Cocurrent Downflow in Networks of Passages ... - ACS Publications

Znd. Eng. Chem. Res. 1990,29,2367-2379 Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The Properties of Gases and Liquids; McGraw-Hill: New York, 1977. Rice, R. G. The Use of Ozone to Control Trihalomethanes in Drinking Water Treatment. Ozone Sci. Eng. 1980,2,75-99. Rice, R. G. The Safe Drinking Water Act Amendments of 1986 and their Impacts on the Use of Ozone for Drinking Water Treatment in the United States. In Proceedings of Ozone in Water Quality Management; Internat. Ozone Assoc. Ed.: London, 1989; pp 13-24. Rook, J. J. Possible Pathways for the Formation of Chlorinated Degradation Products during Chlorination of Humic Acids and Resorcinol. In Water Chlorination Environmental Impact and Health Effects;Jolly, R. L., Cumming, R. B., Jacobs, V. A,, Eds., Ann Arbor Science: Ann Arbor, MI, 1980; Vol. 3. Roth, J. A.; Sullivan, D. E. Solubility of Ozone in Water. Znd. Eng. Chem. Fundam. 1981,20,137-141. Sayre, I. M. International Standards for Drinking Water. J. Am. Water Works Assoc. 1988,80,53-58. Schnitzer, M.; Khan, S. U. Humic Substances in the Enuironment; Marcel Dekker Inc.: New York, 1972. Sotelo, J. L.; Beltrb, F. J.; Benitez, F. J.; Beltran-Heredia, J. Ozone Decomposition in Water: Kinetic Study. Ind. Eng. Chem. Res. 1987,26,39-43.

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Sotelo, J. L.; Beltrb, F. J.; Benitez, F. J.; Beltran-Heredia, J. Henry's Law Constants for the Ozone-Water System. Water Res. 1989, 23, 1239-1246. Sotelo, J. L.; Beltrln, F. J.; Gonzalez, M.; Garcia-Araya, J. F. Ozonation of Aqueous Solutions of Resorcinol and Phloroglucinol. 2. Kinetic Study. Ind. Eng. Chem. Res. 1990,submitted. Staehelin, J.; HoignB, J. Decomposition of ozone in Water in the Presence of Organic Solutes acting as a Promoters and Inhibitors of Radical Chain Reactions. Enuiron. Sci. Technol. 1985, 19, 1206-1213. Steelink, C.; Berry, J. W.; Ho, A.; Nordby, H. E. Alkaline Degradation Products of Soil Humic Acid. Sci. Proc. R. Dublin SOC.1960, Al, 59-67. Throop, W. M. Alternative Methods of Phenol Waste Water Control. J. Hazard. Mater. 1977,1,319-329. Van Krevelen, D. W.; Hoftijzer, P. J. Kinetics of Gas-Liquid Reactions. Part I. General Theory. Recl. Trau. Chim. Pays-Bas 1948, 67, 563-586. Wurm, H. J. Extraction of Phenols from Coking-Plant Effluents. Chem.-Ing.-Tech, 1976,48, 840-845.

Received for review October 10, 1989 Accepted J u n e 11, 1990

Cocurrent Downflow in Networks of Passages. Microscale Roots of Macroscale Flow Regimes Tomls R. Melli,?Juan M. de Santos, William B. Kolb,' and L. E. Scriven* Department of Chemical Engineering and Materials Science, Uniuersity of Minnesota, Minneapolis, Minnesota 55455

Contending trickling, spray, pulsing, and bubbling regimes in cocurrent downflow in packed beds differ hydrodynamically and so also do holdups, pressure drops, transfer rates, and reaction performance. Uncertainties about the flow regimes and competition between them contribute t o unreliability of existing design and scale-up methods for trickle beds. We report flow visualization of microscale hydrodynamics in the spaces between packing particles-the void space of the bed-where gas and liquid compete, and of macroscale flow behavior in nearly two-dimensional packed beds confined between parallel transparent walls. T h e macroscale regimes are the same as those that have been widely reported from beds with transparent walls. We show that these regimes result from a n enormous set of interacting microscale regimes, themselves the outcome of local competitions between liquid and gas for enlargements and junctions of the void space network, on the one hand, and constrictions, on the other.

Introduction Cocurrent two-phase flow occurs in diverse fields of science and technology. Two fluid phases flow cocurrently through micrometer-scale passages in, for example, capillarity-dominated displacement of water-oil systems in sedimentary rocks, through centimeter-scale passages in, for example, steam-water flow in pipes of the cooling system of a nuclear reactor, and through millimeter-scale passages in, for example, hydrogen-hydrocarbon flow in certain trickle-bed reactors. Table I shows the Bond, capillary, and Reynolds numbers that are characteristic of oil displacement in fine porous media, gas-liquid flow in tubes, and two-phase flow in trickle-bed reactors. In oil displacement (Ng et al., 1978; Mohanty, 1981), capillary force is usually much larger than gravity, inertia, and viscous forces; oil displacements are typically capillarity-dominated creeping flows. The characteristic radius of a passage is of the order of a micrometer to hundreds of micrometers. In pipe flow, gravity Research Fellow of CONICET, Repfiblica Argentina. 1 Current address: University of Tulsa, Tulsa, OK 74104.

Table I. Typical Ranges of Force Ratios in Two-Phase Flow in Fine Porous Media, Packed Beds, and Piping force ratios pipe or particle inertial/ viscous/ capillarity/ diameter viscous, capillarity, gravitational, solid support D, m Re Ca 1/Bo fine porous 10-7-10-4 104-10-2 10-7-10-3 102-109 media (petroleum recovery) coarse porous 10-~-10-~10-~-10~ 10-'-10 10-l-10 media (packed beds) piping (nuclear 10-105 10-102 10-3-10-1 technology)

" R e pDV/p is the Reynolds number, Ca wLVL/u is the capillary number, and Bo [D2(pL- p,Jg]/u is the Bond or Eotvos number, where V is the characteristic velocity, p is density, w is viscosity, u is surface tension, and g is gravity. The subscripts L and G refer to liquid and gas, respectively.

and inertia forces together overcome capillarity and viscous forces (Taitel et al., 1980); the characteristic radius is of the order of centimeters. In trickle-bed reactors, all of the 0 1990 American Chemical Society

