Feasibility of underground NPP and its MCDA-based optimization

NUCLEAR ENERGY SCIENCE AND ENGINEERING

Feasibility of underground NPP and its MCDA-based optimization

Hou-Bo Qi，

Feng-Lei Niu，

Yun-Gan Zhao，

Yu Yu，

Sheng-Fei Wang

Nuclear Science and Techniques

Vol.27, No.4

Article number 89

Published in print 20 Aug 2016

Available online 11 Jul 2016

DOI：10.1007/s41365-016-0080-z

53100

The underground nuclear power plant (NPP) makes full use of land resources, reduces costs, makes better use of its passive safety, and avoids radioactivity release into the atmosphere in a serious nuclear accidents. In this paper, for obtaining comprehensive and integrated analyses on this new NPP design, we introduce four kinds of underground NPP designs, analyze the feasibility of each design from various aspects, and use the multiple criteria decision analysis (MCDA) method to choose the best option.

Underground Nuclear Power PlantFeasibilityOptimizationMultiple Criteria Decision Analysis

1 Introduction

All around the world, most nuclear power plants (NPPs) in operation were built on the ground. They occupy a wide area and restrict the environment around the plants. Also, there is the risk of radioactive prolusion of the surrounding areas, if a severe nuclear accident happens. Building underground NPPs may be a solution. It does not only make full use of land resources. It can makes better use of the passive safety system. And, if a nuclear accident occurs, the radioactive substances do not spread into the atmosphere ^[1,2].

The general concept of underground reactor sitting was first suggested by Edward Teller and Andrei Sakharov^[3]. Underground reactor has many progressive factors. Geological stability may ease seismic concerns, unwanted natural and unnatural access are deterred, and the decommissioning is easier to achieve by burial. Historically, Norway was the first country to place a reactor into a rock cavern (a 25 MW heavy water reactor at Halden)^[3]. In 1966, the Chooz-A commercial PWR NPP in Ardennes, France was installed within excavated bedrock, which make the concept of underground nuclear plant available. The Toshiba 4-S is a micro fast neutron reactor that is designed to be underground for 30 years without refuelling ^[3].

Although more countries have recently started their exploration of underground NPPs, related information, over the safety and feasibility, and the scientific analysis and experience as well, is relatively small. In this paper, we analyze the feasibility of underground NPPs, using multiple criteria decision analysis (MCDA) to make a comprehensive evaluation and optimization for each feasible design.

2 Design and feasibility analysis of underground NPP

2.1. Tunnel underground NPP

Existing tunnel underground NPPs do not have containment vessel, using hard rock instead to save construction cost. Granite, layered rock and dome are good choices. Some of them use rib structure with rock arch support (Fig.1a)^[3]. Tunnel underground NPPs use tunnel to connect spent fuel storage tank and the reactor, and the spent fuels are processed and transported underground (Fig.1b)^[4]. Besides, the tunnel underground NPPs are adopted, built and retired on the spot to reduce the cost.

Fig.1.

The tunnel underground NPP in a large constructed cavern (a) and the internal construction (b).

An underground NPP used to be of open loop or closed loop fuel cycle. The new open cycle, combining the two loops, consists of the reactor, the special storage equipment and the waste storage pools (Fig.2). This improves the waste disposal ability of underground nuclear plant^[2].

Fig.2.

Open fuel cycle and closed fuel configuration.

The existing tunnel underground NPPs applications have fully illustrated the feasibility of this design scheme, which is advantageous in safety and cost-effectiveness. However, its construction in a rock tunnel means a certain limit on the plant's location. It is only feasible in places that is rich in geological resources and multiple kinds of rocks conforming to the construction requirements.

2.2. Improvement of tunnel underground NPP

The improved scheme of tunnel underground NPP is a conceptual design proposed in recent years on basis of existing structure, with underground reactor and on-ground steam generator, as shown in Fig. 3. It proposed to remove the main pump and use the height and density difference of natural circulation to provide the driving head, so as to save the main pump power, reduce the cost and eliminate potential failure mode. This scheme takes AP1000 as the research example to carry out thermal hydraulics calculations, and the following formula ^[5] and conservation relations are obtained：

Fig. 3.

Primary circuit loop flow diagram of underground NPP

0.11 {(\frac{ξ}{d})}^{0.25} \times \frac{l}{d} \times \frac{ρ v^{2}}{2} + G^{2} (\frac{1}{ρ_{2}} - \frac{1}{ρ_{1}}) + K \times \frac{ρ v^{2}}{2} = Δ ρ g h,

(1)

where d is the channel diameter; ρ is the fluid density; v is the fluid velocity; l is the channel length; ξ is absolute roughness of the channel surface; G = ρv is the mass flow density;,ρ₁ and ρ₂ are fluid density in Sections 1 and 2, respectively; Δρ is the density difference of pressure between the outlet coolants of vessel and steam generator; and h is the height difference between the steam generator and pressure vessel.

