Ind. Eng. Chem. Process Des. Dev. 1980, 19, 326-328
326
CORRESPONDENCE Effect of Catalyst Particle Size on Performance of a Trickle-Bed Reactor
Sir: The purpose of this correspondence is to point out some corrections that may be made to a communication by Montagna et al. (1977) and to suggest a new interpretation of their reported data on hydrodesulfurization of reduced Kuwait crudes. The authors used the holdup model of Henry and Gilbert (1973) together with the dynamic holdup correlation of Satterfield et al. (1969) to show that for a first-order chemical reaction the performance of a trickle bed is given by cAi
In - a (L)’13(LHSV)-2i3(dp)2!3(u~)1/3 (1) cAo
I submit that a careful application of the correlation of Satterfield et al. (1969) shows that the effect of “catalyst diameter” (dp-2/3)should be corrected to ( d i 4 I 3 ) ,where d , is the “equivalent sphere diameter” of catalyst particles. Thus, if the mass balance equation (-rA)H d V = Q L C A i dnA is combined with the Satterfield (1969) correlation for dynamic liquid holdup
taking into consideration that
Table I. Estimated Values of Parameters and Physical Properties for Desulfurization of 22% Reduced Kuwait Crude temp 750 ’F
where k,,is the intrinsic, specific (first-order) reaction rate (5-l) referred to the unit volume of catalyst particle, 17 is the catalyst effectiveness factor, C, is the reactant concentration on the completely wetted external surface of the particle, t is the void fraction of the bed, QL is the volumetric liquid rate, XAis the reactant conversion, and V is the volume of the bed. If there is no mass-transfer resistance outside the particle, then C, = CAi(l- XA), and eq 4 can be integrated into the form cAi
In - = kL,lv(l- 6 ) CAO
then for a first-order reaction (-rA = hl’CAi(l- X,)) one obtains cAi
In /.I = L Ao
131(1 - C)kl’(A)‘/3(L)’/‘(LHSV)-2/3(~,)-4~~~( v L ) ‘i3 (3)
where the volume of the reactor is V = LA. A major remark should be made with regard to the Henry and Gilbert (1973) holdup model that their main assumption, namely that the global rate of the reaction (expressed per unit volume of bed) is proportional to the dynamic holdup H , really means that they consider the chemical reaction to take place primarily on the external surface of the catalyst particle or in the bulk of the liquid holdup. This assumption may be true in the ordinary case of gas absorption accompanied by chemical reaction on a nonporous packing. However, in the present case of hydrodesulfurization it appears that the reaction takes place within the pores of the catalyst. The authors agree that the catalyst effectiveness factor should be taken into consideration. If this is done, then one may write the global rate of reaction expressed per unit volume of bed as
790 “ F
kinematic viscosity, 0.90 X 10.’ 0.70 X lo-* u L , cm’ls density, p ~ g/cm3 , 0.75 0.69 surface tension, 6.8 5.2 u , dynicm critical surface tension, 61 61 u c , dynicm (taken from Onda et a]., 1 9 6 7 ) bed void fraction, E 0.46 0.46 bed length, L , cm 20, 32 20, 32
3600
LHSV
Comparison of eq 3 and 5 shows that the holdup factor H has disappeared and eq 5 represents the form indicated by the plug-flow model. The effect of the catalyst particle size is now indirectly provided by the effectiveness factor 17 through its relationship with the Thiele modulus. However, as Montagna et al. (1977) and Mears (1974) have pointed out, the catalyst particles are not completely wetted. The authors have employed eq 7 from Mears’ (1974) paper to express the performance of an incompletely wetted bed, namely
Let us derive this equation from fundamental considerations. Mears (1974) used the fraction of the wetted surface a,/a, and the effectiveness factor 7 instead of the holdup H into the mass balance equation, without giving the detailed steps. Thus, one can express the global rate of the reaction per unit volume of bed per unit fraction of wetted surface as
Equation 7 now means that the intrinsic rate constant k, 0196-4305/80/1119-0326$01.00/0
1980 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 2, 1980
327
Table 11. Calculated Values of k , , k ” , , k , , and q , for Desulfurization of 22% Reduced Kuwait Crude exptl temp,
“F
749 750 750 789 753 792 750 788
LIISV, k1.I
Cl.51 0.43 01.5 0 01.53 01.55 ON. 52 0.53 0.51
In CAO
0.954 1.60 2.12 2.56 2.27 2.96 2.31 3.73
k , x 103,
ds
mm 2.5 2.5 1.2 1.2 0.75 0.75 0.40 0.40
may be larger than h,, because not all of the catalytic surface is effective due to incomplete wetting. It is easy to visualize this as far as the external surface of the catalyst particles is concerned, but it is difficult to conceive how the inside pores of the soaked particle can be ineffective, since diffusion of liquid takes place in the pores. As long as there is some contact of the liquid with the pores, one should expect the reactant to diffuse slowly inside the pores everywhere. At any rate, eq 7 can be integrated if we use an adequate correlation for a,/a,. Mears (1974) has used a form given by Puranik and Vogelpohl (1974)-in fact eq 3 of that reference. However, I’uranik and Vogelpohl(1974) pointed out that in the case of absorption accompanied by a chemical reaction, the effective area is given by their eq 5, which was slightly different than their eq 3, namely
where A is the cross-sectional area of the empty reactor, and (QLpL/A) is the specific mass liquid rate. The term a, is the total dry area of the packing per unit volume of bed, i.e., n, = 6(1 - t)/d,. Substituting into eq 7 and integrating, one gets r.
