Method for determining migration distance of nuclide in fractured rock mass by considering multistage decay

Abstract

The invention provides a method for determining the migration distance of nuclide in a fractured rock mass by considering multistage decay, and relates to the technical field of radioactive waste deep geological disposal safety evaluation. According to the method, a random discrete fracture network rock mass model is constructed based on actual site geological information or statistical laws, a unified pipe network method is adopted to discretize a fracture-matrix system into a flow network formed by nodes and pipelines, and a coupling discrete control equation set of multi-nuclide migration is established under the framework; convection, dispersion, diffusion, adsorption retardation and multistage decay processes are synchronously depicted. Spatial and temporal distribution data of nuclide concentration are obtained through numerical solution, the farthest migration distance of mother nuclide is extracted, fracture connectivity density parameters are introduced to carry out quantitative analysis on fracture structure influence, and then an empirical relational expression used for predicting the maximum migration distance is obtained through fitting. According to the method, the nuclide migration ability can be rapidly evaluated under the complex fracture condition, and a quantitative basis is provided for radioactive waste disposal safety evaluation.

Description

Technical Field

[0001] This invention relates to the field of safety assessment technology for deep geological disposal of radioactive waste, and in particular to a method for determining the migration distance of nuclides in fractured rock masses that takes into account multi-stage decay. Background Technology

[0002] Deep geological disposal of high-level radioactive waste typically employs a multi-barrier system to achieve long-term isolation from the biosphere. Fissures in natural barrier rock masses may become advantageous channels for groundwater seepage and radionuclide migration. The migration of radionuclides in fractured surrounding rocks often involves coupled processes of convection, dispersion, matrix diffusion, adsorption / desorption, and radioactive decay. Furthermore, many radionuclides exist in decay chains, forming a multi-level migration-decay coupling problem. Predicting migration behavior is a key scientific issue for long-term safety assessment.

[0003] To better reflect the complex fracture structures at actual sites and improve engineering usability, current methods are gradually moving from idealized single-fracture analytical models to numerical simulation frameworks oriented towards stochastic fracture networks. Based on this, systematic analysis of influencing factors is conducted, and empirical relationships for rapid prediction of migration distances are extracted from a large number of simulation results to support quantitative decisions in the selection of treatment facilities and the design of safety barriers.

[0004] The closest solution to this invention is a single-fracture nuclide migration model based on analytical solutions. Its applicable objects are biased towards single, regular fractures and rely on idealized boundary conditions. At the same time, the decay chain treatment usually only considers the parent nuclide, which is difficult to cover multi-level decay chains of ternary or higher. Moreover, the analytical form is complex and it is difficult to directly form a simple quantitative prediction tool for engineering, thus making it difficult to quantify the comprehensive influence of fracture connectivity, groundwater flow velocity and decay characteristics on migration distance. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, the purpose of this invention is to provide a method for determining the migration distance of nuclides in fractured rock masses that considers multi-stage decay. By coupling numerical simulation of nuclide migration with multi-stage decay in a random fracture network and statistically fitting the simulation results, the maximum migration distance of nuclides can be accurately determined under complex fracture conditions, and an empirical formula for engineering prediction can be formed.

[0006] To achieve the above objectives, the present invention provides the following solution: A method for determining the migration distance of nuclides considering multi-stage decay in fractured rock masses, comprising: Based on actual site geological information or statistical patterns, a two-dimensional or three-dimensional rock mass model containing a randomly distributed fracture network is generated, resulting in a random discrete fracture network rock mass model. The random discrete fracture network rock mass model is discretized using the unified pipeline method, and the random distributed fracture network and matrix blocks are discretized into pipelines, thereby transforming the fracture-matrix system corresponding to the random discrete fracture network rock mass model into a flow network composed of nodes and pipelines. For decay chains containing multiple nuclides, a set of coupled discrete control equations for the migration of multiple nuclides is established at each node of the flow network. The control equations simultaneously characterize convection, dispersion, matrix diffusion and adsorption retardation, and simultaneously introduce the self-decay loss term of each nuclide and the decay generation source term of its parent nuclide into the source and sink terms, so that each nuclide achieves chain coupling through the decay chain relationship. The coupled discrete control equations are numerically solved to obtain a simulation dataset of the spatiotemporal distribution of each nuclide concentration; Based on the simulated dataset, the farthest migration distance of the parent nuclide when its concentration drops to a preset threshold is extracted, and the fracture connectivity density parameter is calculated based on the random discrete fracture network rock mass model. The fracture connectivity density parameter is obtained by summing the squares of the lengths of the randomly distributed fracture network in the study area and normalizing it according to the area of ​​the study area. Using the simulated dataset as input, statistical analysis and fitting are performed on the farthest migration distance obtained under different fracture connectivity density parameters, different groundwater flow velocities, and different decay characteristics. The fitting yields an empirical relationship for predicting the farthest migration distance. This empirical relationship characterizes the relationship between the farthest migration distance and fracture connectivity density parameters, groundwater flow velocity, delay factor, porosity, equivalent hydraulic half-width of fractures, and comprehensive diffusion coefficient. The maximum migration distance is then determined based on this empirical relationship.

