Simulation calculation method for predicting radioactive waste solidified body geological disposal process

Abstract

The invention relates to a simulation calculation method for predicting a radioactive waste solidified body geological disposal process. The simulation calculation method comprises a solid deformation module, a fluid flow module, a heat balance module, a chemical reaction module and a nuclide migration module. The method comprises the following steps: firstly, constructing a deep geological treatment geometric model comprising a solidified body, a buffer material, a backfill material and surrounding rock through geometric modeling software, carrying out grid division on the model based on porous medium hypothesis, generating a grid suitable for computational fluid mechanics simulation, and then establishing a multi-physics field coupling model. According to the method, through multi-physical field coupling simulation, the evolution of a temperature field, a seepage field, a mechanical field and a chemical field of the solidified body in thousands to thousands of years in the geological disposal process can be dynamically predicted, and the limitation of the time scale of a traditional experimental method is broken through; the method provides support for safety evaluation, repository design and long-term performance evaluation of high-level radioactive waste deep geological disposal, effectively guarantees safety isolation of radioactive waste, and reduces environmental risks.

Description

Technical Field

[0001] This invention belongs to the field of high-level radioactive waste disposal technology research, specifically involving a simulation calculation method for predicting the geological disposal process of solidified radioactive waste. Background Technology

[0002] High-level radioactive waste originates from nuclear fuel production, nuclear power plant operation, and spent reactor fuel reprocessing. It is characterized by high radioactivity, high toxicity, long half-life, and high heat release rate, posing a long-term potential threat to humans and the natural environment.

[0003] The Law of the People's Republic of China on the Prevention and Control of Radioactive Pollution clearly stipulates that my country adopts the internationally recognized deep geological disposal technology route to treat high-level radioactive waste, which involves fixing radionuclides in host materials such as glass or mineral ceramics, and then burying them deep underground in disposal repositories 500-1000 meters away from the biosphere.

[0004] Currently, high-level radioactive waste is mainly solidified using glass, ceramics, and artificial rock as solidification substrates. The chemical stability of the solidified body is assessed using standard testing methods such as PCT (Standard Product Consistency) and MCC (Materials Characterization Center), with GB 7023-86 being the primary reference in China.

[0005] Standard testing methods such as PCT and MCC take about a month or less to complete. Such a timescale is insufficient to reflect the radionuclide migration behavior of solidified waste over thousands or even tens of thousands of years after the geological disposal repository is closed.

[0006] Therefore, based on existing experimental data, it is necessary to establish a numerical model of the evolution of radioactive waste solidification over a long time scale and the release and migration of radionuclides during the process. Summary of the Invention

[0007] The purpose of this invention is to provide a simulation calculation method for predicting the geological disposal process of solidified radioactive waste, thereby guiding the safety assessment of high-level radioactive waste geological disposal.

[0008] The objective of this invention is achieved through the following technical solution:

[0009] A simulation calculation method for predicting the geological disposal process of solidified radioactive waste includes the following steps:

[0010] Step 1: Establish a geometric model for deep geological disposal of radioactive waste solidification, including solidified body, buffer material, backfill material and surrounding rock, and satisfy the porous media assumption;

[0011] Step 2: meshing the geometric model and verifying mesh independence;

[0012] Step 3: establishing solid deformation control equations based on linear elasticity theory, and coupling temperature field and seepage pressure field;

[0013] Step 4: establishing fluid flow control equations based on Darcy's law, respectively describing saturated and unsaturated porous medium flow;

[0014] Step 5: establishing heat balance equations, taking the solidified body as a heat source and coupling fluid flow heat transfer;

[0015] Step 6: establishing nuclide migration equations, coupling convection, diffusion and chemical reaction mechanisms;

[0016] Step 7: importing the multi-physical field model of steps 3-6 into finite element software for coupled iterative solution until a converged solution is obtained.

[0017] Further, the geometric model in step 1 further includes a disposal tank.

[0018] Further, the solid deformation control equation in step 3 is:

[0019]

[0020] where C ijkl represents a fourth-order tensor; u i，kk , u k，ki represents displacement components; a T represents a thermal expansion coefficient; represents a Hamiltonian operator; T represents temperature a represents a specific coefficient; P represents fluid pressure; f i is a volume force component.

