Oxygen and Sulfur Isotope Systematics of Dissolved Sulfate in a Nonvolcanic Geothermal System: Sulfate Source, Evolution and Impact on Geothermometers

Abstract

Dual isotopes of sulfate (δ³⁴S_SO4 and δ¹⁸O_SO4), along with isotopes in water and trace elements of geothermal waters, are systematically investigated to quantitatively elucidate sulfate sources and oxygen and sulfur isotopic behaviors during deep groundwater circulation and to constrain reservoir temperatures in the Jimo nonvolcanic geothermal system on the eastern coast of China. The results show that δ³⁴S_SO4 and δ¹⁸O_SO4 values in geothermal waters ranged from −21.0 to 5.7‰ and from 1.1 to 8.8‰, respectively. An increase in SO₄ concentrations (140–796 mg/L) with a systematic decrease in δ³⁴S_SO4 and δ¹⁸O_SO4 values was observed along the flow path from the central to eastern and western parts. The sulfate in the Middle Group was predominantly from atmospheric deposition, with sulfide oxidation contributions of <27%. In contrast, 80–85% of SO₄ in the Eastern Group is derived from pyrite oxidation. In the Western Group, the oxidation of multiple metal sulfides contributed 43–66% of SO₄. Sulfate oxidation and mixing of shallow groundwater caused reservoir temperatures to be underestimated by 9 ± 6–14 ± 16% using silica and K-Mg geothermometers but overestimated by up to 52–62% using sulfate–water oxygen isotope geothermometers. The estimated average target reservoir temperature was 144 ± 8 °C, with geothermal waters circulating to depths of 3.6–4.6 km. This study offers new insights into the significant impact of sulfate-related processes on geothermometric estimates, a factor often overlooked when using aqueous geothermometers. It also provides valuable guidance for accurately estimating target geothermal reservoir temperatures and advancing exploration in nonvolcanic geothermal systems.

1. Introduction

Hydrochemical and isotope investigations of geothermal fluids are among the most economical and effective tools for geothermal exploration and development and utilization and can reflect thermal conditions at depth and provide critical information on the origin of geothermal fluids, subsurface flow direction and subsurface temperatures [1,2,3,4,5]. Estimating the target geothermal reservoir temperatures based on the chemical and isotopic compositions of geothermal water is one of the first steps in determining the potential use of a particular geothermal reservoir [1,6,7]. A wide variety of effective geothermometers, including chemical geothermometers (e.g., silica, Na-K, Na-K-Ca, K-Mg, Na-K-Mg and Na-Li), isotopic geothermometers (e.g., sulfate–water oxygen isotope geothermometer (¹⁸O(SO₄-H₂O)) and geothermometric modeling based on the chemical compositions of geothermal fluids, have been developed since the mid-1960s [6,7,8,9,10,11,12,13,14,15,16,17,18]. When applying these geothermometers, a principal assumption is always made that chemical and isotopic equilibrium between water and minerals is achieved in the source aquifer and cannot be significantly modified by secondary processes as the water ascends to the point of sampling [1,19]. However, this assumption is not necessarily true for all areas, especially where shallow secondary processes such as mixing re-equilibrium [20,21], mineral precipitation/dissolution reactions and degasification [7,17] are universal. In this case, the species concentrations and isotopic compositions can be altered, resulting in an apparent temperature discordant with the actual reservoir temperature [7,13]. Therefore, prior to estimating geothermal reservoir temperatures, it is necessary to acquire a sound understanding of the geochemical evolution of geothermal fluids and evaluate the impact of these processes on geothermometers, which is crucial for the sustainable use of geothermal water resources.

The Jimo geothermal system is located in the southeastern Jiaodong Peninsula, which is an important sector of the eastern coast of China, with abundant low- to medium-temperature geothermal resources [22,23,24]. Previous research based on the analysis of nonreactive elements (e.g., B and Cl), boron isotope (δ¹¹B) and strontium isotope (⁸⁷Sr/⁸⁶Sr) has suggested that high salinity observed in the study area (up to 10.8 g/L) results from the dissolution of marine evaporites and minor seawater mixing [23]. However, the significant variations in SO₄ concentrations and trace metal element concentrations across the western, central and eastern parts of a specific 0.2 km² area remain poorly understood. These variations, particularly regarding the sources and evolution of sulfate, cannot be fully explained by the previously proposed mechanisms for salinity. This also prevents the use of geochemical geothermometers to determine the proper geothermal reservoir temperature.

Sulfur and oxygen isotopes of sulfate (δ34S_SO4 and δ¹⁸O_SO4) have been proven to be robust tools for elucidating the evolution of sulfate in volcanic and nonvolcanic geothermal fluids [2,25,26,27]. The distinct δ34S_SO4 and δ¹⁸O_SO4 of dissolved sulfate derived from various sources, e.g., atmospheric deposition, seawater, evaporites, sulfide oxidation and magmatic degassing, may reveal sulfate origins in natural waters [2,26,28,29,30,31,32,33,34]. Furthermore, the original sulfur and oxygen isotope signals of sulfate are easily modified by secondary abiotic and biological processes, including sulfate reduction [35,36], disproportionation of magmatic SO₂ to H₂S and SO₄ [25] and oxygen isotope exchange between sulfate and water [37,38], that can be identified by the trend of the evolution in δ34S_SO4 values, δ¹⁸O_SO4 values and SO₄ concentrations.

Here, we combine new data on δ34S_SO4 and δ¹⁸O_SO4 values as well as trace elements in geothermal waters and shallow groundwaters with previously reported data on major ions (i.e., Na, K, Mg, Ca, HCO₃, SO₄ and Cl) to elucidate sulfate sources and geochemical processes related to the evolution of sulfate concentrations and sulfur and oxygen isotopes of sulfate and to quantitatively assess the influence of these secondary processes on chemical geothermometers, including chemical (chalcedony, quartz, Na-K, Na-K-Ca, K-Mg and Na-Li) and sulfate–water oxygen isotope geothermometers. We determined the deep geothermal reservoir temperature based on proper geothermometers. The Jimo geothermal system can serve as a model system for the quantitative identification of shallow secondary processes, especially sulfate-related processes, and for the assessment of their impact on aqueous geothermometers.

