Elsevier

Journal of Hydrology

Volume 286, Issues 1–4, 30 January 2004, Pages 87-112
Journal of Hydrology

Age and flow pattern of groundwater in a Jurassic limestone aquifer and related Tertiary sands derived from combined isotope, noble gas and chemical data

https://doi.org/10.1016/j.jhydrol.2003.09.004Get rights and content

Abstract

Multi-tracer study of the Malm (Upper Jurassic) limestone aquifer in north-western part of Cracow, Poland, revealed the existence of much older waters than those estimated from Darcy's law. The following environmental tracers were used: 3H, 14C, δ13C, δ18O, δ2H, 4He, Ne, Ar, Kr, Xe, 3He/4He and 40Ar/36Ar in combination with water chemistry. The natural drainage of unconfined parts of the aquifer is by springs and streams, with a dominant presence of modern and pre-bomb era Holocene waters, whereas the confined part is drained only by upward leakage through thick Miocene clays in river valleys, mainly in the Vistula (Wisła) river valley. As a consequence, the confined part contains much older waters. Their glacial ages are indicated by δ18O and δ2H values significantly more negative than those found for modern recharge and by noble gas temperatures reduced by ca. 4.5 °C when compared to the present-day mean annual air temperatures. Quantitative age interpretation of 14C is regarded unreliable due to isotope exchange between dissolved and solid carbonates as suggested by δ13C values of DIC in the range of −0.6 to −6.1‰ for the confined part of the aquifer. Similarly, quantitative 4He dating turned out to be unreliable, though 4He excess values (0.93–5.45×10−6 cm3 STP/g) and very low 14C contents (0.0–5.5 pmc) suggest glacial ages. Changes in hydrochemistry also indicate a long-lasting water–rock interaction probably dominated by diffusion-controlled exchange with overlying and underlying formations. Admixture of older water ascending from underlying formations is observed at two sites. That older water is also supposed to be of Quaternary age as the 40Ar/36Ar of the mixture remains equal to the atmospheric ratio. Great tracer ages are shown to result mainly from the delay of solute velocity with respect to the velocity of mobile water, caused by diffusive exchange between mobile water in the fissures (porosity of 0.0001–0.001) and stagnant water in the matrix (porosity of ∼0.06). This stagnant water in the porous matrix is the main water reservoir in the Malm aquifer. In the erosion structures of the Malm limestones, close to the Cracow centre on the southern side of the Vistula river, Tertiary sands are deposited under clay cover. Prior to this study, the origin and age of mineral water exploited from these sands was controversial. However, tracer data indicated meteoric water recharged at the end of the last glacial, and excluded an admixture of connate marine water from adjacent formations. In one well a 10% admixture of modern water was observed with the mean age of about 30 years as determined from the lumped-parameter modelling of the tritium data. The recharge is supposed to take place indirectly through nearby Malm horsts and/or by seepage through Miocene clays in unidentified areas, with dissolution of evaporites as the main source of chemical components. The glacial ages of waters in the confined parts of the Malm aquifer and in Tertiary sands indicate their low vulnerability to anthropogenic pollution.

Introduction

Environmental isotope methods are now regarded as routine tools for solving various problems in hydrology (e.g. Clark and Fritz, 1997, Kendall and McDonnel, 1998, Cook and Herczeg, 2000). They serve particularly well in early stages of investigations when the flow paths, mixing pattern, renewal rates and the vulnerability to anthropogenic pollution of aquifers with little known or complex geology are to be assessed.

Though the Malm limestone aquifer in the Cracow area, southern Poland, is intensively exploited, little was known prior to this study about the flow pattern and ages of water due to a complex geology and possible presence of obstacles to flow caused by the presence of numerous faults and horsts. Similarly, the origin of elevated contents of some chemical constituents was unclear. This paper presents the results of multiple tracer study concentrated mainly on the confined part of the aquifer. That aquifer is considered a major strategic reserve of potable water for the entire Cracow municipal area (ca. 1 million inhabitants) in case of a catastrophic pollution of surface intakes and Quaternary aquifers, which are the main suppliers of water for the city. Several samples taken from the unconfined areas were supposed to serve as reference data of the present-day input. For the central confined area of the Malm aquifer, Darcy's law yielded ages in the range of 15–300 years, depending on the assumed fissure porosity. On the other hand, preliminary radiocarbon and stable isotope determinations suggested the presence of glacial water in a number of wells. Therefore, a multi-tracer approach (3H, 14C, δ13C, δ18O, δ2H, 4He, Ne, Ar, Kr, Xe, 3He/4He and 40Ar/36Ar as well as main and some trace chemical constituents) was used to obtain an assessment of the age of water, flow pattern, mixing processes and origin of the main chemical components.

