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Modeling of Hydrogenation of Nitrate in Water on Pd−Sn/Al2O3 Catalyst: Estimation of Microkinetic Parameters and Transport Phenomena Properties Elém Patrícia Alves Rocha, Fabio Barboza Passos, and Fernando Cunha Peixoto* Departamento de Engenharia Química e de Petróleo, Universidade Federal Fluminense, Niterói, Rio de Janerio 24210-900, Brazil ABSTRACT: Excess nitrate in water is a known environmental problem, the remediation of which can be accomplished by catalytic reduction of nitrate to N2 and NH4+. This work presents a model for the microkinetic modeling of a system that uses a Pd−Sn/γ-Al2O3 catalyst taking into account the inherent transport phenomena. The pH control, which was carried out by flowing CO2, was also modeled, leading to a considerably large (and stiff) system of ordinary differential equations, which was dependent on a set of empirical parameters to be fitted. This regression was conducted using a maximum statistical likelihood criterion, employing tailor-made optimization techniques. The results indicated mass-transfer effects should be considered to obtain a complete description of the reaction system, especially regarding the pH profile.

1. INTRODUCTION Underground water usage is a crucial factor for the subsistence and 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 internal supply for a great part of the world’s population.1 Brazilian authorities estimate that 51% of the potable water in Brazil is obtained from this source.2 However, a gradual deterioration of water quality from these sources is being observed throughout the world as a consequence of increasing nitrate concentration.3 Underground water nitrate concentrations can naturally range from 0.1 to 10 mg/L, and contaminated sources can exhibit levels as high as 1000 mg/L.4 Nitrate intake leads to nitrite, which can combine with blood hemoglobin and reduce hemoglobin’s ability to carry oxygen to body cells, a disease known as methemoglobinemia. Children, especially those under 6 years old, are very susceptible to this disease because of some bacteria commonly found in their digestive systems that are able to convert nitrate to nitrite.5,6 Nitrate can also interact with secondary amines to form N-nitrosamines, which are carcinogenic.6 The main causes of the increase in nitrate contamination are related to human activities, especially the use of nitrogen-based fertilizers and inadequate sewage storage and/or transportation. One of the technologies under investigation to solve this problem is the catalytic reduction of nitrate,7,8 which exhibits environmental and economic advantages when compared to other methods.9 Briefly, in the catalytic removal of nitrate, contaminated water is treated by a reductant, such as formic acid or hydrogen in the presence of a metallic catalyst, converted to nitrogen and ammonium ion, which in turn is an undesirable side product.10,11 Several works have pointed out that bimetallic catalysts, such as Pd−Cu10 or Pd−Sn11−13 are more effective, as they are more active and selective for the reduction reaction. The presence of bimetallic ensembles is essential for the occurrence of the nitrate reduction. It is already established that the distribution of products depends on not only the catalyst employed but also the © 2014 American Chemical Society

reaction conditions, which indicates that special attention must be given to operational variables to avoid secondary pollutants in the liquid phase (NO2− and NH4+) or in the gaseous phase (N2O). Therefore, a reliable model for the reaction mechanism is important for predictive purposes.12,14 Different mechanisms for this system can be found in the literature. Basically, for palladium bimetallic catalysts, two consecutive steps are usually proposed on the basis of experimental evidence: the reduction of nitrate, adsorbed on bimetallic sites, to nitrite and the further reduction of nitrite to nitrogen and/or ammonium on palladium monometallic sites.15−17 The first step is usually modeled by a redox mechanism in which an interaction between the nitrate and the bimetallic site takes place;18 nitrate is converted to an intermediate, and the promoter metal is oxidized and then regenerated by adsorbed hydrogen. The second step is believed to proceed easily over palladium monometallic sites, with the formation of adsorbed intermediates (NO*, NH*). The NO* species is believed to be important in the formation of hydrogen, while NH* would lead to the formation of NH4+.12 Prusse et al.12 reported the presence of N2O in the gaseous phase, and its formation is considered, by some authors, to be the main source of N2 formation.19,20 Ebbesen et al.21 did not find any experimental evidence of N2O generation as a byproduct but indicated that this species could be an intermediate that reduces quickly to N2. Wärna et al.,16 on the basis of kinetic studies, proposed that N2 formation takes place 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* decomposition but claimed that the reaction suggested by Wärna et al.16 is unlikely. For Ilinith et al.,12 the interaction between NO* and Received: Revised: Accepted: Published: 8726

