Identification of aquifer transmissivity with multiple sets of data using the Differential System Method

The mass balance equation for stationary flow in a confined aquifer and the phenomenological Darcy s law lead to a classical elliptic PDE, whose phenomenological coefficient is transmissivity, T, whereas the unknown function is the piezometric head. The differential system method (DSM) allows the computation of T when two independent data sets are available, i.e., a couple of piezometric heads and the related source or sink terms corresponding to different flow situations such that the hydraulic gradients are not parallel at any point. The value of T at only one point of the domain, x0, is required. The T field is obtained at any point by integrating a first order partial differential system in normal form along an arbitrary path starting from x0. In this presentation the advantages of this method with respect to the classical integration along characteristic lines are discussed and the DSM is modified in order to cope with multiple sets of data. Numerical tests show that the proposed procedure is effective and reduces some drawbacks for the application of the DSM.