A method for predicting nuclide migration

Abstract

The application provides a method for predicting nuclide migration, which comprises the following steps: determining the liquid pressure of the region where the buffer material is located at the current moment, the gas pressure of the region where the buffer material is located, the water vapor pressure field value and the stress-strain field value according to the temperature value of the buffer material at the current moment; updating the temperature value of the buffer material at the next moment according to the temperature value at the current moment, the liquid pressure of the region where the buffer material is located, the gas pressure of the region where the buffer material is located and the water vapor pressure field value; determining whether the buffer material reaches saturation according to the temperature value of the buffer material at the next moment; if the buffer material does not reach saturation, repeating the above steps until the buffer material reaches saturation, and accordingly, the time corresponding to the saturation state of the buffer material is predicted. The method provided by the application can accurately predict the time when the nuclide leaks at a certain moment in the future.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of radioactive material disposal, and in particular to a nuclide migration prediction method. BACKGROUND

[0002] Nuclear technology provides valuable energy for human beings, while also produces a large amount of radioactive waste. The classification of radioactive waste is based on the "characteristics of radioactive waste and its potential harm to human health and the environment", which is divided into high-level waste, medium-level waste and low-level waste. And according to the classification, corresponding management is carried out. For low-level radioactive waste with short half-life, it can be disposed of as a glass solidification body before near-surface landfill. High-level waste is not only highly toxic, long half-life, long-term heating, but also a kind of radioactive spent fuel, which is very difficult to safely dispose of. Many countries in the world have conducted extensive research on how to dispose of high-level waste, but considering the risk and cost, deep geological disposal is still the only feasible solution at present.

[0003] According to the engineering practice, the research idea of "multi-barrier system" is often adopted, and the combination of engineering barrier and natural barrier is adopted. The high-level waste (nuclide) is buried in the rock layer 300-1000 meters underground, which is called "high-level waste disposal repository". The "multi-barrier system" from inside to outside is: waste solidification body, waste tank, buffer material and surrounding rock. The glass solidification body made of radioactive waste (nuclide), the waste tank for storing the glass solidification body and the outer buffer material are called "engineering barrier", and the rock geology outside the waste tank is called "natural barrier".

[0004] However, the current method for predicting nuclide migration only includes the migration process when the buffer material reaches the saturation state, but there is no method for predicting the migration of nuclides at a certain time in the future when the buffer material has not reached the saturation state. SUMMARY

[0005] The purpose of the present application is to solve the defects of the prior art, and to provide a nuclide migration prediction method.

[0006] A nuclide migration prediction method, comprising the following steps:

[0007] Step 1: obtaining the saturation degree of the buffer material at the initial time, the temperature value of the buffer material at the initial time, and the initial distribution parameters of the buffer material deformation variable; the initial distribution parameters include: the elastic modulus of the buffer material itself, the porosity n of the buffer material, the internal pressure difference of the buffer material and the external initial pressure difference;

[0008] Step 2: predicting the temperature value of the buffer material at the current time according to the saturation degree, the initial distribution parameters of the buffer material deformation variable, and the temperature value of the buffer material at the initial time;

[0009] Step 3: determining the liquid pressure of the region where the buffer material is located at the current time according to the temperature value of the current time;

[0010] Step 4: determining the gas pressure of the region where the buffer material is located at the current time according to the temperature value of the current time;

[0011] Step 5: determining the water vapor pressure field value of the buffer material at the current time according to the temperature value of the current time, the liquid pressure of the region, and the gas pressure of the region;

[0012] Step 6: determining the stress-strain field value of the buffer material at the current time according to the water vapor pressure field value of the buffer material at the current time and the gas pressure of the region;

[0013] Step 7: updating the temperature value of the buffer material at the next time according to the temperature value of the buffer material at the current time, the liquid pressure of the region, the gas pressure of the region, and the water vapor pressure field value;

[0014] Step 8: determining the liquid pressure of the region where the buffer material is located at the next time according to the temperature value of the buffer material at the next time, and determining whether the buffer material reaches saturation according to the liquid pressure of the region where the buffer material is located at the next time;

[0015] Step 9: if it is determined that the buffer material does not reach saturation at the next time according to the liquid pressure of the region where the buffer material is located at the next time, repeating steps 2-7 until the buffer material reaches saturation, thereby predicting the time corresponding to the saturation state of the buffer material, which is the time when the nuclide starts to migrate.

[0016] Further, the nuclide migration prediction method as described above, the step 2 of predicting the temperature value of the buffer material at the current time according to the saturation degree, the initial distribution parameter of the deformation variable of the buffer material, and the temperature value of the buffer material at the initial time includes:

[0017] the saturation degree, the initial distribution parameter of the deformation variable of the buffer material, and the temperature value of the buffer material at the initial time into an energy conservation equation, and determining the temperature value T of the buffer material at the current time according to the energy conservation equation;

[0018] The formula of the energy conservation equation is:

[0019]

[0020] wherein g is the gas phase value, l is the liquid phase value, and s is the solid phase value; p is the density value; c is the specific heat capacity; l is the thermal conductivity; T is the temperature value of the buffer material, T l is the liquid temperature of the region where the buffer material is located.g T is the temperature of the gas in the region where the buffer material is located s T is the temperature of the solid in the region where the buffer material is located, according to the local quasi-equilibrium hypothesis l T = T g T = T s T = T; S is the liquid saturation in the buffer material unit; n is the porosity of the buffer material, which is regarded as a constant value due to its small variation range; ω is the liquid phase migration coefficient; k is the intrinsic permeability tensor of the medium; k lr k is the relative permeability of the water body; μ l μ is the dynamic viscosity coefficient of water; c l c is the compressibility coefficient of the water body, which is expressed as: β l β is the thermal expansion coefficient of the water body, which is expressed as: k gr k is the relative permeability of the gas phase; k gT k is the thermal drive coefficient of the mixed gas; g is the acceleration of gravity; μ g μ is the dynamic viscosity coefficient of the gas; K is the compressibility coefficient of the mixed gas, β is the thermal expansion coefficient of the mixed gas; ε v ε is the stress-strain field value of the buffer material; ρ g ρ is the liquid density in the region where the buffer material is located; c g c is the gas compressibility coefficient; K g K is the volumetric strain modulus of the gas phase; n is the porosity; μ is the gas pressure gradient; μ l μ is the dynamic viscosity coefficient of water; ρ l ρ is the groundwater density; c l c is the compressibility coefficient of the water body, which is expressed as: K is the volumetric strain modulus of the liquid phase; β l β is the thermal expansion coefficient of the water body, which is expressed as: μ is the liquid pressure gradient; k lT k is the relative permeability of the water body; ρ s ρ is the solid density; c s c is the specific heat capacity of the solid; p l p is the liquid pressure in the region where the buffer material is located, K l K is the volumetric strain modulus of the liquid phase; K g K is the volumetric strain modulus of the gas phase.

