Model the fluidized bed

The physical situation in a fluidized bed reactor is obviously too complicated to be modeled by an ideal plug flow reactor or an ideal stirred tank reactor although, under certain conditions, either of these ideal models may provide a fair representation of the behavior of a fluidized bed reactor. In other cases, the behavior of the system can be characterized as plug flow modified by longitudinal dispersion, and the unidimensional pseudo homogeneous model (Section 12.7.2.1) can be employed to describe the fluidized bed reactor. As an alternative, a cascade of CSTR s (Section 11.1.3.2) may be used to model the fluidized bed reactor. Unfortunately, none of these models provides an adequate representation of reaction behavior in fluidized beds, particularly when there is appreciable bubble formation within the bed. This situation arises mainly because a knowledge of the residence time distribution of the gas in the bed is insuf-... 

Lennox, B. Montague, G.A. Frith, A.M. Gent, C. Bevan, V. Industrial apphcations of neural networks—an investigation. J. Process Control. 2001, 11, 497-507. Murtoniemi, E. Merkku, P. Yliruusi, J. Comparison of four different neural network training algorithms in modelling the fluidized bed granulation process. Lab. Microcom-put. 1993, 12, 69-76. 

In a single-phase model, the fluidized bed is regarded essentially as a continuum (Figure 8.4). Heat and mass balances are applied over the fluidized bed. It is assumed that particles in the bed are perfectly mixed. Equations 8.22 and 8.23 are the equations of moisture balance and energy balance, respectively [34]. 

Murtoniemi E, Yliruusi J, Kinnunen P, Merkke P, Leiviska K. The advantages by the use of neural networks in modeling the fluidized bed granulation process. Int J Pharm 1994 108(2) 155-164. 

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). 

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. 

An overly simplified model of fluidized-bed combustion treats the solid fuel as spherical particles freely suspended in upward-flowing gas. Suppose the particles react with zero-order kinetics and that there is no ash or oxide formation. It is desired that the particles be completely consumed by position z = L. This can be done in a column of constant diameter or in a column where the diameter increases or decreases with increasing height. Which approach is better with respect to minimizing the reactor volume Develop a model that predicts the position of the particle as a function of time spent in the reactor. Ignore particle-to-particle interactions. 

Adsorption equilibrium of CPA and 2,4-D onto GAC could be represented by Sips equation. Adsorption equilibrium capacity increased with decreasing pH of the solution. The internal diffusion coefficients were determined by comparing the experimental concentration curves with those predicted from the surface diffusion model (SDM) and pore diffusion model (PDM). The breakthrough curve for packed bed is steeper than that for the fluidized bed and the breakthrough curves obtained from semi-fluidized beds lie between those obtained from the packed and fluidized beds. Desorption rate of 2,4-D was about 90 % using distilled water. 

Because of the inadequacies of the aforementioned models, a number of papers in the 1950s and 1960s developed alternative mathematical descriptions of fluidized beds that explicitly divided the reactor contents into two phases, a bubble phase and an emulsion or dense phase. The bubble or lean phase is presumed to be essentially free of solids so that little, if any, reaction occurs in this portion of the bed. Reaction takes place within the dense phase, where virtually all of the solid catalyst particles are found. This phase may also be referred to as a particulate phase, an interstitial phase, or an emulsion phase by various authors. Figure 12.19 is a schematic representation of two phase models of fluidized beds. Some models also define a cloud phase as the region of space surrounding the bubble that acts as a source and a sink for gas exchange with the bubble. 

On the basis of different assumptions about the nature of the fluid and solid flow within each phase and between phases as well as about the extent of mixing within each phase, it is possible to develop many different mathematical models of the two phase type. Pyle (119), Rowe (120), and Grace (121) have critically reviewed models of these types. Treatment of these models is clearly beyond the scope of this text. In many cases insufficient data exist to provide critical tests of model validity. This situation is especially true of large scale reactors that are the systems of greatest interest from industry s point of view. The student should understand, however, that there is an ongoing effort to develop mathematical models of fluidized bed reactors that will be useful for design purposes. Our current... 

An advantage of this approach to model large-scale fluidized bed reactors is that the behavior of bubbles in fluidized beds can be readily incorporated in the force balance of the bubbles. In this respect, one can think of the rise velocity, and the tendency of rising bubbles to be drawn towards the center of the bed, from the mutual interaction of bubbles and from wall effects (Kobayashi et al., 2000). In Fig. 34, two preliminary calculations are shown for an industrial-scale gas-phase polymerization reactor, using the discrete bubble model. The geometry of the fluidized bed was 1.0 x 3.0 x 1.0 m (w x h x d). The emulsion phase has a density of 400kg/m3, and the apparent viscosity was set to 1.0 Pa s. The density of the bubble phase was 25 g/m3. The bubbles were injected via 49 nozzles positioned equally distributed in a square in the middle of the column. 

