Method for determining thermal power of isotope heat source

Abstract

The present application provides a method for determining the thermal power of an isotope heat source, which can be applied to the field of spent fuel reprocessing technology. The method includes: calibrating a calorimeter using an electrically heated standard sample; measuring the thermal power of the isotope heat source using the calibrated calorimeter to obtain a first thermal power value and a first uncertainty of the isotope heat source; analyzing the composition of the isotope heat source; calculating a second thermal power value of the isotope heat source and a second uncertainty corresponding to the second thermal power value based on the composition of the isotope heat source; and determining the thermal power of the isotope heat source based on the first thermal power value and the second thermal power value, when the first thermal power value and the second thermal power value, as well as the first uncertainty and the second uncertainty, match.

Description

Technical Field

[0001] The present application relates to the technical field of spent fuel reprocessing, and more specifically to a method for determining the thermal power of an isotope heat source. Background Art

[0002] Spent fuel, also known as irradiated nuclear fuel, is nuclear fuel used within a reactor. Reprocessing of spent fuel is a step in the final stage of the nuclear fuel cycle and the most widely used method for disposing of spent fuel discharged from nuclear reactors. Reprocessing allows for timely assessment of the dynamic inventory and fate of nuclear materials, maximizing resource utilization. During spent fuel reprocessing, ensuring the closed balance of reprocessing facilities requires the use of highly accurate and precise measuring instruments and methods to minimize errors. Therefore, precise calibration and calibration of measuring instruments, such as calorimeters, can improve the accuracy of measurement results and enhance the reliability of the resulting treatment measures.

[0003] Instrument calibration typically uses isotope standard heat sources or electrically heated standard samples (electric weights). Isotope standard heat sources, in particular, offer high thermal power stability due to their isotope decay, which is unaffected by the external environment. This makes them ideal measuring tools for calibration. However, calibration requires first determining the thermal power of the isotope standard heat source. The related art of determining the thermal power of isotope heat sources is complex and costly. Summary of the Invention

[0004] In view of the above problems, the present application provides a method for determining the thermal power of an isotope heat source, in order to at least partially solve the above technical problems.

[0005] An embodiment of the present application provides a method for determining the thermal power of an isotope heat source, comprising: calibrating a calorimeter using an electrically heated standard sample to obtain a calibrated calorimeter; measuring the thermal power of the isotope heat source using the calibrated calorimeter to obtain a first thermal power value of the isotope heat source and a first uncertainty corresponding to the first thermal power value; calculating a second thermal power value of the isotope heat source and a second uncertainty corresponding to the second thermal power value based on the composition of the isotope heat source; and determining the thermal power of the isotope heat source based on the first thermal power value and the second thermal power value when the first thermal power value and the second thermal power value and the first uncertainty and the second uncertainty match.

[0006] According to the method for determining the thermal power of an isotope heat source provided in an embodiment of the present application, the thermal power of the isotope heat source is determined by using the calorimetry method and the composition analysis method respectively, and the results obtained by the two methods are compared and mutually verified. If the comparison and mutual verification are passed, the thermal power of the isotope heat source can be determined. Thus, while meeting the current accuracy requirements for isotope heat sources, the costly process of high purification and enrichment of isotope products required in related technologies when determining the thermal power of isotope heat sources is eliminated, thereby achieving the technical effect of reducing process costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] The above contents and other objects, features and advantages of the present application will become more apparent through the following description of the embodiments of the present application with reference to the accompanying drawings, in which:

[0008] Figure 1 A system structure diagram schematically illustrates a method for determining the thermal power of an isotope heat source according to an embodiment of the present application;

[0009] Figure 2 The flowchart of the method for determining the thermal power of an isotope heat source according to an embodiment of the present application is schematically shown.

[0010] It should be noted that the drawings are not necessarily drawn to scale, but are merely shown in a schematic manner that does not affect the reader's understanding. DETAILED DESCRIPTION

[0011] Hereinafter, embodiments of the present application will be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the present application. In the detailed description below, for ease of explanation, many specific details are set forth to provide a comprehensive understanding of the embodiments of the present application. However, it is apparent that one or more embodiments may also be implemented without these specific details. In addition, in the following description, descriptions of known structures and technologies are omitted to avoid unnecessarily confusing the concepts of the present application.

[0012] The terms used herein are only for describing specific embodiments and are not intended to limit this application. The terms "comprise", "include" and the like used herein indicate the presence of the features, steps, operations and / or components, but do not exclude the presence or addition of one or more other features, steps, operations or components. All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein should be interpreted as having meanings consistent with the context of this specification and should not be interpreted in an idealized or overly rigid manner.

