JP2014059238A - Thermal analysis device and thermal analysis method and thermal analysis program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To efficiently and properly perform thermal analysis when a plurality of heating elements such as radioactive waste are disposed.SOLUTION: A thermal analysis device 10 for performing thermal analysis in a region where a plurality of heating elements are disposed includes: a unit information input part 11 for inputting information related to the region and a unit number of heating elements; a base case calculation part 12 for calculating the influence of temperature due to the heating elements corresponding to positions from the unit number of heating elements on the basis of the input information; a heating element information input part 13 for inputting information showing the positions where the plurality of heating elements are disposed and the number of the heating elements; a temperature influence calculation part 14 for calculating the influence of temperature at the evaluation points of the heating elements on the basis of influence due to the unit number of heating elements and distances from the positions where the heating elements are disposed to the evaluation points; an addition part 15 for adding the calculated influence of temperature at the evaluation points of the heating elements; and an output part 17 for outputting information showing the added influence of temperature at the evaluation points.

Description

  The present invention relates to a thermal analysis apparatus, a thermal analysis method, and a thermal analysis program that perform thermal analysis in a region where a heating element is disposed.

  In geological disposal of high-level radioactive waste, the temperature limit of an artificial barrier (artificial barrier material) installed around the waste is adopted as a design condition for the disposal tunnel. There are about 40,000 high-level wastes envisaged for geological disposal. On the other hand, according to the conventional model, it is assumed that disposal tunnels and wastes in the tunnels are arranged indefinitely at the same pitch, and a rectangular parallelepiped region occupied by one waste is taken out and a reflection boundary is used. Thermal analysis was performed. For this thermal analysis, for example, FEM (finite element method) analysis as shown in Patent Document 1 has been used.

JP 2011-226855 A

  However, if the design is performed by thermal analysis for each rectangular parallelepiped region that one waste body occupies as described above, the size of the cuboid region that one waste body occupies regardless of the position where the waste body is disposed. Are the same size. That is, the waste disposed at the center of the disposal tunnel and surrounded by other wastes and greatly affected by the heat generated by the other wastes, and the heat generated by other wastes disposed at the end of the disposal tunnel The waste body having a small influence from the occupies a rectangular parallelepiped region having the same size. Therefore, the exclusive area of the entire disposal tunnel is very large and irrational.

  Further, if the thermal analysis considering all wastes is to be performed by FEM analysis, a very large analysis mesh is required because 40,000 wastes need to be modeled. For this reason, trial examination work at the design stage is very complicated and burdensome, and thermal analysis cannot be performed in a realistic time.

  The present invention has been made in view of the above, and a thermal analysis apparatus, a thermal analysis method, and a thermal analysis apparatus capable of performing thermal analysis efficiently and appropriately when a plurality of heating elements such as radioactive waste are disposed. The purpose is to provide an analysis program.

  In order to achieve the above object, a thermal analysis apparatus according to the present invention is a thermal analysis apparatus that performs thermal analysis in an area where a plurality of heating elements are arranged, and inputs information related to the area and the number of heating elements. A unit information input unit; a base case calculation unit that calculates an influence of temperature by the heating element according to a position from the unit number of heating elements based on information input by the unit information input unit; A heating element information input means for inputting information indicating the position where the heating element is disposed and the number of heating elements, an influence calculated by the base case calculation means, and a heating element indicated by the information input by the heating element information input means Temperature influence calculation that calculates the influence of the temperature at the evaluation point of the heating element on the basis of the distance from the position where the heater is disposed to the evaluation point at the predetermined position in the region Means for adding the temperature influence at the evaluation point of each heating element calculated by the temperature influence calculation means, and output means for outputting information indicating the temperature influence at the evaluation point added by the addition means And comprising.

  In the thermal analysis apparatus according to the present invention, the calculation of the influence of temperature by the heating element according to the position is calculated for a unit number of heating elements. Since the calculation is for a unit number of heating elements, this calculation can be performed with a small load. On the other hand, the influence of the temperature by a plurality of heating elements arranged in the region is the influence of the temperature by the number of heating elements according to the calculated position, and the influence of the temperature by each heating element is added. Calculated. Since the load of addition is calculated by a small calculation, this calculation can also be performed with a small load. Therefore, the thermal analysis apparatus according to the present invention can efficiently perform the thermal analysis of the heating element. On the other hand, in the thermal analysis apparatus according to the present invention, since the influence of temperature is calculated in consideration of the arrangement of the heating elements, thermal analysis can be performed appropriately. For example, the influence of the temperature by the heating element can be calculated according to the arrangement of the heating element at the center and the end of the region.

  The unit information input means inputs information indicating the heat generation amount of the unit number of heating elements as information on the unit number of heating elements, and the heating element information input means inputs information indicating the heat generation amount of the arranged heating elements. The temperature influence calculating means calculates the temperature influence at the evaluation point of each of the arranged heating elements according to the amount of heat generated by the unit number of heating elements and each of the arranged heating elements. It can be. According to this configuration, it is possible to appropriately perform the thermal analysis even in the case where variations in the amount of heat generation occur in the heating elements that are arranged.

  The heating element information input means can determine the arrangement of each heating element according to the amount of heat generated by each heating element. According to this structure, the thermal analysis according to arrangement | positioning of each heat generating body according to the emitted-heat amount of each heat generating body can be performed.

  The heating element information input means can input information indicating the probability distribution of the heat generation amount and determine the heat generation amount of each heating element according to the probability distribution. According to this configuration, it is possible to perform an appropriate thermal analysis even when there is variation in the amount of heat generated by the heating element and the probability distribution is followed.

  The heating element information input means determines a plurality of heating amounts of each heating element according to the probability distribution, and the temperature influence calculation means and the adding means determine the heating amount of each heating element determined by the heating element information input means. Processing may be performed for each of a plurality of sets. According to this configuration, it is possible to perform thermal analysis on a plurality of sets of the calorific values of the respective heat generating elements, and it is possible to consider the influence of the temperature at the evaluation point corresponding to the variation in the calorific value.

  The thermal analysis apparatus determines whether or not the influence of the temperature at the evaluation point added by the adding means satisfies a preset condition. If it is determined that the temperature is not determined, information indicating a position where a plurality of heating elements different from the influence of the temperature at the evaluation point is arranged is input to the heating element information input means, and the temperature at the evaluation point based on the position is input. It can be further provided with a determination means for calculating the influence again. According to this configuration, it is possible to easily design how to arrange the plurality of heating elements.

  By the way, the present invention can be described as an invention of a thermal analysis apparatus as described above, and can also be described as an invention of a thermal analysis method and a thermal analysis program as follows. This is substantially the same invention only in different categories and the like, and has the same operations and effects.

  That is, the thermal analysis method according to the present invention is a thermal analysis method for performing thermal analysis in an area where a plurality of heating elements are arranged, and a unit information input step for inputting information on the heating element in the area and the unit number; Based on the information input in the unit information input step, a base case calculation step for calculating the influence of temperature by the heating element according to the position from the unit number of heating elements, and a plurality of heating elements in the region are arranged From the heating element information input step for inputting information indicating the position and the number of heating elements, the influence calculated in the base case calculation step, and the position where the heating element indicated by the information input in the heating element information input step is arranged Based on the distance to the evaluation point that is a predetermined position in the region, the temperature shadow that calculates the influence of the temperature at the evaluation point of the heating element A calculation step, an addition step for adding the influence of the temperature at the evaluation point of each heating element calculated in the temperature influence calculation step, and information indicating the influence of the temperature at the evaluation point added in the addition step are output. An output step.

  The thermal analysis program according to the present invention is a thermal analysis program for performing thermal analysis in an area where a plurality of heating elements are arranged, and is a unit information input for inputting information about the area and the number of heating elements. And a base case calculating means for calculating an influence of temperature by the heating element according to the position from the unit number of heating elements based on information input by the unit information input means, and a plurality of heating elements in the region. A heating element information input means for inputting information indicating the position to be arranged and the number of heating elements, an influence calculated by the base case calculation means, and a heating element indicated by the information input by the heating element information input means are arranged. The temperature at which the influence of the temperature at the evaluation point of the heating element is calculated based on the distance from the position to the evaluation point at the predetermined position in the region. An influence calculating means, an adding means for adding the influence of the temperature at the evaluation point of each heating element calculated by the temperature influence calculating means, and information indicating the influence of the temperature at the evaluation point added by the adding means are output. Function as output means.