[0021] Further, the buffer material and backfill material in step 4 are initially in a non-saturated state, and the surrounding rock is in a saturated state; the fluid flow control equation is:

[0022]

[0023] The fluid mass conservation equation in the saturated porous medium is:

[0024]

[0025] The fluid mass conservation equation in the unsaturated porous medium is:

[0026]

[0027] where u w represents the flow rate of the fluid; k represents the permeability; and μ represents the dynamic viscosity of the fluid. represents the Hamiltonian operator; P represents fluid pressure; p represents fluid density; g represents gravitational acceleration; f represents porosity; Q s represents the fluid source term; S e represents the saturation of pore fluid in the porous medium.

[0028] Further, the saturation of pore fluid in the porous medium S e in the fluid mass conservation equation in the unsaturated porous medium

[0029]

[0030] where the pore fluid pressure head P represents fluid pressure; p represents fluid density; g represents gravitational acceleration; a v , n represents the VG model parameters.

[0031] Further, the solidified body in step 5 is regarded as a heat source, and the heat balance equation is:

[0032]

[0033] ( pC p ) eff = fS e pC + (1 - f) p s C s

[0034] b T = fS e b + (1 - f) b s

[0035] where ( pC p ) eff represents the equivalent volumetric heat capacity; T represents temperature; t represents time; f represents porosity; S e represents the saturation of pore fluid in the porous medium; p represents fluid density; C represents fluid specific heat capacity; u w represents the flow velocity of the fluid; represents the Hamiltonian operator; b T represents the equivalent heat transfer coefficient; Q r represents the heat source term; p s represents the density of the porous medium skeleton; C s represents the specific heat capacity of the porous medium skeleton; b represents the thermal conductivity of the fluid; b s represents the thermal conductivity of the porous medium skeleton.

[0036] Further, the nuclide migration equation in step 6 is:

[0037]

[0038] wherein c represents the nuclide dissolution concentration; t represents time; φ represents porosity; u w represents the flow rate of the fluid; ▽ represents the Hamiltonian operator; D represents the effective diffusion coefficient; R i represents the chemical reaction source term.

[0039] Further, the chemical reaction source term R i is determined by a solidification body leaching kinetics model, and the leaching kinetics model is:

[0040]

[0041] wherein rate is the leaching rate; A is a pre-exponential factor; E a is the reaction activation energy; k0 is the solidification body dissolution constant;

[0042] η is a constant describing the influence of pH value on the solidification body leaching; R is the gas constant; T represents temperature; r0 is the long-term dissolution constant; r(t) is the leaching rate of the leached element in the solidification body leaching process;

[0043] The accumulation amount m(t) of the leached element in the solidification body leaching process is:

[0044]

[0045] wherein k1, k2 and k3 are model parameters fitted.

[0046] Further, the step 7 obtains a converged solution including the temperature field of the solidification body, the disposal tank and the surrounding rock; the water pressure field and the saturation field of the buffer / backfill material; the seepage field water pressure; and the nuclide Cs concentration.

[0047] The present application has the following beneficial effects:

[0048] By using the high-level waste solidification body disposal process simulation calculation method disclosed by the present application, the solidification body disposal process in the high-level waste geological disposal can be simulated by a theoretical calculation method; the temperature change of the solidification body, the disposal tank, the buffer material, the backfill material and the surrounding rock and the water pressure and the saturation change of the buffer material, the backfill material and the surrounding rock in the simulation time range can be obtained; meanwhile, the leaching rate of the nuclide and the migration behavior thereof can be calculated; according to the simulation results, the high-level waste geological disposal safety evaluation work can be guided, the actual design and operation can be supported, the radioactive waste safety isolation can be effectively guaranteed, and the environmental risk can be reduced. BRIEF DESCRIPTION OF DRAWINGS

[0049] Figure 1 is the calculation flowchart of the present application;

[0050] Figure 2A two-dimensional geometric model diagram of the present application;

[0051] Figure 3 A geometric model meshing diagram;

[0052] Figure 4 A boundary condition diagram;

[0053] Figure 5 A temperature field result evolution diagram;

[0054] Figure 6 A buffer material and backfill material saturation evolution diagram;

[0055] Figure 7 A seepage field water pressure evolution diagram;

[0056] Figure 8 A radionuclide Cs concentration distribution evolution diagram. DETAILED DESCRIPTION

[0057] The present application is further described below in conjunction with the accompanying drawings.