[0013] In spent fuel reprocessing facilities, the flux of nuclear materials such as uranium and plutonium is high. The deeper the spent fuel burnup, the greater the plutonium content. Assuming a reprocessing facility with a spent fuel burnup of 33,000 MWt / Tu and an annual processing capacity of 200 tons, the plutonium 2δMUF (Material Unaccounted For) within a six-month accounting cycle would be approximately 20 kg. This value is far greater than the significant amount of nuclear material, necessitating the processing of this nuclear fuel to monitor its dynamics in real time and maximize resource utilization. Implementing technical monitoring and control of the fuel facilitates timely detection of its dynamic inventory and material flow, enabling the timely identification of abnormal operating conditions and illicit transfers of concern to nuclear security plans.

[0014] The δMUF used in nuclear material accountancy at spent fuel reprocessing facilities is primarily determined by the random and systematic errors of the various measuring and analytical instruments. To ensure closed-ended accountancy at reprocessing facilities, selecting highly accurate and precise measuring instruments and methods is fundamental to minimizing these errors. Furthermore, to ensure the precision and accuracy of these instruments and methods, they must be calibrated and calibrated using reference materials traceable to international standards. Reference materials, as the "measuring tools" of the analytical measurement industry, play an indispensable role in calibrating measuring instruments and devices, evaluating measurement and analytical methods, measuring nuclear material characteristics, and controlling product quality during the production process.

[0015] Nondestructive assay (NDA) technology is widely used in nuclear material accountancy, primarily encompassing three categories: energy spectrum measurement, neutron signal measurement and analysis, and calorimetry. To ensure the accuracy of measurement results, NDA measurement systems used in nuclear material accountancy and nuclear security regulation require the use of certified reference materials (CRMs) or working reference materials (WRMs) for calibration, verification, and verification. This allows for instrument performance verification, quality control of the measurement process, and traceability of results.

[0016] Isotope standard heat sources are excellent measuring instruments for calibrating calorimeters because their isotope decay is unaffected by the external environment, resulting in highly stable thermal power. However, determining the thermal power of an isotope standard heat source generally requires complex technical means. This typically requires purification or even enrichment of the isotopes, followed by determination of their composition and abundance through detection methods such as mass spectrometry. Finally, the thermal power value and uncertainty of the isotope heat source are calculated based on the isotope feed amount and decay heat. This method is costly, particularly due to the high purification and enrichment of the isotope product.

[0017] In view of this, an embodiment of the present application provides a method for determining the thermal power of an isotope heat source, which is used to simplify the process flow and reduce process costs while meeting the current accuracy requirements for isotope standard heat sources. Specifically, the method includes: calibrating a calorimeter using an electrically heated standard sample to obtain a calibrated calorimeter; measuring the thermal power of the isotope heat source using the calibrated calorimeter to obtain a first thermal power value and a first uncertainty of the isotope heat source; analyzing the composition of the isotope heat source; calculating the second thermal power value and the second uncertainty of the isotope heat source based on the composition of the isotope heat source; and determining the thermal power of the isotope heat source based on the first thermal power value and the second thermal power value when the first thermal power value and the second thermal power value, as well as the first uncertainty and the second uncertainty, all match.

[0018] Figure 1 The system structure diagram of the method for determining the thermal power of an isotope heat source according to an embodiment of the present application is schematically shown.

[0019] like Figure 1 As shown, the system according to this embodiment may include an isotope heat source 101 , an electrically heated standard sample 102 , a calorimeter 103 , a component analysis device 104 , and a processor 105 .

[0020] Isotope heat source 101 can be an isotope standard heat source, such as a plutonium-238 nuclide standard heat source. Electrically heated standard sample 102 can be understood as an electric weight and can be used to calibrate calorimeter 103. Optionally, there can be multiple electrically heated standard samples, such as 0.01W, 0.02W, 0.05W, 0.1W, 0.2W, 0.5W, 1.0W, 2.0W, 5.0W, etc.

[0021] The calorimeter 103 can be used to measure the thermal power of the isotope heat source to obtain a first thermal power value, and the processor 105 can determine a first uncertainty based on the first power value.

[0022] The component analysis device 104 may be configured to analyze the components of the isotope heat source, specifically, the nuclides contained in the isotope heat source and the content of each nuclide. The processor 105 may determine the second thermal power value and the second uncertainty of the isotope heat source based on the components of the isotope heat source.

[0023] After obtaining the first thermal power value, the first uncertainty, the second thermal power value, and the second uncertainty of the isotope heat source, the processor 105 may compare the first thermal power value with the second thermal power value, and the first uncertainty and the second uncertainty, respectively. If the first thermal power matches the second thermal power, and both the first uncertainty and the second uncertainty match, the thermal power of the isotope heat source is determined based on the first thermal power value and the second thermal power value.

[0024] It should be understood that Figure 1 The number of isotope heat sources 101, electrically heated standard samples 102, calorimeters 103, component analysis devices 104, and processors 105 is merely illustrative. Any number of isotope heat sources 101, electrically heated standard samples 102, calorimeters 103, component analysis devices 104, and processors 105 may be provided as needed.

