Approximate Analytical Solutions for Two-Region Non-Darcian Flow to a Partially Penetrating Well

Non-Darcian flow is likely to occur in the region near a pumping well because of high velocities, while flow becomes Darcian again in the region far away from the pumping well as the velocity decreases. To describe these characteristics, a two-region non-Darcian flow model toward a partially penetrating well is developed in this study. The flow in the region near the pumping well is assumed to be non-Darcian which can be described by the Izbash equation. The flow in the region far away from the pumping well was assumed to be Darcian as well as the vertical flow due to the low velocities. A linearization procedure associated with the Laplace transform and finite cosine transform is used to work out such two-region non-Darcian flow model. The characteristics of the drawdowns under such flow conditions are examined. It is concluded that: (1) the drawdown in the non-Darcian flow region is the same as that of the fully non-Darcian flow model at early times, and it is the same at that of the fully Darcian flow model and larger than that of the fully non-Darcian flow model at late times. (2) the drawdown in the Darcian flow region is larger than that of the fully Darcian flow model and smaller than that of the full non-Darcian flow model at early times; (3) the drawdown-distance behavior indicates that the drawdown in the non-Darcian flow region increases as the power index n in the Izbash equation increases, while the value of n has a little effect on the drawdown in the Darcian flow region. The results of this study will be of great theoretical significance for the aquifer parameters estimation with the pumping test data in a partially penetrating well.