February 25, 2014 May 5, 2014 May 7, 2014 May 7, 2014 dx.doi.org/10.1021/ie500820a | Ind. Eng. Chem. Res. 2014, 53, 8726−8734

Industrial & Engineering Chemistry Research

Article

“surface” path comprises all mass-transfer effects. As already stated, because of operational conditions, the concentration of both H2 and CO2 in the gaseous phase is considered to be constant; any gaseous product is immediately “swept” from the system. In the “bulk” phase, several chemical equilibria are assumed to take place as well as mass transfer from the gas and to 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 sites occurs in equilibrium with the liquid (“bulk”) phase. (2) The reduction of nitrate occurs because of the interaction with hydrogen, but each one adsorbed to a different site of the catalyst. (3) The regeneration of the promoter metal from metal oxide is fast and promoted by hydrogen transfer on active bimetallic sites. (4) The adsorption and the Hspillover action on bimetallic sites is 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 conclusions found in the literature,11,12,14,22,30 the proposed reaction model comprises the following steps:

H* produces N* and oxygenated species, whereas NH* is formed 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 also proposed.22 It can be seen that despite the intense effort in studying the catalytic reduction of nitrate to nitrogen, the actual mechanism is not a consensus and efforts must still be made to develop a reliable model for this reaction. In addition, it is important to establish a better understanding of the hydroxyl formation and the role of the pH control in the reaction selectivity. This is due to the fact that the hydrogenation leads to a stoichiometric production of OH−,10,23 causing a significant decrease in the conversion rate, once the OH− concentration in the catalyst pores inhibits the adsorption of NO2−.24 Therefore, the pH affects the catalyst activity, increasing the selectivity to NH4+.15 A decrease in the pore size of the support caused an increase in NH4+ concentration.25 Addition of formic acid, carbon dioxide, or even hydrogen chloride is commonly applied to control the pH. Organic buffers showed nitrate removal higher than that of inorganic buffers, but the chemical structure of the organic buffer influenced nitrate reduction.26 In addition, the use of a cation exchange resin improved the buffering properties near the active site, with consequent improvement in N2 selectivity.27 However, the mentioned hydroxyl formation takes place inside the catalyst pore and the local pH within the porous media can be significantly different from that of the solution.24 Because any pH control method will be performed in the solution, a reliable model must also take into account the mass-transfer effects. A higher selectivity to N2 was obtained because of enhanced mass transfer near the catalytic sites when a structure catalyst was used.28 Isotopic labeling experiments showed the selectivity for N2 increased with the concentration of adsorbed NO on the catalytic sites.29 A previous work30 focused on establishing a reaction model without taking into account the mass-transfer effects (gas− liquid and liquid−catalyst porous media) and some equilibrium relations in the aqueous phase (ammonia, water, and the carbonate−bicarbonate−CO2 system). Therefore, the present work is devoted to coupling a reliable microkinetic mechanism30 with transport phenomena and physical-chemical aspects;14 because this effort drastically increases the number of equations, variables, and parameters, some mathematical strategies were also developed.

k1

(NO3−)s + (#) ↔ (NO3−)# k2

(1)

k3

(H 2)s + 2( ∗) ↔ 2(H)* k4

(2)

k5

(NO3−)# + 2(H)* → (NO2−)* + (H 2O)s + (#) + ( ∗) (3) k6

(NO2−)* ↔ (NOs−)s + ( ∗) k7

k8

(NO2−)* + (H)* → (NO)* + (OH−)* k9

(NO)* + (H)* → (N)* + (OH)* k10

2(N)* → N2 + 2( ∗)

