Patterns dispersed flow, dispersion coefficient

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. 

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. 

Axial dispersion, D When a band migrates along a column packed with non-porous particles, it spreads axially because of the combination effects of axial diffusion and the inhomogeneity of the pattern of flow velocity in a packed bed. This combination of effects is accounted for by a single term, proportional to the axial dispersion coefficient. It is independent of the mass transfer resistance and of the other contributions of kinetic origin to band broadening. 

Early SBCR models were reviewed by Ramachandran and Chaudhari (5) and by Deckwer (9). They require hold-up correlations as an input and do not compute flow patterns. The most complete and useful of these models applied to the Fischer-Tropsch (F-T) conversion of synthesis gas in a SBCR is that of Prakash and Bendale (79). They sized commercial SBCR for DOE. They gave syngas conversion and production as a function of temperature, pressure and space velocity. Input parameters with considerable uncertainty that influenced production rates were the gas hold-up, the mass transfer coefficient and the dispersion coefficient. Krishna s group (77) extended such a model to compute product distribution using a product selectivity model. Air Products working with Dudukovic measured dispersion coefficients needed as an input into such model. The problem with this approach is that the dispersion coefficients are not constant. They are a function of the local hydrodynamics. 

Possible optimization of pastes and the according apparatus in process engineering by MRI flow experiments were described. The spatially resolved determination of velocities in suspensions by means of NMR imaging techniques was applied to steady tube flows (with regard to the total flow rate) in different geometries. Three types of suspensions with different solid volumetric concentrations were examined in order to demonstrate the effect of the material-specific flow-behavior and of the geometry of the experimental set-up on the observed flow pattern. The local probability distribution of single velocity components is determined and then both the local mean value and the standard deviation can be derived from the probability distribution. The standard deviation can be interpreted as the local dispersion coefficient of the velocity component. 

This review deals mainly with the discussion of various macroscopic hydro-dynamic, heat, and mass transfer characteristics of bubble columns, with occasional reference to the analogous processes in modified versions of bubble columns with a variety of internals. The hydrodynamic considerations include determination of parameters like flow patterns, holdup, mixing, liquid circulation velocities, axial dispersion coefficient, etc., which all exert strong influence on the resulting rates of heat and mass transfer and chemical reactions carried out in bubble columns. Different correlations developed for estimating the aforementioned parameters are presented and discussed in this chapter. 

The two equations for the mass and heat balance, Eqs. (4.10.125) and (4.10.126) or the dimensionless forms represented by Eqs. (4.10.127), (4.10.128) and (4.10.130), consider that the flow in a packed bed deviates from the ideal pattern because of radial variations in velocity and mixing effects due to the presence of the packing. To avoid the difficulties involved in a rigorous and complicated hydrodynamic treatment, these mixing effects as well as the (in most cases negligible contributions of) molecular diffusion and heat conduction in the solid and fluid phase are combined by effective dispersion coefficients for mass and heat transport in the radial and axial direction (D x, Drad. rad. and X x)- Thus, the fluxes are expressed by formulas analogous to Pick s law for mass transfer by diffusion and Fourier s law for heat transfer by conduction, and Eqs. (4.10.125) and (4.10.126) superimpose these fluxes upon those resulting from convection. These different dispersion processes can be described as follows (see also the Sections 4.10.6.4 and 4.10.7.3) ... 

Optimal reactor design is critical for the effectiveness and economic viability of AOPs. The WAO process poses significant challenges to chemical reactor engineering and design, due to the (i) multiphase nature of WAO reactions (ii) temperatures and pressures of the reaction and (iii) radical reaction mechanism. In multiphase reactors, complex relationships are present between parameters such as chemical kinetics, thermodynamics, interphase/intraphase intraparticle mass transport, flow patterns, and hydrodynamics influencing reactant mass transfer. Complex models of WAO are necessary to take into account the influence of catalyst wetting, the interface mass-transfer coefficients, the intraparticle effective diffusion coefficient, and the axial dispersion coefficient. " ... 

In addition to scale-up difficulties, there are a number of problems related to the stable operation of a bubble column associated with hydrodynamics. For example, consider the important commercial application of bubble columns in hydroprocessing of petroleum resids, heavy oils and synthetic crudes. Hydrodynamic cold flow and hot flow studies on the Exxon Donor Solvent coal liquefaction process (Tarmy et al., 1984) showed that much of the literature correlations for the hydrodynamic parameters (holdup, interfacial area and dispersion coefficients) obtained with cold flow units, at ambient conditions, are not applicable for commercial units operating at relatively higher pressures. In addition, the flow pattern in commercial units was considerably different. In the hydroprocessing of petroleum residues by the H-Oil and LC-Fining processes, refinery operations have experienced problems with nonuniform distribution of gas and liquid reactants across the distributor, maintaining stable fluidization and preventing temperature excursions (Beaton et al., 1986, Fan, 1989 and Embaby, 1990). Catalyst addition, withdrawal and elutriation have also been identified as problems in these hydrotreaters. 

It has been described elsewhere [12] that the flow pattern in the tanks investigated and described by the dimensionless dispersion number (DN = D/[u.L], where D is the turbulent dispersion coefficient, u the convective transport, and L a characteristic length) has, in conjunction with the floe properties, a more pronounced effect upon the separation effectivity than can be concluded from the coagulation rate alone. 

Experimental evidence show that the liquid axial velocity is far from being flat and independent of the radial space coordinate [29], and the use of a cross-sectional average velocity variable seems not to be sufficient. The back mixing induced by the global liquid flow pattern was commonly accounted for by adjusting the axial dispersion coefficient accordingly. However, while (slurry) bubble column performance... 

While attempts have been made to assign axial dispersion coefficients to the gas flow in fluidized beds or to represent the flow field in terms of a series of well-mixed vessels, none of these methods is really satisfactory. Perhaps the most promising approach to the problem of gas flow patterns is provided by a bubbling model [47]. 

The nature of dispersion. The effect which the solid packing has on the flow pattern within a tubular reactor can sometimes be of sufficient magnitude to cause significant departures from plug flow conditions. The presence of solid particles in a tube causes elements of flowing gas to become displaced randomly and therefore produces a mixing effect. An eddy diffusion coefficient can be ascribed to this mixing effect and becomes superimposed on the transport processes which normally occur in unpacked tubes—either a molecular diffusion process at fairly low Reynolds... 

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