[0025] The following will be based on Figure 1 The system structure described by Figure 2 The method for determining the thermal power of the isotope heat source in the embodiment of the present application is described in detail.

[0026] Figure 2 The flowchart of the method for determining the thermal power of an isotope heat source according to an embodiment of the present application is schematically shown.

[0027] like Figure 2 As shown, the method for determining the thermal power of the isotope heat source in this embodiment includes operations S201 to S205.

[0028] In operation S201 , a calorimeter is calibrated using an electrically heated standard sample to obtain a calibrated calorimeter.

[0029] In operation S202 , the thermal power of the isotope heat source is measured using a calibrated calorimeter to obtain a first thermal power value of the isotope heat source and a first uncertainty corresponding to the first thermal power value.

[0030] In operation S203 , the composition of the isotope heat source is analyzed.

[0031] In operation S204 , a second thermal power value of the isotope heat source and a second uncertainty corresponding to the second thermal power value are calculated according to the composition of the isotope heat source.

[0032] In operation S205 , when the first thermal power value and the second thermal power value and the first uncertainty and the second uncertainty all match, the thermal power of the isotope heat source is determined according to the first thermal power value and the second thermal power value.

[0033] According to the embodiments of the present application, the method for calibrating the calorimeter using an electrically heated standard sample is not limited. For example, the calorimeter can be automatically calibrated using an automated program or automated device using an electrically heated standard sample; or, the calorimeter can be calibrated manually using an electrically heated standard sample according to a preset calibration method.

[0034] According to the embodiments of the present application, electric heating standard samples are used to calibrate the calorimeter. For example, electric heating plates, electric heating elements, and other samples with clear thermal power or thermal power scales can be selected. The scales of the electric heating standard samples used in the embodiments of the present application can include 0.01W, 0.02W, 0.05W, 0.1W, 0.2W, 0.5W, 1.0W, 2.0W, 5.0W, etc.

[0035] According to an embodiment of the present application, the calibrated calorimeter can measure the thermal power of the isotope heat source, and the obtained thermal power value is used as the first thermal power value.

[0036] Since the electric heating standard sample itself may have errors in actual measurements, that is, it also has sample uncertainty, there will be a certain calibration error when using the electric heating standard sample to calibrate the calorimeter. This will cause the calorimeter to have measurement errors when measuring thermal power, resulting in the measurement uncertainty of the calorimeter, namely Class A uncertainty. Class A uncertainty refers to the uncertainty obtained by statistical analysis of the observation series. Class A uncertainty is based on repeatability or reproducibility tests, and the results are more real, objective, and convincing. By combining the sample uncertainty of the electric heating standard sample itself and the measurement uncertainty of the calorimeter, the first uncertainty can be obtained.

[0037] According to the embodiments of the present application, when analyzing the composition of an isotope heat source, the composition analysis methods used may include isotope dilution analysis, mass spectrometry, solution density calibration, thermal ion mass spectrometry, secondary ion mass spectrometry, etc.

[0038] According to an embodiment of the present application, an isotope heat source may contain multiple nuclides. For example, a plutonium isotope heat source may contain plutonium-236, plutonium-238, plutonium-239, plutonium-240, plutonium-241, and americium-241. The above-mentioned composition analysis method can be used to measure the content of each nuclide, and thus the thermal power and uncertainty of each nuclide can be calculated based on the content of each nuclide.

[0039] According to an embodiment of the present application, the second power value of the isotope heat source may be obtained by synthesizing the thermal power value of each nuclide. The uncertainty of the isotope heat source may be obtained by synthesizing the uncertainty of the thermal power of each nuclide.

[0040] According to an embodiment of the present application, the first thermal power value and the second thermal power value, the first uncertainty, and the second uncertainty of the isotope heat source are compared. If the first thermal power value and the second thermal power value match, and the first uncertainty and the second uncertainty both match, the thermal power value of the isotope heat source can be determined based on the average of the first thermal power value and the second thermal power value. Similarly, the uncertainty of the thermal power of the isotope heat source can be determined by averaging the first uncertainty and the second uncertainty.

[0041] According to the method for determining the thermal power of an isotope heat source provided in an embodiment of the present application, the thermal power of the isotope heat source is determined by using the calorimetry method and the composition analysis method respectively, and the results obtained by the two methods are compared and mutually verified. If the comparison and mutual verification are passed, the thermal power of the isotope heat source can be determined. Thus, while meeting the current accuracy requirements for isotope heat sources, the costly process of high purification and enrichment of isotope products required in related technologies when determining the thermal power of isotope heat sources is eliminated, thereby achieving the technical effect of reducing process costs.

[0042] According to an embodiment of the present application, the thermal power of the electrically heated standard sample itself has a sample uncertainty. Based on this, operation S202 may also include the following operations: when calibrating the calorimeter using the electrically heated standard sample, determining the sample uncertainty corresponding to the thermal power of the electrically heated standard sample; determining the measurement uncertainty of the calorimeter based on the first thermal power value; and synthesizing the first uncertainty of the isotope heat source based on the sample uncertainty and the measurement uncertainty.

