Two‐region flow caused by pumping at a partial penetration well in a leaky confined aquifer

Abstract

An analytical model for depicting two‐region flow caused by constant‐rate pumping at a partially penetrating well in a leaky confined aquifer is established. The two‐region flow is described by the radial Izbash non‐Darcy flow in the vicinity of the abstraction well and Darcy flow away from the abstraction well in the pumped aquifer. The model considers the effects of aquitard storage, wellbore storage, and wellbore skin. The semi‐analytical solutions of drawdown are developed by means of a linearization procedure combined with Laplace transform and separation of variables. The time‐domain drawdowns are then obtained by using the Stehfest method for numerical Laplace inversion. The solutions encompass previous solutions for one or two‐region flow to a partially penetrating well in a (non‐)leaky confined aquifer. The drawdown response in the abstraction well, non‐Darcy region, and Darcy region is investigated, and sensitivity analysis is made to assess the impact of various controlling parameters. The results demonstrate that the intermediate and late‐stage drawdowns in the abstraction well and non‐Darcy region for the two‐region flow model are larger than the corresponding values for the non‐Darcy flow model. The drawdown in the Darcy region for the two‐region flow model is larger than that for the Darcy flow model throughout the pumping duration. The results of sensitivity analysis show that the drawdowns in the abstraction well, non‐Darcy region, and Darcy region are most sensitive to the non‐Darcy constant n, and is very sensitive to the well configuration, and horizontal hydraulic conductivity of the Darcy region.

A fractional Darcian model‐based analytical solution for non‐Darcian flow toward a fully penetrating well in a confined aquifer

“…The following parameters are used in this scenario: Q = 50 m 3 /h, α = 0.6, k = 0.1 m/h, S = 0.001 m −1 , b = 20 m, and r = 5 m. Similar parameter values are normally found in many previous studies. 11,13,[17][18][19]32 It can be observed in Figure 2 that the proposed analytical solution in Equation ( 22) corresponds very well with the results of Sen 11 and Wen et al 13 at late times, and becomes less accurate at early times. Such similar features were also found in aforementioned studies.…”

“…13,17,34,36,37 Also, a considerable number of studies with such similar features have proven that the error at early times might be acceptable under some circumstance particularly for the relatively large pumping time. 13,[17][18][19]32,34,36,37 Thus, the fractional Darcian model-based analytical solution in this study can be applied to describe the behavior of non-Darcian flow toward a fully penetrating well in a confined aquifer.…”

“…Following these two equations, a variety of (approximate or semi) analytical solutions are presented for non-Darcian flow toward a fully or partially penetrating well in different aquifer systems. [11][12][13][14][15][16][17][18][19] Quite a number of the Forchheimer equation-based analytical solutions for characterizing non-Darcian flow toward wells in various aquifer systems are available in many studies. [20][21][22][23] For instance, Sen presented an analytical solution for describing non-Darcian flow toward large-diameter wells in confined aquifers based on the Forchheimer equation.…”

“…18 An analytical solution for describing the Izbash type non-Darcian flow to a fully penetrating well in a confined aquifer was presented by Feng et al 38 Feng and Zhan proposed an analytical model for depicting two-region flow described using the radial Izbash non-Darcian flow at a partially penetrating well in a leaky aquifer, taking into account the effects of aquitard storage, wellbore storage, and wellbore skin. 19 In addition to analytical solutions, a few Izbash's equation-based numerical solutions have also been developed in the literature. 29,[39][40][41][42] However, it should be pointed out that the Forchheimer and I zbash equations used in the above-mentioned studies for describing non-Darcian flow have a more or less empirical nature.…”

“…To be the best of our knowledge, many efforts have been made to develop the Forchheimer equation and the Izbash equation based (approximate or semi) analytical solutions for describing non-Darcian flow characteristics toward fully or partially penetrating wells in various aquifer systems for few decades, [11][12][13]17,19,23,26,27,31,32 while no analytical solution has so far considered non-Darcian flow described by the fractional Darcian model in a confined aquifer with a fully penetrating well. Therefore, this work makes the attempt to introduce the fractional Darcian model for describing non-Darcian flow toward a fully penetrating well in a confined aquifer instead of the Forchheimer equation and the Izbash equation.…”