += θ (5)

3 3

2 2 2 6 2 6

m 2 m 13 3 O O C H C H *r k (K p ) K p += θ (6)

4 4

2 2 2 4 2 4

m 2 m 14 4 O O C H C H *r k (K p ) K p += θ (7)

5 5

2 2 2 4 2 4

m 2 m 15 5 O O C H C H *r k (K p ) K p += θ (8)

Since the fraction coverage of different species on the catalytic surface is conserved all the

time, the global balance of the fraction sites corresponds to Eq. (9):

2 6 2 4 2 2* O C H C H H O CO CO 1θ + θ + θ + θ + θ + θ + θ = (9)

The fraction coverage of a specific component is defined as the number of sites occupied

by such a species relative to the total number of available sites corresponding to Eq. (10) for

oxygen and Eq. (11) for the species different to oxygen:

2 2

1 2O O O *(K p )θ = θ

(10)

n n n * 2 6 2 4 2 2K p n C H , C H , CO , CO and H Oθ = θ = (11)

The fraction of free active sites is obtained by combining eqs. (9) to (11) resulting in Eq.

(12):

2 2 2 6 2 6 2 4 2 4 2 2 2 2

* 1 2O O C H C H C H C H H O H O CO CO CO CO

1

1 (K p ) K p K p K p K p K pθ =

+ + + + + + (12)

The combination of the specific reaction rates gives the net reaction rate of component n,

which is expressed by Eq. (13) [42]:

5

n n,i ii 1

R r=

= ν∑ (13)

where n,iν is the stoichiometric coefficient of the component n in the i-th reaction (vide steps I to

V displayed in Table 2).

3.2 Mars-van Krevelen model

Kinetic models based upon MvK formalism are frequently used to describe the (partial)

oxidation of organic compounds over noble metals as well as metal oxide catalysts [43,44].

According to the MvK mechanism, the reaction takes place through alternating cyclically the

catalyst’s active sites from oxidized to reduced states [45]. In the reaction, more specifically, the

labile oxygen species from lattice is responsible for ethylene and COx formations, and these

oxygen species are restored by gas phase oxygen [46]. For the particular case of the ODH-Et

studied in this work, Table 3 presents the reaction steps accounted for constructing the

corresponding kinetic model. The reactions involve catalyst’s lattice oxygen as well as gas phase

hydrocarbons to produce, as corresponds, ethylene, COx and/or water in accordance with steps 2-

5. Step O, additionally, represents the re-oxidation of lattice by gas phase oxygen and, hence,

catalyst’s reduced sites.

Table 3 is shown here.

The rate corresponding rate expressions for the MvK model derived on the basis of the

steps displayed in Table 3 are given by eqs. (14) to (18):

2 61 1 C H OXr k p= θ (14)

2 62 2 C H OXr k p= θ (15)

2 63 3 C H OXr k p= θ (16)

2 44 4 C H OXr k p= θ (17)

2 45 5 C H OXr k p= θ (18)

The rate of re-oxidation of the reduced catalyst in the presence of gas phase oxygen to

restore the lattice oxygen is represented by Eq. (19):

2

mO O O redr k p= θ (19)

ki denotes the rate coefficient for the i-th reaction, ko corresponds to the rate coefficient of the re-

oxidation reaction (Step O in Table 3), θox and θred represent the fraction of oxidized and reduced

sites respectively, pn is the partial pressure of the reactants and m is the number of moles of

oxygen used in the re-oxidation of reduced catalyst.

Additionally, the surface site balance in terms of the aforementioned fraction of oxidized

and reduced sites corresponds to Eq. (20):

ox red 1θ + θ = (20)

When reaching the steady-state, the oxidation rate of the catalyst equals that of the

reduction rate and, therefore, after combining eqs. (14) - (20) it is possible to derive an expression

to compute the fraction of oxidized sites, vide Eq. (21):

2

2 2 6 2 4

nO O

OX nO O 1 1 2 2 3 3 C H 4 4 5 5 C H

k p

k p ( k k k )p ( k k )pθ =

+ ν + ν + ν + ν + ν (21)

where iν is the stoichiometric coefficient of oxygen for the i-th reaction, i.e., the number of moles

of oxygen that reacts per mole of hydrocarbon (vide steps I to V in Table 2). The net reaction

rates (Rn) can be finally obtained from the Eq. (13) after accounting for eqs. (14) - (18).

3.3 Combined Mars-van Krevelen and Langmuir-Hinshelwood-Hougen-

Watson models

As stated above MoVTeNbO catalysts mostly consist of two crystalline phases designated

M1 and M2. It has been suggested that terminating [001] planes of the M1 phase contain the most

active and selective surface sites for ODH-Et, and hence phase M2 seems to be active for the

deep oxidation reactions leading to COx species and water [13]. Based on this, two additional

kinetic models named MvK-LHHW-1 and MvK-LHHW-2, obtained as a result of combining the

MvK and the LHHW formalisms, are constructed. Table 4 includes all the reaction steps

accounted for building them. In these two kinetic approaches it is assumed the catalyst consists of

two types of active sites, viz., (i) one type denoted as “M”, which is responsible for the ethylene

formation via the ODH-Et reaction (steps 1 and O in Table 4) via a redox mechanism and, (ii) a

second type designated “S” over which the adsorption of both oxygen and ethane occurs leading

to the formation of carbon oxides and water (steps 2 - 5 in Table 4). Notice that the products

formed out of reactions 2 to 5 are susceptible to be re-adsorbed over the sites S corresponding

specifically to the steps C - F included in Table 4. The main difference between MvK-LHHW-1

and MvK-LHHW-2 is that the later model considers that the re-adsorption of all reaction

products on the active sites responsible of ethylene formation (vide steps G to I) can occur, a

scenario that the former model neglects.

Table 4 is shown here.

The MvK-LHHW-1 model is represented by eqs. (5) - (8), (12), (14), (19), (20) and (22).

Particularly, Eq. (14) expresses the rate of reaction 1 corresponding to the formation of ethylene

out of ethane (step 1 in Table 4), and Eq. (19) denotes the re-oxidation of reduced sites (step O in

Table 4). The reaction rate expressions for reactions 2 - 5 (steps 2 - 5 in Table 4) are represented

by eqs. (5) - (8) respectively; whereas the fractional coverage for the free active sites is given by

Eq. (12). After combining the corresponding steady-state of reaction rates represented by eqs.

