I n d . Eng. C h e m . Res. 1987,26, 32-39
32
Theoretical Study of the Influence of Nonuniform Active-Phase Distribution on Activity and Selectivity of Hydrodesulfurization Catalysts Jose M. Asua* Departamento de Qulmica Tecnica, Facultad de Ciencias Qdmicas, L'niuersidad del Pals Vasco, P.O. Box 1072, 20080 S a n Sebasticin, Spain
Bernard Delmon Groupe de Physico-Chimie Minerale et de Catalyse, UniversitP Catholique de Louuain, B-1348 Louuain- la- Neuue, Belgium
In hydrodesulfurization catalysts, much of the active elements are in the form of separate sulfides (MoS, or similar structures and Cogss). Therefore, in contrast with the prevalent theory focusing on a mixed phase, the so-called "Go-Mo-S", we suppose that spillover hydrogen emitted by Cogss creates and controls the catalytic centers on the surface of MoS2 The present study is an investigation of the influence of the shape of the concentration profiles of Go and Mo, nonuniformly distributed in hydrodesulfurization catalyst pellets, according to our assumption. Our rate expressions use the product of two terms: the first corresponds t o the variable number of active sites; the second corresponds to a classical Langmuir-Hinshelwood expression. The influence of external gas-phase conditions on the intrinsic activity profiles, particle-average reaction rate, selectivity, and effectiveness factor is analyzed. At low concentrations of H2S, the performance of the catalyst pellet is very sensitive to the shape of the active-phase distribution profile. It is shown that the results cannot be explained by classical diffusional effects alone. Much attention has been given, both theoretically and in practice, to the modification of activity and selectivity in a porous catalyst brought about by a nonuniform distribution of the catalytically active species. For example, pellets or spheres within which only a thin zone or shell near the external surface contains the active metal are used in some processes. One advantage, when secondary reactions may take place, is increased selectivity. Another advantage is that the active species are used with maximum effectiveness, even if diffusional limitations exist. In the studies that attempt to describe activity and selectivity of catalysts with nonuniform profiles (Kasaoka and Sakata, 1968; Shadman-Yazdi and Petersen, 1972; Corbett and Luss, 1974; Villadsen, 1976; Cervelld et al., 1977; Nystron, 1978; Wang and Varma, 1978,1980; Yortsos and Tsotsis, 1982; Do and Bailey, 1982; Juang and Weng, 1983), it has been assumed that each portion of the active species has an identical catalytic behavior, whatever is its position within the catalyst pellet. More precisely, the same rate equation (e.g., a Langmuir-Hinshelwood equation) is supposed to hold; i.e., one assumes that the nature and number of active sites occupied by this active species per unit weight or per unit surface area are constant and that differences of the reaction rates at different depths are due only to differences of the reactant concentrations brought about by diffusion. However, for a number of catalytic systems, several experimental results suggest that the reaction conditions act on the structure of the catalyst through processes other than deactivation (Pirotte et al., 1979; Delmon, 1979; Broderick et al., 1978). For example, Pirotte et al. (1979) measured the activities for thiophene hydrodesulfurization of a series of catalysts with different compositions, Co/ (Co + Mo), at several pressures in conditions excluding diffusional limitations and found very large differences in behavior. In particular, taking the results Co/(Co + Mo) = 0.33 and 0.15, they found that the experimental ratio
* Author to whom correspondence should be addressed.
of activities in hydrodesulfuration, a0.33/u0,15, increased with pressure. This suggested that, in addition to a classical rate effect due to higher occupancy of the active sites by reactants, the number of active sites changed with pressure (Delmon, 1979). Besides, several authors (Broderick et al., 1978; Delmon, 1979) have reported that the catalytic activities only readjust slowly after a change in the reaction conditions. The experiments of Broderick et al. (1978) are typical in this respect. During dibenzothiophene hydrodesulfurization, H2S added to the feed induced a longlasting change in activity. The authors attributed the effect to a structural change of the catalyst. One of us (Delmon 1979, 1980), accounting for those facts and the various special characteristics of hydrodesulfurization reactions (HDS), proposed a "remote control hypothesis". In agreement with most authors, MoS2 (or compounds with the MoS, structure) is assumed to carry the active centers. According to the remote control model, the origin of synergy between MoS2 and cogs8 is the creation of catalytic centers on MoS2 by the action of spillover hydrogen emitted by Cogs8. Actually, all hydrodesulfurization catalysts possess both hydrodesulfurizing and hydrogenating activities. The model supposes that a mild reduction of MoS, forms hydrogenation (HYD) centers; a strong reduction gives centers active for the hydrogenolysis of the removal of sulfur (HDS in the strict sense). Indeed, catalysts rich in S are very selective in HYD, whereas strongly reduced catalysts are mainly hydrodesulfurizing (HDS) (Pirotte et al., 1979). The increasing promoting (reducing) action of cogs89 when present in increasing quantities, explains why catalysts richer in Co possess a higher HDS/HYD selectivity (Delvaux et al., 1979; Pirotte et al., 1981). If this interpretation is correct, Cogs8controls the active sites on MoS,. It is clear that the local H2S/H, ratio, potentially modified by diffussional limitations, would change the number of active centers of each type. The above-reported results and, more specifically, the remote control model require a modification of the
08S8-5885/8~/2626-0032$01.50/0 0 1987 American Chemical Society
Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987 33 mathematical formulation of the kinetic equations. In the classical Langmuir-Hinshelwood kinetics, the rates (e.g., rHDS for hydrodesulfurization) are represented by equations of the form rHDS