2. METHODOLOGY The main objective of the present work is devoted to the modeling and parameter estimation of the catalytic reduction of nitrate over a Pd−Sn/γ-Al2O3 catalyst. The experimental apparatus as well as all operational conditions employed can be found in a previous work30 and will not be described here. Nevertheless, whenever an experimental condition is found to be relevant for understanding an assumption, it will be clearly stated. Briefly, a Pd−Sn catalyst was admitted to an aqueous solution of nitrate under a gaseous atmosphere of H2 and CO2 of constant concentration, supplied by a continuous feed of the gaseous 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-

k11

(N)* + (H)* → (NH)* + ( ∗) k12

(NH)* + (H)* → (NH 2)* + ( ∗) k13

(NH 2)* + (H)* → (NH3)* + ( ∗) k14

(NH3)* → (NH3)s + ( ∗) k15

(OH−)* → (OH−)s + (*) k16

(OH−)* + (H)* → (H 2O)s + 2( ∗)

(4) (5) (6) (7) (8) (9) (10) (11) (12) (13)

The Arrhenius relation was used to model the dependence of each rate constant kn(s−1) to the temperature T (K): kn = k 0, ne−Ea,n / RT 8727

(14)

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


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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 r1 = k1C(NO3−)Sθ# − k 2θ(NO3−)#

(36)

The water dissociation constant is given by32,33 K w = exp[148.96502 − 13847.26/T − 23.6521 ln T ] (37)

(15)

The carbonic acid dissociation constants are given by

2 r2 = k 3C(H2)Sθ∗2 − k4θ(H) *

r3 = k5θ

Kb = 10−[4.75595 − 2729.33(1/298.15 − 1/ T )]

(16)

2 θ(H) *

(NO3−)#

(17)

34

K1 = 10−[−14.8435 + 34471.0/ T + 0.032786T ]

(38)

K 2 = 10−[−6.4980 + 2903.9/ T + 0.02379T ]

(39)

r4 = k6θ(NO2−) * − k 7C(NO2−)Sθ *

(18)

r5 = k 8θ(NO2−) *θ(H) *

(19)

r6 = k 9θ(NO) *θ(H) *

(20)

2 r7 = k10θ(N) *

(21)

r8 = k11θ(N) *θ(H) *

(22)

r9 = k12θ(NH) *θ(H) *

(23)

r14 = k17(C(NO3−)b − C(NO3−)S)

(40)

r10 = k13θ(NH2) *θ(H) *

(24)

r15 = k18(C(H2)b − C(H2)S)

(41)

r11 = k14θ(NH3) *

(25)

r16 = k19(C(NO2−)b − C(NO2−)S)

(42)

r12 = k15θ(OH−) *

(26)

r17 = k 20(C(H2O)b − C(H2O)S)

(43)

r13 = k16θ(OH−) *θ(H) *

(27)

r18 = k 21(C(N2)g − C(N2)S)

(44)

r19 = k 22(C(NH3)b − C(NH3)S)

(45)

r20 = k 23(C(H2)g − C(H2)b)

(46)

r21 = k 24(C(CO2)g − C(CO2)b)

(47)

r22 = k 25(C(OH−)b − C(OH−)S)

(48)

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 uniformly distributed over catalyst particles. Because the mass-transfer effects from the “bulk” phase to the “surface” were grouped, the related rates were therefore written in terms of the corresponding driving forces and mass-transfer coefficients:35

where θ , θ#, θe, and Ce, are the fraction of void monometallic * sites, the fraction of void bimetallic sites, the fraction of sites occupied 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 the following equilibrium reactions take place: b Kb

b

+ b

− b

(NH3) + (H 2O) ↔ (NH4 ) + (OH ) Kw

(H 2O)b ↔ (H+)b + (OH−)b K1

(CO2 )b + (H 2O)b ↔ (HCO3−)b + (H+)b K2

(HCO3−)b ↔ (CO32 −)b + (H+)b

These equations are able to predict an eventual OH− accumulation on the surface of the catalyst, as suggested by experimental evidence.24 It must be noticed that the way the model is formulated, no a priori assumption concerning the relative 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 initial estimates for their values. Roughly, each constant can be expressed by

(28) (29) (30) (31)

Therefore, the following equilibrium relations can be stated: Kb =

C(NH4+)bC(OH−)b C(NH3)b

K w = C(H+)bC(OH−)b K1 =

K2 =

kn = (32)

(34)

C(CO32−)bC(H+)b C(HCO3−)b

(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 be emphasized that no accurate description of these entities is needed at this point because they will be statistically fitted. However, some order of magnitude analysis is useful for establishing good initial guesses for the regression algorithm, and this was made employing typical values found in the literature35 and reasonable assumptions made on the basis of the experimental conditions.30 Therefore, when “n” is an electrolyte, the model to be fitted was set to be

