Modeling of Hydrogenation of Nitrate in Water on Pd–Sn/Al 2 O 3 Catalyst: Estimation of Microkinetic Parameters and Transport Phenomena Properties

Modeling of Hydrogenation of Nitrate in Water on Pd−Sn/Al2O3Catalyst: Estimation of Microkinetic Parameters and TransportPhenomena PropertiesElem Patrícia Alves Rocha, Fabio Barboza Passos, and Fernando Cunha Peixoto*

Departamento de Engenharia Química e de Petroleo, Universidade Federal Fluminense, Niteroi, Rio de Janerio 24210-900, Brazil

ABSTRACT: Excess nitrate in water is a known environmental problem, the remediation of which can be accomplished bycatalytic reduction of nitrate to N2 and NH4

+. This work presents a model for the microkinetic modeling of a system that uses aPd−Sn/γ-Al2O3 catalyst taking into account the inherent transport phenomena. The pH control, which was carried out byflowing CO2, was also modeled, leading to a considerably large (and stiff) system of ordinary differential equations, which wasdependent on a set of empirical parameters to be fitted. This regression was conducted using a maximum statistical likelihoodcriterion, employing tailor-made optimization techniques. The results indicated mass-transfer effects should be considered toobtain a complete description of the reaction system, especially regarding the pH profile.

1. INTRODUCTION

Underground water usage is a crucial factor for the subsistenceand food safety of 1.2 to 1.5 billion families living in rural and/or poor areas of Asia and Africa, as well as for the internalsupply for a great part of the world’s population.1 Brazilianauthorities estimate that 51% of the potable water in Brazil isobtained from this source.2 However, a gradual deterioration ofwater quality from these sources is being observed throughoutthe world as a consequence of increasing nitrate concentration.3

Underground water nitrate concentrations can naturallyrange from 0.1 to 10 mg/L, and contaminated sources canexhibit levels as high as 1000 mg/L.4 Nitrate intake leads tonitrite, which can combine with blood hemoglobin and reducehemoglobin’s ability to carry oxygen to body cells, a diseaseknown as methemoglobinemia. Children, especially thoseunder 6 years old, are very susceptible to this disease becauseof some bacteria commonly found in their digestive systemsthat are able to convert nitrate to nitrite.5,6 Nitrate can alsointeract with secondary amines to form N-nitrosamines, whichare carcinogenic.6

The main causes of the increase in nitrate contamination arerelated to human activities, especially the use of nitrogen-basedfertilizers and inadequate sewage storage and/or transportation.One of the technologies under investigation to solve thisproblem is the catalytic reduction of nitrate,7,8 which exhibitsenvironmental and economic advantages when compared toother methods.9

Briefly, in the catalytic removal of nitrate, contaminatedwater is treated by a reductant, such as formic acid or hydrogenin the presence of a metallic catalyst, converted to nitrogen andammonium ion, which in turn is an undesirable sideproduct.10,11 Several works have pointed out that bimetalliccatalysts, such as Pd−Cu10 or Pd−Sn11−13 are more effective, asthey are more active and selective for the reduction reaction.The presence of bimetallic ensembles is essential for theoccurrence of the nitrate reduction.It is already established that the distribution of products

depends on not only the catalyst employed but also the

reaction conditions, which indicates that special attention mustbe given to operational variables to avoid secondary pollutantsin the liquid phase (NO2

− and NH4+) or in the gaseous phase

(N2O). Therefore, a reliable model for the reaction mechanismis important for predictive purposes.12,14

Different mechanisms for this system can be found in theliterature. Basically, for palladium bimetallic catalysts, twoconsecutive steps are usually proposed on the basis ofexperimental evidence: the reduction of nitrate, adsorbed onbimetallic sites, to nitrite and the further reduction of nitrite tonitrogen and/or ammonium on palladium monometallicsites.15−17

The first step is usually modeled by a redox mechanism inwhich an interaction between the nitrate and the bimetallic sitetakes place;18 nitrate is converted to an intermediate, and thepromoter metal is oxidized and then regenerated by adsorbedhydrogen. The second step is believed to proceed easily overpalladium monometallic sites, with the formation of adsorbedintermediates (NO*, NH*). The NO* species is believed to beimportant in the formation of hydrogen, while NH* would leadto the formation of NH4

+.12

Prusse et al.12 reported the presence of N2O in the gaseousphase, and its formation is considered, by some authors, to bethe main source of N2 formation.