=
h D S f hDS(Ki,Pi)
(1)
where Ki and Pi are, respectively, the adsorption coefficients and pressures of the various substances that adsorb on the active centers. But, in this representation, the rate constant, which includes the number of active sites, is supposed to depend only on temperature khDS
= g’HDS(n
(2)
One supposes that the number of active centers remains constant. The previous results obtained in hydrodesulfurization suggest that it would be more adequate to use, instead of a classical Langmuir-Hinshelwood equation, an expression of the form (Asua and Delmon, 1984) rHDS
=
kHDSfHDS(KitPi)
(3)
with kHDS
= gHDS(T,PH&PH2)
(4)
Here, the function gHDS(T&&pHP) can take into account the number of active sites, turnover frequency, and their variations with the experimental conditions. The function fm(KiPi)accounts for the competition for the active sites, according to the Langmuir-Hinshelwood model. The previous arguments are also valid for the hydrogenation reactions that generally accompany hydrodesulfurization. Therefore, the hydrogenation rate equation can be written as rHYD
= kHYDfHYD(KirPi)
(5)
= gHYD( T,pH2S,pHz)
(6)
with kHYD
The remote control model is successful in accounting, at least qualitatively, for the changes of activity in hydrodesulfurization and in hydrogenation which are observed with different catalyst preparations, with different r = Co/(Co + Mo) ratios, and when the experimental conditions change. The model predicts that the activities per unit surface area of the active phase, and therefore the kinetic constants, k H D s and kHYD, vary differently in hydrodesulfurization (hydrogenolysis of C-S bonds) and in hydrogenation (saturation of olefinic or aromatic molecules). They depend on the size of the MoSz and cogs, particles, on the intimacy of their contact, on r, and on the H2 and H2S partial pressures. As the essential feature of the model is that, instead of being constant, the number of active sites for hydrodesulfurization and for hydrogenation change as a function of the composition of the reacting fluid mixture. Activity and selectivity should vary differently, unlike the variations deduced from former models with a constant number of active sites. As activity and selectivity are particularly important for the economy of hydrodesulfurization and for hydrotreating processes in general, it was worth examining the consequences of the remote control model in the case of the corresponding catalysts. One can hope to modify activity and selectivity by better controlling the number and nature of active sites as functions of the depth inside the pores. This can be done by using special nonuniform profiles of the active phases inside the catalyst pellets. The form of these profiles interacts with the H2 and H2S concentration profiles. By proper design of catalysts and choice of re-
action conditions, one can hope to treat widely different feeds optimally, especially the new difficult (“bottom of the barrel”) feeds that the petroleum industry must transform today. On the other hand, compositions are different a t different levels of the catalyst bed in the industrial reactor. One can also envisage optimization of reaction conditions (e.g., choice of liquid or gaseous phases and selection of the rete of hydrogen injection) and the architecture of the catalysts used at various levels, in order to maximize activity and to obtain desirable selectivity. Although at present neither the precise values of the parameters of the model nor the exact dependency on H2 and H2Sconcentrations is known, it is of interest for both the catalyst and reactor design to investigate from a purely theoretical point of view the behavior of a single catalyst pellet having a nonuniform composition. This is the object of our work. Kinetic Implications of t h e Remote Control Model The remote control model (Delmon, 1979,1980)predicts that the rate constants for hydrodesulfurization and hydrogenation depend on the catalyst characteristics and on the H2 and H2S partial pressures, according to the equations kHDs
= Cst[P(l-M-N)(l - r)]”
(7)
= CSt[PN(1 - r)]”’
(8)
kHyD
where r is the composition, Co/(Co + Mo), of the catalyst, N is the fraction of the MoS2 surface which is slightly reduced and contains the active centers for hydrogenation, 1-M-N is the deeply reduced fraction which contains the active centers for hydrodesulfurization, P is the catalyst content of the active phase, and n and n’are the number of active sites involved in the rate-controlling step of each reaction. The fractions of the MoS2surface which carry the active sites are given by the expressions
N = p/(h’cS
+ p + d’p2/cs)
(9)
where p is the surface concentration of spillover hydrogen, Hs,, on the surface of MoS2. The Hso concentration is given by the following equation, similar to the one deduced by Delmon (1979,1980), corresponding to a more comprehensive model applicable to supported catalysts (Delmon, 1983)
where c’, h ‘, k $, k,, and k are the parameters of the model; essentially, c’, h‘, and d‘ are the intensive parameters characteristic of the conversion of H2to Hso on C09S8and of the reaction of Hso to form HDS centers on MoS2,and kh, k,, and k ; are the extensive parameters corresponding to the formation, transfer and consumption of Hso. Parameters OM and ac, respectively, are MoS2 and Cogss surface areas; S, is the specific area of the support, and
34 Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987
t = Ss/aM(3. If t equals zero, the catalyst is unsupported. For supported catalysts, t is greater than zero. The values of the parameters used in the calculations are (Delmon, 1979, 1980) as follows: c' = 100 (kg-mol of Hso.m3 of fluid)/(kg-mol of H&m2 of Co9S8);h' = 100 (kg-mol of Hso.m3 of fluid)/(kg-mol of H2S.m2 of MoS,); d' = (kg-mol of H2S.m2of MoS,)/(kg-mol of Hso.m3of fluid); (3 = 1.876 X kg-mol of (Co + Mo)/kg of catalyst; 4krf/k,a, = 30.4, ksa,/2k$ = 21.32, and t = 2, see Nomenclature section for units.