The calculation took just the acceleration friction pressure drop and pressure drop into consideration. And it divided the coolant from the pressure vessel to the steam generator of circulation process into four parts. The following simplifications were considered for a rough calculation:

(1) Only one loop of AP1000 coolant pipes. One cold pipe and one heat pipe in the loop, and the longest heat pipe of the steam generator were calculated, assuming that the heat transfer tube is 26 m long ^[6].

(2) The heat transfers bend connecting the steam generator and pressure vessel was a quarter of a circular arc, about 1570 m in length.

(3) The acceleration pressure drop in the loop was so smaller than the frictional pressure drop that it can be neglected.

(4) The total pressure drop of 0.3076 MPa in the pressure vessel was taken as a reference value. Using AP1000 related parameter ^[6] in various available situations, at the heights of 1000 and 2000 m, the low velocities are 1.7 and 2.2 m/s, and the flow quantities are 0.84 and 1.08 m³/s, respectively.

Other losses ignored in the calculation include the local pressure drop and acceleration pressure drop. However, with the heat pipe being 2000 m in height, the flow rate of 1.08 m³/s is far smaller than the normal amount of 11.207 m³/s. So, it is not practical to increase the height of steam generator and remove the main pump to get primary circuit natural circulation.

2.3. Combined hydro power plant and NPP

Moving an NPP to mountains can make full use of resources, by combining the NPP with a hydropower station. In China, the design of an underground NPP construction in the Three Gorges region has been proposed. Its internal sketch is shown in Fig.4.^[7]

Fig.4.

Sketch of combined underground NPP

The plan puts the nuclear part underground, whereas the normal part is on the ground. In this design, high temperature and high pressure steam generated by the nuclear part will be transferred to normal part through the pipe in the tunnel. The nuclear part can use the reservoir water as coolant to save water cycle energy consumption. The nuclear plant bears the basic power load, while hydropower station takes the waste load and peak load in power load curve, so a strong and no-emissions clean energy is formed ^[7]. Thus, the problem of season- and climate-affected power generation of hydropower stations can be solved.

The different kinds of terrains and rocks in the Three Gorges reservoir ^[8] provide the material premise for building underground NPPs around the hydropower station. Combining underground NPP with a hydropower station solves the coolant problem of underground NPP, and the height difference between the reservoir and the nuclear part makes it possible to have passive safeguards injection. This design is feasible for a hydropower station with qualified construction technology of underground factory and proved shock resistance ^[7].

2.4. Mined-out areas underground NPP

This scheme is a conceptual design (Fig.5). The underground NPP is built in mined-out areas, making full use of waste resources. As the surrounding rocks are unstable after being dug empty ^[9], underground NPP construction needs to take effective measures to repair the mined-out areas and surrounding rocks, and to have a containment structure much like the ground NPP. The pressure vessel is placed in a container full of boric acid water and surrounded by a layer of stainless steel and ferroconcrete. Thus, if the pressure vessel is damaged, there is still the boron water as a neutron absorber and coolant. In addition, the whole device is embedded in the entire unit composed of a mixture of activated carbon and dry cement, which can absorb radioactive gas once the stainless steel and reinforced concrete material is broken. Dry cement can prevent leakage of radioactive fluid in the pressure vessel. The whole structure uses multi-layer protection to guarantee the plant safety. In this design, the reactor uses a small pile of only a few meters in diameter, so whole area of the plant is not so large.

Fig.5.

Sketch of mined-out areas underground NPP

China has a wide distribution of underground coal mine areas, if the productive area satisfies the requirements of underground NPP construction and the depth meets the requirements of passive safeguards injection of cooling water, building underground NPPs in mined-out areas is a good case to make full use of recycled resources and save the digging cost as well. Groundwater, and production water produced in the exploitation process of coal mines ^[8], can be used as cooling water of underground NPP after being processed, thus solving the cooling water shortage problem for inland underground NPPs.

The ore body is an extra barrier to prevent radioactive material, and it reduces the plant elevation to make full use of the gravity of coolant water. This scheme is feasible for mined-out areas after construction analysis.

3 Optimization of the underground NPP construction scheme based on MCDA

The designs of underground NPPs above have their advantages and disadvantages. In this section, MCDA is used to analyze the underground plant schemes. We take safety, economic benefit, environmental impact and construction difficulty as evaluation indexes to select the optimal design scheme from the underground NPPs.

