TRICKLE BED WETTING FACTORS FROM PRESSURE DROP AND LIQUID HOLDUP MEASUREMENTS

Chem.Eng.Comm., 189: 1653 1670, 2002 Copyright # 2002 Taylor & Francis 0098-6445/02 $12.00 +.00 DOI: 10.1080/00986440290013022 TRICKLE BED WETTING FACTORS FROM PRESSURE DROP AND LIQUID HOLDUP MEASUREMENTS YANINA LUCIANI DOSINDA GONZA LEZ-MENDIZABAL Departamento determodina mica y Feno menos de Transferencia, Universidad Simo n Bol var, Sartenejas, Caracas,Venezuela FILIPPO PIRONTI Inelectra S.A., Edif. Oficentro, San Luis, Caracas,Venezuela In this work, solid-liquid wetting factors were determined from liquid holdup and pressure drop measurements according to the model proposed by Pironti et al. for different air-liquid systems: distilled water and CMC solutions at viscosity values of 3, 6, 9, and 12 mpa. s. The experiments were carried out at atmospheric conditions in a column of 10.2 cm internal diameter and 2 m high, packed with a cylindrical material. The superficial mass velocities varied from 0.67 to 18.6 kg=m 2 s for liquid flow and from 0.024 to 0.31 kg/m 2 s for gas flow. Under these operating conditions, regime of continuous gas flow was observed. The wetting factors obtained were in agreement with those reported by other methods, which allow us to confirm that the model used in this work is applicable to fluids of different properties at low gas velocities. Keywords: Wetting factor; Wetting efficiency; Trickle bed reactor; Pressure drop; Liquid holdup; Shear stress Received 3August 2000; in final form 30 May 2001. Address correspondence to Dosinda Gonzalez-Mendizabal, Departamento de Termodinamica y Fenomenos de Transferencia, Universidad Simon Bol var, Sartenejas, Apartado Postal 89000, Caracas 1080-A, Venezuela. E-mail: dosinda@usb.ve 1653

1654 Y. LUCIANI ET AL. INTRODUCTION A trickle bed reactor (TBR) is a system in which two phases, one liquid and the other gas, flow in a descending and concurrent way through a fixed packed bed, usually filled with catalysts or reactant solids. These reactors are extremely important, judging by the tons of material that are annually processed through them. They are widely used in the oil industry in hydrodesulfuration processes, residual oil hydrocracking, lubricating oils hydrotreatment, demetallization, etc. They are also frequently used in chemical processes such as the hydrogenation of glucose to sorbitol and treatments for the control of water and air pollution through bacteriological processes, in addition to also being used in biological, agricultural, and pharmaceutical processes. Different flow regimes can be found in these reactors depending on the physical properties of the fluids involved (density, viscosity, surface tension), the characteristics of the packed bed (porosity, size and shape of the particles), and the dimensions of the reactor and the superficial mass velocities of both phases. The design and scaleup parameters are affected in a different manner in each flow regime as the hydrodynamics change from one to the other. In the low interaction regime the gas has practically no effect on the fluidodynamic behavior of the fluid; however, the problem of incomplete wetting of the solid surface presents itself due to the low velocities of the liquid being used. In porous particles, the wet area or solid-liquid contact surface can be external or internal. However, it has been shown that even at very low liquid velocities, in the order of 0.05 cm=s, the internal wetting of the porous particles is total, probably by the capillary phenomenon (Colombo et al., 1976; Al-Dahhan and Dudukovic, 1995; Llano et al., 1997). Schwartz et al. (1976) reported that the internal wetting factor is constant and equal to 0.92. For this reason, the internal wetting fraction can be taken as 1 for practical effect. However, this assumption is not always valid when the reactions are strongly exothermic (Mills and Dudukovic, 1993). In contrast, the efficiency or external wetting factor f increases with the liquid and gas speeds, and equals 1 only at high liquid velocity. The knowledge of this factor is essential for the design and scaling of the reactors, since it allows the calculation of the utilization degree. From the literature data f has been obtained either with a chemical method comparison of reaction rates in a two-phase operation and in a reactor completely filled with the liquid or with physical techniques. The physical tracer method is based on the analysis of the reactor behavior after a step change perturbation in the tracer concentration is carried out at the entrance, obtaining as a result a kinetic constant or an apparent interparticle diffusivity. It has been shown that the wetting factor is proportional to the ratio of these apparent values with those

