Groundwater flow to a pumping well in a sloping fault zone unconfined aquifer

Abstract

This study develops a mathematical model for simulating the hydraulic head distribution in response to pumping in a sloping fault zone aquifer under a water table boundary condition. A twodimensional equation with a sink term representing the pumping is used for describing the head distribution in the aquifer. In addition, a first-order free surface equation is adopted to represent the change in water table at the outcrop. The analytical solution of the model, derived by the Laplace and finite Fourier cosine transforms, is expressed in terms of a double series. A finite difference solution within a deformable grid framework is developed to assess the solution obtained by specifying the free surface equation at the outcrop. Based on the analytical solution, we have found that the model's prediction tends to overestimate drawdown in a late pumping period. The temporal head distribution is independent of the aquifer slope if the water table change is small, and exhibits a double-humped shape due to the effect of the free surface. The temporal drawdown predicted from the analytical solution is further compared with those measured from a pumping test conducted in northern Portugal.

Analytical solutions of seawater intrusion in sloping confined and unconfined coastal aquifers

“…In fact, the topic of flow in a sloping aquifer has long been investigated [e.g., Henderson and Wooding, 1964;Huang et al, 2014]. Steady state solutions of the nonlinear Boussinesq equation for homogeneous unconfined flow in sloping aquifers with recharge have been derived analytically by McEnroe [1993], Verhoest and Troch [2000], Chapuis [2002], and Lo aiciga [2005].…”

Solutions for Groundwater Flow to a Pumping Well with an Exponentially Decreasing Variable‐Rate in a Sloping Aquifer

“…Comparison of the drawdown distribution versus time presented by our numerical solution and the solution of Huang et al (2014) with field data reported by Antonio and Pacheco (2002). …”

“…Generally, the upper boundary condition at the outcrop can be regarded as an infiltration curve which is treated as a boundary with recharge. Therefore, as shown in the study of Huang et al (2014), the outcrop boundary can be characterized by the free surface equation (similar to the water table), which can be expressed as: $$$$ K\frac{\partial s}{\partial z}=-{S}_y\frac{\partial s}{\partial t},z=W\sin \theta -s\ \mathrm{and}\ {x}_0\le x\le {x}_r, $$$$ where S y [−] represents the specific yield, W [L] represents the total length of the aquifer, $$$ {x}_0=W\cos \theta -B/\left(\sin \theta \right) $$$, representing the location of the pumping well in the x ‐direction. $$$ {x}_r=W\cos \theta $$$, representing the location of the outcrop in the x ‐direction.…”

“…Similarly, the values of K and S s at E5 were chosen as 0.009 m/d and 5.6 × 10 −7 1/m, respectively. Considering that the pumping test was conducted in a fracture zone aquifer, the actual value of the specific yield ( Sy ) was set to a small scale (i.e., Sy = 0.01), as Huang et al (2014) reported.…”

“…The numerical solution (finite difference code), on the other hand, was developed using MATLAB software considering the water table movement at the outcrop of the surface as well as wellbore storage. Both solutions were compared with the solution of Huang et al (2014). The behavior of the drawdown relative to pumping rate was elucidated.…”