AI
In - = 223h1q(1 - ~)08L6L030~(L,HSV)-0693 X CAO pLO 133r,L4041u 0 133d 0 174(,c/a)0 8
182
(9)
Comparison of eq 9 with eq 6 points out the discrepancies which have inadvertently appeared in Mears‘ (1974) paper and which have been carried over by Montagna et al. (1977). The data of the authors deserve a reinterpretation now. Let us examine them in view of eq 3 (corrected holdup model), of eq 5 (pore diffusion model-complete wetting), and of eq 9 (pore diffusion-incomplete wetting). The data for sulfur removal of 22% reduced Kuwait crude (2000 psig, 100 cm3 of catalysjt) reported in Table I11 of Montagna et al. (1977) are used as an illustration. Estimated values of parameters and physical properties used in these calculations are summarized in Table I here. Calculated values (of rate constant h,’ from eq 3 are tabulated in Table 11. It can be seen that hl’ is not a constant a t a given temperature; in fact, it appears to decrease with decreasing particle diameter. Thus, the holdup model as depicted by eq 3 does not seem to explain the effect of catalyst particle size adequately. Calculated values of rate constant h,, from eq 5 are also listed. In fact, the value of the product (hLlq)was obtained a t each temperature; noting that the effectiveness factor approaches unity for the smallest particle, all q values can be calculated a t the corresponding temperature. A similar calculation was performed for rate constant h , and 7 from eq 9.
kUl x
k,
104,
r,
S-’
S-,
1.56 2.34 1.14 1.55 0.71 0.96 0.30 0.51
6.25 6.32 6.26 9.83 6.42 9.78 6.30 9.79
01
(from eq 9 )
(from eq 5 )
(from eq 3 ) CAi
02
03
04
lo’, tl
5.76 5.77 5.73 8.31 5.74 8.24 5.72 8.25
0.40 0.56 0.87 0.71 1.00 0.81 1.00 1.00
1
01
X
S-’
35 C607@50910
Ffi,
0.29 0.43 0.73 0.58 0.90 0.72 1.00 1.00
2
3
k l 0 3 oT$ +‘&,IX
4
5
I
6 ’ 9 9 ’ 0
.c3
Figure 1. Catalyst effectiveness factor for hydrodesulfurization of 22% reduced Kuwait crude. Data of Montagna et al. (1977).
It can be seen from Table I1 that h,, or h , remain remarkably constant a t around 750 or 790 O F . It is also observed that h,, is one order of magnitude smaller than kl. This may be explained by the fact that the model of incomplete wetting predicts that only 15% of the catalyst surface area is wetted and thus the intrinsic rate hl exhibits a value higher than h,,, respectively. The values of the calculated effectiveness factors are plotted in Figure 1 against the group (ds/2)(kLJ1’2 or (ds/2)(h1)1’2,respectively, as suggested by the Thiele modulus for a sphere. A satisfactory correlation is obtained for both models. Of course, the missing parameter (which is presently unknown) is the effective diffusivity of the sulfur compounds, De,, in the pores of the catalyst. Analysis of the data points to a value of Deffof the order of lo-‘ cm2/s for complete wetting and to a value of the order of cm2/s for the incomplete wetting model. The above discussion and interpretation of the data points to the general conclusion that the effect of catalyst particle size on sulfur removal is adequately explained by both models discussed. The present data are not sufficient for model discrimination.
