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Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer

Summary
This document details a thermodynamically sound method for calculation of flare tip pressure. The
pressure of a flare tip is an important parameter in predicting flare operational performance. The
justification for this document is because standard reference document1 API-RP-521 entirely omits
details for determination of flare tip pressure. Another standard reference document2 GPSA
Engineering Data Book uses Straitz method a to l to determine flare tip pressure. The Straitz method
determines pressure drop as 1.5 velocity heads. However Straitz method uses a form of velocity
head strictly suitable to liquids. The Straitz method is not suitable where pressure change is
greater than 10% of initial pressure, (Crane4 pg. 3-3). The approximate limits of Straitz method are
between 0.25 Mach and 0.4 Mach for methane and propane respectively. Another recently
published3 pressure drop method is similar to the Straitz method. This paper concurs the
recommendation Crane TP-410: gas flow across a nozzle is adiabatic (Crane4 pg. 1-9). The
adiabatic pressure drop calculation has been applied successfully to a wide range of flow nozzles
such as gas well chokes, metering orifices, and relief/ control valves.
Flare Tip Pressure
Perhaps pressure of the flare tip is the most critical parameter in evaluation and design of flares.
This is due to flare tip sizing parameters relate to tip velocity and tip velocity relates to pressure.
The tip pressure sets the pressure profile through out the entire flare header. Ignoring Flare tip
pressure drop will result in under estimation of noise level by between 7 and 13 decibels.
Additionally ignoring flare tip pressure will under rate the flow capacity of subsonic flare.
However most discussions on flare sizing omit details on calculation of tip pressure or relegate tip
pressure to a set of ranges8. Some methods t, u relates tip velocity to the radiant heat11 fraction
emitted by a flame.
The proposed method expresses pressure drop as an implicit function, based on the adiabatic gas
flow equation.

This method is generally applicable to a wide variety of nozzle flows, such as orifice plates, relief
valves at subsonic flow, control valves, etc. The details of this equation are presented in the
following Table, based on common field units, as applied to gas well choke nozzles. Since a flare tip
is an engineered piece of equipment just like a choke valve, basic performance parameters should
therefore be specifiable.
A calculation spreadsheet was prepared to allow pressure drop calculation per the adiabatic
method. The solver routine was implemented since pressure drop is an implicit value in equation
5.2, above. The Crane method4 is used to generate the initial estimate for the implicit solution.

[1]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer

The Choke Valve Method9
Mach number is a ratio between sound velocity in gas
divided into gas flow velocity.
Determination of Critical Pressure Drop or Critical
Pressure Ratio, CPR

The CPR is the minimum pressure ratio for sonic
flow, and for any larger pressure ratio, flow inside
a nozzle is subsonic, M<1.
The pressure ratio is conventionally defined as
pressure upstream divided into downstream
pressure. Since flow is always in a direction of
decreasing pressure, pressure upstream will be
larger than pressure downstream. At pressure
ratio of 1, flow is zero. From thermodynamics CPR
is determined by formula 5.1.
d/D = 33/36 = 0.92

C = 0.92 + 0.33 + 0.09 = 1.34
Since Nre>1E6, use C =1.2, as per example

Nre = 20 (651,430)*0.9883/(0.01245*33) =3.2E7

[2]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer

The following charts offer a comparison of spreadsheet results using the Zink Company
publication5. A certain amount of variation is expected, given the lack of accurate flare tip pressure
from most flare tip performance calculation methods.

[3]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer
References:
1.

Anon., Guide for Pressure-Relieving and De-pressuring Systems, RP-521, 5th edition, The American Petroleum
Institute (API), Washington, D. C., January 2007 & update ISO 23251, {no change to procedures offers no specific directives to
calculate pressure drop and pressure drop is required to determine tip pressure, which is required to determine Velocity or Mach Number} : With a
proper tip design, most commercial flares have flame retainers that restrict flow area by 2 percent to 10 percent; the flame of the main stream can be
anchored in the boundary regions where velocity gradient would otherwise far exceed the critical value for blowoff . There is evidence; 16, 17, 18; that
flame stability can be maintained at relatively high velocities depending on the discharge properties and the type of tip used. Both blowoff and flashback
velocities are greater for fuels that have high burning velocities. Small amounts of hydrogen in a hydrocarbon fuel widen the stability range because
blowoff velocity increases much faster than flashback velocity. Designs may be based on velocities of 0.5 Mach or higher, if pressure drop, noise, and
other factors permits. Flare stack diameter is generally sized on a velocity basis, although pressure drop should be checked. One may want to permit a
velocity of up to 0.5 Mach for a peak, short-term, infrequent flow, with 0.2 Mach maintained for the more normal and possibly more frequent
conditions for low-pressure flares, depending on the following: (a) volume ratio of maximum conceivable flare flow to anticipated average flare flow; (b)
the probable timing, frequency, and duration of those flows; and (c) the design criteria established for the project to stabilize flare burning. 5.4.3.1.1
However, sonic velocity operation may be appropriate for high-pressure flares. Smokeless flares should be sized for the conditions under which they are
to operate smokeless. Equation 23 or 24 can be used to calculate the Mach number (see 5.4.1.3.2). Velocity limitations imposed by CFR 60.18 do not
apply to flares in emergency relief service. Pressure drops as large as 2 psi (14 Kpa) have been satisfactorily used at the flare tip. Too low a tip
velocity can cause heat and corrosion damage..//offers no specific directives to calculate pressure drop//

2.
3.

4.

Anon., Engineering Data Book, 10th edition, Section 5 - Relief Systems, Gas Processors Suppliers Association,
1987. Sizing based on Straitz method, see below citations A to L
Anon, Quick Estimate of Flare Tip Pressure Drop, Chemical & Process Technology pp11-14, March 2009 AFSA or

FLARENET is commonly used for flare network modeling. In calculating back pressure at the PRV, flare tip pressure drop is required.
However, the pressure drop of flare is subject to Flare tip vendor design. How shall engineer determine the pressure drop of flare tip
without vendor information especially during conceptual design ? … Pressure drop provided by vendor shall always be used during
detailed design For a sonic flare tip, pressure drop may range: … 3 - 5 bar. (or) .. up to 7 bar …. For a subsonic flare tip, pressure drop
is generally very small (possibly lower than 1 bar) equation offered: dKpa= 10 ^ {a(Log (scm/hr/3.6))+b}., a<1.5,2>, b<-8.3,-5.3>,
standard definition is 101.325 kPa abs and 15 deg C DN250 tip, dP = 10 ^ ( 1.77 x Log Q - 5.29) = 10 ^ ( 1.77 x Log 30000/3.6 5.29) = 46 kPa //note; this is not adiabatic pressure drop, Crane TP-410 states: flow across nozzle is an adiabatic process//

Anon, “Flow of Fluids Through Valves, Fittings, and Pipe,” Technical Paper Number 410, Crane Co., New
York, 1957, p1-9 compressible fluids discharge … considered to be adiabatic.. supported by experimental data discharging air to
atmosphere pp. 3-3 compressible flow… when dP less than 10% of P1…2-14&15, and A-19 to A-21 detail Y method for gas flow

5.

6.
7.

