Bubbling flow reactor modeling

Figure 23.8 Flow/kinetics scheme for bubbling-bed reactor model for reaction A(g) +. -> product(s)...

Industrial reactors generally operate at very high velocities (of order 1 m/s) much in excess of terminal falling velocity for at least the finest powder fractions. Powder is continually elutriated and returned to the bed via cyclones. Under these conditions there is disagreement as to whether or not bubbles retain their identity and such beds have been described as "turbulent" or "fast fluidised". What little evidence there is supports the continued existence of bubbles but now in a much disturbed or heterogeneous dense phase and with a less definite shape. Until more is known about this physical situation it is not easy to see how the bubbling bed reactor models should be modified correctly to describe this flow regime. 

Van der Laan [82] reported attempts to model FT in a bubble column reactor. His model exhibited well-mixed liquid and two gas bubble regimes small bubbles that were well mixed and large bubbles that showed plug flow behavior (Figure 12.21). Van der Laan [82] also provided a summary of bubble column reactor models that others have utilized (Tables 12.1 and 12.2). He concluded that the FT slurry bubble column reactor is reaction controlled due to the low activity of the iron catalyst and the... 

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. 

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. 

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-... 

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. 

In a bubble-column reactor for a gas-liquid reaction, Figure 24.1(e), gas enters the bottom of the vessel, is dispersed as bubbles, and flows upward, countercurrent to the flow of liquid. We assume the gas bubbles are in PF and the liquid is in BMF, although nonideal flow models (Chapter 19) may be used as required. The fluids are not mechanically agitated. The design of the reactor for a specified performance requires, among other things, determination of the height and diameter. 

This approach is proven for design and prediction of the performance of multiple-bed down-flow reactors. The complication, and a critical difference between this and a bubble column, is that the gas bubbles are formed in situ. The gas flux, and thus gas hold-up, will vary over the bed height. For the down-flow beds, a simplified linear gas hold-up profile was inherent in the design models, but with no apparent penalty in design accuracy. 

In general, the material balances and the corresponding solutions for trickle and bubble bed reactors are the same, under the assumption that the plug-flow condition holds for both phases. Of course, the appropriate correlations should be used for the estimation of mass transfer coefficients. However, in packed bubble bed reactors, the liquid-phase is frequently found in a complete mixed state, and thus some adjustments have to be made to the aforementioned models. Two special cases will be presented here. 

Concerning packed bubble bed reactors, the evaluation of the Peclet number of the liquid-phase is important in order to decide if we have to use a plug- or backmixed-flow model. The liquid-phase can be considered well mixed if (Ramachandran and Chaudhari, 1980)... 

In the following sections, the solutions of the models as well as examples will be presented for the case of trickle-bed reactors and packed bubble bed reactors. Plug flow and fust-order reaction will be assumed in order to present analytical solutions. Furthermore, the expansion factor is considered to be zero unless otherwise stated. Some solutions for other kinetics will be also given. The reactant A is gas and the B is liquid unless otherwise stated. 

Concerning packed bubble bed reactors, the evaluation of the Peclet number of the liquid phase is important in order to decide if we have to use a plug- or backmixed-flow model. For the specified Reynolds number, the Peclet number for the liquid phase using the Stiegel-Shah correlation (eq. (3.422)) is 0.15, much lower than in the trickle bed, which was expected as the backmixing in the liquid phase in packed bubble bed reactors is relatively high. The liquid phase can be considered to be well mixed if (Ramachandran, and Chaudhari, 1980) (eq. (3.423))... 

After the investigation of hydrodynamics and mass transfer, the next step is the examination of the reactor model. For example, let us consider here the two-phase model with plug flow of gas in both bubble and emulsion phase and first-order reaction (see Section 3.8.3). The first step at this stage is to transform its equations to dimensionless forms. 

Although the most realistic model for a bubble column reactor is that of dispersed plug-flow in both phases, this is also the most complicated model in view of the uncertainty of some of the quantities involved, such a degree of complication may not be warranted. Because the residence time of the liquid phase in the column... 

Chemical reactor models invariably start from the two-phase theory (12). The interstitial flow is assumed to be in good and continuous contact with solids whilst some by-passing occurs in the bubble phase. There is, however, very little axial or radial mixing of the gas. There may be some exchange between the two phases and Figure 4 depicts this kind of model. 

As part of the work undertaken by APCI under contract to the DOE, to develop a slurry phase Fischer-Tropsch process to produce selectively transportation fuels, a study of the hydrodynamics of three phase bubble column reactors was begun using cold flow modelling techniques (l ). Part of this study includes the measurement of solid concentration profiles over a range of independent column operating values. 

Bubble columns Loop reactors Stirred tanks Hydrocyclones Reasonable Reasonable Reasonable Reasonable Modeling of chum-turbulent flow regime Modeling of chum-turbulent flow regime Improved geometrical representation of impeller and baffles Improved geometrical representation of system... 

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