2. Geologic Setting

The Jimo geothermal system is located in the southeastern Jiaodong Peninsula in China, which neighbors the Yellow Sea in the east (Figure 1). Tectonically, the study area is situated in the Mouping–Jimo fault zone, which is an important part of the giant Tanlu strike–slip fault system, and forms the boundary between the North China Block and the Sulu orogenic belt [39] (Figure 1a). The Jimo geothermal field is located at the junction of the NE-trending Wenquan–Cangkou fault and the NW-trending Dongkuang–Shuibo fault (Figure 1b). The primary NE-trending Wenquan–Cangkou fault is a tensional fault at an early stage and a compressional fault at a later stage and provides a suitable geothermal pathway [40]. The NW extensional fault is a small-scale water-conducting fault. The dominant strata are Early Cretaceous Laiyang Group clastic rocks (K₁l) and Qingshan Group (K₁q) pyroclastic rocks. The Laiyang Group is a fluvial–lacustrine sedimentary sequence that includes sandstone, conglomerate and mudstone. The Qingshan Group consists of intermediate-acid and intermediate-basic volcanic rocks [23,41,42,43] (Figure 1b). Quaternary unconsolidated sediments are widely distributed in geothermal fields at depths of 10–25 m and consist of Holocene black marine mud, brown lagoon clay and lacustrine silty sediment from bottom to top [40]. Magmatic activity was intense during the Early Cretaceous, with widespread intrusive rocks such as granite, andesite, quartz monzonite and adamellite. Geothermal wells with depths ranging from 125 to 394 m are distributed at the junction of the NE and NW faults, with an area of 0.2 km² (Figure 1c). The maximum yield of a single well reaches 1019 m³/d. The lithology of the geothermal reservoir is dominated by Early Cretaceous Laiyang Group sandstone. The geothermal waters are rich in Br, K, Ca, Mg, I, Ra and Rn, with a content of 58.1 Bq/L, and are used for spas and baths [44,45].

3. Materials and Methods

3.1. Sampling and Laboratory Analysis

Geological field campaigns and sample collections were conducted in July and November 2017. Fourteen geothermal waters were sampled from geothermal wells at depths of 120 to 200 m. Sixteen additional shallow cold groundwaters were sampled from wells at depths of 10–40 m and three seawater samples were collected from the Yellow Sea at a depth of 1–1.5 m (Figure 1b). Sampling from geothermal wells and cold groundwater wells was performed after continuous pumping of the wells for more than 20 min. The temperature, pH, electrical conductivity (EC) and electromotive potential (Eh) were measured at the site with a portable multiparameter (HQ40D, Hach). The portable multiparameter was calibrated to a standard solution at 25 °C before sampling. Total alkalinity was titrated with a digital titrator (16900, Hach, Loveland, CO, USA) with 0.16 N sulfuric acid. All water samples were filtered at the site using a 0.45 μm syringe filter before the storage of water in HDPE bottles sealed with parafilm. Samples for major cation and trace element analysis were acidified to pH < 2 using 6 N redistilled HNO₃. Once collected, all the samples were stored at 4 °C for geochemical and isotope analysis within 3 months.

Major cations (K, Na, Ca and Mg) were analyzed with inductively coupled plasma optical emission spectroscopy (ICP–OES). Trace elements (e.g., Sr, Al, Fe, Mn, Mo, Zn, Tl and Pb) were analyzed with inductively coupled plasma–mass spectrometry (ICP–MS). The analytical precisions for major ions and trace elements were less than 0.5%. Major anions (Cl, SO₄ and NO₃) were analyzed with a DIONEX-500 ion chromatograph with a detection limit of 0.05 mg/L [23]. The oxygen isotopic compositions of water (δ¹⁸O_H2O) were measured in the Water–Rock Interaction Laboratory, Institute of Geology and Geophysics, Chinese Academy of Sciences (IGG-CAS) using a laser absorption water isotope spectrometer analyzer (Picarro L 1102-i). Calibration was performed using three reference materials: GBW04458 (δ¹⁸O = −0.15‰), GBW04459 (δ¹⁸O = −8.61‰) and GBW04460 (δ¹⁸O = −19.13‰). The precision (1σ) for δ¹⁸O_H2O was better than 0.1‰. The sulfur and oxygen isotopic composition of sulfate (δ³⁴S_SO4 and δ¹⁸O_SO4) were determined at the Laboratory for Stable Isotope Geochemistry, IGG-CAS using a Flash 2000 HT elemental analyzer coupled to a Delta V Advantage isotope ratio mass spectrometer (Thermo Fisher Scientific, Waltham, MA USA). Samples were prepared through acidification to pH < 3, boiling and precipitation of BaSO₄ by addition of BaCl₂ solution. The BaSO₄ was recovered by washing several times with deionized water and then oven-dried at 80 °C. The dried BaSO₄ was subsequently thermally decomposed in an elemental analyzer to produce SO₂ for δ³⁴S_SO4 analysis and in a pyrolysis reactor to generate CO for δ¹⁸O_SO4 analysis [47]. For δ³⁴S_SO4, two international standards (NBS127 and IAEA-SO-5) were used for normalization. The δ¹⁸O_SO4 was calibrated using two international standards (NBS127 and IAEA-601). The analytical uncertainties (1σ) were better than ±0.3‰ for δ³⁴S_SO4 and ±0.3‰ for δ¹⁸O_SO4. The oxygen and sulfur isotope ratios are expressed as δ-notions as per mil (‰) (δ = (R_sample/R_standard − 1) × 1000) relative to the Vienna Standard Mean Ocean Water (V-SMOW) standard (δ¹⁸O_H2O and δ¹⁸O_SO4) and to the Vienna Canyon Diablo Troilite (V-CDT) standard (δ³⁴S_SO4), respectively.

3.2. Interpretation Techniques

Geothermometric modeling is based on fundamental methods for calculating multicomponent chemical equilibria in aqueous systems [48]. During the modeling process, the chemical compositions of geothermal water are used to determine the temperature at which a set of minerals is in equilibrium with the geothermal water. This is achieved by plotting log(Q/K) versus temperature for various minerals. The average equilibrium temperature of the minerals can be regarded as the best estimate of the subsurface temperature. Geothermometric modeling in this study was conducted using the SOLVEQ-XPT program, along with the SOLTHERM-XPT data file [49]. This program allows for computing aqueous–mineral–gas equilibria at any specified pressure up to 5 kbar and temperature up to 600 °C.

