Introduction

The Taiyuan Basin is a typical Cenozoic rift basin, located in Shanxi Province, northern China. Groundwater is the principal water resource for water supply in the Taiyuan Basin area. As a result of economic development and population growth, water demand has risen sharply. Overexploitation of groundwater has caused many environmental and geological problems, such as regional decline in groundwater levels, the formation of depression cones, and groundwater quality deterioration (Wu 2018; Zhang 2009). This has increased concerns regarding groundwater supply security and sustainability. These problems have a close relationship with the complex hydrogeological setting, changes in recharge amounts, and long groundwater residence times. Some regional hydrogeological surveys have previously been done in the Taiyuan Basin. Their focus was on geochemical evolution, and recharge and flow paths in the karst groundwater system of the mountain areas (Liao et al. 2014; Ma et al. 2011; Qiao et al. 2015; Sun et al. 2016). Because of the unique topography, geomorphologic features, and aquifer structures, the groundwater in the Taiyuan Basin is rich in fluoride and iodine (Guo et al. 2007a; Li et al. 2011; Tang et al. 2013). Human activities have increased the contamination of groundwater by arsenic and other pollutants (Guo et al. 2007b; Liao et al. 2014). The previous work paid little attention to groundwater age, recharge, and the flow regime of the Quaternary System in the basin area. Although Li et al. (2006) analyzed the hydrochemical characteristics of different groundwater systems and evaluated the recharge ratio of karst groundwater and fissure water using the Sr and Na balance method, the flow pattern and storage were not studied in detail. The present study intends to address these knowledge gaps by providing new insights into the flow regime and flow rates using groundwater age-dating methods.

Groundwater age dating is informative and effective for delineating recharge areas, estimating flow velocities and recharge rates, and describing flow characteristics (Cao et al. 2018; Chen et al. 2011; Gardner and Heilweil 2014; Kamtchueng et al. 2015; Liu et al. 2014; Mcmahon et al. 2010). Groundwater age can also be used to map groundwater renewability and to describe resource attributes, thus facilitating the sustainable use of groundwater resources (Huang et al. 2017; Zhai et al. 2013; Zhang et al. 2017). Radiocarbon (14C) and tritium (3H) are important radioactive isotopes for groundwater dating. The 3H isotope is often used for determining whether “modern” recharge exists, while 14C is suited for dating old groundwater. The combination of 3H and 14C enables an accurate determination of groundwater age in regional aquifers. Estimating the 14C age of groundwater is difficult because of factors such as dead-C dilution, mixing along the flow path, and carbon mass transfer (Geyh 2000). Therefore, 14C dating of groundwater should be corrected by several models and combined with more information from the hydrogeological setting. Many models have been proposed to carry out the correction (Fontes and Garnier 1979; Kalin 2000; Mook 1976; Pearson and Hanshaw 1970; Tamers 1975; Vogel 1970). No single method can accurately estimate 14C age, and thus, additional field samples should be taken, especially in recharge areas, to ensure that the groundwater age is determined as accurately as possible.

In this study, 3H and 14C were combined to date the age of medium-depth groundwater (50–200 m) in the Taiyuan Basin. The flow regime and velocity of the medium-depth groundwater were then delineated using groundwater age.

Study area

General description

The Taiyuan Basin (36° 50′–38° 15′ N, 111° 15′–113° 15′ E) lies in northern China, and covers an area of about 6000 km2. It is surrounded by the Lvliang Mountains in the west and by the Taihang Mountains in the east (Fig. 1). The climate is continental semi-arid, with a mean annual temperature of 9.75 °C. The mean annual precipitation ranges from 259.8 to 655.0 mm, and is high in the mountains and low in the basin area. The area is dominated by the Asia summer monsoon, and more than 58.4% of the annual precipitation falls in the rainy season (June–September). The Fen River is the main river of the Taiyuan Basin, and extends from north to south throughout the entire length of the center of the basin.

