Hysteresis in Trickle-Bed Reactors: A Review - American Chemical

Ind. Eng. Chem. Res. 2006, 45, 5185-5198

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REVIEWS Hysteresis in Trickle-Bed Reactors: A Review Rabindranath Maiti, Rajesh Khanna, and K. D. P. Nigam* Department of Chemical Engineering, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India

A concise review of the hysteresis in cocurrent down-flow trickle-bed reactors (TBRs) is presented. The effects of several factors on the hysteresis, such as the type of particles (porous/nonporous), the size of the particles, the operating flow ranges, and the start-up conditions (wet/dry) are described. Also, some limited information that is available about the effects of other factors, such as addition of wetting agents (surfactants) and inlet liquid distribution, are also discussed. Empirical and theoretical models developed to predict hysteresis are briefly described. Most of the studies have reported an appreciable amount of hysteresis in key hydrodynamic parameters such as pressure drop, liquid holdup, and wetting efficiency, especially with small packing material (∼1.6-3.5 mm). The hysteresis is attributed to the different degrees of wetting, which occurs because of the flowing of liquid in two different modes, such as film and rivulet. The hysteresis behavior of a packed bed with porous particles is observed to be significantly different than that of nonporous particles. These differences are linked to the dual nature of pores, i.e., the pores act both as an accelerator and brakes on the spreading drop edge over the porous surface. This pore-level concept is further enhanced by the concept of participating and nonparticipating particles to understand the different hysteretic behavior of TBRs. Few mathematical modeling efforts have been attempted to capture the trend that is observed in hysteresis behavior with nonporous particles only. Recently, an attempt has been made to understand the comprehensive hysteretic behavior of both porous and nonporous particles with the conceptual framework of hysteresis. The present review focuses the attention to enhance the further understanding of the physics of the flow of fluids through TBRs, which may be responsible for the phenomena of hysteresis, especially in porous particles. 1. Introduction A trickle-bed reactor (TBR) is a reactor in which gas and liquid flow downward cocurrently over solid packing materials. Its use is widespread in the petroleum and chemical industries.1-5 Therefore, any advances in TBR technology will thus represent substantial savings and this stimulates the continued research efforts that are aimed at improving the understanding of TBR performance. Generally, the reaction occurs between the dissolved gas- and liquid-phase reactants at the interior surface of the catalyst. The external surfaces of the catalyst happen to be partially or fully covered with liquid for maximum utilization of the catalyst, based on mass-transfer limitations with gas or liquid.6 At the macroscopic level, the existence of gas or liquid phase is wellrecognized7-11 as various flow regimes, such as trickling flow, pulsing flow, spray flow, and bubble flow (Figure 1). At the microscopic or particle level, the liquid flow textures in a bed consist of several features:12 liquid flows as films, rivulets over the particles, pendulum structures, liquid-filled channels, and liquid-filled pockets (Figure 2). The relative amounts of these features are expected to vary with factors such as the inlet distribution of gas and liquid, the size and shape of the packing, the wetting properties, the presence of inert fines, the methods of packing, the start-up procedures, the flow rates of gas and liquid, and the physical properties of the fluid. Various amounts of these features in same operating flow means the existence * To whom correspondence should be addressed. Tel.: (011) 26591020. Fax: (011) 26591020. E-mail address: [email protected].

of multiple pressure drop, liquid holdup, flow regime, wetting efficiency, flow distribution, etc. Therefore, the performance of the reactor also varies with these parameters, because these factors directly affect the wetting of the catalyst. The importance of the aforementioned parameters to the TBR performance has attracted numerous review papers by several authors for the last 15 years1,3-6,13-19 covering experimental observations and modeling of the reactors at atmospheric pressure, as well as at elevated pressure. Much attention was given by all of the authors on reviewing the various aspects of TBRs, such as pressure drop, liquid holdup, catalyst wetting efficiency, catalyst dilution with inert fines, flow regime transition, mass transfer, heat transfer, gas liquid interfacial area, inlet liquid distribution, periodic flow modulation, evaluation of reactor models (including computational fluid dynamics (CFD) modeling), and various instrumentation techniques of measurement for TBRs. However, very little attention was given to understanding the physics behind the occurrence of hysteresis. Close scrutiny of the literature revealed that many authors have reported the phenomena of hysteresis or multiplicity of hydrodynamic states in TBRs.20-36 Differences in pressure drop (up to 100%) and in liquid holdup (up to 30%) were reported to be due to hysteresis. Current design procedures are invariably based on liquid holdup in the reactor, which determines the residence time of the reactants in the liquid phase. Because the liquid holdup is dependent on the prevailing hydrodynamic state, so must the performance of the reactor. In addition, the pressure drop in one hydrodynamic state can differ from that of another by as

10.1021/ie060238h CCC: $33.50 © 2006 American Chemical Society Published on Web 06/17/2006

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Figure 1. Flow regime in trickle-bed reactors (TBRs).

Figure 2. Flow textures in TBRs.

much as 100%, so the operating costs must also be affected. Finally, the scaleup from laboratory/pilot-plant reactor data to commercial scale becomes further complicated because of the existence of hysteresis. Over the past few years, some attempts have been made to understand the physics of hysteresis phenomena in TBRs.37-40 However, the mystery, as far as the magnitude of hysteresis is concerned, still exists, with respect to porous and nonporous particles. The objective of the present review is to compile the experimental observations and conceptual development made to explain the physics, which may be responsible for the phenomena of hysteresis, especially in porous particles, and also to examine the literature data in light of the aforementioned physics. 2. Hysteresis in Trickle-Bed Reactors Many experimental observations have been reported, in regard to the presence of hysteresis in pressure drop, liquid holdup, and wetting efficiency with porous and nonporous packing