(14), (19) and (20), an expression that allows computing the fraction of oxidized sites is obtained,

vide Eq. (22):

2

2 2 6

nO O

OX nO O 1 1 C H

k p

k p k pθ =

+ ν (22)

In the case of the MvK-LHHW-2 model, it is given by eqs. (5) - (8), (12), (14), (19), (23) -

(25). As stated above, eqs. (14) and (19) denote the rate of the reaction 1 and reaction O,

respectively, vide steps 1 and O in Table 4, respectively. Notice that all reaction products, i.e.,

ethylene, carbon oxides and water, are susceptible to be adsorbed over re-oxidized sites, a

situation that must be accounted for in the corresponding sites balance. Thus, by assuming that

the re-adsorption of all products over oxidized sites is also quasi-equilibrated (steps G-J in Table

4), the original fraction site balance based on the conventional MvK formalism, vide Eq. (20),

was adapted to give Eq. (23):

2 4 2 2OX red OX C H OX H O OX CO OX CO 1− − − −θ + θ + θ + θ + θ + θ = (23)

where the fractional coverage of each species is given by Eq. (24):

OX n OX n n OX 2 4 2 2K p n C H , H O, CO and CO− −θ = θ = (24)

By assuming pseudo-steady-state approximation for the formation intermediate species

adsorbed on the catalyst surface and combining eqs. (14), (19), (23) - (24), the fraction of

oxidized sites is accessible by means of the expression of Eq. (25):

2

2 2 4 2 4 2 2 2 2 2 6

nO O

OX nO O OX C H C H OX CO CO OX CO CO OX H O H O 1 1 C H

k p

k p (1 K p K p K p K p ) k p− − − −

θ =+ + + + + ν

(25)

The rate expressions for reaction steps 2 to 5 in Table 4 are represented by eqs. (5) - (8),

respectively. Notice that, the corresponding fractional coverage for the free active sites has to be

computed by means of Eq. (12).

3.4 Parameters estimation

Kinetic parameters were estimated by minimizing a weighted objective function referred to

as RSS(β), which includes the residual sum of squares of the molar flow rates of all the species

accounted for in the reaction network of Fig. 1:

resp exp

1 2 n

n n, ,...,2

n k,n k,nn 1 k 1

ˆRSS( ) w (F F ) minβ β β

= =

β = − →∑ ∑ (26)

where β is optimal parameters vector, nexp is the number of independent experiments, nresp is the

number of responses, Fk,n and k,nF̂ are the n-th experimental and predicted responses for the k-th

observation, respectively, and wn is the weight factor assigned to the n-th response.

The molar flow rate of component n was calculated by solving a system of ordinary

differential equations (ODEs) given by Eq. (27), which corresponds to the experimental reactor

model equations. Needless to say as that both intra and inter-particle transport limitations were

found to be negligible according to criteria given in Table 1, Eq. (27) stands for an isobaric,

isothermal, one-dimensional pseudo-homogeneous continuous integral fixed-bed reactor model:

nn

cat

dFR

dW= (27)

With the following initial conditions:

n noF F ,= when catW 0= (28)

where Fn is the molar flow rate of component n, Fno is the inlet molar flow rate of component n

and Wcat is the mass of the catalyst loaded into the reactor. The subroutine VODE was used to

solve the corresponding set of ODEs [47]. The initial minimization of the objective function, vide

Eq. (26), in the model regression was carried out using the Rosenbrock method [48] and then, the

ODRPACK subroutines were called for fitting calculated values to the corresponding

experimental data points [49]. These subroutines can perform either weighted orthogonal distance

regression or nonlinear least square problems for explicit and implicit models using multi-

response data with an implementation of the Levenberg-Marquardt method, as documented

elsewhere [50].

In order to obtain activation energies values and pre-exponential factors as well as standard

adsorption enthalpies and entropies during the parameters estimation procedure, a nonisothermal

multi-response parameter estimation was achieved. Aimed at overcoming the correlation between

corresponding parameters both Arrhenius and Van’t Hoff equations were used in the

reparameterized form. Specifically, after reparameterizing the Arrhenius equation, the

corresponding rate coefficients were computed using the expression of Eq. (29):

A,ii i *

E 1 1k exp A'

R T T

= − −

(29)

For the i-th reaction, iA ' is the natural logarithm of the pre-exponential factor, and EA,i is

the activation energy, T is the reaction temperature, T* is the averaged reaction temperature.

The reparameterization of the Van’t Hoff expression leads to Eq. (30), which was used to

compute the corresponding adsorption coefficients:

o on n

n *

S H 1 1K exp

R R T T

∆ ∆ = − −

(30)

onS∆ is the standard adsorption entropy of component n, o

nH∆ is the standard adsorption enthalpy

of component n and R is the universal gas constant.

An additional aspect accounted for during the parameter estimation was related to statistical

issues. For the four kinetic models described above, the F-test for the global significance of the

regression as well as the individual t-test and the confidence limits for the estimates were

computed. Parity diagrams were also built to visualize the agreement between experimental

observations and models predictions. Aside, the parameters correlation between pairs of

estimated parameters was accounted for by computing the so-called binary linear correlation

coefficients (ρij). When the value of ρij is close to ±1 a strong linear relationship between the

estimated parameters i and j occurs.

4 Results and discussion

4.1 Experiments

4.1.1 Temperature and space-time effect

This part of the manuscript deals with the results obtained for a reactor feedstock

containing ethane, oxygen and nitrogen at the operating conditions specified in Section 2.2. The

GC analyses indicated that the reaction products spectra consisted of ethylene, CO2 and CO. Fig.

2a shows the manner ethane conversion varies as a function of temperature at three different

values of Wcat·Fethane,o-1 [23, 46.5 and 70 gcat·h·molethane

-1] and an inlet molar ratio of ethane to

oxygen equal to 1.3. Ethane conversion ranges from 17 to 85 %, the largest value corresponding

to an experiment performed at 480 °C/70 gcat·h·molethane-1. In fact, ethane conversion increases

linearly with augmenting reaction severity, i.e., temperature and space-time.

Fig. 2b displays the evolution of the selectivity to ethylene, CO2 and CO as a function of

the ethane conversion for a set of experiments within the region 400 - 480 °C and 23 - 70

gcat·h·molethane-1, feeding a mixture containing ethane, oxygen and nitrogen with an inlet molar

ratio ethane to oxygen of 1.3. The selectivity to the reaction products detected in the reactor

effluent decreases in the following order: ethylene >> CO > CO2. At the investigated conditions,

the selectivity ranged from 76 to 96 % for ethylene, 2.5 to 16.5 % for CO and 1.5 to 7.5 % for

CO2. On the basis of what was discussed previously, the region of high ethane conversion

demands operating at large values of temperature and space-time, an scenario at which the

selectivity to COx is favored in detriment to that of ethylene, as can be observed in Fig. 2b. A

previous publication [22] was devoted to study systematically the combined effect of temperature

and space-time on a set of catalytic responses over the same catalyst formulation.

Figure 2 is shown here.

4.1.2 Partial pressure effect

The effect of the inlet partial pressure of the reactants, ethane and oxygen, on the

MoVTeNb mixed oxide for the ODH-Et was also dealt with. For this end, the inlet partial

pressure of one reactant was systematically varied maintaining constant the inlet partial pressure

of the other. Fig. 3 summarizes the effect of the inlet partial pressure of the reactants on ethane

conversion for a set of experiments effectuated at a reaction temperature of 440 ºC and space-

time from 10 - 140 gcat·h·molethane-1. It is first detected that an increase of the inlet partial pressure

of ethane and/or oxygen has a positive effect on ethane conversion. Evidently, the ethane

conversion is appreciably more sensitive to changes in the inlet partial pressure of ethane. More

precisely, on the basis of the information included in Fig. 3a, augmenting 2

oOp from 5 to 22 kPa

leads to a relatively small increase in the ethane conversion, ca. 8 % absolute. The data plotted in

Fig. 3b shows that after increasing 2 6

oC Hp from 5 to 22 kPa, the augment in the ethane conversion

is as high as 20 % absolute. All these observations are in agreement with other publications in

which ODH-Et was performed over vanadium-based catalysts [31,32].

