Pressure drop particles

The Poppe plot is a log-log plot of H/uq = t(JN versus the number of plates with different particle sizes and with lines drawn at constant void time, t(). H is the plate height, Vis the number of plates, and u() is the fluid velocity (assumed equal to the void velocity). The quantity H/u() is called the plate time, which is the time for a theoretical plate to develop and is indicative of the speed of the separation, with units of seconds. In the Poppe plot, a number of parameters including the maximum allowable pressure drop, particle diameter, viscosity, flow resistance, and diffusion coefficient are held constant. 

A packed and a capillary column are observed to have flowrates of (2, and Q2, respectively. If the diameter of both tubes are tripled while all other parameters (e.g., pressure drop, particle diameter, viscosity) are held constant, what are the new flow-rates ... 

C 20 line cohesive interparticle forces e.g., flour channel rather than fluidize pressure drop < particle weight fluidization improved by stirring vibration addition of submicrons anti-electrification ... 

Much of the information on hydrate processes has come from macroscopic studies, that is, from the observation of gas consumption, pressure drop, particle size measurements, or crystal morphology observations. However clathrate hydrates in many ways are unique materials that make it imperative that studies on the molecular scale are also carried out. For instance, several structures of hydrate may coexist, and often this is not obvious from phase equilibrium studies ... 

A considerable reduction in particle size separation can be achieved at the expense of increased pressure drop using a Venturi scrubber (see Fig. 11.2c). 

Bag filters. Bag filters, as discussed in Chap. 3 and illustrated in Fig. 3.66, are probably the most common method of separating particulate materials from gases. A cloth or felt filter material is used that is impervious to the particles. Bag filters are suitable for use in very high dust load conditions. They have an extremely high efficiency, but they suflFer from the disadvantage that the pressure drop across them may be high. ... 

Centrifugal demister or cyclone) devices rely on high velocities to remove liquid particles and substantial pressure drops are required in cyclone design to generate these velocities. Cyclones have a limited range over which they operate efficiently this is a disadvantage if the input stream flowrate is very variable. 

Macroscopic properties often influence tlie perfoniiance of solid catalysts, which are used in reactors tliat may simply be tubes packed witli catalyst in tlie fonii of particles—chosen because gases or liquids flow tlirough a bed of tliem (usually continuously) witli little resistance (little pressure drop). Catalysts in tlie fonii of honeycombs (monolitlis) are used in automobile exliaust systems so tliat a stream of reactant gases flows witli little resistance tlirough tlie channels and heat from tlie exotlieniiic reactions (e.g., CO oxidation to CO,) is rapidly removed. 

Catalyst particles are usually cylindrical in shape because it is convenient and economical to fonii tliem by extmsion—like spaghetti. Otlier shapes may be dictated by tlie need to minimize tlie resistance to transport of reactants and products in tlie pores tlius, tlie goal may be to have a high ratio of external (peripheral) surface area to particle volume and to minimize the average distance from tlie outside surface to tlie particle centre, witliout having particles tliat are so small tliat tlie pressure drop of reactants flowing tlirough tlie reactor will be excessive. 

Elution volume, exclusion chromatography Flow rate, column Gas/liquid volume ratio Inner column volume Interstitial (outer) volume Kovats retention indices Matrix volume Net retention volume Obstruction factor Packing uniformity factor Particle diameter Partition coefficient Partition ratio Peak asymmetry factor Peak resolution Plate height Plate number Porosity, column Pressure, column inlet Presure, column outlet Pressure drop... 

Pressure Drop. The prediction of pressure drop in fixed beds of adsorbent particles is important. When the pressure loss is too high, cosdy compression may be increased, adsorbent may be fluidized and subject to attrition, or the excessive force may cmsh the particles. As discussed previously, RPSA rehes on pressure drop for separation. Because of the cychc nature of adsorption processes, pressure drop must be calculated for each of the steps of the cycle. The most commonly used pressure drop equations for fixed beds of adsorbent are those of Ergun (143), Leva (144), and Brownell and co-workers (145). Each of these correlations uses a particle Reynolds number (Re = G///) and friction factor (f) to calculate the pressure drop (AP) per... 