(33)

C(HCO3−)bC(H+)b C(CO2)b

hn a n δnVn

(35)

where Kb, Kw, K1, and K2 are the corresponding equilibrium constants. Ammonia dissociation constant is calculated by31 8728


Industrial & Engineering Chemistry Research −1 ⎡A B ⎤ kn = ⎢ n + n ⎥ ⎣T T⎦

Article

dC(NH3)S

otherwise ⎤−1 ⎡ An B k n = ⎢ 1.75 + n + Cn ⎥ ⎦ ⎣T T

dC(NO3−)b dt

dt dθ(NO3−)#

dC(H2)b

dt

dC(NO2−)b (52)

r1 − r3 αC S

(53)

dC(N2)b

(54)

dC(NH3)b

−r + r3 dθ# = 1 dt αC S

dt

dt

= −r2 + r15

dt

(55)

dC(CO2)b

− 2r2 + 2r3 + r4 + 2r7 + r8 + r9 + r10 + r11 + r12 + 2r13 dθ * = dt (1 − α)CS (56)

dθ(H)* dt

=

dθ(NO2−)* dt dC(H2O)S

dC(NO2−)S dt dθ(NO) *

dθ(OH−) * dt

dt

r5 − r6 (1 − α)CS

r + r6 − r12 − r13 = 5 (1 − α)CS

r − 2r7 − r8 = 6 (1 − α)CS

dC(N2)S dt

= r7 + r18

dθ(NH) * dt

dθ(NH2) * dt dθ(NH3) * dt

= r3 + r4 + r16

=

dt

dθ(N) *

−r4 − r5 = (1 − α)CS = r3 + r13 + r17

dt

dt dC(OH−)S

2r2 − 2r3 − r5 − r6 − r8 − r9 − r10 − r13 (1 − α)CS

=

=

=

dt (57)

(70)

= −r16

(71)

(72)

= −r19

(73)

= r21

(74)

= r12 + r22

(75)

where α is the fraction of bimetallic sites. Considering that all tin is associated with bimetallic sites (monometallic sites are palladium sites), it is easily shown that30

(58)

α=

(59)

(60)

mSn MSn mSn MSn

+

(

mPd MPd

−

mSn MSn

)

(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

(61)

CS =

%Pd Ccat 100MPd

(77)

(62)

where %Pd is the amount of palladium on the catalyst, mcat the mass of catalyst (g), and Ccat the “concentration” of the catalyst in the reaction mixture (g/L). The remaining degree of freedom in the mathematical model is removed by the assumption of the electrical neutrality of the solution:

(63)

(64)

r8 − r9 (1 − α)CS

(69)

= −r18

dt

dC(H2)S

= −r14

= −r15 + r20

dt

= −r1 + r14 =

(68)

(51)

2.1.4. Material Balance. The mechanisms and rate equations described in the previous sections can be used to express the material balance over all species as follows: dC(NO3−)S

= r11 + r19

dt

(50)

C(Na+)b + C(H+)b + C(NH4+)b = C(NO3−)b + C(NO2−)b

(65)

+ C(OH−)b + 2C(CO32−)b + C(HCO3−)b

r9 − r10 (1 − α)CS

(66)

r10 − r11 (1 − α)CS

(67)

(78)

in which the concentration of Na+ is constant and equal to the initial nitrate concentration. Therefore, combining the relevant equations, the rate of change of H+ concentration in the “bulk” phase, becomes 8729


Industrial & Engineering Chemistry Research dC(H+)b dt

⎡ C(H+)bKb dC(NH3)b − ⎢⎣ − K w dt

=

⎡ ⎢⎣1 +

C(NH )bKb 3

Kw

+

dC(CO

b 2)

K1 C(H+)b

K w + K1C(CO

b 2)

2

(C(H+)b)

dC(NO −)b ⎡ 2K a dC(CO2)b 3 + ⎢⎣ − (C + b)2 dt + dt (H ) + C(NH )bKb ⎡ K w + K1C(CO )b 3 2 ⎢⎣1 + K w + (C + b)2 + (H )

dt

+

Article

⎤ ⎥⎦

4KAC(CO

b 2) 3

(C(H+)b)

