Accurately projecting the rate of contaminant recovery is important for evaluating remediation performance. No rational decisions can be made with respect to judging cleanup timeframes without this capability. Based on an analogy between charge transport in disordered solids and contaminant transport in heterogeneous porous media, we propose that the stretched exponential equation is a relatively simple analytical expression with a sound theoretical underpinning that can accurately project contaminant recovery rates from a limited dataset.
Initial work with data from the M-Area pump-and-treat system at the DOE Savannah River Site (SRS) demonstrates the power of the charge transport/contaminant transport analogy. The RWM-01 well has been in essentially continuous operation since December of 1982. Monthly tetrachloroethene (PCE) concentration data from the first five years of operation were used to develop two models for the PCE recovery: a standard exponential model and a stretched exponential model. The fits to the five year “calibration” period were reasonably comparable, with the standard exponential model appearing to provide a slightly better fit. The standard error of the residuals (SE) for the standard exponential model was 5.16 mg/L, while the SE for the stretched exponential model was 5.56 mg/L. The projected model results were then compared with monthly PCE concentrations through January 2006, a 19 year projection. The much greater accuracy of the stretched exponential projection rapidly becomes apparent. The standard exponential model quickly begins to under-predict recovered PCE concentrations, while the stretched exponential model matches the concentrations over the whole period. The SE for the standard exponential model for the whole dataset was 8.17 mg/L. The SE for the stretched exponential model, by comparison, was 5.09 mg/L. The fit of the projection of the stretched exponential model was actually better than the fit to the calibration dataset! Model assumptions and robustness will be presented and evaluated.