~ ENVIRONMENTAL HEALTH SECTION 

,gaNT sg~` /

Gold Seal Center, 918 E. Divide Ave. 

/

NORTH DAKOTA Bismarck, ND 58501-1947 

DEPARTMENTof HEALTH 701.328.5200 (fax) 

www.ndhealth.gov oFNoRTK ~P 

MEMO TO : Air Quality Staff 

FROM : Steve Weber 1-Y 61 

Environmental Scientist 

Division of Air Quality 

RE : Model Input Parameters for Flares 

DATE : November 10, 2010 

Most refined air quality models, including AERMOD and ISC-Prime, do not provide for direct 

modeling of flares. Therefore, the treatment of plume rise from flares is not straightforward, 

because traditional input values of stack temperature, diameter, and exit velocity have no 

physical significance once combustion has occurred at the top of the stack. To properly model 

flare plume rise, therefore, virtual values of stack temperature, diameter, and exit velocity must 

be developed which allow the model to calculate a buoyancy representative of conditions above 

the flare. In addition, a virtual (effective) stack height may be calculated which accounts for the 

length of the flame. These virtual values are then entered for traditional model input. 

The North Dakota Department of Health (NDDH) recommends a new approach for flare stack 

plume rise which is based on the method used in the EPA SCREEN3 model. This new approach 

supersedes the method previously used by the NDDH as outlined in the North Dakota Guideline 

for Air Quality Modeling Analyses (1990). To be more consistent with the SCREEN3 

methodology, the new approach assumes a different entrainment heat loss (55% vs. 25%), and 

adds the provision to revise (increase) stack height by calculated flame length. 

A primary component of plume rise calculations in air quality models is the buoyancy flux 

parameter. Necessary virtual stack parameters for flare modeling can be established by equating 

two versions of the buoyancy flux parameter. The buoyancy flux parameter incorporated in the 

ISC-Prime and AERMOD models (Briggs) is defined: 

F— gV S•(T s — Ta) (1) 

7c TS 

where 

F is the buoyancy flux parameter (m 4/sec3 ), 

g is acceleration of gravity (9.8 m/sec Z), 

VSis volume flow rate of stack gases at stack conditions (m 3 /sec), 

Tais ambient air temperature (K), and 

TS is stack gas temperature (K). 

Environmental Health Division of Division of Division of Division of 

Section Chief's Office Air Quality Municipal Facilities Waste Management Water Quality 

701.328.5150 701.328.5188 701.328.5211 701.328.5166 701.328.5210 

Printed on recycled paper. 
Air Quality Staff 2 November 10, 2010 

For calculating plume rise from flare stacks, SCREEN3 uses the following equivalent form of 

the buoyancy flux parameter: 

F = (2 ) 

p rcC PTa 

where 

Q is the net heat release from combustion of gas stream (calories/sec), 

Cp is the specific heat of air (0.24 calories/gram-K), and 

P is the density of air (1205 gram/m 3). 

Setting Equation 1 equal to Equation 2, and solving for Vs provides: 

V 

_ Q Ts (3) 

s CpPTa (Ts — Ta) 

or 

D 

[TpPTa 

QTs 4~ o.s 

(

4

s (Ts— Ta) rcWs ) 

where 

Ds is the stack diameter (m) and 

Wsis the stack exit velocity (m/sec). 

Therefore, if the heat release is known and ambient temperature is assumed, arbitrary virtual 

values of stack velocity, diameter, and temperature can now be established which satisfy this 

equation, and ensures that the model correctly calculates the buoyancy flux parameter for flares. 

The formulation of Equation 4 is consistent with the treatment in SCREEN3, which solves for 

stack diameter in terms of set values for stack velocity and temperature. 

In its policy for flare plume rise, the NDDH now recommends the use of Equation 4 with set 

values of 293 K for ambient temperature, 1000 K for stack temperature, and 40 m/sec for stack 

exit velocity. The use of 293 K for ambient temperature is consistent with SCREEN3 and other 

screening methods. The use of a relatively large value for stack temperature minimizes 

sensitivity of the equation to variations in ambient temperature. Finally, the use of 40 m/sec for 

stack exit velocity is intended as a compromise to ensure the value is not too low to trigger 

inappropriate stack-tip downwash, or too high to trigger inappropriate assumption of momentum 

dominated plume rise in refined models. 
Air Quality Staff 3 November 10, 2010 

Substituting standard values for Cp and P, (as noted above), and assuming fixed values of 

ambient temperature, stack gas temperature, and stack exit velocity, as discussed above, 

Equation 4 reduces to: 

DS = 7.29 x 10-4(Q)0.5 (5) 

for calculating virtual stack diameter. Note that Q is specified as the net heat release from the 

flare. Consistent with SCREEN3, the NDDH assumes that 55 percent of the total heat released is 

lost due to entrainment of ambient air. Therefore, the net heat release, Q, equals 45 percent of 

the total calculated heat release (calories/sec) for the combusted gas stream. 

As in SCREEN3, effective stack height is calculated by adding flame length on to the physical 

stack height: 

and 

hSe = hs+ hf (6) 

h f= 4.56 x 10 -3(Qt)0.4711 (6') 

where 

hSe is the effective stack height for model input (m), 

hsis the physical stack height (m), 

h f is the flame length (m) (Beychok, 1979), and 

Qt is the total heat release from the flare (calories/sec). 

In summary, the following procedure is now used to develop model input parameters for flares. 

1) Set stack exit velocity to 40 ni/sec and stack gas temperature to 1000 K. 

2) Obtain the total flare heat release (calories/sec) by summing the heat of combustion of the 

individual flared gas components, based on the volume flared in one second. Volumetric 

heating values for natural gas stream components are provided in the attached table (one 

Btu = 252 calories). Alternatively, a total of 1200 Btu/ft 3 (302,400 calories/ft) can be 

assumed for typical sweet gas streams in western North Dakota. 

3) Obtain the net heat release, Q, by multiplying the value obtained in Step 2 by 0.45 

(accounts for 55 percent heat loss due to entrainment of ambient air). 

4) Calculate the virtual stack diameter using Equation 5. 

5) Calculate the effective (model input) stack height using Equation 6. 
Air Quality Staff November 10, 2010 

Heat of Combustion* 

Substance Formula 

Molecular 

Weight 

Cubic Ft 

per Lb 

Btu per 

Cubic Ft 

Btu per 

Lb 

Hydrogen H2 2.016 187.723 275.0 51,623 

Carbon Monoxide CO 28.010 13.506 321.8 4,347 

Methane CH4 16.041 23.565 913.1 21,520 

Ethane C2H6 30.067 12.455 1641.0 20,432 

Propane C3H8 44.092 8.365 2385.0 19,944 

Butane C4H I o 58.118 6.321 3113.0 19,680 

Pentane C5H12 72.144 5.252 3709.0 19,517 

Benzene C6H6 78.107 4.852 3601.0 17,480 

Toluene C7H8 92.132 4.113 4284.0 17,620 

Xylene CgHlo 106.158 3.567 4980.0 17,760 

Acetylene C2H2 26.036 14.344 1448.0 20,776 

Napthalene C10H8 128.162 2.955 5654.0 16,708 

Methyl Alcohol CH30H 32.041 11.820 768.0 9,078 

Ethyl Alcohol C2HSOH 46.067 8.221 1450.5 11,929 

Ammonia NH3 17.031 21.914 365.1 8,001 

Hydrogen Sulfide H2S 34.076 10.979 596.0 6,545 

*From American Gas Association 

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