Minimum Fluidization Velocity and Bed Expansion Characteristics of

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Energy & Fuels 2004, 18, 1149-1155

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Minimum Fluidization Velocity and Bed Expansion Characteristics of Hydrotreating Catalysts in Ebullated-Bed Systems R. S. Ruiz,*,†,‡ F. Alonso,†,§ and J. Ancheyta† Instituto Mexicano del Petro´ leo, Eje Central La´ zaro Ca´ rdenas 152, 07730 Me´ xico, D.F., Mexico, Area de Ingenierı´a Quı´mica, Universidad Auto´ noma Metropolitana-Iztapalapa, Me´ xico, D.F., Mexico, and Instituto Tecnolo´ gico de Ciudad Madero, Juventino Rosas y Jesu´ s Urueta, Col. Los Mangos, Cd. Madero, Tamps., 89440 Mexico Received November 19, 2003

Experiments were conducted to study the hydrodynamic characteristics of a gas-liquid-solid fluidized bed containing commercial hydrotreating catalyst extrudates with both water and oil distillates as the liquid phase. The minimum fluidization velocity and bed expansion data were contrasted with predictions from empirical correlations reported in the literature. Empirical correlations tend to yield relatively smaller errors in reproducing the systems with water than with the organic liquids. Bed expansion predictions for the petroleum distillates systems were substantially improved when the sphericity factor of the extrudates was incorporated to the Begovich-Watson equation.

Introduction Industrial applications of three-phase fluidized beds are widespread in diverse fields of fuel conversion and purification. Many industrial operations such as H-Oil and LC-Fining employ fluidized-bed technology for upgrading heavy oil and residual feedstocks to high quality synthetic crude oils. Cylindrical catalyst particles are commonly used in these reactors. Unfortunately, most of the hydrodynamic studies reported in the literature refer to air-water-glass beads systems, and therefore the current design correlations have been mainly derived for such systems. Important parameters in the operation of fluidized bed reactors include the minimum fluidization velocity and the bed expansion. The minimum fluidization velocity, ULmf, represents the smallest superficial liquid velocity, which at a given superficial gas velocity brings particles in the bed from rest to motion. Many studies have been published on the minimum fluidization velocity of three-phase fluidized beds (see, for example, refs 1-4); however, most of them utilized water or * Author to whom correspondence should be addressed. Fax: (+52) 9175 8429. E-mail: [email protected]. † Instituto Mexicano del Petro ´ leo. ‡ Universidad Auto ´ noma Metropolitana-Iztapalapa. § Instituto Tecnolo ´ gico de Cuidad Madero. (1) Begovich, J. M.; Watson, J. S. Hydrodynamic Characteristics of Three-Phase Fluidized Beds. In Fluidization; Davidson, J. F., Kearins, D. L., Eds.; Cambridge University Press: Cambridge, 1978; pp 190195. (2) Costa, N.; De Lucas, A.; Garcia, P. Fluid Dynamics of GasLiquid-So1id Fluidized Beds. Ind. Eng. Chem. Process Des. Dev. 1986, 25, 84. (3) Song, G. H.; Bavarian, F.: Fan, L. S.; Buttke, R. D.; Peck, L. B. Hydrodynamics of Three-Phase Fluidized Bed Containing Cylindrical Hydrotreating Catalysts. Can. J. Chem. Eng. 1989, 67, 265-275. (4) Zhang, J. P.; Epstein, N.; Grace, J. R.; Zhu, J. Minimum Liquid Fluidization Velocity of Gas-Liquid Fluidized Beds. Chem. Eng. Res. Des. 1995, 73, 347-353.

