Quantitative calculation method for hydrogen and oxygen isotopes in surface water bodies during the evaporation fractionation process

Abstract

The present invention discloses a quantitative calculation method for the hydrogen and oxygen isotopes in surface water during the evaporation fractionation process in the field of isotope tracing technology, aiming to solve the problems of low calculation accuracy and large uncertainty in the existing calculation methods. It includes: analyzing the kinetic effect of the evaporation fractionation process; constructing the probability mass function of the isotope body and decomposing the ratio of the heavy / light isotope body; quantitatively describing the dissipation rate of the heavy / light isotope body in the evaporation fractionation; combining the water evaporation rate to obtain the change efficiency of the heavy / light isotope body during the evaporation fractionation process; and calculating the isotope body content in the remaining surface water. The present invention enhances the application adaptability of the calculation method to various conventional and extreme situations, reveals the isotope fractionation change law in surface water during the evaporation process, and improves the reliability of the results.

Description

Technical Field

[0001] The present invention relates to a quantitative calculation method for the fractionation process of hydrogen and oxygen isotopes in surface water bodies during evaporation, belonging to the technical field of isotope tracing. Background Art

[0002] In the study of basin hydrological processes, it is necessary to fully consider the complex interaction and mixing processes among multiple water sources. Currently, using isotope tracing methods to study hydrological processes such as basin runoff sources and water transfer is a hot topic in international research. Stable hydrogen and oxygen isotopes are components of water molecules, with stable chemical properties, and are effective tools for studying water source analysis and water volume interaction. By monitoring the signal changes of hydrogen and oxygen isotopes in multiple water sources, the formation and transmission processes of fine-scale water flow in the basin can be revealed from the perspective of microscopic water molecule tracing, and hydrological process information that cannot be directly obtained by traditional hydrological monitoring means can be obtained.

[0003] In the analysis of basin hydrological processes based on stable hydrogen and oxygen isotopes, the most important uncertainty comes from the accuracy of isotope data, which is mainly affected by the errors in isotope sample collection and data testing processes, and the fractionation effect caused by the evaporation of isotopes themselves, which is often ignored in practical applications. The fractionation effect of isotopes is more important in the fine-scale water flow-isotope coupling simulation. In order to reduce the uncertainty brought by the isotope fractionation effect to the water flow-isotope coupling simulation application, it is necessary to first conduct quantitative research on the isotope fractionation mechanism under the hydrological evaporation effect, so as to eliminate the influence of hydrogen and oxygen isotopes by evaporation fractionation and improve the accuracy of analyzing key hydrological processes in the basin based on hydrogen and oxygen isotope tracing technology.

[0004] Currently, the commonly used calculation method based on the Rayleigh fractionation principle sets many assumptions in the simplification process, making it difficult for this method to achieve efficient and accurate calculation for many extreme scenario cases. At the same time, since this method analyzes the change in the overall isotope abundance of the water body, it cannot directly quantitatively describe the differential dissipation processes of heavy / light isotope bodies during evaporation, and it is difficult to apply to more refined tracer analysis at the atomic level. Summary of the Invention

[0005] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a quantitative calculation method for the fractionation process of hydrogen and oxygen isotopes in surface water bodies during evaporation, enhance the application adaptability of the calculation method to various conventional and extreme situations, reveal the isotope fractionation change law in surface water bodies during the evaporation process, and improve the reliability of the results.

[0006] To achieve the above purpose, the present invention is implemented by the following technical solutions:

[0007] A quantitative calculation method for the fractionation process of hydrogen and oxygen isotopes in surface water bodies during evaporation, comprising the following steps:

[0008] Analyze the kinetic effects of the evaporation fractionation process;

[0009] Construct the probability mass function of isotopologues and decompose the ratio of heavy / light isotopologues;

[0010] Quantitatively describe the dissipation rate of heavy / light isotopologues in evaporation fractionation;

[0011] Combined with the evaporation rate of water bodies, obtain the change efficiency of heavy / light isotopologues in the evaporation fractionation process;

[0012] Calculate the content of isotopologues in the remaining surface water bodies.