19,20 Ebbesen et al.21 did notfind any experimental evidence of N2O generation as abyproduct but indicated that this species could be anintermediate that reduces quickly to N2. Warna et al.,16 onthe basis of kinetic studies, proposed that N2 formation takesplace through the decomposition of the NH* intermediate,generated through a reaction of NO* and H*. Ilinith et al.12

also stated that nitrogen is formed from NH* decompositionbut claimed that the reaction suggested by Warna et al.16 isunlikely. For Ilinith et al.,12 the interaction between NO* and

Received: February 25, 2014Revised: May 5, 2014Accepted: May 7, 2014Published: May 7, 2014

Article

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© 2014 American Chemical Society 8726 dx.doi.org/10.1021/ie500820a | Ind. Eng. Chem. Res. 2014, 53, 8726−8734

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H* produces N* and oxygenated species, whereas NH* isformed through interaction between N* and H*.NH3* could be formed because of gradual addition of

hydrogen to NO*,16 but a hydrogenation of N* step was alsoproposed.22

It can be seen that despite the intense effort in studying thecatalytic reduction of nitrate to nitrogen, the actual mechanismis not a consensus and efforts must still be made to develop areliable model for this reaction. In addition, it is important toestablish a better understanding of the hydroxyl formation andthe role of the pH control in the reaction selectivity. This is dueto the fact that the hydrogenation leads to a stoichiometricproduction of OH−,10,23 causing a significant decrease in theconversion rate, once the OH− concentration in the catalystpores inhibits the adsorption of NO2

−.24 Therefore, the pHaffects the catalyst activity, increasing the selectivity to NH4

+.15

A decrease in the pore size of the support caused an increase inNH4

+ concentration.25

Addition of formic acid, carbon dioxide, or even hydrogenchloride is commonly applied to control the pH. Organicbuffers showed nitrate removal higher than that of inorganicbuffers, but the chemical structure of the organic bufferinfluenced nitrate reduction.26 In addition, the use of a cationexchange resin improved the buffering properties near theactive site, with consequent improvement in N2 selectivity.27

However, the mentioned hydroxyl formation takes place insidethe catalyst pore and the local pH within the porous media canbe significantly different from that of the solution.24 Becauseany pH control method will be performed in the solution, areliable model must also take into account the mass-transfereffects. A higher selectivity to N2 was obtained because ofenhanced mass transfer near the catalytic sites when a structurecatalyst was used.28 Isotopic labeling experiments showed theselectivity for N2 increased with the concentration of adsorbedNO on the catalytic sites.29

A previous work30 focused on establishing a reaction modelwithout taking into account the mass-transfer effects (gas−liquid and liquid−catalyst porous media) and some equilibriumrelations in the aqueous phase (ammonia, water, and thecarbonate−bicarbonate−CO2 system). Therefore, the presentwork is devoted to coupling a reliable microkinetic mecha-nism30 with transport phenomena and physical-chemicalaspects;14 because this effort drastically increases the numberof equations, variables, and parameters, some mathematicalstrategies were also developed.

2. METHODOLOGYThe main objective of the present work is devoted to themodeling and parameter estimation of the catalytic reduction ofnitrate over a Pd−Sn/γ-Al2O3 catalyst. The experimentalapparatus as well as all operational conditions employed canbe found in a previous work30 and will not be described here.Nevertheless, whenever an experimental condition is found tobe relevant for understanding an assumption, it will be clearlystated. Briefly, a Pd−Sn catalyst was admitted to an aqueoussolution of nitrate under a gaseous atmosphere of H2 and CO2of constant concentration, supplied by a continuous feed of thegaseous mixture.2.1. Model Formulation. 2.1.1. Microkinetic Mechanism.

For modeling purposes, the system was split into four “phases”or subsystems: gas (g), bulk phase (b), surface (s), and catalyst(# for the bimetallic sites and * for the monometallic ones).The last one denotes the adsorbed condition, and the “bulk”-to-

“surface” path comprises all mass-transfer effects. As alreadystated, because of operational conditions, the concentration ofboth H2 and CO2 in the gaseous phase is considered to beconstant; any gaseous product is immediately “swept” from thesystem. In the “bulk” phase, several chemical equilibria areassumed to take place as well as mass transfer from the gas andto the “surface”.On the basis of the proposed redox mechanism, the following

assumptions were employed:14,18

(1) The adsorption of NO3−, H2, and NO2

− on metallic sitesoccurs in equilibrium with the liquid (“bulk”) phase.