A partial correlation analysis was applied to evaluate the influence of secondary processes on geothermometers and to identify the most influential processes. Statistical analyses were performed using SPSS 25.0.

4. Results

4.1. Geochemical Characteristics of Geothermal Fluids

The chemical and isotopic results for geothermal water, shallow groundwater and seawater are shown in

Table 1. Physical and chemical parameters and sulfur and oxygen isotopes of sulfate in geothermal waters, shallow groundwater and seawater.

Sample ID	Water Type	Tem a	pH a	Eh a	TDS a	SO4 a	δ18OH2O	δ34SSO4	δ18OSO4
		°C		mV	mg/L	mg/L	‰V-SMOW	‰V-CDT	‰V-SMOW
C63	SG	14.2	7.0	−19.8	651	113	−6.2	1.6	10.5
C64	SG	18.2	7.7	−64.4	661	25.4	−6.9	3.7	8.8
C66	SG	15.2	7.2	−31.6	889	94.5	−6.4	3.9	7.5
S2	SW	nd	7.9	−40.2	33,778	2316	−0.2	19.7	10.0
S3	SW	nd	8.0	−49.3	33,731	2327	−0.3	20.1	8.4
HW01	GW-M	89.5	6.8	−7.1	10,832	140	−8.3	5.7	6.1
HW03	GW-M	88.0	7.0	−21.9	8961	178	−8.3	0.6	7.6
HW04	GW-M	80.0	6.9	−16.4	6723	156	−7.9	−0.3	8.7
HW10	GW-M	86.0	6.7	1.3	6982	153	−7.9	nd	nd
HW13	GW-M	88.1	7.2	−19.5	8600	162	−8.2	−0.0	8.8
HW14	GW-M	86.7	7.1	−9.0	10,462	158	−8.4	1.1	8.4
HW06	GW-W	74.3	7.2	−30.5	2722	240	−7.1	−4.1	4.3
HW07	GW-W	70.0	7.4	−44.6	5077	247	−7.2	−4.5	6.2
HW11	GW-W	60.0	7.3	−39.6	2472	174	−6.1	nd	nd
HW12	GW-W	70.2	7.1	−27.6	3609	299	−6.6	nd	nd
HW15	GW-W	48.2	7.5	−18.3	4189	314	−6.4	−15.4	6.4
HW02	GW-E	66.8	6.8	−5.4	7182	603	−7.5	−14.0	3.5
HW05	GW-E	66.9	6.7	−1.7	7725	722	−7.9	−15.1	2.6
HW09	GW-E	60.0	4.2	157.2	8057	796	−7.9	−21.0	1.1

Note(s): SG: shallow groundwater, SW: seawater, GW-M: Middle Group geothermal water, GW-W: Western Group geothermal water, GW-E: Eastern Group geothermal water, Tem: wellhead temperature. ^a Data from [23].

and

Table 2. Trace elements in geothermal waters.

Sample ID	Water Type	Si a	Sr a	Al a	Fe	Mn	Mo	Zn	Tl	Pb
		mg/L	mg/L	μg/L	μg/L	μg/L	μg/L	μg/L	μg/L	μg/L
HW01	GW-M	54.9	52.8	4.21	242	243	13.9	16.0	7.9	0.11
HW03	GW-M	54.9	40.6	1.30	27	280	63.8	57.3	6.7	0.49
HW04	GW-M	51.7	34.6	2.36	7	256	35.7	11.6	8.2	2.08
HW10	GW-M	53.5	32.1	1.98	37	210	45.8	55.4	7.1	1.75
HW13	GW-M	54.6	41.1	0.81	21	280	36.4	16.5	7.5	0.03
HW14	GW-M	61.4	49.8	0.91	8	275	22.9	19.9	10.8	0.03
HW06	GW-W	25.7	7.89	1.47	11	118	63.4	148	3.4	9.97
HW07	GW-W	33.0	23.1	2.48	14	359	36.5	11.4	15.2	0.34
HW11	GW-W	35.8	6.53	0.61	42	79.7	9.9	32.8	0.8	0.28
HW12	GW-W	28.0	12.9	2.18	25	365	67.7	52.9	22.4	0.29
HW15	GW-W	28.5	16.5	0.81	94	366	10.1	18.4	4.0	1.74
HW02	GW-E	35.0	32.1	0.56	20	693	12.6	39.4	5.8	133
HW05	GW-E	35.9	36.6	0.47	<0.002	1280	10.7	51.7	19.4	80.6
HW09	GW-E	65.2	34.8	272	12,100	3390	1.4	245	161	99.4

Note(s): ^a data from [23].

. Major cations and anions of 14 geothermal waters, 12 shallow groundwaters and 3 seawaters from the previous study [23] are presented in Table S1. The geothermal water is dominated by Cl-Na·Ca and Cl-Na with high total dissolved solids (TDS) (2472–10,832 mg/L) and significant variations in the concentrations of trace elements, e.g., Al (0.47–272 μg/L), Fe (<0.002–12,100 μg/L), Mn (80–3390 μg/L), Mo (1.4–67.7 μg/L), Zn (11.4–245 μg/L), Pb (0.03–133 μg/L), Tl (0.8–161 μg/L), Sr (6.5–52.8 mg/L) and Si (25.7–65.2 mg/L). The TDS and wellhead temperatures exhibited similar decreasing patterns from the central to the western and eastern parts (Figure 2a,b), consistent with the flow pattern for deep hot water that upwells from the middle area close to the junction of the NE-trending Wenquan–Cangkou fault and NW-trending Dongkuang–Shuibo fault and then flows to the west and east (Figure 1c). In contrast, the pH and Eh data indicate a gradual transition in the geothermal environment, from acidic and oxidizing conditions (pH = 4.2, Eh = 157.2 mV) in the eastern parts to weakly alkaline and reducing conditions (pH = 7.5, Eh = −44.6 mV) in the central and western parts (Figure 2c,d). Geothermal water samples were classified into three groups according to their geographical distribution, temperature and physicochemical characteristics: the Middle Group, Western Group and Eastern Group. The Middle Group samples were characterized by the highest TDS (6.7–10.8 g/L) and lowest SO₄ concentration (140–178 mg/L) and SO₄/Cl molar ratio (0.008–0.015) (Table 1). The Western Group samples exhibited lower TDS (2.5–5.1 g/L) but higher SO₄ (174–314 mg/L) and SO₄/Cl molar ratios (0.032–0.063) than the Middle Group samples. The Eastern Group samples exhibited the highest SO₄ concentration (603–796 mg/L) and SO₄/Cl molar ratio (0.057–0.069) with relatively constant TDS (7.2–8.1 g/L). Compared with geothermal waters, shallow groundwater samples had lower TDS (559–1118 mg/L), SO₄²⁻ (25.4–156 mg/L), Si (4.1–12.6 mg/L), Sr (0.56–2.2 mg/L) and Al (<0.002–1.25 μg/L) concentrations but higher SO₄/Cl molar ratios (0.23–1.27) (Table S1).

