NERS 442

Final Report

Mixed-spectrum Supercritical Water Reactor

WINTER 2013

Team 3 - Yuan Gao, Douglas Kripke, Nishant Patel, and Eric Welch

Department of Nuclear Engineering and Radiological Sciences

University of Michigan

Ann Arbor, Michigan

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TABLE OF CONTENTS

I. ABSTRACT ..................................................................................................................................3

II. PROJECT DEFINITION AND REFERENCE CORE BENCHMARK ........................................................3

1. Background on SCWR concept

2. US reference design

3. Introduction to our unique reactor concept and design specifications

III. FUEL SELECTION AND ANALYSIS ................................................................................................8

1. Fuel and enrichment selection

2. Fuel Cycle Analysis

i. k-infinity

ii. Isotopic depletion analysis

IV. THERMAL-HYDRAULIC COUPLED NEUTRONICS AND BEGINNING OF CYCLE ANALYSIS ............11

1. Coolant and moderator channel temperature profiles and feedback

2. Coolant and moderator pressure drop calculations

3. Radial and axial power distribution

V. SAFETY ANALYSIS ....................................................................................................................14

VI. PROLIFERATION RISK .............................................................................................................. 15

VII. ECONOMIC ANALYSIS............................................................................................................. 15

VIII. SUMMARY ............................................................................................................................. 16

IX. REFERENCES ............................................................................................................................ 17

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I. Abstract

The mixed-spectrum supercritical water reactor (MSWR) is designed to meet the current

demands of the nuclear energy industry. It is modular to reduce capital costs and streamlined to

include passive safety features. As name implies, it utilizes supercritical water as the coolant to

achieve a thermal efficiency of 44% (compared to 33% in typical LWRs) as well as the full

spectrum of neutron energies. The MSWR was benchmarked using the US supercritical water

cooled reactor (SWR). From the US SWR design, the MSWR was scaled down from a power

output of 3400 MWth to around 800 MWth. The macroscopic design is most similar to the

economic simplified BWR design; but the utilization of high pressure (25 MPa) eliminates the

need for a steam separator, steam dryer, and recirculation pump due to the single phase flow of

the coolant, thus greatly reducing capital costs. Fuel cycle analysis indicated 8% enriched

uranium dioxide (UO2) as the most cost effective fuel choice corresponding to a three cycle

rotation of the fuel assemblies. With this configuration, the busbar cost of MSWR will be

around 67 mill/kWhr compared to 75 mill/kWhr of the AP100. Favorable reactivity coefficients

demonstrate the safety of MSWR design, and isotopic analysis show an increased proliferation

risk.

II. PROJECT DEFINITION AND REFERENCE CORE BENCHMARK

The super-critical water-cooled reactor (SCWR) is a generation IV conceptual design

employing super-critical water as both the coolant and moderator. In order to achieve this, the

system must be kept above water’s critical point of 22 MPa and 374°C. Utilizing super-critical

water allows the reactor to share in the same thermal efficiency experienced by super-critical

coal fired power-plants. With a core inlet/outlet temperature difference of 220°C (compared to

30°C for standard LWR systems), thermal efficiency is improved from 35% to nearly 45%. This

corresponds to the core outlet temperature reaching around 500°C. Once the water has passed its

critical point, properties such as density, specific heat, and enthalpy undergo drastic changes as

seen in Fig. 1. The rapidly increasing enthalpy allows one to achieve heat removal comparable

to current LWR systems while using a coolant flow rate that is up to an order magnitude lower.

Moreover the single-phase property of super-critical water eliminates the need for a steam

separator, a dryer, and recirculation pumps. These design simplifications will make the SCWR

cheaper to manufacture by reducing capital costs.

4

.

