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XYLENE POWER LTD.

FAST NEUTRON REACTOR (FNR) DESIGN

By Charles Rhodes, P.Eng., Ph.D.

INTRODUCTION:
LIQUID SODIUM COOLED FAST NEUTRON REACTORS (FNRs) ARE REQUIRED FOR ECONOMIC DISPOSAL OF HIGH LEVEL NUCLEAR WASTE, FOR EFFICIENT ENERGY EXTRACTION FROM URANIUM AND FOR LOAD FOLLOWING ELECTRICITY GENERATION.
 

PURPOSE:
This web page sets out preliminary design calculations for a 962 MWt Fast Neutron Reactor (FNR) which is assembled from road and railway transportable modules. The purpose of these calculations is to provide a starting point for the detailed design of a power FNR that can be mass produced and widely deployed.
 

DESIGN OBJECTIVE:
The object of this web page is to set out the design of a practical modular Fast Neutron Reactor that is not dependent on close proximity to a large water body such as an ocean or the great lakes for either heat sinking or component transportation. The concept is that the FNR is field assembled from factory fabricated modules. Each such module is of a size and weight that lends itself to inexpensive transportation via road or rail. The practical implication of this concept is that the length of any single long rigid component must be less than 20 m (60 feet) and the outside diameter of any cylindrical object must be less than 6 m (20 feet) and the total module weight, including any required shielding, must be less than 100 tons. Depending on the location of a reactor site there may be even tighter dimensional or weight constraints imposed by highway overpasses, bridges, railway tunnels, etc. Transportation costs decrease substantially if the module length is less than 52 feet (15.8 m), the module diameter is less than 14 feet (4.5 m) and the module weight is less than 70 tons. Thus, if possible, the smaller module dimension and weight constraints should be adopted.
 

COOLANT CHOICE:
Liquid sodium is used as the primary coolant in a fast neutron reactor because it provides:
1) Low melting point;
2) A high thermal coefficient of expansion;
3) Good thermal conductivity;
4) Sufficiently high boiling point;
5) Acceptable heat capacity;
6) Chemically compatible with other metals such as iron, chromium, uranium, plutonium, zirconium;
7) A moderate neutron scattering cross section;
8) A low neutron absorption cross section;
9) Little cumulative buildup of long lived radioisotopes. Sodium-23, the only stable sodium isotope, absorbs neutrons and becomes radioactive sodium-24, which has a 15 hour half life and decays via electron emission to become stable Mg-24.
10) Relatively low cost.

Disadvantages of liquid sodium are:
1) Dangerously incompatible with water;
2) Flammable in air;
3) Must be kept above 98 degrees C during maintenance shutdown periods to keep it in its liquid phase.
4) Its high thermal coefficient of expansion can lead to large pipe and tube thermal stresses at temperatures below the melting point of liquid sodium.
5) Sodium-24 naturally decays to become stable Mg-24. Magnesium has a melting point of 650 degrees C which is above the highest normal FNR liquid sodium operating temperature. Sodium-23 impacted by a fast neutron will form stable F-19 and stable He-4. The F-19 will immediately chemically react with the Na to form NaF which has a melting point of 993 C. Any accidental contact between hot liquid sodium and air will lead to formation of Na2O and NaOH which have melting points of 1132 C and 318 C respectively. Hence the primary liquid sodium must be constantly filtered to remove entrained magnesium and NaF particles that otherwise will tend to form a sludge. The filter system inlet should be at the lowest point in the primary liquid sodium pool. The NaOH can only be filtered out when the reactor is in cold shutdown. However, during reactor operation liquid NaOH will tend to collect at the lowest point in the primary liquid sodium pool.
6) The lowest normal operating temperature of the secondary liquid sodium should be 320 degrees C to prevent NaOH precipitating on heat exchange surfaces or scouring those surfaces. There must be a mechanism for filtering NaOH out of the secondary loop after discharge from the steam generator. We need to be able to safely operate the liquid sodium discharge from the steam generator at 320 C to prevent any internal NaOH deposition within the steam generator tubes. That requirement in combination with the saturated vapor pressure of water at 320 degrees C implies a high working pressure rating for the intermediate heat exchanger.

These properties of sodium together dictate numerous aspects of liquid sodium cooled FNR power plant design.
 

STEAM GENERATOR MAXIMUM WORKING PRESSURE:
The temperature of the water in the steam generator is 320 deg C = 608 deg F. The corresponding saturated vapor pressure for water is:
1637.3 psia
= 1637. 3 psia X 101 kPa / 14.7 psia X 1 MPa / 1000 kPa
= 11.249 MPa
This pressure is maintained in the steam generator by the steam generator pressure regulating valve, the discharge from which drives the steam turbine.

P>Thus the steam generator and the liquid sodium secondary circuit should be rated for a working pressure of up to 12 MPa.
 

MINIMUM PRIMARY SODIUM TEMPERATURE:
Allowing for a 15 degree C temperature drop across the intermediate heat exchanger gives a minimum primary liquid sodium temperature of 320 C + 15 C + 15 C = 350 C
 

MAXIMUM PRIMARY SODIUM TEMPERATURE:
The maximum primary liquid sodium temperature is chosen to be 445 degrees C so that, allowing for a 15 degree C temperature drop across a fuel tube wall the maximum fuel tube material temperature is 460 degree C. This temperature choice is made to prevent a Fe-Cr fuel tube material phase transition which can occur at temperatures in excess of 460 degrees C.
 

MAXIMUM SECONDARY SODIUM TEMPERATURE:
Allowing for a 15 degree C temperature drop across the intermediate heat exchanger gives the full load maximum secondary sodium discharge temperature as:
445 C - 15 C = 430 degrees C

At light loads this temperature will rise to almost 445 C.
 

SODIUM RELATED FNR DESIGN ISSUES:
1) Except at the steam generator, water and liquid sodium should not be present in the same building because when water and liquid sodium contact hydrogen is released explosively along with sufficient heat to trigger spontaneous hydrogen ignition. Hydrogen is flamable in air over a wide range of hydrogen concentrations.

2) The fluid used for transporting heat away from the primary liquid sodium pool is non-radioactive liquid sodium pressurized by the inert gas argon. Hence an intermediate heat exchanger tube rupture has little serious consequence other than adding non-radioactive sodium to the radioactive sodium pool. In the event of a steam generator tube rupture the object is to immediately vent the steam to keep the intermediate liquid sodium pressure slightly above the water pressure (steam pressure) to minimize liquid sodium leakage through the rupture and to prevent water or steam entering the intermediate liquid sodium circuit.

3) When sodium-24 decays it emits 1.389 MeV electrons and emits 1.369 MeV gamma rays. Hence manual service work in the proximity of the radioactive primary liquid sodium must be delayed for about a week (11 Na-24 half lives) after reactor shut down to allow the Na-24 to naturally decay. To avoid this maintenance delay there are almost no moving parts within the reactor building and almost all service work in the reactor building is done via robotic equipment. The likely service issues within the reactor building are fuel bundle repositioning, heat exchange bundle replacement, control system service and primary sodium filter service.

4) A major issue with use of liquid sodium as a coolant and heat transport medium is that the density of liquid sodium is 0.927 X (density of water) and the (heat capacity of liquid sodium) is about (0.3 X the heat capacity of water). For the same differential temperature and the same flow velocity liquid sodium heat transport pipes need to be double the diameter of otherwise equivalent pressurized water heat transport pipes.

5) In order for liquid sodium to convey heat with approximately the same size pipes and fluid velocity as would be used for water the heat transport loop temperature differential must be increased about four fold. That increased loop temperature differential causes significant thermal stress relief design issues in the intermediate heat exchanger and in the steam generator. The heat exchange systems and the intermediate sodium pump flow rate must be carefully designed to minimize the temperature difference across the intermediate heat exchange tube walls and across the steam generator tube walls.

6) Liquid sodium is used as the intermediate coolant in a fast neutron reactor because sooner or later due to an intermediate heat exchanger tube or manifold failure high pressure intermediate liquid sodium will leak into the low pressure primary liquid sodium. There should be a sufficient number of isolated intermediate liquid sodium circuits to ensure that a single intermediate heat transfer circuit fault will not force a total reactor shutdown.

7) Note that the intermediate sodium circuits must be designed to accommodate high thermal stress both at the design operating temperature and at temperatures below the melting point of sodium.
 

FNR DESIGN OVERVIEW:
The FNR described herein consists of a primary liquid sodium pool 25.4 m long X 18.4 m wide X 13.5 m deep, in which the liquid sodium depth is 12.5 m. The pool inside walls and bottom are lined with sheet stainless steel outside of which is a 3 m thick layer of porous lava rock which serves as a thermal insulator. On top of the pool bottom is a sheet steel layer which protects the pool bottom against accidental damage. Surrounding the outside of the lava rock is another sheet stainless steel containment layer. Outside this sheet stainless steel layer is a 1 m thick air gap for air cooling and maintenance access and outside that air gap is a 1 m thick concrete wall.

On top of the pool bottom are 14 inch X 6 inch X 0.5 inch rectangular steel tubes which serve as the base for mounting the fuel bundle support tubes. On top of this base is a 14 inch thick layer of solid B4C spheres whose function is to stop melted fuel forming a critical mass.

There are no penetrations of the liquid sodium pool walls or floor. All reactor and heat exchange components are inserted into the liquid sodium pool via the top of the pool.

Allowing for 0.5 m of base gravel thus this reactor requires a below grade excavation of at least:
35.4 m long X 28.4 m wide X 18.5 m deep
= 18,599.16 m^3.

The volume of the required saw cut lava rock blocks is:
(31.4 m X 24.4 m X 16.5 m) - (25.4 m X 18.4 m X 13.5 m)
= (12,641.64 m^3 - 6309.36 m^3
= 6332.28 m^3

Within the air gap is structural steel which maintains the 1 m air gap between the outer layer of stainless steel and the concrete. The structural steel I beams supporting the pool bottom must bear the entire weight of the FNR and the surrounding lava rock and heat exchange bundles. The sheet steel outside the lava rock side walls must be sufficiently reinforced that it can withstand the liquid sodium hydraulic head in the event that there is an inner sheet stainless steel pool liner failure.

The liquid sodium pool deck is at grade level. The top of the liquid sodium in the pool is nominally 1 m below grade level. However, the exact elevation of the top of the primary liquid sodium may be vary over a 0.5 m range. The 1 m thick concrete walls extend straight upwards above grade for 5 m and then curve to form a half cylinder roof with outside dimensions 35.4 m long X 28.4 m wide X 19.2 m high above grade. The inside radius of curvature of the concrete roof is 13.2 m. The concrete normally is at ambient temperature. Inside the concrete is the 1 m air gap which is used for circulating cooling air and which allows maintenance access to the ventilation space and inside roof structure when the pool gamma emission is sufficiently low. Above grade there are both inner and outer sheet stainless steel walls separated by 1 m of ceramic fiber thermal insulation. These sheet stainless steel walls are gas tight. The closed space containing the ceramic insulation is filled with argon but has an over pressure relief vent. The ceramic insulation prevents the inner and outer sheet metal ceilings collapsing together when the absolute pressure in the insulation space is below one bar. The inner sheet stainless steel wall is used to contain the argon cover gas and the neutron activated sodium vapor. The outer sheet stainless steel wall is used to exclude air. The inner sheet stainless steel wall operates at 450 deg C and the outer sheet stainless steel wall operates at ambient temperature. The inner sheet stainless steel wall radius of curvature is 11.2 m. Hence the outer stainless steel sheet radius of curvature is 12.2 m. There is an evacuated low pressure between the inner and outer sheet stainless steel walls and ceiling that is used to detect leaks in either the inner or the outer sheet stainless steel wall/ceiling coverings.
 

REACTOR SIZE CONSTRAINT:
The inside width of the liquid sodium pool must be 18.4 m to allow for a 10.4 m diameter reactor core, a 1.2 m wide perimeter blanket and a 2.8 m wide layer of surrounding liquid sodium. It is anticipated that there will be a 3.0 m thickness of lava rock insulation around the sides and bottom of the sodium pool. There will need to be about a 1 m wide air space outside the lava rock for service access and for forced air heat removal. Hence the pool assembly width to the outside of this air space is 26.4 m.

The reactor roof design is constrained by the use of prefabricated structural steel beams that are limited by road and rail transportation constraints to ~ 20 m in length. It is anticipated that the reactor roof will be of semi-cylinder concrete construction with a maximum inside height above grade of 18.2 m to limit the individual roof construction support component lengths to less than 20 m. However, assuming that the gantry crane is supported by the adjacent concrete walls the sliding gantry crane cross memeber I beams will be almost 26.4 m long. This cross member may need to be fabricated by joining two shorter I beam lengths.
 

CONCRETE PURPOSE:
The concrete remains at ambient temperature unless both the inner stainless steel wall and the outer stainless steel wall rupture. The main function of the concrete is to contain gamma radiation. Other functions of the concrete include:
1) Exclusion of ground water;
2) Exclusion of rain water;
3) Exclusion of flood water;
4) Physical protection from grade level or air borne physical attack;
5) Reserve containment of liquid sodium;
6) Reserve fire containment;
7) Supporting the inner ceiling structure, the ceramic fiber insulation and the fuel bundle discharge temperature monitoring systems;
8) Supporting the gantry crane;
9) Supporting the gamma ray camera;
10) Guiding cooling air flow;
11) Reserve radio isotope containment.
 

STAINLESS STEEL PURPOSE:
The functions of the inner sheet stainless steel wall include:
1) Primary sodium vapor containment;
2) Cover argon containment;
3) Reserve air exclusion.

The functions of the outer stainless steel wall include:
1) Primary air exclusion;
2) Argon containment;
3) Reserve sodium vapor containment;

The functions of the air gap include:
1) Space for circulation of cooling air;
2) Space for inspection and service access;
3) Space for emergency sump pumping of either liquid sodium or water.
 

REACTOR ASSEMBLY:
The assembly of fuel bundles is located in the lower centre of the primary liquid sodium pool between 3 m and 9 m above the pool inside bottom.

In plan view the reactor is a square 32 fuel bundles X 32 fuel bundles = 1024 fuel bundles with 55 fuel bundles clipped off each corner of the square for a total of:
1024 - 4(55) = 804 fuel bundles in an octagon shape.

In plan view the active fuel bundles form a 26 bundle X 26 bundle square = 676 active bundles with 36 bundles clipped off each corner of the square for a total of:
676 - 4(36) = 532 active fuel bundles.

The passive fuel bundles form a perimeter belt 3 fuel bundles thick. This perimeter belt contains:
804 - 532 = 272 passive fuel bundles.

The fuel bundle assembly maximum diameter is 12.8 m from one octagonal face to the opposite octagonal face. The minimum distance from a fuel bundle octagonal face to the nearest primary liquid sodium containment wall or the nearest intermediate heat exchange component is 2.8 m.

There is space in the corners of the primary sodium pool for storing up to 312 used fuel bundles out of the neutron flux. Between the stored used fuel bundles and the intermediate heat exchange bundles is a channel 0.8 m long. This channel is used for adding new fuel bundles to the pool or for removing used fuel bundles from the pool via a door in the enclosure side wall.


 

This plan view details only one quarter of the FNR. The other three quarters are symetrically identical. Each colored square on this plan view represents a 0.40 m X 0.40 m fuel bundle space allocation. The red squares are active bundles. The orange squares are passive bundles. The green squares are used fuel bundle storage positions outside the neutron flux. The blue rectangles at the pool ends are heat exchange bundles. The heat exchange bundle 320 degree C inlet pipes are adjacent to the pool ends. The heat exchange bundle 430 degree C discharge pipes are adjacent to the reactor zone.
 

FUEL BUNDLE DETAIL:
Every second active fuel bundle has a dedicated insertion actuator. Each fuel bundle has a maximum horizontal length allocation of 0.400 m (15.748 inch) and a maximum horizontal width allocation of 0.400 m (15.748 inch).

The nuclear reactions take place within the fuel bundles. Each fuel bundle in plan view is square and contains:
24 X 24 = 576 potential vertical fuel tube positions. The fuel tubes are positioned on a square grid with (5 / 8) inch center to center spacing. However the 4 X 5 corner fuel tube positions are required for shroud structure reinforcement girders, and 4 X 3 fuel tube positions are required for control bundle corner girders leaving 544 actual fuel tubes per fuel bundle.

The nominal face to face size of a fuel bundle exclusive of its shroud is:
(24 tubes X (5 / 8 ) inch / tube) = 15.00 inch

The fuel tube bundles are designed so that individual fuel tubes can linearly swell without the external length or width of the fuel bundle materially changing. Fuel bundles are intended to be replaced after 15% linear swelling of the most intensely neutron irradiated sections. The fuel tube array center-to-center spacing is established by end gratings that are located out of the main fast neutron flux and hence are protected from swelling.
 

INDICATOR TUBES:
Each fuel bundle has an indicator tube about 3 m long. The indicator tube must be strong enough to allow lifting the fuel bundle. The indicator tube shows the vertical position of the fuel bundle, allows measurement of gamma flux, and allows measurement of fuel bundle discharge temperature.
 

FUEL TUBE DETAIL:
Each fuel tube is 0.500 inch OD X 6.0 m long. The bottom 2.8 m of each fuel tube contains uranium alloy fuel rods. The top 3.2 m of each fuel tube is known as its plenum and contains liquid sodium and inert gas. The fuel tubes are sealed around the fuel rods to prevent intensely radioactive fuel and fission products spreading through the primary liquid sodium and depositing on relatively cool heat exchange surfaces.

The FNR top and bottom blankets each consist of 2 rods 0.600 m long. This blanket rod configuration allows a small amount of fuel tube bending. Even so these blanket rods still need to initially be straight to within +/- 1 mm over each 600 mm length.The individual blanket rods are made longer than the individual core rods to allow easy rod sorting and to prevent accidents resulting from rod type mix up.

The FNR core fuel rods are on average initially 1 X 0.350 m long but over time swell to average lengths of 1 X 0.400 m long. This core rod length achieves the desired zone reactivity and allows a small amount of fuel tube bending. Even so these core fuel rods still need to initially be straight to within +/- 1 mm over each 350 mm length.

The following diagram shows a side elevation of the FNR. The primary liquid sodium is shown in yellow.


_________FIX  

Note that the 0.30 m to 0.40 m high core region is surrounded by blanket regions each 1.2 m thick.

Note the fuel tube 3.2 m high plenum region above the highest blanket zone.