materials (Table 1). Hysteresis, i.e., the difference in pressure drop, liquid holdup, and wetting efficiency between increasing and decreasing modes of operation, have been studied by several researchers, in terms of major controlling parameters such as start-up procedures (dry/wet), cycling of gas/liquid flow, particle sizes, addition of surfactants, porous/nonporous particles, operating flow ranges, gas flow rate, column diameters, and inlet liquid distributions. In the following section, the reported experimental observations, along with the effects of the aforementioned controlling parameters on hysteresis, are discussed. 2.1. Start-Up Procedures: Dry/Wet Bed. Several researchers have performed hysteresis experiments starting with a dry bed or after wetting the bed by flowing only liquid or both gas and liquid simultaneously. In the experiments with dry-bed startup conditions, the liquid flow is introduced directly into the dry bed of particles at a low flow rate and increased to the desired flow rate, and then a gas flow is initiated.26,33,36 The liquid flow is then increased gradually step by step to a higher value and decreased in same way, collecting the steady-state value of different hydrodynamic parameters (e.g., pressure drop, liquid holdup, wetting efficiency) in each step. Under wet-bed start-up conditions, one way of wetting the bed is by flooding the bed initially by introducing a high liquid flow rate and then it is reduced to the desired flow level.20 Sometimes, the liquid is introduced at a low flow rate and allowed to fill the bed by closing the outlets to ensure complete wetting of the particles. When the liquid reaches the top of the packing, the liquid flow rate is set to the desired value by opening the outlets gradually to drain the excess liquid.33 Hysteresis data are collected either by varying the gas flow rate, keeping the liquid flow rate constant, or vice versa. The other way of wetting the bed is to flood the bed by introducing both gas and liquid simultaneously at a high flow rate until pulsing occurs, and then the bed is drained for ∼20 min. Afterward, the liquid flow is allowed to increase up to the desired flow level and the gas flow is initiated24 or the gas flow is allowed

∆P, L, η ∆P, exit liquid distribution 0. 02-0.08 0.05

0.8-8.4 0.5-0.55 3.0 1.9 3.5 6.3 γ-alumina γ-particle γ-particle R-particle

air-water, dry, P ) 1 atm

air-water, dry, wet bed, P ) 1 atm air-water, dry, wet bed, P ) 1 atm

Ravindra et al.33

Gunjal et al.36

Lazzaroni et al.25,26 Ravindra et al 33

Nominal diameter.

water, water + ethanol, dry, wet, P ) 1 atm nitrogen-water, wet, P ) 1 atm air-water, water + CMC, water + C12H25SO3Na, dry, P ) 1 atm air-water, dry, wet bed, P ) 1 atm Lutran et al.29

Studies with Porous Particles glass column, diameter/height ) 3.05 cm/50 cm, D/dp ) 10.1 column plexiglass, diameter/height ) 6.0 cm × 8.0 cm/20 cm, D/dp ) 16-55

Figure 3. Hysteresis behavior of a bed wetted in different ways (L ) 4.42 kg/(m2 s), glass beads, dp ) 2.7 mm, air-water system, D ) 7 cm). The procedures are defined as follows: Wet bed-I, wetted by flowing liquid only; Wet bed-II, wetted by flowing gas and liquid simultaneously; and Wet bed-III, data points from various hysteretic curves with varying liquid flow rates at a fixed gas flow rate for beds wetted by flowing gas and liquid simultaneously. (From Wang et al.32)

a

∆P, L 0.11-0.44

0.05

1-10 3, 6 glass beads

∆P, exit liquid distribution 1.6, 3.5, 5.7 glass beads

air-water, wet bed, P ) 1 atm Christensen et al.24

Rode et al.30 Wang et al.32

air-water, wet bed, P ) 1 atm Levec and co-workers22,23

column plexiglass, diameter/height ) 6 cm × 8 cm/20 cm, D/dp ) 16-55 column Perspex, diameter/height ) 11.4, 19.4 cm/100 cm, D/dp ) 19-65

1-10 0.02-1.0 air-water, wet bed, P ) 1 atm Kan and Greenfield20,21

G

0.5-5.5

5 2.7,4,8 glass spheres glass spheres

βL ∆P 4.0-27.1 1-22.7 0.01-0.13 0.05-0.55

3, 6 glass spheres

flow features, X-ray tomography

1-10.5 0.27-1.0 3a glass beads

∆P, L

∆P, L 0.06-25.7 0.0-0.37 3, 6 spherical glass

∆P, L 0.5, 1.0, 1.8 spherical glass

L size, dp (mm) type

Studies with Nonporous Particles acrylic column, diameter/height ) 2.5 cm/45-80 cm; D/dp ) 14-50 Plexiglas column, diameter/height ) 17.2 cm/130 cm; D/dp ) 28-57 column Plexiglas, diameter/height ) 5.1 cm × 45.7 cm/183 cm; D/dp ) 30.5 Plexiglas, diameter/height ) 6 cm × 6.03 cm/30.48 cm; D/dp ) 13-26 column Perspex, diameter/height ) 5.0 cm/130 cm, D/dp ) 10 Plexiglas, diameter/height ) 7 cm/100 cm, D/dp ) 8.5-26

bed properties system studied authors

Packing Material

Table 1. Experimental Studies on the Hysteresis in Trickle-Bed Reactors (TBRs): Studies with Nonporous and Porous Particles

Operating Range (kg/(m2 s))

parameter(s) studied

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to increase up to the desired level and then the liquid flow is initiated.22-24 Hysteresis in the pressure drop and liquid holdup are observed under both dry-bed and wet-bed start-up conditions. These data cannot be compared except for a few cases (stated below), because these were not studied under similar conditions. Wang et al.32 compared the hysteresis between different wet beds, i.e., those wetted by flowing liquid only and those wetted by flowing gas and liquid simultaneously (conditions identified as wet bed I and wet bed II in Figure 3). They observed different pressure drops in the wet beds but a very small difference in hysteresis. Ravindra et al.33 compared the hysteresis in the pressure drop between wet- and dry-bed start-up procedures under similar conditions with various sizes of particles (1.6-1.9 mm, 3.5 mm) as shown in Figures 4a and 4b and Table 2 (parts a and b). Figure 4a and Table 2a indicate that hysteresis was less pronounced under wet-bed start-up conditions for the first cycle but it was more pronounced in the subsequent cycle of operation. In the case of smaller-sized particles, hysteresis was more pronounced for the first cycle under wet-bed start-up conditions (see Figure 4b and Table 2b), compared to the dry-bed start-up procedure. 2.2. Cycling of Gas/Liquid Flow. Christensen et al.24 compared the hysteresis data (Figure 5) at constant liquid flow run (data obtained by varying the gas flow rate at constant liquid flow) with data at a constant gas flow run (data obtained by varying liquid flow rate at a constant gas flow). It was observed that hysteresis is more pronounced for the constant gas flow experiment. Similar observations were made by Rode et al.30 (Figure 6). Wang et al.32 plotted the different hysteresis data obtained at a constant gas flow rate and compared it with data obtained at constant liquid flow run, as shown in Figure 3 (identified as wet bed II and III in the figure). These figures also show that hysteresis is slightly more pronounced with the constant gas flow experiment. 2.3. Particle Sizes. Kan and Greenfield20 were the first to observe the presence of hysteresis in TBRs packed with small glass particles, and the hysteresis decreased as the particle size increased. They observed higher hysteresis for smaller-sized particles (0.5 mm), compared to larger-sized particles (1.8 mm).

