Asymmetrical fixed-bed breakthrough curve modelling: Comparing simplistic, log-modified, fractal-like, and probability distribution function models

Abstract

Column adsorption studies frequently adopt classical breakthrough curve models such as semi-mechanistic Bohart-Adams and Thomas models. They are logistic functions which simulate symmetrically sigmoidal curves centrosymmetric at 50% breakthrough; consequently, they fail and estimate erroneous results when dealing with asymmetric breakthrough curves. This work analyses and compares the trend of how log-modified, fractal-like modified, and probability distribution function models simulate asymmetric breakthrough curves with varied extents of tailing. We generated the asymmetric breakthrough curves by varying the bed depth: 6 mm, 9 mm, and 12 mm on a glass microcolumn of 100 mm length and 5.5 mm inner diameter at a fixed flow rate of 1 mL/min using 10 mg/L bisphenol-A as adsorbate and polyaniline as adsorbent. The asymmetrical curves were a consequence of polyaniline’s low specific surface area of 6.96 m²/g, heterogeneous particle size distribution, slow intraparticle and surface diffusion. The log-Bohart-Adams and fractal-like Bohart-Adams models perfectly fit the curves regardless of symmetry although log-Bohart-Adams performed subpar with increased tailing. The fractal-like Bohart-Adams model accurately estimated the breakthrough times of 13 min, 26 min, and 90 min for the 6 mm, 9 mm, and 12 mm bed depths with a critical bed depth of 5.65 mm. The normal and Gompertz probability distribution functions were unable to adapt to asymmetry of the curves owing to their fixed inflection points at c/cc = 0.5 and 0.37 respectively. Although the Weibull, log-normal, and log-Gompertz functions have floating inflection points, only log-Gompertz function had a satisfactory fit (Radj2>0.98) regardless of symmetry.