Introduction

Remarkable technological and industrial growth has been achieved through the use of fossil fuels; however, this has also led to the emission of large quantities of greenhouse gases such as carbon dioxide (CO2) into the atmosphere, resulting in environmental disasters such as acid rain and global warming. Carbon dioxide geological storage (CGS) has been considered as one effective technology for mitigation of the detrimental effects of CO2. However, because CGS technology injects CO2 into deep subsurface environments, a range of minerals such as silicates and carbonates can be dissolved and/or precipitated as a result of changes in groundwater properties. Such water–rock interactions might occur over a long time span; however, our knowledge of these processes is limited due to the relatively recent adoption of CGS technology (Kharaka et al. 2006; Gaus 2010). For this reason, natural analogue studies using CO2-rich spring water (CSW) have been conducted to advance our knowledge of CGS-driven geochemical processes over geological timescales (Watson et al. 2004; Moore et al. 2005; Pearce 2006; Pauwels et al. 2007; Flaathen et al. 2009; Lu et al. 2011; Choi et al. 2012, 2014; Chopping and Kaszuba 2012).

There have been a number of studies using naturally occurring CSW that have investigated relatively long-term geochemical processes in deep groundwaters after CO2 injection (Balashov et al. 2013, 2015). CSW is most frequently observed in South Korea in the Kangwon (KW), Chungbuk (CB), and Gyeongbuk (GB) districts. The main geology where CSW occurs is granite and banded gneiss for the KW area, granite and alluvial deposits for the CB province, and sedimentary deposits for the GB region (Bong and Chung 2000; Lee et al. 2003; Yun et al. 2003; Noh et al. 2004; Hwang et al. 2013). Previous studies have compared the properties of CSW between areas and investigated the origin and evolutionary pathway of CSW using isotope studies (Koh et al. 1999, 2000, 2008; Choi et al. 2000, 2002, 2005, 2009; Jeong and Lee 2000; Kim et al. 2000, 2001, 2008; Yun and Kim 2000; Jeong 2002, 2004; Jeong et al. 2001, 2005, 2011; Chae et al. 2013). Although the isotope composition of specific elements has been used to investigate the origin and evolutionary pathways of CSW, such approaches are not appropriate for characterizing water–rock interactions resulting from the carbonate water produced in deep subsurface environments on CSW occurring on the surface. Instead, a number of studies have attempted to understand the water–rock interactions using geochemical modeling. Choi et al. (2014) studied the geochemical pathways of two types (Na–HCO3 and Ca–HCO3) of CSW in the GW district using geochemical (reaction path) modeling, including mixing and ion-exchange reactions. Additionally, there have been many attempts to calculate the saturation indices of minerals within carbonate aquifers using equilibrium reaction modeling (Zanini et al. 2000; Kharitonova et al. 2010; Akin et al. 2015; Jin et al. 2015; Nyirenda et al. 2015).

There are two types of approaches for using multivariate statistical analyses with hydrogeochemical data. One is to use traditional statistical techniques, and the other is to use compositional data analysis. Despite being commonplace, traditional techniques cannot treat the data as compositional data and implicitly invoke spurious correlations caused by scaling because they employ amalgamation, which does not preserve distances within an already restricted sample space (called the simplex) (Egozcue and Pawlowsky-Glahn 2005; Bacon-Shone 2006; Pawlowsky-Glahn and Egozcue 2006; Owen et al. 2016). This occurs because hydrochemical data are compositional by nature; in particular, they are quantitative data in which each component is a proportion of a given total (Owen et al. 2016). Compositional data refer to data in which the relevant information is contained in the ratios between the values of the variables. Aitchison (1986) introduced log ratio approaches, such as additive log ratios (alt) and centered log ratios (clr), to treat compositional data in percentages, proportions, concentrations, etc. (Filzmoser et al. 2016). More recently, the isomeric log ratio (ilr) approach was developed, which ultimately led to recognition that compositions can be represented in orthogonal (Cartesian) coordinates in the simplex (Egozcue and Pawlowsky-Glahn 2005; Owen et al. 2016). Collectively, these methods are called compositional data analysis. Recently, there have been several applications of compositional data analyses in the fields of geochemistry and hydrogeochemistry (Blake et al. 2016; Buccianti and Zuo 2016; Tolosana-Delgado and McKinley 2016). Fačevicová et al. (2016) reported a statistical characterization of the Devonian–Carboniferous boundary, in which results obtained by a log ratio method were compared with those obtained from a classical point of view, without any prior transformation. The paper proposed that using a combination of the two approaches brings more insights than using either of any of the two methods separately. Furthermore, Owen et al. (2016) applied compositional data analysis techniques to describe the variability of major ions within and between coal seam gas-bearing (or coal bed methane-bearing) groundwater. Using the compositional data analysis, they described fundamental compositional similarities/differences between coal seam gas and groundwater, provided a robust and descriptive means of comparing water types, and assessed hydrochemical variability within and between large and highly variable datasets with respect to the hydrochemical evolution of coal seam gas or groundwater associated with high gas concentrations.