The design optimization of underground NPPs is based on the following route: Establishment of target system — Identification of evaluation index weight — Generate alternatives set — Scheme optimization and comparison. The concrete steps include：

(1) The underground nuclear target system includes four scheduling evaluation targets namely safety, economic benefit, environmental impact and construction difficulty.

(2) The scheduling weights of evaluation indexes are determined by the form of questionnaire survey, combined with statistical analysis and fuzzy theory according to the related personnel (the importance of the evaluation index) to get different weights of each evaluation index.

(3) The underground plant scheme collection is determined according to the underground NPP designs above and the questionnaire survey results, with different solutions based on the statistical analysis method.

(4) Alternative scheduling schemes of an underground NPP are compared by using the MCDA method, so as to optimize each of the design schemes.

In the process of plan optimization, “Questionnaire” is an efficient way to obtain opinions and ideas of the nuclear experts towards the optimal solution. We designed a questionnaire which mainly includes: 1) survey the importance of underground NPP evaluation index in four levels of very important, important, moderately important and not important, so as to obtain different index weights to scheduling evaluation; and 2) expert table opinions for each scheme different evaluation indexes in different angles of selection sorting, so as to do a statistical analysis to calculate the average classification and score different evaluation targets.

3.1. MCDA based on the fuzzy theory

3.1.1 The Method of Determining the Weight

Weights of different attributes are needed when using different MCDA methods for optimization. Assuming that the evaluation index system includes n attribute indexes and each attribute index contains r evaluation levels, and then the weights of attributes can be expressed as:

S_{j} = \sum_{h = 1}^{r} P_{j h} W P_{h} \begin{matrix} j = 1, 2, \dots ., n \end{matrix} ，

(2)

W_{j} = \frac{S_{j}}{\sum_{j = 1}^{n} S_{j}},

(3)

where P_jh is the proportion at the attribute index j under the evaluation level h, and WP_h is the crisp numbers that corresponds to evaluation level h. WP_h is a given crisp number corresponding to fuzzy terms, or the crisp number obtained after converting fuzzy terms to the corresponding fuzzy set based on the average L - R scoring method ^[10].

3.1.2 Matrix standardization method

The matrix shall be standardized to meet the evaluation index system when using different MCDA methods for optimization. We chose vector standardization method as Eq.(3-2) for decision analysis:

r_{i j} = \frac{x_{i j}}{\sqrt{\sum_{i = 1}^{m} x_{i j}^{2}}} \begin{matrix} i = 1, 2, ..., m; j = 1, 2, ..., n \end{matrix},

(4)

where, i is decision alternatives, j is attribute index,and x_ij is attribute parameter values.

3.1.3 MCDA method

The method to analyze each scheme mainly uses ideal solution and the negative ideal solution of multi-objective problem to sort the alternatives. The basic steps in this method are as follows ^[11-14]:

(1) Building standardized matrix R= {r_ij}: change judgment matrix into standardized matrix using Eq. (3-2).

(2) Building standardization of weighted matrix V = {v_ij}: based on the weight coefficient of attribute index and standardized matrix (R), Eq.(3-3a) can be obtained:

v_{i j} = w_{j} r_{i j}, i = 1, 2, ..., n,

(5)

where, w_j is the weight coefficient of j attribute index; and r_ij is the value after standardizing attribute vector.

(3) Determining the ideal solution (IA) and the negative ideal solution (WA):

I A = {(\max v_{i j} | j \in J_{1}), (\min v_{i j} | j \in J_{2}) | i = 1, 2, ..., M} = {v_{1}^{I}, v_{2}^{I}, ..., v_{n}^{I}},

(6)

W A = {(\min v_{i j} | j \in J_{1}), (\max v_{i j} | j \in J_{2}) | i = 1, 2, ..., M} = {v_{1}^{W}, v_{2}^{W}, ..., v_{n}^{W}},

(7)

where, J₁ is the benefit attribute index number, and J₂ is the cost type attribute index number.

(4) Determining comprehensive index of each alternative U_i: By calculating the Euclidean distance, the distance to ideal solution (IS_i) and non-ideal solution (WS_i) of alternatives, and the comprehensive evaluation value of each program, are obtained, as shown in Eqs.(3-3d)–(3-3f).

I S_{i} = \sqrt{\sum_{j = 1}^{n} {(v_{i j} - v_{j}^{I})}^{2}}, i = 1, 2, ..., m,

(8)

W S_{i} = \sqrt{\sum_{j = 1}^{n} {(v_{i j} - v_{j}^{W})}^{2}}, i = 1, 2, ..., m,

(9)

U_{i} = W S_{i} / (I S_{i} + W S_{i})

(10)

Determining the quality of decisions based on the size of U_i after calculating the comprehensive evaluation value of decision alternatives U_i, and a larger U_i means a better alternative it corresponds to.