Note the 804 X 12.750 inch OD X 0.500 inch wall X 2.5 m long steel pipes that support the fuel bundles;

Note the 804 X 3.0 m long indicator tubes that reach above the top surface of the primary liquid sodium to provide buoyancy, to show the actual bundle position, to signal the fuel bundle liquid sodium discharge temperature and to provide a lifting point.

Note that the intermediate heat exchange bundles extend 3 m above the fuel tube bundles to enhance natural circulation of the primary liquid sodium.

REACTOR FUEL ALLOYS:
The FNR core rods are initially 70% metalic U-238 with 20% Pu-239 and 10% zirconium alloyed with it. The purpose of the zirconium is to prevent formation of a low melting point eutectic between plutonium and iron. (Til & Yoon P.105 - 106). The purpose of the Pu-239 is to fuel the nuclear reaction. The purpose of the U-238 is to absorb surplus neutrons to breed more Pu-239. The reactor fuel core rods are 8.08 mm diameter metallic rods that loosely slide into the steel fuel tubes. The core rod diameter is intentionally only about 86% of the steel fuel tube initial ID. Inside the steel fuel tubes, along with the fuel rods is liquid sodium, which provides a good thermal contact between the fuel rods and the steel fuel tubes and which chemically absorbs the otherwise gaseous reaction products iodine and bromine.

The blanket rods are 90% uranium plus 10% zirconium. Since fissioning in the blanket rods is minimal their initial outside diameter is 9.0 mm, which is about 4.2% less than the initial fuel tube ID.
 

FNR TRADEOFFS:
It is contemplated that the reactor core fuel rods are initially 0.35 m long and are contained in 0.500 inch OD X 0.065 inch wall steel tubes positioned laterally on 0.625 inch square centers. In the vertical channels between the fuel tubes liquid sodium coolant flows upwards to remove heat. Implications of this design are a small liquid sodium circulation power (natural circulation), negligible fuel tube erosion, reasonable fuel temperature, reasonable reactor dimensions, an acceptable liquid sodium temperature rise and a reasonable requirement with respect to filtering particulates out of the liquid sodium.

The size of the gap between the steel tubes is a compromise between the requirements for heat transport and the requirements for average fuel density. As the gap between the fuel tubes becomes smaller the problems of primary sodium circulation and of filtering particulates out of the liquid sodium rapidly become larger. As the gap becomes larger the required concentration of fissionable material in the core rods rapidly increases.

Practical operating experience with the EBR-2 showed that during normal operation formation of fission products causes the core rod cross sectional area to swell by about 33%. Hence the initial reactor core fuel rod diameter is restricted to:
[(steel fuel tube ID) X 0.86].
The only practical ways to increase the average fuel density in the reactor core are to reduce the gap between the steel fuel tubes or to increase the concentration of Pu-239 in the core fuel rods. Note that the initial blanket fuel rod outside diameter can be larger than the initial core fuel rod outside diameter because the blanket fuel rods are less subject to fission product induced swelling.

An important issue in FNR design is neutron conservation. Almost all the excess neutrons emitted by the reactor core zone are captured by the surrounding 1.2 m thick breeding blanket.
 

REACTOR THERMAL POWER:
If we assume a 15.0 deg K temperature drop across the fuel tube wall as shown at FNR Fuel Tubes the approximate heat transfer rate per core tube is given by:
15.0 deg C X 26.2 W / m-deg C / (.065 inch X .0254 m / inch) = 238,037 W / m^2

The active tube external heat transfer surface area is:
Pi X (.500 inch) X (.0254 m / inch) X 0.35 m / fuel tube = 0.013964 m^2 / active fuel tube

The thermal power per active fuel tube is:
238,037 W / m^2 X 0.013964 m^2 / active fuel tube = 3323.95 Wt / active fuel tube

Hence, subject to sufficient primary sodium flow the corresponding maximum allowable reactor thermal power is:
544 fuel tubes / bundle X 532 active bundles X 3323.95 Wt / active fuel tube = 961,977,721.6 Wt
= 961.98 MWt

Each active fuel tube bundle supplies:
544 tubes / bundle X 3323.95 Wt / active tube = 1808228.8 Wt / active fuel tube bundle
= 1.808 MWt / active fuel bundle
 

INTERMEDIATE HEAT EXCHANGER:
The fuel bundle and heat exchanger installation - removal pathway is along a central corridor. There are 32 heat exchange bundles immersed in the liquid sodium and used to extract heat from the primary liquid sodium pool. Each heat exchange bundle is rated for at least:
962 MWt / 32 = 30.06 MWt.

The intermediate heat exchange tube bundles are located at the ends of the primary sodium pool between 6 m and 12 m above the pool bottom. The primary liquid sodium circulates by natural convection. In the middle of the primary sodium pool the top surface of the liquid sodium is about 12 m above the pool bottom. During reactor operation the elevation of the top surface of the liquid sodium slightly increases in the center of the pool and slightly decreases at the ends of the pool. The top surface of the liquid sodium is about 1.0 m below grade.

There are 16 independent intermediate heat transfer circuits, each consisting of two parallel baffled counter flow intermediate heat exchange bundles, extended pipes and fittings, a drain down tank, an induction type intermediate liquid sodium circulation pump, a steam generator, and a cushion tank. Liquid sodium is transferred from the drain down tank into the secondary loop by application of argon pressure in the drain down tank. The intermediate heat exchange tube bundle and the steam generator tube bundle both operate at a working pressure of 11.5 MPa. The intermediate heat exchange tube material is always under tensile stress. The intermediate heat exchanger design and the steam generator design are constrained by the high temperature yield stress and creep properties of the heat exchange tube material and by the tube wall thickness required to resist high thermal stress at temperatures below the melting point of liquid sodium.

Each heat exchange bundle is dedicated about 1.0 m of one end of the liquid sodium pool width and functions to remove heat from the upper layer of hot liquid sodium. Natural circulation of the primary liquid sodium conveys heat from the nuclear fuel bundle discharge near the center of the pool to the heat exchange bundles near the ends of the pool. The liquid sodium recirculates along the bottom of the pool.

The intermediate heat exchanger secondary fluid is non-radioactive sodium. The heat exchanger secondary fluid conveys the heat to steam generators which are located in abutting buildings. The secondary sodium is circulated via electromagnetic induction pumps. In adjacent buildings steam from the steam generators is expanded through turbines. Water cooled condensers connected to cooling towers condense the steam. The condensate is pumped at a high pressure (~ 11.25 MPa) back into the steam generators via recuperator heat recovery coils located in the condensers. The condensate injection rate into the steam generator is adjusted to maintain the desired water level in the steam generator.

At the fuel bundle pool insertion-removal point the interior ceiling over the liquid sodium pool must be at least 13 m above the liquid sodium surface. The fuel bundles are lifted with a 10 ton rated gantry crane. Due to the semi-cylinder roof geometry the outside peak of the reactor building roof is about 19.2 m above grade.
 

REACTOR BUILDING:
The reactor building above grade outside foot print is 35.4 m long X 28.4 m wide. Abutting the ends of the reactor building are the steam generator building extensions which are each 28.4 m wide X 15 m long. Above grade shielded fresh air intakes in the middle of the building side walls increase the reactor building's width by about 6 m. The fresh air is ducted down to the outside bottom of the primary sodium pool and over the higher suspended roof. Thus the total footprint is 65.4 m long X 34.4 m wide. Also at the ends of the reactor building are 2 truck docks for ongoing delivery and removal of fuel bundles and intermediate heat exchange bundles. On the top center line of the reactor building are multiple exhaust fans.

The required 16 turbo-generators, 16 condensers, 2 cooling towers, electrical switch yards, transformers, control room, water supply, emergency generator, reserve sodium pool, sodium drum storage lot, railway siding, fuel reprocessing, fuel bundle assembly-disassembly, fuel bundle storage, argon and liquid sodium injection/recovery equipment, argon production and reserve argon tanks, warehouse and vehicle parking lot all require additional land area.

All of the FNR components are designed for factory fabrication and are sized for easy truck and/or rail transport with no special provisions for load over width, over height or over weight. The sheet stainless steel panels forming the inner pool liner, outer pool wall, inner metal ceiling, inner above grade metal wall, outer metal ceiling and outer above grade wall must be field welded together. These welds must be air tight and free of defects.
 

PRIMARY SODIUM POOL DIMENSIONS:
The primary liquid sodium pool is rectangular with inside dimensions: 18.4 m wide by 25.4 m long X 13 m deep. The nominal liquid sodium depth is 12 m.

The 3.5 m long heat exchange bundle sections near each end of the pool are 6.0 m deep, and are supported by front and back vertical pipes. The sodium pool's reactor zone is 18.4 m long X 18.4 m wide X 12 m deep.

In plan view the primary liquid sodium pool has a 2.8 m wide neutron absorption guard band around the fuel bundle assembly. This guard band allows insertion, removal and relocation of fuel bundles. The spent fuel bundles are stored out of the neutron flux in the corners of the reactor zone to allow fission product decay. The central 12.8 m long by 12.8 m wide area is occupied for the reactor fuel bundles. The two end areas, each 3.5 m long by 18.4 m wide are occupied by the intermediate heat exchange bundles. The 2.8 m guard band gap between the blanket fuel bundles and the nearest wall or heat exchange bundle assembly protects the walls and heat exchange bundles from cumulative neutron damage. Fuel bundles and intermediate heat exchange bundles enter or leave the reactor building via side door air locks at truck deck level. These side doors are aligned with the 0.8 m wide gaps between the intermediate heat exchange bundles and the spent fuel bundles located in the corners of the reactor zone.
 

GUARD BAND:
The guard band is a region 2.8 m wide outside the fuel bundle assembly perimeter. The guard band contains no equipment. The guard band prevents neutrons originating in the reactor from being absorbed by the cooling bundles, heat exchange bundles and the pool wall. The purpose of the guard band is to extend equipment life and minimize formation of decommissioning waste. Above the tops of the fuel tubes are 3 m of liquid sodium that prevent neuton emission upwards. Below the bottoms of the fuel tubes are 3 m of liquid sodium that prevent neutron absorption by the primary sodium pool floor.
 

SPENT FUEL BUNDLE STORAGE SPACE:
The corners of the reactor zone have space for storing up to:
4 (78) = 312 fuel bundles
out of the neutron flux. This space is used to allow fission products to decay to a level compatible with fuel reprocessing before a fuel bundle is removed from the primary liquid sodium pool.
 

FLOATS:
In normal operation the entire top surface of the primary liquid sodium pool is covered by an array of 0.4 m X 0.4 m squate steel floats. The purpose of these floats is to minimize the liquid sodium surface area that is exposed to the atmosphere amd to stabilize the relative positions of the indicator tubes. In theory the atmosphere above the liquid sodium is argon. However, from time to time some air will mix with this cover gas, in which event the floats minimize sodium-air chemical reactions which will tend to pollute the liquid sodium.

An important function of these floats is to minimize the fire risk and to minimize sodium vapor condensation on the interior walls, ceiling, gantry cranes and optical scanning equipment. The floats have 6 holes in their centers to allow passage of the indicator tubes. At the ends of the reactor are floats that are shaped to cover the sodium over the heat exchange bundles.
 

REACTOR CONCRETE ENCLOSURE:
The space immediately above the primary sodium pool is filled with an inert cover gas (argon) that will not chemically react with the liquid sodium. The immediately overhead roof (the lowest roof) must be high enough to allow fuel bundle and heat exchange bundle remote manipulation via the gantry cranes and must be gas tight. The lowest roof is sheet stainless steel and is suspended from the concrete roof structure above it. The suspension rods have thermal breaks. The lowest roof operates at about 480 degrees C. On top of the lowest roof is a 1 m thick layer of high temperature rated ceramic fibre insulation (fiberfrax). On top of this insulation is the outer metal roof. On top and outside of the outer metal roof is a 1 m thick space for circulation of cooling air. This space also allows human access for roof service commencing about one week after the reactor is shut down.

Above the air space is the 1 m thick arched concrete roof. This roof is assembled from interlocking precast concrete sections. The purpose of the concrete is to:
1) Attenuate gamma radiation emitted by fuel bundles and the liquid sodium pool;
2) Exclude rain water and snow melt water;
3) Provide severe storm protection for the FNR.
4) Provide physical protection for the FNR from either overhead or grade level physical attack;
5) Contain and smother a sodium fire;
6) Provide reserve radio isotope confinement.

In plan view the inside dimensions of the bottom of the concrete walls are: 26.4 m X 33.4 m.

Each fuel bundle is brought in horizontally from a truck mounted transport container via a port in the middle of the reactor enclosure end wall and is rotated to a vertical position over the sodium pool where the ceiling is high. When the fuel bundle reaches vertical its bottom is immersed in liquid sodium. It is then moved horizontally through the liquid sodium to its desired rest position. To accommodate a truck compatible end port the enclosure straight side wall height extends 5 m above grade which gives an inside center line ceiling height of:
5 m + (26.4 m / 2) - 2 m = 16.2 m

The concrete roof consists of precast interlocking sections similar in concept to the prefabricated sections used to line subway tunnels.

The overall concrete enclosure outside height is:
5 m + 13.2 m + 1.0 m = 19.2 m

The concrete footing requirement is about:
1 m X 35.4 m X 28.4 m = 1005.3 m^3

Below grade the load bearing concrete walls extend down 17 m and rest on the bottom concrete slab. Hence the straight side and end walls above and below grade contain:
(17 m + 5 m) X (2 (35.4 m + 26.4 m) X 1 m
= 22 m X 2 X 61.8 m X 1 m = 2719.0 m^3 concrete

The curved portion of the upper roof contains:
Pi (13.7 m) X 1 m X 35.4 m = 1523.61 m^3

The semi-circular end wall portions contain:
Pi (13.2 m)^2 X 1 m = 547.4 m^3

Assume that the concrete is everywhere 1 m thick. Then the volume of concrete required is given by:
(volume of base) + (volume of straight walls) + (volume of semi-circular end wall tops) + (volume of arched roof)
= [35.4 m X 28.4 m X 1 m] + [22 m X 2 (35.4 m + 26.4 m) X 1 m] + [Pi (13.2 m)^2 X 1 m] + [Pi (13.7 m) 35.4 m]
= 1005.36 m^3 + 2719.20 m^3 + 547.39 m^3 + 1523.61 m^3
= 5795.56 m^3 concrete

The concrete roof must be covered by a durable waterproof membrane that is easily serviceable. The upper roof arch must be able to exclude rain water under the most adverse circumstances, including violent storms, tornados, long term corrosion and deliberate aerial attack. Ensuring a long term reliable upper roof is a major issue in safe liquid sodium cooled FNR implementation.

There should also be an argon fire suppression system sufficient to prevent sodium combustion in the event of a major roof failure or in the event of a heat transfer circuit failure.
 

LIQUID SODIUM POOL CONSTRUCTION:
There are no through holes in either the side walls or the bottom of the liquid sodium pool. The cover gas above the pool is inert (argon). The ceiling above the pool center line is about 16.2 m above the liquid sodium surface to permit fuel bundles, heat exchange bundles and their associated support pipes to be individually lifted, moved, stored, removed and replaced using two remotely controlled overhead gantry cranes. The reactor enclosure ceiling is insulated and the gas above the pool is maintained slightly above the pool surface temperature (~ 445 deg C) to prevent sodium vapor condensation on the ceiling and on the overhead gantry crane structure. The gantry cranes must be rated for continuous use in a 450 degree C sodium vapor environment.

The pool floor holds a steel frame with a 0.400 m square grid of ~ 10.0 inch diameter ~ 2.8 m deep plugs that are used to position, support and stabilize the fuel bundles. A small central hole in each socket provides controlled amounts of high pressure liquid sodium for mobile fuel bundle vertical positioning.

The primary liquid sodium pool has a double wall and a double sub-floor formed from sheet stainless steel for containment reliability. The inner and outer walls are separated by a 3 m thickness of saw cut lava rock that limits heat loss through the pool walls and floor and limits the decrease in primary sodium pool depth in the event of a failure of the inner wall. The liquid sodium pool must be sited at sufficient elevation that the liquid sodium will never be exposed to flood water or ground water. The ground surrounding the pool must be sufficiently above the local water table that in the event of a major earthquake or other event that ruptures the pool inner, the pool outer wall and the concrete wall the contained radio active sodium still cannot go anywhere or react with significant quantities of ground water.

The primary liquid sodium pool requires a below grade excavation of at least:
35.4 m long X 28.4 m wide X 18 m deep
= 18,096 m^3.

The volume of the required saw cut lava rock blocks is:
(24.4 m X 31.4 m X 16 m) - (18.4 m X 25.4 m X 13 m)
= (12,258.56 m^3 - 6075.68 m^3
= 6182.88 m^3

The area of the stainless steel sheet forming the primary sodium pool outside bottom is:
(24.4 m X 31.4 m) = 766.16 m^2

The area of the stainless steel sheet forming the primary sodium pool outside wall is:
2 [(16 m X 24.4 m) + (16 m X 31.4 m)]
= 1785.6 m^2

The area of the stainless steel sheet covering the primary sodium pool inside bottom is:
(18.4 m X 25.4 m) = 467.36 m^2

The area of the stainless steel sheet covering the primary sodium pool inside walls is
2 [(13.0 m X 18.4 m) + (13.0 m X 25.4 m)]
= 1138.8 m^2

The area of stainless steel sheet metal covering the primary sodium pool pool deck is:
(22.4 m X 29.4 m) - (18.4 m X 25.4 m)
= 658.5 m^2 - 467.36 m^2
= 191.14 m^2

The pool floor must be well supported because it carries the entire weight of the liquid sodium plus the weight of the fuel bundles and their control rod apparatus plus the weight of the immersed heat exchangers and their associated piping plus the weight of the fuel bundles in storage plus the weight of the pool walls and floor, including the 3 m thickness of lava rock insulation.
 

After pouring the concrete foundation slab the straight concrete walls are erected first to support the gantry cranes. Two gantry cranes are used for lifting and positioning all other reactor components. The main issue with the gantry cranes is that they must be rated for continuous remotely controlled operation in a high temperature environment. The cranes must have a high positioning accuracy so that they can easily plug a fuel bundle support pipe into its matching socket in the steel rack on the bottom of the pool without a visual reference. Each crane must have at least a ten tonne lifting capacity.
 

STABLE STRATIFIED PRIMARY LIQUID SODIUM:
The reactor is designed to operate with hot liquid sodium (445 deg C) occupying the upper 3.0 m of the pool depth, and with cooler liquid sodium (335 deg C) occupying the bottom 4.2 m of the pool depth. In the: (12 m - 4.2 m - 3.0 m) = 4.8 m
between these two extremes the temperature in the primary liquid sodium pool changes depending on reactor loading. The design temperature difference between the top and bottom of the primary liquid sodium pool is 110 degrees C.

