Coastal zone soil and underground water radionuclide decay migration simulation method

Abstract

The invention provides a coastal zone soil and underground water radionuclide decay migration simulation method, which comprises the following steps: collecting soil and hydrological data of a research area, including permeability, porosity and salinity distribution; constructing a variable saturation seepage model, a variable density flow model and a radionuclide decay migration model based on the soil and hydrological data; and carrying out coupling calculation on the variable saturated seepage model, the variable density flow model and the radionuclide decay migration model so as to simulate the spatial and temporal distribution of radionuclides in the underground water system. According to the invention, the migration behavior of radionuclides in the coastal zone underground water system can be accurately simulated.

Description

Technical Field

[0001] The invention belongs to the field of ecological environment restoration, and specifically relates to a method for simulating the decay and migration of radioactive nuclides in coastal soil and groundwater. Background Art

[0002] With the widespread application of nuclear energy technology, the release and migration of radionuclides in different media have received increasing attention, especially in coastal areas, where the discharge of marine nuclear contaminated water may enter groundwater through seawater intrusion and other means. These radionuclides will undergo decay processes during migration, making their migration characteristics more complex. At present, the existing radionuclide migration models fail to effectively integrate the interaction between the decay process and flow and diffusion, resulting in inaccurate predictions of changes in nuclide concentrations. In addition, the existing models lack specialized mathematical expressions for decay processes when describing nuclide migration. Therefore, a more comprehensive and effective radionuclide migration model is urgently needed to accurately simulate the diffusion, convection, decay and other processes of nuclides in complex hydrological environments. Summary of the invention

[0003] The main purpose of the present invention is to construct a more accurate and effective radionuclide decay migration model, which is suitable for the study of the diffusion, convection and decay processes of radionuclides in coastal soil and groundwater systems.

[0004] The technical solution of the present invention is as follows:

[0005] A method for simulating the decay and migration of radioactive nuclides in coastal soil and groundwater, the method comprising:

[0006] Collect soil and hydrological data on the study area, including permeability, porosity, and salinity distribution;

[0007] Constructing a variable saturated seepage model, a variable density flow model and a radionuclide decay migration model based on the soil and hydrological data;

[0008] The variable saturation seepage model, the variable density flow model and the radionuclide decay migration model are coupled and calculated to simulate the temporal and spatial distribution of radionuclides in the groundwater system.

[0009] Furthermore, the variable saturation seepage model is constructed based on the Richards equation and the Van Genuchten equation, and the specific formula is:

[0010]

[0011] Where ρ is the pressure; C m is the water storage rate of unsaturated porous media; S e is the effective saturation; S is the water storage rate; K sis the saturated permeability; μ is the fluid dynamic viscosity; k r is the relative permeability coefficient; g is the acceleration of gravity; D is the elevation; Q m is the source and sink term, p is the pressure, is the gradient operator.

[0012] Furthermore, the variable density flow model is constructed based on the relationship between salinity distribution and density to simulate the impact of seawater intrusion on groundwater salinity distribution. The specific formula is:

[0013]

[0014] Among them, D e is the fluid diffusion coefficient; θ is the fluid volume fraction; u is the Darcy velocity, c s is salinity, D e is the diffusion coefficient of the fluid, is the gradient operator.

[0015] Furthermore, the relationship between the salinity distribution and density is specifically:

[0016]

[0017] Where ρ0 is the density of fresh water; ρ1 is the density of sea water; c s is salinity; c0 is the standardized salinity of fresh water; c1 is the standardized salinity of sea water.

[0018] Furthermore, the radionuclide decay migration model is constructed based on diffusion and advection effects to simulate the migration and decay of nuclides under tidal fluctuation conditions. The specific formula is:

[0019]

[0020] Among them, D D is the diffusion term; D e is the diffusion coefficient of the fluid; ∈ P is the porosity; c is the radionuclide concentration; M decay is the decay quantity of radioactive nuclide; S is the source and sink term, u is the Darcy velocity, is the gradient operator.

[0021] Furthermore, the change of the radionuclide concentration over time during the decay process is expressed by the following equation:

[0022]

[0023] Among them, c t is the concentration at time t; c t+1 is the concentration at t+1; L 1 / 2 is the half-life of the nuclide; delt is the time step.

[0024] Furthermore, the specific formula for the decay amount of the radionuclide is:

[0025]

[0026] Among them, c t is the concentration at time t; L 1 / 2 is the half-life of the nuclide, and delt is the time step.

[0027] Furthermore, the finite difference method is used to gradually calculate the salinity distribution and radionuclide concentration changes at each time step for the variable saturation seepage model, the variable density flow model and the radionuclide decay migration model.

