A methodology for segmenting large metal components from nuclear power plants has been developed with a view to minimizing the number of containers to emplace segmented pieces. Spherocylinder-type and rectangular prism-type objects are modeled in shapes, and equations to calculate heights, widths, lengths, or angles for segmentation and the number of pieces are derived using geometric theorems, with a hypothetical ‘virtual rectangle’ being introduced for simplification. Applicability of the new methodology is verified through case studies assuming that each segmented piece is packaged into a 200 L container, and a procedure for adjusting potential overestimation of the segmented pieces due to the virtual rectangle is proposed. The new approach results in fewer segmented pieces but more containers than an existing segmentation study using 3D modeling. It is demonstrated that the number of containers can be further reduced, however, if the generalized methodology is followed by 3D modeling. In addition, it is confirmed that the generalized approach is also applicable to a nonstandard shapes such as ellipsoidal shape but only under limited conditions. Sensitivity analyses are conducted by changing dimensions of the objects and container, which brings about an optimal dimension of container as well. The generalized approach would be utilized either alone in decommissioning planning to estimate waste from segmentation of large metal components or combined with 3D modeling to optimize segmentation operation.

The International Atomic Energy Agency (IAEA) estimates that about 6200 tons of radioactive waste is to be generated from decommissioning of a unit of 900–1300 MWe pressurized water reactor (PWR), and approximately 67% of the waste is in a form of either surface-contaminated or neutron-activated metal [

If a large metal component is decided to be segmented, a segmentation strategy, which can be defined as a process to find a set of lengths and/or angles to segment an object with a view to optimizing subsequent management of resulting segmented pieces, should be considered early in planning for decommissioning. It has been reported that the segmentation strategy can be driven by various factors such as the type of waste container, disposal cost, and transportation requirements [

Various experiences in segmentation of large metal components at nuclear power plants (NPPs) under decommissioning can be found in literature. For instance, the segmentation strategy using 3D modeling software (e.g., CAD-CAM), the segmentation techniques adopted for large components, and the results have been reported in various literature works including decommissioning experience reports for actual NPPs and a few technical papers [

Relatively recently, a few investigators have attempted to calculate angles or lengths for segmentation based upon the geometric shapes of large metal components using 3D modeling software in order to establish the segmentation strategy. In 2013, Lee et al. have suggested an approach to segmenting the cylindrical part of an RPV at an angle derived using a 3D digital model based upon two constraints on dimensions (i.e., width and depth) of segmented pieces being packaged into cuboid-shape containers [

Based on the above literature review, this study aims at proposing a new generalized and geometrical approach to optimal segmentation of representative types of large metal components from NPPs with consideration of the dimensions of both the large metal component and the container in which the segmented pieces are to be emplaced. Applicability of the generalized approach is to be verified through comparison with comparable techniques; however, the method proposed by Lee et al. (2013) [

Though various types of large metal components are generated from NPPs, the representative shapes of them are firstly categorized into the followings: (i) a spherocylinder-type object such as RPV, SG, and PRZ and (ii) a rectangular prism-type object representing walls of spent fuel storage rack. It is assumed that the spherocylinder-type object simply consists of a cylindrical part and two hemispherical parts with the same thickness, while the rectangular prism-type object is assumed to be in a hollow cuboid shape with a constant thickness without lid or bottom. The shapes of the spherocylinder-type and rectangular prism-type objects are schematically shown in Figure

Schematic view of two types of objects representing large metal components: (a) spherocylinder-type object; (b) rectangular prism-type object.

Even for the same object of large metal component, the derived segmentation strategy would be widely varied depending upon the volume and/or the shape of containers to be used. In this study, a cylindrical storage container widely used at NPPs in operation or under decommissioning is assumed to be used to emplace the segmented pieces as shown in Figure

Schematic view of a cylindrical storage container into which segmented pieces are to be emplaced.