The elevation of the center of the transition region between the hot liquid sodium on top and the cooler liquid sodium on the bottom is referred to as the transition elevation. If the transition elevation increases natural circulation through the intermediate heat exchanger primary decreases causing accumulation of hot liquid sodium on top of the pool, which tends to restore the transition elevation to its desiqn level.

If the transition elevation decreases natural circulation through the reactor decreases so that there is net accumulation of cool liquid sodium in the bottom of the pool, which tends to restore the transition elevation to its design level.

The intermediate heat exchanger draws hot primary liquid sodium from near the liquid sodium top surface and discharges cool primary liquid sodium below the transition layer.

Note that to operate at a high thermal power requires high liquid sodium natural circulation which requires a high primary liquid sodium pool top to bottom temperature differential. Hence the reactor power rating is dependent on the steam generator design being consistent with this high liquid sodium temperature differential.

Material property limitations limit the primary liquid sodium top surface operating temperature to a maximum of 445 degrees C. However, more generally the reactor power is limited by fuel tube, heat exchanger and steam generator material and performance constraints. In normal operation the temperature at the top of the primary sodium pool is 445 C and the temperature at the bottom of the primary sodium pool is about 335 C.
 

PRIMARY LIQUID SODIUM FLOW PATH:
The primary liquid sodium flows along two vertical loop paths. Both paths start at the bottom center of the primary liquid sodium pool. The liquid sodium rises between the reactor fuel tubes. As the liquid sodium rises it absorbs heat, expands and becomes less dense and hence more buoyant relative to the surrounding cooler liquid sodium. At the pool top surface the liquid sodium flow splits with half of the hot liquid sodium flowing along the pool top surface toward one end of the pool and the other half of the hot liquid sodium flowing along the pool top surface toward the other end of the pool.

Near the ends of the pool the liquid sodium flows down thermally isolated vertical ducts containing the single pass of vertical intermediate heat exchange tubes.
 

DESIGN FOR FNR SAFETY:
This FNR design uses high pressure liquid sodium secondary heat transport loops. This heat transport fluid choice places two pressure rated metal barriers between the high pressure water/steam and the low pressure radioactive primary liquid sodium. The pressure in the intermediate heat transport loops is maintained by high pressure argon in the heat transport loop cushion tanks. This argon pressure is automatically controlled to track the steam pressure in the relevant steam generator.

In the event of a steam generator tube failure the high secondary sodium loop pressure prevents water from entering the secondary sodium circuit. In the event of an intermediate heat exchanger tube failure the liquid sodium from only one or two of the 32 separately isolated secondary circuits leaks into the primary sodium pool with little practical consequence. The argon in the leaking secondary sodium circuit's cushion tank is chemically inert and will not chemically react with either hot water or hot liquid sodium.

The surface of the primary liquid sodium pool is covered by 0.4 m X 0.4 m square steel floats which minimize sodium oxidation or combustion in the event that oxygen leaks into the sodium pool's argon cover gas. In the event of a significant air leak the liquid sodium is cooled as fast as possible to below 200 degrees C which is its threshold for combustion in air.

The primary liquid sodium pool is located sufficiently above the local water table that it will never be exposed to flood water.

The primary liquid sodium naturally circulates. This natural circulation system avoids many practical complications and reliability issues relating to pumped circulation of the primary liquid sodium.

The fuel bundles are configured such that the sliding control portion moves vertically with respect to the fixed surround portion.

Two adjacent fuel bundles are separated by 2 X (1 / 16) inch thick steel shroud walls to prevent tube swelling and distortion causing adjacent tube rubbing which could threaten the reactor safety.
 

RESERVE POOL:
Sooner or later it will be necessary to do maintenance work on the sodium pool inner wall. To do such work it will be necessary to pump the radioactive primary sodium out of the pool. Hence there must be another adjacent empty pool of sufficient capacity to hold the entire volume of radioactive primary liquid sodium while the maintenance work is being carried out. Viewed another way, a cluster of three FNRs requires four pools. For maintenance flexibility there should be practical means for transferring liquid sodium and fuel bundles from pool to pool.
 

THERMAL POWER CONTROL:
The reactor core zone attempts to maintain its own temperature setpoint of 445 degrees C. With the control bundles 0.6 m withdrawn the corresponding setpoints are intended to be less than 0 C to ensure total reactor shutdown.

As the liquid sodium in the reactor core zone warms up it thermally expands increasing neutron diffusion out of the core zone and hence stopping the nuclear chain reaction in the core zone. Then the only heat produced is fission product decay heat. Provided that the mobile fuel bundle insertion is correct and that there is adequate decay heat removal the liquid sodium discharge temperature from that zone will always stabilize at its design temperature. If heat is removed from the liquid sodium faster than decay heat is produced the liquid sodium temperature decreases causing the liquid sodium density to increase. This liquid sodium density increase reduces neutron diffusion out of the core zone which restarts the nuclear chain reactions.

Care must be used to ensure that every fuel bundle remains within its safe and stable thermal control range. If the fuel is too rich or if the control bundle insertion is too great the fuel in the core zone can potentially get too hot and melt. Hence the discharge temperature of each fuel bundle and the corresponding gamma power emission are individually monitored. The contro bundle insertion is precisely controlled.

The control bundle positions and the fuel bundle discharge temperatures are indicated by indicator tubes that project above the surface of the liquid sodium. The horizontal position of each indicator tube is stabilized by the indicator tube's buoyancy and by its 0.400 m X 0.400 m steel float.

The control bundles are vertically positioned so that as the fuel bundle liquid sodium discharge temperature reaches its design maximum (445 degrees C) the reactor core zone becomes subcritical. Thereafter the fuel bundle discharge temperature remains at its discharge setpoint value.
 

THERMAL SHUTDOWN:
If the control bundles are properly positioned, as the reactor's external thermal load decreases the primary liquid sodium temperature rises and the primary liquid sodium thermally expands causing an increase in neutron diffusion out of the reactor core zone and hence a reduction in reactor heat output. When a fuel bundle discharge temperature reaches its setpoint the reactor core zone becomes subcritical and the fission reactions in that fuel bundle totally cease.

Note that at all times the external thermal load must be sufficient to remove fission product decay heat.
 

REACTOR THERMAL POWER MODULATION:
The reactor thermal power output is modulated by modulating the secondary sodium flow rate. As the secondary sodium flow rate decreases the thermal power delivered to the thermal load decreases. The steam generator must be designed to accommodate the changing secondary liquid sodium flow. The pressure regulator on the steam generator effectively sets the secondary liquid sodium return temperature by modulating the steam discharge valve to maintain the steam pressure in the steam generator at about 11.25 MPa.
 

REACTOR TRIP CONDITION:
Since the working pressure of the secondary sodium heat transport system is 11.4 MPa the steam pressure must always be kept under 11.4 MPa. The reactor must be tripped off by a controlled shut down if for any reason the steam pressure exceeds 11.4 MPa.
 

STRESS RELIEF:
In this equipment arrangement the secondary sodium circuit is designed to safely operate with an internal working pressure of up to 11.4 MPa. The net working pressure stress on the steam generator tubes is minimized by controlling the secondary sodium pressure to be slightly above the steam pressure. Intermediate heat exchanger material thermal stress is minimized by the use of a counter flow heat exchange configuration which limits the temperature difference across the steam generator tube walls and hence limits the tube material thermal stress. These tubes normally operate with an internal sodium pressure of about 11.4 MPa.
 

FUEL TUBE MATERIAL SELECTION:
A material suitable for use in fuel tubes is HT-9. Over its working life part of the Fe atoms transmute into chromium and He-4. Part of the chromium further transmutes into Ti and more He-4. Due to its low nickel content, the iron BCC lattice and the Cr BCC lattice HT-9 minimizes fuel tube material swelling in a fast neutron flux. However, when loaded with He-4 after prolonged exposure to a fast neutron flux the fuel tube material is very brittle.
 

POWER BREEDER REACTOR CONCEPT:
The power breeder reactor contemplated herein has one octagonal shaped core zone, 10.4 m in diameter X (0.35 m to 0.40 m) high that is sandwitched between two breeding blanket zones each 1.2 m high. The perimeter of this stack is surrounded by a 1.2 m thick breeding blanket. The whole is in turn surrounded by a 2.8 m thick layer of liquid sodium for complete neutron absorption.

The reactor is an assembly of 804 fuel bundles. Each active fuel bundle is an assembly of 544 adjacent vertical fuel tubes. Each fuel tube contains a vertical stack of fuel rods.

Each active fuel bundle has 1 X (0.35 m to 0.40 m) high FNR core zone sandwitched between 2 X 1.20 m high blanket zones one above another for an overall fuel rod stack height of (2.75 m to 2.8 m).

The reactor core fuel rods initially consist of an alloy of 70% uranium, 20% plutonium + transuranium actinides, 10% zirconium. The plutonium + transuranium actinides are obtained by reprocessing spent fuel from water moderated nuclear reactors. In the FNR core the isotopes U-235, Pu-239 and transuranium actinides fission. Each Pu-239 fission releases about 3.1 energetic neutrons. Each U-235 fission releases about 2.6 energetic neutrons.

One neutron per Pu-239 fission is required to sustain the fission chain reaction. One neutron per Pu-239 fission is required to sustain the plutonium Pu-239 production required to provide future fuel for this reactor. Approximately 0.5 neutrons per Pu-239 fission are lost to various unproductive neutron absorption processes in sodium and steel. The remaining 0.6 neutons per Pu-239 fission are used for breeding additional plutonium for starting other breeder reactors.

The 0.600 m high breeding blanket fuel rods are made from 90% uranium and 10% zirconium.
 

TUBE AND PIPE WALL THICKNESS:
One of the design issues with liquid sodium is that the containing tubes and pipes must have sufficient wall thickness to safely absorb the stresses that can occur during melting of the sodium. Consider a round steel pipe which is plugged at both ends and which is full of solid sodium at room temperature.

Define:
P = radial pressure on inside pipe surface
Wp = pipe wall thickness
Dp = pipe outside diameter
Syp = pipe steel yield stress at 100 degrees C
TCEp = thermal coefficient of expansion of pipe
Ys = Youngss modulus for sodium
TCEs = Thermal coefficient of expansion for sodium

Barlow's formula for round pipes gives:
P (Dp - 2 Wp) < Syp (2 Wp)

As the pipe warms from 20 degrees C to 100 degrees C its inside diameter linearly expands by the amount:
(Dp - 2 Wp) TCEp (100C - 20 C)

As solid sodium warms from 20 deg C to 100 deg C it linearly expands by the length:
TCEs (Dp - 2 Wp)(100 C - 20 C)

Hence the compressive strain on the sodium is:
[TCEs (Dp - 2 Wp)(100 C - 20 C) - (Dp - 2 Wp) TCEp (100C - 20 C)] / (Dp - 2 Wp)
= (TCEs - TCEp) (80 C)

The corresponding stress on the sodium is P.

Thus:
Ys = stress / strain = P / [(TCEs - TCEp) (80 C)]
or
P = Ys [(TCEs - TCEp) (80 C)]

Substitution of this expression for P into Barlow's formula gives:
Ys [(TCEs - TCEp) (80 C)](Dp - 2 Wp) < Syp (2 Wp)
or
(Ys / Syp) [(TCEs - TCEp)(80 C)] < (2 Wp) / (Dp - 2 Wp)

This relationship sets the minimum wall thickness Wp for metal pipe or tube containing sodium.

For sodium:
Ys = 10 GPa TCEs = 71 X 10^-6 / deg C

For mild steel pipe or tube:
TCEp = 15 X 10^-6 / deg C
Syp = (30,000 psi) X (101,000 Pa / 14.7 psi) = 206.1 X 10^6 Pa = 0.2061 GPa

(Ys / Syp) [(TCEs - TCEp)(80 C)] = (10 GPa / .2061 GPa)[(71 - 15) X 10^-6 X 80] = 0.21737

Thus for mild steel pipe to safely contain sodium:
[(2 Wp) / (Dp - 2 Wp)] > 0.21737
or
2 Wp > (Dp - 2 Wp)(0.21737) or
2 Wp (1 + 0.21737) > Dp (0.21737)
or
Wp > Dp [(0.21737) / (2 (1.21737))]
or
Wp > Dp [.0893]
or
(Wp / Dp) > .0893

Note that this value of (Wp / Dp) provides no safety margin. For safety it is prudent to make (Wp / Dp) significantly larger than its theoretical minimum value.

For the intermediate loop steel piping (Schedule 160 steel pipe):
(Wp / Dp) = (1.312 inchs / 12.75 inches)
= 0.1029
which as compared to the theoretical value of .0893 gives a safety factor of:
0.1029 / .0893 = 1.152

For the selected steel fuel tubes:
(Wp / Dp) = (.065 inch / 0.500 inch)
= 0.130
which as compared to the theoretical value of .0893 gives a safety factor of:
0.130 / .0893 = 1.456

Note that fuel tubes are subject to wall deterioration due to fast neutron damage to which the intermediate sodium circuit is not subject. Hence it is important to use thicker wall fuel tube than this minimum design requirement indicates.

For reasons related to the technology of steel tube manufacture only a few manufacturers can meet the required (Wp / Dp) ratio for 0.500 inch OD tube.
 

FUEL AGING ISSUES:
The nuclear fuel material within the reactor core and blanket is in the form of rods. The core rods are metallic and are initially 0.35 m long but in use gradually swell to:
(1.0 / .86) X 0.35 m = 0.40 m long.

The initial core rod diameter is:
0.86 X 0.37 inch = 0.3182 inch
= 0.3182 inch X 25.4 mm / inch
= 8.08 mm
which over time swells to:
0.37 inch X 25.4 mm / inch = 9.398 mm.

The 0.600 m long blanket rod sections are formed from an alloy consisting of 90% U and 10% Zr.

Within the reactor core Pu-239 and other actinide fission reactions produce fission products, some of which have high neutron absorption cross sections. Simultaneously, as the fuel and blanket rods absorb surplus neutrons from the Pu-239 fission reactions the U-238 atoms gradually transmute into more Pu-239 and a spectrum of trans-uranium actinides.

Periodically, at a time interval known as the fuel cycle time, the core and blanket rods are removed and reprocessed. The effect of this reprocessing is to extract fission products, to move plutonium and transuranium actinides generated in the blanket rods into new core rods and to replace the lost blanket rod mass with an equal mass of depleted U, which may be also be obtained from spent CANDU fuel. A typical fuel cycle time is about 30_________ years. About 3.3%__________ of the fuel bundles are reprocessed every year so the average reactor performance does not significantly change with time and the fuel reprocessing is nearly continuous. The scheduled annual reactor shutdowns are only for a few hours to permit repositioning and exchange of fuel bundles.
 

FAST NEUTRON POWER REACTOR DESIGN CONCEPTS:
Most of the power FNR design concepts have been extensively tested in small research reactors such as the EBR-2. However, the EBR-2 had only about (1 / 16) of the THERMAL power rating of the contemplated power reactor. The design concepts are reviewed below:
 
1) The main component of a fast neutron reactor is a large stainless steel tank (like a deep swimming pool) that contains the primary liquid sodium (Na). For fire safety the top surface of the liquid sodium is covered by steel floats and over the floats there is an argon cover gas.
 
2) For safety there are no penetrations through the bottom or the vertical side walls of the liquid sodium tank;
 
3) The liquid sodium thermally stratifies so that the hotest liquid sodium floats on the top of the primary liquid sodium pool;
 
4) This reactor contains 532 active fuel bundles and 272 passive blanket bundles Each fuel bundle occupies 0.4 m X 0.4 m X 6 m.
 
5) Each surround fuel bundle consists of 300 vertical fuel tubes within a square vertical shroud. The shroud walls are parallel (1 / 16) inch thick sheet steel. The shroud and its corner girders support the surround fuel tube gratings and prevent an unanticipated problem in one fuel bundle from affecting adjacent fuel bundles;
 
6) The control bundles consist of 244 fuel tubes which are raised and lowered by a liquid sodium hydraulic piston. The piston rings and piston tube providing the hydraulic seal are located outside the fast neutron flux.
 
7) Each fuel bundle has an associated: 3.0 m long indicator tube. Each indicator tube is _______ inch OD X 0.134 ________inch wall steel tube with closed ends. At the inside bottom of the indicator tube is a pond of liquid mercury the vapor pressure of which indicates the fuel bundle discharge temperature. This temperature is used for fine adjustment of the control bundle position setpoint. This vapor pressure indicates temperature via a metal diaphragm. Deflection of the diaphragm causes laser interference rings. The height of the indicator tube top indicates the control bundle vertical position. The indicator tube vertical position and the fuel bundle liquid sodium discharge temperature are acquired via laser optics.
 
8) Each indicator tube has a 0.4 m X 0.4 m square guide float with a central hole for guiding the vertically sliding indicator tube.
 
9) Each active fuel tube contains 4 X 0.600 m long blanket fuel rods, 1 X 0.35 m long core fuel rod, liquid sodium and an empty space on top known as the plenum.
 
10) Each passive blanket fuel tube contains 5 X 0.600 m long blanket fuel rods, liquid sodium and an inert gas filled space on top known as the plenum.
 
11) Each fuel tube has top and bottom end plugs that mate with the appropriate top and bottom gratings..
 
12) The external end face of each fuel tube plug has (5 / 32) inch wide saw cut crossed notches that mate with the fuel tube support gratings located at the bottom and top of the fuel bundle.
 
13) To control fuel tube spacing along its length each fuel tube is wound with spacing wire.
 
14) Each fuel bundle bottom grating is formed from 48 4 inch X 1/8 inch steel strips that have saw cut notches so that the steel forms a square grating similar to the dividers separating wine bottles in a box of wine. There are welds at each metal junction for strength and rigidity. The fuel tube bottom plugs mate to the grating at each grating strip intersection. the gratings are welded to the fuel bundle girders. The bottom grating must reliably support the entire weight of the fuel tubes. The openings in this grating are 0.5 inch X 0.5 inch and allow liquid sodium to flow vertically between the fuel tubes. There are bottom notches in the bottom grating to allow liquid sodium cross flow in the event that the bottom grating is partially obstructed. The space between the fuel tubes is sufficient to allow liquid sodium cross flow if an individual cooling channel is obstructed.
 