2368 Ind. Eng. Chem. Res., Vol. 29, No. 12, 1990

forces are comparable in magnitude and none can be neglected a priori. The characteristic radius of a passage is of the order of millimeters-a centimeter down to perhaps tenths of a millimeter, or hundreds of micrometers. Similarities are noticeable in these three examples. Some of the flow regimes found in millimeter-scale passages are qualitatively the same as those found in pipes, namely, trickling, bubbling, and pulsing. The bridged regime in millimeter-scale passages has a parallel that is prevalent in the displacement of oil by water in sedimentary rocks. What makes the differences is the competition among the forces that are active at each scale. Those forces are inertial, viscous, capillary, and gravitational. Their effects can be described in terms of seven dimensionless numbers: the Reynolds number of each phase, the ratio between inertial and viscous forces, ReL E pLVLD/pLand ReG 3 pGV&/pc; the capillary number of each phase, the ratio between viscous and capillary forces, CaL pLVL/o and CaG E pGVG/a;the Bond number, the ratio between gravitational and capillary forces, Bo [ 0 2 ( p -~ & ) g / o ; the viscosity ratio, pG/pL;and the density ratio, p G / p L . Here p G and pL are the densities of the gas and liquid, pG and pL are the viscosities of the gas and liquid, D is the characteristic length, V , and VL are the characteristic velocities of gas and liquid, and a is the surface tension. Cocurrent downflow of gas and liquid in a fixed bed of catalyst particles is widely used in the petroleum and petrochemical industries: trickle-bed cocurrent downflow reactors find extensive applications in hydrodesulfurization, hydrocracking, hydrodenitrogenation, hydrogenation, and oxidation of organic compounds (Tarmy, 1982). The physicochemical properties and the flow rates of the gas and liquid phases, together with the size and shape of catalyst particles, determine the reactor parameters, namely, pressure drop, heat- and mass-transfer coefficients, reaction rate, and liquid holdup. The prediction of these parameters is critical in reactor design and operation. Current practice in trickle-bed reactor design relies on empirical correlations and laboratory data that require scale-up to industrial conditions. However, heatand mass-transfer coefficients and reaction rates depend strongly on the flow regimes, i.e., the hydrodynamic conditions, of the reactor. Expensive pilot-plant testing seems to be usual in scale-up engineering. Several review papers (Satterfield, 1975; Giannetto et al., 1978; Herzkowitz and Smith, 1983) summarize the correlations used for the prediction of the various parameters just mentioned. The flow regimes found in a trickle-bed reactor are as follows. The trickling regime, a gas-continuous situation, prevails at low gas and low liquid flow rates. In it, the liquid moves down the bed in continuous liquid films on the catalyst surface and the gas phase flows as a continuous phase through the core of the passages. When the liquid does not completely wet the particles, the liquid films do not completely cover the surface of the particles, and “rivulets”, or streams of liquid, are noticeable. Here we put aside partial wetting conditions and focus on complete wetting situations. The pulsing regime appears at intermediate gas and liquid rates. In it, liquid-rich and gas-rich slugs pass down the column alternately. The spray regime occurs at high gas and low liquid rates. In it, liquid flows in continuous liquid films and also as entrained drops in a continuous gas phase. The bubbling regime appears at high liquid flow rates. In it, the gas phase is dispersed as bubbles in a continuous liquid stream. For industrial applications, it is, of course, vital to know how the flow regimes change with operating conditions,

i.e., to have the “flow regime map”. Because bed behavior depends on many variables and often on their histories, it is difficult to construct generalized flow maps, i.e., flow maps that can be used for particles of different sizes and shapes, and different fluid properties-densities, viscosities, and surface tension. Many searches have been made during the last two decades for flow maps (Charpentier and Favier, 1975; Talmor, 1978; Blok and Drinkenburg, 1981; Tosun, 1984). All that have been found have come from experiments on pilot-plant or laboratory-scale reactors, and to a great extent, scaling-up with them to industrial conditions has proved unreliable (Tarmy, 1982). To improve trickle-bed reactor design techniques, the fundamental mechanisms that give rise to the different flow regimes have to be elucidated. These mechanisms are rooted at the scale of the particles, which is where the two phases flow and compete for the available space. Here we report an experimental study of two-phase cocurrent downflow regimes and their transitions, with emphasis on the relationship of the macroscale or bed-scale flow regimes to the flow mechanisms in the “void spaces” or pores, where the “particle-scale” or “microscale” flow regimes reside. Here the bed-scale regimes, widely reported and described in the literature, are for the first time demonstrated to be the outcome of local competitions for the void space. The experiments were made in a transparent, almost two-dimensional network that is described in the next section and was used to mimic the void space of packed beds.

Experimental Procedure Figure 1 shows the experimental apparatus. A pump drove tap water to a distribution chamber. After passing through the network, the water was sent to a container and recirculated. The gas supply was compressed air, free of oil and essentially saturated with water, drawn from the laboratory line. Rotameters from Omega Engineering Inc., Stamford, CT, were used to measure gas and liquid flow rates. A t low gas rates, the Model FL 103 C-7643 rotameter, maximum air capacity of 233 m L / s std (measured and flowing at 1 atm and 70 OF), was used. At high gas flow rates, the Model FL 113 D5000 rotameter, maximum air capacity of 600 mL/s std, was used. Three rotameters were employed to measure the liquid flows; their maximum capacities were 110,53, and 30 mL/s to cover low, intermediate, and high liquid flow rates. The distribution chamber was an air-tight transparent Plexiglas cylinder of 35.4-cm diameter and 30.5-cm length. The air entered at the top of the chamber, where a cylindrical Styrofoam baffle, 25 cm in diameter and 10 cm long, redirected the air radially outward toward the chamber walls. Depending on the gas and liquid flow rates, the pressure in the chamber ranged from slightly subatmospheric to as much as 2 atm. The liquid was carried through a Tygon tube, 1.25 cm in diameter, to the bottom of the chamber where eight equal-size rectangular baffles, 2.5 cm x 7.5 cm, damped the liquid movement and the waves on the liquid surface. As shown in Figure 1, a pair of oppositely inclined wooden planes distributed the liquid supply as two films into the entrance of the network of passages. The planes were rectangular in shape, 7.5 cm wide and 9 cm long, with either a smooth upper edge and surface to provide even liquid distribution or a grooved upper edge and surface to provide pointwise distribution. The grooved surface had six equally spaced rectangular channels around 0.5 cm wide carved out of the wood. The two inclined planes were held in the desired position by a clamp that consisted of two transparent 15 cm X 10 cm X 2 cm

