The response of aquifers to Earth's solid tides (Earth tides) has increasingly been used as a tool for monitoring the hydraulic properties of groundwater systems. Recent studies of the tidal response of the Arbuckle aquifer opened to a USGS deep well in Oklahoma (Wang et al., 2018; Barbour et al., 2019), which has been injected with an enormous amount of toxic wastewater, showed evidence that this aquifer may be leaking. Quantitative interpretation of the tidal response of this aquifer was made with a one-dimensional analytical solution (Wang et al., 2018) that showed that substantial leakage is occurring. However, the analytical model has inherent simplifications such as conductivity isotropy, small aquifer thickness, absence of aquitard storage, and no basement leakage. In this study we revisit the tidal response of leaky aquifers with a finite-element, multi-layered model where such simplifications are removed. We found that the simplifications in the analytical model lead to overly conservative estimates of leakage. We revisit the tidal response of the Arbuckle aquifer in Oklahoma with the numerical simulation and estimate an average vertical hydraulic conductivity of 2 x 10-6to7 x 10-5 m/s for the aquitard overlying the Arbuckle. Thus the 'aquitard' above the Arbuckle is not confining at this location but is as conductive as the aquifer itself. Given the fast rise of fluid level in many Arbuckle wells in response to the injection of hundreds of millions of barrels of wastewater into this aquifer across Oklahoma and Kansas, the present result calls for vigilant monitoring of leakage of wastewater from the Arbuckle aquifer into the overlying freshwater reservoirs and the surface environment. Plain Language Summary: Earthquakes can damage the confinement of groundwater aquifers and thus can cause seismic hazard by letting freshwater in some aquifers to be contaminated or stored toxic wastewater in other aquifers to leak out into the environment. Thus it is important to monitor possible leakage of aquifers in earthquake countries. Analysis of the aquifer response to Earth's solid tides in a USGS deep well in Oklahoma (Wang et al., 2018; Barbour et al., 2019), which has been used as the repository of an enormous amount of injected toxic wastewater, shows that the aquifer may be leaking. An analytical solution (Wang et al., 2018) that contains several simplifications was used to quantify the aquifer leakage from the tidal response. Here we use a two-dimensional, multilayered numerical simulation without these simplifications to explore the limitations of the analytical model. We find that aquitard storage and basement leakage have important effects on the tidal response of aquifers and the omission of these factors in the analytical solution may have caused underestimation of the aquifer leakage. We then apply the numerical model to interpret the tidal response of water level documented in a USGS deep monitoring well installed in the Arbuckle aquifer in Oklahoma, where an enormous amount of toxic wastewater has been stored. With reasonable estimates of the aquitard storage, our simulations yield an estimate of 2 x 10(-6)to7 x 10(-5) m/s for the vertical hydraulic conductivity of the aquitard. Thus the 'aquitard' is not at all confining but is as conductive as the aquifer itself. Given the fast rise of fluid level in many Arbuckle wells in response to the injection of hundreds of millions of barrels of wastewater into this aquifer across Oklahoma and Kansas, the present result calls for vigilant monitoring of leakage of wastewater from the Arbuckle aquifer into the overlying freshwater reservoirs and the surface environment.
