A comparative numerical analysis of three approaches for the breakthrough curve modeling has been performed using the experimental data of packed-bed fluoride adsorption on a novel aluminum-doped bone char using micro-columns. The performance of traditional Thomas and Yan breakthrough equations, a mass transfer model for a mobile fluid flowing through a porous media, and an artificial neural network with the optimal brain surgeon approach have been studied and discussed in the data fitting of asymmetric fluoride breakthrough curves. Results of this study highlighted the relative merits of tested breakthrough curve models for the non-linear adsorption data analysis involved in water defluoridation using a new adsorbent. In particular, the application of artificial neural networks is reliable for fitting highly non-linear adsorption patterns of priority water pollutants.