# 4 Effects of Mixing on Groundwater Ages

Mixing of water can occur within aquifers and at the point of sampling, particularly if samples are pumped from wells with long intake zones. Because the components of any mixture are likely to have different ages (and hence different tracer concentrations), it is important to understand how mixing affects apparent age measured on the mixed sample.

The effect of mixing on tracer concentrations has already been discussed in Section 3.1. The effect of mixing on groundwater ages depends on the relationship between recharge time and tracer concentration. In the case of a tracer whose concentration decreases exponentially with age, the mean concentration of a mixed sample will not accurately reflect the mean age of the mixture but will be biased towards the younger components (Figure 46b). To illustrate this point, suppose two waters are mixed in equal proportions: one with an age of 1000 years and one with an age of 10,000 years. Clearly, the mean age of the water in this mixture is 5,500 years. However, the young water will have a ^{14}C activity of 88.6 pmC (assuming an initial activity of 100 pmC) and the old water will have a ^{14}C activity of 29.8 pmC (using Equation 1). The mixture will therefore have a ^{14}C activity of 59.2 pmC. The apparent age measured on a sample with this activity is 4,330 years, which is younger than the true (hydraulic) age of the mixture. In fact, the apparent age of any mixture will only accurately reflect the mean age of the mixed sample for tracers whose concentration is a linear function of age (Figure 46a). This is potentially the case with accumulating tracers such as helium, if the production rate of helium is spatially constant. It may also be the case for SF_{6}, whose atmospheric concentration has increased almost linearly with time since about 1980. However, for most other tracers, the apparent age of a mixed sample is unlikely to equal the mean age of the water in the mixture.

The magnitude of the effect of mixing on measured groundwater ages will vary depending on the extent of groundwater mixing and can sometimes be determined by comparing ages obtained from different tracers (Section 5.1). As groundwater mixing often affects different tracers in different ways, the extent to which different tracers indicate different ages is an indicator of the extent of mixing. Groundwater mixing during sampling can be minimized by collecting groundwater samples from wells with relatively short intake zones (i.e., screen lengths). In many cases, however, such piezometers are not available, and samples are collected from municipal, irrigation or mine wells, with very long screen intervals. In these cases, samples are mixed from various levels of the aquifer that produce water along the screened interval. This can be envisioned by considering the ages of water that would enter a long screen in Figure 14. In a homogeneous unconfined aquifer, the extent of mixing caused by long-screened wells can be estimated from the ratio of the screen length to the vertical water velocity as shown in Equation 13.

(13) |

where:

t_{mix} |
= | extent of well mixing (measured in years) (T) |

R |
= | aquifer recharge rate (L/T) |

θ |
= | Porosity (dimensionless) |

z_{well} |
= | length of the well intake zone (L) |

Thus, for example, if the aquifer porosity is 0.4 and the recharge rate is 100 mm/y, then a 2 m long well screen will mix water over an age range of approximately 8 years. Therefore, if the well is screened immediately below the water table, the water at the top of the screen would have an age of zero, and the water at the bottom of the screen would have an age of 8 years. In comparison, a well with a 20 m well screen would mix water over an age range of 80 years, which would severely limit the ability to determine groundwater ages within the last 100 years.