Fluid and solid flow

On the basis of different assumptions about the nature of the fluid and solid flow within each phase and between phases as well as about the extent of mixing within each phase, it is possible to develop many different mathematical models of the two phase type. Pyle (119), Rowe (120), and Grace (121) have critically reviewed models of these types. Treatment of these models is clearly beyond the scope of this text. In many cases insufficient data exist to provide critical tests of model validity. This situation is especially true of large scale reactors that are the systems of greatest interest from industry s point of view. The student should understand, however, that there is an ongoing effort to develop mathematical models of fluidized bed reactors that will be useful for design purposes. Our current... 

The temperature difference for heat transfer is the log-mean temperature difference when the particles are large and/or the beds packed, or the difference between the inlet fluia temperature and average exhausting fluid temperature expressed for small particles. The use of the log mean for packed beds has been confirmed by Thodos and Wilkins (Second American Institute of Chemical Engi-neers-IIQPR Meeting, Paper SOD, Tampa, May 1968). When fluid and solid flow directions are axially concurrent and particle size is... 

Individual Coefficient of Heat Transfer Because of the comphcated structure of a turbulent flowing stream and the impracti-cabifity of measuring thicknesses of the several layers and their temperatures, the local rate of beat transfer between fluid and solid is defined by the equations... 

Determination of Controlling Rate Factor The most important physical variables determining the controlhng dispersion factor are particle size and structure, flow rate, fluid- and solid-phase diffu-sivities, partition ratio, and fluid viscosity. When multiple resistances and axial dispersion can potentially affect the rate, the spreading of a concentration wave in a fixed bed can be represented approximately... 

Rheology is the study of the deformation and flow behavior of materials, both fluids and solids. See, e.g., Barnes et al. (1989). 

In this equation, V0 is the relative velocity between the unhindered particle and the fluid. However, in a hindered suspension this velocity is increased by the velocity of the displaced fluid, which flows back up through the suspension in the void space between the particles. Thus, if Fs is the (superficial) settling velocity of the suspension (e.g., swarm ) and VL is the velocity of the fluid, the total flux of solids and liquid is relative velocity between the fluid and solids in the swarm is Vr = Vs — VL. If the total net flux is zero (e.g., batch settling in a closed-bottom container with no outflow), elimination of VL gives... 

Continuous reactors for fluid-solid reactions involve continuous flow for both fluid and solid phases. With the assumptions made in Section 22.2.1 about the fluid, we focus only... 

After introducing some types of moving-particle reactors, their advantages and disadvantages, and examples of reactions conducted in them, we consider particular design features. These relate to fluid-particle interactions (extension of the treatment in Chapter 21) and to the complex flow pattern of fluid and solid particles. The latter requires development of a hydrodynamic model as a precursor to a reactor model. We describe these in detail only for particular types of fluidized-bed reactors. 

When a chemical reaction occurs in the system, each of these types of behavior gives rise to a corresponding type of reactor. These range from a fixed-bed reactor (Chapter 21-not a moving-particle reactor), to a fluidized-bed reactor without significant carryover of solid particles, to a fast-fluidized-bed reactor with significant carryover of particles, and ultimately a pneumatic-transport or transport-riser reactor in which solid particles are completely entrained in the rising fluid. The reactors are usually operated commercially with continuous flow of both fluid and solid phases. Kunii and Levenspiel (1991, Chapter 2) illustrate many industrial applications of fluidized beds. 

A one-parameter model, termed the bubbling-bed model, is described by Kunii and Levenspiel (1991, pp. 144-149,156-159). The one parameter is the size of bubbles. This model endeavors to account for different bubble velocities and the different flow patterns of fluid and solid that result. Compared with the two-region model, the Kunii-Levenspiel (KL) model introduces two additional regions. The model establishes expressions for the distribution of the fluidized bed and of the solid particles in the various regions. These, together with expressions for coefficients for the exchange of gas between pairs of regions, form the hydrodynamic + mass transfer basis for a reactor model. 

We find experimentally that when ite>O(103) the flow is no longer laminar, i.e. the flow becomes unstable and vortices are formed. These are first seen at the boundaries between the fluid and solid surfaces. These chaotic flows should be avoided in our laboratory equipment in the course of viscometric characterisation. The conclusion that we draw is that we should make measurements at low Reynolds numbers in order to ensure that only the viscous dissipation is making a significant contribution to our measurements. 

This revolution will spread to all chemical and petroleum processes that are large enough in scale to justify the investment in model building and experimental verification. Further progress needs better chemical kinetic data. The most deficient area remains in predicting the fluid mechanical and solid flow behaviors in reactors, where progress is sorely needed to round out the science of reaction engineering. 

Mucociliary transport in the airways that constantly drains fluid and solid particles (bacteria) in a counter-current flow to the oral cavity. A drug that is deposited in the airways can... 

The branch of science related to the study of deformation and flow of materials was given the name rheology by Bingham, whom some call the father of modern rheology. The prefix rheo is derived from the Greek rheos, meaning current of flow. The study of rheology includes two vastly different branches of mechanics—fluid and solid. The polymer scientist is usually concerned with viscoelastic materials that act as both solids and liquids. 

Energy coupling between the reactor and regenerator are crucial in designing the FCC reactor, because the heat liberated from burning off the coke from the catalyst suppHes the heat to maintain the temperature in the reactor where reactions are endothermic. Therefore, the energy balance equations and the description of flow of fluid and solid phases must be considered carefully in this reactor. 

Filtration is the separation of undissoived particulate solids from a mixture of fluid and solid. The separation is brought about by passage of the fluid thru a pervious septum (filter medium) in or on which the solids are retained. A driving force (gravity, vacuum, pressure, or centrifugal force) produces the flow. Filter aids may be added to the fluid before filtering to counterbalance the unfavorable characteristics of badly filtering materials... 

The amount of adsorption is limited by the available surface and pore volume, and depends also on the chemical natures of the fluid and solid. The rate of adsorption also depends on the amount of exposed surface but, in addition, on the rate of diffusion to the external surface and through the pores of the solid for accessing the internal surface which comprises the bulk of the surface. Diffusion rates depend on temperature and differences in concentration or partial pressures. The smaller the particle size, the greater is the utilization of the internal surface, but also the greater the pressure drop for flow of bulk fluid through a mass of the particles. 

Radioisotopes are widely used in die measurement of process variables, including the level of liquids and solids in tanks, silos, and other vessels, the density and specific gravity of fluids and solids, the thickness of sheets and coatings, the moisture content of soils and other solids, the mass flow of materials in pipelines or on belts, and the determination of chemical composition of raw materials, in-process materials, and end-products. Representative examples of these applications are given in Table 6. 

There have been few studies reported in the literature in the area of multi-component adsorption and desorption rate modeling (1, 2,3., 4,5. These have generally employed simplified modeling approaches, and the model predictions have provided qualitative comparisons to the experimental data. The purpose of this study is to develop a comprehensive model for multi-component adsorption kinetics based on the following mechanistic process (1) film diffusion of each species from the fluid phase to the solid surface (2) adsorption on the surface from the solute mixture and (3) diffusion of the individual solute species into the interior of the particle. The model is general in that diffusion rates in both fluid and solid phases are considered, and no restrictions are made regarding adsorption equilibrium relationships. However, diffusional flows due to solute-solute interactions are assumed to be zero in both fluid and solid phases. 

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