Correlations stirred-tank reactor

Over 25 years ago the coking factor of the radiant coil was empirically correlated to operating conditions (48). It has been assumed that the mass transfer of coke precursors from the bulk of the gas to the walls was controlling the rate of deposition (39). Kinetic models (24,49,50) were developed based on the chemical reaction at the wall as a controlling step. Bench-scale data (51—53) appear to indicate that a chemical reaction controls. However, flow regimes of bench-scale reactors are so different from the commercial furnaces that scale-up of bench-scale results caimot be confidently appHed to commercial furnaces. For example. Figure 3 shows the coke deposited on a controlled cylindrical specimen in a continuous stirred tank reactor (CSTR) and the rate of coke deposition. The deposition rate decreases with time and attains a pseudo steady value. Though this is achieved in a matter of rninutes in bench-scale reactors, it takes a few days in a commercial furnace. 

Two complementai y reviews of this subject are by Shah et al. AIChE Journal, 28, 353-379 [1982]) and Deckwer (in de Lasa, ed.. Chemical Reactor Design andTechnology, Martinus Nijhoff, 1985, pp. 411-461). Useful comments are made by Doraiswamy and Sharma (Heterogeneous Reactions, Wiley, 1984). Charpentier (in Gianetto and Silveston, eds.. Multiphase Chemical Reactors, Hemisphere, 1986, pp. 104—151) emphasizes parameters of trickle bed and stirred tank reactors. Recommendations based on the literature are made for several design parameters namely, bubble diameter and velocity of rise, gas holdup, interfacial area, mass-transfer coefficients k a and /cl but not /cg, axial liquid-phase dispersion coefficient, and heat-transfer coefficient to the wall. The effect of vessel diameter on these parameters is insignificant when D > 0.15 m (0.49 ft), except for the dispersion coefficient. Application of these correlations is to (1) chlorination of toluene in the presence of FeCl,3 catalyst, (2) absorption of SO9 in aqueous potassium carbonate with arsenite catalyst, and (3) reaction of butene with sulfuric acid to butanol. 

Many correlations allow estimation of the gas-liquid volumetric mass transfer coefficient kLa in mechanically stirred tank reactors. The following intends not to provide a comprehensive review but rather a critical evaluation of selected correlations adapted to hydrogenations [Eqs. (40) to (43)] [25, 51-53]. 

Correlations are available for mixing times in stirred-tank reactors with several types of stirrers. One of these, for the standard Rushton turbine with baffles [13], is shown in Figure 7.9, in which the product of the stirrer speed N (s ) and the mixing time t (s) is plotted against the Reynolds number on log-log coordinates. For (Re) above approximately 5000, the product N t (-) approaches a constant value of about 30. 

Scale-up factors have been developed for changes in density, viscosity, surface tension and correlations using these factors have been successful for certain reactor geometries, i. e. stirred tank reactors, and well defined systems, i. e. air/water (Zlokamik, 1978) ... 

The volumetric mass transfer coefficient k-a has been used by most Investigators to characterize mass transfer capability of stirred tank reactors. It would seem preferable to be able to predict k a from separate correlations for its constituent parameters kL and a, since their values are predominantly dependent on different physical properties of the system. 

No correlations of G (fr) or rigriang have been achieved in terms of operating variables. At present, the chief value of RTD studies is for the diagnosis of the performance of existing equipment for instance, maldistribution of catalyst in a packed reactor, or bypassing or stagnancy in stirred tanks. Reactor models made up of series and/or parallel elements also can be handled theoretically by these methods. 

Form and size of support The particle size will have an influence on filtration times from stirred tank reactors in repeated batch mode. Furthermore, this factor is important for the performance in column reactors regarding back pressure and flowrates, which of course are correlated. For this purpose a size of spherical particles in the range of 150-300 pm is preferred. 

For non-isothermal or non-linear chemical reactions, the RTD no longer suffices to predict the reactor outlet concentrations. From a Lagrangian perspective, local interactions between fluid elements become important, and thus fluid elements cannot be treated as individual batch reactors. However, an accurate description of fluid-element interactions is strongly dependent on the underlying fluid flow field. For certain types of reactors, one approach for overcoming the lack of a detailed model for the flow field is to input empirical flow correlations into so-called zone models. In these models, the reactor volume is decomposed into a finite collection of well mixed (i.e., CSTR) zones connected at their boundaries by molar fluxes.4 (An example of a zone model for a stirred-tank reactor is shown in Fig. 1.5.) Within each zone, all fluid elements are assumed to be identical (i.e., have the same species concentrations). Physically, this assumption corresponds to assuming that the chemical reactions are slower than the local micromixing time.5... 

Kinetic models can be used to link the reactor design with its performance. The reaction rate may be expressed by power law functions, by more complex expressions, as Langmuit-Hinselwood-Hougen-Watson (LHHW) correlations for catalytic processes, or by considering user kinetics. There are two ideal models, continuous stirred tank reactor (CSTR) or plug flow (PFR), available in rating mode (reaction volume fixed) or design mode (conversion specified). 

In this chapter, correlations for heat transfer in reactors are presented, and the requirements for stable operation are discussed. The continuous stirred-tank reactor is treated first, since it is the simplest case, and uniform temperature and concentration are assumed for the fluid in the tank. For a homogeneous reaction in a pipeline, there are axial gradients of temperature... 

Chemical engineers intuitively work under the assumption that to improve the mass-transfer characteristics of a gas-liquid reactor, more energy must be dissipated in the fluids to effect a more vigorous contacting of the fluids. For singlephase flow in turbulent systems, this concept has become known as the Chilton-Colburn analogy. Another example of the coupling of hydrodynamics and mass transfer in multiphase systems is the common correlation of the mass transfer and the power input for stirred-tank reactors. 

TABLE 6.1 Gas Holdup Correlations for Stirred-Tank Reactors... 

Whitton, M.J., and Nienow, A.W. (1993), Scale-up correlations fr gas hold-up and mass transfer coefficients in stirred tank reactors in Proceedings of the 3rd International Conference on Bioreactor and Bioprocess Fluid Dynamics, 135-149. 

Combining Highbie s Penetration theory and Kolmogoroff s theory on isotropic turbulence, it has been shown recently [34l that experimental data on aerated liquids in stirred tank reactors can be correlated for coil as well as wall heat transfer by the equation... 

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