Method for evaluating multiphase methane release flux in forming process of cold spring chimney body
Through comprehensive analysis and numerical model simulation methods, the release flux of multiphase methane in the formation of cold spring chimneys is accurately calculated, which solves the problem that the existing technology cannot accurately evaluate and improves the understanding of marine carbon cycle.
Patent Information
- Application Number
- CN202411813972.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-11
- Publication Date
- 2025-03-25
AI Technical Summary
Existing research methods cannot accurately quantify the release flux of the multiphase methane in the formation of cold spring carbonate chimneys, resulting in the inability to accurately evaluate its impact on the marine carbon cycle.
The three-dimensional columnar reaction-diffusion model was constructed using methods of comprehensive mineralogical analysis, petrochemical analysis, geological chronological analysis and numerical model, and the release flux of multiphase methane was quantitatively calculated.
The accurate assessment of the release flux of the multiphase methane in the formation of cold spring chimneys has been achieved, and the understanding of carbon exchange between sediment lithosphere and marine hydrosphere has been improved, which is of great scientific significance.
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Abstract
Description
Technical Field
[0001] The invention belongs to the field of marine sediment geochemistry and marine geology research, and specifically relates to a method for evaluating multiphase methane release flux during the formation of cold spring chimneys. Background Art
[0002] Methane is the most threatening greenhouse gas in the atmosphere after carbon dioxide. Marine sediments are the world's largest reservoir of methane. Even slight fluctuations in methane in the sediments can lead to exponential growth in methane content in the ocean and even the atmosphere, which in turn can have serious impacts on marine ecosystems and global climate change.
[0003] The anaerobic oxidation of methane (AOM) in marine sediments is a strong sink for methane, which consumes almost all the methane in the bottom sediments, making it impossible for methane to break through the sediments and affect the water body. However, as an extreme marine environment, cold seeps release a large amount of methane in two phases, dissolved and bubbled, directly to the seawater due to the instability of the bottom natural gas hydrate. At the same time, the high flux of methane release in the cold seep area strengthens the AOM process in the sediments, increases the total alkalinity of the pore water, promotes the precipitation of authigenic carbonates in the sediments, and leads to the formation of cold seep carbonate chimneys. Although most (>90%) of the methane in the marine sediments is consumed by the anaerobic oxidation of methane (AOM) involving sulfate ions. However, as a "high-speed channel" between the marine lithosphere and the hydrosphere, the dissolved or bubbled methane in the cold seep chimneys can break through the interception of the AOM process in the sediments and be directly transported to the seawater or even the atmosphere during its formation, which poses a serious threat to the marine ecological environment and the atmospheric greenhouse effect.
[0004] As the product of submarine methane oxidation reaction, cold seep carbonate chimneys truly record the geological environment information of submarine methane leakage events. Simulating the formation process of cold seep chimneys can accurately evaluate the release flux of multiphase methane during their life cycle, and can provide an important quantitative evaluation method for studying the marine methane cycle process. The current research methods mainly use geochemical methods to qualitatively analyze the formation process of cold seep carbonate chimneys. There is still a lack of quantitative simulation of the release of multiphase methane and the process of authigenic carbonate carbon fixation in the formation of chimneys, and thus it is impossible to accurately quantify the release flux of multiphase methane in the formation of cold seep carbonate chimneys. Summary of the invention
[0005] In order to solve the problem that existing research methods cannot accurately quantify the release flux of multiphase methane in the formation of cold seep carbonate chimneys, the present invention proposes a method for evaluating the release flux of multiphase methane in the formation process of cold seep chimneys, which combines mineralogical analysis, petrological analysis, geochronological analysis and numerical models to quantitatively simulate the formation process of cold seep chimneys in order to accurately calculate the release flux of multiphase methane in the formation of chimneys.