Figure 3 is shown here.

4.1.3 Catalytic reaction feeding ethylene

The contribution of ethylene to the formation of carbon oxides in the ODH-Et was assessed

by means of a set of experiments using a feedstock containing ethylene instead of ethane. Such

experiments are performed at 440 ºC, space-time between 10 and 130 gcat·h·molethylene-1 and inlet

molar ratios of ethylene to oxygen 0.5 - 2.0 (vide Section 2.2.1). At these conditions, ethylene

conversion is 3 - 14 %, the only carbon-containing products detected via chromatographic

analyses being CO and CO2. The larger the space-time, the higher the ethylene conversion is.

Systematically, the CO is produced in an appreciably higher amount in comparison with CO2, the

selectivity to the former ranging 73 - 78 % and the selectivity to the latter ranging 22 - 27 %, vide

Fig. 4a. On the basis of the information discussed above, it is evident that (i) part of the ethylene

formed via oxydehydrogenation converts into COx, (ii) ethylene is more difficultly activated over

the MoVTeNbO catalyst than ethane is, and (iii) ethylene converts preferentially into CO.

As in the case of ethane, the effect of varying the inlet partial pressure of the ethylene

(2 4

oC Hp ) and oxygen (

2

oOp ) on ethylene conversion as well as COx selectivity was also addressed.

It can be observed in Fig. 4b that increasing the inlet partial pressure of oxygen at a given inlet

partial pressure of ethylene has a slight positive effect on ethylene conversion, a behavior which

is also observed in the case of ethane conversion in the first set of experiments. Fig. 4c shows that

augmenting the inlet partial pressure of ethylene also leads to higher ethylene conversions.

Contrasting Fig 4b with Fig 4c, it is clear that ethylene conversion is appreciably more sensitive

to changes in the inlet partial pressure of ethylene than in that of oxygen.

The way that the experiments are defined (vide Section 2.2.1) allowed us filtering out the

contribution of ethylene conversion to the ethane oxidative dehydrogenation. Thus, it was

detected that ethane and ethylene are source of both CO2 and CO. For the set of experiments

discussed in Section 4.1.2, after removing the contribution of ethylene, the ratios CO/COx and

CO2/COx varied from 0.27 to 0.64 and 0.33 to 0.76, respectively, a value that appears to be very

sensitive to the operating conditions, in particular, to the hydrocarbon to oxygen ratio in the

feedstock contrary to what is detected in the experiments with ethylene.

Figure 4 is shown here.

4.2 Kinetic modeling

The mathematical procedure for the estimation of the kinetic parameters is a crucial step in

the construction of kinetic models, which has to be invariably accompanied by a careful

assessment of the model parameters from a physicochemical perspective and a statistical point of

view. Kinetic parameters should be not only capable to represent adequately the occurred

physicochemical phenomena but also exhibit thermodynamic consistency. Besides, regression

results must be statistically tested to verify the model adequacy and estimate confidence limits.

When confronting a set of kinetic models, all this information is of a great utility to define the

best candidate.

4.2.1 Statistical analysis: model adequacy and t-test on parameters

Fig. 5 shows the so-called parity diagrams for the four kinetic models described in Section

3. In the case of this work, they are utilized to compare the model computed flow rates with

experimentally measured ones for all the components accounted for in the reaction network of

Fig. 1. Evidently, the LHHW is the model that best represents the experimental observations. It is

in fact observed in Fig. 5a, that the LHHW formalism is capable to fit experimental observations

with an error margin below 10 % without detecting the presence of any undesired statistical

trend. Also notice that the random error is constant over the range of the operating variables at

which the kinetic data are collected and, therefore, no systematic association of the random error

for one data point with the random error of any other data point is detected.

The parameter estimation results for LHHW, MvK, MvK-LHHW-1 and MvK-LHHW-2

models are summarized in tables 5 to 8. The best fitting of the LHHW model compared with the

others is confirmed by contrasting the corresponding F-values. Specifically, the F-value obtained

for the LHHW model amounted to 7567, a value that is 3.7, 12.4 and 9.5 times greater compared

with that achieved for model MvK (2038), MvK-LHHW-1 (609) and LHHW-2 (796),

respectively.

The LHHW kinetic model also exhibits the best statistics related to the significance of the

parameters estimates, i.e., t-value as well as confidence intervals, in accordance with the

information included in tables 5 to 8. As a matter of fact, most of the computed t-values of

individual parameters for the LHHW are two orders of magnitude higher than the tabulated t-

value for a 95 % probability level. Regarding the binary linear correlation coefficients (ρij),

values exhibited by the model LHHW model are mostly below 0.6, whereas models MvK, MvK-

LHHW-1 and MvK-LHHW-2 displayed higher values, closer to 1.0. On the basis of the set of

statistical criteria outlined above, it is clear that the LHHW model, which is based on an

adsorption-surface reaction-desorption mechanism, exhibits the best behavior.

Figure 5 is shown here.

4.2.2 Physicochemical assessment of model parameters

After verifying the statistical consistency of the model parameters, they have to be

contrasted with a series of thermodynamic criteria in order to determine whether they are

physically meaningful or not. Where the Vant’t Hoff equation parameters (standard adsorption

enthalpy and entropy) are concerned, estimated values are to be confronted with a set of criteria

defined by Boudart [51]. Since adsorption is an exothermic process, the adsorption enthalpy has

to satisfy the inequality:

oH 0−∆ > (31)

the adsorption entropy must be higher than zero and lower than the corresponding standard

entropy of the gas phase specie ( on,gS ), namely:

o on n,g0 S S< −∆ < (32)

where onS∆ is the standard entropy of adsorption.

The entropy in fact decreases when a gaseous molecule is transferred from a three-

dimensional phase, i.e, the gas phase, to a two-dimensional phase, i.e, the catalyst surface. The

gas phase standard entropy values of ethane, oxygen, ethylene, CO, CO2 and water are computed

at 440 ºC amounting to 275, 231, 257, 223, 246 and 218 J·(mol·K)-1, respectively, based on

reference [52].

An additional criterion to be satisfied during the nonisothermal parameter estimation

related to adsorption reaction, relates to the change in volume that occurs when a gaseous

molecule is adsorbed over the surface of a solid. This is specifically expressed in the following

form:

o o41.8 S 51.04 1.4 H< −∆ < − ∆ (33)

Related to the Arrhenius equation parameters, the activation energy should be lower to 210

kJ·mol-1 [53] since larger values indicate the presence of catalyst deactivation, for instance, by

sintering [54]. Besides, the activation energy of the reactions of total oxidation is expected to be

larger than that of the ethylene formation from ethane.