[0007] Preferably, based on actual site geological information or statistical patterns, a two-dimensional or three-dimensional rock mass model containing a randomly distributed fracture network is generated, resulting in a random discrete fracture network rock mass model, including: Obtain the actual site geological information, or determine the statistical law when the actual site geological information is insufficient, to obtain geological statistical parameters used to characterize the geometry and distribution of fractures; wherein, the geological statistical parameters include fracture length distribution, fracture orientation distribution, fracture density, and fracture spatial location distribution; Multiple randomly distributed fracture networks are generated based on the aforementioned geological statistical parameters; The random distributed fracture network is embedded into a two-dimensional or three-dimensional rock mass model within the study area to obtain the random discrete fracture network rock mass model.

[0008] Preferably, based on actual site geological information or statistical patterns, a two-dimensional or three-dimensional rock mass model containing a randomly distributed fracture network is generated, resulting in a random discrete fracture network rock mass model, including: Using the aforementioned statistical regularity as a constraint, the geological statistical parameters used to generate the fracture network are determined; The randomly distributed fracture network is generated using a discrete fracture network simulation method based on geostatistics, based on the aforementioned geostatistical parameters. The stochastic discrete fracture network rock mass model is constructed from the fracture spatial distribution results output by the discrete fracture network simulation method.

[0009] Preferably, based on actual site geological information or statistical patterns, a two-dimensional or three-dimensional rock mass model containing a randomly distributed fracture network is generated, resulting in a random discrete fracture network rock mass model, including: Obtain field survey data from the actual site geological information, and extract the spatial location, orientation, dip angle and length information of the fractures from the field survey data; The fracture network is reconstructed based on the spatial location, orientation, dip angle, and length information. In areas where fracture information is insufficiently covered, the randomly distributed fracture network is generated based on the statistical laws to obtain the random discrete fracture network rock mass model.

[0010] Preferably, the coupled discrete control equations are numerically solved to obtain a simulated dataset of the spatiotemporal distribution of each nuclide concentration, including: Set concentration boundary conditions, wherein the concentration boundary conditions are either an infinite source release scenario with constant inlet concentration or a finite source release scenario with inlet concentration decaying over time. The coupled discrete control equations are numerically solved under the concentration boundary conditions. Output the spatiotemporal distribution simulation dataset of the concentrations of each nuclide.

[0011] Preferably, numerically solving the coupled discrete control equations under the concentration boundary conditions includes: The random discrete fracture network rock mass model is simplified into a fracture-matrix system corresponding to a single horizontal fracture to form a simplified calculation example for verification. The fracture-matrix system is discretized using the unified pipeline method, with the fractures discretized into pipes and the matrix blocks discretized into nodes, and the coupled discrete control equations are established on the flow network. The coupled discrete control equations are numerically solved under the concentration boundary conditions, and the numerical solution is compared with the analytical solution considering the ternary decay chain to verify the correctness of the coupled discrete control equations.

[0012] Preferably, using the simulated dataset as input, statistical analysis and fitting are performed on the furthest migration distance obtained under different fracture connectivity density parameters, different groundwater flow velocities, and different decay characteristics. The fitting yields an empirical relationship for predicting the furthest migration distance, including: Multiple sets of the aforementioned random discrete fracture network rock mass models are constructed and the corresponding fracture connectivity density parameters are calculated respectively to form different fracture connectivity density parameter conditions; Under different groundwater flow velocities and decay characteristics, the coupled discrete control equations corresponding to each group of random discrete fracture network rock mass models are numerically solved to obtain the corresponding spatiotemporal distribution simulation datasets of each nuclide concentration, and the farthest migration distance is extracted from each spatiotemporal distribution simulation dataset. Using the farthest migration distance and the corresponding fracture connectivity density parameter, groundwater flow velocity, and decay characteristics as a sample set, the statistical analysis and fitting are performed, and the migration distance prediction empirical relationship is output to predict the farthest migration distance.

[0013] Preferably, under different groundwater flow velocities and decay characteristics, the coupled discrete control equations corresponding to each group of stochastic discrete fracture network rock mass models are numerically solved to obtain the corresponding spatiotemporal distribution simulation datasets of each nuclide concentration, and the farthest migration distance is extracted from each spatiotemporal distribution simulation dataset, including: Under the condition of fixing the random discrete fracture network rock mass model and the preset groundwater flow rate, different decay characteristics are formed by setting different half-life combinations for the decay chain; Numerical solutions are performed on the coupled discrete control equations under each decay characteristic condition to obtain the corresponding spatiotemporal distribution simulation dataset of each nuclide concentration. The farthest migration distance is extracted from each of the aforementioned spatiotemporal distribution simulation datasets.

[0014] Preferably, under different groundwater flow velocities and decay characteristics, the coupled discrete control equations corresponding to each group of stochastic discrete fracture network rock mass models are numerically solved to obtain the corresponding spatiotemporal distribution simulation datasets of each nuclide concentration, and the farthest migration distance is extracted from each spatiotemporal distribution simulation dataset, including: Under the condition of fixing the random discrete fracture network rock mass model and the preset decay characteristics, multiple sets of groundwater flow velocities are set, wherein the groundwater flow velocity is the average flow velocity of groundwater in the fractured rock mass; Numerical solutions were performed on the coupled discrete control equations under the groundwater flow velocity conditions described in each group to obtain the corresponding spatiotemporal distribution simulation dataset of each nuclide concentration. The farthest migration distance is extracted from each of the aforementioned spatiotemporal distribution simulation datasets.

