Particle mass transfer

Modelling of the interactions between water and air in MBR systems is important as aeration plays a key role in the mass transfer, particle size distribution and back transport of particles from the membrane surface. In addition, the behaviour of bubbles (shape and size. Fig. 15.8) is recognised to be affected by the injection method, sparger type and aeration rate. Table 15.2 summarises the models for the evaluation of effects of air bubbling in MBRs. 

Fig. 6. Concentration profiles through an idealized biporous adsorbent particle showing some of the possible regimes. (1) + (a) rapid mass transfer, equihbrium throughout particle (1) + (b) micropore diffusion control with no significant macropore or external resistance (1) + (c) controlling resistance at the surface of the microparticles (2) + (a) macropore diffusion control with some external resistance and no resistance within the microparticle (2) + (b) all three resistances (micropore, macropore, and film) significant (2) + (c) diffusional resistance within the macroparticle and resistance at the surface of the...

External Fluid Film Resistance. A particle immersed ia a fluid is always surrounded by a laminar fluid film or boundary layer through which an adsorbiag or desorbiag molecule must diffuse. The thickness of this layer, and therefore the mass transfer resistance, depends on the hydrodynamic conditions. Mass transfer ia packed beds and other common contacting devices has been widely studied. The rate data are normally expressed ia terms of a simple linear rate expression of the form... 

In certain adsorbents, notably partially coked 2eohtes and some carbon molecular sieves, the resistance to mass transfer may be concentrated at the surface of the particle, lea ding to an uptake expression of the form... 

The term dqljdt represents the overall rate of mass transfer for component / (at time t and distance averaged over a particle. This is governed by a mass transfer rate expression which may be thought of as a general functional relationship of the form... 

Diffusion and Mass Transfer During Leaching. Rates of extraction from individual particles are difficult to assess because it is impossible to define the shapes of the pores or channels through which mass transfer (qv) has to take place. However, the nature of the diffusional process in a porous soHd could be illustrated by considering the diffusion of solute through a pore. This is described mathematically by the diffusion equation, the solutions of which indicate that the concentration in the pore would be expected to decrease according to an exponential decay function. 

To obtain an indication of the rate of solute transfer from the particle surface to the bulk of the Hquid, the concept of a thin film providing the resistance to transfer can be used (2) and the equation for mass transfer written as ... 

Gas—solids fluidization is the levitation of a bed of solid particles by a gas. Intense soflds mixing and good gas—soflds contact create an isothermal system having good mass transfer (qv). The gas-fluidized bed is ideal for many chemical reactions, drying (qv), mixing, and heat-transfer appHcations. Soflds can also be fluidized by a Hquid or by gas and Hquid combined. Liquid and gas—Hquid fluidization appHcations are growing in number, but gas—soHds fluidization appHcations dominate the fluidization field. This article discusses gas—soHds fluidization. 

M ass Transfer. Mass transfer in a fluidized bed can occur in several ways. Bed-to-surface mass transfer is important in plating appHcations. Transfer from the soHd surface to the gas phase is important in drying, sublimation, and desorption processes. Mass transfer can be the limiting step in a chemical reaction system. In most instances, gas from bubbles, gas voids, or the conveying gas reacts with a soHd reactant or catalyst. In catalytic systems, the surface area of a catalyst can be enormous. Eor Group A particles, surface areas of 5 to over 1000 m /g are possible. 

This equation predicts that the height of a theoretical diffusion stage increases, ie, mass-transfer resistance increases, both with bed height and bed diameter. The diffusion resistance for Group B particles where the maximum stable bubble size and the bed height are critical parameters may also be calculated (21). 

Catalyst Particle Size. Catalyst activity increases as catalyst particles decrease in size and the ratio of the catalyst s surface area to its volume increases. Small catalyst particles also have a lower resistance to mass transfer within the catalyst pore stmcture. Catalysts are available in a wide range of sizes. Axial flow converters predorninanfly use those in the 6—10 mm range whereas the radial and horizontal designs take advantage of the increased activity of the 1.5—3.0 mm size. 

Sedimentation is also used for other purposes. For example, relative motion of particles and Hquid iacreases the mass-transfer coefficient. This motion is particularly useful ia solvent extraction ia immiscible Hquid—Hquid systems (see Extraction, liquid-liquid). An important commercial use of sedimentation is ia continuous countercurrent washing, where a series of continuous thickeners is used ia a countercurrent mode ia conjunction with reslurrying to remove mother liquor or to wash soluble substances from the soHds. Most appHcations of sedimentation are, however, ia straight sohd—Hquid separation. 

Suspended Particle Techniques. In these methods of size enlargement, granular soHds are produced direcdy from a Hquid or semiliquid phase by dispersion in a gas to allow solidification through heat and/or mass transfer. The feed Hquid, which may be a solution, gel, paste, emulsion, slurry, or melt, must be pumpable and dispersible. Equipment used includes spray dryers, prilling towers, spouted and fluidized beds, and pneumatic conveying dryers, all of which are amenable to continuous, automated, large-scale operation. Because attrition and fines carryover are common problems with this technique, provision must be made for recovery and recycling. 