4.2.3 Kinetic parameters assessment

4.2.3.1 Langmuir-Hinshelwood-Hougen-Watson model

As discussed above in Section 4.2.1 and considering the information included in Fig. 5 and

Table 5, the LHHW model, which is represented by eqs. (4) - (8), (29) and (30), exhibited the

best statistical results among the developed kinetics. Notwithstanding, a physical analysis of the

estimated parameters is also compulsory in order to evaluate the absolute adequacy of this model.

It is noted in Table 5 that activation energy values of the five reactions accounted for in the

network of Fig. 1 are within the range 76 - 149 kJ·mol-1. In particular, the main reaction

responsible for ethylene formation out of ethane (r1) is the one demanding the lowest activation

energy, i.e., 76.6 kJ·mol-1. Total oxidation reaction producing CO2 and CO from ethane (r2 and

r3), in contrast, are the reactions with the largest activation energy amounting to 149.6 and 132.0

kJ·mol-1, respectively. These results also indicate that reaction of COx formation out of ethane are

particularly sensitive to temperature changes, namely, their relative importance increases at

relatively high temperature operation as observed in Fig. 2. Concerning the reactions of COx out

of ethylene, they are less energetically demanding compared with total oxidations involving

ethane. Ethylene would be, in principle, more easily activated than ethane to yield total oxidation

products. Because kinetic studies for the ODH-Et over MoVTeNbO based catalysts are scarce in

open literature, the results reported here in are relevant for academy and industry. Additionally,

values of activation energy obtained in this work (76 - 150 kJ·mol-1) are in a good agreement

with previous reports (50 - 140 kJ·mol-1) [36,55,56]. Besides, pre-exponential factors associated

to the total oxidations of ethane to produce COx are lower than those of total oxidations of

ethylene, indicating that active sites kinetically favor total the oxidation of ethylene which is in

agreement with observations presented in Fig. 4. It is also observed in Table 5 that reaction

orders related to the fraction of sites occupied by oxygen are positive and below 1.0, specifically,

between 0.13 and 0.55. This is in agreement with experimental evidences concerning the lower

dependency of ethane conversion to the inlet partial pressure of oxygen compared with that of

hydrocarbons.

Table 5 is shown here.

With respect to the parameters of the Van’t Hoff’s equation, vide Eq. (30), both standard

adsorption enthalpy and entropy are physically consistent according to the criteria given by

Boudart et al. [51], vide eqs. (31) and (33). More specifically, standard adsorption enthalpies are

systematically negative while the values of standard adsorption entropies are between 41.8

J·(mol·K)-1 and the corresponding gas phase molecular standard entropy, vide Section 4.2.2.

Notice that the lowest standard adsorption enthalpy stands for water, - 90.0 kJ·mol-1, while the

largest values are exhibited by oxygen and ethane, - 42.5 and - 42.7 kJ·mol-1, respectively. For

CO2 the standard adsorption enthalpy amounted to -72.6 kJ·mol-1. The order of magnitude of the

adsorption enthalpies estimated is, in fact, similar to values reported in the literature [57-60];

namely, the standard adsorption enthalpy of oxygen ranged from -19 to -98 kJ·mol-1 [57], that of

water on metal oxides are from -36 to -113 kJ·mol-1 [58,60] and that of CO2 from -54 to -95

kJ·mol-1 [60]. From this end, the fractional coverage of water at the outlet of the laboratory-scale

reactor varied from 38.6 to 73.3 %, ethane and oxygen fractional coverage oscillated from 7.5 to

38.0 % and 6.5 to 25.2 % respectively, and the fractional coverage of carbon oxides and ethylene

never exceeded 1 %. Adsorption phenomena involved in LHHW formalism indicated that ethane

and oxygen are two of the main components along with water to be strongly adsorbed on catalyst

surface. Nevertheless, water, being one of the main reaction products in ODH-Et, is, therefore,

the main component impacting negatively on reaction rates.

The presence of oxygen is crucial for the oxidative dehydrogenation of ethane and total

oxidations of ethane and ethylene to occur. Catalytic studies over MoVTeNbO materials suggest

that lattice oxygen participates in the reaction, particularly, oxygen coming from the first layers.

Thus the catalyst’s activity strongly depends on the oxygen’s lability, which is intimately related

to its chemical composition and crystalline structure [20,21,61]. In this respect, MoVTeNbO

catalysts which mainly consist of M1 crystalline phase, show a relatively large capacity of

oxygen recombination, in other words, the oxygen is rapidly released from the first layers and

took from the gas phase. In fact, this may be the reason why the LHHW mechanism adequately

represents such a kinetic phenomenon instead of the MvK mechanism. Recall that reaction orders

associated to the partial pressure of oxygen were found to be far below 1.0. This indicates that

reaction rates are only weakly affected by changes in the oxygen partial pressure, explaining the

high selectivity to ethylene of MoVTeNb mixed oxide catalyst [20, 21, 61].

4.2.3.2 Mars-van Krevelen model

Table 6 displays the main values of activation energies as well as reparameterized pre-

exponential factors with corresponding t-values and 95 % probability confidence intervals for the

kinetic model denoted as MvK. Being given by eqs. (14) - (19) and Eq. (29), this model exhibits

an appreciably lower F-value compared with that of the LHHW model discussed above.

Activation energies, however, also exhibited a good physicochemical and, in agreement with the

LHHW model estimates, indicate that the formation of CO2 and CO out of ethane requires the

highest activation energies 145.0 and 131.2 kJ·mol-1, respectively. The activation energy of the

ethylene oxidation to produce CO2 and CO from ethylene corresponds to 122.0 and 107.4 kJ·mol-

1, respectively. Besides, ethylene formation requires the lowest activation energy to occur, i.e.,

77.6 kJ·mol-1. Evidently, the values of the activation energy of MvK model for corresponding

reactions are very similar to those reported for the LHHW model above and, consequently, online

with values reported by others [62,63]. Additionally, the activation energy of active site

reoxidation is, in turn, as high as 100 kJ·mol-1, a value that is larger than the activation energy of

the ethylene formation from ethane and lower than total oxidations. The reaction order of the re-

oxidation reaction is also low, amounting to 0.211. As stated above, this order reaction suggests

that oxygen is rapidly released from the first layers of the catalyst and rapidly took from the gas

phase. On the basis of this value, the MvK formalism appears to be questionable at the studied

kinetic conditions [64-67]. However, future studies are necessary to confirm this model-based

conclusion.

Table 6 is shown here.

4.2.3.3 Mars-van Krevelen – Langmuir-Hinshelwood-Hougen-Watson models

Tables 7 and 8 contains the main values of Arrhenius and Van’t Hoff parameters as well as

corresponding 95 % probability t-values and confidence limits for kinetic models designated

MvK-LHHW-1 and MvK-LHHW-2. As indicated above, models MvK-LHHW-1 and MvK-

LHHW-2 displayed a relatively low capacity to represent the available experimental data

compared with the LHHW model on the basis of the corresponding F-values and parity plots.

Activation energies and Boudart’s criteria exhibited, however, kinetic and thermodynamic

consistency with results that are close to those found for both LHHW and MvK models.