  ADVANTAGE OF THE INVENTION According to this invention, when a several heat generating body, such as radioactive waste, is arrange | positioned, a thermal analysis can be performed efficiently and appropriately.

It is a figure which shows the functional structure of the thermal analyzer which concerns on embodiment of this invention. It is a figure which shows the example of arrangement | positioning when radioactive waste is geologically disposed of. It is a figure which shows the image of the thermal analysis using the superimposition by the thermal analysis apparatus which concerns on embodiment of this invention. It is a figure which shows the FEM analysis model used for the thermal analysis of a base case. It is a graph which shows the spatial distribution of the temperature rise amount of a base case. It is another graph which shows the spatial distribution of the temperature rise amount of a base case. It is a figure which shows the example of the distance from the position where each waste body is arrange | positioned to an evaluation point. It is a flowchart which shows the process (thermal analysis method) performed with the thermal analysis apparatus which concerns on embodiment of this invention. It is a graph which shows the comparison of a temperature temporal change with respect to a bedrock bed setting model. It is a figure which shows the model (FEM mesh) of FEM analysis. It is a figure which shows the setting of the time-dependent change of the emitted-heat amount per waste body. It is a graph which shows the time-dependent change (case A) of the buffer material inner side temperature of the waste body of a FEM analysis and the thermal analysis which concerns on this embodiment. It is a graph which shows the time-dependent change (case B) of the buffer material inner side temperature of the waste body of a FEM analysis and the thermal analysis which concerns on this embodiment. It is a graph which shows the time-dependent change (case C) of the buffer material inner side temperature of the waste body of a FEM analysis and the thermal analysis which concerns on this embodiment. It is a figure which shows the analysis mesh around the disposal mine shaft of (a) 12 models and (b) 12 models. It is the figure which showed the waste object used as the object of analysis in this embodiment. It is a graph which shows the time-dependent change of the temperature of a FEM analysis and the thermal analysis which concerns on this embodiment. It is a figure which shows the setting of the initial heating value of 12 waste bodies. It is a figure which shows the idea of expansion of a waste body exclusive area. It is a figure which shows an example of an underground panel layout (disposal hole standing type, crystalline rock). It is a figure which shows the classification | category of the waste according to the emitted-heat amount ((a) In the case of 2 divisions (b) In the case of 4 divisions (c) In the case of 8 divisions). It is a figure which shows the order which allocates the emitted-heat amount to each waste body. It is a graph which shows the example of the maximum temperature of the buffer material in each realization. It is a graph which shows the result of the required exclusive area ratio. It is a figure which shows the 6,669 waste body arrangement | positioning supposing the part for 1 panel. It is a figure which shows the contour (the waste-body initial heating value is uniform) of the buffer material internal temperature maximum value. It is a graph which shows distribution of the buffer material maximum temperature of a panel edge part at the disposal mine shaft direction. It is a figure which shows the structure of the related document extraction program which concerns on embodiment of this invention with a recording medium.

  Hereinafter, preferred embodiments of a thermal analysis device, a thermal analysis method, and a thermal analysis program according to the present invention will be described in detail with reference to the drawings. In the description of the drawings, the same elements are denoted by the same reference numerals, and redundant description is omitted.

  FIG. 1 shows a thermal analysis apparatus 10 according to this embodiment. The thermal analysis device 10 is a device that performs thermal analysis in a region where a plurality of heating elements are arranged. This thermal analysis is performed by information processing performed by the thermal analysis apparatus 10 using information input to the thermal analysis apparatus 10 by inputting information necessary for the analysis. Specifically, the thermal analysis apparatus 10 corresponds to an information processing apparatus such as a workstation or a PC (Personal Computer), and is configured by hardware such as a CPU (Central Processing Unit) and a memory. The thermal analysis apparatus 10 exhibits each function described later when these components are operated by a program or the like. In the present embodiment, the thermal analysis device 10 is realized by a single device, but may be realized by an information processing system in which a plurality of information processing devices are connected to each other via a network.

  Here, an example of a target of thermal analysis in the present embodiment will be described. In the present embodiment, an example is described in which geological disposal is performed in which a waste of high-level radioactive waste is used as a heating element (heat source) and is placed (embedded) in a deep underground. When the waste is disposed of in the geological formation, a mine is provided in a place several hundred meters below ground, and the waste is placed in the mine to be backfilled. A section composed of a group of disposal tunnels for placing waste and a tunnel surrounding it is called a panel (disposal panel).

  When wastes are disposed of in geological formations, an artificial barrier is usually provided to prevent the disposal environment from being affected. FIG. 2 shows an example of the arrangement when the waste is disposed of. FIG. 2A shows an example of the horizontal placement method, and FIG. 2B shows an example of the vertical placement method. As shown in FIG. 2, the artificial barrier 100 includes a vitrified body 101, an overpack 102, and a buffer material 103. In the case of the laying method as shown in FIG. 2 (b), the vitrified body 101, the overpack 102 and the buffer material 103 are arranged in the hole provided in the bedrock 200, and the tunnel backfilling material 201 is disposed thereon. cover. In the present embodiment, a hard rock cage case will be described as an example.

  The vitrified body 101 takes in the radionuclide into a stable glass structure and suppresses elution into the groundwater. The overpack 102 is a rigid container for storing the waste body (the glass solidified body 101), and prevents contact between the glass solidified body 101 and the groundwater for a certain period. The cushioning material 103 is a member filled between the overpack 102 and the rock mass 200. The buffer material 103 protects the vitrified body 101 by its physical and chemical buffering functions, suppresses the penetration of groundwater from the surroundings and the flow therein, and further adsorbs radionuclides eluted in the groundwater. This suppresses the movement of radionuclides. The buffer material 103 is made of bentonite, for example.

  The waste body disposed as described above generates heat, and the influence of the heat generation extends around the waste body. Due to this influence, the temperature of the artificial barrier 100 varies. As described above, the temperature limit of the artificial barrier 100 (specifically, for example, the temperature limit of the overpack) is adopted as the design condition of the tunnel. Therefore, how the waste body is arranged, that is, how the tunnel is designed depends on the temperature of the artificial barrier 100 when the waste body is arranged. The thermal analysis device 10 according to the present embodiment is a device that performs thermal analysis of a region when a plurality of waste bodies are arranged in a specific region. For example, the time change of the temperature at a predetermined position such as the position of the artificial barrier 100 is calculated.

  Subsequently, the functional configuration of the thermal analysis device 10 will be described. As shown in FIG. 1, the thermal analysis apparatus 10 includes a unit information input unit 11, a base case calculation unit 12, a heating element information input unit 13, a temperature effect calculation unit 14, an addition unit 15, and a determination unit 16. And an output unit 17.

  Here, an outline of thermal analysis by the thermal analysis apparatus 10 according to the present embodiment will be described. In this thermal analysis, a unit number of waste bodies (for example, one) is first placed in a region where the waste body is placed, and it is assumed that there is no thermal influence from the other adjacent waste bodies (base case) Is subjected to thermal analysis to obtain the spatial distribution of temperature in that case. Subsequently, as shown in FIG. 3, based on the positions where the plurality of waste bodies 300 are arranged, evaluation points (positions where the waste bodies 300a are arranged in FIG. 3) and the respective waste bodies are calculated. Find the distance to 300. Based on the distance, the temperature distribution at the evaluation point by each waste body 300 is calculated with reference to the spatial distribution of the temperature of the base case. Here, the target of the thermal analysis is, for example, the arrangement of waste bodies on the panel scale (panel unit).

  Subsequently, the temperature at the evaluation point by each waste body 300 is added (superimposed) to calculate the temperature at the evaluation point. In addition, the method of superimposing the case (base case) where only one waste body is used and the surrounding waste body is calculated as a bedrock as described above is based on the thermal analysis, the area of the waste body itself is compared to the entire area. It is reasonable because it is small enough to be ignored. At this time, as shown in FIG. 3, the initial heat generation amount of each waste body 300 may be calculated as different for each waste body 300. For example, the heat generation amount of each waste body 300 may be determined according to a preset probability distribution. The above is the outline of the thermal analysis by the thermal analysis apparatus 10 according to the present embodiment.

  Note that the thermal analysis according to the present embodiment is an evaluation method in which a large number of trials of thermal analysis are performed in consideration of the design of the disposal tunnel in consideration of the design of the disposal tunnel. In other words, the ground where the disposal mine is planned is a relatively homogeneous rock, and the isolation between the wastes is relatively larger than the outer diameter of the mine where the wastes are installed. And the thermal characteristics of the backfilling material are focused on the condition that the influence on the temperature distribution is small. Subsequently, the function of each component of the thermal analysis apparatus 10 will be described in detail.

