3.3  Quantifying Groundwater Velocities in Confined Aquifers

Peter Cook

3.3 Quantifying Groundwater Velocities in Confined Aquifers

While groundwater ages in unconfined aquifers can be used to estimate vertical flow velocities and recharge rates, groundwater ages in confined aquifers enable estimation of horizontal groundwater flow velocities. Figure 22 shows the distribution of travel times in a simple confined aquifer of constant thickness. In the confined part of the aquifer, flow lines are horizontal, and groundwater age increases downgradient. The horizontal groundwater velocity (dx/dt) is the inverse of the horizontal age gradient (dt/dx). In practice, the horizontal groundwater velocity (v_h) is usually estimated as shown in Equation 12.

$\displaystyle v_h=\frac{x_2-x_1}{t_2-t_1}$

(12)

In Equation 12, t₁ and t₂ are groundwater ages at two points in the confined part of the aquifer and (x₂–x₁) is the distance between these points, measured in the direction of flow. It is apparent from Figure 22 that groundwater ages in the confined part of the aquifer also show an increase in age with depth. This vertical age gradient is created within the unconfined part of the aquifer and preserved as the water flows downgradient in the confined part of the aquifer. In many cases, though, the vertical age stratification within the confined part of the aquifer is much less than the horizontal increase in age. Thus, groundwater samples collected from confined aquifers often show an increase in age with distance downgradient, irrespective of the sampling depth.

Figure showing flow lines, equipotential lines and distribution of travel times in a homogeneous aquifer of constant thickness — **Figure 22 –** Flow lines (orange), equipotential lines (blue) and distribution of travel times (green) in a homogeneous aquifer of constant thickness, which is confined in the downstream part. Age increases with depth in the unconfined part of the aquifer, as indicated in Figure 14. Where the aquifer is confined, flow lines are horizontal, and travel times increase in the horizontal direction, as well as with depth. Values are not shown for equipotential lines or travel times because it is the shape of the lines, rather than their value that is important. The left and lower boundaries for the simulation are no flow, and the right boundary is constant head (After Cook and Solomon, 1997).

One of earliest studies that used radioactive ¹⁴C as a groundwater dating tool was an investigation into the rate of groundwater flow in the Carrizo-Wilcox aquifer (Figure 23) in south-central Texas (Pearson and White, 1967). The Carrizo-Wilcox aquifer is a confined aquifer that outcrops roughly 200 – 300 km inland from the coast of the Gulf of Mexico, and dips to the southeast (towards the coast) at an angle of 1 to 2 degrees. In northern Atascosa County, the aquifer outcrops on rolling hills as a band that is only 15 to 20 km wide. The thickness of the aquifer is approximately 200 m in the outcrop area but increases towards the southeast.

Water samples were collected for ¹⁴C and δ ¹³C analysis on dissolved carbonate. pH and alkalinity were also measured and used to calculate the total carbonate content and degree of saturation with respect to calcite. ¹⁴C values ranged from 77 pmC (percent modern Carbon; Table 1) in the outcrop area to background values (< 0.7 pmC) in the most downgradient samples. Total carbonate content was lowest (2.6 to 2.8 equivalents per million; epm) and δ ¹³C was most negative (-18.9 to -17.9 ‰) close to the outcrop area, with most downgradient samples having carbonate contents above 5 epm and δ ¹³C values between -8 and -12 ‰.

Comparison of total carbonate and δ ¹³C values indicated that most samples could be explained by dilution of ¹⁴C by dissolution of geologic layers of marine carbonate formations. However, some samples had high total carbonate concentrations, but did not have correspondingly enriched δ ¹³C values, indicating that some other process (perhaps dissolution of plant or petroleum-derived carbonate within aquifer materials) was affecting the carbonate chemistry. Therefore, the ¹⁴C values were corrected based on the ratio of the measured carbonate concentration to an assumed initial value. After correcting for dilution with geologic carbonate, ¹⁴C ages of groundwater increase from less than a few hundred years in the outcrop area to more than 20,000 years at distances greater than 40 km from the outcrop area (Figure 24). The mean groundwater velocity is therefore calculated to be approximately 2 m/y and is in good agreement with hydraulic calculations based on measured hydraulic heads, porosities and hydraulic conductivities.