Fig. 1
figure 1

Study area and sampling sites. Stratigraphic boundary around Taiyuan basin refers to Guo et al. (2007a)

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Geological and hydrogeological setting

The Taiyuan Basin is a typical Cenozoic fault basin, and has an asymmetrical hydrogeological structure. The thicknesses of the Cenozoic sediments range from 50 to 3800 m. In the geological history of the area, the Lvliang Mountains rose dramatically, and alluvial-pluvial sediment developed in the western part of the Taiyuan Basin. There are different scales of loess hills and platforms between the mountains and the plains. Bedrock in the mountain areas consists of Cambrian–Ordovician carbonate rocks, Carboniferous–Permian coal-bearing strata, and Triassic clastic rocks (Fig. 1). As a result, the groundwater system in and around the Taiyuan Basin comprises pore groundwater systems in loose sediments, karst groundwater systems in carbonate rocks, and fissure groundwater systems in clastic rocks. The Quaternary aquifer in the basin area can be vertically divided into four groups (Fig. 2): Holocene phreatic aquifer (shallow groundwater, 0–50 m); Middle and Upper Pleistocene confined aquifer (medium-depth groundwater, 50–200 m); Lower Pleistocene confined aquifer (deep groundwater, 200–400 m); and a Tertiary confined aquifer. The medium-depth groundwater aquifer (50–200 m) is the main resource that is exploited.

Fig. 2
figure 2

Hydrogeological cross section along the I–I′ line and groundwater ages. Lithologic features originated from the China Geological Survey project (No. 200310400008)

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The medium-depth groundwater flow direction is controlled by the terrain, and groundwater moves laterally from the edge to the center of the basin, except in the northern part where groundwater flows out of the basin. Because of overexploitation, the natural flow characteristics have changed, and some groundwater depression cones have formed, and there is essentially no groundwater flow out of the basin. The medium-depth aquifer is mainly recharged by vertical infiltration and lateral inflows. Vertical infiltrations include precipitation, leakage from the Fen River in the piedmont area, and irrigation along the rivers. The major discharge is from human abstraction.

Methods

Sampling and measurement

In July 2014, 72 groups of groundwater were collected at depths of 50 to 200 m from wells used for domestic and agricultural purposes. The locations of the sampling points are shown in Fig. 1. Each well was pumped for about half an hour before in situ parameters were measured and groundwater was sampled. In situ parameters included water temperature, pH, dissolved oxygen (DO) concentration, oxidation-reduction potential (ORP), and electric conductivity (EC). These parameters were measured using a HACH HQ30d, Single-Input Multi-Parameter Digital Meter (HACH, USA). In situ parameters were monitored until values reached a steady state. Isotope analyses (3H, 14C, and δ13C–DIC) were carried out for each sample at the Laboratory of Groundwater Sciences and Engineering of the Institute of Hydrogeology and Environmental Geology, Chinese Academy of Geological Sciences (IHEG-CAGS). The 3H isotopes were electrolytically enriched and measured using the liquid scintillation counting method with Quantulus–1220 (Pharmacia LKB, Sweden). The results were reported in tritium units (TU), with an analytical precision of ± 1 TU. The 14C isotope of dissolved inorganic carbon was determined radiometrically using the liquid scintillation counting method (with the Quantulus–1220) after synthesis to benzene. The specific 14C activity was reported in units of percentage modern carbon (pMC). The δ13C–DIC isotopes were measured on a mass spectrometer (Finnigan MAT253, Finnigan, Germany). The results for δ13C–DIC were reported as ‰ deviation from the Vienna Peedee Belemnite (VPDB, 0‰) with an analytical precision of ± 0.1‰.

Tritium model

Mathematically, the transport of 3H in a hydrogeological system can be best described by the following convolution integral (Chatterjee et al. 2018; Maloszewski and Zuber 1982):

$$ {C}_{out}(t)=\underset{0}{\overset{\infty }{\int }}{C}_{in}\left(t-{t}^{\prime}\right)g\left({t}^{\prime}\right)\exp \left(-{\lambda t}^{\prime}\right){dt}^{\prime } $$
(1)

where Cout(t) is the output concentration of 3H at time t(TU), Cin is the input concentration of 3H (TU), g(t') is the transit time distribution function, t is the time of sampling (a); t' is the lag time between output and input tracer composition (a), and λ is the radioactive decay constant of 3H (λ=0.55764 a−1).