[0043] Specifically, when calibrating the calorimeter using an electrically heated standard sample, the electrically heated standard sample can be connected in series with a standard resistor, and then the sample uncertainty can be determined based on the voltage of the electrically heated standard sample, the voltage of the standard resistor, and the resistance value of the standard resistor during calibration.

[0044] According to the embodiment of the present application, when calibrating the calorimeter using an electrically heated standard sample, a voltage is applied to both ends of the electrically heated standard sample, and the voltage component applied to the electrically heated standard sample is U 加载 When the electric heating standard sample is heated to a certain temperature, the thermal power of the electric heating standard sample is U 加载 2 / R 标定 , or according to the measured current I 实测 2 With R 标定 Product, U 加载 with I 实测 The product representation, that is, P 标定 =U 加载 2 / R 标定 =I 实测2 R 标定 =U 加载 I 实测 .

[0045] When determining the sample uncertainty of the electric heating standard sample, it can also be understood as determining the uncertainty of the thermal power of the electric heating standard sample. Considering that the resistance of the electric heating standard sample will change with the change of temperature, the voltage (U 加载 ) and the current (I 实际测量 , referred to as I 实测 ) is multiplied by the thermal power (P 标定 ).

[0046] Furthermore, when determining the current passing through the electric heating standard sample, the electric heating standard sample can be connected in series with a standard resistor. Since the resistance value of the standard resistor is constant, the current passing through the electric heating standard sample can be calculated by the voltage across the standard resistor (U 标准 ) and the resistance of the standard resistor (R 标准 ) is expressed as the ratio of 实测 =U 标准 / R 标准 , so P 标定 =U 加载 U 标准 / R 标准 .

[0047] Based on this, the thermal power (P 标定 ) can be used to apply a voltage (U 加载 ), the voltage on the standard resistor (U 标准 ) and the resistance of the standard resistor (R 标准 ), as shown in formula (1).

[0048] f (P标定) =f(U 加载 , U 标准 , R 标准 ) (1)

[0049] Among them, f (P标定) Can be expressed with P 标定 The related function, f(U 加载 , U 标准 , R 标准 ) can be expressed with U 加载 , U 标准 , R 标准 Related functions.

[0050] When determining the uncertainty of the thermal power of the electrically heated standard sample, the uncertainty synthesis formula can be used, as shown in formula (2).

[0051]

[0052] Among them, u c It can represent the uncertainty after synthesis; i and j can represent different types of uncertain factors, which can be nuclides, measurement times, measuring instruments, etc.; N can represent the number of uncertain factors; x i 、x j The factor value that can represent different uncertain factors; u xi 、u xj It can express the uncertainty of different uncertain factors; ρ ij It can represent the correlation coefficient.

[0053] Because U 标准 、U 标准 、R 标准 No correlation, ρ ij =0, so the uncertainty of the thermal power of the electrically heated standard sample can be expressed as formula (3).

[0054]

[0055] Based on this, the uncertainty of the thermal power of the electric heating standard sample will be affected by the measuring equipment and devices, that is, it will be affected by the voltmeter measuring the electric heating standard sample, the voltmeter measuring the voltage of the standard resistor, and the resistance value of the standard resistor.

[0056] According to the embodiments of the present application, when considering measurement uncertainty, it is necessary to consider the uncertainty caused by the calorimeter's hardware, such as the thermopile, voltage signal acquisition equipment, line resistance, and connector resistance. It is also necessary to consider the uncertainty caused by external environmental factors such as air temperature, water temperature, and vibration. This can be considered comprehensively. Because the calorimeter is calibrated using an electrically heated standard sample and then used to measure the isotope heat source, in order to ensure accurate measurement, the thermal power range of the isotope heat source should be roughly the same as the thermal power range of the electrically heated standard sample.

[0057] Specifically, when determining the first thermal power and first uncertainty of the isotope heat source, the thermal power of the isotope heat source can be measured multiple times using a calibrated calorimeter to obtain multiple thermal power measurement values. For example, the calorimeter can be calibrated using a 0.1W electrically heated standard sample, and the thermal power of the isotope heat source can be measured six or more times. The first thermal power and measurement uncertainty (i.e., Type A uncertainty) can be calculated based on the measurement results.

[0058] After multiple measurements, the first thermal power value of the isotope heat source can be calculated based on the multiple thermal power measurement values. Specifically, the first thermal power value can be the total average value of the thermal power measurement values ​​obtained by the multiple measurements, which can be calculated using the following formula (4).

[0059]

[0060] After multiple measurements, the measurement uncertainty of the calorimeter can be calculated based on the multiple thermal power measurement values ​​and the first thermal power value. The measurement uncertainty determination process can be shown in formula (5).

