Approximate analytical solution for non-Darcian flow toward a partially penetrating well in a confined aquifer

- Non-Darcian flow to a partially penetrating well was investigated.
- Approximate analytical solutions for the drawdowns were obtained.
- The impacts of different parameters on the drawdowns were analyzed.
- The drawdown is very sensitive to the power index n in the Izbash equation.

SummaryIn this study, non-Darcian flow to a partially penetrating well in a confined aquifer was investigated. The flow in the horizontal direction was assumed to be non-Darcian, while the flow in the vertical direction was assumed to be Darcian. The Izbash equation was employed to describe the non-Darcian flow in the horizontal direction of the aquifer. We used a linearization procedure to approximate the non-linear term in the governing equation enabling the mathematical model to be solved using a combination of Laplace and Fourier cosine transforms. Approximate analytical solutions for the drawdown were obtained and the impacts of different parameters on the drawdown were analyzed. The results indicated that a larger power index n in the Izbash equation leads to a larger drawdown at early times, while a larger n results in a smaller drawdown at late times. The drawdowns along the vertical direction z are symmetric if the well screen is located in the center of the aquifer, and the drawdown at the center of the aquifer is the largest along the vertical direction for this case. The length of the well screen w has little impact on the drawdown at early times, while a larger length of the well screen results in a smaller drawdown at late times. The drawdown increases with Kr at early times, while it decreases as Kr increases at late times, in which Kr is the apparent radial hydraulic conductivity. A sensitivity analysis of the parameters, i.e., the specific storage Ss, w, n and Kr, indicated that the drawdown is not sensitive to them at early times, while it is very sensitive to these parameters at late times especially to the power index n.