Segmentation of the object is not needed, and just direct packaging of one-piece object without cutting is practical enough under the following conditions:

Spherocylinder-type object:

Rectangular-prism-type object:

The cylindrical part and the two hemispherical parts of a spherocylinder-type object (see Figure

Schematic view of sequential segmentation strategy for the spherocylinder-type object shown in Figure

When the cylindrical part of a spherocylinder-type object is segmented in horizontal direction, the height of segmented pieces should be lower than the reference value (i.e., the height of container,

After being horizontally segmented to the uniform height

Top view of the piece resulting from horizontal and subsequent vertical segmentations of the cylindrical part of a spherocylinder-type object emplaced into a container together with a virtual rectangle assumed in this study.

Once the virtual rectangle is introduced as in Figure

Likewise,

Accordingly,

Based upon the same approach adopted in horizontal segmentation, it is assumed that the horizontally segmented cylindrical part is to be cut in vertical direction into pieces all having the same segmentation angle. Accordingly, the uniform segmentation angle for vertical cutting

Finally, the number of segmented pieces to be generated from the cylindrical part

When the cylindrical part of a spherocylinder-type object is segmented in horizontal direction as depicted in Figure

Side view of the piece resulting from horizontal and subsequent vertical segmentations of a hemispherical part of a spherocylinder-type object.

The hemispherical part is also assumed to be segmented into pieces at the same horizontal angle and with the same chord length. Therefore, the uniform segmentation angle for horizontal cutting

After horizontal segmentation of the hemispherical part at the uniform angle

Top view of the piece resulting from horizontal and subsequent vertical segmentations of a hemispherical part of spherocylinder-type object emplaced into a container together with the virtual rectangle assumed in this study.

As shown in Figure

It is noted that (

On the other hand, the uniform angle for vertical cutting

Therefore, the number of segmented pieces

Finally, the total number of segmented pieces from the spherocylinder-type object

The rectangular prism-type object considered in this study consists of four rectangular walls of the same height and thickness without ceiling or bottom as shown in Figure

Schematic view of sequential segmentation strategy for the rectangular prism-type object shown in Figure

The rectangular prism-type object whose four walls have been separated is to be further segmented horizontally at height

The horizontally segmented pieces are to be subsequently segmented in vertical direction and then emplaced into the cylindrical container (see Figure

Top view of a finally segmented piece from the rectangular prism-type object placed into the container: (a) a segmented piece from front/back walls; (b) a segmented piece from left/right walls.

In Figure

As shown in Figure

The total number of final pieces from the rectangular prism-type object

Based upon a set of descriptions and equations in Sections

Flow chart of generalized approach to establishing segmentation strategy for large metal components developed in this study.

The generalized approach to establishing segmentation strategy proposed in this study (see Figure

The uniform segmentation height _{C,S} = 189) from the cylindrical part is calculated by multiplying _{C,Z,S}(=9) by _{C,V,S}(=21) and that

Segmentation strategy derived for the spherocylinder-type object assumed in this study and comparison with the results from 3D modeling using Rhino [

Target | Parameter | Equation | Results | Relative error of general approach | ||
---|---|---|---|---|---|---|

This study | 3D modeling (C) | |||||

General approach (A) | Adjustment (B) | |||||

Cylindrical part | ( | 0.844 m | 0.844 m | 0.844 m | — | |

( | 17.1° | 18° | 18° | −4.78% | ||

( | 9 | 9 | 9 | — | ||

( | 21 | 20 | 20 | +5.00% | ||

( | 189 | 180 | 180 | +5.00% | ||

Hemispherical parts | ( | 30° | 30° | 30° | — | |

( | 17.1° | 18° | 18° | −4.78% | ||

( | 3 | 3 | 3 | — | ||

( | 21 | 20 | 20 | +5.00% | ||

( | 126 | 120 | 120 | +5.00% | ||

Total | ( | 315 | 300 | 300 | +5.00% |

Potential gaps between the number of segmented pieces generally derived in Column (A) of Table

General top view of a finally segmented piece from the cylindrical part of a spherocylinder-type object depicted for deriving adjustment algorithm for errors induced by the virtual rectangle.

