Ind. Eng. Chem. Res. 2005, 44, 7529-7539
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Holdup and Residence Time Distributions in Inclined Dishes Paul C. Chadwick,† Sarah L. Rough,‡ and John Bridgwater*,‡ School of Chemical Engineering, University of Birmingham, Edgbaston, Birmingham B15 2TT, U.K., and Department of Chemical Engineering, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, U.K.
Inclined rotating dishes are commonly used for particle processing, but the flow behavior of the bed has received little attention. Experiments using nongranulating solids showed that the fractional volumetric holdup was related to the material flow pattern, being dependent upon the rotational Froude number, the dish aspect ratio (rim height/diameter), and the angle of dish inclination. A magnetic tracer method was used to determine the particle exit age distributions. For a monosized feed, the dimensionless variance of the exit age distribution and the rotational Froude number were linearly related and independent of the dish diameter. For two-component feeds, the exit age distributions of the components were not the same and considerable differences were found when one component was present in a small proportion. If the components were of equal proportions, there was a marked and fairly consistent extent of segregation, whatever the operating conditions. 1. Introduction Despite widespread significance, the internal flow behavior in many pieces of processing equipment for fine powders remains unknown. For example, fine powders can readily be formed into granular masses by spraying a liquid phase onto the surface of a bed in a rotating inclined dish, employing the agitation arising from the rotation. Solids are fed batchwise or continuously onto the central part of the dish and are discharged as agglomerates over the rim (Figure 1a). Particle size enlargement is then achieved by collisions of moist particles within the bed. However, design and operation take place with little detailed understanding of the flow patterns occurring within the dish. A characteristic of the inclined dish is its pronounced size-segregating action. This causes the larger particles to be discharged preferentially from the surface of the bed over the rim, while smaller particles are retained for further processing. There are many detailed designs including ones with a side-wall scraper (to promote a more efficient rolling action) or a bottom-wall scraper (to promote the development of a uniform protective layer of particles on the base of the dish). The design and operation of dishes for agglomeration in various industries have been reviewed extensively.1,2 For large tonnages, the dish finds its main application in the granulation of mineral ores, fertilizers, and material for cement kilns. For instance, Young and McCamy3 used dishes for the manufacture of highnitrogen-content fertilizers, yielding products that were nondusting and hard, with excellent handling and storage properties. There is now an increased use in the small- and medium-scale production of higher value products in many industries, such as detergents and pharmaceuticals. Despite the lack of scale-up procedures, the dish granulator offers an attractive proposition for making trial quantities, as well as for commercial operation. * To whom correspondence should be addressed. Fax: +441223-334796. E-mail:
[email protected]. † University of Birmingham. ‡ University of Cambridge.
Figure 1. (a) Schematic diagram of the dish at low speeds of rotation and (b) notation used.
The literature contains little coherent quantitative data pertaining to the dish. Primarily, studies have been concerned with specific agglomerating conditions, and at best, qualitative descriptions of solids movement have been given. Dish operation, thus, remains an art, since the optimum conditions are found by trial and error in the development stage. The common design features discussed are dish diameter D, rim height h, angle of
10.1021/ie040252z CCC: $30.25 © 2005 American Chemical Society Published on Web 08/20/2005
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Ind. Eng. Chem. Res., Vol. 44, No. 19, 2005
Figure 2. Some typical flow patterns and regimes encountered in the inclined dish.
