The principle of reciprocity, called Maxwell-Betti theorem, initially used in mechanics in an elastic structure, establishes a relation of equality between two distinct strains under different loads. In this paper, we extend and apply this principle to flow and solute transport equations in porous media, in order to perform the pollution sources identification in aquifers. We developed general 2D expressions of the reciprocity principle for transient transport problems. This model leads to a linear equations set, with point sources coordinates, concentrations and associated water fluxes as unknowns The proposed model is then applied to the Rocky Mountain Arsenal aquifer (Konikow in Modeling Chloride Movement in the Alluvial Aquifer at the Rocky Mountain Arsenal, Colorado. Technical Report Water-Supply Paper 2044, USGS, 1979), where polluted water is injected into a well in the domain. The used inverse technique successfully recovered the position and the pollutant concentration in addition to the associated water flux. In addition, we developed and implemented the inverse method for different knowledge levels of the degrees of the aquifer contamination, i.e. more or less data available in the field. Multiple pollution point sources and noisy data situations are also developed and tested with high efficiency. The proposed method would be easy and useful to be implemented in the modeling software now widely used by researchers and groundwater managers. It can thus be applied in real case studies, to help authorities and regulators to efficiently identify the polluters and the contamination process, i.e. its location, onset, duration and the associated mass and water fluxes.
© 2022. The Author(s).