Correction: Pushpull tests for estimating effective porosity: expanded analytical solution and in situ application
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Erratum: « Pushpull » tests pour estimer la porosité efficace: solution analytique étendue et application in situ
Erratum: Ensayos “pushpull” para estimar la porosidad efectiva: solución analítica expandida y su aplicación in situ
勘误: 进行推拉试验估算有效孔隙度:扩展解析解决方案及现场应用
Erratum: Testes “pushpull” para estimativa de porosidade efetiva: solução analítica expandida e aplicação in situ
Correction: Hydrogeology Journal (2018) 26:381393
https://doi.org/10.1007/s1004001716723
 Q _{i}

injection rate [L^{3}/T]
 t _{i}

total injection time [T]
 b

saturated aquifer thickness [L]
 n _{e}

effective porosity [dimensionless]
 v

average linear groundwater velocity [L/T]
 Δt_{a1}

time elapsed during injection [T]
 Δt_{a2}

time elapsed during drift [T]
 Q _{e}

extraction rate [L^{3}/T]
 t _{e}

total extraction time [T]
 Δt_{a3}

time elapsed during extraction [T]
 \( \frac{dh}{dr} \)

hydraulic gradient [L/L]
 K

hydraulic conductivity [L/T]
 t _{i}

time elapsed during injection [T]
 t _{d}

time elapsed during drift [T]
 τ _{e}

time elapsed from start of extraction until onehalf of tracer mass is recovered [T]
 Ѵ _{e}

volume of water extracted until onehalf of tracer mass is recovered [L^{3}]
Equation (C4), like Eq. (C3), describes effective porosity but does not account for the onedimensional displacement of the center of mass of the tracer due to ambient groundwater flow during the injection phase (t_{i}).
Effective porosity calculated from the incorrect Paradis et al. (2018) solution (Eq. (18) in Paradis et al. (2018), n_{e1}), the Hall et al. (1991) solution (Eq. (C4), n_{e2}), and the corrected Paradis et al. (2018) solution (Eq. (C3), n_{e3}) for tests from Paradis et al. (2018) (FW220FW225), Hall et al. (1991), and Istok (2013)
Moreover, all other conclusions from Paradis et al. (2018) that include: “(1) the analytical solution to describe the displacement of the center of mass of a tracer during a pushpull test can be expanded to account for displacement during the injection phase, (2) the transport of a tracer during the injection phase of a pushpull test may not be truly negligible,” and “(4) singlewell pushpull tests can be readily applied to multiple wells within a study site to assess the spatial variability of effective porosity, and (5) the errorpropagated uncertainty in the value of effective porosity can be mitigated to a reasonable level by careful consideration for the precise determination of the aquifer properties and the pushpull test parameters”, also hold true.
In summary, Eq. (C3) given here is the corrected version of Eq. (18) in Paradis et al. (2018) to describe effective porosity when accounting for the onedimensional displacement of the center of mass of the tracer due to ambient groundwater flow during the injection phase (t_{i}). The authors would like to sincerely thank Felix Tritschler from the Helmholtz Center for Environmental Research  UFZ for bringing the error to light and for assisting in the correction to the error.
References
 Hall SH, Luttrell SP, Cronin WE (1991) A method for estimating effective porosity and groundwater velocity. Ground Water 29(2):171–174. https://doi.org/10.1111/j.17456584.1991.tb00506.x CrossRefGoogle Scholar
 Istok JD (2013) Pushpull tests for site characterization. SpringerVerlag, Berlin HeidelbergCrossRefGoogle Scholar
 Paradis CJ, McKay LD, Perfect E, Istok JD, Hazen TC (2018) Pushpull tests for estimating effective porosity: expanded analytical solution and in situ application. Hydrogeol J 26(2):381–393. https://doi.org/10.1007/s1004001716723 CrossRefGoogle Scholar