RTD models

Dispersion In tubes, and particiilarly in packed beds, the flow pattern is disturbed by eddies diose effect is taken into account by a dispersion coefficient in Fick s diffusion law. A PFR has a dispersion coefficient of 0 and a CSTR of oo. Some rough correlations of the Peclet number uL/D in terms of Reynolds and Schmidt numbers are Eqs. (23-47) to (23-49). There is also a relation between the Peclet number and the value of n of the RTD equation, Eq. (7-111). The dispersion model is sometimes said to be an adequate representation of a reaclor with a small deviation from phig ffow, without specifying the magnitude ol small. As a point of superiority to the RTD model, the dispersion model does have the empirical correlations that have been cited and can therefore be used for design purposes within the limits of those correlations. 

FIG. 23-12 Comp arison of RTD models, all with the same variance and skewness. Values of C/Cq of segregated conversion of a first-order reaction with kt = 3 original, 0.1408 gamma, 0.1158 Gauss, 0.1148 GC, 0.1418. 

RTD Models. The next class of models relied on the RTD to calculate conversions. But since the rate of catalytic reaction of an element of gas depends on the amount of solid in its vicinity, the effective rate constant is low for bubble gas, high for emulsion gas. Thus any model that simply tries to calculate conver-... 

Contact Time Distribution Models. To overcome this difficulty and still use the information given by the RTD, models were proposed which assumed that faster gas stayed mainly in the bubble phase, the slower in the emulsion. Gilliland and Knudsen (1971) used this approach and proposed that the effective rate constant depends on the length of stay of the element of gas in the bed, thus... 

For the SCC of type II an example of a RTD modelled is shown in Figure 7, The model used is the dispersion model (sec Esq. 6). The values of the model parameters determined arc a Bodenstein number of 8.8 and a mean residence time of 0.6 s. It clearly shows that the model for the RTD explains the frequency response measurement up to a frequency of 2 Hz, At the frequency of 2 Hz the signal-to-noise ratio of 100 is reached. Any mixing processes which affect the transfer function above this frequency cannot be identified. 

Laquerbe, C Laborde, J.C. Soares, S. Floquet, P. Pibouleau L. Domenech, S. Synthesis of RTD models via stochastic procedures simulated annealing and genetic algorithms. Comput. Chem. Eng. 2001, 25, 1169-1183. 

Gilliland and Kundsen (1970) then modified the RTD models and assumed that the faster gas stayed mainly in the bubble phase and the slower in the emulsion. Their approach was to distinguish the effect of the two classes of gas with different effective rate constant. The overall conversion equation in their proposed model is... 

The above equation describes the conversion and is referred to as the contact time distribution (CTD) model. Although improvement was made over the RTD models, the problem with this approach involves obtaining a meaningful E function to use in Eq. (3)... 

The Pdclet number thus defined is the one classically used in RTD models. It differs from the one more commonly introduced in turbulence theories. Pet = Kt k Urmdt) k, where K is the molecular diffusivity of constituents. 

The two approaches are not conflictive but rather complementary. The fluid mechanics description may give a physical and theoretical meaning to the phenomenological parameters introduced in the RTD models and an indication on the way these parameters are affected by the operating conditions. In turn, the RTD models give a more accurate global description of fluid flow pattern. In this paper, we will present an application of this twosided approach to the analysis of the liquid flow hydrodynamics and the RTD models in trickle-bed reactors. 

RTD models for trickle-bed reactors are quite numerous. They are reviewed in part 2 in order to evidence the main fluid flow characteristics that have been considered by the authors developing these models. The fluid mechanics description is based on percolation concepts. The main implications of these concepts are analyzed in part 3 whereas part 4 is devoted to the development of a percolation model describing the liquid flow distribution in a trickle-bed reactor. This model is then applied to derive correlations for the wetting efficiency and the dynamic liquid holdup (part 5) and, finally, for the axial dispersion coefficient (part 6) a classical example... 

RTD models have been developed to characterize mixing in both gas and liquid phases. Actually, mixing in the gas phase has received very little attention because its influence on the behaviour of trickle flow reactors is rather weak. 

The numerous RTD models developed for trickle bed reactors may be grouped into two classes ... 

Actually, the RTD models reported in this section evidence some questions that cannot be answered by RTD experiments but rather by a detailed analysis of the liquid flow hydrodynamics the scale of mixing (e.g. the number of stages in a stage-wise model)... 

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