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Figure 4. Hysteresis loops under dry- and wet-bed conditions (air-water system) with various packing types: (a) 3.5-mm glass beads and 3.5-mm alumina particles and (b) 1.6-mm glass beads and 1.9-mm alumina particles. G ) 0.05 kg/(m2 s), bed cross-section: 6 cm × 8 cm (from Ravindra et al.33). The label “1,2,3-i” indicates increasing operating mode in the first, second, and third cycle, and the label “1,2,3-d” indicates decreasing operating mode in the first, second, and third cycle. The term “Glass” is used to indicate the type of packing, and the term “dry” refers to dry-bed conditions.

Levec et al.22 also observed more hysteresis in the case of smaller (3-mm) glass beads, compared to 6-mm glass beads (Figure 7). The similar trends in variation of hysteresis with particle sizes, were observed by Wang et al.,32 Ravindra et al.,33 and Gunjal et al.,36 not only with nonporous glass particles but also with porous alumina particles. 2.4. Addition of Surfactants. The addition of different surfactants means a reduction in the surface tension of the liquid. Kan and Greenfield20,21 observed that, with the addition of a wetting agent, hysteresis was reduced, although the pressure drops in all paths were increased slightly. Levec et al.22 reported that the addition of a surfactant reduced the hysteresis substantially, as shown in Figure 8. Christensen et al.24 observed that, with the decrease in the surface tension, the hysteresis was

reduced but the pressure drop increased. It was observed that both the lower and upper limiting curve was located above that of pure water when superimposed. Wang et al.32 also reported that, with the decrease in the surface tension, the pressure drop was increased but the hysteresis decreased. 2.5. Porous/Nonporous Particles. Most of the reported hysteresis studies were with nonporous glass particles. Very few studies were reported with porous alumina particles. Lazzaroni et al.25,26 observed hysteresis in the pressure drop, liquid holdup, and wetting efficiency with porous alumina particles under drybed conditions. To see the difference of hysteresis, if any, with porous and nonporous particles, the data reported by Lazzaroni et al.25,26 for 3-mm porous alumina particle are plotted against the data reported by Gunjal et al.36 for nonporous 3-mm glass

Ind. Eng. Chem. Res., Vol. 45, No. 15, 2006 5189 Table 2. Hysteresisa in Pressure Drop and Deviation in Starting Point in First Cycles and in Subsequent Cycles Dry parameter

porous

nonporous

porous

first cycle first cycle second cycle onward second cycle onward second cycle onward

(a) dp ) 3.5 mm hysteresis (cmwc.kg/(m2 s)) 291 × 10-2 end point shifted from starting point? yes hysteresis (cmwc. kg/(m2 s)) 0 deviation in end point no pressure drop variation (cmwc) in the flow range 2.0-2.1

240 × 10-2 yes (negligible) 79 × 10-2 no 2.0-3.8

153 × 10-2 no 91 × 10-2 no 3.2-6.5

152 × 10-2 no 152 × 10-2 no 2.2-4.5

first cycle first cycle second cycle onward second cycle onward second cycle onward second cycle onward

hysteresis (cmwc. kg/(m2 s)) end point shifted from starting point? hysteresis (cmwc. kg/(m2 s)) deviation in end point pressure drop variation (cmwc) in the flow range

(b) dp ) 1.6-1.9 mm 504 × 10-2 yes 184 no 4.5-8.0

266 × 10-2 yes (negligible) 216 × 10-2 no 2.5-7.0

634 × 10-2 no 634 × 10-2 no 6.0-16.0

682 × 10-2 no 661 × 10-2 no 3.5-10.2

a

nonporous

Wet

Area of the pressure drop hysteresis loop or area between increasing and decreasing operating branch (according to Maiti et al.40).

Figure 5. Hysteresis in pressure drop (L ) 5.4 kg/(m2 s), glass beads, dp ) 3 mm, air-water system, wet-bed start-up procedure, bed cross-section ) 5.1 cm × 45.7 cm) at a constant liquid flow rate and constant gas flow rate under similar conditions. (From Christensen et al.24)

Figure 6. Mean values of liquid saturation (5-mm glass spheres, N2water system, wet-bed start-up procedure, D ) 5 cm) obtained by different approaches of the flow pattern. (From Rode et al.30)

particles under almost similar conditions (Figure 9). It shows more hysteresis with nonporous glass particles, compared to porous alumina particles, even if some changes are considered to be due to slide variation in the operating liquid flow range and gas mass velocity. Ravindra et al.33 studied the hysteretic

Figure 7. Effect of particle size on the hysteresis in dynamic liquid holdup for the following conditions: stagnant gas-phase operation, air-water system, wet-bed start-up procedure, D ) 17.2 cm. (From Levec et al.22)

Figure 8. Effect of the addition of surfactant on the hysteresis in dynamic liquid holdup for the following conditions: stagnant gas-phase operation with 3-mm glass beads, air-water system, wet-bed start-up procedure. (From Levec et al.22)

behavior of porous alumina particles of different sizes (1.9, 3.5, and 6.3 mm). Maiti et al.40 plotted the hysteresis in the pressure drop of porous and nonporous particles as observed by Ravindra et al.,33 in Figure 4a and b and compiled the data in Table 2. This table and Figure 4a and b show that strikingly different hysteretic behavior is observed with porous particles, compared

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Figure 9. Comparison of hysteresis data of different authors between porous and nonporous particles under dry-bed conditions (3-mm particles).

Figure 11. Effect of operating range for asymptotic inner hysteresis loop 2 (starting point of L ) 10.86) and loop 3 (starting point of L ) 2.7 kg/(m2 s)) cycling between L ) 2.7 and 10.86 kg/(m2 s). Conditions: air-water system, wet-bed start-up procedure, D ) 5.1 cm. (From Christensen et al.24)

Figure 10. Effect of operating range on the hysteresis, under the following conditions: air-water system,, wet-bed start-up procedure, glass particles with dp ) 1 mm, L ) 1.0 kg/(m2 s), D ) 2.5 cm. (From Kan et al.21)

to that of nonporous particles. The porous particles show lesspronounced hysteresis, compared to nonporous particles in the first cycle, but more-pronounced hysteresis in the subsequent cycles with dry-bed start-up conditions. Under wet-bed startup conditions, the porous particles show more-pronounced hysteresis both in the first and subsequent cycles. 2.6. Operating Flow Ranges. Kan and Greenfield20,21 observed that hysteresis in the pressure drop was dependent on the maximum operating gas flow experienced and more hysteresis was observed with higher operating gas flow rate that was reached. During the experiment, the pressure readings were recorded in each step of increasing gas flow (Path 0) until a predetermined maximum (Gmax,1) was reached, as shown in Figure 10. When the maximum was reached, the gas flow rate was then reduced to a low level following Path 1, where the pressure drop was less. When the gas flow rate was increased again from the end point in Path 1 (called subsequent cycles of operation), it adhered to the same Path 1, provided that Gmax,1 is not exceeded. When the gas flow rate was increased beyond Gmax,1, to Gmax,2, the path followed was Path 0-A, which is an extension of Path 0. On decreasing the gas flow rate from Gmax,2, a new path (Path 2) was followed that runs more or less parallel to Path 1. Similar trends also were reported for the liquid holdup.

