Chemical Engineering February 2011 - 34

TABLE 2. TYPICAL RESULTS FROM THE APPLICATION OF BAKER'S METHOD
FOR ESTIMATION OF BLAST OVERPRESSURE [3]
Cover Story
at a test pressure of 101 barg. The
resulting Rblast for an overpressure
of 0.5 psig (0.0345 barg) was 156 m.
For comparison, the range predicted
by Equation (4) (to be introduced later
in this article) for fragment range for
brittle fracture (Rbrittle) was 908 m.
Exclusion zones were chosen to insure
that overpressures from rupture
of the piping system could not exceed
0.5 psig (0.0345 barg) at the boundary
of the exclusion zone radius, regardless
of the mode of fracture of the piping
system.
Hazards from projectiles
Rupture of a piping system may occur
due to either ductile fracture or brittle
fracture. Under the planned test conditions
for one LNG project, it was
determined that the carbon-steel systems
might exhibit ductile or brittle
fracture and that the stainless-steel
piping systems might exhibit ductile
fracture. The number of fragments
and the methods of estimating the velocities
of the resulting projectiles differ
for brittle and ductile fracture.
Rupture of a piping system under
pressure may produce projectiles.
Here are Mannan's [1] introductory
remarks on fragmentation resulting
from either brittle or ductile fracture:
" The number of missiles formed in
an explosion involving rupture of containment
varies widely. At one extreme
is the bursting of a weapon such as a
high explosive shell or grenade, which
normally gives a large number of fragments.
Large numbers of missiles are
also produced by fragmentation of a
gas-filled pressure-vessel. At the other
extreme is the ejection of a single item,
such as a valve component, due to failure
in a high pressure system.
Of particular interest here is rupture
of a pressure vessel. This may involve
either brittle or ductile fracture.
... In general, failure is more likely
to be ductile. Ductile failure does not
usually produce missiles, but if it does
they are likely to be small in number
but may have the potential to do
severe damage. It is brittle fracture
which is most likely to produce failures
in which quite a large number of
fragments are generated. "
Theoretical maximum velocity and
range of projectiles. One method of
Input data:
Vessel burst pressure:
102 bar abs Heat capacity ratio:
Distance from vessel center: 156 m
Vessel volume:
Final pressure:
18.84 m3
1.013 bar
abs
Speed of sound in ambient
gas:
475 MJ
7.39
1.4
Molecular weight of gas: 28
Gas temperature:
298 K
298
m/s
Calculated results:
Energy of explosion using Brode's equation for constant volume expansion:
Energy of explosion:
TNT equivalent:
101.4 kg TNT
Effective energy of explosion (X 2): 951 MJ
Scaled distance:
Interpolated scaled overpressure: 0.0244
Interpolated scaled impulse:
Vessel shape:
Overpressure multiplier for vessel
shape:
Corrected scaled overpressure:
Actual overpressure:
1.1
0.0268
0.0272 bar
0.39 psi
Impulse multiplier for vessel shape: 1
Corrected scaled impulse:
Actual impulse:
estimating the theoretical maximum
velocity is to assume that the pressure
energy stored in a piping system is completely
converted into kinetic energy of
the piping system under test [2-3]:
E = (m × v2)/2
(2)
Where E is the energy released upon
piping system rupture; m is the total
mass of projected piping system fragments;
and v is the velocity of each
fragment of the piping system.
The theoretical maximum range
(neglecting air friction) is then calculated
assuming that the projectiles
are launched at a 45-deg angle from
horizontal. An angle of 45 deg is the
optimum angle for the maximum projectile
travel distance. Equation (3)
is based on Newton's second law of
motion and Newton's law of gravitation;
its derivation is found in many
college-level physics textbooks:
Rmax = v2/g
(3)
Where Rmax is the theoretical maximum
range; and g is the acceleration
due to gravity. Distances calculated
with this conservative method are
very large, as can be seen in Table 1.
Calculated values range from 35 to
2,497 m.
The Health and Safety Executive
(HSE) report [2] indicates that only
about 40% of the pressure energy
would be translated into kinetic energy
for brittle fracture of a cylindrical
container during testing, and less en32
CHEMICAL ENGINEERING WWW.CHE.COM FEBRUARY 2011
0.0069
0.00690
Spherical
Cylindrical
1.4
0.0341
0.0346 bar
0.50 psi
1
0.0069
39.3 kPa - ms 39.3 kPa - ms
ergy would be translated into kinetic
energy for ductile fracture of the container.
Thus for brittle fracture, Equation
(4) gives a better estimate of the
theoretical range of missiles:
Rbrittle = 0.4 × Rmax
(4)
Brittle fracture ranges estimated with
Equation (4) are tabulated in Table 1
in the column labeled Rbrittle.
Predicted velocities and ranges of
projectiles from brittle fracture.
Naturally, most fragments would not
launch at the optimum angle, and air
friction would reduce the range as
well. Finally, when two or more fragments
result from rupture of a piping
system, the resulting projectiles will
usually have a distribution of sizes
and initial velocities.
Baker [6] developed methods to estimate
fragment ranges taking shape and
air friction into account. Spreadsheets
developed by the CCPS [3] to apply
these methods were used to develop the
results shown in Table 3 for a 20-in., carbon-steel,
schedule 80 pipe that has broken
into two fragments at a test pressure
of 101 barg. Each of the two fragments is
a section of pipe, flying end-wise with a
lift-to-drag ratio of zero. For comparison,
the range predicted by Equation (4) is
709 m. Representative values calculated
with Equation (4) in Table 1 are used as
estimates of the maximum range of missiles
from brittle fracture.
Field data on projectiles from
ruptured vessels. Mannan [1] pres
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Chemical Engineering February 2011

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