Asif et al. (1991) studied distributor effects in liquid-fluidized beds of low-density particles by measuring RTDs of the system by pulse injection of methylene blue. If PF leads into and follows the fluidized bed with a total time delay of 10 s, use the following data to calculate the mean-residence time and variance of a fluid element, and find N for the US model. 

The discussion above suggests a hydrodynamic flow model based on two distinct regions in the fluidized bed a bubble region made up mostly of gas, but also containing solid... 

A one-parameter model, termed the bubbling-bed model, is described by Kunii and Levenspiel (1991, pp. 144-149,156-159). The one parameter is the size of bubbles. This model endeavors to account for different bubble velocities and the different flow patterns of fluid and solid that result. Compared with the two-region model, the Kunii-Levenspiel (KL) model introduces two additional regions. The model establishes expressions for the distribution of the fluidized bed and of the solid particles in the various regions. These, together with expressions for coefficients for the exchange of gas between pairs of regions, form the hydrodynamic + mass transfer basis for a reactor model. 

A fluidized-bed reactor consists of three main sections (Figure 23.1) (1) the fluidizing gas entry or distributor section at the bottom, essentially a perforated metal plate that allows entry of the gas through a number of holes (2) the fluidized-bed itself, which, unless the operation is adiabatic, includes heat transfer surface to control T (3) the freeboard section above the bed, essentially empty space to allow disengagement of entrained solid particles from the rising exit gas stream this section may be provided internally (at the top) or externally with cyclones to aid in the gas-solid separation. A reactor model, as discussed here, is concerned primarily with the bed itself, in order to determine, for example, the required holdup of solid particles for a specified rate of production. The solid may be a catalyst or a reactant, but we assume the former for the purpose of the development. 

Using the Kunii-Levenspiel bubbling-bed model of Section 23.4.1 for the fluidized-bed reactor in the SOHIO process for the production of acrylonitrile (C3H3N) by the ammoxidation... 

Figure 9.14 shows that the score T1 for the acoustic model and T1 for the process data have similar trend lines for the start-up procedure on the 20 February 2001, however the acoustic T1 has a significantly faster response than T1 for the process data when the fluidized bed is filled with granules. 

Taking the density, thermal conductivity and latent heat of fusion of the peas to be 1050 kg m , l.OWm K and 250kjkg respectively and the bulk density within the fluidized bed as 525kgm , the Plank/ Nagaoka model can be used to estimate the time required for the product outlet temperature to reach -20°C. 

Table IV shows the restrictions which must be placed on this general model to obtain each of the special cases studied. Also shown are the number of parameters for each of the models. What is now needed is an evaluation of these models to find those models which fit the fluidized bed in its wide range of behavior, and then to select from these the simplest model of good fit. Practically every one of these models is flexible enough to correlate the data of any single investigation consequently a proper evaluation would require testing every model under the extremely wide variety of operating conditions of different investigators.

Figure 7-4 Slurry reactor (left) for well-mixed gas-solid reactions and fluidized bed reactor (center) for liquid-solid reactions. At the right is shown a riser reactor in which the catalyst is carried with the reactants and separated and returned to the reactor. The slurry reactor is generally mixed and is described by the CSTR model, while the fluidized bed is described by the PFTR or CSTR models.

An advanced cracking evaluation-automatic production (ACE Model AP) fluidized bed microactivity unit was used to study the catalyst and feed interactions. The fluidized bed reactor was operated at 980°F (800 K). Every feed was tested on two different catalysts at three cat-to-oil ratios 4, 6, and 8. Properties of laboratory... 

The modeling of real immobilized-enzyme column reactors, mainly the fluidized-bed type, has been described (Emeiy and Cardoso, 1978 Allen, Charles and Coughlin, 1979 Kobayashi and Moo-Young, 1971) by mathematical models based on the dispersion concept (Levenspiel, 1972), by incorporation of an additional term to account for back-mixing in the ideal plug-flow reactor. This term describes the non-ideal effects in terms of a dispersion coefficient. 

Two approaches have been used to calculate A. One of them is based on the two-phase model of fluidized beds and the other is based on the stability theory. In the two-phase model [75], the flow of gas in excess to that corresponding to the minimum fluidization velocity traverses the fluidized bed as bubbles. On this basis, one can write the following equation for the volume fraction i// occupied by the bubbles ... 

As in the fluidized beds analysis (Section 3.8.3), a similar simplification has been made in Kunii-Levenspiel model for the material balances in the emulsion phase, where again the corresponding derivatives have been omitted (eqs. (3.529) and (3.530)). As in the case of liquid flow in trickle beds, the flow of the gas in the emulsion phase is considered too small and so the superficial velocities can be neglected. Thus, in trickle beds, from eq. (3.367),... 

---