[0015] Preferably, using the furthest migration distance and the corresponding fracture connectivity density parameter, groundwater flow velocity, and decay characteristics as a sample set, the statistical analysis and fitting are performed to output the migration distance prediction empirical relationship for predicting the furthest migration distance, including: Establish a corresponding data table for the sample set; the corresponding data table includes the farthest migration distance and the fracture connectivity density parameter, groundwater flow velocity and decay characteristics that correspond one-to-one with the farthest migration distance; Correlation analysis is performed on the corresponding data table to determine the empirical relational structure for fitting, so that the empirical relational structure can characterize the response trend of the farthest migration distance as the fracture connectivity density parameter, groundwater flow velocity and decay characteristics change. The empirical relation structure is fitted with parameters using a numerical fitting method, and the empirical relation for predicting migration distance is output.

[0016] The present invention discloses the following technical effects: (1) This invention constructs a two-dimensional or three-dimensional rock mass model containing a randomly distributed fracture network, and on this basis forms a random discrete fracture network rock mass model, so that nuclide migration analysis is no longer limited to idealized single fractures or regular geometric conditions, thereby reflecting the randomness and heterogeneity of fracture spatial distribution in actual sites, effectively overcoming the defects of existing technologies where the model has a single applicable object and is difficult to represent the real fracture structure.

[0017] (2) The present invention uses a unified pipeline method to discretize the randomly distributed fracture network and matrix block into pipelines, and establishes a set of coupled discrete control equations for multi-nucleon migration in the flow network, so that the transmission process between fracture and matrix can be uniformly described in the same computational framework, thereby avoiding the problem of insufficient coupling caused by the separation modeling of fracture migration and matrix diffusion in the prior art, and improving the completeness of the migration process characterization.

[0018] (3) In this invention, the self-decay loss term of each nuclide and the decay generation source term of its parent nuclide are introduced into the coupled discrete control equations of multi-nuclide migration. This allows the generation and loss of nuclides due to decay chain relationships during migration to be characterized synchronously, thus breaking through the limitation of existing technologies that are only applicable to low-order or simplified decay cases, and realizing the unified simulation of nuclide migration behavior under multi-level decay conditions.

[0019] (4) The present invention obtains a spatiotemporal distribution simulation dataset of each nuclide concentration by numerically solving the coupled discrete control equations, and extracts the farthest migration distance of the parent nuclide when the concentration drops to a preset threshold based on the simulation dataset, so that the determination of the maximum migration distance is based on the complete spatiotemporal evolution results, avoiding the migration distance evaluation deviation caused by relying on local analytical solutions or single-moment judgment in the prior art.

[0020] (5) The present invention further uses the simulation dataset as input to perform statistical analysis and fitting on the farthest migration distance obtained under different fracture connectivity density parameters, different groundwater flow velocities and different decay characteristics, and directly fits to obtain the migration distance prediction empirical relationship for predicting the farthest migration distance. Thus, without introducing additional assumptions, the complex numerical simulation results are transformed into a prediction tool that can be used for rapid engineering evaluation, making up for the lack of unified and intuitive prediction methods in the prior art. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 A flowchart of the method provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the technical route provided for an embodiment of the present invention. Detailed Implementation

[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] The purpose of this invention is to provide a method for determining the migration distance of nuclides in fractured rock masses that considers multi-stage decay. Based on a randomly distributed fracture network, a multi-stage decay migration model of nuclides is constructed, and the numerical results of multi-nuclide coupling are transformed into a prediction relationship of the maximum migration distance, thereby improving the applicability and reliability of nuclide migration distance assessment under actual site conditions.

[0025] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0026] Figure 1 The method flowchart provided in the embodiments of the present invention is as follows: Figure 1 As shown, this invention provides a method for determining the migration distance of nuclides considering multi-stage decay in fractured rock masses, comprising: Step 100: Based on the actual site geological information or statistical patterns, generate a two-dimensional or three-dimensional rock mass model containing a randomly distributed fracture network to obtain a random discrete fracture network rock mass model; Step 200: The random discrete fracture network rock mass model is discretized using the unified pipeline method. The randomly distributed fracture network and matrix blocks are discretized into pipelines, thereby transforming the fracture-matrix system corresponding to the random discrete fracture network rock mass model into a flow network composed of nodes and pipelines. Step 300: For a decay chain containing multiple nuclides, establish a set of coupled discrete governing equations for the migration of multiple nuclides at each node of the flow network; the set of governing equations simultaneously characterizes convection, dispersion, matrix diffusion and adsorption retardation, and simultaneously introduces the self-decay loss term of each nuclide and the decay generation source term of its parent nuclide into the source and sink terms, so that each nuclide can achieve chain coupling through the decay chain relationship. Step 400: Numerically solve the coupled discrete control equations to obtain a simulation dataset of the spatiotemporal distribution of each nuclide concentration; Step 500: Extract the farthest migration distance of the parent nuclide when its concentration drops to a preset threshold based on the simulated dataset, and calculate the fracture connectivity density parameter based on the random discrete fracture network rock mass model; the fracture connectivity density parameter is obtained by summing the squares of the lengths of the randomly distributed fracture network in the study area and normalizing it according to the area of ​​the study area. Step 600: Using the simulated dataset as input, perform statistical analysis and fitting on the farthest migration distance obtained under different fracture connectivity density parameters, different groundwater flow velocities, and different decay characteristics. The fitting yields an empirical relationship for predicting the farthest migration distance. The empirical relationship for predicting the migration distance characterizes the relationship between the farthest migration distance and fracture connectivity density parameters, groundwater flow velocity, delay factor, porosity, equivalent hydraulic half-width of fractures, and comprehensive diffusion coefficient. The maximum migration distance is determined based on the empirical relationship for predicting the migration distance.

