Method for predicting effective diffusion coefficient of nuclide in bentonite

Abstract

The invention provides a method for predicting the effective diffusion coefficient of nuclides in bentonite. The method comprises the steps of obtaining a data set; the data set comprises the pH value of underground water; and constructing a nuclide effective diffusion coefficient model by using the data set, and predicting the effective diffusion coefficient of a certain radioactive element in bentonite by using the constructed nuclide effective diffusion coefficient model. According to the method provided by the invention, the prediction precision of the effective diffusion coefficient of the nuclide can be effectively improved.

Description

Technical Field

[0001] The invention relates to the technical field of high-level radioactive waste disposal, and in particular to a method for predicting the effective diffusion coefficient of nuclides in bentonite. Background Art

[0002] Bentonite is often selected as the backfill material for high-level radioactive waste disposal repositories, playing the role of isolating and delaying the migration and diffusion of radioactive nuclides. Due to the toxicity and long half-life of high-level radioactive waste, the design life of high-level radioactive waste disposal repositories is required to be no less than 10,000 years. High-level radioactive waste in the disposal environment is affected by a combination of factors such as heat, stress, microorganisms, groundwater, and chemistry. It is extremely difficult to predict the evolution and migration of radioactive nuclides in bentonite on a scale of thousands or tens of thousands of years.

[0003] The effective diffusion coefficient is a physical quantity that measures the migration and diffusion of radionuclides in mineral materials and is an important input parameter in the safety assessment of disposal repositories. This parameter is related to the properties of groundwater, the properties of the solid-liquid interface, the properties of the nuclides, and the physicochemical properties of bentonite. At present, the methods for predicting the effective diffusion coefficient of nuclides in bentonite include numerical simulation methods such as reaction transport model, pore scale model, molecular dynamics model, multi-porosity model and adsorption-diffusion model. However, the numerical simulation model involves a large amount of calculations under complex conditions and has low prediction efficiency. With the development of artificial intelligence, machine learning models have become an effective way to solve the problem of prediction efficiency. However, the current use of machine learning models to predict the effective diffusion coefficient of nuclides in bentonite has the problem of low prediction accuracy. Summary of the invention

[0004] The invention provides a method for predicting the effective diffusion coefficient of nuclides in bentonite, which is used to solve the defect that the prediction accuracy of the effective diffusion coefficient of nuclides in the prior art is not high enough.

[0005] A method for predicting the effective diffusion coefficient of nuclides in bentonite, comprising:

[0006] Acquire a data set; the data set includes a pH value of groundwater;

[0007] The data set is used to construct a nuclide effective diffusion coefficient model, and the constructed nuclide effective diffusion coefficient model is used to predict the effective diffusion coefficient of a certain radioactive element in bentonite.

[0008] Furthermore, in the above-mentioned method for predicting the effective diffusion coefficient of nuclides in bentonite, the data set also includes:

[0009] Compacted density of bentonite ρ d , montmorillonite content m, external specific surface area A ext 、Number of montmorillonite stacking layers n c , particle density ρ s , total porosity εtot ;

[0010] Groundwater temperature T, ionic strength I;

[0011] The partition coefficient K of the solid-liquid interface d , rock capacity factor α;

[0012] The ionic molar conductivity λ, ionic radius r, and diffusion coefficient D of a certain nuclide in water w , ion charge number z, molecular weight MW.

[0013] Furthermore, in the above-mentioned method for predicting the effective diffusion coefficient of nuclides in bentonite, the method of constructing a nuclide effective diffusion coefficient model using the data set, and predicting the effective diffusion coefficient of a radioactive element in bentonite using the constructed nuclide effective diffusion coefficient model includes:

[0014] Step 1: Use the PSO-LightGBM model to build a pH prediction model, and use the constructed pH prediction model to predict the groundwater pH value;

[0015] Step 2: adding the predicted groundwater pH value to the data set to obtain an updated data set;

[0016] Step three: using the updated data set to calibrate the nuclide effective diffusion coefficient model, and using the calibrated nuclide effective diffusion coefficient model to predict the effective diffusion coefficient of a radioactive element in bentonite.

