Peclet numbers internal

GP 9] [R 16[ The extent of external transport limits was made in an approximate manner as for the internal transport limits (see above), as literature data on heat and mass transfer coefficients at low Peclet numbers are lacking [78]. Using a Pick s law analysis, negligible concentration differences from the bulk to the catalyst sur-... 

Note that our program runaxialdispDa is specialized to run for just two sets of values for Pen and PeM as 4 and 8 or as 8 and 4, respectively. We have not attempted to make runaxialdispDa truly global by internal parameterizations for other Peclet data. It is obvious, however, how our readers can modify the program with a bit of trial and error to work for other sets of Peclet numbers PeH and PeM- The main task for this consists of figuring out - by trial and error - how to set up the various integration subintervals differently and to experiment with the direction of integration and the step size used for different Damkohler numbers. 

Figure 34 compares the residence time distribution in the influence zone of a single set of ring internals at location 3, which is 0.55 m downstream of tracer injection, with and without the ring set. The decrease of solids backmixing is shown by an increase of the Peclet number from 1.06 to 2.46, and from 1.97 to 3.61, when the ring set is used, for gas velocities of 1.75 and 2.62 m/s, respectively. 

Axial and radial Peclet numbers as a function of Reynolds number for packed-beds. [Adapted from R, H. Wilhelm, Pure App. Chem., 5 (1962) 403, with permission of the International Union of Pure and Applied Chemistry.]... 

Particle-based Peclet number, dj,v/Dt Amount of component i injected with feed, mol Separation factor [Eqs. (16-30), (16-32)] particle radial coordinate, m Column internal radius, m... 

Polyanin, A. D., Qualitative features of internal problems of transient convective mass and heat exchange at large Peclet numbers, Theor. Found. Chem. Eng., Vol. 18, No. 3, pp. 171-181, 1984. 

If potential flow and constant surface temperature are assumed, an equation analogous to Eq. (18) is obtained for the internal Nusselt number. Note, however, that the reference velocity in the internal Peclet number is the drop velocity. Similar results will be obtained from the penetration theory, according to which the film is assumed infinite with respect to the depth of heat penetration during the short contact time of a fluid element sliding over the interface. Licht and Pansing (L13) report West s equation, based on the transient film concept, for the case of mass transfer through the combined film resistance. In terms of the overall heat-transfer resistance, l/U (= l//jj + I/he) and if the contact time is that required for the drop to traverse a distance equal to its diameter. West s equations yield... 

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... 

The subscript i refers to gas-phase reactants and products the superscript c refers to gas-phase cell threads. The accumulation term in (3.43) is equalized to the sum of the convective and reactive fluxes. The reactive term is computed only when a control volume has a face adjacent to the catalytic geometrical surface Fext), while the other terms are considered for internal faces Pint). Face variables, denoted by the subscript f, are computed with a first-order upwind scheme. If Peclet number, defined as shown in (3.44), is significantly greater than 1 (as happens for the LNT case study described later), it is possible to neglect the diffusion term vL... 

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