Petroleum Exploration and Development >

2024 , Vol. 51 >Issue 3: 753 - 766

DOI: https://doi.org/10.1016/S1876-3804(24)60503-3

Genetic source, migration and accumulation of helium under deep thermal fluid activities: A case study of Ledong diapir area in Yinggehai Basin, South China Sea

  • FENG Ziqi 1, 2, 3 ,
  • HAO Fang , 1, 2, * ,
  • HU Lin 4 ,
  • HU Gaowei 4 ,
  • ZHANG Yazhen 4 ,
  • LI Yangming 1, 2 ,
  • WANG Wei 1, 2 ,
  • LI Hao 1, 2 ,
  • XIAO Junjie 1, 2 ,
  • TIAN Jinqiang 1, 2
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  • 1. State Key Laboratory of Deep Oil and Gas, China University of Petroleum (East China), Qingdao 266580, China
  • 2. School of Geosciences, China University of Petroleum (East China), Qingdao 266580, China
  • 3. Laboratory for Marine Mineral Resources, Qingdao Marine Science and Technology Center, Qingdao 266237, China
  • 4. Hainan Branch of CNOOC (China) Co., Ltd., Haikou 570312, China
*E-mail:

Received date: 2023-12-11

  Revised date: 2024-04-20

  Online published: 2024-06-26

Supported by

National Natural Science Foundation of China(41821002)

National Natural Science Foundation of China(42272163)

National Natural Science Foundation of China(42072167)

Laoshan Laboratory Science and Technology Innovation Project(LSKJ202203403)

Hainan Branch Project of CNOOC(KJZH-2021-0003-00)

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Abstract

Based on the geochemical parameters and analytical data, the heat conservation equation, mass balance law, Rayleigh fractionation model and other methods were used to quantify the in-situ yield and external flux of crust-derived helium, and the initial He concentration and thermal driving mechanism of mantle-derived helium, in the Ledong Diapir area, the Yinggehai Basin, in order to understand the genetic source, migration and accumulation mechanisms of helium under deep thermal fluid activities. The average content of mantle-derived He is only 0.001 4%, the 3He/4He value is (0.002-2.190)×10−6, and the R/Ra value ranges from 0.01 to 1.52, indicating the contribution of mantle-derived He is 0.09%-19.84%, while the proportion of crust-derived helium can reach over 80%. Quantitative analysis indicates that the crust-derived helium is dominated by external input, followed by in-situ production, in the Ledong diapir area. The crust- derived helium exhibits an in-situ 4He yield rate of (7.66- 7.95)×10−13 cm3/(a·g), an in-situ 4He yield of (4.10-4.25)× 10−4 cm3/g, and an external 4He influx of (5.84-9.06)×10−2 cm3/g. These results may be related to atmospheric recharge into formation fluid and deep rock-water interactions. The ratio of initial mole volume of 3He to enthalpy (W) is (0.004-0.018) ×10−11 cm3/J, and the heat contribution from the deep mantle (XM) accounts for 7.63%-36.18%, indicating that deep hot fluid activities drive the migration of mantle-derived 3He. The primary helium migration depends on advection, while the secondary migration is controlled by hydrothermal degassing and gas-liquid separation. From deep to shallow layers, the CO2/3He value rises from 1.34×109 to 486×109, indicating large amount of CO2 has escaped. Under the influence of deep thermal fluid, helium migration and accumulation mechanisms include: deep heat driven diffusion, advection release, vertical hydrothermal degassing, shallow lateral migration, accumulation in traps far from faults, partial pressure balance and sealing capability.

Key words： deep thermal fluid; helium; genetic source; migration and accumulation mechanism; Yinggehai Basin

Cite this article

FENG Ziqi , HAO Fang , HU Lin , HU Gaowei , ZHANG Yazhen , LI Yangming , WANG Wei , LI Hao , XIAO Junjie , TIAN Jinqiang . Genetic source, migration and accumulation of helium under deep thermal fluid activities: A case study of Ledong diapir area in Yinggehai Basin, South China Sea[J]. Petroleum Exploration and Development, 2024 , 51(3) : 753 -766 . DOI: 10.1016/S1876-3804(24)60503-3

Introduction

Helium is an important strategic noble gas resource related to national security and the upgrading of high- tech industries. Since the natural gas containing 1.84% helium was discovered in Kansas in 1903, the United States has been the largest producer, consumer and exporter of helium in the world, and the country’s helium reserves account for nearly 40% of the global total [1]. Currently, China has imported over 95% of its helium demand for a long period, and the demand is increasing year on year, which brings a serious challenge to the national resource security [2-3]. The helium-rich gas fields discovered in China are mainly distributed in central and western basins and oil- and gas-bearing basins on both sides of the eastern Tan-Lu fault belt [2].
The Yinggehai Basin is one of the important oil- and gas-bearing basins in the South China Sea, with widespread mud diapir structures. Development and evolution of the mud diapir structures and uptrusion of deep thermal fluid provide channels for the migration and infiltration of natural gas and other fluids, thus providing conducive conditions to the release and migration of deep helium [4⇓⇓-7]. As early as 1993, geochemical studies on helium had been conducted in the Yinggehai Basin. The results revealed that helium was primarily derived from the crust while a small amount from mantle [8]. Subsequent researches have assisted in understanding the formation mechanism of natural gas reservoirs in diapir areas, by taking the isotopic composition of helium as the basis for determining the origin and proportions of crust-derived and mantle-derived helium in natural gas. By 2010, the discovery of LD22-1 and LD15-1 gas fields and a group of gas bearing structures in the Ledong diapir area in the southeast of the Yinggehai Basin has made it one of the major exploration fields for natural gas in the South China Sea [4-5,9⇓ -11]. Along with the discovery of an ultra-high-temperature and high-pressure gas field (LD10-1) with proved petroleum initially-in-place of nearly 180×108 m3 in 2015, the exploration for the deep formations has been accelerated in the Yinggehai Basin. The basin has become an important exploration area characterized by high temperature and strong overpressure, mud-fluid diapirism, and frequent thermal fluid uptrusion, and it contributes more to the natural gas industry development and energy transition in China [6,9⇓ -11].
Different from hydrocarbon gases, helium has a distinct and independent transport system, and its migration process is closely related to non-hydrocarbon gases such as CO2 and N2 in natural gas reservoirs [12-13]. The solubility and gas-liquid partition coefficient of CO2 affect the occurrence of helium since N2 can act as a "carrier" to help transport helium from deep to shallow strata and its further migration and accumulation [1-2,12 -13]. Non-hydrocarbon gases (CO2 and N2) in the natural gas reservoirs in the Ledong diapir area show significantly different contents. Diapirism results in a local impact of mantle source so that high CO2 abundance appears in some gas layers (CO2 content higher than 50%) [6,10], and even zoned, layered and locally enriched in gas reservoirs [10-11]. The complex transport system, pressure evolution, and oil- gas-water contact serve as a "natural" laboratory for identifying and analyzing the genesis and sources of helium. As an important indicator of deep fluid migration, helium has never been studied as a special resource in previous research on the Yinggehai Basin, or no systematic research has been carried out on its source, generation potential and migration. Basic geological research on helium is essential for revealing deep crustal tectonic movements [5⇓⇓-8], hydrocarbon generation mechanism of source rocks in the basin, natural gas migration and accumulation patterns, and overpressure evolution process [9⇓⇓-12]. The helium in the Ledong diapir area is originated from both mantle and crustal sources, with their contributions unknown yet. Furthermore, there is a lack of quantitative analysis regarding the in-situ production and external input of helium from crustal sources. As a result, research on the origin and migration mechanism of helium under the influence of deep geothermal fluid activities is relatively limited.
On the basis of preceding main results and geochemical data, this study systematically analyzes the initial He concentration, thermal driving mechanism, in-situ yield and external flux of helium, as well as its migration and accumulation mechanism in the Ledong diapir area in the Yinggehai Basin (including LD8-1 gas-bearing structure, gas fields of LD15-1 and LD22-1). The findings are expected to provide a reference for understanding of the enrichment and accumulation processes of helium under the influence of hydrothermal activities.