Material Balance A simplified reaction scheme for dibenzothiophene hydrodesulfurization is
m-@--pJ\
s
'
+H,S
The boundary conditions for i = 1-4 are x =0 dCi/dX = O C, = C'i
x =1 The kinetics of hydrodesulfurization have generally been expressed based on the equations of the Langmuir-Hinshelwood type (Vrinat, 1983). In this work, we have to take into account the effect of the reaction environment on the number of active sites by using eq 3-11. The kinetic equations used in the simulation include rate constants of the types of eq 7 and 8. These take into account the variation of the number of active sites, in addition to Langmuir-Hinshelwood terms which account for the competition for active sites. The Langmuir-Hinshelwood terms were taken from the literature. Thus, for dibenzothiophene hydrodesulfurization, the equation obtained by Broderick and Gates (1981) was used; for biphenyl hydrogenation, the equation derived by Vrinat (1981) was employed. The equations used are
kg-mol kg of cata1yst.s
CBFCH 0.063p(1 - r)N term a (1 + ~ C E F ) term
kg-mol kg of catalyst-s
)
(13)
where term a is the remote control term and term b is the Langmuir-Hinshelwood term. The remote control term is squared in eq 12 because the square of the concentration of active sites was used in the kinetic equation obtained by Broderick and Gates (1981). The Langmuir-Hinshelwood term is identical with the one reported by the authors. Equation 13 features a modified adsorption constant for biphenyl because Vrinat (1981) derived the kinetic equation in the gas phase, whereas liquid phase will be assumed in the present work. The values of the numerical factors in the remote control terms are arbitrary, but they yield reaction rate values of the same order as the ones reported by those authors. The material balance for a spherical catalyst at steady state and isothermal conditions may be written in terms of nondimensional variables.
(18) (19)
where the fractional radial distance x = r'/R; C, = = cBF/coBF;c3 = CH/c'H; c4 = CS/c'S; CODBT, cDBT/coDBT; cOBF, cOH, and cos are the concentrations at the pellet surface. As suggested by Villadsen and Michelsen (1978), important computational savings can be achieved for calculating C3 and C4 by the following expressions instead of eq 16 and 17 1-C4=
DDBTC'DBT (C, - 1) DSCOS
DBFC'BF 1) - 3(C2 - 1) (21) DHC'H DHCOH Differential eq 14 and 15, together with boundary conditions 18 and 19 and eq 20 and 21, have been solved by means of orthogonal collocation (Villadsen and Stewart, 1967), using five collocation points. The particle density used in our calculations was 1000 kg m-3. The diffusion coefficients have been determined by the random-pore model (Wakao and Smith, 1962) for a catalyst with a pore volume of 0.5 cm3 g-' and a pore radius of 40 A. It is assumed that the reactions occur in liquid phase at 1.8 X lo7 Pa and 598 K. Their values are DDBT = 2.2 X m2 s-l, DBF = 2.05 X m2 s-l, DH = 2.05 x m2 s-l, and Ds = 1.5 X m2 s-l. These values were used to calculate the standard 4i. The Co-Mo catalyst can be prepared, and many have indeed been prepared by previous authors, by successive impregnation, namely, by impregnating a y-alumina support f i s t with Mo, calcinating, and then impregnating with the other active phase and calcining. Such a method can lead to catalysts with independent and different concentration profiles of Mo and Co (Fierro et al., 1986). Therefore, the profies of Mo and Co have to be considered separately. In the frame of the present work, each profile type is characterized by using the profiles of /3 and r vs. position r' in the pellet. Keeping p constant, i.e., with the same total content of active phase at every position within the catalyst pellet, 16 different r profile types were computed, including convex, uniform, and concave shapes. Also, profile types combining r and (3 vs. r' changes were studied. In order to be able to compare the different profile types, the total amount of both Mo and Co in the catalyst pellet was kept C3-1=
5DDBTCoDBT
(C,
-
Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987 35 Table I. Profiles of r Used in Calculations” profile type profile equation r = 0.9947 - 2.638 X 102r’ 1-1 r = 0.84 - 1.813 X 102r’ 1-2 r = 0.68 - 0.961 X 102J 1-3 r = 0.52 - 0.108 X 10%’ 1-4 r = 0.5 1-5 r = 0.48 + 0.108 X 102r’ 1-6 r = 0.32 + 0.961 X 10%’ 1-7 r = 0.16 + 1.813 X 102r’ 1-8 r = 5.33 X + 2.638 X lo2+ 1-9 + 5.33r’ + 12.9 X 104r” r = 5.33 X 1-10 + 5.33 X lo-$-’ + 13.16 X 104f2 1-11 r = 5.33 X + 5.33r’ + 10.17 X 104f2;r’ < 2.4 1-12 r = 5.33 X 10-3 r = 0.85; r‘ > 2.4 X + 2.459 X 102r‘;r’ < 2.4 X 1-13 r = 5.33 X r = 0.9; r‘ > 2.4 X + 2.393 X 102r‘; r‘ < 2.4 X 1-14 r = 5.33 X r = 0.99; r’ > 2.4 X + 1.866 X 102r’;r‘ < 2.2 X 1-15 r = 5.33 X r = 0.9; r’ > 2.2 x + 1.61 X 10%’;r‘ < 2.2 X 1-16 r = 5.33 X r = 0.99; r’ > 2.2 x
