Radial design method

The wall boundary condition applies to a solid tube without transpiration. The centerline boundary condition assumes S5anmetry in the radial direction. It is consistent with the assumption of an axis5Tnmetric velocity profile without concentration or temperature gradients in the 0-direction. This boundary condition is by no means inevitable since gradients in the 0-direction can arise from natural convection. However, it is desirable to avoid 0-dependency since appropriate design methods are generally lacking. 

An analysis of radial flow, fixed bed reactor (RFBR) is carried out to determine the effects of radial flow maldistribution and flow direction. Analytical criteria for optimum operation is established via a singular perturbation approach. It is shown that at high conversion an ideal flow profile always results in a higher yield irrespective of the reaction mechanism while dependence of conversion on flow direction is second order. The analysis then concentrates on the improvement of radial profile. Asymptotic solutions are obtained for the flow equations. They offer an optimum design method well suited for industrial application. Finally, all asymptotic results are verified by a numerical experience in a more sophisticated heterogeneous, two-dimensional cell model. 

Examples 13-3 to 13-5 illustrate the simplified design method for different cases. The first is for the endothermic styrene reaction, where the temperature decreases continually with catalyst-bed depth. Example 13-4 is for an exothermic reaction carried out under conditions where radial temperature gradients are not large. Example 13-5 is also for an exothermic case, but here the gradients are severe, and the simplified solution is not satisfactory. 

Figure 2.7. Tubular turbulent apparatus of cylindrical (a, c) and divergent-convergent (b) designs with coaxial (a, b) and radial (c) methods of reagents introduction. Ind - introduction of indicator. Reactors working regimes P - plan front T - torch Z - drift regime.

There is a tendency for both axial and radial dispersion of mass to occur when a fluid flows through a packed bed. Since the bed diameter is normally far greater than the particle diameter in an adsorption bed, it is common not to have to consider the effects of radial dispersion. Hence the prevalence of plug and axially dispersed plug flow models in rigorous design methods. 

Beckman Elutriation Method. The Beckman elutriation method uses a chamber designed so that the centrifugal effect of the radial inward fluid flow is constant (Fig. 3). The separation chambers are made of transparent epoxy resin which faciUtates observation of the movements of the cell boundary in strobe light illumination. This enables detection of the radius at which the cells are separating. When a mixture of cells, eg, mononuclear white cells, enters the chamber, separation can be achieved by fine tuning centrifuge speed and inward fluid flow to the specific cell group. This is a laboratory method suitable for relatively small numbers of cells. Chambers are available in sizes to handle 2-3 x 10 , 1 2 x 10 , and 1 x 10 ° cells. The Beckman chambers can be appHed to collect mononuclear cells from bone marrow aspirates. 

On the basis of the information gathered here, three methods are possible for the design of agitated gas dispersion. In all cases the size of the tank, the ratio of impeller and tank diameters and the gas feed rate are specified. The data are for radial turbine impellers with six vertical blades. 

The space velocity for a given conversion is often used as a ready measure of the performance of a reactor. The use of equation 1.25 to calculate reaction time, as if for a batch reactor, is not to be recommended as normal practice it can be equated to VJv only if there is no change in volume. Further, the method of using reaction time is a blind alley in the sense that it has to be abandoned when the theory of tubular reactors is extended to take into account longitudinal and radial dispersion and other departures from the plug flow hypothesis which are important in the design of catalytic tubular reactors (Chapter 3, Section 3.6.1)... 

While catalytic HDM results in a desirable, nearly metal-free product, the catalyst in the reactor is laden with metal sulfide deposits that eventually result in deactivation. Loss of catalyst activity is attributed to both the physical obstruction of the catalyst pellets pores by deposits and to the chemical contamination of the active catalytic sites by deposits. The radial metal deposit distribution in catalyst pellets is easily observed and understood in terms of the classic theory of diffusion and reaction in porous media. Application of the theory for the design and development of HDM and HDS catalysts has proved useful. Novel concepts and approaches to upgrading metal-laden heavy residua will require more information. However, detailed examination of the chemical and physical structure of the metal deposits is not possible because of current analytical limitations for microscopically complex and heterogeneous materials. Similarly, experimental methods that reveal the complexities of the fine structure of porous materials and theoretical methods to describe them are not yet... 

In this chapter, emphasis will be given to heat transfer in fast fluidized beds between suspension and immersed surfaces to demonstrate how heat transfer depends on gas velocity, solids circulation rate, gas/solid properties, and temperature, as well as on the geometry and size of the heat transfer surfaces. Both radial and axial profiles of heat transfer coefficients are presented to reveal the relations between hydrodynamic features and heat transfer behavior. For the design of commercial equipment, the influence of the length of heat transfer surface and the variation of heat transfer coefficient along the surface will be discussed. These will be followed by a description of current mechanistic models and methods for enhancing heat transfer on large heat transfer surfaces in fast fluidized beds. Heat and mass transfer between gas and solids in fast fluidized beds will then be briefly discussed. 

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