[0021] Further, in step 3 of the prediction method of nuclide migration as described above, the liquid pressure in the region where the buffer material is located at the current time is determined according to the temperature value at the current time, which includes:

[0022] The temperature value of the buffer material at the current time is brought into the water mass conservation equation, and the liquid pressure p of the region where the buffer material is located at the current time is determined according to the water mass conservation equation l ;

[0023] The water mass conservation equation is expressed by the following formula:

[0024]

[0025] Wherein, ε v is the stress-strain field value of the buffer material; P sv is the saturated vapor pressure of groundwater; P v is the vapor pressure of groundwater; S is the saturation degree; c lp is the compressibility coefficient of the water body, which is expressed as: is the saturation degree suction influence coefficient; p l is the liquid pressure of the region where the buffer material is located; p g is the gas pressure of the region where the buffer material is located; μ l is the dynamic viscosity coefficient of water; p l is the liquid pressure of the region where the buffer material is located; g is the acceleration of gravity; ω is the liquid phase migration coefficient; k lT is the bentonite water body thermal driving coefficient; c sT is the temperature influence coefficient of saturation; c lT is the thermal expansion coefficient of the liquid; k lr is the relative permeability of the water body.

[0026] Further, the prediction method of nuclide migration as described above, the gas pressure of the region where the buffer material is located at the current time is determined according to the temperature value at the current time, which comprises:

[0027] The temperature value of the buffer material at the current time is brought into the solid mass conservation equation, and the gas pressure p of the region where the buffer material is located at the current time is determined according to the solid mass conservation equation g ;

[0028] The solid mass conservation equation is expressed by the following formula:

[0029]

[0030] Wherein, K s is the solid strain modulus; χ is the Bishop effective stress parameter, which is replaced by saturation S, β sT is the solid phase particle volume thermal expansion coefficient; p g is the gas pressure of the region where the buffer material is located.

[0031] Further, in the step 5 of the method for predicting the nuclide migration as described above, the step of determining the water vapor pressure field value in the buffer material at the current time according to the temperature value at the current time, the liquid pressure in the region, and the gas pressure in the region comprises:

[0032] applying the temperature value at the current time, the liquid pressure in the region, and the gas pressure in the region of the buffer material into the water vapor mass conservation equation, and determining the water vapor pressure field value P in the buffer material at the current time according to the water vapor mass conservation equation. v :

[0033] The water vapor mass conservation equation is expressed as follows:

[0034]

[0035] wherein c vp is the water vapor compressibility coefficient; D v is the effective diffusion coefficient of water vapor molecules; c sp is the saturation degree suction influence coefficient; c sT is the temperature influence coefficient of saturation degree; c vT is the thermal expansion coefficient of water vapor; p v is the water vapor density; is the density gradient of water vapor; is the temperature gradient; P sv is the saturated vapor pressure; and P v is the water vapor pressure field value in the buffer material.

[0036] Further, in the step 6 of the method for predicting the nuclide migration as described above, the step of determining the stress and strain field value of the buffer material at the current time according to the water vapor pressure field value in the buffer material at the current time and the gas pressure in the region comprises:

[0037] applying the water vapor pressure field value in the buffer material at the current time and the gas pressure in the region into the water vapor bulk mass conservation equation, and determining the stress and strain field value ε v of the buffer material at the current time according to the water vapor bulk mass conservation equation.

[0038] The water vapor bulk mass conservation equation is as follows:

[0039]

[0040] wherein, is the temperature gradient, k gT is the thermal drive coefficient of mixed gas; k gr is the relative permeability of gas; k lr is the relative permeability of water; p gμ is the dynamic viscosity coefficient of the liquid in the region where the buffer material is located l μ is the dynamic viscosity coefficient of the liquid in the region where the buffer material is located l μ is the dynamic viscosity coefficient of the liquid in the region where the buffer material is located g μ is the dynamic viscosity coefficient of the liquid in the region where the buffer material is located gT μ is the dynamic viscosity coefficient of the liquid in the region where the buffer material is located lT μ is the dynamic viscosity coefficient of the liquid in the region where the buffer material is located ap μ is the dynamic viscosity coefficient of the liquid in the region where the buffer material is located sp μ is the dynamic viscosity coefficient of the liquid in the region where the buffer material is located gT μ is the dynamic viscosity coefficient of the liquid in the region where the buffer material is located aT μ is the dynamic viscosity coefficient of the liquid in the region where the buffer material is located sT μ is the dynamic viscosity coefficient of the liquid in the region where the buffer material is located sv μ is the dynamic viscosity coefficient of the liquid in the region where the buffer material is located v μ is the dynamic viscosity coefficient of the liquid in the region where the buffer material is located μ is the dynamic viscosity coefficient of the liquid in the region where the buffer material is located a μ is the dynamic viscosity coefficient of the liquid in the region where the buffer material is located gp μ is the dynamic viscosity coefficient of the liquid in the region where the buffer material is located

[0041] Further, the prediction method of the nuclide migration as described above, if it is determined that the buffer material has reached saturation according to the liquid pressure in the region where the buffer material is located at the next time point, the next time point is taken as the initial time point of the nuclide migration;

[0042] According to the initial time point of the nuclide migration, the corresponding diffusion parameter of the buffer material in the saturated state is determined;

[0043] According to the diffusion parameter, the nuclide diffusion equation is determined, and the concentration distribution field of the nuclide at a future time point is determined through time iteration;

[0044] According to the concentration distribution field of the nuclide at a future time point, the corresponding migration state of the nuclide at the future time point is determined.

[0045] The method provided by the present application can obtain the saturation, temperature value, gas pressure in the region where the buffer material is located, liquid pressure in the region where the buffer material is located, and water vapor pressure in the buffer material, so that the obtained field values are more accurate when the buffer material reaches saturation, and the time required for the buffer material to reach saturation from not reaching saturation can be accurately obtained. Since the time required to reach saturation is an important indicator in the complete life cycle of waste disposal, which may be thousands of years in length, the method provided by the present application can accurately predict the time point at which the nuclide begins to leak. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 Buffering the interaction relationship between the multi-field coupling diagram;

[0047] Figure 2 The flow chart of the prediction method of nuclide migration provided by the present application. DETAILED DESCRIPTION

[0048] To make the objectives, technical solutions and advantages of the present application clearer, the technical solutions in the present application are described below clearly and completely. Obviously, the described embodiments are some of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the protection scope of the present application.

