TY - JOUR

T1 - Equivalent and effective conductivities of heterogeneous aquifers for steady source flow, with illustration for hydraulic tomography

AU - Bellin, Alberto

AU - Fiori, Aldo

AU - Dagan, Gedeon

N1 - Publisher Copyright:
© 2020 Elsevier Ltd

PY - 2020/8

Y1 - 2020/8

N2 - 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.

AB - 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.

KW - Characterization of aquifer hydraulic properties

KW - Effective hydraulic conductivity

KW - Hydraulic tomography, Heterogeneous aquifers

KW - Source flow

KW - Well flow

UR - http://www.scopus.com/inward/record.url?scp=85085270007&partnerID=8YFLogxK

U2 - 10.1016/j.advwatres.2020.103632

DO - 10.1016/j.advwatres.2020.103632

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AN - SCOPUS:85085270007

SN - 0309-1708

VL - 142

JO - Advances in Water Resources

JF - Advances in Water Resources

M1 - 103632

ER -