[0017] Furthermore, in the above-mentioned method for predicting the effective diffusion coefficient of nuclides in bentonite, before constructing the effective diffusion coefficient model of nuclides, the data of the data set is first preprocessed, and the effective diffusion coefficient model of nuclides is constructed using the preprocessed data.

[0018] Furthermore, according to the above-mentioned method for predicting the effective diffusion coefficient of nuclides in bentonite, the total porosity ε of bentonite tot The calculation formula is as follows:

[0019]

[0020] Among them, ρ d represents the compacted density of bentonite, ρ s Indicates the particle density of bentonite.

[0021] Furthermore, according to the above-mentioned method for predicting the effective diffusion coefficient of nuclides in bentonite, the calculation formula of the ionic molar conductivity λ of the nuclides is as follows:

[0022]

[0023] Among them, Dw represents the diffusion coefficient of the nuclide in water, F represents the Faraday constant, z represents the charge number of the ion, R represents the molar gas constant, and T represents the temperature.

[0024] Furthermore, according to the above-mentioned method for predicting the effective diffusion coefficient of nuclides in bentonite, the calculation formula of the ionic radius r of the nuclide is as follows:

[0025]

[0026] Where k represents the Boltzmann constant, η represents the viscosity of the medium, T represents the temperature, and D w Represents the diffusion coefficient of the nuclide in water.

[0027] Furthermore, in the above-mentioned method for predicting the effective diffusion coefficient of nuclides in bentonite, the pH value prediction model adopts the determination coefficient R 2 , mean absolute error MAE, mean square error MSE and root mean square error RMSE to evaluate its performance:

[0028]

[0029]

[0030] Among them, y i exp is the experimentally measured effective diffusion coefficient, y i pred is the effective diffusion coefficient calculated by the model, y ave exp is the average effective diffusion coefficient measured experimentally.

[0031] The method for predicting the effective diffusion coefficient of nuclides in bentonite provided by the present invention uses the PSO-LightGBM regression interpolation method to predict the array that does not contain the pH value, so that the number of arrays containing the pH value is effectively expanded, and then the expanded array is used to construct a nuclide effective diffusion coefficient model, and the trained nuclide effective diffusion coefficient model is used to predict the effective diffusion coefficient of nuclides in a high-level waste disposal repository, which can effectively improve the prediction accuracy of the effective diffusion coefficient of nuclides. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0033] Figure 1It is a schematic flow chart of the method for predicting the effective diffusion coefficient of nuclides in bentonite provided by the present invention. DETAILED DESCRIPTION

[0034] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the drawings of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0035] The geological repository for high-level radioactive waste adopts a "multiple barrier" design, including disposal tanks, backfill materials and natural clay. Different barriers have different migration and diffusion rates of nuclides. Bentonite is the backfill material of the geological repository for high-level radioactive waste and is the last artificial barrier to block the diffusion of nuclides. The purpose of this invention is to evaluate the diffusion state of backfill materials blocking nuclides.

[0036] Figure 1 The flow chart of the method for predicting the effective diffusion coefficient of nuclides in bentonite provided by the present invention is as follows: Figure 1 As shown, the method includes:

[0037] Step 1: Acquire a data set; the data set includes the pH value of groundwater.

[0038] Specifically, the data set is used to construct a nuclide effective diffusion coefficient model. The data set includes various parameters related to the physicochemical properties of bentonite, groundwater properties, solid-liquid interface properties, and nuclide properties. The input of the nuclide effective diffusion coefficient model is the pH value of the groundwater and other parameters that affect the nuclide effective diffusion coefficient model, and the output is the effective diffusion coefficient.

