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Section summary |
---|

1. Introduction |

2. Pre-requisites
to the sizing of dust explosion vents |

3. Method limitations |

4. Calculation procedure |

5. Dust explosion vent ducts |

6. Other calculation methods |

It is mandatory for a factory operator to perform a dust explosion
risk assessment and put in place all the measures required to
prevent explosions. Sometimes however the residual risk is too high
and **explosion mitigation measures must be implemented such as
explosion panels on hopper, silos, filters on some conveyors**.
This page is explaining how are built explosion panels and propose
approximates methods to size them.

**The methods presented here are not accurate,
they are used only as illustration of the concepts guiding the
design and as a 1st approximation for budgetting for instance but
MUST NOT BE USED FOR DETAIL DESIGN. FOR ACTUAL IMPLEMENTATION
ALWAYS CONTRACT A REPUTABLE COMPANY TO SIZE AND INSTALL THE PANEL.**

In order to be able to size an explosion panel allowing to relieve the pressure of a dust explosion, it is necessary to know "how" the dust will explode, that is to say it is required to measure the dust explosion properties of a material. Especially, the following must be known :

- Kst
- Pmax

The sizing of the explosion panel will change according to the volume, shape and the design pressure of the vessel to protect. It is therefore required to gather the following :

- Maximum allowable working pressure
- Volume of the vessel
- Ratio length (height) over diameter : L/D

The method presented is only valid with the following assumptions :

- Volume in between 0.1 and 10000 m3
- Static activation pressure of the vent in between 0.1 and 1 bar g
- Reduced explosion pressure in between 0.1 and 2 bar g, and should be at least equal to the static activation pressure 2 times the vent burst pressure tolerance
- Pmax in between 5 and 10 bar if Kst is in between 10 and 300 bar.m.s-1
- Length/Diameter ration L/D in between 1 and 20 ; with vertical shaped hoppers (if the shape is horizontal, this method will not apply)
- Pressure at ignition < 110 kPa and oxygen concentration < 21%

As explained above

Considering a vertical cylindrical hopper, the ratio height over
diameter L/D will depend on the position of the vent which typically
can be either install on the top, or on the side. The "length" is
then the maximum length that the flame, L_{eff}, will have
to travel in order to exit the vessel through the explosion vent.

In case a cone is present, the contribution of the cone to the flame effective length is considered to be 1/3 of the cone height [SHAPA 1].

The "diameter" is also actually an effective diameter that must be calculated thanks to the calculation of the effective volume.

*Note that in some cases, the longest flame path can be from the
top of the hopper to the bottom of the explosion panel. It can be
the case for some filters.*

A = B*[1+C*log_{10}(L/D)]

B = [3.264*10^{-5}*P_{max}*Kst*P_{red}^{-0.569}+0.27*(P_{stat}-0.1)*P_{red}^{-0.5}]*V^{0.753}

C = [-4.305*log_{10}(P_{red})+0.758]

With :

A = required vent area in m^{2}

V = actual volume of the vessel in m^{3}

Kst = explosion pressure increase rate in bar.m/s

P_{max} = maximum explosion pressure in bar

P_{red} = reduced explosion pressure in bar (it is the
target maximum pressure in the vessel reached after the explosion
vent has burst open)

P_{stat} = static opening pressure of explosion vent in bar
(it is the design static pressure at which the explosion vent will
open)

L/D = L/D_{eff} = shape ratio of the vessel protected by the
explosion vent

**[SHAPA 2] is mentioning that an efficiency** must be taken
into account to correct the calculated venting area. It is then
critical to design the vent with the manufacturer which will then be
able to determine the efficiency of the explosion vent. Such design
should not be done alone by factory operators.

If the efficiency is, let's say 90%, then the actual area required will be A/0.9

The hopper to protect is located at the end of a pneumatic
conveying line. It is a conical hopper equipped with a filter and
for which the factory has determined by its dust explosion risk
analysis that it will have to be fitted with a side explosion panel.
The factory would like to check the size of the panel required, to
make sure it can install it, and then get an idea of the cost. This
work is done during basic design **and then the company plans to
hire a specialized company to confirm during detail design**.

