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Unformatted text preview: WTAQ Program (Barlow and Moench, 1999) includes analytical solutions for drawdown at a pumped well (or an observation well) for a variety of cases, including that of a partially penetrating pumped well. The WTAQ Program implements the Laplace-transform solution of Moench (1997) for flow in a water-table aquifer, a modified solution of Dougherty and Babu (1984) for flow to a partially penetrating well in a confined aquifer, and the Theis solution for flow to a fully penetrating well in a confined aquifer. The Laplace-transform solutions are numerically inverted to the time domain by means of the Stehfest (1970) algorithm (Barlow and Moench, 1999). The numerical solution for the first test was generated using one model layer to represent the 100-ft thick aquifer and an initial time step of 2.41×10-7 days, which was increased by a factor of 1.2 in each successive time step (requiring a total of 100 time steps to simulate a representative 100-day stress period). Because the cell where the pumping well is located has a grid spacing of 5 ft by 5 ft, the equivalent well radius (computed using eq. 6 of Halford and Hanson, 2002, p. 9) is ro = 0.99 ft. Thus, the analytical solution for the drawdown in the pumping well is based on a specified well radius of 0.99 ft to maximize comparability and eliminate the need to correct for any difference between the well radius and the effective radius of the cell (that is, LOSSTYPE = NONE). The MODFLOW numerical results show excellent agreement with equivalent analytical solutions (fig. 3) for the pumping well and for observation wells at various distances (r) from the pumping well. These results indicate that the numerical model of the hypothetical confined aquifer system is adequate to evaluate methods (described later in the report) to compute additional drawdown caused by partial penetration and other sources of well loss. Long, Unpumped Observation Well (Reilly Problem) Reilly and others (1989) used numerical experiments in a hypothetical ground-water system to demonstrate that appreciable wellbore flow can occur in observation wells screened through multiple layers, even in homogeneous aquifers having small vertical head differences (less than 0.01 ft between Model Features and Processes the top and bottom of the screen). Konikow and Hornberger (2006a,b) slightly modified this test problem to evaluate solute transport through a multi-node well. This same test problem (herein called the “Reilly” test problem) is used in this study to help evaluate the MNW2 Package. As described by Konikow and Hornberger (2006b), the hypothetical unconfined ground-water system represents regional flow that is predominantly lateral but includes some vertical components because of diffuse areal recharge [at a rate of 4.566×10-3 feet per day (ft/d)] and a constant-head boundary condition at the surface of the right side of the regional groundwater system that controls discharge (fig. 4). No-flow boundaries are on all other external boundaries. The system is substantially longer (10,000 ft) than it is thick (205 ft) or wide (200 ft); the width was selected to eliminate any important effect of the position of the lateral no-flow boundary on the solution in the area of the well. A nonpumping borehole with a 60-ft screen is located close to the no-flow boundary on left side of the system (252 ft from that boundary) (fig. 4). Other properties of the system and the model are listed in table 2. Reilly and others (1989) simulated the regional system with a two-dimensional crosssectional model, arguing that the width of the cross section was irrelevant for their analysis, and applied a local (approximately a 100-ft-by-100-ft area) three-dimensional flow model in the vicinity of the wellbore. Their local model was discretized vertically into 5-ft layers and used a variably spaced areal grid with a minimum spacing of about 0.33 ft by 0.33 ft around the borehole. They represented the borehole using a relatively high vertical hydraulic conductivity, the value of which was based on equivalence of Darcy’s law to the equation for laminar pipe flow (Reilly and others, 1989, p. 272). Konikow and Hornberger (2006a,b) simulated the regional flow system with a three-dimensional model with a domain 9 width sufficient to minimize any effects of that dimension on the flow field close to the borehole; they represented the borehole using the MNW Package (Halford and Hanson, 2002). Because a vertical plane of symmetry is present and passes through the well, they only simulated one-half of the domain outlined by Reilly and others (1989). The grid has a variable spacing (fig. 5). In the local area around the well, however, a relatively fine and uniform areal cell spacing of 2.5 ft by 2.5 ft was used. This finest part of the grid included 20 rows, 40 columns, and 41 layers of cells. Outside the uniformly spaced part of the grid, the lateral grid spacing was increased geometrically to a maximum spacing of 50.25 ft in the row (x) direction and 9.55 ft in the column (y) direction (fig. 5). The vertical discretization (Δz) was 5 ft everywhere in the model domain, and the top layer was...
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This document was uploaded on 01/20/2014.

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