Flow to a horizontal well in an aquitard–aquifer system

A horizontal well is sometime installed in an aquifer beneath a water reservoir to get significant amount of groundwater with better quality. An aquitard often separates the surface water body from the underneath aquifer. Previous studies in vertical wells related to this subject treated leakage from the aquitard as a volumetric source term in the governing equation of flow in the main aquifer, a hypothesis termed ‘Hantush's approximation for partially penetrating wells’. In this study, flow in the aquitard and aquifer is treated as two systems which are linked through the continuity of flux and head at the aquitard–aquifer boundary. In particular, we treat leakage as a boundary at the aquitard–aquifer interface, not as a volumetric source. The leakage induced by the pumping horizontal well depends on several parameters such as the aquitard thickness, the vertical hydraulic conductivity of the aquitard, the aquitard specific storage, the well location, and the well length. In general, we find that the solution based on the Hantush's approximation to some extent deviates from that obtained based on the actual scenario of leakage through the interface during the transient flow condition, particularly at the early time. For steady-state flow, the Hantush's approximation works reasonably well under realistic conditions of aquitard thickness and hydraulic conductivity as long as the aquitard thickness is relatively thick (aquitard–aquifer ratio greater than 0.001). This approximation also works reasonably well under realistic horizontal well length and well location as long as the well is not too close to the aquitard–aquifer boundary.