Particle-Tracking Analysis of Contributing Areas of Public-Supply Wells in Simple and Complex Flow Systems, Cape Cod, Massachusetts

U.S. Geological Survey, Water-Supply Paper 2434

Paul M. Barlow

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Steady-state, two-and three-dimensional, finite-difference ground-water-flow models coupled with particle tracking were evaluated to determine their effectiveness in delineating contributing areasofexisting and hypothetical public-supply wells pumping from two different flow systems of Cape Cod, Mass. The flow systems represent the range of hydrogeologic complexityofflow systems of Cape Cod and are typical of shallow, highly permeable stratified-drift aquifers. The first flow system (the simple flow system) consists of a thin (up to 100 feet thick), single-layer aquifer with near-ideal boundary conditions and no large-capacity public-supply wells. The second flow system (the complex flow system) consists of a thick (approximately 250-500 feet), multilayered aquifer with nonideal boundary conditions (including streams, ponds, and spatial variability of recharge rates) from which 32 partially penetrating public-supply wells currently (1987) pump water. Analytical methods previously used to delineate contributing areas to wells of Cape Cod were found to be incapable of accounting for all of the hydrogeologic and well-design characteristics that affect the delineation of contributing areas, including spatial variability of recharge, aquifer heterogeneity, nonideal boundary conditions, and multiple, partially penetrating supply wells.

Results of the investigation indicate that the choice of either a two- or a three-dimensional model for delineation of contributing areas depends largely on the complexity of the flow system tapped by the well. Contributing areas delineated for hypothetical wells in the simple flow system were not significantly different for the two- or three-dimensional models of the natural system at pumping rates greater than or equal to 0.25 million gallons per day. For this relatively thin, single-layer aquifer with near-ideal boundary conditions, the use of a three-dimensional model to delineate contributing areas of supply wells may not be warranted. Several of the contributing areas delineated by use of the three-dimensional model of the complex flow system and by use of the three-dimensional model of the simple flow system for hypothetical conditions, however, did not conform to simple ellipsoidal shapes that are typically delineated by use of two-dimensional analytical and numerical modeling techniques, included discontinuous areas of the water table, and did not surround the wells. Because two-dimensional areal models do not account for vertical flow, they cannot adequately represent many of the hydrogeologic and well-design characteristics that were shown to complicate the delineation of contributing areas in these systems, including the presence and continuity of discrete lenses of low hydraulic conductivity, ratios of horizontal to vertical hydraulic conductivity greater than the stratified-drift aquifers, shallow streams, partially penetrating supply wells, low (less than about 0.1 Mgal/d) pumping rates, and spatial variability of recharge rates. Under these conditions, accurate delineation of contributing areas may require the use of a three-dimensional model.

Particle tracking helped identify the source of water to simulated wells. In the simple flow system, precipitation recharge was the only source of water to the wells. The size of the contributing area of each well in this flow system is equal to the pumping rate of the well divided by the uniform recharge rate to the aquifer within the contributing areas of the wells. In the complex flow system, precipitation recharge, wastewater return flow, and pond throughflow were the predominant sources of water to the wells. Pond throughflow and wastewater return flow accounted for up to 73 and 40 percent of well discharge, respectively. Contributing areas in the complex flow system are not linearly related to the pumping rate at each well because of the inclusion of ponds and pond contributing areas within the contributing areas to wells, and because recharge rates to the aquifer are spatially variable. Elevated nitrate (as nitrogen) concentrations, an indicator of contamination from septic systems and wastewater-treatment facilities, were found in wells for which estimates of the volume of captured wastewater were large; this pattern indicates a correlation between the quality of water discharged by the wells and the simulated source of water to the wells.

Although particle tracking was shown to be of value in the delineation of contributing areas in simple and complex flow systems, the method requires a large amount of data, which must be collected and analyzed, especially for three-dimensional simulations. In addition, several limitations of the method affect the accuracy with which a contributing area can be defined. These limitations include those caused by uncertainty in the definition of boundary conditions, stresses, and model parameters; limitations caused by discretization of the flow system by a finite-difference grid; and limitations in the data base used for model calibration. Contributing areas of several wells in the complex flow system were affected by the scale of discretization used to represent internal boundary sinks (such as wells, streams, and lakes). Internal boundary sinks affected contributing areas delineated by use of the two-dimensional model more than those delineated by use of the three-dimensional model because the single-layer model does not adequately represent the vertical location of the screened interval of supply wells or the location of shallow streams and lakes. Nevertheless, accurate flow simulation coupled with particle tracking provides a technically rigorous and defensible means of delineating contributing areas of supply wells for the purpose of wellhead protection.

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