(2) The reduction of nitrate occurs because of the interactionwith hydrogen, but each one adsorbed to a different siteof the catalyst.

(3) The regeneration of the promoter metal from metaloxide is fast and promoted by hydrogen transfer on activebimetallic sites.

(4) The adsorption and the Hspillover action on bimetallic sitesis very fast.

(5) The elementary hydrogenation steps are irreversible.(6) The desorption of N2 and the desorption of NH3 are

both irreversible.(7) There is only one molecular layer of adsorbed species on

the catalyst.

On the basis of the above assumptions and other conclusionsfound in the literature,11,12,14,22,30 the proposed reaction modelcomprises the following steps:

+ # ↔− − #(NO ) ( ) (NO )k

k3

s3

2

1

(1)

+ ∗ ↔ *(H ) 2( ) 2(H)k

k2

s

4

3

(2)

+ * → * + + # + ∗− # −(NO ) 2(H) (NO ) (H O) ( ) ( )k

3 2 2s5

(3)

* ↔ + ∗− −(NO ) (NO ) ( )k

k2 s

s

7

6

(4)

* + * → * + *− −(NO ) (H) (NO) (OH )k

28

(5)

* + * → * + *(NO) (H) (N) (OH)k9

(6)

* → + ∗2(N) N 2( )k

210

(7)

* + * → * + ∗(N) (H) (NH) ( )k11

(8)

* + * → * + ∗(NH) (H) (NH ) ( )k

212

(9)

* + * → * + ∗(NH ) (H) (NH ) ( )k

2 313

(10)

* → + ∗(NH ) (NH ) ( )k

3 3s14

(11)

* → + *− −(OH ) (OH ) ( )k s15

(12)

* + * → + ∗−(OH ) (H) (H O) 2( )k

2s16

(13)

The Arrhenius relation was used to model the dependence ofeach rate constant kn(s

−1) to the temperature T (K):

= −k k en nE RT

0,/na, (14)

Industrial & Engineering Chemistry Research Article

dx.doi.org/10.1021/ie500820a | Ind. Eng. Chem. Res. 2014, 53, 8726−87348727

where the pre-exponential factor k0,n (s−1) and the activation

energy Ea,n (J/mol) are all subject to estimation.On the basis of the framework described in eqs 1−13, rate

equations are given by

θ θ= −#− − #r k kC1 1 (NO ) 2 (NO )3S

3 (15)

θ θ= −∗ *r k kC2 3 (H )2

4 (H)2

2S (16)

θ θ= *− #r k3 5 (NO ) (H)2

3 (17)

θ θ= − **− −r k k C4 6 (NO ) 7 (NO )2 2S (18)

θ θ= * *−r k5 8 (NO ) (H)2 (19)

θ θ= * *r k6 9 (NO) (H) (20)

θ= *r k7 10 (N)2

(21)

θ θ= * *r k8 11 (N) (H) (22)

θ θ= * *r k9 12 (NH) (H) (23)

θ θ= * *r k10 13 (NH ) (H)2 (24)

θ= *r k11 14 (NH )3 (25)

θ= *−r k12 15 (OH ) (26)

θ θ= * *−r k13 16 (OH ) (H) (27)

where θ*, θ#, θe, and Ce, are the fraction of void monometallicsites, the fraction of void bimetallic sites, the fraction of sitesoccupied by species “e”, and the concentration of species “e”,respectively.2.1.2. Chemical Equilibria. As already stated, the pH of the

liquid phase remains approximately constant, even though OH−

is produced, because of the presence of CO2 and once thefollowing equilibrium reactions take place:

+ ↔ ++ −(NH ) (H O) (NH ) (OH )K

3b

2b

4b bb

(28)

↔ ++ −(H O) (H ) (OH )K

2b b bw

(29)

+ ↔ +− +(CO ) (H O) (HCO ) (H )K

2b

2b

3b b1

(30)

↔ +− − +(HCO ) (CO ) (H )K

3b

32 b b2

(31)

Therefore, the following equilibrium relations can be stated:

=+ −

KC C

Cb(NH ) (OH )

(NH )

4b b

3b (32)

= + −K C Cw (H ) (OH )b b (33)

=− +

KC C

C1(HCO ) (H )

(CO )

3b b

2b (34)

=− +

−K

C C

C2(CO ) (H )

(HCO )