Models commonly used in hydrogeological studies are (Cartwright and Morgenstern 2016; Maloszewski and Zuber 1982) piston-flow model (PFM), exponential mixing model (EMM), exponential piston-flow model (EPM), partial exponential model (PEM), and dispersion model (DM). Of these models, the EPM is the most appropriate model for the study area because it considers flow in both horizontal and vertical directions. Each model has a different mathematical form for the transit time distribution function g(t'). The g(t') for the EPM model is as follows (Cartwright and Morgenstern 2016):

$$ g\left({t}^{\prime}\right)=0,\kern0.5em {t}^{\prime }<\left(1-1/\eta \right){t_m}^{\prime } $$
(2a)
$$ g\left({t}^{\prime}\right)=\left(\eta /{t_m}^{\prime}\right)\exp \left(-{\eta t}^{\prime }/{t_m}^{\prime }+\eta -1\right),\kern0.5em {t}^{\prime}\ge \left(1-1/\eta \right){t_m}^{\prime } $$
(2b)

where tm' is the transit time (a) and η is the ratio of the total volume to the exponential volume.

The lumped parameter method can provide estimates of the unknown parameters in the above transit time distribution function by calibrating simulations to fit the measured 3H output composition (Chatterjee et al. 2018; Hagedorn et al. 2018; Jurgens et al. 2016). This is accomplished by numerically integrating the convolution integral (Eq. (1)) in the time domain. The computer code FLOWPC (Maloszewski and Zuber 1996) has been used for evaluating the mean transit time of groundwater in this study.

Radiocarbon model

Radiocarbon dating of dissolved inorganic carbon (DIC) in groundwater began in 1957, and continues to be used widely (Aravena et al. 1992; Han and Plummer 2016; Zhang et al. 2016). The 14C age of DIC in a groundwater sample can be calculated from the half-life of 14C decay, the initial 14C content, and the measured amount of 14C (Han and Plummer 2016):

$$ t=-\frac{T_{1/2}}{\ln 2}\ln \frac{A_t}{A_0} $$
(3)

where t is the groundwater age (a), At is the measured 14C of DIC (pMC), A0 is initial 14C (pMC), and T1/2 is the half-life of 14C (T1/2 = 5730 a).

The theoretical principles behind the 14C age calculation begin with dissolved CO2 in precipitation entering the top soil with an initial content of 100 pMC. Then, influenced by complex geochemical and physical processes along the flow path, A0 is altered. Thus, A0 activity needs to be determined by a geochemical model that accounts for various sources and sinks of inorganic carbon.

Results and discussion

Groundwater age dating by 3H

The 3H values for medium-depth groundwater ranged from < 1 to 13.5 TU (Table 1). Fourteen samples had a 3H content of more than 2TU. This indicates that they are probably recharged by modern water of less than 60 a. The depths of the wells from which the samples were taken are mainly between 100 and 150 m (Fig. 3). These wells are located in the piedmont area or near the Fen River (Fig. 1). The 3H ages of groundwater in the wells were determined by using the lumped parameter method.

Table 1 Analytical results for groundwater samples in Taiyuan Basin
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Fig. 3
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The change of 3H concentrations with well depth

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The calculation of groundwater age requires that the input concentration of 3H in precipitation is known. However, observations of 3H concentrations in precipitation in the Taiyuan Basin are only available for 1986 and 1988. Therefore, the data were reconstructed using the Doney model (Doney et al. 1992) for 1960–1986, and then corrected using monitoring data from Shijiazhuang (a city not far from Taiyuan) for the years when data were not available. The reconstructed 3H input concentration in precipitation is shown in Fig. 4.

Fig. 4
figure 4

3H input concentration in precipitation in the Taiyuan basin

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The medium-depth aquifers of the Taiyuan Basin are recharged by lateral flow from the mountain areas, and by the infiltration of surface water and shallow groundwater. Therefore, the EPM model was chosen to obtain young groundwater ages. Trial calculations were carried out by adjusting the η value and the transit time (tm') to fit the observed 3H values in 2004. The best fitting was obtained when η = 7.5, and tm' =7. These parameters were then used to obtain the 3H output concentration curve (Fig. 5). The groundwater age was estimated from this curve. Final ages were determined by considering the samples’ location and the hydrogeological characteristics of the area (Table 2). Most samples had ages of more than 60 a, while T31, T45, T48, T49, and T57 were recharged in recent years (Table 2 and Fig. 1). T49 is the youngest groundwater, and is located in the piedmont area of the single layer aquifer. Its young age is probably caused by the infiltration of surface water from the Wenyu River (Fig. 2).