[0049] Some concepts involved in the present application are introduced as follows:

[0050] Temperature field: a physical field indicating the distribution of temperature in a space (one-dimensional, two-dimensional or three-dimensional) at a certain moment (for steady-state problems, there is no time concept), which is a continuous field distribution in physical sense, and is simulated as a continuous distribution of the whole space by calculating the temperature of discrete points and using interpolation and other methods in simulation calculation.

[0051] Stress field: a physical field indicating the distribution of stress in a space (one-dimensional, two-dimensional or three-dimensional) at a certain moment (for steady-state problems, there is no time concept), which is a continuous field distribution in physical sense, and is simulated as a continuous distribution of the whole space by calculating the stress of discrete points and using interpolation and other methods in simulation calculation. In the present application, stress is caused by phase change and pressure change of water (representing groundwater) in the porous medium due to the action of heat, as well as deformation of the solid framework of the porous medium.

[0052] Seepage field: a physical field indicating the distribution of groundwater in a space (one-dimensional, two-dimensional or three-dimensional) at a certain moment (for steady-state problems, there is no time concept), which is a continuous field distribution in physical sense, and is simulated as a continuous distribution of the whole space by calculating the saturation of discrete points and using interpolation and other methods in simulation calculation.

[0053] Nuclide concentration field: a physical field indicating the distribution of nuclide concentration in a space (one-dimensional, two-dimensional or three-dimensional) at a certain moment (for steady-state problems, there is no time concept), which is a continuous field distribution in physical sense, and is simulated as a continuous distribution of the whole space by calculating the nuclide concentration of discrete points and using interpolation and other methods in simulation calculation.

[0054] Multi-field coupling: refers to the complex physical process of interaction and mutual influence between multiple physical fields, in the present invention, mainly refers to the coupling effect of temperature field-stress field-seepage field and other three fields on the nuclide migration process (nuclide concentration field).

[0055] THM: respectively value temperature, seepage and stress.

[0056] Buffer material: English: backfill material, including the early called buffer material, refers to various materials placed around the radioactive waste package and filled in the excavated part of the disposal library, at present, bentonite is mainly used in China, which is a porous medium material.

[0057] Porous medium: is the common space occupied by multiphase substances, and is a combination of coexistence of multiphase substances. The part of space without solid skeleton is called pore, which is occupied by liquid or gas or gas-liquid two phases, and other phases are dispersed in one phase, and some cavities of void space are connected.

[0058] The high-level waste disposal library is introduced as follows:

[0059] High-level waste deep geological disposal is the only way to dispose of high-level waste (nuclide), so the multi-field coupling research in high-level waste deep geological disposal library (HLW for short) becomes the focus of research. After the operation of high-level waste disposal library, the following situations may occur: high-level waste heat release; stress and strain of buffer material and rock mass; fluid seepage field changes; near-field geochemical process is affected; high-level radioactive nuclide is continuously released. In the closed high-level waste disposal library, the stability of surrounding rock and buffer material and the nuclide migration process are completed under the condition of coupling with each other in a long time and temperature change process. In order to reflect the operation condition of high-level waste disposal library under the action of high temperature, water flow and pressure, based on the mixed physical theory and the continuous medium mechanics, the unsaturated medium is regarded as a mixed continuum of three independent superposed phases, and the coupling mathematical model of heat, water flow and force of unsaturated medium and the coupling mathematical model of heat-water-force-chemical of saturated medium are sorted out and derived. The unsaturated model averages and continuous processes the intrinsic property parameters of mixed system of solid phase, liquid phase and gas phase in space from the perspective of characterization unit, and considers the coupling between variables; the saturated model considers the coupling of temperature, water flow, stress and solute transport under the premise of saturated state of buffer material.

[0060] Figure 1 The interaction relationship diagram between multi-field coupling of buffer material, in the heat-water-force coupling of buffer material, the interaction relationship between each field can be represented by Figure 1The heat-water-force coupling in the buffer material is coupled with the solute migration field on this basis. Therefore, the theory of heat-water-force-chemical coupling of the buffer material not only contains the solid phase structure of the porous medium, but also includes the internal fluid transmission and temperature transfer, thereby generating the coupling effect between the multiple physical fields. The control equation contains the coupling terms between the two fields and the three fields, and the physical field and the physical quantity parameter are also coupled with each other in the constitutive relation. Due to the multiple physical field coupling, two or more mathematical equations must be used for solving, and therefore, it is necessary to study the numerical solution method, the universality of the solution and the new problems caused by the coupling.

[0061] The high radioactivity nuclides in the deep geological disposal repository of high-level waste not only release decay heat and radiation, but also the underground water flow penetrates into the disposal repository under the action of high pressure, and the complex THM coupling effect occurs in the buffer material. In order to fully understand these coupling processes, numerical modeling is an indispensable tool, because the safety of the disposal repository must be ensured for 100,000 years or more.

[0062] In summary, the buffer material cannot be predicted in this stage (the time may last for thousands of years) before saturation, and the results of the interaction between the temperature field, the stress field and the seepage field are not revealed. The results of the multiple physical field interaction in this stage will directly affect the saturation degree and the time of reaching full saturation of the buffer material. However, there is no scheme for predicting the nuclide migration in this stage, so that the prediction of the nuclide migration process in the unsaturated stage is missing, and the saturation judgment (time and degree) is deviated.

[0063] The purpose of the present application is to provide a multiple field coupling control equation set according to the characteristics of different control equations in the unsaturated condition of the buffer material, and to predict the time of nuclide leakage at a future time in the unsaturated condition of the buffer material through the multiple field coupling control equation set.

[0064] Figure 2 The flow chart of the nuclide migration prediction method provided by the present application is shown in Figure 2 The method comprises the following steps:

[0065] Step 1: obtaining the saturation degree of the buffer material at the initial time, the temperature value of the buffer material at the initial time, and the initial distribution parameters of the deformation variable of the buffer material; the initial distribution parameters include the elastic modulus of the buffer material itself, the porosity n of the buffer material, the internal pressure difference of the buffer material and the initial external pressure difference.

