Capillary Impact on Tidal Response of Groundwater in Unconfined Aquifers With Finite Thickness, Anisotropy and Wellbore Storage—An Analytical Model

Abstract

This study develops a novel, two‐dimensional analytical model to study capillary effects on Earth tidal responses of groundwater in unconfined aquifers. It differs from the previous model by accounting for effects of finite aquifer thickness, anisotropy and wellbore storage. We test the present model against the previous model and numerical simulations and apply it to the field data. Several significant results are obtained: (a) At high conductivity (Kr>10−5 ${K}_{r} > {10}^{-5}$ m/s), the effect of capillary zones dominates tidal responses of groundwater and causes higher amplitude ratio and smaller phase shift compared with that predicted by the unconfined aquifer model without a capillary zone. At low conductivity (Kr<10−5 ${K}_{r}< {10}^{-5}$ m/s), the effect of capillary zones on the tidal responses diminishes. (b) The impact of the finite thickness on the tidal response is regulated by the anisotropy. If the anisotropic ratio is small (Kz/Kr<1 ${K}_{z}/{K}_{r}< 1$), the impact of thickness may be negligible; at high anisotropic ratio (Kz/Kr>1 ${K}_{z}/{K}_{r} > 1$), however, the amplitude ratio decreases and the phase shift increases, and the response differs substantially from that of the previous model, which is caused by a change in the flow pattern. (c) Wellbore storage have significant impacts on the tidal response at low conductivity (Kr< ${K}_{r}< $ 10−5 m/s) but negligible impact at higher conductivity. (d) The present model marginally improved the fit by the half‐space model to the field data from a well in SW China, showing that the remaining misfit to the field data by models with capillarity cannot be due to finite aquifer thickness, anisotropy, or wellbore storage.

Impact of Depth‐Dependent Heterogeneity in Aquifers on the Response of Unsaturated‐Saturated Flow to Earth Tides

“…The findings reveal that vadose zone thickness ( b ) significantly affects both the amplitude ratio and phase shift of the tidal response of groundwater. Smaller b values result in lower amplitude ratios and larger phase shifts, consistent with previous studies (Liang et al., 2022; Zhang et al., 2023). Additionally, b influences the impact of the decay coefficient ( c s ) of hydraulic conductivity on the tidal responses of groundwater.…”

“…and the definitions of the other parameters C′ 1 ,C′ 2 ,C′ 3 ,and C′ 4 in Equation 17and the details of their derivation are given in Supporting Information S1 (Text S4). The parameter δ usually denotes as the "skin depth" of the tidal responses of groundwater flow (Detournay & Cheng, 1993), which regulates the impacts of the aquifer thickness (Zhang et al, 2023). The corresponding amplitude ratio and phase shift of the tidal response of hydraulic head in a homogeneous aquifer are, respectively,…”

“…However, it is worth noting that the changes in hydraulic heads caused by Earth tides are relatively small compared to most aquifer thickness. Therefore, we may employ the perturbation method to linearize the Richards equation and fix the water table at a known position (Kroszynski & Dagan, 1975), as done in previous studies in solving the coupled unsaturatedsaturated flow equations (Chang et al, 2018;Liang, Zhan, Zhang & Liu, 2017;Liang, Zhan, Zhang, & Schilling, 2017;Liang, Zhan, Zhang, et al, 2018;Liang, Zhan, & Zhang, 2018;Lin et al, 2017;Mathias & Butler, 2006;Mishra & Neuman, 2010;Tartakovsky & Neuman, 2007;Zhang et al, 2023). Moreover, Liang et al (2022) conducted a thorough comparison between the analytical solution obtained through linearizing the Richards equation and the numerical solution of the nonlinear Richards equation.…”

“…Recent studies conducted by C.-Y. Wang et al (2019), Liang et al (2022), and Zhang et al (2023) have highlighted the significant influence of the unsaturated zone on the Earth tide response of groundwater. C.-Y.…”

“…Extending this line of research, Zhang et al. (2023) expanded the analytical model by incorporating additional factors like finite aquifer thickness, anisotropy, and wellbore storage, further underscoring the importance of the unsaturated zone and its interplay with aquifer characteristics.…”