Figure 12. Effect of operating range on the hysteresis (3-mm glass sphere, water and stagnant air system, wet-bed start-up procedure, D ) 17.2 cm) in dynamic liquid holdup: (2) Run 1, with maximum Re/L ) 41.09; (]) Run 2, with Re/L ) 70.44; and (9) Run 3, with Re/L ) 93.92. (From Levec et al.22)

Christensen et al.24 obtained a unique loop (Loop 1) on the cyclic variation of liquid rate between two fixed limits (zero and pulsing) of flow rates (Figure 11). Loops 2 and 3 are the asymptotic loops obtained on the cyclic variation of liquid rate between L1 and L2, starting from the pulse flow regime and low liquid rates, respectively. Starting with a low liquid flow rate (L1) return path is dependent on the various maximum liquid flow rates and maximum point always on the lower curve. Similarly, starting with a maximum fixed liquid flow rate (L2) return path is dependent on the various minimum liquid flow rate and minimum point always on the higher curve. Levec et al.23 studied the possible effects of the maximum liquid flow rate on hysteresis (Figure 12) under stagnant gas flow conditions where the liquid flow rate was increased to various maximum liquid Reynolds numbers (e.g., 93.92, 70.44, and 41.09 for runs 1, 2, and 3, respectively). Each run consists of two cycles and began with the draining of the column. Each cycle started with a lower liquid Reynolds number (1.17),


Figure 13. Effect of operating range on the hysteresis with beds of 3-mm alumina particles, air-water system, D ) 3.05 cm, dry-bed start-up procedure. (From Lazzaroni et al.26)

gradually increased to the highest Reynolds number, and then decreased to a minimum value to end the cycle. Subsequent cycles started immediately after the first cycle by increasing the liquid flow rate but did not show any notable hysteresis. The next run (Run 2) started after draining the bed where the liquid flow rate was increased to the second-highest Reynolds number and then decreased to a minimum value to complete the cycle. As shown in Figure 12, the paths for increasing liquid flow in all three runs were almost the same but the decreasing paths were different, based on the maximum Reynolds number that was attained. Similar trends in the pressure drop, liquid holdup, and wetting efficiency hysteresis were observed by Lazzaroni et al.,25,26 using porous particles; e.g., in the case of pressure drop hysteresis, the return path was different with different maximum liquid flows that were reached (see Figure 13). 2.7. Higher Gas Flow Rate. Gunjal et al.36 observed that hysteresis in the pressure drop was not very sensitive to the gas velocity. At a higher gas flow rate, the observed hysteresis was slightly lower, compared to the hysteresis at a lower gas flow rate (see Figure 14a). 2.8. Column Diameter. Gunjal et al.36 studied the hysteresis in TBRs with columns that had two different diameters (11.4, 19.4 cm). Figure 14b shows that, as the column diameter increasesd, the hysteresis in the pressure drop was reduced but the observed pressure drop increased slightly. They also observed that this variation in the hysteresis with column diameter becomes negligible with increasing particle size. Similar trends with hysteresis in liquid holdup were also evident from their experiment. 2.9. Inlet Liquid Distributions. Gunjal et al.36 examined the effect of the initial distribution of liquid on hysteresis. The magnitude of the pressure drop hysteresis observed with the spray distributor (with better liquid distribution) was smaller than that for the perforated plate distributor. Similar trends with the hysteresis in liquid holdup were also observed. 3. Concepts of Hysteresis Several authors20-22,24-26,32,33,36 have speculated that hysteresis is related to the different degree of wetting of packing between increasing and decreasing modes of operation. Various factors are responsible for the different degrees of wetting, such as the variation in gas flow path density and tortuosity, liquid flows in two modes (such as film and rivulet), the difference in capillary pressure, the generation of new liquid paths in

Figure 14. Effect of (a) gas flow rate (D ) 11.4 cm) and (b) column diameter on the hysteresis (3-mm glass beads, column diameter ) 11.4 cm, air-water system, dry-bed start-up procedure) in pressure drop. (From Gunjal et al.36)

increasing mode and their survival in decreasing mode. Kan and Greenfield20,21 speculated that the hysteresis is due to decreased gas flow path tortuosity, as a result of an irreversible breakup of liquid bridges transverse to the direction of the flow with increasing gas flow rate. The flow pattern is retained during the decreasing flow of gas, because of the high surface tension effect. In the bed of large packing, the surface tension effect is low, no large variation in tortuosity is possible, and the liquid phase trickles down the bed in drops and films, giving less hysteresis. However, this can poorly explain the hysteresis observed in single-phase flow conditions, because there is no gas flow to change the tortuosity. All other speculations primarily converge to a general perception, i.e., hysteresis is due to a difference in wetting between two modes of operation, i.e., increasing or decreasing mode. Starting from zero liquid flow rates in a dry bed, as the liquid flow commences, the liquid flows in rivulets or channels. At the beginning, the cross-sectional area or the number of particles that are covered in a channel is small. At this stage, the pressure drop is equivalent to the pressure drop in the dry bed and the liquid flows as rivulets. When the bed is pre-flooded and then drained (wet bed), dry regions are formed locally and the liquid

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Figure 15. Comparison of hysteresis data of the first cycle obtained by different authors under similar conditions (glass beads, dp ) 3.0-3.5 mm, air-water system).