Equilibrium phase modeling (EPM) can be used to target the solid, liquid, and gas phases and has been actively used to compute a variety of aqueous chemical reactions in equilibrium. In particular, EPM has recently been used in numerous CGS and natural analogue studies of carbonate water and CSW. Springer et al. (2012) conducted a study using EPM to simulate the dissolution of CO2 according to the temperature and pressure of the saline aquifer in which a CGS project had been implemented. In addition, Bollengier et al. (2013) performed an EPM study to estimate phase changes of water and CO2 at a specific temperature and pressure and to evaluate the stability of CO2 hydrates in deep sea environments. EPM was used to investigate chemical equilibrium reactions taking place in the groundwater of karst regions (White 1997) and to observe the phase changes of carbon in deep groundwater aquifers when magmatic CO2 moved up from the upper mantle (Manning et al. 2013). EPM has also been used in numerous laboratory studies to simulate diverse carbonate water and groundwater environments (Evans and Derry 2002; Garcia-Rios et al. 2014; Martos-Rosillo and Moral 2015; Raju et al. 2015). However, EPM is not likely to be reliable when it is applied to a wide study area or large datasets. To overcome such drawbacks, multivariate statistical analysis can be used in conjunction with EPM when geochemical modeling is applied in groundwater studies (Sharif et al. 2008; Belkhiri et al. 2010; Ryzhenko and Cherkasova 2012; Tallini et al. 2014; Ledesma-Ruiz et al. 2015; Sanchez et al. 2015; Rafighdoust et al. 2016).

Even though there have been a number of studies of CSW in South Korea, most have been limited to a local area. The lack of an overall understanding of CSW on a national scale motivated this study. The objectives of this study were therefore: (1) to compare the hydrochemical properties of CSW occurring in three typical districts in South Korea and (2) to determine the evolutionary pathways of carbonate water and CSW. To achieve these objectives, compositional data analyses and geochemical modeling were utilized. In particular, past geochemical processes in CSW were described by EPM to interpret the carbonate water–rock interactions arising in subsurface environments and relate them to the occurrence of surface CSW.

Geology of the study area

The typical areas where CSW occurs in South Korea are in the KW, CB, and GB provinces. The geology of these areas and the location of CSW sampling sites are given in Fig. 1. The KW province is located in northeastern South Korea and predominantly consists of Precambrian metamorphic rocks, including porphyroblastic, banded, and leucocratic gneisses, together with Jurassic biotite granites and sedimentary rocks (Yun and Kim 2000; Choi et al. 2014). The dominant mineral composition in this area is quartz (33.4%), albite (24.5%), K-feldspar (21.5%), anorthite (11.3%), biotite (3.8%), and hematite (2.8%), with minor components of magnetite, muscovite, and pargasite (Choi et al. 2014). The main geology of the KW area, where CSWs of Na–HCO3 type frequently occur, has been reported to be Cretaceous Bulguksa granite, which has a mineralogy of albite (35.4%), quartz (30.1%), K-feldspar (26.7%), anorthite (2.2%), magnetite (1.2%), ferrosilite (0.1%), and enstatite (0.1%) (Min and Kim 1996). The CB province, located in central South Korea, mainly consists of Precambrian gneisses and Jurassic granites extending to the KW province, with minor components of Paleozoic metamorphic sedimentary rocks (Jeong et al. 2001; Koh et al. 2008). The main mineral composition of the CB area is quartz (27.4%), plagioclase (38.0%), K-feldspar (26.3%), biotite (6.2%), and muscovite (1.6%), with some calcite and pargasite (Koh et al. 2008). The GB province is located in eastern South Korea. The main geology of the GB area is Jurassic sedimentary and Cretaceous granitic rocks (Yun and Kim 2000). Lee and Lee (1991) conducted petrological research on the granite of the GB area and reported that the main mineralogy of this area was quartz (27.9%), plagioclase (44.5%), biotite (12.9%), K-feldspar (11.4%), epidote (1.8%), ripidolite (0.6%), and pargasite (0.3%). In addition, Jeong and Jeong (1999) studied the sedimentary rocks conformably or unconformably covering granitic rocks within the GB area and reported that the mineralogy of the sedimentary rocks was quartz (33.4%), plagioclase (22.8%), K-feldspar (5.2%), muscovite (0.6%), and carbonate minerals including calcite and dolomite (36.9%).

