Dispersion in packed beds

Dispersion is the general term which denotes the various types of self-induced mixing processes which can arise during the flow of a fluid. The effects of dispersion are important in packed beds, though they are also present in the 

In turbulent flow, molecular diffusion is augmented by the presence of turbulent eddies and mixing is more intensive though, due to the flatter velocity profiles in tubes, the role of velocity gradient in dispersion diminishes. 

Longitudinal dispersion coefficients can be evaluated by injecting a flat pulse of tracer into the bed so that dC/dr = 0. The values of Dl can be estimated by 

Wen and Yim [1971] reported a few results on axial dispersion coefficients (Dl) for the flow of two weakly shear-thinning polymer (PEO) solutions (n = 0.81 and 0.9) through a bed packed with glass spheres (d = 4.76 and 14.3 mm) of voidages 0.4 and 0.5. Over the range (7 Rei 800), then-results did not deviate substantially from the correlation developed by these authors previously for Newtonian fluids  

In the only reported study of radial mixing of non-Newtonian rubber solutions in packed beds [Hassell and Bondi, 1965], the quality of mixing was found to deteriorate rapidly with the increasing viscosity. 

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The original Rate Theory which describes dispersion in packed beds evolved over a number of years, probably starting with the work of Lapidus and Amundson [6] in 1952, extended by that of Glueckauf [7] and Tunitski [8] in 1954. The final form of the equation that described dispersion in packed beds as a function of the linear... 

They convert the initial value problem into a two-point boundary value problem in the axial direction. Applying the method of lines gives a set of ODEs that can be solved using the reverse shooting method developed in Section 9.5. See also Appendix 8.3. However, axial dispersion is usually negligible compared with radial dispersion in packed-bed reactors. Perhaps more to the point, uncertainties in the value for will usually overwhelm any possible contribution of D. ... 

The general question of whether or not plug flow can be attained is discussed in Volume 3, Section 1.7. (Tubular Reactors) and the special case of Plug-Flow (Fermenters) is considered in Chapter 5, Section 5.11.3. A more detailed consideration of dispersion in packed bed reactors and those effects which enhance and invalidate plug flow is given in Chapter 3, Section 3.6.1. 

Gunn, D. J. and PRYCE, C. Trans. Inst. Chem. Eng. 47 (1969) T341. Dispersion in packed beds. 

Fig. 8. Axial dispersion in packed beds, dispersed plug flow model (L13).

Fig. 14. Radial dispersion in packed beds, general dispersion model. Adapted from (F2).

Carberiy (C7) and Epstein (E6) discussed the magnitudes of the corrections necessary for dispersion in packed beds. It was found that for many practical cases of interest, the axial mixing effect was very small. 

The importance of dispersion and its influence on flow pattern and conversion in homogeneous reactors has already been studied in Chapter 2. The role of dispersion, both axial and radial, in packed bed reactors will now be considered. A general account of the nature of dispersion in packed beds, together with details of experimental results and their correlation, has already been given in Volume 2, Chapter 4. Those features which have a significant effect on the behaviour of packed bed reactors will now be summarised. The equation for the material balance in a reactor will then be obtained for the case where plug flow conditions are modified by the effects of axial dispersion. Following this, the effect of simultaneous axial and radial dispersion on the non-isothermal operation of a packed bed reactor will be discussed. 

The conditions presented above have been formulated for the case that the values of the Peclet numbers for heat and mass dispersion in a bed are indentical. However, recent experimental research on axial heat dispersion in packed beds has indicated that the values of the Peclet number for heat transfer may be different from those for mass transfer (48). Fortunately, the aforementioned conditions are still valid, however, the critical values of B and Pe as well as the bounds Dan,in and Da x are dependent on the ratio q = PeH/PeM. From the theoretical results may be inferred that for highly exothermic reactions multiple steady states may... 

Dispersion in Packed Beds. For the case of gas-solid catalytic reactions which take place in packed-bed reactors, the dispersion coefficient, can be esti-... 

I Ian, N, J, Bhakta, and R.G. Carbonell. 1985. Longitudinal and lateral dispersion in packed beds effect of column length and particle size distribution. AIChE J, 31 277—288. 

Rasmuson, A., and I. Neretnieks. 1980. Exact solution of a model for diffusion in particles and longitudinal dispersion in packed beds. AIChE J. 26 686-690. 

D. Vortmeyer, Axial Heat Dispersion in Packed Beds, Chem. Engng. Sci., (30) 999-1001,1975. 

Cao is the inlet molar density of reactant A at z = 0, a. interpeiiet is the interpellet diffusion coefficient of species A which accounts for axial dispersion in packed beds, the dimensionless rate of the 7 th reaction is... 

If there is only one chemical reaction on the internal catalytic surface, then vai = — 1 and subscript j is not required for all quantities that are specific to the yth chemical reaction. When the mass transfer Peclet number which accounts for interpellet axial dispersion in packed beds is large, residence-time distribution effects are insignificant and axial diffusion can be neglected in the plug-flow mass balance given by equation (22-11). Under these conditions, reactor performance can be predicted from a simplified one-dimensional model. The differential design equation is... 

Axial dispersion in packed beds, and Taylor dispersion of a tracer in a capillary tube, are described by the same form of the mass transfer equation. The Taylor dispersion problem, which was formulated in the early 1950s, corresponds to unsteady-state one-dimensional convection and two-dimensional diffusion of a tracer in a straight tube with circular cross section in the laminar flow regime. The microscopic form of the generalized mass transfer equation without chemical reaction is... 

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