[0006] The present invention is implemented by adopting the following technical scheme: a method for evaluating the multiphase methane release flux during the formation of a cold spring chimney structure, comprising the following steps: Step A: Qualitative analysis of the formation mode of the cold spring chimney structure: (1) Conduct petrological and mineralogical analyses on the collected chimney samples to identify the main carbonate components of the chimneys and clarify the key geochemical processes that occurred during the formation of the chimneys; (2) Conduct geochronological analysis on the collected chimney samples to accurately establish the geological time framework of chimney growth and provide the necessary boundary conditions for subsequent simulation work; Step B: Construct a reaction-diffusion model to quantitatively analyze the formation of cold spring chimney structures: (1) Model the key geochemical processes in the formation of the chimneys and quantitatively simulate the reaction rates of each geochemical process; (2) Based on the obtained chimney formation age framework distribution data, a three-dimensional columnar cold spring chimney formation model was constructed to simulate the chimney formation process; Step C: Combined with the chimney formation simulation process in step B, the release flux of multiphase methane in the chimney formation is quantitatively calculated to achieve a comprehensive assessment of the contribution of the multiphase methane release flux in the cold spring chimney formation to the regional ocean carbon cycle.
[0007] Furthermore, in step A, the organic matter and carbonate content in the chimney body sample is determined by experimental analysis. The total organic carbon (TOC) in the chimney body sample is analyzed using an elemental analyzer connected to a continuous flow system. In addition, the collected chimney body samples are subjected to X-ray diffraction analysis (XRD) to obtain their mineralogical composition; some typical samples are classified according to macroscopic characteristics, and micrometer-scale morphological observations are performed under a scanning electron microscope (SEM), and energy spectrum analysis (EDS) tests are performed on characteristic mineral crystals to confirm the type of minerals by elemental composition.
[0008] Furthermore, in step A, based on the stratified sampling for mineralogical research, samples are sampled with a dental drill at key strata, ground to 200 mesh, and then dissolved. The purified sample is inhaled into the nebulizer chamber of CETAC AridusII using a PFA ESI-50 nebulizer, heated and atomized into an aerosol, which is introduced into a mass spectrometer by argon (Ar2) and nitrogen (N2), and the age distribution data of the chimney sample is determined by U and Th isotopes.
[0009] Furthermore, in step B, the geochemical processes involved in the formation of the cold spring chimney include: organic matter degradation, sulfate reduction, anaerobic oxidation of methane, and precipitation of authigenic carbonate. For the organic matter degradation process, a continuous organic matter degradation model is used for simulation, as follows:
[0010] (1) Where G(t) is the content of organic matter at time t during the degradation process, k is the first-order kinetic degradation coefficient, G(0) is the content of organic matter at the sediment-seawater interface (SWI), and g(k,0) is the distribution of organic matter activity in the sediment surface.
[0011] For the sulfate reduction process, the following model is used for simulation: The organic matter degradation rate (R OM ), the reaction rate of sulfate reduction (R SR ) is closely related to the degradation rate of organic matter. According to the stoichiometric relationship between the two, R SR It can be expressed as: (2) For the anaerobic oxidation of methane, the AOM reaction intensity in sediments is mainly related to the concentrations of methane and sulfate. The second-order kinetic model is used to describe the reaction rate R of the anaerobic oxidation of methane. AOM ,Right now: R AOM = k AOM ∙ [ CH 4 ]∙[ SO 4 2- ] (3) In the formula, k AOM is the reaction coefficient, [] represents the concentration.
[0012] The following model is used to simulate the precipitation process of authigenic carbonate: The rate of formation of authigenic carbonate (R AC ) shows a good linear relationship with the saturation of calcium ions in pore water (Ω), R AC The model is expressed as follows: Ω = [ Ca 2+ ] ⋅ [ CO 3 2- ] K SP * → R AC = k Ca ⋅ Ω - 1 (4) In the formula, K * SP is the solubility constant of solid carbonate, K Ca is the reaction coefficient, [] represents the concentration.
[0013] Furthermore, in step B, the formation of the chimney involves the precipitation process of dissolved calcium ions into the solid phase. Due to the limitation of Gibbs free energy, this process is always a process of contraction from the outside to the inside. This scheme adopts the following phase field model simulation, as follows: (5) Where φ represents the phase state of calcium ions (when φ=0, calcium ions are dissolved; when φ=1, calcium ions are solid). φ Characterizes the growth coefficient of the chimney sample (this coefficient is proportional to the precipitation rate of the authigenic carbonate in formula 4, which is limited by the age data of the chimney sample), and F is the free energy limit that calcium ions need to break through to transform from the dissolved state to the solid state. Based on formula (5), combined with the dating data of the chimney carbonate, the formation process of the chimney from the outside to the inside is accurately simulated.