Fig. 1
figure 1

Geological map of the study area with the locations of CO2-rich spring water (CSW). a Kangwon (KW) area, b Chungbuk (CB) area and c Gyeongbuk (GB) area

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Methodology

Data collection and processing

For this study, we investigated a number of previous studies of CSW undertaken within the three districts and collected CSW hydrochemical data from 54 sites. The data were classified into three groups: (1) on-site measurements such as pH, temperature, electrical conductivity (EC), and total dissolved solid (TDS), (2) major constituents such as cations (Na, Ca, K, and Mg) and anions (Cl, HCO3, SO4, and NO3), and (3) minor elements (Al, Fe, and Si). Data collection was restricted because the analytical items were different between studies, and for this reason, the use of dissolved oxygen (DO) and oxidation–reduction potential (ORP) data was excluded in this study. It was possible to acquire analytical data on major ion constituents from most previous studies, whereas data on minor elements differed significantly between studies, and only three elements (Al, Fe, and Si) commonly analyzed in previous studies were collected and used. In terms of EC and TDS, when only one item was acquired from the literature, the other was calculated using a first-order equation (y = ax + b) because the relationship between them is commonly assumed to be linear. The data acquired from the literature are summarized in Tables 1 and 2. The CSW hydrochemical data were also characterized by Piper diagrams, ternary principal components plots, and relationships between molar ratios of major constituents and TDS/HCO3.

Table 1 Physical and chemical data of CO2-rich spring water (CSW) used in this study
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Table 2 Elemental concentrations of CO2-rich spring water (CSW) used in this study (unit: mg/L)
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Compositional data analyses

To statistically interpret the CSW data collected from the literature, a total of 12 parameters (pH, Na, Ca, K, Mg, HCO3, Cl, SO4, NO3, Al, Fe, and Si) were used for the statistical analyses. pH values were converted to hydrogen (H+) ion concentrations in mg/L to match the unit with that of the other variables.

Compositional data have several weaknesses for direct application of conventional multivariate statistical analysis, e.g., spurious correlation (Pearson 1896). For this reason, compositional data analyses were conducted using R package (v. 3.3.2), CodaPack (v. 2.02.04), and IBM® SPSS (v. 22) programs. In this work, two log ratios were applied when analyzing the dataset: (1) D-dimensional centered log ratio (clr) coordinates [\( \log \frac{{x_{1} }}{{\left( {x_{1} \cdots x_{p} } \right)^{1/D} }}, \ldots ,\log \frac{{x_{p} }}{{\left( {x_{1} \cdots x_{D} } \right)^{1/D} }} \)] of D-dimensional original data (x1, …, xD) and (2) the (D − 1)-dimensional isomeric log ratio (ilr) coordinates

$$ \left( {\sqrt {\frac{{r_{1} s_{1} }}{{r_{1} + s_{1} }}} \log \frac{{\left( {\mathop \prod \nolimits_{{ + \in B_{D - 1} }} x_{i} } \right)^{{1/r_{1} }} }}{{\left( {\mathop \prod \nolimits_{{ - \in B_{D - 1} }} x_{i} } \right)^{{1/s_{1} }} }}, \ldots \sqrt {\frac{{r_{D - 1} s_{D - 1} }}{{r_{D - 1} S_{D - 1} }}} \log \frac{{\left( {\mathop \prod \nolimits_{{ + \in B_{D - 1} }} x_{i} } \right)^{{1/r_{D - 1} }} }}{{\left( {\mathop \prod \nolimits_{{ - \in B_{D - 1} }} x_{i} } \right)^{{1/s_{D - 1} }} }}} \right), $$