[0066] Specifically, the elastic modulus is not embodied in the equation, which is one of the basic properties of the buffer material, and is obtained by directly reading the example attribute data from the program. The initial distribution quantity includes: the temperature distribution in the temperature field, i.e. the temperature distribution inside the buffer material at the initial time, which can be considered as a uniform room temperature distribution; the saturation in the seepage field, which is all 0 at the initial time, i.e. it is considered that all is dry at the initial time; and the absolute pressure value (or pressure difference) inside and outside the buffer material, the stress and strain in the stress field, which are all considered as 0 at the initial time, i.e. no stress and strain occurs at the initial time.

[0067] Step 2: predicting the temperature value of the buffer material at the current time according to the initial distribution parameters of the saturation and the deformation variable of the buffer material, and the temperature value of the buffer material at the initial time.

[0068] Specifically, the initial distribution parameters of the saturation and the deformation variable of the buffer material, and the temperature value of the buffer material at the initial time are brought into the energy conservation equation, and the temperature value T of the buffer material at the current time is determined according to the energy conservation equation;

[0069] The formula of the energy conservation equation is:

[0070]

[0071] Wherein, g is the gas phase value, l is the liquid phase value, and s is the solid phase value; ρ is the density value; c is the specific heat capacity; λ is the thermal conductivity; T is the temperature value of the buffer material, T l is the liquid temperature of the region where the buffer material is located; T g is the gas temperature of the region where the buffer material is located; T s is the solid temperature of the region where the buffer material is located, according to the local quasi-equilibrium assumption, T l =T g =T s =T; S is the liquid saturation in the buffer material unit; n is the porosity of the buffer material, which is considered as a constant value due to its small change range; ω is the liquid phase migration coefficient; k is the intrinsic permeability tensor of the medium; k lr is the relative permeability of the water body; μ l is the dynamic viscosity coefficient of water; c l is the compressibility coefficient of the water body, which is expressed as: β l is the thermal expansion coefficient of the water body, which is expressed as: k gr is the relative permeability of the gas phase; k gT is the thermal driving coefficient of the mixed gas; g is the acceleration of gravity; μ g is the dynamic viscosity coefficient of the gas; is the compressibility coefficient of the mixed gas, is the thermal expansion coefficient of the mixed gas; εv ε is the stress-strain field value of the buffer material; p g p is the liquid density in the region where the buffer material is located; c g K is the compressibility coefficient of the gas; K g K is the volumetric strain modulus of the gas phase; n is the porosity; μ is the gas pressure gradient; p l p is the dynamic viscosity coefficient of water; p l p is the density of groundwater; c l K is the compressibility coefficient of the water body, expressed as: K l K is the volumetric strain modulus of the liquid phase; β l β is the thermal expansion coefficient of the water body, expressed as: k is the liquid pressure gradient; p lT p is the relative permeability of the water body; p s p is the density of the solid; c s c is the specific heat capacity of the solid; p l p is the liquid pressure in the region where the buffer material is located; K l K is the volumetric strain modulus of the liquid phase; K g K is the volumetric strain modulus of the gas phase.

[0072] Since energy can be presented in the form of heat, i.e., the equation containing the temperature term (generally represented by T) can be generally considered as an energy equation. The main variable in this equation is T, i.e., the temperature term. When the temperature changes, the energy changes. Therefore, the solution of this equation is the field value distribution of T, i.e., this equation can be used to calculate / predict the temperature value.

[0073] Step 3: determining the liquid pressure in the region where the buffer material is located at the current time according to the temperature value of the buffer material at the current time.

[0074] Specifically, the temperature value of the buffer material at the current time is brought into the water body mass conservation equation, and the liquid pressure p l in the region where the buffer material is located at the current time is determined according to the water body mass conservation equation.

[0075] The water body mass conservation equation is expressed as follows:

[0076]

[0077] wherein ε v is the stress-strain field value of the buffer material; p sv P is the saturated vapor pressure of groundwater; p v P is the vapor pressure of groundwater; S is the saturation degree; c lp K is the compressibility coefficient of the water body, expressed as: c spis the coefficient of the saturation degree suction effect; p l is the liquid pressure in the region where the buffer material is located; p g is the gas pressure in the region where the buffer material is located; p l is the dynamic viscosity coefficient of water; p l is the liquid pressure in the region where the buffer material is located; g is the acceleration of gravity; k lT is the coefficient of the swelling of the bentonite in the water; c sT is the temperature effect coefficient of the saturation degree; c lT is the thermal expansion coefficient of the liquid; k lr is the relative permeability of the water.

[0078] In the above formula, only T, s v , p l and p g are unknown fields, and the rest are either constants or can be solved using third-party formulas. In step 2, the physical field distribution of T (i.e., temperature) has been solved, where represents the gradient of the temperature field that has been calculated, and can be solved to calculate represents the partial derivative of temperature with respect to time, which can be approximated using the difference method. At the initial time, it can be considered that s v has not occurred, so this term can be ignored. In the time iteration process, s v is the field value obtained at the previous time step; p g Similarly, at the initial time, it is the normal atmospheric pressure, and in the time iteration, it is the field value obtained at the previous time step; then the four unknown fields to be solved are simplified to only p l an unknown, at this time, the finite element method can be used to solve this equation to obtain p l , i.e., the field distribution of the liquid pressure. At this time, the formula is used, where s is the suction (i.e., the pressure acting on the liquid), and the obtained p l is brought in, i.e., the saturation degree can be obtained.

[0079] Step 4: determining the gas pressure in the region where the buffer material is located at the current time according to the temperature value of the current time.

[0080] Specifically, the temperature value of the buffer material at the current time is brought into the solid mass conservation equation, and the gas pressure p g in the region where the buffer material is located at the current time is determined according to the solid mass conservation equation.

[0081] The solid mass conservation equation is expressed by the following formula:

[0082]

[0083] where K s is the solid strain modulus; χ is the Bishop effective stress parameter, which is replaced by using saturation S, β sT is the solid phase particle volume thermal expansion coefficient; p g is the gas pressure of the region where the buffer material is located.

[0084] There are three unknowns p g , T and ε v in this formula, where T has been obtained in step 2, can be obtained according to the previous method; ε v can be obtained according to the previous assumption, which is 0 at the initial time and is the value calculated at the last time at the new time, p g is unknown, and the rest are constants or can be calculated by third-party formulas. In this way, the three variables in this formula become only one unknown, and the distribution of the gas pressure can be calculated by using the finite element method.

[0085] Step 5: Determine the water vapor pressure field value in the buffer material at the current time according to the temperature value at the current time, the liquid pressure of the region, and the gas pressure of the region.