Ind. Eng. Chem. Res., Vol. 29, No. 12, 1990 2369

SCHEMATIC DIAGRAM OF THE EXPERIMENTAL APPARATUS

I

I I

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SIDE VIEW Figure 1. Experimental setup. The network dimensions are 30 cm long and 9 cm wide. A U-tube manometer measures low pressure drop (trickling regime). A pressure transducer measures high pressure drop (pulsing and bubbling regimes).

polycast plates joined with four threaded rods. The two inclines and the clamp made up a removable, self-contained liquid distribution unit. This unit rested on top of soft, 1/4-in.thick, fluorosilicone pads, positioned inside the distribution chamber, directly above the column entrance. The unit was secured to the bottom of the distribution chamber by four threaded rods with wingnuts for easy adjustment. The positioning of the adjusting rods in the four corners of the distribution unit in combination with the soft fluorosilicone pads allowed for easy adjustment of the distributor and thus of the position of the inclined planes. Visualization of microscale and macroscale flows was accomplished with the aid of a high-speed video camera (SP2000 Kodak Motion Analyzer, San Diego, CA). The pressure drop through the network was measured with a differential pressure transducer, Model PX236 (Omega Engineering, Stamford, CT), range 0-30 psi, a digital readout (Model DP350 benchtop pressure indicator, Omega Engineering), and a chart recorder. The chart recorder aided in determining the magnitude of pressure fluctuations. Figure 2 shows the “two-dimensional” network of passages, the simplest mimic of a packed bed that allows visualization of the complete pore space, or void space. The particles of the “solid” phase of the network consisted of Parker Seals rubber O-rings, Hardness 70, clamped into position between two transparent polycast plates of dimensions 30 cm X 9 cm X 0.65 cm. Two different networks were used. In one of them, the O-rings were 9-mm diam-

TRANSPARENT WALLS 9

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x 30

cm 2.2 mm

CLAMP SCREWS

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Figure 2. “Two-dimensional” packed bed. The arrangement of O-rings creates a diamond (rotated square) network in the void space.

eter and 2.3 mm thick; in the other, the O-rings were 7-mm diameter and 1.8 mm thick. The network assembly was mounted in a slit in the bottom of the distributor chamber and set through the fluorosilicone pad. Clay and Parafilm paper (American Can Co., Greenwich, CT) served as sealers


in the case of the smaller O-rings. In the latter case, the height of the bed was spanned by 24 rows of 9 sites each; consequently, rows of 17 passages alternated with the rows of sites. The bigger O-rings were arranged in a longer network of 30 rows of 5 sites each. The results from both networks were qualitatively the same, but flow visualization was easier with the bed packed with bigger O-rings. Before each use, the network was cleaned with a solution of Alconox Pipet Detergent and rinsed with tap water.

PASSAGE

(RUBBER O-RINGS

Figure 3. Flow network structure. Sites are cruciform wide spaces between the O-rings. Passages are convergent-divergent narrow spaces connecting sites.

between the slit and the outside walls of the network assembly. Figure 3 shows the void space between the O-ring particles in the experimental two-dimensional network. The space is a collection of enlargements (the sites of the network) connected by convergent-divergent flow passages (the bonds of the network). The O-rings were arranged in a rotated square array, in which each site has two inlet and two outlet bonds. The rotated square or diamond arrangement gives cruciform sites of dimensions approximately 7 mm X 5 mm X 2.3 mm interconnected by converging-diverging passages of rectangular cross section and throat dimensions of 2 X 2.3 mm in the case of the larger O-rings and sites of 5 mm X 3 mm X 1.8 mm interconnected by passages of throat dimensions 1.2 mm X 1.8mm

(I-

GAS-CONTINUOUS REGIME

e- BURBLING REGIME LOW GAS FLOW RATE

b- SPRAY REGIME

Microscale Flow States in Passages (Bonds) and Connections (Sites) De Santos et al. (1989) studied by experiment and theory the two-phase cocurrent downflow of air and water in single vertical constricted tubes, the constriction diameters being of the order of a millimeter, in the range of the sizes of pores in a trickle bed. In these tubes, the transitions between flow regimes occur a t gas and liquid Reynolds numbers (based on constriction diameter) that depend on the shape and size of the constricted tube. The same flow regimes as those described by de Santos et al. (1989) in cylindrical constricted tubes appeared in the passages of the two-dimensionalnetwork, which have rectangular cross sections. What follows is a description of the flow regimes found in a constricted tube with constriction radius r, = 1.2 mm, body radius-the radius of the tube outside of the constricted section-rb = 2.4 mm, and length of the constricted section I = 29.4 mm; the flow regimes were the same as we found in the 2 mm X 2.3 mm rectangular passages of the network packed with O-rings of 9-mm diameter. In what follows, the Reynolds numbers given are based on the constriction diameter and a velocity equal to the volumetric flow rate divided by the constriction area. Trickling flow appears in the tube a t low and intermediate liquid flow rates corresponding to ReL 5 1500, over a wide range of gas flow rates corresponding to ReG 5 600.

C-

BRIDGED REGIME

f-BUBBLING REGIME INTERMEVIATE GAS FLOW RATE

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d F W O D E D REGIME

6- DISPERSED BUBBLlh'G REGIillE

HIGH GAS FI.OIV RATE

Figure 4. Local or microscale flow regimes in the passages of the "two-dimensional" packed bed. (a) Trickling regime and (b) spray regime are gas-continuous regimes; liquid flows as a film over the network walls and particles (O-rings), and the gas flows through the remaining core space. (c) Bridged regime: gas is accessible to both ends of the passage, and liquid bridges the constriction. (d) Flooded regime: gas is not accessible to the passage, and liquid floods the passage. (e-g) Bubbling regime: bubble size and shape depend on gas flow rate.


