Selection of the optimal option for the transformation of the “Shelter” object into an environmentally safe system using the factor-criterion model of scenario analysis

The paper presents a comprehensive analysis of potential scenarios for Shelter Object transformation into an environmentally safe system after the commissioning of the New Safe Confinement. The analysis of scenarios is based on the developed factor-criteria model, which includes two groups of indicators in the scenario assessment: groups of factors and sets of criteria for each factor. The assessment of a separate scenario is carried out using the global value indicator. The global value of the scenario is determined taking into account the criterion content of all assessment factors. Characteristics of groups of factors and their criteria were determined by means of peer review. The assessment of the global values of scenarios allowed us to rank them. Based on the analysis, the most reasonable and realistic strategy for the phased removal/transfer to a controlled state of fuel-containing materials was proposed. The strategy also includes processes for further management of these materials and associated radioactive waste. As well as “Shelter” Object transformation processes in the process of its transformation into an environmentally safe system and determination of its final state. Based on the results of the comparative analysis of scenarios, it was found that the scenario that provides for the removal of known accumulations of fuel-containing materials during the life cycle of the New Safe Confinement is optimal if the activities on the phased retrieval of fuel-containing materials are properly financed.


Introduction
Despite the completion of construction and commissioning of the New Safe Confinement (NSC), the accumulation of fuel-containing materials (FCM) formed as a result of the beyond-design basis accident at Unit 4 remains the main source of hazard of the "Shelter" Object (SO).Moreover, the potential danger of FCM may increase over time due to the spontaneous destruction of the surface of paw-shaped FCM with the formation of highly active dust.The formation of such dust in the "Shelter" Object is a radio-ecological hazard not only of a local but also of a global nature since the NSC is not a hermetic structure.The problem of FCM IOP Publishing doi:10.1088/1755-1315/1254/1/012101 2 degradation and methods of their evaluation and subsequent removal is extremely important not only for the SO but also for other facilities with similar conditions, such as the decommissioning of damaged reactors of the Fukushima Daiichi NPP [1].Therefore, it is extremely important to remove or transfer to a controlled state FCM before the process of their destruction can acquire a large-scale character.
Resolution of the Presidium of the National Academy of Sciences of Ukraine No. 141 dated 16.05.2018[2] states that scientific research on the transformation of the "Shelter" Object into an environmentally safe system is one of the priority areas of fundamental and applied research of specialized institutions of the National Academy of Sciences of Ukraine.
In work [3], the main directions of such research were determined and the following works were carried out: • definition and analysis of factors affecting the choice of scenarios for the transformation of the "Shelter" Object; • assessment of the risks of adverse effects on the environment of each of the FCM accumulations both during the life cycle of the NSC and after its decommissioning; • analysis of possible options for the transformation of the "Shelter" Object; • determination and substantiation of criteria for the final state of the "Shelter" Object; • development of scenarios for the step-by-step transformation of the "Shelter" Object.
The ultimate goal of ensuring the nuclear and radiation safety of the "Shelter" Object -New Safe Containment" system (SO-NSC) should be the removal of all FCMs, and the organization of their safe storage and/or processing.An approach that considers the technological space of SO as a system of interconnected zones of FCM extraction, which are significantly different from each other, is promising.At the same time, for each extraction zone, one should consider individual technological approaches or scenarios for the extraction of FCM and handling of associated RAW.
It is also necessary to take into account the guaranteed service life of the NSC, which is only 100 years, and the half-life periods of the nuclear materials contained in it are many orders of magnitude longer, and therefore their danger to the environment will remain for more than one millennium.This indicates that the problem of further transformation of the "Shelter" Object into an environmentally safe system (ESS) remains relevant even after the commissioning of the NSC and requires special scientific research.Thus, as of 2022, the following scenarios for the transformation of the "Shelter" Object into an environmentally safe system [5] have been determined, presented in table 1.The object of the study is the SO-NSC system.The research object is a complex system in which its technical, technological, security, financial, infrastructural, and other parameters are connected.Therefore, the main method of his research is a systematic analysis of factors affecting the solution of the problems of transforming the "Shelter" Object into an environmentally safe system.
The subject of the research is a comprehensive analysis of the scenarios of transformation of the "Shelter" Object into an environmentally safe system.The complexity of the analysis processes is ensured by taking into account all the parametric and non-parametric component characteristics of the scenarios, as well as their internal technical, economic, safety, technological, etc. structure.
In work [6], a methodology for detailed assessment of nuclear power systems (NPS) was developed, including key assessment areas: economy, infrastructure, waste management, proliferation, resistance to proliferation, environment, etc.Comprehensive decision-making support is necessary for the comparative evaluation of alternative options and the selection of the most promising solution.But estimates according to the INPRO methodology [7] require sufficiently detailed design information for NPS components.For the SO-NSC system, such information is at the stage of development.The most adequate use of the multi-criteria optimization technique for the comparative evaluation of the scenarios of the transformation of the "Shelter" Object into an environmentally safe system is the work [8], using which it was decided to apply the expert evaluation of the criteria that characterize the scenarios.
The main tasks of the research presented in the work are: • complex analysis of scenarios based on the grouping of factors and the determination of criteria relevant to them; • the creation of a comprehensive evaluation model based on the global value of the scenario; • practical use of the scenario evaluation model based on collegial expert evaluation of factors and criteria for the studied scenarios.
The article aims to rank the scenarios by their global (complex) value.A comprehensive analysis of the scenarios of step-by-step extraction of FCM after the commissioning of the NSC is being carried out for the first time.