[0086] Specifically, the temperature value of the buffer material at the current time, the liquid pressure of the region, and the gas pressure of the region are brought into the water vapor mass conservation equation, and the water vapor pressure field value P v in the buffer material at the current time is determined according to the water vapor mass conservation equation.

[0087] The water vapor mass conservation equation is expressed by the following formula:

[0088]

[0089] In the formula, c vp is the water vapor compressibility coefficient; D v is the effective diffusion coefficient of water vapor molecules; c sp is the saturation degree suction influence coefficient; c sT is the temperature influence coefficient of saturation degree; c vT is the thermal expansion coefficient of water vapor; ρ v is the density of water vapor; is the density gradient of water vapor; is the temperature gradient; P sv is the saturated vapor pressure; P v is the water vapor pressure field value in the buffer material.

[0090] There are ε v , p g , p v, T, etc. four unknown quantities, the rest are constants or can be calculated by third party formula. As described above, the previous steps have been solved (assuming) ε v , p g , T three field values, only p v unknown, so you can use the finite element method to solve p v , namely the water vapor pressure value.

[0091] Step 6: According to the water vapor pressure field value in the buffer material at the current time, the gas pressure in the region determines the stress and strain field value of the buffer material at the current time.

[0092] Specifically, the water vapor pressure field value in the buffer material at the current time, the gas pressure in the region is brought into the water vapor mass conservation equation, and the stress and strain field value ε v of the buffer material at the current time is determined according to the water vapor mass conservation equation.

[0093] The water vapor mass conservation equation is as follows:

[0094]

[0095] Where, is the temperature gradient, k gT is the thermal drive coefficient of the mixed gas; k gr is the gas relative permeability; k lr is the water relative permeability; ρ g is the liquid density in the region where the buffer material is located, μ l is the dynamic viscosity coefficient of water, k is the intrinsic permeability tensor of the medium, ρ l is the groundwater density; μ g is the dynamic viscosity coefficient of gas, k gT is the thermal drive coefficient of the mixed gas; k lT is the water relative permeability; H is the Herry dissolution coefficient; c ap is the dry air compression coefficient; c sp is the saturation suction influence coefficient; c gT is the gas phase thermal expansion coefficient; S is the saturation; c aT is the thermal expansion coefficient of the mixed gas in the gas phase; c sT is the temperature influence coefficient of saturation; P sv is the saturation vapor pressure of groundwater; P v is the vapor pressure of groundwater; is the gradient of gas pressure; ρ a is the density of the mixed gas; c gp is the compression coefficient of the mixed gas.

[0096] There are pg , p v , T and ε v Four unknown quantities, where p g , p v , T have been obtained previously, only ε v is left to be calculated. The equation is calculated above by the assumption, so here the equation is solved to obtain the field value of the stress and strain of the buffer material, i.e. ε v field value at the new time.

[0097] Step 7: Update the temperature value of the buffer material at the next time according to the temperature value of the buffer material at the current time, the liquid pressure in the region, the gas pressure in the region, and the water vapor pressure field value.

[0098] Specifically, since there are various substances in a unit body, such as solids, liquids and gases, when calculating the total temperature drop, the average specific heat capacity value and the average density of the mixture in the unit body need to be calculated (which can be calculated by weighting according to the volume proportion), and then the specific heat capacity and density of each specific substance (such as solids, liquids and gases) need to be calculated separately.

[0099] The temperature field obtained in step 2 is an ideal temperature field, i.e. all energy (i.e. heat energy) does not change. After obtaining the liquid pressure, saturation, air pressure and water vapor pressure, it can be considered that these physical phenomena will all cause heat transfer, which is described in detail as follows:

[0100] 1. Saturation represents the presence of a certain amount of liquid in a unit body. In the case of low liquid flow rate, it can be approximately considered that this part of the liquid will absorb heat and rise in temperature;

[0101] 2. The pressure of air and water vapor can be calculated by the ideal gas state equation to calculate its temperature, and it can be considered that the energy source of this part of the temperature rise is also provided by the temperature field;

[0102] 3. The heat absorption of the solid in the unit body can be approximately calculated (calculated by thermal conductivity, mass, porosity and time, etc.), and this part of the energy also comes from the temperature field;

[0103] 4. According to the quasi-equilibrium assumption, the temperatures of gas, solid and liquid should be equal, so the temperature conservation equation can be obtained, i.e.

[0104] The heat lost in the unit body = the heat absorbed by the liquid in the unit body + the heat absorbed by the gas + the heat absorbed by the solid (not considering external heat exchange)

[0105] According to the quasi-equilibrium assumption, the temperature conservation equation is determined, and the temperature field prediction data of the buffer material at the next time corresponding to the time is determined according to the temperature conservation equation;

[0106] wherein the heat lost in the unit volume = (initial temperature - Tx) * average specific heat capacity * unit volume * average density;

[0107] the heat gained by the liquid in the unit volume = (Tx - initial temperature) * liquid specific heat capacity * liquid volume * liquid density;

[0108] the heat gained by the gas = (Tx - initial temperature of the gas) * gas specific heat capacity * gas volume * gas density;

[0109] the heat gained by the solid = (Tx - initial temperature of the solid) * solid specific heat capacity * solid volume * solid density;

[0110] the Tx is the final equilibrium temperature, i.e. the temperature field prediction data corresponding to the buffer material.

[0111] Since finally all are in thermal equilibrium (i.e. equal temperature), by the above equation can be obtained in each unit volume inside each time step of the equilibrium temperature, so as to update the original predicted temperature field, i.e. to achieve the update of the temperature field.

[0112] Step 8: according to the temperature value of the buffer material at the next time, determine the liquid pressure of the buffer material at the next time, according to the liquid pressure of the buffer material at the next time, determine whether the buffer material reaches saturation.

[0113] Specifically, in the buffer material, only when the pores of the porous medium are all filled with groundwater, the nuclides permeated through the surface cracks of the solidification tank can begin to migrate in the buffer material with the migration of groundwater, so the sufficient and necessary condition for determining whether the nuclides can begin to migrate is whether the buffer material currently contacting the solidification tank is filled with groundwater. Since the groundwater permeates from the outer wall of the buffer material to the inside, the calculation condition for characterizing whether the nuclides can migrate is that the saturation S of all unit volumes in the calculation domain corresponding to the buffer material is 1.0. When the saturation of the buffer material is 1, it represents that the buffer material has reached saturation. Considering the calculation error, a relaxed factor (for example, the error is 2%, i.e. the saturation of all unit volumes is not less than 98%) can be introduced. After reaching this condition, the nuclides begin to migrate, and at this time, the multi-field coupling equation set in the unsaturated stage is no longer needed to be calculated, and the nuclide migration equation in the saturated stage is started to be calculated.

