An overall isotherm for activated carbon adsorption of dissolved natural organic matter in water

Design and analysis of activated carbon processes in water treatment often requires the adsorption isotherm for dissolved natural organic matter (NOM). Of the isotherm models available, the Summers and Roberts (SR) equation, capable of describing the adsorbent dose effect with the fewest parameters, has been successfully used to normalize NOM isotherm data. In this study, we show that the adsorbent dose in the SR equation can be eliminated as an intermediate variable and the initial concentration effect on NOM adsorption is then described explicitly. Comparing with the original SR equation, the derived isotherm equation is in a form more amenable to analysis. To ensure that the prediction is physically attainable, we introduced the limiting adsorption capacity by taking the adsorbent pore volume and size exclusion into consideration. Subsequently, we develop a simple relationship that can be used to determine the minimum adsorbent usage required for any desirable level of treatment. By comparing with extensive isotherm data previously published by Li et al. [2003a. Polydisperse adsorbability composition of several natural and synthetic organic matrices. J. Colloid Interface Sci. 265(2), 265–275], we demonstrated that the isotherm equation derived herein yields predictions that agree with the much more complicated fictive component-ideal adsorbed solution theory (IAST)-based model for NOM from different sources and over a range of initial concentrations.