[0061]

[0062] Among them, u A Can express the Type A uncertainty, It can represent the standard deviation of the thermal power value of the isotope heat source; i and m can represent the number of measurements; The thermal power measurement value of the isotope heat source for each measurement can be expressed; It can represent the total average thermal power of the isotope heat source.

[0063] The sample uncertainty of the thermal power of the electric heating standard sample is synthesized with the measurement uncertainty to obtain the first uncertainty. The process of the first uncertainty is shown in formula (6).

[0064]

[0065] Among them, u c电标样 As shown in formula (3), u A It can be shown as formula (5).

[0066] According to an embodiment of the present application, in operation S203, the nuclides contained in the isotope heat source and the nuclides' contents can be measured. Furthermore, in operation S204, the thermal power of each nuclide and the uncertainty of the thermal power of each nuclide can be determined based on the contents of each nuclide; a second thermal power can be synthesized based on the thermal power of each nuclide; and the second uncertainty can be synthesized based on the uncertainty of the thermal power of each nuclide.

[0067] Specifically, the raw materials for preparing the isotope heat source can be chemically dissolved to obtain a mixed solution; the mixed solution can be measured multiple times to determine the content of each nuclide in the mixed solution; and the thermal power of each nuclide and the uncertainty of the thermal power of the nuclide can be determined based on the average of the nuclide content obtained from the multiple measurements. When analyzing the nuclides in the mixed solution, isotope dilution, mass spectrometry, and solution density calibration can be used to determine the nuclides in the mixed solution.

[0068] According to the embodiments of the present application, a certain mass of raw materials for preparing an isotopic heat source can be weighed, chemically dissolved, and the solution diluted to meet measurement requirements. The content of each nuclide in the diluted solution (mol / kg-Liq) is then determined using mass spectrometry combined with solution density calibration. Finally, the content of each nuclide per unit mass of the raw materials is calculated. Each nuclide should be measured multiple times to calculate the average thermal power and the thermal power uncertainty based on the multiple measurement results.

[0069] Optionally, when measuring and analyzing the composition of the isotope heat source, thermal ion mass spectrometry and secondary ion mass spectrometry can also be used to directly measure the composition and isotope abundance of the solid sample.

[0070] In addition, the measured data of the content of each nuclide should be calculated back to the same day or time through the decay formula (10) to ensure the consistency of the measured data.

[0071] According to the embodiments of the present application, using plutonium dioxide as an isotopic heat source as an example, 1g of plutonium dioxide raw material can be weighed, chemically dissolved, and then the solution is diluted proportionally to meet measurement requirements. The content of each nuclide in the diluted solution (mol / kg-Liq) is then determined through isotope dilution, mass spectrometry, and solution density calibration. Finally, the content of each nuclide per unit mass of plutonium dioxide is calculated. Each nuclide should be measured multiple times to determine the mean thermal power and the uncertainty of the thermal power.

[0072] According to an embodiment of the present application, when determining the thermal power of a nuclide, the thermal power of the nuclide can be determined based on the nuclide content, the half-life of the nuclide, and the heat energy released by a single decay of the nuclide. Specifically, the thermal power of the nuclide can be determined based on the measured solution concentration of the nuclide, the half-life of the nuclide, the heat energy released by a single decay of the nuclide, the relative atomic mass, the dilution factor, the weight of the dissolved raw material of the isotope heat source, the weight of the raw material of the isotope heat source after dissolution, and the weight of the isotope-containing material in a single isotope heat source.

[0073] When determining the uncertainty of a nuclide's thermal power, the uncertainty of the nuclide's thermal power can be synthesized based on the uncertainty of the nuclide content, the uncertainty of the nuclide half-life, and the uncertainty of the heat energy released by a single nuclide decay. Specifically, the uncertainty of the nuclide's thermal power can be determined based on the uncertainty of the measured nuclide solution concentration, the uncertainty of the nuclide half-life, the uncertainty of the heat energy released by a single nuclide decay, the uncertainty of the relative atomic mass, the uncertainty of the dilution factor, the uncertainty of the weight of the dissolved raw material of the isotope heat source, the uncertainty of the weight of the dissolved raw material of the isotope heat source, and the uncertainty of the weight of the isotope-containing material in a single isotope heat source.

[0074] According to an embodiment of the present application, operation S204 may further include the following operations: synthesizing the thermal power of the nuclide to obtain a second thermal power value of the isotope heat source; synthesizing the uncertainty of the thermal power of the nuclide to obtain a second uncertainty of the isotope heat source.

[0075] According to an embodiment of the present application, the nuclides in the isotope heat source decay, and the second thermal power value calculated here can be the thermal power of the isotope heat source at the initial moment (before decay begins) and the uncertainty of the thermal power. The process of synthesizing the second thermal power value can be as shown in formula (7). The process of synthesizing the second uncertainty can be as shown in formulas (8) and (9).

