Modeling of trickle bed reactors

A. Gianetto and F. Berruti, Modelling of trickle-bed reactors, ibid., pp.631-685. 

Examples of several models and their numerical solutions were given by Attou et al. [30], whose model is limited to the descriptions of hydrodynamics, and by Khadilkar et al. [31] as well as Jiang et al. [32], who present general trickle-bed reactor models. The two latter papers originate from the well-known Dudukovic research group and show the latest state-of-the-art modeling of trickle-bed reactors in stationary operation. 

As conclusion of this first approach of the two-dimensional modelling of trickle-bed reactors, it seems possible to describe the radial liquid flow spreading in terms of a percolation process. The numerical simulations presented above evidence the liquid flow trapping. This phenomenon affects the quality of the liquid flow distribution. It should be accounted for when designing a distributor, a redistributor or any other internal. 

Lopes JG, Quinta-Ferreira RM. Multiphase CFD modeling of trickle-bed reactor hydrodynamics. In Proceedings of the World Congress on Engineering and Computer Science, San Frandsco, CA, USA, 2007. 

More recent modeling mainly follows the approach outlined in Sections 14.2.4 and 14.2.5. Mills and Dudukovic [1983] applied a generalized dispersion model with partially wetted pellets. A review by Gianetto and Specchia [1992] and the text books of Ramachandran and Chaudhari [1983] and of Shah [1979] provide further insight into the modeling of trickle bed reactors. 

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. 

Industrial gas-liquid hydrogenation reactions are carried out in slurry and trickle-bed reactors (Ref. 3). Modeling of the latter has been advanced significantly in the last two decades (Refs. 4-6). Predictions of trickle-bed reactors performance were in good agreement with experimental data (Ref.7). 

Trickle-bed reactors are widely used in the oil industry because of reliability of their operation and for the predictability of their large-scale performance from tests on a pilot-plant scale. Further advantages of trickle-bed reactors are as follows The flow pattern is close to plug flow and relatively high reaction conversions may be achieved in a single reactor. If warranted, departures from ideal plug flow can be treated by a dispersed plug-flow model with a dispersion coefficient for each of the liquid and gas phases. 

The design and the scale-up of trickle-bed reactors are still rather difficult problems despite of the high research activity in this area for many years. As a matter of fact an accurate modelling of these reactors should basically involve the knowledge of the fluid flow hydrodynamics as well as of the various heat and mass transport resistances between the three phases. The various attempts in modelling these processes and in predicting... 

An appropriate model for trickle-bed reactor performance for the case of a gas-phase, rate limiting reactant is developed. The use of the model for predictive calculations requires the knowledge of liquid-solid contacting efficiency, gas-liquid-solid mass transfer coefficients, rate constants and effectiveness factors of completely wetted catalysts, all of which are obtained by independent experiments. 

A pure phenomenological model of such an intricate process, taking into account all possible reaction steps, is therefore a powerful tool for the scale up and the prediction of performances of trickle-bed reactors. Such a model (20 has proved to be able to correctly reproduce experimental data using only two adjustable parameters. It has been checked in several cases (hydrogenation of alphamethylstyrene (3J, hydrogenation of 2-butanone (, hydrorefining (J5) ), with more or less volatile liquid reactants and it appeared to be also useful to calculate a posteriori the extent of the different types of wetted catalyst area and their different effectiveness factor. 

The above issues associated with prediction of trickle-bed reactor performance has motivated a number of researchers over the past two decades to perform laboratory-scale studies using a particular model-reaction system. These are listed in Table I. Although a more detailed summary is given elsewhere (29), a general conclusion seems to be that both incomplete catalyst wetting and mass transfer limitations are significant factors which affect trickle-bed reactor performance. 

A review of previous reaction studies used to support the development of trickle-bed reactor models is presented. This review suggests that these previous models have neglected the effect of incomplete liquid-solid contacting even though it was experimentally observed in a number of cases. For the few cases where it was included, it was used as an adjustable parameter to match the measured conversion versus liquid mass velocity data to the model. 

MODELS BASED ON EFFECTIVENESS OF CONTACT, WITH NO EXTERNAL MASS-TRANSFER RESISTANCES (MODELS FOR TRICKLE-BED REACTORS)... 