Since MvK-LHHW-1 and MvK-LHHW-2 models are less significant than LHHW and

MvK models from a statistical point of view, they cannot be considered at this stage as suitable

models for the studied catalytic system. Nevertheless, a physicochemical revision of the kinetic

parameters estimated from MvK-LHHW-1, vide Table 7, and MvK-LHHW-2, vide Table 8,

confirms the results obtained with the LHHW model. Namely, oxydehydrogenation ethylene is

the least energetically demanding reaction; the total oxidation products (COx) are more easily

formed out of ethylene than out of ethane; and reaction rates, even that of catalyst re-oxidation,

are weakly affected by changes in the oxygen partial pressure.

Table 7 is shown here.

Table 8 is shown here.

5 Conclusions

Four kinetics models based on macroscopic LHHW and MvK formalisms are built to

describe the ODH-Et. For a reaction network including four carbon-content species as well as

five reactions, the corresponding rate equations are derived and then used to fit via a nonlinear

regression laboratory scale observations obtained over a high activity-selectivity MoVTeNb

mixed oxide. Experimental results, which demonstrated that ethylene is a primary nonstable

product and that COx are formed out of both ethane and ethylene, are used to define a consistent

reaction network. Reaction rates over the MoVTeNbO catalyst are found to be fairly less

sensitive to changes in the partial pressure of oxygen than it is to changes in the partial pressure

of hydrocarbons (ethane and ethylene). This partially justifies the remarkably high activity and

selectivity of this catalytic system. The resulting kinetic information is used to better

understanding of some aspect of the macro reaction mechanism involved in the ODH-Et. Both

physicochemical and statistical criteria are employed to compare the performance of the

constructed kinetic models and to define the most suitable one. Although the four models

reported, in general, physical meaningful parameters and consistent statistics, the LHHW model

is found to exhibit the best capacity to reproduce the referred the experimental information. An

assessment of reaction rate and corresponding parameters indicates that: ethylene formation from

ethane is the reaction demanding the lowest amount of energy to proceed while the formation of

COx and water products is more difficult departing from ethane than out of ethylene; and ethane,

water and oxygen are the main components adsorbing on catalyst surface. Furthermore, since

water is the main reaction product adsorbed on catalyst active sites according to its fraction

coverage, this compound seems the main factor affecting reaction rates.

Acknowledgments

Consejo Nacional de Ciencia y Tecnología (CONACYT) under project No. 181104 and

Instituto Mexicano del Petróleo. Gamaliel Che-Galicia also thanks CONACYT for providing a

postgraduate fellowship.

Nomenclature

Roman letters

av specific external surface area, m2·m-3

An chromatographic area of the component n

A i'

natural logorithm of pre-exponential factor, mmol· (g·h)-1

Bo Bodenstein number

Cn concentration of component n, mol·kg-1

C carbon number

d diameter, m

dn calibration factor of the component n

Dn diffusion coefficient for component n, m2·s-1

EA activation energy, kJ·mol-1

Fno inlet molar flow rate of the component n, mmol·h-1

Fn molar flow rate of the component n, mmol·h-1

h heat transfer coefficient between pellet and gas phase, kJ·m-2· (K·s)-1

kg mass transfer coefficient, m·s-1

kn reaction rate coefficient, dep.

Kn adsorption equilibrium coefficient for component n, Pa-1

L catalyst bed length, m

m partial reaction order for oxygen, model number

M active sites for MvK mechanism

Mn molecular mass of the component n, g·mmol-1

pn partial pressure of component n, Pa

rn specific reaction rate of reaction n, mmol·(g·h)-1

R universal gas constant, kJ·(mol·K)-1

Rn net reaction rate of the component n, mmol·(g·h)-1

RSS objective function

S active sites for LHHW mechanism

S

g standard entropy of gas phase molecule, J·(mol·K)-1

Sn selectivity of component n on carbon basis, %

T temperature, K

u velocity, m·s-1

wn objective function weight factor of each response

W mass of catalyst, g

XHC hydrocarbon conversion on carbon basis, %

Greek letters

α

vector of parameters accounted for in the objective function

β

vector of parameters accounted for in the objective function

onH∆ standard enthalpy of adsorption for component n, kJ·(mol·K)-1

rH∆ reaction enthalpy, kJ·mol-1

onS∆

Standard entropy of adsorption for component n used in Eq. (30), kJ·(mol·K)-1

onS∆

Standard entropy of adsorption for component n, J·(mol·K)-1

ε

void fraction

*θ fraction coverage of vacant sites

nθ fraction coverage of component n

OXθ fraction coverage of oxidized sites

OX n−θ fraction coverage of component n on oxidized sites

redθ fraction coverage of reduced sites

pλ particle conductivity, J·(m·s·K)-1

µ viscosity, Pa·s

iν stoichiometric number

ρ density, kg·m3

σj Horiuti number

Subscripts

b bed, bulk

cat catalyst

eff effective

exp experiment

f fluid

g gas phase

HC hydrocarbon

i.s. internal standard

n component n

o inlet, superficial

obs observed

p particle

r response

s surface

t tube

tab tabulated

tot total

w wall

Superscripts

^ calculated

o inlet, standard

* reference

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r r

rr

r

2

1

4

53

C

C

C

2CO

H

O

2

2

6H O2O2

12

O 272

2

3HO2

C H2 4

2HO

2

2O2

3HO2

2HO2

3O

2

O

2

52

Figure 1. Reaction network describing the ODH-Et.

100

80

60

40

20

0

Eth

ane

conv

ersi

on [

%]

480460440420400

Temperature [ºC]

a) Wcat/Fethane,o=23.0 gcat·h·molethane-1

Wcat/Fethane,o=46.5 gcat·h·molethane-1

Wcat/Fethane,o=70.0 gcat·h·molethane-1

100

80

60

40

20

0

Sel

ecti

vity

[%

]

100806040200

Ethane conversion [%]

b)

C2H4

CO CO2

Figure 2. a) Ethane conversion versus temperature at different values of Wcat·Fethane,o-1. b)

Selectivity to ethylene, CO2, and CO versus ethane conversion. (T = 400-480 °C; space-time =

23-70 gcat·h·molethane-1; nominal inlet molar ratio C2/O2/N2 = 9/7/84).

80

60

40

20

0

Eth

ane

conv

ersi

on [

%]

2520151050

Inlet partial pressure of oxygen [kPa]

a)

Wcat/Fethane,o=22.0 gcat·h·molethane-1

Wcat/Fethane,o=35.0 gcat·h·molethane-1

Wcat/Fethane,o=70.0 gcat·h·molethane-1

60

40

20

0

Eth

ane

conv

ersi

on [

%]

2520151050

Inlet partial pressure of ethane [kPa]

b)

Wcat/Fethane,o=35.0 gcat·h·molethylene-1

Wcat/Fethane,o=40.0 gcat·h·molethylene-1

Wcat/Fethane,o=44.0 gcat·h·molethylene-1

Figure 3. a) Ethane conversion versus oxygen inlet partial pressure. b) Ethane conversion versus

ethane inlet partial pressure. (T = 440 °C; ethane (or oxygen) inlet partial pressure ranged from

5.1 to 22.3 kPa; space-time ranged between 10 and 140 gcat·h·molethane-1).