32 b b

3b (35)

where Kb, Kw, K1, and K2 are the corresponding equilibriumconstants. Ammonia dissociation constant is calculated by31

= − − −K 10 Tb

[4.75595 2729.33(1/298.15 1/ )] (36)

The water dissociation constant is given by32,33

= − −K T Texp[148.96502 13847.26/ 23.6521 ln ]w(37)

The carbonic acid dissociation constants are given by34

= − − + +K 10 T T1

[ 14.8435 34471.0/ 0.032786 ](38)

= − − + +K 10 T T2

[ 6.4980 2903.9/ 0.02379 ](39)

leading to Ka = K1K2, which is the total dissociation constant.2.1.3. Mass-Transfer Rates. For the transport phenomena

involved, it was assumed that each subsystem is homogeneous,the system is isothermal, and the active sites are uniformlydistributed over catalyst particles. Because the mass-transfereffects from the “bulk” phase to the “surface” were grouped, therelated rates were therefore written in terms of thecorresponding driving forces and mass-transfer coefficients:35

= −− −r k C C( )14 17 (NO ) (NO )3b

3S (40)

= −r k C C( )15 18 (H ) (H )2b

2S (41)

= −− −r k C C( )16 19 (NO ) (NO )2b

2S (42)

= −r k C C( )17 20 (H O) (H O)2b

2S (43)

= −r k C C( )18 21 (N ) (N )2g

2S (44)

= −r k C C( )19 22 (NH ) (NH )3b

3S (45)

= −r k C C( )20 23 (H ) (H )2g

2b (46)

= −r k C C( )21 24 (CO ) (CO )2g

2b (47)

= −− −r k C C( )22 25 (OH ) (OH )b S (48)

These equations are able to predict an eventual OH−

accumulation on the surface of the catalyst, as suggested byexperimental evidence.24 It must be noticed that the way themodel is formulated, no a priori assumption concerning therelative magnitude of kinetic and mass-transfer rates is made.Even though the constants in the previous equations are

subject to fitting, some relations can be used to establish initialestimates for their values. Roughly, each constant can beexpressed by

δ=k

h aVn

n n

n n (49)

where an is the effective interfacial area, Vn the volume of the“phase”, and δn the film thickness; hn refers to a diffusion and/or convective coefficient, depending on the scenario. It must beemphasized that no accurate description of these entities isneeded at this point because they will be statistically fitted.However, some order of magnitude analysis is useful forestablishing good initial guesses for the regression algorithm,and this was made employing typical values found in theliterature35 and reasonable assumptions made on the basis ofthe experimental conditions.30 Therefore, when “n” is anelectrolyte, the model to be fitted was set to be



= +−⎡

⎣⎢⎤⎦⎥k

AT

BTn

n n1

(50)

otherwise

= + +−⎡

⎣⎢⎤⎦⎥k

AT

BT

Cnn

1.75n

n

1

(51)

2.1.4. Material Balance. The mechanisms and rateequations described in the previous sections can be used toexpress the material balance over all species as follows:

= − +−C

tr r

d

d(NO )

1 143

S

(52)

θ

α=

−− #

tr r

C

d

d(NO ) 1 3

S

3

(53)

θα

=− +#

tr r

Cdd

1 3

S (54)

= − +C

tr r

d

d(H )

2 152

S

(55)

θα

* =− + + + + + + + + +

−tr r r r r r r r r r

Cdd

2 2 2 2(1 )

2 3 4 7 8 9 10 11 12 13

S(56)

θα

=− − − − − − −

−*

tr r r r r r r r

C

d

d2 2

(1 )(H) 2 3 5 6 8 9 10 13

S (57)

θα

=− −

−*−

tr r

C

d

d (1 )(NO ) 4 5

S

2

(58)

= + +C

tr r r

d

d(H O)

3 13 172

S

(59)

= + +−C

tr r r

d

d(NO )

3 4 162

S

(60)

θα

=−

−*

tr rd

d (1 )C(NO) 5 6

S (61)

θα

=+ − −

−*− r r r r

C

d

dt (1 )(OH ) 5 6 12 13

S (62)

θα

=− −

−*

tr r r

C

d

d2

(1 )(N) 6 7 8

S (63)

= +C

tr r

d

d(N )

7 182

S

(64)

θα

=−

−*

tr r

C

d

d (1 )(NH) 8 9

S (65)

θα

=−

−*

tr r

C

d

d (1 )(NH ) 9 10

S

2

(66)