4.2. Sulfur and Oxygen Isotopes (δ¹⁸O_SO4 and δ³⁴S_SO4) in Sulfate

The δ³⁴S_SO4 values for dissolved sulfate in geothermal waters varied from −21.0‰ to 5.7‰, which were much lower than those of seawater (19.7 to 20.1‰) and overlapped with those of shallow groundwater (1.6 to 3.9‰) (Table 1). The δ³⁴S_SO4 values for dissolved sulfate in geothermal waters in the study area are also much lower than those in volcanic geothermal waters worldwide (−2.0‰ to +24.7‰ [3,50]) and in nonvolcanic geothermal waters, e.g., 26‰ to 30‰ for the Tangquan Karst geothermal system [26] and 3.17‰ to 17.89‰ for in Pearl River Delta region [2] in the east China region (Figure 3). The δ¹⁸O_SO4 values for sulfate in geothermal waters ranged from 1.1‰ to 8.8‰, which were lower than those of seawater (8.4 to 10.0‰) and shallow groundwater (7.5 to 10.5‰). Besides, in geothermal waters, the δ¹⁸O_SO4 values for dissolved sulfate were 9–17‰ higher than the δ¹⁸O_H2O values for water (−8.4 to −6.1‰). The measured δ³⁴S_SO4 and δ¹⁸O_SO4 for seawater sulfate around the Jimo geothermal systems were close to those of modern seawater sulfate (δ³⁴S_SO4 = 21.0 ± 0.2‰ [51], δ¹⁸O_SO4 = 9.5‰ [52]). The decreasing trends of the δ³⁴S_SO4 and δ¹⁸O_SO4 values for the geothermal waters from the Middle Group to the Western Group and Eastern Group (Table 1) were consistent with those of the TDS and temperature, while they contrasted with the increasing trend of the SO₄ concentration.

5. Discussion

5.1. Geochemical Evolution of Geothermal Water

The geochemical variations in the Middle Group, Western Group and Eastern Group samples indicate that processes occurred along the flow pathway (Figure 4). Sample HW01 in the Middle Group is located at the cross-section of faults with the highest TDS and temperature and can be regarded as a deep-sourced fluid compared with the other samples. The significant increases in the concentrations of metal elements such as Fe, Mn, Zn, Pb and Tl, especially Fe, in HW09 were 50 times higher than those in HW01. This was accompanied by a much lower pH and higher Eh, SO₄ concentration and SO₄/Cl ratio, suggesting that the excess sulfate in Eastern Group samples may have resulted from the oxidization of metal sulfides, predominantly pyrite oxidization [31]. Moreover, the acidic environment further accelerated silicate and carbonate dissolution, as indicated by the synchronous increases in Al/Cl, Si/Cl, Ca/Cl and Mg/Cl.

In contrast to the SO₄ concentrations in the Middle Group samples, those in the Western Group samples slightly increased with increasing pH. The slight increases in the concentrations of Zn, Mn, Mo and Tl compared with those in HW01 indicated that oxidization of assemblages of metal sulfides (ZnS, MnS, MnS₂, MoS₂) also occurred. Unlike in HW09, which is dominated by pyrite oxidization, the multimetal oxidization effect is relatively weaker and might be partially covered by mixing of shallow groundwater, as indicated by the lowest TDS and Cl concentrations and temperatures among the three groups. The significant increase in SO₄/Cl ratios with a slight increase in SO₄ for the Western Group samples could be the result of the compatible effect of mixing and metal sulfide oxidization. The lower variations in SO₄, pH, temperature and SO₄/Cl for the Middle Group samples indicate the lower influence of shallow secondary processes, but a tiny fraction of metal-sulfide oxidization cannot be ruled out due to the difference in trace metal elements, such as the increase in Zn, Mn and Mo, compared with those in HW01.

5.2. Sources of Sulfate Constrained by Sulfur and Oxygen Isotope Systematics

Sulfate derived from natural sources, including sulfide oxidation, gypsum dissolution, soil sulfate and atmospheric deposition, exhibits different δ¹⁸O_SO4 and δ³⁴S_SO4 values (Figure 5, [28,36]). Physical and biogeochemical processes, including the mixing of potential sources with different isotopic compositions, bacterial sulfate reduction and oxygen isotope exchange between sulfate and water, cause the evolutions of δ¹⁸O_SO4 and δ³⁴S_SO4 values to have different trends (Figure 5a). The diagram of δ³⁴S_SO4 vs. δ¹⁸O_SO4, combined with the lithology of the geothermal reservoirs (e.g., sandstone with overlying Quaternary sediments) and the recharge sources of geothermal water in the study area, was used to constrain the dominant sulfate sources in Jimo geothermal waters.