Mineral waters exploited from Tertiary sediments within the city limits were also investigated. They were earlier regarded as vulnerable to anthropogenic pollution as supposedly being a mixture of modern and sedimentary waters. The presented study was aimed at clarifying their origin, age and potential vulnerability to anthropogenic pollution.

Volumetric flow rate through a unit cross-section area defines Darcy's velocity (vD), which in turn defines the travel time of mobile water, assuming that the movement of water takes place only in the fissures:vD=nevf≅nfvf=nfx/tw=(ΔH/Δx)Kwhere ne is the effective porosity defined as that in which the water movement takes place, nf is the fissure porosity assumed in a good approximation to be equal to the effective porosity, vf is the mean velocity of water in the fissures, tw is the mean travel time (age) of mobile water (tm=Vm/Q, where Vm is the volume of mobile water in groundwater system and Q is the volumetric flow rate through that system), ΔHx is the mean hydraulic gradient along flow distance x, and K is the hydraulic conductivity.

The dominant influence of matrix diffusion on tracer transport in fissured media with a porous matrix was indicated by experiments and mathematical models (e.g. Grisak et al., 1980, Neretnieks, 1981, Sudicky and Frind, 1982, Małoszewski and Zuber, 1985, Małoszewski and Zuber, 1991). Due to molecular diffusion between mobile water in the fissures and stagnant water in the matrix, the water ages obtained from tracer data significantly exceed the mobile water ages, i.e. the ages deduced from hydrodynamic data. For densely fissured rocks and sufficiently large time scale, the ratio of these ages is expressed by a factor approximately equal to the ratio of total interconnected porosity to fissure porosity (Neretnieks, 1981, Małoszewski and Zuber, 1985). In such a case, a conservative solute (tracer or pollutant) travels as if the flow were through the total interconnected porosity, i.e. through nf+np, where np is the interconnected matrix porosity. Then, the mean travel time (age) of both water molecules and an ideal tracer (tt) is related to the mobile water age by:vf/vt=tt/tw=(np+nf)/nf−np≅(np+nf)/nf

In that equation the mean tracer age is equal to Vtotal/Q, where Vtotal is the sum of mobile water in the fissures and stagnant water in the matrix. By inserting Eq. (2) into Eq. (1), the following formula is obtained (Małoszewski and Zuber, 1993, Zuber and Motyka, 1994):(nf+np)vt=(nf+np)(x/tt)=(ΔH/Δx)K

Usually nf is much smaller than np and can be neglected in Eq. (3). This means that though K depends strongly on nf, its value can be found from the tracer age, or vice versa, when K is known, the mean solute velocity can be estimated, without any knowledge on the fissure system.

In the hydrogeologic literature, the tracer age (tt) is often wrongly identified with the mobile water age (tw). See for instance Małoszewski and Zuber (1991) for the discussion of 14C ages and their relations to the hydraulic parameters of a chalk aquifer in France. The effective porosity (nenf) is also sometimes wrongly identified with the total interconnected porosity (nf+np). The age of mobile water (tw) should not be identified with the age of water, i.e. the age of water molecules (the time spent in the groundwater system by water molecules from the recharge event to the time of sampling). The age of water is expressed by properly determined tracer age both for mobile and stagnant water systems. However, for stagnant water systems, the hydraulic parameters are not related to tracer and water ages.

If the fissure spacing is large, ages determined from decaying tracers can be somewhat lower than those deduced form non-decaying tracers, or from tracers with long half-lives. That effect results from the decay in the matrix, which, for relatively short-lived tracers, prevents them from penetrating the whole matrix. As a consequence, only a part of the matrix porosity in Eqs. , is available for the tracer. Age corrections for that effect are usually neglected because they are difficult to estimate due to a complex dependence on the fissure network and matrix parameters (Małoszewski and Zuber, 1984, Małoszewski and Zuber, 1985).