[0013] Furthermore, the steps of analyzing the kinetic effects of the evaporation fractionation process include:

[0014] S1. When the same molecular system is in different phases and undergoes two phase transitions, the isotope fractionation coefficient α is used to describe this dynamic process, and the expression is:

[0015]

[0016] In the formula, N i is the number of heavy isotopes, N j is the number of light isotopes, and R is the isotope ratio;

[0017] S2. Under the action of thermodynamics, the gas-liquid water at the water surface is in a relative equilibrium state, that is

[0018] dN i / dN j =(N i / N j ) 气 (2)

[0019] Combining formulas (1) and (2), we get:

[0020]

[0021] In the formula, k H and k L are the change efficiencies of heavy and light isotopologues respectively;

[0022] Subsequently, the kinetic isotope effect KIE can be expressed as:

[0023]

[0024] Furthermore, the isotope fractionation coefficient in open water bodies can be calculated through an empirical formula:

[0025] α 气-液 =1 / α 液-气 (5)

[0026] Combined with α can be obtained 气-液 ; where T is the Kelvin temperature (K).

[0027] Furthermore, the construction of the probability mass function of heavy / light isotope species includes:

[0028] Based on the binomial distribution function, construct the binomial distribution of oxygen heavy / light isotope species:

[0029]

[0030] In the formula, P i is the probability of the occurrence of hydrogen-oxygen isotope species, n i is the number of hydrogen and oxygen atoms, H i is the number of heavy hydrogen and oxygen atoms, n i -H i corresponds to the number of light hydrogen and oxygen atoms, π R is the relative abundance of heavy hydrogen and oxygen atoms

[0031]

[0032] In the formula, δ 18 O is the initial oxygen isotope abundance in the measured water body, Vienna Standard Mean Ocean Water value ( 18 O / 16 O) 标准 =(2005.2±0.45)×10 -6 .

[0033] Furthermore, based on the established probability mass function of heavy / light isotope species, taking oxygen isotope as an example, the ratio R H and R L of heavy / light isotope species of oxygen can be decomposed into:

[0034] ①H2- 18 O

[0035] n i =1, H i =1 (9)

[0036]

[0037] ②H2- 16 O

[0038] n i =1, H i =0 (11)

[0039]

[0040] Further, when analyzing the content of heavy / light oxygen isotope species in the test water body, the ratio R of heavy / light oxygen isotope species in the evaporated water body H and R L The actually measured data can also be directly used.

[0041] Further, for the water body during the evaporation process at the gas-liquid interface, affected by the fractionation effect, the dissipation rates rate H and rate L show differences, and its relationship with the change efficiency k H and k L as well as the isotope ratio R H and R L can be expressed as:

[0042] rate H = k H ·R H (13)

[0043] rate L = k L ·R L (14)

[0044] The sum of the dissipation rates rate H and rate L of heavy / light oxygen isotope species is equal to the dissipation rate of all water molecules, that is, the water body evaporation rate rate evap , and combined with formula (4), it can be expressed as:

[0045]

[0046] After deformation, the change efficiency of heavy / light oxygen isotope species during the evaporation fractionation process is obtained:

[0047]

[0048]

[0049] Further, the specific calculation of the isotope species content in the remaining surface water body includes: assuming that the initial water depth is h, and the initial decomposition results of heavy / light oxygen isotope species are R H t and R L t , the actually measured evaporation rate is rate evap , after a short time (ΔT), the amounts of heavy / light oxygen isotope species dissipated into the air are Δ H and Δ L :

[0050]

[0051]

[0052] That is, the heavy / light isotope body content R of the remaining oxygen in the surface water body H t+1 , R L t+1 can be expressed as:

[0053]

[0054]

[0055] Furthermore, according to the isotope permil difference expression:

[0056]

[0057] the oxygen isotope abundance in the remaining surface water body can be obtained That is:

[0058]

[0059] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0060] The present invention decomposes the hydrogen and oxygen isotope information into the concept of heavy / light isotope bodies, analyzes the kinetic effect of isotopes during the evaporation process, identifies the quantitative relationship between the change efficiency of heavy / light isotope bodies and the fractionation coefficient during the fractionation process, constructs the probability mass function of heavy / light isotopes, decomposes the measured overall isotope abundance into the proportions of heavy / light isotope bodies, and through the calculation of the migration and transformation of heavy / light isotope bodies with water flow respectively, it is beneficial to realize the quantitative description of the isotope evaporation fractionation effect considering the different fractionation rates of heavy / light isotope bodies, thereby revealing the isotope fractionation change law of surface water bodies during the evaporation and migration process of water molecules.

[0061] The present invention has no specific limitation on the initial isotope abundance of water bodies, is applicable to various extreme conditions, the research results obtained are reliable, and the result reproducibility is good. In addition, in addition to analyzing the change of the isotope abundance of the remaining water body with the evaporation process from the perspective of water molecules, the present invention can also quantitatively analyze the change laws of heavy / light isotope bodies in the remaining water body with the evaporation process respectively, providing a basis for more refined research at the atomic level.