4 -
3-
2 -
1-
X
\ I
,
0
1X-x
0
0.2
0.6
04
0
10
08 X
Figure 1. Effect of the external concentration of HzS on the profiles of intrinsic activity in hydrodesulfurization for profile 1-1 (Table I), for cDBT = 0.03, cBF = 0.01, CH = 0.2, and R = 2.5 X m. The figure also shows the concentration profile r (right-hand ordinate) vs. fractional radial distance n. ~HOS’O* 18 1-0-0
\
Case of p constant along the radius of the catalyst pellet. Total amount of active phase: kg-mol of Co = kg-mol of Mo = 6.139 X lo4, R = 2.5 X m.
Table 11. Profiles of B and r Used in Calculations4 profile type profile equations 11-1 p= 4.673 X 10%’; r = (3 X + 3.4 X 10-’r‘)/lp r = 0.16 + 1.813 X 10%’ 11-2 p = 1.876 X + 3.4 - 1.193 X 10%’; r = (3 X 11-3 0 = 2.1 X IO+ ?/@ 11-4 p= + 4.673 X lo-%’; r = 0.5 fl = 1.876 X r = 0.5 11-5 - 1.193 X lo-%’; r = 0.5 11-6 p = 2.1 X 11-7 0= 4.673 X 10%’; r = (6 X + 1.803 X ~~
~
~
+
X
+
lo-’r‘)/p
11-8 11-9
p = 1.876 X p = 2.1 X 3.403
X
r = 0.84 - 1.813 X 102r‘ 1.193 X 10-lr’; r = (1.576 X lO-’r’)/p -
-
OCase of both p and r varying along the radius of the catalyst pellet. Total amount of active phase: kg-mol of Co = kg-mol of m. Mo = 6.139 X lo”, R = 2.5 X
constant. For each profile type, the effect of the external gas-phase composition was analyzed. We summarize the profile types studied in Tables I and 11. It is worth pointing out that such profiles have been chosen not with the aim of obtaining an optimum of activity or selectivity but in an attempt to include very different cases. This was supposed to illustrate the differences between the results obtained by using the remote control model, with a varying number of active sites, and the ones obtained in the classical studies, with a contant number of active sites. I. Profile Types Corresponding to Variations of the Ratio Co/Mo ( r )with the Total Content of the Active Phase, Co Mo, (8) Being Kept Constant. The effect of the external concentration cs of H2S on the intrinsic (or local) HDS activity profiles vs. fractional radial distance x , for profile type 1-1from Table I, is presented in Figure 1. The r vs. x profile is also included in this figure. Notice that the local activity profiles differs from the profile of r within the particle and that activity increases with the external concentration of H2S. Similar results are obtained with other r-profile types, showing that the activity profile inside the particle and, therefore, total activity depend both on the profile of composition and on the external gas-phase conditions.
+
Profile t y p e
Figure 2. Effect of the concentration of H,S on the overall hydrodesulfurization reaction rates, for profiles of r from Table I: cDBT = m. cs = 0.003 (XI, 0.005 0.03, cBF = 0.01, CH = 0.2, and R = 2.5 X (O), 0.01 ( O ) , 0.015 (O), 0.02 (+), 0.03 (A).
The effect of the concentration of H2S outside the pellet on the overall hydrodesulfurization reaction rates for the r-profile types from Table I is presented in Figure 2. The overall reaction rates were calculated by averaging the local reaction rate over the particle volume by the equation N+l ~ H D S=
WirHDSi i=l N+l
(22)
C wi
i=l
where N is the number of collocation points and the wi’s are the weighting factors given by the collocation theory (Villadsen and Stewart, 1967). The effect of the external concentration of H2 is shown in Figure 3. From Figures 2 and 3, it is evident that, for each particular set of external conditions, there is a profile of r which maximizes the reaction rate. When the external concentration of H2S is high, the optimal performance of the catalyst pellet is not very sensitive to the profile type, but when the concentration of H2Sis low, slight changes in the profile type of r are able to provoke strong variations on the catalyst performance. For instance, a t cs = 0.003 and CH2= 0.2, the overall reaction rate corresponding to profile type 1-10 is more than 10 times the one corresponding to profile 1-9, whereas the profiles are not very different. Therefore, a t the inlet of the reactor where the concentration of H2Sis low, the profiles of active phases in the particle must be carefully controlled.