where Bi is the ith sequential binary partition and ri and si are the number of parts coded in Bi as + and −, respectively (Wickham 2009; Owen et al. 2016). Sequential binary partitions define D − 1 orthonormal coordinates (ilr coordinates), called balances, which can be modeled by standard statistical methods (Egozcue et al. 2003). The clr transformation produces D coordinates, which are useful for constructing biplots to describe variability (Egozcue et al. 2003; Pawlowsky-Glahn and Egozcue 2006). However, the clr-transformed coordinates are constrained to a subspace of real space and are represented on a hyperplane in D-dimensional real space because they ultimately sum to zero; consequently, the covariance and correlation matrices are singular (Egozcue et al. 2003; Pawlowsky-Glahn and Egozcue 2006). Therefore, care should be needed during the interpretation of clr-transformed data because the clr-coordinates represent the proportion in the numerator concerning the geometric mean of all the parts in the composition (Owen et al. 2016). We used the information derived from the biplot to develop meaningful sequential binary partitions for ilr transformation. Finally, a hierarchical cluster analysis (HCA) based on Euclidean square distance and Ward linkage was applied to the ilr coordinates. This method of performing an HCA means that the clustered groups represent compositional similarities in the simplex, rather than simply similarities in individual ion concentrations. Before applying the procedures described above, the data below the detection limit (typically NO3 and Al) were imputed using the log ratio data augmentation function (lrDA) in the R package zCompositions, which is a function based on the log ratio Markov chain Monte Carlo data augmentation (DA) algorithm (Palarea-Albaladejo and Martín-Fernández 2015). This algorithm provides a method of estimating values below the detection limit while preserving the relative structure of the data.

Geochemical modeling

Geochemical modeling was performed using PHREEQC (Parkhurst and Appelo 1999, 2013) with the Lawrence Livermore Laboratory (LLNL) database. Biotite, which is not included in the LLNL database, was added by the command PHASES, and its solubility constant (log K) of − 12.55 and enthalpy (ΔH) of 22 kJ/mol were used (Palandri and Kharaka 2004). Plagioclase was replaced by albite and anorthite (Choi et al. 2014; Gaus et al. 2005). To simulate the evolution of carbonate water, we formulated a hypothesis that the carbonate water originated from interactions between magmatic CO2, deep groundwater, and bedrock-forming minerals, and then the carbonate water moved up to the shallow groundwater aquifer along various geological structures (faults and fractures), finally resulting in the generation of CSW through a diverse range of processes including mixing, dilution, and water–rock interactions (Fig. 2). Based on this hypothesis, the evolutionary pathway of carbonate water in the deep environment as well as the formation of CSW was simulated by EPM in the PHREEQC code. EPM is considered to be a powerful tool for estimating aqueous phase concentrations of many elements using their saturation indices, which are included in the LLNL database. To simulate the primary stage for the generation of carbonate water in the deep bedrock aquifer, the deep groundwater was assumed to be meteoric water that has permeated into the deep bedrock aquifer under high CO2 conditions (Koh et al. 2000; Yun and Kim 2000; Choi et al. 2014). As the meteoric water moved into the deep environment, water–rock interactions might be enhanced due to the increase in the residence time and geothermal gradient. As a result, the meteoric water would change to groundwater with high ionic concentration. Choi et al. (2005) conducted a study to estimate the temperature at which the carbonate water was formed and reported a range of 100–251 °C. In the present study, the temperature for the generation of carbonate water was assumed to be 150 °C. The redox potential was also an important parameter in the simulation, with 70 mV (pe = − 0.833) assumed here based on the result provided by Koh et al. (2000). Another key parameter influencing the formation of carbonate water is the partial pressure of CO2 (\( P_{{{\text{CO}}_{2} }} \)) originating from magmatic gases. Schaller et al. (2012) reported the \( P_{{{\text{CO}}_{2} }} \) values of lavas erupted from numerous volcanoes with a maximum value of 4500 ± 1200 ppm; therefore, a CO2 concentration of 4500 ppm (0.102 mol/kg of water) was used in this study. All the simulations were conducted with the assumptions of a pressure of 1 atm and water density and mass of 1 g/cm3 and 1 kg, respectively. A full set of simulation parameters for each area is given in Table 3. The simulation of CSW formation was conducted by stepwise sequences. First, the evolution of carbonate water was simulated via interactions of magmatic CO2 with deep groundwater and the bedrock-forming minerals listed in Table 3. Second, the formation of CSW was simulated by mixing between the modeled carbonate water and shallow groundwater with interactions with the minerals included in weathered rocks (Table 3). The mixing ratios were adjusted in nine steps from 1:9 to 9:1. Third, the simulations of each mixing ratio were iterated 25 times with the change of temperature ranging from the average measured value of each CSW (16.8, 16.6, and 14.0 °C for the KW, CB, and GB areas, respectively) to 150 °C. Accordingly, 225 runs were undertaken for the simulations of each area. Finally, by comparing the hydrochemical properties between the simulated and real CSWs, the most relevant mixing ratio and temperature were obtained.