[0062] Based on the content of the present invention, the influence of hydrogen and oxygen isotope evaporation fractionation can be eliminated, thereby improving the accuracy of analyzing key hydrological processes in the basin based on the hydrogen and oxygen isotope tracing technology. At the same time, the discretized calculation method of the present invention can facilitate its integration with the modules of the hydrological model to carry out refined water flow-isotope coupling simulation. Description of the Drawings

[0063] Figure 1 Schematic flow chart of an embodiment of the present invention;

[0064] Figure 2 Schematic comparison of the evaporation fractionation process of water bodies with a lower initial oxygen isotope abundance over time in an embodiment of the present invention;

[0065] Figure 3 Schematic comparison of the evaporation fractionation process of water bodies with a higher initial oxygen isotope abundance over time in an embodiment of the present invention. Detailed implementation manners

[0066] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention and should not be used to limit the protection scope of the present invention.

[0067] Embodiment 1:

[0068] The present invention sets an ideal research object with a water depth h = 1.0 m. In an open environment, it is subject to a stable water surface evaporation rate (rate evap = 5 mm / day), and based on the measured results of isotope samples in the small watershed of Mukeng Source, a common lower scenario of the initial oxygen isotope abundance (δ 18 O = -11.18‰) is selected, and the corresponding air temperature during sampling is 13°C.

[0069] As Figure 1 shown, the quantitative calculation method of hydrogen and oxygen isotopes in surface water bodies during the evaporation fractionation process, taking oxygen isotopes as an example, is calculated through the following steps:

[0070] The first step is to quantitatively analyze the kinetic isotope fractionation effect of the oxygen isotope body (the number of heavy isotope atoms n = 1 in the oxygen isotope body) based on the quantitative description results of the kinetic isotope effects (KIE):

[0071] When the same molecular system is in different phases and undergoes a phase transition between two phases (from phase A to phase B), the isotope fractionation coefficient α is used to describe this dynamic process, and the expression is:

[0072]

[0073] In the formula, N i is the number of heavy isotopes, N j is the number of light isotopes, and R is the isotope ratio;

[0074] Under the action of thermodynamics, the gas-liquid water at the water surface is in a relatively equilibrium state, that is

[0075] dNi / dN j =(N i / N j ) 气 (2)

[0076] Combining equations (1) and (2), we get:

[0077]

[0078] where k H and k L are the change efficiencies of the heavy and light isotope bodies, respectively;

[0079] Subsequently, the kinetic isotope effect KIE can be expressed as:

[0080]

[0081] The isotope fractionation coefficient in the open water body can be calculated through the empirical formula:

[0082] α 气-液 =1 / α 液-气 (5)

[0083] Combining we can obtain α 气-液 =0.9897.

[0084] Second, construct the probability mass function of the isotope body and decompose the ratio of the heavy / light isotope body;

[0085] Based on the binomial distribution function, construct the binomial distribution of the oxygen heavy / light isotope body:

[0086]

[0087] where P i is the probability of the hydrogen-oxygen isotope body appearing, n i is the number of hydrogen and oxygen atoms, H i is the number of heavy hydrogen and oxygen atoms, n i -H i corresponds to the number of light hydrogen and oxygen atoms, π R is the relative abundance of the heavy hydrogen and oxygen atoms, and satisfies the following formula (8),

[0088]

[0089] where δ 18 O is the measured initial oxygen isotope abundance in the water body, Vienna Standard Mean Ocean Water value ( 18 O / 16 O) 标准 =(2005.2±0.45)×10 -6。

[0090] Based on the established probability mass function of heavy / light isotope species, taking oxygen isotope as an example, the ratio R of heavy / light isotope species of oxygen H and R L can be decomposed into:

[0091] ①H2- 18 O

[0092] n i =1, H i =1 (9)

[0093]

[0094] ②H2- 16 O

[0095] n i =1, H i =0 (11)

[0096]

[0097] When analyzing the content of heavy / light isotope species of oxygen in the test water body for the oxygen isotope abundance, the ratios R of heavy / light isotope species of oxygen in the evaporated water body calculated in the second step H and R L can also use the actually measured data.