[0058] The present application is a simulation calculation method for predicting the geological disposal process of a radioactive waste solidification body, and a calculation flowchart is shown in Figure 1 .

[0059] As shown in Figure 2 , the embodiment of the present application provides a two-dimensional geometric model for the geological disposal of a radioactive waste solidification body, which includes a solidification body, a disposal canister, a buffer material, a backfill material, and a surrounding rock.

[0060] The established geometric model is meshed by meshing software to form a mesh for computational fluid dynamics simulation, and mesh independence verification is combined to determine whether the mesh requirements are met. The meshing result is shown in Figure 3 , in which the mesh is divided using free triangular meshing, the maximum unit size is set to 52 mm, the minimum unit size is set to 0.6 mm, and a total of 93786 units are included.

[0061] The boundary conditions of the calculation model are shown in Figure 4 . The buffer material, backfill material, and surrounding rock meet the porous medium assumption, and the flow of seepage in the porous medium meets Darcy's law. The solidification body, disposal canister, buffer material, backfill material, and surrounding rock meet the linear elasticity theory.

[0062] The solid deformation equilibrium differential equation, i.e., the solid deformation control equation, is shown below:

[0063]

[0064] In the formula: C ijklis the fourth order tensor; u i,kk , u k,ki is the displacement component; α T is the thermal expansion coefficient; ▽ is the Hamiltonian operator; T represents the temperature; α is the Biot coefficient; P represents the fluid pressure; f i is the volume force component.

[0065] wherein -C ijkl α T ▽T embodies the influence of the temperature change on the deformation of the porous medium domain; -α▽P embodies the influence of the fluid seepage pressure on the deformation of the porous medium domain.

[0066] The fluid flow equation can be described by Darcy's law, assuming that the buffer material, backfill material is initially in a non-saturated state, the surrounding rock is in a saturated state, the fluid flow control equation:

[0067]

[0068] wherein u w represents the flow rate of the fluid; k is the permeability; μ is the dynamic viscosity of the fluid; ▽ is the Hamiltonian operator; P represents the fluid pressure; ρ is the fluid density; g is the acceleration of gravity.

[0069] The fluid mass conservation equation in the saturated porous medium is as follows:

[0070]

[0071] wherein φ is the porosity; ρ is the fluid density; t is the time; u w represents the flow rate of the fluid; ▽ is the Hamiltonian operator; Q s is the fluid source term, which is taken as 0 here.

[0072] The fluid mass conservation equation in the non-saturated porous medium is as follows:

[0073]

[0074] wherein S e is the saturation of the pore fluid in the porous medium; φ is the porosity; ρ is the fluid density; t is the time; u w represents the flow rate of the fluid; ▽ is the Hamiltonian operator; Q s is the fluid source term, which is taken as 0 here.

[0075] The change of the saturation of the pore fluid in the non-saturated porous medium can be described according to the Van Genuchten water retention curve model, and the VG model judges whether the material domain is in a saturated state through the positive and negative of the pore pressure P, and the VG model is as follows:

[0076]

[0077] where H p is the pore fluid pressure head; P represents fluid pressure; p is fluid density; g is gravitational acceleration; S e is the saturation of pore fluid in porous media; a v , n are the VG model parameters.

[0078] In the temperature field setting, the solidified body is regarded as a heat source. According to the basic law of thermodynamics, the temperature field control equation in the heat transfer process is as follows:

[0079]

[0080] ( pC p ) eff = fS e pC + (1-f)p s C s

[0081] b T = fS e b + (1-f)b s

[0082] where ( pC p ) eff is the equivalent volume heat capacity; T represents temperature; t is time; f is porosity; S e is the saturation of pore fluid in porous media; p is fluid density; C is the specific heat capacity of fluid; u w represents the flow rate of fluid; D is the Hamiltonian operator; b T is the equivalent heat transfer coefficient; Q r is the heat source term, which is taken as the evolution data of waste body heat release rate in the Japanese H12 report; p s is the density of the porous medium skeleton; C s is the specific heat capacity of the porous medium skeleton; b is the thermal conductivity of the fluid; b s is the thermal conductivity of the porous medium skeleton.

