Granular flow reactive flows

In a series of papers Lathouwers and Bellan [43, 44, 45, 46] presented a kinetic theory model for multicomponent reactive granular flows. The model considers polydisersed particle suspensions to take into account that the physical properties (e.g., diameter, density) and thermo-chemistry (reactive versus inert) of the particles may differ in their case. Separate transport equations are constructed for each of the particle types, based on similar principles as used formulating the population balance equations [61]. 

Moreover, very few parameterizations are reported on the wall- and fluid-granular material convective thermal heat transfer coefficients. For introductory studies, the work of Natarajan and Hunt [55], Gunn [25], Kuibe and Broughton [40], Kuipers et al [41] and Patil et al [59] might be consulted. To enable validation and reliable predictions of non-isothermal non-adiabatic reactive granular flows the thermal conductivity and the convective heat transfer coefficients have to be determined with sufficient accuracy. For certain processes this may be an important task for future research in the field of granular flows in fluidized beds. 

In this section the application of multiphase flow theory to model the performance of fluidized bed reactors is outlined. A number of models for fluidized bed reactor flows have been established based on solving the average fundamental continuity, momentum and turbulent kinetic energy equations. The conventional granular flow theory for dense beds has been reviewed in chap 4. However, the majority of the papers published on this topic still focus on pure gas-particle flows, intending to develop closures that are able to predict the important flow phenomena observed analyzing experimental data. Very few attempts have been made to predict the performance of chemical reactive processes using this type of model. 

For reactive flows the governing equations used by Lindborg et al [92] resemble those in sect 3.4.3, but the solid phase momentum equation contains several additional terms derived from kinetic theory and a frictional stress closure for slow quasi-static flow conditions based on concepts developed in soil mechanics. Moreover, to close the kinetic theory model the granular temperature is calculated from a separate transport equation. To avoid misconception the model equations are given below (in which the averaging symbols are disregarded for convenience) ... 

Chapter 10 contains a literature survey of the basic fluidized bed reactor designs, principles of operation and modeling. The classical two- and three phase fluidized bed models for bubbling beds are defined based on heat and species mass balances. The fluid dynamic models are based on kinetic theory of granular flow. A reactive flow simulation of a particular sorption enhanced steam reforming process is assessed. 

Extending the Kinetic Theory of Granular Flow to Reactive Systems... 

The success in deriving the Maxwellian type macroscopic transport equations and in obtaining appropriate source and flux closures based on the kinetic theory of granular flow relies heavily on the knowledge about the distribution function involved. In principle, for reactive systems the single particle distribution function should satisfy... 

The outcome of this procedure is, in addition to the previously described kinetic theory of granular flow (KTGF) transport equations with the given flux and source closures, characteristic transport equations for species mass and thermal temperature. It is noted that the use of second order velocity moments or higher moments usually requires some kind of manipulation in order to obtain equations in the desired form. The derivation of the thermal temperature equation for reactive systems is certainly not trivial. The application of this theory to reactive systems is extensively discussed in the following two sections. 

In the literature numerous two-fluid models of different complexity have been proposed to predict the fluidized bed reactor cold flow and reactive flow behaviors. Four decades ago emphasis was placed on the modeling of the velocity fluctuation co-variance terms in the dispersed particle fluid phase momentum equations. The early one-dimensional models were normally closed by an elasticity modulus parameterization for the particle phase collisional pressure and a constant viscosity parameter for the corresponding shear stresses. Later, with the improved computer memory and speed capacities, multi-dimensional flow models and more advanced model closures were developed based on the kinetic theory of granular flow (KTGF). Moreover, the... 

Step algorithm was employed for the solution of an unsteady two-fluid granular flow model [136], The latter semi-implicit procedure has also been extended in order to simulate reactive flows in fluidized beds [138],... 

This funnel is placed to encompass and direct the flow of contaminated water to a "gate" or "gates" containing a permeable zone of granular Fe° or other reactive material. 

The data from 1987 on the use of activated carbons for liquid-phase applications in the US shows that 15,900 tons of activated carbon was used for wastewater treatment, 7,300 in the granular form and 8,600 in the powdered form [66]. Of 15,900 tons, 13,000 tons was used industrially and 2,900 tons municipally. Industrial applications of activated carbon are related to, in decreasing order, decolorization, treatment of chemical effluents, pharmaceuticals or mining groundwater. The organic contaminants removed include BOD, TOC, phenol, color, cresol, polyethers, toluene, xylene, nitro- and chlorophenols, insecticides, refinery wastes and acetic acid. Generally, the flow being treated is less than 80 m d and thermal reactivation of the carbon is used [67]. 

Dependence of degradation rates on flow velocity indicates rate limitation by transport processes, e.g. reported by Sivavec and Homey (1995) or Burris et al. (1995) for the degradation of trichloroethene (TCE) by zerovalent iron in batch reactors. Even if there has been no real explanation for the different degradation behaviour at the two column experiments, it must be dependent on the characteristics of the granular iron, because of the similar experimental conditions. The diverse granulate shape or the distribution of reactive surface as well as mineral precipitations usually present in iron... 

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