Figure 1: Macroscopic view of the reactor (left) and thermo-physical properties of water (right)

[Hu08]

The US reference SCWR design was chosen as a starting point to benchmark to before

beginning any work on the MSWR. We initially hoped to use the mixed spectrum design as our

reference core, however, the literature on this reactor concept proved insufficient. As a result,

we switched to using the more established US design. Figure 2 displays the planned core and

fuel assembly of the US reference design. This design features square fuel elements as opposed

to the hexagonal array of the MSWR design. Furthermore, the US design uses a thermal

spectrum and low enriched UO2 fuel compared with a mixed spectrum and various potential

Figure 2: Cross-section of fuel assembly (left) and water rod (right) for the US reference SCWR

design [Hu08]

Moderator rod

Coolant Channel

Fuel Rod

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Table I: Parameters of the US reference SCWR design [Hu08]

combinations of UO2 and thorium mixed-oxide (TMOX) fuel for the MSWR design. Table 1

quantifies all of the design details necessary for benchmarking the MSWR design. The water

rods are a unique feature of the US reference design, which are shown with greater detail in

figure 2. In the blue region, the coolant water goes down with a higher density of about 0.7

g/cm3. The higher density supercritical water can be used as a moderator. In the red region,

coolant water go up with a lower density of about 0.15 g/cm3. With a lower density and higher

temperature, the water losses its moderating function. The green region represents the fuel rod.

As coolant enters the core, about 90% of the feed-water goes into the upper plenum of the core,

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and then flows downward in the water rods. At the lower plenum it mixes with the rest of feed-

water, and the mixture then flows upward as coolant.

In meeting the benchmark, the thermal-hydraulics was not coupled with the neutronics

due to time restriction. To benchmark our results with the reference design, a core radial power

distribution was created with some control rods partially inserted. The results showed good

agreement with the reference design. Additionally, the assembly level k-infinite value was

modeled as a function of burn-up. The results were very close to that of the reference paper,

with error of about 1%. At this point, the benchmarking was considered satisfactory enough to

move forward with determining the parameters of an ideal and modular MSWR design.

The size of the reference design was reduced in order to make the MSWR design

modular. As a result, the MSWR has a power output of 355 MWe (the reference design was

scaled down from 3400 MWth to 807 MWth). This was done by reducing the size of the

assemblies to 17x17 and reducing the number of assemblies in the core to 61. The layout of the

core is shown in figure 3. Apart from the dimensions, the overall design of the MSWR remained

unchanged from the reference design shown in figure 1.

As the name implies, the MSWR operates using a mixed spectrum of neutron energies.

Unlike the US SCWR, the MSWR does not have any water rods for extra moderation. Instead,

the flow of the coolant was redesigned such that each assembly has the coolant either flowing

upward or downward. The core has three types of assemblies fresh burnt assemblies are the only

assemblies that have coolant flowing down through them. The fresh fuel assemblies and the

once burnt assemblies have coolant flowing upward. The coolant from inlet initially flows down

Figure 3: Cross-section of core (left) and fuel assembly (right) for the MSWR design

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through the twice burnt assemblies, and then flows upward through the fresh fuel and the once

burnt assemblies. The water becomes supercritical towards the bottom of the core, and therefore

it has a high enough density to be a good moderator as it is flowing through the twice burnt

assemblies. Thus, the twice burnt assemblies primarily capture thermal neutrons. When the

water is flowing upward, it is supercritical and has low density with poor moderating

capabilities. Therefore, the fresh fuel and the once burnt assemblies are the fast assemblies. The

assembly design for the MSWR is shown in figure 3. The cladding material was also changed to

silicon carbide from stainless steel in the reference design because SiC has a lower neutron

absorption cross section (the value of kinf increased to 1.45 with SiC up from 1.16, which was

previously determined by altering the number of control rods, burnable absorbers, and the fuel

enrichment). Thus SiC was chosen as the cladding material. Table II displays various properties

of the MSWR core.

Table II: Summary of the MSWR core properties

CORE DESIGN

MSWR uses uranium dioxide (UO2) fuel pellets with a uranium enrichment of 8 wt% U-235 in a 17x17

square fuel assembly. The fuel will spend six years in the core through three two-year cycles in which

each assembly spends two cycles with a fast spectrum and one cycle with a thermal spectrum. This

mixed spectrum ideas comes from the very large density drop that water undergoes at the

supercritical temperature. Silicon carbide was chosen to be the cladding material, due to its low

neutron absorption and favorable corrosion characteristics at supercritical temperatures.