TRICKLE BED WETTING FACTORS 1655 Table I Wetting Efficiency Models Satterfield (1975), Scwhartz et al. f ¼ ðk AÞ apparent (1) ðk A Þ liquid full bed (1976) Colombo et al. (1976) f ¼ ðdeffþ 2 phase (2) ðdeffþ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi liquid filled ðdeffþ Dudukov c (1977), Mills and f ¼ 2 phase ðdeffþ liquid filled Dudukov c (1981), Al-Dahhan and (3) Dudukov c (1995, 1996) Lakota and Levec (1990), f ¼ ðk S a LS Þ 2 phase ðk S aþ liquid filled Gonzalez-Mendizabal et al. At the same v L (4) (1998) Pironti et al. (1999) f ¼ ðt LS a LS Þ 2 phase ðt LS aþ liquid full bed At the same v L and v G (5) obtained in experiments when the particles are totally wetted. Models widely used in the literature for wetting efficiency are summarized in Table I. The external fraction of wetted area f has been correlated basically as a function of dimensionless numbers that include physical properties and operative parameters. Some of the oldest expressions are the ones reported by Onda et al. (1967) and Puranik and Vogelpohl (1974). A brief summary of proposed correlations to estimate wetting efficiencies in TBR is included in Table II. It should be noted that Equation (11) leads asymptotically to physically bounded values of wetting factor approaching unity. In effect, substituting Equations (12) and (13) into Equation (11) and simplifying yields: f ¼ e L e B þ DP 2 phase DP gas filled Lgðr L r G Þ 1 þ DP liquid full bed DP gas filled Lgðr L r G Þ ð16þ e L =e B is lower or equal to one, since the liquid holdup is always less than void fraction; it will be one if no gas is present. On the other hand, twophase pressure drop is also lower than liquid full-bed pressure drop under the assumption that pressure drop is due only to frictional losses. So according to Equation (16), f is bounded to a maximum value of one, excluding of course experimental errors that may lead to inaccuracies on determined variables. If two-phase pressure drop increases in lieu of a large gas velocity or a high pressure (gas density), both liquid holdup and liquid thickness will decrease and induce liquid separation from solid surface. Under these circumstances nonfrictional losses will become

Table II Wetting Efficiency Models and Correlations 2! 0:0615 Mills and Dudukovic (1981) f ¼ tgh 0:664 r 0:333 LvLdp m 0:195 4 L L L g r L v 2 L p sa e 2 B 5 (6) 2 0:171 ad 2 v 2 a Re 0 0:1461 Ga 0 0:0711 or f ¼ ð bld Þ 0:224 (7) El-Hisnawi et al. (1982) f ¼ 1:617 L 3 Alicilar et al. (1994) f ¼ 1 25:626 Re 0 0:96 35 < Re 0 L < 180 (8) L 1=9 Al-Dahhan and Dudukovic (1995) f ¼ 1:104Re 1=3 1 þ½ðdp=lþ=r L gš (9) L Gonzalez-Mendizabal et al. (1998) f ¼ 1 exp 4:265 10 2 Re 0:745 L Re 0:079 G 6:71 ReL 117:90 and 32:00 ReG 204:19 (10) GaL Pironti et al. (1999) f ¼ g ½ r LeL þ r G ðeb elþ ŠþeB DP2 phase L ðtgs aþ gas filled (11) ðtls aþ liquid filled bed ðtgs aþ gas filled ðtls aþ liquid full bed ¼ e BðDPÞ liquid full bed L þ ebr L g (12) Double-Slit Model, Iliuta et al. (2000) ðtgs aþ gas filled ¼ e BðDPÞ gas filled L þ ebr G g (13) Ga L f ¼ f2 2E1 8 < þ : 2 el CL 1 þ r G fs eb r L ReL " f 2 2 el CL 1 þ r # G Ga 2 L fs 2E1 eb r O L ReL O ¼ f2 E1 2 el e B CL 1 þ r G GaL rl ReL fs þ 2f2 3E1 9 1=2 = (14) ; 3 el Ga L e B CL (15) ReL 1656