θ

α=

−−

*

tr r

C

d

d (1 )(NH ) 10 11

S

3

(67)

= +C

tr r

d

d(NH )

11 193

S

(68)

= −−C

tr

d

d(NO )

143

b

(69)

= − +C

tr r

d

d(H )

15 202

b

(70)

= −−C

tr

d

d(NO )

162

b

(71)

= −C

tr

d

d(N )

182

b

(72)

= −C

tr

d

d(NH )

193

b

(73)

=C

tr

d

d(CO )

212

b

(74)

= +−C

tr r

d

d(OH )

12 22

S

(75)

where α is the fraction of bimetallic sites. Considering that alltin is associated with bimetallic sites (monometallic sites arepalladium sites), it is easily shown that30

α =+ −( )

mM

mM

mM

mM

Sn

Sn

Sn

Sn

Pd

Pd

Sn

Sn (76)

where mi is the mass of i (g) and Mi is the molecular mass of i(g/(g mol)).The total “concentration” of catalytic sites Cs is given by

=CC

M%Pd100S

cat

Pd (77)

where %Pd is the amount of palladium on the catalyst, mcat themass of catalyst (g), and Ccat the “concentration” of the catalystin the reaction mixture (g/L).The remaining degree of freedom in the mathematical model

is removed by the assumption of the electrical neutrality of thesolution:

+ + = +

+ + +

+ + + − −

− − −

C C C C C

C C C2

(Na ) (H ) (NH ) (NO ) (NO )

(OH ) (CO ) (HCO )

b b4

b3

b2

b

b3

2 b3

b (78)

in which the concentration of Na+ is constant and equal to theinitial nitrate concentration.Therefore, combining the relevant equations, the rate of

change of H+ concentration in the “bulk” phase, becomes



=− −

+ + +

+− + +

+ + +

+

+

+

+

+

+ +

+

− −

+ +

⎡⎣⎢

⎤⎦⎥

⎡⎣⎢

⎤⎦⎥

⎡⎣⎢

⎤⎦⎥

⎡⎣⎢

⎤⎦⎥

C

t

d

d1

1

C K

K

C

tK

C

C

t

C K

K

K K C

C

K C

C

KC t

C

t

C

t

C K

K

K K

C

K C

C

(H )

d

d

d

d

( )

4

( )

2( )

dC

d

d

d

d

d

C

( )

4

( )

b

(H )b b

w

(NH3)b1

(H )b

(CO2)b

(NH3)b b

w

w 1 (CO2)b

(H )b2

A (CO2)b

(H )b3

a

(H )b2

(CO2)b (NO3 )b (NO2 )b

(NH3)b b

w

w 1 (CO2)b

(H )b2

A (CO2)b

(H )b3

(79)

which is a “key” equation for the formulation other rateequations:

=−−

+

+C

tK

C

C

t

d

d ( )

d

d(OH ) w

(H )2

(H )b

b

b

(80)

= −+

− −

−C

tK

C

C

t

C

C

C

t

d

d

d

d ( )

d

d(NH ) b

(OH )

(NH ) (NH )

(OH )2

(OH )4b

b

3b

3b

b

b

(81)

2.1.5. Initial Conditions. Once the concentrations of CO2and H2 in the gas phase remain constant in each run(depending only on the temperature), Henry’s law was usedto calculate the initial concentration of these species in the“bulk” phase:36

=CC

H(CO )(CO )

CO2 0

b2

g

2 (82)

=CC

H(H )(H )

H2 0

b2

g

2 (83)

where HCO2and HH2

are the solubility constants of CO2 and H2,respectively, given by36

= − + −

+

HT T

T

1exp[1n( 159.8741 5528/ 0.0011026

21.66941 ln( )]

CO2

(84)

= − + +H

T T1

exp[1n( 125.939 5528/ 16.8893 ln )]H2

(85)

It must be said that this was performed only to generate a setof adequate initial conditions; once equilibria 30 and 31 takeplace, Henry’s law would not be applicable.The initial concentrations of NO3

−, NH4+, and Na+ were

known, whereas NO2− and N2 were not initially present.