100

80

60

40

20

0

Sel

ecti

vity

[%

]

1614121086420

Ethylene conversion [%]

a)

CO CO2

20

15

10

5

0

Eth

ylen

e co

nver

sion

[%

]

2520151050

Inlet partial pressure of oxygen [kPa]

b) Wcat/Fethylene,o=22.0 gcat·h·molethylene-1

Wcat/Fethylene,o=35.0 gcat·h·molethylene-1

Wcat/Fethylene,o=70.0 gcat·h·molethylene-1

10

8

6

4

2

0

Eth

ylen

e co

nver

sion

[%

]

2520151050

Inlet partial pressure of ethylene [kPa]

c)

Wcat/Fethylene,o=35.0 gcat·h·molethylene-1

Wcat/Fethylene,o=40.0 gcat·h·molethylene-1

Wcat/Fethylene,o=44.0 gcat·h·molethylene-1

Figure 4. a) Selectivity of CO and CO2 versus ethylene. b) Ethylene conversion versus oxygen

inlet partial pressure. c) Ethylene conversion versus ethylene inlet partial pressure. (T = 440 °C;

ethylene (or oxygen) inlet partial pressure ranged from 5.0 to 24.2 kPa; space-time ranged

between 10 and 130 gcat·h·molethylene-1).

46

50

40

30

20

10

0

Fn

calc

ulat

ed [

mm

ol/h

]

50403020100

Fn observed [mmol/h]

+10 %

-10 %

a)

50

40

30

20

10

0

Fn

calc

ulat

ed [

mm

ol/h

]

50403020100

Fn observed [mmol/h]

+10 %

-10 %

b)

47

50

40

30

20

10

0

Fn

calc

ulat

ed [

mm

ol/h

]

50403020100

Fn observed [mmol/h]

+10 %

-10 %

c)

50

40

30

20

10

0

Fn

calc

ulat

ed [

mm

ol/h

]

50403020100

Fn observed [mmol/h]

+10 %

-10 %

d)

Figure 5. Parity plots comparing experimental with calculated reactor outlet molar flow rates for the four kinetic models: a) LHHW. b) MvK. c) MvK-LHHW-1 and d) MvK-

LHHW-2. The full lines are the first bisector and the dashed lines represent a deviation of 10 %.

48

Table 1. Summary of results after assessing the various criteria for plug flow regime as

well as concentration and temperature gradients at the pellet scale in the ODH-Et

experiments.

Criterion Mathematical form (A < B) A B

1a Assumption plug flow regime t

p

d8

d<

8.0 66

1b Assumption plug flow regime

2 6C H p

8 1 Lm ln

Bo 1 X d<

−

8.0 56

2 Pressure drop 22f b f b tot

o o2 3 3p b p b

0.15 L(1 ) 0.00175 L(1 ) pu u 0.2

d d m

µ − ε ρ − ε+ <

ε ε

48 95

3 External mass transfer limitation

2 6

obs

g v C H ,b

r 0.05

k a C m<

3.1 × 10-4 5.0

4 Internal mass transfer limitation

2 6 2 6

2

pobs

C H ,eff C H ,b

dr 1

D C 6 12m

<

3.3 × 10-3 8.0

5 External heat transfer limitation 2obs r p f

A

r ( H )d 0.05RT

6h E

∆<

0.017 2.35

6 Internal heat transfer limitation 2 2obs r p f

p A

r ( H )d 0.05RT

60 E

∆<

λ

1.23 × 10-3 2.35

7 Radial reactor heat transfer

limitation

2 2obs r b t w

A

r ( H )(1 )(1 b)d 0.05RT

6h E

∆ − ε −<

1.3 2.35

49

Table 2. Reaction steps and catalytic cycles considered for the LHHW model to describe

the ODH-Et.

Step Elementary reaction step σI σII σIII σIV σV

A O2 + 2S � 2O-S 1 7 5 3 2

B C2H6 + S � C2H6-S 2 2 2 0 0

1 C2H6-S + O-S → C2H4-S + H2O-S 2 0 0 0 0

2 C2H6-S + 7O-S → 2CO2-S + 3H2O-S + 3S 0 2 0 0 0

3 C2H6-S + 5O-S → 2CO-S + 3H2O-S + S 0 0 2 0 0

4 C2H4-S + 6O-S → 2CO2-S + 2H2O-S + 3S 0 0 0 1 0

5 C2H4-S + 4O-S→ 2CO-S + 2H2O-S + S 0 0 0 0 1

C C2H4-S � C2H4 + S 2 0 0 1 1

D CO2-S � CO2 + S 0 4 0 2 0

E CO-S � CO + S 0 0 4 0 2

F H2O-S � H2O + S 2 6 6 2 2

I C2H6 + 0.5O2 → C2H4 + H2O

II C2H6 + 3.5O2 → 2CO2 + 3H2O

III C2H6 + 2.5O2 → 2CO + 3H2O

IV C2H4 + 3.5O2 → 2CO2 + 2H2O

V C2H4 + 2.5O2 → 2CO + 2H2O

50

Table 3. Reaction steps and catalytic cycles considered for the MvK model to describe the

ODH-Et.

Step Elementary reaction step σI σII σIII σIV σV

1 C2H6 + Mox → C2H4 + H2O + Mred 1 0 0 0 0

2 C2H6 + Mox → 2CO2 + 3H2O + Mred 0 1 0 0 0

3 C2H6 + Mox → 2CO + 3H2O + Mred 0 0 1 0 0

4 C2H4 + Mox → 2CO2 + 2H2O + Mred 0 0 0 1 0

5 C2H4 + Mox → 2CO + 2H2O + Mred 0 0 0 0 1

O Mred + mO2 → Mox 1 1 1 1 1

51

Table 4. Reaction steps and catalytic cycles considered for the MvK-LHHW to describe

the ODH-Et.

Step Elementary reaction step σI σII σIII σIV σV

A O2 + 2S � 2O-S 0 7 5 3 2

B C2H6 + S � C2H6-S 0 2 2 0 0

1 C2H6 + Mox → C2H4 + H2O + Mred 1 0 0 0 0

2 C2H6-S + 7O-S → 2CO2-S + 3H2O-S + 3S 0 2 0 0 0

3 C2H6-S + 5O-S → 2CO-S + 3H2O-S + S 0 0 2 0 0

4 C2H4-S + 6O-S → 2CO2-S + 2H2O-S + 3S 0 0 0 1 0

5 C2H4-S + 4O-S→ 2CO-S + 2H2O-S + S 0 0 0 0 1

C C2H4-S � C2H4 + S 0 0 0 1 1

D CO2-S � CO2 + S 0 4 0 2 0

E CO-S � CO + S 0 0 4 0 2

F H2O-S � H2O + S 0 6 6 2 2

G C2H4 + Mox � C2H4-Mox 0 0 0 0 0

H CO2 + Mox � CO2-Mox 0 0 0 0 0

I CO + Mox � CO-Mox 0 0 0 0 0

J H2O + Mox � H2O-Mox 0 0 0 0 0

O Mred + mO2 → Mox 1 0 0 0 0

52

Table 5. Kinetic parameters values and corresponding 95% probability confidence intervals

of the LHHW model used to describe the ODH-Et over the MoVNbTeO catalyst.

