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XYLENE POWER LTD.

FNR NaK LOOP

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

INTRODUCTION:
A nuclear reactor produces heat. That heat is used to produce high pressure steam. Then expansion of that steam through a turbine drives a line synchronous generator to produce 60 Hz 3 Phase electric power.

This web page describes how heat is transported from the FNR primary liquid sodium pool to the nitrate salt.

In a liquid sodium cooled Fast Neutron Reactor (FNR) power plant, due to the chemical incompatibility between sodium and water, for safety purposes the primary sodium is triple isolated from the steam genertor water. Heat moves from the atmpspheric pressure (0.1 MPa) primary sodium to the higher pressure (0.5 MPa) secondary NaK by thermal conduction through the intermediate heat exchange bundles that are immersed in the primary sodium pool. The secondary NaK is then pumped through a NaK-salt heat exchanger. The NaK flow rate is controlled to keep the NaK/nitrate salt heat exchanger discharge temperature at 350 degrees C. This equipment is located in a heat exchange gallery outside the upper perimeter of the FNR's primary sodium pool enclosure.

Then the heat moves from the secondary NaK through the NaK-salt heat exchangers to atmospheric pressure (0.1 MPa) nitrate salt by thermal conduction. The molten nitrate salt is circulated by a pump and flows through through below grade pipes to transport the heat from the NaK-salt heat exchangers to steam generators that are located in turbogenerator halls that are outside of the laneway around the nuclear building.

The reactor power is controlled by controlling the speed of the nitrate salt pump.

The secondary NaK loop is rated for a maximum working pressure of 2.0 MPa but operates at only 0.5 MPa. The NaK referred to herein is a low temperature melting point alloy consisting of 60% Na and 40% K by weight. A major feature of this NaK is that it is liquid from room temperature up to over 500 degrees C while minimizing its K fraction. This feature enables primary sodium melting by transfer of heat backward from an organic heat transfer fluid loop through the NaK to the primary sodium pool. NaK is not used in the primary sodium pool due to its inferior neutronic properties as compared to pure sodium.
 

GASKETED PIPE MECHANICAL JOINTS:
A major constraint on assembly and service of liquid sodium cooled FNRs is the gasketed flanged pipe joints necesssary for repeatedly connecting and disconnecting pipes in the field. The issue is that graphite gaskets are only rated to 454 degrees C. The whole issue of the optimum gasket impregnation material needs more study.
 

CONTROL STRATEGY:
The control strategy is to use a variable speed induction pump to control the discharge temperature of the NaK from the NaK/nitrate salt heat exchanger at 350 degrees C. Due to the passive FNR temperature control the NaK inlet temperature is nearly constant in the range 450 C to 460 C. Hence this strategy maintains a nearly constant temperature across the NaK loop.

The nitrate salt return temperture is locked at about 310 C by the superheated water in the steam generator. The nitrate salt dischaarge temperature is locked at about 440 C by the NaK/nitrate salt heat exchanger characteristics. Hence the Nak/nitrate salt heat exchanger flows are in a constant ratio. Then the reactor power is controlled by varying the speed of the nitrate salt pump. Note that this control arrangement relies on there being some flow through both the NaK loop and the nitrate salt loop to maintain temperature stability which means that the reactor output power cannot be smoothly modulated down to

An advantage of this arrangement is that the temperature across the nitrate salt loop is stabilized which stabilizes the steam temperature. Another advantage of this control strategy is that by maintaining constant high differential temperatures across both the NaK loop and the nitrate salt loop the thermal stress in the NaK/nitrate salt heat exchanger is minimized.
 

HEAT TRANSPORT LOOP ISOLATION:
There are 48 identical independent heat transport circuits, 6 connecting to each of the 8 heat exchange galleries located around the perimeter of the primary sodium pool. Failure of any individual heat transport circuit does not cause a failure of the whole. Likewise, any electricity generator can be operated at part power using only a fraction of its 6 allocated heat transport circuits.

Each intermediate heat exchanger supplies hot secondary NaK to a dedicated NaK-salt heat exchanger which has three parallel connected dedicated secondary NaK dump tanks, a dedicated variable speed electric induction pump, a dedicated argon filled cushion tank and dedicated pressure relief vents. Any heat transport circuit can be shut down for service while the other heat transport circuits remain in operation.

Typically two heat transport circuits are fitted with heat transport fluid rather than nitrate salt and are reserved for supporting warm up/cool down operations.

Each of eight heat exchange galleries has six associated secondary NaK heat transport loops. Each heat transport loop must have the capacity to transport:
1000 MWt / (6 X 8) heat transport loops = 20.833 MWt / heat transport loop
at a secondary NaK differential temperature of:
120 degrees C________.

Each heat transfer loop transfers up to 20.833 MWt of heat which in turn can be used to provide:
20.833 MWt X 0.300 = 6.25 MWe
of turbo-electricity generation. Thus the maximum possible system electricity output is limited by the available heat transport circuits to about:
(48 - 2) X 6.25 MWe = 287.5 MWe

Each secondary NaK heat transport loop is executed using 12.000 inch inside diameter (ID) schedule 40S stainless steel pipe. This pipe has an OD of 12.75 inch, a wall thickness of 0.375 inch and a linear weight of 49.56 lb / ft.

At full load the differential temperature drop across each NaK pipe loop is about 50 degrees C ____and the fluid flow velocity in each pipe is ~ 3 m / s.______
 

CHOICE OF SECONDARY HEAT TRANSPORT FLUID:
The FNR requires a secondary heat transport fluid that is compatible with the heat exchange tube material (Inconel 600) and will not chemically react with the hot radioactive primary liquid sodium in the event of an intermediate heat exchange bundle tube failure. The secondary heat transport fluid must to be chemically stable liquid over the temperature range 15 C to 600 C.

This same secondary heat transport fluid must react with molten nitrate salt in a predictable manner to allow safe loop shutdown in the event of a NaK-salt heat exchange tube failure.

To meet these specifications modest pressure (~ 0.5 MPa) non-radioactive NaK is used as the secondary heat transport fluid. This modest pressure permits use of gasketed flanged pipe joints in the NaK pipes with minimal NaK gasket leakage problems at the flanged pipe joints. However, apart from the gaskets, the secondary NaK loop is rated for 2.0 MPa working pressure at 800 degrees K (527 C) to allow safe management of sudden NaK-salt heat exchange tube ruptures and/or steam generator tube ruptures.