The plot of δ³⁴S_SO4 vs. δ¹⁸O_SO4 shows that sulfate in shallow groundwater samples derives from atmospheric deposition. The sulfate in Middle Group geothermal water samples also originates from atmospheric deposition, but it is much older than that in shallow groundwater. This is supported by the geothermal water samples plotted on the local meteoric water line in the δ¹⁸O_H2O–δ²H_H2O diagram, depleted in ²H and ¹⁸O relative to shallow groundwater, and by the ¹⁴C age of geothermal water (~10,010 years; ¹⁴C: 17.40 pMC), which is older than that of shallow groundwater (~2500 years; ¹⁴C: 72.5 pMC) [23]. Thus sulfur-containing atmospheric deposits with high δ³⁴S_SO4 values are carried by paleometeoric water into the deep geothermal reservoirs. The δ³⁴S_SO4 and δ¹⁸O_SO4 values for sulfates in Eastern Group geothermal water samples are comparable to those of sulfate derived from the oxidation of reduced inorganic sulfide. This is additionally confirmed by the typical characteristics of sulfide oxidation, i.e., increases in SO₄ concentrations and SO₄/Cl ratios with decreases in δ³⁴S_SO4 and δ¹⁸O_SO4 (Figure 6). Combined with the evidence from the major and trace elements shown in Section 5.1, the sulfide is dominated by pyrite. The δ¹⁸O of sulfate formed by pyrite oxidation depends on oxidation processes; more specifically, this process involves the incorporation of oxygen atoms dominated by oxygen molecules (δ¹⁸O_O2 =23.8‰, Equation (1)) or water molecules (generally depleted ¹⁸O, Equation (2)) [36,57,58,59]. In reaction (1), 87.5% of the sulfate oxygen is derived from oxygen molecules and the remaining 12.5% is derived from water molecules, which yielded a relatively ¹⁸O-rich sulfate. In reaction (2), 100% of the oxygen in sulfate is contributed by water molecules, and sulfate is depleted of ¹⁸O [31]. In addition, the process of pyrite oxidation by ferric (Fe³⁺) iron adds more moles of H⁺ for each mole of pyrite oxidized and causes a lower pH compared with that of reaction (1) [60].

FeS₂(s) + 7/2O₂(g) + H₂O(l)→Fe²⁺(aq) + 2SO₄²⁻(aq) + 2H⁺(aq)

(1)

FeS₂(s) + 14Fe³⁺(aq) + 8H₂O(l)→15Fe²⁺(aq) + 2SO₄²⁻(aq) + 16H⁺(aq)

(2)

To determine the predominant oxidation pathway of pyrite, the relative percentages of oxygen in sulfate incorporated by atmospheric O₂ and water were quantified using the δ¹⁸O_SO4 for sulfate and the δ¹⁸O_H2O values for water based on the stable isotope mass balance (Equation (3), [31,61]).

δ¹⁸O_SO4 = f × (δ¹⁸O_H2O + ε_SO4-H2O) + (1 − f) × [0.875 × (δ¹⁸O_O2 + ε_SO4-O2) + 0.125 × (δ¹⁸O_H2O + ε_SO4-H2O)]

(3)

where f is the fraction of water-derived oxygen in sulfate through Equation (2), and (1 − f) represents the fraction of oxygen in sulfate derived from atmospheric oxygen and water through Equation (1).

Notably, ε_SO4-H2O (+4.1‰) and ε_SO4-O2 (−11.2‰) are the isotopic enrichment factors for the incorporation of oxygen from water and atmospheric oxygen, respectively [57,62]. The oxygen mass balance suggests that the process of pyrite oxidation by ferric iron (Equation (2)) contributed to 51–66% of the oxygen in sulfate in Eastern Group geothermal waters (Figure 5b). Geothermal waters containing a greater percentage of water-derived oxygen in SO₄ are expected to have a lower pH since the H⁺ produced from the process of pyrite oxidation by ferric iron is much greater than that produced by atmospheric oxygen (Equation (1)), which was further confirmed by the lowest pH of 4 observed in HW09, which has the highest SO₄/Cl molar ratio (0.069) (Figure 4).

Western Group geothermal waters exhibit large variations in δ³⁴S_SO4 values and relatively constant δ¹⁸O_SO4 values (Figure 5). This cannot be explained by a dominant single source (e.g., atmospheric precipitation or oxidation of sulfide minerals) or the influence of bacterial sulfate reduction, which generally results in a 1:4 kinetic relationship between the δ¹⁸O_SO4 and δ³⁴S_SO4 of sulfate [35,36]. The δ³⁴S_SO4-δ¹⁸O_SO4-SO₄-SO₄/Cl relationship suggests both the influence of sulfide oxidation and mixing of shallow groundwater with low SO₄²⁻ concentrations but higher δ³⁴S_SO4 values and SO₄/Cl ratios (Figure 6), which is consistent with the explanation of geochemical characteristics in Section 5.1. Due to the involvement of multiple metal sulfides and the significant influence of shallow groundwater, it is challenging to identify sulfide oxidation pathways.

The exchange of oxygen isotopes between sulfate and water may also add a degree of uncertainty to the interpretation of δ¹⁸O_SO4. The isotope exchange rate depends on the temperature and is inversely proportional to the pH of the aquifer water. Five hundred years is sufficient to reach 90% equilibrium at 100 °C at a pH of 7 [1]. Under the conditions of a deep reservoir, the pH, high temperature (>the highest measured wellhead temperature of 89.5 °C) and fluid residence time (about 10,010 years) are sufficient to achieve oxygen isotope exchange equilibrium between sulfate and water. However, the reservoir temperature is estimated to reach 198 °C for Eastern Group samples, which is 50 °C higher than that estimated for HW01 (Figure 5c). This suggests that the pyrite oxidation process disturbed the oxygen isotopic equilibrium between sulfate and water in the deep reservoir. In addition, the observed fractionation of oxygen isotopes between sulfate and water (10³lnα_SO4-H2O) in geothermal waters ranges from 9 to 17‰, which is lower than the expected fractionation of 20–26‰ when oxygen isotope exchange equilibrium is achieved at a wellhead temperature of 48.2–89.5 °C (Figure 5d), especially for the Eastern Group and Western Group samples, suggesting that oxygen isotope re-equilibrium at shallow depth has not been achieved. Overall, sulfide oxidation at shallow depths disturbs the oxygen isotope exchange equilibrium between sulfate and water in deep reservoirs and is not completely masked by the shallow oxygen isotope exchange between sulfate and water.

5.3. Quantitative Contributions of Sulfate Sources and Sulfur Isotope of Sulfides

Dissolved sulfate in geothermal water originates from sulfide oxidation, mixing of shallow groundwater (atmospheric precipitation in ~2500 BP) and deep geothermal water represented by HW01 (atmospheric precipitation in the late Pleistocene), which can be quantified based on the mass balance of sulfate and chloride.