water-based solutions as the liquid phase. Larachi et al.5 evaluated many of the available correlations and phenomenological models for ULmf and proposed two different empirical correlations based on a wide historic database set up from the open literature. Soung6 studied bed expansion using cylindrical catalysts fluidized by n-heptane and nitrogen. A correlation for bed expansion three-phase fluidization is proposed based on particle Reynolds number, particle sphericity, and expansion characteristics of the respective liquidsolid system. Sinha et al.7 studied and compared expansion characteristics of catalyst extrudates and polydisperse beads using a hydrocarbon-nitrogen system. They reported similar expansion characteristics for the catalyst bed and polydisperse beads of different size distributions. Song et al.3 studied bed expansion in beds containing cylindrical catalysts using water and an aqueous t-pentanol solution as the liquid phase, the latter in an attempt to simulate high gas holdup conditions. They reported bed porosity correlations for both the water and the surfactant systems. More recently, Larachi et al.8 compared the predictions of several of the most named phase holdup correlations with those of their own correlations derived from an upto-date broad fluidization database. They reported for their correlations smaller mean absolute errors than those obtained with other published correlations. (5) Larachi, F.; Illiuta, I.; Rival, O.; Grandjean, B. P. A. Prediction of Minimum Fluidization Velocity in Three-Phase Fluidized-Bed Reactors. Ind. Eng. Chem. Res. 2000, 39, 563-572. (6) Soung, W. Y. Bed Expansion in Three-Phase Fluidization. Ind. Eng. Chem. Process Des. Dev. 1978, 17, 33-36. (7) Sinha, V. T.; Butensky, M. S.; Hyman, D. Comparison of Cylinders and Spheres in Three-Phase Fluidization. Ind. Eng. Chem. Process Des. Dev. 1986, 25, 321-324. (8) Larachi, F.; Belfares, L.; Illiuta, I.; Grandjean, B. P. A. ThreePhase Fluidization Macroscopic Hydrodynamics Revisited. Ind. Eng. Chem. Res. 2001, 40, 993-1008.

10.1021/ef030184d CCC: $27.50 © 2004 American Chemical Society Published on Web 06/12/2004

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Figure 2. Effect of gas velocity on minimum fluidization velocity.

Figure 1. Schematic diagram of cold flow equipment. Table 1. Physical Properties of the Catalysts Used

Table 2. Properties of the Liquids

physical properties

fresh catalyst

equilibrium catalyst

shape length (×103) m diameter (×103) m relative density pore vol. (×103) m3/kg

cylindrical 4.39 0.79 0.945 0.73

cylindrical 1.93 0.79 1.87 0.12

kg/m3

density, viscosity (×103) kg/m s @ 20 °C surface tension (×103) N/m

The objective of this work is to study the minimum fluidization velocity and bed expansion of three-phase expanded beds containing commercial catalysts of cylindrical shape fluidized by oil fractions. The experimental results are compared with the predictions of different available correlations and phenomenological models. Experimental Section A schematic diagram of the experimental set-up is shown in Figure 1. A cylindrical glass column of 0.1 m internal diameter and 1.4 m height was used. The column is made up of three sections, namely, the gas-liquid distributor section, the test section, and the gas-liquid disengagement section. A perforated plate was used as the distributor. The height of bed expansion was determined from the axial pressure profiles as the position where there is an abrupt change in the slope of the axial pressure profile.9 For this purpose, pressure tappings were fitted along the column at every 7.5 cm interval, with the first one located 10 cm above the distributor. The bed expansion was related to the bed porosity through the following equation:

WS S ) 1 -  ) FSACSH

physical properties

(1)

The minimum fluidization velocity was determined from pressure drop versus liquid velocity relationship. For these measurements, the superficial liquid velocity was decreased step-by-step from an initial fluidized state to zero while maintaining the gas velocity constant. Fresh and equilibrium hydrocracking catalysts were used in the experiments, which consist of nickel and molybdenum oxide on an extruded porous alumina support. The physical properties of the catalysts are shown in Table 1. The equivalent diameter and sphericity were calculated based on the definitions of Song et al.3 The particle dry density and pore volume were determined according to standard procedures (9) Lee, D. H.; Macchi, A.; Epstein, N.; Grace, J. R. Transition Velocities and Phase Holdups at Minimum Fluidization in GasLiquid-Solid Systems. Can. J. Chem. Eng. 2001, 79, 579-583.

