Improved fixed bed models for correlating asymmetric adsorption breakthrough curves

Abstract

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.

Metal–Organic Framework Aerogel for Full pH Range Operation and Trace Adsorption of Arsenic in Water

“…The Thomas model describes the adsorption capacity of the flowing liquid adsorbate onto the adsorbent in the fixed-bed column. − The curve-fitting equation is given below where C is the effluent concentration at time t , C 0 is the feed concentration in ppm, k Th is the Thomas rate coefficient, q e is the amount of As adsorbed onto the adsorbent in mg g –1 , x is the adsorbent mass, and Q is the volumetric flow rate.…”

A Modified Belter Model for Correlating Asymmetric Breakthrough Curves of Water Pollutants

“…A logarithmic transformation method (Apiratikul and Chu, 2021) is used to modify the Belter model. The main idea is to convert the parameter t in the Belter model to ln(t).…”

“…Restricted by their functional form, the three models are confined to describing symmetric breakthrough curves. Some attempts have been made to improve their ability to represent asymmetric breakthrough curves, as discussed by Apiratikul and Chu (2021). The model of Belter et al, by comparison, has The two-parameter model of Belter et al was first used by Brady et al (1999) to describe fixed bed adsorption of copper ions.…”

Fixed bed adsorption of water and air contaminants: analysis of breakthrough curves using probability distribution functions

“…From a practical perspective, this is a serious limitation because a poorly fitted model is likely to predict grossly inaccurate estimates of breakthrough and exhaustion times. Limited efforts have been made to enhance the data fitting abilities of the three models, as summarized by Apiratikul and Chu (2021).…”