[0098] Step 3: Quantitatively describe the dissipation rate of heavy / light isotope species in evaporation fractionation;

[0099] For the water body in the evaporation process at the gas-liquid interface, affected by the fractionation effect, the dissipation rates rate of heavy / light isotope species H and rate L show differences, and their relationship with the change efficiency k of heavy / light isotopes in the evaporation process H and k L as well as the isotope ratio R H and R L can be expressed as:

[0100] rate H =k H ·R H (13)

[0101] rate L =k L ·R L (14)

[0102] Step 4: The dissipation rates rate of heavy / light isotope species H and rate LThe sum of the two is equal to the dissipation rate of all water molecules, i.e., the evaporation rate rate of the water body evap , and combined with formula (4), it can be expressed as:

[0103]

[0104] After deformation, the change efficiency of the heavy / light isotope body in the evaporation fractionation process is obtained:

[0105]

[0106]

[0107] Step 5, calculate the isotope body content in the remaining surface water body;

[0108] Assume that the initial heavy / light isotope body decomposition result is R H t and R L t , after a short time (ΔT), the amounts of heavy / light isotope bodies dissipated into the air are Δ H and Δ L :

[0109]

[0110]

[0111] That is, the heavy / light isotope body content R H t+1 of the remaining oxygen in the surface water body, R L t+1 can be expressed as:

[0112]

[0113]

[0114] It can also be based on the isotope per mil difference expression:

[0115]

[0116] The oxygen isotope abundance in the remaining surface water body can be obtained, that is:

[0117]

[0118] Secondly, compare the above method of the present invention with the fractionation process calculation method based on the Rayleigh fractionation principle.

[0119] The fractionation process calculation method based on the Rayleigh fractionation principle can be expressed as:

[0120]

[0121] In the formula, is the ratio of the remaining isotope, which is the ratio of the remaining water volume to the initial water volume. Therefore, 1 - f corresponds to the ratio of the evaporated water volume (rate evap ·ΔT / h), and are the current and initial isotope abundances respectively. ε 气-液 is the enrichment coefficient when water changes from the gaseous state to the liquid state, which can be calculated by ε 气-液 = α 气-液 - 1 = -0.01027. It should be noted that this method is for the equilibrium fractionation situation and many assumptions are used to obtain this simplified equation. At the same time, it is required that and are much less than 1 and approach 0, otherwise the error is large.

[0122] Given different evaporation calculation durations, the variation process of the oxygen isotope abundance in the surface water body with time can be calculated. Under the condition of a relatively low initial oxygen isotope abundance (-11.18‰), the calculation results are shown in Table 1:

[0123] Table 1: Calculation results of the evaporation fractionation process of water bodies with a relatively low initial oxygen isotope abundance

[0124]

[0125] Example 2:

[0126] The present invention sets an ideal research object with a water depth h = 1.0 m. In an open environment, it is subject to a stable water surface evaporation rate (rate evap = 5 mm / day). Considering extreme conditions, a scenario with a relatively high initial oxygen isotope abundance is set (δ 18 O is equal to 0‰). Also considering the air temperature of 13°C, the corresponding empirical fractionation coefficient is: α 气-液 = 0.9897. Combining the new method of the present invention and the method based on the Rayleigh fractionation principle, with the same steps as in Example 1, the variation process of the oxygen isotope abundance in the surface water body with time under the condition of a relatively high initial oxygen isotope abundance (0‰) can be calculated. The calculation results are shown in Table 2:

[0127] Table 2: Calculation results of the evaporation fractionation process of water bodies with a relatively high initial oxygen isotope abundance

[0128]

[0129] Analyze the calculation results of Examples 1 - 2:

[0130] Combined with Figures 2-3 , it can be seen that the calculation results of the evaporation fractionation process of the present invention are generally in good agreement with the calculation results based on the Rayleigh fractionation principle, especially when the evaporation duration is short. However, when the evaporation amount exceeds 10-20% of the total water volume (after 40 days in the case), the relative error between the two calculation results reaches 5% and increases with further evaporation.

[0131] According to the calculation principle of the evaporation process based on Rayleigh fractionation, the calculation of the change in the isotope abundance of the final surface water body with evaporation uses an approximate simplification of the logarithmic function, that is, when the isotope abundance in the surface water body is a minimum value, Therefore, as the evaporation process continues, the isotope abundance in the surface water body continuously increases, resulting in an increasingly large error. To effectively avoid this error, in the discrete calculation of the isotope fractionation process, the calculation step size can be controlled to ensure that within a single-step calculation, the evaporation water volume does not exceed 10% of the total water volume.

[0132] Compared with the method based on Rayleigh fractionation, the calculation method of the present invention has fewer simplified limiting conditions and stronger adaptability to extreme application conditions. At the same time, the principle of the method of the present invention is to calculate the fractionation change laws of heavy / light isotope bodies with the evaporation process respectively, which can effectively trace the movement of substances at the atomic level. Compared with the traditional fractionation calculation at the water molecule level, it can meet more refined research requirements.