[0076]

[0077] Among them, P t0 It can represent the thermal power of the isotope heat source at the initial time (time t0), or it can be the second thermal power value; i can represent the type of nuclide. If the isotope heat source uses plutonium-238, then i can represent plutonium-236, plutonium-238, plutonium-239, plutonium-240, plutonium-241, and americium-241; P it0 It can represent the thermal power value of each nuclide at the initial moment; A it0 It can express the radioactivity of each nuclide at the initial moment; E i It can represent the heat energy released by a single decay of each nuclide; i Can be expressed as the decay constant, N A Avogadro constant (constant, 6.02214076mol -1 );C i0 It can represent the concentration of each nuclide solution measured (mol / kg); ε can represent the dilution factor, which is the reciprocal of the dilution factor and is dimensionless; m Liq It can represent the weight (kg) of the raw material of the isotope heat source after dissolution. If the isotope heat source is plutonium dioxide, then m Liq It can express the weight of dissolved plutonium dioxide; A r is the relative atomic mass; m0 can be the weight (kg) of the dissolved raw material of the isotope heat source. If the isotope heat source is plutonium dioxide, then m0 can represent the weight of dissolved plutonium dioxide; m' can represent the weight (kg) of the isotope-containing material in a single isotope heat source; T i1 / 2 The half-life of each nuclide can be expressed.

[0078]

[0079] in, It can represent the uncertainty of the second thermal power at the initial moment (t0); It can represent the uncertainty of the thermal power of the isotope heat source caused by each nuclide i at the initial time (time t0); i can represent the type of nuclide; It can be shown as formula (9).

[0080]

[0081] in, It can represent the uncertainty of the thermal power of the isotope heat source caused by nuclide i at the initial time (time t0); It can express the uncertainty of the thermal power of the isotope heat source caused by measuring the solution concentration of each nuclide; u ε It can express the uncertainty of the thermal power of the isotope heat source caused by the dilution factor; It can express the uncertainty of the thermal power of the isotope heat source caused by the weight of the raw material of the isotope heat source after dissolution; It can express the uncertainty of the thermal power of the isotope heat source caused by the relative atomic mass; u m‘ It can express the uncertainty of the thermal power of an isotope heat source caused by the weight of the isotope-containing material in a single isotope heat source; It can express the uncertainty of the thermal power of the isotope heat source caused by the weight of the dissolved raw materials of the isotope heat source; It can express the uncertainty of the thermal power of the isotope heat source caused by the half-life of each nuclide; It can express the uncertainty of the thermal power of the isotope heat source caused by the heat energy released by a single decay of each nuclide. i It can represent the heat energy released by a single decay of each nuclide; i 、N A 、C i0 ,ε,m Liq 、A r 、m0、m'、T i1 / 2 、E i The meanings of are the same as those in formula (7) and will not be repeated here.

[0082] According to the embodiments of the present application, the fixed value of the thermal power of the isotope heat source refers to the thermal power value of the isotope heat source at a certain moment, which can be understood as the initial value of the thermal power of the isotope heat source in some embodiments. However, the isotope heat source will cause the thermal power to continuously decay due to the decay of the isotope. When the isotope heat source is in use, it is necessary to determine the thermal power value of the isotope heat source at the time of use. Assuming that the thermal power value of the isotope heat source at a certain moment is P CRM , the change of the thermal power value of the isotope heat source over time can be shown as formula (10). Formula (10) can be used as a decay formula.

[0083]

[0084] Among them, P CRM It can represent the thermal power of the isotope heat source at a certain moment; i can represent the type of nuclide; P i The thermal power of each nuclide in the isotope heat source at the initial moment; T i1 / 2 It can represent the half-life of each nuclide; t can represent the time.

[0085] Assume that the initial thermal power value of the isotope heat source at a certain moment is P CRM0 , (P here CRM0 The second thermal power value P obtained by component analysis can be expressed as t0 , or, in the case of the same determination time as the component analysis method, the first thermal power value measured or calculated using a calorimeter), then P CRM0 The determination process of can be shown as formula (11).

[0086] The initial uncertainty of the isotope heat source at a certain moment is u CRM0 (The u here CRM0 The second uncertainty obtained by component analysis can be expressed as Or, in the case of the same determination time as the composition analysis method, the first uncertainty u is obtained by measuring or calculating with a calorimeter. c第一不确定度 ).

[0087]

[0088] Among them, P i It can be the initial thermal power of each nuclide in the isotope heat source at a certain moment; i can indicate the type of nuclide.

[0089] Since there is decay inside the isotope heat source, the initial thermal power P of each nuclide at a certain moment is i This will also cause uncertainty in the thermal power of each nuclide, and the P i The uncertainty of the thermal power of each nuclide caused by i ; P of each nuclide i The total uncertainty caused at a certain moment is recorded as It can also be understood that at a certain moment, the uncertainty of the thermal power of the isotope heat source caused by nuclide i can be recorded as The determination process is shown in formula (12).