[0027] This embodiment first generates a two-dimensional or three-dimensional rock mass model containing a large number of randomly distributed fracture networks based on actual site geological information or statistical patterns. The Unified Pipe Network Method (UPM) is then used to discretize this fracture-matrix system. This method discretizes fractures as "pipes" and matrix blocks as "nodes," thereby transforming the continuous medium problem into a pipe network flow and mass transfer problem.

[0028] For a decay chain containing N nuclides (e.g., matter 1 (parent nucleus) → matter 2 (first-order daughter nucleus) → matter 3 (second-order daughter nucleus) → ...), within the UPM framework, this embodiment designs a new discrete form of the migration control equation for the i-th nuclide at each node k. This equation simultaneously considers convection, dispersion, matrix diffusion, adsorption retardation, and multi-stage decay (self-decay loss and parent nucleus decay source term).

[0029] To verify the correctness of the UPM model, it was applied to a classic example with a single horizontal fissure, and the numerical simulation results were compared with the analytical solution considering the ternary decay chain proposed by Sudicky et al. The simulation results (nuclide concentration distribution along the fissure) are in high agreement with the analytical solution, demonstrating the reliability of the numerical method used in this invention in simulating convection, diffusion, adsorption, and multi-stage decay processes.

[0030] Based on verifying the reliability of the model, systematic numerical experiments were conducted to quantitatively analyze the impact of key factors on the migration behavior of multi-stage decay nuclides. Rift connectivity: Defines a dimensionless connectivity density parameter Multiple sets of stochastic discrete fracture network rock mass models with different d values ​​(from disconnected to highly connected) were designed to simulate and analyze the variation of nuclide migration distance and peak concentration with d.

[0031] Nuclide decay characteristics: By fixing the fracture network and changing the half-life of each nuclide in the decay chain (such as setting short, medium and long half-life combinations), the effects on the spatial distribution of nuclides and the peak concentration of daughter nuclides are studied.

[0032] Groundwater flow velocity: In the same fracture network, different Darcy velocities were set to analyze how the velocity changes altered the competitive relationship between "convective migration" and "decay consumption", thereby affecting the migration front and peak position of each nuclide.

[0033] Concentration boundary conditions: Constant concentration boundary (infinite source) and exponentially decaying concentration boundary (finite source, simulating the release scenario after waste container failure) were simulated respectively. The differences in the spatiotemporal evolution of nuclide migration under the two conditions were compared. The latter is closer to engineering reality.

[0034] Based on the extensive and systematic numerical simulation results described above, statistical analysis was performed on the nuclide migration data at quasi-steady state or specific moments. Characteristic migration distances of nuclides were discovered (e.g., the farthest migration distance of the parent nuclide). Peak position of daughter nuclide , There is a clear functional relationship between the prediction formula and the key parameters. Through data fitting, the following prediction formula was established (taking the furthest migration distance of the parent nuclide as an example): Where d is the fracture connectivity density, v is the flow velocity, R is the retardation factor, and λ_1 is the parent nucleus decay constant. denoted as porosity, b as fracture half-width, and D as diffusion coefficient. and These are empirical constants determined through fitting. Similarly, empirical formulas for predicting the peak positions of first- and second-order sub-nuclides can be obtained.

[0035] As an optional implementation method, such as Figure 2 As shown, the technical approach of this embodiment is as follows: Step 1: Establish a geometric model of a stochastic fracture network Input: Geological statistics of the target area, including fracture length distribution, orientation distribution, density, etc.

[0036] Processing: Based on the above input, a two-dimensional rock mass geometric model containing a large number of randomly distributed fracture networks is generated using a stochastic simulation method. This model needs to be able to characterize the heterogeneity and randomness of the actual fracture network.

[0037] Output: A digitized, stochastic, discrete fracture network rock mass model. This step provides a complex computational domain that conforms to actual geological statistical laws for subsequent simulations.

[0038] Step 2: Discretization and parameter assignment using numerical simulation methods. Input: The geometric model of the random fracture network output from the first step, and hydrogeological parameters (porosity) (e.g., permeability coefficient k), nuclide migration parameters (dispersion coefficient D, adsorption partition coefficient K) d decay constant (etc.) and boundary conditions (inlet concentration, hydraulic gradient, etc.).

[0039] deal with: 1. Establishing an improved governing equation: Within the UPM framework, for any node k in the network, this embodiment establishes a matter conservation equation for the i-th nuclide in its decay chain. The fundamental improvement of this embodiment over the traditional single-nuclide equation lies in considering, simultaneously, the following factors in the source and sink terms of the equation: Self-decay loss term: ( (where i is the concentration of nuclide i at node k); The decay of the parent nucleus generates the source term (when i>1): .

[0040] This allows the equations for different nuclides at the node to couple with each other through decay terms, forming a set of equations.

[0041] 2. Numerical Discretization: The improved equations described above are discretized in both time and space (network). An implicit time-difference scheme is used to ensure numerical stability. For node k and nuclide i, the discretized equations at time steps n to n+1 are as follows: In this formula, the superscript of the parameter Indicates the type of medium. =f represents a crack. =m represents the rock matrix, superscript and These represent the current time step and the next time step, respectively. Indicates the first in the decay chain One nuclide, Indicates the current computing node. Represents nodes Connected adjacent nodes, For nodes The set of adjacent nodes; and They represent the first Nuclide at the node With nodes Different media Concentration values ​​in; Represents a node With nodes Between along the direction The diffusion or diffusive transport coefficient, Represents a node With neighboring nodes Between different media convective transport coefficient; This indicates the porosity of the corresponding medium. This represents the delay factor of the corresponding medium. Represents a node The volume of the corresponding control body; For time step; Indicates the first The radioactive decay constant of each nuclide This represents the decay constant of its parent nuclide; the entire equation represents the decay constant of the first nuclide within the discrete time step. Nuclide at the node The conserved equilibrium relationship between convection, diffusion, accumulation effects, and generation and loss processes in the decay chain.