15) Natural circulation moves primary liquid sodium coolant upwards through the cooling channels between the fuel tubes;
 
16) Within the primary liquid sodium pool the active fuel bundles and the passive blanket fuel bundles are positioned in concentric octagons;
 
17) Outside the reactor core zone is a 1.20 m thick layer of neutron absorbing blanket rods. The design concept is to absorb all neutrons that escape from the blanket in the surrounding 2.8 m guard band of liquid sodium so that the neutrons do not activate or cause long term damage to the walls or bottom of the liquid sodium tank, the intermediate heat exchange bundles or the overhead gantry crane or the roof structure.
 
18) The 2.8 m wide liquid sodium guard bands, in addition to absorbing neutrons, provide additional thermal mass that limits the rate of change of the primary sodium pool temperature.
 
19) There is corner space in the primary liquid sodiuum pool for storage of neutron activated fuel bundles to allow fission products to naturally decay before these fuel bundles are removed from the liquid sodium pool.
 
20) The steel fuel bundle girders and shroud in and near the core zones are subject to intense fast neutron bombardment. These components are replaced with each fuel cycle. Hence, these components are designed for easy removal and reprocessing while still being highly radioactive;
 
21) The FNR is intended for partial refuelling via 3.3%_______ fuel bundle changes each year. The fuel bundles are designed to remain immersed in liquid sodium while they are transferred from their operating positions in the reactor to their storage positions in the corners of the primary liquid sodium tank. These storage positions are outside the neutron flux;
 
22) The control bundles can be withdrawn as a group by releasing the high pressure liquid sodium into the primary sodium pool. If a fuel bundle is running hotter than average its discharge temperature setpoint can be lowered by selectively extracting a small amount of liquid sodium from its actuator.
 
23) On a loss of control system power all of the high pressure sodium is automatically released into the primary sodium pool to withdraw the control bundles to their cold shutdown position. The control bundle travel is about 1.0 m.
 
24) The actual vertical position of each control bundle is indicated by the height of the top of its indicator tube. The relative vertical position setpoint of each control bundle should be slowly adjusted to achieve the desired fuel bundle discharge temperature.
 
25) The core zone in each active fuel bundle acts as its own temperature control system. As a core zone warms up and thermally expands the fraction of fission neutrons diffusing out of that core zone increases, which reduces that zone's reactivity and thermal power output. Similarly as the liquid sodium contained in a core zone cools and contracts the fraction of fission neutrons diffusing out of that core zone decreases which increases that zone's reactivity and thermal power output. Hence, at a particular control bundle vertical position when the primary liquid sodium discharge temperature is high the fuel bundle thermal power output is low and as its primary liquid sodium discharge temperature decreases the fuel bundle thermal power output increases;
 
26) Thus every core zone of every active fuel bundle in the fast neutron reactor spontaneously seeks an operating temperature at which the rate of heat generation equals the rate of heat removal by the natural convection flow of primary liquid sodium through the bundle. This rate is not uniform in the reactor because some fuel bundles will have been in the reactor longer than other fuel bundles, so the fuel tube swelling, fission product accumulation and dirt accumulation vary from bundle to bundle;
 
27) As long as the fuel in each bundle is uniform and the control bundle is vertically positioned so that the safe liquid sodium discharge temperature of 445 degrees C is not exceeded the fast neutron reactor is passively thermally stable;
 
28) Due to fuel bundle aging issues control bundle insertions should be periodically optimized to achieve the desired fuel bundle discharge temperature.
 
29) A square fuel tube lattice is used so that the natural convection liquid sodium flow is never dangerously reduced by fuel tube swelling. A square fuel tube lattice allows full rated power reactor operation with up to 15% linear fuel tube swelling.
 
30) Provided that there is adequate intermediate liquid sodium coolant flow and an adequate heat sink the primary liquid sodium natural circulation is always sufficient to remove fission product decay heat;
 
31) For safety every cold isolated fuel bundle must always be subcritical;
 
32) For safety on a turbo/generator fault trip there should be sufficient redundant cooling and/or natural secondary sodium circulation to remove fission product decay heat to prevent the primary liquid sodium pool overheating. The fuel tubes must be temperature rated to safely accommodate worst case thermal transients;
 
33) In normal operation overall reactor thermal power is nearly constant or tracks the grid load. Thermal power turn down is achieved by allowing the primary liquid sodium temperature to rise causing chain reaction shutdowns in the fuel bundle core zones. This temperature increase will occur on the reduction of the rate of heat transfer out of the reactor due to reduction of the secondary sodium flow rate;
 
34) An advantage of fast neutron reactors is that they are almost unaffected by slow neutron poisons. Hence the thermal power of a fast neutron reactor can ramp relatively rapidly to follow a changing electricity load.
 
35) Cold shutdown of a fast neutron reactor is achieved by withdrawing all the control bundles;
 
36) The maximum permitted liquid sodium discharge temperature from any active fuel bundle is 445 degrees C. This temperature is chosen to keep the maximum fuel tube material temperature under 460 degrees C.
 
37) For safety the portion of the liquid sodium pool depth in bedrock is made 13.0 m deep whereas the liquid sodium is 12.0 m deep. Thus there is 1.0 m of tank depth allowance to withstand unforseen surface waves in the liquid sodium that might arise as a result of an earthquake.
 
38) The 5 m high straight inside sheet metal walls should be sufficiently reinforced to the surrounding concrete to contain the large liquid sodium wave that might be produced by a large earthquake.
 
39) The insulated inner walls and inner ceiling of the reactor building extend 17.2 m above the liquid sodium surface to confine the primary sodium in the event of a really large earthquake and to provide sufficient clearance for lifting individual fuel bundles together with their indicator rods out of the primary liquid sodium tank.
 
40) It is important to constantly filter the primary liquid sodium to keep the liquid sodium clean to prevent buildup of impurities on heat exchange surfaces or obstruction of the liquid sodium flow channels between the fuel tubes and between the intermediate heat exchange tubes.
 
41) An important issue is making the fuel tube gas plenum sufficiently large to safely contain both the spare sodium and the inert gas fission products.
 
42) The service life of the intermediate heat exchange bundles is long because the liquid sodium guard band protects them from cumulative neutron damage and primary sodium filtering minimizes surface deposits.
 
43) The service life of the primary liquid sodium pool is very long because there are no relevant corrosion or erosion mechanisms.
 

NEUTRON STOPPING CONSTRAINTS:
Two very important material constraints are that the probability of fast neutrons being absorbed by the 1.2 m thick blanket is close to unity and the probability of absorption of neutrons that escape from the blanket into the surrounding 2.8 m thick liquid sodium layer is close to unity.
 

FIXED TO HERE

FUEL BUNDLE TRANSPORTATION:
A practical constraint on FNR design is transportation of fuel bundles back and forth between the FNR and the nearby fuel bundle assembly-disassembly facility. This transportation must be by truck. There are both fuel bundle length and weight constraints imposed by this transportation mode and the related shielding requirement.

Another consideration is that each fuel bundle is fabricated from HT-9 steel tubes, each 6.1 m long, so availability of suitable steel tubing at a competitive price is an important consideration.

Consider a fuel bundle that is 9.0 m long and 15.50 inches to 15.50 inches face to face. An assembled fuel bundle must be transported within a lead container that has an inside cross section 0.4 m X 0.4 m, 12 inch thick walls and 12 inch thick end caps. The wall thickness is:
12 inch X .0254 m / inch = .3048 m The lead volume of in this fuel bundle transport container is:
[(4 X .3048 m X .4 m X 9.6 m)] + [(2 X .4 m X .4 m X .3048 m)] + [Pi (.3048 m)^2 (9.6 m)]
 
= 4.6817 m^3 + .0975 m^3 + 2.8018 m^3
= 7.581 m^3

The mass of the fuel bundle lead shield is:
7.581 m^3 X 11.34 X 10^3 kg / m^3 = 85.969 tonnes.

This weight is close to the maximum that can be easily transported by road. Hence there is no merit in contemplating a larger fuel bundle. Note that a fuel bundle has add-on indicator tube.

The volume of the indicator tube shield would be about:
[Pi (.3048 m + .08636 m)^2 X 3 m] - [Pi (.08636 m)^2 X 3 m] + [Pi (4 / 3)(.3048 m + .08636 m)^3]
= 1.442 m^3 - 0.0704 m^3 + .2507 m^3
= 1.6222 m^3

The corresponding mass of the indicator tube transportation container is:
1.6222 m^3 X 11.34 X 10^3 kg / m^3 = 18.4 tonnes
 

ISSUES AFFECTING REACTOR SIZE:
1) From the perspective of reliable power generation it is essential for a FNR to have multiple independent intermediate heat transport and electricity generation systems so that a shutdown of one such system has only a small affect on the remaining electric power generation capacity. The present intent is to have 16 intermediate heat transport systems so as to make each electricity generator have a rated electricity output capacity of about 20 MWe. That is likely the largest steam turbine that is readily transportable by rail.

2) The reactor tube height is 6.0 m.

3) There is a reactor core zone height related to average reactor core zone fuel density that is necessary to realize core criticality. With 20% Pu fuel that core zone height works is about 0.35 m. Provision for fuel expansion due to fission product formation may eventually increase the reactor core zone height to about:
(0.35 m / 0.86) = 0.40 m.

The reactor core zone diameter is about:
26 X 0.4 m = 10.4 m
Note that there is a maximum tolerance allowance of about:
[0.4 m / (.0254 m / inch) - 15.500 inch] / 2 = 0.139 inch
in the overall fuel bundle outside dimensions.

The total tube bundle assembly diameter is:
32 X 0.4 m = 12.8 m.

The fuel bundle support frame which rests on the bottom of the primary liquid sodium pool is shipped to the site in multiple numerically machined parts.

In the passive fuel tubes the fuel stack is 3.0 m high. In the active tubes the fuel stack is initially 2.8 m high but in use can swell to 3.0 m.

There is 0.1 m of fuel tube length allocated to the two end plugs. There is 3.0 m of fuel tube length allowance for plenum. Hence the steel fuel tube length of 8.6 m is fully allocated.

To minimize the roof and gantry crane construction costs it is desirable to minimize the sodium pool width so as to minimize the required unsupported gantry beam span and the roof span.
 

FNR TUBE BUNDLE ASSEMBLIES:
The reactor core is an octagonal assembly of 6.0 m high square cross section fuel bundles based on a 26 bundle X 26 bundle square with straight sides 10 bundle widths long and diagonal sides of length:
[2 X (8 bundle widths)^2]^0.5 = 11.3 bundle widths long. This shape is realized by cutting 36 bundles off each corner, so that the total number of core bundles is given by:
26^2 - 4(36) = 676 -144
= 532 core bundles

If the blanket bundles are included the assembly is based on a square of 32 bundles X 32 bundles with 55 bundles clipped off each corner. The four straight sides are each 12 bundle widths long. The nominal length of each diagonal side is given by:
1.41 X 10 = 14.1 bundle widths

The total number of fuel bundles is:
32^2 - 4(55) = 804 bundles

Hence the number of blanket bundles is:
804 - 532 = 272 blanket bundles
 

FIXED TO HERE

CORE FUEL RODS:
The steel fuel tube initial ID is 0.37 inches. Hence allowing for 74% smear density (Till & Yang P. 123) the initial core fuel rod diameter is:
[(.74)^0.5] (0.37 inch) X 25.4 mm / inch = 8.08 mm

In terms of allowance for core fuel rod swelling:
1 / [(0.74)^0.5] = 1.162
or
16.2% linear core rod swelling before there is significant stress on fuel tubes.
 

The core fuel rods are nominally 10% zirconium, 20% plutonium and 70% uranium by weight. The density of zirconium is:
6.52 gm / cm^3
The density of plutonium is about:
19.8 gm / cm^3
The density of uranium is about 18.9 gm / cm^3

Let:
Vz = volume of zirconium in a core rod
Vp = volume of plutonium in a core rod
Vu = volume of uranium in a core rod.
Mz = mass of zirconium in a core rod
Mp = mass of plutonium in a core rod
Mu = mass of uranium in a core rod

Total volume V is given by:
V = Vz + Vp + Vu

Core fuel rod mass M is given by:
M = Mz + Mp + Mu

Mz = 0.1 M
Mp = 0.2 M
Mu = 0.7 M

Mz / Vz = 6.52 gm / cm^3
Mp / Vp = 19.8 gm / cm^3
Mu / Vu = 18.9 gm / cm^3

The average core rod density is:
M / V = (Mz + Mp + Mu) / (Vz + Vp + Vu)
= (Mz + Mp + Mu) / ((Mz / 6.52) + (Mp / 19.8) + (Mu / 18.9))
= M / ((0.1 M / 6.52) + (0.2 M / 19.8) + (0.7 M / 18.9))
= 1 / ((0.1 / 6.52) + (0.2 / 19.8) + (0.7 / 18.9))
= 1 / (.015337 + .010101 + .037037)
= 1 / .062475
= 16.006 gm / cm^3

The mass of each core fuel rod is given by:
Pi X (8.08 X 10^-3 m / 2)^2 X 0.35 m / rod X 16.006 g / cm^3 X 10^6 cm^3 / m^3 X 1 kg / 10^3 g
= 0.28725 kg / core rod

Hence:
Mass Mu of U-238 in each core fuel rod is:
Mu = .7 (0.287252 kg)
= .20107 kg

Mass of Pu in each core fuel rod is:
Mp = 0.2 (0.287252 kg)
= 0.05745 kg

Mass of Zr in each core fuel rod is:
Wz = 0.1 (0.287252 kg)
= 0.0287252 kg

BLANKET FUEL RODS:

The blanket rods must slide easily into the fuel tubes but are subject to much less swelling because their only fissionable content comes from breeding. Hence the initial blanket rod diameter is:
(0.37 inch X 0.95) X 25.4 mm / inch = 8.93 mm

The blanket fuel rods are nominally 10% zirconium, 90% uranium by weight.
The density of zirconium is:
6.52 gm / cm^3
The density of uranium is about 18.9 gm / cm^3

Let:
Vzb = volume of zirconium in a blanket rod
Vub = volume of uranium in a blanket rod.
Mzb = mass of zirconium in a blanket rod
Mub = mass of uranium in a core rod

Total volume V is given by:
Vb = Vzb + Vub

Blanket fuel rod mass Mb is given by:
Mb = Mzb + Mub

Mzb = 0.1 Mb
Mu = 0.9 Mb

Mzb / Vzb = 6.52 gm / cm^3
Mub / Vub = 18.9 gm / cm^3

The average blanket rod density is:
Mb / Vb = (Mzb + Mub) / (Vzb + Vub)
= (Mzb + Mub) / ((Mzb / 6.52) + (Mu / 18.9))
= Mb / ((0.1 Mb / 6.52) + (0.9 Mb / 18.9))
= 1 / ((0.1 / 6.52) + (0.9 / 18.9))
= 1 / (.015337 + .047619)
= 1 / .062956
= 15.884 gm / cm^3

The mass of each blanket fuel rod is given by:
Pi X (8.93 X 10^-3 m / 2)^2 X 0.600 m / rod X 15.884 g / cm^3 X 10^6 cm^3 / m^3 X 1 kg / 10^3 g
= 0.59690 kg / blanket rod

Hence:
Mass Mub of U-238 in each blanket fuel rod is:
Mub = .9 (0.397935 kg)
= .53721 kg

Mass of Zr in each blanket fuel rod is:
Mzb = 0.1 (0.53721 kg)
= 0.053721 kg

The mass of each fuel tube bundle is significant. The major mass components consist of:

Control Rod: consists of slugs of uranium-zirconium of length totalling 2.375 m.
__________________ Mass = [Pi X (3 inch)^2 X 2.375 m _______X (.0254 m / inch)^2 X 15.884 X 10^3 kg / m^3]
=
= 827.5.0 kg

Bottom Rod 6.0 inch dia X 4.0 m long
Mass = Pi X 3 inch^2 X 4.0 m X (.0254 m / inch)^2 X 7.874 X 10^3 kg / m^3
= 574.5 kg

Indicator Tube: 5.563 inch OD X 0.258 inch wall X 10.0 m long
Mass = Pi X 5.563 inch X 0.258 inch X 10.0 m X (.0254 m / inch)^2 X 7.874 X 10^3 kg / m^3
= 229.06 kg

Central Support Pipe 6.625 inch OD X .280 inch wall, 6.1 m long
Mass = Pi X 6.625 inch X .280 inch X 6.1 m X (.0254 m / inch)^2 X 7.874 kg / m^3
= 180.58 kg

456 steel tubes 0.5 inch OD, 0.37 inch ID, 300 inch long
Mass = 456 X Pi [(0.5 inch)^2 - (0.37 inch)^2] / 4 X 8.5 m X (.0254 m / inch)^2 X 7.874 X 10^3 kg / m^3
= 1749.03 kg

8 X 456 = 3648 blanket fuel rods
Mass = 3648 X 0.59690 kg / blanket rod
= 2177.5 kg

1368 core fuel rods
Mass = 1368 X 0.28725 kg / core rod
= 392.958 kg

912 tube end plugs
Mass = 912 X Pi X (.25 inch)^2 X .05 m X (.0254 m / inch)^2 X 7.874 X 10^3 kg / m^3 = 45.48 kg

Miscellaneous steel parts for shroud rods, bottom grating, end frames, spacer rods:
92.149 kg

Liquid Sodium =

Piston rings

TOTAL MASS PER ACTIVE FUEL BUNDLE:
MASS = 827.5 kg + 574.5 kg + 229.06 kg + 180.58 kg + 1749.03 kg + 2177.5 kg + 392.958 kg + 45.48 kg + 92.149 kg
= 6268.7 kg

TOTAL REACTOR:
Total reactor core rod mass = (532 X 544) core fuel rods X 0.28725 kg / core rod)
= 83,132 kg
= 83.132 tonnes

The required plutonium mass is:
0.2 (83.132 tonnes) = 16.626 tonnes

This plutonium can be obtained by reprocessing of spent CANDU fuel.

The amount of plutonium readily available from spent CANDU fuel is about:
0.0038 X 50,000 tonnes = 190 tonnes. Hence at this time in 2017 in Canada there is only enough plutonium available to start about:
190 / 16.626 = 11.4
full size power FNRs. It is clear that in FNR planning a very important objective is breeding additional plutonium for starting future FNRs.
 

REACTOR CORE:
In choosing the gap between the steel fuel tubes the issue is one of maximizing the average fuel density in the fuel bundle while not unduely decreasing the liquid sodium circulation and not imposing unreasonable cleanliness restrictions on the liquid sodium pool.

A related issue is that the maximum sodium temperature as liquid sodium passes through the fuel bundle needs to be limited to provide sufficient temperature safety margin at the upper end of the liquid sodium operating temperature range.