water

diesel fuel

jet fuel

997 1.00 72.8

834 4.45 30

798 1.51 26

(ASTM C128-01).10 The particle density saturated with a given liquid is calculated from the particle dry density, pore volume, and liquid density. The gas-liquid flow is co-current and upward. The liquids used were water, diesel fuel, and jet fuel, for which the physical properties are given in Table 2. Air and nitrogen at atmospheric pressure and room temperature were used as the gas phase. Gas and liquid flow rates were measured by rotameters, with UG varying from 0 to 24.3 mm/s and UL from 0 to 22 mm/s. In order for the experimental results to be independent of the column size, the bed diameter should be large enough so as to minimize wall effects. This can be achieved in systems where the average particle and bubble diameters are both much smaller than the bed diameter.11 In the present work, the systems with petroleum distillates were expected to operate predominantly in the disperse bubble regime, which is characterized by the presence of small bubbles with relatively uniform size distribution. Furthermore, for the larger particles used, the column diameter was more than 20 times larger than the particle length, thus minimizing wall effects.12,13

Results and Discussion Minimum Fluidization Velocity. The minimum liquid fluidization velocity at fixed UG, defined as the point at which the particles settle to form a fixed bed, as observed both visually and by the sharp break in the plot of pressure gradient versus UL, was measured by decreasing the superficial liquid velocity.9 Figure 2 shows the variation of the minimum fluidization velocity with superficial gas velocity. For the systems considered, (10) ASTM Test Method C128-01: Standard Test Method for Density, Relative Density (Specific Gravity), and Absorption of Fine Aggregate, 2001. (11) Safoniuk, M.; Grace, J. R.; Hackman, L.; McKnight, C. A. Use of Dimensional Similitude for Scale-Up of Hydrodynamics in ThreePhase Fluidized Beds. Chem. Eng. Sci. 1999, 54, 4961-4966. (12) Macchi, A.; Bi, H.; Grace, J. R.; McKnight, C. A.; Hackman, L. Dimensional Hydrodynamic Similitude in Three-Phase Fluidized Beds. Chem. Eng. Sci. 2001, 56, 6039-6045. (13) McKnight, C. A.; Hackman, L.; Grace, J. R.; Macchi, A.; Kiel, D.; Tyler, J. Fluid Dynamic Studies in Support of an Industrial ThreePhase Fluidized Bed Hydroprocessor. Can. J. Chem. Eng. 2003, 81, 338-350.

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Energy & Fuels, Vol. 18, No. 4, 2004 1151

Table 3. Empirical Correlations for Minimum Liquid Fluidization Velocity references al.15

Ermakova et Bloxom et al.2323 Begovich & Watson1 Begovich & Watson1 Fortin2424 Costa et al.2 Song et al.3 Nacef2525 Larachi et al.5 Larachi et al.5

correlations

equation

ULmf ) U°Lmf(1 - 0.5UG - mfβGmf) ULmf ) 5.359 × 10-17UG-0.14µL-0.497dc-0.423FS3.75 ReLmf ) 0.00512ArL0.662FrG-0.118 ULmf ) U°Lmf(1 - 1.62 × 103UG0.436µL0.227dv0.598(FS - FL)-0.305) ULmf ) 0.427UG-0.198dv1.539(FS - FL)0.775 ULmf ) 6.969 × 10-4UG-0.328µL-0.355(φdv)1.086dc0.042(FS - FL)0.865 ULmf ) U°Lmf(1 - 376UG0.327µL0.227dv0.213(FS - FL)-0.423) ln(ULmf) ) ln(U°Lmf) - 13.8FrG0.35(FS - FL)-0.38 neural network ULmf ) f(UG;µL;φ;dv;FS - FL;σL;dv/dc) neural network ReLmf ) f(ReG;ArL;φdv/dc;MoL)

(2) (3) (4a) (4b) (5) (6) (7) (8) (9a) (9b)

