Fluid velocity distribution in nitrifying trickling filters: mathematical model and NMR calibration

Abstract

Modeling trickling filter performance requires knowledge of the distribution of flow velocities within the packed column. A probability density function (PDF) is developed for the likelihood of finding a given flow (Reynolds number) over a point on the packing material surface. The model predicts an exponential relationship between the Reynolds number and the probability of finding that flow rate. Wetted area, minimum flow rate to wet the packing material, and maximum flow rate before flooding of the packing material are calculated by methods presented by other authors. The PDF is subject to the constraints that the sum of probabilities for all non-zero flow rates must equal the wetted fraction, the sum of all local flows must equal the total flow applied to the filter, and only Reynolds numbers between the minimum and maximum are possible. Miniature trickling filters (25.4 mm in diameter, with 6.4 mm spherical polystyrene packing) are used to verify the filter flow models. Six nitrifying biofilm-coated filters and eleven new (no biofilm) filters are imaged using nuclear magnetic resonance (NMR) to characterize the flow through the filter. NMR images are taken while a nutrient medium trickles over the columns at superficial flow rates of 75, 150, and 300 m/d. Addition of a bi-polar velocity-encoding gradient in the NMR sequence allows water velocity measurement. The occurrence of Reynolds numbers calculated from the images agreed with the model predictions within 1.4% for low Re (<30) and within 0.3% for the higher Reynolds numbers (>30).