Based on all of these issues the center to center spacing between the square lattice fuel tubes was chosen to be:
(5 / 8) inch = 0.625 inch.

This dimensional choice sets the smallest initial intertube gap in the assembly at (1 / 8) inch, so filtering should be used to eliminate particulates larger than (1 / 32) inch in longest dimension.

Each fuel tube position has associated with it a reactor top surface area of about 1 tube per [0.625^2 inch^2]
= 1 tube / .3906 inch^2

The cross sectional area initially occupied by each fuel tube is:
Pi (.25 inch)^2 = 0.1963 inch^2

Thus the remaining cross sectional area per core fuel tube initially available for natural convection liquid sodium coolant flow is:
0.3906 inch^2 - 0.1963 inch^2 = 0.1943 inch^2
= 0.1943 inch^2 X (.0254 m / inch)^2
= 1.2535 X 10^-4 m^2

Note that initially the cross sectional area of a fuel tube OD and the cross sectional area of a flow channel are almost equal.

Note that a scale diagram shows that initially the flow channel wall area is almost equal to the OD wall area of a fuel tube.

Hence the initial effective cross sectional area for natural circulation through the reactor is:
1.2535 X 10^-4 m^2 / core fuel tube X 544 tubes / bundle X 532 core bundles = 36.2772 m^2

If the fuel tube radius linearly swells by 10% the cross sectional area occupied by each fuel tube becomes:
1.21 X 0.1963 inch^2 = 0.237523 inch^2

Thus the remaining cross sectional area per core fuel tube available for natural convection liquid sodium coolant flow after 10% linear tube swelling is:
0.3906 inch^2 - 0.237523 inch^ = 0.1531 inch^2
= 0.1531 inch^2 X (.0254 m / inch)^2
= 9.8759 X 10^-5 m^2

Fuel tube swelling also increases viscous effects that further reduce primary liqud sodium circulation.

The length of the reactor core perimeter is about:
Pi X 10.4 m = 32.67 m

Hence, prior to fuel tube swelling, the thickness of the radially horizontally moving liquid sodium layer at the active region perimeter is about:
(30.4089 m^2) / (32.67 m = .9307 m.
 

PRIMARY SODIUM NATURAL CIRCULATION:
The natural circulation of the primary liquid sodium occurs due to a decrease in liquid sodium density with increasing temperature. Nuclear heating of the sodium in the reactor causes the sodium to locally expand in the core zones. If this expansion takes place within a surrounding pool of cooler liquid sodium the buoyancy of the warmer liquid sodium will cause it to rise. This warm liquid sodium flows over the top surface of the pool toward the ends of the pool where it cools, contracts and sinks as it flows between the cooler heat exchange tubes. The higher density cooled liquid sodium flows along the bottom of the primary sodium pool back to the pool bottom center where it again rises due to heating by the reactor fuel tubes.

In order to naturally circulate the primary liquid sodium there must be a large temperature difference between the top and bottom of the liquid sodium pool. At full power the bottom of the transition region between the hot liquid sodium and the cool liquid sodium should be at the top of the fuel tubes. At low power the bottom of this trasition region is 1.0 m above the bottom of the fuel tubes.

An accurate closed form expression for the maximum primary liquid sodium flow is developed at FNR PRIMARY LIQUID SODIUM FLOW. This viscous flow limits the FNR power output.
 

SHUNT HEAT FLOW IN THE PRIMARY LIQUID SODIUM POOL:
Due to the fuel stack design the transition region between the hot liquid sodium and the cool liquid sodium is 3.6 m thick. Assume that the temperature difference between the hot liquid sodium and the cool liquid sodium is 160 degrees C. The thermal conductivity of liquid sodium is 142 W / m-K. Hence the conducted vertical shunt heat flow is:
142 W / m-K X (1 MW / 10^6 W) X 18.4 m X 25.4 m X (160 K / 3.6 m) = 2.949 MW/P>

At steady state conditions the primary sodium mass flow through the reactor is equal to the primary sodium mass flow through the intermediate heat exchanger. Hence if the reactor thermal power is 2400 MWt and the temperature drop across the intermediate heat exchanger primary is 150 deg C, then the temperature rise along the reactor fuel tubes is:
[(2400 + 2.949) / 2400] X 150 C = 150.184 deg C
 

UPPER TEMPERATURE LIMIT:
When the reactor is operating at full rated power the liquid sodium temperature discharged from the top of the active fuel tube bundles must be less than 910 F or 488 C (Til & Yoon Figure 7-2, P. 149).
 

REACTOR CORE DESCRIPTION:
The steel fuel tubes are 6.0 m long. The steel fuel tubes are sealed closed at both the top and bottom ends.

The steel tubes are clustered in square bundles. Each tube bundle is centrally supported by a 6.625 inch OD steel pipe 20 foot long. This pipe has a bottom interior rod 4 m long that plugs into a matching ~ 6.0 inch diameter X 3.0 m deep blind hole in the bundle support rack. The bottom tip of this interior rod has a conical tapered lower tip to allow easy insertion.

Each fuel bundle is supported by a square steel grating 15.0 inches to a side which is attached to the central support pipe. Around the support pipe are 6 concentric square rings of 0.5 inch OD vertical steel fuel tubes on 0.625 inch square centers. The fuel tubes of each fuel bundle are position stablized by the bottom grating and (1 / 16) inch diameter bent criss cross rods.

Each fuel tube bundle has a sliding central ~ 6 inch diameter indicator tube attached to a control rod that slides within the bundle central support pipe to control the core zone reactivities in the fuel bundle. This control rod is set and held in position by liquid sodium pressure applied to the control rod bottom such that when sodium pressure is lost the control rod falls into its fully inserted position, which reduces reactivity of the fuel bundle. At the time of fuel insertion into the reactor the control rod should be fully inserted and locked. The control rods are then unlocked and individually positioned. Each central support pipe has an internal bottom rod which prevents the control rod going too deep into the central pipe. If the fuel bundle support grating connection to the central pipe fails and the fuel bundle slides down the outside of the central support pipe, the fuel bundle reactivity is reduced by the bottom rod. This bottom rod should be contain a high neutron cross section material.

Each tube bundle is laterally stabilized by is shroud and by adjacent fuel bundles. The tube bundles are placed in position by the gantry crane that spans the width of the pool. The weight of the tube bundle assemblies is borne by the pool floor. The tube bundles are repositioned or replaced from time to time using the gantry crane and remote manipulation.

The first step in tube bundle replacement is reactor shutdown and full insertion and locking of its indicator tube into its keyhole slot. Then the gantry crane uses the indicator tube to lift the selected tube bundle by the height of its frame insertion (< 3.0 m) before moving the bundle horizontally to a perimeter storage position. During this process the spent fuel bundle remains covered by over 3 m of liquid sodium. The spent fuel bundle is moved to a perimeter storage position where it is inserted in another frame hole. The spent fuel bundle remains for several years in the liquid sodium until it loses most of its fission product decay heat. Then the spent fuel bundle is lifted out of the primary sodium pool for fuel reprocessing. Note that to access interior fuel bundles it is necessary to temporarily move other fuel bundles out of the way.
 

CONTROL RODS AND INDICATOR TUBES:
Each fuel bundle has associated with it a ~ 5.5 inch diameter X 6 m long reactivity control rod assembly attached to the bottom of the indicator tube. During normal reactor operation this control rod assembly is positioned by liquid sodium pressure applied to its bottom. There are piston rings to achieve a good sliding seal between the bottom of the contol rod ands the ID if the central fuel bundle support pipe. By appropriate control rod positioning the reactor thermal load is evenly distributed.

Each control rod has an attached indicator tube which indicates both the vertical position of the control rod and the fuel bundle liquid sodium discharge temperature. The indicator tube also provides a gamma ray propagation path for indicating fuel bundle thermal power. At the bottom of the indicator tube, immediately above the control rod, is a pond of liquid mercury which has a well known vapor pressure versus temperature characteristic. At the top of the indicator tube is a metal diaphragm which bends in response to the mercury vapor pressure deflecting an incident laser beam coming from overhead. This laser beam deflection indicates the fuel bundle's liquid sodium discharge temperature. The inside of the indicator tube should be lined with a thermally insulating material to minimize mercury vapor condensation on the indicator tube inside walls.

The indicator tube must be sufficiently strong for lifting and positioning the fuel bundle.

The indicator tube has two projecting side studs that mate with locking slots located near the top of the fuel bundle support pipe. When the indicator tube is fully down and rotated into the locked position it can be used to lift and move the fuel bundle together with its 0.4 m X 0.4 m steel float.
 

MAXIMUM TEMPERATURE:
Assume that when the reactor is operating at full rated power the liquid sodium discharge temperature from the core fuel bundles should remain less than 910 F or 488 C (Til & Yoon Figure 7-2, P. 149).
 

|THERMAL ANALYSIS:
A CANDU E6 REACTOR SUPPLIES 2084 MWt OF HEAT TO STEAM GENERATORS VIA CIRCULATED HEAVY WATER AT 310 C TO 265 C AT A PRESSURE OF ABOUT 10 MPa.

The contemplated FNR is rated at 2000 MWt using HT-9 fuel tubes with a theoretical stress safety margin of over 2:1. At full rated power the maximum core rod temperature should normally be about 548 C. The fuel tubes heat an atmospheric pressure primary liquid sodium coolant that is everywhere less than 488 degrees C.

These temperatures allow for a 10.0 deg C temperature drop across each HT-9 steel fuel tube wall, a 50 deg. C temperature drop between the inner HT-9 steel wall and the interior of the core fuel rod and a 25 deg C temperature drop between the outside of the HT-9 steel wall and the bulk liquid sodium. Note that within the reactor flow channels the liquid sodium flow is laminar, so there is a significant temperature difference between the fuel tube outside wall temperature and the average passing liquid sodium temperature.

The primary liquid sodium pool heats an intermediate liquid sodium heat transport loop that normally operates from 310 C to 470 C. In the steam generator of the contemplated FNR at full load the water temperature is about 300 C and the corresponding saturated steam pressure is about 8.6 MPa. At lower thermal power the pressure in the steam generator can potentially rise to 16.67 MPa, the system pressure limit, corresponding to a water temperature in the steam generator of: 351.1 C which will be reached at an intermediate liquid sodium return temperature of about 360 C. The intermediate sodium pumping rate must be reduced to keep this steam generator water temperature sufficiently low as otherwise the pressure in the steam generator will become too high. Hence the flow in the intermediate sodium loop is automatically adjusted to keep its return temperature in the range 310 C to 350 C.

The chosen steam temperature and pressure allows FNR operation with a natural draft cooling tower heat sink.

The pressure within each intermediate heat transport loop is controlled by the expansion tank argon head pressure that operates in the range 0.1 MPa to 16.67 MPa. The intermediate liquid sodium pressure is kept slightly higher than the steam pressure so that in the event of a steam generator tube rupture the potential sodium leakage flow from the intermediate loop to the water is minimized and hydrogen generation is confined to the water side of the steam generator which is easily vented.
 

PRIMARY LIQUID SODIUM POOL:
The peak temperature in the primary liquid sodium pool is about 488 degrees C. Due to this high temperature conventional cement materials that set up via absorption of water of hydration are unsuitable for thermally unprotected liquid sodium containment.

The cavity for the liquid sodium pool is cut from bed rock. The entire cavity should be above the local water table. For certain long term safety the bed rock should have a melting point over 600 degrees C. Sedimentary rock may be unsuitable if it breaks down at FNR liquid sodium operating temperatures.

Near the cavity walls the drill holes and explosive used should be chosen to minimize cracking of the remaining rock. The bedrock cavity should be about 35.4 m long X 26.4 m wide X 22.5 m minimum depth to allow for a 3 m thickness of lava rock (basalt) insulation thickness, a 1 m air gap and a 1 m thck concrete wall. Any cracks discovered in the cavity must be water sealed with clay. The outside of the concrete below grade should be sealed with hot bitumen.

The water tightness of the bedrock cavity is checked by temporarily filling the bedrock cavity with water. If there is any sign of water leakage the entire cavity wall should be be lined with clay.

The bottom of the bedrock cavity is leveled with igneous rock pea gravel. On top of the pea gravel foundation is laid a layer of structural steel I beams that will support the liquid sodium pool, reactor and lava rock while permiting cooling air to circulate beside and beneath the pool to remove heat conducted through the lava rock.

On top of the I beams is the steel sheet that forms the outer liquid sodium containment floor. External vertical I beams with horizontal spreaders reinforce the vertical side walls. The vertical side walls are precisely positioned using threaded rods with turnbuckles that are attached to the adjacent concrete face. The details of this steel wall construction are similar to the construction of the hull of a ship.

The water tightness and strength of the outer steel wall and its supporting members should be demonstrated by temporarily filling the outer stainless steel wall with water.

Inside the outer sheet steel liquid sodium containment wall is a 3 m thickness of saw cut interlocking low density lava rock blocks that provide the thermal insulation between the inner and outer steel walls of the liquid sodium pool. These interlocking blocks are shaped like childrens Lego or Duplo blocks. Suitable lava rock for forming these blocks is plentiful on the main island of Hawaii. The saw cutting of the lava rock must be numerically controlled to be dimensionally accurate so that there are no gaps between the lava rock blocks. If the inner stainless steel containment wall for liquid sodium leaks the amount of liquid sodium that flows into the space between the inner and outer steel walls must be low and the thermal leakage to the outer stainless steel liquid sodium containment wall must be minimal. The lava rock used should have a melting point over 600 degrees C and should not be reduced by hot liquid sodium.

The maximum ongoing heat leakage through the lava rock can be estimated assuming a lava rock thermal conductivity of 2.0 W / m-K. Thus:
Heat leakage = (Area / thickness) X (2.0 W / m-deg K) X (440 deg K)
= {[2 (16.5 m) (18.4 m + 25.4 m) + (18.4 m X 25.4 m)] / 3 m} X (2.0 W / m-deg K) X (480 deg K)
= {[1445.4 m^2 + 467.36 m^2] / 3 m} X (2.0 W / m-deg K) X (480 deg K)
= 0.612 MWt
which is the maximim ongoing parasitic heat load on the reactor that must be removed by forced air circulation. The effective air duct cross sectional area is 25.4 m^2. The maximum allowable air temperature rise is about 10 degrees C. The heat capacitry Cp of dry air at 300 degrees K is:
Cp = 1.005 kJ / kg-K.

The density of air is: 1.225 kg / m^3

The heat flow is given by:
0.612 MWt X 10^6 J / s-MWt = 25.4 m^2 X V m / s X 1.225 kg / m^3 X 1.005 kJ / kg-K X 1000 J / kJ X 10 K
or
V = [(0.612 X 10^6 ) / (25.4 X 1.225 X 1.005 X 10^4)] m / s
= 1.957 m / s
which is an acceptable ongoing ventilation air flow velocity.

Inside the saw cut lava rock interlocking blocks is the inner liquid sodium containment wall which is fabricated from sheet stainless steel.

The inner and outer sheet steel walls are tied to the lava blocks via thin steel rods that penetrate at least one lava block layer before reaching a tie plate situated between adjacent lava block layers.

The water tightness and strength of the inner steel wall should be confirmed by temporarily filling the inner steel wall with water.

In normal operation the inner stainless steel sheet vertical walls are in tension. In the event of an inner wall failure the outer wall will become in tension. Hence both walls must be rated for the hydrostatic stress potentially imposed by the liquid sodium.

In normal operation the outer steel wall and its components are only slightly above room temperature. We must be concerned about long term corrosion of the outer steel wall due to it being exposed to an ongoing flow of cooling air drawn from the outside.

Another potential concern is wall stress and wall movement during earth quakes. The steel rods between the outer wall reinforcing I beams and the concrete wall should be sufficiently strong and resiliant to be earthquake tolerant.

Thus the liquid sodium has four hydraulically tested containment barriers, the inner stainless steel wall, the outer stainless steel wall, the concrete wall and the bedrock cavity.

The approximate volume of primary liquid sodium is:
25.4 m X 18.4 m X 16.5 m = 7711.44 m^3 which weighs about:
0.927 X 7711.44 = 7148.5 tonnes.
 

REACTOR SECTION FLOOR LINER:
An FNR designed for utility power production has many thousands of fuel rods. Sooner or later through accident, negligence or malevolent behavior a defective fuel bundle and/or related reactivity control system will be loaded into the reactor. In these circumstances a significant concern is fuel melting. If a steel fuel tube fails high density fuel rods, droplets or pellets might sink through the liquid sodium and will collect on the pool floor. It is essential that this material does not accumulate together sufficiently to form a critical mass. Thus the tube bundle support frame should be covered with a liner that has a high neutron absorption cross section and has controlled size bumps or cavities so that a critical mass cannot form. There should be a practical means of selectively removing and cleaning portions of this liner.
 

PRIMARY SODIUM CONTAMINANT FILTERING:
A power FNR will contain about 5600 m^3 of primary liquid sodium. In spite of best efforts to prevent sodium contamination the hot liquid sodium will gradually become contaminated. Hence a dedicated sump pump is required to run continuously to pump liquid sodium out of the bottom of the primary sodium pool, through a cleanup filter apparatus and back into the pool.

The reactor tube bundle contains numerous narrow internal sodium flow channels. Thus it is imperative that there be a filter process that constantly removes sodium contaminants. The primary sodium filter must trap and remove all particulate matter with any dimension in excess of (1 / 32) inch. This filter system must run for a long time before the steel tube bundles are inserted into the liquid sodium.

eg if the sump pump runs at 0.5 m^3 / minute the time required to pump one pool volume is:
7711.44 m^3 X 1 minute / 0.5 m^3 X 1 hour / 60 minutes X 1 day / 24 hour = 10.71 days.
Hence it will require at least a month to appreciably filter the liquid sodium.

Over time the liquid sodium will gradually become polluted with unwanted material including magnesium particles, radio active fuel, other metals, sodium oxide, sodium hydroxide, etc. The contaminants will include:
Na2O, NaOH, Na3N, NaNO2, NaNO3

Na2O must be removed by density separation and filtering. It has a specific gravity of 2.27 and sublimates at 1275 degrees C.

NaOH melts at 318.4 degrees C and has a boiling point of 1390 degrees C. It has a specific gravity of 2.130. It can be removed by density separation and filtering at a temperature less than 318 degrees C. NaOH may tend to form on the surface of the cooler parts of the intermediate heat exchange bundles. From time to time the low temperature of these bundles must be raised to melt any acciumulated NaOH.