  The unit information input unit 11 is a unit information input unit that inputs information related to a region (tunnel) where a waste is disposed and a unit number of wastes. The information input to the unit information input unit 11 is information necessary to calculate the temperature spatial distribution in the base case described above. The information on the area where the waste body is disposed is, for example, information indicating the thermal conductivity, specific heat, and density of the rock mass (hard rock system) that is the area to be disposed of. In addition, the area | region where a unit-number waste body is arrange | positioned shall be a single disposal tunnel in a homogeneous uniform formation, for example. Further, the unit information input unit 11 may input information indicating the initial temperature of the rock mass in order to calculate the temperature of the rock mass calculated by the adding unit 15 described later.

  The information on the unit number of waste bodies is, for example, information indicating the thermal conductivity, specific heat, and density of the vitrified body, overpack, and buffer material that constitute the waste bodies. The unit information input unit 11 may input information indicating the thermal conductivity, specific heat, and density of the backfill material. In addition, the unit information input unit 11 may input information indicating the amount of heat generated by the unit number of waste bodies as information on the unit number of waste bodies. As the information indicating the heat generation amount, specifically, for example, information indicating an initial heat generation amount that is a heat generation amount at the stage where the waste body is disposed is used.

  The number of units, which is the number of waste bodies included in the base case, may be one, but may be two or more. When the number of units is 2 or more, the unit information input unit 11 inputs information necessary for calculating the temperature spatial distribution from the set of waste bodies, such as information indicating the positional relationship of the waste bodies.

  The unit information input unit 11 may also input information used by calculation by the base case calculation unit 12, for example, information on parameters of the analysis model. This input of information may be performed based on an operation by a user of the thermal analysis device 10 or may be performed by reading information stored in the thermal analysis device 10 in advance. The input of information to be described later is performed in the same manner as described above. The unit information input unit 11 outputs the input information to the base case calculation unit 12.

  The base case calculation unit 12 is a base case calculation unit that calculates the influence of the temperature of the waste according to the position from the waste of the unit number based on the information input from the unit information input unit 11. The temperature influence calculated at this time is calculated assuming that there is no influence from (adjacent) waste bodies other than the unit number of waste bodies. Specifically, the influence of the temperature by the waste body is, for example, the amount of increase in the temperature at the position due to the presence of the waste body (the amount of increase from the initial temperature of the region (rock)). That is, the base case calculation unit 12 calculates the spatial distribution of the temperature rise amount by the unit number of waste bodies. The base case calculation unit 12 performs thermal analysis (heat conduction analysis) with a model in which a waste body is embedded in the center of a rock area that can be considered infinite (for example, a three-dimensional area of 2000 m × 2000 m × 12000 m). To obtain the spatial distribution of the temperature rise. The thermal analysis of the base case is performed by FEM analysis similar to the conventional method, for example. Note that the base case thermal analysis may be performed by any method other than the FEM analysis as long as the thermal analysis according to the distance of the waste body can be performed.

4A and 4B show FEM analysis model diagrams. As the analysis model, a 1/4 cut-out model (a model in which a waste body and a region that are symmetrical at an angle of 90 degrees at the center of the waste body are cut out) can be used from the symmetry of the boundary condition. Table 1 below shows examples of physical property values used in the analysis.

For example, the boundary condition is set as shown in FIG. As for the heat generation condition of the waste body, for example, the initial heat generation amount and the fluctuation of the heat generation amount are appropriately set.

  The base case calculation unit 12 calculates the amount of increase in temperature at each position according to the horizontal distance from the center of the waste body and the elapsed time from the arrangement by the thermal analysis. The spatial distribution of the temperature increase obtained under the above conditions is shown in FIGS. The graph shown in FIG. 5 is a graph showing the relationship between the horizontal distance from the waste (horizontal axis, unit is cm) and the temperature rise (vertical unit, unit is ° C.). The type of line indicates the elapsed time since the waste was placed (in years). The graph shown in FIG. 6 is a graph showing the relationship between the elapsed time (horizontal axis, unit is year) and the temperature rise (vertical axis, unit is ° C.) since the waste body is disposed. The line type indicates the horizontal distance from the waste (unit: m). As shown in FIGS. 5 and 6, the amount of increase in temperature decreases as the horizontal distance increases. Further, with respect to the elapsed time after the waste body is disposed, the temperature rise amount decreases as the elapsed time increases after reaching the maximum temperature once it rises from the waste body placement time point. The base case calculation unit 12 creates a database of information indicating the spatial distribution of the calculated temperature rise amount as a function of the horizontal distance from the waste center and the elapsed time from the arrangement so that the temperature effect calculation unit 14 and the like can refer to the information. Keep it.

  The heating element information input unit 13 is a heating element information input unit that inputs information indicating a position where a plurality of waste bodies are arranged in a region and the number of heating elements, which is the number of waste bodies. The information input to the heating element information input unit 13 is information necessary for calculating the temperature influence at the evaluation point when a plurality of waste bodies are arranged using the temperature spatial distribution in the base case described above. It is. The information indicating the position where the plurality of waste bodies are arranged and the number of heating elements is, for example, the coordinates of each waste body corresponding to the number of heating elements. In addition, the heating element information input unit 13 includes the total number of waste bodies, the number and interval of tunnels in the region where the waste bodies are disposed (distance between disposal tunnels), and the number of waste bodies provided in the tunnel (number of disposal holes). And the information which shows a space | interval (disposal hole fixed space | interval) may be input, and the coordinate of each waste body may be calculated from those information.

  Since the heating element information input unit 13 is used to calculate the influence of the temperature at the evaluation point, the heating element information input unit 13 may input information indicating the heat generation amount of each disposed waste body. The heat generation amount of the waste body is specifically an initial heat generation amount that is a heat generation amount at the stage where the waste body is disposed, as in the case of the base case described above.

  For example, information indicating the calorific value is input for each waste body (a method of setting a representative value deterministically). Alternatively, the heating element information input unit 13 may input information indicating a probability distribution, set the heat generation amount by randomly extracting the heat generation amount according to the probability distribution (giving a probability distribution, random sampling) How to set by). As the probability distribution of the heat generation amount, for example, a normal distribution can be used. When the normal distribution is used, the heating element information input unit 13 inputs an average value and a variance. Moreover, when determining the calorific value according to the probability distribution, a plurality of calorific values of each waste body may be determined. That is, it is good also as determining the emitted-heat amount of each waste body of a some group. When determining the heat generation amount of a plurality of groups, thermal analysis is performed by the temperature influence calculation unit 14 and the addition unit 15 for each group.

  Further, the heating element information input unit 13 may determine the arrangement of each waste body according to the amount of heat generated by each waste body. For example, as will be described in detail later, a waste body having a high calorific value and a waste body having a low calorific value are combined in a combination of those having an absolute value close to the average value of the calorific value so that the effect of canceling heat becomes the highest May be arranged alternately. In addition, as a result, there is as little bias as possible due to the temperature effect of the waste. The heating element information input unit 13 outputs the input information to the temperature influence calculation unit 14.

  Based on the information created in the database by the base case calculation unit 12 and the information input from the heating element information input unit 13, the temperature influence calculation unit 14 determines the evaluation points for each of the plurality of waste bodies arranged in the region. It is a temperature influence calculation means for calculating the influence of temperature (the contribution of the influence of the temperature of each waste body). The temperature influence calculation unit 14 inputs information indicating an evaluation score. The information indicating the evaluation point is, for example, coordinates on the area. The evaluation point may be one point on the region or a plurality of points. Based on the information input from the heating element information input unit 13, the temperature influence calculation unit 14 obtains the distance from the position where each waste body is disposed to the evaluation point.

  FIG. 7 shows an example of the distance from the position where each waste is placed to the evaluation point. FIG. 7 is an example in which the calculation is performed on the arrangement of 3 rows of disposal mine shafts arranged at a hard rock basin × 4 waste bodies. Here, the inside of the cushioning material 103 of the waste body 300 (1) is set as the evaluation point (the temperature inside the cushioning material 103 is obtained). The distance from the center point of each disposed waste body 300 to the evaluation point is obtained. The temperature influence calculation unit 14 calculates the influence of the temperature at the evaluation point of each waste body based on the distance.

