A new correlation for the initial filter coefficient under unfavorable surface interactions

Abstract

In deep-bed filtration, if the surface interactions between particles and collectors (i.e., filter grains) are unfavorable, particle deposition will be retarded. The extent of the reduction in deposition may be expressed as the ratio of the actual filter coefficient to that if the unfavorable surface interactions are absent, or α, the collision efficiency. Attempts have been made to relate α with operating and systems variables, but none of the proposed correlations is complete to include all the relevant variables. In the present study, by applying the Buckingham-π theory, α is shown to be a function of 11 dimensionless parameters. Further, by conducting partial regression analysis to available experimental data, only 4 of the 11 dimensionless parameters were found to exert strong influence on α. A correlation between α and the 4 dimensionless parameters identified from the partial regression analysis was established. This correlation was found to agree with experiments well. However, in view of the relatively small data base, the correlation must be regarded as a preliminary one.