The modeling of fluidized beds remains a difficult problem since the usual assumptions made for the heat and mass transfer processes in coal combustion in stagnant air are no longer vaUd. Furthermore, the prediction of bubble behavior, generation, growth, coalescence, stabiUty, and interaction with heat exchange tubes, as well as attrition and elutriation of particles, are not well understood and much more research needs to be done. Good reviews on various aspects of fluidized-bed combustion appear in References 121 and 122 (Table 2). 

If requited, the drydown can be hastened by increasing desiccant mass, particle surface area, or mass-transfer coefficient. The mass-transfer coefficient can be altered to some extent by the design of the desiccant container. 

Convection heat transfer is dependent largely on the relative velocity between the warm gas and the drying surface. Interest in pulse combustion heat sources anticipates that high frequency reversals of gas flow direction relative to wet material in dispersed-particle dryers can maintain higher gas velocities around the particles for longer periods than possible ia simple cocurrent dryers. This technique is thus expected to enhance heat- and mass-transfer performance. This is apart from the concept that mechanical stresses iaduced ia material by rapid directional reversals of gas flow promote particle deagglomeration, dispersion, and Hquid stream breakup iato fine droplets. Commercial appHcations are needed to confirm the economic value of pulse combustion for drying. 

Thermodynamics Hendrick C. Van Ness, Michael M. Abbott Heat and Mass Transfer James G. Knudsen, Hoyt C. Hottel, Adel F. Sarofim, Phillip C. Wankat, Kent S. Knaebel Fluid and Particle Dynamics Janies N. Tilton Reaction Kinetics Stanley M. Walas... 

Mass-Transfer Coefficient Denoted by /c, K, and so on, the mass-transfer coefficient is the ratio of the flux to a concentration (or composition) difference. These coefficients generally represent rates of transfer that are much greater than those that occur by diffusion alone, as a result of convection or turbulence at the interface where mass transfer occurs. There exist several principles that relate that coefficient to the diffusivity and other fluid properties and to the intensity of motion and geometry. Examples that are outlined later are the film theoiy, the surface renewal theoiy, and the penetration the-oiy, all of which pertain to ideahzed cases. For many situations of practical interest like investigating the flow inside tubes and over flat surfaces as well as measuring external flowthrough banks of tubes, in fixed beds of particles, and the like, correlations have been developed that follow the same forms as the above theories. Examples of these are provided in the subsequent section on mass-transfer coefficient correlations. 

To determine the mass-transfer rate, one needs the interfacial area in addition to the mass-transfer coefficient. For the simpler geometries, determining the interfacial area is straightforward. For packed beds of particles a, the interfacial area per volume can be estimated as shown in Table 5-27-A. For packed beds in distillation, absorption, and so on in Table 5-28, the interfacial area per volume is included with the mass-transfer coefficient in the correlations for HTU. For agitated liquid-liquid systems, the interfacial area can be estimated... 

TABLE 5-26 Mass-Transfer Correlations for Particles, Drops, and Bubbles in Agitated Systems... 

Stainless steel flat six-blade turbine. Tank had four baffles. Correlation recommended for ( ) < 0.06 [Ref. 156] a = 6( )/<, where d p is Sauter mean diameter when 33% mass transfer has occurred. dp = particle or drop diameter <3 = iuterfacial tension, N/m ( )= volume fraction dispersed phase a = iuterfacial volume, 1/m and k OiDf implies rigid drops. Negligible drop coalescence. Average absolute deviation—19.71%. Graphical comparison given by Ref. 153. ... 

Fluidized Beds When gas or liquid flows upward through a vertically unconstrained bed of particles, there is a minimum fluid velocity at which the particles will begin to move. Above this minimum velocity, the bed is said to be fluidized. Fluidized beds are widely used, in part because of their excellent mixing and heat and mass transfer characteristics. See Sec. 17 of this Handbook for detailed information. 

Glaser and Thodos [Am. Jn.st. Chem. Eng. J., 4, 63 (1958)] give a correlation involving individual particle shape and bed porosity. Kunii and Suzuki [Jnt. ]. Heat Mass Tran.sfer, 10, 845 (1967)] discuss heat and mass transfer in packed beds of fine particles. 

Retention of a given solids particle in the system is on the average veiy short, usually no more than a few seconds. This means that any process conducted in a pneumatic system cannot be diffusion-controlled. The reaction must be mainly a surface phenomenon, or the solids particles must be veiy small so that heat transfer and mass transfer from the interiors are essentially instantaneous. 

Spray Dryers A spray diyer consists of a large cyhndrical and usu ly vertical chamber into which material to be dried is sprayed in the form of small droplets and into which is fed a large volume of hot gas sufficient to supply the heat necessary to complete evaporation of the liquid. Heat transfer and mass transfer are accomphshed by direct contact of the hot gas with the dispersed droplets. After completion of diying, the cooled gas and solids are separated. This may be accomplished partially at the bottom of the diying chamber by classification and separation of the coarse dried particles. Fine particles are separated from the gas in external cyclones or bag collectors. When only the coarse-particle fraction is desired for fini ed product, fines may be recovered in wet scrubbers the scrubber liquid is concentrated and returned as feed to the diyer. Horizontal spray chambers are manufactured with a longitudinal screw conveyor in the bottom of the diying chamber for continuous removal of settled coarse particles. 

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