Using Probability Distribution Functions to Correlate Breakthrough Curves of Water and air Contaminants

Abstract

This paper reports the use of five probability cumulative distribution functions (normal, log-normal, logistic, Gompertz, and Weibull) to correlate published breakthrough data of water and air contaminants (ciprofloxacin, ammonium, hydrogen chloride, and hydrogen sulfide). Because the shape of the ciprofloxacin breakthrough curve is fairly symmetric, it is well correlated by all five functions (R2 > 0.99). They also provide a good representation of the overall shape of the ammonium breakthrough curve (R2 > 0.99). However, none can describe the leakage of ammonium during the initial period of column operation. The log-normal and Weibull functions give an excellent representation of the tailing HCl data while the normal, logistic, and Gompertz functions are quite poor. This difference in performance can be explained by the different characteristics of their inflection points. The log-normal and Weibull functions have a floating inflection point, which gives them flexibility in tracing the shape of the tailing data. The invariant inflection points of the normal, logistic, and Gompertz curves restrict their data fitting ability. Only the log-normal function can provide a reasonable fit to the H2S data with strong tailing. It is shown that the invariant inflection point of a probability function can be converted to a floating one. A version of the Gompertz function so modified provides a good quantitative correlation of the tailing data of H2S (R2 = 0.99).