Impact of external stresses on steady state plume lengths

Sandhya Birla1, Falk Händel2, Prabhas Kumar Yadav3, Rudolf Liedl2, Bhagu Ram Chahar1
1 IIT Delhi, Department of Civil Engineering
2 Technische Universität Dresden, Institut für Grundwasserwirtschaft
3 Sharda University, Department of Civil Engineering

P 13.2 in Reactive transport modeling

Knowing the extent of contamination is the most important aspect in the field of contamination management. A number of studies have been carried out in the past to determine the maximum plume length (Lmax); the emphasis is on Lmax because it represents the worst case scenario, which is very relevant in the assessment of contamination cases. Frequently, this assessment is based on analytical models, which, however, are inappropriate in quantifying the impact of external stresses, like groundwater recharge, on plume extension. Reactive numerical transport models can overcome this difficulty in principle but require advanced knowledge in adjusting spatial and temporal discretization to the various conservative and non-conservative processes involved. In our contribution we propose to reduce this discrepancy by combining a purely conservative modelling approach with a mathematical transformation suggested, for instance, by Liedl et al. (2011). The presentation is intended to illustrate this combined method and to show some impacts of external stresses on maximum plume length. 

One of the two key elements of our approach is a standard numerical technique (as coded e.g. in MT3D) to simulate advective-dispersive solute transport in groundwater. The second key element is a straightforward transformation provided in Liedl et al. (2011) and Yadav et al. (2013) that allows to replace the reactive transport problem by a conservative one and to recalculate concentrations of reactive compounds after the conservative transport problem has been solved numerically.

As a first step, this method was validated using analytical results. After that, the numerical model was used to simulate scenarios with different recharge rates including the influence of spatial and temporal variations. The results clearly support the phenomenon of downward diversion and decreased longitudinal extension of plumes due to these external stresses. The evaluation also suggests that the percentage reduction in plume lengths with respect to analytical results as obtained from Liedl et al. (2011) is directly proportional to aquifer thickness and recharge rate. For this purpose, sensitivity analyses as shown in the figure were carried out and evaluated.

Additionally, it was found that spatial and temporal variations of recharge rates do not have a significant effect on plume lengths as opposed to the influence of averaged recharge rate. An empirical equation as provided below, was also proposed in line with Maier and Grathwohl (2006):


This result can be satisfactorily used to calculate plume lengths depending on the effect of average recharge rates valid in Germany. For the future it is planned to deal with more complex scenarios, e.g. non-homogeneous aquifers, partially penetrating contamination sources and other external stresses like pumping activities. 




LIEDL, R., YADAV, P. K., & DIETRICH, P. (2011). Length of 3-d mixing-controlled plumes for a fully penetrating contaminant source with finite width. Water Resour. Res., 41 (12), w12501. 

MAIER, U., & GRATHWOHL, P. (2006). Numerical experiments and field results on the size of steady state plumes. J. Contam. Hydrol., 85(1-2), 33–52.

YADAV, P. K., LIEDL, R., & DIETRICH, P. (2013). Influence of source thickness on steady-state plume length. Environ. Earth Sci., 1–6.