Analytical and Numerical Analyses of Hydrologic Well-Bore Experiments

摘要

An analytical approximate method and a finite-difference numerical model (based on the rate at which a borehole fills with water) were developed to estimate permeability of the Magenta Formation in southeastern New Mexico near the proposed Waste Isolation Pilot Project (WIPP) site. The analytical treatment applies to certain simple geometries with idealized boundary conditions (constant properties, ground water compressibility negligible). Permissible geometries include water-collecting cylinders with large needle-like aspect ratios located beneath the water table. The analytical treatment clearly shows the sensitivity of inferences and conclusions to material properties and geometries. Much of the existing well-bore fill-rate data fall within the range of validity of this simplified analysis. Admission of compressibility effects into the generalized Darcy law, and a nondimensionalization of the equations identify the range of experimental conditions and material properties for which the approximations are invalid. In the numerical capability to complement this analytical treatment, numerous restrictions have been removed so that the code can treat complex geometries for a variety of boundary conditions and variable properties. The compressibility term that is excluded in the analytical treatment is maintained in these numerical solutions. The resulting equations are formally parabolicand can be solved by an implicit integrator with guaranteed stability. The two methods, applied to several different experimental situations, agree with each other. 9 figures, 3 tables. (ERA citation 06:026909)