[0042] in, ,in Density of the rock mass For allocation coefficients, Porosity.

[0043] Output: A fully parameterized computational model of a discrete system with multi-stage decay coupling control equations.

[0044] In existing single-nuctopic migration models, each nuctopic is typically treated as an independent computational object, with closed-loop migration control equations established and solved independently for each nuctopic. These models only introduce a decay term for the nuctopic itself into the equations to describe its mass loss during migration, without simultaneously describing and tracking the daughter nuclides generated after decay. Therefore, these models can only characterize the migration, decay, and adsorption processes of a single nuctopic, and their physical meaning is equivalent to assuming that the nuctopic "disappears without transforming" after decay, failing to reflect the objective physical process of one-to-one correspondence and continuous transformation between parent and daughter nuclides in the radioactive decay chain.

[0045] This implementation breaks away from the aforementioned independent modeling approach. Within the same discrete computational framework, it simultaneously establishes migration control equations for each level of nuclide in the decay chain, and couples the control equations for different nuclides through decay generation terms. Specifically, in the discrete control equation established for a certain level of nuclide at any node, in addition to including the nuclide's own migration, adsorption hindrance, and decay loss terms, it also introduces a decay generation source term for its direct parent nuclide at the same node. This ensures that decay occurring at any position and time during the migration of the parent nuclide can be instantly and quantitatively converted into a contribution to the generation of daughter nuclides. Through this method, the migration and transformation processes of each level of nuclide in the decay chain remain consistent in time and space, forming a multi-level decay coupling control equation set that is solved simultaneously, thereby achieving a closed-loop description of the decay and migration processes at the mathematical model level.

[0046] Unlike the common "step-by-step cascaded calculation" method in existing technologies, this embodiment does not use the parent nuclide migration result as a fixed source term to calculate the daughter nuclide migration. Instead, it solves the coupled control equations simultaneously, allowing nuclides at each level to evolve together within the same time step. Although the step-by-step cascaded method can formally introduce daughter nuclide generation, its calculation process is artificially split in time, failing to reflect the actual process of daughter nuclides being generated anytime and anywhere during the parent nuclide migration and immediately participating in their own migration and decay. This can easily lead to systematic deviations in the peak position and intensity of daughter nuclide concentrations. This embodiment, by introducing decay chain coupling terms into a unified calculation model, avoids the error accumulation and physical process fragmentation problems caused by step-by-step calculations, thus more realistically reflecting the spatiotemporal evolution of nuclide migration and transformation under multi-level decay conditions.

[0047] Step 3: Model Validation and Benchmark Case Simulation Input: A simplified single-crack model (7m long, 2m wide) and its parameters, and the corresponding classical analytical solution (Sudicky, 1984).

[0048] Processing: Using the UPM simulation framework established in the second step, nuclide migration simulation (considering multi-stage decay) was performed on the single-crack model.

[0049] Output: Distribution curve of nuclide concentration along the fissure.

[0050] Objective and Results: The UPM simulation results (numerical solutions) were compared with classical analytical solutions. The high consistency of the results verifies the correctness of the UPM discretization method and multi-stage decay processing adopted in this invention, ensuring the reliability of subsequent complex simulations. This is a crucial verification step in transitioning from simple to complex models.

[0051] Step 4: Systematic numerical experiments and analysis of influencing factors Input: Multiple stochastic discrete fracture network rock mass models with different fracture connectivity densities d (e.g., d=0.14, 0.44, 1.02, 1.79, 2.70), as well as different combinations of nuclide decay constants, different groundwater flow rates (v), and different concentration boundary conditions (constant source vs. exponentially decaying source).

[0052] Processing: Based on the UPM model established in the second step, multiple sets of numerical simulations were conducted using the controlled variable method.

[0053] Connectivity analysis: With other parameters fixed, the models with different d values ​​were simulated sequentially, and the spatiotemporal evolution data of the concentration field of each nuclide were recorded, especially the advancing distance of the parent nuclide front and the peak position of the daughter nuclide concentration.

[0054] Decay characteristics analysis: With a fixed fracture network (e.g., d=1.02) and flow velocity, the half-life of the nuclides in the decay chain is changed (i.e., the λ value is changed). i Simulations were conducted to analyze the impact of half-life on migration patterns.

[0055] Velocity analysis: With the fracture network and decay chain fixed, the groundwater flow velocity v is varied to conduct simulations and analyze the effect of the velocity.

[0056] Boundary condition analysis: Compare the differences in nuclide migration behavior under constant concentration inlet and concentration inlet that decays exponentially over time.

[0057] Output: A massive, systematic dataset of simulation results, including concentration contour maps under different operating conditions, concentration distribution curves along specific paths, and extracted key feature values ​​(such as...). , wait).

[0058] This step is crucial for generating the core insights in this embodiment. Through a systematic numerical experiment, for the first time, it comprehensively and quantitatively reveals how the three key factors—fracture connectivity (d), groundwater flow velocity (v), and nuclide decay constant (λ)—jointly control the spatiotemporal evolution of multi-stage decay chains in complex stochastic fracture networks, and discovers specific phenomena such as peak hysteresis of daughter nuclides.