that remains in the bed (static holdup) is retained by means of a counterbalance of forces, which includes gravitational forces and interfacial tension. As the liquid flow rate is increased from these static situations, a liquid flow pattern is established in which dry regions still remain. The increase in the liquid flow rate induces a larger accumulation of liquid in the wet regions. As the liquid flow rate increases, the rivulets will grow in size and an enlargement of the existing channels or the formation of additional channels also occurs. Also, it is understood that, with increasing liquid flow rate, the three-phase contact line must advance over the dry surface and will spread less, because of the higher contact angle (higher capillary pressure), i.e., rivulet-type flow. Therefore, the pressure drop increases, because of lower effective porosity and larger liquid-solid and liquidgas interactions. As the liquid flow decreases, liquid retracts from the peripheral regions of the channel, leaving a thin film of liquid over the packings and gas flowing in the resultant voids. The central core of the channel remains in filament mode. Although the actual liquid coverage of the solid remains approximately the same, the effective porosity still is higher and the gas/liquid interfacial area becomes greater, because of the simultaneous presence of a central core and surrounding film in place of the liquid filament. This combined effect of increased solid-liquid and gas-liquid interactions more than offsets the decrease that is due to increased voidage. This results in a greater pressure drop during the decreasing mode than during the increasing mode at the same flow rate. Therefore, liquid flowing in a film flow in decreasing mode justify the increase in pressure drop and liquid holdup. In the following section, an attempt was made to study the effects of several controlling parameters on the hysteresis as described in section 2, based on the aforementioned perceptions. In the wet bed or in subsequent cycles of operation, liquid will spread over the film already formed over the wetted particles and three-phase contact line also will retract over the

wetted surface, thus bringing the values of advancing and receding contact angles closer to each other. Therefore, it is expected that there will be a negligible amount of hysteresis in the wet bed, compared to that in a dry bed, but substantial hysteresis was observed in the former case. When the bed is wetted under different wet-bed start-up conditions, a different degree of wetting of the packing may exist, resulting in different extents of hysteresis and the same was also reported. In the case of hysteresis studies with a cycling of gas flow at constant liquid flow, at the beginning of the cycle, liquid may be flowing in channels with film flow at peripheral particles (at the starting point, the bed is normally flooded with a high liquid flow and then reduced to the desired flow). When the gas flow rate is increased (increasing mode of operation), the film over the peripheral particles breaks apart and liquid flows through the core of the channel as a filament. After a higher gas flow rate is attained, when the gas flow starts to decrease (decreasing mode of operation), liquid tries to flow as rivulets (less spreading over a dry surface is observed), resulting in a lower pressure drop, compared to the upper limiting curve (obtained during increasing mode of operation). Because of less influence of gas cycling on hysteresis, sometimes the trend changes, within the experimental uncertainty, as observed in Figures 3, 5, and 10. As the diameter of the particles increases, capillary pressure decreases and the liquid reverts to film flow quickly and causes lower hysteresis. When pulsing is reached, the liquid spreads evenly over the packing. When the liquid flow rate is reduced, the evenly spread distribution is apparently maintained and no coalescence of these thin films into rivulets could be observed. As surfactant is added, the surface tension of the liquid is reduced. As the surface tension decreases, the contact angle at the three-phase contact line decreases (i.e., less capillary pressure) and more film flow occurs, which causes more wetting in the bed. As the surface tension decreases, hysteresis is reduced but the pressure drop increases. This occurs because rivulets


spread and split more easily if the surface tension is reduced and the gas/liquid interactions increase. During decreasing mode of operation, more wetting occurs, as has been explained previously. Thus, the difference in wetting between the increasing and decreasing modes will be less (i.e., less hysteresis), which is consistent with the earlier observations. Under higher gas flow conditions, the flow situation is toward the pulsing regime and hysteresis is expected to be less. With a uniform inlet distribution of liquid, more wetting occurs in both modes of flow (increasing and decreasing), resulting in less hysteresis. Increasing the operating range of liquid within the trickle flow regime causes more dry regions (in both dry and wet bed) to become active for film/rivulet flow, which causes more hysteresis. In the case of different types of packing, no difference in hysteresis is expected, as per the general perceptions of hysteresis. However, from the experimental observations of Ravindra et al.33 and subsequent analysis by Maiti et al.,40 it was found that the variation of hysteresis in porous particles is strikingly different than that in nonporous particles depending on start-up procedure and size of the particles used. This indicates that physics of hysteresis still need to be explored. Even when hysteresis data for nonporous particles by different authors were plotted under similar conditions (Figure 15), it was found that there is hardly any agreement. Therefore, it could be considered that, although many studies have been performed, the phenomenon of hysteresis still is poorly understood and explained. 4. Models for Hysteresis 4.1. Mathematical Models. Most of the knowledge about the multiplicity of hydrodynamic states has been obtained through experimental studies by several investigators. They observed that the hysteresis in the pressure drop and liquid holdup was dependent on the history of the process, i.e., the mode of operation, the start-up procedure, the porous and nonporous nature of the particles, the particle sizes, the addition of a wetting agent (such as a surfactant), and the initial distribution of liquid. They speculated that the hysteresis was due to an irreversible breakup of liquid bridges transverse to the direction of the flow, i.e., the tortuosity of the flow path, the difference between advancing and receding contact angles at gas-liquid-solid contact lines, the rivulet and film flow, a nonuniform distribution of liquid, the capillary pressure, etc. Some researchers have focused their efforts on characterizing the history of the process by including several criteria/additional parameters and have proposed correlations for quantifying the hysteresis. Kan and Greenfield21 developed a channel-flow model to explain the hysteresis in TBRs where the gas phase is considered to flow in channels with a circular cross section. Under the maximum gas flow rate conditions, the number of gas channels may be assumed to be proportional to the fractional voidage that remains after the space occupied by the liquid holdup is taken into account and a correlation is used to predict the number of flow channels. Under reduced gas flow conditions, the tortuosity and number of gas flow channels remain unchanged as the gas flow rate is reduced, i.e., they remain the same as that for the corresponding maximum gas flow rate from which the reduction in gas flow commences. The model gives a satisfactory explanation to the existence of hysteresis. The disadvantage of the model is that the correlations under both maximum and reduced gas flow conditions require fitting

