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Elsewhere on this website Fast Neutron Reactors (FNRs) have been identified as the primary source of energy for meeting mankind's future energy needs. This web page focuses on the design of the FNR's primary sodium pool.
PRIMARY SODIUM POOL MATERIAL:
The EBR-2 primary sodium pool had no visible corrosion of its stainless steel alloy after 30 years of operation. The exact alloy is detailed in the attached file referred to as: EBR-II stainless steel alloy analysis.
Web sites dealing with stainless steel indicate that its corrosion resistance decreases after prolonged exposure to temperatures greater than 425 degrees C. In this respect 316 SS is believed to be significntly more corrosion resistant than 304 SS. Since the primary sodium pool is extremely difficult to replace it should be formed from 316 SS. Note that 316 SS is slightly more expensive than 304 SS.
PRIMARY SODIUM POOL OVERVIEW:
The inside diameter of the primary sodium pool should be 20.0 m to allow for a 12.6 m nominal diameter reactor core, a 1.333 m wide perimeter reactor blanket, a 0.666 m wide ring for storing used active fuel bundles and a 1.7 m wide ring for intermediate heat exchangers. The primary sodium depth must be 15 m to allow 6 m high intermediate heat exchanger tubes, 6 m high fuel tubes and a 3 m guard band underneath the fuel tubes.
The bottom 3 m of the primary sodium pool is divided into a 1.5 m height for the open steel lattice and 1.5 m for the fuel bundle bottom supports. In the case of movable fuel bundles the central bottom support penetrates 1.2 m into the open steel lattice when fully withdrawn.
There are no penetrations of the primary liquid sodium pool walls or floor below the pool deck, which is 1 m above the normal sodium surface. The ball bearings, the open steel lattice, the reactor fuel assembly, the intermediate heat exchange bundle supports and the intermediate heat exchange bundles are all inserted into the primary liquid sodium pool via the top surface of the primary sodium pool.
The top surface of the liquid sodium in the pool is nominally 1 m above grade level.
The sodium pool is assembled after the polar gantry crane is in place but before the steel dome roof panels are added, so that sodium pool components can be unloaded from a truck and lowered into the pool space using an external construction crane.
Once assembled the primary sodium pool is permanent. There are no plans to replace it at any time during the reactor working life. Should it need repair it can be field patched. The primary sodium pool walls and floor are protected by sufficient thicknesses of sodium and gadolinium that their neutron exposure is negligible. However, the inner steel cup is subject to prolonged exposure to 460 degree C primary sodium.
The common stainless steels 304 and 316 are believed to be long term thermally stable at 460 degrees C when air is excluded.
BALL BEARING LAYER:
The open steel lattice rests on a layer of 1.000 inch diameter ball bearings. The ball bearings form a hexagonal close packed layer. The average area occupied by each ball bearing is:
(3^0.5 / 2) inch^2 = 0.8660 inch^2
By comparison the cross sectional area of the ball bearing is:
Pi (1 / 2 inch)^2
= 0.785 inch^2
The fuel bundles have an overall height of 7.9 m. To relocate a fuel bundle it must be lifted about 8.0 m to clear other fuel bundles. When lifted the top 2.4 m of the fuel bundle are above the primary sodium surface.
There must be adequate room for primary sodium natural circulation. At the primary sodium pool perimeter the available cross sectional area is:
Pi [(10 m)^2 - (8.3 m)^2]
= 31.11 Pi m^2
For radial flow between the open lattice and the fuel tube bottoms the cross sectional area is:
Pi (2)(8.3 m)(1.5 m)
= Pi (24.9 m^2)___________
Thus about 0.5 m of the open steel lattice height must be truly open to allow adequate radial primary sodium natural circulation._________
The nominal primary sodium volume is:
Pi (10 m)^2 (15 m) = 1500 Pi m^3
= 4712 m^3
The primary sodium that is displaced by solid items within the primary sodium pool is approximately offset by the volume of the secondary sodium.