As shown in Figure

Points C and D should be within the inner area of the container (i.e.,

That is, (

In order to adjust the possible gap which may be caused by the virtual rectangle assumed in the generalized segmentation approach of this study, the range of new segmentation angle

Likewise, it is shown in Table

Though the gap in the number of vertically segmented pieces between the general approach and the adjustment is “

In order to evaluate the relative efficiency of the generalized segmentation approach and the adjustment methodology proposed in this study, the same spherocylinder-type object has been virtually segmented using the well-known 3D modeling software Rhinoceros® (i.e., Rhino) in a manual way under the same constraints addressed in Section

In addition, the result from 3D modeling turns out to be the same as the adjusted result in terms of segmentation height, angles, and resulting number of pieces (see Table

The generalized segmentation approach developed has been implemented to a rectangular prism-type object of specified dimensions (

The uniform segmentation height

Segmentation strategy derived for the specified rectangular prism-type object assumed in this study and comparison with the results from 3D modeling using Rhino [

Target | Parameter | Equation | Results | Relative error of general approach | ||
---|---|---|---|---|---|---|

This study | 3D modeling (C) | |||||

General approach (A) | Adjustment (B) | |||||

Front and back walls | ( | 0.8 m | N/A | 0.8 m | — | |

( | 0.52 m | N/A | 0.52 m | — | ||

( | 10 | N/A | 10 | — | ||

( | 19 | N/A | 19 | — | ||

Left and right walls | ( | 0.8 m | N/A | 0.8 m | — | |

( | 0.50 m | N/A | 0.50 m | — | ||

( | 10 | N/A | 10 | — | ||

( | 19 | N/A | 19 | — | ||

Total | ( | 760 | N/A | 760 | — |

The same rectangular prism-type object has been virtually segmented using the 3D modeling software Rhino, under the same constraints given in Section

Additional consideration of potential adjustment of segmentation height, width, and length or the number of segmented pieces resulting from the general segmentation approach as above is not needed, since the virtual rectangle has not been assumed in the segmentation of the rectangular prism-type object (see Figure

The generalized approach proposed in this study is additionally compared with a comparable technique reported in the past study on segmentation of a large metal component from an NPP in which geometries and dimensions of the target component and container are specified [

Geometries and dimensions of the RPV and storage container assumed for comparison with the past study [

Target | Part | Parameter | Value (m) |
---|---|---|---|

RPV | Cylindrical part | 8.24 | |

1.68 | |||

0.17 | |||

Hemispherical parts | 1.68 | ||

0.17 | |||

M II-10T MOSAIK® cask | 1.22 m | ||

0.86 m |

The procedure for deriving the segmentation strategy for the spherocylinder-type object adopted in Section

Comparison of segmentation strategies derived in this study and reported in the past study for the same target object and container defined in Table

Target | Parameter | Equation | Results | Relative error of this study with respect to past study | ||
---|---|---|---|---|---|---|

This study | Past study [ | |||||

General approach (A) | Adjustment (B) | |||||

Cylindrical part | ( | 1.18 m | 1.18 m | 1.03 m | +14.3% | |

( | 25.7° | 25.7° | 10° | +157% | ||

( | 7 | 7 | 8 | −12.5% | ||

( | 14 | 14 | 36 | −61.1% | ||

( | 98 | 98 | 288 | −66.0% | ||

Hemispherical parts | ( | 30° | 30° | 30° | — | |

( | 25.7° | 25.7° | 10° | +157% | ||

( | 3 | 3 | 3 | — | ||

( | 14 | 14 | 36 | −61.1% | ||

( | 84 | 84 | 216 | −61.1% | ||

Total | ( | 182 | 182 | 504 | −63.9% | |

— | 98 | 98 | 126 | −22.2% |

However, the number of containers (i.e.,

In order to compare the number of resulting containers from the two studies under the same conditions, therefore, we tried to reduce the total number of containers by assuming that multiple pieces derived from the general approach can be emplaced into a container. The volume of each piece in Type C is the same as or higher than any other pieces in Types