Na3N dissociates at 300 degrees C and hence nitrogen accumulates in the cover gas. At temperatures below 300 C the nitrogen will react with the sodium. Then Na3N can be remved by filtering.

NaNO2 MP = 271 degrees C, dissociates at 320 deg C, SG = 2.16, can be removed by filtering at less than 271 degrees C or by cryogenic separation of cover gas.

NaNO3 MP = 306.8 deg C, dissociates at 380 deg C, SG = 2.261, can be removed density separation and filtering at less than 306.8 degrees C

The primary liquid sodium temperature must drop below 300 degrees C to permit complete contaminent removal by filtering. Hence the filter system inlet should be at the intermediate heat exchanger primary sodium discharge where the primary liquid sodium temperature is lowest. At this point the pool floor should be deepest. To clean the intermediate heat exchange tubes it is necesary to run the reactor at part load to raise the intermediate sodium return temperature.
 

SAFETY SYSTEM CONCEPT:
For safety reasons the pressure of the argon gas over the secondary sodium is kept slightly higher than the steam pressure. Any unanticipated change in secondary sodium level in the secondary sodium expansion tank indicates a tube leak somewhere, as does any presence of hydrogen in either the steam / condensate circuit or the secondary sodium circuit. In response the reactor is shut down by control bundle withdrawal and steam/hydrogen is released via the steam circuit vent. This safety concept keeps both water and hydrogen out of the secondary sodium circuit where they could potentially cause catastrophic damage to the pipes and/or intermediate heat exchanger by liquid sodium fluid hammer.

The reactor has 16 independent intermediate heat removal loops. In the event that one heat removal loop has any sort of fault that loop can be shut down and isolated while the other heat removal loops continue to operate. Each heat removal loop has its own intermediate heat exchange bundles, steam generator, and intermediate liquid sodium circulation pump. Each heat removal loop has its own turbogenerator, condenser, condensate injection pump. Cooling towers, transformers, switchgear and auxillary power are shared.

The maximum permitted liquid sodium temperature in normal circumstances is 445 deg C. At that temperature the yield stress of the steel tubes and pipes starts to decrease. If the primary liquid sodium temperature exceeds 488 deg C at any point that temperature should trigger a total reactor shutdown via control bundle withdrawal.

A steam pressure in excess of 11.5 MPa should also trigger a complete reactor shut down.

If for some reason the release of the control bundles fails to shut down the reactor and if the heat removal rate is insufficient the primary liquid sodium temperature will rise until thermal expansion of the core fuel bundles reduces the core reactivity, which will by itself shut down the reactor. However, even with a total fission shut down it is necessary to maintain sufficient cooling to remove fission product decay heat.
 

NEUTRON RANGE TO SCATTERING IN LIQUID SODIUM:
The cross section for high energy neutron scattering in sodium is 2.62 b. Hence the distance Ls between successive high energy scatters in pure liquid sodium is given by:
Ls = 1 / [(2.62 X 10^-28 m^2 / atom) X (6.023 X 10^23 atoms / 23 gm) X (.927 gm / 10^-6 m^3)]
= 23 m / [ 2.62 X 6.023 X .927 X 10]
= .1572 m

In each scattering event total momentum is conserved.
Define:
Mn = neutron mass
Ms = scattering mass
Vn = neutron velocity
Vs = scattering mass velocity
Conservation of momentum gives:
Mn Vn = Ms Vs
or
(Vs / Vn) = (Mn / Ms)

The fractional loss of neutron kinetic energy in each scattering event is:
Ms Vs^2 / Mn Vn^2 = (Ms / Mn)(Mn / Ms)^2
= (Mn / Ms)
= 1 / (23)

Hence the neutron energy after a scattering event is (22 / 23) of its energy before the scattering event until the neutron kinetic energy reaches thermal energy.

(22 / 23)^2 = .9149338374
(22 / 23)^4 = .8371039268
(22 / 23)^8 = .7007429843
(22 / 23)^16 = .49104073
(22 / 23)^32 = .2411209985
(22 / 23)^64 = .0581393359
(22 / 23)^128 = .0033801824

Thus after about 128 scattering events a 3 MeV neutron has lost sufficient energy to drop to 10 keV.

Since scattering takes place in a 3 dimensional random walk the required thickness of liquid sodium required to provide this energy loss along a single axis is:
[(128)^0.5 X (.1572 m / 3^0.5)] = 1.03 m

For neutrons with energies of less than 10 keV the average sodium atom absorption cross section is 0.310 barns = 0.31 X 10^-28 m^2 and the scattering cross section is 122.68 barns. Hence the probable number of scatters before absorption is 122.68 / .31 = 395.74.

The density of liquid sodium is 927 gm / lit. The atomic weight of sodium is 23. Avogadro's number is 6.023 X 10^23 atoms / mole. Hence the range Ls between scatters in liquid sodium for neutrons with midrange energies less than 10 keV is given by:
Ls = 1 / [927 gm / lit X 1000 lit /m^3 X 1 mole / 23 gm X 6.023 X 10^23 atoms / mole X 122.68 X 10^-28 m^2 / atom]
= 23 m / [927 X 1000 X 6.023 X 10^23 X 122.68 X 10^-28]
= 23 m / [9.27 X 6.023 X 122.68]
= .003357 m

Hence the expected distance along one axis that a neutron travels before absorption is:
(395.74)^0.5 X (.003357 m / 1.732) = .0385 m

However, after that distance there are still a lot of thermal neutrons. For thermal neutrons the scattering cross section is 3.090 b and the absorption cross section is 0.417 b. Hence the average number of scatters before absorption is:
3.090 / 0.417 = 7.41 scatters.

The distance between scatters is:
Ls = 1 / [927 gm / lit X 1000 lit /m^3 X 1 mole / 23 gm X 6.023 X 10^23 atoms / mole X 3.090 X 10^-28 m^2 / atom]
= 23 m / [927 X 1000 X 6.023 X 10^23 X 3.090 X 10^-28]
= 23 m / [9.27 X 6.023 X 3.090]
= 0.1333 m

Thus the expectation distance for thermal neutron travel along a single axis for a single scatter is:
0.1333 m / 1.732 = 0.07696 m

Over 1.7 m the number of scatters N is given by;
(N)^0.5 = 1.7 m / .07696 m
= 22.089
or
N = (22.089)^2 = 487.9

Assume that in 7.41 scatters the neutron flux is reduced by a factor of 2.71. Thus the neutron flux reduction factor is about:
exp (487.9 / 7.41) = exp(65.847)
which is sufficient.

Thus a 2.8 m wide liquid sodium guard band around the reactor is sufficient for absorbing all emitted neutrons.

The issue with a breeder reactor is that as the breeding progresses neutrons start to be emitted by the blanket. To absorb all these neutrons we need 2.8 m of sodium between the outside edge of the blanket and the reactor wall and the heat exchange bundles. This issue substantially impacts the overall sodium pool dimensions.

Hence the corresponding liquid sodium pool dimensions are:
25.4 m long X 18.4 m wide X 16.5 m deep
.

The neutrons exiting the reactor blanket vertically can avoid the sodium between the tubes by travelling through the fuel tubes. Hence there must be 3 m of liquid sodium both above and below the fuel tubes. The tube end plugs may be subject to severe neutron irradiation.
 

STRUCTURAL ISSUES:
As previously calculated the mass of each tube bundle assembly is about 5084 kg.

Clearly the overhead gantry must be rated for at least 10 tonnes to allow for the circumstance when two or three fuel bundles stick together.

The corresponding floor load due to the fuel bundles is:
5100 kg / 0.16 m^2 = 31.875 tonne / m^2

The floor load due to the liquid sodium is:
16.5 m X 0.927 tonne / m^3 = 15.3 tonne / m^2

There is an additional floor load due to the steel fuel bundle support frames.

There is a floor load due to lava rock under the pool of about:
3 m X 2 tonnes / m^3 = 6 tonnes / m^2

It is clear that the total floor load, including the pool structure, is ~ 54 tonnes / m^2, which requires a suitable bedrock foundation. The corresponding ground pressure is:
(54 X 10^3 kg / m^2) X 9.8 m /s^2 / 1 m^2 = 529 X 10^3 Pa
= 529 kPa

The load bearing capacity of shale bedrock is believed to be about 5000 kPa

Under the inner pool floor liner are 3 m of saw cut lava rock blocks, then the outer pool liner, then a 1 m layer of I beams resting on a 1.0 m thick concrete/gravel foundation with a sump pit. The I beams must be long term protected from corrosion.
 

REACTIVITY REQUIREMENT
In order to sustain the nuclear chain reaction in the reactor core while controlling the reaction by thermal expansion the mean fast neutron travel along the Z axis between successive Pu-239 fissions must be greater than the core zone height. On the web page_________it was determined that a practical core zone height is about 0.35 m.

The neutron path between successive fissions is inversely proportional to the average fissionable fuel density in the reactor. Hence a major issue in FNR design is maximizing the ratio of metallic core fuel volume to total reactor core volume while maintaining adequate cooling and while minimizing unwanted neutron absorption.

In order for an FNR to run there must be a self sustaining chain reaction. This requirement imposes a constraint on the average atomic density of Pu-239 in the reactor core as compared to the average atomic density of U-238, Na-23, Fe, Cr and probability of neutron leakage out the surface of the active core zone.

In order to control the nuclear reaction full insertion of the control rod must render a fuel bundle subcritical under all conditions. Fully removing a control rod should make the reactor run provided that other 8 adjacent contol rods are also removed. In order to conserve neutrons the control rods should be made out of blanket rod material, so that the neutrons that the control rods absorb usefully convert U-238 into Pu-239.

Each core zone of a fuel bundle has volume Vcz of: Vcz = 0.400 m X 0.400 m X 0.35 m
= 0.0560 m^3

Within core zone volume Vcz are uranium-plutonium-zirconium fuel rods with a uranium-plutonium-zirconium volume of:
544 X Pi X (8.08 X 10^-3 m / 2)^2 X 0.35 m = .009762 m^3

within volumeVcz are steel fuel tubes with a steel volume of:
544 X 0.35 m X Pi X [(.25 inch)^2 - (0.185 inch)^2] X (.0254 m / inch)^2 = .0109115512 m^3

Within volume Vcz are 4 girders with a combined steel volume of:
4 X 0.35 m X 0.25 inch^2 X 5 X (.0254 m / inch)^2 = 0.00112903 m^3

Within volume Vcz are 4 girders with a combined steel volume of:
4 X 0.35 m X 0.25 inch^2 X 3 X (.0254 m / inch)^2 = 0.000677418 m^3

Within volume Vcz are 4 shroud walls with a combined steel volume of:
4 X 0.35 m X (1 / 16) inch X 15 inch X (.0254 m / inch)^2 = 0.00084677 m^3

Within volume Vcz are 4 control bundle walls with a combined steel volume of:
4 X 0.35 m X (1 / 16) inch X 10 inch X (.0254 m / inch)^2 = 0.0005645 m^3

Thus the steel volume Vi within Vcz is given by:
Vi = .0109115512 m^3 + 0.00112903 m^3 + 0.000677418 m^3 + 0.00084677 m^3 + 0.0005645 m^3
= 0.014129 m^3

The remaining core region volume consisting of:
Vs = 0.0560 m^3 - 0.014129 m^3 - .009762 m^3
= 0.032109 m^3
is filled with liquid sodium.

Define:
Ns = average number of sodium atoms / unit volume in reactor core zone
Ni = average number of iron atoms per unit volume in reactor core zone
Nc = average number of chromium atoms per unit volume in ractor core zone
Np = average number of plutonium atoms per unit volume in the reactor core zone with control bundle inserted at start
Npw = averge number of plutonium atoms per unit volume in reactor core zone with contro bundle withdrawn
Nz = average number of zirconium atoms per unit volume in the reactor core zone
Nu = average number of U-238 atoms / unit volume in reactor core zone with control bundle inserted
Nuw = average number of U-238 atoms / unit volume in reactor core zone with control bundle wiothdrawn
Nf = average number of fission product atoms / unit volume in reactor core at end of fuel bundle life with control bundle inserted
Rhos = mass density of liquid sodium = .927 gm / cm^3
Rhoi = mass density of iron = 7.874 gm / cm^3
Rhou = mass density of U-238 = 19.1 gm / cm^3
Rhop = mass density of Pu-239 = 19.8 gm / cm^3
Rhoc = average mass density of control rod slug material Aws = atomic weight of sodium = 23
Awi = atomic weight of iron = 55.845
Awc = atomic weight of Chromium = __________
Awu = atomic weight of uranium = 238
Awz = atomic weight of zirconium = 91.22
Awc = atomic weight of control rod atoms Av = Avogadro's Number

OK TO HERE

At the end of a fuel bundle life as set by fuel tube material swelling:
Nf = 2 (0.59 Np)
= 2 (0.59) (Np / Nu) Nu
= 2 (0.59) (2 / 7) Nu
= 0.33714 Nu

Recall that:
Mass Mu of U-238 in each core fuel rod is:
Mu = .7 (0.28725 kg / core rod)
= 0.201075 kg

Mass of Pu in each core fuel rod is:
Mp = 0.2 (0.28725 kg / core rod)
= 0.05745 kg

Mass Mz of Zr in each core fuel rod is:
Mz = 0.1 (0.28725 kg / core rod kg)
= 0.028725 kg / core rod

Mc = control rod mass in a core zone consisting of blanket rod material

Mc = (Pi (3.0 inch)^2 X 0.35 m) X (.0254 m / inch)^2 X (15.884 X 10^3 kg / m^3)
= 101.41 kg

Nuc = Mc X 0.9 X (1 mole / .238 kg) X Av / 0.056 m^3

Ns = (0.0369377 m^3) X (927 kg / m^3) X (1 mole / .023 kg) X Av] / (0.056 m^3)

Nu = [456 core rods X 0.201075 kg / core rod X (1 mole / .238 kg) X Av] / (0.056 m^3)
= [(456 core rods X 0.201075 kg / core rod) X (1 mole / .238 kg) X 6.023 X 10^23 atoms / mole] / (0.056 m^3)
= 41.435 X 10^26 U atoms / m^3

Hence:
(Nuc / Nu) = Mc X 0.9 X (1 mole / .238 kg) X Av / 0.056 m^3
/ [(456 core rods X 0.201075 kg / core rod) X (1 mole / .238 kg) X Av] / (0.056 m^3)
 
= [101.41 kg X 0.9] / [(456 core rods X 0.201075 kg / core rod)]
 
= 0.9954

(Ns / Nu) = {[ 0.0369377 m^3 X (927 kg / m^3) X (1 mole / .023 kg) X Av] / (0.056 m^3)}
/ [456 core rods X 0.201075 kg / core rod X (1 mole / .238 kg) X Av] / (0.056 m^3)
 
= {[ 0.0369377 m^3 X (927 kg / m^3) X (1 mole / .023 kg)]}
/ [456 core rods X 0.201075 kg / core rod X (1 mole / .238 kg)]
= 3.86434

Similarly:

Ni = [ 0.0108787 m^3 X Rhoi X (1 mole / Awi) X Av] / (0.056 m^3)

Hence:
(Ni / Nu) = {[ 0.0108787 m^3 X Rhoi X (1 mole / Awi) X Av] / (0.056 m^3)}
/ [456 core rods X 0.201075 kg / core rod X (1 mole / .238 kg) X Av] / (0.056 m^3)
 
= {[ 0.0108787 m^3 X 7874 kg / m^3 X (1 mole /0.055845 kg)]}
/ [456 core rods X 0.201075 kg / core rod X (1 mole / .238 kg)])
 
= 3.9815

Nz = [456 core rods X (Mz / core rod) X (1 mole / Awz) X Av] / (0.06 m^3)

Hence:
(Nz / Nu) = {[456 core rods X (Mz / core rod) X (1 mole / Awz) X Av] / (0.056 m^3)}
/ [456 core rods X 0.201075 kg / core rod X (1 mole / .238 kg) X Av] / (0.056 m^3)
 
{[(Mz / core rod) X (1 mole / Awz)]}
/ [0.201075 kg / core rod X (1 mole / .238 kg)]
 
{[(0.028725 kg / core rod) X (1 mole / .09122 kg))]} / [0.201075 kg / core rod X (1 mole / .238 kg)]
= 0.372725
 

Np / Nu = (.2 / .7) = 0.2857

Re-define:
Np = number of fissionable plutonium atoms per unit volume
Gu = number of neutrons emitted per average U-235 atomic fission = 2.6
Gp = number of neutrons emitted per average Pu-239 atomic fission = 3.1
Ge = number of neutrons emitted per average atomic fission that are absorbed by breeding
Data from Kaye & Laby for a FNR core:
Sigmaas = fast neutron absorption cross section of sodium = 0.0014 b
Sigmass = fast neutron scatter cross section of sodium = 2.62 b
Sigmaai = fast neutron absorption cross section of iron = .0086 b
Sigmasi = fast neutron scatter cross section of iron = 4.6 b
Sigmaaf = fast neutron absorption cross section of fission products = ____ b
Sigmaau = fast neutron absorption cross section of U-238 = 0.25 b
Sigmasu = fast neutron scatter cross section of U-238 = 9.4 b
Sigmaap = fast neutron absorption cross section of plutonium-239 = 0.040 b
Sigmaaz = fast neutron absorption cross section of zirconium = 0.0066 b Sigmafp = fast neutron fission cross section of plutonium-239 = 1.70 b
Sigmafu = fast neutron fission cross section of uranium-238 = 0.041 b
 

WITH NO CONTROL ROD PRESENT CONSIDER THE DISTANCE Lsc TRAVELLED BY A NEUTRON IN A CORE ZONE BETWEEN SUCCESSIVE SCATTERS:
Lsc = 1 / [Ns Sigmass + Ni Sigmasi + Nu Sigmasu]
= 1 / {Nu [(Ns / Nu) Sigmass + (Ni / Nu) Sigmasi + (Nu / Nu) Sigmasu]}
= 10^28 (b / m^2) / {(41.435 X 10^26 U atoms / m^3) [(3.86434) (2.62 b) + (3.9815)(4.6 b) + (1) (9.4 b)]
= 100 m / {41.435 [10.12 + 18.3149 + 9.4]}
= 100 m / {41.435 [37.835]}
= 0.063787 m
Note that as Lsc increases when Ns, Ni, Nu decrease. Hence Lsc increases with increasing temperature.
 