3.2. Generation X and analysis of decision scheme weight

Safety, economic benefit, environment impact and construction difficulty were chosen as the scheme selection of evaluation indexes. The experts questionnaire is the main reference for optimizing underground NPPs. Different scheduling evaluation index ratios were obtained under different evaluation levels based on the statistical results of questionnaire survey. Endowing fuzzy evaluation with crisp numbers (very important,10; important,7.5; medium, 5; not important,2.5; ignored,0), the scheduling weights of evaluation indexes (Fig. 6) were obtained using Eq.(3-1).

Fig. 6.

Evaluation index weight of underground NPPs.

The results show that different scheduling evaluation index has different weights. The size of weight represents the importance of each underground NPP index. Safety is the most important, followed by environmental impact, economic benefits, and difficulty of construction.

3.3. Analysis of expert judgment

The 40 copies questionnaires distributed to nuclear experts were fully taken back. The membership function of each index based on the expert questionnaire results is shown in Fig. 7. The abscissa is the expert score, and the ordinate is function value. The following points can be obtained from Fig.7.

Fig.7.

Membership function of each index.

(1) For the safety index (■), the turning point appeared in 6–8, namely scoring less than 6, the scheme is not safe and not desirable; while scoring higher than 8, the scheme achieves the maximum security.

(2) For the economic benefit (Δ), the turning point appeared in 6.5–7, namely scoring less than 6.5, the economic efficiency is too low; while scoring higher than 7, the scheme achieves the maximum economic benefits.

(3) For the environmental impact (○), the turning point appeared in 4–8, namely scoring less than 4, the scheme has too much negative influence for the environment; while scoring higher than 8, the scheme reaches the maximum degree of friendliness to the environment.

(4) For the construction difficulty (◇), the turning point appeared in 5–7, namely scoring less than 5, the construction is easy to achieve; while scoring is higher than 7, the construction is too difficult to achieve.

3.4. Analysis of decision results

3.4.1 Optimization and analysis under the monomial index

After expert questionnaire, using the statistical principle to calculate the average and get the average score of different indicators of the program (Table 1).

Score of each underground NPP under the different indexes

Index	Tunnel underground NPP	Combined hydro power and NPP	Mined-out areas underground NPP
Safety	8.34	7.65	6.70
Economic benefit	6.88	8.37	7.55
Environmental impact	8.49	7.28	7.94
Construction difficulty	8.05	7.94	7.68

In this study, the higher the scores of security, economic benefits and environment impact indexes, the better the scheme is, while for the score of construction difficulty index, the lower the better. Table 1 shows that tunnel underground NPP is the optimal scheme from the perspective of security and environmental impact; the combined hydro power and NPP is the optimal scheme from economic point of view, and mined-out areas underground NPP is the optimal scheme from the perspective of construction difficulty. Optimization results show that each plant design has its advantages and focus.

3.4.2 The plan optimization and analysis based on the fuzzy MCDA

According to the analysis method, experts’ score are inputted into a matrix. Then after dealing with the normalized and weighted, it is changed into a weighted matrix. Weighted matrix will get the ideal solution and non-ideal solution of each scheme as shown in Tables 2 and 3. The synthetic appraisal values (U_i) of tunnel underground NPP, combined hydro power and NPP, and mined-out areas underground NPP are 0.60, 0.53 and 0.35, respectively.

Ideal solution of each evaluation index

Index	Tunnel underground NPP	Combined hydro power and NPP	Mined-out areas underground NPP
Safety	0.175	——	——
Economic benefit	——	0.144	——
Environmental impact	0.165	——	——
Construction difficulty	——	——	0.127

Non-Ideal Solution of Each Evaluation Index

Index	Tunnel underground NPP	Combined hydro power and NPP	Mined-out areas underground NPP
Safety	——	——	0.142
Economic benefit	0.119	——	——
Environmental impact	——	0.141	——
Construction difficulty	0.134	——	——

In this analysis method, the larger the synthetic appraisal value, the greater the corresponding decision alternative. After combining the indexes of security, economic benefits, environmental impact and construction difficulty, it can be concluded that the tunnel underground NPP is the best, followed by the combined hydro power and NPP, and the mined-out areas underground NPP.

4 Conclusion

After analysis, the design of tunnel underground NPP, combined hydro power and NPP, and the mined-out areas NPP are all feasible under the existing conditions.

Based on MCDA, in optimizing for feasibility scheme on safety, economic benefit, environmental impact and construction difficulty selection, it can be seen that each scheme has its own advantages and focus, but the tunnel underground NPP is the best solution. The integrated optimization results show that the safety and environmental impact of the underground NPP construction are important, and they are also the primary concern in construction and operation of a nuclear power plant.

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