  Specifically, the temperature influence calculation unit 14 extracts a temperature increase amount corresponding to the distance from the information stored in the database by the base case calculation unit 12. If the analysis result of the base case (temperature rise amount according to the distance) is discrete data and the distances do not match, the temperature rise amount according to the corresponding distance is calculated by interpolation.

  If the heat generation amount of the base case and the heat generation amount of the disposed waste body are the same, the temperature increase amount related to the base case obtained as described above can be used as the temperature increase amount related to each waste body. it can.

If the calorific value of the base case and the calorific value of the disposed waste body are different (the calorific value of the individual waste bodies are different from each other), for example, the following is related to the individual waste body as follows: The amount of temperature rise can be calculated. In that case, the temperature influence calculation part 14 calculates the influence of the temperature in the said evaluation point of each said heat generating body arrange | positioned according to each calorific value of each waste body arrange | positioned of the base case. Specifically, for waste bodies with different calorific values, the temperature rise amount may be calculated from the following equation using the analysis result of the base case and the linearity of the thermal analysis.
Temperature rise by each waste [° C.] = Temperature rise by base case analysis [° C.] × initial heat generation [W] of each waste / initial heat generation [W] in the base case
The above formula is obtained by multiplying the temperature increase amount of the base case analysis by the ratio of the initial heat generation amount of the target waste body and the initial heat generation amount of the base case. By calculating the temperature rise amount of each waste body according to the above formula, it is possible to perform temperature evaluation in consideration of the heat generation amount that differs for each waste body.

  The temperature influence calculation unit 14 performs the temperature increase amount at the evaluation point by each waste body for each elapsed time (each time) after the waste body is arranged. As described above, the temperature increase amount by the base case analysis is calculated for each elapsed time since the waste body is disposed, and therefore may be calculated for each elapsed time. Thereby, a time-series temperature history (time-series change) can be obtained. The temperature influence calculation unit 14 outputs information indicating the amount of temperature increase at the evaluation point by each waste body to the addition unit 15.

  Since the thermal contribution from waste that is more than a certain distance from the evaluation point is negligibly small, it is necessary to calculate the temperature at one evaluation point by adding the temperature rises of all the wastes on the model. Not always efficient from a time perspective. Therefore, in the calculation of the influence of the temperature at the evaluation point of each waste described above, the influence of all the wastes on the evaluation point may be taken into account, but the wastes disposed at a certain distance from the evaluation point ( The waste body in a range in which the thermal influence is considered to be negligible may be excluded from the object of the addition calculation because the influence of the temperature on the evaluation point is extremely small. That is, the temperature influence calculation unit 14 may calculate the temperature influence at the evaluation point only for the waste disposed within a predetermined distance from the evaluation point.

  The adding unit 15 is an adding unit that adds the influence of the temperature at the evaluation point of each waste body calculated by the temperature effect calculating unit 14. Specifically, the adding unit 15 obtains the sum by adding (superimposing) the values of the temperature rise amounts of all the wastes calculated for each evaluation point. Further, the adding unit 15 may calculate the temperature at the evaluation point by adding the value of the temperature increase amount to the initial temperature (initial ground temperature) of the rock at the evaluation point inputted in advance. The calculation of the temperature rise amount and the temperature at the evaluation point by the adding unit 15 is also performed for each elapsed time after the waste body is arranged. The addition unit 15 outputs information indicating the calculated temperature of the evaluation score to the determination unit 16.

  The determination unit 16 is a determination unit that determines whether or not the temperature increase amount at the evaluation point calculated by the addition unit 15 satisfies a preset condition. Note that the object of determination may be the temperature, not the amount of temperature rise at the evaluation point. The determination by the determination unit 16 is, for example, determining whether or not the arrangement of the waste body satisfies the design condition of the mine shaft. Then, as described later, the above calculation is performed again by changing the arrangement so that the arrangement of the waste body satisfies the design condition of the mine shaft or the arrangement of the waste body is more desirable. That is, the determination unit 16 is a means for designing the arrangement of the waste bodies. Therefore, when the thermal analysis device 10 is not intended for designing the layout of the waste body, or merely for calculating information indicating the temperature at the evaluation point, the thermal analysis device 10 is not necessarily the determination unit. 16 need not be provided. In that case, the result of the calculation by the adding unit 15 is output by the output unit 17.

  Specifically, the determination unit 16 compares the temperature increase amount at the evaluation point with a preset threshold value (allowable value) corresponding to the design condition of the mine shaft, and determines whether the temperature increase amount at the evaluation point falls below the threshold value. Judge whether or not. In addition, let the temperature rise amount at this time be the highest temperature (the future highest temperature rise) among the temperature rise amounts in each elapsed time after the waste is disposed. When the determination unit 16 determines that the temperature increase amount at the evaluation point is equal to or greater than the threshold value, that is, when it is determined that the design condition of the tunnel is not satisfied, the position where the waste body is disposed is changed again. The temperature rise amount at the evaluation point is calculated. Specifically, the arrangement of the waste body different from the arrangement of the waste body when the temperature increase amount at the evaluation point is equal to or greater than the threshold value is input to the heating element information input unit 13, and the above-described processing based on the arrangement again. The temperature rise amount is calculated in the same manner as above. Here, if the temperature increase amount at the evaluation point is equal to or greater than the threshold value, the arrangement of the waste body is changed in a direction to decrease the temperature increase amount (again, if it has been changed before that). Specifically, the interval between the waste bodies is made wider. In order to widen the interval, the arrangement of the individual waste bodies may be changed, or the interval between the mine shafts and the interval of the arrangement positions of the waste materials in the mine shaft may be increased.

  When it is determined that the temperature increase amount at the evaluation point is lower than the threshold value, that is, when the determination unit 16 determines that the design condition of the tunnel is satisfied, the temperature at the evaluation point in that case and the arrangement of the waste body are indicated. Information is output to the output unit 17. Even if the determination unit 16 determines that the temperature increase amount at the evaluation point is lower, it is desirable to make the area (occupied space) where the waste is disposed under the restrictions of the site as small as possible. The temperature may be calculated again by narrowing the interval. Thus, it is good also as setting the magnitude | size of a mine shaft and a mine shaft space | interval from which an occupation space becomes the minimum under the restrictions of a site so that a future maximum temperature rise may become the minimum waste body space | interval below an allowable value. If the determination unit 16 determines that the distance between the mine shafts and the like is optimum based on a predetermined determination criterion, the determination unit 16 outputs information indicating the temperature at the evaluation point and the arrangement of the waste body to the output unit 17.

  Further, as described above, when the heating element information input unit 13 performs random extraction of the heating value according to the probability distribution and sets the heating value of each waste body, the temperature increase amount at the calculated evaluation point Variation also occurs. Therefore, the calorific value of each waste body is set for the preset number of times (the number of realizations), and a Monte Carlo simulation is performed to calculate the temperature rise amount at the evaluation points for the number of realizations for each set calorific value. Also good. In that case, the determination unit 16 performs the above determination for each trial and determines that the condition is satisfied in any case (or a certain number of times or more) when the temperature increase at the evaluation point falls below the threshold value. It is good to do.

  The output unit 17 is an output unit that outputs information indicating the influence of the temperature at the evaluation point added by the adding unit 15. Specifically, the output unit 17 outputs information indicating the temperature rise amount or temperature at the evaluation point. The temperature rise amount or temperature may be output as information for each elapsed time from the disposition of the waste body, or the maximum value thereof may be output. In addition, when the above-described determination is made by the determination unit 16, information (for example, coordinates of each waste body) indicating the arrangement of each waste body when the condition is satisfied may be output. The output by the output unit 17 may be, for example, a display output to a display device or the like so that the user of the thermal analysis device 10 can confirm the result of the thermal analysis, or information may be output to another device. . The functional configuration of the thermal analysis device 10 has been described above.

  Subsequently, processing (thermal analysis method) executed by the thermal analysis apparatus 10 according to the present embodiment will be described with reference to the flowchart of FIG. In the thermal analysis apparatus 10 according to the present embodiment, first, the unit information input unit 11 inputs information about a region where wastes are disposed and one (unit number) of wastes (S01, unit information input). Step). The input information is information necessary for analyzing the base case. The input information is output from the unit information input unit 11 to the base case calculation unit 12.