dish inclination θ, and rotational speed ω, as defined in Figure 1b, together with the power requirement P. These parameters interact and determine the internal flow and product properties such as shape, size, and porosity. Usually these parameters are studied one by one.4 For continuous operation, the residence time in the dish can be increased either by decreasing the throughput or by raising the holdup, the latter being achieved by increasing the dish depth or decreasing the angle of inclination. A decreased angle of inclination increases the surface area of the dish in contact with the solids, and this, in turn, increases the amount of material carried to higher trajectories at the top of the dish, raising the solids holdup. According to Sherrington and Oliver,2 increasing the ratio of the rim height to the dish diameter (h/D) further increases the segregating action. Excessive speed can, however, lead to loss in the segregating action and degradation of the particles. In some processes, the mean residence time is insufficient to describe the process at its optimum performance, since more details are required of the history of the particles inside the dish. In such cases, the residence time distribution can be helpful. This distribution was investigated by Bhrany et al.5 using salt as a tracer; the results were fitted to an exponential decay function derived on the assumption of perfect mixing. The mean residence time calculated from a stimulus response technique was in good agreement with experimentally determined values of holdup. Bitsianes6 argued that the exponential decay was due to the feed material being quickly and uniformly distributed over the cascading surface layer and that, accordingly, some material leaves immediately and some is retained indefinitely. However, no attempt was made by Bhrany et al.5 to relate the residence time to the operating variables. Delwel and Veer7 investigated residence time distributions using methylene blue as a tracer; their results were interpreted in terms of a flow model of two tanksin-series. Chadwick and Bridgwater8 have shown the effect of dish and material properties on the material flow patterns and the power requirement. Results for different dish diameters could be unified using a dimensionless representation. At very low speeds of dish rotation, the surface of the bed is flat and, as the speed of rotation increases, the material forms a profile looking rather like a kidney (Figure 2). The surface profile becomes more crescent-shaped as the speed of rotation increases, with the material then cascading onto the surface, forming a “tongue” which extends up the slope opposite to the main bed. Direct observation of the
internal structure of mixtures developed in a batch inclined dish using positron emission particle tomography (PEPT) was given by White et al.9,10 They argued that different mechanisms of segregation were present in the rising and falling regimes of the bed. A better understanding of the flow of solids within dish granulators would assist in optimizing performance, thus reducing capital investment and operating costs and improving product quality. For instance, when the speed is less than the optimum, the material does not reach the top point of the vertical diameter. When the speed is raised above the optimum, a crater is formed in the center of the dish: the material is often deflected by a scraper and rolls downward in a rapid, narrow stream, inhibiting size segregation. In both cases, incomplete use of the dish surface, whether for liquid addition or heat transfer, occurs. Here it is shown how insight into the behavior of close-sized and two-component materials in a rotating inclined dish, as may be used for granulation, drying, and reaction, can be obtained. The specific aims are as follows: (i) to investigate the volumetric holdup and its internal distribution using dimensional analysis for a continuously operating inclined dish; (ii) to develop and apply a technique to allow the ready measurement of residence time distributions; and (iii) to study the properties of the residence time distribution for a continuous system for both monosized or binary feed materials. 2. Equipment and Materials 2.1. Dishes. Two geometrically similar stainless steel dishes were used, with diameters 0.25 and 0.5 m. Each was mounted on an inclining frame, which allowed the angle of inclination to be varied between 0° and 90° with an accuracy of (0.25°. The speed of rotation ranged from 0 to 300 rpm for the smaller dish and from 0 to 50 rpm for the larger one. Up to 50 rpm, the speed was accurate to (0.1 rpm, and above 50 rpm, it was accurate to (1 rpm. Dish rims could be exchanged so that the ratio of rim height to dish diameter could be 0.25, 0.5, and 0.75 for each dish. The internal surfaces of the dishes were lined with grade P36 abrasive paper to avoid erratic bed slip near the rim. Before commencing each test, the rim height, angle of inclination, and speed were fixed. Solids were charged via a hopper, which emptied into a trough mounted on a vibratory feeder. This feeder transported the solids to a chute positioned over the bed in the dish. The solids flow rate was adjusted by a vibratory feed controller, and the position at which the solids hit the bed surface was controlled by maneuvering the chute. Material was fed at a rate of 5-10% of the maximum dish volume per minute, based on the bulk density of the solids, until it began to cascade over the rim into a container. The system was then assumed to be operating in a steady continuous state. Extended sidearms of the inclining frame could provide side-wall and base scrapers inside the dish. For experiments on holdup, a special bed divider could be used to sample the material in each of six equal-width regions into which the contents of the dish were sectioned. The divider, consisting of equally spaced semi-circular metal sheets (the diameter of which corresponded to the dish being used), was attached to a shaft that was positioned axially within the dish. This divider was dropped into the bed after the dish rotation
Ind. Eng. Chem. Res., Vol. 44, No. 19, 2005 7531 Table 1. Physical Properties of the Uncoated and Magnetically Coated Solid Particles material
coating
particle diameter, µm
particle density, kg m-3
bulk density, kg m-3
poured angle of repose, deg
drained angle of repose, deg
400-500 µm glass ballotini 2 mm glass ballotini
none none
