Inverse Green element simulations of instantaneous pollutant injections into a 2-D aquifer

Abstract

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.

Keywords:

• The Green element method
• inverse simulations
• point & distributed instantaneous pollution injections
• Tikhonov regularisation