Gas and vapor venting to the
atmosphere from tanks and equipment may provoke hamful effects
due to the flammable, toxic and corrosive properties of the
released substances. Venting lines are generally connected to
flaring or treatment systems, where they are burned or
processed with the aim of preventing harm to personnel and the
environment. Nevertheless, cold vents may not always be
avoided, and, when they are feasible and environmentally acceptable, they
offer significant advantages over alternative methods.
Cold venting is frequent in both
onshore and offshore installations, despite efforts made in the
design phase to prevent or properly manage the emissions. In these cases,
applicable regulations and standards require identification of
the quantitative features of the released streams. This narrows
the engineering choices to consider the acceptability of a
safe, open discharge by implementing the necessary protection.
A general reference is given by API RP 521,1 which
says that disposal can be accomplished without creating a
potential hazard or causing other problems, such as the
formation of flammable mixtures at grade level or on elevated
structures. Also, Norsok standards2 require
that cold vents be based on dispersion calculation results to
prove that explosive mixtures are not created in the installation
vicinity and to ensure that the concentration therein does not
exceed a fraction of the lower flammable limit.
Open discharges should be
Safety valve releases from atmospheric tanks
storing hydrocarbons or organic compounds, in case of process
offset or instrument failure
Releases from rupture disks or emergency-relief
valves (ERVs) from atmospheric tanks storing hydrocarbons or
organic substances, in case of external fire
Emissions from pressure equipment in
onshore and offshore facilities; examples include methane
emissions from common vent stacks or
low-boiling, pressurized compounds.
Release from atmospheric tanks.
Flammable and combustible liquids
stored in atmospheric tanks are assumed to be blanketed with
nitrogen working at a low relative pressure, as shown in Fig.
1. The working conditions are the operating temperature
(TOP ) and the operating pressure
(POP). The relieving scenario assumed for
the pressure relief valve (PRV) is a control valve failure,
with a setting pressure (PS1) and a
corresponding temperature equal to TOP.
Vapor pressure is given by the Antoine equation:
The gas molar fraction corresponding to the set pressure can be
and the nitrogen molar fraction as:
The assumed relieving scenario for the ERVs is external fire,
with a setting pressure
(PS2). The nitrogen
content in the tank head space is assumed to remain the same,
whereas the gas amount will increase due to heating from fire.
Accordingly, if the headspace volume does not change
significantly, the second law of Gay Lussac may be applied:
and the gas molar fraction (XS2)
corresponding to PS2 is:
where PVAP-Tfire is the vapor pressure at
Fig. 1. Atmospheric tank relief
The gas outlet characteristics have now been completely
identified. For the purpose of this work, the released mass
flowrate is essential information, being a venting design issue
covered by the standard API 520.3 The described
scenario has been summarized in Table 1, where input design
data and calculated values have been included. The gas
stripping from a solution can be approached in the same manner,
using gas-liquid equilibrium equations, such as the Henry
Release from pressure vessels.
Cold venting from pressure vessels
is much less frequent than atmospheric venting, and it consists
of a pressurized gas or a vapor in equilibrium with its liquid.
The first case, natural gas in offshore facilities, is completely defined by
the pressure and the geometrical characteristics of the jet,
and the second case can be treated as atmospheric blanketed
storage, being that the substance in both of these cases is
formed by a single compound under pressure.
Modeling aims to describe the
concentration contour of a gas jet downstream from a nozzle
outlet, with reference to specific toxic or fire end points. As
the gas leaves the nozzle, it is entrained by air, strongly
depending on the fluodynamic features and on the wind velocity
and direction. This results in a progressive gas concentration
dilution as both the axial and the radial distance from the
outlet increase (Fig. 2).
Fig. 2. Jet flow showing gas concentration
The theory of turbulent and laminar jet is based on the
original studies of Ricou and Spalding4 and
Schlichting,5 respectively. Momentum driven
turbulent jets from relief valves are also covered by the API
521 standard, and its conclusions fit well with the Ricou and
Spalding theory of entrainment approach.