36 Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987
I O'
1'1
1'2
1'3 i 4
1'5 " 6
I"'
1'8 1'9
1'10 I'll 1'12
'13
P r o f i l e type
Figure 3. Influence of hydrogen concentration on the overall hydrodesulfurization reaction rate, for profiles of r from Table I: CDBT = 0.03, cBF = 0.01, cs = 0.01, and R = 2.5 X m. CH = 0.1 ( O ) ,0.15 (X), 0.20 (O), 0.25 (0).
'14 1'15 l ' 6
'
Prof l e t y p e
Figure 5. Effect of the external concentration of H,S on the overall hydrodesulfurization rate for profiles of r from Table I. Cave of the model with a constant number of active sites: cDBT = 0.03, cBF = 0.01, CH = 0.2, and R = 2.5 X m. cs = 0.003 (X), 0.005 (O),0 01 ( O ) , 0.015 (O), 0.02 (+I, 0.03 (A). 8
rHDSlo
20
9 t
I
! I'
/
>
8
I2
13
I4
1
1
8
15 16 ' 7
I
l
I
f
/
t
'
/
4
1 6 1 9 I10 1 1 1 112 113 I 1 4 1 1 5 1-16
1 0
P r o f le ty)e
Figure 4. Effect of the concentration of H2S on the overall hydrodesulfurization rates for the case of a rate constant proportional to the remote control term. The symbols are the same as those in Figure 2.
In order to show the effect of the power of the remote control term (power 2) in eq 12, some calculations have been carried out by using a rate constant proportional to the remote control term a t power 1. The effect of the external concentration of H2Son the hydrodesulfurization reaction rate for different r-profile types is presented in Figure 4. It can be seen that the behavior is similar to the case of a squared remote control term (Figure 2). In order to compare the results obtained by using the remote control model with the ones obtained with a model of a constant number of active sites, some calculations have been carried out with the model KHDs = K'HDs(pr)' = 18.3(pr)2 r < 0.35 (23)
KHDS= K"HDs(P(~- r))' = 5.3@(1 - r))2 r > 0.35 (24)
This simple model takes into account the well-established fact that catalysts with an intermediate composition show a maximum of activity. The results are presented in Figure 5. When the external concentration of H2S is low, this model, unlike the remote control model, does not show any strong sensitivity to the profile of r. That finding could be used to discriminate between both models. Figure 6 shows that the plot of rHDS vs. cs presents maxima for the r-profile types studied. The maxima occur
0 01
002
003 CS
Figure 6. Influence of cs on the hydrodesulfurization reaction rate a t CDBT = 0.03, cBF = 0.01, CH = 0.2, and R = 2.5 X m.
1 07
Profile t y p e
Figure 7. Effect of the external concentration of H2S on the selectivity for profiles of r from Table I: CDBT = 0.03, CBF = 0.01, CH = 0.2, and R = 2.5 X m. cs = 0.003 (X),0.005 (O),0.01 (e),0.015 (O), 0.02 (-I-), 0.03 (A).
owing to the 1-M-N term, and therefore, the numerator in eq 12 increases with cs, while the increase of the denominator makes the reaction rate decrease. At low concentrations of H2S, the effect of the increase of 1-M-N is more important and the reaction rate increases. At high concentrations of H2S,the effect of the adsorption term in the denominator predominates and the reaction rate decreases.
Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987 37
07
06
-
05-
04 -
03-
0 02
I
I
t
,
1
,
1
,
I
,
I
,
,
,
,
(15
10
15
$:
I
2D
25
$;st a n d a r d
Figure 10. Effect of $12 on the effectiveness factor: cDBT = 0.01, cBF = 0.01,and CH = 0.2. cs = 0.005 (O), 0.02 (+).
P r o f i l e type
--
1.3-
1-9 -
-0
I
o.L
I
0
-_--_
11-1 11-2 11-3 11.4 11-5 11.6 11-7 11-8 11-9
Protile t y p e 0
05
10
15
$:
20 $1
25
2 standard
Figure 9. Influence of 612 on the selectivity: cDBT = 0.03, cBF = 0.01, and CH = 0.2. cs = 0.005 (O), 0.02 (+).
