Distributional Scaling in Heterogeneous Aquifers

Abstract:

An investigation is undertaken into the fractal scaling properties of the piezometric head in a heterogeneous unconfined aquifer. The governing equations for the unconfined flow are derived from conservation of mass and the Darcy law. The Dupuit approximation will be used to model the dynamics. The spatially varying nature of the tendency to conduct flow (e.g. the hydraulic conductivity) is represented as a stochastic process. Experimental studies in the literature have indicated that the conductivity belongs to a class of non-stationary stochastic fields, called H-ss fields. The uncertainty in the soil parameters is imparted onto the flow variables; in groundwater investigations the potentiometric head will be a random function. The structure of the head field will be analyzed with an emphasis on the scaling properties. The scaling scheme for the modeling equations and the simulation procedure for the saturated hydraulic conductivity process will be explained, then the method will be validated through numerical experimentation using the USGS Modflow-2005 software. The results of the numerical simulations demonstrate that the head will exhibit multi-fractal scaling if the hydraulic conductivity exhibits multi-fractal scaling and the differential equations for the groundwater equation satisfy a particular set of scale invariance conditions.