Schwartz, R. E. and White, J. W. Flare Radiation Prediction: A Critical Review ZINK Corp., AIChE 1996 Annual
LP Symp. Session 12 Flare Stacks The authors have designed hundreds of flares which have discharge velocities greater than 0.5

Mach at maximum flow. . In choosing a discharge velocity one must always take care to avoid over pressuring the relief system. //
offers no calc guidance except refer to API//

Beychok, M.R. Fundamentals of Stack Gas Dispersion, Ch11 Flare Stack Plume Rise, 4thed. New Port Beach CA.
2005
Vatavuk, B., Pollution Control Equipment Cost, U.S. EPA, OAQPS Ch7 Flares Radian Corp RTP NC 1998 discuss

need to know velocity and pressure at tip but offers no calc guidance) (7.1) The EPA requirements for flares used to comply with EPA
air emission standards are specified in 40 CFR Section 60.18. The requirements are for steam-assisted, air-assisted, and non-assisted
flares. Requirements for steam-assisted, elevated flares state that the flare shall be designed for and operated with: C an exit velocity at
the flare tip of less than 60 ft/sec for 300 Btu/scf gas streams and less than 400 ft/sec for >1,000 Btu/scf gas streams. For gas streams
between 300-1,000 Btu/scf the maximum permitted velocity (V, ft/sec) is determined by the following max equation:
log10(Vmax)=((Bv+1214)/852), where B is the net heating value in Btu/scf, v, The actual maximum capacity of a flare tip is usually
limited by the vent stream pressure available to overcome the system pressure drop. Elevated flares diameters are normally sized to
provide vapor velocities at maximum throughput of about 50 percent of the sonic velocity of the gas subject to the constraints of CFR
60.18. The physical limitation on the quantity of steam that can be delivered and injected into the flare flame determines the smokeless
capacity of the flare. Smokeless capacity refers to the volume of gas that can be combusted in a flare without smoke generation. The
smokeless capacity is usually less than the stable flame capacity of the burner tip. A pressure drop calculation is required at this point to
ensure that the vent stream has sufficient pressure to overcome the pressure drop occurring through the flare system at maximum flow
conditions. The pressure drop calculation is site specific but must take into account losses through the collection header and piping, the
knock-out drum, the liquid seal, the flare stack, the gas seal, and finally the flare tip. Piping size should be assumed equal to the flare tip
diameter. Schedule 40 carbon steel pipe is typically used. The design pressure drop through the flare tip can range from 0.1 to 2 psi
with the following approximate pressure drop relationships:[5] Gas seal: 1 to 3 times flare tip pressure drop Stack: 0.25 to 2 times flare
tip pressure drop Liquid seal and Knock- 1 to 1.5 times flare tip pressure drop plus out drum: pressure drop due to liquid depth in the
seal, which is normally 0.2 to 1.5 psi. Gas collection system: calculated based on diameter, length, and flow. System is sized by designer
to utilize the pressure drop available and still leave a pressure at the stack base of between 2 and 10 psi. Typical total system pressure
drop ranges from about 1 to 25 psi.[5] This approach will encourage higher flare tip exit velocities, which promote higher combustion
efficiencies..

[4]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer
8.

9.
10.

Czaikowski, M., P. Process Engineering Design Guide Relief System Design: 3DGV88D1, Bechtel Corp. 2004
11.5 Super-sonic Furnace Burner used offshore to save weight. 11.5.3.1 The tip diameter and pressure drop through the stack, for
elevated flares, should be checked and confirmed by the flare vendor to ensure that excessive back pressure has not been imposed in
the header system. 11.3 For initial estimating purposes the following guidelines may be used: Equipment Pressure Drop (psi) Flare
Tip 0.5 – 2.0 Molecular Seals 0.5 – 1.0 Fluidic Seals 0.1 Seal Pots 1.0 – 1.5 Note: For ground flares, additional pressure drop should
be allowed for staging valve operation. The staging control valve differential pressure is usually 5 - 10 psi or more. The ground flare
vendor should be consulted to confirm the pressure drop. Note that the API method (Example 1 in API 521 Appendix C) provides
satisfactory results when the target is relatively far from the flare tip, but overestimates the radiation when the target is close by (meaning
API not good means for determination of flare stack height: opa). Section 3.19 should be followed. This section should be interpreted to read
that the depressuring target of 50% of design pressure or 100 psig (whichever is lower) in 15 minutes should be used whenever leakage
of vessel contents leading to a fire is a concern. A standard of 50% of design pressure in 15 minutes is used when the depressuring is
for process reasons only, not fire, and the vessel wall thickness is 1‖ or greater. John Zink Co. suggests a 0.01 ft/sec minimum purge
gas rate under most conditions, with up to 0.03 ft/sec minimum in special circumstances. In general, the purge gas rate should be
specified by the molecular seal vendor. vendor of the device should confirm the steam requirements for smokeless burning. Most often
it is impossible or economically impractical to supply sufficient steam to render the flare smokeless under maximum relieving
conditions. ergo.

Gao, B. & Ghalambor, A. Natural Gas Engineering Handbook, Ch7 Choke Performance GPC Houston TX 2005
This reference provided the adiabatic pressure drop equations recommended for Tip Pressure Drop calculation, this equation was
selected as it is in a field units format. The examples are direct cuts from this document.

Ludwig, E.E., Applied Process Design For Chemical and Petrochemical Plants, Vol. 1, 3rd Gulf Publishing Co.,
Houston, TX, Section 9.125-9.129 Flares/Flare Stacks 1995. {Offers no calc method on flare pressure drop, most material offered
follows GPSA (Straitz Method)or API methods: 9.127: For specific details, consult a flare system design manufacturer (who use proprietary systems?),
9.126: Pressure drops across the tip of the flare have been used satisfactorily up to 2psi. It is important not to be too low and get flashback (without a
molecular seal) or blow off where the flame blows off the tip; 9.137, V, fpsexit, = 550√((dpinchH2O)/55), (the method leads to the a quadratic tip pressure
as density depends on pressure} 

11. Guidard, S.E., Kindzierski, W.B. and Harper N.,. Heat Radiation from Flares. Report prepared for Science and
Technology Branch, Alberta Environment, ISBN 0-7785-1188-X, Edmonton, Alberta, 2000 ―A matrix summarizing
which parameters have been used to determine the fraction of heat radiated for each of these relationships is ‗detailed‘. The
applicability of these relationships to the general case is limited. The theoretical or empirical conditions for which many of these
relationships are based upon are situation-specific. In addition, limited information was provided in many instances on numerous
parameters that are known to influence flare heat radiation losses (e.g. stack exit velocity, crosswind velocity, aerodynamics of the
flame, etc.) .. Determination of the thermal radiation emitted from flares is important in facility design, since it establishes the required
flare site and stack height in order that workers and equipment are protected‖ Chamberlain (1987) noted that Equation 8
(Ludwig‘60/API Heat Rad. Eqn.) has been successfully applied to onshore refinery flares for many years. However, he indicated that it
is of limited use offshore because it can only predict thermal radiation accurately in the far field (the opposite to what Brzustowski and
Sommer (1973) reported).”

12. Banerjee, K. Flare Gas Systems Pocket Handbook 1st Ed. Gulf Publishing Co., Houston, TX, 1985 {Offers no calc
method on flare pressure drop, most material offered follows API methods or based on Kent‘s method:}

13. Zelensky M.J. Sour Well Test Flaring Permit Application Process and Dispersion Modeling Nonographs,
Alberta Energy Utilization Board, Calgary 09/2001 4.3.2 The minimum recommended exit velocity at the flare tip is based on the flare
research at the University of Alberta (1998). They found that the flare efficiency was strongly sensitive to crosswinds and that higher exi t velocity flares
are less prone to becoming inefficient. In general, flare efficiency exceeded 99 percent if the flare tip exit velocity exceeded the wind speed at the flare
tip. The wind speed at the flare tip changes hour-by-hour while flaring so a statistical approach was taken. The 99th percentile wind speed (U99, m/s)
for Alberta was determined to be 10.28 m/s at the standard 10 m reference height, based on AENV‘s six regional meteorological data sets. U99 at 10 m
is adjusted to the wind speed at flare tip height (h, m) using a power profile with an exponent of 0.15 for the neutral stabi lity conditions associated with
high wind speeds. The approach adopted by the U.S. EPA (1992b) from Beychok (1979) was used to account for the flame height required for
combustion. The effective stack height (Hs, m) is based on the flare stack tip height (H, m) and a portion of the flame lengt h (Hf, m) that depends on
the maximum heat release rate (EM). Hf = 0.00456*(EM)0.478 Hs = Hf+h The flame length correlation is based on the maximum heat release rate
assuming complete combustion. The constant of 0.00456 assumes the flame is tilted at an angle of 45 degrees to the horizontal by the wind and that the
effective stack height is the center of the tilted flame. Using one-half of the flame length is a conservative assumption. High wind speeds are required to
tilt the flame 45 degrees. This approach is a reasonable compromise and avoids the complications of making the effective height a function of wind
speed and actual flare tip exit velocity

[5]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer

Citation References as critical in the developmental concepts of flaring technology
a.
b.
c.
d.
e.