Fig. 5
figure 5

3H output concentration curves from the EPM (in 2014). The curve was constructed by using the precipitation correction of the monitoring data in Shijiazhuang

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Table 2 3H age calculated from EPM
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Groundwater age dating by 14C

The measured 14C of DIC values ranged from 0.6 to 75.76 pMC, with an average of 24.27 pMC (Table 1). Samples with a high content of 14C are consistent with samples with a high 3H content. This shows that these samples are mixtures of modern and old water. The δ13C of DIC exhibits a wide range of values (from − 20 to − 4‰) with an average of − 11.1‰ (Table 1). Based on the relationship between δ13C–DIC and 14C (Fig. 6), two groups could be identified: group 1 (14C content less than 25 pMC) with a wide range of δ13C–DIC values and an average of − 11.6‰ and group 2 (14C content more than 25 pMC) with a wide range of δ13C–DIC values and an average of − 10.3‰. The differences in these groups indicate that (1) groundwater is recharged under various conditions (humid-dry, open-closed, different aquifer matrices); and (2) the geochemical evolution of some of the samples has progressed further than others, for example, in the dissolution of carbonate (Stadler et al. 2010). If it is assumed that, for a given sample pH and temperature, the soil CO2 is in equilibrium with the δ13C of DIC, then the soil CO2 can be calculated from the δ13C value of DIC. The calculated values for soil CO2 in the recharge area ranged from − 28.6 to − 7.4‰ with an average of − 19.7‰, which reflect that the input carbon originated from C3-plants.

Fig. 6
figure 6

Plot of 14C activities of groundwater samples versus their δ13C–DIC values

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Groundwater with a 3H less than 2TU was recharged before the 1950s, and the age of these samples was determined using 14C. To calculate the appropriate age of groundwater, correction models are needed to be employed. Seven models were used in this study: (1) Vogel (Vogel 1970), (2) IAEA (Mook 1976), (3) Tamers (Tamers 1975), (4) Pearson (Pearson and Hanshaw 1970), (5) Fontes and Garnier (Fontes and Garnier 1979), (6) Alkalinity (ALK) (Tamers 1975), and (7) chemical mass balance (CMB) (Kalin 2000). These models consider either chemical mixing between carbon compounds and/or isotopic fractions. The samples’ pH and temperature are needed in the calculation process. In addition, δ13C values of soil CO2 gas and soil carbonate (0‰) are needed for the IAEA, Pearson, and Fontes and Garnier models. The average A0 values calculated using these models showed that the Vogel model gives the largest A0 (80 pMC); the ALK and CMB models give very low A0 (averages of 18.0 pMC and 24.8 pMC, respectively); the Tamer, Pearson, and Fontes and Garnier models yielded similar A0 values (averages of 52.5 pMC, 49.8 pMC, and 53.1 pMC, respectively). The actual A0 is therefore probably about 50 pMC. The 14C age of the medium-depth groundwater was calculated from the three models. The average values from the three models were taken as the final ages (809–25,894 a) (Table 3).

Table 3 14C age determined by comparing various models
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Groundwater flow regime and velocity

Groundwater flow regime

The groundwater flow field was mapped from the groundwater-level data observed and collected in this study (Fig. 1). Groundwater flows from the piedmont area to the basin center area, or to the depression cones. Three large groundwater depression cones (at Taiyuan, Qingxu, and Jiexiu) have formed in the center of the basin. Because of the groundwater depression in Qingxu, a watershed has appeared between Qiaocheng and Wenshui Counties. Thus, two large, local, groundwater flow systems were formed as the result of intensive exploitation.

Groundwater ages become older along the flow path, and thus can help to delineate the flow path and flow regime. The distribution of groundwater age as determined by 14C is shown in Fig. 2 and Fig. 7, and shows that groundwater flow in the center of the basin is complex. Most of the groundwater in the piedmont area is relatively young, with ages < 10,000 a, while the groundwater in the depression cone at Taiyuan City is relatively old, with an age of 12,508 a. Two high-age zones (ages > 20,000 a) exist in the center part of the basin: one is located in the south of Qingxu (high-age area I), and the other is located in Fenyang (high-age area II) in the south of the Taiyuan Basin which was the only discharge zone for the whole basin in the past. The two high-age zones’ distribution characteristics also indicate the presence of a watershed.