Sudicky and Frind (1981) showed that for thin aquifers, diffusive exchange with water in the aquitards leads to overestimation of 14C ages. Similarly, Sanford (1997) showed that less permeable interbeds with stagnant or quasi-stagnant water also lead to overestimation of 14C ages. Diffusive exchange between aquifers and aquitards influences the transport of all tracers and pollutants, but following the estimations given by Sudicky and Frind (1981) its influence was neglected within the present work due to relatively large thickness of the Malm aquifer.

Tritium, 3H/3He and some other recently developed tracer methods may serve for age determination of young unconfined waters (usually up to several tens of years). Within the present study tritium was used to identify modern waters. In some cases 3H/3He ratio and 4He excess were helpful for determining binary mixing between modern and older Holocene waters, or modern and glacial waters. Available time records of tritium were interpreted by the lumped-parameter approach described in detail by Małoszewski and Zuber (1982), with the aid of the FLOWPC program (Małoszewski and Zuber, 1996). The tritium input-function was calculated using the method described by Grabczak et al. (1984), with the ratio of summer-to-winter infiltration coefficient equal to 0.7 obtained from the stable isotope data of the precipitation and modern groundwater in the Cracow region. For these calculations the summer months were taken from April to September, and winter months from October to March. Precipitation and tritium data for the Cracow station in the period of 1974–1999 are available in the IAEA Database (http://isohis.iaea.org). Earlier data were obtained by correlation with the Vienna station, and for recent years they were taken from Duliński et al. (2001) and their unpublished data. Mean tritium ages significantly larger than the period of the hydrogen bomb-era result from assumed flow distribution in the lumped-parameter approach whereas, measurable tritium contents are contributed only by short flow lines (Zuber et al., 2001). For instance, the exponential model has distribution of ages from zero to infinity. Any decaying tracer, with the half-life time distinctly shorter than the mean water age, will not be measurable at the end of flow lines with large ages.

Confined waters are commonly characterised by long residence times and quantitative determination of their ages requires the use of 14C and/or other suitable tracers, e.g. accumulated 4He. The 14C method, based on measurements of 14C in the dissolved inorganic carbon (DIC), is particularly useful for dating waters in the range of about 2–30 ka, though some controversies occur when this method is used in carbonate aquifers. Some researches apply the 14C data either to calibrate transport models (e.g. Wei et al., 1990), or for dating water in carbonate aquifers with simple corrections of the initial 14C content (e.g. Blavoux et al., 1993). More often geochemical reaction models are used to account for the influence of carbon hydrochemistry on the 14C dating (e.g. Fontes and Garnier, 1979, Kemp et al., 2000, Plummer and Sprinkle, 2001). In such models δ13C is used as an indicator of isotopic exchange between the phases, and of the dissolution of solid carbonate material. Recently, Gonfiantini and Zuppi (2003) reviewed 14C–δ13C correlations in a number of aquifers and showed that isotope exchange caused by equilibrium dissolution–precipitation process, expressed in terms of apparent 14C decay, in some cases may lead to a significant overestimation of ages. If the isotopic exchange partly takes place on the solid surface already modified by the exchange process, the δ13C value of the DIC remains unchanged by that part of the process. As a consequence, the transport of 14C can additionally be delayed without significant changes in the δ13C value and the 14C ages become additionally overestimated (Małoszewski and Zuber, 1991). Similarly, Aeschbach-Hertig et al. (2002) showed that 14C content in a sandy aquifer, with 5–25% carbonate shell debris and calcareously cemented sand, was affected by isotopic exchange leading to too high ages, which were difficult to correct. As stated by Mook (2000, p. 136), the chemical conditions underground are so complicated that geochemical models may be reasonable approaches but are not to be considered clean correction methods.

For the calculations of apparent 14C ages of waters in siliceous aquifers, one of the simplest approaches can sometimes be used, i.e. the piston flow model with the initial 14C activity changed by the dissolution of ‘dead’ carbonates in the soil zone (Ingerson and Pearson, 1964, Cook and Herczeg, 2000).14Cage(ka)=8.3ln[(100/C14)(δ13C/−25)]where C14 is the 14C activity measured in DIC expressed in pmc (percent of modern carbon). In that model, the 13C value of DIC produced by plants in moderate climates is taken as equal to −25‰ (Deines, 1980, Mook, 2000), and the 13C value of the marine carbonates as equal to 0‰. Within the present work, Eq. (4) was used just to support the conclusions derived from the stable isotope data on the climatic period in which the recharge into the Tertiary sands took place, and to show trends in apparent 14C ages caused by withdrawal of water from that formation.