[0083] The accumulation amount of leached elements of the solidified body in the aqueous solution can be described by a semi-empirical mathematical model:

[0084]

[0085] where m(t) is the accumulation amount of leached elements of the solidified body in the leaching process, in g / m 2 ; t is time; the leaching amount can be obtained by leaching experiments meeting the national standard, and k1, k2 and k3 are fitting model parameters.

[0086] The derivative of the above formula with respect to time t is:

[0087]

[0088] wherein r(t) is the leaching rate of the leached element during the leaching of the solidified body, in g / (m2·s) 2 ·d).

[0089] The hydrolysis reaction kinetics of the solidified body can be described by the following formula:

[0090]

[0091] wherein rate is the leaching rate; A is the pre-exponential factor; E a is the reaction activation energy; k0 is the dissolution constant of the solidified body; η is a constant describing the influence of pH on the leaching of the solidified body; R is the gas constant; T represents the temperature; r0 is the long-term dissolution constant.

[0092] The above formula is set as the boundary condition of the solidified body to describe the migration of radionuclides, the evolution of the radioactive waste solidified body at a long time scale, and the migration of radionuclides during the process.

[0093] The migration process of the nuclide in the porous medium can be described by the following formula:

[0094]

[0095] wherein c is the dissolution concentration of the nuclide; t is time; φ is the porosity; u w represents the flow rate of the fluid; ▽ is the Hamiltonian operator; D is the effective diffusion coefficient; R i is the chemical reaction source term.

[0096] The above-established mathematical model is introduced into the finite element analysis software for iterative solution, so that the physical field cloud chart of the radioactive waste solidified body disposal process can be obtained, as shown in Figs. Figure 5 、 6 、7、8.

[0097] Figure 5 The temperature distribution of the calculation domain at the simulation time of 0.1, 1, 5, 10 and 50 years is shown.

[0098] Figure 6 The evolution of the saturation of the buffer material and the backfill material at the simulation time of 0.1, 1, 5, 10 and 20.3 years is shown, and the buffer material and the backfill material basically reach saturation when the simulation time reaches 20.3 years.

[0099] Figure 7 The fluid pressure change and the flow line of the calculation domain at the simulation time of 0.1, 1, 5, 10 and 20.3 years are shown.

[0100] Figure 8The Cs concentration distribution of the calculation domain at the simulation time of 0.1, 1, 5, 10 and 50 years is shown.

[0101] It can be seen from the above examples that the simulation and calculation method for predicting the dissolution behavior in the geological disposal process of a radioactive waste solidified body comprises the establishment and solving of temperature field, seepage field, mechanical field and chemical field models.

[0102] By using the calculation method of the present application, the mass conservation, momentum conservation and energy conservation theoretical models are comprehensively applied, and the geological disposal process of a radioactive waste solidified body is simulated by a numerical simulation method, thereby providing suggestions and guidance for the safety evaluation of high-level waste geological disposal.

[0103] The present application further provides a simulation and calculation system for predicting the geological disposal process of a radioactive waste solidified body, which comprises a memory, a processor and a computer program stored in the memory, and the processor executes the computer program to realize the steps of the simulation and calculation method for predicting the geological disposal process of a radioactive waste solidified body, which will not be described herein again.