A full development of the jet air
dispersion model relative to both turbulent and laminar regimes
has been carried out by the author,6,7 with the aim
of predicting the endpoint concentration contour of hazardous
areas due to flammable substances. This method gives much more
realistic results than those provided by the standard IEC
60079-10,8 as confirmed by Webber et al.9
The same models may be used to investigate whether (and to what
extent) gas cold venting is harmful.
According to literature
data6 and to the standard API RP 521, the fully
turbulent regime exists from the Reynolds number of
104 upward. If it is verified, air entrainment works
reducing the jet gas concentration according to the following
Within the equation, Me and M(y)
are the initial and the overall entrained gas mass flowrates at
a distance y from the exit, D is the outlet diameter
and Ce is the coefficient of entrainment,
which is 0.32 according to Ricou and Spalding4 and
0.264 according to the standard API RP 521. This approach has
been followed6 in order to define the distance along
the axis, where the lower flammable or toxic endpoint is
reached. Assuming a cross sectional average gas concentration,
the jet development is as outlined in Fig. 3. Indicating with
EP the flammable or toxic endpoint, with
MWG and MWA as the gas
and air molecular weight, and XMo as the
initial gas mass fraction, the mentioned distance is given by
the following equation:
Fig. 3. Turbulent discharge illustrating
to flammable or toxic endpoint.
The laminar jet theory is based on
the original work of Schlichting.5 Accordingly, the
same calculation carried out for turbulent jet has been
developed7 for the laminar regime, resolving the
mass and momentum equations and obtaining an exact solution for
the axial and radial concentration gradient. The jet surface,
as defined by the points of space where the concentration is
the end point, is given by the following formula:
Within the formula, ∆ is the gas diffusivity in air;
ve is the gas velocity at the outlet;
µ is the gas viscosity; Xo is the
initial gas mass fraction; EP is expressed in the same unit;
and Me is the initial average momentum. As
for the turbulent jet, the distance along the axis, where the
lower flammable or toxic end point is reached, has been
Meanwhile, the maximum transversal distance
REP is calculated as:
In Fig. 4, the endpoint contour has been depicted for a typical
application. In the previous equations, XMo
and Xo are equal to 1 for pure gases.
Fig. 4. Laminar discharge illustrating
to flammable or toxic endpoint.
End points for venting.
Flammable and toxic endpoints must
be defined for the substances under investigation. For fire and
explosion cases, the lower explosion limit (LEL) is entered
into Eq. 8 or Eq. 10, depending on the existing regime. Toxic
clouds can be described in terms of immediately dangerous to
life and health (IDLH), temporary emergency evaluation levels
(TEELs), emergency response planning guides (ERPGs) and acute
emergency guidance levels (AEGLs) or, in accordance with the
applicable safety philosophy, more stringent values can be
assumed. Basic information can also be obtained relative to the
occupational impact of venting, considering TLV-TWA and
The model can easily be adjusted in
the case of a gas mixture containing more than one substance,
other than the inerting gas only. In this case, with reference
to the flammable endpoint, a mixture limit can be calculated
using the Le Chatelier equation:
Within this equation, Xi is the single
component molar fraction.
The same additive mixture formula
applies, as per the ACGIH guidelines,10 to two or
more hazardous substances having a similar toxicological effect
on the same target organs or systems.
Table 2 includes data relative to
an ethyl acrylate storage tank blanketed with nitrogen. The
Reynolds number is higher than 10.000, so the turbulent model
is to be used. The calculation has been carried out considering
both the LEL and the IDLH, obtaining two very different
results. Roughly, it could be concluded that fire and explosion
hazards are unlikely, whereas the toxic scenario does not seem
negligible. A further confirmation of the accuracy of the
method may be found in the volume of J. L. Woodward edited by
the CCPS.11 Here, the concentration profile drawn
for a methane turbulent jet would fit very well with the values
calculated through the model.
