AN INTEGRATED APPROACH IN EVALUATING ISOTOPE DATA OF THE NUBIAN SANDSTONE
3. RECHARGE, FLOW AND DISCHARGE OF THE GROUNDWATER
3.2. Evaluation of the 36 Cl and 81 Kr data
In comparison to 14C, the average 81Kr and 36Cl values in deep groundwater are in general insignifi cantly affected by small contributions of shallow (young) groundwater. Assuming for example that the proportion of young groundwater (initial ratio of 81Kr/Kr and 36Cl/Cl of 100%) is 4% in the bulk of deep groundwater with an average age of 200 kyr (81Kr/Kr of 54.6% and
36Cl/Cl of 63.1%), groundwater mixing would result in 81Kr/Kr of 56.8% and
36Cl/Cl of 64.5%, which corresponds to a shift of the apparent 81Kr and 36Cl ages to 187 kyr and 191 kyr, respectively. Thus, the shift of the apparent age is insignifi cant in comparison to 14C, which would result in a nearly ten times lower apparent age (25 kyr if a 14C initial content of 85 pMC is assumed).
The 81Kr and 36Cl groundwater ages of the NSAS in Egypt [6, 7] range from a few ten thousand years to about 1 million years. A good agreement has been found between the 81Kr and 36Cl ages of selected samples. Patterson et al. [7]
used a two-dimensional hydraulic model to discuss the dating results in terms of groundwater fl ow and replenishment in the aquifer system. The model assumes that the system is recharged by base fl ow through the southern boundary (at East Uweinat) and discharge occurs through the northern boundary north of Bahariya oasis. Thus, the model ignores recharge over the unconfi ned part of
the system between Uweinat and Dakhla oasis, which implies negligible vertical age stratifi cation. This assumption, however, is in contrast to measurements of
14C in the East Uweinat region that show a well-developed vertical change of the 14C values (Fig. 4) and, thus, unequivocally prove rain-fed local recharge in that unconfi ned aquifer region. Also for other parts of the aquifer system, local recharge during pluvial phases is recognized [1, 5].
In this paper a more realistic recharge regime is proposed, on the basis of which the available 81Kr, 36Cl and related data are re-evaluated. An evolutionary trend of the 36Cl and 81Kr data has been examined, which suggests an appropriate conceptual model of the recharge and fl ow regime. This approach avoids an
„a priori”calculation of apparent ages of the individual groundwater samples which gives preference to the simple piston-fl ow regime and, moreover, requires
Fig. 5. 14C content as function of depth of the sampling well (a) and of the latitude of the sampling sites (b). Given that the main fl ow direction of the groundwater is from south to north (Fig. 1, right part), the latitude differences in Fig. 5b are about proportional to the distance differences between the sampling sites in fl ow direction. It should also be noted that in Fig. 5b the 14C values are normalized to an assumed 14C initial content of 85 pMC.
a
*initial 14C content = 85 pMC 14C pMC
laborious (sometimes diffi cult to verify) geochemical corrections. To examine a possible trend along the main fl ow direction, the coordinates of the sampling sites, not listed in the relevant papers, have been re-constructed. Plotting the
36Cl and Cl– values versus the latitude of the sites, rather high values and high fl uctuations have been found in the unconfi ned part of the aquifer system. If atmospheric fallout (wet and dry) is anticipated as dominating source of the
36Cl and Cl– concentrations, this fi nding can be explained by build-up of chloride over several thousand years during arid phases followed by dissolution during pluvial phases. Since there is no remarkable difference in the enrichment of
36Cl and Cl– by evaporation and precipitation, the ratio of 36Cl/Cl should be unaffected. This concept appears to be proved by the evolution of 36Cl/Cl which shows no signifi cant fl uctuations in the unconfi ned part of the aquifer but a continuous decrease from the East Uweinat/Toshka area in northern direction (main fl ow direction). — Only one outlier with very high 36Cl/Cl has been identifi ed (site BA4 in the Kharga oasis). One of the possible explanations is additional 36Cl production due to nuclear reaction of cosmic-ray neutrons with 35Cl of salt deposits at the surface of this site. — By extrapolation in a semi-logarithmic plot of 36Cl/Cl versus latitude of the sampling sites, the initial isotopic ratio 36Cl/Cl has been estimated to be 130 × 10–15. In this way, the relative 36Cl and 81Kr isotopic ratios could be plotted.
FIG. 6. Relative 36Cl/Cl and 81Kr/Kr ratios versus latitude of the sampling sites: Ba – Bahariya, Da – Dakhla, Fa – Farafra, EU-To – East Uweinat/Toshka. Full symbols represent 36Cl values, the open symbols stand for 81Kr values. The lines have been drawn to indicate possible evolutionary trends. The upper full and dashed lines suggest a trend in the main fl ow direction, while the lower line (only for 36Cl because of insuffi cient data for
81Kr) suggests a separate fl ow path to the eastern part of Kharga oasis.
Fig. 6 suggests two different fl ow paths from south to north, one is connecting East Uweinat, Dakhla, Farafra, and Bahyriya oases and the other in the east includes sites of the Kharga oasis. This separation into two fl ow paths could be related to the Kharga Uplift, which stretches from East Uweinat (near Safsat) to the western part of the Kharga oasis (Thorweihe, [10], Fig.3).
