Ground water flow model for fractured media

In fractured rock systems, ground water flow is not as simple and as methodical as in a porous medium. To create a numerical model of such a flow system, a four-part algorithm was written, which included MATLAB$\sp\circler$ as a fundamental component. It was intended that the model output define the zone of influence of pumping stresses. The four model parts are, sequentially: generation of the interconnected fracture geometry; generation of the linear finite element grid; the hydraulic calculations and the influence zone delineation. MATLAB$\sp\circler$ is used to stochastically generate the fracture geometry from empirical estimates of the probability distributions of: fracture length, orientation, width and density. This first part not only yields the fracture geometry but also develops two matrices: the interconnectivity matrix and the fracture endpoint matrix. In the second part, a matrix of linear finite elements is generated from the matrices of the first part. The solution of the flow equations in the third part gives the hydraulic head at each node of the finite element grid. From this, internodal velocities can be calculated in the last part of the model in order to delineate the influence zone. An application of the hydraulic model was performed using the data set from the Blackwater Brook site in Dover, NH. The fitting of the hydraulic model to these field data represents an important step toward the use of this model with a larger set of field data not only to verify the hydraulic behavior of fractured media, but also to yield information for delineation of time-related capture zones for various hydraulic stresses which can be imposed. Finally, sensitivity analyses were performed using adjoint operators in order to identify the parameters to which the system responds most strongly. The system was more sensitive to the areal recharge on a fracture segment. In addition to widespread application for hydrogeologic studies, this model promises to contribute to the surge of studies in ground water science spurred by the strong interest by federal agencies in ground water protection and contamination at hazardous waste sites