[0039] Among them, the pH value of groundwater affects the properties of nuclides and the properties of the solid-liquid interface, and the properties of nuclides and the properties of the solid-liquid interface play a vital role in the prediction of the effective diffusion coefficient. Therefore, the present invention predicts the effective diffusion coefficient of nuclides by adding the parameter of the pH value of groundwater, which can effectively improve the prediction accuracy of the model.

[0040] Step 2: construct a nuclide effective diffusion coefficient model using the data set, and use the constructed nuclide effective diffusion coefficient model to predict the effective diffusion coefficient of a certain radioactive element in bentonite.

[0041] Specifically, different radioactive elements have different nuclide effective diffusion coefficients, and different radioactive elements have correspondingly different solid-liquid interface properties and nuclide properties. Therefore, by inputting parameters related to the target radioactive element into the model, the effective diffusion coefficient of the target radioactive element can be obtained.

[0042] The method for predicting the effective diffusion coefficient of nuclides in bentonite provided by the present invention constructs a data set through the parameter of the pH value of groundwater, and uses the data set to train a nuclide effective diffusion coefficient model, so that the trained nuclide effective diffusion coefficient model can more accurately predict the nuclide effective diffusion coefficient.

[0043] Furthermore, the relevant parameters involved in the physicochemical properties of bentonite include: the compaction density of bentonite ρ d , montmorillonite content m, external specific surface area A ext 、Number of montmorillonite stacking layers n c , particle density ρ s , total porosity ε tot The relevant parameters involved in the groundwater properties include: groundwater temperature T, ionic strength I, and pH value.

[0044] The relevant parameters involved in the solid-liquid interface include: the distribution coefficient K of the solid-liquid interface d , rock capacity factor α.

[0045] The relevant parameters of the nuclide include: ionic molar conductivity λ, ionic radius r, diffusion coefficient D of a certain nuclide in water w , ion charge number z, molecular weight MW.

[0046] Furthermore, the step 2 specifically includes the following steps:

[0047] Step 21: Use the PSO-LightGBM model to build a pH prediction model, and use the constructed pH prediction model to predict the groundwater pH value.

[0048] Specifically, the machine learning model is a model based on data modeling, which can make regression predictions. The premise of regression prediction is to have a database with enough data. A large amount of experimental data can be collected in professional databases and literature databases to provide data sets for the application of machine learning models. However, the current professional databases and literature databases lack reports on the parameter of groundwater pH value, which makes the number of samples in the current database that can construct the effective diffusion coefficient model of nuclides relatively small, and the small number of samples will lead to the reduction of the accuracy of the model predicting the effective diffusion coefficient of nuclides. In order to solve this problem, the present application first uses the PSO-LightGBM regression interpolation method to supplement the pH value data set and increase the number of samples in the data set. Then all parameters containing pH value are used as the data set for constructing the effective diffusion coefficient model of nuclides.

[0049] Specifically, since there are 316 arrays containing pH values ​​in the original data set, the number of samples is relatively low. If only this data set is used to build the model, the accuracy of the model prediction will not be ideal. Therefore, it is necessary to expand the number of arrays in the data set. The way to expand is to use the PSO-LightGBM regression interpolation method to supplement the array that does not contain the pH value and predict the pH value corresponding to the array. Then add the array with the predicted pH value to the data set, so that the number of arrays in the data set is updated and expanded. Finally, the updated data set is used to build the effective diffusion coefficient model of the nuclide.

[0050] The method of constructing the pH value prediction model is as follows: d , temperature T, ionic strength I, diffusion coefficient of ions in water D w , ion charge number z, molecular weight MW, distribution coefficient K d , montmorillonite content m, external specific surface area A ext , particle density ρ s , total porosity ε tot , rock capacity factor α, ion molar conductivity λ, ion radius r, number of montmorillonite stacking layers n c As the input parameter of the pH value prediction model, pH is taken as the output parameter of the model.