As an initial trial, therefore, 84 segmented pieces of three types (i.e., Types

It is noted that the resulting number of containers may decrease by

The generalized approach to establishing segmentation strategy proposed in this study can be comprehensively applied to the ‘cylindrical part of spherocylinder-type’ and ‘rectangular prism-type’ objects of any components or structures. If the top or bottom head of RPV is not perfectly hemispherical, however, the methodology in this study may not be fully applicable. In order to show the applicability of the new methodology for nonhemispherical head of pressure vessel, the generalized approach to establishing segmentation strategy proposed in this study has been implemented to the bottom head of VVER-1000 reactor whose shape is reported to be ‘ellipsoidal’ in accordance with the categories of head shapes in the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code (BPVC) Section VIII Division 1 [

Comparison of geometry and dimensions of actual ellipsoidal-type bottom head (blue solid line) of VVER-1000 with hemispherical-type shape assumed in the study (red dotted line).

As shown in Table

Segmentation strategy derived for an ellipsoidal-type bottom head of VVER 1000 RPV and comparison with the results from 3D modeling using Rhino.

Target | Parameter | Equation | Result | Relative error of general approach | |
---|---|---|---|---|---|

This study general approach (A) | 3D modeling (B) | ||||

Ellipsoidal shape | ( | 22.5° | 22.5° | — | |

( | 14.4° | 15° | −4.00% | ||

( | 4 | 4 | — | ||

( | 25 | 24 | +4.17% | ||

( | 100 | 96 | +4.17% |

Using the segmentation angles derived from the generalized approach (

Results of 3D modeling using Rhino for emplacement of all types of segmented pieces into a 200 L container for (a) actual ellipsoidal-type bottom head of VVER 1000 RPV and (b) hypothetical hemispherical model assumed to apply the generalized approach to the ellipsoidal-type object.

A series of sensitivity analyses has been conducted by varying geometry and dimensions of the target objects and container, in order to demonstrate the applicability of the generalized segmentation strategy to various conditions and to quantify the effect of major parameters on the number of segmented pieces.

The volume of a spherocylinder-type object

As shown in Figure

Number of segmented pieces along with variation of the volume of spherocylinder-type object from

In Case 1A (_{C} <

The constraint _{C} < _{D} is applied for the vertical segmentation of the cylindrical part. The depth of the segmented piece _{H} (i.e., _{H} in (

In Case 1B (_{H,V,S} in (_{c} can be attributed to the increment of _{H,V,S} with increasing _{c} as well (see (

In Case 1C (

When

The volume of a rectangular prism-type object

Accordingly,

Number of segmented pieces along with variation of the volume of rectangular prism-type object from ^{3} by changing one parameter only for each case (i.e., thickness in Case 2A, length or width in Case 2B, and height of object in Case 2C). Case 2D represents a priori segmentation in half of the same object assumed in Case 2A and application of generalized segmentation approach.

In Case 2A (

It is observed, in Case 2B (

The number of segmented pieces increases steeply to the infinity if

In order to investigate the effect of variable dimensions of a 200 L cylindrical container on the number of segmented pieces and determine optimal dimensions of the container, the generalized segmentation strategy has been applied to the spherocylinder-type object for the reference case in Section

Total number of segmented pieces and volume of steel used for manufacturing all containers with increasing height (or decreasing radius) of 200 L container. (A) and (B) are the points of the minimum values for the total number of segmented pieces and the volume of steel for all containers, respectively.

The plot of total number of segmented pieces versus height (or radius) of container shows a U-shape curve in general, which has its minimum ^{3}.

All through the range of

Some irregularities are observed in the general U-shape curve in Figure

The curves in Figure

On the other hand, the segmented pieces and volume of steel for containers have been also analyzed for the rectangular prism-type object in the reference case defined in Section

Most of publicly reported practices and studies on segmentation of large metal components from NPPs have focused on introducing the results of 3D modeling to specific cases without detailed descriptions of methodology and/or technical basis. Based upon a few assumptions for simplification, however, generalized equations and procedure for calculating heights, lengths, widths, lengths, or angles for segmentation and the number of resulting pieces using geometric dimensional information of the objects and the container have been derived in this study.

