Improved fixed bed models for correlating asymmetric adsorption breakthrough curves

Breakthrough curves of water contaminants are usually analyzed using simple fixed bed models such as the Bohart-Adams, Thomas, and Yoon-Nelson equations, which are by design symmetric. Because breakthrough data often follow an asymmetric pattern, the use of models that do not account for asymmetry could lead to poor fits, consequently resulting in erroneous estimates of breakthrough and exhaustion times. To address this issue, the Bohart-Adams, Thomas, and Yoon-Nelson models were modified by a logarithmic transformation to enhance their data fitting ability. The three modified models were found capable of providing robust fits to seven separate sets of previously reported asymmetric breakthrough data of water contaminants (fluoride, methylene blue, salicylic acid, lead, mercury, nickel, and arsenic), with reported residual root mean square error (RRMSE) values ranging from 0.019 to 0.046. In consequence, the new models were found capable of providing reliable estimates of breakthrough and exhaustion times corresponding to any predetermined concentration level. By contrast, the three original models were found to perform poorly, reporting inferior RRMSE values ranging from 0.038 to 0.086 for data fits and providing grossly inaccurate estimates of breakthrough and exhaustion times. The new models contain only parameters that appear in the original models, and are highly flexible, being able to assume virtually all monotonically increasing sigmoid shapes. They represent a far more accurate alternative to the original models.