1. Geological setting

The Yinggehai Basin is located in the transitional zone between the circum-Pacific tectonic domain and the Paleo-Tethys Ocean tectonic domain. It includes three first-order tectonic units from west to east: the Western Yinggehai Slope, the Central Depression, and the Eastern Yinggehai Slope (Fig. 1a) [4⇓-6,11 -12]. As a Cenozoic sedimentary basin, the Yinggehai Basin has experienced two evolutionary stages: early rifting and late depression. The late depression created the Neogene Sanya, Meishan, Huangliu and Yinggehai formations, and the Quaternary strata. In the rapid subsiding and filling process since the Neogene period, large-scale mud-fluid diapirs were developed [14⇓-16].
Fig. 1. Structural location (a) and composite stratigraphic column (b) of the Ledong diapir area in the Yinggehai Basin.
The Ledong diapir area is located in a diapiric structure belt in the southeast of the Central Depression, and adjacent to the southern part of the Eastern Yinggehai Slope. The major source rocks consist of the mudstone of shore-shallow-semi-deep marine facies developed in the Middle Miocene Sanya (N1s) and Meishan formations (N1m) of the Neogene. The primary exploration targets include the Middle Miocene Huangliu Formation (N1h), Upper Miocene Yinggehai Formation (N2y), and Neogene Ledong Formation (Q1) (Fig. 1b) [4-5,11]. The mud-fluid diapirism and thermal fluid activities in the Ledong diapir area led to local superimposition of geothermal fields, promoted the thermal evolution of organic matter, and made the source rocks enter the hydrocarbon generation threshold in advance [14⇓-16]. LD8-1 gas-bearing structure, LD15-1 and LD22-1 gas fields are located in the study area, and LD22-1 is one of the southernmost major gas fields in China. It is primarily a structural gas reservoir controlled by diapiric anticlines, with local litho- structural and lithologic gas reservoirs [15]. Diapiric faults and their associated microfractures developed in the study area connect upper traps with the lower Meishan-Sanya formations source rocks, and facilitate the vertical migration and accumulation of natural gas [5,10 -11].

2. Source and geochemical characteristics of helium and its carrier gas

Helium is produced by the radioactive decay of elements U and Th in crust rocks. It scatters throughout the crust [12⇓⇓⇓-16] after generation, and requires carriers, such as N2, CO2, groundwater and other fluids, to be transported into gas reservoirs, where it accumulates to form helium- rich gas reservoirs under appropriate conditions [17-18]. CO2 is the dominant carrier gas for mantle-derived noble gases. Scouring by inorganic CO2 from deep-seated magmatic system usually leads to the strong mixing of 3He and 4He in the crust [13,19⇓⇓⇓ -23]. N2 serves as an effective carrier gas for radiogenic helium and has a direct correlation to its accumulation [2,24⇓ -26]. Although generated in different ways, they always pre-mix in groundwater, enter into pre-existing traps through degassing in shallow layers, and simultaneously accumulate in gas reservoirs [13,18⇓⇓ -21]. At the same time, shallow gaseous CO2 releases from helium-containing groundwater, facilitating helium accumulation [18-19].