Fig. 2
figure 2

Conceptual diagram showing the geochemical evolution of CO2-rich spring water (CSW). DGW deep groundwater, MC magmatic CO2, BRFM bedrock-forming mineral, SCW simulated carbonate water, SGW shallow groundwater, and WRFM weathered rock-forming mineral

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Table 3 Conditions of equilibrium phases modeling for the simulation of geochemical evolution of CO2-rich spring water (CSW)
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Results and discussion

Water chemistry of CSW

The hydrochemical data of CSW used in this study are given in Tables 1 and 2. Based on the concentrations of the major ionic species, the hydrochemical facies of CSW in each area were analyzed using Piper plots (Fig. 3). Most CSWs were of the Ca–HCO3 type, but Na–HCO3-type CSWs were observed in five sites in the KW province. The Na–HCO3 type CSWs have a higher Na, K, and Si content than the Ca–HCO3 type CSWs, whereas the Ca–HCO3-type CSWs have higher Ca, Mg, and Fe concentrations (Table 2). This indicates that the Na–HCO3-type CSWs have undergone more severe silicate weathering processes than the Ca–HCO3-type CSWs (Choi et al. 2014). Despite their convenience, traditional Piper plots make meaningful interpretations about hydrochemical evolution difficult because of a messy arrangement of overlapping data (Owen et al. 2016). To compensate for this drawback of conventional Piper plots (Fig. 3), ternary principal components plots were prepared using CodaPack (Fig. 4). Figure 4 condenses the compositional variability into a descriptive tool for identifying the water types of CSW for each area based on the relationships between the relative proportions of major constituents (Owen et al. 2016). Overall, the CSW was much more affected by PC1 than by PC2. More specifically, 87% of the CSW seemed to be influenced dominantly by the behavior of Ca and Mg (PC1), while 13% of the CSW was characterized by Ca and Na + K (PC2) (Fig. 4a). On the other hand, 85% of the CSW appeared to be affected by Ca and HCO3 (PC1) and 15% was characterized by HCO3 and Cl (PC2), as shown in Fig. 4b. Using the relative proportions of K–Si–Fe shown in Fig. 4c, the relative effects of K-feldspar (Si–K, PC1) and biotite (Si–Fe, PC2) were interpreted. Most (95%) of the CSW tended to be influenced by PC1, while only 5% of the CSW was more likely affected by PC2. Finally, it was confirmed that 87 and 13% of the CSW were characterized as Ca–HCO3 and Mg–HCO3 types, respectively (Fig. 4d).

Fig. 3
figure 3

Piper diagram showing the hydrochemical facies of CO2-rich spring water (CSW) in each study area

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Fig. 4
figure 4

Ternary principal components plot. a Mg–Ca–Na + K, b Ca–Cl–HCO3, c K–Si–Fe and d Ca–Mg–HCO3

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To delineate the effect of water–rock interactions on the hydrochemical properties of the CSW, the relationship between molar ratios of major elements and TDS and HCO3 is presented in Fig. 5. First, the relative effects of albite and anorthite were elucidated using the molar ratio of Na and Ca (Fig. 5a). The lower ratios indicated that most of the CSW seemed to be affected by anorthite, except for five samples from the KW area of Na–HCO3 type. Comparing the relative effects of albite and K-feldspar using the molar ratio of K and Na (Fig. 5b), the CSW was more influenced by albite than by K-feldspar, except for one sample in the GB area. A significantly lower ratio of Si/Al was observed in most of the CSW (Fig. 5c), indicating that dissolution of primary minerals was dominant in most of the CSW. To examine the source of Fe, the molar ratios of Fe/SO4 were investigated (Fig. 5d). Most of the CSW from the KW area exhibited a relatively high molar ratio of Fe/SO4, indicating that these CSWs were predominantly affected by primary minerals bearing Fe or secondary minerals such as hematite, rather than pyrite. As shown in Fig. 4d, the effect of Ca was more dominant than that of Mg (Fig. 5e). Lastly, the relatively low ratios of Ca/HCO3 (Fig. 5f) indicate that the CSW likely originated from magmatic evolution rather than the interactions with carbonate minerals.