[0104] The above only describes the preferred embodiments of the present application and is not used to limit the present application, and the present application can have various modifications and changes for those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method of predicting a simulation calculation in a geological disposal process of a solidified radioactive waste, characterized by: The method comprises the following steps: Step 1: establishing a geometric model of radioactive waste solidification body deep geological disposal including solidification body, buffer material, backfill material and surrounding rock, and satisfying the porous medium assumption; Step 2: meshing the geometric model and verifying the mesh independence; Step 3: establishing a solid deformation control equation based on the linear elasticity theory, and coupling the temperature field and the seepage pressure field; Step 4: establishing a fluid flow control equation based on the Darcy's law, and respectively describing the saturated and unsaturated porous medium flow; Step 5: establishing a heat balance equation, taking the solidification body as a heat source and coupling the fluid flow heat transfer; Step 6: establishing a nuclide migration equation, coupling the convection, diffusion and chemical reaction mechanisms; Step 7: importing the multi-physical field model of steps 3-6 into a finite element software for coupled iterative solution until a convergent solution is obtained.

2. The method of claim 1, wherein the method is characterized by: The geometric model in step 1 further comprises a disposal tank.

3. The method of claim 1, wherein the method is characterized by: The solid deformation control equation in step 3 is: Among them, C ijkl Represents a fourth-order tensor; u i,kk u k,ki Represents the displacement component; α T Indicates the coefficient of thermal expansion; The Hamiltonian operator is represented by T; temperature is represented by α; Biot coefficient is represented by P; and fluid pressure is represented by f. i This represents the volume force component.

4. The method of claim 1, wherein the method is characterized by: The buffer material and the backfill material in step 4 are initially in unsaturated state, and the surrounding rock is in saturated state; the fluid flow control equation is: The fluid mass conservation equation in the saturated porous medium is: The fluid mass conservation equation in the unsaturated porous medium is: where u w represents the flow rate of the fluid; k represents the permeability; μ represents the dynamic viscosity of the fluid; represents the Hamiltonian operator; P represents the fluid pressure; p represents the fluid density; g represents the gravitational acceleration; φ represents the porosity; Q s represents the fluid source term; S e represents the saturation of the pore fluid within the porous medium.

5. The method of claim 4, wherein the method is characterized by: The saturation S of the pore fluid within the porous medium in the fluid mass conservation equation in the non-saturated porous medium e : where the pore fluid pressure head P represents fluid pressure; p represents fluid density; g represents gravitational acceleration; a v , n represents the VG model parameters.

6. The method of claim 1, wherein: The solidification body is regarded as a heat source in step 5, and the heat balance equation is: (ρC p ) eff = φS e ρC+(1-φ)ρ s C s β T = φS e β + (1 - φ)β s where (pC p ) eff represents the equivalent volumetric heat capacity; T represents the temperature; t represents the time; φ represents the porosity; S e represents the saturation of the pore fluid within the porous medium; p represents the fluid density; C represents the specific heat capacity of the fluid; u w represents the flow velocity of the fluid; represents the Hamiltonian operator; β T represents the equivalent heat transfer coefficient; Q r represents the heat source term; p s represents the density of the porous medium skeleton; C s represents the specific heat capacity of the porous medium skeleton; β represents the thermal conductivity of the fluid; β s represents the thermal conductivity of the porous medium skeleton.

7. The method of claim 1, wherein: The nuclide migration equation in step 6 is: ​ where c denotes the nuclide solubility concentration; t denotes time; φ denotes porosity; u w denotes the flow rate of the fluid; denotes the Hamiltonian operator; D denotes the effective diffusion coefficient; R i denotes the chemical reaction source term.

8. The method of claim 7, wherein the method further comprises: determining a time period for the simulation; and determining a time period for the simulation of the waste package. said chemical reaction source term R i determined by a solidification body leaching kinetics model, said leaching kinetics model: where rate is the leaching rate; A is the pre-exponential factor; E is the activation energy for the reaction a k0 is the solubility constant of the solidified body; k is the rate constant of the reaction; η is the constant describing the effect of pH on the leaching of the solidified body; R is the gas constant; T indicates the temperature; r0 is the long-term solubility constant; r(t) is the leaching rate of the leached element during the leaching process of the solidified body; The accumulated amount m(t) of leaching elements in the solidification body leaching process is: Wherein, k1, k2 and k3 are fitting model parameters.

9. The method of claim 1, wherein: The convergent solution obtained in step 7 comprises: the temperature field of the solidification body, the disposal tank and the surrounding rock; the water pressure field and the saturation field of the buffer / backfill material; the seepage field water pressure; and the Cs concentration of radioactive nuclides. ​

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