The effect of the external concentration of H2S on the selectivity of several profiles of r is presented in Figure 7. Selectivity is defined as moles of H2 reacted in hydrogenolysis s = total moles of H2 reacted ~ ~ H D S
+ 3rHYD This selectivity is calculated by the equation 2KHDS
(27)
N+l
C~W,(~HDS)~
s =
i=l
N+ 1
(28)
Figure 11. Influence of cs on the overall hydrodesulfurization reaction rate for the profiles of r and fl given in Table I 1 CDBT = 0.03, cBF = 0.01, CH = 0.2, and R = 2.5 X lo9 m. cs = 0.003 (X), 0.005 (O), 0.01 ( O ) , 0.015 (O),0.02 (+), 0.03 (A).
crease. However, when the concentration of H2S is low, surprisingly, the selectivity increases with increasing diffusional limitations. This effect is due to increasing cs within the particle as C#J? increases: it has been shown that, when cs is low, an increase of cs improves the hydrodesulfurization reaction rate and therefore the selectivity. When @ is further increased, the decrease of cDBT makes up for the effect of cs and the selectivity decreases. The effect of $i2 on the effectiveness factor for several profile types is shown in Figure 10. The effectiveness factor is defined as the ratio of the actual reaction rate to that which would exist in the absence of any diffusional resistance and is given by N+l
C w .r ;.
i=l
Figure 7 shows that the selectivity has a behavior similar to the hydrodesulfurization reaction rate. Similar calculations, but with a rate constant proportional to the remote control term of power 1, are presented in Figure 8. Comparison betwen Figures 7 and 8 together with Figures 2 and 4 indicates that the remote control concept, i.e., the variation of the number of active sites in response to the local H2Sconcentration, not the details of the kinetics of the reaction on the surface, is the origin of the difference observed with a classical Hougen-Watson model. The effect of the modulus, C#Jt, on selectivity for several r-profiie types is presented in Figure 9. For a high external concentration of H2S, Figure 9 shows classical behavior: the selectivity of the intermediate products of a series reaction decreases when the diffusional limitations in-
q = N + 1
C WirS,
i=l
where rs, is the rate of reaction with surface conditions at the ith collocation point. For cs = 0.02, classical behavior is obtained and further explanation is not needed; for cs = 0.005, the curve presents a maximum which can be explained as in the case of the selectivity. 11. Mixed Profile Types: r and j3 Variables. The effect of the external concentration of H2S on the hydrodesulfurization reaction rates is presented in Figure 11for the profile types given in Table 11. It is evident from this figure that profile types for which fl increases in the direction of the pellet surface improve the reaction rate. The plot, rHDS vs. cs, presents a maximum similar to the one
38 Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987
presented by the r-profile types in the previous section because the effect of cs on 1-M-N is opposite to the effect on the adsorption term. The effect of the modulus, 412,on the selectivity is similar to the one found for the profile types in Table I: when the external concentration of H2S is low, the selectivity increases with @12 first and later decreases with 4:. Again, accumulation of H2S within the particle is responsible for this effect. For high concentrations of H2S at cs = 0.02, the effectiveness factor decreases monotonously with increasing pellet size; for cs = 0.005 such a plot presents a maximum. Conclusions The intrinsic activity profiles depend both on the profile type of the active-phase composition and on the external gas-phase conditions. The dependence is not simply a function of the profiles of active-phase concentration. The fact that both models, using either the power 2 or the power 1 of the number of active sites in the remote control term (either [P(1 - r ) ( l - M - N ) l 2 or [P(1 - r ) ( l - M N)]), give similar and quite conspicuous variations of activity and selectivity in the function of the active-phase profile type proves that the remote control concept, namely, the variation of the number of active sites in response to the local H,S concentration, and not the details of the kinetics of reaction on the surface is the origin of the difference observed between the present model and a classical Hougen-Watson model. For each external condition, there are profiles of r and P which maximize the hydrodesulfurization reaction rate. These profile types show maxima situated near the surface of the pellet, At low concentrations of H2S,namely, at the inlet of the reactor, the performance of the catalyst pellet is very sensitive to the r-profile type. It follows that r must be carefully controlled. At low concentrations of H2S, the reaction rate and the selectivity increase with cs, and after a maximum, both present a decreasing curve. For high concentrations of H2S,the selectivity and the effectiveness