POOL WALL CONSTRUCTION:
Below the pool deck the primary liquid sodium pool wall and bottom consist of three upright flat bottom nested stainless steel cups with bottoms separated from one another by 1 m thicknesses of fire brick between adjacent cups. The fire brick will retain its shape and dimensions over the long term thus preventing pool bottom shape distortion potentially related to use of silica sand instead of fire brick for intercup bottom separation.
The intercup spaces between the stainless steel pool walls are separated by dry silica sand. For the inner cup and the middle cup the sand head pressure almost balances the liquid sodium head pressure which reduces the material hoop stress.
The sand must not chemically react with either the stainless steel pool walls or with hot liquid sodium.
The sand must remain loose and liquid like so that as the distance between nested stainless steel cup walls changes due to thermal expansion and contraction and as the sand volume changes due to thermal expansion and contraction the sand level between the walls rises or falls to provide stress relief. In this respect it may be necessary to control the sand grain size and the particle smoothness. Possibly the sand should be prefired to get rid of volatile components that might lead to sand particles sticking together. Possibly the sand should be replaced by silica or alumina marbles. Consider use of sand composed of NaCl or NaF. Ideally the average density of the sand should be about (3 / 4) the average density of the liquid sodium so as to provide partially balancing counter pressure to the liquid sodium. That may require replacing the silica sand by a low density volcanic lava gravel.
The fire brick and sand provide thermal insulation and also act as a gamma ray shield.
The innermost stainless steel cup is 20 m diameter X 16 m deep X 0.75 inch wall. The middle stainless steel cup is 22 m diameter X 17 m deep X 0.5 inch wall. The outermost stainless ssteel cup is 24 m diameter X 18 m deep X 0.75 inch wall.
This nested cup configuration is shown on the following FNR side elevation diagram.
This nested steel cup design faces a number of engineering challenges including:
a) Operating hoop stress;
b) Thermal expansion;
c) Field welding;
d) Bottom top surface grinding;
e) Seal testing;
f) Potential sodium absorption by fire brick;
g) Corrosion prevention;
The corrosion of stainless steel by liquid Na as reported by the EBR-2 experiment was negligibly small. However, we do not have good information with respect to the temperature and impurity concentration in the EBR-2. Here is a reference relevant to corrosion of various steels by caustic soda.
FIRE BRICK AND SAND VOLUMETRIC CONSTRAINT:
In the event that the two inner steel cylinders fail the FNR geometry must be such that fission product decay heat can still be removed from the FNR. Hence the primary sodium inlets feeding the intermediate heat exchangers and part of the heat exchanger tube length must remain below the liquid sodium surface.
The fire brick and silica sand provide thermal insulation and will not react with the hot liquid sodium in the event of an inner cup leak. The density of the fire brick is chosen to ensure that in the event of leaks in both of the inner two steel cups the liquid sodium level in the primary sodium pool will remain sufficient to allow reliable extraction of fission product decay heat via the intermediate heat exchangers.
Fine sand has a density of 1.60 kg / lit. The same sand saturated with water has a density of 2.01 kg / lit. Thus if liquid sodium seeps into the dry sand the volume of liquid sodium that can potentially be absorbed is 0.41 lit Na / lit fine dry sand.
For comparison the fractional unfilled volume in a stack of spheres is: (8 - (4 / 3) Pi) / 8 = 0.476
The volume of fire brick and sand between the side walls below the primary sodium pool 11 m mark is:
Pi [(12 m)^2 - (10 m)^2] 11 m
= Pi (484 m^3)
The volume of sodium potentially absorbed by the sand between the cups is:
Pi (484 m^3) (0.476) = Pi (230.4 m^3)
The volume of fire brick between the cup bottoms is:
Pi (2 m) (12 m)^2 = Pi (288 m^3)
Assume that the volume of sodium absorption by fire brick is:
0.476 lit sodium / lit fire brick
Then the maximum possible sodium absorption by the fire brick between the cup bottoms is:
Pi (288 m^3)(0.476) = Pi (137.1) m^3
Thus the volume of liquid sodium that can potentially be absorbed by the fire brick and sand is:
Pi (137.1 + 230.4) m^3 = Pi (367.4) m^3
Note that Pi (367.4) m^3 < Pi (400) m^3
which implies that even if both the innermost cup and the middle cup fail the liquid sodium level in the inner most cup will drop less than 4.0 m.
