Axial dispersion of mass in flow through fixed beds

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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 well‐known 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 Reynolds‐number functionality, are of lower magnitude.A theory based upon bed‐v⊙id 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 diffusion 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 diffusivity of this gas system.