A t higher gas rates, over the same range of liquid rates, gas tears drop off the liquid film so that the liquid flows not only as a film along the walls but also as entrained drops in the continuous gas phase; this is the spray regime. Figure 4a shows the trickling regime in the passages of the network. The liquid flows as a film on the surfaces of the particles and on the confining walls. Figure 4b shows the sprav flow regime, a special case of the more general gas-continuous flow regime. In the spray regime, the high gas flow rate thins the 1iquid.film and causes it to tremble below the constriction. There drops are torn off and carried away in the continuous gas flow. The same phenomenon was observed by de Santos et al. (1989) in single con str icted tubes. The bridged regime appears in the tube a t intermediate liquid rates corresponding to ReL i 2000. The liquid fills the throat of the passage; if the gas flow is zero, the liquid bridge is stable. IC'hen the gas flow is not zero, the gas arriving pushes the bridge down and opens the channel for a temporary gas-continuous flow. The pressure difference between the ends of the passage falls, the liquid film thickens, and finallv the liquid bridges the throat again. This alternation of the trickling and bridged regimes, called the pulsing regime, appears in the ranges 1500 IReL i ZOO0 and ReG 5 150. When ReL > 2O00, the liquid fills the tube completely and the bridged regime is replaced by the flooded regime. Figure 4c shows the bridged regime in the passages. The liquid clogs constrictions, and the gas-liquid interfaces take up positions inside them. A t high liquid rates, the gas is displaced from the adjacent sites and the liquid floods the passages as Figure 4d shows; this is the flooded regime in the passages. The bubbling regime appears in the tube at high liquid rates corresponding to RcL 2 2000 and low gas rates corresponding to ReG i 200. The gas flows as more-or-less spherical bubbles in a liquid stream. As the gas flow is raised, the bubbles deform and elongate. High liquid and gas rates corresponding to ReL 1 5000 and ReG 2 600 give a regime described elsewhere as dispersed bubbling. Figure 4e,f shows the bubbling regime in the passages of the network. When liquid flows down the network a t high rates, it fills most of the passages and junctions and the flowing gas is broken up into bubbles and entrained by the liquid. Figure 4e-g shows the effect of gas rate in the bubbling regime. Low gas rates produce small and spherical bubbles, whereas high gas rates produce the larger deformed bubbles of the dispersed bubbling regime. Trickling, bubbling, bridged, and flooded local flows are the elemental flow regimes a t the passage scale, that is, a t the microscale, in packed beds. These microscale flow regimes are ubiquitous in two-phase cocurrent downflow, and the macroscopic flow regimes are combinations of them. The pulsing regime, the alternation of bridged and trickling regimes, found in tubes in the transition between gas-continuous (trickling) and gas-discontinuous (bridged) regimes, also appears in the passages of the network, as Figure 5 shows. Gas and liquid compete not only for the passages but also for the enlargements, or sites, of the network. There are three different states of sites, according to what occupies them. Gas-dominated sites are those occupied mainly by the gas, with liquid present as films along the walls and the surfaces of the particles as seen in Figure fia. When the liquid is evenly distributed a t the top of the network a t low liquid Reynolds numbers, ReL i 200, all sites in the network are gas-dominated. Pendant drops appear on the

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Figure S. Pulsing regime in a passage of the network. Bridged and trickling regimes alternate in time.

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Figure 6. Types of sites in the 'two-dimensional" network. (a) Gas-dominated site, low gas flow rate: liquid flows as films over the surface of walls and particles, pendant drops hang from the O-rings, and gas occupies the remaining space. (h) Gas-dominated site, high gas flow rate: pendant drops shrink, liquid films are thin, and droplets are torn and carried away by the gas. (c) Contested sites: gas and liquid occupy the site in comparable amounts. (d) Liquid-dominated site: gas is present only as dispersed bubbles.

bottoms of the particles and grow by accumulating some of the liquid arriving locally. The size of the enlargements is critical to the existence of pendant drops. Rig enlargements, like those of the network used here and those of millimeter-size spherical particles and commercial packings, allow drops to hang from the solid surfaces. In tighter porous media that consist of smaller particles, liquid accumulates in the interstices between the particles, but there is no space for pendant drops to develop. From another point of view, the Bond number is constrained to be small, i.e., Ho between and because the diameters of the particles are small; that is, the gravitational effect responsible for pendant drops is limited by the small size of the particles. This can be understood in greater detail by noting that capillary pressure force, which arises in surface tension, tends to hold the liquid in the drop whereas gravity force


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Figure 7. Ten possible combinations of flow regimes in the two passages leading out of a site of a four-coordinated network. Gas-continuous (trickling) regime, bridged regime, and their combinations appear a t low local liquid flow rates in wide passages. Flooded and bubbling regimes appear at high liquid flow rates and in tight passages.

on the liquid tends to detach the drop. The same forces control the stability of drops hanging from the tip of a round tube (e.g., Adamson, 1982). In the present instance, viscous forces in the flowing phases also contribute to elongation and to detachment of the drop. In essence, the pendant drops are means of liquid accumulation and then, when they spawn droplets, of transport within a site while the gas phase is continuous there and in the connecting passages. The other liquid-transfer mechanism is also seen in Figure 6a and is through a liquid bridge to the nearestneighbor site. A t high gas rates corresponding to Rec 2 1400 and low liquid rates such that ReL I200 and where the flow is near or in the macroscale spray regime, bridges no longer appear in the constrictions and liquid droplets are torn off the pendant drops and carried away in the gas stream. In this situation, the pendant drops become smaller, and a substantial amount of liquid dispersed as drops is entrained by the gas, as Figure 6b shows. Contested sites are those where comparable amounts of both phases occupy the enlargement, as seen in Figure 6c. In contested sites, the accumulated liquid clogs one or more of the passages leading out of the site and breaks the continuity of the gas phase. In the experimental network with uniform liquid distribution a t the top, contested sites appear when the liquid flow is raised to intermediate values corresponding to 200 IReL 5 400, a t low and intermediate gas rates corresponding to 400 5 Rec I600. Liquid-dominated sites are those occupied mainly by liquid. The gas phase, if present, is dispersed as bubbles, as Figure 6c shows. Liquid-dominated sites appear in the

network as the liquid rate is raised so that ReL 3 600. If every site has 2 inflow passages and 2 outflow passages, and if there are 4 flow regimes-trickling, bubbling, bridged, and flooded-then there are 10 alternative combinations of outflow regimes in any 4-coordinated network like that used in the experiments. The possible combinations in the two passages leading out of a site are shown in Figure 7. The 10 combinations populate the network, and the statistical combinations of them define the different flow regimes a t the macroscale, as shown in the following sections.