Parameter Estimated value Lower limit Upper limit t-value

A'1, mmol·(g·h)-1 5.04E+00 5.02E+00 5.06E+00 4.71E+02

A '2, mmol·(g·h)-1 8.07E-02 8.03E-02 8.10E-02 5.17E+02

A '3, mmol·(g·h)-1 1.64E+00 1.63E+00 1.64E+00 4.15E+02

A '4, mmol·(g·h)-1 2.96E+00 2.89E+00 3.02E+00 8.99E+01

A '5, mmol·(g·h)-1 4.46E+00 4.39E+00 4.52E+00 1.41E+02

E

A ,1, kJ·mol-1 7.66E+01 7.62E+01 7.70E+01 3.65E+02

E

A ,2, kJ·mol-1 1.49E+02 1.48E+02 1.50E+02 3.05E+02

E

A ,3, kJ·mol-1 1.32E+02 1.31E+02 1.33E+02 3.68E+02

E

A ,4, kJ·mol-1 1.20E+02 1.17E+02 1.24E+02 6.32E+01

E

A ,5, kJ·mol-1 1.09E+02 1.07E+02 1.10E+02 1.51E+02

2

oOS−∆ , J·(mol·K)-1 4.66E+01 4.63E+01 4.68E+01 3.45E+02

2 6

oC HS−∆ , J(mol·K)-1 5.71E+01 5.68E+01 5.73E+01 4.75E+02

2 4

oC HS−∆ , J(mol·K)-1 9.01E+01 8.96E+01 9.05E+01 4.20E+02

2

oH OS−∆ , J(mol·K)-1 5.17E+01 5.15E+01 5.18E+01 6.29E+02

2

oCOS−∆ , J(mol·K)-1 6.61E+01 6.58E+01 6.65E+01 3.63E+02

oCOS−∆ , J(mol·K)-1 8.34E+01 8.29E+01 8.39E+01 3.21E+02

2

oOH−∆ , kJ·mol-1 4.25E+01 4.22E+01 4.28E+01 3.03E+02

2 6

oC HH−∆ , kJ·mol-1 4.27E+01 4.24E+01 4.29E+01 3.28E+02

53

2 4

oC HH−∆ , kJ·mol-1 6.15E+01 6.11E+01 6.20E+01 2.77E+02

2

oH OH−∆ , kJ·mol-1 9.00E+01 8.96E+01 9.04E+01 4.90E+02

2

oCOH−∆ , kJ·mol-1 7.26E+01 7.18E+01 7.33E+01 1.81E+02

oCOH−∆ , kJ·mol-1 8.80E+01 8.70E+01 8.91E+01 1.65E+02

m2 1.42E-01 1.42E-01 1.43E-01 4.26E+02

m3 5.49E-01 5.47E-01 5.51E-01 5.41E+02

m4 1.30E-01 1.27E-01 1.33E-01 9.31E+01

m5 4.92E-01 4.84E-01 5.00E-01 1.19E+02

Note: F value = 7567, Ftab = 2.79, ttab = 1.97 at 1-α = 0.95 and 388 degrees of freedom.

54

Table 6. Kinetic parameters values and corresponding 95% probability confidence intervals

of the MVK model used to describe the ODH-Et over the MoVNbTeO catalyst.

Parameter Estimated value Lower limit Upper limit t-value

A '1, mmol·(g·h·Pa)-1 3.45E+00 3.40E+00 3.50E+00 1.35E+02

A'2 , mmol·(g·h·Pa)-1 6.48E-06 6.37E-06 6.59E-06 1.15E+02

A'3 , mmol·(g·h·Pa)-1 1.02E-03 9.98E-04 1.04E-03 8.77E+01

A'4 , mmol·(g·h·Pa)-1 7.79E-04 7.69E-04 7.89E-04 1.50E+02

A'5 , mmol·(g·h·Pa)-1 7.20E-04 7.05E-04 7.36E-04 9.29E+01

A'O , mmol·Pa-m·(g·h)-1 4.60E-01 4.54E-01 4.66E-01 1.55E+02

E

A,1, kJ·mol-1 7.76E+01 7.63E+01 7.88E+01 1.21E+02

E

A ,2, kJ·mol-1 1.45E+02 1.43E+02 1.47E+02 1.28E+02

E

A ,3, kJ·mol-1 1.31E+02 1.29E+02 1.34E+02 1.14E+02

E

A ,4, kJ·mol-1 1.22E+02 1.22E+02 1.22E+02 7.68E+02

E

A ,5, kJ·mol-1 1.07E+02 1.07E+02 1.08E+02 9.65E+02

E

A ,O, kJ·mol-1 9.99E+01 9.83E+01 1.02E+02 1.20E+02

m 2.11E-01 2.08E-01 2.13E-01 1.66E+02

Note: F value = 2038, Ftab = 2.79, ttab = 1.97 at 1-α = 0.95 and 401 degrees of freedom.

55

Table 7. Kinetic parameters values and corresponding 95% probability confidence intervals

of the MVK-LHHW-1 model used to describe the ODH-Et over the MoVNbTeO catalyst.

