Linear programming method for investigating the disposal histories and locations of pollutant sources in an aquifer

A linear programming based methodology has been used to identify the unknown sources of groundwater pollution. A source identification model is demonstrated and evaluated using hypothetical groundwater systems for a steady state case and a transient case. The concept of linear super-position is employed to find waste disposal rates at disposal sites from concentrations at measurement wells. In the steady state case, the identification model finds the unknown location and magnitude of leaks in a pipe among the probable leak locations. Contamination data are obtained from sparsely located wells. Subsequently, the transient case source identification problem is tested for unsteady case of flow and transport with several disposal periods in the aquifer. The model results show that in the steady state case problem with perturbed data, the pipe leak is identified within 1% of the true flux value when the maximum error tolerance is set to 15%. In the transient case, a large number of measurements of concentration data spread over time and space are necessary to satisfactorily identify possible unknown sources of groundwater pollution. The injection rate values were found with a relative error of 13% to 32% and a normalized error of 17% when the disposal locations were known. The results remain unchanged after entering a dummy source to the unknown potential sources. Ignoring a measurement well location changes the identification results to a normalized error value of 21%. The linear programming model can be very useful in source identification with available measurement and aquifer parameters.