Search

Regional groundwater flow systems often contain both strong sinks and weak sinks. A strong sink extracts water from the entire aquifer depth, while a weak sink lets some water pass underneath or over the actual sink. The numerical groundwater flow model MODFLOW may allow a sink cell to act as a strong or weak sink, hence extracting all water that enters the cell or allowing some of that water to pass. A physical strong sink can be modeled by either a strong sink cell or a weak sink cell, with the latter generally occurring in low-resolution models. Likewise, a physical weak sink may also be represented by either type of sink cell. The representation of weak sinks in the particle tracing code MODPATH is more equivocal than in MODFLOW. With the appropriate parameterization of MODPATH, particle traces and their associated travel times to weak sink streams can be modeled with adequate accuracy, even in single layer models. Weak sink well cells, on the other hand, require special measures as proposed in the literature to generate correct particle traces and individual travel times and hence capture zones. We found that the transit time distributions for well water generally do not require special measures provided aquifer properties are locally homogeneous and the well draws water from the entire aquifer depth, an important observation for determining the response of a well to non-point contaminant inputs. [ABSTRACT FROM AUTHOR]

Regional finite-difference models tend to have large cell sizes, often on the order of 1–2 km on a side. Although the regional flow patterns in deeper formations may be adequately represented by such a model, the intricate surface water and groundwater interactions in the shallower layers are not. Several stream reaches and nearby wells may occur in a single cell, precluding any meaningful modeling of the surface water and groundwater interactions between the individual features. We propose to replace the upper MODFLOW layer or layers, in which the surface water and groundwater interactions occur, by an analytic element model (GFLOW) that does not employ a model grid; instead, it represents wells and surface waters directly by the use of point-sinks and line-sinks. For many practical cases it suffices to provide GFLOW with the vertical leakage rates calculated in the original coarse MODFLOW model in order to obtain a good representation of surface water and groundwater interactions. However, when the combined transmissivities in the deeper (MODFLOW) layers dominate, the accuracy of the GFLOW solution diminishes. For those cases, an iterative coupling procedure, whereby the leakages between the GFLOW and MODFLOW model are updated, appreciably improves the overall solution, albeit at considerable computational cost. The coupled GFLOW–MODFLOW model is applicable to relatively large areas, in many cases to the entire model domain, thus forming an attractive alternative to local grid refinement or inset models. [ABSTRACT FROM AUTHOR]

Regional finite-difference models often have cell sizes that are too large to sufficiently model well-stream interactions. Here, a steady-state hybrid model is applied whereby the upper layer or layers of a coarse MODFLOW model are replaced by the analytic element model GFLOW, which represents surface waters and wells as line and point sinks. The two models are coupled by transferring cell-by-cell leakage obtained from the original MODFLOW model to the bottom of the GFLOW model. A real-world test of the hybrid model approach is applied on a subdomain of an existing model of the Lake Michigan Basin. The original (coarse) MODFLOW model consists of six layers, the top four of which are aggregated into GFLOW as a single layer, while the bottom two layers remain part of MODFLOW in the hybrid model. The hybrid model and a refined "benchmark" MODFLOW model simulate similar baseflows. The hybrid and benchmark models also simulate similar baseflow reductions due to nearby pumping when the well is located within the layers represented by GFLOW. However, the benchmark model requires refinement of the model grid in the local area of interest, while the hybrid approach uses a gridless top layer and is thus unaffected by grid discretization errors. The hybrid approach is well suited to facilitate cost-effective retrofitting of existing coarse grid MODFLOW models commonly used for regional studies because it leverages the strengths of both finite-difference and analytic element methods for predictions in mildly heterogeneous systems that can be simulated with steady-state conditions., (© 2015, National Ground Water Association.)

Noxious weeds threaten the Sheyenne National Grassland (SNG) ecosystem and therefore herbicides have been used for control. To protect groundwater quality, the herbicide application is restricted to areas where the water table is less than 10 feet (3.05 m) below the ground surface in highly permeable soils, or less than 6 feet (1.83 m) below the ground surface in low permeable soils. A local MODFLOW model was extracted from a regional GFLOW analytic element model and used to develop depth-to-groundwater maps in the SNG that are representative for the particular time frame of herbicide applications. These maps are based on a modeled groundwater table and a digital elevation model (DEM). The accuracy of these depth-to-groundwater maps is enhanced by an artificial neural networks (ANNs) interpolation scheme that reduces residuals at 48 monitoring wells. The combination of groundwater modeling and ANN improved depth-to-groundwater maps, which in turn provided more informed decisions about where herbicides can or cannot be safely applied., (Published 2012. This article is a U.S. Government work and is in the public domain in the USA.)