[0014] Cold spring chimneys often present regular features of cylinders, so a three-dimensional cylindrical chimney formation model based on a three-dimensional cylindrical reaction-diffusion model is established: (6) Among them, z is the longitudinal length, r is the radial length, t is the time, D i is the phase diffusion coefficient of solution i, τ is the tortuosity, C i is the concentration of dissolved phase i, v z,r are the longitudinal and radial flow rates, and R is the reaction rate.
[0015] Furthermore, in step C, the formation process of the chimney can be simulated according to the modeling process in step B. DM ) and bubble methane (TF BM ) is calculated as follows:
[0016] (7) (8) In the above formula: T represents the simulation time (based on the geological age test), R represents the simulated radius of the cylindrical chimney (2πr is the circular surface integral of the chimney cross section). In the formation of the chimney, the leakage flux at each transverse radius node (r) is calculated by Flux DM(r, t) represents (this value can be quantitatively calculated by formula 6). The phenomenon of methane bubble plumes in the cold spring area indicates the supersaturated methane concentration in the pore water. Therefore, the dissolved methane concentration at the bottom of the model is set as the saturated concentration of methane in the pore water. The saturated concentration of methane in the pore water of the sediment is related to the ambient pressure (P), temperature (T) and salinity (S). The saturated concentration of methane in the pore water is usually calculated by the following polynomial C mes :
[0017] (9) The spatial distribution of dissolved methane saturation in the chimney sediments is calculated by Equation 9, which is related to Flux DM The difference between (r, t) is the flux of bubble-state methane at each transverse radius node (r). BM Then, based on the obtained release flux of dissolved methane and bubbling methane, combined with the specific content of methane in different depth layers of the ocean in the exploration area, the contribution of methane released from cold seep chimneys to the regional ocean carbon cycle is evaluated.
[0018] Compared with the prior art, the advantages and positive effects of the present invention are: This project uses cold seep carbonate chimney samples collected in the cold seep area as the research object, and uses petrology, mineralogy, geochronology and other analytical methods to qualitatively restore the chimney formation process; secondly, a three-dimensional columnar chimney formation model is constructed based on a three-dimensional cylindrical reaction-diffusion model, and the leakage flux of multiphase methane in the chimney formation is quantitatively calculated; finally, the formation mechanism of cold seep carbonate chimneys is constructed to evaluate the contribution of chimney formation to the regional marine carbon cycle. This project not only helps to invert the multiphase methane cycle process in the formation of cold seep chimneys and enhance the understanding of carbon exchange between sediment lithosphere and ocean hydrosphere, but also has important scientific significance for further understanding the geological, environmental and biological co-evolution of cold seep areas. BRIEF DESCRIPTION OF THE DRAWINGS
[0019] Figure 1 This is a schematic diagram of the method flow of an embodiment of the present invention; Figure 2 This is a schematic diagram of the numerical model of a three-dimensional columnar cold seep carbonate chimney. The arrows represent dissolved methane, the circles represent bubbling methane, and the central area is the release channel of the bubbling methane. DETAILED DESCRIPTION
[0020] In order to more clearly understand the above-mentioned purpose, features and advantages of the present invention, the present invention is further described below in conjunction with the accompanying drawings and embodiments. In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention can also be implemented in other ways different from those described herein. Therefore, the present invention is not limited to the specific embodiments disclosed below.
[0021] Embodiment, the present invention proposes a method for evaluating the multiphase methane release flux during the formation of cold spring chimneys, combining Figure 1 As shown, the following steps are included: Step A: Qualitatively analyze the formation mode of cold spring chimneys through geochemical analysis: Step A1, collect chimney samples and perform petrological and mineralogical analysis on them to identify the main carbonate components of the chimneys and clarify the important geochemical processes that occurred during the formation of the chimneys; The experiment analyzed the organic matter and carbonate content in the chimney samples. The total organic carbon (TOC) in the chimney samples was analyzed using an elemental analyzer connected to a continuous flow system. In addition, the collected chimney samples were subjected to X-ray diffraction analysis (XRD) to obtain their mineralogical composition; some typical samples were classified according to their macroscopic characteristics, and micrometer-scale morphological observations were performed under a scanning electron microscope (SEM), and energy spectrum analysis (EDS) tests were performed on characteristic mineral crystals to confirm the type of minerals based on elemental composition.
