Least cost search algorithm for the identification of a DNAPL source

The overall objective of this work is to develop, test and evaluate a computer assisted analysis algorithm to help the groundwater professional identify, at least cost, the location of a DNAPL source. The DNAPL source location is generally too small to identify via borings or geophysical methods. On the other hand, the plume emanating from a DNAPL source is typically quite large and easily discovered. The algorithm presented here defines how to achieve an acceptable level of source-location accuracy with the least possible number of water quality samples. The overall strategy includes the construction of a stochastic groundwater flow and transport model assuming a number of potential locations of the DNAPL source. Each location is associated with an initial weight that reflects our confidence that it is the true source location. This is done using a Choquet integral. The hydraulic conductivity is considered the main source of uncertainty, other than the source location, and the Latin hypercube sampling strategy is used to obtain the hydraulic conductivity field. Using the hydraulic conductivity field and the uncertain source location weights as input to the groundwater flow and transport simulator, the concentration random field and its associated uncertainty is calculated. An optimal sampling point is selected using a method that combines the minimization of the total field variance and the proximity to the potential source locations. A Kalman filter is used to update the simulated concentration field using the real data and the updated plume is compared to the individual plumes (that are calculated using the groundwater flow and transport simulator considering only one source at a time) using a method that involves representing the normalized concentrations as fuzzy sets and comparing several of their α-cuts. The comparison provides new weights for each potential source location that are used as input to the groundwater flow and transport model and the above steps are repeated until the weights stabilize and the optimal source location is found. The algorithm has been successfully tested using synthetic example problems that include homogeneous and heterogeneous aquifers, a pumping well, multiple true DNAPL sources, two dimensional and three dimensional problems. A field application is considered as another test of the proposed algorithm.