The intermediate heat exchange bundles isolate the radioactive primary liquid sodium from the non-radioactive secondary NaK. Should an intermediate heat exchange bundle fail, due to its higher pressure secondary NaK will always flow into the primary sodium, not vice versa.

Thus the heat exchange galleries are always radiation free.

To achieve the desired level of safety it is essential that, even during system transients, at the NaK-salt heat exchanger the secondary NaK pressure must always be greater than the molten nitrate salt pressure. Hence, if the secondary NaK starts to lose argon cover gas pressure or NaK level the nitrate salt should automatically immediately drain to its dump tank.

Both ends of the nitrate salt loop are vented to the atmosphere via tall large diameter (16 inch OD) vents.

The secondary NaK has a pressure head (0.5 MPa) sufficient to ensure that even during a rupture of a NaK-salt heat exchange tube and consequential nitrogen production in the nitrate salt circuit the secondary NaK pressure will always be greater than the nitrate salt pressure in the NaK-salt heat exchanger. Then if there is a NaK-salt heat exchanger tube failure secondary NaK always flows into the salt, not vice-versa. That injection of secondary NaK into the nitrate salt rapidly forms nitrogen gas which will escape to the atmosphere via the local nitrate salt vent. This gas will likely also violently expel molten nitrate salt out the same vent. The volume of the secondary NaK cushion tank is minimized to minimize the maximum amount of NaK that can leak into the nitrate salt loop.
 

SECONDARY NaK LOOPS:
Each heat exchange gallery has an internal width of 8.0 m. Each heat transfer loop has one NaK-salt heat exchanger. There are 6 NaK- nitrate salt heat exchangers per heat exchange gallery. The heat transfer loops are spaced at 1.5 m and have 1.25 m off each side. Hence the overall gallery length occupied by equipment is:
5 (1.5 m) + 2 (1.25 m) = 10.0 m.

At the end of the Heat Exchange Gallery furthest from the airlock is the door to the stairwell.

Intermediate heat exchange bundles are immersed in the upper perimeter of the primary sodium pool. The 12.75 inch OD Pipes connecting the NaK-nitrate salt heat exchangers to the intermediate heat exchange bundles go straight through the primary sodium pool enclosure wall before bending down to reach the desired intermediate heat exchange bundle position. Each pipe carrying hot secondary NaK from an intermediate heat exchange bundle goes directly to its companion NaK-salt heat exchanger top manifold inlet port. Each pipe carrying cooler secondary NaK back from a NaK-nitrate salt heat exchanger to its companion intermediate heat exchange bundle is routed through a flow meter (F) and then an induction pump which in normal operation sets the secondary NaK circulation rate and hence the thermal power conveyed by the heat transport circuit. Note that this NaK cirulation rate is controlle dto keep the NaK return temperature at 350 degrees C.

There is a secondary NaK drain to 2 MPa pressure rated NaK dump tanks located at a low point on the secondary NaK return pipe between the NaK-salt heat exchanger and the intermediate heat exchanger. This drain pipe is connected so as to fully drain the NaK in the induction pump.

The lower NaK-salt heat exchanger manifold cover has a small drain plug to allow drainage of trapped secondary NaK from that manifold when service access inside that manifold is required.

Below a nitrate salt temperature of about 260 degrees C the nitrate salt will no longer flow. Thermal fluid cooling in place of molten nitrate salt cooling is required to dump sufficient primary sodium heat to enable work inside the reactor space. For cooling below 300 degrees C the nitrate salt is drained to its dump tanks. Heat transfer is then done by an organic heat transfer fluid in a dedicated warmup / cool down heat transfer circuit which cools the NaK down to less than 110 degrees C and hence cools the primary sodium pool down to about 120 degrees C, which permits fuel bundle repositioning and intermediate heat exchange bundle service.
 

In the event of a NaK-salt heat exchanger tube rupture the higher pressure (0.5 MPa) secondary NaK will enter the molten nitrate salt circuit where it will rapidly chemically react with the molten salt producing nitrogen. The nitrogen gas will displace salt in the Nak-salt heat exchanger shell, and will force molten nitrate salt to discharge out the adjacent large diameter nitrate salt vent.

Loss of NaK to the heat transfer fluid does not cause a violent chemical reaction but it will likely start a fire if expoosed to air. In this respect it is important that the density of the NaK be greater than the density of the heat trnsfer fluid._____________

As the NaK loses pressure and/or its level decreases the air pressure over the nitrate salt/heat transfer fluid dump tank is released and the nitrate salt/heat transfer fluid in the NaK-nitrate salt heat exchanger will drain to the nitrate salt/heat transfer fluid dump tank. The nitrogen producing chemical reaction in the nitrate salt will continue as long as there is any liquid NaK above the NaK-salt heat exchanger tube rupture. Thus the nitrate salt vent diameter and the various pressure ratings must be sufficient to safely manage this rapid nitrogen production and discharge.

As soon as the nitrate salt level drops below the bottom of the NaK-salt heat exchanger the NaK should be dumped to the NaK dump tanks.

An important ongoing operating issue is maintenance of sufficient thermal flux and molten salt flow to prevent the molten nitrate salt from freezing in the external pipes and in the steam generator.

The steam pressure in the steam generator shell must be set sufficiently high to keep the steam generator water temperature and hence the molten nitrate salt return temperature at 320 C, well above the salt melting point. The molten nitrate salt supply upper temperature is limited by the primary Na temperature and hence the NaK high temperature. The molten nitrate salt return temperature should be kept at about 340 degrees C to prevent NaOH and KOH in the NaK depositing on heat exchange surfaces.

If the molten nitrate salt temperature falls below its melting point there will be no heat transport away from the NaK-salt heat exchanger. When it is necessary to cool the primary sodium below 300 degrees C for service or other purposes heat should be removed from the NaK using thermal fluid cooling instead of nitrate salt cooling. The nitrate salt is drained to its dump tank. Then heat transfer fluid from its dump tanks is used to replace the nitrate salt in a dedicated heat transfer circuit. The steam bypass valve from the steam generator to the turbine condenser is openned. Then evaportion of steam generator water will extract heat from the heat transfer fluid, the NaK and hence the primary sodium pool. The steam generator water level control system will automatically add replacement water as this water evaporates.
 

CONSTRUCTION:
The high pressure NaK piping is 12 inch schedule 40S pipe (12.75 inch OD, 12.000 inch ID, 0.375 inch wall.