  Subsequently, the base case calculation unit 12 calculates the amount of temperature rise by the waste according to the distance from one waste based on the information input from the unit information input unit 11 (S02, base case calculation). Step). Further, the temperature rise amount is calculated according to the elapsed time after the waste body is disposed. This calculation is performed by FEM analysis, for example. Information on the temperature increase calculated by the base case calculation unit 12 is made into a database so that the temperature effect calculation unit 14 and the like can refer to it. The above is a process necessary for performing a thermal analysis when a plurality of waste bodies are arranged. The calculation process of the base case does not need to be performed every time the thermal analysis is performed when a plurality of waste bodies are arranged, and may be performed only once. Moreover, it does not need to be performed continuously with the process of performing thermal analysis when the following plurality of waste bodies are arranged.

  The following thermal analysis process when multiple wastes are placed is an example in which the heat generation amount of each waste follows a probability distribution, and the placement of wastes that meet the conditions using the results of thermal analysis The position is to be calculated.

  In this process, information on positions where a plurality of waste bodies are arranged is input by the heating element information input unit 13 (S03, heating element information input step). Further, information indicating a probability distribution related to the heat generation amount of the waste body is input by the heat generation body information input unit 13, and the heat generation amount of each waste body is determined based on the information. These pieces of information are output from the heating element information input unit 13 to the temperature influence calculation unit 14.

  Subsequently, the temperature influence calculation unit 14 evaluates each of the plurality of waste bodies arranged in the region based on the information stored in the database by the base case calculation unit 12 and the information input from the heating element information input unit 13. The temperature rise amount at the point is calculated (S04, temperature influence calculation step). This calculation is performed based on the temperature increase amount obtained by acquiring the temperature increase amount of the base case according to the distance between the evaluation point and each waste body. Information indicating the calculated temperature rise amount is output from the temperature influence calculation unit 14 to the addition unit 15.

  Subsequently, the temperature increase amount at the evaluation point of each waste body calculated by the temperature influence calculation unit 14 is added (summed) by the adding unit 15 to calculate the temperature increase amount at the evaluation point ( S05, addition step). Information indicating the amount of temperature increase at the calculated evaluation score is output to the determination unit 16.

  Subsequently, the determination unit 16 determines whether or not the temperature increase amount at the evaluation point calculated by the addition unit 15 satisfies a preset condition (temperature requirement) (S06, determination step). When it is determined that the condition is not satisfied (No in S06), the disposal position of the waste body is reset (S07), and the processes after S04 are repeated again based on the reset position. In the above processing flow, if there is one that does not satisfy the condition, the arrangement position is reset. In addition to this, after performing the calculation for the predetermined number of realizations, the arrangement position may be reset when the condition that does not satisfy the condition (the temperature exceeds the threshold) exceeds a certain ratio.

  If it is determined that the condition is satisfied in S06 (Yes in S06), whether or not the determination unit 16 has performed the calculation of the number of times set in advance in one arrangement in each waste body (the processes in S04 and S05). Is determined (S08, determination step). For example, it is determined whether a total of 10,000 realization calculations have been performed. When it is determined that the set number of times has not been calculated (No in S08), the heating element information input unit 13 again causes the heating value of each waste body according to the probability distribution (the value is different from the previous calculation). A different calorific value) is determined, and the calorific value of each waste body is reset (S09). The reset heat generation amount is used, and the processes after S04 are repeated.

  When it is determined that the number of times set in S08 has been calculated (Yes in S08), information indicating the thermal analysis result is output by the output unit 17 (S10, output step), and the process ends. The above is the process executed by the thermal analysis apparatus 10 according to the present embodiment.

  As described above, in this embodiment, the calculation of the influence of the temperature by the waste according to the position is calculated for one waste body (base case) which is the unit number. Although this calculation is performed by an analysis method such as FEM analysis, it is a calculation for one waste body. Therefore, this calculation should be performed with a smaller load compared to FEM analysis that considers all disposed waste bodies. Can do. In addition, the temperature effect of multiple waste bodies arranged in the area is calculated by adding the temperature effect of each waste body using the temperature effect of the base case heating element according to the calculated position. Is done. Since the calculation is performed by a calculation with a small load of addition, this calculation can also be performed with a very small load compared to FEM analysis or the like considering all the disposed wastes.

  Therefore, in this embodiment, the thermal analysis of the waste body can be performed efficiently. On the other hand, in the present embodiment, the constant influence is not repeated under the same conditions, and the influence of the temperature is calculated in consideration of the arrangement of the waste bodies, so that the thermal analysis can be appropriately performed. For example, the influence of the temperature due to the waste can be calculated at the center and the end of the region according to the arrangement of the waste.

  In this way, for example, in the planning stage of disposal tunnels and disposal holes, trial calculation is required while various conditions change, so the disposal tunnel interval and the waste body placement interval (disposal hole interval) are set. Trial calculation to do this can be performed easily.

  Moreover, it is good also as performing a thermal analysis in consideration of the information of the emitted-heat amount of each disposed waste body. According to this configuration, it is possible to appropriately perform thermal analysis even when the generated waste varies in the amount of heat generated. Thereby, a rational design can be performed. In the case where there is a variation in the heat generation amount of the waste due to differences in the manufacturing conditions of the waste, etc., it is not possible to perform calculation in a realistic calculation time by the conventional FEM analysis method. Accordingly, the thermal analysis of the present embodiment is particularly useful when variation occurs in the heat generation amount of the waste. In addition, the one where the dispersion | variation in the emitted-heat amount of a waste body is smaller can narrow a tunnel interval.

  Moreover, it is good also as determining the position where each waste body is arrange | positioned according to the emitted-heat amount of a waste body. According to this structure, the thermal analysis according to arrangement | positioning of each waste body according to the emitted-heat amount of each waste body can be performed. For example, in the region where the waste body is disposed as described above, it is possible to perform a thermal analysis with an arrangement that minimizes the deviation of the temperature rise from the waste body. However, when it can be assumed that the information on the calorific value of each waste body is constant, the above-described configuration is not necessarily required.

  Further, the heat generation amount of the waste body can be set according to the probability distribution. According to this configuration, it is possible to perform an appropriate thermal analysis even when the heat generation amount of the waste body varies and follows the probability distribution. Furthermore, in this case, thermal analysis is performed on a plurality of sets of calorific values of each waste body, specifically, for example, Monte Carlo simulation can be performed. According to this configuration, thermal analysis can be performed on a plurality of sets of calorific values of each waste body, and the influence of temperature at an evaluation point corresponding to variations in calorific values can be taken into consideration. In addition, the probability distribution of the calorific value does not necessarily need to use a normal distribution, and an arbitrary probability distribution can be used.

  Further, as in the present embodiment, it is possible to determine whether or not the result of the thermal analysis satisfies a preset condition, and to perform the thermal analysis by changing the conditions for disposing the waste body. According to this configuration, it is possible to easily design how to dispose a plurality of waste bodies. However, when it is intended to know the temperature in the region at the time of disposing a certain waste body (when it is not intended to design the disposition of the waste body), the above-described configuration is not necessarily required.

  In the present embodiment, the example of the heating element is a high-level radioactive waste, but any other heating element can be applied as long as a plurality of heating elements are arranged in the region.

  An example of performing a thermal analysis according to the present embodiment will be described. The validity of the thermal analysis according to this embodiment was verified by comparing the thermal analysis according to this embodiment with the result of the conventional FEM analysis.

1) 1/4 cut-out model Thermal analysis according to this embodiment is performed on a model of a hard rock cage case (a side heat insulation model for a dedicated area of one waste body), and the internal temperature of the cushioning material is Changes over time were compared. In the thermal analysis, 100 tunnels × 100 waste bodies were arranged, and the buffer material internal temperature of the waste body set at the center was obtained.

  FIG. 9 shows a result of comparison of the temperature change obtained by the three-dimensional FEM analysis with the result of the thermal analysis (superposition calculation) according to the present embodiment. In FIG. 9, the horizontal axis represents the elapsed time from the placement (unit is year), and the vertical axis is the temperature at each position (unit is [° C.]). In the above graph, what is indicated by a solid line is the result obtained by FEM analysis, and what is indicated by a circle is the thermal analysis result according to the present embodiment. Although the maximum value of the buffer material internal temperature is slightly smaller in the result of the thermal analysis according to the present embodiment, it can be said that the change with time can be substantially reproduced. However, the error is slightly larger after several hundred years. Possible reasons for this error include the effect of the accuracy of the base case analysis result used for the thermal analysis according to the present embodiment and the effect of an error when adding and approximating the contributions from an infinite number of solidified bodies.