Considering that the reaction system was previously exposed to an excess of H2 for the catalyst activation, the initial concentration of H2 on the surface of the catalyst was equal to the one in the “bulk” phase and all monometallic sites were occupied by H2; no other species was adsorbed, and the fraction of void bimetallic sites was 100%. 2.2. Model Integration and Parameter Estimation Methods. Some attempts were made to solve the system of differential-algebraic equations (DAE) composed by the material balances and the chemical equilibrium equations along with the restriction of electrical neutrality of the solution. Several standard DAE-solving algorithms and some modified ones were tested without success, probably because of the stiffness of the differential equations.30 Therefore, the insertion of the algebraic equations into the differential, which lead to a system of ordinary differential equations (ODEs), was crucial to the numerical strategy employed. It must be noted that the integration of such a system of ODEs corresponds to the dynamic simulation of the reaction system and is completely dependent on the empirical parameters, which is adequate for a statistical fitting procedure (as far as experimental data were available). The numerical integration method used is described in detail in a previous work,30 but basically involves a backward differentiation formulas (BDF) scheme in a vector−matrix format. 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 the following optimization:

⎤ ⎥⎦

⎤ ⎥⎦ 4KAC(CO )b ⎤ 2 (C(H+)b)3 ⎥ ⎦ dC(NO

−b 2 )

dt

(79)

which is a “key” equation for the formulation other rate equations: dC(OH−)b

=

dt dC(NH4+)b dt

=

dC(H+)b

−K w 2

(C(H+)b)

dt

Kb

dC(NH3)b

C(OH−)b

dt

(80)

−

C(NH3)b dC(OH−)b (C(OH−)b)2

dt (81)

2.1.5. Initial Conditions. Once the concentrations of CO2 and H2 in the gas phase remain constant in each run (depending only on the temperature), Henry’s law was used to calculate the initial concentration of these species in the “bulk” phase:36 C(CO2)0b = C(H2)0b =

C(CO2)g HCO2

(82)

C(H2)g HH 2

exp exp t β ̂ = min[C̲ (NO − C̲ (NO3−)b( β̲ )] − b − C̲ (NO −)b( β̲ )] W[C̲ 3 ) (NO −)b

(83)

{ β}

3

(88)

where HCO2 and HH2 are the solubility constants of CO2 and H2, respectively, given by36

exp where C̲ (NO − b is the vector of all experimental points and W is ) 3

a diagonal matrix of weights. Because small experimental values tend to be close to the measurement precision, each weight was set as the inverse of the value of the corresponding experimental point. The final problem involves an optimization of an objective function that demands the integration of all ODEs using the decision variables (the parameters to be estimated). Once again, the present work employed the previously developed strategy, which consisted of a hybrid scheme, in which a simplex search preceded a quasi-Newton method with a Broyden−Fletcher−Goldfarb−Shanno approximation of the Hessian matrix.30 A total of 150 experimental points were used to fit the 50 empirical parameters. All routines were written with Scilab 5, a free and open source software (distributed under CeCILL license, GPL compatible) developed by Scilab Enterprises (http://www. scilab.org).

1 = exp[1n( −159.8741 + 5528/T − 0.0011026T HCO2 + 21.66941 ln(T )]

3

(84)

1 = exp[1n(− 125.939 + 5528/T + 16.8893 ln T )] HH 2 (85)

It must be said that this was performed only to generate a set of adequate initial conditions; once equilibria 30 and 31 take place, 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 solution could be applied at the initial time, leading to C(H+)0b + C(NH4+)0b = C(OH−)0b + 2C(CO32−)0b + C(HCO3−)0b (86)

3. RESULTS AND DISCUSSION Once the regression was concluded, fitted parameters for the kinetic and mass-transfer models were available; these can be found in Tables 1−3. The predictive model thus obtained can be compared to experimental data. In Figure 1, a normalized scale for the nitrate concentration was used, dividing each experimental value by the initial concentration of the corresponding run.