FIRE BRICK THERMAL CONDUCTIVITY:
The fire brick used in this application should have low thermal conductivity. The issue of fire brick thermal conductivity is discussed in the Stack Thesis.
The density of fire brick is 1.6 X the density of water. The ratio of the fire brick or sand thickness to 30 cm of lead is:
2 m / 0.30 m = 6.66
Hence if the fire brick or sand was compressed into a layer 30 cm thick its density would be:
6.66 X 1.6 = 10.656 gm / cm^3
In addition there is the weight of steel. There are 3 layers of steel, (1 X 0.5 inch thick + 2 X 0.75 inch thick) for a total of 2.0 inches. The density of steel is about:
7.874 gm / cm^3.
Distributing this additional mass over a 30 cm thickness gives an additional shield material density of:
40.0 gm / cm^2 / 30 cm = 1.333 gm / cm^3
Thus the equivalent shield material density is:
10.656 gm / cm^3 + 1.333 gm / cm^3 = 11.989 gm / cm^3
This is more than the density of lead which is: 11.36 gm / cm^3
Hence a 2 m thickness of fire brick plus 2.0 inch steel is a better gamma ray shield than is a 30 cm thickness of lead.
HYDRAULIC HEAD ISSUES:
The sheet steel cups must be sufficiently strong that they can safely withstand the worst case hydraulic heat issues of liquid sodium with fire brick and sand.
WALL HOOP STRESS:
At the bottom of the inner most nested stainless steel cup there is a 15 m head of liquid sodium.
The density of the liquid sodium is about 927 kg / m^3
The acceleration of gravity is about 9.8 m / s^2
Hence the static head pressure at the bottom of the pool is given by:
15.0 m X 927 kg / m^3 X 9.8 m / s^2 = 136,269 Pa
On a 1 m high strip of inner cup side wall this pressure exerts a force of:
1 m X 20 m X 136269 Pa = 2,725,380 Newtons.
Let W = inner most cup wall thickness.
Then if no sand is present the hoop stress on the inner most cup wall material near the bottom of the primary liquid sodium pool is:
(2,725,380 Newtons) / (2 X W X 1 m) = (1,362,690 / W) Pa
where W is in m.
The maximum allowable working stress for stainless steel at 500 degrees C is:
10,000 psi X 101,000 Pa / 14.7 psi = 68,707,483 Pa
Hence the smallest allowable value of W is given by:
W = 1,362,690 / 68,707,483 = 0.0198 m
= 0.0198 m / .0254 m /inch
= 0.7808 inch
which indicates that near the bottom of the inner and outer most cups the wall must be composed of 3 / 4 inch thick low carbon stainless steel. The wall thicknesses of the middle cup can be less due to the counter pressure provided by the sand.
FIELD FABRICATION METHODOLOGY:
For practical field fabrication the walls of each nesting cup are made of vertical plate strips. Associated with each vertical plate strip is a triangular bottom piece. These strips are pre-rolled to provide the required 10 m radius of curvature. These strips are prefabricated for shipping and have beveled edges for field welding. The wall strip lengths are 16 m, 17 m and 18 m. The bottom of each cup is made from triangular plates cut from flat steel steel sheets. The tops of the pool side wall strips have holes for lifting. The heaviest single pool wall component is:
18 m X 60 inch X 0.75 inch X (.0254 m / inch)^2 X 7.85 g / cm^3 X 10^6 cm^3 / m^3 X 1 kg / 1000 g X 1 tonne / 1000 kg
= 4.10 tonnes
Thus a crane with a 10 tonne lifting capacity is required at the reactor site for primary sodium pool assembly. The gantry crane with one enclosure end wall not yet installed should be adequate for this purpose.