Map showing location of the Carrizo-Wilcox aquifer in south-central Texas, USA — **Figure** 23 – Location of the Carrizo-Wilcox aquifer in south-central Texas, USA which was the focus of one of the earliest studies to use ¹⁴C to estimate groundwater flow rates (Figure 24). The area shown in Figure 24 is indicated by the blue rectangle on the aquifer map (Eckhardt, 2020).

**Figure** 24 – Carbon-14 ages of groundwater within the Carrizo-Wilcox aquifer, Texas. Blue lines represent approximate lines of equal groundwater age, estimated from contouring the measured age data. The inset shows the increase in age with distance from the outcrop area. Figure 23 for location of the Carrizo-Wilcox aquifer (After Pearson and White, 1967).

The value of combining different groundwater age tracers to cover the range of ages in large flow systems is illustrated in a study of the confined aquifers of the Atlantic Coastal Plain, Maryland, USA (Plummer et al., 2012). The Atlantic Coastal Plain (Figure 25) consists of a series of wedge-shaped unconsolidated sedimentary deposits that thicken in the direction of groundwater flow. Pumping has greatly changed the flow systems in these aquifers, and so wells were selected along two transects in the Upper Patapsco aquifer that were believed to follow pre-development flow lines. Samples were analyzed for ¹⁴C, ³⁶Cl and He, as well as several other environmental tracers.

Map showing location of the Northern Atlantic Coastal Plain Aquifer System, USA — **Figure** 25 – Location of the Northern Atlantic Coastal Plain Aquifer System, USA (shown in green on right image created by Trapp and Horn, 1997), which has been the focus of several groundwater studies. The red lines are the locations of north and south well transects used for groundwater-dating in the confined Upper Patapsco aquifer, and the blue circle is the location of the Locust Grove agricultural catchment. Data from the Locust Grove catchment is discussed in Sections 3.9 and 3.10.

¹⁴C concentrations were measurable only within the first 40 km of the flow system and decreased from 109 pmC near the outcrop area to below detection limit further downgradient (Figure 26). The piezometers with highest concentrations of ¹⁴C also contained measurable ³H and CFCs, confirming that the water was very young. The ³⁶Cl/Cl ratio also decreased downgradient, but measurable concentrations were observed for at least 80 km, due to the longer half-life of this tracer. ³⁶Cl ages in this part of the aquifer increased from 23,000 years to 328,000 years on the northern flow path and from 185,000 to 503,000 years on the southern flow path. The most downgradient sample (at 120 km) was close to background and appears to have an age of more than 2 million years. Helium concentrations increased from close to atmospheric values (negligible subsurface production) to more than 8 × 10^–⁶ cm³ STP/g furthest downgradient. The rate of increase in helium concentration with distance is consistent with the ages obtained from ¹⁴C and ³⁶Cl data, within the range of uncertainties of the He production rate.

Ages within the aquifer increase in a non-linear fashion, with flow rate significantly decreasing downgradient. This is consistent with an increase in aquifer thickness with distance in the wedge-shaped aquifer, and with a decreasing volume of flow as water leaks out through confining layers into overlying and underlying aquifers. The average groundwater velocity is estimated to be approximately 1 m/y in the upgradient parts of the aquifer (at about 10 km) and decreases to 0.13 m/y and 0.04 m/y at 40 km and 80 km downgradient, respectively.

Comparison of the <sup>14</sup>C activity of total dissolved inorganic carbon, values of the <sup>36</sup>Cl/Cl ratio, and radiogenic <sup>4</sup>He concentrations in groundwater along flow paths in the Upper Patapsco aquifer — **Figure** 26 – Comparison of the ¹⁴C activity of total dissolved inorganic carbon (TDIC), values of the ³⁶Cl/Cl ratio, and radiogenic ⁴He concentrations in groundwater along flow paths in the Upper Patapsco aquifer, Atlantic Coastal Plain, Maryland, USA. Data is from two flow lines, whose locations are shown in Figure 25, although this Figure combines data from the two flow lines (After Plummer et al., 2012).

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