Fig. 5
figure 5

Schematic diagrams showing the relationships between molar ratios of major elements and TDS/HCO3 of CO2-rich spring water (CSW) in each study area. a Molar ratio (Na/Ca) versus TDS. b Molar ratio (K/Na) versus TDS. c Molar ratio (Si/Al) versus TDS. d Molar ratio (Fe/SO4) versus TDS. e Molar ratio (Ca/Mg) versus HCO3. f Molar ratio (Ca/HCO3) versus HCO3

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Results of compositional data analyses

The CSW within each area was classified statistically and interpreted using R, CodaPack, and SPSS programs. First, the R package zCompositions was used for imputation of values below the detection limit of compositional data based on the methodology proposed by Palarea-Albaladejo and Martín-Fernández (2015). The results of the imputation are given in Table 2. After the imputation, principal component analyses (PCA) were conducted using the CodaPack program. The clr biplots obtained from the PCA are presented in Fig. 6. The PCA results show that constituents such as Si, SO4, Mg, Cl, and H were distributed in the first component (PC1) with positive values, whereas others such as K, Na, HCO3, Ca, Fe, and Al had negative values on PC1. Additionally, the constituents with positive PC1 values were dominant in the CB and GB areas, but those with negative PC1 values appeared in the KW and in part of the CB area. Furthermore, the CSW of the CB area appeared to have positive PC1 and negative PC2 values, the CSW samples in the GB area dominantly had positive PC1 and PC2 components, and the CSW of the KW area tended to have negative PC1 and PC2 values. The reason why the density of the clr biplot was different between areas can be explained easily by the data shown in Table 2. It was confirmed that the constituents having the largest Euclidean distance from the center were Fe, NO3, and Mg (Fig. 6): their concentrations were much higher than those of other constituents. A hierarchical cluster analysis (HCA) was applied to classify the CSW according to area. Prior to the HCA, the ilrs of proportions of major ions derived from an intuitive sequential binary partition (SBP) were used to characterize the hydrochemical variability within and between the areas. There are two methods for developing a SBP: by experience and by PCA (Pawlowsky-Glahn and Egozcue 2011). In this study, the SBP was derived using the Euclidean distance of PCA (Table 4). Figure 7 presents an ilr dendrogram acquired from the SBP of CodaPack and explains the different behaviors of constituents in each area. In the CB area, a significant difference was not observed between the two groups of constituents (K, Na, and HCO3 vs. Ca, Al, and Fe). However, the K, Na, and HCO3 group was more dominant than that of Ca, Al, and Fe in the GB area, and vice versa in the KW area. Additionally, the effects of Mg, H, and NO3 were more dominant than those of Si, Cl, and SO4 in the CB area, but the tendency was the opposite in the GB and KW areas. Overall, the CSW of the GB area was more affected by Si, Cl, SO4, Mg, H, and NO3 than by K, Na, HCO3, Ca, Al, and Fe, but the opposite was true in the KW area. However, no significant difference was observed in the CB area. Using the ilr coordinates derived from the SBP, a HCA was conducted using SPSS (Fig. 8). The CSW was classified into five groups. The first cluster (C1) is characterized by having a lower concentration of Fe and a higher concentration of NO3, indicating that it was likely produced in a relatively shallow aquifer that had a relatively high recharge rate or was vulnerable to pollution. The second cluster (C2) tended to have lower concentrations of Fe and NO3 and may have formed in a shallow environment with a relatively low recharge. The CSW of the third cluster (C3) was characterized by higher Fe concentration and lower Al content, indicating that it was influenced by Fe-bearing minerals, such as hematite. The fourth cluster (C4) was Na–HCO3 type CSW. Finally, the CSW of the fifth cluster (C5) was likely affected by Fe-bearing silicate minerals, such as biotite, because of the relatively high concentrations of Fe and Al. Based on the HCA results, the proportions of CSW samples in each cluster are listed in Table 5. C1 encompassed 13 and 1 CSW samples from the CB and GB areas, respectively. Most of the CSW samples in the GB area appeared to belong to C2. Clusters C3 and C4 included only 5 CSW samples from the KW area. Finally, C5 was composed of 10 and 7 CSW samples from the KW and CB areas, respectively, which seemed to have been affected by biotite in the granite and metamorphic rocks that are distributed in those two areas. Consequently, the HCA conducted via calculation of clr and ilr revealed the structural variability of th CSW in each area, and the characteristics of water–rock interactions, external effects, and formation environments could be inferred from the HCA results.

Fig. 6
figure 6

A centered-log ratio (clr) biplot of data set for each study area. Cum.Prop.Exp = cumulative proportion of explained variance

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Table 4 Sequential binary partition (SBP) of a 11-part composition (x1, x2, …, x11) for describing isometric log ratio (ilr) coordinates for the hierarchical cluster analysis (HCA)
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Fig. 7
figure 7

Balance dendrogram showing distinctions in the isometric log ratio (ilr) as defined in Table 4

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Fig. 8
figure 8

Dendrogram showing the hierarchical cluster analysis (HCA) of CO2-rich spring water (CSW)

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Table 5 HCA results showing the CSW distribution of each area in five clusters
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Simulation of the geochemical evolution of CSW using equilibrium phase modeling