factor present classical behavior. Both decrease monotonously with increasing diffusional resistance. Conversely, for low concentrations of H2S, both the selectivity and the effectiveness factor increase with 4: until they reach maxima. When q ! ~is ~further ~ increased the selectivity and the effectiveness factor decrease. The very different predicted behaviors of a catalyst pellet could be used to discriminate experimentally between models representing a constant and a varying number of active sites. From a practical point of view, our results indicate that, if the external gas composition governs catalytic activity in a given reaction, parameters which have not yet been taken into account in catalyst design must play an important role. This offers new perspectives for improving the selectivity of certain catalysts. Acknowledgment We thank Prof. G. F. Froment for a very valuable suggestion concerning the role of the active centers. Nomenclature c = molar concentration, kmol m-3 c’ = parameter of the remote control model, (kg-mol of H s m 3 of fluid)/(m2 of Co9S8-kg-molof M,S) C = dimensionless concentration Cst = constant d’ = parameter of the remote control model, (kg-mol of H2S.m2 of MoS,)/(kg-mol of Hso.m3of fluid)
D = effective diffusion coefficient, m3 of fluid/ (m of solid-s) h’ = parameter of the remote control model, (kg-mol of Hwm3
of fluid)/(m2of MoS,.kg-mol of H,S) Hso = spillover hydrogen k ’ , = parameter of the remote control model, (kg-mol of Hso.kg-mol of H,)/(s.m3 of fluid.m2 of MoSz slightly reduced) k f f= parameter of the remote control model, (kmol of HSo-m3 of fluid)/(kg-mol of H,.s.m2 of Cogss) k , = parameter of the remote control model, (kg of catalyst.m2 of catalyst)/(s-m2of CogSs-m2of (MoS, + support)) K , = adsorption coefficient of substance i, Pa-’ 1-M-N = fraction of the MoS2 surface deeply reduced n, n’ = number of active sites involved in the rate-controlling step of hydrodesulfurization and hydrogenation reactions N = fraction of the MoSz surface slightly reduced P, = partial pressure of substance i, Pa r = fraction of Co in the active phase, kg-mol of Co/kg-mol of (Co + Mo) r’ = radial distance, m rHDS= hydrodesulfurization reaction rate, kg-mol/ (kg of cata1yst.s) rWD= hydrogenation reaction rate, kg-mol/ (kg of catalyst-s) R = radius of the catalyst pellet, m s = selectivity defined by eq 27, kg-mol of H2 reacted in hydrogenolysis/total kg-mol of H2 reacted S , = specific area of support not covered by active phase m2/kg of catalyst T = temperature, K w, = weighting factor x = fractional radial distance, rf/R Greek Symbols
p = catalyst content of active phase, kg-mol of (Co + Mo)/kg of catalyst q = effectiveness factor p = surface concentration of spillover hydrogen oc = Cogss surface area, m2 kg mol uIM= MoS, surface area, m /kg-_mol p = particle density, kg of catalyst/m3 = modulus given in eq 14-17
1
fi
Subscripts
DBT = dibenzothiophene BF = biphenyl S = hydrogen sulfide H = hydrogen Registry No. Co, 7440-48-4; Mo, 7439-98-7.
Literature Cited Asua, J. M.; Delmon, B. Appl. Catal. 1984, 12, 249. Broderick, D. H.; Gates, B. C. AICHE J. 1981, 27, 663. Broderick, D. H.; Schmit, G. C. A.; Gates, B. C. J . Catal. 1978, 54, 94. Cervelld, J.; Melendo, F. J.; Hermana, E. Chem. Eng. Sci. 1977, 32, 155. Corbett, W. E.; Luss, D. Chem. Eng. Sci. 1974, 29, 1473. Delmon, B. Bull. SOC.Chim.Belg. 1979, 88, 979. Delmon, B. React. Kinet. Catal. Lett. 1980, 13, 203. Delmon, B. 5th International Symposium on Heterogeneous Catalysis, Varna, 1983; Bulg. Acad. Sci., Comm. Dept. Chem. 1984, 17, 107.
Delvaux, G.; Grange, P.; Delmon, B. J. Catal. 1979, 56, 99. Do, D. D.; Bailey, J. E. Chem. Eng. Sci. 1982, 37, 545. Fierro, J. L. G.; Grange, P.; Delmon, B. Presented at the 4th International Symposium Scientific Bases for the Preparation of Heterogenous Catalysts, Louvain la Neuve, Sept 1-4, 1986. Juang, H. D.; Weng, H. S. Znd. Eng. Chem. Fundam. 1983,22,224. Kasaoka, S.; Sakata, Y. Kagaku Kogaku ( A b .Ed. Engl.) 1968 1,138. Nystron, M. Chem. Eng. Sci. 1978, 33, 379. Pirotte, D.; Grange, P.; Delmon, B. Presented a t the 4th International Symposium on Heterogeneous Catalysis, Varna, 1979, Part 2, p 127. Pirotte, D.; Zabala, J. M.; Grange, P.; Delmon, B. Bull. SOC.Chim. Belg. 1981, 90, 1239. Shadman-Yazdi, F.; Petersen, E. E. Chem. Eng. Sci. 1972, 27, 227. Villadsen, J. Chem. Eng. Sci. 1976, 31, 1212.
Ind. Eng. C h e m . Res. 1987,26,39-43 Villadsen, J.; Michelsen, M. L. Solution of Differential Equation Models by Polynomial Approximation; Prentice Hall: Englewood Cliffs, NJ, 1978; p 304. Villadsen, J.; Stewart, W. E. Chem. Eng. Sci. 1967, 22, 1483. Vrinat, M. L. Ph.D. Dissertation, Claude Bernard University-Lyon I, Lyon, 1981. Vrinat, M. L. Appl. Catal. 1983, 6, 137.
39
Wakao, N.; Smith, J. M. Chem. Eng. Sci. 1962, 17, 825. Wang, J. B.; Varma, A. Chem. Eng. Sci. 1978, 33, 1549. Wang, J. B.; Varma, A. Chem. Eng. Sci. 1980, 35, 631. Yortsos, Y. C.; Tsotsis, T. T. Chem. Eng. Sci. 1982, 37, 237.