2) Verification by model considering spatial variation in calorific value of multiple wastes In order to confirm the applicability of thermal analysis according to this embodiment for multiple wastes with different calorific values, 15 wastes were modeled A three-dimensional unsteady FEM thermal analysis was performed, and the result was compared with the thermal analysis according to the present embodiment.

(A) FEM analysis conditions and analysis case In the hard rock standing type, modeling was performed for a system in which five waste bodies were buried in three disposal tunnels. The disposal depth was set to 1000 m, and the stationary density of the waste was set to a disposal tunnel separation distance = 10 m and a disposal hole interval = 4.44 m. The artificial barrier specifications and material property values were the same as in the base case analysis. A range of 1000 m × 1000 m × 1200 m was modeled as an analysis region. An excerpt of the analysis mesh (total number of nodes = 646,728, total number of elements = 648,748) is shown in FIGS. 10 (a) and 10 (b) (only the central portion).

The analysis was carried out for the three cases shown in Table 2 below.

Here, the numbers of waste bodies shown in Table 2 are as shown in the layout diagram of FIG. 13A, μ is an average value of initial calorific value, and σ is a standard deviation of initial calorific value (waste body). Refer to Fig. 11 showing the setting of the change over time in the calorific value per bottle, where the horizontal axis is the elapsed time from the placement (unit is year), and the vertical axis is the calorific value of one waste body (unit is [W]). Here, μ = 350 [W] and σ = 50 [W].

(B) Comparison between FEM analysis result and thermal analysis result according to this embodiment Thermal analysis (overlay calculation) according to this embodiment was performed on the same waste body arrangement conditions as the FEM analysis. As a comparison of the analysis results of Case A, FIG. 12 shows the change over time of the buffer material inner temperature of each waste body, and Table 3 below shows a comparison focusing on the buffer material maximum temperature.

As a comparison of the analysis results of Case B, FIG. 13 shows the change over time of the buffer material inner temperature of each waste body, and Table 4 below shows a comparison focusing on the buffer material maximum temperature.

As a comparison of the analysis results of Case C, FIG. 14 shows the change over time of the buffer material inner temperature of each waste body, and Table 5 below shows a comparison focusing on the buffer material maximum temperature.

In the graph of the change over time of the buffer material inner temperature of each waste body, the upper side of the legend is the FEM analysis result, and the lower side is the thermal analysis result according to the present embodiment. From these charts, the results of the thermal analysis (overlay calculation) according to the present embodiment for a plurality of waste bodies having different waste heat generation amounts were almost the same as the FEM analysis results, and the applicability was confirmed.

3) Comparison with 12 waste FEM model As a verification of thermal analysis (superimposition calculation) according to this embodiment, thermal analysis according to this embodiment is performed on the FEM model with 12 waste, and the results are compared. did. FIG. 15 (a) and FIG. 15 (b) show the 12 models used for this verification. The twelve model is a model in which twelve waste bodies 300 are arranged in the mine shaft 400 in the rock 200. The twelve model is a side heat insulation model using symmetry, and it is assumed that every 12 wastes having the same heat generation condition are infinitely spread while maintaining symmetry.

In the thermal analysis according to the present embodiment, as shown in FIG. 16, 1764 waste bodies (disposal tunnel 21 × waste body 84) are considered, and the buffer material inner temperature of 12 waste bodies in the center is evaluated. Compared. FIG. 17 shows changes with time in the temperature near each waste body. In FIG. 17, the horizontal axis represents the elapsed time from the placement (unit is year), and the vertical axis is the temperature at each position (unit is [° C.]). Table 6 below shows a comparison focusing on the maximum temperature inside the cushioning material.

From these, it can be seen that the result of the thermal analysis according to the present embodiment can approximate the FEM analysis result with high accuracy.

The input data of the system used for the examination described above is as follows.
-Pre-calculated base case analysis results (data of distance and temperature rise for each hour)
・ Coordinates of evaluation points ・ Initial geothermal temperature of rock mass ・ Total number of wastes, number of disposal tunnels, number of disposal holes per tunnel, distance between disposal tunnels, placement distance of disposal holes ・ Initial calorific value of each waste (deterministically When setting)
・ Number of realizations (when set probabilistically)
・ Average initial calorific value, standard deviation, upper and lower limits (when set probabilistically)
・ Number of evaluation points to be output and their numbers

  In this system, as described above, the calculation algorithm is devised so that the wastes in the range where the thermal influence on the evaluation point can be ignored are excluded from the target of the addition calculation. In the program created this time, the calculation time when using a PC of 3.33 GHz for the overlay calculation of 6,669 waste bodies (27 × 247), 1 type step, 1 realization is about 2 seconds.

  In addition, the following points may be considered for the necessary waste-occupying area and a rational waste-space layout method using the thermal analysis according to the present embodiment described above. Here, for the bedrock stand, the quantitative effect of the planned placement considering the calorific value of each waste body and the quantitative effect of the "heat removal effect" at the panel edge are considered.

(1) Examination of the effect of systematic placement considering the calorific value of each waste 1) Purpose The variation in the calorific value of each waste upon confirmation when receiving the vitrified body and placing the waste in the underground facility Consider how to deal with. Unlike the thermal analysis according to the present embodiment, the following description is based on a study using an evaluation model that assumes a situation in which the heat generation distribution for each waste body extends infinitely while maintaining symmetry. Since it became clear that the management of the calorific value is important as a property of the solidified glass, the thermal analysis that models multiple wastes with different calorific values was conducted, and a study on how to handle the variation in calorific value was conducted. Started. Regarding the handling of the variation in the calorific value, as shown in Table 7 below, three patterns were considered according to the difference in the waste arrangement method and the design concept.

*) Since an upper limit value of the calorific value is set at the time of manufacturing the vitrified body, an upper limit value naturally exists also in the calorific value at the time of stationary (assuming storage after 50 years).

  The plan A in Table 7 assumes that the thermal design is performed assuming that the calorific value of all wastes is equal to the upper limit value, and the design concept is the most conservative and clear. However, on the other hand, the above study showed that the required area occupied by the waste (the product of the distance between the disposal tunnels and the distance between the disposal holes) becomes excessive. The plan B, like the plan A, randomizes the arrangement of the underground waste, but aims at a more rational design in consideration of the calorific value distribution. For the plan B, 12 waste bodies (refer to FIG. 18, in which the calorific value indicated by the arrow is set) with the calorific value variation set as a normal distribution of the calorific value variation, the buffer material maximum temperature is The thermal analysis was carried out by placing it conservatively so as to be the largest. As a result, the area occupied by the required waste was smaller than that of Plan A, and it was expected that a rational design was possible from Plan A.

  Unlike plan A and plan B, plan C is a case where the arrangement is devised in consideration of the amount of heat generated for each waste body. In the above study, as a result of conducting a thermal analysis by rearranging the waste materials so that the maximum temperature of the buffer material becomes smaller than the conservative waste material layout assumed in the above B plan, the maximum temperature of the buffer material is It became smaller than B plan. From this, the prospect that more rational design is possible by devising the arrangement of the waste body according to the calorific value was obtained.

  However, the evaluation model used in the above examination divides the probability distribution of the calorific value and assigns it to 12 waste bodies (see FIG. 18), and the heat generation distribution for each of the 12 waste bodies is infinite while maintaining symmetry. It is assumed that the situation is widespread, and lacks generality as an evaluation model. Although the evaluation model used in the above discussion can discuss qualitative trends, it sets the interval between the waste bodies in a way that can reasonably explain the spatial variation in the calorific value (design). Is not necessarily an appropriate evaluation model.

  Therefore, considering the uncertainty of the calorific value of the waste, according to the case where the waste is randomly placed (plan B in Table 7) and the calorific value using a more general temperature evaluation system Temperature evaluation is performed for the case where the arrangement method is devised (C plan in Table 7). Based on these results, the area occupied by the waste body required is calculated, and the effect of managing the waste heat generation amount is quantitatively investigated.

2) Study policy Conduct temperature evaluations in the following two cases, calculate the waste-occupied area required in each case, and quantitatively clarify the latter effect by comparing the two.
・ When placing randomly without considering the difference in calorific value of each waste ・ When devising the arrangement considering the difference in calorific value of each waste

(A) Preconditions In this study, it is a requirement that the maximum temperature of each surrounding cushioning material does not exceed 100 ° C in all wastes considered in the evaluation model.