(1)

The proportion of solutes from shallow groundwater (x) in the mixing process of shallow groundwater and HW01 is determined based on the Cl mass balance model:

$$x{\mathrm{n}}_{\mathrm{Cl}\left(\mathrm{SG}\right)\mathrm{Mea}}+(1-x){\mathrm{n}}_{\mathrm{Cl}\left(\mathrm{HW}01\right)\mathrm{Mea}}={\mathrm{n}}_{\mathrm{Cl}\left(\mathrm{GW}\right)\mathrm{Mea}}$$

(4)

(2)

The expected SO₄ concentrations formed by the mixing of shallow groundwater and HW01 are as follows:

$$x{\mathrm{n}}_{\mathrm{SO}4\left(\mathrm{SG}\right)\mathrm{Mea}}+(1-x){\mathrm{n}}_{\mathrm{SO}4\left(\mathrm{HW}01\right)\mathrm{Mea}}={\mathrm{n}}_{\mathrm{SO}4\left(\mathrm{GW}\right)\mathrm{Cal}}$$

(5)

(3)

The excess sulfate derived from sulfide oxidation:

$$\Delta {\mathrm{n}}_{\mathrm{SO}4}={\mathrm{n}}_{\mathrm{SO}4\left(\mathrm{GW}\right)\mathrm{Mea}}-{\mathrm{n}}_{\mathrm{SO}4\left(\mathrm{GW}\right)\mathrm{Cal}}$$

(6)

(4)

Contributions from different sources:

Sulfide oxidation:

$$Y_{\mathrm{SO}}=\Delta {\mathrm{n}}_{\mathrm{SO}4}/{\mathrm{n}}_{\mathrm{SO}4\left(\mathrm{GW}\right)\mathrm{Mea}}$$

(7)

Shallow groundwater:

$$Y_{\mathrm{SG}}=x(1-Y_{\mathrm{SO}})$$

(8)

HW01:

$$Y_{\mathrm{HW}01}=(1-x)(1-Y_{\mathrm{SO}})=1-Y_{\mathrm{SO}}-Y_{\mathrm{SG}}$$

(9)

where n_SO4(SG)(n_Cl(SG)), n_SO4(GW)(n_Cl(GW)) and n_SO4(HW01)(n_Cl(HW01)) refer to the concentration of SO₄²⁻ (Cl⁻) in the shallow groundwater (SG), geothermal water except for HW01 (GW) and HW01; Δn_SO4 refers to the excess sulfate; and _Mea and _Cal represent the measured and calculated values, respectively. x is the proportion of solutes from shallow groundwater during the mixing process of shallow groundwater and HW01. Y_SO, Y_SG and Y_HW01 are the proportions of sulfate from sulfide oxidation, shallow groundwater and HW01, respectively.

With an average SO₄ concentration of 0.94 ± 0.31 mmol/L and a Cl concentration of 3.25 ± 0.83 mmol/L for shallow groundwater (Figure 7), the results show that the sulfates of the Middle Group geothermal water samples are less affected by the mixing of shallow groundwater (0–31%) and sulfate oxidation (<27%) and are dominated by sulfate from HW01 (46–85%). In contrast, sulfide oxidation contributes significantly to the sulfate content in the Western Group and Eastern Group geothermal water samples. For the Western Group samples, the proportions of sulfate produced by sulfide oxidation range from 43 to 66%, with the contributions of shallow groundwater (23–47%) being greater than those of deep geothermal water (8–19%). For Eastern Group samples, sulfide oxidation contributes 80–85% of the total SO₄, with higher proportions of sulfate from HW01 (10–12%) than from shallow groundwater (5–8%).

Due to the lack of direct measurements of δ³⁴S values for sulfides in the study area, the δ34S values for sulfides (R_sulfide) are calculated based on isotope mass balance using the δ34S_SO4 values of shallow groundwater (R_SG), geothermal water (R_GW, excluding HW01) and HW01 (R_HW01) (Equation (10)). It was assumed that there is no discernible difference between δ³⁴S_sulfide in the parent sulfides and associated dissolved sulfate during the inorganic oxidation of sulfide (Δ_SO4-Sulfide ≈ 0, [29,63]). The expected δ34S values for sulfides range widely from −35.9‰ to −13.2‰ in the western area; however, the δ34S values for pyrite in the eastern area are relatively constant, ranging from −29.5‰ to −21.9‰ (Figure 5). The inferred δ³⁴S values for sulfides are generally lower than those of igneous rocks but fall within the range of sedimentary sulfides from a variety of settings (Figure 3). Considering that Quaternary sediments, consisting of black marine mud, brown lagoon clay and lacustrine silty sediment, are widely distributed in the Jimo geothermal field at depths of 10–25 m [40], the sulfide minerals with inferred low δ³⁴S values are mostly likely to be derived from Quaternary sediments.

$$Y_{\mathrm{SO}}{\Delta \mathrm{n}}_{\mathrm{SO}4}{\mathrm{R}}_{\mathrm{sulfide}}+Y_{\mathrm{SG}}{\mathrm{n}}_{\mathrm{SO}4\left(\mathrm{SG}\right)\mathrm{Mea}}{\mathrm{R}}_{\mathrm{SG}}+Y_{\mathrm{HW}01}{\mathrm{n}}_{\mathrm{SO}4\left(\mathrm{HW}01\right)\mathrm{Mea}}{\mathrm{R}}_{\mathrm{HW}01}={\mathrm{n}}_{\mathrm{SO}4\left(\mathrm{GW}\right)\mathrm{Mea}}{\mathrm{R}}_{\mathrm{GW}}$$

(10)

