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Scientific Investigations Report 2009–5205

Prepared in cooperation with the city of Rapid City

Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units in the Rapid City Area, South Dakota

By Larry D. Putnam and Andrew J. Long

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The city of Rapid City and other water users in the Rapid City area obtain water supplies from the Minnelusa and Madison aquifers, which are contained in the Minnelusa and Madison hydrogeologic units. A numerical groundwater-flow model of the Minnelusa and Madison hydrogeologic units in the Rapid City area was developed to synthesize estimates of water-budget components and hydraulic properties, and to provide a tool to analyze the effect of additional stress on water-level altitudes within the aquifers and on discharge to springs. This report, prepared in cooperation with the city of Rapid City, documents a numerical groundwater-flow model of the Minnelusa and Madison hydrogeologic units for the 1,000-square-mile study area that includes Rapid City and the surrounding area.

Water-table conditions generally exist in outcrop areas of the Minnelusa and Madison hydrogeologic units, which form generally concentric rings that surround the Precambrian core of the uplifted Black Hills. Confined conditions exist east of the water-table areas in the study area.

The Minnelusa hydrogeologic unit is 375 to 800 feet (ft) thick in the study area with the more permeable upper part containing predominantly sandstone and the less permeable lower part containing more shale and limestone than the upper part. Shale units in the lower part generally impede flow between the Minnelusa hydrogeologic unit and the underlying Madison hydrogeologic unit; however, fracturing and weathering may result in hydraulic connections in some areas. The Madison hydrogeologic unit is composed of limestone and dolomite that is about 250 to 610 ft thick in the study area, and the upper part contains substantial secondary permeability from solution openings and fractures. Recharge to the Minnelusa and Madison hydrogeologic units is from streamflow loss where streams cross the outcrop and from infiltration of precipitation on the outcrops (areal recharge).

MODFLOW–2000, a finite-difference groundwater-flow model, was used to simulate flow in the Minnelusa and Madison hydrogeologic units with five layers. Layer 1 represented the fractured sandstone layers in the upper 250 ft of the Minnelusa hydrogeologic unit, and layer 2 represented the lower part of the Minnelusa hydrogeologic unit. Layer 3 represented the upper 150 ft of the Madison hydrogeologic unit, and layer 4 represented the less permeable lower part. Layer 5 represented an approximation of the underlying Deadwood aquifer to simulate upward flow to the Madison hydrogeologic unit. The finite-difference grid, oriented 23 degrees counterclockwise, included 221 rows and 169 columns with a square cell size of 492.1 ft in the detailed study area that surrounded Rapid City. The northern and southern boundaries for layers 1–4 were represented as no-flow boundaries, and the boundary on the east was represented with head-dependent flow cells. Streamflow recharge was represented with specified-flow cells, and areal recharge to layers 1–4 was represented with a specified-flux boundary. Calibration of the model was accomplished by two simulations: (1) steady-state simulation of average conditions for water years 1988–97 and (2) transient simulations of water years 1988–97 divided into twenty 6-month stress periods.

Flow-system components represented in the model include recharge, discharge, and hydraulic properties. The steady-state streamflow recharge rate was 42.2 cubic feet per second (ft3/s), and transient streamflow recharge rates ranged from 14.1 to 102.2 ft3/s. The steady-state areal recharge rate was 20.9 ft3/s, and transient areal recharge rates ranged from 1.1 to 98.4 ft3/s. The upward flow rate from the Deadwood aquifer to the Madison hydrogeologic unit was 6.3 ft3/s. Discharge included springflow, water use, flow to overlying units, and regional outflow. The estimated steady-state springflow of 32.8 ft3/s from seven springs was similar to the simulated springflow of 31.6 ft3/s, which included 20.5 ft3/s from Jackson-Cleghorn Springs. Simulated transient springflow ranged from 25.7 to 42.3 ft3/s. Steady-state water-use rates for the Minnelusa and Madison hydrogeologic units were 3.4 and 6.7 ft3/s, respectively. Total transient water-use rates ranged from 3.4 to 19.1 ft3/s. Flow from the Minnelusa hydrogeologic unit to overlying units was 2.0 ft3/s. Steady-state and transient regional outflows from the Minnelusa and Madison hydrogeologic units were 12.9 and 12.8 ft3/s, respectively.

Linear regression of the 252 simulated and observed hydraulic head values for the steady-state simulation had a coefficient of determination (R2 value) of 0.92 with an average absolute difference of 37.6 ft. For the transient simulation, the average absolute difference between simulated and observed hydraulic head values for 19 observation wells ranged from 3.5 to 65.1 ft with a median value of 18.3 ft.

Calibrated horizontal hydraulic conductivity values for model layer 1 ranged from 1.0 to 5.2 feet per day (ft/d). Horizontal hydraulic conductivity values for model layer 3 ranged from 0.1 to 388.8 ft/d. Horizontal hydraulic conductivity for layers 2 and 4 were 10 percent of hydraulic conductivity values for layers 1 and layer 3, respectively, except near the outcrop where it was 50 percent of the values for layers 1 and 3, respectively. Vertical hydraulic conductivity for layers 1, 3, 4, and 5 was 10 percent of the respective horizontal hydraulic conductivity for those layers. Vertical hydraulic conductivity for layer 2 ranged from 0.000001 to 0.25 ft/d. Conductance for head-dependent cells representing springs ranged from 3,000 to 86,400 feet squared per day.

Simulation of increased hypothetical pumping of more than about 10 ft3/s may require modification of the boundaries to allow flow into the model. The model is limited by simplifying assumptions necessary to represent material having secondary porosity as a porous media. With additional data, further refinement of the model would be possible, which could improve the accuracy of model estimates of the effects of additional stresses on the system, such as increased withdrawals or drought. The model can yield simulations of future conditions, which can guide management decisions and planning. The model provides a useful tool for general characterization of the effects of stresses and management alternatives on a regional basis.

Posted October 20, 2009

For additional information contact:
Director, USGS South Dakota Water Science Center
1608 Mt. View Rd.
Rapid City, SD 57702
(605) 394–3200

Part or all of this report is presented in Portable Document Format (PDF); the latest version of Adobe Reader or similar software is required to view it. Download the latest version of Adobe Reader, free of charge.

Suggested citation:

Putnam, L.D., and Long, A.J., 2009, Numerical groundwater-flow model of the Minnelusa and Madison hydrogeologic units in the Rapid City area, South Dakota: U.S Geological Survey Scientific Investigations Report 2009–5205, 81 p.




Description of Study Area

Numerical Groundwater-Flow Model

Response to Stress

Model Limitations


References Cited

Supplemental Information

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