(B) Target of study This study is intended for hard rock anchors. The investigation will be conducted based on a disposal depth of 1,000m (assuming that the ground surface temperature is 15 ° C, the temperature gradient is + 3 ° C / 100m, and the initial ground temperature is 45 ° C). However, in the case of the standing type, the area occupied by the waste body is determined by the dynamic conditions of the bedrock. Is done. Therefore, in order to clarify such conditions, evaluation is performed when the disposal depth is changed based on the result of the disposal depth of 1,000 m using the linearity of the thermal analysis.

(C) Calculation method of necessary area occupied by required waste In this study, random sampling using the thermal analysis of this embodiment, assuming a probability distribution of the amount of heat generation, as a temperature evaluation taking into account variations in the amount of heat generated by multiple waste bodies Carry out Monte Carlo simulation with The number of realizations in the Monte Carlo simulation is 10,000. Regarding the concept of the required area occupied by the waste body, in this study, it is a necessary condition that the maximum temperature of the buffer material is 100 ° C. or less for all of the modeled waste bodies in all 10,000 calculation results. To do. That is, the exclusive area is determined such that the probability that there is a waste body having a maximum buffer material temperature exceeding 100 ° C. is 1 / 10,000 or less.

  Specifically, taking into account the dynamic conditions of the rock mass, for example, the disposal tunnel spacing = 10m and the disposal hole spacing = 4.4m are the initial values, and the area occupied by the waste is increased until the above conditions are satisfied. To do.

(D) Method of expanding the exclusive area From the viewpoint of efficiently reducing the buffer material temperature, when expanding the exclusive area of the waste body (product of the distance between the disposal tunnel and the disposal hole), It is effective to increase isotropically. However, in view of cost advantage, in this study, the disposal hole interval is fixed and only the disposal tunnel interval is increased (see FIG. 19).

(E) Variation in calorific value and its spatial distribution It is assumed that the probability distribution of the waste calorific value is a normal distribution. Here, considering that wastes are manufactured in batch units (1 batch = equivalent to about 12 wastes), the amount of heat generated varies depending on the production time, etc., and the identification (bias) for each batch The possibility of having it is considered. However, in this study, it is assumed that the variation in calorific value is uniform across the entire disposal panel. In other words, the calorific values of all the waste bodies follow the same probability distribution, and the spatial bias of the waste body calorific values is not considered.

3) Examination Method (a) Analysis Method A temperature evaluation is performed in consideration of spatial variations in the amount of heat generated by a plurality of waste bodies by an approximate evaluation using the thermal analysis (“superposition method”) according to the present embodiment.

(B) Analytical model In this study, the waste body for one panel is handled as an analysis target with reference to the waste body layout in the underground facility layout shown in FIG. That is, the number of disposal tunnels = 27, the number of wastes per disposal tunnel = 247, and the total number of wastes = 6,669 (27 × 247). However, the panel shape is rectangular for simplicity.

(C) Analyzed physical property values The physical property values used for the analysis are shown in Table 1 above.

(D) Parameters relating to distribution of waste body The probability distribution of the initial heat generation amount of the waste body is assumed to be a normal distribution, and the following parameters are considered.

a) Average value of initial calorific value The average value of initial calorific value is 350 [W].

b) Standard deviation of initial calorific value In this study, the standard deviation of initial calorific value is set to 50 [W].

c) Upper limit value and lower limit value of initial heating value The upper limit value of initial heating value is set to 430 [W]. Further, 200 [W] (μ−3σ) is set as the lower limit value of the initial calorific value.

(E) Device arrangement for waste according to the amount of heat generated When considering an arrangement method that can effectively reduce the temperature of the buffer material, if all the waste for one panel is prepared at the start of placement, the buffer material Considering that the maximum temperature of the waste is the minimum, it is considered as an optimal placement problem of the waste body with an objective function. For example, an optimization method such as “genetic algorithm” or “annealing method” may be applied.

  In practice, the calorific value of the waste is measured and managed, so it is considered that an optimum arrangement method of the waste for each receiving unit is deterministically required. Here, in order to reduce the maximum temperature of the cushioning material, it is basically effective to place a waste body with a small calorific value next to a waste body with a large calorific value. Examine the effect of the placement method.

[Draft 1] Two-partition method FIG. 21A shows a distribution image of the heat generation amount of the waste body for one panel. As shown in FIG. 21A, waste bodies are classified into two groups according to the amount of heat generation, and the one with the larger amount of heat generation is called group (A), and the one with the smaller amount of heat generation is called group (B). I will decide. This method is a method in which wastes are placed in the following order in the disposal tunnel, and the wastes of the groups (A) and (B) are always managed adjacent to each other (hereinafter referred to as “two-division method”).

a ₁ → b ₁ → a ₂ → b ₂ → a ₃ → b ₃ → ... → a _i → b _i → ...
(A _i and b _i are wastes randomly extracted from groups (A) and (B), respectively)
In addition, wastes adjacent to each other in the direction perpendicular to the disposal tunnel are also considered in the arrangement so that the order is as described above.

[Draft 2] Quadrant Method Extending the above idea, as shown in FIG. 21 (b), waste materials are classified into four groups according to the amount of heat generation, and the groups ( A), group (B), group (C), and group (D) will be referred to. This method is a method in which wastes are placed in the following order in the disposal tunnel, and a waste body with a large calorific value is always managed so as to be adjacent to a waste body with a small calorific value (hereinafter referred to as “four-division method”).
_{a 1 → d 1 → b 1} → c 1 → a 2 → d 2 → b 2 → c 2 → a 3 → d 3 → b 3 → c 3 → ...
... → a _i → d _i → b _i → c _i → ...
(A _i , b _i , c _i and d _i are wastes randomly extracted from the groups (A), (B), (C) and (D), respectively)
In addition, wastes adjacent to each other in the direction perpendicular to the disposal tunnel are also considered in the arrangement so that the order is as described above.

[Draft 3] Eight-division method Extending the same idea as described above, the wastes are classified into eight groups according to the amount of heat generation as shown in FIG. These are called (A), group (B),..., Group (H). In the 8-division method, as an example of the disposal order of waste bodies, management is performed so that they are placed in the following order.
a ₁ → h ₁ → d ₁ → e ₁ → c ₁ → f ₁ → b ₁ → g ₁ →
a ₂ → h ₂ → d ₂ → e ₂ → c ₂ → f ₂ → b ₂ → g ₂ →
... → a _i → h _i → d _i → e _i → c _i → f _i → b _i → g _i → ...
(A _i , b _i ,..., H _i are wastes randomly extracted from groups (A), (B),..., (H), respectively)
In addition, wastes adjacent to each other in the direction perpendicular to the disposal tunnel are also considered in the arrangement so that the order is as described above.

(F) Setting of calorific value of each waste body in analysis Setting of the calorific value of each waste body in the analysis is performed by the following method. In the case of random arrangement, 6,669 random samplings are performed per realization according to the probability distribution of the calorific value assumed in each case. These calorific values are taken as Q ₁ , Q ₂ ,..., Q ₆₆₆₉ in order. As shown in FIG. 22, the heat generation amounts Q _{1 to} Q ₆₆₆₉ are assigned to the respective waste bodies in order from the waste bodies at the corners of the panel.

When arranging the heat generation according to the heat generation amount (in the case of the two-division method), similar to the above, 6,669 random samplings are performed per realization according to the probability distribution of the heat generation amount, and these heat generation amounts are sequentially arranged. Q ₁ , Q ₂ ,..., Q ₆₆₆₉ . The calorific values of Q _{1 to} Q ₆₆₆₉ are divided into two groups (A) and (B) according to their sizes (hereinafter, Q ₁ (A) indicates whether each calorific value belongs to (A) or (B). , Q ₂ (B) etc.). When the order of Q ₁ , Q ₂ , Q ₃ ,... Is alternating between groups (A) and (B), they are placed as they are in the order shown in FIG. If any of the groups (A) and (B) is not continuously alternated, the most recent heat generation amount is exchanged and adjustment is performed so that (A) and (B) alternate. For example, when Q ₁ (A), Q ₂ (B), Q ₃ (B), Q ₄ (A), Q ₅ (A),..., Q ₁ (A), Q ₂ (B), Q ₃ (A), Q ₄ (B), Q ₅ (A),...

(G) Analysis Case and Analysis Procedure Monte Carlo simulation is performed on the six cases shown in Table 8 below, and the waste-occupied area required in each case is obtained by trial and error.

