A method for estimating the content of mantle-derived volatile

Abstract

The present application provides a mantle source volatile content estimation method, which belongs to the technical field of rare gas geochemistry research. The estimation method comprises the following steps: obtaining sampling data of a target area; dividing the target area into the center, middle and outside of the tectonic-thermal response area in the order of the non-hydrocarbon gas carbon dioxide content in associated natural gas from large to small; calculating the proportion of carbon dioxide from mantle source volatiles in each region respectively; and calculating the content of mantle source volatiles in the target area according to the proportion of carbon dioxide from mantle source volatiles and the content of non-hydrocarbon gas carbon dioxide in associated natural gas in the corresponding region. The proportion of carbon dioxide from mantle source volatiles is calculated by different methods for different carbon dioxide content regions, which effectively improves the accuracy of the estimation of the content of mantle source volatiles. Therefore, the migration range of mantle source volatiles can be more accurately determined, the exploration range of strategic resources of helium and hydrogen in oil and gas field development is accurately demarcated, and the exploration risk is reduced.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of rare gas geochemistry, and particularly relates to a mantle source volatile content estimation method for tectonic-thermal response zones. BACKGROUND

[0002] Mantle source volatiles are volatile substances released from the earth's interior mantle, mainly existing in the central region of tectonic thermal events, and the main components are carbon dioxide and nitrogen, which are closely related to helium and hydrogen. Among these volatiles, carbon dioxide is not only the core component of deep mantle source volatiles, but also plays a key role in its migration process.

[0003] In the deep mantle, carbon dioxide can exist together with helium and hydrogen, and under the driving of geological tectonic activity, high-concentration mantle source carbon dioxide as the dominant carrier carries helium and hydrogen to form a multiphase percolation or gas capacity phase, and migrates upward through channels such as faults. In the migration process, as the content of mantle source carbon dioxide decreases, the migration system transitions to a CO2-N2 mixed carrier phase; when the mantle source carbon dioxide signal completely disappears, nitrogen becomes a single carrier gas, continuing to affect the migration of helium and hydrogen. During this period, the dissolution and mineralization of carbon dioxide have an important influence on the enrichment of helium and hydrogen. For example, in the oil and gas basins in eastern China, the formation of mantle source carbon dioxide reservoirs is closely related to the enrichment of helium. The dissolution and mineralization of carbon dioxide relatively increase the concentration of helium in the gas phase, thereby promoting the enrichment of helium and being beneficial to oil and gas field exploration and development.

[0004] It is of great significance to study the carbon isotope behavior and evolution mechanism in the migration process of mantle source volatiles. Especially in areas where the influence of mantle source fluids such as deep faults or diapirism is significant, it not only helps to deeply understand the geochemical characteristics of natural gas, but also helps to identify the potential sources of helium and hydrogen, which can provide important clues for the formation and enrichment of helium and hydrogen, and provide important scientific basis for the exploration of helium and hydrogen, reduce the risk of exploration, and promote the development and utilization of unconventional energy resources. SUMMARY

[0005] Based on the above background, the present application aims to provide a mantle source volatile content estimation method, which is suitable for oil and gas fields in tectonic-thermal response zones such as deep faults, volcanoes and diapir structures, and realizes the accurate characterization of the content of mantle source volatiles, providing more accurate data support for natural gas geochemical research and exploration.

[0006] To achieve the above purpose, the solution adopted by the present application is: a mantle source volatile content estimation method, comprising the following steps:

[0007] S100, obtaining sampling data of a target region, the target region being a tectonic-thermal response zone, the sampling data including helium-3 content, carbon isotope value and non-hydrocarbon gas carbon dioxide content in associated natural gas;

[0008] S200, dividing the target region into a tectonic-thermal response zone center, a tectonic-thermal response zone middle and a tectonic-thermal response zone outer part in order of non-hydrocarbon gas carbon dioxide content in associated natural gas from large to small;

[0009] S300, calculating the mantle source volatile carbon dioxide proportion of the tectonic-thermal response zone center, the tectonic-thermal response zone middle and the tectonic-thermal response zone outer part respectively;

[0010] S400, calculating the mantle source volatile content of the target region according to the mantle source volatile carbon dioxide proportion and the non-hydrocarbon gas carbon dioxide content in associated natural gas of the corresponding region.

