Accidental release source terms

Accidental release source terms

Accidental release source terms are the mathematical equations that quantify the flow rate at which accidental releases of air pollutants into the ambient environment can occur at industrial facilities such as petroleum refineries, petrochemical plants, natural gas processing plants, oil and gas transportation pipelines, chemical plants, and many other industrial activities. Governmental regulations in a good many countries require that the probability of such accidental releases be analyzed and their quantitative impact upon the environment and human health be determined so that mitigating steps can be planned and implemented.

There are a number of mathematical calculation methods for determining the flow rate at which gaseous and liquid pollutants might be released from various types of accidents. Such calculational methods are referred to as "source terms", and this article on accidental release source terms explains some of the calculation methods used for determining the mass flow rate at which gaseous pollutants may be accidentally released.

Accidental release of pressurized gas

When gas stored under pressure in a closed vessel is discharged to the atmosphere through a hole or other opening, the gas velocity through that opening may be choked (i.e., it has attained a maximum) or it may be non-choked.

Choked velocity, also referred to as sonic velocity, occurs when the ratio of the absolute source pressure to the absolute downstream pressure is equal to or greater than [("k" + 1) ÷ 2 ] "k"÷("k" - 1 ), where "k" is the specific heat ratio of the discharged gas (sometimes called the isentropic expansion factor and sometimes denoted as gamma).

For many gases, "k" ranges from about 1.09 to about 1.41, and therefore [("k" + 1) ÷ 2 ] "k"÷("k" - 1 ) ranges from 1.7 to about 1.9, which means that choked velocity usually occurs when the absolute source vessel pressure is at least 1.7 to 1.9 times as high as the absolute downstream ambient atmospheric pressure.

When the gas velocity is choked, the equation for the mass flow rate in SI metric units is:"Perry's Chemical Engineers' Handbook", Sixth Edition, McGraw-Hill Co., 1984.] "Handbook of Chemical Hazard Analysis Procedures", Appendix B, Federal Emergency Management Agency, U.S. Dept. of Transportation, and U.S. Environmental Protection Agency, 1989. Also provides the references below:
– Clewell, H.J., "A Simple Method For Estimating the Source Strength Of Spills Of Toxic Liquids", Energy Systems Laboratory, ESL-TR-83-03, 1983.
– Ille, G. and Springer, C., "The Evaporation And Dispersion Of Hydrazine Propellants From Ground Spill", Environmental Engineering Development Office, CEEDO 712-78-30, 1978.
– Kahler, J.P., Curry, R.C. and Kandler, R.A.,"Calculating Toxic Corridors" Air Force Weather Service, AWS TR-80/003, 1980.
[ Handbook of Chemical Hazard Analysis, Appendix B] Scroll down to page 391 of 520 PDF pages.] "Risk Management Program Guidance For Offsite Consequence Analysis", U.S. EPA publication EPA-550-B-99-009, April 1999. [ Guidance for Offsite Consequence Analysis] ] "Methods For The Calculation Of Physical Effects Due To Releases Of Hazardous Substances (Liquids and Gases)", PGS2 CPR 14E, Chapter 2, The Netherlands Organization Of Applied Scientific Research, The Hague, 2005. [ PGS2 CPR 14E] ]

Q;=;C;A;sqrt{;k; ho;P;igg(frac{2}{k+1}igg)^{(k+1)/(k-1)

or this equivalent form:


For the above equations, it is important to note that although the gas velocity reaches a maximum and becomes choked, the mass flow rate is not choked. The mass flow rate can still be increased if the source pressure is increased.

Whenever the ratio of the absolute source pressure to the absolute downstream ambient pressure is less than [ ( "k" + 1 ) ÷ 2 ] "k" ÷ ( "k" - 1 ), then the gas velocity is non-choked (i.e., sub-sonic) and the equation for mass flow rate is:

Q;=;C;A;sqrt{;2; ho;P;igg(frac{k}{k-1}igg)Bigg [,igg(frac{;P_A}{P}igg)^{2/k}-;,igg(frac{;P_A}{P}igg)^{(k+1)/k};Bigg] }

or this equivalent form:

Q;=;C;A;P;sqrt{igg(frac{2;M}{Z;R;T}igg)igg(frac{k}{k-1}igg)Bigg [,igg(frac{;P_A}{P}igg)^{2/k}-;,igg(frac{;P_A}{P}igg)^{(k+1)/k};Bigg] }

"The U.S. EPA method"

The following equations are for predicting the rate at which liquid evaporates from the surface of a pool of liquid which is at or near the ambient temperature. The equations were developed by the United States Environmental Protection Agency using units which were a mixture of metric usage and United States usage. The non-metric units have been converted to metric units for this presentation.

E = frac{0.1268cdot Acdot Pcdot M^{0.667}cdot u^{0.78{T}

Adiabatic flash of liquified gas release

Liquified gases such as ammonia or chlorine are often stored in cylinders or vessels at ambient temperatures and pressures well above atmospheric pressure. When such a liquified gas is released into the ambient atmosphere, the resultant reduction of pressure causes some of the liquified gas to vaporize immediately. This is known as "adiabatic flashing" and the following equation, derived from a simple heat balance, is used to predict how much of the liquified gas is vaporized.

X = 100;frac{H_s^L - H_a^L}{H_a^V - H_a^L}

If the enthalpy data required for the above equation is unavailable, then the following equation may be used.

X = 100cdot c_pcdot (T_s - T_b)/H

ee also

*Choked flow
*Orifice plate
*Flash evaporation


External links

* [ Ramskill's equations] are presented and cited in this pdf file (use search function to find "Ramskill").
*More release source terms are available in the feature articles at []
* [ Choked flow of gases]
* [ Development of source emission models]

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