An exact method has been presented
with the aim of predicting the outcome of an open discharge
from tanks and equipment. The method has been split into two
different equations, depending on the fluodynamic regime
existing at the jet outlet. The equations can be used in a very
flexible way, since the contour describes the concentration
field of the specific endpoint used, whatever it is. The
results expected could be considered satisfactorily reliable,
provided that the following boundary conditions exist:
A steady state can be assumed
The jet does not impinge over adjacent obstacles
The equipment under investigation is not installed
in a congested zone, where closed spaces and a cul-de-sac can
provoke hazardous gas accumulations and significant
modifications of the concentration profile obtained using the
Borderline cases or specific lay outing and spacing
concerns should be further investigated through CFD and more
accurate dispersion models; the method is very useful in giving
a first estimate of the predictable outcome.
A specific mention must be made
relative to the action of the wind, both on the laminar and the
turbulent jets. Even if it results in an increased air
entrainment, an uncertainty might exist about the direction of
the plume and its profile. This is the case even if the
standard API 521 states that, for high Reynolds numbers, the
turbulent equation is valid anyway, provided that jet velocity
is higher than about 12 m/s or the jet-to-wind velocity ratio
is more than 10. The same standard shows how the effect of the
wind, in terms of wind velocity to initial jet velocity ratio,
is effective in reducing the endpoint vertical downwind
distance; whereas, the horizontal distance is much less
As a conservative application of
the presented model, engineering judgment suggests extending
the hazardous zone to the whole hemispherical volume of radius
equal to the endpoint distance (Fig. 5), and to use an endpoint
concentration equal to 25% of its real value.
Fig. 5. Hemispherical approach to endpoint
1 ANSI/API Standard 521,
Pressure-Relieving and Depressuring Systems, Fifth
Edition, January 2007 (addendum May 2008).
2 NORSOK Standard S-001, Technical Safety,
Fourth Edition, February 2008.
3 API Standard 520, Sizing, Selection and
Installation of Pressure-Relieving Devices in Refineries,
Eighth Edition, December 2008.
4 Ricou, F. P. and D. B. Spalding,
Measurements of entrainment by axisymmetrical turbulent
jets, Journal of Fluid Mechanics, 11(1), 21 e
32, Cambridge University Press, 1961.
5 Schlichting, H., Boundary Layer Theory,
Sixth Edition, McGraw Hill, New York, 1968.
6 Benintendi, R., Turbulent jet modeling for
hazardous area classification, Journal of Loss
Prevention in the Process Industries, Vol. 23, Issue
pp. 373378, May 2010.
7 Benintendi, R., Laminar jet modelling for
hazardous area classification, Journal of Loss
Prevention in the Process Industries, Vol. 24, Issue
pp. 123130, March 2011.
8 IEC 60079-10-1 ed 1.0, Explosive atmospheres,
Part 10-1: Classification of areasExplosive gas
9 Webber, D. M., Ivings, M. J. and R. C. Santon,
Ventilation theory and dispersion modeling applied to
hazardous area classification, Health and Safety
Laboratory, Journal of Loss Prevention in the Process
Industries, Vol. 24, Issue 5, pp. 612621, September
10 ACGIH, Threshold limits values for chemical
substances and physical agents and biological exposure
11 Woodward, J. L., Estimating the flammable
mass of a vapor cloud, CCPS, American Institute
of Chemical Engineers, 1998.
Renato Benintendi is a loss prevention
and process specialist at Foster Wheeler Energy Ltd. in
Reading, UK. He holds a degree in chemical engineering
from the University of Naples Federico II in Italy. He
has been working for 25 years in process safety and environmental projects and has been a
lecturer and a professor of process safety and environmental engineering at
Salerno University and Naples University.