Daniel B. Abrams

Modeling Flow into Horizontal Wells in a Dupuit-Forchheimer Model

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.

Predicting Redox Conditions in Groundwater at a Regional Scale.

Defining the oxic-suboxic interface is often critical for determining pathways for nitrate transport in groundwater and to streams at the local scale. Defining this interface on a regional scale is complicated by the spatial variability of reaction rates. The probability of oxic groundwater in the Chesapeake Bay watershed was predicted by relating dissolved O2 concentrations in groundwater samples to indicators of residence time and/or electron donor availability using logistic regression. Variables that describe surficial geology, position in the flow system, and soil drainage were important predictors of oxic water. The probability of encountering oxic groundwater at a 30 m depth and the depth to the bottom of the oxic layer were predicted for the Chesapeake Bay watershed. The influence of depth to the bottom of the oxic layer on stream nitrate concentrations and time lags (i.e., time period between land application of nitrogen and its effect on streams) are illustrated using model simulations for hypothetical basins. Regional maps of the probability of oxic groundwater should prove useful as indicators of groundwater susceptibility and stream susceptibility to contaminant sources derived from groundwater.

On Modeling Weak Sinks in MODPATH

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.

Correcting Transit Time Distributions in Coarse MODFLOW‐MODPATH Models

In low to medium resolution MODFLOW models, the area occupied by sink cells often far exceeds the surface area of the streams they represent. As a result, MODPATH will calculate inaccurate particle traces and transit times. A frequency distribution of transit times for a watershed will also be in error. Such a distribution is used to assess the long-term impact of nonpoint source pollution on surface waters and wells. Although the inaccuracies for individual particles can only be avoided by increased model grid resolution or other advanced modeling techniques, the frequency distribution can be improved by scaling the particle transit times by an adjustment factor during post-processing.

How Aquifer Characteristics of a Watershed Affect Transit Time Distributions of Groundwater: D. Abrams and H. Haitjema Groundwater x, no. x: x-xx

Transit time distributions (TTDs) have a number of applications in the hydrologic sciences. Our work aligns with the group of researchers who use groundwater flow models to assess the transit time distribution of groundwater, not considering the other components of flow that comprise stream water (Kauffman et al., 2008; Sanford et al., 2012; Engdahl, 2017). If the input of a solute is ubiquitous over the watershed and known through time, then a convolution of the TTD and solute input yields the output concentration of groundwater discharging to a well or stream in the watershed over time (Małoszewski and Zuber, 1982).

Developing Potentiometric Surfaces and Flow Fields with a Head-Specified MODFLOW Model

Investigating changes in an aquifer system often involves comparison of observed heads from different synoptic measurements, generally with potentiometric surfaces developed by hand or a statistical approach. Alternatively, head-specified MODFLOW models, in which constant head cells simulate observed heads, generate gridded potentiometric surfaces that explicitly account for Darcys Law and mass balance. We developed a transient head-specified MODFLOW model for the stratified Cambrian-Ordovician sandstone aquifer system of northeastern Illinois to analyze flow within its 275 m deep cone of depression. Potentiometric surfaces were developed using static heads from production wells regardless of open interval; hence assuming no vertical head difference. This assumption was tested against steady-state, head-specified models of each sandstone strata for 1980 and 2014. The results indicate that the original conceptual model was appropriate in 1980 but not 2014, where a vertical head difference had developed at the center of the cone of depression. For earlier years, when the head difference was minimal, the transient head-specified model compared well with a traditional, flow-specified model. In later years, the transient head-specified model overestimated removal of water from storage. MODFLOW facilitates the development of a time-series of potentiometric surfaces and can easily be modified to test the impacts of different conceptual models, such as assumptions on vertical head differences. For this study of a deep confined aquifer, MODFLOW also offers advantages in generating potentiometric surfaces and flow fields over statistical interpolation techniques, although future research is needed to assess its performance in other settings.