Model of complex analysis of scenarios of transformation of the "Shelter" Object 2.1. Formation of a data array for complex analysis of scenarios
According to the recommendations of the IAEA [9][10][11][12], the decision-making criteria include: • radiation protection criteria, which are: implementation of anti-radiation protection of personnel, the population, and the environment in accordance with the requirements of the Laws, norms, and rules in force in Ukraine; implementation of anti-radiation protection of personnel in accordance with the ALARA principle [13]; assessment of radiation consequences for personnel, which takes into account exposure caused both by activities during the implementation of the main task and by being in the exclusion zone; assessment of radiation consequences of potential accidents for personnel, population, and environment; • criteria for handling RAW; • general technical criteria, which are: creation of deep echelon defense; quality assurance; exchange of experience; consideration of the human factor; application of proven engineering and technical practice.
For the practical application and implementation of the environmental safety analysis of work execution options in the implementation of scenarios of phased removal of FCM, the criteria given in table 2 are defined.
The comparative analysis of the proposed scenarios for the phased removal of FCM is performed based on expert evaluations of the values of an array of criteria, which reflect various aspects of the condition of the "Shelter" Object and the specifics of its transformation into an environmentally safe system.The key goal in determining expert evaluations is the indicator of "achieving a given level of environmental safety".A nine-point scale is proposed for expert evaluation of criteria [14].
All the specified criteria are evaluated non-parametrically by a group of experts (in points), collegially, with the definition of a jointly agreed point evaluation of the criteria for each scenario.

Formalization of the model of the comparative analysis of scenarios of the conversion of SO
The array of criteria presented in table 2 can be grouped by factorial features, namely: • factor 1 -security components of scenarios: risks of changes in properties (degradation) of FCM over time R D , %; risks of destruction of protective barriers around FCM accumulations over time R DP B , %; radiological risks R Rad , person/year; project implementation time (scenario) T, years; • factor 2 -financial components of the scenarios: costs for creating protective barriers for containment and isolation of FCM after decommissioning NSC OE CP B , thousand UAH; costs for the creation of additional infrastructure for the removal and further handling of FCM and other RAW after the decommissioning of the NSC OE CAI , thousand UAH; operational costs for ensuring the current security of the OE ECS "Shelter" Object, thousand UAH; risks of underfunding of works on the phased removal of FCM and their further handling by R U F W , thousand UAH / year; • factor 3 -infrastructural components of the scenarios: the degree of use of the infrastructure of the NSC for the extraction and further handling of FCM and other RAW, L U I , %; risks of non-readiness of storage facilities for intermediate storage of recovered FCM R U ISF , %; risks of unpreparedness of the geological repository for the final disposal of the FCM R U GR , %; By analogy with [15], we will introduce the concept of "scenario values" SF i , (significance function).For practical use in accordance with the purpose and objectives of the research, this indicator is identically equal to the predicted level of environmental safety in the implementation of the i-th scenario with the corresponding groups of factors Φ i and their constituent criteria: where: -safety factor of scenarios with its own criteria; -the financial factor of the scenarios with its criteria; -the infrastructural factor of the scenarios with its criteria.Thus, the initial conditions for using the scenario evaluation method based on collective expert evaluations are a set of factors Φ 1 , Φ 2 and Φ 3 with groups of criteria defined for them.
Then a separate i-th scenario will be represented by a complex or integral value criterion W i , which is determined based on the weight of factors and criteria that form them.This will allow you to rank the scenarios according to their relative value: where