[0114] The criterion for determining whether the nuclide starts to migrate is whether the buffer material has reached saturation, which is verified in relevant tests. In such tests, when pressure is applied to the simulated buffer material while water is added, water gradually penetrates into the buffer material under the action of the internal and external pressure difference. When the buffer material has not reached saturation, no nuclide (or tracer) can be found in the test material when sampling and detection are performed. When and only when the buffer material has reached saturation, the nuclide (or tracer) starts to migrate outward with water and is detected.

[0115] Therefore, when the physical model (i.e., the control equation set) is established, the entire process will inevitably be divided into two stages, i.e., the unsaturated and saturated stages. In the former stage, the nuclide does not migrate, and the mutual coupling among the temperature field, the seepage field, and the stress field plays a leading role, which changes the distribution of parameters such as the temperature distribution, the groundwater distribution, the stress, the density, the water vapor proportion, and the water vapor pressure in the buffer material. In the saturated stage, it is considered that the temperature field, the seepage field, and the stress field have reached stability and will not change significantly, so only the nuclide migration equation needs to be solved in this stage. Obviously, there is a criterion between the two stages. According to the previous test, it can be determined that the criterion is the saturation of the buffer material. Since the groundwater seeps into the buffer material from all directions under the action of the internal and external pressure difference, it can be regarded as an isotropic seepage process (there may be slight differences in the Z-axis direction due to gravity), so a reasonable physical simplification assumption is made here: when the saturation of all cells in the buffer material corresponding to the calculation grid is 1 (i.e., saturation is reached), it is considered that the buffer material corresponding to the calculation grid has reached saturation, and at this time, the nuclide will start to migrate outward with the groundwater.

[0116] In the actual computer implementation level, a field quantity S can be set, which has a value range of [0, 1], 0 represents dryness (i.e., no groundwater exists in the cell), and 1 represents saturation. At the initial moment, S can be set (generally, it can be set to 0, i.e., dryness, or a value less than 1, i.e., there is a certain amount of groundwater at the initial moment). Then at the beginning of each time iteration, whether saturation has been reached is determined through the traversal of the field quantity. If saturation has been reached, the nuclide migration control equation is solved, otherwise, the control equation set of the multi-physical field coupling is solved.

[0117] Step 9: If it is determined according to the liquid pressure of the buffer material in the region at the next moment that the buffer material has not reached saturation at the next moment, steps 2-7 are repeated until the buffer material reaches saturation, and the moment corresponding to the saturation state of the buffer material is predicted, which is the moment when the nuclide starts to migrate.

[0118] Specifically, the multi-field coupling control equation set in the unsaturated state is as follows:

[0119] Water mass conservation equation:

[0120]

[0121] If the change of porosity n is ignored, the above formula can be simplified as:

[0122]

[0123] If it is considered that the density of water remains unchanged, the above formula can be further simplified as:

[0124]

[0125] Gas mass conservation equation:

[0126]

[0127] If the change of porosity n is ignored, the above formula can be simplified as:

[0128]

[0129] If it is considered that the density of water remains unchanged, the above formula can be further simplified as:

[0130]

[0131] Water vapor mass conservation equation:

[0132]

[0133] If the change of porosity n is ignored, the above formula can be simplified as:

[0134]

[0135] If it is considered that the density of water remains unchanged, the above formula can be further simplified as:

[0136]

[0137] Solid mass conservation equation:

[0138]

[0139] If the change of porosity n is ignored, the above formula can be simplified as:

[0140]

[0141] If it is considered that the density of water remains unchanged, the above formula can be further simplified as:

[0142]

[0143] Energy conservation equation:

[0144]

[0145] Nucleus migration control equation in saturated state:

[0146] The original equation is as follows:

[0147]

[0148] In the formula, R d is a linear retardation coefficient; D is a hydrodynamic dispersion coefficient, which can be approximated as an apparent diffusion coefficient Da, m2 / a when the water flow velocity is small; β lT and c lp are constants; C is the concentration of the nucleus.

[0149] In the saturated state, it can be assumed that the temperature field, pressure field and strain field no longer change, so the above formula can be simplified as follows:

[0150]

[0151] In the formula, v r represents the velocity of the fluid relative to the solid, that is, the average flow velocity of the liquid relative to the solid skeleton. Considering the Soret effect and Dufour effect, the generalized Darcy law considers that in addition to the hydraulic gradient, the temperature gradient and the concentration gradient will also change the motion of the fluid, which is expressed as follows:

[0152]

[0153] In the formula: D t is the water flow diffusion rate under the action of the temperature gradient; K c is the water flow diffusion rate under the action of the concentration gradient. Considering that in the saturated state, the liquid pressure p l and the temperature T can be approximately considered to no longer change, the above formula can be simplified as:

[0154]

[0155] At the same time, in the Darcy law, the velocity actually refers to the velocity of the fluid relative to the solid, that is, the average flow velocity of the liquid relative to the solid skeleton:

[0156]

[0157] In the formula, n is the porosity.

[0158] Bring back the 12th formula, and the following formula for the migration of the nucleus in the saturated state can be obtained:

[0159]

[0160] Therefore, in the unsaturated stage, only the equations of temperature-stress-seepage coupling are involved, and the nuclide does not start to migrate in this stage, so only the equations related to the three fields are solved (such as the previous equations 1-9). In the saturated stage, since the groundwater reaches saturation, it can be approximately considered that the temperature field and the stress field no longer change, so only the nuclide migration equation in the saturated stage needs to be solved (such as the previous equation 15).

[0161] In the unsaturated stage, the relationship between the three physical fields of temperature, seepage, and stress is analyzed, and it can be seen that temperature and seepage are the main variables that will cause changes in the stress field, so the order of solving the physical fields is: temperature field -> seepage field -> stress field.

[0162] ①Among them, the temperature field equation (i.e. the energy conservation equation) contains variables ε v , T, S and n, which represent deformation, temperature, saturation and porosity, respectively, and the rest are constants or variables to be closed by other equations. Since it has been proved in experiments that the change of porosity is small, it can be approximately treated as a constant, and ε v and S need to be determined according to the initial conditions at the initial time. It can be reasonably assumed that at the initial time, there is no deformation in all unit bodies in the buffer material, and there is no groundwater (i.e. completely dry, of course, it can also be considered as partially dry, i.e. the value of S is a small value, for example 0.1%), so at the initial time, ε v and S of all unit bodies are known, which are brought into equation (9) to directly calculate the distribution of temperature in the buffer material corresponding to the calculation domain at the next time layer (if it is not the initial time, then the saturation and deformation variables calculated at the previous time layer are brought into the equation to solve).