Therefore, the restriction of electrical neutrality of the solutioncould be applied at the initial time, leading to

+ = + ++ + − − −C C C 2C C(H ) (NH ) (OH ) (CO ) (HCO )0b

4 0b

0b

32

0b

3 0b

(86)

This was combined with chemical equilibrium equations togive:

+ − + =+ + + +C C C K K C C( ) ( ) [ ] 0(H )3

(NH ) (H )2

w 1 (CO ) (H )0b

4 0b

0b

2 0b

0b

(87)

which in turn was solved by Cardano’s method.36

After (H+)0b was caluculated, the initial concentration of both

OH− and NH3 could be calculated by eqs 32 and 33.

Considering that the reaction system was previously exposedto an excess of H2 for the catalyst activation, the initialconcentration of H2 on the surface of the catalyst was equal tothe one in the “bulk” phase and all monometallic sites wereoccupied by H2; no other species was adsorbed, and thefraction of void bimetallic sites was 100%.

2.2. Model Integration and Parameter EstimationMethods. Some attempts were made to solve the system ofdifferential-algebraic equations (DAE) composed by thematerial balances and the chemical equilibrium equationsalong with the restriction of electrical neutrality of the solution.Several standard DAE-solving algorithms and some modifiedones were tested without success, probably because of thestiffness of the differential equations.30 Therefore, the insertionof the algebraic equations into the differential, which lead to asystem of ordinary differential equations (ODEs), was crucial tothe numerical strategy employed. It must be noted that theintegration of such a system of ODEs corresponds to thedynamic simulation of the reaction system and is completelydependent on the empirical parameters, which is adequate for astatistical fitting procedure (as far as experimental data wereavailable).The numerical integration method used is described in detail

in a previous work,30 but basically involves a backwarddifferentiation formulas (BDF) scheme in a vector−matrixformat.For the model regression, a maximum likelihood statistical

criterion was employed, as also described in a previous work.30

The set of estimated parameters (β ) is, therefore, given by thefollowing optimization:

β β β = − − β

− − − −min[C C ( )] W[C C ( )]t

{ } (NO )exp

(NO ) (NO )exp

(NO )3

b 3b

3b 3

b

(88)

where −C(NO )exp

3b is the vector of all experimental points and W is

a diagonal matrix of weights. Because small experimental valuestend to be close to the measurement precision, each weight wasset as the inverse of the value of the correspondingexperimental point.The final problem involves an optimization of an objective

function that demands the integration of all ODEs using thedecision variables (the parameters to be estimated). Onceagain, the present work employed the previously developedstrategy, which consisted of a hybrid scheme, in which asimplex search preceded a quasi-Newton method with aBroyden−Fletcher−Goldfarb−Shanno approximation of theHessian matrix.30 A total of 150 experimental points wereused to fit the 50 empirical parameters.All routines were written with Scilab 5, a free and open

source software (distributed under CeCILL license, GPLcompatible) developed by Scilab Enterprises (http://www.scilab.org).

3. RESULTS AND DISCUSSION

Once the regression was concluded, fitted parameters for thekinetic and mass-transfer models were available; these can befound in Tables 1−3.The predictive model thus obtained can be compared to

experimental data. In Figure 1, a normalized scale for the nitrateconcentration was used, dividing each experimental value bythe initial concentration of the corresponding run.



http://www.scilab.org

http://www.scilab.org

After the model is fitted, any other state variable could haveits dynamics simulated, which is important for model validation.Figure 2 depicts the evolution of the most important N-basedentities present in the “bulk” phase (for simplicity, only theresults corresponding to 35 °C are shown).

It is important to notice that these results are in accordancewith the literature.8,11,14 The NO2

− concentration in the bulkphase was quite low during the reaction time, with anincreasing profile reaching a maximum for a time lower than100 min, followed by a decrease associated with a rapidadsorption on the surface of the catalysts and subsequentconversion to NO. The low concentration values wereconsistent with the fact that NO2

− could not be observedexperimentally.30 Figure 3 depicts the evolution of the nitrite

concentration gradient between the “bulk” phase (thicker lines)and the “surface” (thinner lines). The results shows that thehigher the temperatures, the sooner the nitrite reaches amaximum both in the “bulk” phase and in the “surface”. This isconsistent with the effect of temperature on the conversion ofnitrate as described in the literature.28

The pH control was performed by a stream of CO2,30 and it

is useful to verify whether it was effective using the mass-transfer effects evaluated by the present model. For that, inFigure 4, the pH on both “bulk” phase (thicker lines) and“surface” (thinner lines) are represented.The prediction of a higher pH inside the porous media in

comparison with the one in the “bulk” phase is consistent withthe literature.15 The addition of CO2 to control the pH hasproven to be a better option than the addition of HCl.7,8,37