MSWR produces 807 MW of thermal power, translating to 355 MW of electric power. The active fuel

height is 2.60 m with an effective diameter of 2.17 m. This gives a thermal power density of 85

W/cm3, making the MSWR comparable to the standard PWR or BWR. The normalized power

distributions for our thermally coupled core at BOC are shown in figure 4.

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III. FUEL SELECTION AND ANALYSIS

At the process of fuel selection, three types of nuclear fuel were considered to be the fuel

of our core, MOX, (Th+Pu+U)O2, UO2. The MOX was considered to be a fuel for the light water

reactor, and the (Th+Pu+U)O2 was chosen as a mixed spectrum reactor fuel. UO2 has a relative

high melting point, which goes to 2865°C. UO2 has cheaper enrichment price, which leads to a

much cheaper fuel cost. The uranium dioxide has less weapon grade products compare to the

MOX and (Th+Pu+U)O2. So the UO2 was chosen as our reactor fuel.

The fuel enrichment is a big issue in our design. Two factors were considered in the

selection of the fuel enrichment, one is the k-infinity and the fuel enrichment cost. From figure 4,

we can see that the k-infinity of 7% enrichment uranium dioxide goes down to 0.89876 smaller

than 0.9 at the 50 (GWD/UT), which does not meet our design requirement. The 8% and 10%

enriched fuel has a k-infinity higher than 0.9, which meet our design requirement. If we only

consider the k-infinity factor, both 8% and 10% enrichment fuel can satisfy our design

requirement. But the enrichment cost is another important factor that we have to consider.

Figure 4 is a plot of the fuel cost versus fuel tails enrichment. We can see that the price of the 10%

enrichment fuel is 25% more expensive than the 8% enrichment fuel. So the 8% enrichment

UO2 was chosen as our fuel.

Figure 4: Cost versus tails enrichment for MSWR design

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 0.001 0.002 0.003 0.004 0.005 0.006

Co

st (

$/k

gU

)

Tails Enrichment (%)

7% Fuel enrichment8% Fuel enrichment10% Fuel enrichment

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Figure 5: k-infinity versus fuel discharge burn-up from SCALE for MSWR design

Figure 6: Fuel burn-up analysis for MSWR design from SCALE

MSWR uses standard UO2 fuel pellets, but with an initial enrichment of 8 wt% U-235.

The fuel will be shuffled in the core in two year cycles until being discharged after the third

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

0 10 20 30 40 50

K-I

nfi

nit

y

Fuel discharge burnup (MWd/kgU)

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cycle when the average urnup is near 60 MWd/kgU. Depletion calculations at the assembly

level were carried out with SCALE and the resulting kinf values are shown in figure 6. The

important thing to notice is that the fuel spends two cycles in a fast spectrum region (where

neutron moderation is limited). The fuel then moves to a thermal spectrum region for its third

cycle and receives a boost in reactivity from increased neutron moderation. At this transition

period, the fuel composition is still mostly U-238, but with 4.5% U-235 and 3% fissile

Plutonium. When the fuel is discharged after the third cycle, it contains 3.2% U-235.

Full core depletion was done with PARCS without any thermal hydraulic feedback. The

value of keff starts at 1.1 and drops to just below 1 after the third cycle. To help control the extra

reactivity at BOC, the MSWR would utilize control rods with small insertions. We were unable

to complete a full TH-coupled depletion analysis due to our hand calculation method and a lack

of extended time.