[0059] Step 5: Fitting to obtain the empirical formula for predicting migration distance (this part is the final prediction method; based on the empirical relationship, the migration distance of each substance can be predicted). Input: The systematic simulation dataset output from step four, especially the feature migration distance of each nuclide under different d, v, and λ conditions. , , (Data).

[0060] deal with: Data analysis: Correlation analysis of the data revealed a clear functional relationship between feature transfer distance and key parameters.

[0061] Formula fitting: Based on physical mechanisms and data analysis, an empirical formula form containing key parameters is constructed, and numerical fitting methods are used to determine the coefficients in the formula.

[0062] For example, the farthest migration distance of the parent nuclide Through fitting, it was found that it satisfies the following relationship with the main parameters: The parameters in the above formula are explained as follows: : The furthest migration distance (m) when the concentration of the parent nuclide drops to a preset threshold.

[0063] d: Fractal connectivity density, dimensionless, d = (1 / (4A)) Σ Li 2 A is the area of ​​the model (m²) 2 ), where Li is the crack length (m).

[0064] : Average groundwater flow velocity in the fissure (m / s).

[0065] Delay factor, dimensionless.

[0066] The decay constant of the parent nuclide (s -1 ).

[0067] : Fracture porosity, dimensionless.

[0068] b: Equivalent hydraulic half-width of the fracture (m).

[0069] D: Overall diffusion coefficient (m) 2 / s).

[0070] , The empirical constants determined by fitting specific simulation data according to the present invention, for example, based on a set of specific implementation data. ≈ 3.61, ≈ -0.20.

[0071] Similarly, the peak positions of first-order nuclides can be obtained by fitting. and peak positions of second-order nuclides The empirical formula is similar in form, but the coefficients are different.

[0072] Specifically, regarding the concentration peak migration behavior of first-order nuclide (substance 2) under steady-state conditions, this invention analyzes the distribution of peak positions under different connectivity conditions and establishes the following prediction formula through fitting: In the formula: L peak,2 : The peak concentration distance of first-order nuclides under steady-state conditions, in meters (m). m ); λ 2: Decay constant of first-order nuclides (unit: s -1 ); m 2 = 0.23, which is the fitting parameter, representing the sensitivity of the peak position of the first-order sub-nuclide to connectivity; c 2 = 4.23, which represents the correction factor when only connectivity is considered; Furthermore, regarding the concentration peak migration behavior of the second-order nuclide (substance 3) under steady-state conditions, this invention analyzes the distribution of peak positions under different connectivity conditions and establishes the following prediction formula through fitting: L peak,3 : The peak concentration distance of second-order nuclides under steady-state conditions, in meters (m). m ); λ 3: Decay constant of second-order nuclides (unit: s -1 ); m =3=0.24, which is the fitting parameter, representing the sensitivity of the peak position of the first-order sub-nuclide to connectivity; c 3 = 5.08, which represents the correction factor when only connectivity is considered.

[0073] Output: A set of empirical formulas for predicting the characteristic migration distance of multi-stage decay nuclides in fractured rock masses (i.e., the core result of this embodiment).

[0074] This step is the most innovative and practically valuable aspect of this invention. It "black-boxes" the complex numerical simulation process, extracting concise formulas directly applicable to engineering projects. This solves the problems mentioned in the background art, namely, the "lack of practical prediction tools" and "insufficient quantification of the impact on key parameters." Engineers no longer need to run complex UPM simulations; they only need to input easily obtainable or estimable parameters (d, v, λ, R, etc.) to quickly predict the potential migration range of nuclides, greatly improving the efficiency and convenience of safety assessments for high-level radioactive waste repositories.

[0075] In this embodiment, a complex fracture network containing a randomly distributed fracture network is discretized using the unified pipe network method. Fractures are uniformly represented as pipes, and matrix blocks are represented as nodes, thus constructing a flow network model suitable for numerical solutions. Within this unified discretization framework, coupled control equations for convection, dispersion, diffusion, adsorption retardation, and multi-stage radioactive decay processes are simultaneously established and solved, ensuring that each physical process is consistently characterized within the same spatiotemporal scale. This approach avoids the coupling deficiencies caused by the separate modeling of different physical processes in traditional methods, providing a unified and stable computational foundation for subsequent quantitative analysis of nuclide migration behavior.

[0076] Building upon the aforementioned coupling modeling, this embodiment further introduces a fracture connectivity density parameter to characterize the overall connectivity between fractures in a random fracture network. Through numerical calculations under different fracture connectivity densities, the dominant role of fracture connectivity in controlling nuclide migration capability is revealed, indicating that fracture connectivity density is a key structural factor determining whether nuclides can undergo long-distance migration. The calculation results show that the characteristic distance of nuclide migration exhibits a clear power-law variation trend with fracture connectivity density, thus achieving a quantitative expression of its impact on the structural complexity of the fracture network.

[0077] While keeping other parameters constant, this implementation method systematically analyzes the combined regulatory effects of fracture connectivity density, groundwater flow velocity, and nuclide decay characteristics on the migration behavior of nuclides at each level in the decay chain using the controlled variable method. It comprehensively characterizes the spatiotemporal evolution of the parent nuclide and its daughter nuclides, including the lag distribution of daughter nuclide concentration peaks relative to the parent nuclide. Based on this, empirical formulas for predicting the farthest migration distance of the parent nuclide and the location of daughter nuclide concentration peaks are extracted from numerous numerical simulation results. This directly correlates measurable or estimable geological parameters with key nuclide migration indicators, enabling engineers to quickly assess the potential migration range of nuclides without repeatedly conducting complex numerical simulations. This significantly improves the efficiency and practicality of radioactive waste disposal safety assessments, site selection justifications, and barrier optimization.