WITH NO CONTROL ROD PRESENT CONSIDER THE DISTANCE Lac TRAVELLED BY A NEUTRON IN THE REACTOR CORE ZONE BEFORE ABSORPTION:
Lac = 1 / [Ns Sigmas + Ni Sigmaai + Nu Sigmaau + Nu Sigmafu + Np Sigmaap + Np Sigmafp]
= 1 / {Nu [(Ns / Nu) Sigmaas + (Ni / Nu) Sigmaai + (Nu / Nu) Sigmaau + (Nu / Nu) Sigmafu + (Np / Nu) (Sigmaap + Sigmafp)]}
= 10^28 (b / m^2) / {(41.435 X 10^26 U atoms / m^3) [(3.86434) (.0014 b) + (3.9815)(.0086 b) + .25 b + .041 b + (0.2857)(.040 + 1.70)]
= 100 m / {41.435 [.00541 + .03424 + .25 + .041 + .497118]}
= 100 m / {41.435 [.82776]}
= 2.915 m
Note that Lac increases when Ns, Ni, Nu, Np decrease. Hence Lac increases with increasing temperature.
 

Hence the number of neutron scatters before absorption is:
(Lac / Lsc) = 2.915 m / 0.063787 m
= 45.71

Since neutron scattering takes place in a 3 dimensional random walk the distance travelled by a neutron along a single axis before absorption is:
[(La / Ls)^0.5 X (Ls / 3^0.5)]
= [(La Ls) / 3]^0.5 = [(2.915 m X 0.063787 m) / 3]^0.5
= .2489 m

Note that diffusion distance [(La Ls) / 3]^0.5 increases with increasing temperature.

Note that by comparison the core zone height is 0.35 m and the adjacent blanket thickness is 1.20 m. The diffusion distance is more than half the core zone height. Hence about half of the fission neutrons diffuse out of the core zone into the blanket zone and do not contribute to maintenance of the chain reaction. An increase in temperature decreases Ns, Ni, Nu, Np which increases:
[(La Ls) / 3]^0.5 which increases the fraction Fp of neutrons diffusing out of the core zone and hence not supporting the chain reaction. Hence the chain reaction will stop at a sufficiently high temperature.
 

OK TO HERE FIND Lsb AND Lab USE DEDICATED WEB PAGE FOR NEXT SECTION

CONSIDER THE CASE OF THE CONTROL ROD FULLY WITHDRAWN:
With respect to a flux neutrons in reactor the condition for criticality is:
(- Ns Sigmaas - Ni Sigmaai - Nu Sigmaau - Nz Sigmaaz - Np Sigmaap - Nf Sigmaaf + Gp Fp Np Sigmafp) > 0
where:
Gp = 3.1 neutrons / fission
Fp ~ 0.8 = Fraction of fission neutrons that remain in core region to potentially participate in subsequent fusion reactions
giving:
[(Gp Fp Np Sigmafp)- (Np Sigmaap)] > Ns Sigmaas + Ni Sigmaai + Nu Sigmaau + Nz Sigmaaz + Nf Sigmaaf or
Np [(Gp Fp Sigmafp) -(Sigmaap)] > Ns Sigmaas + Ni Sigmaai + Nu Sigmaau + Nz Sigmaaz + Nf Sigmaaf or
(Np / Nu) >
[(Ns / Nu) Sigmaas + (Ni/ Nu) Sigmaai + Sigmaau + (Nz / Nu) Sigmaaz + (Nf / Nu) Sigmaaf)] / [(Gp Fp Sigmafp) - Sigmaap)]

As indicated at FNR FUEL TUBE WEAR at the end of the fuel tube's useful life when the number of plutonium atom fissions equals 0.59 of the number of plutonium atoms initially present:
(Nf / Nu) = 2 (0.59 Np / Np) (Np / Nu)
= 2 (0.59) (.2857) = 0.3371.

Then numerical substitution gives:
(Np / Nu)
> [(Ns / Nu) Sigmaas + (Ni / Nu) Sigmaai + Sigmaau + (Nz / Nu) Sigmaaz + (Nf / Nu) Sigmaaf] / [(Gp Fp Sigmafp) - Sigmaap]
or
(Np / Nu) > [3.72135 (.0014 b) + 4.4816 (.0086 b) + .25 b + 0.372725 (.0066 b) + 0.3371 (Sigmaaf)] / [(3.1 Fp X 1.7 b) - .40 b]
or
[0.00521 b + .03854 b + .25 b + .00246 b + .3371 (Sigmaaf)] / [(Fp 5.27 b) - 0.40 b]
or
(Np / Nu) > [.29621 b + .3371 (Sigmaaf)] / [(Fp 5.27 b) - 0.40 b]
or
[(Fp 5.27 b) - 0.40 b] > [.29621 b + .3371 (Sigmaaf)] / (Np / Nu)
or
[(Fp 5.27 b) - 0.40 b] > [.29621 b + .3371 (Sigmaaf)] / (.2857)
or
[(Fp 5.27 b) - 0.40 b] > [1.03678 b + 1.1799 (Sigmaaf)]
or
[(Fp 5.27 b)] > [1.43678 b + 1.1799 (Sigmaaf)]
or
Fp > 0.2726 + 0.2239 (Sigmaaf / b)

This is the condition that must be satisfied for the chain reaction to run when the control rod is fully withdrawn. At the beginning of the fuel life the 2nd term is zero.
 

NOW CONSIDER THE CASE OF THE CONTROL ROD FULLY INSERTED:
With respect to a flux neutrons in reactor the condition for ensuring non-criticality is:
(Np / Nu)
< [(Ns / Nu) Sigmaas + (Ni / Nu) Sigmaai + Sigmaau + (Nz / Nu) Sigmaaz + (Nf / Nu) Sigmaaf + (Nuc / Nu) Sigmaau]
/ [(Gp Fp Sigmafp) - Sigmaap]
 
or
(Np / Nu) < [.29621 b + .3371 (Sigmaaf) + (1.3299) (.25 b)] / [(Fp 5.27 b) - 0.40 b]
or
(Np / Nu) < [.628685 b + .3371 (Sigmaaf)] / [(Fp 5.27 b) - 0.40 b]
or
[(Fp 5.27 b) - 0.40 b] < [.628685 b + .3371 (Sigmaaf)] / (Np / Nu)

This is the condition that must be satisfied for the chain reaction to stop when the control rod is fully inserted. Note that at the beginning of the fuel life the 2nd term is zero.

For compliance with this equation at the beginning of the fuel life:
[(Fp 5.27 b) - 0.40 b] < [.628685 b] / (Np / Nu)
or
R giving:
[(Fp 5.27 b) - 0.40 b] < [.628685 b] / 0.2857
or
Fp 5.27 b < 2.600 b
or
Fp < 0.4934
 

SUMMARY:
Reactor operation is highly dependent on the correct choice of core region height to give the desired value of Fp.

0.2726 + 0.2239 (Sigmaaf / b) < Fp < 0.4934

For safe shutdown and to realize operationinthe face of accumulated fission products we need to choose Fp ~ 0.45.

We must solve the diffusion equationto find the diffusion fluxes of neutrons from the core regioninto the adjacent blanket regions to accurately determine Fp in terms of the core rod length Lc.

If Fp is less than 0.27 the reactor will never run. If Fp is larger than 0.49 the chain reactin cannot be stopped by inserion of the contemplated U-238 control rod.

To find Fp we must solve the equation for the diffusion flux of neutronsinto the blanket regions above and below the core region.

Once fission products start to accumulate the condition for operation until the end of the fuel tube life is:
0.2726 + 0.2239 (Sigmaaf / b) < Fp
For Fp = 0.45: 0.2726 + 0.2239 (Sigmaaf / b) < 0.45
or
(Sigmaaf / b) < 0.794
or
(Sigmaaf) < 0.794 b

Thus to make maximum use of the fuel tube material the fast neutron cross section of the fission products must be less than 0.794 b. Based on the Kaye & Laby data it appears for fast neutrons the fission product cross sections are much smaller than 0.794 barnes so fuel bundle working life is determined by fuel tube swelling rather than by fission product accumulation.
 

SAFETY REQUIREMENT:
Note that for safety there must be absolute certainty that the chain reaction can be shut down, so Fp must be significantly less than 0.49. A safe initial choice is Fp = 0.45
 

THERMAL POWER CONTROL:
In a liquid sodium cooled FNR the primary means of thermal power control is thermal expansion which changes the fraction of fission neutrons that diffuse out of the core zone and hence regulates the chain reaction.
 

FUEL BUNDLE REACTIVITY:
The fuel bundles are engineered such that all core zones are sub-critical with the control rods fully inserted. Ideally if a single core fuel bundle in an array of core fuel bundles with their control rods inserted has its control rod withdrawn that fuel bundle should remain subcritical. This feature is desirable to prevent problems if a single control rod jams in a withdrawn position.

As the reactor core zone exceeds its design operating temperature its thermal expansion should cause the core zone to drop below criticality.

CORE ZONE HEIGHT:
On average each U-235 fission produces 2.6 neutrons and each Pu-239 fission produces 3.1 neutrons. In order for criticality to be maintined one of these three neutrons must be captured by a plutonium atom. That capture must happen before the neutron leaves the core zone.

Once a neutron leaves the core zone the probability of it being captured within the adhacent blanket zone must be vey high.

In a true breeder started with U-235 there is very little margin for neutron loss. Plutonium is a much more practical start fuel.

CRITICALITY MAINTENANCE:
Maintenance of criticality in the core zone requires a minimum core zone size together with a minimum plutonium density within the core zone. From each fission the chain reaction must use at least one neutron to sustain the chain reaction and will likely lose an additional 0.2 neutrons in the core. Hence roughly speeking, if La is the average total neutron travel distance from emission to fission:

However, in travelling distance La the neutron goes through about 50 scattering events so its linear travel distance is not that large.

BREEDING CONDITION:
The probability of surplus neutron capture by the surrounding U-238 needs to be at least 95%.

Let Lb = thickness of the blanket surrounding the reactor core.

The blanket is composed of fuel rods that do not contain fissionable material. Then the required minimum blanket thickness Lb is given by:
Lb = 3 /(Sigmaab Nub)
where Nub = average uranium atomic density in the blanket.

Nub =
[(3 X 546) blanket rods X (0.3112 kg / blanket rod) X (238 kg uranium / 260 kg blanket rod) X (6.023 X 10^23 atoms uranium / 0.238 kg uranium) / 0.2400 m^3
= 4.9201 X 10^27 atoms / m^3

Data from the UK Nuclear Data Library indicates that in the blanket the transport cross section is:
Sigmaab = 10.3 b. Hence the minimum required blanket thickness Lb is given by:
Lb = 3 /(Sigmaab Nu)
= 3 / {10.3 X 10^-28 m^2 X 4.9201 X 10^27 atoms / m^3}
= 0.592 m

I have provided for a blanket that is 1.2 m thick to ensure completeness of neutron absorption by U-238.
 

OPERATIONAL NOTE:
The Pu-239 concentration in the breeding blanket may be less than 2% by weight whereas in the core the Pu-239 concentration must be about 20% by weight. The Pu-239 concentration in the breeding blanket is gradually bred up to 2%. Then blanket rod reprocessing is used to remove almost 90% of the uranium and zirconium from the breeding blanket material to leave behind 20% Pu-239 material which is suitable as fuel for the reactor core.
 

PLUTONIUM DOUBLING TIME:
An issue of great importance in large scale implementation of FNRs is the FNR run time required for one FNR to breed enough excess Pu-239 to allow startup of another identical FNR. This time may be calculated using the approximation that each plutonium atom fission releases of 3.1 neutrons of which 2.5 neutrons are required for sustaining reactor operation leaving 0.6 neutrons for breeding extra Pu-239. Thus one atom of Pu-239 has to fission to form 0.6 atoms of extra Pu-239.

Hence the plutonium doubling time, which the time required to double the available amount of plutonium via breeding within the FNR is:
(10 / 6) X (time to consume the initial Pu supply)
= [(10 / 6) X (1 cycle time )] / 0.59
= 2.825 (1 fuel cycle time)
= 2.825 X (47.78 years)
= 136 years

This is the time required for one FNR to form enough excess Pu to allow starting another FNR. Clearly this doubling time is too long to enable rapid deployment of FNRs.

With large scale implementation of FNRs the available supply of plutonium and trans uranium actinides will soon be exhausted. Hence the issue of the Pu-239 doubling time physically constrains the rate of growth of the FNR fleet.

Thus FNRs are viable for disposing of transuranium actinides but due to the Pu-239 doubling time will not in the near future provide enough power capacity for complete displacement of fossil fuels.
 

FUEL BUNDLE TRACKING:
Each fuel bundle requires an individual code identifier on its indicator tube to allow tracking of its neutron exposure history.
 

FISSION PRODUCT DECAY HEAT REMOVAL:
One of the most important aspects of reactor design is provision for fission product decay heat removal under adverse circumstances. If an event occurs which causes a sudden reactor shutdown the reactor will continue to produce fission product decay heat at 5% to 10% of its full power rating. Hence it is essential to ensure ongoing removal of fission product decay heat under the most adverse circumstances.

Hence:
1) Under no circumstances, including a sodium pool inner wall leak, should the liquid sodium level ever fall to the point that the fuel tubes are not fully immersed in liquid sodium.
2) The gap and lava rock fill between the inner and outer pool walls must be designed such that if the inner wall fails and the liquid sodium leaks into the space between the two walls, the sodium pool surface level will not drop below the tops of the upper blanket rods.
3) At least 3 of the 36 intermediate liquid sodium circulation pumps must always be functional to remove fission product decay heat from the primary liquid sodium pool;
4) In the event of an intermediate liquid sodium circuit fault it is essential that reactor cooling be maintained. Hence multiple redundant intermediate heat transport systems are required. The current design contemplates 36 independent heat removal systems.
 

PRIMARY SODIUM TEMPERATURE MAINTENANCE:
To prevent prolonged equipment restart problems due to sodium freezing it is essential to keep the primary liquid sodium above 100 degrees C at all times. Hence, there should be at least four 0.5 MWt oil fired boilers on site connected to separate intermediate liquid sodium circuits to ensure maintenance of the primary liquid sodium pool temperature.
 

FNR THERMAL TIME CONSTANT:
The volume of primary liquid sodium is about:
25.4 m X 18.4 m X 17.5 m = 8178.8 m^3

The sodium volume displaced by fuel tubes is:
804 bundles X 456 tubes / bundle X 8.6 m X Pi X (.25 inch)^2 X (.0254 m / inch)^2
= 399.4 m^3

The primary liquid sodium volume displaced by the intermediate heat exchange bundle tubes is:
36 bundles X 1664 tubes / bundle X 6.0 m X Pi X (.25 inch)^2 X (.0254 m / inch)^2
= 45.53 m^3

The primary liquid sodium volume displaced by the immersed pipes and headers is ~ 45.53 m^3.

The maximum primary liquid sodium temperature slew rate at rated power is:
(2400 MW X 10^6 J / s-MW) / [(8178.8 m^3 X 927 kg / m3 X 1000 gm / kg X 28.230 J / mole deg K X (1 mole / 22.9897 gm)]
= (2400 X 10^6 / s) / [8178.8 X 927 X 1000 X 28.230 / deg K X (1 / 22.9897 )]
= [2400 X 10^6 deg K / s X 22.9897] / [8178.8 X 927 X 1000 X 28.230]
= 0.2577 deg K / s

= 0.2577 deg K / s X 60 s / minute = 15.46 deg K / minute

This slew rate has limited meaning because the FNR acts as a constant temperature source.
 

INTERMEDIATE SODIUM:
The FNR requires a heat exchanger secondary fluid that is compatible with the heat exchange bundle material (Inconel 600) and will not chemically react with the hot radioactive liquid sodium in the event of a heat exchange bundle failure. This fluid must to be chemically stable over the temperature range 0 C to 600 C.

To meet these specifications non-radioactive sodium is used as the heat exchanger secondary fluid.

In the event of an internal failure in the steam generator there is potential for a violent chemical reaction between the heat exchange secondary sodium and water used as the turbine working fluid. If this chemical reaction took place in the secondary sodium circuit a hydrogen pressure pulse from this reaction might cause a liquid sodium hammer analogous to water hammer, possibly leading to major facility damage. Hence the heat exchanger must be designed to safely withstand large pressures and the secondary liquid sodium should always be at a higher pressure than the water in the steam generator to prevent water entering the secondary sodium circuit.

The intermediate heat exchanger secondary fluid is pressurized by expansion tanks containing variable pressure argon. These expansion tanks will also assist by attenuating any pressure pulses in the liquid sodium.
 

Some important physical properties of water, sodium and argon, are:
PROPERTYWATERSODIUMARGON
Liquid Thermal Conductivity: 0.58 W / m-deg C 142 W / m-deg C
Density Rho: 1.0 kg / lit .927 kg / lit 1.784 g / lit@101.025 KPa, 0 deg C
(1 / Rho) dRho / dT:2.71 X 10^-4 / deg K
Heat Capacity (J / mol deg K): 75.2428.23020.786
Heat of Vaporization@101 kPa: 40.68 kJ / mole 97.42 kJ / mole
Molecular Weight (gm / mole): 18 22.9897 39.948
Viscosity Muv (kg / m-s): 7 X 10^-4
Melting Point@101kPa (deg C): 0 97.72
Boiling Point@101 kPa (deg C): 100 883
Vapor Pressure@46 C: 10.094 kPa
Vapor Pressure@70 C: 31.176 kPa
Vapor Pressure@100 C: 101.32 kPa
Vapor Pressure@134 C: 303.93 kPa
Vapor Pressure@180 C: 1001.9 kPa
Vapor Pressure@234 C: 3005.9 kPa
Vapor Pressure@281 C: 6510.5 kPa 1 Pa
Vapor Pressure@311 C: 9995.8 kPa
Vapor Pressure@344 C: 15.342 MPa 10 Pa
Vapor Pressure@373 C: 21.779 MPa
Vapor Pressure@424 C: 100 MPa
Vapor Pressure@529 C: 1 GPa
Vapor Pressure@673 C: 10 GPa
Vapor Pressure@880 C: 100 GPa

 

INTERMEDIATE HEAT EXCHANGE TUBE MATERIAL:
One of the best heat exchange tube materials for use in the intermediate heat exchanger and steam generator is Inconel 600.
 

MATERIAL STRESS ISSUES:
A major issue in FNR design is combined pressure stress and thermal stress in the intermediate heat exchanger and the steam generator caused by high working pressures and potentially high differential temperatures across the tube walls.
 

TEMPERATURE CONSTRAINT:
At low steam loads the intermediate sodium flow will decrease and the intermediate sodium temperature will rise to the highest primary liquid sodium temperature. As the steam load increases the intermediate sodium flow will increase and the intermediate sodiuum temperature will decrease.

