Moment Method Applied to Solute Transport with Binary and Ternary Exchange

Abstract

AbstractWhen modeling transport of exchanging solutes in soils, it is sometimes conveniently assumed that the solutes interact linearly with the solid phase of the soil. In this study, an attempt was made to quantify the influence of nonlinear cation exchange on solute spreading with the moment method. Theoretical expressions for the first four moments were derived based on the equilibrium and physical nonequilibrium models of the advection‐dispersion equation (ADE). Displacement experiments were conducted in which either a NaCl pulse (binary exchange) or a pulse of KBr and NaBr (ternary exchange) was applied to a CaBr2‐saturated medium. Values for the transport parameters were determined with moment analysis and curve fitting. The observed breakthrough curves were somewhat better reproduced with parameters obtained from curve fitting than from the moment method. However, the curve‐fitting program produced some unrealistic parameter estimates for the nonequilibrium model. A disadvantage of the moment method was that the fourth‐order moment sometimes yielded unstable results for the nonequilibrium model. Parameters form the anion displacement were used to estimate the theoretical variance due to hydrodynamic dispersion and nonequilibrium spreading for the cation breakthrough curves. The difference between the variance of the observed cation breakthrough curve and these theoretical variances was used as an approximation of the variance due to nonlinear exchange. Particularly for the ternary exchange, the variance due to nonlinear exchange was often several times greater than predicted according to the transport model. The results enabled us to quantify errors in dispersion coefficient (D) values directly determined from cation‐displacement experiments.