[0011] Further, the non-hydrocarbon gas carbon dioxide content in associated natural gas of the tectonic-thermal response zone center is >50%; the non-hydrocarbon gas carbon dioxide content in associated natural gas of the tectonic-thermal response zone middle is 5%-50%; and the non-hydrocarbon gas carbon dioxide content in associated natural gas of the tectonic-thermal response zone outer part is <5%.

[0012] Further, the mantle source volatile carbon dioxide proportion of the tectonic-thermal response zone outer part is calculated based on the following formula:

[0013] (C / A) MEA =α / f1 VOL +β / f1 DEC +γ / f1 DIC +δ / f1 EVO +∈ / f1 DOC (1)

[0014] (B / C) MEA =α / f2 VOL +β / f2 DEC +γ / f2 DIC +ε / f2 EVO +∈ / f2 DOC (2)

[0015]

[0016] β=σx (4)

[0017] γ=σ(1-x) (5)

[0018]

[0019] ε=τy (7)

[0020] ∈ = τ (1 - y) (8)

[0021] σ + τ = 1 - α (9)

[0022] Wherein, A is the normalized carbon isotope value, B is the helium-3 content, C is the non-hydrocarbon gas carbon dioxide content in associated natural gas; subscript MEA represents the sample measurement value;

[0023] VOL, DEC, DIC, EVO and DOC respectively refer to mantle source volatile, shell source carbonate mineral thermal decomposition, basement carbonate mineral dissolution inorganic carbon DIC, organic matter thermal evolution release, shallow fluid dissolved organic carbon DOC;

[0024] α, β, γ, ε, ∈ respectively refer to the proportion of carbon dioxide from mantle source volatile, the proportion of carbon dioxide from shell source carbonate mineral thermal decomposition, the proportion of carbon dioxide from basement carbonate mineral dissolution inorganic carbon DIC, the proportion of carbon dioxide from organic matter thermal evolution release, the proportion of carbon dioxide from shallow fluid dissolved organic carbon DOC, σ and τ are respectively the proportion of inorganic source carbon dioxide and the proportion of organic source carbon dioxide; x and y are the normalized variables set;

[0025] f1 VOL , f1 DEC , f1 DIC , f1 EVO and f1 DOC The values of f2 VOL , f2 DEC , f2 DIC , f2 EVO and f2 DOC are respectively 1.5×10 9 , 0.9×10 13 , 1.5×10 13 , 0.8×10 13 , 1.2×10 13 .

[0026] Further, the proportion of carbon dioxide from mantle source volatile in the middle of the tectonic-thermal response zone is calculated based on the following formula:

[0027] (C / A) MEA = α / f3 VOL + β / f3 DEC + γ / f3 DIC + ε / f3 EVO (10)

[0028] (B / C) MEA = α / f4 VOL + β / f4DEC + γ / f4 DIC + ε / f4 EVO (11)

[0029]

[0030] β = σx (13)

[0031] γ = σ (1 - x) (14)

[0032] σ + ε = 1 - α (15)

[0033] wherein A is the normalized carbon isotope value, B is the helium-3 content, C is the non-hydrocarbon gas carbon dioxide content in associated natural gas; subscript MEA represents the sample measurement value;

[0034] VOL, DEC, DIC and EVO respectively refer to mantle source volatile, thermal decomposition of crust source carbonate mineral, inorganic carbon DIC from dissolution of basement carbonate mineral, and release from thermal evolution of organic matter;

[0035] α, β, γ, ε respectively refer to the proportion of carbon dioxide from mantle source volatile, the proportion of carbon dioxide from thermal decomposition of crust source carbonate mineral, the proportion of carbon dioxide from inorganic carbon DIC from dissolution of basement carbonate mineral, and the proportion of carbon dioxide from thermal evolution of organic matter, σ is the proportion of inorganic source carbon dioxide; x is a normalized variable set; f3 VOL , f3 DEC , f3 DIC and f3 EVO respectively are -0.15‰, 0.33‰, -0.5‰ and -0.067‰; f4 VOL , f4 DEC , f4 DIC and f4 EVO respectively are 1.5 x 10 9 , 0.9 x 10 13 , 1.5 x 10 13 , 0.8 x 10 13 .