Table 1. Fitted Kinetic Parameters

k0,n Ea,n (kJ/mol)

k0,1 4.02 Ea,1 8.12k0,2 8.69 × 10−12 Ea,2 2.69k0,3 0.14 Ea,3 8.62k0,4 0.000 057 Ea,4 1.71k0,5 0.091 Ea,5 24.52k0,6 0.0024 Ea,6 12.11k0,7 0.33 Ea,7 1.67 × 10−16

k0,8 0.000 26 Ea,8 10.75k0,9 0.000 26 Ea,9 10.75k0,10 1097.02 Ea,10 25.65k0,11 16.52 Ea,11 49.11k0,12 0.61 Ea,12 31.60k0,13 2.62 Ea,13 34.50k0,14 0.51 Ea,14 34.35k0,15 3648.78 Ea,15 62.92k0,16 0.0080 Ea,16 1.26

Table 2. Fitted Mass-Transfer Parameters for NonelectrolyteSpecies

An (s K) Bn (s K1/2)

A18 410 843.46 B18 −22 496.44A20 527 269.88 B20 −28 871.61A21 606 914.02 B21 −33 232.74A22 459 904.04 B22 −25 182.81A23 2.58 × 109 B23 −1.43 × 108

A24 −7.42 × 108 B24 86 222 578.0

Table 3. Fitted Mass-Transfer Parameters for ElectrolyteSpecies

An (s K1.75) Bn (s K) Cn (s)

A17 4.67 × 1010 B17 −1.09 × 109 C17 1 499 880.6A19 4.18 × 1010 B19 −9.72 × 108 C19 1 315 111.1A25 1.18 × 1010 B25 −2.73 × 108 C25 366 220.94

Figure 1. Fitted model and experimental data (normalized nitrateconcentration).

Figure 2. Evolution of NO3−, NH4

+, N2, and NO2− concentration in

the “bulk” phase (T = 35 °C).

Figure 3. Evolution of nitrite concentration in the “bulk” phase(thicker lines) and on the “surface” (thinner lines).



However, our results show that although the presence of CO2improves the pH control, a pH gradient within the pores stillremains. Thus, the present model allowed to us to follow theintrapore pH gradient, what was not possible for the modelused before.30 This indicates the need to couple mass-transferand kinetic steps to get a complete picture of the system. Thismodel explains why better selectivities were obtained for largepore supports25 and when an acidic cation exchange resin wasused as support.27

The simulation of the dynamics of occupation of catalystactive sites is also of great interest. As expected, it was foundthat an almost instantaneous complete occupation of bimetallicsites takes place, as can be seen in Figures 5 and 6. The

decrease in the fraction of bimetallic sites occupied by nitrate isassociated with the reaction progress. The occupation is shorterfor higher temperatures, and this may be related to the higherconversion to nitrite. As the nitrite leaves the bimetallic sites,these are able to adsorb new nitrate species.Figure 7 depicts the evolution of the fraction of

monometallic sites occupied by NO. The fraction of NOincreases initially and reaches a maximum because of its

combination with H to form NH species. The fraction of themonometallic sites occupied by hydrogen is high at initial times(Figure 8), with a steep decrease due to the hydrogenation ofnitrate and consequent formation of other intermediates. Forlonger times, as hydrogen is continuously fed to the system,and because of desorption of products, there is an increase inthe fraction of the occupied sites by hydrogen. The selectivityfor N2 is influenced by the relative ratio of sites occupied byNO and hydrogen.12,21,28 Also, a higher occupation of NOleads to an increase in selectivity for N2.

29 In fact, when thefraction of sites occupied by NO increases, there is an increasein the formation of NH4

+ (Figure 9).The proposed model showed good predictive power (Figure

9) as shown by the comparison of the experimental formationof NH4

+ at 25 °C and the curve predicted by the model. It mustbe stressed that the experimental data for NH4

+ concentrationwas not included in the regression procedure.A model variance of 3.8 × 10−9 (mol/L)2 was estimated,

denoting low uncertainties of predicted values, taking intoaccount that experimental nitrate concentrations were around0.0007 mol/L, which denotes an improvement from a previouswork.30

Figure 4. Evolution of the pH in the “bulk” phase (thicker lines) andon the “surface” (thinner lines).

Figure 5. Evolution of the fraction of bimetallic sites occupied bynitrate.