Nomenclature A = cross section of empty reactor, cm2 CA, = concentration of A entering reactor, mol/cm3 CAo = concentration of A leaving reactor, mol/cm3 C, = concentration of A on catalyst surface, mol/cm3 d, = equivalent sphere diameter of catalyst particle, cm d, = catalyst particle diameter, cm Deff= effective diffusivity of A in catalyst pores, cm2/s g = acceleration of gravity, cm/s2 hD = dynamic liquid holdup, g H = dynamic liquid holdup ratio, cm3 of liquid cm3 of bed k l = intrinsic rate constant defined by eq 9, shl’ = intrinsic rate constant defined by eq 3, s-l k , = intrinsic rate constant defined by eq 5 , s-l LkSV = liquid hourly space velocity of feed at reactor inlet conditions, h-’ L = catalyst bed length, cm N = number of catalyst particles in bed
i
Ind. Eng. Chem. Process Des. Dev. 1900, 19, 328
320 QL -rA
= volumetric liquid flowrate, cm3/s = rate of conversion of A, mol of A/(s) (cm3 of liquid
holdup) V = volume of reactor bed, cm3 X A = conversion fraction of A a, = wetted area of catalyst particles per unit volume of bed, cm2/cm3 a, = total area of catalyst particle per unit volume of bed, cm2/cm3 e = catalyst bed void fraction 7 = catalyst effectiveness factor c(L = viscosity of liquid, g/(cm)(s) uL = kinematic viscosity of liquid, cmz/s pL = density of liquid, g/cm3 T
= 3.1415.-
Sir: In our opinion Marangozis (1980) has not only confused the purpose of our paper (Montagna et al., 1977) but has also misunderstood the aim of our other papers on the same subject (Paraskos et al., 1975; Montagna and Shah, 1975). Our reasons are as follows. (1)The purpose of the paper by Montagna et al. (1977) was to discriminate between holdup and effective wetting models in pilot plant reactors. These two correlating models predict different dependence of conversion (or more specifically In (CAi/CAq),where CAiand CAoare the reactor inlet and outlet concentrations) on the catalyst particle diameter. We cannot derive the relationship In (CAi/CAo)0: dp-4/3(where d, is the catalyst particle diameter) suggested by Marangozis (1977). Even if the holdup model suggests In (CAi/CAo)a di4I3,this relationship will not be satisfied by the data of Montagna et al. (1977). Also, as pointed out by Mears (1974), the use of eq 2 of Marangozis for correlating trickle-bed data is questionable. Thus, the data of Montagna et al. (1977) show the effective wetting model to be a better correlating model than the holdup model. (2) Equation 5 of Marangozis (1977) is simply the plug-flow model for a trickle-bed reactor. With the help of data obtained at various liquid hourly space velocity and length of catalyst beds, Paraskos et al. (1975) and Mon-
0196-4305/80/1119-0328$01 .OO/O
u = surface tension of liquid, dyn/cm uc = critical surface tension of bed packing,
dyn/cm
Literature Cited Henry, H. C., Gilbert, J. E., Ind. Eng. Chem. Process Des. Dev., 12, 328-334
(1973). Mears. D. E., Adv. Chem. Ser., No. 133, 218-227 (1974). Montagna, A. A.. Shah, Y. T I Paraskos, J. A,, Id.Eng. Chem. Process Des. Dev.. 16, 152-155 (1977). Puranik, S. S., Vogelpohl, A., Chern. Eng. Sci., 29, 501-507 (1974). Onda, K., Takeuchi, H. Koyama, Y., Kagaku Kogaku, 31, 126 (1967). Satterfield, C. N., Pelossof. A. A,. "herwood, T. K.. AIChEJ., 15, 226-234
(1989).
School of Chemical Engineering National Technical Uniuersity Athens, Greece
John Marangozis
tagna and Shah (1975) showed that this equation does not satisfactorily correlate small pilot scale data. This equation should be used only in the absence of significant wetting, dispersion, etc. effects. Thus, this equation cannot be used to correlate the effect of particle size on the conversion in pilot scale operation. Equation 5 of Marangozis predicts In (CAi/CAo)a 7 (where '7 is the catalyst effectiveness factor) whereas eq 9 of Marangozis predicts In (CAi/CAo) 0: d,0.17*. These two proportionalities are close. However, they cannot be compared because eq 5 is not applicable to the dat, of Montagna et al. (1977).
Literature Cited Marangozis, J., Ind. Eng. Chem. Process Des. Dev., preceding paper in this Issue (1980). Montagna, A. A., Shah, Y . T.. Paraskos, J. A,, Ind. Eng. Chem. Process Des. Dev.. 16. 152 (1977). Paraskos. J.' A,, F;ayer,'J. A,, Shah, Y. T., Ind. Eng. Chem. Process Des. Dev., 14, 315 (1975). Montagna, A. A., Shah, Y. T., Ind. Eng. Chem. Process Des. Dev., 14, 479
(1975). Mears. D. E., Adv. Chem. Ser., No. 133, 218 (1974).
Department of Chemical and Petroleum Engineering University o f Pittsburgh Pittsburgh, Pennsylvania 15261
Q 1980 American Chemical Society
Yatish T. Shah