TRICKLE BED WETTING FACTORS 1657 predominant, and this model is not applicable since wetting factors greater than one will be obtained. Recently, Iliuta and Larachi (1999) proposed a generalized slit model for the prediction of frictional two-phase pressure drop, external liquid holdup, gas-liquid interfacial area, and wetting efficiencies in TBR. The wetting factor may be calculated from the relationship in Equation (14), shown in Table II, knowing the velocities and properties of each fluid, Ergun s constants (E 1,E 2 ), and the shear and velocity slip factors (Iliuta et al., 2000). The applicability of the empirical correlations that have been developed to determine the degree of wetting of the packing as a function of the liquid and gas velocities, the physical and chemical properties of the liquid, and the size of the packing is questionable, as it requires the performance of experiments under conditions corresponding to such operations (Satterfield, 1975). In this work the solid-liquid wetting factor was experimentally determined using the model proposed by Pironti et al. (1999). This model was validated with experimental data reported by Al-Dahhan and Dudukovic (1994) and data obtained by same authors for the air-water system. The main objective of this work is to determine if the model applies to different air-newtonian liquid systems. EXPERIMENTAL The experimental facility, bench scale, used to measure pressure drops and liquid holdup for both single-phase and trickle-bed operation is shown in Figure 1. This facility consists of a trickle-bed reactor setup, the gas and liquid delivery systems, and data acquisition system. The reactor was made of a 10.16 cm internal diameter and 2 m high carbon steel tube with four 0.635 cm pressure taps, each one separated 0.6 m. The column has a thick optically clear acrylic window to observe the behavior of the two-phase flow near the wall surface. The gas-liquid distributor designed is similar to the one used by Herskowitz and Mosseri (1983) to ensure uniform liquid and gas distribution at the bed inlet. The liquid phase from its storage in a 200 L reservoir was pumped through a rotameter up to the top of the column. The flow was regulated manually by needle valves. Distilled water and four aqueous solutions of CMC in different concentrations were used as liquid substances. In order to characterize the substances being used, the densities of the fluids were measured utilizing pycnometers, a Brookfield viscosimeter to measure the viscosities, and the pendant drop method (Lopez de Ramos et al., 1993) to measure the surface tension. These properties are summarized in Table III. The steady shear stress-rate data obtained for the aqueous solutions of CMC was shown to be linear, so Newtonian behavior was assumed to prevail for the range used in this work. Additionally, during

1658 Y. LUCIANI ET AL. Figure 1. Schematic diagram of the experimental setup. B1: pump; D: distributor; PT: pressure transducer; R: reactor; R1, R2, R3, R4: rotameters; S1, S2: solenoid valves; St: terminal section; V1 to V9: valves. the course of experiments, periodical measurements of rheological properties were done to ensure that no mechanical degradations of CMC aqueous solutions may have occurred. Compressed air, regulated to a fixed pressure of 515 kpa, was driven through gas rotameters and introduced to the top of the column at a given flow manually fixed by a needle valve. For all the experimental runs, the liquid and gas phases were at ambient conditions (25 C and atmospheric pressure). The column is packed with cylindrical extruded catalyst material with 3.19 mm mean diameter and 5.33 mm mean height. The characteristics of the column and bed properties are shown in Table III Characteristics of Fluids Employed Fluid Air Water CMC-3CMC-6 CMC-9 CMC-12 Density (kg=m 3 ) 1.184 997 1001.31002.2 1002.3 1002.4 Viscosity (mpa.s) 0.0182 1 36 9 12 Surface tension (mn=m) 70.8 55.8 54.9 53.3 53.0

TRICKLE BED WETTING FACTORS 1659 Table IV Characteristics of Solids and Column Column diameter 10.16 cm Column volume 16.86 L Void fraction of the bed (e B ) 0.41±0.01 Static holdup (e LS ) 0.036±0.001 Mean equivalent diameter of the particles 3.68±0.01 mm Table IV. The column to particle diameter ratio is about 26, enough to avoid channeling and to ensure a uniform distribution of liquid through the packing (Al-Dahhan and Dudukovic, 1996). On the top and at the bottom of the column there are two solenoid valves connected to a switch that suddenly and simultaneously interrupts the entrance and the exit of fluids to the column and thus allows the measurement of external liquid holdup. The exit valve of the column is opened, allowing the liquid to drain for at least 30 min. After that the liquid collected is weighted. Then the dynamic liquid holdup is calculated by: e Ld ¼ W L r L V ð17þ Pressure drops across the particle bed were measured with pressure transducers connected to the top and bottom of the reactor bed. Then the signal was recorded by a data acquisition system. For each gas and liquid flow rate, a minimum of 20 min was allowed for the pressure drop and liquid holdup measurements to ensure the data reflected true steady state (Holub et al., 1993). The mass flux range adopted in this work varied from 0.67 to 18.6 kg=m 2 s for liquid flow and varied from 0.024 to 0.31 kg/ m 2 s for gas flow. Under these operating conditions, visual observation through the acrylic window indicated the existence of continuous gas flow regime in the column. This was corroborated by stable and steady pressure drop measurements. To determine the wetting factor, according to the model employed in this work (Equations (11) (13), Table II), single-phase pressure drops are needed as well for different gas and liquid flows under two-phase flow, and liquid holdup for two-phase runs. To predict pressure drop when only one-phase experiments are carried out through the column, Ergun s equation can be used (Ergun, 1952). The Ergun constants E1 and E2 were determined for the packed bed using only gas flow on dry packing. The values obtained were E 1 ¼ 150 and E 2 ¼ 1.8 (Pironti et al., 1999). Previous to each two-phase flow experiment the packing bed was extensively prewetted by flooding the bed, then the exit valve of the