Concentrations of Ne, Kr, Ar and Xe in groundwater originate from the atmosphere, and usually serve for determining the temperature at the water table at the time of recharge after correcting for the so-called air excess and altitude (Mazor, 1972, Herzberg and Mazor, 1979, Heaton and Vogel, 1981, Stute and Schlosser, 1993, Stute and Schlosser, 2000, Aeschbach-Hertig et al., 1999). If the dependence of surface air temperature on altitude is known, noble gases can also be used for determining the altitude of recharge (Zuber et al., 1995, Manning and Solomon, 2003). The temperature of recharged water derived from the concentrations of noble gases is usually called the noble gas temperature (NGT). Noble gas temperatures were mainly studied for well-known large groundwater systems to obtain paleoclimatic information (e.g. Stute and Deák, 1989, Stute et al., 1993, Clark et al., 1997, Beyerle et al., 1998), or to confirm the pre-Holocene origin of water dated by other methods (e.g. Blavoux et al., 1993, Clark et al., 1997, Clark et al., 1998, Zuber et al., 2000).

Concentrations of 4He in groundwater often exceed those resulting from equilibrium with the atmosphere and the presence of air excess. There are four main sources of 4He excess in groundwater: (a) in situ production within the aquifer matrix and diffusive release from the solid material (Bath et al., 1979, Rudolph et al., 1984, Bottomley et al., 1984, Andrews et al., 1985, Torgersen and Ivey, 1985, Weise and Moser, 1987, Stute et al., 1992, Castro et al., 2000); (b) diffusive release of 4He accumulated in aquifer solids in their earlier geological history in the form of a hard rock, which may exceed the in situ production for about 50 million years of the existence of a granular aquifer (Solomon et al., 1996); (c) diffusion of 4He from deeper formations of crust or mantle (Andrews et al., 1985, Weise and Moser, 1987, Torgersen and Ivey, 1985, Deák et al., 1987, Stute et al., 1992, Torgersen et al., 1995, Castro et al., 2000); and (d) admixture of much older waters (Mazor, 1972, Clark et al., 1998, Zuber et al., 2000).

Usually 4He excess is used as a relative age indicator within aquifer systems containing old waters (e.g. Clark et al., 1997, Clark et al., 1998, Blavoux et al., 1993, Lehmann et al., 1995, Zuber et al., 2000). Solomon et al. (1996) showed that when the release rate can be measured in laboratory, 4He can also be used for dating groundwater as young as 10 years. In general, the 4He excess serves for dating in a much wider range of ages than 14C (e.g. Castro et al., 2000), in some cases also yielding more reliable chronology than the 14C method (e.g. Aeschbach-Hertig et al., 2002). Quantitative dating is possible if one source of 4He dominates (e.g. Solomon et al., 1996, Aeschbach-Hertig et al., 2002), or if the crustal flux can be estimated from the 4He distribution within the aquifer (e.g. Torgersen and Ivey, 1985, Stute et al., 1992, Castro et al., 2000). In age estimations of some groundwater systems, the crustal 4He flux was assumed as known on the basis of literature data (e.g. Wei et al., 1990, Marty et al., 1993).

When 4He excess results from an admixture of older water, that component may mix directly with young water at the drainage site (Mazor, 1972), or may enter the aquifer by upward leakage from underlying formations (Clark et al., 1998, Zuber et al., 2000). If the contribution of older water is irregular along flow paths, quantitative dating using 4He can be difficult due to lack of adequate models. In the cited works the contribution of older water was identified by correlations between Cl content and 4He excess whereas Lehmann et al. (1995) discussed several underground systems where Cl4He correlations occur and came to a conclusion that both components probably resulted from in situ processes.

