Bulk density, packed beds

In scale-up from laboratory quantities (up to 10 kg) to production batches (300 kg and up), bed depth increases significantly. The most notable consequence is an increase in finished product bulk density, typically in the range of 15% to 20%. In some instances, this is a disadvantage (if product is packed by volume and a low density is desired). However, granule strength is usually greater as a result of the decreased interstitial void space. 

Void Fraction in the packed bed was calculated as 1 — (bulk density)/ (particle density). 

A non-linear mathematical model, which is a set of ordinary differential equations, for the process in the SPBER was developed.19 The model accounts for the heterogeneous electrochemical reaction and homogeneous reaction in the bulk solution. The lateral distributions of potential, current density and concentration in the reactor were studied. The potential distribution in the lateral dimension, x, of the packed bed was described by a one dimensional Poisson equation as ... 

Bulk density, or packing density, includes all pores and voids (interparticle spaces) in its calculation. It is determined by filling a graduated cylinder, with or without tapping. It follows that the value obtained is dependent upon the form of the catalyst (powder, tablets, extrudates) because of the different contribution of interparticle void space to the pore volume. Tap density is the apparent density of a bed of particles in a container of stated dimensions when a given amount of powder is vibrated or tapped under controlled conditions. The use of the term bulk density should be... 

Based on the definition of density, two new terms are defined. Porosity is defined as the proportion of a powder bed or compact that is occupied by pores and is a measure of the packing efficiency of a powder and relative density is the ratio of the measured bulk density and the true density ... 

The catalyst consists of 0.32 cm diameter spheres that have a bulk density of 0.84 g cm and pack into a fixed bed with a void fraction of 0.4. The mass velocity of the gas through each tube will be 0.075 g cm s , which corresponds to an overall heat transfer coefficient between the tube wall and the reacting fluid of about 10 cal cm s K . ... 

For a packed-bed reactor, we can write Equation (8-44) in terras of catalyst weight by simply dividing by the bulk catalyst density... 

Note. We have converted the specific reaction rates to a per unit volume basis by multiplying the k on a per mass of catalyst basis by the bulk density of the packed bed. 

We will now caleulate the fluidized CSTR catalyst weight necessary to achieve the same conversion as in the packed-bed reactor at the same operating conditions. The bulk density in the fluidized reactor is 0.4 g/cm. The design equation is... 

Commercial fluid cracking catalysts are predominantly particles with diameters ranging from 20 to 100 microns and densities of the order of 1.0 to 1.6 g./cc. (based on geometric volume of particles including pores). Gas velocities of 1 to 2.5 ft./second are ordinarily used in the reaction vessels of fluid cracking units. Within this range, the bulk density of the dense-phase fluidized bed is typically 40 to 60% of the bulk density of the packed static bed. 

Fluidized This is an expanded condition in which the solids particles are supported by drag forces caused by the gas phase passing through the interstices among the particles at some critical velocity. The superficial gas velocity upward is less than the terminal setting velocity of the solids particles the gas velocity is not sufficient to entrain and convey continuously all the solids. Specifically, the sohds phase and the gas phase are intermixed and together behave as a boU-ingjluid (Fig. 12-28). The gas forms the continuous phase, but the bulk density is not much lower than a continuous packed bed of solids. 

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