A 3-D Analytical Model for Aquifers Contaminated with Organic Contaminants

A 3-D model is developed to estimate plume lengths for hydrocarbon or similar contaminant contaminated aquifers based on the previous  2-D model suggested by Liedl et al.,  (2005).  The conceptual model has finite source dimensions, vertical (M) and horizontal (W), and all the assumptions in its development are based on the previous 2-D model, which assumes infinite lateral source extension. The developed model is capable of deriving the maximum plume length, i.e., where the source concentration equals zero in the plume’s profile, and any plume length that is defined by any pre-set concentration.

Results obtained from the model, especially at higher vertical transverse dispersivities (α_TV>10 mm), were able to estimate plume lengths typically observed in hydrocarbon-contaminated sites. This was also true at larger source thickness where 2-D models tend to fail. The results suggested that the divergence between the 2-D and the 3-D model was linearly related to the finite W, and possibly the horizontal transverse dispersivity (α_TH), defined in the 3-D model and which is absent in the 2-D model.

Also, the largest plume lengths from the 3-D models were obtained for the source that is approximately square in shape. This was true for any combination of dispersivities, α_TV and α_TH  relevant in field conditions. Results also suggested that the α_Tv/α_Th ratio is a critical ratio in defining the size of the plume. From the sensitivity analysis, the following ranking for influence of 3-D model parameters on plume lengths was established: M> α_TV >W>α_TH. M was also ranked as the most influential parameter on the plume length  by LIEDL et. al., (2005).

Further analyses have  to be performed to confirm the validity of the developed 3-D model.

Literature

Liedl, R., Valocchi, A. J., Dietrich, P., & Grathwohl, P. (2005): Finiteness of steady state plumes, Water Resour, Res., doi: 10.1029/2005WR004000.