The pool wall outside surface area is:
Pi (18 m) 2 (12 m) + Pi (12 m)^2
= Pi (12 m) (48 m)
= Pi (576 m^2)
The thermal conductivity of sand is in the range:
0.15 W / m-deg C to O.27 W / m-deg C
The maximum heat loss via thermal conduction through the pool walls and floor is:
Pi (576 m^2) X 0.27 W / m-deg C X 505 deg C X (1 / 2 m)
= 123,366 Wt
= 123.4 kWt
PRIMARY SODIUM POOL MELTING
The FNR primary pool needs 50 kW of immersion heater capacity for liquid sodium melting at startup. This heat may be applied by one or more of the secondary sodium loops. Note that it is impossible to install or remove any fuel bundles until after the primary liquid sodium has completely melted.
The thermal coefficient of expansion of stainless steel is:
17 um / m deg C
Thus the radial expansion of the innermost cup in transitioning from 15 deg C to 500 deg C is:
485 deg C X 17 X 10^-6 / deg C X 10 m = 0.0824 m = 8.2 cm.
The corresponding radial expansion of the second cup will be about 4 cm.This 4 cm of differential expansion must be absorbed by the sand between the walls of the nested steel cups.
The pool liner side walls will also vertically expand:
505 deg C X 17 X 10^-6 / deg C X 16.0 m = 0.137 m
Thus the hot pool deck must be free to move up and down with respect to adjacent cool walls.
The walls above the pool deck will vertically expand by:
505 deg C X 17 X 10^-6 / deg C X 14 m = 0.12 m
Hence the 1 m thick fiber ceramic insulation between the pool enclosure metal ceilings must compress by:
.137 m + .12 m = 0.257 m or 25.7% insulation compression.
The pool deck is rigidly welded to the inner nesting cup. Hence the fiber ceramic in the 1 m thick walls above the pool deck must accommodate pool deck radial expansion of about 9 cm or 9% insulation compression.
On top of the exposed fire brick is a sheet steel pool deck. The pool deck is welded to the inner most stainless steel nested cup and slides over the other two stainless steel nested cups to permit stress free thermal expansion and contraction.
On top of the inner most cup bottom is a sheet steel layer which protects the underlying stainless steel cup bottom from accidental damage.
On top of this protective sheet is the ball bearing layer and then the 1.5 m high open steel lattice which supports all the fuel bundles and contains the 340 hydraulic actuators and related liquid sodium hydraulic pressure tubes for the movable fuel bundles.
Inside the pool and around its perimeter are steel columns which support the intermediate heat exchangers.
At the bottom of the steel lattice is a layer of solid B4C spheres which act as ball bearings and have the secondary function of preenting bits of melted reactor fuel from forming a critical mass. Note that these B4C spheres are outside the neutron flux and hence will not form C-14.
Underneath the outermost nested steel cup bottom is 1 m thick space set by a row of steel I beams which rest on the concrete foundation and support the primary sodium pool and its contents.
CONNECTION TO PRIMARY SODIUM POOL ENCLOSURE:
Outside the outer cup wall is a > 1 m wide air gap for air cooling and for maintenance access to the below pool ventilation space. Within the air gap between the outer stainless steel pool wall and the concrete wall inner face are structural steel radial elements which stabilize the outer pool wall. In the event of inner and middle nested steel cup failures this structural steel relieves hoop stress in the outer nested cup steel wall.
