Dense-phase transport modeling

A starting model can be selected depending on the type of dense phase transport. Modeling a homogeneous dense phase would use the same approach as dilute phase with a new frictional term. This approach would have two contributions due to the gas alone and the linear combination with the solids contribution. 

Tsuji et al. (1990) have modeled the flow of plastic pellets in the plug mode with discrete dynamics following the behavior of each particle. The use of a dash pot/spring arrangement to account for the friction was employed. Their results show remarkable agreement with the actual behavior of real systems. Figure 28 shows these flow patterns. Using models to account for turbulent gas-solid mixtures, Sinclair (1994) has developed a technique that could have promise for the dense phase transport. 

Blasco et al. [12] proposed two-dimensional mathematical model for the drying process of dense phase pneumatic conveying. However, heat and mass transfer were not considered and therefore their model may be used for dense phase pneumatic transport only. In their paper, both experimental and numerical predictions for axial and radial profiles for gas and solid velocity, axial profiles for solid concentration and pressure drop were presented. 

In effect, such a multi-scale analysis resolves a macro-scale heterogeneous system into three meso- to micro-scale subsystems—dense-phase, dilute-phase and inter-phase. Thus, modeling a heterogeneous particle-fluid two-phase system is reduced to calculations for the three lower-scale subsystems, making possible the application of the much simpler theory of particulate fluidization to aggregative fluidization and the formulation of energy consumptions with respect to phases (dense, dilute and inter) and processes (transport, suspension and dissipation). 

For the separation of gas mixtures (permanent gases and/or condensable vapors) where the feed and permeate streams are both gas phase, the driving force across the membrane is the partial pressure difference. The membrane is typically a dense film and the transport mechanism is sorption-diffusion. The dual-mode transport model is typically used with polymer materials that are below their glass transition temperature. 

Starting from the energy conservation equation of the gas phase, we may restore the energy balance defined in the EMMS model. Note that Fjc is defined in the whole dense phase, while Ugc applies only in the gas part of the dense phase, then, for the averaged energy consumption for suspending and transporting particles in any cell. 

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. 

When the gas-solid flow in a multiphase system is dominated by the interparticle collisions, the stresses and other dynamic properties of the solid phase can be postulated to be analogous to those of gas molecules. Thus, the kinetic theory of gases is adopted in the modeling of dense gas-solid flows. In this model, it is assumed that collision among particles is the only mechanism for the transport of mass, momentum, and energy of the particles. The energy dissipation due to inelastic collisions is included in the model despite the elastic collision condition dictated by the theory. 

Employing 1-hexene isomerization on a Pt/y-ALOj reforming catalyst as a model reaction system, we showed that isomerization rates are maximized and deactivation rates are minimized when operating with near-critical reaction mixtures [2]. The isomerization was carried out at 281°C, which is about 1.1 times the critical temperature of 1-hexene. Since hexene isomers are the main reaction products, the critical temperature and pressure of the reaction mixture remain virtually unaffected by conversion. Thus, an optimum combination of gas-like transport properties and liquid-like densities can be achieved with relatively small changes in reactor pressure around the critical pressure (31.7 bars). Such an optimum combination of fluid properties was found to be better than either gas-phase or dense supercritical (i.e., liquid-like) reaction media for the in situ extraction of coke-forming compounds. 

Kimura and Sourirajan have offered a theory of preferential adsorption of materials at interfaces to describe liquid phase, selective transport processes in portms membranes. Lonsdale et al. have ofiered a simpler explanation of the transport behavior of asymmetric membranes which lack significant porosity in the dense surface layer. Their solution-diffusion model seems to adequately describe the cases for liquid transport considered to date. Similarly gas transport should be de-scribable in terms of a solution-diffusion model in cases where the thin dense membrane skin acts as the transport moderating element. 

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