0.075

Table 4. Statistics for the Correlations in Table 3 and Models in Table 5 to Predict ULmf for the Present Data air-water-catalyst system references

AARE (%)

σ (%)

nitrogen-diesel fuelcatalyst systems AARE (%)

nitrogen-jet fuelcatalyst system

total data

σ (%)

AARE (%)

σ (%)

AARE (%)

σ (%)

Ermakova et al.15 Bloxom et al.23 Begovich & Watson1 (a) Begovich & Watson1 (b) Fortin24 Costa et al.2 Song et al.3 Nacef25 Larachi et al.5 (b) equation 13

36 49 33 8 13 32 15 11 22

Empirical Correlations 8 35 21 138 14 27 6 37 14 152 20 49 11 24 8 32 15 28

18 115 24 32 82 52 21 33 17

10 201 5 79 57 35 54 65 11

6 79 6 24 12 12 18 16 11

29 131 23 40 91 41 30 35 23 19

17 103 21 36 83 38 23 31 16 13

Costa et al.2 Song et al.3) Song et al. modified by Zhang et al.4 Zhang et al.4

39 19 9 49

Phenomenological Models 18 81 11 49 6 79 13 76

29 43 45 8

48 6 17 43

32 4 13 7

61 28 44 60

32 34 46 18

regardless of the liquid used, ULmf decreased with an increase in UG, as reported by other researchers.1,3,9,14 It seems that the presence of gas reduces the liquid holdup and hence increases the interstitial liquid velocity. This in turn increases the drag exerted on the particles which leads to earlier fluidization. It is also evident from Figure 2 that the three-phase system with diesel fuel as the liquid phase has lower minimum fluidization velocities than the corresponding one with water. This difference can be attributed to both the nature of the fluids and properties such as the viscosity and density of the liquid and the density of the particle saturated with the liquid. According to the empirical eq (a) of Begovich and Watson,1 the ratio of minimum fluidization velocities for these two systems, (ULmf)water/(ULmf)diesel, was calculated to be 2.1, which is relatively similar to the approximately 2.0 obtained experimentally, in contrast to other values such as the 1.6 predicted by the correlation of Costa et al.,2 for instance. Several empirical correlations are reported in the literature for predicting ULmf, and some of the most often cited are presented in Table 3.5 Most of these correlations have been derived from data obtained from experiments based on water or aqueous solutions, and where the solid particles used are often glass beads. For the purpose of evaluating their prediction ability for systems where the liquid phase is an oil fraction and the solid particles are catalyst extrudates, the experimental minimum fluidization velocities have been compared

with the predicted values from each of the correlations in Table 3. The experimental value of the minimum fluidization velocity of the liquid-solid system, U°Lmf, was used for calculations in the correlations that refer to this parameter. The average absolute relative error (AARE) has been calculated for each of the gas-liquidsolid systems mentioned in Figure 2 and are presented in Table 4. It can be seen that in general terms the error for almost all correlations was found to be smaller for the system fluidized with water as the liquid phase than with diesel fuel. This is probably not surprising since, as was mentioned above, most of them were derived from experiments where water or water-based solutions were utilized. Several correlations have relatively small errors in predicting ULmf for the air-water-catalyst system; however, eq (b) of Begovich and Watson1 presented in Table 3 showed the smallest AARE as well as the smallest error dispersion as given by the standard deviation. The smallest obtained average absolute relative errors for the predictions of the gas-diesel fuelcatalyst systems were slightly below 29% as they were for the correlation of Song et al.,3 the dimensionless version (eq (b)) of Larachi et al.5 and eq (a) of Begovich and Watson.1 For the gas-jet fuel-catalyst systems the best predictions were from eqs (a) of Begovich and Watson,1 Ermakova et al.,15 and the dimensionless equation of Larachi and co-workers,5 for which the AARE were 5, 10, and 11%, respectively. For all the experimental data of the present work the most favorable predictions are provided by eq (a) of Begovich and

(14) Briens, L. A.; Briens, C. L.; Margaritis, A.; Hay, J. Minimum Liquid Fluidization Velocity in Gas-Liquid-Solid Fluidized Beds. AIChE J. 1997, 43, 1180-1189.

