Comparison of methods for predicting ternary exchange from binary isotherms

Methods for predicting ternary and higher order cation exchange from binary isotherms are required because it is impossible to measure isotherms for all possible combinations when there are three or more competing ions. One important use for ternary and higher order exchange predictions is for modeling cation transport in multicomponent systems. We review several existing methods for predicting ternary exchange from binary isotherm data and introduce a new method based on the Rothmund-Kornfeld approach. Existing methods include the Valocchi and Gapon equations as well as the Wilson and subregular models used in conjunction with the Vanselow-Argersinger exchange formulation. The methods were used with three data sets: Na-K-Ca exchange at 50 and 200 mol(c) m(-3) in Brucedale soil, and NH4-Ba-La exchange at 100 mol(c) m(-3) in montmorillonite. The resulting predictions were compared with measured ternary exchange data. It was found that all methods that account for the variation of the exchange coefficient and/or the exchanger phase cation activity coefficients performed similarly well. Their performance was much better than methods that assume that conditional exchange coefficients are constant, such as the Valocchi and Gapon methods. For the data examined, the Gaines-Thomas formulation of the Rothmund-Kornfeld equation consistently gave the best predictions for the least computational effort.