Straitz, J.F., and R.J. Altube, ―Flares: Design and Operation‖, Pub. National Air-Oil Burner Co., Inc. 1980
Straitz, J.F., ―Make the Flare Protect the Environment‖, Hydrocarbon-Processing, (56), pp131/35, Oct 1977
Straitz, J.F., "Flaring for Safety and Environmental Protection" Drilling-DCW, November, 45-48. (1977)
Straitz, J.F., "Solving Flare Noise Problems" Inter. Noise 78, San Fran. 8-10 May pp1-6 (1978)
Straitz, J. F. "Nomograph Determines Proper Flare-Stack Height." Oil, Gas, & Petrochem Equipment, v.25n.10, p.25
August, 1979 (ISSN 00301353)

f.
g.
h.
i.
j.

Straitz, J. F. "Smokeless Flaring at High Rates." ASME Pet Mech Eng Symp, Philadelphia, PA, pp.105/11, Sept.1982
Straitz, J. F. ―High Performance Offshore Flares." 4th International flare seminar Norway, 1986
Straitz, J.F., "Flare Technology Safety" Chem. Eng. Progress, v.83n.7 July, pp53-62, (1987)
Straitz, J.F., "Improve Flare Design" Hydrocarbon Processing, v.73n.10 October, pp61-66, (1994)
Straitz, J.F., et-al., "Flare Pilot Design" 1996 International Symposium, Combustion in Industry—Status and Needs
into the 21st Century, Baltimore, MD 1996
k. Straitz, J.F., "Clearing the Air, About Flare Systems" Chemical Engineering, 103(9) 1996
l. Straitz, J.F.,"Improve Flare Safety to meet ISO-9000 Standards" Hydrocarbon-Processing. v.75n.6,4pp Jun 1996,
m. Brzustowski, T.A. and Sommer E.C., ―Predicting Radiant Heating from Flames‖, Proceedings Div. of Refining,
API v. 53, pp. 865-893, 1973.
n. Brzustowski, T. A., A Model for Predicting the Shapes and Lengths of Turbulent Diffusion Flames Over
Elevated Industrial Flares, Proceedings 22nd Canadian Chemical Engineering Conference, Toronto, 1972.
o. Oenbring, P.R. and Sifferman T.R., ―Flare Design: Are Current Methods Too Conservative?‖ HydrocarbonProcessing, v59n5, pp124-129, 1980
p. Kent, G. R., ―Practical Design of Flare Stacks‖ Hydrocarbon Processing, v43n8 pp121-125, 1964
q. Hajek J. D. and Ludwig E. E., ―How to Design Safe Flare Stacks,‖ Part 1, Petro/Chem. Engineer; 1960, v32, n6, pp.
C31-C38; Part 2, Petro/Chem. Engineer; 1960, v32n7, pp. C44-C51, 1960
r. Narasimhan, N.D., ―Predict Flare Noise‖, Hydrocarbon-Processing, v.65, n4. p133, 1986
s. Tan, S. H., ―Flare System Design Simplified‖, Hydrocarbon-Processing , v46n1, p172-176, 1967
t. Chamberlain, G. A. ‗Developments in Design Methods for Predicting Thermal Radiation from Flares’, Chemical
Engineering, Research and Design, Volume 65, July 1987
u. Cook, D. K., Fairweather, M., Hammonds, J. and Hughes, D. J. ‗Size and Radiative Characteristics of Natural
Gas Flares. Part 1 – Field Scale Experiments, Part 2 – Empirical Model, Chemical Engineering, Research and
Design, Volume 65, July 1987, pp318-325, 310-317., 1987 method for rad of sonic flares
v. Barnwell, J. & Marshall, B. K. ‗Offshore Flare Design To Save Weight‘ American Institute of Chemical Engineers
Meeting, November 1984, San Francisco, California, 1984
w. Smith-SK; Selle-GK, Supersonic, High Pressure, Low Radiation Flare System Design, Offshore-TechnologyConference,-Annual-Proceedings. v 4 1997, Offshore Tech Conf, Richardson, TX, USA. 14p Proceedings of the 1997
29th Annual Offshore Technology Conference, OTC'97. part 4 of 4. Houston, TX, USA
x. Magda-W; Marcinkowski-T; Mazurkiewicz-B-K Cantilevered flame boom – the effect of wind on flare exit angle
Proceedings of the Sixth (1987) International Offshore Mechanics and Arctic Engineering Symposium. Houston, TX,
USA Publ by ASME, New York, NY, USA p 275-279
y. Bjorge T, Bratseth A, Measurement of radiation heat flux from large scale flares JOURNAL OF HAZARDOUS
MATERIALS 46: (2-3) 159-168 APR 1996
z. Beeri Z, Blunsdon CA, Malalasekera WMG, Dent JC Comprehensive modeling of turbulent flames with the
coherent flame-sheet model .2. High-momentum reactive jets JOURNAL OF ENERGY RESOURCES
TECHNOLOGY-TRANSACTIONS OF THE ASME 118: (1) 72-76 MAR 1996

[6]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer

F Factor
Use
0.15
Hydrogen
0.2
Methane
0.3
Higher MW Hydrocarbons
The following thermal radiation limits apply for personnel: Conditions Maximum Heat Intensity BTU/hr/
sf Operating areas where personnel are not shielded from radiation 1000 Operation areas where

personnel are shielded from radiation, by virtue of equipment, pipeways and the like 1500 Operating
areas where no shelter exists and only escape is required 3000 Operating area in which personnel
normally do not work and where shelter is available 5000 The issue of whether or not these limits

include solar radiation is left open in APIRP 521.
The use of a molecular seal (See Section 11.6.2) should allow substantial reduction of the
purge gas rate. John Zink Co. suggests a 0.01 ft/sec minimum purge gas rate under most
conditions, with up to 0.03 ft/sec minimum in special circumstances. In general, the purge gas
rate should be specified by the molecular seal vendor. Manufacturer of the device should
confirm the steam requirements for smokeless burning. Most often it is impossible or
economically impractical to supply sufficient steam to render the flare smokeless under
maximum relieving conditions. The following guidelines are offered as reasonable compromises
for smokeless flare design basis: Design for the maximum individual requirement, such as the
FCC relief gas, that is normally large and contains large quantities of unsaturates. Design for
20% of maximum rate that typically results in about 95% of the relief occurrences being
smokeless. Design for maximum rate but provide remote (adjustment from control house)
control of steam addition. Governing regulations or permits should always be consulted for
verification of smokeless operation requirements.
In cases where specific direction or data is not available, the practice outlined in API RP 521

The basic formula used to calculate the flows discharging from ruptured tubes is:
W = 1891 K Y d2 (ΔP ρ1)0.5
Where: W = Flow, lb/hr at sonic flow conditions
K = Discharge Coefficient
Y = Expansion Factor
d = Tube ID, in
ΔP = Pressure drop, psi
ρ1 = Upstream density, lb/ft3
This is the formula for flow through nozzles and orifices given in Crane Technical Paper
410 Equation 3-21 and 3-22. To account for flow from both ends of the ruptured tube,
the calculated flow rate must be multiplied by a factor of two. In calculating discharge
due to tube rupture, assume that both halves of the break behave as square edged
orifices with K = 0.7. The expansion factor Y is unity for a liquid and is given by the figure
in Appendix H for a gas or by the equation:
Y = 1 – ( 0.41 / n ) ( ΔP / P1 ) where: Y = Expansion Factor n = k = Cp/Cv for an ideal gas
ΔP = Pressure drop, psi P1 = Upstream Pressure, psia
log10(Vmax)
[7]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer

This minimum velocity is dependent on both gas composition and diameter and can range from
insignificant amounts on small flares to 0.5 ft/sec on greater than 60-inch diameter units.[5]
The average pilot gas consumption based on an energy-efficient model is 70 scf/hr (of typical 1000 Btu
per scf gas) per pilot burner.[6, 7, 8, 9, 10] The number of pilot burners, N, based on flare size is:[6, 7, 8,
9, 10] 60‘=4pilot
4.3.1 Minimum Flare Tip Diameter
The minimum recommended flare tip diameter (DMIN, mm) is based on the maximum flaring rate (QMAX, 103m3/d) divided by the maximum
recommended exit velocity (VMAX, m/s). It is set to prevent flame lift-off with the following equations: DMIN = 1000 mm/m*{(4*QMAX*103
m3/103m3)/(24 h/d*3600 s/h*π*VMAX)}1/2 VMAX = MIN {122, 10[(NHV+28.8)/31.7]} MIN is the minimum function. EUB Guide 60
references a U.S. EPA relationship (U.S. CFR Part 60) that specifies the maximum exit velocity (VMAX) as a function of the net heating value
(NHV, MJ/m3). Higher heating value flare gas can maintain a stable flame at higher exit velocities than lower heating value flare gas. The upper
limit of 122 m/s corresponds to a heating value of 51.1 MJ/m3, and is approximately a Mach number of 0.3 (i.e. 30% of the speed of sound).
The U.S. EPA equation is consistent with the rule of thumb for flare tip design to not exceed a Mach number of 0.2 for continuous flares and 0.5
for emergency flares
4.3.2 Maximum Flare Tip Diameter
The maximum recommended flare tip diameter (DMAX, mm) is based on a representative average flaring rate of one-half of the maximum
flaring rate (0.5*QMAX, 103m3/d) divided by the minimum recommended exit velocity (VMIN, m/s) at the flare tip. It is set to avoid flame
downwash with the following equation: DMAX = 1000 mm/m*{(4*0.5*QMAX*103 m3/103m3)/(24 h/d*3600 s/h*π*VMIN)}1/2
VMIN = U99*(h/10)0.15 DMAX is provided for guidance in sizing the flare tip and does not effect the dispersion modeling. VMIN is used in
the flare tip downwash adjustment described in the next section. The representative average flaring rate used in the calculation avoids having the
maximum recommended diameter less than the minimum recommended diameter. flaring rate is much less than the one half of the requested
maximum flaring rate, then the flare tip should be sized closer to the minimum recommended diameter.
4.5 Ground Level Radiation
EUB Guide 60 specifies that flares must be designed so that the maximum radiant heat intensity at ground level will not exceed 1500BTU/hr/sf.
The following equation is based on the GPSA (1998) and API (1997) procedures referenced in EUB Guide 60, but are simplified to result in
conservative predictions. The ground level thermal radiation intensity depends on the maximum flaring rate (QMAX,), net heating value (NHV),
radiation loss (RAD, fraction), and the effective stack height (Hs, m), and is given by: IR = (QMAX*NHV*RAD)/(4*π*Hs2)
Both referenced procedures require the background thermal radiation to be included in the total radiation calculation. A maximum background
thermal radiation of 1.04 kW/m2, the upper range of maximum values according to the GPSA (1998), is added to the predicted value to compare
to the guideline. Maximum background thermal radiation values in Alberta would be less. For sour gas flares, ground level radiation is not a
limiting factor in the selection of the stack height; the dispersion of SO2 determines the required height. A 12 m flare handling about 569
103m3/d of methane equivalent heating value gas meets the thermal radiation guideline. An 18.3 m flare can handle about 1206 103m3/d and
meet the guideline. Where C is the velocity of sound (m/s), L the sound level (dB), L30 the sound level at 30 m (dB), M the mass flow (kg/s) and
PR the ratio of the upstream to the downstream pressure. For L in the function A12.4.2 API RP 521 gives a correlation with linear scale for L
and logarithmic scale for PR. The correlation is two straight lines with a break point at the two lines being defined by the additional points. For
other distances the sound level may be Lp is the sound level (dB) and r the distance from the stack tip (m). Green states that emergency relief
vents tend to be the most powerful noise sources on chemical plant. The noise from a jet is greatest in the 60 cone about the axis and hence a
vertical orientation is usually to be desired. He indicates that a vent should be so located that the sound level does not exceed 125 dB in areas
where operators might be, however infrequently. The jet noise is proportional to the sixth to eighth power of the exit velocity. Methods of
reducing noise include velocity reduction and silencing, but reduction of velocity is in direct conflict with the need for a high velocity to promote
dispersion.
5.9.2 EPA Requirements EPA (1988) published criteria for flare operation (40 CFR 60.18) which apply to normal process flare systems as
follows. (Even though smokeless is not normally required for emergency flares, this information is included for reference purposes since local
regulations may require smokeless flaring.)• Steam-assisted or air-assisted flares require the gas to have a minimum net heating value of 300
Btu/SCF. • Nonassisted flares require the gas to have a minimum net heating value of 200 Btu/SCF. • No visible emissions. A five minute
exception period is allowed during any two consecutive hours. • A flame must be present at all times when emissions may be vented. The
presence of a pilot flame shall be monitored using a thermocouple or equivalent device. • Maximum tip velocity is defined as a function of net
heating value of the feed to the flare in Table 5.3 • The equation for maximum tip velocity for heating values between 300 and 1000 Btu/SCF:
(5.9.1) where Vmax is the maximum permitted velocity at flare tip, ft/s, and Bv is the net heating value of feed to flare, Btu/SCF.
TABLE 5.3
Maximum Tip Velocity
Heating Value of Gas, Btu/SCF Maximum Tip Velocity, ft/s .
<300 60 300-1000 See Eq. (5.9.1) >1000 400
Stone et al. (1992) state that it is standard practice to size the flare tip so that the design velocity is 80% of Vmax. Too low a tip velocity can cause
heatand corrosion damage. The equation for minimum tip diameter is then (5.9.2) where
Dmin= minimum tip diameter, inches Qtot = total volumetric flow rate, actual CFM Vmax = maximum tip velocity, ft/s; determined from
Table 5.3. The selected flare tip diameter, D, is the calculated diameter, £>min, (inches), rounded up to the next commercially available size. The
minimum flare size commercially available is 1 inch; larger sizes are available in 2-inch increments from 2 to 24 inches and in 6-inch increments
above 24 inches. API method. API 521 recommends a maximum tip velocity corresponding to a Mach Number of up to 0.5 for peak, short-term,
infrequent flow emergency discharges. The Mach Number for a given tip diameter and flow rate may be calculated from where M 2 = Mach
Number at flare tip outlet W = gas flow rate, Ibm/h P — pressure of gas just inside flare tip, psia D = flare tip diameter, ft Z = compressibility
factor of gas under conditions at tip T = absolute temperature of the gas just inside the flare tip, 0R k = ratio of specific heats, C^/CV Mw =
molecular weight of the gas. The tip diameter calculated by the API method [Eq. (5.9-3)] may be smaller than that calculated by the EPA criteria

[8]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer
(Table 5.3), and if so, the larger diameter should be selected (Shore 1995). Too low a tip velocity can result in combustion taking place inside the
stack—this is called burn-back, or sometimes a flame dip. This can occur when a slow upward flow of lighter-than-air gas allows air to flow
downward along the stack wall. A diffusion flame propagates down into this region and it is quenched at the wall. Air then flows downward
again causing another burn-back, and the cycle is repeated again. Seebold (1984) suggests that a tip velocity of 1-3 ft/s is required to prevent
flame dip. Straitz (1996) suggests that an effective air seal will prevent burn-back and burning inside the flare tip at flare burner tip velocities as
low as 0.03 ft/s. The approximate limiting tip velocity is given by equation: where D is the flare tip diameter, ft, and V is the tip velocity
required to prevent flame dip, ft/s. A pressure drop calculation should be made to ensure that the vent stream has sufficient pressure to
overcome the pressure drop occurring through the flare system at maximum flow conditions. The pressure drop calculation is site specific but
must take into account losses through the collection header and piping, the knock-out drum, the liquid seal, the flare stack, the air seal, and finally
the flare tip. If sufficient pressure is not available, the economics of either a larger flare system or a gas mover such as a fan or compressor must
be considered. A pressure drop as high as 2 psi across the flare tip has been used satisfactorily. This pressure drop is the result of a flame retainer
at the flare tip included in most commercial flares, which restricts flow area by 2-10% (API 521).
RP 521 gives a correlation with linear scale for L and logarithmic scale for PR. For other distances the sound level may be obtained from Lp
where Lp is the sound level (dB) and r the distance from the stack tip (m). Green states that emergency relief vents tend to be the most powerful
noise sources on chemical plant. The noise from a jet is greatest in the 60 cone about the axis and hence a vertical orientation is usually to be
desired. He indicates that a vent should be so located that the sound level does not exceed 125 dB in areas where operators might be, however
infrequently. The jet noise is proportional to the sixth to eighth power of the exit velocity. Methods of reducing noise include velocity reduction
and silencing, but reduction of velocity is in direct conflict with the need for a high velocity to promote dispersion