The NaK dump tanks are formed from 48 inch outside diameter stainless steel with 1.25 inch thick walls.

The induction pump is formed from 16 inch Schedule 40S pipe (16 inch OD, 15.250 inch ID, 0.375 inch wall). It is assumed to have the same open area, net of its torpedo, as does a 12 inch pipe.

The stainless steel alloy used in the NaK-salt heat exchanger must be chosen for nitrate salt resistance.

The cross sectional area of the 12 inch pipes is:
Pi (6 inch)^2 X (.0254 m / inch)^2
= 0.072966 m^2

The overall length of equivalent 12 inch pipe containing secondary sodium is:
58.35 m

The equivalent 12 inch pipes have a contained NaK volume of:
58.35 m X 0.072966 m^2 = 4.258 m^3

The intermediate heat exchange bundle contains a NaK volume of 1.0595 m^3.

The NaK-salt heat exchanger contains a NaK volume of 3.3869 m^3.

Hence the NaK dump tank capacity must be more than:
4.258 m^3 + 1.0595 m^3 + 3.3869 m^3 = 8.704 m^3

We have not accounted for the cushion tank or drain down pipe volumes. Prudence suggests that we design for some excess NaK dump tank capacity.
 

NaK DUMP TANK SIZING:
The cross sectional open area of the proposed NaK dump tank material is:
Pi[45.5 inch /2]^2 X [0.0254 m / inch]^2 = 1.049 m^2.
In order to form the contemplated dump tanks we need more than:
8.704 m^3 / 1.049 m^2 = 8.297 m of dump tank material. Choose each NaK dump tank section to be 3 m high. Hence we need 3 such parallel sections for each heat exchange circuit. Each section with its insulation is about 1.5 m in diameter. They can be slightly staggered for improved service access.
 

NaK REQUIREMENT:
The previous calculation indicates that in sourcing NaK we must plan on acquiring:
48 heat transport circuits X 9 m^3 / heat transport circuit = 432 m^3
of NaK.
 

MAINTENANCE:
There is no radioactivity in the heat exchange galleries which allows safe service work or NaK fire suppression in selected heat exchange galleries without causing a total reactor shutdown.
 

DIAGRAM:
A diagram showing an end view of a heat exchange gallery. Each gallery has 6 heat transport loops, one behind the other. Note that the NaK-salt heat exchangers are staggered in position, so that part of the 2nd loop is visible behind the first loop.

The left hand side of this diagram shows the intermediate heat exchange bundle and the NaK pipes. This diagram shows the molten salt heat transport pipes on the right hand side and the three parallel connected NaK dump tanks in the lower left middle. The horizontal induction pump, the NaK flow meter and the vertical NaK-salt heat exchanger are in the middle of the diagram. Above the NaK-salt heat exchanger from left to right are the NaK argon filled cushion tank and the molten nitrate salt pressure relief vent.

Note the dedicated steel I beam equipment supports. The maximum width of each such I beam is 0.20 m to allow installation and subsequent replacement of the 1.3 m wide NaK dump tanks.

Note that NaK-nitrate salt heat exchanger staggering enables a NaK-salt heat exchanger shell diameter of 1.2 m (~ 48 inches). Note that the NaK-nitrate salt heat exchanger centerline to end wall clearance is 1.25 m which is sufficient for the NaK-salt heat exchanger end manifold flanges + insulation.

Note the 2.0 m wide space between adjacent heat exchange galleries that is dedicated to the airlocks that are required for moving fuel bundles and intermediate heat exchange bundles from their truck load/unload points into or out of the primary sodium pool space.
 

HEAT EXCHANGE GALLERY LOWER LEVELS:
Each heat exchange gallery has a lower level where the NaK dump tanks are located. Personnel access to the various heat exchange gallery levels is via a stairwell at the gallery end farthest from the airlock truck load/unload point.

The drives for the NaK induction pumps are wall mounted adjacent to the induction pumps.

Equipment in the heat exchange galleries is installed and removed from above using a mobile crane parked at the airlock truck load/unload point. The roof over the heat exchange galleries must be easily removable and replaceable.

There must be a large air vents in heat exchange galleries for outside air cooling.

An important issue in the heat exchange gallery is isolation of potential NaK drips. A likely source of these drips are the NaK pipe flange connections. Drip collection pans should be provided to isolate dripped NaK. Note that these drips will self ignite in air.

In the basement under each heat exchange gallery is an isolated space that is used for an argon bladder. This space is air flow connected to the service access space under the pool deck. Any water penetrating this space must flow along the floor and into the FNR bottom drain located about 18 m below grade.
 

NaK PIPING:
The intermediate heat exchanger is counter flow and is realized with a single pass vertical tube bundle.

The intermediate heat exchange bundle tube side top manifold connects to the NaK-salt heat exchanger tube side top manifold via a 12.75 inch OD schedule 40S stainless steel pipe. The intermediate heat exchange bundle bottom connects to the NaK-salt heat exchanger tube side bottom via a 12.75 inch OD schedule 40S stainless steel pipe. This pipe contains an induction pump that circulates NaK from the bottom of the NaK-salt heat exchanger to the bottom of the intermediate heat exchanger. This configuration provides heat exchange counterflow and permits removal and replacement of individual NaK-salt heat exchangers and induction pumps via an overhead crane lift. There is a gravity drain to three parallel connected NaK dump tanks which also acts as cushion tanks. A small top tank is still required for each NaK circuit to trap gases and to indicate the NaK level.
 

PIPE WALL SEALING AND SUPPORT:
Flexible air and argon bellows wall seals are required at locations where the NaK pipes pass through the inner reactor enclosure wall to accommodate thermal expansion/contraction. Under ordinary operation the reactor power is modulated by controlling the nitrate salt circulation rate and hence the NaK circulation rate. This control methodology causes significant loop differential temperatures.

The NaK pipes and the induction pump must be supported with threaded support hardware so that the pipes and pump remain in their correct positions when an intermediate heat exchanger is disconnected.
 

NaK TEMPERATURE CONSTRAINTS:
Inside the tubes of the intermediate heat exchange bundle is non-radioactive NaK normally at a pressure of about 0.5 MPa. The normal low temperature limit on the circulated NaK at full load is 330 degrees C to prevent NaOH precipitation on the inside of the tubes within the NaK-salt heat exchanger and to prevent nitrate salt solidification. The normal high temperature limit on the circulated NaK is ~ 460 degrees C. We are assuming a full load 10 degree C temperature difference across the intermediate heat exchange tube bundle wall. At full load the dry steam in the steam generator will reach about:
(460 deg C - 10 deg C -10 C - 40 deg C) = 400 deg C.