It is very interesting, after all this discussion of hydrodynamics, mass transfer, and other properties of trickle beds, to see what people have aetually done when they get down to the task of trickle-bed reactor design. Things get fairly basie quite rapidly, and while we don t retreat all the way to the ideal triekle-bed reactor model, neither do we attempt the presumption of three or four parameters. Some have proposed simplified heterogeneous models, others consider only the degree of contact between the liquid and solid phases, and still others base the approach on the mass-transfer factors appearing in the three-phase reactor/reaction system. Finally, there are some approaches based on the directly-determined residenee time distribution funetion. We will take a brief look at each. 

The simulation results show that in addition to precise microkinetics, knowledge of the fluid dynamics, especially the liquid holdup, is an essential prerequisite for modeling a trickle-bed reactor. The advantage of a simulation program is not so much the calculation of the conversion for a concrete situation rather, it is the splitting of a complex problem into individual steps, which allows parameter smdies to be carried out [10]. 

The following will explain one way of essentially process intensification of trickle-bed reactors by periodic operation. The unsteady-state operation was considered as square waves cycling liquid flow rate at the reactor inlet. The hydrogenation of alpha-methylstyrene to cumene C6H5(CH3) = CH2(L) + H2(g) C6H5CH(CH3)2(l) over a palladium catalyst (0.7% Pd/y-Al203) was selected as a model reaction. Own experimental trickle-bed reactor investigations showed for this reaction system that the periodic variations of liquid flow rates by on/off... 

The performance of trickle-bed reactors may be affected by many factors, such as interphase mass transfer, intraparticle diffusion, axial dispersion and incomplete catalyst wetting. Therefore, knowledge about these influenced factors is important for their mathematical description by an unsteady-state reactor model. Until now, the literature analysis shows the experimental and theoretical understanding of trickle-bed reactors under unsteady-state-operation conditions has improved, but not considerably. The following studies are focused on the trickling regime under unsteady-state-operation conditions. 

The momentum balance will not be discussed in more detail here, because the first simulation tests for periodic process control of trickle-bed reactors do not consider the momentum balance. A complete mathematical model for a three-phase reactor would thus be made up of the respective material, heat and momentum balances for the gas phase , for the liquid phase , and for the solid phase (catalyst) , but their complete solution currently encounters major difficulties. 

The previously described mathematical models for simulating the periodic operation of trickle-bed reactors are limited to liquid-throughput variations both in the trickle and in the pulse regimes, because these strategies have so far given the most efficient improvement of reactor performance. 

The modeling of the periodic process management is chiefly based on the extension of steady-state models for trickle-bed reactors. Their applications to nonsteady-state systems have several drawbacks, as summarized in the following points ... 

In general, it can be concluded that substantial progresses have been made in the experimental and theoretical analysis of trickle-bed reactors under unsteady-state conditions. But until now these results are not sufficient for a priori design and scale-up of a periodically operated trickle-bed reactor. The mathematical reactor models, which are now available are not detailed enough to simulate all of the main transient behavior observed. For solving this problem specific correlations for specific model parameters (e.g. Hquid holdup, mass transfer gas-solid and liquid-solid, intrinsic chemical kinetic, etc.) determined under dynamic conditions are required. The available correlations for important hydrodynamic, mass-and heat-transfer parameters for periodically operated trickle-bed reactors leave a lot to be desired. Indeed, work for unsteady-state conditions on a larger scale may also be necessary. 

Remarks. Close inspection of the nonequilibrium model outputs reveals that assumption of nonequilibrium capillary pressure in the studied range of experimental conditions was not necessary and static equilibrium described by PcxPg-Pe was sufficient to account for the interfacial forces [54], However, recourse to empirical capillary relationships, such as the Leverett /-function, is unnecessary as the nonequilibrium two-phase flow model enables access to capillary pressure via entropy-consistent constitutive expressions for the macroscopic Helmholtz free energies. Also, the role of mass exchange between bulk fluid phase holdups and gas-liquid interfacial area was shown to play a nonnegligible role in the dynamics of trickle-bed reactor [ 54]. By accounting for the production/destruction of interfacial area, they prompted much briefer response times for the system to attain steady state compared to the case without inclusion of these mass exchange rates. 

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