[9]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer

Summary
Capacity of 33 inch nozzle was checked by five methods, Table 1. The resultant capacity calculated by
these methods, meet or exceeded requirements (570#/sec or 2.05MM#/hr) as given in Table 2. An
additional constraint is that Flare Nozzle Mach Number must not exceed 0.8 Mach number. Mach
number is calculated by API-RP-521 equation 23. An additional constraint is that nozzle pressure must
be less than critical pressure ratio. The critical pressure ratio is the maximum pressure ratio that is
achieved prior to sonic flow conditions. This pressure ratio, PCR, is determined as given below. All
methods are described in the following write up.
Table 1
Method

calc'd cap
#/sec
Tube Rupture RV 572.0
Orifice Plate
678.0
Crane TP410 K=0.5 678.0
Choke Nozzle
663.9
Mach #
684.2
P(w) TP410-b K=0.5 570.0

tip size Pup P down
inch
psia psia
33.0
25.90 14.7
33.0
26.40 14.7
33.0
26.40 14.7
33.0
26.00 15.0
33.0
26.40 14.7
33.0
23.90 14.7

MW
#/mol
28.66
28.66
28.66
28.66
28.66
28.66

K
cp/cv
1.25
1.25
1.25
1.25
1.25
1.25

T
R
520
520
520
520
520
520

Ma ch #
RP521.e 23

0.68
0.79
0.79
0.79
0.80
0.74

Max Pup
psia
26.49
26.49
26.49
27.03
26.49
26.49

#
1
2
3
4
5
6

Table 2 HP Flare Upset Sizing Conditions, PFD Stream 215-◊ of G80-NA-J-54992

As seen from Table 2, sufficient pressure is available at flare KO Drum to achieve a pressure necessary for flaring
570#/sec of gas, 23.9 psia. This leaves 37psia less 23.9 or about 13 psi for pipe and flare system pressure losses.
The ability of a 60 inch flare header to achieve required relief rate with pressure losses at or below 13 psi is
detailed in this write up. Since limiting case is for emergency depressurization, a review is made for heat
radiation limits under transient flow conditions. It is pointed out that high values of transient heat radiation are
permitted by API-RP-521. The heat flux requirement for a transient condition is not same as that for continuous
operation.
A simplified Flare Tip sizing routine by Mach number is as follows: 1) calculate Critical Pressure and select tip pressure slightly
less than calculated critical pressure, 1b) check pressure balance to verify tip pressure. 2) Use MW, mass rate, and
th
Temperature from PFD 3) Calculate Cp/Cv from Figure 16-2 of GPSA 9 Edition. 4) Use formula 23 of API-RP-521 to find
required tip diameter for allowable Mach number, 0.80 in this instance.. The same method may be used to determine
capacity of a tip.
(k/(k-1))
PCR = (2/(k+1))

[10]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer

Overview
No small amount of deliberation has been made over whether or not an old flare, F3, will pass a mass
rate of 569 pounds per second of 28.7MW hydrocarbon gas available at 37 psia from flare KO drum. F3
is a decommissioned unit. It has a 12 foot diameter base with a 36” Flare Tip (point 3) sitting atop an 82
inch molecular seal, point 1. Between the 12 foot base and the 82 inch section is another section of
approximately 10 foot diameter. It is the premise given here that a 36 inch tip is adequate for the
specified service. Considerations are given from a basic engineering point. Also additional witness are
called to support this position, namely, Mr. Farris Relief Valve, Mr. Daniel Orifice, and Mr. Crane TP-410
method of example 4.21, Mr. Choke Valve, and Mr. ISA C. Valve. All these witness are credible by
virtue of regular application.
I) Basic Diagram with Energy Balance Considerations

The Bernoulli energy balance equation for above condition is:
144(P/ρ) 2 + V22/62.4 = 144 (P/ρ)3 + V32/64.4 + Hf

EQN. 1

If ρ is in #/CF with pressure in #/sq-in, the following conversion factor must be introduced, 144 in2/ft2,
so pressure head is in feet, as is velocity head when V is ft/sec and g is 32.2 ft/s/s.
The friction losses, Hf , are expressed in terms of V2. They may consist of following basic terms:

[11]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer

1.
2.
3.
4.
5.
6.
7.
8.

Acceleration of gas from low velocity state to higher velocity state, Ka
Turbulence losses in contraction (vena cava) section, Kv
Deceleration losses as gas expands to P3, Kd
And lastly a thermodynamic term, to account for adiabatic expansion density changes, Kt
Collectively these terms are called+ ΣKi to keep algebra simple
As will be shown, the Crane method just lumps all terms into a ΣKi to keep algebra simple
Losses are expressed in terms of inlet V, since V in dispersion cone is not precisely known
It will be shown for reasonable amounts of expansion this velocity head becomes insignificant
and that inclusion of adiabatic expansion factor eliminates need for item 4.

144(P/ρ) 2 + V22/62.4 = 144 (P/ρ)3 + V32/64.4 + ( ΣKi) V22/64.4

EQN. 2

Velocity may be expressed in terms of mass rate as V=(w/(A ρ)) or V(Aρ) =w.

EQN 3 a&b

Since continuity requires w2 = w3, then (VAρ)2 = (VA/ρ)3 & V3 =(VAρ)2/(Aρ)3 =(Vρ)2*(d2/d3)2 /ρ3
For any gas ρ = PM/10.73zT, where P is psia and M lb/mol and T is degree Rankin. For adiabatic
expansion density changes are related to pressure ratio raised to inverse of heat capacity ratio.
The area ratio is accounted for by term beta, β. Area ratio is just a ratio of diameters squared. For the
velocity head term it is to the forth power.
Consider situation where the diameter triples (as shown in above diagram) and initial conditions are: V2
=800fps MW=29 P2=27, T2=520R, beta =3, k=1.25, den2=27*29/10.7/520=0.14
Conditions at 3: den3 =0.14*(15/27)^(1/1.25) =0.09, V3=800*(.14/.09)*(1/3)^2=142,
the Vhead3= (0.09)*142^2/64.4/144 = 0.20psi, Vhead2 = 0.14*800^2/64.4/144= 9.7psi.
V head 3 is less than 2% of initial V head and only 3% of exit pressure head.
Thus for any reasonable expansion, velocity head on Right hand side is not especially significant and is
dropped. A second simplification is to carry all density in terms of initial density. A third simplification is
to carry initial velocity head in the term: ( ΣKi). Application to Eqn. 2 of this method yields Eqn 4:
(P)2 = (P)3 + ρ ( ΣKi) V22/64.4 /144

EQN. 4

(P) 2 = (P)3 + ρ ( ΣKi) (w/(A ρ))22/64.4 /144

=> (ρP) 2 = ρ2(P)3 + ( ΣKi) (w/(A))22/64.4 /144 & use density:

application of Eqn 3a, V=(w/(A ρ)) gives

(PMP/(zRT)) 2 = (PM/(zRT))2(P)3 + ( ΣKi) (w/(A))22/64.4 /144 => (P2)2 -(P)2(P)3 -zRT( ΣKi) (w/(A))22/9274/M=0
Simplify the constants by using A in terms d4 to give: 1.273^2 *12^4/9274 = 3.62 (same as Crane Constant in 3.20-g)

P22 -P2P3 -3.6ZRT( ΣKi)(w)2/(Md4))2 =0
ΣKi)(w2)/(Y2Md4))=0

compare to Crane 3.20-g:

P22 -P2P3 -3.6ZRT(

The adiabatic expansion factor corrects for the simplifications made in derivation, as endorsed by APIRP521. The Crane method is given in example 3.
The following five (5) validations are offered to confirm use of 36” Flare Nozzle for the listed pressure
available and other requirements:

[12]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer

Witness #1

RESULT OF FARRIS RV PROGRAM:

The Farris Relief valve program
calculates a capacity of 4.22 MM#/hr for
a 33 inch id tube at 25.9 psia pressure.
Also provided are the equations used by
the Farris Program to calculate capacity
of flow nozzle for given conditions. The
factor of 2 is because tube rupture flows
from 2 ruptured sides. Capacity for 1
ruptured 33 inch tube is 2.06MM#/hr or
572#/sec.
For these conditions density is:
#/CF = 25.9*28.66/10.7/520 = 0.134
The area in square feet is:
A, sf = (33/12)^2/1.273 = 5.94
For required mass flow of 2.06MM #/hr (572#/sec) velocity in feet/sec is:
V= (#/sec)(cf/#)/(A, SF) = 572/0.134/5.94
V, fps = 719, & Mach# =719/1025= 0.70
This relief valve routine uses a method for flow at subsonic conditions thru a flow nozzle. The Farris RV
Tube Rupture routine shows a 36” flare tip with 33” port is entirely adequate. It also shows that for
required capacity, velocity need not approach sonic conditions.

