A new inverse method for contaminant source identification under unknown solute transport boundary conditions

Abstract

A new solute transport inverse method is proposed for estimating plume trajectory and source release location under unknown solute transport boundary conditions in a steady-state, non-uniform groundwater flow field. Solute concentration is modeled by proposing a set of local approximation solutions (LAS) of transport that are discretized over the problem domain. At a given time step, the inverse method imposes continuities of concentration and total solute mass flux at a set of collocation points in the inversion grid, whereas the LAS are conditioned to measured breakthrough concentrations. By enforcing transport physics at selected points in space and time, the inverse problem becomes well-posed and a single system of inversion equations is assembled and solved with a parallel iterative solver. Unlike most of the inversion techniques that minimize a model-data mismatch objective function, the inverse method does not require the simulation of a forward transport model for optimization, thus both solute initial and boundary conditions can be recovered. Assuming dispersivity estimates are available, the method was demonstrated using synthetic breakthrough data from various sampling densities and designs, i.e., irregular versus uniformly spaced well networks. Different measurement errors and source release histories (e.g., uniform-in-time, single, and multiple pulses) were also investigated. Results suggest that for the source release histories tested, 1) inversion is stable under increasing measurement errors up to 5% of the maximum observed concentration; 2) accurate plume trajectory and source release location can be estimated from solute breakthrough concentrations; 3) inversion accuracy appears the most sensitive to sampling well density and its information content.