Flow Regimes at the Macroscale To studv and describe the macroscale flow regimes in terms of the microscopic flow mechanisms, two sets of experiments were conducted. On the one hand, in 14 experiments at constant liquid flow rate (at ReL between 0 and 1500),the gas flow rate was raised from 0 by 12 equal increments up to a value corresponding to Rec = 1700. After the maximum flow was attained, the gas flow was reduced by equal decrements, so that the pressure drop and flow regimes were recorded again at the same flow rate settings. On the other hand, in 12 experiments et constant gas flow rates corresponding to Rec between 0 and 1700, the liquid rate was raised in 14 equal increments from 0 to a value corresponding to ReL = 1500 and subsequently was reduced. There was no appreciable hysteresis in the pressure drop or in the visual appearance of liquid distribution. Videotape images of macroscale flow spanning nine rows ( 6 5 cm) a t the center of the network and from two sites were recorded to make plain the macroscale and microscale


0

- GAS-CONTINUOUS

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BED SCALE SITE SCALE Figure 8. Macroscale gas-continuous (trickling) regime, transition between macroscale trickling and macroscale bubbling regimes, and bubbling regime when the liquid is fed uniformlv across the network entrance. (a) and (b) show the trickling regime a t the bed scale. Sites are gas-dominated everywhere: drops pendant from the bottom of the O-rings are noticeable. In passages, the regime is trickling. (c) Transition between the trickling and bubbling regimes. All types of sites (gas-dominated, liquid-dominated, and contested) and all types of regimes in passages (bubbling, flooded, bridged, and trickling) are present. (d and e) Macroscale bubbling regime. All sites are liquid-dominated, and the regime in the passages is buhhling (gas is dispersed as bubbles).

flows in each experiment (Melli, 1989). Trickling, Bubbling, and Spray Regimes. A t the bed scale, trickling flow appears a t low liquid and low gas rates. When the liquid is distributed uniformly over the upper boundary of the bed, it trickles over all the surfaces of the O-ring particles and walls of the network. The gas flows through the unoccupied pore space that remains. The trickling regime dominates the passages. Pendular drops form at the bottom of most particles, grow, and either drip over the particle below or are diverted laterally by the flowing gas as it falls. In this latter instance, the drop is likely to touch a neighboring particle and temporarily clog the passage-the locally bridged regime-so that liquid is transferred to the next particle. Liquid is then transferred directly from the particle to i t s neighbor; however, liquid is always being transferred along the two walls between which the O-ring particles are clamped. A t ReLI200, the state of the sites is gas-dominated everywhere, and pressure fluctuations in the chamber are negligible (in the range of 50 Pa, which is the sensitivity of the pressure transducer that was used). Figure 8b shows a close-up on the site scale. Here the dimensionless numbers, based on the constriction hydraulic diameter (d, 4 A / P , where A is the cross-sectional area of the constriction and P is the wetted perimeter), are ReL = 100, Rec = 200, CaL = 5 X and Bo = 0.61. As the liquid rate is raised so that the Reynolds number is above ReL= 250 at low gas rates (Rec i 300),the liquid holdup in the network increases. The competition for site space begins. The liquid clogs some of the flow passages, and sequences of liquid-bridged passages form streams of

liquid through the pore space--"liquid filaments" in the terminology of Ng (1986). Then some sites become contested or dominated by liquid, and more compact clusters rather than strings of liquid-dominated sites are formed. Whereas in the trickling regime, gas and liquid flow locally in those portions of the bed where the sites are gas-dominated, the bubbling regime appears in passages connected to liquid-dominated sites. The distribution of gas and liquid changes. Liquid and gas follow parallel paths, or channels, along the network; the "channeling" phenomenon, so much reported in countercurrent operation, becomes noticeable. All flow regimes in the passages, as shown in Figure 4, and all types of sites, as shown in Figure 6, are found at the microscale as seen in Figure &. In this region of operation, the transition region between trickling and bubbling regimes extends to ReL around 500. A t still higher liquid rates corresponding to ReLabove 600 and a t low gas rates, the gas is totally dispersed as bubbles. Gas-dominated and contested sites are scarce, and liquid fills most passages and sites. The bubbling and flooded regimes dominate the passages. The macroscale flow regime is bubbling and is shown in Figure tM. Figure 8e shows a closeup of sites in the bubbling regime. The bubbling regime region studied here covers the range of capillary numbers, eaL,between 4 X and 1 X and liquid Reynolds numbers between 600 and 1500. The maximum gas Reynolds number, ReCmax, in the bubbling regime increases as the liquid rate is raised. A t the lowest liquid rate in the bubbling regime, which corresponds to ReL = 600, the maximum gas Reynolds number is ReCmax = 300; at the high liquid rate studied, corresponding to ReL


I.YCREA.Sl,I'G l.lQt5rll) F1.0~1' RATE

-

Figure 9. Macroscale gas-continuous (trickling) regime, transition between macroscale trickling and macroscale bubbling regimes,and bubbling regime when the liquid is fed only at the sides of the network entrance. (a and b) Local bubbling regime and liquid-dominated sites at the network's sides: in the center of the network, gas f l o w alone. ( c and d) Liquid bridges and trickling regime appear in the passages at the center of the network, pendant drops appear in the sites there, and the gas-dominated region shrinks. (e) The macroscale flow regime is bubbling all across the network. (f) At very high liquid flow rates, the liquid floods the sides of the network and gas is carried as dispersed bubbles though the center of the network.

