Transient Solutions to Groundwater Mounding in Bounded and Unbounded Aquifers

Abstract

In this study, the well-known Hantush solution procedure for groundwater mounding under infinitely long infiltration strips is extended to finite and semi-infinite aquifer cases. Initially, the solution for infinite aquifers is presented and compared to those available in literature and to the numerical results of MODFLOW. For the finite aquifer case, the method of images, which is commonly used in well hydraulics, is used to be able to represent the constant-head boundaries at both sides. It is shown that a finite number of images is enough to obtain the results and sustain the steady state. The effect of parameters on the growth of the mound and on the time required to reach the steady state is investigated. The semi-infinite aquifer case is emphasized because the growth of the mound is not symmetric. As the constant-head boundary limits the growth, the unbounded side grows continuously. For this reason, the groundwater divide shifts toward the unbounded side. An iterative solution procedure is proposed. To perform the necessary computations a code was written in Visual Basic of which the algorithm is presented. The proposed methodology has a wide range of applicability and this is demonstrated using two practical examples. The first one is mounding under a stormwater dispersion trench in an infinite aquifer and the other is infiltration from a flood control channel into a semi-infinite aquifer. Results fit very well with those of MODFLOW.

Estimating Groundwater Mounding in Sloping Aquifers for Managed Aquifer Recharge

“…The absolute difference commonly reduces with distance away from the recharge source, thereby further improving quality of estimates. Various numerical revisions of linearization (e.g., Korkmaz ) have not challenged the validity of previous research. For example, numerical experiments found that for flow perturbations s max / h 0 = 1, the relative difference between analytical and numerical results is on the order of 5%, and is under 14% for s max / h 0 = 2 (Bansal et al , Tables 4 and 5, respectively).…”

Simulation of Groundwater Level in Ephemeral Streams with an Improved Groundwater Hydraulics Model

“…The vertical cross section of the flow system under consideration is shown in Figure 2. The water level is initially horizontal with a depth of h 0 from the bedrock and is subject to recharge from an infinite strip of width 2 L. The following assumptions are made about the flow in the aquifer (Hantush 1967;Oritz et al 1978;Basak 1979;Rao and Sarma 1984;Serrano and Workman 1998;Rai et al 2001;Korkmaz 2013).…”

“…To evaluate the accuracy, we compare the GH solution of the 1-D Boussinesq equation with the solutions obtained by other researchers. Figure 3 shows a comparison of the GH solution (Equation 16) results with those of Rai's solution (Rai et al 2001) ( Figure 3A) and Korkmaz's solution (Korkmaz 2013) ( Figure 3B). The fitting results for the groundwater level change (h − h 0 ) are without obvious deviations at different time scales.…”

“…In the past half century, researchers have developed both analytical and numerical methods for determining the groundwater peaks during artificial recharge and the subsequent decreases after infiltration has stopped (Hantush 1967;Singh 2012;Chipongo and Khiadani 2015). Many studies have used linearized solutions of the Boussinesq equation to calculate the water table fluctuations in response to recharge from ephemeral streams (Oritz et al 1978;Basak 1979;Rao and Sarma 1984;Serrano and Workman 1998;Rai et al 2001;Korkmaz 2013). However, most published studies use data from a single event to simulate transient conditions over a short recharge period, and systematic and multiyear observations of groundwater dynamics in ephemeral stream catchments are very rare (Shentsis and Rosenthal 2003;Carling et al 2012;Chipongo and Khiadani 2015;Cuthbert et al 2016).…”

Estimating stream filtration from a meandering stream under the Robin condition

“…Analytical solutions based on the image well theory are reviewed below. Korkmaz [2013] developed an analytical solution describing a spatiotemporal groundwater mound subject to regional recharge between two Dirichlet boundaries. The derivation of the solution was based on the application of the method of images and Hantush [1967] solution.…”