[0090]

[0091] Among them, T i1 / 2It can represent the half-life of each nuclide; i can represent the type of nuclide, and t can represent the time. When t is selected as the initial time (t0), the formulas (8) to (9) can also be obtained by formula (12):

[0092] Since the isotope heat source decays internally, the half-life of each nuclide is T i1 / 2 It also causes uncertainty in the thermal power of the isotopes, which is the half-life T of each nuclide. i1 / 2 The uncertainty of the thermal power of the isotope caused by The half-life T of each nuclide i1 / 2 The total uncertainty caused at a certain moment is recorded as The determination process is shown in formula (13).

[0093]

[0094] in, It can be expressed by the half-life T of each nuclide i1 / 2 Uncertainty caused by; i can be marked to indicate the type of nuclide; T i1 / 2 It can represent the half-life of each nuclide; t can represent the time.

[0095] According to the embodiments of the present application, Table 1 is the basic data of the main heating elements. Table 1 shows the types of nuclides included in the case of plutonium as the isotope heat source, as well as the atomic mass, half-life, and decay energy corresponding to the nuclide type. In the process of calculation using formulas (1) to (13), the process involving atomic mass, half-life, and decay energy can be determined by Table 1.

[0096] Table 1 Basic data of main heating elements

[0097]

[0098] According to an embodiment of the present application, operation S205 may also include the following operations: unifying the first thermal power value and the second thermal power value at the same moment; comparing the first thermal power value and the second thermal power value, the first uncertainty and the second uncertainty at the same moment; and when the difference between the first thermal power value and the second thermal power value, and the difference between the first uncertainty and the second uncertainty both meet the preset threshold, it is considered that the first thermal power value and the second thermal power value, the first uncertainty and the second uncertainty all match.

[0099] According to an embodiment of the present application, the first thermal power value and the second thermal power value are unified at the same moment. Based on the decay of the nuclide over time, a decay relationship of the first thermal power value over time can be constructed; based on the decay of the nuclide over time, a decay relationship of the second thermal power value over time can be constructed; based on the decay relationship of the first thermal power value over time and the decay relationship of the second thermal power value over time, the first thermal power value and the second thermal power value at the same moment are determined.

[0100] According to the embodiments of the present application, the first thermal power value and the first uncertainty determined by the calorimeter method, and the second thermal power value and the second uncertainty determined by the composition analysis method, all need to take into account the decay of the nuclides in the isotope heat source, and all need to draw a curve showing the change of power over time, that is, they all need to determine the change of thermal power over time according to the decay formula, draw a thermal power-time curve, and respectively construct the decay relationship of the first thermal power value over time and the decay relationship of the second thermal power value over time. The determination of the change relationship of thermal power over time can be determined according to the process shown in formulas (10) to (13).

[0101] According to an embodiment of the present application, since the thermal power of the isotope heat source will continue to slowly decrease as the radioactive nuclide decays, the thermal power values ​​of the isotope heat source obtained on different test dates are constantly changing. Therefore, it is necessary to convert the first thermal power value measured by the calorimeter method, the first uncertainty determined based on the first thermal power value, and the second thermal power value and the second uncertainty determined by the composition analysis method to the same date, such as the same day or the same time, so as to accurately compare the results obtained by the two methods. When comparing, the difference between the first thermal power value and the second thermal power value, and between the first uncertainty and the second uncertainty can be made respectively to obtain the difference. When the difference meets the preset threshold, or meets the preset threshold range, it is considered that the results obtained by the two methods match. Among them, the preset threshold or the preset threshold range can be adaptively adjusted according to actual needs.

[0102] According to the embodiments of the present application, the present application compares and verifies the results obtained by calorimetry and composition analysis. This not only allows the comparison of the results to determine if they are identical, but also proves the rationality and accuracy of the measurements. Uncertainty analysis, calculation, and synthesis are used to determine the uncertainty value of the initial thermal power of the isotope heat source. The thermal power variation curve over time is then determined through decay calculations. In the process of determining the thermal power of the isotope heat source, the high purification and enrichment process of the isotope product is omitted. While meeting the accuracy requirements for the isotope heat source, the process cost of determining the thermal power of the isotope heat source can be greatly reduced.

[0103] It should be noted that, unless it is clearly stated that there is a sequence of execution between different operations shown in the flowcharts in the embodiments of the present application, or there is a sequence of execution between different operations in technical implementation, otherwise, the execution order between multiple operations may not be prioritized, and multiple operations may also be executed simultaneously.

[0104] Those skilled in the art will appreciate that various combinations and / or combinations of features described in the various embodiments and / or claims of this application may be made, even if such combinations or combinations are not explicitly described in this application. In particular, various combinations and / or combinations of features described in the various embodiments and / or claims of this application may be made, without departing from the spirit and teachings of this application. All such combinations and / or combinations fall within the scope of this application.