2.1. Source and geochemical characteristics of helium

Helium has two stable isotopes (3He and 4He) that have different origins. 3He is primordial helium in the mantle, and brought by the cosmic nebula when the Earth was formed. It is a major product of nuclear fusion reaction at the time of elements formation and released to shallower layers and the surface during mantle degassing, it can be used as a stable indicator of mantle source. 4He belongs to a radioactive origin. It is produced by the alpha decay of elements, U and Th (238U, 235U and 232Th), in the crust [13⇓⇓⇓⇓⇓-19]. The geochemical characteristics of helium mainly depend on He content, isotopic abundance ratio of 3He and 4He, and R/Ra value. R is the 3He/4He value of a sample, and Ra is the 3He/4He value of air (1.4×10−6) [20-21]. R/Ra value greater than 1 indicates a significant mantle source of helium [17⇓-19].
In the Ledong Formation natural gas of Ledong diapir area, the helium content ranges from 0.000 3% to 0.004 5%, with an average of 0.001 4%, and lower than the industrial standard for liquefied natural gas (0.04%). The 40Ar/36Ar value varies from 292.0 to 787.0, with an average of 366.6, and generally higher than the characteristic 40Ar/36Ar value for atmospheric argon (295.5) [20⇓⇓⇓-24]. The 3He/4He value is in the range of (0.043-2.130)×10−6, with an average of 0.968×10−6. The R/Ra value ranges from 0.03 to 1.52 (Table 1). Higher values are mainly distributed in LD8-1, ranging from 0.60 to 1.52, indicating the contribution of mantle-derived helium. In the Yinggehai Formation natural gas, the helium content ranges from 0.001 1% to 0.002 6%, with an average of 0.001 6%. The 40Ar/36Ar value ranges from 293 to 341, with an average of 306. The 3He/4He value is (0.020-2.190)×10−6, with an average of 0.920×10−6. In the Yinggehai Formation in LD22-1 gas field, the R/Ra values range from 0.01 to 0.05, suggesting the dominance of crust-derived He. Most geochemical data of noble gases in the Ledong diapir area are close to the crust-derived gas, but some data are close to the Zambales Ophiolite Complex (ZO) zone, suggesting possible influence of deep fluids (Fig. 2). The 3He/4He values of mantle and crust end members are 1.1×10−5 and 1×10−8, respectively [20-21]. According to the crust and mantle hybrid model [15,17], it is determined that the mantle-derived He accounts for 0.09%-19.84% (up to 7.51%-19.84% in LD8-1). It is thus inferred that over 80% of helium in the study area is originated from crustal source.
Table 1. Distribution characteristics of non-hydrocarbon and noble gases in the Ledong diapir area, Yinggehai Basin
Area Forma-
tion		 Well Depth/m N2
content/
%		 CO2 content/
%		 He
content/
%		 δ15N2/
‰		 δ13Cco2/
‰		 40Ar/
36Ar		 (3He/
4He)/
10−6		 R/Ra (CO2/
3He)/
109		 M/% L/% S/%
Ledong diapir area Q1 LD8-1-2 1 194-1 216 2.00 78.00 0.000 7 −4.0 −3.3 295 2.130 1.52 1.34 74.5 25.5
3.00 41.00 0.000 7 −4.0 −4.5 293 2.130 1.52 2.01 49.7 50.3
LD8-1-3 342-352 2.27 78.90 0.000 3 −5.0 −2.5 292 1.390 0.99 5.44 18.4 77.4 4.3
2.00 17.00 0.000 3 −5.7 −2.5 292 1.390 0.99 4.80 20.8 75.4 3.7
LD8-1-5 1 115-1 125 1.66 4.52 0.000 4 −7.0 −3.3 301 2.040 1.46 2.03 49.2 50.4 0.5
2.00 7.00 0.000 4 −0.9 −3.3 301 2.040 1.46 2.45 40.8 56.9 2.3
LD8-1-5 1 245-1 264 3.92 59.74 0.001 3 −2.2 −8.5 298 0.835 0.60 3.61 27.7 50.0 22.3
LD15-1-1 1 417-1 557 14.65 16.81 0.004 5 −3.3 −6.9 787 0.248 0.08 13.12 7.6 70.8 21.6
LD15-1-4 1 587-1 605 9.80 42.04 0.004 5 −3.3 −6.4 787 0.105 0.08 20.74 4.8 75.0 20.2
LD20-1-2 1 190 7.08 45.22 0.000 5 −3.0 −3.4 295 0.506 0.36 27.98 3.6 85.9 10.6
1 217-1 220 6.24 44.70 0.000 5 −3.1 −3.4 295 0.506 0.36 24.67 4.0 85.5 10.5
1 056-1 065 4.09 52.16 0.000 5 −8.0 −3.9 296 0.119 0.09 68.74 1.4 85.9 12.7
LD22-1-5 1 595-1 600 18.53 0.35 0.001 9 −6.0 −5.3 300 0.043 0.03 228.97 0.4 82.0 17.6
LD22-1-6 587-593 18.53 0.35 0.002 4 −7.0 −2.2 301 0.068 0.05 113.73 0.9 92.2 7.0
N2y- LD8-1-1 1 723-1 737 3.78 69.33 0.001 1 −5.0 −3.7 302 2.190 1.56 1.36 57.9 42.1
LD8-1-2 1 335-1 352 - 2.00 22.00 0.001 2 −6.0 −4.6 341 1.470 1.05 1.36 73.5 26.5
2.00 22.00 0.001 2 −6.0 −3.7 1.470 1.03 1.73 73.5 26.5
LD8-1-5 1 245-1 264 3.92 59.74 0.001 3 −7.0 −3.3 2.040 1.46 1.92 52.0 48.0
LD22-1-5 1 595-1 600 - 18.08 0.90 0.002 1 −6.0 −5.3 300 0.073 0.05 118.43 0.8 81.7 17.5
16.50 0.13 0.002 6 −9.0 −5.3 293 0.042 0.03 148.93 0.7 81.8 17.5
LD22-1-6 1 582-1 600 16.86 0.25 0.001 7 −3.0 −2.0 298 0.020 0.01 486.07 0.2 93.2 6.6
1 468-1 482 13.79 34.77 0.001 7 −7.0 −2.2 302 0.051 0.04 150.23 0.7 92.3 7.0
Ledong Slope area N1h LD10-1-10 4 000-4 020 4.28 70.10 0.005 4 −1.8 308 0.051 0.07 156.64 1.3 92.9 5.9
4 022-4 062 4.28 70.10 0.005 4 −1.8 309 0.101 0.04 79.10 0.6 93.4 6.0
N1m LD10-2-1 4 101-4 170 6.85 62.17 0.005 4 −0.9 775 0.025 0.02 519.66 0.2 96.7 3.2
LD10-3-1 4 151 4.44 33.58 0.005 4 −0.8 528 0.778 0.56 10.66 9.4 90.0 0.6

Note: M, L, and S represent the calculated relative contributions of CO2 components sourced from mantle (mid-ocean ridge basalt, MORB), marine limestone, and organic sediment by MATLAB based on the values of δ13CCO2 and CO2/3He, respectively.

Fig. 2. Correlation of CH4/3He vs. R/Ra of natural gases in the Ledong diapir area, Yinggehai Basin (EPR represents the geothermal fluids of the Pacific Uplift [20]; ZO represents the gas seep in the Zambales Ophiolite Complex, Philippines [21]; the crust-source endmember values refer to Ref. [22]; basemap is modified from Refs. [20,23]).