The hopper has the following dimensions :

- D = 2 m diameter
- Cylindrical height H
_{shell}= 3 m - Position of vent must be above the level of product, it is 1 m
from top of hopper, H
_{vent}= 2 m - Cone height h
_{cone}= 2.5 m - Cone outlet diameter d
_{o}= 0.25 m

STEP 1 : gather the dust explosion characteristics

The product being stored has the following characteristics :

- Kst = 150 bar.m/s
- Pmax = 8.5 bar

Considering the mechinal resistance of the hopper, the factory wishes that the vent opens at 0.2 bar g and the residual pressure Pred do not exceed 0.5 bar g.

STEP 2 : define the ration L/D

- Effective flame length L
_{eff}= 2.5/3+2 = 2.8 m (see case 2 of paragraph 4.2) - The effective volume V
_{eff}= π.D^{2}/4*H_{vent}+(2*π/3*(D^{2}/4+(D/_{2}*d_{o}/2)+d_{o}^{2}/4)/3 = 7.08 m3 - The effective diameter is then D
_{eff}= 2*(V_{eff}/L_{eff}/π)^{0.5}= 1.78 m - The ratio L/D
_{eff}= 2.8/1.78 = 1.58

The required vent size can then be calculated :

- V = 12.4 m3 (the top cover is considered flat here to simplify calculations)
- B =0.66
- C =2.05
**A = 0.94 m2**

**It is required to install a vent with a size >0.94 m2 to
protect the hopper.**

**WARNING : the calculation above is
only for illustration on this website, it cannot be used for
detail design, any other use is at the own risk of the user.
Detail design must be done with a company specialized.
**

It is sometimes required to direct the explosion flame and pressure
wave away from the equipment, outside a building for example. It is
done through the implementation of a duct at the outlet of the
explosion vent. **The presence of the duct is an important design
parameter as it will influence the actual reduced explosion
pressure reached in the vessel protected**. After calculating
the required venting area through the method explained above, it is
therefore ** required to correct the reduced explosion pressure
due to the presence of a vent**. If the reduced explosion
pressure is too high, then the vent design must be adjusted.

In any case, the diameter of the duct must at least be equal to the diameter of the vent. [SHAPA 2] is mentioning that the duct should be straight.

The reduced pressure in the presence of a vent can be calculated, for vessels of a maximum size of 100 m3 by the following formula [Laurent] :

P'_{red}/P_{red} = 1+17.3*(A/V^{0.753})^{1.6}(L/D)

With :

P'_{red} = reduced pressure with a duct (bar g)

P_{red} = reduced pressure without duct (bar g)

L = length of the duct (m)

D = diameter of the duct

One important point to consider is for flameless venting (flame arrestors) : a study [Gregoire] showed that the formula above were not directly applicable for these kind of vents as the fluid dynamics are totally different due to the present of a filter. Those systems are presenting a lot of advantages but their sizing must definitively be given to their sole manufacturers, only entities with enough data to size these vent adequately.

The method given above is actually derived from an earlier method called "nomograph" method. It is a graphical method that was proposed as a german VDI norm from 1979 and revised several times then. This method was used as a basis of other norms in US, France...etc...

[Laurent] is reporting that the equations above can be slightly modified in order to take into considering the turbulence in the vessel at the moment of the explosion, which is a very important parameters influencing it.

A coefficient of turbulence τ is introduced, with τ that should be in between 0 and 3.5 :

Source

[SHAPA 1] Sizing of explosion relief vents, SHAPA Technical
Bulletin 10

[SHAPA 2] Sizing of explosion
relief vents, SHAPA Technical Bulletin 10 revised, 2013

[Laurent] Securite des procedes
chimiques, Andre Laurent, Tec et Doc, 2003, pages 257-261

[Gregoire] Flameless venting,
achievements and difficulties, Gregoire et al, Ineris, 2016