[0036] Further, the proportion of carbon dioxide from mantle source volatile in the center of the tectonic-thermal response zone is calculated based on the following formula:

[0037] (V / A) MEA = α / f5 VOL + β / f5 DEC + γ / f5 DIC (16)

[0038] (B / C) MEA = α / f6 VOL + β / f6 DEC + γ / f6DIC (17)

[0039] β+γ=1-α (18)

[0040] Wherein, A is the normalized carbon isotope value, B is the helium-3 content, C is the non-hydrocarbon gas carbon dioxide content in associated natural gas; subscript MEA represents sample measurement value;

[0041] VOL, DEC and DIC respectively refer to mantle source volatile, shell source carbonate mineral thermal decomposition, and inorganic carbon DIC of base carbonate mineral dissolution;

[0042] Alpha, beta and gamma respectively refer to the proportion of carbon dioxide from mantle source volatile, the proportion of carbon dioxide from shell source carbonate mineral thermal decomposition, and the proportion of carbon dioxide from inorganic carbon DIC of base carbonate mineral dissolution;

[0043] f5 VOL , f5 DEC and f5 DIC The values of f6 VOL , f6 DEC and f6 DIC are respectively 1.5*10 9 , 0.9*10 13 , 1.5*10 13 .

[0044] Further, the value range of epsilon is 0% to 50%.

[0045] Further, the content of mantle source volatile is calculated based on the following formula:

[0046]

[0047] Wherein, alpha is the proportion of carbon dioxide from mantle source volatile, C is the non-hydrocarbon gas carbon dioxide content in associated natural gas of the corresponding region, is the content of mantle source volatile.

[0048] The beneficial effects of the present application are:

[0049] Because of being close to the center of deep large fault and crust deep diapir and other tectonic thermal events, the content of carbon dioxide is particularly high, which is directly upwelling in form. Through the 'radiation' of the tectonic center, it diffuses to the periphery, and the content of carbon dioxide gradually decreases in this process. Therefore, the content of carbon dioxide can be used to represent the relative distance from the center of tectonic thermal event to the shallow surface. For the oil and gas field with deep large fault or diapir structure, the present application creatively uses the above phenomenon to divide the target area into the center of tectonic-thermal response zone, the middle of tectonic-thermal response zone and the outside of tectonic-thermal response zone, and uses different methods to calculate the proportion of carbon dioxide from mantle volatile in different regions, which effectively improves the accuracy of the estimation of the content of mantle volatile. Thus, the migration range of mantle volatile can be more accurately determined, the exploration range of strategic resources of helium and hydrogen in oil and gas field development is accurately demarcated, and the exploration risk is reduced.

[0050] The present application further proposes that the region with the content of carbon dioxide in non-hydrocarbon gas > 50% is divided into the center of tectonic-thermal response zone, the region with the content of carbon dioxide in non-hydrocarbon gas 5% ~ 50% is divided into the middle of tectonic-thermal response zone, and the region with the content of carbon dioxide in non-hydrocarbon gas < 5% is divided into the outside of tectonic-thermal response zone, and the content of mantle volatile is calculated by setting conditions in stages, and the calculation efficiency can be improved by combining with Matlab programming. BRIEF DESCRIPTION OF DRAWINGS

[0051] Figure 1 Statistical graph of the content of mantle volatile for each typical well of A gas field;

[0052] Figure 2 Planar position distribution graph of each typical well of A gas field; DETAILED DESCRIPTION

[0053] In order to make the purpose, technical scheme and advantages of the embodiments of the present application more clear, the technical scheme of the present application will be described clearly and completely below in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments described in the present application document, all other embodiments obtained by those skilled in the art without making creative efforts fall within the scope of protection of the present application technical scheme.

[0054] Embodiment:

[0055] A mantle volatile content estimation method for geological tectonic background of tectonic-thermal response zone with deep large fault, diapir structure and the like, comprising the following steps:

[0056] First step: obtaining sampling data of target area, the target area is tectonic-thermal response area, the sampling data includes natural gas geochemical related data of the target area, specifically including helium content and helium isotope content (such as helium-3 content), carbon isotope value and the content of non-hydrocarbon gas carbon dioxide in associated natural gas. The embodiment selects a typical well in A gas field with tectonic thermal event for implementation, and the A gas field is the target area.