2.2. Carrier gases CO2 and N2

Previous research found that high 3He/4He values almost fall in the gas layer with a high CO2 content in the Ledong diapir area. Among the non-hydrocarbon gases, CO2 has a content ranging from 0.13% to 78.90% (averaged 31.67%), and δ13CCO2 ranges from −8.5‰ to −2.2‰ (averaged −4.0‰) (Table 1). As shown in Fig. 3, most of the CO2 in the study area is of inorganic origin [27-28]. It is primarily derived from the thermal decomposition of carbonate minerals in the calcareous mudstone of the Meishan and Sanya formations, including the contribution of deep-seated fluids. Some CO2 of organic origin has α value close to the minimum (1.02), indicating it is the result from the cracking of the same reactant (organic matter). This is because the superimposition of local temperature field caused by thermal fluid activities accelerates organic matter maturation and hydrocarbon generation.
Fig. 3. Correlation of δ13CCO2 vs. δ13C1 values of the natural gas in the Ledong diapir area, Yinggehai Basin (α is the fractionation coefficient of carbon isotope between CO2 and CH4, according to Ref. [29]).
The value of CO2/3He can be used to analyze the genetic evolution of helium and its carrier gas CO2. As shown in Fig. 4, the CO2 in the study area is located closer to the mixed zone of thermal decomposition endmember of carbonate rock (limestone). This is because rapid thermal subsidence and upward migration of thermal fluids generated by diapir activities along the Ledong fault since 5.5 Ma provided an important heat source for the decompo-sition of carbonate minerals, which further led to the generation and accumulation of a large amount of CO2 (Table 1) [11,14 -15].
Fig. 4. Correlation of CO2/3He vs. δ13CCO2 values of the natural gas in the Ledong diapir area, Yinggehai Basin (the basemap was modified from references [19-20,23]).
In nature, CO2 mainly has three carbon sources: mantle (MORB), marine limestone, and sedimentary organic carbon. The CO2/3He values at different endmembers are distinctly different, namely (1.0±0.5)×109, 1.0×1013, and 1.0×1013 [18⇓⇓-21,30]. Therefore, the relative contributions of these three carbon sources to the CO2 in natural gas are quantitatively characterized by their δ13C values [23]. In summary, the δ13C and CO2/3He values (Y) observed in samples can be determined by the following equations:
δ 1 3 C C O 2 = M δ 1 3 C C O 2 , M O R B + L δ 1 3 C C O 2 , L I M + S δ 1 3 C C O 2 , S E D
1 / Y O B S = M / Y M O R B + L / Y L I M + S / Y S E D
The calculated relative contributions are listed in Table 1. In the natural gas with R/Ra value greater than 1 in the Ledong diapir area, the contribution of mantle-derived CO2 ranges from 40.8% to 74.5%, indicating that a large amount of CO2 works as a carrier when deep mantle-derived helium migrates toward shallow formations. When R/Ra is approximately 0.99, the contribution of mantle-derived CO2 is 18.4%-20.8%. When R/Ra is significantly less than 1, inorganic CO2 is mainly from the thermal decomposition of carbonate minerals (such as calcareous mudstone). For example, R/Ra of 0.08 indicates 70.8%-75.0% contribution from carbonate thermal decomposition-derived CO2, and 20.2%-21.6% contribution from sedimentary organic carbon-derived CO2.
In the Ledong diapir area, the natural gas has a relatively high N2 content ranging from 1.66% to 18.53% (avg. 8.24%) (Table 1), and a higher N2 content exceeding 25% has been reported [4⇓-6]. The significant difference in the N2 content is partly due to the small molecular size of N2 that makes it prone to migrate. With the increasing migration pathways, it accumulates more [31⇓-33]. Additionally, in the migration process, nitrogen isotope fractionation occurs due to the secondary action at the gas-rock-fluid interface [34]. N2 associated with high He concentration often corresponds to a narrow range of δ15N. The δ15N values of N2 in the Ledong and Yinggehai formations range from −8.0‰ to −0.9‰ (avg. −4.5‰) and −9.0‰ to −3.0‰ (avg. −6.1‰), revealing the N2 is primarily originated from the thermal ammonification of mature to highly mature organic matter and atmosphere (Fig. 5).
Fig. 5. The δ15N values in the natural gas in the Ledong diapir area, Yinggehai Basin (source data of N2 and chemical reaction sourced from references [31⇓⇓-34]).

3. Discussion

3.1. Genetic mechanisms of helium

3.1.1. Thermal driving mechanism of mantle-derived 3He

Deep thermal fluid activities have dual effects of matters (e.g. 3He, CO2) and energy (heat), and the thermal effect affects the geothermal field distribution in the basin. The 3He/4He value of the natural gas in the Ledong diapir area typically suggests an influence of mantle-derived 3He which migrates through the fault systems formed by graben faulting or diapirism as transport pathways. The mantle-derived 3He either comes directly from the mantle, or is derived from the cooling and degassing of mantle- derived thermal fluids intruding into the crust [35].
The Ledong diapir area has experienced multi-phase thermal fluid activities. During the thermal fluid charging periods at 1.2-2.0 Ma and 0.3-0.8 Ma, the Miocene hydrocarbon source rocks became mature and generated a large 6of hydrocarbons, while the thermal decomposition of carbonate minerals produced a significant amount of CO2 [13⇓⇓-16]. In that process, heat transfer associated with diapir activities inevitably affected the 3He in thermal fluids from the deep mantle or intruding into the crust. As two main types of heat sources in the geothermal system [35-36], W, the unique ratio of initial mole volume of 3He to enthalpy (Z) from the mantle and the crust (radiogenic), is used to analyze the thermal driving mechanism and the relative impact of different heat sources on the origin of helium in the Ledong diapir area, but the initial 3He concentration under reservoir conditions should be given through inversion. This study adopts the following heat conservation equation [35⇓⇓⇓-39]:
C i , o = C i , l 1 − γ + γ C i , v
γ = Z o − Z l / Z v − Z l
Since volatile components are preferentially partitioned into the gas phase, the concentration of dissolved gas in the liquid or gas phases needs to be calculated based on the gas-liquid partition coefficient (KD). The initial gas concentration under reservoir conditions is obtained:
K D i = C i , v / C i , l
C i , o = C i , v [ ( 1 − γ ) / K D i + γ ]
The molar concentration ratio of CO2 to 3He of the sample, CO2/3He, is denoted as Y:
Y = C C O 2 , v / C H 3 e , v
Combining Eqs. (6) and (7), Eq. (8) is obtained:
C H 3 e , o = C C O 2 , l K D C O 2 , l Y 1 − γ K D 3 H e + γ
Eq. (8) allows us to obtain the initial concentration of 3He, C H 3 e , o, and γ under reservoir conditions. K D 3 H e is calculated using the gas-liquid partition coefficient equation[35-36,40⇓ -42]:

ln K D i = q F + E T / K f ( τ ) + F + G τ 2/3 + H τ exp 2 7 3 . 1 5 − T K 1 0 0

where q is −0.023 767, and E, F, G, H are equilibrium distribution constants for Eq. (9). For He, E is 2 267.408 2, F is −2.961 6, G is −3.260 4, and H is 7.881 9. For CO2, E is 1 672.937 6, F is 28.175 1, G −112.461 9, and H is 85.380 7 [35-36,40⇓ -42].
f τ = ρ 1 / ρ c l − 1
τ = 1 − T w T c l
Eq. (10) indicates the relationship between liquid density and saturation temperature. By using Eqs. (7)-(9), we can obtain the gas-liquid partition coefficients of He and CO2 at different temperatures. Finally, the enthalpy value (Z) is calculated through the IAPWS-95 Formulation [36⇓⇓⇓-40], and W, the ratio of the initial 3He molar volume to the corresponding enthalpy value (Z) under standard conditions (STP) is determined. The W values for noble gases in the Ledong diapir area are (0.006-0.018)×10−12 cm3/J (Table 2).
Table 2. Calculated result of hydrochemical analysis, CO2 concentrations and 3He/Z values in the formation water in the Ledong diapir area, Yinggehai Basin
Well Depth/m Ion concentration of formation
water/(mg•L-1)		 pH CO2(1)/
(10−5 mol·kg−1)		 CO2(2)/
(mol·kg−1)		 3He(3)/
(10−12 mol·kg−1)		 3He(4)/
(10−8 cm3·kg−1)		 Z(5)/
(kJ·kg−1)		 W(6)/
(10−11 cm3·J−1)		 XM(7)/
%
Cl− SO42− Ca2+ Mg2+ K++Na+
LD8-1-1 1 723-1 737 19 279 2 614 729 1 432 10 773 6.3 3.49 0.003 5 6.21 13.92 766.81 0.018 36.18
LD15-1-3 1 447-1 607 18 542 2 614 80 611 13 611 7.7 23.90 0.466 8 2.06 4.62 313.40 0.015 29.34
LD15-1-3 1 572-1 577 4 524 679 114 209 3 501 7.7 16.30 0.318 8 0.89 1.99 313.40 0.006 12.52
LD22-1-3 1 486-1 496 2 304 181 160 53 2 213 7.3 12.40 0.206 7 0.99 2.22 334.38 0.007 13.10
LD22-1-3 579-590 19 081 2 634 457 1 224 11 139 7.0 23.00 0.798 1 0.42 0.93 238.00 0.004 7.63

Note: (1) CO2 molality in the liquid phase calculated by PHREEQC, according to hydrogeochemical parameters; (2) CO2 molality in the fluid under reservoir conditions calculated by Eqs. (7)-(9); (3) 3He molality in the fluid under reservoir conditions calculated by Eq. (6); (4) 3He concentration converted into the molar volume under STP; (5) Enthalpy value calculated by IAPWS-95 Formulation (according to Refs. [36⇓⇓⇓-40]); (6) The ratio of the initial molar volume of 3He to the corresponding enthalpy under STP, i.e., the initial W; (7) The relative heat contribution from mantle source in the Ledong diapir area, obtained by heat balance equation (Eq. (12)).

In theory, W values of the mantle and crust are 0.5× 10−12 and 1×10−15 cm3/J respectively [36⇓⇓⇓-40], and their relative heat contributions to the diapir area can be evaluated through the heat conservation equation [35]:
W c a l = X M W m a n + 1 − X M W c r u
XM indicates the contribution fraction of the mantle-derived heat in sample. The results show the heat contribution from the mantle is 7.63%-36.18% in these wells. It reveals a thermal driving effect of thermal fluids in deep diapir area on mantle-derived 3He. Specifically, these fluids promote the upward migration of 3He from the deep mantle and its strong mixing with crust-derived helium in shallow layers [13,18 -19], facilitating He accumulation to some extent. In the context of helium exploration, helium concentration is prone to be diluted by highly concentrated CO2 and its associated gases near the activity centers connected with deep diapir area. Thus, helium is required to migrate a relatively long distance to return to normal concentration [29]. With more hydrological data, accurate formation temperature and detailed noble gas data, the relationship between mantle-derived 3He and heat in the diapir area will be deeply investigated.

3.1.2. Genetic mechanism of crust-derived 4He

In the Ledong diapir area, helium is primarily crust-derived and radioactive 4He [8,10 -11]. It is mainly generated in the upper-middle crust, and migrates upward to shallower layers through episodic diffusion related to tectonic events [24]. On the basis of the genetic mechanism, helium is classified into in-situ yield and external flux. In-situ yield refers to the in-situ release of radiogenic decay products of elements U and Th within helium source rocks [41].
According to the principle of mass balance of helium, the yield of crust-derived 4He is the sum of the in-situ yield of 4He ( Q H 4 e , i n) and the external yield of 4He ( Q H 4 e , e x).
Q H 4 e , t l = Q H 4 e , i n + Q H 4 e , e x
The in-situ yield of 4He is calculated using Eq. (14) [39]:
Q H 4 e , i n = P H 4 e ρ r Λ 1 − ω ω ρ w t
P H 4 e = 1.207 × 10 − 13 J U + 2.867 × 10 − 14 J T h
The unit of the coefficients, 1.207×10−13 and 2.867×10−14, is 106 cm3/(a·g), representing the amount of 4He generated per gram of U and Th per year. When the formation is a closed system, the in-situ 4He yield rate of helium source rocks can be calculated through Eq. (13), and is primarily controlled by the concentrations of trace elements U and Th. When it is an open system (or has been destroyed in the late closed stage), the 4He generation potential needs to be carefully evaluated based on geological evolution characteristics. In this study, two adjacent wells (LD10-3-1 and LD11-1-1) in the study area were selected for a comparison. The calculated results (Table 3) show wells LD10-3-1 and LD11-1-1 have similar in-situ 4He yield rates, 7.66×10−13 and 7.95×10−13 cm3/(a·g), respectively.
Table 3. Calculated 4He yield rates from wells LD10-3-1 and LD11-1-1 in the Ledong diapir area, Yinggehai Basin
Well Depth/m Formation Density/
(g·cm−3)		 JTh/10−6 Ju/10−6 P H 4 e/
(10−13 cm3·a−1·g−1)		 Q H 4 e , i n/
(10−4 cm3·g−1)		 Q H 4 e , e x/(10−2 cm3·g−1)
LD10-3-1 3 746-4 096 N1m 2.55 13.85 3.06 7.66 4.10 5.84
LD11-1-1 3 560-4 778 N1s-N1m 2.55 14.41 3.17 7.95 4.25 9.06
The external flux of crust-derived 4He refers to the 4He accumulating along the basement boundary after released from basement rocks after in-situ weathering, and a small portion of deep 4He that migrates upward with fluids [39⇓−41]. It is widespread in sedimentary basins and requires particular attention when identifying the origin and source of helium. It can be calculated using Eq. (16) [39]:
Q H 4 e , e x = P H 4 e ρ cru H 1 ω h ρ w t
The lowest closure temperature of 4He recorded in apatite, 70 °C, is used as the limit for 4He release from the crust, above which 100% of 4He atoms are released from minerals [13].
As shown in Table 3, for wells LD10-3-1 and LD11-1-1, the in-situ yields are low (4.10×10−4 and 4.25×10−4 cm3/g), and the external fluxes of 4He are significant (5.84×10−2 and 9.06×10−2 cm3/g) are found. This is possibly related to the replenishment of atmospheric fluid and deep rock- water interaction. Fluid migration is accompanied by the addition of external flux of 4He (such as deep fluid). A similar phenomenon is observed in the Antrim shale in the Michigan Basin, where the external flux of 4He far outstrips its in-situ yield. It is attributed to the complex formation fluid derived from evaporation and concentration of seawater [42⇓⇓−45]. Significantly, the source of external flux of 4He is not necessarily confined in gas fields, and factors such as the release efficiency of helium, helium loss during erosion period, and structural uplifting during geological period may all influence the accumulation and migration of 4He. It is challenging to determine the true source of helium in reservoirs solely based on the principles of mass balance [30,42⇓⇓ −45]. An in-depth understanding of helium migration mechanism and accumulation process is required.

