Packed beds continuum models

The application of CFD to packed bed reactor modeling has usually involved the replacement of the actual packing structure with an effective continuum (Kvamsdal et al., 1999 Pedernera et al., 2003). Transport processes are then represented by lumped parameters for dispersion and heat transfer (Jakobsen... 

The model presented here is a significant step forward in the simulation of fixed bed catalytic reactors. It is an early computational fluid dynamics (CFD) model of the continuum type. In recent years supercomputers have led to an increased application of CFD to studies of heat transfer in packed beds. In modeling the fluid flow in the voids confined by the catalyst particles, Nijemeisland and Dixon [2004] investigated the possibility of deriving values for the heat transfer coefficient between the bed and the wall in terms of the local properties of the flow field, but found no statistically valid correlation. They... 

The Eulerian continuum approach, based on a continuum assumption of phases, provides a field description of the dynamics of each phase. The Lagrangian trajectory approach, from the study of motions of individual particles, is able to yield historical trajectories of the particles. The kinetic theory modeling for interparticle collisions, extended from the kinetic theory of gases, can be applied to dense suspension systems where the transport in the particle phase is dominated by interparticle collisions. The Ergun equation provides important flow relationships, which are useful not only for packed bed systems, but also for some situations in fluidized bed systems. 

Reactor Model. The design of an industrial packed-bed reactor requires a reactor model as well as the chemical and the heat and mass transfer parameters of the catalyst bed - gas stream system. Since these parameters are model-specific, it seemed advisable to employ a continuum model for the reactor calculation. This is the only model to date for which the literature contains consistent data for calculating heat and mass transfer parameters (5,6,7). This model in its... 

Extensive experimental determinations of overall heat transfer coefficients over packed reactor tubes suitable for selective oxidation are presented. The scope of the experiments covers the effects of tube diameter, coolant temperature, air mass velocity, packing size, shape and thermal conductivity. Various predictive models of heat transfer in packed beds are tested with the data. The best results (to within 10%) are obtained from a recently developed two-phase continuum model, incorporating combined conduction, convection and radiation, the latter being found to be significant under commercial operating conditions. 

Mechanistic equations describing the apparent radial thermal conductivity (kr>eff) and the wall heat transfer coefficient (hw.eff) of packed beds under non-reactive conditions are presented in Table IV. Given the two separate radial heat transfer resistances -that of the "central core" and of the "wall-region"- the overall radial resistance can be obtained for use in one-dimensional continuum reactor models. The equations are based on the two-phase continuum model of heat transfer (3). 

The use of two-phase homogeneous continuum models in packed bed modelling has often been avoided due to the computational difficulties. Recently, Paspek and Varma (15) have found a two-phase model to be necessary to describe an adiabatic fixed-bed reactor, while Dixon and Cresswell (16) have shown that the effective parameters of the one-phase model may be interpreted in terms of the more fundamental parameters of a two-phase model, thus demonstrating more clearly their qualitative dependencies on the operating and design characteristics of the bed. When two phases and several species are involved, the computational advantages of the cubic Hermite method may be anticipated to be high. 

In this paper the coupled elliptic partial differential equations arising from a two-phase homogeneous continuum model of heat transfer in a packed bed are solved, and some attempt is made to discriminate between rival correlations for those parameters not yet well-established, by means of a comparison with experimental results from a previous study (, 4). 

Both radial and axial diffusion can be taken into account and the final equations to be solved are relatively simpler than those of the continuum model. Although, the equations of the model at steady state are algebraic equations, the dimensionality of the system increases considerably. McGuire and Lapidus (1965) used this model for the study of the stability of a packed bed reactor which included both interphase and intraparticle mass and heat transfer resistances. 

Fig. 15 Categories of continuum models for concurrently operated multiphase catalytic packed bed reactors...

What is the difference between the qnasi-continuum model and the cell model in designing packed-bed reactors both in terms of the physical pictnre and the mathematics involved ... 

ETC is an important parameter describing the thermal behavior of packed beds with a stagnant or dynamic fluid and has been extensively investigated experimentally and theoretically in the past. Various mathematical models, including continumn models and microscopic models, have been proposed to help solve this problem, but they are often limited by the homogeneity assumption in a continuum model (Wakao and Kaguei, 1982 Zehner and Schliinder, 1970) or the simple assumptions in a microscopic model... 

Soo and Radke (11) confirmed that the transient permeability reduction observed by McAuliffe (9) mainly arises from the retention of drops in pores, which they termed as straining capture of the oil droplets. They also observed that droplets smaller than pore throats were captured in crevices or pockets and sometimes on the surface of the porous medium. They concluded, on the basis of their experiments in sand packs and visual glass micromodel observations, that stable OAV emulsions do not flow in the porous medium as a continuum viscous liquid, nor do they flow by squeezing through pore constrictions, but rather by the capture of the oil droplets with subsequent permeability reduction. They used deep-bed filtration principles (i2, 13) to model this phenomenon, which is discussed in detail later in this chapter. 

The combined CFD-DEM approach, incorporated with heat transfer models of convection, conduction, and radiation, has been developed and can be used in the study of heat transfer in packed and fluidized beds. It has various advantages over the conventional experimental techniques and continuum simulation approaches. For example, the detailed conductive heat transfer between particles can be examined and the factors such as local particle-fluid structure and materials properties in determining heat transfer can be investigated. 

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