[0163] ②At this time, the development of groundwater in the buffer material can be predicted according to the pressure difference between the inside and outside of the buffer material, and the groundwater saturation in the unit body is calculated according to equations (2b) and (8b). In these two equations, the main variables are ε v , T, p g , ω, ρ l , P sv and P v , where ρ l is the density of groundwater, which can be considered as a constant, P sv and P v are the saturated vapor pressure and vapor pressure of groundwater, which can be calculated according to the current temperature of the unit body, ω is the liquid phase migration coefficient, which can also be calculated by a third party formula from the temperature, and T is the temperature, which has been calculated in the previous step. ε vThen the gas pressure value p inside the unit cell can be solved by the third-party formula based on the known assumption / calculated value, and the gas pressure value p inside the unit cell can be calculated by the two equations g .

[0164] ③Next, the water vapor pressure p is calculated according to equations (4b) and (6b) v .

[0165] ④After the above field values are calculated, the temperature field calculated by the prediction of 10 is corrected according to the heat consumed by the processes of transferring to groundwater, water vapor phase change, etc. inside each unit cell, and the corresponding temperature value is deducted from the ideal temperature field to obtain the corrected temperature field.

[0166] ⑤Based on the various field data obtained at the last time layer, steps ①-④ are repeated until the entire time cycle is completed.

[0167] Since the multiple physical fields are coupled with each other, i.e. multiple physical variables are included in the same equation, in addition to using functions and additional equations to close part of the variables, assumptions need to be made for other physical quantities that cannot be closed. After solving, the physical quantity is corrected by calculating other physical quantities, i.e. the distributed solving strategy of "assumption -> solution -> correction" is adopted.

[0168] For the nuclide migration equation in the saturation stage, it can be solved by solving the single migration equation, and there is no need for correction. The weighted residual method of the finite element method is used for solving.

[0169] Considering the unified solution of the unsaturated state and the saturated state, i.e. completely covering the two sub-processes of nuclide migration, the calculation domain needs to be divided according to the set conditions of nuclide migration. The logical flow corresponding to the determination condition is to traverse the saturation degree of each unit cell of the calculation domain. If all the set conditions are met, it can be considered that the saturation stage has been reached, and only the nuclide migration equation needs to be calculated, and the multiple physical field coupling equation set in the unsaturated stage does not need to be calculated.

[0170] Step 10: If it is determined that the buffer material has reached saturation according to the liquid pressure of the region where the buffer material is located at the next time, the next time is taken as the initial time of nuclide migration.

[0171] Step 11: Determine the diffusion parameter of the buffer material in the saturated state according to the initial time of nuclide migration.

[0172] Step 12: Determine the nuclide diffusion equation according to the diffusion parameter, and determine the concentration distribution field of the nuclide at a future time through time iteration.

[0173] Step 13: determining the migration state of the nuclide at the future time according to the concentration distribution field of the nuclide at the future time.

[0174] The present application has the following beneficial effects:

[0175] 1. The nuclide migration control equation group in the complex porous medium can be solved, and the multi-physical field data obtained by calculation can predict the expected distribution of the nuclide in the buffer material in the medium and long term, and can provide a more scientific evaluation method for the construction of the nuclear waste underground disposal library.

[0176] 2. The multi-physical field data obtained by solving the nuclide migration control equation group in the porous medium can scientifically evaluate the corresponding buffer material properties and evaluate the long-term retardation and adsorption effect of the specific nuclide.

[0177] 3. The present application can provide a scientific numerical simulation evaluation basis for the medium and long term migration of the nuclide in the buffer material, make up for the short period (in years) test of the current indoor test, and provide a new evaluation method and method for the nuclear waste disposal industry.

[0178] Finally, it should be pointed out that: the above examples are only used to illustrate the technical solutions of the present application, but not to limit them; although the present application has been described in detail with reference to the foregoing examples, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing examples, or make equivalent replacement for part of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for predicting nuclide migration, characterized in that, Includes the following steps: Step 1: Obtain the initial saturation of the buffer material, the initial temperature of the buffer material, and the initial distribution parameters of the deformation of the buffer material; The initial distribution parameters include: the elastic modulus of the buffer material itself, the porosity n of the buffer material, the internal pressure difference of the buffer material, and the external initial pressure difference; Step 2: Based on the initial distribution parameters of the saturation and deformation of the buffer material, and the initial temperature value of the buffer material, predict the current temperature value of the buffer material. Step 3: Determine the liquid pressure in the area where the buffer material is located at the current moment based on the current temperature value; Step 4: Determine the gas pressure in the area where the buffer material is located at the current moment based on the current temperature value; Step 5: Determine the water vapor pressure field value in the buffer material at the current moment based on the current temperature value, the liquid pressure in the area, and the gas pressure in the area; Step 6: Determine the stress-strain field value of the buffer material at the current moment based on the water vapor pressure field value in the buffer material and the gas pressure in the area at the current moment; Step 7: Update the temperature value of the buffer material for the next moment based on the current temperature value of the buffer material, the liquid pressure of the area, the gas pressure of the area, and the water vapor pressure field value. Step 8: Based on the temperature value of the buffer material at the next moment, determine the liquid pressure in the area where the buffer material is located at the next moment, and determine whether the buffer material has reached saturation based on the liquid pressure in the area where the buffer material is located at the next moment. Step 9: If, based on the liquid pressure in the area where the buffer material is located at the next moment, it is determined that the buffer material has not reached saturation at the next moment, then repeat steps 2-7 until the buffer material reaches saturation. Based on this, the moment when the buffer material reaches saturation is predicted. The moment when the buffer material reaches saturation is the moment when the nuclide begins to migrate.