[0028] Compared with the prior art, the present invention has the following advantages:

[0029] The present invention is applicable to the study of the diffusion, convection and decay processes of radionuclides in coastal soil and groundwater systems. The model effectively integrates the interaction between the decay process and flow and diffusion, so that the migration behavior of radionuclides in groundwater can be described more accurately. It not only improves the accuracy of the prediction of nuclide concentration changes, but also provides a more comprehensive understanding for scientific research. Considering the nuclide decay process makes the model more flexible and targeted when dealing with the migration of radionuclides, which helps to better assess the risks of groundwater resources in practical applications. In addition, the present invention provides important theoretical support for groundwater management and pollution control, and has significant practical value and application prospects in predicting the migration of radionuclides and their decay characteristics. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] The accompanying drawings generally illustrate various embodiments by way of example and not limitation, and together with the description and claims, serve to illustrate the embodiments of the invention. Where appropriate, the same reference numerals are used throughout the drawings to refer to the same or similar parts. Such embodiments are illustrative and are not intended to be exhaustive or exclusive embodiments of the present apparatus or method.

[0031] Figure 1 A flow chart of model construction of the present invention is shown;

[0032] Figure 2 The model solving flow chart of the present invention is shown;

[0033] Figure 3 Shows the different levels of seawater intrusion 90 Concentration distribution diagram of Sr migration and diffusion in coastal groundwater. DETAILED DESCRIPTION

[0034] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0035] like Figure 1-Figure 3 As shown, the present invention simulates the migration process taking into account the decay of radionuclides based on the variable saturation seepage model, the variable density flow model and the radionuclide decay migration model.

[0036] First, soil and hydrological data of the study area were collected, including permeability, porosity and salinity distribution, and a variable saturated seepage model was established using the Richards equation, and the dynamic changes of water in the soil were described by the Van Genuchten equation. On this basis, a variable density flow model was constructed, and the relationship between salinity and density was used to analyze the impact of different degrees of seawater intrusion on salinity distribution. Finally, combined with the diffusion and advection effects, the migration and decay of nuclides under tidal fluctuation conditions were simulated through the radionuclide decay migration model, and the salinity distribution and radionuclide concentration changes at each time step were gradually calculated using the finite difference method through numerical solution.

[0037] The results show that tidal fluctuations significantly affect the dynamic changes of groundwater level and salinity, causing the migration speed and concentration distribution of radionuclides in groundwater to show temporal and spatial variation characteristics.

[0038] Specific:

[0039] (1) Constructing a variable saturation seepage model

[0040] In coastal areas, the groundwater environment involves complex interactions between soil and groundwater. The groundwater dynamics in the area lead to the emergence of variable saturation in the underground environment, which plays a vital role in the migration and transformation of pollutants. In order to describe the flow characteristics in a specific underground environment, the Richards equation is used to describe the flow in a variable saturated aquifer. The Van Genuchten equation summarizes the relationship between water content and pressure head. The mathematical equation is generalized as follows:

[0041]

[0042] Where p is the pressure (kg m -1 s -2 );C m is the water storage capacity of unsaturated porous media (m -1 );S e is the effective saturation (dimensionless); S is the water storage rate (m -1 );K s is the saturated permeability (m 2 ); μ is the fluid dynamic viscosity (kg m -1s -1 );K r is the relative permeability coefficient (dimensionless); g is the gravitational acceleration (ms -2 );D is the elevation (m);Q m is the source and sink term (kg m -3 s -1 ).

[0043] (2) Variable density flow model

[0044] Seawater intrusion makes coastal groundwater vulnerable, especially near the coastline, where tidal fluctuations affect groundwater levels and salinity distribution. Specifically, fluid density is directly related to salinity, and the mathematical equation is summarized as follows:

[0045]

[0046] Where ρ0 is the density of fresh water (kg m -3 ), ρ1 is the density of seawater (kg m -3 );c s is salinity (dimensionless); c0 is the standardized salinity of fresh water (dimensionless); c1 is the standardized salinity of sea water (dimensionless).

[0047] Throughout the wave process, the change in salinity is controlled by density-driven advection. Specifically, salinity is propagated entirely through advection and molecular diffusion, and the mathematical equation is summarized as follows:

[0048]

[0049] Where D e is the fluid diffusion coefficient (m 2 s -1 );θ is the fluid volume fraction;u is the Darcy velocity (ms -1 ).