[0051] In order to predict pH value and improve the number of samples, the present invention divides 316 data sets containing pH values ​​into training sets, validation sets and test sets, and obtains the best pH value prediction model through training with the training set. The pH value prediction model is constructed using the PSO-LightGBM model, thereby filling the problem of reduced sample number caused by the lack of pH value.

[0052] Step 22: adding the predicted groundwater pH value to the data set to obtain an updated data set;

[0053] Step 23: calibrate the nuclide effective diffusion coefficient model using the updated data set, and use the calibrated nuclide effective diffusion coefficient model to predict the effective diffusion coefficient of a radioactive element in bentonite.

[0054] Specifically, in order to predict the effective diffusion coefficient of nuclides, the present invention divides the data set into a training set, a validation set and a test set, optimizes the hyperparameters, and uses a random forest algorithm to construct a nuclide effective diffusion coefficient model. Cross-validation is used to evaluate the robustness of the model and obtain the optimal nuclide effective diffusion coefficient model. The hyperparameter optimization method uses a particle swarm optimization algorithm (PSO). Cross-validation uses a 5-fold cross-validation.

[0055] The performance evaluation method is: determination coefficient (R 2), mean absolute error (MAE), mean square error (MSE) and root mean square error (RMSE).

[0056]

[0057]

[0058] Here i exp is the experimentally measured effective diffusion coefficient, y i pred is the effective diffusion coefficient calculated for the model. ave exp is the average effective diffusion coefficient measured experimentally.

[0059] The present invention collects nuclide diffusion experimental data from professional databases and literature databases, and the input parameters include bentonite physicochemical properties, groundwater properties, solid-liquid interface properties and nuclide properties, which are used as data sets for constructing the effective diffusion coefficient model of nuclides. Professional databases include: the nuclide diffusion database of the Japan Atomic Energy Agency, Web of Science, China National Knowledge Infrastructure, and Wanfang Database.

[0060] Furthermore, before constructing the nuclide effective diffusion coefficient model, the present invention first preprocesses the data of the data set, and constructs the pH value prediction model with the preprocessed data.

[0061] Specifically, the present invention preprocesses the data set in the following manner: normalize the data set and use the Mahalanobis distance method to remove outliers.

[0062] The normalized formula is as follows:

[0063]

[0064] Among them, x normal is the result of normalizing a certain eigenvalue, x min and x max Represent the minimum and maximum values ​​of the eigenvalue respectively.

[0065] The Mahalanobis distance formula is:

[0066]

[0067] Where C, Xi and μ are the sample covariance matrix, target vector and arithmetic mean vector respectively. i Set to 6 to ensure that all data have a skewness less than 10.

[0068] Furthermore, the total porosity of bentonite ε tot The formula is as follows:

[0069]

[0070] Among them, ρ d (kg / m 3 ) represents the compacted density of bentonite, ρ s (kg / m 3 ) represents the particle density of bentonite.

[0071] Furthermore, the relationship between rock capacity factor α and porosity (ε) can be expressed as:

[0072] α=ε+K d ·ρ d , (8)

[0073] When the distribution coefficient of the radionuclide K d >0, ε=ε tot . And K d = 0, porosity ε = 1-0.39·ρ d .

[0074] Furthermore, the calculation formula of ionic molar conductivity λ is as follows:

[0075]

[0076] Among them, D w (m 2 / s) represents the diffusion coefficient of the nuclide in water, F represents the Faraday constant, z(-) represents the charge number of the ion, R represents the molar gas constant, and T(K) represents the temperature.

[0077] Furthermore, the calculation formula of the ionic radius r is as follows:

[0078]

[0079] Here k represents the Boltzmann constant and η represents the viscosity of the medium.

[0080] Furthermore, the montmorillonite stacking number n c The calculation formula is as follows:

[0081]

[0082] N A (6.022×10 -23 molecules / mol) represents Avogadro's constant, MW represents the molecular weight of montmorillonite, A ext (m 2 / g) represents the external specific surface area of ​​bentonite, where a×b×c*=0.523×0.905×0.96nm 3 , n a =nb =200.

