Influence of time-dependent ground surface flux on aquifer recharge with a vadose zone injection well

Vadose zone well (VZW) injection is an effective method for aquifer recharge in semiarid and arid regions where groundwater table is deep or sufficiently permeable soils and/or sufficiently large land areas for surface infiltration are not available. Several analytical and numerical models have been developed for the injection well in the vadose zone. However, those models usually ignore the ground surface flux (GSF) generated by infiltration or evapotranspiration, which may cause errors and hinder the success of artificial recharge and groundwater management. This study takes GSF generated by these two processes into consideration with the purpose of understanding their influences on the hydraulic responses and recharge efficiency. An innovative mathematical model is established based on a three-dimensional (3D) governing equation for saturated flow and a linearized 3D Richards' equation for unsaturated flow. The Laplace-Hankel transforms are applied to derive solutions for the hydraulic head increments and recharge rate. The solutions are tested by a finite-element numerical model developed using COMSOL Multiphysics. The obtained solutions are utilized to assess the influences of time-dependent GSF generated by infiltration or evapotranspiration. The magnitude of these influences depends on unsaturated and saturated aquifer properties and the value of GSF. The impacts of three important properties are investigated: the constitutive exponent of the unsaturated zone omega, the specific yield S-y, and the hydraulic conductivity anisotropy K-D = K-z/K-r. Smaller values of dimensionless constitutive exponent D and dimensionless specific yield S-yD lead to larger changes of hydraulic head increments in both unsaturated zone (u(D)) and saturated zone (s(D)) when GSF is the same. A small value of K-D can delay the changes of u(D) and s(D), but the value of K-D does not affect the final values of u(D) and s(D). Larger values of GSF generated by surface infiltration lead to larger increases of u(D) and s(D); larger absolute values of GSF generated by evapotranspiration lead to larger decreases of u(D) and s(D). The proposed semi-analytical solutions can be used to improve the feasibility and efficiency of artificial recharge in semiarid and arid regions.