Models for macromixing in the reactor

Once the data for the RTD are obtained, the backmixing characteristics for each phase of a multiphase reactor can be quantitatively evaluated by fitting appropriate models to these data. The models for backmixing can be largely divided into two 

Commercial reactors are non isothermal and often adiabatic. In a noniso-thermal gas-liquid reactor, along with the mass dispersions in each phase, the corresponding heat dispersions are also required. Normally, the gas and liquid at any given axial position are assumed to be at the same temperature. Thus, in contrast to the case of mass, only a single heat-balance equation (and corresponding heat-dispersion coefficient) is needed. Under turbulent flow conditions (such as in the bubble-column reactor) the Peclet number for the heat dispersion is often assumed to be approximately equal to the Peclet number for the mass dispersion in a slow-moving liquid phase. 

Methods for evaluating the axial dispersion coefficient from RTD data As mentioned earlier, the one-parameter axial-dispersion model is widely used to correlate RTD data. The nature of the RTD depends upon the nature of the tracer input and the nature of the. flow, characteristics. For the RTD shown in Fig. 3-4 o), the axial dispersion coefficients for the liquid and solid phases can be obtained by fitting the equation 

In the vast majority of experimental studies, the backmixing characteristics of a flowing phase are examined using a -pulse tracer input. For the fixed-bed systems shown in Fig. 3-2, if a perfect pulse input is used, then, as shown by Levenspiel,5 6 the axial dispersion coefficient or the Peclet number can be obtained from the variance of the RTD curve. For example, for a closed system and large extent of dispersion, the variance, it, is related to the Peclet number by the equation 

Although the above method can give a simple evaluation of Peclet number for the system, the tailing in the RTD curve can cause significant inaccuracy in the evaluation of the Peclet number. Michell and Furzer67 suggested that a better estimation of the axial dispersion coefficient is obtained if the observed RTD is statistically fitted to the exact solution of the axial dispersion model equation with appropriate boundary conditions. For example, a time-domain solution to the partial differential equation describing the dispersion model, i.e., 

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RESIDENCE-TIME DISTRIBUTION AND MODELS FOR MACROMIXING IN THE REACTORS... 

In a continuous reaction process, the true residence time of the reaction partners in the reactor plays a major role. It is governed by the residence time distribution characteristic of the reactor, which gives information on backmixing (macromixing) of the throughput. The principal objectives of studies into the macrokinetics of a process are to estimate the coefficients of a mathematical model of the process and to validate the model for adequacy. For this purpose, a pilot plant should provide the following ... 

An alternative method to RTD theory for treating non-ideal reactors is the use of zone models. In this approach, the reactor volume is broken down into well mixed zones (see the example in Fig. 1.5). Unlike RTD theory, zone models employ an Eulerian framework that ignores the age distribution of fluid elements inside each zone. Thus, zone models ignore micromixing, but provide a model for macromixing or large-scale inhomogeneity inside the reactor. 

The first combination - well macromixed and well micromixed - is just the CSTR model for a stirred reactor wherein the scalar is assumed to be constant at every point in the reactor. The second combination - well macromixed and poorly micromixed - corresponds to a statistically homogeneous flow and is often assumed when deriving CRE micromixing models. The third combination - poorly macromixed and well micromixed - is often... 

As far as first order reactions are concerned, the only quantity determining conversion is the time spent by reacting species in the reactor. Therefore, conversion can be calculated from batch kinetics - e.g. Cg(t) - and from macromixing characteristics only - e.g., RTD or lAD. For instance, in a continuous reactor, by merging all streamlets issuing from the tubes of the BPT-Model, one obtains the well-known relationship... 

Validation and Application. VaUdated CFD examples are emerging (30) as are examples of limitations and misappHcations (31). ReaUsm depends on the adequacy of the physical and chemical representations, the scale of resolution for the appHcation, numerical accuracy of the solution algorithms, and skills appHed in execution. Data are available on performance characteristics of industrial furnaces and gas turbines systems operating with turbulent diffusion flames have been studied for simple two-dimensional geometries and selected conditions (32). Turbulent diffusion flames are produced when fuel and air are injected separately into the reactor. Second-order and infinitely fast reactions coupled with mixing have been analyzed with the k—Z model to describe the macromixing process. 

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