[0022] Step A2, conducting geochronological analysis on the collected chimney samples, accurately establishing the geological age framework of chimney growth, and providing necessary boundary conditions for subsequent simulation work; On the basis of stratified sampling in mineralogical research, samples were taken from key layers by dental drills, ground to 200 mesh, and then dissolved. The purified samples were inhaled into the nebulizer chamber of CETAC Aridus II using a PFA ESI-50 nebulizer, heated and nebulized into aerosols, which were introduced into the mass spectrometer by argon (Ar2) and nitrogen (N2). The age distribution data of the chimney samples were determined by U and Th isotopes.
[0023] Step B, constructing a three-dimensional cylindrical reaction-diffusion model to simulate the formation of cold spring chimneys; Step B1, modeling the key geochemical processes in the chimney formation process obtained in A1, and quantitatively simulating the reaction rates of each geochemical process; The main geochemical processes involved in the formation of cold spring chimneys include: organic matter degradation, sulfate reduction, anaerobic oxidation of methane, and precipitation of authigenic carbonates. For the organic matter degradation process, this scheme uses a continuous organic matter degradation model to simulate the specific model as follows:
[0024] (1) Where G(t) is the content of organic matter at time t during the degradation process, k is the first-order kinetic degradation coefficient, G(0) is the content of organic matter at the sediment-seawater interface (SWI), and g(k,0) is the distribution of organic matter activity in the sediment surface.
[0025] For the sulfate reduction process, this scheme adopts the following model simulation: The organic matter degradation rate (R) can be obtained by taking the derivative of the time term of model (1). OM The reaction rate of sulfate reduction (R SR ) is closely related to the degradation rate of organic matter. Therefore, according to the stoichiometric relationship between the two, R SR It can be expressed as:
[0026] (2) For the anaerobic oxidation process of methane, this scheme adopts the following model simulation: The intensity of AOM reaction in sediments is mainly related to the concentration of methane and sulfate. This scheme uses a second-order kinetic model to describe the reaction rate (R AOM , Model 3).
[0027] R AOM = k AOM ∙ [ CH 4 ]∙[ SO 4 2- ] (3) In the formula, k AOM is the reaction coefficient, [] represents the concentration.
[0028] For the precipitation process of authigenic carbonate, this scheme adopts the following model simulation: The rate of formation of authigenic carbonate (R AC ) shows a good linear relationship with the saturation of calcium ions in pore water (Ω), so R AC The model is as follows: Ω = [ Ca 2+ ] ⋅ [ CO 3 2- ] K SP * → R AC = k Ca ⋅ Ω - 1 (4) In the formula, K * SP is the solubility constant of solid carbonate, KCa is the reaction coefficient, [] represents the concentration.
[0029] Step B2, constructing a 3D columnar cold spring chimney formation model based on the chimney formation age grid distribution data obtained in A2 to simulate the chimney formation process; The formation of chimneys involves the precipitation process of dissolved calcium ions into the solid phase. Limited by Gibbs free energy, this process is always a process of contraction from the outside to the inside. This process is mainly shown by the dating data of chimney samples, and the age data of the chimney periphery is smaller than the age data of the interior. In order to simulate the growth process of chimneys from the outside to the inside, this scheme uses the phase field model simulation, as follows:
[0030] (5) Where φ represents the phase state of calcium ions (when φ=0, calcium ions are dissolved; when φ=1, calcium ions are solid). φ Characterizes the growth coefficient of the chimney sample (this coefficient is proportional to the authigenic carbonate precipitation rate in Model 4 and is constrained by the age data of the chimney sample), and F is the free energy limit required for calcium ions to transform from a dissolved state to a solid state.
