Solute transport under non-linear sorption and decay

Contaminant transport in aquifers is usually represented by a solution to t he advective-dispersive differential equation. When the contaminant is subj ect to non-linear degradation or decay, or it is characterized by a chemica l constituent that follows a non-linear sorption isotherm, the resulting di fferential equation is non-linear. Using the method of decomposition, serie s solutions were obtained for the non-linear equation. The series were used to derive and test "simulant" solutions that arise using the concept of do uble decomposition. Simulant solutions are closed-form analytic expressions that approximate part of the series. These expressions are simple, stable, and flexible. They permit an accurate forecasting of contaminant propagati on under non-linearity in laboratory or field investigations at early or pr olonged times after the spill. In this article, the practical scenario of a n instantaneous spill, and that of a constant concentration boundary condit ion, is studied for situations of non-linear decay, non-linear Freundlich i sotherm, and non-linear Langmuir isotherm. The solutions are verified with limited well-known analytical solutions of the linear reactive and non-reac tive equations with excellent agreement, and with limited finite difference solutions. Plumes undergoing non-linear decay experience a profile re-scaling with res pect to that of linear decay, the degree of which is controlled by the magn itude of the non-linear parameter b. The direction of the scaling (scaling up or scaling down with respect to the linear decay plume) is controlled by the magnitude of C (whether greater or less than 1) in relation to the mag nitude of b (whether greater or less-than 1). When C > 1, values of b >1 pr oduce plumes that experience less decay (i.e., are scaled up) than that of the linear decay, whereas values of b < 1 produce non-linear plumes that ex perience more decay (i.e., are scaled down) than that of the linear decay. The opposite effect is observed when concentrations are less than 1. In oth er words, when C >1, values of b <1 produce non-linear plumes that experien ce more decay (i.e., are scaled down) than that of the linear decay, wherea s values of b <1, produce non-linear plumes that experience less decay (i.e ., are scaled up) than that of the linear decay. A plume undergoing non-linear sorption according to a Freundlich isotherm r etards the processes of advection and dispersion with respect to a plume wi th no sorption. Similar to the case of non-linear decay, whether this retar dation is more or less pronounced than that of the linear sorption plume de pends on whether the values of b and C are greater or less than 1. The solu tion presented here for the advective dispersive equation subject to a Freu ndlich sorption isotherm is restricted to concentration greater than 1. Whe n C > 1 and b <1, the decrease in mobility in the non-linear plume is not a s pronounced as that of a plume modeled by a linear isotherm. Plume shape m ay be quite sensitive to the values of the non-linear parameters. Plumes wi th parameter values b < 1 (and C > 1) exhibit the well-known lack of symmet ry with respect to their center of mass, sharp fronts, and the tailing effe cts observed at hazardous waste sites. As the magnitude of the non-linear p arameter increases, the non-linear plume approaches the linear one. This pa rtial non-linear "retardation" can now be observed quantitatively with the models presented herein. The models developed also simulate the case of b > 1 (i.e., "unfavorable" sorption), which produce a plume even more retarded than the linear. The shape of a contaminant plume following a non-linear La ngmuir isotherm is very sensitive to the magnitude of the non-linear parame ter cr. Approximate solutions for mild non-linearity are presented. (C) 200 1 Elsevier Science Ltd. All rights reserved.