[0105] The embodiments of the present application have been described above. However, these embodiments are for illustrative purposes only and are not intended to limit the scope of the present application. Although each embodiment has been described separately above, this does not mean that the measures in each embodiment cannot be advantageously used in combination. The scope of the present application is defined by the appended claims and their equivalents. Without departing from the scope of the present application, those skilled in the art may make various substitutions and modifications, which should all fall within the scope of the present application.

Claims

1. A method for determining the thermal power of an isotope heat source, comprising: calibrating the calorimeter using an electrically heated standard sample to obtain a calibrated calorimeter; Measuring the thermal power of the isotope heat source using the calibrated calorimeter to determine a first thermal power value of the isotope heat source and a first uncertainty corresponding to the first thermal power value; Analyze the composition of isotope heat sources; calculating a second thermal power value of the isotope heat source and a second uncertainty corresponding to the second thermal power value according to the composition of the isotope heat source; When the first thermal power value and the second thermal power value, and the first uncertainty and the second uncertainty all match, the thermal power of the isotope heat source is determined according to the first thermal power value and the second thermal power value.

2. The method according to claim 1, wherein Determining a first thermal power value of the isotope heat source and a first uncertainty corresponding to the first thermal power value includes: When calibrating a calorimeter using an electrically heated standard sample, determining the sample uncertainty corresponding to the thermal power of the electrically heated standard sample; determining a measurement uncertainty of the calorimeter based on the first thermal power value; The first uncertainty of the isotope heat source is synthesized according to the sample uncertainty and the measurement uncertainty.

3. The method according to claim 2, wherein: Determining a first thermal power value of the isotope heat source and a first uncertainty corresponding to the first thermal power value includes: Using the calibrated calorimeter to measure the isotope heat source multiple times to obtain multiple thermal power measurement values; Calculating a first thermal power value of the isotope heat source according to the plurality of thermal power measurement values; The measurement uncertainty of the calorimeter is calculated based on the multiple thermal power measurement values ​​and the first thermal power value.

4. The method according to claim 2, wherein: When calibrating a calorimeter using an electrically heated standard sample, determining the sample uncertainty corresponding to the thermal power of the electrically heated standard sample includes: Connecting the electrically heated standard sample and a standard resistor in series; The sample uncertainty is determined according to the voltage of the electric heating standard sample, the voltage of the standard resistor, and the resistance value of the standard resistor during calibration.

5. The method according to claim 1, wherein Calculating a second thermal power value of the isotope heat source and a second uncertainty corresponding to the second thermal power value according to a component in the isotope heat source includes: measuring the nuclides contained in the isotope heat source and the content of the nuclides; Determining the thermal power of each nuclide and its uncertainty based on the content of each nuclide; synthesizing the second thermal power according to the thermal power of each of the nuclides; The second uncertainty is synthesized according to the uncertainty of the thermal power of each of the nuclides.

6. The method according to claim 5, wherein: Determining the thermal power and uncertainty of each nuclide includes: chemically dissolving the raw materials for preparing the isotope heat source to obtain a mixed solution; Performing multiple measurements on the mixed solution to determine the content of each nuclide in the mixed solution; The thermal power of each nuclide and the uncertainty of the thermal power of the nuclide are determined according to the average value of the content of each nuclide obtained from the multiple measurements.

7. The method according to claim 6, wherein: Determining the thermal power of the nuclide and the uncertainty of the thermal power of the nuclide includes: Determining the thermal power of the nuclide based on the content of the nuclide, the half-life of the nuclide, and the heat energy released by a single decay of the nuclide; The uncertainty of the thermal power of the nuclide is synthesized based on the uncertainty of the nuclide content, the uncertainty of the nuclide half-life, and the uncertainty of the heat energy released by the single decay of the nuclide.

8. The method according to claim 5, wherein The first thermal power value and the second thermal power value, as well as the first uncertainty and the second uncertainty, all match, including: unifying the first thermal power value and the second thermal power value at the same time; comparing the first uncertainty and the second uncertainty of the first thermal power value and the second thermal power value at the same moment; and When the difference between the first thermal power value and the second thermal power value, and the difference between the first uncertainty and the second uncertainty both meet the preset threshold, it is considered that the first thermal power value and the second thermal power value, and the first uncertainty and the second uncertainty all match.

9. The method according to claim 8, wherein The unifying the first thermal power value and the second thermal power value at the same time includes: Based on the decay of the nuclide over time, constructing a decay relationship of the first thermal power value over time; Based on the decay of the nuclide over time, constructing a decay relationship of the second thermal power value over time; The first thermal power value and the second thermal power value at the same moment are determined according to the decay relationship of the first thermal power value over time and the decay relationship of the second thermal power value over time.

10. The method according to claim 1, wherein Determining the thermal power of the isotope heat source according to the first thermal power value and the second thermal power value includes: The thermal power of the isotope heat source is determined according to the average of the first thermal power value and the second thermal power value.

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