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Modeling Diffusivity Tests in Heterogeneous Aquifers: A Stochastic First‐Order Approach
Author(s) -
Cheng Kan Bun,
Dagan Gedeon,
Rabinovich Avinoam
Publication year - 2020
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2020wr027672
Subject(s) - aquifer , hydraulic conductivity , thermal diffusivity , harmonic mean , log normal distribution , anisotropy , variance (accounting) , mathematics , mechanics , flow (mathematics) , soil science , statistics , geology , geotechnical engineering , physics , thermodynamics , groundwater , optics , business , accounting , soil water
The diffusivity test considered here consists of injecting (or pumping) a volume of water through short segments of a well for a short time and measuring the travel time of the peak of the head signal at different points in the surrounding aquifer volume. The specific storage is assumed to be constant, while the hydraulic conductivity of the heterogeneous aquifer is modeled as a random lognormal field. The axi‐symmetric anisotropic structure is characterized by a few parameters (logconductivity mean and variance and horizontal and vertical integral scales). The paper determines the mean and variance of the peak travel time as function of distance from an instantaneous source by solving the flow equation using a first‐order approximation in the logconductivity variance. The mean travel time is recast in terms of the equivalent conductivity, which decreases from the harmonic mean near the source to the effective conductivity in uniform flow for a sufficiently large distance. Similarly, the variance drops from its maximum near the source to a small value. Application to field test is discussed and topics of future investigations are suggested.