5.4. Impact on Geothermometers and Estimation of Geothermal Reservoir Temperature

5.4.1. Evaluation of the Influence of Secondary Processes on Different Geothermometers

Based on the geochemistry of geothermal waters, the temperatures of the Jimo geothermal reservoir have been estimated by 21 geothermometers, including silica geothermometers (chalcedony and quartz [8,10,64,65]), cation geothermometers (Na-K [12,13,64,66,67,68], Na-K-Ca [14], Na-K-Ca with Mg correction [9], K-Mg [13] and Na-Li [69,70], Li-Mg [71]) and sulfate–water oxygen isotope geothermometers [16,35,72] (Figure 8, Table S2). The temperatures estimated by different chalcedony and quartz geothermometers range from 104 ± 18 °C to 133 ± 17 °C (Table S3). The Mg-corrected Na–K–Ca geothermometer yielded a relatively lower temperature (147 ± 11 °C) than the Na–K–Ca geothermometer without correction (168 ± 11 °C). K-Mg geothermometers record a temperature of 115 ± 8 °C, which is similar to that of chalcedony. Sulfate–water oxygen isotope geothermometers yield temperatures ranging from 135 ± 34 °C to 142 ± 30 °C. The Na-K geothermometers yield much higher reservoir temperatures (156 ± 10 °C to 201 ± 8 °C) than the other geothermometers. The Na–K–Mg triangle diagram suggests that not all of the geothermal water has reached the equilibrium and is partially equilibrated and immature; thus, Na-K geothermometers are not applicable in low- to medium-temperature Jimo geothermal systems (Figure S1). In contrast, the reservoir temperatures estimated by the Na-Li (69 ± 9–79 ± 9 °C) and Li-Mg (90 ± 4 °C) geothermometers are even lower than the wellhead temperatures and thus are not applicable to the Jimo geothermal system. In addition to the abnormally high and low temperatures measured by the Na-K, Na-K-Ca without Mg correction, Li-Na and Li-Mg geothermometers, the other geothermometers yield reservoir temperatures ranging from 105 ± 19 to 147 ± 11 °C. However, temperatures estimated by the same geothermometer vary up to 50–100 °C among different samples, suggesting the influence of secondary processes.

The impacts of different secondary processes on quartz, chalcedony, Na-K-Ca, K-Mg and sulfate–water oxygen isotope geothermometers were evaluated using the partial correlation relationships between the geothermometer and sulfate contributions from sulfide oxidation (Y_SO), shallow groundwater (Y_SG) and HW01 (Y_HW01) (

Table 3. Partial correlation relationships of geothermometers and secondary processes, and the extent to which the reservoir temperatures estimated for geothermal samples (except for HW01) deviate from those estimated for HW01.

Methods	Geothermal Reservoir Temperature, T (°C)			Partial Correlation Coefficient			ΔT = (T − THW01)/THW01 (%)
	HW01	HW09	Average ± SD a (n = 14)	YSO	YSG	YHW01	Max-Derivation	Average ± SD b
Chalcedony [8]	121	132	105 ± 19	−0.395	−0.562 *	0.383	−36	−14 ± 15 (n = 13)
Chalcedony [64]	118	129	104 ± 18	−0.395	−0.562 *	0.383	−34	−13 ± 15 (n = 13)
Quartz [10]	147	157	132 ± 17	−0.395	−0.562 *	0.383	−27	−11 ± 11 (n = 13)
Quartz [8]	146	157	132 ± 17	−0.396	−0.562 *	0.383	−27	−10 ± 12 (n = 13)
Quartz [65]	146	157	132 ± 17	−0.396	−0.562 *	0.383	−27	−10 ± 12 (n = 13)
Na-K-Ca Mg corr [9]	156	134	147 ± 11	−0.447	−0.424	0.306	−17	−6 ± 7 (n = 13)
K-Mg [13]	126	109	115 ± 8	−0.730 ***	−0.652 **	0.437	−18	−9 ± 6 (n = 13)
18O(SO4-H2O) [72]	128	196	141 ± 31	0.898 ***	−0.624 *	−0.725 **	53	11 ± 24 (n = 10)
18O(SO4-H2O) [16]	130	198	142 ± 30	0.899 ***	−0.624 *	−0.730 **	52	10 ± 24 (n = 10)
18O(SO4-H2O) [35]	121	196	135 ± 34	0.897 ***	−0.623 *	−0.718 **	62	13 ± 28 (n = 10)

Note(s): the significance levels are indicated: *** p < 0.01, ** p < 0.05, * p < 0.1. ^a The average geothermal reservoir temperatures with standard deviations (average ± SD) of 14 geothermal water samples (Table S3). ^b The average values with standard deviations (average ± SD) of 10–13 geothermal water samples, representing the extent to which the reservoir temperatures estimated for these geothermal samples (except for HW01) deviate from those estimated for HW01 (ΔT = (T − T_HW01)/T_HW01 (%)) (Table S4).

). The extent to which the reservoir temperatures estimated for the geothermal samples (T) deviated from those estimated by HW01 (T_HW01) was also assessed (ΔT = (T − T_HW01)/T_HW01 (%)) (Table S4). The partial correlation coefficient of the Y_SG and silica (chalcedony and quartz) geothermometers is −0.562 at a significance level of p < 0.1. The mixing of shallow groundwater may cause the deep reservoir temperature to be underestimated by 10 ± 12–14 ± 15% on average, with the largest deviations of 27–36% for the Western Group samples. In addition, the reservoir temperature is overestimated by 7–9% for HW09, suggesting that sulfate oxidation can play a dominant role in silica geothermometers when the pH is low enough to dissolve silicate. The K-Mg geothermometer is strongly affected by sulfate oxidation, with a partial correlation coefficient of −0.730 at a significance level of p < 0.01. Sulfate oxidation accelerates water–rock interactions by differential dissolution of rock minerals and precipitation of secondary minerals, destroying the original K²/Mg by decreasing K²/Mg. The K-Mg geothermometer is also influenced by the mixing of shallow groundwater due to a decrease in temperature, which causes unsaturated water with primary rock minerals and enhances the mineral dissolution rate and decreases the K²/Mg ratio [1]. In general, the deep reservoir temperatures are underestimated by 9 ± 6% on average, with the largest deviation of 18% by the K-Mg geothermometer. The sulfate–water oxygen isotope geothermometer is sensitive to the environment and is significantly influenced by sulfide oxidation, other undetermined reasons and mixing of shallow groundwater, with partial correlation coefficients of 0.897~0.899 (p < 0.01), −0.718~−0.730 (p < 0.05) and −0.623~−0.624 (p < 0.1), respectively. Sulfide oxidation can lead to a higher reservoir temperature, as estimated by sulfate–water oxygen isotope geothermometers, because the addition of oxygen from water to sulfate decreases the difference in δ¹⁸O values between sulfate and H₂O. The undetermined factors lowering the predicted temperatures may be the exchange of oxygen isotopes between sulfate and water at lower temperatures at shallow depths. The temperatures estimated by the sulfate–water oxygen isotope geothermometer, on average, were overestimated by 10 ± 24–13 ± 28%, especially for Eastern Group samples, which are significantly influenced by sulfate oxidation, for which the temperature can be abnormally overestimated by up to 52–62%. The influence of secondary processes on the Na-K-Ca geothermometer with Mg correction is not significant, as the partial correlation coefficient is less than 0.5 (p > 0.1), indicating that the reservoir temperature was underestimated by 6 ± 7% on average. Generally, the degree to which the estimated temperatures based on the geothermometers in the middle group deviated from those in the HW01 group is small, ranging from 0–6%, except for those estimated by the sulfate–water oxygen isotope geothermometer, which underestimated the reservoir temperature by 11–20% (Table S4).