At full load the NaK temperature differential can drop to:
450 -330 = 120 deg C
without threat of NaOH precipitation. There is feed water temperature mixing in the lower part of the steam generator to minimize thermal stress on the lower ends of the steam generator tubes. The injection water temperature rise from 25 deg C to 320 C is realized by feed water recuperator heat recovery from the steam immediately upstream from the turbine condenser followed by water mixing in the bottom of the steam generator shell.
 

TEMPERATURE CONSTRAINT:
At low steam loads the NaK flow through the intermediate heat exchanger will decrease and the NaK discharge temperature from the intermediate heat exchange bundle will rise to about 460 degrees C. As the steam load increases the NaK flow will increase and the NaK discharge temperature from the intermediate heat exchange bundle will decrease to about 450 degrees C.
 

INDUCTION PUMP:
Induction pumps are used to circulate the NaK. The induction pumps must be sized to overcome the flow pressure head in the NaK loops. Note that these pumps should be located on the low temperature return pipes near the primary sodium pool deck level to ensure both cool operation and sufficient positive suction head.

The induction pump operates by inducing a circular current in the liquid sodium. This current crosses a radial magnetic field component and hence experiences an axial force. External 3 phase coils, analogous to the stator coils of a 3 phase AC motor, create a suitable time varying magnetic field.

In normal operation the pumped NaK temperature is about 340 degrees C and the induction pumps are oil cooled to protect the electrical insulation from heat damage.

When the nitrate salt cooling of the NaK-salt heat exchanger is replaced by thermal fluid cooling the NaK temperature at the induction pump falls to about 110 C, at which point the induction pump does not need oil cooling.

However, under circumstances when the NaK-salt heat exchanger is uncooled either natural or pumped circulation of the secondary sodium can potentially cause the NaK temperature at the induction pump to rise to about 460 degrees C. Under these circumstances the induction pump can easily be damaged if it has insufficient pumped oil cooling. To prevent wide temperature excursions the nitrate salt loop should be charged with nitrate salt before the NaK is transferred from its dump tank back into the NaK heat transfer loop.

The induction pumps have 16.000 inch OD schedule 40S (0.375 inch wall) 316 SS input pipes and 12.75 inch OD schedule 40S (0.375 inch wall) 316 SS discharge pipes. The 16.000 inch OD pipe runs through the induction pump but is partially obstructed by the induction pump's internal magnetic flux torpedo.

The ID of the 16 inch pipe is:
16.000 inch - 2 (0.375 inch) = 15.25 inch

Induction pump details are set out at FNR Induction Pump.
 

GASKET CONSTRAINT:
A major constraint on the FNR design is gasket material properties. This FNR operates at too high a (temperature X pressure) product for use of normal elastomeric gaskets. Soft metal or compressed carbon gaskets must be used. Such gaskets do not tolerate pipe misalignment, manifold distortion or high pressures. Hence gasketed mechanical joints need near optical precision fabrication. All the NaK flanges are sealed with such gaskets.The flange bolts must have a smaller TCE than the flange material.
 

THERMAL EXPANSION:
The NaK-nitrate salt heat exchangers are in fixed positions with respect to the concrete structure. The intermediate heat exchange bundles move due to connecting pipe thermal expansion and contraction. Also the primary sodium pool inside wall moves due to thermal expansion. When the system is cold the insulation of the cooler intermediate heat exchange bundle supply pipes should be almost touching the primary sodium pool inside wall. When the system is hot there is about a 0.2 m gap between this pipe insulation and the primary sodium pool inside tank wall.
 

FULL LOAD SYSTEM TEMPERATURE PROFILE (deg C):_______
FUEL
CENTER
Primary  
Na HIGH
Primary  
Na LOW
Secondary  
NaK HIGH
Secondary  
NaK LOW
STEAM  
HIGH
STEAM  
LOW
WATER  
HIGH
WATER  
LOW
10%550544322543321503320320____
100%550440340429329440320320____

 

NaK FLOW:
Some of the FNR NaK flow issues are discussed in the paper titled Improving SFR Economics Through Innovation.

The FNR NaK loops take advantage of the relatively large thermal coefficient of expansion of liquid sodium to promote natural circulation of the NaK. Even with no pumping the position of the NaK-salt heat exchanger above the intermediate heat exchange bundles causes the NaK to naturally circulate.

There is an induction pump for larger controlled circulation of NaK.

The NaK pipe is chosen to be 12.75 inch OD, schedule 40S (0.0.375 inch wall). Then the pipe ID is:
12.75 inch - 2 (0.375 inch) = 12.000 inch

Then the pipe cross sectional area A is:
A = Pi [(12.000 inch / 2) (.0254 m / inch)]^2
= .072966 m^2

The maximum pipe working pressure rating Pm is given by:
Pm (12.000 inch) X L = 39 MPa X 2 X (0.375) inch X L
or
Pm = 39 MPa (2) (0.375 inch‌) / 12.000 inch)
= 2.4375 MPa
 

Define:
Rho = 0.927 gm /cm^3 = density of liquid sodium;
V = average sodium linear velocity in 12.75 inch OD pipe;
Cp = 1.23 J / gm-deg C = heat capacity of liquid sodium;

NaK Loop Thermal power = Rho A V Cp (120 deg C)

20.833 MWt X 10^6 Wt = 0.927 gm /cm^3 X 10^6 cm^3 / m^3 X 0.06557 m^2 X V X 1.23 J / gm deg C X 120 deg C
= 8.9716 X 10^6 V J / m

Hence:
V = 20.833 Wt / 8.9716 J/ m
= 2.322 m / s
which is an acceptable liquid flow velocity.

Hence the maximum NaK flow rate in each heat transport loop is:
A V = .06557 m^2 X 2.322 m / s
= 0.156619 m^3 / s

Hence the NaK flow rate for the entire reactor is:
0.15226 m^3 / s X 48 = 8.3085 m^3 / s
which must be matched by the primary sodium flow rate.

Herein lies a potential problem. to provide the same heat flux with a 60 degree C primary sodium temperature differential the primary sodium flow must be twice as great.