Algorithm for determining complex values of scenarios based on group expert evaluation
Determining the complex values of scenarios based on group expert evaluation is a step-by-step process.
At stage 1, arrays of scenario evaluation criteria are formed where: i is a separate scenario, i = 1, p, p is the number of scenarios.
As a result, we get an array of criteria with a definition of their characteristics.At stage 2, criteria are grouped by qualitatively homogeneous factors Φ j .The result is the formation of three groups of factors for p scenarios with their own criteria (1): At stage 3, a group expert evaluation of factors and criteria within the factors is carried out according to point evaluations according to the proposed scale.
The result is the formation of point scores expert assessment matrices for factors and their criteria for p scenarios: ... ...
At stage 4, the matrix of advantages for factors is formed based on the factor scores: where: a Φ i,j -advantage of the i-th factor over the j-th.For the i-th scenario, the benefits matrix looks like this: The result is an estimate of the weight of the factors for the i-th scenario according to the formulas: At stage 5, a preference matrix is formed for criteria based on point scores: where: a KP i,j -advantage of the i-th criterion over the j-th.For the i-th scenario, the benefits matrix looks like this: • for the array of criteria grouped in "Factor 1 -security components of scenarios" • for the array of criteria grouped in "Factor 2 -financial criteria of scenarios" • for the array of criteria grouped in "Factor 3 -infrastructural criteria of scenarios" The result is an assessment of the weight of the criteria for the relevant factors for the i-th scenario as a ratio of the geometric mean from a separate row of the matrices ( 9), ( 10), (11) to the sum of the geometric means of all rows of the matrices: where: m -the number of criteria in the corresponding factor.
For the specified factors, we will obtain the vectors of the relative values of the criteria: At stage 6, a vector of complex indicators W (Ω, ω) is formed, containing evaluations of the criteria that form them ω i 1 , , ω i k and groups of factors based on determining their weights where: k, l, z -the number of criteria that form the relevant factor.The result is the determination of the complex indicators of the weight (values) of the scenarios W = ω, Ω taking into account the determination of the weight of the relevant criteria ω based on the weight of the structural factors Ω.It is performed using a geometric weighted multiplicative convolution of the form: where: S Cj ∈ S c -the array of scripts; ω j i -weights of the criteria that form the factors of the corresponding scenarios; Ω j -factor weights for scenarios.
For expression (15), we obtain the vectors of the relative values of the scenarios defined by (16): Scenarios are ranked by the value of their complex value according to (2): where:

Practical implementation of a comparative analysis of scenarios for the transformation of the "Shelter" Object into an environmentally safe system
According to clause 1 of the article, the comparative analysis of scenarios will be carried out on the basis of factorial-criterion group expert evaluation (EE).A working group of experts was created to perform the work according to the EE method, which meets the requirements of qualification and competence, which will ensure the reliability of the implementation of the EE.In the work of the group of experts on scenario evaluation, collective expert evaluations are applied.The input conditions for EE scenarios are: • number of scenarios -10; • all expert assessments for all stages of practical use of the model are carried out on a nine-point scale (from 1 to 9 points).
Each factor or criterion within the scenario is assigned a collegial assessment in points, which can be equivalent for different indicators and different scenarios.The process of collegial point expert evaluation is carried out in two stages: • stage 1 -scoring of three groups of FACTORS for ten scenarios; • stage 2 -scoring of the CRITERIA, which are included in the relevant groups of factors, for ten scenarios.
Based on the results of expert scoring for ten scenarios, the relative complex values of the scenarios are determined according to the proposed model.Based on the determined relative complex values of the scenarios, the scenarios are ranked according to their relative complex value.
At the first stage of the model implementation, a group expert evaluation of defined groups of scenario factors was carried out.The results of a collegial group expert survey and evaluation of factor weights for the scenarios calculated according to formulas (6), (7) and ( 8) are given in table 3.
At the second stage of the model implementation, a group expert evaluation of the criteria for the relevant groups of scenario factors was performed.The results of the collegial group expert survey are given in tables 4-6.
The determination of the complex indicators of the values of the scenarios taking into account the determination of the weight of the relevant criteria based on the weight of the structural factors of the type (15) was carried out according to the formula (16).
The results of the comprehensive assessment of the scenarios can be provided either in the form of a vector or in a tabular format.T7 presents the results of calculations in tabular format.The vector of complex relative values of the scenarios defined by ( 16): The results of the ranking of the scenarios by the value of the complex value:

Conclusions
Thus, on the basis of the conducted research, the following conclusions can be drawn: • collegial expert assessments conducted for factors and their criteria are competent and consistent; • calculated based on EE weights of the factors Ω Φj i for the considered scenarios and the weights of the criteria ω j i for the corresponding Ω j factors for the scenarios based on the comparison matrices are reliable and significant which is confirmed by the calculated consistency indices that do not exceed 10%; • the vector of relative complex values of scenarios (15) is the basis for making managerial decisions; • according to the argmax(W i ) principle the best scenario is "scenario 1" -the base scenario.
The value of the relative complex value is W * i = argmax(W i ) = 0.6642; • the worst scenario according to the argmin(W i ) principle is "scenario 2".The value of the relative complex value of which is the minimum among the estimates and is W 0 i = argmin(W i ) = 0.6212; • a series of scenario evaluations ranked by relative complex value: > W 0 i = W 1 0 0.6642 > 0.6461 > 0.6453 > 0.6449 > 0.6429 > 0.6382 > 0.6369 > 0.6333 > 0.6328 > 0.621 Therefore, with proper financing of the step-by-step extraction of FCM, the priority is the basic scenario -Scenario 1, which provides for the removal of all FCM accumulations (except FCM localized in man-made soil under NSC structures) during the life cycle of NSC.When implementing such a scenario, the NSC infrastructure is used to the maximum, the costs of creating protective barriers to contain and isolate FCM are reduced, as well as the costs of creating additional infrastructure for the extraction and further handling of FCM and other RAW after decommissioning of the NSC.
Since the values of the values of the relative complex value of all scenarios do not differ significantly, under certain circumstances (mostly due to the financial component) other scenarios, which provide for the delayed removal of individual accumulations of FCM, may become better.

Figure 1 .
Figure 1.FCM extraction zones.Zone 1 -upper marks of the SO (Central Hall and other rooms are above the mark 18,000); Zone 2 -intermediate grades of SO (utility room, other rooms on the marks from 9,000 to 18,000); Zone 3 -lower marks of SO (premises below the mark 9,000); Zone 4 -part of the Machinery Hall within the SO; Zone 5 -the space behind the Pioneer walls; Zone 6 -rubble under the cascading wall; Zone 7 -local zone of the SO.

Table 1 .
Potential scenarios for the implementation of the strategy "staged removal of FCM".

Table 2 .
Criteria for the comparative analysis of scenarios of phased extraction of FCM.
D 9 Risks of underfunding of works on the phased removal of FCM and their subsequent handling, thousand UAH/year R U F W 10 Risks of the destruction of protective barriers around FCM accumulations over time, % R DP B 11 Project implementation time (scenario), years T

Table 3 .
Results of group expert assessment of scenario factors.

Table 4 .
Group expert evaluation of criteria for groups of scenario factors (safety factor).DP B R Rad T ω(R D ) ω(R DP B ) ω(R Rad ) ω(T )

Table 5 .
Group expert evaluation of criteria for groups of scenario factors (financial factor).OE CAI OE ECS R U F W ω(OE CP B ) ω(OE CAI ) ω(OE ECS ) ω(R U F W )

Table 6 .
Group expert assessment of criteria for groups of scenario factors (infrastructure factor).
U I P U ISF P U GR ω(L U I ) ω(P U ISF ) ω(P U GR )

Table 7 .
Complex factorial and criterion evaluation of scenarios.