As the liquid sodium flows through the reactor at full power its temperature increases from 250 C to 450 C. In this temperature range in a fast neutron flux HT-9 undergoes goes material embrittlement.
 

INTERMEDIATE SODIUM HEAT TRANSPORT:
Define:
Fmi = intermediate sodium mass flow.
Cpi = intermediate sodium heat capacity = 1.26 kJ / kg-deg K for sodium
Delta Ti = change in intermediate sodium temperature = 160 deg K
Then for sodium:
Fmi Cpi (Delta Ti) = 2000 MWt
or
Fmi = [2000 MWt] / [Cps (Delta Ti)]
= {[2000 MWt]
/ [(1.26 kJ / Kg-deg K) (160 deg K)]} X {1 kJ / kWt-s} X {10^3 kWt / MWt}
= [(2000) / (1.26 X 160)] X 10^3 kg / s
= 9.92 tonnes / s
= (9.92 tonnes / s) / (0.927 tonnes / m^3
= 10.70187 m^3 / s
= required intermediate volumetric sodium flow.

Since there are 36 intermediate heat exchange bundles, the sodium mass flow rate in each bundle must be: (10.70187 X m^3 / s) / 36 = 0.2973 m^3 / s

The flow cross sectional area of each 12.75 inch OD, 10.126 inch ID pipe is:
Pi (5.063 inch)^2 X (.0254 m / inch)^2 = 0.05195565 m^2

Let V = average axial flow velocity of secondary liquid sodium. Then:
V = (0.2973 m^3 / s) / [0.05195565 m^2)]
= 5.7217 m / s

This intermediate liquid sodium flow will develop a momentum change pressure at a 90 degree elbow of:
(5.7217 m / s)^2 X 1 m^2 X 927 kg / m^3 = P X 1 m^2
or
P = (5.7217 m / s)^2 X 927 kg / m
= 30,347 kg / m s^2
= 30,347 Pa
=0.300 bar
 

INTERMEDIATE SODIUM CIRCULATION PUMP:
The open cross sectional area of the intermediate heat exchanger secondary is much larger than the external pipe cross sectional area which means that the secondary sodium circulation pump must be sized to create the kinetic flow power in the secondary external piping. Since the same issue pertains to the steam generator the intermediate liquid sodium circ pump must be sized to create more than twice the kinetic flow power in the external piping. Note that this pump should be located on the low temperature return pipe and should be physically near the bottom of the secondary pipe loop.
 

INTERMEDIATE LIQUID SODIUM PUMPING POWER:
The intermediate liquid sodium acceleration power associated with each straight pipe section is:
[(mass flow rate) / 2] X (flow velocity)^2
(mass / volume)(area)(flow velocity /2)(flow velocity)^2
= (927 kg / m^3)(Pi)(10.126 inch / 2)^2 (.0254 m / inch)^2 (5.7217 m / s)^3(.5)
= 4510 kg m^2 / s^3
~ 4.51 kW

There are at least two such accelerations in a typical secondary sodium circuit and the pumps are unlikely to be more than 20% efficient.

Each loop needs about 10 kW 0f mechanical circulating energy. If the induction pump is 20% efficient each intermediate loop needs:
5 X 10 = 50 kWe
of pumping electric power. Hence the total intermediate sodium pumping electricity requirement is about:
36 X 50 kW = 1800 kWe
 

GASKET CONSTRAINT:
A major constraint on the FNR design is gasket properties. This FNR operates at too high a (temperature X pressure) product for use of elastomeric gaskets. Soft metal gaskets must be used. Hence the intermediate heat exchanger, its secondary sodium pump and its related steam generator need precision fabrication and alignment.
 

INTERMEDIATE LIQUID SODIUM FLOW:
There are 36 heat exchange bundles, 18 at each end of the primary liquid sodium pool.

The heat exchange bundles are completely isolated from one another. Each bundle feeds a dedicated steam generator. Hence in the event of a heat exchange tube problem any heat transport system can be shut down while keeping the other heat transport systems fully operational.

There are 12.75 inch OD, 10.126 inch ID pipes from each end of each heat exchange bundle manifold up to 90 degree elbows and then back towards argon tight wall penetrations. All the heat exchange bundle manifolds and the liquid sodium pipe and fitting disconnection flanges are fitted with soft metal gaskets.

The hot secondary liquid sodium is passes through the adjacent wall to the nearby steam generator. Under ordinary operation the reactor power is set by adjusting the control rod positions.

The immersed heat exchange bundles are realized with vertical tube bundles. To minimize longitudinal thermal stress on the tubes the lower tube manifolds are unsupported except by the tubes and external pipes. The upper tube manifolds are positioned near the liquid sodium surface level and are supported by the 12.75 inch OD pipes. Threaded pipe support hardware provides fine adjustment of each heat exchange maniflold position to precisely align the 12.75 inch OD pipe disconnection flanges. These flanges have an OD of about 24 inches.

The heat exchange tubes are Inconel 600, 20 feet (6.1 M) long. They are 0.500 inch OD, 0.065 inch wall thickness. The immersed heat exchange bundles are single pass with one bypass tube connected to the lower manifold to permit easy expulsion of liquid sodium from this loop using compressed argon. The upper manifold has a main chamber and a small vent chamber. The vent chamber has a small vent valve.

The tube bundles are baffled on the primary sodium side to realize a counter flow heat exchange configuration with a smooth temperature transition. Liquid sodium flows over the baffle top, down along the tubes and out under the baffle bottom. Each heat exchange bundle manifold is piped to a dedicated steam generator with the secondary circulation pump on the lower cool side of the loop. A pipe loop bypass reduces the steam generator liquid sodium inlet temperature. This arrangement minimizes the requirement for valves. The liquid sodium injection/removal port has a low temperature valve.

This configuration balances flows, optimizes heat transfer and minimizes thermal stresses. The standard manifold piping connection arrangement for each heat exchange bundle has one 12 inch circulation pump, one 12 inch wall penetration, one 12 inch straight pipe section, one 12 inch 90 degree elbow, one 12 inch vertical pipe section, the heat exchange bundle lower manifold, the heat exchange bundle tubes, the heat exchange bundle upper manifold, one vertical 12 inch pipe section, one 90 degree elbow, one horizontal straight pipe section, one more wall penetration, one argon cushion tank, the steam generator inlet, the steam generator tubes and a straight pipe section back to the circulation pump. There is one small drain valve on each heat exchange bundle. This arrangement permits practical and safe identification, isolation, draining, replacement and refilling of any defective heat transport loop component.The heat exchange bundles must have sufficient positioning play to allow for pipe thermal expansion-contraction and possible earthquake related movement.
 

INTERMEDIATE HEAT EXCHANGE BUNDLE SIZING:
The intermediate heat exchange bundles are in two rows adjacent to the primary liquid sodium pool end walls. Each heat exchange bundle has 12.75 inch OD, 10.126 inch ID inlet and discharge pipes that run directly above the bundle. The inlet pipe is lower and closer to the pool end and the discharge pipe is higher and closer to the pool middle. This configuration provides heat exchange counterflow and permits removal and replacement of individual heat exchange bundles together with their service pipes. The heat exchange bundles are connected single pass, with the inlet port closer to the pool end and the discharge port closer to the pool centre.

The heat exchange bundle sizing is largely determined by the required thermal power and discharge temperature, the thermal conductivity characteristics of the heat exchange bundle tubes and the temperature profile of the primary liquid sodium.

One of the principal constraints on heat transfer is the wall thickness of the heat exchange bundle tubes. The heat exchange tubes in the intermediate heat exchanger are chosen to be .500 inch OD tubes with .065 inch wall spaced on 0.75 inch square centers.

Hence the ID of this heat exchange tube is:
0.500 inch - 2(.065 inch) = 0.370 inch

The long term yield stress of Inconel 600 at less than 600 deg. C is about 579 MPa. Ontario pressure vessel safety codes require a safety factor of 3. Hence the maximum material working stress at 600 deg. C should be (579 MPa / 3) = 193 MPa. The combined tube wall thickness is:
2 X .065 inch = 0.13 inch.
The tube inside diameter is:
(0.500 inch - .13 inch) = .370 inch

Application of Barlow's formula gives the maximum allowable internal working pressure with no thermal stress as:
193 MPa X (.13 / .370) = 67.81 MPa. This pressure is divided by two again to allow for thermal stress, so the maximum rated working pressure is 33.90 MPa. However, the normal working pressure of the steam system is less than 16.67 MPa. Thus the heat exchange tubes in the intermediate sodium loop have a large pressure/stress safety margin.

The condensate feed pump control system should be designed such that the maximum design system operating pressure of 16.67 MPa is never exceeded.

The immersed heat exchange bundles are single pass to realize a counter current heat exchanger.

The width of the individual heat exchange bundles is limited by the pressure withstand capabilities of the top and bottom manifolds. Assuming the two halves of each manifold are bolted together the strength of the flange bolts limits the heat exchanger manifold width. Standard flanging for nominal 12 inch pipe sets the manifold width as 24 inches. The portion of the manifold that can accommodate tubes is the 12 inch wide central strip.

To withstand the high liquid sodium working pressure the chosen 12.75 inch OD pipe has:
ID = 10.126 inch
OD = 12.75 inch
Wall = 1.312 inch

At 600 degrees C the yield stress of pipe steel is 193 MPa.

The yield pressure at 600 deg C is:
193 MPa X (2) (1.312 inch/ 10.126 inch) = 50.01 MPa

Hence for safety the secondary heat transport system should be pressure limited to:
50.01 MPa / 3 = 16.67 MPa
= 165.05 bar
= 2426 psi
which is the maximum intermediate sodium working pressure for the intermediate sodium piping.

The corresponding saturated steam temperature is:
664 deg F = 351 deg C
 

INDIVIDUAL HEAT EXCHANGE BUNDLES:
Assume that each heat exchange bundle is intermediate liquid sodium connected to a steam generator using 12.75 inch OD, 10.126 inch ID steel pipe. Assume use of 0.500 inch OD inconel tubes with .065 inch wall thickness. Then neglecting viscosity considerations for cross sectional area matching each heat exchange bundle should have:
(10.126 inch / 0.37 inch)^2 = 749 tubes / bundle.

However, the above calculation does not take into consideration either viscosity or thermal loading.

In the above calculation the total active intermediate heat exchange tube length is: 36 bundles X 749 tubes / bundle X (6.0 m) / tube = 161,784 m

This parameter compares with a reactor active heat exchange tube length of:
456 tubes per fuel bundle X 532 core bundles X 1.5 m / core tube = 363,888 m

Hence to match the tube thermal loading in the intermediate heat exchanger to the reactor the number of tubes must be increased to about:
(363,888 / 161,784) X 749 tubes = 1684.7 tubes / bundle

Assume that the heat exchange tubes are located on 0.75 inch rectangular grid to allow external primary liquid sodium to easily penetrate the tube bundle. Hence a 12 inch width for tubes allows:
(12 inch / row) / (0.75 inch / tube) = 16 tubes / row.

Then the required minimum number of rows is:
1555 / 16 = 97 rows.

Decide to use almost all the availble heat exchange header length which permits 104 rows.

The length of 104 rows is:
104 rows X .75 inch / row = 76 inches

The final number of tubes is:
104 rows X 16 tubes / row = 1664 tubes per intermediate heat exchange bundle.

The required length of this heat exchange bundle, including two 12 inch pipe end supports and a manifold divider is:
76 inch + 2(24) inch + 2(6) inch = 136 inch
= 3.45 m

For ease of assembly and maintenance allow 15 inchs of clearance space between adjacent heat exchange bundles. Then each heat exchange bundle occupies 39 inches (1 m) of pool width. The number of heat exchange modules at each end of the pool is:
18.4 m / (39 inch X .0254 m / inch) = 18.57
Hence we design for 18 heat exchange bundles at each end of the pool.
 

FIX FROM HERE ONWARDS

STEAM GENERATOR:
The steam generator must withstand the steam pressure and must have approximately the same tube heat transfer area as the intermediate heat exchanger tube bundle.

The contemplated steam generator is realized using two 20 foot lengths of 2 foot diameter thick wall pipe. This pipe is available in sufficient wall thickness to safely withstand the steam pressure on the shell side of the steam generator.

Thus a 12.75 inch OD liquid sodium pipe from the secondary heat exchanger feeds approximately 1023 0.500 inch OD X .065 inch wall tubes in each 24 inch diameter pipe section. The two 24 inch diameter pipe sections are assembled horizontally one above the other so that steam easily rises to the top. Thus about 25 feet outside each end of the reactor building is fully occupied by steam generator components.

The next 20 feet outside each end of the reactor building must be left clear to allow steam generator service, removal and replacement. Thus at each end of the reactor building is a 15 m long building extension dedicated to steam generators. Including flanges each steam generator requires about a 1.0 m width allocation.

Note that The TCEs of the steam generator tubes and the steam generator shells must be closely matched to minimize longitudinal thermal stress. In practise both the tubes and the shell must be fabricated from the same material. If the material is Inconel 600 the steam generators are expensive. A better solution may be a floating turn around tube manifold.

At the water inlet and steam output ports on the shell side the 2 foot diameter steam generator must be heavily reinforced. The shell must safely contain the steam pressure. The steam pressure compresses the 0.500 inch OD tubes which operate at a slightly higher internal pressure.

The flanges on the 2 foot diameter shell ends must have soft metal gaskets that are liquid sodium tight. The whole issue of liquid sodium tight gaskets that continuously operate at high temperatures and pressures needs further investigation.

The steam generator steam outputs can be manifolded together to provide turboelectricity generation at:
16 X 20 MWe
 

INTERMEDIATE SODIUM VOLUME:
The volume of each intermediate sodium circuit can be estimated by assuming that everywhere along that circuit the cross sectional area is approximately the same as the cross sectional area of a 12 inch diameter pipe.

Thus the minimum pipe length equivalents are:
Intermediate heat exchanger = 16 m
Steam generator = 18 m
Horizontal pipes = 2 X (4 m + 8 m + 2 m) = 28 m
Vertical pipes = 2 X 3 m = 6 m

Hence total equivalent pipe length = 68 m

Pipe volume = Pi (6 inch)^2 X 68 m X (.0254 m / inch)^2 = 4.96 m^3

Thus the total secondary sodium volume is about:
36 X 4.96 m^3 = 178.56 m^3
 

STEAM GENERATOR HEAT EXCHANGE AREA:
Assume each intermediate heat exchanger bundle feeds heat to two series connected steam generators.

Each 20 foot long X 2 foot diameter OD steam generator shell will accept: (19.876 / .625 )^2 ~ 1000 tubes. Within each steam generator bundle there is a heat exchange area of:
1000 tubes X 220 inches / tube X Pi X .37 inch = 255,725 inch^2
= 165 m^2

The corresponding heat flow rate per bundle limited by Inconel 600 conductivity is: 20.9 Wt / m-deg K X 165 m^2 X (1 / .065 inch) X (1 inch / .0254 m) = 2,088,734 Wt / deg K
= 2.09 MWt / deg K

Thus with a 20 degree K drop across the heat exchange bundle tube wall the conducted thermal power transfer is:
2.09 MW / deg K X 20 K = 41.8 MWt

On this basis the total heat exchange capacity is:
72 heat exchange bundles X 41.8 MW / bundle = 3009 MW

To realize 2007 MWt the average temperature drop across the steam generator tube wall must be:
(2007 / 3009) X 20 C = 13.34 C

 

SUMMARY OF MAJOR MATERIAL REQUIREMENTS FOR ONE FNR:
804 fuel bundle shrouds;
804 Fuel bundle support grates;
804 Fuel bundle support pipes;
804 Fuel bundle bottom extension pipes;
532 Fuel bundle control rod tubes;
804 Fuel bundle indicator tubes X 10.5 m long;
804 fuel bundle indicator tube top caps;
804 fuel bundle indicator tube bottom plug;
221,312 active fuel tubes;
156,672 passive fuel tubes;
377,984 fuel tube top plugs
377,984 fuel tube bottom plugs;
663,936 core fuel rods;
1,770,496 blanket fuel rods for active fuel tubes;
1,681,920 blanket fuel rods for passive fuel tubes;
179 m^3 intermediate liquid sodium
7477 m^3 primary liquid sodium;
804 0.4 m X 0.4 m steel floats with 6.1 inch diameter holes in the center;
1312 0.4 m X 0.4 m steel floats with a lifting eye but no central hole;
38 heat exchange bundle floats;
72 X 20 foot lengths of 24 inch OD thick wall steel pipe rated for 10 MPa working pressure for steam generators
1224 m of 12.75 inch OD, 1.312 inch wall pipe rated for 18 MPa working pressure for secondary sodium
36 induction type 12 inch nominal diameter liquid sodium pumps
36 X 1664 = 59,904 X 20 foot inconel 0.5 inch dia intermediate heat exchange tubes rated for 16.67 MPa working pressure at 500 deg C
36 intermediate heat exchanger top headers;
36 intermediate heat exchanger bottom headers;
59,904 steam generator tubes rated for 16.67 MPa working pressure at 500 deg C
144 steam generator tube header plates about 2 foot diameter
144 steam generator end plates
22,620.6 m^3 of below grade excavation;
1533 m^2 primary sodium pool inside side wall stainless steel liner;
467.36 m^2 primary sodium pool inside bottom liner;
7527.48 m^3 saw cut lava rock blocks;
766.16 m^2 primary sodium pool outside bottom sheet stainless steel;
2287.8 m^2 primary sodium pool outside wall sheet stainless steel;
6351.76 m^3 concrete;
Exhaust fans;
38 independent argon pressure systems;
2 steam boilers for primary sodium melting via intermediate heat exchange systems;
532 laser range finders;
532 laser temperature measurement systems;
1 set of fuel bundle support stands, 1244 bundle capacity with 532 liquid sodium hydraulic control fittings;
532 liquid sodium hydraulic control rod positioning systems;
1 reserve primary sodium tank;
1137 m^3 ingeous rock gravel for foundation;
24.4 m long X 1 m deep I beams for bottom support of lava rock, primary sodium pool and its contents;
~ 1 km^2 elavated granite rock water front property;
> ~ 50,000 55 gallon open top steel drums with covers for sodium;
~ 6 X 150 MWe steam turbogenerators;
~ 6 turbogenerator enclosures;
~ 6 X 300 MWt cooling towers;
~ 6 transformers;
~ 6 sets of switchgear;

The cost of the aforementioned items x 2 is the floor price for a FNR.
 

This web page last partially updated January 29, 2017

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