Field Validation of the Backward-in-time Advection Dispersion Theory

We have recently developed a theory that can be used to locate the source of contamination captured by a pumping well [1]. Accounting for advection, dispersion, linearequilibrium sorption, aquifer heterogeneity, and regional natural recharge, the theory is based on the concept of travel time probability. This probability describes the time for a particle to travel from a source location to the pumping well, and can be directly computed by solving adjoint partial differential equations backwards-in-time, with a third type probability boundary condition at the pumping well. We apply a two-dimensional version of the theory, implemented numerically using the Laplace Transform Galerkin method, to the analysis of a recent tracer test conducted at the Borden Site in Ontario, Canada [2]. The test was designed to validate common conceptual models of pumping well capture zones. Tracers were injected at 15 locations upgradient of a pumping well. Their arrival in the well was observed with weekly concentration measurements. A single twodimensional backward-in-time simulation was used to predict separate travel time probabilities for each injection site. These were compared to normalized experimental breakthrough curves, and arriving tracer mass was assigned to 11 of the injection locations. Tracer from 4 injection sites was predicted to miss the pumping well. The assignments of mass and source location and the predicted tracer recovery compare favorably with independent interpretations of the experiment which were based on multiple three-dimensional forward simulations [3]. Satisfactory performance of the method on the field test data supports its validation as a standard tool and certainly demonstrates its practical use.