3.2. Helium migration mechanism

Helium migration channels are characterized by cross-sphere, diversity, and complexity [2]. Due to its rarity in nature, absence of a primary gas generation period, and inability to form independent free gas, its effective migration and diffusion processes rely on the migration of underground water and carrier gases [24]. Its migration processes include primary migration and secondary migration. The former explains how helium is released from hydrocarbon source rocks, and the latter determines how helium moves a considerable distance from source rocks to reservoirs [18−19,46⇓ −48].

3.2.1. Primary migration

Primary migration of helium refers to the process of 4He generated by the in-situ decay of U and Th in basement rocks or helium source rocks and released to the surface [30]. It is essentially the relative diffusion of helium when underground temperature is higher than the closure temperature of minerals [13]. The radiogenic 4He produced from the α decay of 238U, 235U and 232Th is typically found within 10-20 μm to the parent radioelement, which is also defined as the penetration distance of the original α particle [29]. As this distance is often smaller than the grain size of the host mineral, 4He can be trapped within the mineral matrix and on the mineral grain boundary. Therefore, the primary migration of helium includes two stages. The first stage is the diffusion of helium from producing minerals into surrounding pores or fractures. A higher helium concentration in the matrix minerals than in the pores is required to allow its outward migration from the helium source rocks [49−50].
Diapirs, deep and large faults, and related thermal fluid activities can promote primary migration of helium, primarily in two ways: mass diffusion or fluid advection of accumulated 4He [13,35]. Mass diffusion is a relatively insignificant contributor to the observed 4He concentration in reservoirs (less than 0.1%). The reason is that even at high temperature (150 °C), the diffusion rate of helium is only 1×10−22-1×10−18 cm2/s [49−50]. Since the Eocene, the Yinggehai Basin has experienced three stages of CO2 thermal fluid activities associated with strike-slip extensional movements, and the basin basement heat flow reached its peak during the third stage (0.4-1.9 Ma), with a value of 70 mW/m2 [4−5]. This results in a significant increase in the regional thermal gradient, which can overcome the closure temperature in the mineral that confines helium. In addition, under the influence of hot fluid, the contents of carrier gases, N2 and CO2, in the study area are relatively high, with an average of 8.24% and 31.67%, respectively. Especially near the fracture zone at the top of the diapir and the micro-fracture zone at the upper part of the mud diapir, hot fluid strongly invades upward, and the concentration of the carrier gases is high, which can effectively promote the release of helium and advective flow. Advection mainly refers to the upward flow of fluids generated by dehydration and carbonation reactions due to lower density than the surrounding rocks during progressive metamorphism [39,41⇓⇓ −44]. This process results in significant helium migration, with a migration at rate of 1×10−6 cm2/s to 1×10−5 cm2/s, and controls the helium accumulation over a short period [49−50].

3.2.2. Secondary migration

Secondary migration is the lateral and vertical migration of helium and other associated gases (such as N2 or CO2) after primary migration. The balance between hydrostatic pressure and lithostatic pressure is the primary drive for secondary migration of helium, followed by the influences of porosity, permeability, and capillary pressure [39⇓⇓−42].
As shown in Fig. 6, noble gases in the study area are distributed between air-saturated-water (ASW) and air. The Yinggehai Formation natural gas has a high He content which is close to that of the left side of the mantle-derived fluid mixture area. Particularly in LD8-1, the 3He/4He value is high, indicating a significant contribution from mantle-derived fluid. But the helium content is only 0.000 6%, and falls among ASW, air and subduction zone-derived gases, indicating rapid migration and loss of He associated with fluid activity. These fluids may be deep thermal fluids migrating vertically to shallow layers or shallow groundwater migrating laterally. This is similar to that of hot spring gases in the northern fault belt of Tanzania [39].
Fig. 6. Ternary diagram of N2, He and Ar in natural gas in the Ledong diapir area, Yinggehai Basin ( φ   N 2 , ϕHe, ϕAr represent the relative contents of N2, He and Ar; the base map is modified from Reference [38], where the blue circles, ES, LS and B, are the average values of mantle-derived helium in different regions of the European Cenozoic Rift System (ECRS)).
As shown in Table 4, the secondary migration of helium occurs as free-gas-phase migration, degassing of helium-bearing supersaturated water, and gas stripping via hydrocarbon (CH4) or magmatic gas phase (CO2) (i.e., gas-liquid separation effect) [39⇓-41]. Due to the interaction between circulating groundwater and deep fluids, the vertical flux of 4He generated by degassing controls helium accumulation on a relatively long-time scale [42]. To analyze the influence of hydrothermal degassing on secondary migration of helium, this study adopts the Rayleigh distillation model [35]:
Y fin = Y ini f α − 1
Table 4. Secondary migration of helium (modified from references [13,30])
Secondary migration Description
Free-gas-phase migration He of free-gas-phase from primary migration migrates into traps
Degassing from helium-
bearing groundwater		 Migrate with groundwater containing N2:
(1) Free-gas-phase from primary migration contacts with groundwater, and then degases from groundwater when contacting other gases
(2) Free-gas-phase is dissolved in groundwater, and then absorbs crust-derived gas (N2) and migrates. When the groundwater is oversaturate/water temperature changes/salinity changes/pressure drops/contacts with another gas phase, degassing will occur
Gas-liquid separation Stripping gas from groundwater through migrated CO2 or CH4, that is, CO2 and/or CH4 of free-gas-phase driven by independent buoyancy displace 4He and associated gases from groundwater (helium removal process)
f represents the fraction of volatiles remaining in the fluid after hydrothermal degassing, and α is the fractionation coefficient, which can be represented by the reverse solubility ratio of CO2 to He in water. The ratio can be calculated using PHREEQC and REFPROP. As shown in Table 2, under reservoir temperature, the 3He concentration in fluid decreases from 6.21×10−12 mol/kg to 0.42×10−12 mol/kg (f=0.026), indicating large-scale CO2 precipitation and noticeable 3He dispersion. Hydrothermal degassing may lead to carbon isotope fractionation between gaseous CO2 and dissolved carbonate (HCO3−) in residual fluid, which is controlled by the main carbon species in fluid and temperature. It is worth noting that when temperature rises to around 125 °C, α decreases to around 1.000 (without fractionation) [48]. The reservoir temperature in the Ledong diapir area is usually higher than 125 °C, and hydrothermal degassing doesnot significantly alter the δ13C values of the fluids released from the residual phases, but most of the δ13CCO2 values are lower than those of marine limestone (δ13CCO2,LIM is (0±2)‰), indicating a certain degree of calcite precipitation after hydrothermal degassing.