[0057] Second step, according to the content of non-hydrocarbon gas carbon dioxide in associated natural gas, the target area is divided into three categories, which are: tectonic-thermal response area center, the content of non-hydrocarbon gas carbon dioxide in this area is > 50%. Tectonic-thermal response area middle, the content of non-hydrocarbon gas carbon dioxide in this area is 5%-50%. Tectonic-thermal response area outside, the content of CO2 in non-hydrocarbon gas in this area is < 5%.

[0058] Third step, when in the tectonic-thermal response area outside, the content of CO2 in non-hydrocarbon gas is < 5%, the proportion of mantle source volatile carbon dioxide is calculated according to the following formula:

[0059] (C / A) MEA = α / f1 VOL + β / f1 DEC + γ / f1 DIC + ε / f1 EVO + ∈ / f1 DOC (1)

[0060] (B / C) MEA = α / f2 VOL + β / f2 DEC + γ / f2 DIC + ε / f2 EVO + ∈ / f2 DOC (2)

[0061]

[0062] β = σx (4)

[0063] γ = σ(1-x) (5)

[0064]

[0065] ε = τy (7)

[0066] ∈ = τ(1-y) (8)

[0067] σ + τ = 1-α (9)

[0068] In the above formula, A is the normalized carbon isotope value, B is the helium-3 content, and C is the non-hydrocarbon gas carbon dioxide content in the associated natural gas; subscript MEA represents the measured value of the sample; VOL, DEC, DIC, EVO and DOC respectively refer to the mantle source volatile, the thermal decomposition of the crust source carbonate mineral, the dissolved inorganic carbon DIC of the basement carbonate mineral, the released organic matter thermal evolution, and the dissolved organic carbon DOC of the shallow fluid; α, β, γ, ε and ∈ respectively refer to the proportion of carbon dioxide from the mantle source volatile, the thermal decomposition of the crust source carbonate mineral, the dissolved inorganic carbon DIC of the basement carbonate mineral, the released organic matter thermal evolution, and the dissolved organic carbon DOC of the shallow fluid; σ and τ respectively refer to the proportion of inorganic source carbon dioxide and the proportion of organic source carbon dioxide; x and y are the normalized variables set; f1 VOL , f1 DEC , f1 DIC , f1 EVO , and f1 DOC respectively are -0.15‰, 0.5‰, -0.5‰, -0.029‰ and -0.025‰; f2 VOL , f2 DEC , f2 DIC , f2 EVO , and f2 DOC respectively are 1.5×10 9 , 0.9×10 13 , 1.5×10 13 , 0.8×10 13 , and 1.2×10 13 . In order to ensure the accuracy and reasonableness of the final result, the value of ε is limited to 0% to 50%.

[0069] When the content of carbon dioxide in the non-hydrocarbon gas is 5% to 50% in the middle of the tectonic-thermal response zone, the proportion of carbon dioxide from the mantle source volatile is calculated according to the following formula:

[0070] (C / A) MEA = α / f3 VOL + β / f3 DEC + γ / f3 DIC + ε / f3 EVO (10)

[0071] (B / C) MEA = α / f4 VOL + β / f4 DEC + γ / f4 DIC + ε / f4 EVO (11)

[0072]

[0073] β = σx (13)

[0074] γ = σ (1 - x) (14)

[0075] σ + ε = 1 - α (15)

[0076] In the above formula, A is the normalized carbon isotope value, B is the helium-3 content, and C is the non-hydrocarbon gas carbon dioxide content in associated natural gas; subscript MEA represents the sample measurement value. VOL, DEC, DIC, and EVO respectively refer to mantle source volatiles, thermal decomposition of crust source carbonate minerals, dissolution of inorganic carbon DIC of basement carbonate minerals, and organic matter thermal evolution release. α, β, γ, and ε respectively refer to the proportion of carbon dioxide from mantle source volatiles, the proportion of carbon dioxide from thermal decomposition of crust source carbonate minerals, the proportion of carbon dioxide from dissolution of inorganic carbon DIC of basement carbonate minerals, and the proportion of carbon dioxide from organic matter thermal evolution release. σ is the proportion of inorganic source carbon dioxide; x is the normalized variable set; f3 VOL , f3 DEC , f3 DIC , and f3 EVO respectively have values of -0.15‰, 0.33‰, -0.5‰, and -0.067‰; f4 VOL , f4 DEC , f4 dIC , and f4 EVO respectively have values of 1.5 x 10 9 , 0.9 x 10 13 , 1.5 x 10 13 , and 0.8 x 10 13 .

