Bed dynamics

The linear driving force (LDF) approximation is obtained when the driving force is expressed as a concentration difference. It was originally developed to describe packed-bed dynamics under linear eqm-librium conditions [Glueckauf, Trans. Far Soc., 51, 1540 (1955)]. This form is exact for a nonlinear isotherm only when external mass transfer is controlling. However, it can also be used for nonlinear sys-... 

Consequently the catalytic activity for the CF3CH2CI fluorination reaction was measured in the presence of an excess of HF in a fixed bed dynamic reactor (fig. 2). 

Newby, R. A., and Keaims, D. L., Test of the Scaling Relationships for Fluid-bed Dynamics, Fluidization V, (K. Ostergaard and A. Sorensen, eds.), Engineering Foundation, New York (1986)... 

A. Heim, T. Gluba, A. Obraniak, Bed dynamics during granulation in rotating drums, In Proceedings of the 7th International Symposium on Agglomeration, Albi, 2001. 

Among the variety of methods which have been proposed for simulation of packed bed dynamics three techniques have been used with success (1) Crank-Nicholson technique [10], (2) transformation to integral equation [11], (3) orthogonal collocation on finite elements [12]. In the following computation, we have used the Crank-Nicholson method with the nonequidistant space steps in the Eigenberger and Butt version [10]. 

To design and develop PSA process, detailed analysis of the fixed-bed dynamics must be preceded, because the key step to developing an optimum PSA process lies in the design and operation of the adsorption step. Also, on the condition that the theoretical models of the adsorption breakthrough can predict its experimental results well, it can be used to investigate the breakthrough dynamics in a bed and predict PSA performance without any specific experiment. 

The oxidation of SO2 over the vanadium catalyst takes place in the liquid melt phase of active species (mainly V2O5 and K2SO4). This observation, described extensively in the literature (e g [6, 7, 8]) seems to have been proved beyond any doubt, and will be discussed here only with regard to consequences it may have in the description of the bed dynamics. 

For the most part we have labored over the analysis of steady-state problems, although there have been some important side trips into the unsteady state. Principal among these were the analysis of CSTR startup, visits to fixed-bed and CSTR dynamics arising from catalyst deactivation, and some discussion on adsorption variations. The purpose of this chapter is to pursue some of these topics in more detail the range of interests here is rather broad, but all can be linked through a common concern with fixed-bed dynamics. 

Figure 2. The error versus the CPU time in seconds for different methods for System C and D. The computations for System D are initiated from two different starting values an empty bed and a saturated bed — dynamic simulation, O Broyden s method, + Newton-Picard method, Newton s method.

As far as industrial adsorption processes are concerned it always should be taken into account that isotherms which are favorable for adsorption normally are unfavorable for desorption processes. Also, for column performance, for example packed bed dynamics, the velocity of the mass break through front is inverse proportional to the steepness of the adsorption isotherm. Hence it can be decisive to have accurate equilibria data at hand to get reasonably accurate values of the respective differential quotients [7.2, 7.4, 7.40]. For mixture adsorption this argument becomes even more important. S. D. G. 

Further verification of the scaling laws are needed in terms of radial solids distribution and solids diffusivity. These have not been compared between hot and cold beds. In addition, work needs to be carried out to see the lower limit of solids diameter for which the present set of scaling parameters holds. At some point, surface forces will have an important influence on bed dynamics. This will require additional scaling parameters that include these effects. The range of validity of the present set of scaling parameters for fluidized beds for FCC operations and for cyclone separators remains uncertain at the present time. 

Newby RA, Keaims DL. Test of the scaling relationships for fluid-bed dynamics. In Ostergaard K, Sorensen A, eds. Fluidization V. New York Engineering Foundation, 1986. 

Schouten JC, Zijerveld RC, van den Bleek CM. Scale-up of bottom-bed dynamics and axial solids-distribution in circulating fluidized beds of Geldart-B particles. Chem Eng Sci 54 2103-2112, 1999. 

Solsvik and Jakobsen [140] performed a set of one-dimensional two-fluid model simulations in order to elucidate whether such simple models can be suitable for further simulations of two interconnected fluidized bed reactor units with a dynamic solid flux transferred between these reactor units which collectively is denoting a circulating fluidized bed. Dynamic solid circulation between two fluidized bed units that operate at different conditions (e.g., temperatures and feed compositions) is an inherent requirement for the novel SE-SMR technology operated in fluidized bed reactors. A less computational demanding one-dimensional model to study the performance of interconnected reactor units will be an important contribution to the progress of the commercialization of circulating fluidized bed reactors intended for the SE-SMR technology. 

Figure 5.6 Packed bed dynamics (a) breakthrough curve (single transition) and (b) mass transfer zone inside the bed (redrawn from Keller et al. 1987, p. 672).

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