This was combined with chemical equilibrium equations to give: (C(H+)0b)3 + C(NH4+)0b(C(H+)0b)2 − [K w + K1C(CO2)0b]C(H+)0b = 0 (87)

which in turn was solved by Cardano’s method.36 After (H+)b0 was caluculated, the initial concentration of both OH− and NH3 could be calculated by eqs 32 and 33. 8730



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Table 1. Fitted Kinetic Parameters k0,n k0,1 k0,2 k0,3 k0,4 k0,5 k0,6 k0,7 k0,8 k0,9 k0,10 k0,11 k0,12 k0,13 k0,14 k0,15 k0,16

Ea,n (kJ/mol) Ea,1 Ea,2 Ea,3 Ea,4 Ea,5 Ea,6 Ea,7 Ea,8 Ea,9 Ea,10 Ea,11 Ea,12 Ea,13 Ea,14 Ea,15 Ea,16

4.02 8.69 × 10−12 0.14 0.000 057 0.091 0.0024 0.33 0.000 26 0.000 26 1097.02 16.52 0.61 2.62 0.51 3648.78 0.0080

8.12 2.69 8.62 1.71 24.52 12.11 1.67 × 10−16 10.75 10.75 25.65 49.11 31.60 34.50 34.35 62.92 1.26

Figure 2. Evolution of NO3−, NH4+, N2, and NO2− concentration in the “bulk” phase (T = 35 °C).

It is important to notice that these results are in accordance with the literature.8,11,14 The NO2− concentration in the bulk phase was quite low during the reaction time, with an increasing profile reaching a maximum for a time lower than 100 min, followed by a decrease associated with a rapid adsorption on the surface of the catalysts and subsequent conversion to NO. The low concentration values were consistent with the fact that NO2− could not be observed experimentally.30 Figure 3 depicts the evolution of the nitrite

Table 2. Fitted Mass-Transfer Parameters for Nonelectrolyte Species Bn (s K1/2)

An (s K) A18 A20 A21 A22 A23 A24

−22 496.44 −28 871.61 −33 232.74 −25 182.81 −1.43 × 108 86 222 578.0

B18 B20 B21 B22 B23 B24

410 843.46 527 269.88 606 914.02 459 904.04 2.58 × 109 −7.42 × 108

Table 3. Fitted Mass-Transfer Parameters for Electrolyte Species An (s K1.75) A17 A19 A25

4.67 × 1010 4.18 × 1010 1.18 × 1010

Bn (s K) B17 B19 B25

−1.09 × 109 −9.72 × 108 −2.73 × 108

Cn (s) C17 C19 C25

1 499 880.6 1 315 111.1 366 220.94

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

concentration gradient between the “bulk” phase (thicker lines) and the “surface” (thinner lines). The results shows that the higher the temperatures, the sooner the nitrite reaches a maximum both in the “bulk” phase and in the “surface”. This is consistent with the effect of temperature on the conversion of nitrate 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 masstransfer effects evaluated by the present model. For that, in Figure 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 with the literature.15 The addition of CO2 to control the pH has proven to be a better option than the addition of HCl.7,8,37

Figure 1. Fitted model and experimental data (normalized nitrate concentration).

After the model is fitted, any other state variable could have its dynamics simulated, which is important for model validation. Figure 2 depicts the evolution of the most important N-based entities present in the “bulk” phase (for simplicity, only the results corresponding to 35 °C are shown). 8731



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

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

However, our results show that although the presence of CO2 improves the pH control, a pH gradient within the pores still remains. Thus, the present model allowed to us to follow the intrapore pH gradient, what was not possible for the model used before.30 This indicates the need to couple mass-transfer and kinetic steps to get a complete picture of the system. This model explains why better selectivities were obtained for large pore supports25 and when an acidic cation exchange resin was used as support.27 The simulation of the dynamics of occupation of catalyst active sites is also of great interest. As expected, it was found that an almost instantaneous complete occupation of bimetallic sites takes place, as can be seen in Figures 5 and 6. The

Figure 7. Evolution of the fraction of monometallic sites occupied by NO.