If the available primary sodium flow rate is less than 8.77066 m^3 / s it will constrain the reactor thermal output power.

In normal operation hot (460 degree C) primary sodium flows into the intermediate heat exchange bundles just below the pool surface, flows down outside the intermediate heat exchange tubes and is discharged about 6 m below the primary sodium pool surface at a temperature of about 400 degrees C. Simultaneously secondary sodium flows up inside the intermediate heat exchange bundle tubes, entering at about 330 degrees C and leaving at about 450 degrees C.

The intermediate heat exchange bundles are single pass to realize counter current operation and to minimize material thermal stresses.

In the NaK-salt heat exchanger secondary sodium flows downwards inside the tubes while molten nitrate salt flows upwards in the shell.

If there is a NaK leak from an intermediate heat exchange tube or manifold, NaK will leak slowly into the primary sodium pool.

Potential fire problems are NaK leaks from the heat transport piping, NaK-nitrate salt heat exchanger or induction pump. The NaK pressure driving such leaks is moderate (0.5 MPa). In every case the fire can be extinguished by first releasing the air pressure over the molten nitrate salt dump tank to lower the molten salt level below the bottom of the NaK-salt heat excahanger and then immediately releasing the argon pressure over the NaK dump tanks which causes gravity drain down of the NaK into the NaK dump tanks.
 

MAXIMUM SAFE NaK WORKING PRESSURE:
For the NaK 16 inch OD schedule 40S pipe used in the induction pump the ID is:
15.25 inch

The NaK pipe wall thickness is:
0.375 inch

Assume that the induction pump barrel is made of SS pipe. A table of 316 SS yield stress versus temperature is as follows:
TEMPERATURE (degrees K)YIELD STESS (MPa)
300208
400167
500144
600129
700122
800117
900114
1000104

The highest anticipated NaK working temperature is:
520 C + 273 = 793 K
which from the above table indicates a 316 SS yield stress of 117 MPa.

The corresponding maximum 316 SS working stress is:
117 MPa / 3 = 39 MPa.

Let Pm = maximum allowable NaK working pressure. Then:
Pm (15.25 inch) = 2 (0.375 inch)(39 MPa)
or
Pm = 2 (0.375 inch)(39 MPa) / 15.25 inch
= 1.92
which is the maximum safe secondary sodium working pressure due to rapid formation of nitrogen or hydrogen in the atmospheric vent of the sodium-salt heat exchanger. All of the other NaK loop components must be rated for working pressures of at least 2.0 MPa.
 

INTERMEDIATE HEAT EXCHANGE BUNDLES:
The intermediate heat exchange bundles isolate the radioactive primary liquid sodium from the secondary non-radioactive liquid sodium. They also serve as a barrier to other radioactive species in the event of a fuel tube leak.

To attain the desired temperature distribution in the intermediate heat exchanger bundles the NaK mass flow rate must be the same as the primary sodium mass flow rate. However, the primary sodium flow cross sectional area is larger so the primary sodium linear descent velocity is smaller.

There is a ring of 48 intermediate heat exchange bundles that are immersed in the primary sodium pool in a 19 m OD, 17 m ID ring. The heat exchange tubes are located between the pool surface and 6 m below the pool surface.

The weight of the intermediate heat exchange bundles is supported by a ring shaped table located in the primary sodium pool about 8 m above primary sodium pool bottom and about 9 m radially from the pool center. This table is supported by a ring of steel columns and the table is horizontally stabilized by interleg connections and by the adjacent innermost steel cup primary sodium pool liner. The top of this table is flat to allow the supported intermediate heat exchange bundles to move back and forth radially over a distance of about 0.2 m to accommodate thermal expansion/contraction of the primary sodium pool and the radial NaK piping. Apart from thermal expansion the radial position of the intermediate heat exchangers is fixed by the radial NaK pipes which in turn are fixed to the NaK-salt heat exchangers and induction pumps, which are in turn are fixed to the heat exchange gallery concrete structure. Thermal expansion, at points where these pipes pass through gas tight walls, is accommodated by use of metal bellows fittings.

The maximum outside diameter of the intermediate heat exchange manifolds is limited to:
38.8 inches
so that after accounting for thermal expansion 56 of them will fit in the available space on an 18 m diameter circle in the primary sodium pool. Note that with thermal expansion the circle shrinks to 17.6 m diameter.
 

NaK CIRCULATION PUMPING POWER:
The NaK mechanical pumping power is:
(force) X (velocity)
= (pressure head) X (area) X (velocity)
= (pressure head) X (volumetric flow rate)

Recall that for each heat transport loop:
(volumetric flow rate) = 0.10440 m^3 / s
 

NaK FIRES:
Other parties using NaK for heat transport have experienced repeated fires. The problem is that if hot high pressure NaK is inside a pipe the NaK tends to leak out via any mechanical joint that is less than perfect. The NaK operating temperature is too high for use of conventional elastomeric gaskets. Once outside the pipe the NaK spontaneously ignites in air. That situation is unacceptable.

The solution to this problem is to operate the NaK at the lowest practical pressure and to fit every NaK loop with a dump tank and every NaK pipe flange connection with a leak detector. At the first hint of a fire release of argon pressure in the dump tank causes the NaK in the affected loop to drain into its NaK dump tanks. Simultaneously the molten nitrate salt must be drained into its dump tank.
 

DUMP TANKS:
At the low points in the heat transport pipe loops are dump tanks with sufficient volume to accommodate all the fluid in that heat transport loop. The nitrate salt dump tanks have electric heaters for fluid melting and temperature maintenance. Note that the NaK dump tanks must be rated as pressure vessels and must be fitted with high pressure argon relief valves vented to the argon atmosphere over the primary sodium pool. Note that changing the temperature of the argon in the dump tank affects the argon pressure and hence the NaK level. Hence each NaK loop needs its own argon pressure control and NaK level sensor for liquid level regulation.

The NaK level control relies on argon pressure control by external low temperature argon valves. To charge the NaK loop argon is first injected into the top of the dump tanks while the displaced argon in the cushion tank is vented to the primary sodium pool space.

This arrangement requires a reliable valves on small argon pipes connected to the dump tank that either vent the dump tank to the argon atmosphere or connect pressurized argon to drive NaK out of the NaK dump tank. Note that over time NaK vapor may tend to condense in the cooler vent line. This issue may require ongoing maintenance.
 

