Stochastic Characterization of Aquifer Permeability and Macrodispersivity Based on Point Velocity Probes Measurements (With Application to Borden Site)

A recently developed technology of characterization of shallow aquifers is based on the point velocity probes (PVP). At ports along vertical tubes which are inserted in the subsurface, water velocity is measured at the centimeter scale. This technique was applied by Osorno et al. (2022, https://doi.org/10.1029/2020wr029034) to a field test at the Borden aquifer, near the site of the transport experiment conducted by Sudicky (1986, https://doi.org/10.1029/wr022i013p02069). One of the main aims was to validate the method by identifying the aquifer hydraulic conductivity field and to compare it with the one determined by the extensive hydraulic conductivity sampling (Sudicky, 1986, https://doi.org/10.1029/wr022i013p02069). The velocities were measured along a vertical plane, normal to the mean head gradient, in the neighborhood of the previous field test area, at 420 ports along 15 vertical lines. A forced steady flow was created by recharging and pumping wells. The analysis of Osorno et al. (2022, https://doi.org/10.1029/2020wr029034) led to the histogram of the longitudinal log-velocities and to their transverse and vertical semi-variograms. Our main aim is to use these data to derive, by a relatively simple and general method, the statistical moments of the permeability field. We assumed that the log-conductivity is a random, stationary variable of axisymmetric two point covariance. The structure is characterized by the log-permeability mean, variance and transverse as well as vertical integral scales. The transverse and vertical velocity covariances were derived theoretically in a semi analytical form, in terms of the log-conductivity parameters, which were subsequently determined by a best fit with measurements. The resulting log-conductivity variance and integral scales were in fair agreement with those of Sudicky (1986, https://doi.org/10.1029/wr022i013p02069) and the ensuing macrodispersivity was close to the one characterizing the transport experiment. Concluding, we found by a simplified analysis that the PVP is a promising characterization methodology.