Figure 6. Evolution of the fraction of void bimetallic sites.

Figure 7. Evolution of the fraction of monometallic sites occupied byNO.



When it is compared to the previous work,30 which was ableto simulate the evolution of chemical entities in only two“phases” (“bulk phase” and catalyst), the introduction of mass-transfer effects made it possible to simulate relevant statevariables in four “phases” (gas, “bulk phase”, surface, andcatalyst). However, the computational time for systemsimulation increased 60% when the number of variablesincreased from 17 to 53. Therefore, when choosing betweenthe present model or the previous one,30 there is a compromisebetween the level of mathematical detail and the computationaltime required.This new model allowed a better prediction of the selectivity

for the several products, specially NH4+ (Figure 9), which is

highly dependent on local pH. The model developed in thiswork confirmed that a pH gradient remains in the reactionsystem even when CO2 is used to control the pH. This was alsoan improvement; in the previous work,30 the pH wasconsidered to be uniform throughout the system.It must be pointed out that no comparison can be made with

the same previous work30 in terms of the computational timedevoted exclusively to parameter estimation, which is highlydependent on the initial guess. The mentioned previous work30

involved the estimation of 14 parameters, and the present work

involved 50 parameters; it is not even possible to use the sameinitial guess for comparison purposes.Despite the good adherence to experimental data and low

variance achieved, considerably large variations in the fittedparameters set tended to have little impact in the objectivefunction, as in other works devoted to kinetics parametersregression.38,39 This apparent paradox can be explained by thepeculiar topology of the likelihood function when dealing withkinetic models, which seems to exhibit a large flat regionaround its minimum (which leads to low parameter sensitivityand large parameter variances and covariances) but at relativelylow values of the likelihood function itself (which leads to lowmodel fundamental variance). Of course, this jeopardizesestablishing the set of the most relevant parameters to thecomplete model and decreases the reliability of each one butalso guarantees the fluctuations in the fitted parameters (whichcould be caused by experimental errors, for instance) will havelittle effect on the predictive capabilities of the model. Thus, thegood predictive power and the complete statistical descriptionof the model were benefits of the employed methodology.

4. CONCLUSIONThe addition of the mass-transfer effects to the microkineticmodel of the catalytic reduction of nitrates improved theunderstanding of the catalytic reduction of nitrate. Theproposed phenomenological model comprises a system ofdifferential equations related to the molar balances of allreactants and products in the reactor. Coded in an open sourcesoftware, the model allowed a detailed analysis of thecomposition in each phase of the nitrate hydrogenation system,showing a good predictive capability.The main assumptions of the complete kinetic model were

mass transfer between the gas, liquid (“bulk”), and surfacephases. In the “bulk” phase, several chemical equilibria areassumed to take place as well as mass transfer from the gas andto the “surface”. In addition, a redox mechanism was employed,with two different sites being responsible for the reaction. Acomplete description of the adsorbed species was obtained.This model allowed following the gradient of the pH within thepores, which affects the selectivity for N2, and it was able topredict NH4

+ profiles.

■ AUTHOR INFORMATIONCorresponding Author*Rua Passo da Patria 156, 24210-240, Niteroi, Brazil. Tel.: +55-21-2629-5562. E-mail: [email protected] authors declare no competing financial interest.

■ ACKNOWLEDGMENTSCAPES is acknowledged for sponsoring the scholarship forE.P.A.R.

■ REFERENCES(1) United Nations Educational, Scientific and Cultural Organization.Water in a Changing World; UNESCO: Paris, 2009(2) MMA − Ministerio do Meio Ambiente, Plano Nacional deRecursos Hidricos − Iniciando um processo de debate nacional, SRH −Secretaria de Recursos Hidricos, Brasilia - DF, 2005 (in portuguese).(3) World Health Organization. Nitrates and Nitrites in Drinking-Water; WHO: Geneva, Switzerland, 2004(4) Feitosa, F.; Manoel Filho, J. Hidrogeologia: Conceitos e Aplicacoes,2nd ed.; CPRM: Brazil, 2000 (in portuguese).

Figure 8. Evolution of the fraction of monometallic sites occupied byH.

Figure 9. Fitted model and experimental data (NH4+ concentration).



mailto:[email protected]

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Modeling of Hydrogenation of Nitrate in Water on Pd–Sn/Al 2 O 3 Catalyst: Estimation of Microkinetic Parameters and Transport Phenomena Properties