= 1500, the bubbling regime appears a t all gas rates studied. The effect of the liquid distribution a t the top of the network on the transition between the trickling regime and the bubbling regime is shown in Figure 9. In this instance, liquid was fed only a t the left and right sides of the network. The heavier liquid flow a t the sides of the network is made evident by the large clusters of liquid-dominated passages and sites that span the length of the network and resemble the "liquid filaments" described by Ng (1986). In those clusters, the flowing gas is dispersed as bubbles. The lighter liquid flow in the center of the network is evident in the channeling of gas there. Gas and liquid flow in parallel flow paths: see Figure 9, a and b. The width of the gas path spans three sites. A rise in the liquid flow rate widens the lateral liquid filaments, as Figure 9c shows; the gas-dominated channel a t the center of the bed narrows. Gas and liquid channels span the length of the short bed. A t intermediate liquid rates corresponding to ReLnear 400, the bridged regime becomes noticeable in the gas channel, yet the bubbling regime still dominates in the liquid-rich filaments: see Figure 9, d and e. As the liquid rate is subsequently raised, to about ReL = 700, a bubbling regime similar to that in the experiment with well-distributed liquid ensues. As the liquid rate is raised even further, a t ReLaround 1O00, the liquid filaments at the sides of the network become totally flooded by liquid, and gas flows in the bubbling regime in the central part of the network, as can be seen in Figure 9f. In the macroscale trickling regime, the way liquid is distributed a t the top of the bed strongly affects the local

flow regimes. When the liquid distribution is uniform, the trickling regime prevails locally, but when the liquid is maldistributed, channeling arises. Moreover, bubbling, bridged, and flooded local regimes appear in the regions of heavy liquid flows. There the local liquid Reynolds and capillary numbers are on the order of those found in the bubbling regime. In the range of liquid rates such that ReLi 200 and high gas rates such that ReG > 1300, the trickling regime is replaced by another continuous gas regime: the spray regime, shown in Figure 10. Drops are torn off the pendular liquid suspended from the particles as well as from the liquid films. The flow in passages is gas-continuous, the liquid films are thinner than in the trickling regime, and liquid drops are entrained in the gas. All the sites are gas-dominated, and the dripping mechanism of liquid transfer in the sites is negligible. Transition from the Trickling Regime to the Pulsing Regime. Pulse Formation. A t intermediate gas rates corresponding to ReG between 400 and 1300 (again based on the constriction hydraulic diameter), by raising the liquid rate from the low values characteristic of the trickling regime, i.e., ReL i 200, to intermediate values, such that ReL = 500, the flow regime a t the macroscale evolves from the gas-continuous (trickling) regime to a transition between gas-continuous and pulsing. The first indication of local pulses appears in the form of liquid-rich clusters located in small sections of the network, as pictured in Figure l l a . The sites in these clusters are gas-dominated, and the flow passages switch from the trickling to the bridged regime in a cyclic sequence-pulsing a t the microscale regime. The rest of


n

a-SPRAY REGIME

- BED SCALE

-

a END OF GAS-CONTINUOUS REGIME

LOW LIQUID SATURATION

-

b BEGINNING OF TRANSITION

b-SPRAY REGIME

- SITE SCALE

Figure 10. Macroscale spray regime at high gas flow rates at (a) the bed-scale (macroscale) and (b) the site scale. All sites are gas-dominated, pendant drops are small, liquid drops are carried by the gas stream, and the liquid flows down as films over the network walls and O-rings' surfaces.

the network displays trickling flow in the passages. These liquid clusters move along the network a t low velocities-O.5 to 0.7 m/s. The frequency with which they pass a given point is not constant. The overall macroscale flow regime is still gas-continuous, and the liquid saturation is low. The frequency of pulses was measured by counting the number of pulses traveling across the test section per second; the velocity was calculated from the time it takes a pulse to travel across the test section of known length. The pulse velocity was greater than the volumetric flow rate of liquid per unit cross-sectional area. A t higher liquid rates that correspond to ReL = 300 or so, the transition between gas-continuous and pulsing regimes is more evident. The liquid clusters span only one row of sites but grow laterally and extend across almost the entire width of the narrow network (Figure Ilb). In the liquid-rich slugs, the passages perform local bubbling. Ahead of a liquid-rich slug, passages evolve from trickling to pulsing to bubbling regimes, and behind a liquid-rich slug, they evolve in reverse order. In the transition between gas-continuous and pulsing regimes, the pulse frequency is defined better than a t the end of the gas-continuous (trickling) regime. In the gas-rich slugs, the pas-

GAS-CONTINUOUS

- PULSING

Figure 11. Transition between macroscale trickling regime and macroscale pulsing regime. (a) Trickling regime before transition. A liquid-rich cluster appears at the center-right of the network where passages perform in the bridged regime and sites are contested. In the rest of the network, the sites are gas-dominated and the passages perform in the trickling regime. (b) 'T'ransition between macroscale trickling and pulsing regimes. Liquid-rich cluster grows and spans the width of the network.

sages perform in local trickling flow and the sites are dominated bv gas. Several authors-Ng (1986) and Blok and Drinkenburg (1981), among others-have reported that pulses first appear a t the bottom of the reactor while the top section works in the trickling regime. To visualize how pulses form and evolve, two cameras were focused a t two test sections of our network, each 4 cm in height, one located 15 mm from the top and the other 5 mm from the bottom. Then experiment? were made within the transition between the trickling and pulsing regimes, i.e., at ReLbetween 300 and 500 and ReG between 400 and 800. Flow visualization revealed the pulse formation mechanism, as detailed in Figure 12. The upper section operated in the gas-continuous regime with some liquid clusters, called here "protopulses", forming in tight pore spaces. These small liquid clusters are shown in the center and right of Figure 12, a and i. The operation in the lower section was quite different. Pulses that spanned the bed width, shown in Figure 12b-h, entered this section, passed through, and exited. Pulses appeared first a t the bottom of the network, but they had been born as small liquid-rich


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Figure 12. Transition between macroscale trickling regime and macroscale pulsing regime. The top half of each photograph shows a section 15 mm below the network top: the bottom half of each photograph shows a section 5 mm above the bottom of the network. Top operates in trickling regime: all sites are gas-dominated, and all the passages perform in trickling regime although sporadic liquid bridges appear in passages (see a and i). Bottom: a liquid-rich pulse enters the test section (b), travels down (c-g), and leaves the test section (h and i).

clusters or protopulses in the upper part. These protopulses, which seem to be generated where smaller pores happen to prevail, are seeds of bigger and well-defined pulses. Insight into the formation of protopulses can be gained from the experiments in single constricted passages reported by de Santos et al. (1989). A t low gas rates, the liquid flow a t the transition between gas-continuous (trickling) and gas-discontinuous regimes (pulsing and bubbling) depends on the gas rate. Higher gas rates (higher gas velocities in the passages) tend to keep the passages performing in the trickling regime, and therefore higher liquid rates are needed to clog the constrictions. The pressure at the top of the experimental network was higher than at the bottom-for example, a t ReId= 350 and Rec = 650, the pressure drop through the network was 16500 Pa-and consequently the density of the gas was 16% higher in the top than in the bottom of the network. The gas mass rate was constant, so the volumetric gas rate in the top, and therefore the local velocity there, was 16% lower than in the bottom. The limit of the trickling regime was reached first a t the top of the network where the gas velocity was lower. There the liquid blocked the throats of the passages and liquid accumulated in neighboring sites, becoming the seeds of liquid-rich clusters.