Figure 16. Comparison of simulated versus experimental data of hysteresis (wet-bed start-up procedure) in pressure drop. (From Chu and Ng.27)

parameters, and the maximum number of flow channels is a function of the liquid holdup under maximum gas flow conditions, which is supposed to be known experimentally. Chu and Ng27 modeled the packed bed as an array of inclined flow channels, based on the concept of a porous medium model. Basically, it is a three-dimensional, six-coordinated, simple cubic network of cylindrical channels. They considered two gascontinuous flow regimes: annular flow and segregated flow. Relations between pressure drop, holdup, and flow rates were assigned to each flow regime. No mass accumulation was allowed in the junctions. The allowability criterion was simply that, when the overall liquid rate was increased, all channels operated in the segregated regime and, when the overall liquid flow rate was reduced, they all operated in the annular regime. The model successfully predicts the trend of hysteresis, as shown in Figure 16. However, the limitations of the model are that the model requires the number of monofilaments and bifilaments, with their location, and the liquid distribution before starting the calculation. Levec et al.22 attempted to predict hysteresis based on the different relative permeabilities of gas and liquid flow for two modes of operation. The envelope of the relative permeability curve was developed based on the experimental operating range. They could predict the pressure drop and liquid holdup with mean relative deviations of 13% and 3.5%, respectively. Melli and Scriven41 predicted hysteresis in terms of the fluid distribution in the bed, which is defined as a two-dimensional network of passages, and hysteresis is the outcome of different local flow regimes that are operating in the individual passage. The solution of the constituent mass and momentum balance equations is based on allowability and occupancy statistics. Obtaining a solution is a challenge: Melli and Scriven41 did not present any comparison with experimental results. Wang et al.32 developed a “parallel flow zone” model to predict the hysteresis behavior of TBRs, based on the concept that the hysteresis is due to the various degrees of nonuniformity in the gas liquid flow distribution. A reduced pressure drop is related to a less-uniform distribution, whereas the upper branch of the hysteresis loop corresponds to a uniform distribution of gas-liquid flow. As per their model, in portions of the cross section (Figure 17), both the gas and liquid flow downward in the same channel, occupying a cross-sectional area fraction of X3. The gas or liquid flow may also be concentrated locally in some channels to result in single-phase flow of either gas or liquid, constituting fractions of X1 and X2, respectively. This scenario of gas-liquid flow may be represented by a

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Figure 17. Conceptualized flow structure of trickling flow. (From Wang et al.32) Figure 19. Comparison of simulated results of pressure drop hysteresis (glass spheres, dp ) 3 mm, D ) 11.4 cm, air-water system, dry-bed startup procedure,VG ) 0.22 m/s). (From Gunjal et al.36)

Figure 18. Comparison of the model prediction with measurements for hysteresis (G ) 0.208 kg/(m2 s), air-water system,, wet-bed start-up procedure, D ) 7 cm) in pressure drop. (From Wang et al.32)

parallel flow zone model: the gas, liquid, and gas-liquid mixture flow in a segregated fashion in several parallel zones and flow may be assumed to be uniform in each flow zone. Flow in all zones is subject to a common axial pressure drop across the bed. In the model, the modified Ergun equation is used to calculate the pressure drop of single-phase flow zones and the concept of relative permeability is applied to the gasliquid two-phase flow. For the upper branch, the existence of single-phase flow zones X1 and X2 are assumed to be zero. The exact solution of the equation network is not possible. The global minimum of pressure drop was considered for the lower branch. They could obtain an upper-branch and lower-branch curve of the hysteresis loop, as shown in Figure 18. Predicted and simulated data were in agreement, within 25%. However, the disadvantage of the model is the required use of the correlation for permeability, the value of which must be established experimentally. Gunjal et al.36 developed a comprehensive CFD model to predict the hydrodynamic behavior in TBRs and included capillary pressure in the CFD model to predict hysteresis in the pressure drop and liquid holdup in TBRs. They used an empirical factor (f) that is related to the degree of wetting in the capillary pressure formulation. The simulations were performed by setting a value of f ) 0 for the increasing liquid flow rate mode (lower branch) and f ) 1 for the decreasing

liquid flow rate mode (upper branch). The major advantage of the model is that it is based on fundamental concepts and can accurately capture the hysteresis trend (Figure 19). However, the predicted magnitude of the hysteresis is less than that observed in the experiments. The model overpredicts the pressure drop for the increasing liquid branch. The inadequate representation of the factor f for the lower branch is the most likely cause of this discrepancy. 4.2. Conceptual Framework. In the preceding section, it was determined that all the authors have put their efforts to develop the correlations to characterize and quantify hysteresis in reference to nonporous particles. However, there are many differences in the hysteretic behavior of porous and nonporous particles, as observed previously in section 2. Therefore, an understanding of the liquid flow behavior in a bed packed with porous particles has great merit. Khanna and Nigam37 have introduced a pore level concept to understand the presence of particles with a porous nature on hysteresis. They visualized the effect of the wettability of the solid on the wetting efficiency via the movement of the solidliquid-gas contact line over the catalyst particle, based on a thought experiment. They modeled the surface (Figure 20) as alternating patches of saturated pore (of width m) and solid surface (of width n). When the wettability is increased, the wetting efficiency increases as the contact line advances on the solid surface, merging with neighboring rivulets (see from stage A to stage C in Figure 20). When it reaches the edge of the pore, it accelerates across the patch to form a contact with other side of the patch, showing enhanced spreading (see from stage C to stage D in Figure 20). This was also supported by the experimental observations of Ravindra et al.33 and subsequent analysis by Maiti et al.,38 where less-wettable alumina particles show more liquid spreading and more time is required to reach steady state, compared to more-wettable glass beads. When the catalyst wettability is decreased, the contact line starts to retract, which results in a reduction in wetting efficiency. The retracting contact line retracts on a wetted surface differently than on a dry surface during increased wettability. After reaching the edge of the liquid filled pore, it becomes stranded there, thus making any more retraction very difficult (see from stage D to stage E in Figure 20), i.e., the pinning effects of pores. If nonhomogeneities are present (in the form of completely wettable saturated pores and partially wettable solid patches), film rupture occurs,


Figure 20. Change in wetting efficiency, relative to movement of the contact line. (From Khanna and Nigam.37)

showing a sudden dip in wetting (see stage F in Figure 20). This was supported by the experimental observations of Maiti et al.,39 which suggest that the pore not only helps in the lateral spreading of liquid during increasing wettability but also acts as brakes during decreasing wettability. Maiti et al.40 developed a new framework, starting with the pore level concept of liquid spreading that was reported by Khanna and Nigam37 and incorporating the concept of participating and nonparticipating particles in the current understanding of fluid flow in TBRs. Basically, the general perception of hysteresis was enhanced by the concept of wettability.37 As per the general perception with the commencement of liquid, a liquid flow pattern is established through favorable particle clusters. With the increase of flow, liquid spreads laterally, covering more particles in the periphery of the core channel; i.e., the channel diameter increases, as observed in Figure 21a and b (also see panels a1 and b1 in Figure 21). During decreasing flow, the liquid-filled core or filaments retracts, leaving the surrounding region with the film (see panels c and c1 in Figure 21). With further decreases in the flow, one will encounter a stage when peripheral particles are dried and core of the channel reduces to film flow. Thus, the peripheral particles of the channel are the major contributors to the hysteretic behavior. The behavior of these peripheral particles during the spreading and retraction of flow in increasing and decreasing flow modes causes the major differences between porous and nonporous particles. Starting with a dry bed, the liquid will start to flow as a rivulet or film in the channel. With increasing flow, the rivulet will