[0031] Cold spring chimneys often present regular features of a cylinder, so a three-dimensional cylindrical chimney formation model based on a 3D cylindrical reaction-diffusion model was established (Eq. 6, Figure 1 ) (6) Step C, quantitatively calculating the release flux of multiphase methane during the formation of chimneys, thereby evaluating the contribution of methane release from cold spring chimneys to the regional carbon cycle; According to the chimney formation simulation process obtained in B2, the release flux of multiphase methane (bubble state and dissolved state) in chimney formation is quantitatively calculated; According to the modeling process in step B, the formation process of the chimney can be simulated. DM ) and bubble methane (TF BM ) is calculated as follows:
[0032] (7) (8) In the above formula: T represents the simulation time (based on the geological age test), R represents the simulated radius of the cylindrical chimney (2πr is the circular surface integral of the chimney cross section). In the formation of the chimney, the leakage flux at each transverse radius node (r) is calculated by Flux DM(r, t) represents (this value can be quantitatively calculated by Model 6). The phenomenon of methane bubble plumes in the cold spring area indicates the supersaturated methane concentration in the pore water. Therefore, the dissolved methane concentration at the bottom of the model is set as the saturated concentration of methane in the pore water. The saturated concentration of methane in the pore water of the sediment is related to the ambient pressure (P), temperature (T) and salinity (S). The saturated concentration of methane in the pore water is usually calculated by the following polynomial (C mes , Equation 9):
[0033] (9) The spatial distribution of dissolved methane saturation in chimney sediments was calculated by Method 9, which is consistent with Flux DM The difference between (r, t) is the flux of bubble-state methane at each transverse radius node (r). BM (r,t)).
[0034] The comprehensive release flux of dissolved methane and bubble methane, combined with the specific content of methane in different depth layers of the ocean in the exploration area, is used to comprehensively evaluate the contribution of multiphase methane release flux in the formation of cold seep chimneys to the regional ocean carbon cycle, and to evaluate the contribution of methane released from cold seep chimneys to the regional ocean carbon cycle.
[0035] This program innovatively combines mineralogical analysis, petrological analysis, geochronological analysis and numerical models to establish a numerical model of the three-dimensional cold seep carbonate chimney process based on a reaction-diffusion model, simulate the formation process of the chimney, quantitatively calculate the leakage flux of multiphase methane and the solid efficiency of authigenic carbonate, and then evaluate the impact of the multiphase methane release process on the regional carbon cycle during the formation of the chimney. This will enhance the understanding of carbon exchange between the sedimentary lithosphere and the ocean hydrosphere, and has important scientific significance for further understanding the geological, environmental and biological co-evolution of the cold seep area.
[0036] The above description is only a preferred embodiment of the present invention and does not limit the present invention in other forms. Any technician familiar with the profession may use the technical content disclosed above to change or modify it into an equivalent embodiment with equivalent changes and apply it to other fields. However, any simple modification, equivalent change and modification made to the above embodiment based on the technical essence of the present invention without departing from the content of the technical solution of the present invention still falls within the protection scope of the technical solution of the present invention.
Claims
1. A method for evaluating the multiphase methane release flux during the formation of cold spring chimneys, characterized in that: The following steps are involved: Step A, combining petrological analysis and mineralogical analysis to determine the key geochemical processes occurring during the formation of the cold spring chimney, wherein the key geochemical processes include organic matter degradation, sulfate reduction, anaerobic oxidation of methane, and precipitation of authigenic carbonates, and establishing a geological time frame for the growth of the cold spring chimney through geochronological analysis to achieve a qualitative analysis of the formation pattern of the cold spring chimney structure; Step B: constructing a reaction-diffusion model to simulate the formation of cold spring chimneys, including: (1) Model the key geochemical processes in the formation of the obtained cold spring chimneys to quantitatively simulate the reaction rates of each key geochemical process; (2) Based on the geological time distribution data of the cold spring chimney growth, a reaction-diffusion model of the formation of three-dimensional columnar cold spring chimneys was constructed to simulate the formation process of cold spring chimneys; Step C, combining the chimney formation simulation process in step B, quantitatively calculate the release flux of multiphase methane in the chimney formation, where multiphase methane includes dissolved methane and bubble methane, thereby achieving an assessment of the contribution of the multiphase methane release flux in the formation of cold spring chimneys to the regional ocean carbon cycle.