DETECTION OF NaK LEAKS:
Any leak in a NaK circuit will result in loss of NaK volume in the NaK loop. Should such a volume drop occur that entire heat transport circuit should be shut down, the molten salt drained to its dump tank and the NaK drained to its the dump tank.
 

NATURAL CIRCULATION REQUIREMENT:
There must be enough natural circulation of NaK to remove fission product decay heat. This decay heat is quantified in the paper: Decay Heat In Fast Reactors.
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AUXILIARY POWER FOR DECAY HEAT REMOVAL:
There must be enough reliable molten nitrate salt circulation and enough water available at the steam generators to remove the fission product decay heat by evaporation of that water.
 

NaK NATURAL CIRCULATION:
In normal full load reactor operation the reactor produces 1000 MWt of heat. When the chain reaction is off the reactor may still produce as much as:
0.08 X 1000 MWt = 80 MWt
of fission product decay heat.

After a few ____hours this fission product decay heat output diminishes to about 10 MWt

Hence natural circulation of the NaK with the nitrate salt replaced by thermal fluid at atmospheric pressure should run at over 8% of the pumped circulation rate.

The natural circulation rate will be primarily limited by the temperature difference between the NaK rising leg and the NaK falling leg and by the viscous flow pressure drops across the intermediate heat exchange bundle and the NaK-salt heat exchanger. Thus these pressure drops need to be quantified.

The volumetric TCE of liquid sodium is 240 ppm / deg C. Hence if there is a 100 degree C temperature difference between the rising and falling legs the change in sodium density is:
.967 kg / lit X 240 X 10^-6 / deg C X 1000 lit / m^3 X 100 deg C = 0.967 X 24 kg / m^3

Assume an elevation difference of 10 m. Then the corresponding differential pressure is:
0.967 X 24 kg / m^3 X 10 m X 9.8 m / s^2 = 2274 Pa

The molten salt will not transport heat if its temperature is below its melting point of about _____ degrees C.

We need to compare these pressure drops to the viscous pressure drop across the intermediate heat exchange bundle at 1 / 10 of normal flow.
 

CALCULATE NaK VISCOUS PRESSURE DROP AT SUFFICIENT NATURAL CIRCULATION TO REMOVE FISSION PRODUCT DECAY HEAT:
An important issue with the intermediate heat exchange bundles is their ability to remove fission product decay heat by natural circulation. In natural circulation the liquid sodium flow rate is low and laminar, so the heat transfer characteristics are different from when the NaK loop is pumped. It is necessary to have a sufficient number of intermediate heat exchange tubes to allow the required natural circulation and laminar flow limited heat transfer. The viscosity of the NaK must be taken into account.
 

The following equations derived on the web page titled FNR PRIMARY SODIUM FLOW can be used to find the natural circulation volumetric fluid flow Fv per round coolant flow channel.
Fv = {Pi Pg Ro^4 / [Muv Zo (N + 2)(N + 4)]}BR> where:
Pi = 3.14159
Pg ~ 1000 Pa
Ro = (0.37 inch / 2) X (0.0254 m / inch) = 0.004699 m
Muv = 3 X 10^-4 N-s / m^2
(N + 2) = Ro [(Rhos Pg) / 2]^0.25 [1 / [Muv Zo]^0.5]
where:
Zo = 6.0 m
Rhos = 849.4 kg / m^3

Numerical substitution gives:
(N + 2) = Ro [(Rhos Pg) / 2]^0.25 [1 / [Muv Zo]^0.5]
= 4.699 X 10^-3 m [(849.2 kg / m^3) (1000 kg m /s^2 m^2) / 2]^0.25 [1 / [(3 X 10^-4 N^-s / m^2)(6 m)]^0.5]
= 4.699 X 10^-3 m [25.5267 kg^0.5 / s^0.5 m] [ 1 / [4.24264 X 10^-2 (kg m s /s^2 m)^0.5]]
= 2.8272482 kg^0.5 s-0.5 kg^-0.5 s^0.5
= 2.8272482

Hence the NaK natural circulation flow Fv through each tube is given by:
Fv = {Pi Pg Ro^4 / [Muv Zo (N + 2)(N + 4)]} = {3.14159 (1000 N / m^2)(0.004699 m)^4 / [(3 X 10^-4 N - s / m^2) (6 m) (2.8272)(4.8272)]}
= {3.14159 (1000)(487.55294 X 10^-12 m^2 / [(245.654277 X 10^-4 s / m)]}
= 6.23515 X 10^-5 m^3 / s

With 800 ______ tubes intermediate heat exchange / bundle the NaK natural circulation flow rate is:
800 tubes/bundle_____ X 6.23515 X 10^-5 m^3 / s-tube = 0.06378 m^3 / s which is faster _________than the minimum required natural circulation rate.
 

CORROSION:
We need to be concerned about possible long term corrosion of the enclosing materials caused by impurities NaOH amd KOH in the NaK. A relevant reference is corrosion by caustic soda.
 

PROVISIONS FOR SYSTEM MAINTENANCE:
To enable heat transport system service the NaK is transferred into its dump tank.

Application of argon pressure over the NaK dump tank and relief of argon pressure from the top of the NaK loop transfers Nak from the dump tanks into the NaK loop. Reversing this procedure allows the NaK to gravity flow back into its dump tanks.

A NaK level sensor should be provided at the top of each NaK loop to indicate when to close the system fill valve. The supply of argon for presurizing the Nak dump tank and the argon sink from the system top can both be from the primary sodium pool enclosure. Similarly when NaK drain down to its dump tank is required the argon in the dump tank can be vented to the primary sodium pool enclosure and after the argon pressure has sufficiently dropped the argon top vent valve can be openned. Note that for safety this argon top vent valve must be vented over the primary liquid sodium pool.

To expel NaK from the intermediate heat exchanger tubes the NaK level is first drained down to the level of the bottom of the return pipe to the intermediate heat exchanger. Then a blanking disk is installed between the flanges of the intermediate heat exchange bundle NaK discharge pipe. Then argon pressure is applied to the intermediate heat exchange discharge which will drive most of the contained NaK from the intermediate heat exchange bundle into the dump tank.

