The characterization of aquifer geometry using flow dimension

Aquifer hydraulic properties are typically estimated from pumping test data. Analysis of these data often assumes that flow in the aquifer is radial toward the pumping well. This assumption is often violated in highly heterogeneous media, especially fractured rock, where flow is often channelized toward the well. A generalized mathematical formulation of the radial flow equation proposed by J. A. Barker (1988) allows the dimensionality of the flow toward a well to be specified using integer or non-integer flow dimensions, which describe the changing cross-sectional area of flow with respect to distance from the well. Barker's approach simplifies to a linear, radial, or spherical flow equation for integer dimensions of 1, 2, or 3, respectively. Diagnostic plots of drawdown data from pumping tests can be used to directly observe the evolution of flow dimension during pumping tests, and many pumping tests in heterogeneous and fracture rock aquifers show non-integer flow dimensions. The physical meaning of non-integer flow dimensions has long been the subject of debate, with some researchers attributing them to the evolution of pressure fields in fractal media. Non-integer flow dimensions can also arise from pumping in high permeability conduits, where the flow dimension is determined by the geometry of the conduit.;In this research, we focus on the interpretation of flow dimension and aquifer hydraulic properties from pumping tests conducted in high-permeability conduits. We apply Barker's description of changing cross-sectional area of flow to generate conduits with known flow dimension, establish the physical connection between flow dimension and non-fractal geometry, estimate hydraulic properties for generated conduits, and compare their simulated responses to those seen in field data for the Waste Isolation Pilot Plant (WIPP). We then estimated aquifer hydraulic properties in conduits and simplified random fields with varying configurations of pumping and observation wells. We specifically evaluated the benefits of estimating input field parameters using flow dimension as a fitting parameter through optimization of a distributed parameter model. Finally, we combined our conduit simulation methods, site specific geologic knowledge, and recorded observation well responses to reinterpret constant-rate pumping tests conducted at the WIPP site.