1660 Y. LUCIANI ET AL. column was opened, allowing the liquid to drain. This procedure assured a uniform liquid-gas distribution and prevented hysteresis effects in measured pressure drop. RESULTS AND DISCUSSION A total of 125 experimental tests were performed with varying flow rates of both phases. For each fixed liquid flow rate, different air Reynolds numbers were operated: 34, 52, 71, 89, and 107. In Figure 2, the effect of the liquid phase properties over the dynamic retention of a liquid for a constant gas velocity (Re G ¼ 34 and 107) is shown. It is clearly observed that the holdup increases at a higher viscosity and at a lower surface tension. This behavior coincides with that reported by Ellman et al. (1990). Wammnes et al. (1990) indicated that surface tension of the liquid has no drastic influence on the dynamic holdup unless the working system is of the foaming type. For this reason, in this work we can attribute the augmentation of the holdup, in a larger degree, to the increase of the viscosity in the CMC solutions, and not to the decrease of the surface tension of the solutions. Iliuta et al. (1996) found that dynamic liquid holdup increased with increasing CMC concentration, as a result of larger liquid phase stresses in the gas-liquid and solid-liquid interphases. Basically, all correlations reported in the literature for the calculation of the dynamic liquid holdup show a direct power dependency upon liquid superficial velocity or liquid Reynolds number, with an exponent according to the movement of the liquid through the bed (laminar film, turbulent films, or spray) and the particle texture. Generally the values of this exponent oscillate between 1/3for laminar films and 0.5 0.6 for turbulent films (Wammes et al., 1990). However, contradictory results have been found, for instance, Goto and Smith (1975) reported a 1/3power for lower liquid Reynolds numbers, while Kohler and Richarz (1984) related the liquid dynamic holdup, e Ld, with a 0.53power for very low Re L (0.1 5). In this work, the exponents obtained for all the liquids used are around 0.3, which is an indication that the flow regime is laminar film, where the energy loss of the fluid is mainly due to the viscous effects between the liquid and the packing (Wammes et al., 1990). Regarding the effect of the gas upon the liquid holdup, Shah (1979) and Ramachandran and Chaudhari (1983) reported that at atmospheric pressure it was not considerable. Their results are in agreement with those obtained in this work. However, at high pressure, the gas flow reduces the liquid holdup notably due to the increase of the drag force in the liquid-gas interface. Figure 3shows the effect of the liquid properties on the pressure gradient throughout the packed bed for Re G ¼ 34 and 107. As was

TRICKLE BED WETTING FACTORS 1661 Figure 2. Dynamic liquid holdup vs. superficial liquid mass velocity for Re G ¼ 34 and Re G ¼ 107. expected, a larger pressure drop is produced with substances that have a higher viscosity due to the fact that the shear stresses of the liquid side increase at the gas-liquid and liquid-solid interfaces (Iliuta et al., 1996). Furthermore, it is observed in this same figure that for all liquids used, pressure drop increases with liquid and gas flow rates.

