The effective conductivity of heterogeneous aquifers Kefu relates the mean flux to the mean head gradient in mean uniform (natural gradient) flow. While Kefu depends on the hydraulic conductivity K statistical moments (KG, the geometric mean and σY 2, the logconductivity variance for a given structure model) it is not a local property for strongly nonuniform well flow. In hydraulic tomography, flow to a short well segment which is considered here, can be approximated by that toward a source in a three-dimensional heterogeneous medium. We investigate the equivalent conductivity Keq, which unlike Kefu, is a measurable property, directly related to the head H (or its mean) and the discharge. The dependence of Keq on K statistics and distance r from the source is determined for steady source flow in a formation of random stationary and statistically isotropic K. For the first time Keq is derived by numerical simulations for σY 2≤ 4. The derivation of the transition of Keq from the local exact value for r/I < < 1 (I is the integral scale) to Kefu for r/I⪆1 is one of the main results of the study. Application to a synthetic example of hydraulic tomography to derive KG, σY 2and I, from H measurements, demonstrates the promise of the method and calls for its further development and validation.
- Characterization of aquifer hydraulic properties
- Effective hydraulic conductivity
- Hydraulic tomography, Heterogeneous aquifers
- Source flow
- Well flow