IV. THERMAL-HYDRAULIC COUPLED NEUTRONICS AND BOC Analysis

The thermal hydraulic code packages that were available to us for this project cannot

correctly model supercritical water without modifying their source code. Unfortunately, we did

not have this option, so we moved forward with hand calculations to find coolant temperature

profiles for the thermal and fast assemblies. This was done by finding the change in enthalpy of

a core-average channel:

( )

( ) (1)

where W is the mass flow rate (see table III) and M is the wetted perimeter. We split the core

into 30 axial sections and used a discretized version of (1) to find the enthalpy of the nth

section:

∑

(2)

This initial step assumed a cosine shaped axial power distribution. From the enthalpy

distribution, we looked up the corresponding temperature T(z) and density ρ(z) profiles. We

then remodeled our core with SCALE and PARCS using the new ρ(z) for six axial regions. The

resultant axial power distribution is labeled “1st” in figure 7. This entire process was repeated

once to get a neutron-thermal-hydraulic coupled BOC axial distribution, labeled “2nd

” in figure

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7. Figure 8 shows the coolant temperature profile difference between the neutron-coupled and

non-coupled cases. Coupling the thermal hydraulics to the neutronics in the MSWR flattens

the axial power distribution because of the effects of the largely negative MTC. That is, a region

that receives extra power is heated more, which lowers the reactivity of that region, thus

Table III: Summary of the MSWR thermo-hydraulic parameters

lowering its power. The inverse effect happens to regions receiving too little power, so they get

a power boost.

Figure 7: Radial and axial power distribution for MSWR design from PARCS

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Figure 8: Hand calculated coolant temperature distribution of MSWR design

The fuel temperature can be calculated by the axial power density and the coolant

temperature. The relation can be shown by the following equation:

( ) (3)

where q is the axial power density, Tb is the coolant bulk temperature, Tc is the fuel centerline

temperature, and Uc is the overall heat transfer coefficient

(4)

where a is the fuel OR, hg is the gap conductance, kc is the cladding thermal conductivity, h is the

general conductivity coefficient of water, tg is the thickness of the gap, and tc is the thickness of

the cladding. The fuel temperature profile was divided into 30 data points. The fuel temperature

distribution is shown in figure 9. Here, we can see that the temperature on fast assembly is

higher than the thermal assembly. The shape of fuel temperature distribution is quite similar to

that in reference paper.

Our core has two coolant channels, and there is turn around point at the bottom of the

core, so the pressure drop is mainly determined by three factors. The frictional drop,

gravitational pressure drop and the form pressure drop happen on the turnaround point. The

frictional pressure drop can be calculated by the following equation:

0

0.5

1

1.5

2

2.5

3

250 300 350 400 450 500 550

Co

re h

eig

ht(m

)

Temperature(°C) Moderator with feedback Coolant with feedback

Moderator without feedback Coolant without feedback

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(5)

where H is the height, f is the friction factor of the coolant, v is the mass velocity. The

gravitational pressure drop is determined by the density and relative height, and can be

Figure 9: Coupled temperature profile from PARCS for MSWR design

calculated by the following equation:

(6)

The form pressure drop is determined by multiple factors, but the most important one is the bend

angle, and the form pressure drop can be estimated by the following equation:

(7)

The coolant goes down from top to bottom in the moderator assembly. So the total pressure

should be the following equation:

(8)

So the total pressure drop of coolant is tiny in the moderator assembly. The result is 745 Pa. The

coolant goes up from bottom to top in the coolant assembly. So the total pressure come to the

following equation:

(9)

From (9), we can see that the pressure drop is much bigger than the previous one. The result is

13604 Pa, which is not a too much number compare to the 25 MPa core pressure. Thus, the

0

0.5

1

1.5

2

2.5

3

0 200 400 600 800 1000 1200 1400

Co

re h

eig

ht (

m)

Fuel Temperature (°C)

Thermal assembly

Fast assembly

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pressure drop will maintain the water in a supercritical state as it moves through the core as

required by our design.

V. SAFETY ANALYSIS

In designing a reactor, it is important to have a negative power coefficient of reactivity

(PCR) for safety purposes. This means that an increase in power from the reactor results in a

decrease of reactivity, which pushes the power back down. For our MSWR design, it is

important to consider a PCR for the thermal assemblies as well as one for the fast assemblies.