1662 Y. LUCIANI ET AL. Figure 3. Pressure drop for two-phase flow vs. superficial liquid mass velocity for Re G ¼ 34 and Re G ¼ 107. Shear stress for liquid- and gas-full bed was calculated from the Ergun equation with the constants determined by measured single-phase pressure drops. The shear stress for two-phase operation together with the liquid-full bed results for air-cmc-3are shown in Figure 4 as a function of modified liquid Reynolds numbers (Re L * ¼ Re L e B =e Ld ) for

TRICKLE BED WETTING FACTORS 1663 Figure 4. Liquid-solid shear stresses as a function of modified Reynolds number for twophase and single-phase (liquid-full bed) flow. System: air-cmc-3. several gas Reynolds numbers. The same behavior predicted by Lakota and Levec (1990), Gonzalez-Mendizabal et al. (1998), and Pironti et al. (1999) is clearly observed from this figure. As the gas and liquid flow increases, the wetting factor should come closer to unity, since the shear stress for two-phase operation is approaching the liquid-full bed values, even more if the Reynolds number is based on the intrinsic liquid velocity over the particles. The wetting factors were calculated by the model of Pironti et al. (1999), showing that the wetting efficiency increases monotonically to one with the liquid mass velocity and gas Reynolds numbers. Figure 5 shows the effect of liquid properties over the wetting factor for Re G ¼ 34 and 107. As can be observed, the wetting factor increases as the viscosity of the liquid solutions increases and the surface tension decreases. As surface tension decreases, the contact angle between the fluids and solids decreases, favoring the wetting of the packed bed. Additionally, as the viscosity increases, so does the liquid s holdup, favoring an increase in the wetting factor. However, the results do not allow the decoupling of the influences of each isolated property. In Figure 6, all wetting factor values obtained in this work are shown together with some literature data and correlation reported by Gonzalez- Mendizabal et al. (1998) for Re G ¼ 107. As can be observed, the values of f follow similar tendencies as those found in the diverse literature cited. Furthermore, when compared with the correlation proposed by El-Hisnawi et al. (1982) and the mechanistic model proposed by Al-Dahhan and Dudukovic (1995), a maximum divergence of 25% was found (Figures 7 and 8). Additionally, in Figure 9, our results are

1664 Y. LUCIANI ET AL. Figure 5. Solid-liquid wetting factors as a function of superficial liquid mass velocity for Re G ¼ 34 and Re G ¼ 107. compared with those obtained using the Double-Slit Model (Iliuta et al., 2000), and the average deviation was 35%. These results confirm that the model and experimental methodology employed in this work are adequate to calculate solid-liquid wetting factors in three-phase columns

TRICKLE BED WETTING FACTORS 1665 Figure 6. Wetting factors as a function of superficial liquid mass velocity. Comparison between data obtained and values reported in the literature. Figure 7. Parity plot of experimental wetting factors obtained in this work and values calculated from model proposed by El-Hisnawi et al. (1982).

1666 Y. LUCIANI ET AL. Figure 8. Parity plot of experimental wetting factors obtained in this work and values calculated from model proposed by Al-Dahhan and Dudukovic (1995). with a fixed packed bed in a continuous gas regime, for Newtonian liquids with different properties at low air velocities. For large gas velocities at fixed liquid rate, pressure drop increases. This increment improves liquid film spreading, making the external area wetter. However, the model proposed by Pironti et al. (1999) fails to take into account the gas-liquid turbulent stresses now present. Finally, it can be inferred from Figure 6 that the measurement method does not affect the f values, since data obtained from physical techniques were compared with values recollected through physical and chemical methods, and no striking difference was observed. This behavior is contradictory to that reported by Llano et al. (1997), who found that their wetting factor values obtained through chemical method were below those calculated through physical techniques, especially at low liquid velocities. To our knowledge, no other investigator has reported this result explicitly. In fact, other authors (i.e., Mills and Dudukovic, 1981) have used the data originating from chemical and physical techniques without distinguishing them and have even related them with the same empirical expression. Gianetto and Specchia (1992) also reported a graph comparing a large number of data regarding f obtained through both methods, concluding that there exists no evident effect of the

TRICKLE BED WETTING FACTORS 1667 Figure 9. Parity plot of experimental wetting factors obtained in this work and values calculated from model proposed by Iliuta et al. (2000). measurement technique on the results. Additionally, it was concluded that the divergence of the f values is due to the characteristics of the particles used by each researcher (form, size, wettability), and that many did not consider the effects of the gas stream. This effect could be considered if working with the modified Reynolds number instead of the traditional one, as was done during this work. CONCLUSIONS Solid-liquid wetting factors were calculated through a physical nonintrusive method, in continuous gas regime, from liquid holdup and pressure drop measurements. A direct dependency of the wetting fraction with the liquid and gas flows was verified. It was shown that wetting factor increases as the viscosity of the liquid solutions increases and the surface tension decreases; however, these two variables were not studied separately. The experimental values were contrasted against those reported in the literature, and it was found that they are within the ample band of values proposed by other authors for the same liquid and gas flows combination.