3.3. Helium accumulation mechanism

3.3.1. Deep thermal-derived helium release and vertical hydrothermal degassing

Most helium-rich gas reservoirs are typically developed in shallow layers shallower than 2 km, under temperatures lower than the closure temperature of helium-bearing minerals. Therefore, the accumulation of helium requires first released from deeper formations and efficiently migrating to shallower ones [13,30,35⇓⇓ -38]. Deep thermal fluid activities in the Ledong diapir area are conducive to the release and effective migration of helium to shallow layers, which is mainly reflected in two aspects: First, the thermal effect induced by thermal fluid activities breaks through the closure temperature in the mineral that confines helium, which is conducive to the release and advection of helium. Second, deep thermal fluid activities drive mantle-derived 3He to migrate to a certain extent, and at the same time provide an important heat source for the decomposition of carbonate minerals, and the high concentration of CO2 generated also participates in the migration of helium from deep to shallow layers.
Helium migration from deep to shallow formations is controlled by two geological processes. The first process involves the mixing of mantle-derived gases (R/Ra=8, CO2/3He=2×109) with crust-derived gases (R/Ra=0.02, CO2/3He=1011-1012). According to Fig. 7, the distribution of CO2/3He values in the study area is large as (1.34- 486.00)×109. Apart from LD8-1 gas field where the values vary in the range of (1.34-5.44)×109, the values in other areas are much higher than the CO2/3He values of the mantle-derived mid-ocean ridge basalt (MORB) (2×109). Some noble gases in the Ledong Formation are distributed close to the mantle-derived MORB end-member, and during the migration process from mantle to crustal sources, the CO2/3He values remarkably increase from 109 to 1011. This indicates a gradual decreasing contribution of mantle-derived helium.
Fig. 7. Correlation of R/Ra vs. CO2/3He values of the natural gas in the Ledong Diapir area, Yinggehai Basin (The base map refers to Ref. [35]; the SCLM endmember indicates the continental lithospheric mantle).
The second process is that degassing and gas-liquid separation occur with secondary migration during which helium is preferentially lost and degassed into a gas phase, leading to gradually increasing CO2/3He value released from the residual phase. Due to the low solubility of noble gases, He is more easily lost than CO2 in fluids, and during the migration towards the surface, loss of any gas phase during the depressurization process results in rapid precipitation of noble gases [37,50]. For examples, the loss of CO2 is beneficial to He accumulation [12,51]. This process can be characterized by a ternary plot with CO2, 3He, and 4He as end-members (Fig. 8). The Ledong diapir area exhibits a high content of radiogenic 4He. However, some data points in the Ledong Formation are closer to the mantle- derived area, as having a relatively higher proportion of mantle-derived 3He, and exhibit a good linearity, indicating significant helium precipitation during pressure reduction.
Fig. 8. Ternary diagram of relative contents of CO2, 3He and 4He in CO2-rich natural gas in the Ledong diapir area, Yinggehai Basin ( φ   C O 2, φ 3 H e, φ   4 H erepresent the relative contents of CO2, 3He and 4He; the base map refers to Refs. [35,41]).

3.3.2. Lateral migration in shallow layers and accumulation in trap far from faults

In the context of helium exploration, near the center of tectonic activity (such as the center of diapir or volcano), the He concentration in fluid is prone to be diluted by CO2 and its associated gases, so it will not gradually rise again until entering a far and tectonically stable area [21⇓⇓⇓⇓-26]. This necessitates lateral migration in shallow layers where external 4He and its associated N2 are premixed and dissolved in laterally flowing groundwater before degassing and entering pre-existing traps [13,29].
Noble gas, argon (Ar), has been released in a large quantity into the atmosphere in the early stage of the Earth’s formation, and is used as an important tracer for atmosphere-derived noble gases (ANGs) and shallow crust-derived noble gases. As shown in Fig. 9, noble gases in the Ledong diapir area are subjected to a significant influence from atmospheric sources. Some data approach the crust-derived components due to decreased 36Ar/40Ar values, suggesting lateral migration of helium in shallow layers. ANGs migrate into underground along with water. When encountering other fluid phases (such as water or gas phases), due to the different solubilities in groundwater, part of ANGs in groundwater (such as accumulated 4He and dissolved 36Ar) will exsolve. By transiting from water phase to gas phase, an equilibrium between phases is achieved, causing changes in the ANG content in groundwater and fractionation among elements (Fig. 9). The structural traps such as anticlinal and fault-block traps in the study area were formed early, and faults and fractures are well developed. They are connected with the deep helium source, and conducive to the migration of helium from deep to shallow layers. However, nearby faults are prone to causing helium escape, and helium is easily diluted by hot-fluid-carrying high-concentration CO2 and associated gases, which has a negative impact on helium accumulation in the traps. In order to prevent from being diluted, helium needs to horizontally migrate over a certain distance, and gradually accumulates in the traps away from the center of tectonic activity.
Fig. 9. Correlation of N2/40Ar vs. 36Ar/40Ar in CO2-rich natural gas in the Ledong diapir area, Yinggehai Basin (modified according to Ref. [13]).