The geochemical evolution of CSW was simulated using EPM incorporated in the PHREEQC code, and the results are presented in Figs. 9, 10 and 11. As mentioned in “Geochemical modeling,” the evolution of CSW was simulated by a stepwise method. The first step was to simulate the formation of carbonate water in the deep environment as a result of the interaction between deep groundwater–magmatic–rock-forming minerals (Fig. 2), and the CSW was then generated via the geochemical processes of mixing between the simulated carbonate water and shallow groundwaters, and water–rock interaction. Accordingly, EPM was conducted to simulate the evolutionary stage of CSW just before it occurs on the surface. The simulated CSW is hereafter referred to as SCSW, to distinguish simulated results from field CSW data. The model lines on each graph shown in Figs. 9, 10, and 11 were obtained by connecting the lines acquired by simulation with different mixing ratios between the simulated carbonate water and shallow groundwater. For the simulation of each mixing ratio, the temperature was changed from 150 °C for simulation of deep carbonate water to the average values of each CSW (e.g., 16.8, 16.6, and 14.0 °C for the KW, CB, and GB areas). In this way, the final properties of the SCSW were similar to those of the real CSW. In the case of the KW area, two kinds of CSW (Ca–HCO3 and Na–HCO3 types) occurred and the simulations were conducted twice to compute each type of CSW. In the simulation for the Ca–HCO3-type CSW, the best fit was obtained at a temperature of 77.8 °C. On the other hand, the best simulation results were obtained at 150 °C for the Na–HCO3-type CSW. In the cases of the CB and GB areas, the best results were acquired at temperatures of 138.9 and 93.0 °C, respectively. A larger amount of albite was simulated to be dissolved at higher temperature, resulting in an increase in Na concentration. However, Ca concentration increased at lower temperature due to the dissolution of anorthite. By contrast, the concentrations of K, Mg, and Si were not likely to be affected by temperature. Hence, the relative proportion of Ca and Na can be used as an indicator to infer the depth of CSW formation because temperature can be directly linked to depth.

Fig. 9
figure 9

Simulation results for geochemical evolution of CO2-rich spring water (CSW) in Kangwon (KW) area

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Fig. 10
figure 10

Simulation results for geochemical evolution of CO2-rich spring water (CSW) in Chungbuk (CB) area

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Fig. 11
figure 11

Simulation results for geochemical evolution of CO2-rich spring water (CSW) in Gyeongbuk (GB) area

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The simulation results indicate that the depth of carbonate water formation increased with increasing temperature. However, as the carbonate water moved up along the various geological structures, it mixed with shallow groundwater and the temperature gradually changed. In addition to the temperature drop, water–rock interactions have taken place continuously. As a result, the water quality changed significantly and then approached equilibrium with increasing residence time. However, according to Koh and Chae (2008), the residence time of the CSW occurring within the study area was relatively short (15–50 years), indicating that the chemistry of the CSW might not have established a state of equilibrium. However, our simulations were conducted using the EPM of the PHREEQC code, and a state of equilibrium was assumed. For this reason, the water chemistry of the SCSW tended to deviate from that of the real CSW, as confirmed by the simulation results shown in Figs. 9, 10 and 11. The equilibrium state and formation temperature of each CSW could be estimated using the concentration ratio between Na, K, and Mg (Giggenbach 1988). A discrimination diagram is shown in Fig. 12, obtained by the method suggested by Giggenbach (1988). The Na–HCO3-type CSW of five sites within the KW area appeared to be equilibrated, but the other CSWs did not approach equilibrium. Additionally, based on the formation temperature shown in the discrimination diagram (Fig. 12), it can be speculated that the Na–HCO3-type CSW was formed at a relatively higher temperature range (100–230 °C). This indicates that the formation environment was deep and also that the residence time of this CSW was longer. As a result, the possibility of approaching the equilibrium state increased. Based on the simulation results (Figs. 9, 10, 11), the concentrations of K and Mg appeared to be different between the SCSW and the real CSW, which might be attributed to the difference in the degree of equilibrium state.