1668 Y. LUCIANI ET AL. When establishing a comparison between the values of f obtained in this work against those found in diverse literature, there was no evidence that the measurement technique (physical or chemical) could affect the results. ACKNOWLEDGMENTS The authors acknowledge financial support from Seccion de Fenomenos de Transporte, Laboratorio A, Universidad Simon Bol var. Special thanks to Javier Fuentes for his measurement of surface tension. NOTATION a effective interfacial area of particles per unit volume of bed, m 71 A column cross-section, m 2 d e average equivalent particle diameter defined as six times the volume-to-surface ratio, m d p particle diameter, m Deff intraparticle effective diffusivity E 1,E 2 Ergun constants for the single-phase flow on the packing (describes bed tortuosity and roughness) f wetting factor f s interfacial friction factor Ga Galileo number, Ga ¼ r2 gd 3 e e 3 m 2 B ð1 e B Þ 3 Ga 0 modified Galileo number, Ga ¼ r2 gd 3 e m 2 ks.a volumetric liquid-solid mass transfer coefficient without reaction, s 71 K A adsorption equilibrium constant L superficial liquid mass velocity, kg. m 72.s 71 Q volumetric flow, m 3.s 71 Re Reynolds number, Re ¼ (Q=Ae B )(r=m)d e (e B =(1 7 e B )) Re L * modified liquid Reynolds number, Re L * ¼ Re L e B =e Ld Re 0 L modified liquid Reynolds number, Re 0 L ¼ Qrde Am v superficial velocity, m. s 71 v G * intrinsic gas velocity, v G * ¼ Q G =(A (e B 7 e L )) v L * intrinsic liquid velocity, v L * ¼ Q L =(A e Ld ) V column volume, m 3 W L weight of the liquid, kg Greek letters b Ld dynamic liquid saturation (liquid volume per void volume), b Ld ¼ e Ld =e B e B packed-bed void per reactor volume (bed porosity) e L total external liquid holdup per reactor volume (e L ¼ e Ld þ e LS ) e Ld dynamic liquid holdup per reactor volume e LS static liquid holdup per reactor volume f sphericity factor m viscosity, kg. m 71.s 71 r density, kg. m 73 s liquid surface tension, N. m 71

TRICKLE BED WETTING FACTORS 1669 t shear stress, Pa DP=L pressure drop per unit of length, Pa. m 71 C L dimensionless body force on liquid phase, C L ¼ DP=L r L g C G dimensionless body force on gas phase, C G ¼ DP=L r G g Subscripts G referred to gas phase GS referred to gas-solid phases L referred to liquid phase LS referred to liquid-solid phases REFERENCES Al-Dahhan, M. and Dudukovic, M. P. (1994). Pressure drop and liquid holdup in high pressure trickle-bed reactors, Chem. Eng. Sci., 49(24B), 5681. Al-Dahhan, M. and Dudukovic, M. P. (1995). Catalyst wetting efficiency in trickle-bed reactors at high pressure, Chem. Eng. Sci., 50(15), 2377. Al-Dahhan, M. and Dudukovic, M. P. (1996). Catalyst bed dilution for improving catalyst wetting in laboratory trickle-bed reactors, AIChE J., 42(9), 2594. Alicilar, A., Bicer, A. and Murathan, A. (1994). The relation between wetting efficiency and liquid holdup in packed columns, Chem. Eng. Comm., 128, 95. Colombo, A. J., Baldi, G. and Sicardi, S. (1976). Solid-liquid contacting effectiveness in trickle bed reactors, Chem. Eng. Sci., 31, 1101. Dudukovic, M. P. (1977). Catalyst effectiveness factor and contacting efficiency in trickle-bed reactors, AIChE J., 23, 940. El-Hisnawi, A. A., Dudukovic, M. P. and Mills, P. L. (1982). Trickle-bed reactors: Dynamic tracer tests, reaction studies and modeling of reactor performance, ACS Symp. Ser., 196, 431. Ellman, M. J., Midoux, N., Wild, G., Laurent, A. and Charpentier, J. C. (1990). A new improved liquid hold-up correlation for trickle bed reactors, Chem. Eng. Sci., 45(7), 1677. Ergun, S. (1952). Fluid flow through packed columns, Chem. Eng. Prog., 48, 89. Gianetto, A. and Specchia, V. (1992). Trickle-bed reactors: State of art and perspectives, Chem. Eng. Sci., 47, 3197. Gonzalez-Mendizabal, D., Aguilera, M. E. and Pironti, F. (1998). Solid-liquid mass transfer and wetting factors in trickle bed reactors: Effect of the type of solid phase and the presence of chemical reaction, Chem. Eng. Comm., 169, 37. Goto, S. and Smith, J. M. (1975). Trickle reactor performance, AIChE J., 21, 706. Herskowitz, M. and Mosseri, S. (1983). Global rates of reaction in trickle bed reactors: Effects of gas and liquid flow rates, Ind. Chem. Fund., 22, 4. Holub, R. A., Dudukovic, M. P. and Ramachandran, P. A. (1993). Pressure drop, liquid holdup, and flow regime transition in trickle flow, AIChE J., 39(2), 302.