[0077] When in the center of the tectonic-thermal response zone, the content of carbon dioxide in non-hydrocarbon gas is > 50%, the proportion of carbon dioxide from mantle source volatiles is calculated according to the following formula:

[0078] (C / A) MEA = α / f5 VOL + β / f5 DEC + γ / f5 DIC (16)

[0079] (B / C) MEA = α / f6 VOL + β / f6 DEC + γ / f6 DIC (17)

[0080] β + γ = 1 - α (18)

[0081] Where A is the standardized carbon isotope value, B is the helium-3 content, and C is the non-hydrocarbon carbon dioxide content in the associated natural gas; the subscript MEA represents the sample measurement value. VOL, DEC, and DIC refer to the DIC of mantle-derived volatile matter, thermal decomposition of crustal carbonate minerals, and dissolved inorganic carbon in basement carbonate minerals, respectively. α, β, and γ refer to the specific gravity of carbon dioxide from mantle-derived volatile matter, thermal decomposition of crustal carbonate minerals, and dissolved inorganic carbon in basement carbonate minerals, respectively. VOL f5 DEC and F5 DIC The values ​​are -0.15‰, 0.5‰, and -0.2‰, respectively; f6 VOL f6 DEC and F6 DIC The values ​​are 1.5 × 10 9 0.9×10 13 1.5×10 13 .

[0082] Fourth, using MATLAB software, write code based on the above calculation formulas and connect to the database to calculate the specific gravity of carbon dioxide from mantle volatiles at the center of the tectonic-thermal response zone, the middle of the tectonic-thermal response zone, and the outer part of the tectonic-thermal response zone. The execution steps are as follows:

[0083] (1) Use MATLAB's Database Toolbox to connect to the database storing the data (such as MySQL, SQLite, etc.), and extract the non-hydrocarbon carbon dioxide content, helium-3 content, and standardized carbon isotope values ​​of associated natural gas from different well names using SQL queries. Specific operations include:

[0084] % Connect to database

[0085] conn=database('database_name','username','password','Vendor','Server','Port');

[0086] %Query data

[0087] sqlquery='SELECT well_name,CO2,He3,delta13C FROM carbon_data';

[0088] data=fetch(conn,sqlquery);

[0089] % Disconnect

[0090] close(conn);

[0091] (2) According to the content of non-hydrocarbon gas carbon dioxide in associated natural gas, the data is divided into three cases: CO2> 50%, CO2 between 5% and 50%, and CO2<5%. The data subset in each case is extracted using a logical index. The specific operation includes:

[0092]

[0093] (3) Define constants and symbolic variables, use loops to solve equations, and select the above different equation sets according to the value of C to obtain the proportion of carbon dioxide from mantle volatile in each region. The solve function can be used to solve the equation set, and the disp function can be used to output the solution array of each variable. The specific operation includes:

[0094]

[0095]

[0096] Step 5, calculate the content of mantle volatile:

[0097]

[0098] In the formula, a is the proportion of carbon dioxide from mantle volatile, C is the content of non-hydrocarbon gas carbon dioxide in associated natural gas in the corresponding region, is the content of mantle volatile. Since the existing technology cannot accurately calculate the content of mantle volatile, and carbon dioxide is the main component of mantle volatile, the content of carbon dioxide from mantle volatile can be used to approximate the content of mantle volatile.

[0099] Step 6, according to the quantitative calculation result of the content of mantle volatile, combined with the well plane position and sampling depth of the structure-thermal response area of the oil and gas field, analyze the spatial distribution and sweet spot area of mantle volatile.

[0100] The sampling data and calculation results involved in this embodiment are shown in Table 1.

[0101] Table 1. A gas field sample information, test data and Mtalab calculation result statistical table

[0102]

[0103]

[0104] In Table 1, δ 13 C CO2 is the standardized carbon isotope value, and CO2 is the content of non-hydrocarbon gas carbon dioxide in associated natural gas.

