Axial dispersion of mass in flow through fixed beds

Abstract

The axial dispersion of water flowing through fixed beds was determined by measuring and recording the dispersion of a pulse input of dye at one or two points downstream of the injection site. Dispersion coefficients at various flow rates were obtained in systems of 1/2-, 1-, 3-, and 5-mm. spheres and 2-and 6-mm. rings each packed in a 1.5-in. I.D. column. Data were also obtained with 3-mm. spheres in a 1-in. I.D. column. Bed length was varied from 6 to 36 in. Void fractions of from 0.365 to 0.645 were represented by the systems studied. One gas system was studied at Reynolds numbers below unity.The results of the water study indicate that the dispersion coefficient increases linearly with the Reynolds number in the range of Re = 0.5 to 100. Beyond that point the Reynolds number exponent decreases through 0.85 to a value of about 0.25 at a characteristic breakpoint in the region of Re = 350 to 400. Pressure-drop data secured for the systems studied clearly indicate that the cited breakpoint in dispersion behavior is identical with the wellknown region of flow transition as characterized by the friction-factor-Reynolds-number relationship within a given system.The dispersion values for the 5-and 6-mm. particles, while obeying this Reynoldsnumber functionality, are of lower magnitude.A theory based upon bed-vdid cell-mixing efficiency is developed, and this efficiency is shown to be directly proportional to the Peclet number, which at the condition of perfect void-cell mixing should attain a value of about 2.Anomalous behavior was noted in two respects: (1) the pulse amplitude change between two stations is greater than that predicted by either a u s i o n or cell-mixing theory, lending strong support to a bed-capacitance effect, and (2) short-bed studies revealed unusually high dispersion coefficients, reflecting short-circuiting, that is, poor cell-mixing efficiencies in these shallow beds, presumably owing to entrance effects, yet independent of the mode of pulse injection.The dispersion of a pulse of air injected into a stream of helium flowing through a gas chromatographic column was briefly investigated. At Re < 1, E was found to be about equal to the calculated molecular difIusivity of this gas system.I n view of the key position occupied by fixed-bed processes in the chemical and allied industries, it follows that much attention should be focused on the fundamental aspects of heat, mass, and momentum transfer in these systems. Such studies are particularly important where heat and/or mass transfer occur simultaneously with one or more chemical processes. Ion exchange and catalyst regeneration constitute unsteady state examples, and any heterogeneously catalyzed reaction may be cited as a steady state case, in which the chemical kinetic picture is usually rendered more complicated by the transfer as well as the distribution of heat and mass.With regard to mass transport there are aspects to be considered other than transfer or diffusion through a f i l m to the surface of another contacting phase. There is t...

Axial dispersion of liquid in concurrent gas-liquid downflow in packed beds.

“…£ denotes the void fraction of the dry bed, h the volume fraction of the total liquid volume per unit void volume, and <f> the fraction of the dynamic liquid volume in the total liquid volume. The boundary conditions which lead to the solution for the impulse response are as follows cd=09 cs=0 at t=O (5) cd=d(t), cs=0 at z=O (6) Q=0, cs=0 dX z=oo (7) Eqs. (3) to (7) Fig.…”

Axial Dispersion in Liquid Flow Through Packed Beds

“…1, 3,[6][7][8][9]13,15,19,21,24,26 j_n Reynol s num er. There j_s, however, no consensuc~ concerning the absolute magn:i_tud.e of the Peclet number :i.n this J F J8 1 2.,.…”

FLUID-SOLID HEAT TRANSFER STUDY. Final Report, May 1, 1959-September 30, 1964

“…No experimental data are available for superficial Reynolds numbers less than 10, which would be of interest for 5 fluidized systems. However, theoretical work has been reported by Carberry and Bretton (18). A simple theoretical analysis for the case when the ,Reynolds number is zero (or a single spherical particle in infinite fluid at rest) give a Nusselt number of 2.0.…”