5.4.2. Geothermal Reservoir Temperature

Compared with classical geothermometers, which calculate the solubility of a few minerals or (semi-)empirical correlations, geothermometric modeling involves complete fluid analyses and a solid thermodynamic basis [7,73]. It is useful to identify equilibrated and nonequilibrated waters, especially to detect and eliminate mixing and CO₂ loss processes to reconstruct the existing equilibrium information. The geothermal reservoir in the study area is dominated by sandstone, consisting of quartz, plagioclase, K-feldspar, clay, calcite, anhydrite and dolomite (Table S5). Based on the lithology of the geothermal reservoir in the study area and in similar geothermal environments, an assemblage of eight minerals, including chalcedony, microcline, calcite, dolomite, kaolinite, Ca-montmorillonite, Mg-montmorillonite and anhydrite, were selected for thermodynamic simulation. Geothermometric modeling was conducted for samples HW01 and HW04, which are not significantly related to shallow processes of sulfate oxidation.

A Q/K graph for HW01 shows that different mineral curves scatter over a temperature range from 80 to 150 °C (Figure 9a). In addition, the supersaturation of calcite and dolomite at the sampling and chalcedony temperatures indicates that CO₂ degassing occurred. The dilution and CO₂ loss effects were eliminated by the addition of 0.0008 mol/L CO₂ and removal of 0.2 kg of water from the initial 1.0 kg of solvent water (Figure 9b), which changed the pH from the measured value of 6.78 to a computed value of 5.86. The reconstructed Q/K graph with good convergence reveals a reservoir temperature of 143 ± 4 °C, ranging from 135 to 149 °C. The same processes were also conducted on HW04, and a similar equilibrium temperature was achieved at 140 ± 5 °C in the range of 132–147 °C by the addition of 0.0015 mol/L CO₂ and removal of 0.35 kg of water from the initial 1.0 kg of solvent water (Figure 9c,d).

The geothermal reservoir temperature of 142 ± 5 °C calculated by geothermometric modeling agrees well with the average temperature of 147 ± 11 °C calculated by the magnesium correction Na-K-Ca geothermometer. It is reasonable to infer that the geothermal reservoir temperature in the study area is 144 ± 8 °C on average. Accordingly, geothermal water circulates at depths of 3.6–4.6 km based on a geothermal gradient (G) of 29–37 °C/km, a constant temperature zone depth (Z₀) of 20 m and a normal temperature zone temperature (T₀) of 12.3 °C (Equation (11), [48,49]).

Z = Z₀ + (T_z − T₀)/G

(11)

where Z and Z₀ are the circulation depth of the water and the depth of the constant temperature zone, respectively (km); T_z and T₀ are the temperatures (°C) of the geothermal reservoir and the normal temperature zone, respectively; and G is the geothermal gradient (℃/km).

5.5. Conceptual Model of the Sulfur and Oxygen Isotope Evolution of Sulfate

The geothermal fluid evolution history and the conceptual model of the sulfur and oxygen isotope evolution of sulfate in Jimo geothermal water are shown in Figure 10. Paleometeoric water carrying sulfur-containing atmospheric deposits with high δ³⁴S_SO4 values infiltrates into the deep crust at depths of 3.6–4.6 km. The δ¹⁸O_SO4 of dissolved sulfate is influenced by oxygen isotope exchange between sulfate and water at a geothermal reservoir temperature of 144 ± 8 °C. When deep geothermal fluids migrate from the deep reservoir to the surface and flow from the central parts to the eastern and western parts, geothermal water experiences sulfide oxidation and mixing of shallow groundwater. In the middle parts, the sulfate from sulfide oxidation and shallow groundwater mixing were less than 27% and 31% of the total SO₄, respectively. In the eastern parts, 80–85% of the total SO₄ is derived from pyrite oxidation, which increases SO₄ concentrations and decreases δ³⁴S_SO4 and δ¹⁸O_SO4 values. The low pH caused by pyrite oxidation further induces carbonate and silicate dissolution, introducing Ca, Mg, Al and Si into the geothermal water. In the western region, the increasing influence of shallow groundwater and relatively weaker oxidation of multimetal sulfides (e.g., ZnS, MnS, MnS₂ and MoS₂) cause slight increases in SO₄, Mn, Zn and Mo concentrations and decreases in δ³⁴S_SO4 values and relatively constant δ¹⁸O_SO4 values. The proportions of sulfate produced by multimetal sulfide oxidation range from 43 to 66%, with the contributions of shallow groundwater (23–47%) being greater than those of deep geothermal water (8–19%).

6. Conclusions

This study quantifies the sulfate sources, processes controlling sulfur and oxygen isotopes of sulfate in Jimo geothermal waters and their influence on geothermometric estimates. The major findings are as follows:

The δ³⁴S_SO4-δ¹⁸O_SO4-SO₄-SO₄/Cl-trace element systematics suggest that SO₄²⁻ in the Middle Group geothermal waters primarily originates from atmospheric deposition, with sulfide oxidation contributing less than 27%. In contrast, in the Eastern and Western Groups, sulfide oxidation is the dominant sulfate source, accounting for 80–85% and 43–66% of SO₄²⁻, respectively. Isotope mass balance calculations reveal distinct δ³⁴S values of sulfides between the two regions, with values ranging from −35.9‰ to −13.2‰ for multimetal sulfides in the west and from −29.5‰ to −21.9‰ for pyrite in the east.

Dramatic geochemical and isotopic variations are driven by oxygen isotope exchange between sulfate and water, sulfide oxidation and induced carbonate and silicate dissolution and mixing of shallow groundwater. These processes significantly affect geothermometric estimates, with sulfide oxidation leading to temperature overestimations of up to 52–62% by sulfate–water oxygen isotope geothermometers. The reliable geothermal reservoir temperature is estimated to be 144 ± 8 °C.

Further research on geothermometer calibration to account for sulfide oxidation is essential for more accurate reservoir temperature estimates. In addition, deep drilling, direct reservoir temperature measurements and long-term chemical monitoring are needed to validate geothermometric estimates and assess renewability of geothermal water.