[0133] In addition, in the actual research on analyzing the key hydrological processes of the basin based on the hydrogen and oxygen isotope tracing technology, the application of the content of the present invention can eliminate the influence of hydrogen and oxygen isotopes by evaporation fractionation, thereby improving the accuracy of the analysis results. And the discrete calculation method of the present invention can facilitate its module integration with the hydrological model to carry out refined water flow-isotope coupling simulation.

[0134] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the technical principle of the present invention, several improvements and deformations can still be made, and these improvements and deformations should also be regarded as the protection scope of the present invention.

Claims

1. A quantitative calculation method for the oxygen isotope during the evaporation fractionation process in surface water bodies, characterized in that: Including the following steps: Analyze the kinetic effect of the evaporation fractionation process: S1. When the same molecular system is in different phases and undergoes two phase transitions, the isotope fractionation coefficient α is used to describe the dynamic process of the phase transition. The expression is: Where N i is the number of heavy isotopes, N j is the number of light isotopes, and R is the isotope ratio; S2. Under the action of thermodynamics, the gas-liquid water at the water surface is in a relative equilibrium state, that is dN i / dN j =(N i / N j ) 气 (2) Combining formulas (1) and (2), we get: where k H and k L are the change efficiencies of the heavy and light isotope bodies, respectively; Express the kinetic isotope effect KIE as: Construct the probability mass function of the isotope body: Based on the binomial distribution function, construct the binomial distribution of the heavy / light oxygen isotope body: where P i is the probability of occurrence of oxygen isotope species, n i is the number of oxygen atoms, H i is the number of heavy oxygen atoms, n i -H i corresponds to the number of light oxygen atoms, π R is the relative abundance of heavy oxygen atoms; where δ 18 O is the measured initial oxygen isotope abundance in the water body, Vienna Standard Mean Ocean Water value ( 18 O / 16 O) 标准 = (2005.2 ± 0.45) × 10 -6 ; Based on the isotopologue probability mass function, the ratio R H of the heavy / light isotopologues of oxygen and R L is decomposed into: ①H2- 18 O n i = 1, H i = 1 (7) ②H2- 16 O n i = 1, H i = 0 (9) Quantitatively describe the dissipation rate of the heavy / light isotope body in the evaporation fractionation, and combine with the water body evaporation rate to obtain the change efficiency of the heavy / light isotope body in the evaporation fractionation process: For water bodies during the evaporation process at the air-liquid interface, affected by fractionation, the dissipation rates of heavy / light isotope species rate H and rate L exhibit differences, and their relationship with the change efficiency k H and k L as well as the isotope ratio R H and R L can be expressed as: rate H = k H ·R H (11) rate L = k L ·R L (12) Heavy / Light Isotope Body Dissipation Rate rate H and rate L The sum of the two is equal to the dissipation rate of all water molecules, i.e., the water body evaporation rate rate evap , and combined with formula (4), it can be expressed as: After deformation, the change efficiency of the heavy / light isotope body in the evaporation fractionation process is obtained: Calculate the content of the isotope body in the remaining surface water body: Assume that the initial water depth is h, and the initial decomposition result of the heavy / light isotope body is R H t and R L t , the actually measured evaporation rate is rate evap , after a short period of time (ΔT), the amounts of heavy / light isotope dissipated into the air are Δ H and Δ L : i.e., the heavy / light isotope content R of the remaining oxygen in surface water bodies H t+1 , R L t+1 can be expressed as:

2. The quantitative calculation method for oxygen isotope during the evaporation fractionation process in surface water bodies according to claim 1, wherein: The isotope fractionation coefficient is calculated through an empirical formula, and its expression is as follows: α 气-液 ＝1 / α 液-气 (20) Combine α can be obtained 气-液 ; In the formula, T is the Kelvin temperature (K).

3. The quantitative calculation method for the oxygen isotope during the evaporation fractionation process in surface water bodies according to claim 1, characterized in that: When analyzing the content of heavy / light oxygen isotope species in the test water body for oxygen isotope abundance, the ratio R of heavy / light oxygen isotope species in the evaporated water body H and R L The actually measured data can also be directly used.

4. The quantitative calculation method for the oxygen isotope during the evaporation fractionation process in surface water bodies according to claim 1, characterized in that: It can also be based on the expression of the permil difference of isotopes: Obtain the oxygen isotope abundance in the remaining surface water That is:

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