Fig. 12
figure 12

Giggenbach discrimination diagram to estimate the equilibrium state and formation temperature of carbonate water

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When the geochemical evolution of CSW was investigated by modeling, the mixing ratios between simulated carbonate water and shallow groundwater were adjusted. In the case of the Ca–HCO3-type CSWs occurring in the KW and GB areas, the simulation results were obtained by changing the mixing ratio between simulated carbonate water and shallow groundwater from 1:9 to 9:1. Mixing ratios of 1:9–5:5 were simulated for the Na–HCO3-type CSW of the KW area, while mixing ratios of 1:9–3:7 were used for the simulation of the CB area, resulting in a relatively smaller contribution of carbonate water. The results indicate that the CSW in this area was formed by the small amount of carbonate water in the deep environment or the large amount of shallow groundwater. These simulation results could be related to the results of the compositional data analyses. As shown in Table 5 and Fig. 8, the CSW was categorized into five groups. As mentioned in “Results of compositional data analyses,” the CSW belonging to C1 was characterized as having a lower concentration of Fe and a higher concentration of NO3, which indicates that these CSWs were produced in a relatively shallow aquifer with a high recharge. This is supported by the simulation results showing mixing ratios of 1:9–3:7, indicating a greater effect of shallow groundwater. On the other hand, the results of the compositional data analyses indicate that C2 which contained most of the CSW in the GB area was generated in a shallower aquifer with a lower recharge. This is supported by the simulation results in which mixing ratios of 1:9–9:1 were relevant, suggesting that the CSW of the GB area was affected more by carbonate water than by shallow groundwater.

This study proposed a schematic, but relatively simple methodology to simulate the formation of carbonate water in a deep environment and the geochemical evolution of CSW. By estimating the temperature of the groundwater system in each area, the depth of carbonate water formation may be calculated, because the formation temperature of carbonate waters can be speculated from the results of the study. Additionally, it was demonstrated that the behavior of various minerals can be evaluated via a simulation of the mixing of carbonate water with shallow groundwater, together with an interpretation of water–rock interactions.

Conclusions

There are three typical areas of naturally outflowing CSW in South Korea. This study was initiated to compare the hydrochemical properties of CSWs between areas and to classify them on the basis of any similarity in their chemistry. Only 5 CSW samples of the KW area were classified as Na–HCO3 type water; the other samples were Ca–HCO3 water type. Using the ternary principal components plot, the relative effects between major constituents on the properties of the CSW were delineated. Additionally, the CSW within the study area was classified to five groups via HCA analyses. The CSW of C1 was characterized as being formed in a shallower aquifer with a high recharge; most of the CSW in the CB area belonged to this group. Group C2, encompassing the CSW of the GB area, was speculated to have formed in a shallower environment with a lower recharge. The C3 group of CSW seemed to be greatly affected by Fe-bearing minerals, and only five samples of the KW area were included in this group. The CSW of the C4 group was Na–HCO3-type water and included only five samples from the KW area. Finally, group C5 was characterized as being affected by Fe-bearing silicate minerals, such as the biotite in granite and metamorphic rocks. This group was composed of 10 and 7 CSW samples from the KW and CB areas, respectively.

In addition to multivariate statistical analyses, we simulated the geochemical evolution of CSW using EPM. The simulation was conducted using stepwise approaches. First, we simulated the carbonate water originating from a deep environment through interactions among magmatic CO2, deep groundwater, and bedrock-forming minerals. Next, the geochemical evolution of CSW was estimated via the simulation of geochemical processes, including mixing between carbonate water and shallow groundwater and water–rock interactions taking place in a shallow environment. To acquire the best simulation results, modeling conditions, such as the mixing ratios between the simulated carbonate water and shallow groundwater, temperature, and rock-forming minerals, were adjusted according to the area of concern. Generally, the chemistry of simulated CSW was similar to that of real CSW. However, the simulated composition of some elements, such as K and Mg, was somewhat different from the real values, which might be attributed to the difference in the degree of equilibrium state between simulated and real systems. Based on the simulation results, the Na–HCO3-type CSW was interpreted to be formed at a higher temperature range than the Ca–HCO3 type CSW, indicating that the formation environment of Na–HCO3 type CSW was deeper. Furthermore, the simulation results suggest that the relative contribution of carbonate water in producing CSW could be estimated according to the areas of concern. Additionally, the simulation results on the mixing ratios between carbonate water and shallow groundwater and CSW formation temperature were intimately related to the HCA results, particularly for groups C1 and C2.

The significant contributions of the present study were (1) the methodology proposed could be effectively applied to studies investigating CSW distributed over extensive areas, (2) CSW chemistry could be simulated using equilibrium phase modeling and the formation temperature and depth of CSW could be estimated through modeling, with adjustment of the diverse range of temperatures of the system, and (3) the chief factors affecting the geochemical evolution of CSW from carbonate water originating in deep environments could be determined through modeling. Consequently, the methodology used in this study could be applied to predict the behavior of CO2 after its geological storage, as well as to evaluate the stability and security of geologically stored CO2.