Prediction of Frictional Pressure Drop During Water Permeation Through Packed Beds of Granular Particulates

A methodology has been developed based on the Kozeny-Carman equation to predict frictional pressure drops during water permeation of packed columns containing essentially noncompressible, but highly irregular particles. The resulting model accurately predicts pressure drop as a function of liquid flow rate and resin particle size for this system. A total of five particle sieve cuts across the range -20 to +70 mesh were utilized for testing using deionized water as the mobile phase. The Rosin-Rammler equation was used to fit the raw particle size data (wet sieve analysis) for the as-received resin sample and generate a continuous cumulative distribution function based on weight percent passing through the sieve. Probability distribution functions were calculated from the cumulative distribution for each particle sieve cut tested. Nine particle diameter definitions (i.e., number mean, volume mean, etc.) were then selected from the distribution function for each sample to represent the average spherically-equivalent particle diameter as input to the Kozeny-Carman equation. Nonlinear least squares optimization of the normalized pressure drop residuals were performed by parameter estimation of particle shape factor and bed porosity for all samples simultaneously using a given average particle diameter definition. Good fits to the full experimental data set were obtained when utilizing the number mean and the number median diameters. However, the shape factor and porosity values of 0.88 and 0.40, respectively, obtained from fitting the data using the number mean diameter were more consistent with experimental observations