[13]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer

Witness #2

RESULTS FROM Daniel Orifice PROGRAM:

The Daniels Orifice program calculates a capacity of 2.102 MM#/hr for a 33 inch hole with 28 psia
upstream pressure and 15psia downstream pressure. Daniels does not provide sizing equations used by
the Daniels Program to calculate capacity of flow thru an opening at given conditions.
For these conditions density is:
#/CF = 26.4*0.9883*29/10.7/520/0.99 = 0.137
The area in square feet is:
A, sf = (33/12)^2/1.273 = 5.94, square feet, SF
For required mass flow of 2.05MM #/hr (570#/sec) velocity in feet/sec is:
V= (#/sec)(cf/#)/(A, SF) = 570/0.137/5.94 V, fps = 700
Sonic Velocity is calculated by equation 5.7, Vs, fps = 44.8Root(T, R) =44.8√520 =44.8*22.8 =1022
DANIELS Mach# at required capacity =V/Vs =700/1022= 0.68
An orifice bore of 33 inch at 26.4psia Matches Flare Criteria of Mach number less than 0.80
Pressure meets or exceeds requirement of critical pressure ratio
Pressure drop is sufficient to meet flow requirements thru a 60 inch flare header.

[14]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer

Witness #3 RESULTS FROM Crane TP410 Example 4.21:
A comparison is made between results of TP-410, method of example 4.21 and results obtained by
Daniels Orifice calculation method.
Determine inlet pressure to Nozzel discharging to atmosphere
Crane (TP-410 25 th print 1991) formula for pressure loss in gas flow is
given on page 3.4 by equation 3-20-g
w =0.525Yd2(ρΔP/K)) 0.5
symbol
w
Y
d
ρ
ΔP

explanation
lb/sec of flow
expansion factor, pg A-22
id of pipe inches
density in, #/cubic feet
pressure drop psi P in-Pout

Ex4.21
9.19
0.637
3.068
0.265
91.8

F3-36"
678.00
0.665
33.000
0.136
11.7

Dan Orif
678.00
0.665
33.000
0.136
11.7

Pin

psia

139.7

26.4

26.4

Pout
K
0.525

psia

47.9
2.87
0.525

14.7
0.50
0.525

14.7
0.50
0.525

139.7
12.18
1.00

26.4
28.66
1.00

26.4
28.66
1.00

600.0
1.40

520.0
1.25

520.0
1.25

K resistance coefficient of system

dimensional term

ρ=PM/(10.7ZR)
P
Pressure in Psia
M
molecular Weight
Z
Compression factor, ~1
Ro
Temperature, 460+F
k
Cp/Cv
by arrangement:
3.63Kw2/(d4Y2) = ρ ( Pin-Pout)
by density equation
3.63Kw2/(d4Y2) = MPin ( Pin-Pout)/(10.7Ro)
(10.7Ro/M)3.63Kw2/(d4Y2) = Pin ( Pin-Pout)
arranging to quadratic form gives

Pin ( Pin) - ( Pin)(Pout) - (10.7Ro/M)3.63Kw2/(d4Y2) =0
This equation can be solved by xcel solver for Pin given Pout
Spreadsheet solution validated below for example 4.21, pg 4-14
Pin

Pout
139.7
26.4
26.4

#/sec
47.4
14.7
14.7

MW
9.2
678
678

T,R
12.2
28.7
28.7

id in
600
520
520

f(P) den V fps M dP/P1
3.07
0.0 0.265 675.3 0.37 0.66 TP410-E4.21
33.00
0.0 0.136 839.3 0.79 0.44 Tan Flare F3
33.00
0.0 0.136 839.3 0.79 0.44 Dan Orif

[15]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer

Witness #4 Result from Bernoulli Energy Balance
Provided to right is flow solution based on Bernoulli
energy balance method.
The details of the method are developed in section
one of this discussion. The Bernoulli energy balance
is valid at any sonic condition, either sonic, subsonic,
or supersonic.
However the pressure change across tip will vary
depending upon sonic condition.
The Critical
Pressure ratio is used to determine flow conditions,
sonic, subsonic or supersonic. Determination of
critical pressure is given by Equation 5.1 of Appendix
1.
The density change of gas is based on the adiabatic
method.
The friction K is based on an expansion K of 1.0 and
a contraction K of 0.40. The sum of these two K
factors determines friction head based on upstream
velocity.

The mass rate is adjusted until the sum of energy
terms are equal, or difference of terms equals zero.
As is shown by “sum” row to right

Nozzel
Bern'li Eqn. Flow in
Flow out
variable dimension value up
value down
d nozzel inch
33.00 use adiabatic
D Barrel inch
36.00 den change
viscosity'μcp
0.01
0.014
gas vol Q
mscfd
6.45E+05 6.45E+05
gas sg
gas sg
0.99
0.988
mass flow
#/sec
564.67
564.67
k
Cp/Cv
1.25
1.250
Pup
psia
26.45
Pdn
psia
14.700
Temperature R
520.00
462.36
Pmax up psia
26.49
1/k
Den adab =ρu(Pu/Pd)
0.136
0.0852
Area in Sq ft
5.94
Beta, β Beta
4.00
D2 (beta, β) inch
132.000
A d/s out sq ft
95.05
Velocity fps
697.66
69.761
Frict K
Ke=1 Kc=0.4
1.40
2
feet, V /2g
Vhead
7557.89
75.57
P hea d
feet, P/ρ
27955.90 24857.17
frict head ft. K*Vin2/2g
10581.04
adjust mass | sum =
35513.78 35513.78
till Δ=0 Δ=diff |=
0.00 en'gy balance
bernoulli basis (P/ρ+V2 /2g)1 = (P/ρ+V2/2g)2 + hf

Mach Number by API method is as follows:
Where D is tip diameter in feet, and P2 is tip pressure in
psia. Other units need be used as imperial units for the
constant to apply. The Mach for Bernoulli are
1.72E-5*(565*3600)/(26.5/(33/12)

2

))*(1*520/1.25/28.7)0.5

= 0.658

[16]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer

Witness #5 Result from Choke Valve
Mr. Choke Valve is called since some think any pressure above atmospheric causes or implies Mach
number greater than one, M>1. Mach number is a ratio between sound velocity in gas divided into gas
flow velocity.
Determination of Critical Pressure Drop or Critical
Pressure Ratio, CPR

The CPR is the minimum pressure ratio for sonic
flow, and for any larger pressure ratio, flow inside
a nozzle is subsonic, M<1.
The pressure ratio is conventionally defined as
pressure upstream divided into downstream
pressure. Since flow is always in a direction of
decreasing pressure, pressure upstream will be
larger than pressure downstream. At pressure
ratio of 1, flow is zero. From thermodynamics CPR
is determined by formula 5.1.
d/D = 33/36 = 0.92