As a result of the case study on the spherocylinder-type object of reference dimension, the generalized approach overestimates the number of segmented pieces

Through comparison with an existing study on segmentation of an RPV based upon 3D modeling, the generalized approach gives rise to

Sensitivity analyses of geometric parameters on the number of pieces derived from general approach to the spherocylinder-type object show linearly increasing curves with local irregularities for

It is anticipated that the generalized approach including adjustment algorithm proposed in this study can be used in either of the following ways: (i) standalone application in initial decommissioning planning to establish conceptual segmentation strategy, to estimate the waste from large metal components, and so on; (ii) application in actual segmentation planning to derive angles, heights, etc. for segmentation or to optimize the segmentation strategy (e.g., minimizing the need for containers) prior to or in combination with 3D modeling.

Height of cylindrical part of spherocylinder-type object

Height of rectangular prism-type object

Inner height of container

Height of horizontal segmentation of cylindrical part of spherocylinder-type object

Height of horizontal segmentation of rectangular prism-type object

Height of ellipsoidal shape

Inner radius of cylindrical part of spherocylinder-type object

Inner radius of hemispherical part of spherocylinder-type object

Thickness of cylindrical part of spherocylinder-type object

Thickness of hemispherical part of spherocylinder-type object

Thickness of rectangular prism-type object

Inner diameter of container

Length of rectangular prism-type object

Length of vertical segmentation of left and right walls of rectangular prism-type object

Chord length of vertical segmentation of cylindrical part of spherocylinder-type object

Chord length of horizontal segmentation of hemispherical part of spherocylinder-type object

Chord length of vertical segmentation of hemispherical part of spherocylinder-type object

Angle of vertical segmentation of cylindrical part of spherocylinder-type object (degree)

Angle of horizontal segmentation of hemispherical part of spherocylinder-type object (degree)

Angle of vertical segmentation of hemispherical part of spherocylinder-type object (degree)

Angle of horizontal segmentation of ellipsoidal shape (degree)

Angle of vertical segmentation of ellipsoidal shape (degree)

Included angle of virtual rectangle of cylindrical part of spherocylinder-type object (degree)

Included angle of virtual rectangle of hemispherical part of spherocylinder-type object (degree)

Width of rectangular prism-type object

Depth of segmented piece of hemispherical part of spherocylinder-type object

Width of vertical segmentation of front and back walls of rectangular prism-type object

Number of segmented pieces of cylindrical part of spherocylinder-type object (−)

Number of horizontally segmented pieces of cylindrical part of spherocylinder-type object (−)

Number of vertically segmented pieces of cylindrical part of spherocylinder-type object (−)

Number of segmented pieces of hemispherical part of spherocylinder-type object (−)

Number of horizontally segmented pieces of ellipsoidal shape (−)

Number of vertically segmented pieces of ellipsoidal shape (−)

Number of segmented pieces of ellipsoidal shape (−)

Number of horizontally segmented pieces of hemispherical part of spherocylinder-type object (−)

Number of vertically segmented pieces of hemispherical part of spherocylinder-type object (−)

Number of segmented pieces of rectangular prism-type object (−)

Number of segmented pieces of front and back walls of rectangular prism-type object (−)

Number of segmented pieces of left and right walls of rectangular prism-type object (−)

Number of containers (−)

Volume of spherocylinder-type object

Volume of rectangular prism-type object

Volume of container

Spherocylinder-type object

Front and back walls

Left and right walls

Rectangular prism-type object

Cylindrical part of spherocylinder-type object

Hemispherical part of spherocylinder-type object

Container

Horizontal

Vertical

Segmentation

Included

Ellipsoidal shape.

The data used to support the findings of this study are included within the article.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was partly supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grants funded by the Korean government (MOTIE) (no. 20191510301290, Development of Configuration Management Platform for Decommissioning of Nuclear Power Plants (no. 20203210100240), Development of a Platform for Optimization of Interdependences in Packaging-Transport-Disposal of Radioactive Waste and History Management).