[0105] The calculation result of the content of mantle volatile is as follows Figure 1As shown, the results show that in the natural gas of the gas sample of a typical well of the A gas field, the mantle source volatile content is between 0.006% and 6.345%, the histogram presents multiple peaks, and the calculation results of the method can accurately reflect the mantle source volatile migration range and spatial distribution (such as Figure 2 As shown) of the oil and gas field. Among them, the wells A3, A7, A13 and A18 have higher mantle source volatile content than other wells, and can be used as the key exploration "sweet spot" area of deep helium and hydrogen, thereby reducing the exploration risk and improving the production efficiency.

Claims

1. A method of estimating the mantle volatile content, characterized by: The method comprises the following steps: S100, acquiring sampling data of a target region, the target region being a tectonic-thermal response zone, the sampling data comprising helium-3 content, carbon isotope value and non-hydrocarbon gas carbon dioxide content in associated natural gas; S200, dividing the target region into a tectonic-thermal response zone center, a tectonic-thermal response zone middle part and a tectonic-thermal response zone outer part in order of non-hydrocarbon gas carbon dioxide content in associated natural gas from large to small; S300, calculating the mantle source volatile carbon dioxide proportion of the tectonic-thermal response zone center, the tectonic-thermal response zone middle part and the tectonic-thermal response zone outer part respectively; S400, calculating the mantle source volatile content of the target region according to the mantle source volatile carbon dioxide proportion and the non-hydrocarbon gas carbon dioxide content in associated natural gas of the corresponding region; The mantle source volatile carbon dioxide proportion of the tectonic-thermal response zone outer part is calculated based on the following formula: (1) (2) (3) x (4) (5) (6) y (7) (8) (9) The mantle source volatile carbon dioxide proportion of the tectonic-thermal response zone middle part is calculated based on the following formula: (10) (11) (12) x (13) (14) (15) The mantle source volatile carbon dioxide proportion of the tectonic-thermal response zone center is calculated based on the following formula: (16) (17) (18) wherein is the normalized carbon isotope value, is the helium-3 content, is the non-hydrocarbon gas carbon dioxide content in associated natural gas; subscript denotes the sample measurement value; , , and respectively refer to mantle-derived volatile, thermal decomposition of crust-derived carbonate minerals, dissolution of basement-derived inorganic carbon DIC, thermal evolution of organic matter release, and dissolution of organic carbon DOC by shallow fluids; , , , , respectively refer to the proportion of carbon dioxide from mantle-derived volatile, the proportion of carbon dioxide from the thermal decomposition of crust-derived carbonate minerals, the proportion of carbon dioxide from the dissolution of basement-derived carbonate minerals, the proportion of carbon dioxide from the thermal evolution of organic matter, and the proportion of carbon dioxide from the dissolution of shallow fluid, and respectively refer to the proportion of inorganic-derived carbon dioxide and the proportion of organic-derived carbon dioxide; x and y are normalization variables set. , , , values of -0.15‰, 0.5‰, -0.5‰, -0.029‰ and -0.025‰, respectively; , , , and values of 1.5 x 10 9 , 0.9 x 10 13 , 1.5 x 10 13 , 0.8 x 10 13 , 1.2 x 10 13 ; , , values of -0.15 ‰, 0.33 ‰, -0.5 ‰ and -0.067 ‰, respectively; , , values of 1.5 x 10 9 , 0.9 x 10 13 , 1.5 x 10 13 , 0.8 x 10 13 ; , the values of the parameters a, b and c are -0.15 ‰, 0.5 ‰ and -0.2 ‰, respectively; , the values of the parameters a, b and c are 1.5 x 10 9 , 0.9 x 10 13 , 1.5 x 10 13 .

2. The method according to claim 1, wherein: The non-hydrocarbon gas carbon dioxide content in associated natural gas of the tectonic-thermal response zone center is greater than 50%; the non-hydrocarbon gas carbon dioxide content in associated natural gas of the tectonic-thermal response zone middle part is 5% to 50%; and the non-hydrocarbon gas carbon dioxide content in associated natural gas of the tectonic-thermal response zone outer part is less than 5%.

3. The method according to claim 1, wherein: the value range of R is 0%~50%.

4. The method according to claim 1, wherein: The mantle source volatile content is calculated based on the following formula: (19) wherein a is the proportion of mantle-derived carbon dioxide in the volatile component, is the content of non-hydrocarbon gas carbon dioxide in the associated natural gas of the corresponding region, is the mantle-derived volatile content.

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