Radial time-of-travel (TOT) capture zones have been evaluated for unconfined aquifers with and without recharge. The solutions of travel time for unconfined aquifers are rather complex and have been replaced with much simpler approximate solutions without significant loss of accuracy in most practical cases. The current "volumetric method" for calculating the radius of a TOT capture zone assumes no recharge and a constant aquifer thickness. It was found that for unconfined aquifers without recharge, the volumetric method leads to a smaller and less protective wellhead protection zone when ignoring drawdowns. However, if the saturated thickness near the well is used in the volumetric method a larger more protective TOT capture zone is obtained. The same is true when the volumetric method is used in the presence of recharge. However, for that case it leads to unreasonableness over the prediction of a TOT capture zone of 5 years or more., (© 2011, The Author(s). Ground Water © 2011, National Ground Water Association.)

Horizontal wells or radial collector wells are used in shallow aquifers to enhance water withdrawal rates. Groundwater flow patterns near these wells are three-dimensional (3D), but difficult to represent in a 3D numerical model because of the high degree of grid refinement needed. However, for the purpose of designing water withdrawal systems, it is sufficient to obtain the correct production rate of these wells for a given drawdown. We developed a Cauchy boundary condition along a horizontal well in a Dupuit-Forchheimer model. Such a steady-state 2D model is not only useful for predicting groundwater withdrawal rates but also for capture zone delineation in the context of source water protection. A comparison of our Dupuit-Forchheimer model for a radial collector well with a 3D model yields a nearly exact production rate. Particular attention is given to horizontal wells that extend underneath a river. A comparison of our approach with a 3D solution for this case yields satisfactory results, at least for moderate-to-large river bottom resistances., (Copyright © 2010 The Author(s). Journal compilation © 2010 National Ground Water Association.)

Most ground water modeling courses focus on the use of computer models and pay little or no attention to traditional analytic solutions to ground water flow problems. This shift in education seems logical. Why waste time to learn about the method of images, or why study analytic solutions to one-dimensional or radial flow problems? Computer models solve much more realistic problems and offer sophisticated graphical output, such as contour plots of potentiometric levels and ground water path lines. However, analytic solutions to elementary ground water flow problems do have something to offer over computer models: insight. For instance, an analytic one-dimensional or radial flow solution, in terms of a mathematical expression, may reveal which parameters affect the success of calibrating a computer model and what to expect when changing parameter values. Similarly, solutions for periodic forcing of one-dimensional or radial flow systems have resulted in a simple decision criterion to assess whether or not transient flow modeling is needed. Basic water balance calculations may offer a useful check on computer-generated capture zones for wellhead protection or aquifer remediation. An easily calculated "characteristic leakage length" provides critical insight into surface water and ground water interactions and flow in multi-aquifer systems. The list goes on. Familiarity with elementary analytic solutions and the capability of performing some simple hand calculations can promote appropriate (computer) modeling techniques, avoids unnecessary complexity, improves reliability, and is likely to save time and money. Training in basic hand calculations should be an important part of the curriculum of ground water modeling courses.

As part of its Wellhead Protection Program, the U.S. EPA mandates the delineation of "time-of-travel capture zones" as the basis for the definition of wellhead protection zones surrounding drinking water production wells. Depending on circumstances the capture zones may be determined using methods that range from simply drawing a circle around the well to sophisticated ground water flow and transport modeling. The simpler methods are attractive when faced with the delineation of hundreds or thousands of capture zones for small public drinking water supply wells. On the other hand, a circular capture zone may not be adequate in the presence of an ambient ground water flow regime. A dimensionless time-of-travel parameter T is used to determine when calculated fixed-radius capture zones can be used for drinking water production wells. The parameter incorporates aquifer properties, the magnitude of the ambient ground water flow field, and the travel time criterion for the time-of-travel capture zone. In the absence of interfering flow features, three different simple capture zones can be used depending on the value of T . A modified calculated fixed-radius capture zone proves protective when T < 0.1, while a more elongated capture zone must be used when T > 1. For values of T between 0.1 and 1, a circular capture zone can be used that is eccentric with respect to the well. Finally, calculating T allows for a quick assessment of the validity of circular capture zones without redoing the delineation with a computer model.

Contaminant transport models often use a velocity field derived from a MODFLOW flow field. Consequently, the accuracy of MODFLOW in representing a ground water flow field determines in part the accuracy of the transport predictions, particularly when advective transport is dominant. We compared MODFLOW ground water flow rates and MODPATH particle traces (advective transport) for a variety of conceptual models and different grid spacings to exact or approximate analytic solutions. All of our numerical experiments concerned flow in a single confined or semiconfined aquifer. While MODFLOW appeared robust in terms of both local and global water balance, we found that ground water flow rates, particle traces, and associated ground water travel times are accurate only when sufficiently small cells are used. For instance, a minimum of four or five cells are required to accurately model total ground water inflow in tributaries or other narrow surface water bodies that end inside the model domain. Also, about 50 cells are needed to represent zones of differing transmissivities or an incorrect flow field and (locally) inaccurate ground water travel times may result. Finally, to adequately represent leakage through aquitards or through the bottom of surface water bodies it was found that the maximum allowable cell dimensions should not exceed a characteristic leakage length lambda, which is defined as the square root of the aquifer transmissivity times the resistance of the aquitard or stream bottom. In some cases a cell size of one-tenth of lambda is necessary to obtain accurate results.