The process at this time is the process described with reference to FIG. In addition, the reset of the arrangement position of the waste body in S07 is to increase the distance between disposal tunnels by 0.5 m, for example. Further, the waste body exclusive area can be calculated by the product of the distance between the disposal tunnels and the distance between the disposal holes as described above.

4) Examination result As an example of the result of the Monte Carlo simulation, the case where the waste body arrangement is fixed in the standard specification under the heat generation condition of case 1-B shown in Table 8 (disposal depth = 1000 m, average value of initial heat generation amount of waste body = FIG. 23 shows the analysis result of 10,000 realizations at 350 W, standard deviation = 50 W, upper limit value = 430 W, disposal tunnel separation distance = 10 m, random arrangement). FIG. 23 is a plot of 10,000 points of the maximum peak temperature of the buffer material around all waste bodies (6,669) in each realization.

  FIG. 24 shows the result of the waste-occupied area in each case calculated according to the processing described with reference to FIG. From this, the quantitative effect of devising the waste body arrangement according to the calorific value was clarified as compared with the case where the waste bodies are randomly arranged.

(2) Quantitative effect of “heat removal effect” at the panel edge For the area where the “heat removal effect” at the panel edge can be expected, how much the amount of generated heat is increased relative to the “area without heat removal effect” Quantitatively consider the effect of acceptability. Here, as in the case of (1) above, the case where the hard rock is placed and the disposal depth is 1,000 m is targeted, and the evaluation model is also the waste for one panel (27 × 247 = 6,669 pieces, see FIG. 25). ). Here, the waste body heating value is placed deterministically to perform temperature evaluation,
・ Examine the range of the area where the heat removal effect can be expected and the maximum amount of heat generated at the end.

  First, FIG. 26 shows the distribution of the maximum value of the buffer material inner temperature according to the position of the panel when the initial heat generation amount of all the waste bodies is uniformly 350 [W]. From this, it is considered that the range where the “heat removal effect” can be expected is an area of about 50 m from the end of the panel.

  Next, temperature evaluation was performed when the initial calorific value was increased only for the wastes in the outermost disposal tunnel. The buffer material maximum temperature in the outermost disposal tunnel is shown in FIG. Accordingly, when the initial heat generation amount of other waste bodies is uniformly 350 [W], it can be said that the initial heat generation amount of the waste body in the outermost disposal tunnel is allowable up to 460 [W].

  Then, the thermal analysis program for making a computer perform the process by the series of thermal analysis apparatuses 10 mentioned above is demonstrated. As shown in FIG. 28, the thermal analysis program 30 is inserted into a computer and accessed, or stored in a program storage area 21 formed on a recording medium 20 provided in the computer.

  The thermal analysis program 30 includes a unit information input module 31, a base case calculation module 32, a heating element information input module 33, a temperature effect calculation module 34, an addition module 35, a determination module 36, and an output module 37. It is prepared for. It is realized by executing the unit information input module 31, the base case calculation module 32, the heating element information input module 33, the temperature influence calculation module 34, the addition module 35, the determination module 36, and the output module 37. The function includes a unit information input unit 11, a base case calculation unit 12, a heating element information input unit 13, a temperature effect calculation unit 14, an addition unit 15, a determination unit 16, and a thermal analysis apparatus 10 described above. The functions of the output unit 17 are the same.

  Note that a part or all of the thermal analysis program 30 may be transmitted via a transmission medium such as a communication line and received and recorded (including installation) by another device. Each module of the thermal analysis program 30 may be installed in any one of a plurality of computers instead of one computer. In that case, the series of processes of the thermal analysis program 30 described above is performed by the computer system of the plurality of computers.

DESCRIPTION OF SYMBOLS 1 ... Waste body, 10 ... Thermal analysis apparatus, 11 ... Unit information input part, 12 ... Base case calculation part, 13 ... Heating body information input part, 14 ... Temperature influence calculation part, 15 ... Addition part, 16 ... Determination part, DESCRIPTION OF SYMBOLS 17 ... Output part, 20 ... Recording medium, 21 ... Disposal tunnel, 21 ... Program storage area, 30 ... Thermal analysis program, 31 ... Unit information input module, 32 ... Base case calculation module, 33 ... Heating element information input module, 34 ... temperature influence calculation module, 35 ... addition module, 36 ... judgment module, 37 ... output module.

Claims (8)

A thermal analysis device that performs thermal analysis in a region where a plurality of heating elements are arranged,
Unit information input means for inputting information about the region and the number of heating elements;
Base case calculating means for calculating the influence of the temperature by the heating element according to the position from the unit number of heating elements based on the information input by the unit information input means;
Heating element information input means for inputting information indicating positions and the number of heating elements in which the plurality of heating elements are arranged in the region;
Based on the influence calculated by the base case calculation unit and the distance from the position where the heating element indicated by the information input by the heating element information input unit is arranged to the evaluation point which is a predetermined position in the region A temperature influence calculating means for calculating the influence of the temperature at the evaluation point of the heating element;
Adding means for adding the influence of temperature at the evaluation point of each heating element calculated by the temperature influence calculating means;
Output means for outputting information indicating the influence of temperature at the evaluation point added by the adding means;
A thermal analysis apparatus comprising: The unit information input means inputs information indicating the amount of heat generated by the unit number of heating elements as information on the unit number of heating elements,
The heating element information input means inputs information indicating the calorific value of the heating element arranged,
The temperature influence calculation means calculates the influence of the temperature at the evaluation point of each of the arranged heating elements according to the amount of heat generated by the unit number of heating elements and each of the arranged heating elements. The thermal analysis apparatus according to 1.   The thermal analysis apparatus according to claim 2, wherein the heating element information input unit determines an arrangement of the heating elements according to a heating value of the heating elements.   The thermal analysis apparatus according to claim 2 or 3, wherein the heating element information input means inputs information indicating the probability distribution of the heating amount and determines the heating amount of each heating element according to the probability distribution. The heating element information input means determines a plurality of heating amounts of each heating element according to the probability distribution,
The thermal analysis apparatus according to claim 4, wherein the temperature influence calculation unit and the addition unit perform processing for each of a plurality of sets of heat generation amounts of the heating elements determined by the heating element information input unit.   It is determined whether or not the influence of the temperature at the evaluation point added by the adding means satisfies a preset condition. If it is determined that the condition is satisfied, the output by the output means is executed, and is not satisfied If it is determined, the information indicating the position where the plurality of heating elements different from the influence of the temperature at the evaluation point is input to the heating element information input means, and the temperature at the evaluation point based on the position is input. The thermal analysis apparatus according to any one of claims 1 to 5, further comprising a determination unit that calculates the influence again. A thermal analysis method for performing thermal analysis in a region where a plurality of heating elements are arranged,
A unit information input step for inputting information about the region and the number of heating elements;
Based on the information input in the unit information input step, a base case calculation step for calculating the influence of temperature by the heating element according to the position from the unit number of heating elements;
A heating element information input step for inputting information indicating a position where the plurality of heating elements are arranged in the region and the number of heating elements;
Based on the influence calculated in the base case calculation step and the distance from the position where the heating element indicated by the information input in the heating element information input step is arranged to the evaluation point which is a predetermined position in the region A temperature influence calculating step for calculating the influence of the temperature at the evaluation point of the heating element;
An adding step of adding the temperature influence at the evaluation point of each heating element calculated in the temperature influence calculating step;
An output step of outputting information indicating the influence of the temperature at the evaluation point added in the addition step;
Thermal analysis method including A thermal analysis program for performing thermal analysis in an area where a plurality of heating elements are arranged,
Computer
Unit information input means for inputting information about the region and the number of heating elements;
Base case calculating means for calculating the influence of the temperature by the heating element according to the position from the unit number of heating elements based on the information input by the unit information input means;
Heating element information input means for inputting information indicating positions and the number of heating elements in which the plurality of heating elements are arranged in the region;
Based on the influence calculated by the base case calculation unit and the distance from the position where the heating element indicated by the information input by the heating element information input unit is arranged to the evaluation point which is a predetermined position in the region A temperature influence calculating means for calculating the influence of the temperature at the evaluation point of the heating element;
Adding means for adding the influence of temperature at the evaluation point of each heating element calculated by the temperature influence calculating means;
Output means for outputting information indicating the influence of temperature at the evaluation point added by the adding means;
Thermal analysis program to function as