[0078] In the implementation of this invention, the construction method of the fracture network is not limited to a completely random generation method. Besides the random distribution of the fracture network, geostatistical simulation methods can also be used to construct the fracture network. For example, a discrete fracture network model can be used to statistically constrain the spatial distribution, orientation, dip angle, and length of fractures; or the spatial location and geometric characteristics of actual fractures can be reconstructed directly based on field survey data, thereby forming a fracture network model that more closely resembles real geological conditions. Based on this, regardless of the specific generation method of the fracture network, as long as an equivalent fracture network structure can be formed, it can be incorporated into the analytical framework described in this invention for application.

[0079] Furthermore, this invention also offers significant flexibility in numerical solution and empirical formula construction. In the numerical discretization and solution stage, in addition to the unified network method, other numerical methods capable of handling complex fractured media can be employed, such as the solution method coupling the discrete fractured network model with the continuous medium, or high-performance numerical calculations based on the finite element method or finite volume method using unstructured meshes. When performing statistical analysis and empirical formula fitting on the simulation results, besides the combination of exponential and power-law terms proposed in this invention, other forms of empirical formulas, such as polynomial fitting and logarithmic fitting, can be selected based on the distribution characteristics of the simulation data. As long as the empirical formula can effectively characterize the correlation between fracture structure parameters, groundwater flow parameters, and nuclide migration characteristic indicators, it falls within the scope of analysis and application of this invention.

[0080] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0081] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for determining the migration distance of nuclides considering multi-stage decay in fractured rock masses, characterized in that, include: Based on actual site geological information or statistical patterns, a two-dimensional or three-dimensional rock mass model containing a randomly distributed fracture network is generated, resulting in a random discrete fracture network rock mass model. The random discrete fracture network rock mass model is discretized using the unified pipeline method, and the random distributed fracture network and matrix blocks are discretized into pipelines, thereby transforming the fracture-matrix system corresponding to the random discrete fracture network rock mass model into a flow network composed of nodes and pipelines. For decay chains containing multiple nuclides, a set of coupled discrete control equations for the migration of multiple nuclides is established at each node of the flow network. The control equations simultaneously characterize convection, dispersion, matrix diffusion and adsorption retardation, and simultaneously introduce the self-decay loss term of each nuclide and the decay generation source term of its parent nuclide into the source and sink terms, so that each nuclide achieves chain coupling through the decay chain relationship. The coupled discrete control equations are numerically solved to obtain a simulation dataset of the spatiotemporal distribution of each nuclide concentration; Based on the simulated dataset, the farthest migration distance of the parent nuclide when its concentration drops to a preset threshold is extracted, and the fracture connectivity density parameter is calculated based on the random discrete fracture network rock mass model. The fracture connectivity density parameter is obtained by summing the squares of the lengths of the randomly distributed fracture network in the study area and normalizing it according to the area of ​​the study area. Using the simulated dataset as input, statistical analysis and fitting are performed on the farthest migration distance obtained under different fracture connectivity density parameters, different groundwater flow velocities, and different decay characteristics. The fitting yields an empirical relationship for predicting the farthest migration distance. This empirical relationship characterizes the relationship between the farthest migration distance and fracture connectivity density parameters, groundwater flow velocity, delay factor, porosity, equivalent hydraulic half-width of fractures, and comprehensive diffusion coefficient. The maximum migration distance is then determined based on this empirical relationship.

2. The method for determining the migration distance of nuclides considering multi-stage decay in fractured rock masses according to claim 1, characterized in that, Based on actual site geological information or statistical patterns, a two-dimensional or three-dimensional rock mass model containing a randomly distributed fracture network is generated, resulting in a random discrete fracture network rock mass model, including: Obtain the actual site geological information, or determine the statistical law when the actual site geological information is insufficient, to obtain geological statistical parameters used to characterize the geometry and distribution of fractures; wherein, the geological statistical parameters include fracture length distribution, fracture orientation distribution, fracture density, and fracture spatial location distribution; Multiple randomly distributed fracture networks are generated based on the aforementioned geological statistical parameters; The random distributed fracture network is embedded into a two-dimensional or three-dimensional rock mass model within the study area to obtain the random discrete fracture network rock mass model.

3. The method for determining the migration distance of nuclides considering multi-stage decay in fractured rock masses according to claim 1, characterized in that, Based on actual site geological information or statistical patterns, a two-dimensional or three-dimensional rock mass model containing a randomly distributed fracture network is generated, resulting in a random discrete fracture network rock mass model, including: Using the aforementioned statistical regularity as a constraint, the geological statistical parameters used to generate the fracture network are determined; The randomly distributed fracture network is generated using a discrete fracture network simulation method based on geostatistics, based on the aforementioned geostatistical parameters. The stochastic discrete fracture network rock mass model is constructed from the fracture spatial distribution results output by the discrete fracture network simulation method.