[0083] Example 1

[0084] Based on the nuclide diffusion database of the Japan Atomic Energy Agency and according to the input parameter characteristics of the database, the nuclide diffusion experimental data published in Web of Science, China National Knowledge Infrastructure, and Wanfang database were collected to create a dataset.

[0085] The PSO-LightGBM algorithm is used for regression interpolation to improve the missing pH value in the data set. There are 15 input parameters, namely: compaction density ρ d , temperature T, ionic strength I, diffusion coefficient of ions in water D w , ion charge number z, molecular weight MW, distribution coefficient K d , montmorillonite content m, external specific surface area A ext , particle density ρ s , total porosity ε tot , rock capacity factor α, ion molar conductivity λ, ion radius r, number of montmorillonite stacking layers n c The output parameter is: pH. The description of the data set of the regression prediction method for 316 samples is shown in Table 1:

[0086]

[0087] The 316 samples were divided into training set and test set in a ratio of 8:2, and then normalized and cleaned.

[0088] PSO was used for hyperparameter optimization to train the LightGBM model to predict pH value, and the MAE of the test set with five-fold cross validation was obtained. cv is 0.28, MSE cv The RMSE is 0.33. cv is 0.57 and R 2 cv It is 0.88.

[0089] Furthermore, the optimal hyperparameters of the PSO-LightGBM algorithm are: Num_leaves = 30; Max_depth = -1, Learning_rate = 0.01; Min_data_in_leaf = 3; Feature_fraction = 0.4; Bagging_freq = 30; Bagging_seed = 1; Bagging_fraction = 0.75; Lambda_l1 = 0.01; Lambda_l2 = 0.03. The optimal test set results are: MAE is 0.24, MSE is 0.23, RMSE is 0.48 and R2 It is 0.92.

[0090] After regression interpolation, the number of samples increased to 813. The input parameters increased to pH value, a total of 16 input parameters, namely: compaction density ρ d , temperature T, ionic strength I, diffusion coefficient of ions in water D w , ion charge number z, molecular weight MW, distribution coefficient K d , montmorillonite content m, external specific surface area A ext , particle density ρ s , total porosity ε tot , rock capacity factor α, ion molar conductivity λ, ion radius r, number of montmorillonite stacking layers n c , pH value. Output parameters are: effective diffusion coefficient D e The dataset description is shown in Table 2:

[0091]

[0092]

[0093] The 813 samples were divided into training set and test set in a ratio of 8:2, and then normalized and cleaned.

[0094] PSO is used for hyperparameter optimization to train the RF model to predict the effective diffusion coefficient, and the five-fold cross-validation test set is: MAE cv is 0.12, MSE cv is 0.04, RMSE cv is 0.21 and R 2 cv It is 0.82.

[0095] Furthermore, the optimal hyperparameters of the PSO-RF algorithm are: N_estimators = 85; Max_depth = 10, Max_features = "auto"; Min_samples_split = 5; Min_samples_leaf = 1; Min_weight_fraction_leaf = 0.01; Random_state = 57. The optimal test set results are: MAE is 0.11, MSE is 0.04, RMSE is 0.19 and R 2 It is 0.84.

[0096] The present invention uses the through-diffusion method to measure HCrO4 in Wyoming bentonite. - The effective diffusion coefficient of bentonite was 1200kg / m 3 -1800kg / m3 The influence of the effective diffusion coefficient under the conditions is shown in Table 3.

[0097]

[0098] The background solution in the diffusion experiment was 0.5 mol / L NaCl, pH 6.8 ± 0.1, and the initial concentration was 1.8 × 10 - 3 mol / L, temperature is 15±3℃.

[0099] Particle density of Wyoming bentonite ρ s 2760kg / m 3 , montmorillonite content m is 0.85, external specific surface area A ext 49m 2 / g. HCrO4 - The diffusion coefficient in water is 1.13×10 -9 m 2 / s, distribution coefficient K d 0m 3 / kg. The predicted HCrO4 in the compacted Wyoming bentonite in this example - The effective diffusion coefficients are shown in Table 3.