POOL STEEL QUANTITIES:
The area of the stainless steel sheet forming the primary sodium pool outside bottom is:
Pi (12 m)^2 = 452.4 m^2
The area of the stainless steel sheet forming the primary sodium pool outside wall is:
Pi (24 m) (18 m)
= 1357.2 m^2
Primary sodium pool outer stainless steel wall total area is:
452 m^2 + 1357.2 m^2 = 1809.6 m^2
The area of the stainless steel sheet forming the primary sodium pool middle cup bottom is:
Pi (11 m)^2 = 380.1 m^2
The area of the stainless steel sheet forming the primary sodium pool middle wall is:
Pi (22 m) (17 m)
= 1175.0 m^2
Primary sodium pool middle cup stainless steel wall total area is:
380.1 m^2 + 1175.0 m^2 = 1555.1 m^2
The area of the stainless steel sheet covering the primary sodium pool inside bottom is:
= Pi (10 m)^2
= 314.2 m^2
The area of the stainless steel sheet covering the primary sodium pool inside walls is
Pi (20 m) (16 m)
= 1105.3 m^2
Total inner liner area is:
314.2 m^2 + 1105.3 m^2 = 1419.5 m^2
The area of stainless steel sheet metal covering the primary sodium pool deck is:
= Pi (12.0^2 - 10.0^2) m^2
= 138.2 m^2
The fire brick supporting the pool floor must flat 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 sodium piping plus the weight of the fuel bundles in storage plus the weight of the pool walls and floor, including the 2 m thickness of sand insulation. Note that until the sodium is present the inner cup is subject to severe compressive stress by the sand.
After pouring the concrete foundation slab the straight concrete walls are erected first. Then the pool cups are fabricated and fire brick are installed.
Consider the earthquake acceleration and displacement that are necessary to cause the primary liquid sodium level to rise 1 m on one side of the pool and drop 1 m on the other side of the pool. This situation corresponds to a sustained horizontal acceleration of about 0.1 g.
The primary sodium pool half fills a vertical cylinder 20 m diameter X 30 m high. Normally the sodium surface is horizontal. Consider a horizontal earthquake acceleration that causes the sodium surface to be an inclined plane stretching from a bottom corner of this cylinder to an opposite top corner of this cylinder.
The height of this incline is 30 m. The base of this incline is 20 m. A little geometry shows that it takes a sustained 1.5 g horizontal acceleration to cause the liquid sodium surface to adopt this inclined shape.
A earthquake induced 1.5 g vertical acceleration causes a maximum vertical acceleration of 2.5 g. This is about the structural limit of normal engineered structures. Thus the primary sodium pool can reasonably be rated for public safety at up to 1.5 g earthquake induced vertical accelerations.
Note that there are no wall penetrations at wall heights normally exposed to liquid sodium. At wall heights where there are wall penetrions for pipes and air locks the exposure to hot sloshed liquid sodium is only transient and is extremely rare.
The pool ceiling, which carries the gantry crane and monitoring system, is not structurally intended to withstand even sloshed liquid sodium. Hence an earthquake acceleration of greater than 1.5 g will almosst certainly result in a facility repair shutdown for an extended period.
The reason for having three nested cups is that it is absolutely essential to ensure that primary sodium will never leak outside the outer cup. If the inner and middle cups fail primary sodium will fill the gasspaces in the sand and fire brick. That will cause the elevation of the primary liquid sodium surface to drop by about 4 m. Hence the bottom 2 m of the intermediate heat exchange bundles will remain immersed in primary sodium, which is enough to remove fission product decay heat.
However, if due to a further failure of the outer stainless steel cup the primary sodium surface elevation continues to drop, that circumstance is very dangerous because:
a) As the primary sodium surface drops below the intermediate heat exchange bundles heat removal will stop;
b) Fission product decay heat will keep raising the temperature of the fuel and the remaining primary liquid sodium;
c) Eventually the high fuel temperature will cause fuel melting, which should be confined by the fuel tubes;
d) Eventually the liquid sodium temperature will reach its boiling point causing sodium vapor emission;
e) When the sodium boiling drops to the level of the fissile fuel rods the reactor reactivity will increase which will cause a reactor setpoint temperature increase if the fissile fuel geometry is unchanged. This setpoint temperature increase will cause fuel melting even if there is little or no fission product decay heat.
The bottom line is that until the movable fuel bundles are extracted from the matrix of fixed fuel bundles it is crucial to ensure that there are no primary sodium leaks through the outer cup and that there is sufficient cooling by natural circulation to extract fission product decay heat. Hence, from a walkaway safety perspective it is esential to have three redundant primary sodium enclosing steel cups that are spaced such that the largest possible primary sodium surface elevation drop is 4 m.
This web page last updated May 20, 2022.
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