A dual‐porosity model for water level response to atmospheric loading in wells tapping fractured rock aquifers

Abstract

A fractured rock aquifer may be viewed as a permeable fracture network embedded within a less permeable porous matrix. This permeability contrast gives rise to distinct pressure fields in the pore space and fractures, and therefore to a response to atmospheric loading different from that of nonfractured porous media. Assuming that fracture sizes and orientations are uncorrelated and sufficiently random to ensure homogeneous and isotropic elastic behavior of the rock mass at the continuum scale, an effective stress model proposed by Tuncay and Corapcioglu [1995] is used to develop a linear elastic stress‐strain relationship for dual‐porosity media. Elastic constants of the fractured rock mass, required by the model, are estimated using theoretical relations derived by Budiansky and O'Connell [1976]. The stress‐strain relationship and the coupled continuity equations for flow in deformable fractured media are combined to derive expressions for the undrained, static‐confined barometric efficiency of a dual‐porosity medium. Two limiting cases are considered: the initial, instantaneous pressure response in the pore space and fractures due to a change of confining stress, and the later stage of pressure equilibrium between the two phases. The dual‐porosity response model developed here may be used to characterize hydraulic properties in fractured aquifers, including low‐porosity and low‐permeability media. The model is evaluated on water level hydrograph data from a borehole tapping fractured volcanic rocks. Water level and barometric data are supplemented by independent measurements of matrix porosities, fracture spacing, and rock elastic properties, allowing an assessment of total porosity and specific storage at the site. For the observed static‐confined barometric efficiency of 0.78 the instantaneous pressure response model yields plausible values for both parameters.