Fluidization model

Ding, J. and Gidaspaw, D., Bubbling fluidization model using kinetie theory of granular flows, AIChE J, 36, 523, 1990. 

Ding J, Gidaspow D. A bubbling fluidization model using the kinetic theory of granular flow. AIChE J 1990 36 523-538. 

Ding J, Gidaspow D (1990) A Bubbling Fluidization Model Using Kinetic Theory of Granular Flow. AIChE J 36(4) 523-538... 

Figure 6.46. Block diagram of the fluidized bed biofilm reactor model according to Mulcahy and La Motta (1978), containing reactor flow equation, biofilm effectiveness equations, and fluidization model with 13 system (fixed and design) parameters and six empirical correlations.

The fluidization model indicated in Fig. 6.46 is not elaborated on here in detail. An algorithm is proposed by these authors, as already stated, correlating bed porosity e determined through the expansion index n, which corresponds to the bioparticle terminal Re number Ret as a measure of the terminal settling velocity calculated from Newton s law in the following manner With... 

The most common approach, however, in contrast to this strategy for the setup of a fluidization model, is first to define an empirical correlation for an isolated particle and then to extend it to cover multiparticle systems through inclusion of a correction factor dependent on s, as demonstrated by Shieh et al. (1981). For an isolated spherical particle system with defined characteristics (d, Pp, Pl, and v), these workers gave the following expression... 

The performance of fluidized-bed reactors is not approximated by either the well-stirred or plug-flow idealized models. The solid phase tends to be well-mixed, but the bubbles lead to the gas phase having a poorer performance than well mixed. Overall, the performance of a fluidized-bed reactor often lies somewhere between the well-stirred and plug-flow models. 

Fundamental models correctly predict that for Group A particles, the conductive heat transfer is much greater than the convective heat transfer. For Group B and D particles, the gas convective heat transfer predominates as the particle surface area decreases. Figure 11 demonstrates how heat transfer varies with pressure and velocity for the different types of particles (23). As superficial velocity increases, there is a sudden jump in the heat-transfer coefficient as gas velocity exceeds and the bed becomes fluidized. 

The modeling of fluidized beds remains a difficult problem since the usual assumptions made for the heat and mass transfer processes in coal combustion in stagnant air are no longer vaUd. Furthermore, the prediction of bubble behavior, generation, growth, coalescence, stabiUty, and interaction with heat exchange tubes, as well as attrition and elutriation of particles, are not well understood and much more research needs to be done. Good reviews on various aspects of fluidized-bed combustion appear in References 121 and 122 (Table 2). 

In the chemical engineering domain, neural nets have been appHed to a variety of problems. Examples include diagnosis (66,67), process modeling (68,69), process control (70,71), and data interpretation (72,73). Industrial appHcation areas include distillation column operation (74), fluidized-bed combustion (75), petroleum refining (76), and composites manufacture (77). 

The bubble model (Kunii and Levenspiel, Fluidization Engineering, Wiley, New York, 1969 Fig. 17-14) assumes constant-sized bubbles (effective bubble size d ) rising through the suspension phase. Gas is transferred from the bubble void to the mantle and wake at... 

FIG. 17-14 Biihhling-hed model of Kunii and Levenspiel. dy = effective hiih-ble diameter, = concentration of A in hiihhle, = concentration of A in cloud, = concentration of A in emulsion, y = volumetric gas flow into or out of hiihhle, ky,- = mass-transfer coefficient between bubble and cloud, and k,. = mass-transfer coefficient between cloud and emulsion. (From Kunii and Leoen-spiel, Fluidization Engineering, Wiley, New York, 1.96.9, and Ktieger, Malahar, Fla., 1977.)... 

The first commercial fluidized bed polyeth)4eue plant was constructed by Union Carbide in 1968. Modern units operate at 100°C and 32 MPa (300 psig). The bed is fluidized with ethylene at about 0.5 m/s and probably operates near the turbulent fluidization regime. The excellent mixing provided by the fluidized bed is necessary to prevent hot spots, since the unit is operated near the melting point of the product. A model of the reactor (Fig. 17-25) that coupes Iduetics to the hydrodynamics was given by Choi and Ray, Chem. Eng. ScL, 40, 2261, 1985. 

Wen, C. Y. and L. H. Chen, "Flow Modeling Coneepts of Fluidized Beds," n Handbook of Fluids in Motion, N. P. Cheremisinoff (Editor), Butterworth Publishers, Ann Arbor, MI, 1983. 

The effectiveness of a fluidized bed as a ehemical reactor depends to a large extent on the amount of convective and diffusive transfer between bubble gas and emulsion phase, since reaction usually occurs only when gas and solids are in contact. Often gas in the bubble cloud complex passes through the reactor in plug flow with little back mixing, while the solids are assumed to be well mixed. Actual reactor models depend greatly on kinetics and fluidization characteristics and become too complex to treat here. 

Knowledge of these types of reaetors is important beeause some industrial reaetors approaeh the idealized types or may be simulated by a number of ideal reaetors. In this ehapter, we will review the above reaetors and their applieations in the ehemieal proeess industries. Additionally, multiphase reaetors sueh as the fixed and fluidized beds are reviewed. In Chapter 5, the numerieal method of analysis will be used to model the eoneentration-time profiles of various reaetions in a bateh reaetor, and provide sizing of the bateh, semi-bateh, eontinuous flow stirred tank, and plug flow reaetors for both isothermal and adiabatie eonditions. 

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