The evolution from small liquid clusters in the top section to defined pulses in the lower part of the bed also was illuminated by flow visualizations a t the microscale. The pulse velocity, measured experimentally a t either of the sections observed, rose as the pulse size grew. Big pulses moved down faster than small ones and overtook them, generating new and even bigger pulses of higher velocity. As the liquid pulses flowed down the bed, many small pulses coalesced into bigger ones, spanned the entire cross-sectional area, and became noticeable a t the bottom of the bed. The mechanism of formation of pulses, called here the "overtaking mechanism", is shown in Figure 13 for ReL= 450 and RcC = 1080. Figure 13a shows a gas slug and small liquid pulse arriving a t the upper observation section of the bed. The liquid saturation in the gas pulse increases near the bottom of the test section (the tail of the previous liquid-rich slug) and almost all the passages operate in the local gas-continuous regime. In Figure 13, b and c, a small pulse (spanning one row of the packing) can be seen that travels down the column. In the liquid-rich slug, the passages perform in local bubbling. Ahead of a liquid-rich slug, sites evolve from gas-dominated to contested to liquid-dominated and behind from liquid-dominated to contested to gas-dominated.

Ind. Eng. Chem. Res., Vol. 29, No. 12, 1990 2377 D

I

-

-

r CE.\’TER: SMAIJ. IJQl’ID PI ’WE

f GAS PHASE BREAKS IJQUID

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Figure 13. Overtaking of a small pulse by a big pulse in the transition from trickling to pulsing regime. A small pulse spans one row of sites (b and c). A big pulse spans two rows of sites (f and g). The gas-rich slug between liquid-rich slugs shrinks and disappears (h-j). The original two pulses travel out of the section as a single pulse.

In Figure 13d, the front of a big liquid pulse (about twice the size of the small one) appears in the observation section. In the next two photographs, Figure 13, e and f, the gas trapped between the liquid pulses breaks through some of the passages of the small pulse, and the gas slug trapped between the pulses shrinks. Figure 13g shows both liquid pulses connected in the left of the test section and a small gas pocket on the right. In the last three photographs of the sequence, both pulses travel out of the observation section as one big liquid pulse spanning more than four rows of the bed. Within the transition between the trickling and pulsing regimes, as the pulsing regime is approached, liquid-rich pulses of different sizes and velocities can be found. Instead of the diffuse band of pulse frequencies found a t lower liquid flow rates, the pulses have definite velocities and frequencies that increase monotonically with the liquid flow rate. Pulsing Regime. The pulsing regime appears a t ReG > 500 when RcL is between 450 and 800. The pulse size and velocity are clearly defined when compared with the size and velocity of the pulses in the transition between the trickling and pulsing regimes. A t ReL= 600 and Rec = 800, the velocity of pulses is about 2 m/s, and the liquid-rich slugs span four or five rows in the network. The sequences of Figure 14 and 15 show the pulsing regime a t the bed scale and site scale. Figure 14 demonstrates that the liquid saturation changes sharply between the tail of the gas-rich slug and the front of the liquid-rich slug. The sites in the liquid-rich slugs are all liquid-dominated, the passages perform in the bubbling or flooded regime, and the liquid saturation is high. The liquid-rich slug extends across the narrow bed and spans four to five rows of sites. The liquid saturation

subsides smoothly at the back of the liquid-rich slug as the sites evolve from liquid-dominated to contested to gasdominated, and the flow regimes in the passages evolve from bubbling to bridged to trickling in the gas-rich slug. Figure lfia, a close-up of pulsing regime, shows the tail of the gas slug. As the liquid slug approaches, passages are bridged by liquid; then the flooded or bubbling regime takes over. The liquid arriving accumulates in the sites, and the sites evolve from gas-dominated to contested to liquid-dominated; see Figure 15, b and c. In the middle of the liquid slug, the passages perform in the bubbling regime and sites are liquid-dominated, as they are in the bubbling regime a t the macroscale: see Figure E d . The tail of the liquid slug (the front of the following gas-rich slug) leaves contested sites where pendant drops are noticeable and dripping of liquid is the main mechanism of liquid transfer, as it is in the trickling regime a t the bed scale: see Figure 15e. In this example, the total time elapsed in the filling-emptying cyclic sequence is 9 ms; therefore, sites and passages are flooded on a time scale of the order of a millisecond or less. Transition from the Pulsing to the Bubbling Regime. A t high liquid flow rates corresponding to ReL 1 800 and gas rates such that Rec 1 500, the bed-scale pulsing regime evolves to the bubbling regime. In this transition, the liquid-rich slugs are big and the gas-rich slugs are small. As the liquid rate is raised, more gas is entrained as bubbles, the gas saturation inside the liquid-rich slugs increases, and the gas-rich slugs shrink. The gas is trapped in localized pockets that do not span the width of the bed, and more sites perform continuously as liquid-dominated. There is no longer a clear distinction between the tail of a liquid pulse and the front of the following one.


-

a TOP : FRONT OF

LIQUID PUISE CENTER & BOTTOM: GAS S I N G

-

-

b TOP: IJQUID RICH SLUG RO7TOM:TAII. OF GAS SING

C- TOP: IJQUID RICH SLUG ROTTOM:TAII, OF GAS SLUG

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e BOTTOM : LIQUID RICH SLUG f - T A I L OF LIQUID RICH SLUG T0P:TAlL OF LIQUID RICH SIJYG Figure 14. Macroscale pulsing regime a t the bed scale. The liquid-rich cluster spans four rows of the network. The liquid saturation decreases graduallv from the front to the back of the gas-rich slug.

d LIQUID RICH SING

Figure 15. Macroscale pulsing regime a t the site scale. A t the back of the gas-rich slug:, (a) the sites are gas-dominated and the passages perform in the trickling regime. Pendant drops are small. In (b) and (c), the liquid invades passages and sites become contested. (d) In the liquid-rich slug, the sites are liquid-dominated and the passages perform in the bubbling regime. (e) A t the back of the liquid-rich slug and the front of the gas-rich slug that follows, the sites are contested and the passages perform in the bridged regime. (c) A t the t a i l of the gas-rich slug, the sites are gas-dominated and the passages perform in the trickling regime.

