Investigation On Non-Darcian Flow Toward A Partially Penetrating Well

Pumping test is one of the most important ways to estimate aquifer parameters. It’s also of great importance in evaluating groundwater resources in the aquifer in hydrogeology. Compared with fully penetrating well, partially penetrating well (denoted as PPW in the following) is easy to drill and it can save a lot of money. Therefore, PPW is widely used in pumping test. Because of the large flow velocity near a PPW, flow can be non-Darcian, meaning that the relationship between the flow velocity and the hydraulic gradient is no longer valid. Up to now, the research on non-Darcian flow to a PPW is quite too limited. In this study, we will developed a series of non-Darcian flow models for non-Darcian flow to a PPW in different kind of aquifer systems, i.e., non-Darcian flow to a PPW in a confined aquifer, non-Darcian flow to a PPW in the first kind of leaky aquifer, non-Darcian flow to a larger-diameter PPW in a confined aquifer and the two-region non-Darcian flow model near a PPW in a confined aquifer. The approximate analytical solutions of these four non-Darcian models were obtained by using the analytical method. The non-Darcian feature near the PPW were analyzed and summarized.For the flow to a PPW, the vertical flow in the aquifer cannot be neglected. According to the different characteristics of flow in each direction, the flow in the aquifer was divided into two flow directions, i.e., the flow in tha radial direction and the flow in the vertical direction. The flow in the horizontal direction was assumed to be non-Darcian and it can be described by the Izbash equation, while the flow in the vertical direction was assumed to be Darcian. With the initial and boundary conditions, the mathematical models of these four non-Darcian models were established. The linearization procedure was used to approximate the non-linear term in the mathematical models. After that, the mathematical models can be solved by using the Laplace transform associated with the finite cosine Fourier transform. The approximate analytical solutions of these mathematical models were obtained in Laplace domain. We have developed a series of MATLAB programs to calculate the drawdowns in the aquifer for such non-Darcian models. The features of the drawdown curves under different conditions were analyzed. Several findings can be drawn from this study: (1) The impact of specific storage of the aquifer Ss on the drawdowns mainly occurs at early times and a larger Ss results in a smaller drawdown, while the drawdowns are not changeable with the value of Ss at late times. The length of the well screen w has little impact on the drawdown at early times, while with pumping time increases, the drawdown decreases as w increases. The drawdown increases with Kr at early times, while it decreases as KT increases at late times. We also analyzed the impact of vertical position in the aquifer on the drawdown and found that the drawdown is the largest at the center of the aquifer and it decreases symmetrically from the center of the aquifer to the boundary along the vertical direction.(2) The value of n in the Izbash equation indicates the nonlinearity of the flow and a larger n implies greater turbulence of the flow. It was found that different values of n have a different impact on the drawdown during the entire pumping period. A larger n results in a larger drawdown at early times, and leads to a smaller drawdown at late times.(3) A sensitivity analysis of the parameters Ss, w, n, Kr has been done. The results indicated that the normalized sensitivity increases with the pumping time. The value of n is the most sensitive parameter of these parameters and the value of Ss is the least sensitive one.(4) The results of the non-Darcian flow model for flow to a partially penetrating well in the first kind of leaky aquifer indiciated that the leakage has little impact on the drawdowns at the early times. As the pumping time increases, the drawdowns in the main aquifer become larger, which leads to greater difference between the hydraulic head in the main aquifer and that in the adjacent aquifer. Therefore, the leakage becomes larger. In addition, a larger hydraulic conductivity of the aquitard leads to a larger leakage, so the drawdown in the main aquifer is smaller.(5) The pumping rate mainly comes from the water storage inside the well for a larger-diameter PPW. Thus, a late response of the aquifer was found for groundwater flow to a larger-diameter PPW. It was found that the wellbore storage effect only exsist at the early times, and a larger well radius means a greater wellbore storage effect leads to a smaller drawdown at early times and the late response of the aquifer becomes more evident. An analysis of impact of the wellbore storage on the drawdowns for different n values indicated that the drawdown at quasi-steady state and time lag become smaller when n is larger。(6) The results of the two-region non-Darcian flow model indicated that the drawdown in the non-Darcian region is larger than that of the full non-Darcian flow model at late times. The drawdown in the Darcian flow region is larger than that of the full Darcian flow model at early times.