Randomly packed beds of equal spheres exhibit damped oscillatory voidage variation in the near wall region. Models reported in literature were found to be lacking in their ability to relate this variation to average bed porosity. The changing mean of the voidage oscillations and deviations from sinusoidal behavior were not described well either. Experimental data and a new radial bed porosity model are presented. Improved radial bed voidage and average bed voidage predictions were demonstrated. It has further been shown that multiple stable packing configurations exist within the same packing mode, which complicates modeling at a small column to particle diameter ratio.

Voidage variation in packed beds at small column to particle diameter ratio

Considerable evidence indicates that dissolved transition metal ions (TMI) are capable of catalyzing oxidations in atmospheric water droplets, at least in certain circumstances. Wide variations in the importance of TMI chemistry are expected in these systems because concentrations of transition metals in water droplets range over at least 4 orders of magnitude. In the present work we perform an extensive series of model calculations for TMI chemistry in raindrops. The specific TMI discussed are iron, manganese, and copper. The present treatment is restricted to homogeneous processes, that is, those involving dissolved molecules and ions. Results are presented for studies at pH 3 and pH 4, for both daytime and nighttime conditions. Among the results are the following: (1) At pH 3 and pH 4, Fe(III) is present largely as photosensitive hydroxide complexes. Our model results indicate that under atmospheric conditions the photolysis of these complexes is the primary daytime source of reactive free radicals within the droplets, even at quite low TMI concentrations. (2) TMI complex photolysis is not, of course, operative at night. At those times the presence of TMI continues to control the concentration of free radicals in raindrops through “Fenton type” reactions with hydrogen peroxide, for example, Fe(II) + H2O2 → Fe(III) + OH + OH−. (3) The oxidation of S(IV) to S(VI) by H2O2 is the most important daytime sulfite oxidation process in raindrops, but S(IV) oxidation catalyzed by Mn(II) can be significant under certain conditions, particularly at night or in the winter months. (4) Solution nitrogen chemistry is relatively unaffected by TMI. Its most important daytime chemical process is the (rather inefficient) photodissociation of the nitrate ion, a process which generates ozone (and hence HOx radicals). (5) Organic chemistry in atmospheric water droplets is very sensitive to the presence of hydroxyl radicals. Since OH· production is strongly influenced by catalysis involving iron complexes, the presence of soluble iron is a major stimulus for organic chemical processes (such as the conversion of alkyl aldehydes to carboxylic acids). (6) For cases where S(IV) concentrations exceed those of H2O2 the S(IV) effectively “titrates out” the H2O2. If the H2O2 concentration dominates, however, residual H2O2 remains to initiate a variety of solution oxidation chains, particularly those producing organic acids. The presence of H2O2 in the gas phase thus implies acid production in the aqueous phase, the form of the acid depending upon the particular oxidizable species available. (7) The chemical reactions and rate constants used in the calculations are relatively well determined, but our results are quite sensitive to the assumed concentrations of TMI and other species. Increased attention to measurement of species concentrations in fog, clouds, and rain is therefore indicated.

Kinetic model studies of atmospheric droplet chemistry: 2. Homogeneous transition metal chemistry in raindrops

Radial Void Fraction Distributions in Randomly Packed Fixed Beds of Uniformly Sized Spheres in Cylindrical Containers

The packing of spheres in a cylindrical container: the thickness effect

Numerically packing spheres in cylinders

Structural characteristics of packed beds of low aspect ratio

Voidage profile in packed beds by multi-channel model: effects of curvature of the channels

Prediction of location of particles in the wall region of a randomly packed bed of spheres

On the steady state performance of cocurrent bubble column slurry reactors

A rate equation is developed for the liquid phase hydrogenation of aniline over cylindrical catalyst pellets of 30% nickel deposited on clay in a trickle bed reactor. The equation takes into account external and internal diffusional limitations, and describes the experimental data adequately. The hydrogenation reaction is first order with respect to hydrogen and zero order with respect to aniline. Effectiveness factors are in the range 0.003-0.03. Apparent activation energy of the reaction is 12.7 kcal/mol and true activation energy is 39.6 kcal/mol.

Venneti M.H. Govindarao

Papers

Structural characteristics of packed beds of low aspect ratio

Voidage profile in packed beds by multi-channel model: effects of curvature of the channels

Prediction of location of particles in the wall region of a randomly packed bed of spheres

On the steady state performance of cocurrent bubble column slurry reactors

Liquid phase hydrogenation of aniline in a trickle bed reactor