2. The method for evaluating the multiphase methane release flux during the formation of cold spring chimneys according to claim 1, characterized in that: In step B, the reaction rates of key geochemical processes are quantitatively simulated in the following manner: (1) Regarding the degradation process of organic matter: Continuous organic matter degradation model Simulation; where G(t) is the content of organic matter at time t during the degradation process, k is the first-order kinetic degradation coefficient, G(0) is the content of organic matter at the sediment-seawater interface, and g(k,0) is the distribution of organic matter activity in the sediment surface layer; (2) Regarding the sulfate reduction process: The time term of the continuous organic matter degradation model is derived to obtain the organic matter degradation rate R OM , then the sulfate reduction reaction rate R SR It is expressed as: ; (3) Anaerobic oxidation process for methane: The intensity of AOM reaction in sediments is mainly related to the concentrations of methane and sulfate. The second-order kinetic model is used to describe the reaction rate R of the anaerobic methane oxidation process. AOM , , where k AOM is the reaction coefficient, [] represents the corresponding ion concentration; (4) Regarding the precipitation process of authigenic carbonates: The rate of formation of authigenic carbonate R AC It has a linear relationship with the saturation of calcium ions in the pore water, Ω, as shown below: In the formula, K * SP is the solubility constant of solid carbonate, K Ca is the reaction coefficient, [] represents the corresponding ion concentration.
3. The method for evaluating the multiphase methane release flux during the formation of cold spring chimneys according to claim 1, characterized in that: In step B, the specific process of constructing the reaction-diffusion model of the formation of the three-dimensional cylindrical cold spring chimney is as follows: (1) Use the phase field model to simulate the growth process of the chimney from the outside to the inside: In the formula, φ represents the phase state of calcium ions. When φ=0, calcium ions are dissolved; when φ=1, calcium ions are solid. φ Characterizes the growth coefficient of the chimney sample, F is the free energy limit that calcium ions need to break through to transform from dissolved state to solid state; (2) Establish a three-dimensional columnar chimney formation model based on the three-dimensional columnar reaction-diffusion model: Where z is the longitudinal length, r is the radial length, t is the time, and D i is the phase diffusion coefficient of solution i, τ is the tortuosity, C i is the concentration of dissolved phase i, v z,r are the longitudinal and radial flow rates, and R is the reaction rate.
4. The method for evaluating multiphase methane release flux during the formation of cold spring chimneys according to claim 1, characterized in that: In the step A, the key geochemical processes occurring during the formation of the chimney are determined in the following manner: cold spring chimney samples are collected and subjected to petrological and mineralogical analyses, the organic matter and carbonate contents in the cold spring chimney samples are determined by experimental analysis, and the total organic carbon in the cold spring chimney samples is analyzed by using an elemental analyzer connected to a continuous flow system; in addition, the collected cold spring chimney samples are subjected to X-ray diffraction analysis to obtain their mineralogical composition; some typical samples are classified according to their macroscopic characteristics, morphological observations are performed at the micrometer scale under a scanning electron microscope, and energy spectrum analysis tests are performed on characteristic mineral crystals at the same time, and the types of minerals are confirmed by elemental composition to identify the main carbonate components of the chimney.
5. The method for evaluating multiphase methane release flux during the formation of cold spring chimneys according to claim 1, characterized in that: In step A, the following method is used to establish the geological time frame of chimney growth: On the basis of stratified sampling for mineralogical research, samples from key strata are selected and ground to a specific mesh size. After dissolution, the purified samples are inhaled into the nebulization chamber, heated and atomized into aerosols, which are introduced into the mass spectrometer by argon and nitrogen. The age distribution data of the chimney samples are determined by U and Th isotopes to provide necessary boundary conditions for subsequent simulation work.
6. The method for evaluating multiphase methane release flux during the formation of cold spring chimneys according to claim 1, characterized in that: In step C, the formation process of the chimney body is simulated according to the modeling process in step B: Among them, dissolved methane TF DM With bubble methane TF BM The flux is calculated as follows: Where T represents the simulation time, R represents the simulation radius of the cylindrical chimney, and during the formation of the cold spring chimney, the leakage flux at each lateral radius node r is given by Flux DM (r, t) indicates that the methane bubble plume phenomenon in the cold spring area indicates the supersaturated methane concentration in the pore water. Therefore, the dissolved methane concentration at the bottom of the model is set as the saturated concentration of methane in the pore water. The saturated concentration of methane in the sediment pore water is related to the ambient pressure P, temperature T and salinity S. The saturated concentration of methane in the pore water C is calculated by the following polynomial: mes : The spatial distribution of dissolved methane saturation in the chimney sediments is calculated by the above formula, which is consistent with Flux DM The difference between (r, t) is the flux of bubble methane at each lateral radius node r. BM (r,t).