Models three-phase fluidization

The complexity of the three-phase fluidized bed bioreactor is gradually coming under control as more sophisticated models become available. The chief need is for a model that integrates the microbial kinetics with the... 

An example of the application of a unified model to the design of a three-phase, fluidized bed bioreactor is the scale down, scale up procedure. A model of the full scale reactor is developed, then is used to design... 

Zhang, J. P., Jin. Y and Yu, Z. Q. Estimation of General Wake Model Parameters for a Three-Phase Fluidized Bed by Bed Collapse Technique (Chinese), in The Proceeding of 5th National Conference on Fluidization, pp. 327-331 (1990). 

The modeling and design of a three-phase reactor requires the knowledge of several hydrodynamic (e.g., flow regime, pressure drop, holdups of various phases, etc.) and transport (e.g., degree of backmixing in each phase, gas-liquid, liquid-solid mass transfer, fluid-reactor wall heat transfer, etc.) parameters. During the past decade, extensive research efforts have been made in order to improve our know-how in these areas. Chapters 6 to 8 present a unified review of the reported studies on these aspects for a variety of fixed bed columns (i.e., co-current downflow, co-current upflow, and counter-current flow). Chapter 9 presents a similar survey for three-phase fluidized columns. 

In the previous section, stability criteria were obtained for gas-hquid bubble columns, gas-solid fluidized beds, liquid-sohd fluidized beds, and three-phase fluidized beds. Before we begin the review of previous work, let us summarize the parameters that are important for the fluid mechanical description of multiphase systems. The first and foremost is the dispersion coefficient. During the derivation of equations of continuity and motion for multiphase turbulent dispersions, correlation terms such as esv appeared [Eqs. (3) and (10)]. These terms were modeled according to the Boussinesq hypothesis [Eq. (4)], and thus the dispersion coefficients for the sohd phase and hquid phase appear in the final forms of equation of continuity and motion [Eqs. (5), (6), (14), and (15)]. However, for the creeping flow regime, the dispersion term is obviously not important. 

Epstein and co-workers (Bhatia and Epstein, 1974 Epstein, 1976 Epstein and Nicks, 1976 El-Temtamy and Epstein, 1978, 1979) have made very valuable contributions to the understanding of expansion/contraction characteristics of three-phase fluidized beds. Bhatia and Epstein (1974) proposed a wake model in which the solid contents of the liquid wakes behind the gas bubbles is negligible compared to the solid contents of the remaining... 

It was thought desirable to develop an alternative model for the prediction of contraction/expansion. The proposed model is based on the behavior of the particle settling velocity in solid-liquid and three-phase fluidization. 

Joshi (1983) used a simpler form of this model for the prediction of contraction/expansion in three-phase fluidized beds. 

The phenomenon of expansion/contraction in three-phase fluidized beds was analyzed. A brief review of literature has been presented. Epstein and co-workers have made outstanding contributions in this area. An alternative method has been presented. A favorable comparison between the model predictions and the experimental observations was observed. 

Trickle bed reactors Slurry reactors Three-phase fluidized beds No Little Little Modeling on basis of unit cell approach + development of correspondence rules for macroscopic system behavior Modeling of the effect of the solids phase on interfacial transport phenomena Modeling of the effect of the solids phase on interfacial transport phenomena -I- development of refined models for particle-particle and particle-wall interaction... 

On the basis of the generalized wake model of Bhatia and Epstein, " a criterion for the bed contraction was developed. In the generalized wake model, the three-phase fluidized bed is assumed fo consist of three regions, the gas bubble region, the wake region, and the liquid-solid fluidized region. Bed contraction will occur when the following criterion is satisfied, ij/ < 0 where... 

Bhatia, V.K. Epstein, N. Three-phase fluidization generalized wake model. In Fluidization and Its Applications, Proceedings of the International Symposium, Toulose, October 1-5, 1973 Angelion, H. Coudere, J.P. Gibert, H. Laguerie, C., Eds. Cepadues-Editions Toulose, 1974, 380-392. 

The fundamental principles of the gas-to-liquid mass transfer were concisely presented. The basic mass transfer mechanisms described in the three major mass transfer models the film theory, the penetration theory, and the surface renewal theory are of help in explaining the mass transport process between the gas phase and the liquid phase. Using these theories, the controlling factors of the mass transfer process can be identified and manipulated to improve the performance of the unit operations utilizing the gas-to-liquid mass transfer process. The relevant unit operations, namely gas absorption column, three-phase fluidized bed reactor, airlift reactor, liquid-gas bubble reactor, and trickled bed reactor were reviewed in this entry. 

Lee, H. Barnett, S.M. A predictive model for the allowable operating velocities and the biomass concentration in a three phase fluidized biofilm reactor. J. Ind. Eng. Chem. 2003, 9, 202-211. 

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. 

Hamidipour, M., Chen, J., and Larachi, E (2012), CFD study on hydrodynamics in three-phase fluidized beds—Application of turbulence models and experimental validation, Chemical Engineering Science, 78(0) 167-180. 

Warsito, W, and Fan, L.-S. (2003b), ECT imaging of three-phase fluidized bed based on three-phase capacitance model, Chemical Engineering Science, 58 823-832. 

The minimum fluidization velocity can also be effectively described based on the gas-perturbed liquid model (Zhang et al., 1998a). The model assumes that the solid particles in the bed are fully supported by the liquid and there is little direct interaction between gas and solid phases. In this model, the gas phase plays a simple role in the bed by occupying space with particles fluidized by the liquid. The minimum fluidization velocity along with minimum liquid velocity for particle transport for three-phase fluidized beds of relatively large particles (dp > 1mm) (Zhang et al., 1998b) can... 

Figure 13 The regime transition velocity (a) in a bubble column. Open symbols are obtained by standard deviation of pressure fluctuation and drift flux model closed symbols are calculated by the correlation of Wilkinson et al. (1992). (From Lin et al., 1999.) (b) In a three-phase fluidized bed. (From Luo et al., 1997a.)...

Liquid-phase mixing in three-phase fluidized beds can be described using the dispersion model. A two-dimensional model considers both radial and axial dispersions. Both axial and radial dispersion coefficients are strong functions of operating conditions such as liquid and gas velocities and properties of liquid and solid phases. Evaluations of liquid-phase dispersion coefficients are based on a tracer injection method and subsequent analysis of the mean and the variance of the system response curves. 

An understanding of three-phase flows is still limited because of complicated phenomena underlying interactions between phases, such as the particle-bubble interaction and the liquid interstitial effect during particle-particle collision. Recently, several computational fluid dynamics models were reported to simulate three-phase fluidization behavior (Gidaspow et al., 1994 Grevskott et al., 1996 Mitra-Majumdar et al., 1997). These models are based on the multifluid... 

To date, the design of three-phase fluidized beds still relies heavily on experimental observations, empirical correlations, and engineering models. With increasing computer power, the employment of the computational fluid dynamics approach has gained consider-... 

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