In reality, even after this procedure is complete a small amount of NaK will remain in the bottom manifold of the intermediate heat exchange bundle. This small NaK accumulation presents a potential risk to maintenance personnel and a potential fire risk if at some later time oxygen is admitted into the secondary sodium piping. This risk can be minimized by use of a small tube that connects onto the bottom of the intermediate heat exchange bundle lower manifold and removes the remanent secondary sodium by vacuum suction. In general for safety the flange connections of the intermediate heat exchange bundle and the radial piping should be closed with blanking plates while the intermediate heat exchange bundle is still in the argon atmosphere over the primary sodium pool.
 

PROTECTION OF THE INTERMEDIATE HEAT EXCHANGE BUNDLE FROM HIGH TRANSIENT PRESSURES:
In the event of a NaK-salt heat exchanger tube rupture there is potential for a violent chemical reaction between the NaK and the salt. This chemical reaction will cause a rapid transient rise in the NaK loop pressure which if not properly managed could cause a liquid sodium pressure pulse analogous to water hammer, possibly rupturing the intermediate heat exchange bundle and possibly leading to major facility damage. Hence the secondary heat transport system, including the intermediate heat exchange bundles, must be designed to safely withstand large transient pressures and the secondary liquid sodium should normally operate at a pressure of about 0.5 MPa. Sustained high pressure is prevented by venting the molten salt to the atmosphere and by dropping the molten salt level at the first hint of trouble.

In order for the safety mechanisms to reliably function there must also be a rupture disk That can provide instantaneous NaK pressure relief. The aforementioned rupture disk must be able to discharge nitrogen gas from the NaK loop at a rate equal to the maximum possible rate of high pressure nitrogen formation in that loop. That rate is limited by the maximum molten salt flow through the NaK-salt heat exchange tube rupture which is a function of the heat exchange tube inside diameter and the transient differential pressure between the molten salt and the secondary sodium.

In a practical accident scenario the chemical reaction forms nitrogen which rapidly raises the NaK pressure. The nitrogen is vented via the NaK cushion tank rupture disk. Most of the nitrogen forms in the molten salt and is vented to the atmosphere via the molten salt vent.

Each NaK heat transport loop is normally 0.5 Pa above ambient pressure. The secondary sodium dump tank also acts as an expansion tank that attenuates any pressure pulse in the secondary liquid sodium.
 

CONSTRAINTS:

1) The airlock design for primary sodium pool access must be large enough to accommodate the intermediate heat exchangers and related flanged pipe stubs.

2) There must be enough NaK natural circulation to dependably remove fission product decay heat so that the system remains safe on loss of electric power to the sodium induction pumps.

3) Need thick concrete walls between the primary sodium pool and the heat exchange galleries to protect workers in the heat exchange galleries from gamma radiation emitted by decay of Na-24 into Mg-24.
 

THERMAL SIPHON CALCULATIONS:
Define:
V = linear sodium velocity in pipe g = acceleration of gravity
Rho = density of liquid sodium
A = pipe cross sectional area
H =verage height of temperature difference
Cp = heat capacity of sodium ~ 0.3 cal / gm-deg C

Assume that the NaK-salt heat exchanger is mounted so that its bottom is 2 m above the surface of the primary sodium pool. Then the top of the NaK/salt heat exchanger is 10 m above the top surface of the primary liquid sodium pool. This height is consistent with the sodium vapor pressure constraint. For H = 5 m:
V^2 = 1.176 m^2 / s^2 or
V = 1.0844 m / s

Thermal power = Rho A V Cp (150 deg C) = 0.927 gm /cm^3 X 10^6 cm^3 / m^3 X A X 1.0844 m / s X 1.23 J / gm deg C X 150 deg C
= 185.466 X 10^6 J A / m^2 - s
= 185.466 MWt A / m^2

________

Thus neglecting viscosity and assuming ideal heat exchanger and reactor performance the maximum heat transport capacity is:
185.466 MWt / m^2 X 8.705 m^2 = 1614.5 MWt.

However, there will be a reduction in intermediate heat exchanger performance because the primary side of the intermediate heat exchanger operates in the laminar flow region. The effective tube wall thickness is increased by about (1 / 8) inch of sodium. At 700 deg K the liquid sodium has a thermal conductivity of 70.53 W / m-deg K.

Hence the temperature drop delta T across the (1 / 8) inch thick liquid sodium boundary layer is given by:
875 X 10^6 Wt / 56 bundles = [(delta T) (70.53 Wt / m-deg K) X 823 tubes X 6 m X Pi X (0.5 inch) / (1 / 8)] inch
or
(delta T) = [875 X 10^6 Wt / [(56 bundles) X (70.53 Wt / m-deg K) X (823 tubes / bundle) X 6 m X Pi X (0.5 inch) / (1 inch / 8)]
= 3.57 deg K

The web page FNR HEAT EXCHANGE TUBES
indicates that at full rated power the temperature drop across the intermediate heat exchanger tube metal wall is 7.40 deg C. Hence the total temperature drop across the intermediate heat exchange bundles at full power is about:
3.57 deg C + 7.40 deg C = 10.97 deg C.

NaK Thermal Siphon:
The differential pressure established by the falling sodium column is:
P = [(873.2 -849.4) / 2] kg / m^3 x 6 m x 9.8 m / s^2
= 699.72 kg m / s^2-m^2

Neglecting viscosity:
P = Rho V^2 / 2
or
V = [2 P / Rho]^0.5 = [2 (699.72 kg m / s^2-m^2) / (849.4 kg / m^3)]^0.5 = 1.2836 m / s
= maximum possible falling sodium flow velocity

The corresponding falling sodium volumetric flow rate = 1.2836 m / s X 0.3893 m^2 = 0.4996 m^3 / s

This is about twice the required flow rate. However this flow rate will be retarded by viscosity. This flow rate can be further reduced as required by adding a baffle to the primary side of the intermediate heat exchanger.

It is necessary to maintain the design temperature differential across the reactor in order to develop the required primary sodium natural circulation through the reactor.

Note that each intermediate heat exchange tube bundle contains baffles that cause zig-zag downward flow to enhance heat transfer. The baffle design detail may have to be experimentally optimized. Note that the baffle gives each tube bundle an effective open area on the primary sodium side of about 1 m^2_____.


 

TEMPERATURE CONSTRAINT:

As the primary liquid sodium flows through the reactor at full power its temperature increases from 340 C to 460 C. In this temperature range in a fast neutron flux the fuel tube material HT-9 undergoes goes material embrittlement if it contains any nickel.
 