Some empirical equations to predict cyclone pressure drop have been proposed (165,166). One (166) rehably predicts pressure drop under clean air flow for a cyclone having the API model dimensions. Somewhat surprisingly, pressure drop decreases with increasing dust loading. One reasonable explanation for this phenomenon is that dust particles approaching the cyclone wall break up the boundary layer film (much like spoiler knobs on an airplane wing) and reduce drag forces. 

The term essentially a drag coefficient for the dust cake particles, should be a function of the median particle size and particle size distribution, the particle shape, and the packing density. Experimental data are the only reflable source for predicting cake resistance to flow. Bag filters are often selected for some desired maximum pressure drop (500—1750 Pa = 3.75-13 mm Hg) and the cleaning interval is then set to limit pressure drop to a chosen maximum value. 

Table 13 can be used as a rough guide for scmbber collection in regard to minimum particle size collected at 85% efficiency. In some cases, a higher collection efficiency can be achieved on finer particles under a higher pressure drop. For many scmbbers the particle penetration can be represented by an exponential equation of the form (271—274)... 

Type of scmbber Pressure drop. Pa Minimum collectible particle dia, tlm ... 

Venturi scmbbers can be operated at 2.5 kPa (19 mm Hg) to coUect many particles coarser than 1 p.m efficiently. Smaller particles often require a pressure drop of 7.5—10 kPa (56—75 mm Hg). When most of the particulates are smaller than 0.5 p.m and are hydrophobic, venturis have been operated at pressure drops from 25 to 32.5 kPa (187—244 mm Hg). Water injection rate is typicaUy 0.67—1.4 m of Hquid per 1000 m of gas, although rates as high as 2.7 are used. Increasing water rates improves coUection efficiency. Many venturis contain louvers to vary throat cross section and pressure drop with changes in system gas flow. Venturi scmbbers can be made in various shapes with reasonably similar characteristics. Any device that causes contact of Hquid and gas at high velocity and pressure drop across an accelerating orifice wiU act much like a venturi scmbber. A flooded-disk scmbber in which the annular orifice created by the disc is equivalent to a venturi throat has been described (296). An irrigated packed fiber bed with performance similar to a... 

Deep Bed Filters. Deep bed filtration is fundamentally different from cake filtration both in principle and appHcation. The filter medium (Fig. 4) is a deep bed with pore size much greater than the particles it is meant to remove. No cake should form on the face of the medium. Particles penetrate into the medium where they separate due to gravity settling, diffusion, and inertial forces attachment to the medium is due to molecular and electrostatic forces. Sand is the most common medium and multimedia filters also use garnet and anthracite. The filtration process is cycHc, ie, when the bed is full of sohds and the pressure drop across the bed is excessive, the flow is intermpted and solids are backwashed from the bed, sometimes aided by air scouring or wash jets. 

Dewatering of high value products and particle systems sensitive to high pressure drops are the most likely candidates for electrofiltration. The Dorr-OHver Electrofilter is a commercial example of a vacuum filter adapted for electrofiltration. 

The constant given the value 5 in equation 1 depends on particle size, shape, and porosity it can be assumed to be 5 for low porosities. Although equation 1 has been found to work reasonably well for incompressible cakes over narrow porosity ranges, its importance is limited in cake filtration because it cannot be used for most practical, compressible cakes. It can, however, be used to demonstrate the high sensitivity of the pressure drop to the cake porosity and to the specific surface of the soHds. 

The basic concepts of a gas-fluidized bed are illustrated in Figure 1. Gas velocity in fluidized beds is normally expressed as a superficial velocity, U, the gas velocity through the vessel assuming that the vessel is empty. At a low gas velocity, the soHds do not move. This constitutes a packed bed. As the gas velocity is increased, the pressure drop increases until the drag plus the buoyancy forces on the particle overcome its weight and any interparticle forces. At this point, the bed is said to be minimally fluidized, and this gas velocity is termed the minimum fluidization velocity, The bed expands slightly at this condition, and the particles are free to move about (Fig. lb). As the velocity is increased further, bubbles can form. The soHds movement is more turbulent, and the bed expands to accommodate the volume of the bubbles. 

Good gas distribution is necessary for the bed to operate properly, and this requites that the pressure drop over the distributor be sufficient to prevent maldistribution arising from pressure fluctuations in the bed. Because gas issues from the distributor at a high velocity, care must also be taken to minimize particle attrition. Many distributor designs are used in fluidized beds. The most common ones are perforated plates, plates with caps, and pipe distributors. 

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