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USGS NAWQA Transport of Anthropogenic and Natural Contaminants to Supply Wells Study

Two-Component Mixing Equation for Investigating Sources of Recharge for a Well


Relatively simple mixing equations can be used to estimate the proportions of two or more waters that combine in a well, provided that different parts of the aquifer system tapped by the well contain groundwater with distinct concentrations or ratios of conservative constituents. A two-component mixing equation (binary mixing model) and example calculation for a study area in Nebraska are given below. (For more complex mixtures, a computer program such as the USGS program PHREEQC (Parkhurst and Appelo, 1999) might be needed to resolve the mixture.)

A simple mixing equation (binary mixing model)

X1 = (Cmix - C2) / (C1 - C2) * 100

  • Where:
  • X1 is the proportion of end-member 1 in the mixture (in percent)
  • C1 is concentration of end-member 1
  • C2 is concentration of end-member 2
  • Cmix is concentration of the water mixture
  • Cmix
  • C1
  • C2
  • Result (X1):


As an example, for the Nebraska study area, mixing fractions for the public-supply well were calculated using deuterium (2H) values from multiple parts of the groundwater-flow system. End-member 1 represented water from the shallow unconfined aquifer, and end-member 2 represented water from the confined aquifer. Average values from monitoring well samples in each aquifer were used as endmember concentrations (-56.89 for water from the shallow, unconfined aquifer and -77.40 for unmixed water from the confined aquifer). The water mixture (the public-supply wellhead samples) had an average deuterium concentration of -74.97. Results from the mixing calculation indicated that 12 percent of the public- supply wellhead sample was composed of water from the unconfined aquifer.

Once the mixture of waters captured by a public-supply well has been estimated, the maximum concentration of a chemical constituent in the water from the well can be computed. For example, the maximum chloride concentrations for the unconfined and confined aquifers in the Nebraska study area were 187 mg/L and 32 mg/L, respectively. Using these data and assuming that the water from the unconfined aquifer constitutes 12 percent of the mixture, the maximum future chloride concentration in water from the public-supply well will be about 50 mg/L if conditions remain unchanged.

More information:
USGS Circular 1385 (Eberts & others), pg. 111

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URL: http://oh.water.usgs.gov/tanc/NAWQATANC.htm
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Page Last Modified: Tuesday, 22-Sep-2015 14:26:28 EDT