(15) Ermakova, A.; Ziganshin, G. K.; Slin′ko, M. G. Hydrodynamics of a Gas-Liquid Reactor with a Fluidized Bed of Solid Matter. Theor. Found. Chem. Eng. 1970, 4, 84-89.

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Table 5. Phenomenological Models for Minimum Liquid Fluidization Velocity

Watson1 and by the dimensionless equation of Larachi et al.5 The average errors of these two correlations were within the 29% reported by Larachi et al.5 for their ReLmf dimensionless correlation. There are also available in the literature semitheoretical phenomenological models for the prediction of the onset of fluidization in three-phase fluidized beds (Table 5). Accordingly, Costa el al.2 derived a “homogeneous drift-flux” model by applying the drift-flux approach of Wallis16 and the multi-particle drag equation of Wen and Yu,17 modified for the presence of gas, to describe fluid-particle interaction. Song et al.3 derived

a model based on the separate flow approach of Chern et al.18 to derive an equivalent diameter to be used in the Ergun equation expressing the liquid-solids interaction. Zhang et al.4 proposed a correction to the equation of Song et al.3 for calculating the equivalent diameter utilized in this model. Zhang et al.4 also (16) Wallis, G. B. One-Dimensional Two-Phase Flow; McGrawHill: New York, 1969. (17) Wen, C. Y.; Yu, Y. H. Mechanics of Fluidization. Chem. Eng. Prog. Symp. Ser. 1966, 62, 100-112. (18) Chern, S. H.; Muroyama, K.; Fan, L.-S. Hydrodynamics of Constrained Inverse Fluidization and Semifluidization in a GasLiquid-Solid System. Chem. Eng. Sci. 1983, 38, 1167-1174.

Hydrotreating Catalysts in Ebullated-Bed Systems

proposed the gas-perturbed liquid model which assumes that full support of the solids is provided by the exclusive action of the liquid, velocity of which is increased by the presence of gas. The experimental minimum fluidization velocities have been compared with the predicted values from each of these models, and the average absolute relative errors have been calculated and also presented in Table 4. As can be seen, the predictions of the model of Song et al.3 provided the best predictions among the phenomenological models for the gas-oil-catalyst systems and follow closely those of the best empirical correlations reported above. The AARE for the predictions of the other models seem to fall somewhere in the middle of the range of predictions of the empirical correlations. For non-spherical particles, the effect of their shape is being considered in correlations and models by the equivalent particle diameter, dv, or by both this variable and the particle sphericity factor, φ. The sphericity factor is present in all the phenomenological models in Table 5 but only in the correlations of Costa et al.2 and Larachi et al.5 (Table 3). The sphericity factor in the models in most cases is introduced, at least partially, via the Ergun19or the Wen and Yu17 equations. Larachi et al.5 found that the liquid Reynolds number at the onset of fluidization, ReLmf, is correlated by the scale factor, dv/dcφ. These results contrast with the experience of other researchers who have found that the equivalent particle diameter can adequately describe both particle size and shape (e.g., Song et al.3). To test if the prediction of the correlations could be improved by considering the effect of the sphericity factor, it has been incorporated into the two correlations that were found to yield the best predictions after those of the aforementioned of Larachi and co-workers,5 i.e., eq (a) of Begovich and Watson1 and that of Ermakova et al.15 The equation of Ermakova et al.15 modified by φ yields:

ULmf ) U°Lmf(1 - 0.5U0.075 - mfβGmf)φ-0.93 (13) G As it is evident from Table 4, eq 13 permits a significantly better reproduction of the experimental data with a reduction in the AARE values from 29 to 19%. The corresponding results obtained with the equation of Begovich and Watson1 were found to only reduce the AARE values from 23 to 21%. From the above comparison it seems that the equations available tend to predict a wide spectra of values for ULmf; however, eq 13, eq (a) of Begovich and Watson,1 and the dimensionless correlation of Larachi et al.5 were found to predict the liquid minimum fluidization velocities with the smallest errors, altogether for the water and the oil fractions systems with catalyst extrudates. Bed Expansion. The variations of bed expansion, H/Ho, with superficial gas velocity for the gas-waterfresh catalyst and gas-diesel fuel-fresh catalyst systems are shown in Figures 3 and 4, respectively. As is evident from Figure 3, the system that uses water as the liquid phase shows a contraction tendency of the bed with the presence of the gas phase. This result has been reported for systems in the coalesced bubble flow regime where bubbles entrain part of the liquid. This (19) Ergun, S. Fluid Flow Through Packed Column. Chem. Eng. Prog. 1952, 48, 89-94.

Energy & Fuels, Vol. 18, No. 4, 2004 1153

Figure 3. Effect of gas velocity on bed expansion for the airwater-fresh catalyst system.

Figure 4. Effect of gas velocity on bed expansion for the nitrogen-diesel fuel-fresh catalyst system.

reduction in the interstitial liquid velocity reduces the expansion in the liquid-solid region.20 The bed expansion characteristics of the system fluidized with diesel fuel, contrary to that observed with water, were of expansion with gas velocity. It was visually observed that diesel fuel is a liquid that tends to foam and to form smaller bubbles than in the system with water. Similar expansion behavior has been reported for other foaming systems such as those with kerosene, and it has been attributed to their coalescence inhibition characteristics.21 Comparison of the magnitude of the bed expansion of the water and diesel systems (Figures 3 and 4) shows a higher expansion level in the latter under similar gas and liquid superficial velocities. The smaller bubbles present in the diesel fuel system and its higher viscosity are among the main reasons that explain the differences in bed expansion. There are several empirical correlations for estimation of bed porosity that can be used for calculating bed height. The use of these correlations for predicting bed expansions of ebullated bed reactors is somewhat uncertain since most of them have been derived from data from systems based on water or aqueous solutions and on spherical particles. Larachi et al.8 have evaluated the most referred-to correlations in the literature and (20) Epstein, N. Three-Phase Fluidization: Some Knowledge Gaps. Can. J. Chem. Eng. 1981, 59, 649-657. (21) Fan, L. S. Gas-Liquid-Solid Fluidization Engineering, Butterworth Series in Chemical Engineering; Butterworth: Stoneham, MA, 1989.

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Table 6. Porosity Correlations for Three-Phase Fluidized Beds references

correlations

equation

3.93µL0.055UL0.271UG0.041(FS - FL)-0.316dp-0.268dc-0.033 (2.5 + 13.2µL0.64)UL0.271UG0.041(FS - FL)-0.316dp-0.268dc-0.033 3.93φ-0.424µL0.055UL0.271UG0.041(FS - FL)-0.316dp-0.268dc-0.033

) ) ) neural network  ) f(FrL;ReLG;StLG;βL;Eo¨ ;F)

Watson1

Begovich & Grandjean et al.22 Song et al.3 Larachi et al.8

(14) (15) (16) (17)

Table 7. Performance of Literature and Present Correlations To Predict Bed Expansion Fresh catalyst-water system

references Begovich and Watson1 Grandjean et al.22 Song et al.3 Larachi et al.8 equation 18

no. of data

AARE (%)

σ (%)