Fig. 7
figure 7

The counter map of 14C ages in the Taiyuan Basin and flow path sections

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The direction of local groundwater flow system was identified. The flows are mainly to the high-age zones. At Taiyuan, the distribution of the high-age zone coincided with groundwater depression cone. At Qingxu and Fenyang, the two high-age zones were distributed near groundwater depression cones, and groundwater in the high-age zones showed a trend of moving toward the depression cones. These trends can be confirmed by comparing the groundwater ages determined in the present study to those determined in the study by Li et al. (2006). In Li’s research, three medium-depth groundwater samples’ ages were dated (K05, K07, and BK12 with ages of 17,652 a, 21,238 a, and 13,252 a, respectively). The samples’ locations are shown in Fig. 7. With respect to the corresponding groundwater areas in the present study, the groundwater age at BK12 has not changed significantly since Li’s study. The groundwater ages at the positions of K05 and K07 have become younger (10000–12000 a), while to their north, the groundwater ages have increased. The groundwater at sites K05 and K07 have moved toward the center of the depression cones in past years (red arrows show the direction of movement in Fig. 7). As a consequence, the oldest groundwater will be exploited in the depression cones in future if overexploitation in the depression areas continues. Once this groundwater has been used, it cannot be restored.

Groundwater flow velocity

Groundwater flow velocity, the reciprocal of the age gradient, was calculated along the flow path. Two transect sections (A–A′ and B–B′), and several segments, were chosen to estimate groundwater flow velocity. For sections A–A′ and B–B′, the mean flow velocity estimated from the slope of the fitting line (Fig. 8 and Fig. 9) was 2.94 m/a and 1.81 m/a, respectively. The groundwater velocity for the other segments is given in Table 4. The velocities of the medium-depth groundwater ranged from 0.90 to 2.94 m/a. Groundwater in the eastern part of the study area flows faster than in the western part. Groundwater in the northern and Yuci piedmont areas (with velocity of 2.78 m/a and 2.94 m/a, respectively) flow faster than in other areas. The groundwater velocity in the Jiaocheng piedmont area is slowest. On the whole, the medium-depth groundwater of the Taiyuan Basin flows slowly.

Fig. 8
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Variation of groundwater age with groundwater flow path (A–A′ section)

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Fig. 9
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Variation of groundwater age with groundwater flow path (B–B′ section)

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Table 4 Representative flow velocity of groundwater in Taiyuan Basin
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Conclusions

Radioactive isotopes 3H and 14C were used to date groundwater age, delineate the groundwater flow regime, and estimate the groundwater velocity of medium-depth groundwater (50–200 m) in the Taiyuan Basin. The 3H values show that groundwater age ranges from 3.5 to > 60a, indicating that some groundwater was recharged by modern water and mixed with old groundwater. The 14C model gave ages ranging from 809 to 25790 a. The groundwater becomes older from the piedmont area to the center of the basin. Two separate areas with old groundwater are present in the center of the basin. Groundwater flow velocity ranges from 0.90 to 2.94 m/a. Groundwater in the eastern part flows faster than in the western part. Age evolution along the flow line from the mountains to the basin is apparent, indicating recharge from the mountain areas. Two new findings that were not evident in earlier studies were obtained: a watershed has appeared in the center of the basin, and the regional north-to-south groundwater system has disappeared. Although the groundwater flow is very slow, the trend of the oldest groundwater moving to the centers of the depression cones is obvious.

Groundwater renewability can be characterized on the basis of groundwater age and flow regime, and this can provide useful information regarding the sustainable use of groundwater. Groundwater in the southern piedmont area is relatively young and some parts are recharged by modern water. Thus, there is partial groundwater renewal in this area and groundwater can be exploited appropriately here. However, the groundwater in the western piedmont area is not effectively recharged and two groundwater depression cones have formed. It is, therefore, no longer suitable for exploitation. The groundwater in the southern part of the study area (the discharge area in the past) can be exploited relatively highly, although the renewability is small. Increased exploitation here will accelerate groundwater recharge, from lateral inflows and vertical infiltration.