grow in size and an enlargement of the existing channels or the formation of additional channels occurs, covering more particles, or the thickness of the rivulet increases, as per the general perception. Liquid will spread more on the porous particle, because of the combined effect of wettability and capillary action of pore and film flow, which will be present in peripheral particles. In contrast, the liquid will spread less on nonporous solids and, primarily, rivulet flow will dominate. During decreasing flow, the liquid retracts over the previously wetted surface. For the nonporous surface, this retraction is guided by the contact angle, i.e., film flow is due to a lower contact angle. For the porous surface, a completely different route is followed, as outlined in the model of Khanna and Nigam.37 A combination of the following scenarios is likely to happen, viz, (1) The retracting liquid is delayed, because of the pinning force that is provided by the pores, which will result in greater liquid coverage and higher pressure drops; (2) The retracting film breaks free of this pinning, either by rupture that is due to the presence of pore as nonhomogeneity (Konnur et al.42) or drying up by the gas flow, which will result in lower liquid coverage and lower pressure drop. This dry section may be at the particle in the periphery of the channel or in part of the surface of a particle; these features are called participating particles or seasoned particles, as discussed previously. They used this enhanced framework to analyze the present situation. In a dry bed, after the first cycle is over, more dry particles (or seasoned particles) will reappear in channels of porous particles, because of the rupture of film, than in channels of nonporous particles. In the subsequent cycles, the liquid will spread and retract over these particles, in addition to the nonparticipating particles, and constant closed-loop hysteresis will be observed. Because of the presence of a much smaller number of dry or seasoned particles, the hysteresis effect is not pronounced in nonporous particles. In the wet bed, there will be a much-greater number of faVorable clustered particles or channels that will be generated in the wet bed than in a dry bed. As stated previously, each channel will consist of some nonparticipating particles and some participating particles. The total number of such participating particles will be much greater here, in comparison to a dry bed (identified during the descending branch of the first cycle), because of the greater number of favorable clusters. During the first cycle, these participating particles justify the existence of hysteresis, even after prewetting the bed. In nonporous particles, some of the dry particles, which are present, will be covered by liquid and may not be identified as participating particles during the descending branch. Thus, the hysteresis will be openloop for nonporous particles during the first cycle. Note that hysteresis is expected to be closed-loop for porous particles, because these dry portions are expected to be much smaller, because of enhanced spreading, and the participating particles remain unchanged during the ascending and descending branches of all cycles. For nonporous particles, the ascending branch of the first cycle is affected by the presence of dry portions. Because these will not contribute to the hysteresis in subsequent cycles, the extent of hysteresis is expected to be less during subsequent cycles than during the first cycle. They applied this concept to explain the hysteretic behavior of porous and nonporous particles in smaller-sized particles. They considered that, in a bed of smaller-sized particle, the number of particles is greater, so the chances of having favorable clusters also will be greater, compared to larger-sized particles. Based on the aforementioned intuitive arguments, the hysteresis

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Figure 21. Liquid flow in proposed favorable clusters (a, a1) when flow started, (b, b1) at increased flow, and (c, c1) decreased back to initial flow. (From Maiti et al.40)

of smaller-sized (1.6-1.9 mm) porous and nonporous particles, under wet-bed conditions, was also explained. It also explained the limited hysteresis data available for porous particles at other gas flow rates. However, their framework was tested with a limited number of data and has not been verified with other controlling parameters, as mentioned in section 2. 5. Conclusions From the foregoing discussion, the following conclusions regarding hysteresis in trickle bed reactors (TBRs) can be drawn: (1) Pronounced hysteresis is observed for the pressure drop, liquid holdup, and wetting efficiency for both porous and nonporous types of packing materials. Differences in pressure drop (up to 100%) and in liquid holdup (up to 30%) are reported to be due to hysteresis. (2) Several factors are observed to affect the hysteretic behavior of TBRs, such as (a) the type of particle (hysteretic behavior of a bed with porous particles is observed to be strikingly different from that with nonporous particles); (b) the start-up procedure (the amount of hysteresis, following the wetbed start-up procedure, is much less than that observed in the case of the dry-bed start-up procedure; the effect of the startup procedure also is dependent on the size and type (porous/ nonporous) of the particles; again, in the wet-bed start-up procedure, hysteresis in a constant gas flow run is higher, in comparison to that in a constant liquid flow run); (c) particle size (as the particle size increases, hysteresis effect is reduced); (d) the surfactant (the addition of a surface wetting agent reduces surface tension, and, therefore, less hysteresis is observed,

because of the increased film flow with increasing mode of operation); and (e) the inlet liquid distribution (the hysteretic behavior of the bed is dependent on the initial flow distribution in the bed, and the amount of hysteresis is smaller with better liquid distribution). (3) The hysteresis is interpreted as being due to a change in the tortuosity of the gas flow path, film-/rivulet-type liquid flow, the difference in the advancing and receding contact angles, and the difference in capillary pressures in the increasing and decreasing modes of flow. Rivulet flow is likely to be caused by the poor wetting properties of the packing material. When the surface tension is reduced, the rivulets spread and split more easily toward film flow, because of the lower contact angle, and causes more gas/liquid interactions (and, therefore, a greater pressure drop). (4) Different hysteretic behavior of the bed with porous particles is due to a different impact of the pore on liquid spreading. Visually, it is observed that, depending on whether the drop edge is moving toward the pore or away from the pore, the pore acts as an accelerator or brake for the drop edge. This dual nature of the saturated pores can be ascribed to the attraction between the liquid in the drop and the liquid inside the pore. (5) It has been established that hysteresis is dependent on the history of the process by which flow rates have been achieved. Some mathematical modelings have been attempted by incorporating the flow history to predict hysteresis, such as physical model, using correlations or fundamental approaches using computational fluid dynamics (CFD). The CFD model is able to capture the trends that are observed in hysteresis