34 34 34 38

13.2 11.8 31.1 11.6

5.4 5.4 6.3 4.2

Fresh catalystdiesel fuel system no. of AARE data (%) σ (%) 70 70 70 70

28.3 28.1 64.3 31.1

have proposed a correlation that improves predictions over the whole range of operating conditions of data reported in the literature. Since this correlation was fitted over such a broad range of data, the question remains as to how good its predictions can be for particular systems as are those for hydrotreating reactors. For comparison purposes, four correlations have been considered (see Table 6) and contrasted with the experimental bed expansion data of the present work. Besides the correlation proposed by Larachi et al.,8 one of the correlations considered is that proposed by Begovich and Watson,1 which despite its limitations at low gas velocities, has been recommended in the literature since it is based on a large number of data obtained with varying solid and liquid physical properties.21 The other two correlations considered are those of Song et al.3 and Grandjean et al.22 These correlations are based on the Begovich-Watson equation, and incorporate, in the case of Song and co-workers,3 the effect of the sphericity factor for cylindrical particles, while Grandjean et al.22 suggested a different dependence on liquid viscosity. The predictions of porosity obtained with the correlations have been converted to expanded bed height with eq 1. The results of the comparison between the experimental data and the predictions are presented in Table 7 in terms of the AARE. For the case of fresh catalyst systems it is clear that the AARE values for water are nearly half of those for diesel fuel. Given the origin of the correlations considered, it is somewhat understandable that they are more suitable for systems with waterlike liquids. For the systems with water, the correlations of Begovich-Watson,1 Grandjean et al.,22 and Larachi et al.5,8 all have very similar AARE values as well as dispersion values expressed in terms of the standard deviation. Comparatively, much larger errors were found for the expression of Song et al.3 due to the consistently higher bed porosities predicted than those observed experimentally in the present work. (22) Grandjean, B. P. A.; Carreau, P. J.; Nikov, I.; Paris, J. Viscosity Effects in Cocurrent Three-Phase Fluidization. AIChE J. 1990, 36, 1613-1616. (23) Bloxom, V. R.; Costa, J. M.; Herranz, J.; MaxWilliam, G. L.; Roth, S. R. Determination and Correlation of Hydrodynamic Variables in a Three-Phase Fluidized Bed. MIT Report N219; Oak Ridge National Laboratory: Oak Ridge, TN, 1975. (24) Fortin, Y. Re´acteurs a` Lit Fluidise´ Triphasique: Caracte´ristiques Hydrodynamiques et Me´lange des Particules Solides. Ph.D. Thesis, Institut National Polytechnique de Lorraine, Lorraine, France, 1984.

9.6 9.5 23.9 6.7

Equilibrium catalyst- Equilibrium catalyst- Diesel and jet fuels diesel fuel system jet fuel system data no. of data

AARE (%)

σ (%)

no of data

AARE (%)

σ (%)

70 70 70 70

5 4.7 15.3 19.3

3.8 3.6 8.8 6.2

62 62 62 62

7.1 8.0 7.2 31.1

6.5 6.1 6.0 9.9

no. of AARE data (%)

σ (%)

202 202 202 202 202

12.9 12.6 30.0 9.3 3.6

12.8 12.9 29.2 27.7 6.1

Figure 5. Comparison of bed expansion data for the nitrogendiesel fuel-fresh catalyst with predicted values.

Figure 6. Comparison of bed expansion data for the nitrogendiesel fuel-equilibrium catalyst with predicted values.

The bed expansion data for the nitrogen-diesel-fresh catalyst system have been compared in Figure 5 with the predictions of the considered correlations. The equivalent plot for the system with equilibrium catalyst is presented in Figure 6. It is clear that the goodness of the predictions of all the correlations was improved in (25) Nacef, S. Hydrodynamique des Lits Fluidise´s Gaz-LiquideSolide. Effets du Distributeur et de la Nature du Liquide. Ph.D. Thesis, Institut National Polytechnique de Lorraine, Lorraine, France, 1991.

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Energy & Fuels, Vol. 18, No. 4, 2004 1155

The bed expansion characteristics of the gas-waterfresh catalyst system were found to be different from those fluidized with diesel fuel. The bed fluidized with water showed contraction with the presence of gas, while a slight bed expansion was observed with the organic liquid. For given catalyst particles, the bed porosity correlations considered showed better expansion predictions for the systems with water than with diesel fuel. The experimental data from the diesel fuel systems were found to be sensitive to the sphericity factor of the extrudated catalyst particles, and therefore a much better reproduction of the data was observed when the Begovich-Watson equation was modified to account for this parameter.