3.3.3. Partial pressure balance and caprock sealing capability

Based on the different partial pressures of gases in water, formation water plays a role of a "helium pump" in the process of helium accumulation in gas reservoirs [51-52]. In the shallow layers of the crust, N2 and 4He are often dissolved in groundwater. When they come into contact with the separated gas phase in shallow traps (such as CH4), according to the Henry's Law, the dissolved 4He and N2 would be precipitated from the groundwater, and change into free gas phases (degassed) to reach a partial pressure balance [13,30,50]. Hence, when the groundwater becomes supersaturated with N2 associated with highly concentrated 4He, degassing can occur [13,29]. If not supersaturated, to ensure degassing, a pre-existing gas cap such as CH4 or CO2 is necessary, where degassing can occur when the groundwater containing 4He and N2 contacts free gas phase [13,29].
After He and its associated N2 migrate into a trap, their preservation will depend on the relative balance between the generation potential of He and the sealing capacity of cap rock. With a high diffusion coefficient, any destruction to caprock or trap, microfiltration, capillary damage, and other negative factors would lead to helium loss [52]. Particularly, helium has a molecular diameter of about 0.20 nm, which is much smaller than those of CO2, N2, and CH4, which are 0.33, 0.36 and 0.38 nm respectively [17,41]. Therefore, helium requires tight and sealable cap rock, such as evaporite rock (rock salt or anhydrite), to prevent it from losing through diffusion over a long geological time. The Yinggehai Formation in the study area is semi-deep marine thick and undercompacted mudstone. Although it is a regionally effective cap, and has a good sealing ability to oil and gas, it should be higher in integrity and sealing ability to seal helium because the latter is more likely to leak and escape, and there are developed faults and fractures in the diapir area. In order to comprehensively evaluate the exploration potential of helium in the study area, it is necessary to identify a tighter cap rock and strengthen the research on helium storage conditions.

4. Conclusions

In the Ledong diapir area, the crust-derived helium is dominant. The average content of mantle-derived He is only 0.001 4%, the 3He/4He value is (0.002-2.190)×10−6, and the R/Ra value ranges from 0.01 to 1.52, indicating the contribution of mantle-derived He is 0.09%-19.84%, while the proportion of crust-derived helium can reach over 80%.
Quantitative analysis indicates that the crust-derived helium is dominated by external input, followed by in-situ production, in the Ledong diapir area. The crust- derived helium exhibits an in-situ 4He yield rate of (7.66-7.95)×10−13 cm3/(a·g), an in-situ 4He yield of (4.10- 4.25)×10−4 cm3/g, and an external 4He influx of (5.84- 9.06)×10−2 cm3/g. This may be related to atmospheric recharge into formation fluid and deep rock-water interactions.
Heat effect resulted from thermal fluid activities in the deep Ledong diapir area affects the geothermal field, and facilitates helium migration significantly. The ratio of initial mole volume of 3He to enthalpy (W) is (0.004- 0.018) ×10−11 cm3/J, and the heat contribution from the deep mantle (XM) accounts for 7.63%-36.18%, indicating that deep hot fluid activities drive the migration of mantle-derived 3He.
The primary helium migration depends on advection, while the secondary migration is controlled by hydrothermal degassing and gas-liquid separation. From deep to shallow layers, the CO2/3He value rises from 1.34×109 to 486×109, indicating a large amount of CO2 has escaped.
Under the influence of deep thermal fluid, helium migration and accumulation mechanisms include: deep heat driven diffusion, advection release, vertical hydrothermal degassing, shallow lateral migration, accumulation in traps far from faults, partial pressure balance and sealing capability.

Acknowledgments

We highly appreciate Academician Dai Jinxing for his careful guidance and revision on this paper. We thank professors Liu Quanyou, Wu Xiaoqi, Qin Shengfei, and Hu Guoyi for their rigorous and insightful guidance and assistance on this paper.

Nomenclature

Ci—concentration of component i, mol/kg;
f—fraction of volatiles remaining in fluid after hydrothermal degassing, %;
f(τ)—relation function between liquid density and saturation temperature, dimensionless;
h—thickness of helium source rock, m;
H—crust thickness, m;
KD—gas-liquid partition constant, dimensionless;
K D 3 H e—gas-liquid partition coefficient of 3He, dimensionless;
L—relative contribution of CO2 sourced from marine limestone, %;
M—relative contribution of CO2 sourced from the mantle (mid-ocean ridge basalt, MORB), %;
P H 4 e—in-situ yield rate of 4He from helium source rocks, cm3/(a·g);
q—fixed constant in gas-liquid partition coefficient equation, values as −0.023 767 for water;
Q H 4 e , e x—external yield of crust-derived 4He, cm3/g;
Q H 4 e , i n—in-situ yield of 4He, cm3/g;
Q H 4 e , t l—total yield of crust-derived 4He, cm3/g;
R—helium isotope ratio (3He/4He) of samples, dimensionless;
Ra—helium isotope ratio (3He/4He) of air, dimensionless;
S—relative contribution of CO2 sourced from sedimentary organic carbon, %;
t—helium generation time (i.e., age of 4He), a;
T—thermodynamic temperature, K;
Tw—water temperature under reservoir conditions, K;
Tcl—critical temperature of water, K;
JTh—average abundance of Th, 106;
JU—average abundance of U, 106;
W—ratio of initial molar volume of 3He to according enthalpy under standard conditions, cm3/J;
Wcal—the final calculated ratio of initial molar volume of 3He to corresponding enthalpy, cm3/J;
Wcru—ratio of 3He to enthalpy for the crust heat endmember, cm3/J;
Wman—ratio of 3He to enthalpy for the mantle heat endmember, cm3/J;
XM—heat contribution fraction of mantle-derived endmember, %;
Y—molar concentration ratio of CO2 to 3He, dimensionless;
Yfin—molar concentration ratio of CO2 to 3He after degassing, dimensionless;
Yini—molar concentration ratio of CO2 to 3He before degassing, dimensionless;
YOBS—measured CO2/3He value, dimensionless;
YMORB—CO2/3He value of MORB endmember, (1.0±0.5) ×109;
YLIM—CO2/3He value of marine limestone endmember, 1.0×1013;
YSED—CO2/3He value of sedimentary organic carbon endmember, 1.0×1013;
Z—enthalpy of water at liquid-gas boundary, kJ/kg;
α—carbon isotope fractionation coefficient between CO2 and CH4, i.e., (1 000+δ13CCO2)/(1 000+δ13C1), dimensionless;
γ—vapor mass fraction at sampling temperature, %;
ρl—boundary density of liquid phase, g/cm3;
ρcl—density of water at critical temperature, g/cm3;
ρr—rock density, g/cm3;
ρcru—crust density, cm3/g;
ρw—water density, set as 1 g/cm3;
τ—degree from current state to critical state, dimensionless;
ω—reservoir rock porosity, %;
Λ—helium transfer efficiency from rock matrix to water, values as 1;
δ13CCO2—carbon isotope value of non-hydrocarbon CO2, ‰;
δ13CCO2,MORB—δ13CCO2 value of MORB endmember, (−6.5±2.5)‰;
δ13CCO2,SED—δ13CCO2 value of sedimentary organic carbon endmember, (−30±10)‰;
δ13CCO2,LIM—δ13CCO2 value of marine limestone endmember, (0±2)‰.
Subscripts:
l—the state of liquid phase (i.e., water) at gas-liquid separation temperature;
o—the initial state at reservoir temperature;
v—the state of gas phase (i.e., vapor) at gas-liquid separation temperature.

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