Parameter Estimated value Lower limit Upper limit t-value

A'1, mmol·(g·h·)-1 2.33E+00 2.32E+00 2.35E+00 3.04E+02

A'2 , mmol·(g·h·)-1 5.14E-09 -9.78E-08 1.08E-07 9.82E-02

A'3 , mmol·(g·h·)-1 8.28E-06 7.51E-06 9.05E-06 2.13E+01

A'4 , mmol·(g·h·)-1 2.05E-02 2.03E-02 2.06E-02 3.23E+02

A'5 , mmol·(g·h·)-1 2.13E-01 2.11E-01 2.14E-01 2.94E+02

A'o , mmol·Pa-m·(g·h·)-1 7.64E-01 7.59E-01 7.69E-01 2.94E+02

E

A,1, kJ·mol-1 7.73E+01 7.65E+01 7.80E+01 1.94E+02

E

A ,2, kJ·mol-1 1.55E+02 1.52E+02 1.58E+02 9.81E+01

E

A ,3, kJ·mol-1 1.37E+02 1.33E+02 1.41E+02 7.10E+01

E

A ,4, kJ·mol-1 1.30E+02 1.30E+02 1.31E+02 3.72E+02

E

A ,5, kJ·mol-1 1.04E+02 1.03E+02 1.04E+02 4.02E+02

E

A ,O, kJ·mol-1 7.51E+01 7.45E+01 7.56E+01 2.85E+02

2

oOS−∆ , J·(mol·K)-1 9.54E+01 9.49E+01 9.59E+01 3.76E+02

2 6

oC HS−∆ , J·(mol·K)-1 2.00E+02 1.99E+02 2.01E+02 4.41E+02

2 4

oC HS−∆ , J·(mol·K)-1 7.51E+01 7.48E+01 7.55E+01 3.91E+02

2

oH OS−∆ , J·(mol·K)-1 5.18E+01 5.18E+01 5.19E+01 4.68E+03

2

oCOS−∆ , J·(mol·K)-1 4.87E+01 4.84E+01 4.91E+01 2.83E+02

oCOS−∆ , J·(mol·K)-1 4.25E+01 4.23E+01 4.27E+01 3.67E+02

56

2

oOH−∆ , kJ·mol-1 6.43E+01 6.37E+01 6.49E+01 2.14E+02

2 6

oC HH−∆ , kJ·mol-1 5.08E+01 5.06E+01 5.11E+01 3.66E+02

2 4

oC HH−∆ , kJ·mol-1 1.05E+02 1.04E+02 1.05E+02 3.76E+02

2

oH OH−∆ , kJ·mol-1 5.21E+01 5.17E+01 5.25E+01 2.86E+02

2

oCOH−∆ , kJ·mol-1 7.00E+01 6.95E+01 7.05E+01 2.72E+02

oCOH−∆ , kJ·mol-1 6.68E+01 6.64E+01 6.73E+01 2.77E+02

m2 5.95E-01 5.82E-01 6.07E-01 9.33E+01

m3 1.01E+00 9.98E-01 1.03E+00 1.17E+02

m4 8.51E-01 8.46E-01 8.55E-01 3.65E+02

m5 2.75E-01 2.73E-01 2.77E-01 3.21E+02

m 1.45E-01 1.44E-01 1.46E-01 2.86E+02

Note: F value = 609, Ftab = 2.79, ttab = 1.97 at 1-α = 0.95 and 385 degrees of freedom.

57

Table 8. Kinetic parameters values and corresponding 95% probability confidence intervals

of the MVK-LHHW-2 model used to describe the ODH-Et over the MoVNbTeO catalyst.

Parameter Estimated value Lower limit Upper limit t-value

A'1, mmol·(g·h)-1 2.32E+00 2.29E+00 2.35E+00 1.37E+02

A'2 , mmol·(g·h)-1 5.12E-09 5.06E-09 5.19E-09 1.65E+02

A'3 , mmol·(g·h)-1 8.29E-06 8.19E-06 8.39E-06 1.64E+02

A'4 , mmol·(g·h)-1 2.04E-02 2.01E-02 2.07E-02 1.36E+02

A'5 , mmol·(g·h)-1 2.13E-01 2.10E-01 2.15E-01 1.72E+02

A'o , mmol·Pa-m·(g·h)-1· 7.66E-01 7.58E-01 7.74E-01 1.88E+02

E

A,1, kJ·mol-1 7.34E+01 7.29E+01 7.40E+01 2.57E+02

E

A ,2, kJ·mol-1 1.66E+02 1.64E+02 1.68E+02 1.71E+02

E

A ,3, kJ·mol-1 1.47E+02 1.44E+02 1.49E+02 1.28E+02

E

A ,4, kJ·mol-1 1.31E+02 1.29E+02 1.32E+02 1.40E+02

E

A ,5, kJ·mol-1 1.04E+02 1.03E+02 1.05E+02 1.75E+02

E

A ,O, kJ·mol-1 7.50E+01 7.43E+01 7.57E+01 2.15E+02

2

oOS−∆ , J·(mol·K)-1 9.54E+01 9.44E+01 9.63E+01 1.98E+02

2 6

oC HS−∆ , J··(mol·K)-1 1.08E+01 1.06E+01 1.10E+01 1.22E+02

2 4

oC HS−∆ , J··(mol·K)-1 7.53E+01 7.45E+01 7.60E+01 2.03E+02

2

oH OS−∆ , J··(mol·K)-1 4.19E+01 4.15E+01 4.23E+01 2.04E+02

2

oCOS−∆ , J·(mol·K)-1 4.88E+01 4.83E+01 4.93E+01 2.01E+02

oCOS−∆ , J·(mol·K)-1 4.25E+01 4.20E+01 4.31E+01 1.58E+02

58

2

oOH−∆ , kJ·mol-1 6.45E+01 6.40E+01 6.50E+01 2.62E+02

2 6

oC HH−∆ , kJ·mol-1 5.08E+01 5.03E+01 5.13E+01 2.08E+02

2 4

oC HH−∆ , kJ·mol-1 1.05E+02 1.04E+02 1.06E+02 1.96E+02

2

oH OH−∆ , kJ·mol-1 4.21E+01 4.15E+01 4.27E+01 1.32E+02

2

oCOH−∆ , kJ·mol-1 6.99E+01 6.92E+01 7.07E+01 1.89E+02

oCOH−∆ , kJ·mol-1 6.73E+01 6.64E+01 6.81E+01 1.55E+02

m2 5.92E-01 5.86E-01 5.98E-01 1.91E+02

m3 1.01E+00 9.98E-01 1.03E+00 1.29E+02

m4 8.48E-01 8.40E-01 8.57E-01 1.97E+02

m5 2.75E-01 2.70E-01 2.80E-01 1.14E+02

m 1.45E-01 1.43E-01 1.46E-01 1.64E+02

2 4

oC H OXS −−∆ , J·(mol·K)-1 4.77E+01 4.71E+01 4.83E+01 1.60E+02

2

oH O OXS −−∆ , J·(mol·K)-1 6.13E+01 6.07E+01 6.19E+01 1.94E+02

2

oCO OXS −−∆ , J·(mol·K)-1 6.01E+01 5.93E+01 6.09E+01 1.49E+02

oCO OXS −−∆ , J·(mol·K)-1 4.18E+01 4.13E+01 4.23E+01 1.70E+02

2 4

oC H OXH −−∆ , kJ·mol-1 7.02E+01 6.91E+01 7.14E+01 1.20E+02

2

oH O OXH −−∆ , kJ·mol-1 5.47E+01 5.37E+01 5.58E+01 1.05E+02

2

oCO OXH −−∆ , kJ·mol-1 8.59E+01 8.49E+01 8.69E+01 1.74E+02

oCO OXH −−∆ , kJ·mol-1 7.23E+01 7.13E+01 7.34E+01 1.37E+02

Note: F value = 796, Ftab = 2.79, ttab = 1.97 at 1-α = 0.95 and 377 degrees of freedom.

59

Mo V Te Nb

O O O

50

40

30

20

10

0

Fn

calc

ulat

ed [

mm

ol/h

]

50403020100

Fn observed [mmol/h]

+10 %

-10 %

C2H6

O2

C2H4

CO CO2

H2O

r r

rr

r

2

1

4

53

C

C

C

2CO

H

O

2

2

6H O2O2

12

O 2

72

2

3HO2

C H2 4

2HO

2

2O2

3HO2

2HO2

3O

2

O

2

52

60

Highlights:

• We study the kinetics for oxidative dehydrogenation reaction of ethane on

MoVNbTeO.

• We develop four kinetic models based on LHHW and MvK mechanisms.

• The LHHW mechanism provides the best statistical description of experimental data.

• Reaction rates are weakly affected by changes in the oxygen partial pressure.

• COx are formed out of both ethane and ethylene.