The corresponding NaK flow rate in the intermediate heat exchange bundle tubes is:
(321.05 m^2 / hr-exhanger) / (823 tubes / exchanger) = 0.3900 m^3 / hr-tube
= (0.3900 m^3 / hr-tube) X (1 hr / 3600 s)
= 1.08333 X 10^-4 m^3 / s-tube

The corresponding intermediate sodium flow rate in the steam generator tubes is:
(321.05 m^3 / hr-exchanger) / (625 tubes / exchanger)
= 0.51368 m^3 / hr-tube
= (0.51368 m^3 / hr-tube) X (1 hr / 3600 s)
= 1.4268 X 10^-4 m^3 / s-tube

The following equations derived on the web page titled FNR PRIMARY SODIUM FLOW can be used to find the pressure drop Pd per round coolant flow tube neglecting natural circulation:
Fv = [Pi Pd Ro^4] / [Muv Zo (N + 2)(N + 4)]BR> where:
Pd = pressure drop along tube in Pa (1 Pa = 1 kg m /s^2 m^2) Fv = volumetric flow rate / tube Pi = 3.14159
Ro = (0.37 inch / 2) X (0.0254 m / inch) = 0.004699 m = tube inside radius
Muv = 3 X 10^-4 N-s / m^2 = sodium viscosity
(N + 2) = Ro [(Rhos Pd) / 2]^0.25 [1 / [Muv Zo]^0.5]
where:
Zo = 6.0 m = tube length
Rhos = 849.4 kg / m^3 = density of sodium at the reactor operating temperature

Recall that:
Fv = [Pi Pd Ro^4] / [Muv Zo (N + 2)(N + 4)]
or
Pd = [Fv / (Pi Ro^4)] [Muv Zo (N + 2)(N + 4)] Equation #1

Recall that:
(N + 2) = Ro [(Rhos Pd) / 2]^0.25 [1 / [Muv Zo]^0.5]
or
N = {Ro [(Rhos Pd) / 2]^0.25 [1 / [Muv Zo]^0.5]} - 2 Equation #2

Try and initial interim value of N = 1.0 in equation #1 and solve for an interim value of Pd.
Substitute that interim value of Pd into equation #2 and solve for a new interim value of N.

Repeat this process itteratively until N and Pd converge.

Then the sum of the Pd values in combination with the exchanger intermediate sodium flow rate give the mechanical load for an ideal circulation pump.

This intermediate liquid sodium flow will develop a momentum change pressure at a sharp 90 degree elbow of:
(2.010 m / s)^2 X 1 m^2 X 927 kg / m^3 = P X 1 m^2
or
P = (2.010 m / s)^2 X 927 kg / m
= 3746 kg / m s^2
= 3746 Pa
= 3746 Pa X 1 bar / 101,000 Pa
= 0.03709 bar

This pressure change is one possible method of measuring the fluid velocity in the pipe.
 

This intermediate liquid sodium flow will develop a momentum change pressure at a sharp 90 degree elbow of:
(2.010 m / s)^2 X 1 m^2 X 927 kg / m^3 = P X 1 m^2
or
P = (2.010 m / s)^2 X 927 kg / m
= 3746 kg / m s^2
= 3746 Pa
= 3746 Pa X 1 bar / 101,000 Pa
= 0.03709 bar

This pressure change is one possible method of measuring the fluid velocity in the pipe.
 

NaK FLOW PATH:
This configuration balances flows, optimizes heat transfer and minimizes thermal stresses. The standard piping connection arrangement for each NaK circuit starting at the 12 inch induction pump: 1 X 12 inch straight pipe, 1 X 12 inch 90 degree elbow, the intermediate heat exchanger lower manifold, the intermediate heat exchange tubes, the intermediate heat exchanger upper manifold, 1 X 12 inch straight pipe, 1 X 12 inch 90 degree elbow, one 12 inch horizontal straight pipe section, 1 X 12 inch 90 degree elbow, 1 X 12 inch straight pipe section, the NaK-salt heat exchanger upper manifold, the NaK-salt heat exchanger tubes, the NaK heat exchanger lower manifold, 1 X 12 inch straight pipe section, 1 X 12 inch 90 degree elbow, 1 X 12 inch X 16 inch adapter, 1 X 16 X 16 X 16 inch tee, 1 X 16 inch to 6 inch adapter down to a NaK dump tank, and a 16 inch connection to the 16 inch induction pump flow tube. There is one small drain/fill valve for each heat exchange loop. This arrangement permits practical and safe identification, isolation, draining, replacement and refilling of any defective heat transport loop component.The pipes must have sufficient positioning play to allow for thermal expansion-contraction and possible earthquake related movement.
 

NaK VOLUME:
The volume of each NaK loop can be estimated by assuming that everywhere along that loop except in the NaK-salt heat exchanger the cross sectional area is approximately the same as the cross sectional area of a 12.75 inch schedule 40S pipe.

Thus the minimum pipe length equivalents are:
Intermediate heat exchanger tibes = 6 m
Steam generator tubes = 6 m
4 Manifolds = ???? Horizontal pipes = 2 X (2 m) = 4 m
Vertical pipes = 4 X 0.5 m = 2 m

Hence total equivalent pipe length = 30 m

System volume = Pi (6.4 inch)^2 X 30 m X (.0254 m / inch)^2 = 2.49 m^3

Required NaK drain down tank volume = _______

Thus the total NaK volume is about:
56 X 2.49 m^3______ = 79.70 m^3_______
 

INSTALLATION:
Each heat exchange gallery has an internal length of 10 m and an internal width of 8.0 m. There is 1.5 m between adjacent loops. There is a 1.25 m clearance at each end.

Equipment in the heat exchange galleries is lowered by crane from above.

An important issue in the heat exchange gallery basement is separation of water and NaK drips. Water is only likely to leak near the outside wall. Elsewhere there could be NaK drips. A cement ridge should be provided across the basement floor to separate these two accumulations.

As a rule of thumb electrical equipment should be mounted on the inside wall which is less subject to water penetration. There will need to be a large air vent in the access stair well end wall for air cooling.

The heat exchange gallery basement water sump pump should flow to a bottom drain at 18 m below grade.

At the basement level the floor is divided so that any NaK drips stay near the inner wall and any water drips stay near the outer wall.
 

WELDING:
The manifold welds must be deep penetration equal in quality to the welds used on high pressure natural gas distribution pipelines. Possibly a helium leak detector should be used for confirming weld quality.
 

This web page last updated Masy 31, 2022

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