Inverse Green element simulations of instantaneous pollutant injections into a 2-D aquifer
DOI:
https://doi.org/10.13052/17797179.2018.1469834Keywords:
The Green element method, inverse simulations, point & distributed instantaneous pollution injections, Tikhonov regularisationAbstract
When pollution spills occur, they impact on the quality of water in underlying aquifers. Such spills can be modelled as instantaneous pollution sources, and estimating their strengths from the concentration plumes they produce is an inverse problem which is addressed in this paper by the Green element method (GEM). Estimating the strengths of such spills, making use of the concentration data at various locations and times, is an inverse problem whose solution is often associated with non-uniqueness, non-existence and instability. Here the GEM is used to predict the strengths of pollution spills from measured concentration data at internal observation points. The performance of the methodology is illustrated using two numerical examples in which the contaminant plumes are from multiple point and distributed pollution sources. Single and multiple episodes of pollution injections are accommodated in both examples. It is observed that GEM is more accurate in predicting the strengths of distributed instantaneous pollution sources than point sources because of the discontinuities of the latter in both the spatial and temporal dimensions.
Downloads
References
Atmadja, J., & Bagtzoglou, A. C. (2001). Pollution source identification in heterogeneous porous
media. Water Resources Research, 37, 2113–2125.
Bear, J. (1979). Hydraulics of groundwater. New York, NY: McGraw Hill.
Brebbia, C. A. (1978). The boundary element method for engineers. Great Britain: Pentech Press.
Cokca, E., Bilge, H. T., & Unutmaz, B. (2009). Simulation of contaminant migration through a
soil layer due to an instantaneous source. Computer Applications in Engineering Education,
, 385–398.
Datta, B., Chakrabarty, D., & Dhar, A. (2011). Identification of unknown groundwater pollution
sources using classical optimization with linked simulation. Journal of Hydro-environment
Research, 5, 25–36.
Hansen, P. C. (1994). Regularization tools: A Matlab package for analysis and solution of
discrete ill-posed problems. Numerical Algorithms, 6, 1–35.
Jha, M., & Datta, B. (2013). Three-dimensional groundwater contamination source identification
using adaptive simulated annealing. Journal of Hydrologic Engineering, 18, 307–317.
Michalak, A. M., & Kitanidis, P. K. (2004). Estimation of historical groundwater contaminant
distribution using the adjoint state method applied to geostatistical inverse modeling. Water
Resources Research, 40, W08302. doi:10.1029/2004WR003214
Neupauer, R. M., & Lin, R. (2006). Identifying sources of a conservative groundwater
contaminant using backward probabilities conditioned on measured concentrations. Water
Resources Research, 42, W03424. doi:10.1029/2005WR004115
Onyari, E., & Taigbenu, A. (2017). Inverse Green element evaluation of source strength and
concentration in groundwater contaminant transport. Journal of Hydroinformatics, 19,
–96. doi:10.2166/hydro.2016.028
Sun, A. Y., Painter, S. L., & Wittmeyer, G. W. (2006a). A constrained robust least squares
approach for contaminant source release history identification. Water Resources Research,
, W04414. doi:10.1029/2005WR004312
Sun, A. Y., Painter, S. L., & Wittmeyer, G. W. (2006b). A robust approach for contaminant
source location and release history recovery. Journal of Contaminant Hydrology, 88, 29–44.
Taigbenu, A. E. (2012). Enhancement of the accuracy of the Green element method: Application
to potential problems. Engineering Analysis with Boundary Elements, 36, 125–136