Received for review February 21, 1985 Revised manuscript received February 3, 1986
Ozone Decomposition in Water: Kinetic Study Jos6 L. Sotelo,* Fernando J. Beltrln, F. Javier Benitez, and Jesiis Beltrkn-Heredia Departamento de Quimica Tgcnica, Facultad de Ciencias, Universidad de Extremadura, 06071 Badajoz, Spain
Kinetic studies on ozone decomposition in water were performed over a range of temperatures from 10 to 40 "C and p H range from 2.5 t o 9. T h e ozone decomposition rate was determined in eq 24. This expression is supported by a reaction mechanism. The second term is negligible, a t p H values below 3, leading to a first-order kinetic expression. The direct ozonewater reaction and the hydroxide ion initiation step are the main causes of ozone decomposition. Experimental and calculated ozone concentrations agree within &lo% for 95% of the experiments. The use of ozone as an oxidizing agent in both drinking and wastewater treatment and in several processes for organic synthesis has been growing. In water treatment the rate of ozonation of dissolved pollutants is affected considerably by temperature and pH. These variables also influence ozone's self-decomposition, whose kinetics must be known in order to achieve a satisfactory design. This subject has been widely studied by many authors, as can be seen in Table I. Recently, in 1982, three new reports about this subject have been published (see Table I). Forni's work (1982) studies the ozone decomposition under conditions different from those in drinking water processes, using extremely high pH values above 10. Gurol and Singer (1982) indicated that ozone decomposes by a second-order reaction with respect to ozone concentration, but no mechanism was presented in order to support their kinetic equation. Finally, Staehelin and HoignVs work deals mainly with the hydroxide ion's initial action on ozone decomposition. For this purpose they inhibited the action of very active radical species, such as hydroxyl radicals, OH*, using radical scavengers such as carbonate or methylmercury ions. In these circumstances, there is competition between the reactions k = 3 X los mol/(L.s) OH' + O3 0 2 + HOz' (1) k = 4.2
OH' OH'
+ C032k = 1.5 + HCOB-
X lo* mol/(L.s)
X 10'
mol/(L.s)
OH-
+ C03'-
(2)
OH-
+ HC03'
(3)
So, the kinetic equation presented in this work, deduced only a t 20 "C,corresponds to the initiation reaction between ozone and the hydroxide ion. These authors also study the hydrogen peroxide action on ozone decomposition. This is particularly important when the water to be treated has organic micropollutants whose decomposition by ozone produces hydrogen peroxide via organic peroxides (Schultze and Schultze-Frohlinde, 1975). In general, from the works listed in Table I, it can be concluded that there is disagreement among the previous results. Most of these investigations are not supported by reaction mechanisms, and generally, the range of conditions investigated was very narrow; some used only one pH and one temperature. The reaction orders for the ozone and hydroxide ion varied very much, being the main point of disagreement (Table I). The only agreement reached by all the works is that the reaction is catalyzed by the 0888-5885/87/2626-0039$01.50/0
hydroxide ion. Hence, the aim of this work is to deduce a general kinetic expression for ozone decomposition in water involving the action of different species which greatly accelerate the process, such as OH' and OHz' radicals, and which are supported by a reaction mechanism involving these radicals. In addition, since temperature is generally the most important variable affecting reaction kinetics, it would also be interesting to study its influence over a wide range of values.
Experimental Section Materials. Water was first deionized by ion exchange and then distilled. A mixture of KH,PO, and Na2HP04 was used to adjust both the ionic strength (0.15) and the pH of the solutions. The ionic strength was kept constant because this parameter affects ozone decomposition (Gurol and Singer, 1982). Potassium iodide, analytical grade, was used for the analytical measurements. Oxygen was taken directly from a commercial cylinder and dried with silica gel traps before entering the ozonator. Procedure. An ozone-oxygen mixture was produced in an ozonator (SLO Constrema) which is able to operate a t a maximum rate of 6 g of 03/h. The reactor was a 750-cm3 glass vessel with inlets for bubbling, stirring, sampling, venting, and temperature measurement and was submerged in a bath equipped with stirring, heating, and refrigeration systems, which allowed us to keep the temperature constant within rt0.5 "C. Stock buffered water (500 cm3) was added to the reactor and then ozonated with an 02-03 stream, containing about 4% (v/v) ozone, at a flow rate of 40 L/h for 30 min. About this time, saturation of water was reached, and the gas stream was stopped. Subsequently, the ozone decomposition chemical reaction was followed by determining the concentration of dissolved ozone by reaction with a buffered potassium iodide solution, measuring the triodide ions liberated spectrophotometrically at the wavelength of 352 nm (Shechter, 1973). Results and Discussion Effects of Agitation Speed, Temperature, and pH. Though the process studied is only a homogeneous chemical reaction, agitation was provided to keep the temperature of the water uniform during the experiment. Agitation speed was varied between 100 and 700 rpm. A t speeds below 300 rpm, the ozone conversion remained constant at a given reaction time. However, the decom0 1987 American Chemical Society