[0100] The embodiment of the present invention adopts the PSO-LightGBM model to predict the missing pH value. This regression interpolation technology supplements the pH value with the most missing data, and establishes a nuclide diffusion database with 16 input parameters and 813 samples. On this basis, a high-precision prediction model for the effective diffusion coefficient of nuclides in bentonite is obtained, which can more accurately predict the effective diffusion coefficient of a certain radioactive nuclide for use in the safety rating work of high-level waste geological disposal repositories.

[0101] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting the effective diffusion coefficient of nuclides in bentonite, characterized in that: include: Get the dataset; The data set includes pH values ​​of groundwater; The data set is used to construct a nuclide effective diffusion coefficient model, and the constructed nuclide effective diffusion coefficient model is used to predict the effective diffusion coefficient of a certain radioactive element in bentonite.

2. The method for predicting the effective diffusion coefficient of nuclides in bentonite according to claim 1, characterized in that: The dataset also includes: Compacted density of bentonite ρ d , montmorillonite content m, external specific surface area A ext 、Number of montmorillonite stacking layers n c , particle density ρ s , total porosity ε tot ; Groundwater temperature T, ionic strength I; The partition coefficient K of the solid-liquid interface d , rock capacity factor α; The ionic molar conductivity λ, ionic radius r, and diffusion coefficient D of a certain nuclide in water w , ion charge number z, molecular weight MW.

3. The method for predicting the effective diffusion coefficient of nuclides in bentonite according to claim 2, characterized in that: The method of constructing a nuclide effective diffusion coefficient model using the data set and predicting the effective diffusion coefficient of a radioactive element in bentonite using the constructed nuclide effective diffusion coefficient model includes: Step 1: Use the PSO-LightGBM model to build a pH prediction model, and use the constructed pH prediction model to predict the groundwater pH value; Step 2: adding the predicted groundwater pH value to the data set to obtain an updated data set; Step three: using the updated data set to calibrate the nuclide effective diffusion coefficient model, and using the calibrated nuclide effective diffusion coefficient model to predict the effective diffusion coefficient of a radioactive element in bentonite.

4. The method for predicting the effective diffusion coefficient of nuclides in bentonite according to claim 1, characterized in that: Before constructing the nuclide effective diffusion coefficient model, the data of the data set is firstly preprocessed, and the nuclide effective diffusion coefficient model is constructed with the preprocessed data.

5. The method for predicting the effective diffusion coefficient of nuclides in bentonite according to claim 2, characterized in that: Total porosity of bentonite ε tot The calculation formula is as follows: Among them, ρ d represents the compacted density of bentonite, ρ s Indicates the particle density of bentonite.

6. The method for predicting the effective diffusion coefficient of nuclides in bentonite according to claim 2, characterized in that: The calculation formula of the ionic molar conductivity λ of the nuclide is as follows: Among them, D w represents the diffusion coefficient of the nuclide in water, F represents the Faraday constant, z represents the charge number of the ion, R represents the molar gas constant, and T represents the temperature.

7. The method for predicting the effective diffusion coefficient of nuclides in bentonite according to claim 2, characterized in that: The formula for calculating the ionic radius r of a nuclide is as follows: Where k represents the Boltzmann constant, η represents the viscosity of the medium, T represents the temperature, and D w Represents the diffusion coefficient of the nuclide in water.

8. The method for predicting the effective diffusion coefficient of nuclides in bentonite according to claim 3, characterized in that: The pH value prediction model uses the determination coefficient R 2 , mean absolute error MAE, mean square error MSE and root mean square error RMSE to evaluate its performance: Among them, y i exp is the experimentally measured effective diffusion coefficient, y i pred is the effective diffusion coefficient calculated by the model, y ave exp is the average effective diffusion coefficient measured experimentally.

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