ERE Special Seminar - Avinoam Rabinovich
School of Mechanical Engineering
Dynamic Effective Properties of Heterogeneous Aquifers in Unsteady Periodic Flow
We consider time-periodic flow in heterogeneous aquifers, of spatially varying hydraulic conductivity, K and specific storativity s. In steady state flow, it is common to replace the aquifer with a homogeneous one of effective conductivity K = Kef , which depends on the medium heterogeneity structure solely, for given flow conditions. We determine the average pressure head field ‹H› and the associated effective properties Kef , sef for an aquifer with a periodic head drop between the inlet and outlet, such that H is periodic in time. In the first case, the aquifer is modeled by a two-phase medium consisting of a matrix with a dilute concentration of randomly distributed spherical inclusions. In the common quasi-steady approximation Kef is equal to the classical steady solution while sef =sA, the arithmetic mean. We derive expressions for the frequency dependent Kef , sef which are generally complex, i.e. dynamic and delineate the ranges of the parameters: dimensionless frequency and contrasts of conductivity and storativity between the matrix and the inclusions, for which dynamic effects are significant.
In the second case, the analysis is extended to 3D and 2D (regional) confined aquifers modeled as a dense ensemble of spherical (circular) inclusions of lognormal conductivity with constant storativity everywhere. The self consistent approximation is used to derive the dynamic effective conductivity Kef and the average head ‹H› and flux ‹q› fields are subsequently arrived at. It is also shown that the derived Kef applies to 2D phreatic flow with time periodic recharge.