Furthermore, the rapid drop in the isotopic ratios from north to south of the Kharga oasis points to confi ned conditions in this region, increase of the aquifer thickness, and groundwater discharge through leakages in the confi ning beds.
In the following, this fl ow path will not be discussed in more detail because of insuffi cient data.
The semi-logarithmic plot of the relative 36Cl and 81Kr ratios along the groundwater fl ow path from East Uweinat to Bahyriya oasis appears to be linear up to 26.7°N (north of the Dakhla oasis) followed by a rapid drop behind this latitude (Fig.6). Considering the geologic section of the aquifer system (Fig. 7), the strong bend of the lines could be explained by the change from unconfi ned to confi ned conditions. — Due to the geology of the system, this change in the geologic conditions is slightly more southern than the change in the isotope data. — Taking the geometry of the aquifer system into account and assuming constant recharge in the unconfi ned, and constant discharge in the leaky confi ned part, a conceptual model can be developed that describes the change of the isotopic composition along the groundwater fl ow path. For the sake of simplicity of this model, recharge, discharge and hydraulic permeability are assumed to be constant in the aquifer system. Recognizing, that the samples have been taken from pumping wells, it appears to be adequate assuming that the samples represent a mixture of groundwater from the whole aquifer depth.
On the basis of this conceptual model the following relationship has been derived for the isotope ratio (r) in the unconfi ned region
0 0
0 0
1 exp( ( / )
( / ) r x x
x x λτ λτ
− −
= (2)
and for the leaky confi ned region
0 0
0
0 0 0 0
1 exp( )
exp ( )( / L)
x x
r x x x
λτ § λτ ¤ ³¶
¥ ´
¨ ¦ µ·
© ¸
= ¨− ·
λτ τ τ
− − −
(3) where x (x0) is the distance of a sampling site (transition zone from unconfi ned to confi ned conditions) from the southern boundary, and λ is the decay constant of 36Cl and 81Kr, respectively. The parameter τ0 and τL are defi ned by the expressions
0 0
pH
τ = R and L pH0
τ = L (4a, b).
where H0 is the maximum depth of the aquifer system (Fig. 7), p the porosity, R the recharge rate and L the discharge (leakage) rate. The geometric parameter x0 and H0 can be taken from Fig. 7, the average porosity of the aquifer system is known to be at about 10%. Therefore, the model allows to estimate parameter R by fi tting the isotope data of the unconfi ned part to the theoretical curve given in equ.(2) and parameter L by fi tting the data of the leaky confi ned part to equ.(3). In addition to the two parameters characterizing average recharge and discharge, also the fl ow velocity of the groundwater in the two parts of the system can be estimated. Under the given conditions, the groundwater fl ow velocity v follows the expression
0
0 uc
v x R
= H p and 0
0
( )
c uc
x x L v v
H p
= − − (5a, b)
where vuc is the (distance) velocity in the unconfi ned and vc in the leaky confi ned part.
In the following, only the evaluation of the 36Cl ratios is presented.
Although the relevant values derived from 81Kr are close to the ones obtained by 36Cl, the 81Kr results will not be presented because of the insuffi cient 81Kr data points. The fi t of the measured 36Cl ratios to the theoretical curves (Fig. 8) gives the following values of the relevant hydrodynamic parameters:
R = 0.4 mm/yr, L = 0.65 mm/yr, vuc = 0.8 m/yr
FIG. 7. Geologic section through the NSAS from the Sudanese border to Bahariya area in Egypt [12], and simplifi ed geometry of the aquifer system used for modelling the groundwater fl ow and recharge regime. Arrows indicated recharge and discharge over the system.
Recharge
Recharge DischargeDischarge
It should be noted that these parameters represent long-term averages over both pluvial phases (with higher recharge values) and arid phases (with no recharge at all) of the last hundreds of thousands years. Similarly, the discharge rate is higher in, or shortly after, pluvial phases and decreases in arid phases. Considering the relative extension of the recharge and discharge areas (Fig. 7), the estimated values of R and L result in a rather good balance of total recharge and discharge over the whole system. It should also be emphasized that according to this conceptual model, the groundwater fl ow velocity is constant in the unconfi ned part; the estimated value is close to the commonly accepted value of 1 m/yr. In the ‘confi ned’ part the velocity decreases due to leakages in the confi ning beds.
Finally, it should be emphasized that the apparent groundwater ages, estimated by Sturchio et al. [6] and Patterson et al. [7], appeared to be irrelevant for the data evaluation in terms of hydrogeologically (hydrodynamically) relevant parameters. Nevertheless, the groundwater age at a given location and depth of the groundwater can easily be derived from the geometry of the aquifer and the recharge and discharge values. For example, the vertically averaged groundwater age at a given distance x from the outcrop of the aquifer (‘average transit time’) is for the unconfi ned part of the aquifer given by the expression
0
2 0 avg
t x
x
=τ × (6)
FIG. 8. Relative 36Cl ratio and average transit time calculated on the basis of the conceptual model.
The values calculated for both parts of the aquifer are shown in Fig. 8. In fact, this average transit time increases along the fl ow path up to about 1 million years.
REFERENCES
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