Figure 7. Comparison of bed expansion data for fresh and equilibrium catalysts with predicted values.

the case of the equilibrium catalyst with respect to the fresh catalyst system. The observed difference seems to be due to particle properties (see Table 1). Particle density (saturated with liquid) is accounted for in the correlations as well as the equivalent particle diameter; however, particle shape is probably not accounted for adequately. As a result of particle attrition in the reactor, the average particle length is reduced from 4.39 to 1.87 mm, and hence the attrited particles become more rounded in shape. The calculated sphericity values are 0.61 and 0.81 for the fresh and equilibrium catalysts, respectively. The sphericity factor (φ) has been introduced into the Begovich-Watson equation and fitted to the data with the following equation:

 ) 3.93µL0.055UL0.271UG0.041(FS FL)-0.316dp-0.268dc-0.033φ0.378 (18) In Figure 7 the predictions of eq 18 are presented together with those of the Begovich-Watson correlation for fresh and equilibrium catalysts fluidized with diesel and jet fuels as the liquid phase. It is evident from this plot that eq 18 substantially improves the agreement with experimental data. As shown in Table 7, the AARE for this correlation was found to be 6% with a standard deviation of less than 4% in the error distribution.

Acknowledgment. The authors thank Instituto Mexicano del Petro´leo for its financial support. Glossary ACS ArL dc dv Eo¨ F FrG FrL g H, Ho MoL ReLG ReLmf R ˜ eLmf StLG UG UL ULmf Ut U∞ WS

column cross-section area (m2) liquid Archimedes number, ArL ) dv3FL(FS - FL)g/ µL2 column diameter (m) equivalent diameter of sphere having the same volume as the particle (m) Eo¨ tvos group, Eo¨ ) gdp2(FS - FL)/σL wall effect ratio, F ) φdp/dv gas Froude number, FrG ) UG2/gdv liquid-phase Froude number, FrL ) UL2/gdv gravity acceleration (m/s2) expanded and static bed heights (m) liquid Morton number, MoL ) gµL4/FLσL3 composite Reynolds group, ReLG ) (UL + UG)FLdv/ µL liquid Reynolds number at minimum three-phase fluidization ReLmf ) ULmfdvFL/µL liquid Reynolds number based on linear velocity, R ˜ eLmf ) (FLULmfdv/(1 - βGmf)mfUL) composite Stocks group, StLG ) (UL + UG)µL/gFLdv2 gas superficial velocity (m/s) liquid superficial velocity (m/s) minimum fluidization velocity (m/s) transport velocity (m/s) particle terminal velocity in liquid (m/s) catalyst loading (kg)

Greek Letters

Conclusions Minimum fluidization velocities of commercial catalyst extrudates have been measured using water, diesel, and jet fuels as the liquid phase. It has been found that ULmf decreases with the presence of the gas phase in both systems. In general terms, the prediction error of available empirical correlations were mostly found to be comparatively smaller in the gas-water-catalyst systems than in those where the organic liquid was used. The dimensionless correlation of Larachi et al.,5 eq (a) of Begovich and Watson,1 and a modified version of the correlation of Ermakova et al.15 that accounts for particle sphericity were found to yield the smallest errors altogether for the water and the oil fractions systems. For the phenomenological models tested, that of Song et al.3 produced the smallest errors; however, these were generally higher than those for the better empirical correlations.

βG βL  mf φ µ F σL

gas void fraction per unit porous volume liquid-phase velocity ratio, βL ) UL/U∞ bed porosity of fixed bed bed porosity at minimum fluidization sphericity factor dynamic viscosity (Pa s) density (kg/m3) liquid surface tension (N/m)

Subscripts G L mf S

gas liquid at minimum liquid-solid or three-phase fluidization (m/s) solid

Superscripts °

no gas flow

EF030184D