Ind. Eng. Chem. Res., Vol. 29, No. 12, 1990 2379 When the bed-scale bubbling regime is reached, at high enough liquid rates that ReL L 900, the gas is totally dispersed as bubbles, and the liquid saturation and the overall pressure drop in the network increase sharply.

Conclusions The macroscale flow regimes found in the experiments in an almost two-dimensional network resemble those found in trickle-bed reactors (cf. Charpentier and Favier, 1975; Blok and Drinkenburg, 1981) and can be described in terms of the local or pore-scale flow regime. Thus, it appears that the microscale flow regimes in trickle beds and the experimental network also parallel each other. Four main microscale flow regimes-trickling, bridged, flooded, and bubbling-can combine in the 2 outlet passages of a site to give any 1 of 10 different outflow states, all of them found in the experimental study reported in this paper. For the first time, the macroscale flow regimes are described in terms of different combinations of microscale regimes-themselves outcomes of competitions of the gas and liquid for the void space. The macroscale bubbling regime is formed by passages performing in the bubbling and flooded regimes and by liquid-dominated sites. The gas-continuous or trickling regime is formed by gas-dominated sites and the trickling and bridged regimes in the passage. Liquid dripping and bridging are the dominant mechanisms of liquid transfer in the trickling regime. The pulsing regime is formed by liquid-rich slugs that, a t the microscale, resemble the bubbling regime and gas-rich slugs that, at the microscale, resemble the trickling regime. Ahead of and behind the liquid-rich slugs appears the bridged regime in passages and contested sites. The first indication of pulses arises when the bridged regime in the passages becomes noticeable. The pulses can be seen all along the bed, but they are smaller a t the top-where the liquid-rich slugs are generated-and increase in size and velocity toward the middle and bottom of the bed owing to the overtaking of the small and slow pulses by big and fast ones. The microflow visualizations at the site scale reveal the existence of multiple combinations of local flow regimes in passages and of site states and so provide a basis for development of comprehensive theory of cocurrent downflow in packed beds (Melli, 1989; Melli and Scriven, 1991; de Santos et al., 1990). Nomenclature A = cross-sectional area of constriction, m2 Bo = Bond number, [D2(pL- p,$g]/u, dimensionless Ca = capillary number, V / u, dimensionless D = characteristic length, m d , = hydraulic diameter of the constricted passage, 4A/P, m g = accelaration of gravity, m/s2 P = wetted perimeter of constriction, m r b = body radius of the constricted tube, m rt = constriction radius, m

Re = Reynolds number, p V D / p , dimensionless V = characteristic velocity, m/s p = viscosity, kg/(ms) p = density, kg/m3 u = surface tension, kg/s2 Subscripts G = gas L = liquid

Literature Cited Adamson, A. W. Physical Chemistry of Surfaces; John Wiley & Sons: New York, 1982. Blok, J. R.; Drinkenburg, A. A. H. Hydrodynamics and Mass Transfer in Pulsing Trickle Bed Columns;ACS Symposium Series 196; American Chemical Society: Washington, DC, 1981; pp 393-401. Charpentier, J. C.; Favier, M. Some Liquid Holdup Experimental Data in Trickle Bed Reactors for Foaming and Non-foaming Hydrocarbons. AZChE J . 1975,21, 1213-22. de Santos, J. M.; Melli, T. R.; Scriven, L. E. Cocurrent Downflow in Packed Beds: Basic Flow Mechanisms in Individual Passages. Presented at the AIChE Spring National Meeting, Houston TX, April 2-6, 1989; Paper 87B, to be submitted for publication. de Santos, J. M.; Melli, T. R.; Scriven, L. E. Mechanics of Gas-liquid Flow in Packed-Bed Contactors. Ann. Rev. Fluid Mech. 1990, in press. Giannetto, A. G.; Baldi, G.; Specchia, V.; Sicardi, S. Hydrodynamics and Solid-Liquid Contacting Effectiveness in Trickle-Bed Reactors. AZChE J. 1978,24, 1087-93. Herzkowitz, M.; Smith, J. M. Trickle Bed Reactors: A Review. AZChE J . 1983, 29, 1-18. Melli, T. R. Two-Phase Cocurrent Downflow in Packed Beds; Macroscale from Microscale. Ph.D. Dissertation, University of Minnesota, Minneapolis, 1989; Distributed by University Microfilms International, Ann Arbor, MI. Melli, T. R.; Scriven, L. E. The Theory of Two-Phase Cocurrent Downflow in Networks of Passages. Znd. Eng. Chem. Res. 1991, in press. Mohanty, K. K. Fluids in Porous Media. Two-Phase Distribution and Flow. Ph.D. Dissertation, University of Minnesota, Minneapolis, 1981; Distributed by University Microfilms International, Ann Arbor, MI. Ng, K. M. A Model for Flow Regime Transitions in Cocurrent Downflow Trickle Bed Reactors. AIChE J. 1986, 32, 115-22. Ng, K. M.; Davis, H. T.; Scriven, L. E. Visualization of Blob Mechanics in Flow through Porous Media. Chem. Eng. Sci. 1978,33, 1009-17. Satterfield, C. N. Trickle Bed Reactors. AZChE J. 1975,21, 209-21. Taitel, Y.; Barnea, D.; Dukler, A. E. Modelling Flow Pattern Transition for Steady Upward Gas-Liquid Flow in Vertical Tubes. AZChE J . 1980,26, 345-52. Talmor, E. Two-Phase Downflow through Catalyst Beds. Part I; Flow Maps. AIChE J . 1978,23, 868-73. Tarmy, B. L. Reactor Technology. In Kirk-Othmer Encyclopedia o f Chemical Techno1og.y; __ John Wiley & Sons: New York, 1982; Vol. 19, pp 880-914. Tosun. G. A Studv of Cocurrent Downflow of Nonfoamine GasLiquid Systems”in a Packed Bed. 1. Flow Regimes: Search for a Generalized Flow Map. Ind. Eng. Chem. Process Des. Deu. 1984, 23, 29-34.

Received for review November 2, 1989 Revised manuscript received May 10, 1990 Accepted May 23, 1990

Cocurrent Downflow in Networks of Passages ... - ACS Publications

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