1670 Y. LUCIANI ET AL. Iliuta, I. and Larachi, F. (1999). The generalized slit model: Pressure gradient, liquid holdup and wetting efficiency in gas-liquid trickle flow, Chem Eng. Sci., 54, 5038. Iliuta, I., Larachi, F. and Al-Dahhan, M. H. (2000). Double-slit model for partially wetted trickle flow hydrodynamics, AIChE J., 46(3), 597. Iliuta, I., Thyrion, F. C. and Muntean, O. (1996). Hydrodynamic characteristics of two=phase flow through fixed beds: Air=newtonian and non-newtonian liquids, Chem. Eng. Sci., 51(22), 4987. Kohler, M. and Richarz, W. (1984). Untersuchungen des flussigkertsholdup in rieselbettreaktoren, Chemie-Ingr-Tech., 5, 1. Lakota, A. and Levec, J. (1990). Solid-liquid mass transfer in packed beds with concurrent downward two-phase flow, AIChE J., 36(9), 1444. Leung, P. C., Recausens, F. and Smith, J. M. (1987). Hydration of isobutene in a trickle-bed reactor: Wetting efficiency and mass transfer, AIChE J., 33, 996. Llano, J. J., Rosal, R., Sastre, H. and D ez, F. V. (1997). Determination of wetting efficiency in trickle-bed reactors by a reaction method, Ind. Eng. Chem. Res., 36(7), 2616. Lopez de Ramos, A., Redner, R. and Cerro, R. (1993). Surface tension from pendant drop, Langmuir, 9(12), 3691. Mills, P. L. and Dudukovic, M. P. (1981). Evaluation of liquid-solid contacting in trickle bed reactors by tracer methods, AIChE J., 27, 893. Erratum, AIChE J., 28(3), 526 (1982). Mills, P. L. and Dudukovic, M. P. (1993). Reactores qu micos en sistemas multifasicos, CEPET course, Caracas, Venezuela. Onda, K., Takeuchi, H. and Koyama, Y. (1967). Effect of packing material on the wetted surface area, Kagaku Kogaku, 31, 126. Pironti, F., Mizrahi, D., Acosta, A. and Gonzalez-Mendizabal, D. (1999). Liquidsolid wetting factor in trickle-bed reactors: Its determination by a physical method, Chem. Eng. Sci., 54, 3793. Puranik, S. S. and Vogelpohl, A. (1974). Effective interfacial area in irrigated columns, Chem. Eng. Sci., 29, 501. Ramachandran, P. A. and Chaudari, R. V. (1983). Three Phase Catalytic Reactors, 200, Gordon & Breach, New York. Satterfield, C. N. (1975). Trickle bed reactors, AIChE J., 21, 209. Schwartz, T. G., Wegwe, E. and Dudukovic, M. P. (1976). A new tracer method for determination of liquid-solid contacting effectiveness in trickle bed reactors, AIChE J., 22, 894. Shah, Y. T. (1979). Gas-Liquid-Solid Reactor Design, 180, McGraw-Hill, New York. Wammes, W. J. A., Mechielsen, S. J. and Westerterp, K. R. (1990). The influence of pressure on the liquid hold-up in a cocurrent gas-liquid trickle-bed reactor operating at low gas velocities, Chem. Eng. Sci., 46, 409.