C = 0.92 + 0.33 + 0.09 = 1.34
Since Nre>1E6, use C =1.2, as per example

Nre = 20 (651,430)*0.9883/(0.01245*33) =3.2E7

[17]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer

Witness #5 Result from Choke Valve, c’td
For Practical Example consider a flared
gas with k=1.25 & as given to right the
critical pressure ratio is 0.555.
Since gas expands to pressure of 1
atmosphere, which at sea level is about
14.7 psia, the max upstream pressure is
14.7/0.555 = 26.5 psia
Since pressure available at HP flare KO
drum is 37 psia, say by time gas reaches
flare nozzle pressure there is only 26 psia
available; check subsonic:
14.7/26 = 0.57 > 0.555 subsonic exist
Calculate Sonic velocity for 60F
hydrocarbon gas by formula 5.7 above:
=44.8√(520) =1022fps
Flare group limits tip V to 0.8M, &
allowable V = 0.8*1022 = 817fps.
Listed conditions: C=1.2, d=33 P1 =26 for listed Conditions Qsc = 683645>651430 of Table 1
k=1.25, Pd/Pu=0.57 SG=0.988 T=520
Calc. #/sec= (scf/d)(1mol/379scf)(MW,#/mol)(1d/86400sec)
Mr. Choke #/sec =683,645,000/379*28.66/86400 =598#/sec

For 33 inch nozzle the area is 5.94 square
feet. Thus the actual cubic feet per
second equals:
Gas density at Nozzle Condition is
lb/cf = PM/10.7/R = 26*28.66/10.7/520
= 0.134#/actual cubic feet
Thus 33 inch diameter flare tip is
sufficient to pass 650#/sec of 26.66MW
gas at pressure of 26psia and
temperature of 60F (520 Rankin) at
Mach 0.80.
Mr.Choke, what is your Mach#?, “It is =

ACFS =V*A =5.94*817 =4853 actual cubic of gas feet/ second
#/sec =ACF/sec *#/ACF = 4853*0.134 = 650#/sec
The requirements per Zink Table, below, are:
650E6
SCF/Day/(379SCF/MOL)*(28.66#/mol)/(1440min/day)/(60sec
/min) = 569#/sec
Mr. Choke Valve is free to leave the witness stand.

=0.8*598/650=0.74 to meet or exceed
requirements of Maximum Upset case

A summary of Mr. Choke Valve is that:

Zink Cases

The flare tip of F3 is actually 36 inches,
but using 33 inch nozzle is sufficient to
pass 598#/sec at M=0.74, the
requirements are only 569#/sec,
therefore F3 tip is sufficient for the
specified duty. The Mach of Mr. Choke
meets requirements from both capacity
and Mach requirements.

[18]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer

Witness #6

Result From ISA Control Valve

Control Valve Sizing program may also be used with Cv charts to estimate capacity of a flare tip.

The above output is from Fisher
sizing program, FSP14.
The
upstream pressure was selected
to not exceed Mach 0.8.
At the given pressure, flow,
temperature, gas heat capacity
ratio, gas specific gravity and
mass
rate,
the
program
calculates a Cv value. Various
manufacturer offer Cv charts.
Shown at right is Cv chart for
large full port gate valves.
FSP14 calculated a required Cv of 44069. As seen from the Cv chart above a 24” gate valve port will
meet the required Cv. As size increases, the Cv increases. The listed flare orifice size by Zink is 33 inch,
so a 33 inch port is sufficient to pass 2,050,000#/hr or 570#/sec.
Mach number may be estimate as dP/(dP choked) = 8.1/11.1 = 0.73.
Pressure drop, dP is determined as inlet, 22.8 minus outlet, 14.7 = 22.8-14.7 = 8.1psid.
Calculation by API formula with 33 inch nozzle & given conditions yields a Mach Number of 0.78.
In summary, Mr. ISA C. VALVE, also has testified that a 33 inch flare nozzle is adequate to process the
required flow.
More details on calculation equations for subsonic valves are available from the Instrument Society of
America, publication: S75.01-1985 (R 1995), Flow Equations for Sizing Control Valves
[19]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer
Additionally, the following important considerations deserve merit:
Pressure Drop 60” Flare Header, HP Max Upset Condition
The following hydraulic analysis show that for a 60” flare header with a run of 1244 feet of feed pipe from Flare K/O drum, a
flare tip pressure of 31.22 psia is achieved with given flow conditions and starting at a listed pressure of 37psia at flare K/O
drum. While only between 30.1 and 28 psia is required to properly flow the 36 inch nozzle.
L i n e I d e n ti fi c a ti o n

U n i ts

Ca s e

U n i ts

6 0 " s ec ti o n

Pha se

60" run

Ga s
HP F LA RE

GAS

2 7 ,1 4 3 ,0 0 0

SCFH

V i s c o s i ty

0 .0 1 5

cP

D en s i ty

0 .1 9 1

l b /ft3

60
2 2 .3

Tem p er a tu r e
I n l et P r es s u r e

U n i ts

fl a r e p =b a r r el eq u i l

Ga s

F l o w r a te

Fluid in line

U n i ts

3 6 fl a r e ti p

Ga s

HP F LA RE

GAS

Ga s

HP F LA RE

GAS

SCFH

2 7 ,2 6 8 ,0 0 0

SCFH

2 7 ,2 6 8 ,0 0 0

SCFH

0 .0 1 5

cP

0 .0 1 5

cP

0 .0 1 5

cP

0 .1 8 6

l b /ft3

0 .1 7 6

l b /ft3

0 .1 6 1

l b /ft3

d eg F

60

d eg F

60

d eg F

60

d eg F

psig

2 1 .3 3

psig

1 9 .4 7

psig

1 6 .6 3

psig

2 7 ,1 4 3 ,0 0 0

HP F LA RE

S p ec fi c G r a v i ty (S G )

0 .9 8 8

0 .9 8 8

0 .9 8 8

0 .9 8 8

M ol W t

2 8 .6 5

2 8 .6 5

2 8 .6 5

2 8 .6 5

1 .2

1 .2

1 .2

C p /C v o r K

1 .2

M ACH Num be r

0.604

R o u g h n es s F a c to r

0 .0 1 2

P i p e S i ze / S c h ed u l e

6 0 .0 0

I n s i d e D i a m eter

0 .0 1 2
XS

59

V el o c i ty
S o n i c V el o c i ty
P re s s u re D ro p
R e y n o ld 's N u m b e r

GAS

0 .0 1 2

6 0 .0 0

inch

s td

59

0 .0 1 2

4 2 .0 0

inch

s td

42

3 6 .0 0

inch

s td

36

inch

157

ft/s ec

161

ft/s ec

337

ft/s ec

500

ft/s ec

1041

ft/s ec

1041

ft/s ec

1041

ft/s ec

1041

ft/s ec

0.124

p s i /1 0 0 ft

0.127

p s i /1 0 0 ft

0.742

p s i /1 0 0 ft

1.749

p s i /1 0 0 ft

14,566,132

14,566,132

Q ty

20,556,179

Q ty

F eet o f P i p e

23,982,209

Q ty

Q ty

302

Ft

942

Ft

7 5 .2

Ft

6

Ft

9 0 d eg El l s

4

260

Ft

7

455

Ft

4

308

Ft

0

0

Ft

4 5 d eg El l s

0

0

Ft

1

35

Ft

0

0

Ft

0

0

Ft

s o ft T's

0

0

Ft

0

0

Ft

0

0

Ft

0

0

Ft

h a r d T's

1

220

Ft

0

0

Ft

0

0

Ft

0

0

Ft

R ed u c er

0

0

Ft

1

28

Ft

0

0

Ft

0

0

Ft

en tr a n c e l o s s

0

Ft

0

Ft

0

Ft

0

Ft

ex i t l o s s

0

Ft

0

Ft

0

Ft

0

Ft

To ta l Eq u i v Len g th

782

Ft

1460

Ft

3 8 3 .2

Ft

6

Ft

Eq ft d P

0 .9 7

psi

1 .8 6

psi

2 .8 4

psi

0 .1 0

psi

I n l et P r es s u r e

2 2 .3

psi

2 1 .3 3

psi

1 9 .4 7

psi

1 6 .6 3

I n l et El ev a ti o n

0

ft

0

ft

0

ft

0

ft

O u tl et El ev a ti o n

0

ft

0

ft

0

ft

0

ft

psig

S ta ti c H ea d

0 .0 0

psi

0 .0 0

psi

0 .0 0

psi

0 .0 0

psi

Li n e Lo s s es

0 .9 7

psi

1 .8 6

psi

2 .8 4

psi

0 .1 0

psi

C o n tr o l V a l v e

0

psi

0

psi

0

psi

0

psi

Eq u i p m en t

0

psi

0

psi

0

psi

0

psi

0 .9 7

psi

1 .8 6

psi

2 .8 4

psi

0 .1 0

psi

2 1 .3 3

psi

1 9 .4 7

psi

1 6 .6 3

psi

1 6 .5 2

To ta l p r es s u r e l o s s
O u tl et P r es s u r e

psig

N o tes :
O r 651.43 M M S C F D

3 1 .2 2

Psia at nozzle
First; 1300 foot run is only necessary at design of 500BTU/HR/SF which is excessive for maintenance work and two, the 651mmscfd of gas
flow for a plant producing only 50mmscfd is excessive. These concerns are detailed below by depressurization study and review of heat
flux.