combination with H to form NH species. The fraction of the monometallic sites occupied by hydrogen is high at initial times (Figure 8), with a steep decrease due to the hydrogenation of nitrate and consequent formation of other intermediates. For longer times, as hydrogen is continuously fed to the system, and because of desorption of products, there is an increase in the fraction of the occupied sites by hydrogen. The selectivity for N2 is influenced by the relative ratio of sites occupied by NO and hydrogen.12,21,28 Also, a higher occupation of NO leads to an increase in selectivity for N2.29 In fact, when the fraction of sites occupied by NO increases, there is an increase in the formation of NH4+ (Figure 9). The proposed model showed good predictive power (Figure 9) as shown by the comparison of the experimental formation of NH4+ at 25 °C and the curve predicted by the model. It must be stressed that the experimental data for NH4+ concentration was 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 into account that experimental nitrate concentrations were around 0.0007 mol/L, which denotes an improvement from a previous work.30

Figure 5. Evolution of the fraction of bimetallic sites occupied by nitrate.

decrease in the fraction of bimetallic sites occupied by nitrate is associated with the reaction progress. The occupation is shorter for higher temperatures, and this may be related to the higher conversion 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 NO increases initially and reaches a maximum because of its 8732



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involved 50 parameters; it is not even possible to use the same initial guess for comparison purposes. Despite the good adherence to experimental data and low variance achieved, considerably large variations in the fitted parameters set tended to have little impact in the objective function, as in other works devoted to kinetics parameters regression.38,39 This apparent paradox can be explained by the peculiar topology of the likelihood function when dealing with kinetic models, which seems to exhibit a large flat region around its minimum (which leads to low parameter sensitivity and large parameter variances and covariances) but at relatively low values of the likelihood function itself (which leads to low model fundamental variance). Of course, this jeopardizes establishing the set of the most relevant parameters to the complete model and decreases the reliability of each one but also guarantees the fluctuations in the fitted parameters (which could be caused by experimental errors, for instance) will have little effect on the predictive capabilities of the model. Thus, the good predictive power and the complete statistical description of the model were benefits of the employed methodology.

Figure 8. Evolution of the fraction of monometallic sites occupied by H.

4. CONCLUSION The addition of the mass-transfer effects to the microkinetic model of the catalytic reduction of nitrates improved the understanding of the catalytic reduction of nitrate. The proposed phenomenological model comprises a system of differential equations related to the molar balances of all reactants and products in the reactor. Coded in an open source software, the model allowed a detailed analysis of the composition 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 surface phases. In the “bulk” phase, several chemical equilibria are assumed to take place as well as mass transfer from the gas and to the “surface”. In addition, a redox mechanism was employed, with two different sites being responsible for the reaction. A complete description of the adsorbed species was obtained. This model allowed following the gradient of the pH within the pores, which affects the selectivity for N2, and it was able to predict NH4+ profiles.

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

When it is compared to the previous work,30 which was able to simulate the evolution of chemical entities in only two “phases” (“bulk phase” and catalyst), the introduction of masstransfer effects made it possible to simulate relevant state variables in four “phases” (gas, “bulk phase”, surface, and catalyst). However, the computational time for system simulation increased 60% when the number of variables increased from 17 to 53. Therefore, when choosing between the present model or the previous one,30 there is a compromise between the level of mathematical detail and the computational time 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 this work confirmed that a pH gradient remains in the reaction system even when CO2 is used to control the pH. This was also an improvement; in the previous work,30 the pH was considered 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 time devoted exclusively to parameter estimation, which is highly dependent on the initial guess. The mentioned previous work30 involved the estimation of 14 parameters, and the present work

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AUTHOR INFORMATION

Corresponding Author

*Rua Passo da Pátria 156, 24210-240, Niterói, Brazil. Tel.: +5521-2629-5562. E-mail: [email protected]ff.br. Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS CAPES is acknowledged for sponsoring the scholarship for E.P.A.R. REFERENCES

(1) United Nations Educational, Scientific and Cultural Organization. Water in a Changing World; UNESCO: Paris, 2009 (2) MMA − Ministério do Meio Ambiente, Plano Nacional de ́ Recursos Hidricos − Iniciando um processo de debate nacional, SRH − ́ ́ - DF, 2005 (in portuguese). Secretaria de Recursos Hidricos, Brasilia (3) World Health Organization. Nitrates and Nitrites in DrinkingWater; WHO: Geneva, Switzerland, 2004 (4) Feitosa, F.; Manoel Filho, J. Hidrogeologia: Conceitos e Aplicaçoẽ s, 2nd ed.; CPRM: Brazil, 2000 (in portuguese). 8733



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