correctly. However, quantitative predictions of the hysteresis are lower than the experimentally observed values. Most of the model predictions are for nonporous particles and have been validated against only a few data points. No different contribution was considered for porous particles, although the hysteretic behavior is noticeably different from that for nonporous particles. (6) Recently, the research group of Khanna and Nigam (Khanna and Nigam,37 Maiti and co-workers38-40) proposed a new framework that is based on the concept of participating and nonparticipating particles, which could explain various features of hysteresis in porous and nonporous particles. 6. Recommendations for Future Work (1) The wetting efficiency could be correlated in terms of interfacial phenomena, based on the movement of the advancing and receding contact line. (2) More-comprehensive data could be generated, in regard to gas flow, type of packing material, shape of the packing material, and liquid type, especially in regard to porous packing. Hysteresis should be studied at higher pressure, using organic liquids (physical properties representative of industrial operating conditions of high pressure and high temperature). (3) Better capillary model should be developed to predict hysteresis quantitatively. (4) Modeling efforts are required to correlate porosity and the concept of participating/nonparticipating particles to the hysteresis. It is expected that this pore-level analysis of hysteresis between porous and nonporous particles will enhance our understanding to further demystify the hydrodynamic phenomena in TBRs. However, strengthening of the analysis over a wide range of physical properties of the fluids and different particles will help in further exploiting the applicability. Acknowledgment Authors are thankful to Dr. Prashant R. Gunjal, Dr. Zeljko V. Kuzeljevic, and Dr. Pierre-Yves Lanfrey for providing their valuable comments on the manuscript. We wish to acknowledge the support of Center for High Technology, Ministry of Petroleum and Natural Gas, Government of India, for providing research facilities in the area of trickle-bed reactors (TBRs). Nomenclature dp ) packing diameter (m or mm) de ) equivalent diameter of the particles; de ) 6Vp/Sp D ) diameter of bed (cm or m) d1h ) hydraulic diameter; d1h ) dp/(1 - ) EO ) Eotvos number based on hydraulic diameter; EO ) FLgd1h/σL f ) degree of wetting G ) gas mass flux (kg/m2s or kg/m2h) L ) liquid mass flux (kg/m2s, or kg/m2h) m ) width of saturated pore, arbitrary dimension n ) width of solid surface, arbitrary dimension ∆P/∆Z ) pressure drop per unit length of bed (cmwc/m or kPa/ m) ∆P ) pressure drop (cmwc or kPa) Re/L ) Reynolds number of the liquid phase; Re/L ) FLVLde/ (1 - )µL Re/G ) Reynolds number of the gas phase; Re/G ) FGVGde/ (1 - )µG Sp ) external surface areas of the particles (m2)

V ) superficial velocity (m/s) Vp ) volume of the particles (m3) X1 ) fraction of cross sectional area occupied by gas X2 ) fraction of cross sectional area occupied by liquid X3 ) fraction of cross sectional area occupied by both gas and liquid ∆Z ) bed length (m) Greek Letters R ) R-phase of alumina; surface area ) 25-35 m2/g γ ) γ-phase of alumina; surface area ) 200-240 m2/g βL ) total liquid saturation per unit of bed void volume µ ) viscosity (Pa s) δL ) reduced liquid saturation; δL ) L - 0L/(1 - 0L), where L ) L/ and 0L ) 0L/ 0 L ) static holdup ) bed void volume η ) wetting efficiency DL ) dynamic liquid holdup L ) total liquid holdup per unit volume of bed F ) density (kg/m3) σ ) surface tension (N/m) Subscripts L ) liquid G ) gas Literature Cited (1) Saroha, A. K.; Nigam, K. D. P. Trickle Bed Reactors. ReV. Chem. Eng. 1996, 12, 207-347. (2) Larachi, F.; Cassanello M.; Laurent A. Gas liquid interfacial mass transfer in trickle-bed reactors at elevated pressures. Ind. Eng. Chem. Res. 1998, 37, 718-733. (3) Kundu, A.; Nigam, K. D. P.; Verma, R. P. Catalyst wetting characteristics in trickle-bed reactors. AIChE J. 2003, 49, 2253-2263. (4) Kundu, A.; Nigam, K. D. P.; Duquenne, A. M.; Delmas, H. Recent Developments on Hydroprocessing Reactors. ReV. Chem. Eng. 2003, 19, 531-603. (5) Maiti, R. N.; Sen, P. K.; Nigam, K. D. P. Trickle-Bed Reactors: Liquid Distribution and Flow Texture. ReV. Chem. Eng. 2004, 20, 57111. (6) Sie, S. T.; Krishna, R. Process development and scale-up, III: Scaleup and scale down of trickle bed processes. ReV. Chem. Eng. 1998, 14, 203-252. (7) Sato, Y.; Hirose, T.; Takahashi, F.; Toda, M.; Hashiguchi, Y. Flow pattern and pulsation properties of cocurrent gas-liquid downflow in packed beds. J. Chem. Eng. Jpn. 1973, 6, 315-319. (8) Charpentier, J. C.; Favier, M. Some Liquid Holdup Experimental Data in Trickle-bed Reactors for Foaming and Nonfoaming Hydrocarbons. AIChE J. 1975, 21, 1213-1218. (9) Ng, K. M. A Model for Flow Regime Transitions in Cocurrent Downflow Trickle-Bed Reactors. AIChE J. 1986, 32, 115-122. (10) Ng, K. M.; Chu, C. F. Trickle-bed reactors. Chem. Eng. Progr. 1987, 83, 55-63. (11) Larachi, F.; Iliuta, I.; Chen, M.; Grandjean, B. P. A. Onset of pulsing in trickle beds: Evaluation of current tools and state-of-the-art correlation. Can. J. Chem. Eng. 1999, 77, 751-758. (12) Zimmerman, S. P.; Ng, K. M. Liquid distribution in trickling flow trickle bed reactors. Chem. Eng. Sci. 1986, 41, 861-866. (13) Zhukova, T. B.; Pisarenko, V. N.; Kafarov, V. V. Modeling and design of industrial reactors with a stationery bed of catalyst and two-phase gas-liquid flowsA Review. Int. Chem. Eng. 1990, 30, 57-102. (14) Gianetto, A.; Specchia, V. Trickle-bed reactors: State of the art and perspectives. Chem. Eng. Sci. 1992, 47, 3197-3213. (15) Al-Dahhan, M. H.; Larachi, F.; Dudukovic, M. P.; Laurent, A. Highpressure trickle-bed reactors: A Review. Ind. Eng. Chem. Res. 1997, 36, 3292-3314. (16) Dudukovic, M. P.; Larachi, F.; Mills, P. L. Multiphase reactorsrevisited. Chem. Eng. Sci. 1999, 54, 1975-1995. (17) Marcandelli, C.; Lamine, A. S.; Bernard, J. R.; Wild, G. Liquid distribution in trickle-bed reactor. Oil Gas Sci. Technol. 2000, 55, 407415.

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ReceiVed for reView February 25, 2006 ReVised manuscript receiVed May 12, 2006 Accepted May 18, 2006 IE060238H

Hysteresis in Trickle-Bed Reactors: A Review - American Chemical

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