[20]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer
Corrosion Issues:
Exterior Corrosion, Just one Location

Corrosion Issues:
[21]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer

Just a poor weld job, not
result of corrosion.
A
more detailed inspection
appears
in
order.
Corrosion alone does not
condemn
equipment.
Repair of corrosion is a
major function of every
T&I.

[22]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer
Depressurization Evaluation
Determination of Gas Volumes Used for Depressurization Evaluation

[23]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer
Depressurization Evaluation
HP
HP
HP
HP
HP
HP
HP
HP

D203
D204
D106 B
D207
D209
D212
D213
D2

13.0
11.0
11.5
11.0
11.5
5.0
5.0
14.0

24.0
33.0
36.0
23.0
36.0
8.5
13.0
55.5

60.0 LP suct
3186.2
60.0 LP Disch
3136.7
665.0 confy
3740.0
145.0 P/L suct
2186.2
625.0 cont fd 2" 3740.0
650.0 bst suc
166.9
650.0 bst dsc
255.3
50.0 LPTs 1/2
8545.2

2 6372.3
2 6273.4
2 7480.0
2 4372.3
2 7480.0
2 333.9
2 510.6
2 17090.3

0.260
0.260
3.494
0.649
3.284
3.415
3.815
0.217

30
24
4
24
20
8
12
16

150
150
150
150
150
150
150
150

300 1376
300 866
300
15
300 866
300 591
300
80
300 198
300 368

0.432 5098
0.276 5019
0.004 5984
0.396 3498
0.158 5984
0.480
267
0.776
408
0.043 13672

2549
2509
2992
1749
2992
134
204
6836

26.0
25.6
409.9
44.5
385.3 24" 12"V
17.9
30.6
58.1

50
50
615
115
565
600
600

60
60
665
145
625
650
650
50

25.5
25.5
25.5
25.5
25.5
25.5
25.5
25.5

60 26.0 0.98
60 25.6 0.98
665 409.9 0.81
145 44.5 0.95
625 385.3 0.81
650 17.9 0.81
650 30.6 0.73
50 58.1 0.98

Summary of Volumes used for simulation

In summary, there are only a fixed amount of
vessels inside Tanajib Plant. At any given time
these fixed number of vessels contain a finite
amount of gas molecules.

P range

Pmx

mol

#/cf mx

# max

CF, Vo

z

50 to 70

70

259.7

0.33

6622

20269

0.982

150 to175

175

272.6

0.84

6951

8242

0.951

570 to 650

650

1000 -1230

1230

sum all

1817.5
76.4

3.68
7.78

46347
1948

12602
250

0.810
0.725

2426.2

These molecules are released during de-pressure
operations. If the molecules are released at a high rate, then the time to de-pressure is reduced. If the
molecules are released at a moderate rate, as set by release rate requirements of OIM’s and SAES-B-058, then
the rate of release is reduced.
CLEARLY BOTH HIGH RELEASE RATES AND LONG RELEASE TIMES CANNOT BOTH BE SUSTAINED. Either 1)the release time is
reduced with increase in release rate or 2)release rate is reduced with longer release time. This concept is
explored in more detail under section titled, Heat Release Rate. Heat exposure is a time sensitive factor and it is
not possible to consider heat exposure flux without making consideration of the time of heat exposure.
SAES B-058 7.4 Process vessels shall be designed with systems to de-pressure to 50% of the vessel's design gauge
pressure within 15 minutes if:... and..b) The vessel is designed for pressures equal to or greater than a gauge
pressure of 1725 kPa (250 psig).
The depressurization sequences from the OIM of G54 are detailed below.
Page 29 of G54 OIM 34.085
 1. at time t=0 •
o Atmospheric Compressor K-101 HP Flare Valve NV-675 opens •
o LPPT Compressor K-102 HP Flare Valve NV-747 opens •
o Pipeline Compressor K-103 HP Flare Valves NV-809A and NV-809B open
 2. At time 60 seconds •
o Atmospheric Compressor K-201 HP Flare Valve NV-710 opens, if train 2 is operational
o LPPT Compressor K-202 HP Flare Valve NV-777 opens, if train 2 is operational
o Pipeline Compressor K-203 HP Flare Valves NV-846A and NV-846B open, if train 2 is if operational
 3. At time 250 seconds
o Booster Compressor K-105 HP Flare Valves NV-1097 and NV-1050 open
o Booster Compressor K-205 HP Flare Valves NV-1098 and NV-1079 open if train 2 is operational.

[24]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer
Internal Depressurization Simulation results MAX RATE CASE to meet SAES B-058 7.4

The output of this simulation is shows a maximum Mach number of 0.45 is

[25]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer
Depressurization Evaluation
Dynamic Simulation of Depressurization using RO gas flow Equation. Plant G80 + R54
This depressurization Model Indicates Maximum Flow at flare is only 250#/sec, (900,000#/hr) not the 2 million
pound per hour claimed on PFD. This is conservative model as Pressures on PFD at not achieved under current
operation.
Basis as per above Table and condensed to 4 pressure ranges as follows:
P range

mol

Pmx

#/cf mx

# max

CF, Vo

50 to 70

135.7

70

0.36

4344

11989

150 to170

407.9

170

0.88

13053

14833

570 to 625

738.4

625

3.24

23628

7304

1000 to1450

64.2

1450

7.51

2056

274

sum

1346.2

Based on this evaluation Tanajib HP Flare emergency relief case is over specified by a factor of 100%,
if requirements of SAES B-058 7.4. are applied.
In conclusion a 36” flare nozzle was calculated to run at 0.82 Mach by P&CSD based on the relieving rate of 2.05
MM#/HR to meet the requirement of 0.80 Mach number the flow need only be relaxed to 2.00 MM#/HR.
The 2.05MM#/HR was based on specification of Pressure requirements for Operating conditions which are no
longer valid.. This over specification applies to both Conditions shown on PFD & Current Operational Conditions.

[26]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer

SAES_F-007 Table 1 on pg. 10 of 26

Clearly based on criteria listed in F007, Table 1, at heat exposure rates between 1500 BTU/HR/SF and
2000BTU/HR/SF an exposure time between one minute and several minute are permissible. The below
simulation outputs indicate that if PFD maximum release rate of 570#/sec is used, the radiation exposure time
between 1500 BTU/HR/SF and 2000 BTU/H/SF is about 60 second with Flare D of 770 feet...

[27]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer

[28]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer

[29]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer

[30]

Considerations on Flare Parameters by Otis Armstrong, Licensed Professional Engineer

Summing up:
In summary this detailed review finds no reason a 36” Flare Tip cannot be used for this application of a
temporary Flare.

Justifications are repeated as:
1. Less than 2% disagreement between standards requirements and
P&CSD calculated values. P&CSD calculated Mach number is 0.82 as
compared to the limit of 0.80.
2. Current Operational conditions do not require same relief capacity as
shown on PFD because current operational pressures are lower than the
pressures listed on PFD.
3. In house study indicates original sizing basis used more than 100%
safety factor.
4. Internal Considerations for relieving Mach number indicate value less
than 0.8 is to be expected.

[31]


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