Assuming that He is homogeneously distributed along the aquifer depth, and its excess results from the in situ production and/or crustal flux, the age of water can be determined from the following equation (Andrews et al., 1985, Torgersen and Ivey, 1985, Stute et al., 1992):Age=CHenhρf/(J+nhρfΛP)where CHe is the 4He excess measured, n is the total interconnected porosity, h is the thickness of the water system, J is the net crustal flux of 4He to the system from the underlying formations, ρf is the density of fluid, Λ is the gas fraction escaping from the solid phase usually taken as equal to 1, and P is the in situ production rate of 4He. For concentrations of uranium (CU) and thorium (CTh) in ppm, the production rate in cm3 He STP g−1 a−1 is:P=(ρr/n)(1.19×10−13CU+0.288×10−13CTh)where ρr is the density of rock material.

Different values can be found in literature for the crustal flux of 4He (e.g. Andrews and Lee, 1979, Ozima and Podosek, 1983, Mamyrin and Tolstikhin, 1984). Torgersen and Clarke (1985) reported (1.0±0.4)×10−6 cm3 STP cm−2 a−1. In some cases no influence of the crustal flux was observed (e.g. Aeschbach-Hertig et al., 2002).

Helium isotope ratio (3He/4He) is commonly used to distinguish the origin of crustal and mantle gases (Mamyrin and Tolstikhin, 1984). That ratio may also be used for a better identification of water components when tritium is present (Weise and Moser, 1987).

For waters older than several tens of thousand years, the 40Ar/36Ar ratio in groundwater may differ from the atmospheric ratio due to accumulation of 40Ar resulting from both in situ decay of 40K and diffusive flux from the crust (e.g. Torgersen et al., 1989). This ratio can also be used for qualitative identification of very old waters, or for estimation of ages with the aid of Eq. (5) expressed for 40Ar excess.

Section snippets

Hydrogeology of Malm limestones

Malm limestones (Upper Jurassic) in the Cracow region are recharged mainly at their outcrops in the Ojców plateau and probably also at elevated horsts (Fig. 1). They dip irregularly from the plateau towards the south, under confining Miocene clays in the Krzeszowice and Cholerzyn grabens, and towards the east under Cretaceous limestones and marls (Fig. 1, Fig. 2). Marly interbeds in the Cretaceous are often of low permeability and in some areas they separate water levels within the Cretaceous.

Measurement methods

Water samples from 29 wells were analysed for chemistry, δ18O and δ2H mainly under other projects. Within the present tracer study, 26 wells were sampled for 3H, in that 19 for determining 14C and δ13C in TIC, and 17 for noble gas analyses. Non-artesian wells were pumped prior to sampling to remove at least five casing volumes of water. The specific conductivity, temperature and pH were measured in the field (only pH is reported here). Total alkalinity was also determined in the field on

Results

Site names, well depths, open intervals, concentration of chosen chemical components and the values of two hydrochemical indicators of the two investigated systems are listed in Table 1, whereas tracer data, chemical types of water, and qualitative estimates of tracer ages are given in Table 2. Age estimations are based on the analysis of the tabulated data and their graphical presentations discussed further. Fig. 3, Fig. 6, Fig. 7 contain data of both systems for a better visualisation of

Modern and older Holocene waters

The least negative δ18O and δ2H values in Fig. 3 represent wells in the main recharge area in the north-west (1–3) as well as wells in southern Cracow (24 and 25) and a spring (23) situated at elevated horsts. Within the stated analytical uncertainty (Table 2) their isotopic composition is equal to the mean δ-values of local modern waters in Quaternary aquifers, i.e. δ18O≅−10.0‰ and δ2H≅−70‰, and is also close to the long term mean representing annual precipitation (Grabczak et al., 1984,

Conclusions

The present study confirms the importance of tracer methods in investigations of little known groundwater systems with complex geology. Even a relatively low number of sampling sites can supply valuable information especially when tracers used are adequately chosen to the expected ages and mixing characteristics.

Acknowledgements

Partial support under the German-Polish Co-operation (Project No. F5-X085.9), and for A.Z. from the Committee for Scientific Research under Project No. 6.POD4.019.09 is kindly acknowledged. Works of J.M. and K.R. were also partly supported by the Committee for Scientific Research. Chemical data were obtained mainly from the archives of other projects. Thorough and constructive reviews by N.L. Plummer and P.A. Macfarlane greatly contributed to the improvement of the final version of the

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