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Venting vapor streams: Predicting the outcome

04.01.2012  |  Benintendi, R.,  Foster Wheeler Energy Ltd., Reading, UK

Laminar and turbulent jet theories provide strong support when addressing cold venting situations

Keywords: [cold venting] [laminar theory] [turbulent jet theory] [open discharge] [Norsok] [atmospheric tanks] [ jets] [explosions]

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 considered when:
• 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 calculated as:


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 Tfire.

  Fig. 1.  Atmospheric tank relief scenarios.

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 formula.


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.

Turbulent jet.

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 general equation:


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 distance
  to flammable or toxic endpoint.

Laminar jet.

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 determined as:


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 distance
  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 TLV-STEL indices.

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.

Final analysis.

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 and barriers
• 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 entrainment equations
• 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 affected.

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. HP 

  Fig. 5.  Hemispherical approach to endpoint contour.


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 3,
pp. 373–378, May 2010.
7 Benintendi, R., “Laminar jet modelling for hazardous area classification,” Journal of Loss Prevention in the Process Industries, Vol. 24, Issue 2,
pp. 123–130, March 2011.
8 IEC 60079-10-1 ed 1.0, Explosive atmospheres, Part 10-1: Classification of areas—Explosive gas atmospheres.
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. 612–621, September 2011.
10 ACGIH, Threshold limits values for chemical substances and physical agents and biological exposure indices, 2008.
11 Woodward, J. L., “Estimating the flammable mass of a vapor cloud,” CCPS, American Institute of Chemical Engineers, 1998.

The author 

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.  

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