[0050] (3) Radionuclide decay migration model

[0051] It cannot be ignored that the nuclear contaminated water discharged into the ocean may penetrate into the groundwater through seawater intrusion. These sewage contains a large number of radioactive nuclides, which will decay during the migration process, making their migration process extremely complicated. Therefore, the model takes into account the migration process of radioactive nuclides decay, and the mathematical equation is generalized as follows:

[0052]

[0053] Where D D is the diffusion term (m 2 s -1 );D e is the diffusion coefficient of the fluid (m 2 s-1 );∈ p is the porosity (dimensionless); c is the radionuclide concentration (mol m -3 );M decay is the decay reaction term (mol m -3 s -1 ); S is the source and sink term (mol m -3 s -1 ). During the decay process, the change of concentration over time can be expressed by the following equation:

[0054]

[0055] where c t is the concentration at time t (mol m -3 );c t+1 is the concentration at t+1 (mol m -3 );L 1 / 2 is the half-life of the nuclide (a); delt is the time step (s). When the delt time is short enough, the decay of the radionuclide can be expressed as follows:

[0056]

[0057] In order to achieve the numerical solution of the above model, the finite difference method is used to gradually calculate the salinity distribution and radionuclide concentration changes at each time step. The finite difference method discretizes the continuous space and time variables, and recursively calculates the salinity and nuclide concentration changes at each time step, thereby simulating the spatiotemporal distribution of radionuclides in the groundwater system. Specifically:

[0058] Set initial conditions: including initial water level, salinity, radionuclide concentration, permeability and diffusion coefficient, and determine the time step;

[0059] Calculation by coupling model: numerical calculation is performed by coupling the variable saturation seepage model (based on Richards equation), the variable density flow model (considering the relationship between salinity and density) and the radionuclide migration model (following the decay equation);

[0060] Model convergence check: Perform model convergence check during the calculation process to ensure the accuracy and reliability of the results;

[0061] Output results and conduct analysis: Output the spatiotemporal distribution of salinity and radionuclide concentration in groundwater based on the calculation results, and conduct corresponding analysis to evaluate the migration behavior of radionuclides.

[0062] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for simulating the decay and migration of radionuclides in coastal soil and groundwater, characterized in that: The method comprises: Collect soil and hydrological data on the study area, including permeability, porosity, and salinity distribution; Constructing a variable saturated seepage model, a variable density flow model and a radionuclide decay migration model based on the soil and hydrological data; The variable saturation seepage model, the variable density flow model and the radionuclide decay migration model are coupled and calculated to simulate the temporal and spatial distribution of radionuclides in the groundwater system.

2. The method for simulating the decay and migration of radionuclides in soil and groundwater in the coastal zone according to claim 1, characterized in that: The variable saturated seepage model is constructed based on the Richards equation and the Van Genuchten equation, and the specific formula is: Where ρ is the density; C m is the water storage rate of unsaturated porous media; S e is the effective saturation; S is the water storage rate; K s is the saturated permeability; μ is the fluid dynamic viscosity; k r is the relative permeability coefficient; g is the acceleration of gravity; D is the elevation; Q m is the source-sink term, is the rate of change of pressure with time, p is the pressure, is the gradient operator.

3. The method for simulating the decay and migration of radionuclides in coastal soil and groundwater according to claim 1, characterized in that: The variable density flow model is constructed based on the relationship between salinity distribution and density to simulate the impact of seawater intrusion on groundwater salinity distribution. The specific formula is: Among them, D e is the fluid diffusion coefficient; θ is the fluid volume fraction; u is the Darcy velocity, c s is salinity, D e is the diffusion coefficient of the fluid, is the gradient operator.

4. The method for simulating the decay and migration of radionuclides in coastal soil and groundwater according to claim 3, characterized in that: The relationship between the salinity distribution and density is specifically: Where ρ0 is the density of fresh water; ρ1 is the density of sea water; c s is salinity; c0 is the standardized salinity of fresh water; c1 is the standardized salinity of sea water.

5. The method for simulating the decay and migration of radioactive nuclides in coastal soil and groundwater according to claim 1, characterized in that: The radionuclide decay migration model is constructed based on diffusion and advection effects to simulate the migration and decay of nuclides under tidal fluctuation conditions. The specific formula is: Among them, D D is the diffusion term; D e is the diffusion coefficient of the fluid; ∈ P is the porosity; c is the radionuclide concentration; M decay is the decay quantity of radioactive nuclide; S is the source and sink term, u is the Darcy velocity, is the gradient operator.

6. The method for simulating the decay and migration of radionuclides in coastal soil and groundwater according to claim 5, characterized in that: The change of the radionuclide concentration over time during the decay process is expressed by the following equation: Among them, c t is the concentration at time t; c t+1 is the concentration at t+1; L 1 / 2 is the half-life of the nuclide; delt is the time step.

7. The method for simulating the decay and migration of radionuclides in coastal soil and groundwater according to claim 5, characterized in that: The specific formula for the decay amount of the radionuclide is: Among them, c t is the concentration at time t; L 1 / 2 is the half-life of the nuclide, and delt is the time step.

8. The method for simulating the decay and migration of radionuclides in coastal soil and groundwater according to claim 1, characterized in that: The finite difference method is used to gradually calculate the salinity distribution and radionuclide concentration changes at each time step for the variable saturation seepage model, variable density flow model and radionuclide decay migration model.

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