Application of the Dupuit–Forchheimer model to groundwater flow into a well

Existing models are built upon to develop new ones. As a foundational model in porous media flow, the Darcy flow model has been built upon by many researchers. The groundwater flow equation evolved from the Darcy equation. Dupuit–Forchheimer built upon it to develop the simplified forms for both the confined and unconfined aquifers flow, usable for studying groundwater flow into wells. Aside from height, permeability, and availability of water in the aquifers, other factors influence groundwater flow into wells, as enshrined in the flow equation. This paper investigates the roles of storability, hydraulic conductivity, and source/sink strength in both confined and unconfined groundwater flow into wells using the Dupuit–Forchheimer assumption. In this model, the Dupuit–Forchheimer pressure assumption is substituted into the groundwater flow equations and solved using the Bessel form for separation of variable technique, and Mathematica 11.2 computational software to obtain the expressions for the pressure, which are computed and presented quantitatively. The results show that an increase in the hydraulic conductivity and storability have no effect on the flow pressures in the confined and unconfined aquifers but cause fluctuation in the pressure structure in the unconfined aquifer; the source/sink strength factor causes fluctuation in the pressure structures in both confined and unconfined aquifers flow. However, in both confined/unconfined aquifers the pressures increase as the radii of the wells increase. Importantly, the fluctuation in the pressure structures causes a loss of energy for groundwater flow into the wells.