2. The method for predicting nuclide migration according to claim 1, characterized in that, Step 2, which involves predicting the current temperature value of the buffer material based on the saturation, the initial distribution parameters of the buffer material deformation, and the initial temperature value of the buffer material, includes: Substitute the saturation, the initial distribution parameters of the deformation of the buffer material, and the initial temperature value of the buffer material into the energy conservation equation, and determine the current temperature value T of the buffer material based on the energy conservation equation. The formula for the energy conservation equation is: Where g is the gas phase value, l is the liquid phase value, s is the solid phase value; ρ is the density value; c is the specific heat capacity; λ is the thermal conductivity; and T is the temperature value of the buffer material. l T represents the temperature of the liquid in the area where the buffer material is located. g T represents the gas temperature in the area where the buffer material is located. s Given the solid temperature in the region where the buffer material is located, and based on the local quasi-equilibrium assumption, T l =T g =T s =T; S is the liquid saturation within the buffer material unit; n is the porosity of the buffer material, which is considered a constant due to its small variation range; ω is the liquid phase migration coefficient; k is the intrinsic permeability tensor of the medium; k lr The relative permeability of the water body; μ l c is the dynamic viscosity coefficient of water; l The compressibility coefficient of water is expressed as: β l The coefficient of thermal expansion of water is expressed as: k gr The relative permeability of the gas phase; k gT μ is the thermal driving coefficient of the gas mixture; g is the acceleration due to gravity; μ g The dynamic viscosity coefficient of the gas; Let be the compressibility coefficient of the gas mixture. ε is the coefficient of thermal expansion of the gas mixture; v ρ represents the stress-strain field value of the buffer material. g c is the liquid density in the area where the buffer material is located. g K is the gas compressibility coefficient. g is the gas phase bulk strain modulus; n is the porosity. For gas pressure gradient; μ l ρ is the dynamic viscosity coefficient of water; l c is the density of groundwater. l The compressibility coefficient of water is expressed as: K l β is the bulk strain modulus of the liquid phase. l The coefficient of thermal expansion of water is expressed as: For the liquid pressure gradient; k lT ρ is the relative permeability of the water body. S c is the density of the solid. s p is the specific heat capacity of a solid. l K is the liquid pressure in the area where the buffer material is located. l K is the bulk strain modulus of the liquid phase. g This is the gas phase volumetric strain modulus.

3. The method for predicting nuclide migration according to claim 1, characterized in that, In step 3, determining the liquid pressure in the area where the buffer material is located at the current moment based on the current temperature value includes: Substitute the current temperature value of the buffer material into the water mass conservation equation, and determine the liquid pressure p in the region where the buffer material is located at the current moment based on the water mass conservation equation. l ; The water mass conservation equation is expressed by the following formula: Where, ε v P represents the stress-strain field value of the buffer material. sv P is the saturated vapor pressure of groundwater. v S is the vapor pressure of groundwater; S is the degree of saturation; c lp The compressibility coefficient of water is expressed as: c sp p is the saturation suction influence coefficient. l p represents the liquid pressure in the area where the buffer material is located. g The gas pressure in the area where the buffer material is located; μ l p is the dynamic viscosity coefficient of water. l ω is the liquid pressure in the region where the buffer material is located; g is the acceleration due to gravity; ω is the liquid phase migration coefficient; k lT c is the thermal drive coefficient of bentonite in water; sT c is the temperature effect coefficient of saturation. lT k is the coefficient of thermal expansion of the liquid. lr This represents the relative permeability of the water body.

4. The method for predicting nuclide migration according to claim 1, characterized in that, Step 4, determining the gas pressure in the area where the buffer material is located at the current moment based on the current temperature value, includes: Substitute the current temperature value of the buffer material into the solid mass conservation equation, and determine the gas pressure p in the region where the buffer material is located at the current moment based on the solid mass conservation equation. g ; The solid mass conservation equation is expressed by the following formula: Among them, K s χ is the solid strain modulus; χ is the Bishop effective stress parameter, replaced by the saturation degree S; β sT It is the coefficient of thermal expansion of solid particles; p g This refers to the gas pressure in the area where the buffer material is located.

5. The method for predicting nuclide migration according to claim 1, characterized in that, In step 5, determining the water vapor pressure field value in the buffer material at the current moment based on the current temperature value, the liquid pressure in the area, and the gas pressure in the area includes: Substitute the current temperature value of the buffer material, the liquid pressure of the area, and the gas pressure of the area into the water vapor mass conservation equation, and determine the water vapor pressure field value P in the buffer material at the current moment based on the water vapor mass conservation equation. v : The water vapor mass conservation equation is expressed by the following formula: In the formula, c vp It is the water vapor compressibility coefficient; D v It is the effective diffusion coefficient of water vapor molecules; c sp It is the saturation suction influence coefficient; c sT It is the temperature influence coefficient of saturation; c vT It is the coefficient of thermal expansion of water vapor; ρ v It is the density of water vapor; It is the density gradient of water vapor; It is a temperature gradient; P sv Saturated vapor pressure P v This represents the water vapor pressure field value in the buffer material.

6. The method for predicting nuclide migration according to claim 1, characterized in that, In step 6, determining the stress-strain field value of the buffer material at the current moment based on the water vapor pressure field value in the buffer material and the gas pressure in the area includes: Substitute the current water vapor pressure field value in the buffer material and the gas pressure in the surrounding area into the water vapor mass conservation equation, and determine the stress-strain field value ε of the buffer material at the current moment based on the water vapor mass conservation equation. v ; The mass conservation equation for the water vapor is as follows: in, For the temperature gradient, k gT k is the thermal drive coefficient of the gas mixture. gr k is the relative permeability of the gas. lr ρ is the relative permeability of the water body. g The density of the liquid in the region where the buffer material is located, μ l Let ρ be the dynamic viscosity coefficient of water, k be the intrinsic permeability tensor of the medium, and ρ be the viscosity coefficient of water. l Density of groundwater; μ g Let k be the dynamic viscosity coefficient of the gas. gT k is the thermal drive coefficient of the gas mixture. lT The relative permeability of the water body; H is the Herry solubility coefficient; c ap It is the dry air compressibility coefficient; c sp It is the saturation suction influence coefficient; c gT It is the coefficient of thermal expansion of the gas phase; S is the degree of saturation; c aT It is the coefficient of thermal expansion of the gas-phase mixture; c sT It is the temperature effect coefficient of saturation; P sv P is the saturated vapor pressure of groundwater. v This refers to the vapor pressure of groundwater. The gradient of gas pressure; ρ a c is the density of the gas mixture; gp is the compressibility coefficient of the gas mixture.

7. The method for predicting nuclide migration according to claim 1, characterized in that, If the buffer material is determined to be saturated at the next moment based on the liquid pressure in the area where the buffer material is located, then the next moment is taken as the initial moment of nuclide migration. Based on the initial moment of the nuclide migration, determine the diffusion parameters of the buffer material when it has reached saturation. The nuclide diffusion equation is determined based on the diffusion parameters, and the concentration distribution field of the nuclide at a future moment is determined through time iteration. The migration state of the nuclide at a future time is determined based on the concentration distribution field of the nuclide at that future time.

Images