A 3D hybrid model for estimation of steady-state plume lengths with the influence of recharge

Research output: Contribution to journalResearch articleContributedpeer-review


  • Sandhya Birla - , Indian Institute of Technology Delhi (IITD) (Author)
  • Jyotiranjan Barik - , Indian Institute of Technology Delhi (IITD) (Author)
  • P. K. Yadav - , Institute for Groundwater Management (Author)
  • Rudolf Liedl - , Chair of Groundwater Systems, Chair of Groundwater Management (Author)
  • Charles J. Werth - , University of Texas at Austin (Author)
  • B. R. Chahar - , Indian Institute of Technology Delhi (IITD) (Author)


Abstract: The characterization of plume length is a critical aspect in the field of groundwater contamination management. Frequently, this assessment is based on analytical models, which do not have components to account for external stresses like groundwater recharge. Although reactive numerical transport models can overcome this challenge in principle, they require a large number of parameters and are computationally expensive. Several analytical solutions are available to assess steady-state plume length (Lmax), a key variable for risk assessment. However, these solutions work under simplifying assumptions, often substantially deviating from observed field plume lengths. This research extends the applicability of the Liedl et al. (2011) model by introducing an empirical function in combination with the analytical model. This hybrid approach combines the flexibility found in a numerical model with the ease of solution characteristic of an analytical model and may prove useful in estimating Lmax for many of potentially contaminated sites worldwide. In particular, we assess our newly proposed hybrid model's ability to characterize 3D plume lengths, including the impact of groundwater recharge. The empirical function considers variable recharge rates, contaminant source areas, and contaminant perimeter lengths. The impact of the aspect ratio of a rectangular source geometry, i.e., shape factor (M/W) and area to perimeter (A/P) ratio, on Lmax is also investigated. The hybrid empirical–analytical solution is validated with a selection of limited field contamination site data. The hybrid model results (Lmax,hyb) provide a significant improvement in the estimation of plume lengths compared to the analytical model based on the validation results.


Original languageEnglish
Article number46
JournalEnvironmental Earth Sciences
Issue number1
Publication statusPublished - Jan 2023

External IDs

Scopus 85145652083
Mendeley fc179d5e-4f5f-3b63-860b-f0898d0af27d



  • 3D hybrid model, Analytical–empirical model, Contaminant transport, Steady-state plume length

Library keywords