The PCR αP is found by combining the fuel temperature coefficient (FTC) αF with the moderator

temperature coefficient (MTC) αM:

(10)

(11)

(12)

Table IV: Calculated reactivity coefficients for MSWR design from SCALE

Estimates for all of the reactivity coefficients were calculated using outputs from SCALE and are

tabulated in table IV. The two PCRs calculated for the MSWR are both negative, ensuring that

the reactor will self-regulate in the case of a power increase.

VI. PROLIFERATION RISK

At the end of fuel cycle, we have 3.2% transuranium elements, in which 99.5% is plutonium. So

the proliferation resistance is an important issue that we have to think about. The advantage of

Thermal Assembly Fast Assembly

αF (pcm/K) -2.8 -3.4

αM (pcm/K) -80 -60

αP {(%Δk/k)/(% power)} -0.04 -0.13

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our core design in nonproliferation part is that we have a much longer discharge burn-up, is 63

GWd/Mt. We have less mass fuel used in our core, which leads to less mass weapon grade

products. As we have a higher concentration of plutonium in the transuranic elements, we can

reprocess the fuel wastes to MOX fuel. The high concentration of plutonium can help the

reprocessing to MOX fuel, and MOX fuel can be used as fuel of some light water reactors. The

longer burn-up time and the fuel waste reprocessing to MOX fuel can help on the proliferation

resistance work. We still need to control this reactor customer. The background and objective of

the customer should be check. We may not sell the reactor to the country without nuclear

weapon right now, or they may use the wastes to develop nuclear weapons.

VII. ECONOMIC ANALYSIS

The MSWR is designed to be economical. The higher thermal efficiency of the reactor

helps lower the total cost significantly. The principal amount was estimated to be $4B/GWe plus

a 20% increase for making it modular—that is $1.3B for MSWR. Over the Construction period

of four years, the interested accrued is $256M assuming a 10% interest rate per year. This yields

a capital cost of $1.5B. This is to be paid over the period of 40 years. The decommissioning

cost is estimated to be 20% of the capital cost. Management and operations (M&O) cost was

estimated to be 9 mill/kWhr. The busbar cost of the reactor comes out to be 67 mill/kWhr,

which is 10% lower than the busbar cost of AP 1000. Moreover since it only has one coolant

loop and no steam separator, steam dryer or recirculation pump the cost is further reduced (this

however was not taken into account). The breakdown of generation cost is shown in figure 10.

The depleted fuel turns out to be 3% enriched, which is the enrichment used in BWRs.

Therefore, the depleted fuel can be sold to BWR lowering their cost of fuel and our cost of fuel

below 4 mill/kWhr.

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Figure 10: Breakdown of the generation costs (in mill/kWhr) for MSWR design

VIII. SUMMARY

The initial interest of the group was a mixed-spectrum design. The goal to make the reactor

smaller was achieved with an output of 800 MWth. Thermal-hydraulic analysis showed the

viability of using supercritical water to take advantage of a mixed spectrum configuration. A

fuel choice of 8% enriched UO2 along with high burn-up will yield reduced operating costs of

around 67 mill/kWhr. Favorable reactivity coefficients demonstrate the safety of MSWR design,

and isotopic analysis show an increased proliferation risk. Overall cost analysis indicate that the

MSWR design is a viable reactor design that is capable of helping our country meet the

challenges of its increasing energy demands.

IX. REFERENCES

[Hu08] P. Hu, “Coupled Neutronics/Thermal-Hydraulics Analyses of SuperCritical Water

Reactor,” PhD Thesis, University of Wisconsin - Madison (2008).

[INE05] “Feasibility Study of Supercritical Light Water Cooled Reactors for Electric Power

Production,” INEEL/EXT-04-02530, Idaho National Engineering and Environmental

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4

0.24

9

Construction

Fuel

Decomission

M&O

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Laboratory, Nuclear Energy Research Initiative Project 2001-001, Westinghouse Electric

Company Award Number DE-FG07-02SF22533 (2005).