4. The method for determining the migration distance of nuclides considering multi-stage decay in fractured rock masses according to claim 1, characterized in that, Based on actual site geological information or statistical patterns, a two-dimensional or three-dimensional rock mass model containing a randomly distributed fracture network is generated, resulting in a random discrete fracture network rock mass model, including: Obtain field survey data from the actual site geological information, and extract the spatial location, orientation, dip angle and length information of the fractures from the field survey data; The fracture network is reconstructed based on the spatial location, orientation, dip angle, and length information. In areas where fracture information is insufficiently covered, the randomly distributed fracture network is generated based on the statistical laws to obtain the random discrete fracture network rock mass model.

5. The method for determining the migration distance of nuclides considering multi-stage decay in fractured rock masses according to claim 1, characterized in that, Numerical solutions were performed on the coupled discrete control equations to obtain a simulated dataset of the spatiotemporal distribution of each nuclide concentration, including: Set concentration boundary conditions, wherein the concentration boundary conditions are either an infinite source release scenario with constant inlet concentration or a finite source release scenario with inlet concentration decaying over time. The coupled discrete control equations are numerically solved under the concentration boundary conditions. Output the spatiotemporal distribution simulation dataset of the concentrations of each nuclide.

6. The method for determining the migration distance of nuclides considering multi-stage decay in fractured rock masses according to claim 5, characterized in that, Numerical solution of the coupled discrete control equations under the concentration boundary conditions includes: The random discrete fracture network rock mass model is simplified into a fracture-matrix system corresponding to a single horizontal fracture to form a simplified calculation example for verification. The fracture-matrix system is discretized using the unified pipeline method, with the fractures discretized into pipes and the matrix blocks discretized into nodes, and the coupled discrete control equations are established on the flow network. The coupled discrete control equations are numerically solved under the concentration boundary conditions, and the numerical solution is compared with the analytical solution considering the ternary decay chain to verify the correctness of the coupled discrete control equations.

7. The method for determining the migration distance of nuclides considering multi-stage decay in fractured rock masses according to claim 1, characterized in that, Using the simulated dataset as input, statistical analysis and fitting are performed on the farthest migration distance obtained under different fracture connectivity density parameters, different groundwater flow velocities, and different decay characteristics. The fitting yields an empirical relationship for predicting the farthest migration distance, including: Multiple sets of the aforementioned random discrete fracture network rock mass models are constructed and the corresponding fracture connectivity density parameters are calculated respectively to form different fracture connectivity density parameter conditions; Under different groundwater flow velocities and decay characteristics, the coupled discrete control equations corresponding to each group of random discrete fracture network rock mass models are numerically solved to obtain the corresponding spatiotemporal distribution simulation datasets of each nuclide concentration, and the farthest migration distance is extracted from each spatiotemporal distribution simulation dataset. Using the farthest migration distance and the corresponding fracture connectivity density parameter, groundwater flow velocity, and decay characteristics as a sample set, the statistical analysis and fitting are performed, and the migration distance prediction empirical relationship is output to predict the farthest migration distance.

8. The method for determining the migration distance of nuclides considering multi-stage decay in fractured rock masses according to claim 7, characterized in that, Under different groundwater flow velocities and decay characteristics, the coupled discrete control equations corresponding to each group of stochastic discrete fracture network rock mass models are numerically solved to obtain the corresponding spatiotemporal distribution simulation datasets of each nuclide concentration. The furthest migration distance is then extracted from each of these spatiotemporal distribution simulation datasets, including: Under the condition of fixing the random discrete fracture network rock mass model and the preset groundwater flow rate, different decay characteristics are formed by setting different half-life combinations for the decay chain; Numerical solutions are performed on the coupled discrete control equations under each decay characteristic condition to obtain the corresponding spatiotemporal distribution simulation dataset of each nuclide concentration. The farthest migration distance is extracted from each of the aforementioned spatiotemporal distribution simulation datasets.

9. The method for determining the migration distance of nuclides considering multi-stage decay in fractured rock masses according to claim 7, characterized in that, Under different groundwater flow velocities and decay characteristics, the coupled discrete control equations corresponding to each group of stochastic discrete fracture network rock mass models are numerically solved to obtain the corresponding spatiotemporal distribution simulation datasets of each nuclide concentration. The furthest migration distance is then extracted from each of these spatiotemporal distribution simulation datasets, including: Under the condition of fixing the random discrete fracture network rock mass model and the preset decay characteristics, multiple sets of groundwater flow velocities are set, wherein the groundwater flow velocity is the average flow velocity of groundwater in the fractured rock mass; Numerical solutions were performed on the coupled discrete control equations under the groundwater flow velocity conditions described in each group to obtain the corresponding spatiotemporal distribution simulation dataset of each nuclide concentration. The farthest migration distance is extracted from each of the aforementioned spatiotemporal distribution simulation datasets.

10. The method for determining the migration distance of nuclides considering multi-stage decay in fractured rock masses according to claim 7, characterized in that, Using the maximum migration distance and the corresponding fracture connectivity density parameter, groundwater flow velocity, and decay characteristics as a sample set, the statistical analysis and fitting are performed to output the migration distance prediction empirical relationship for predicting the maximum migration distance, including: Establish a corresponding data table for the sample set; the corresponding data table includes the farthest migration distance and the fracture connectivity density parameter, groundwater flow velocity and decay characteristics that correspond one-to-one with the farthest migration distance; Correlation analysis is performed on the corresponding data table to determine the empirical relational structure for fitting, so that the empirical relational structure can characterize the response trend of the farthest migration distance as the fracture connectivity density parameter, groundwater flow velocity and decay characteristics change. The empirical relation structure is fitted with parameters using a numerical fitting method, and the empirical relation for predicting migration distance is output.

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