Packed beds fluid mechanics

FIG. 16-9 General scheme of adsorbent particles in a packed bed showing the locations of mass transfer and dispersive mechanisms. Numerals correspond to mimhered paragraphs in the text 1, pore diffusion 2, solid diffusion 3, reaction kinetics at phase boundary 4, external mass transfer 5, fluid mixing. 

The axial dispersion coefficient [cf. Eq. (16-51)] lumps together all mechanisms leading to axial mixing in packed beds. Thus, the axial dispersion coefficient must account not only for moleciilar diffusion and convec tive mixing but also for nonuniformities in the fluid velocity across the packed bed. As such, the axial dispersion coefficient is best determined experimentally for each specific contac tor. 

Whitaker, S, Diffusion in Packed Beds of Porous Particles, AlChE Journal 34, 679, 1988. Whitaker, S, The Development of Fluid Mechanics in Chemical Engineering. In One Hundred Years of Cheical Engineering Peppas, NA, ed. Kluwer Academic Dordrecht The Netherlands, 1989 47. 

Appendix B consists of a systematic classification and review of conceptual models (physical models) in the context of PBC technology and the three-step model. The overall aim is to present a systematic overview of the complex and the interdisciplinary physical models in the field of PBC. A second objective is to point out the practicability of developing an all-round bed model or CFSD (computational fluid-solid dynamics) code that can simulate thermochemical conversion process of an arbitrary conversion system. The idea of a CFSD code is analogue to the user-friendly CFD (computational fluid dynamics) codes on the market, which are very all-round and successful in simulating different kinds of fluid mechanic processes. A third objective of this appendix is to present interesting research topics in the field of packed-bed combustion in general and thermochemical conversion of biofuels in particular. 

To consolidate the experimental screening data quantitatively it is desirable to obtain information on the fluid mechanics of the reactant flow in the reactor. Experimental data are difficult to evaluate if the experimental conditions and, especially, the fluid dynamic behavior of the reactants flow are not known. This is, for example, the case in a typical tubular reactor filled with a packed bed of porous beads. The porosity of the beads in combination with the unknown flow of the reactants around the beads makes it difficult to describe the flow close to the catalyst surface. A way to achieve a well-described flow in the reactor is to reduce its dimensions. This reduces the Reynolds number to a region of laminar flow conditions, which can be described analytically. 

The word flow implies fluid moving through (or across) a rigid framework or conduit (a container, tube, or packed bed) and not being carried with it as in the case of mechanical transfer. Flow is an integral part of many separation techniques, including chromatography, field-flow fractionation, ultrafiltration, and elutriation. The flow process is not itself selective, but it enables one to multiply by many times the benefits of separations attempted without flow. This point is explained in Chapter 7. 

The main assumptions made in arriving at eq 10 were (1) no interaction between the globules and (2) no slippage at the particle-fluid interface. Most emulsions of practical interest exceed the concentration for which eq 10 is valid. With increasing concentration, the hydrodynamic interaction between the globules increases, and eventually mechanical interference occurs between the particles as packed-bed concentrations are approached. To take into account the increased hydrodynamic interaction, many investigators (30, 38-43) have expanded eq 10 into the polynomial form ... 

The gas flow velocity through the emulsion phase is close to the minimum fluidization velocity When the particles are spherical and have diameters of several tens of microns, this flow condition gives a quite small particle Peclet number, dpUmf/Dc. For example, the Peclet number is estimated as 0.1-0.01 when 122-/Lim-diam. cracking catalyst is fluidized by gas, with Umt = 0.73 cm/sec and Dq = 0.09 cmVsec and it is estimated as 0.001-0.01 for 58-/u.m-diam. particles, with Umt = 0.16 cm/sec. The mechanism of mass transfer between fluid and particles in packed beds is controlled by molecular diffusion under such low Peclet numbers, and the particle Sherwood number kfdp/Dc, is well over 10 (M24). Consequently with intraparticle diffusion shown to be negligible (M21), instantaneous equilibrium is established to be a good approximation [see Eq. (6-24)]. 

When the gas stream flows upwards through a packed bed of particles, there is a pressure drop due to the flow resistance from these particles. This pressure drop increases with the gas velocity based on the theory of fluid mechanics [64], A fluidised bed of particles is formed if the pressure drop across the bed is equal to the weight of the bed particles per unit area, i.e. the pressure (or the force in a unit area) for pushing the particle upwards to form the fluidised bed equals the weight of the particles of the unit area, as shown in Figure 3.36. 

Thompson, K. E., and Eogler, H. S., Modeling flow in disordered packed beds from pore-scale fluid mechanics. AIChE J. 43,1377 (1997). 

Heat Transfer in a Packed Bed (Effective Thermal Conductivity) In a bed of solid particles through which a reacting fluid is passing, heat can be transferred in the radial direction by a number of mechanisms. However, it is customary to consider that the bed of particles and the gas may be replaced by a hypothetical solid in which conduction is the only mechanism for heat transfer. The thermal conductivity of this solid has been termed the effective thermal conductivity k. With this scheme the temperature T of any point in the bed may be related to and the position parameters r and z by the differential equation... 

The number of transfer units for each mechanism can be estimated from known parameters and mass transfer correlations (4). For example, for a column with particles 0.01 cm in diameter, a superficial velocity of 0.01 cm/sec, and a solute bulk diffusivity of 7 x 10-7 cm2/sec, the estimated number of transfer units in a packed bed of length L for the four mechanisms, axial dispersion, external fluid film mass transfer, pore diffusion, and solid homogeneous particle diffusion,are... 

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