Modeling Flares in BEEST

Contents Overview ............................................................................................................................................... 1 SCREEN3 procedure .............................................................................................................................. 1 Texas procedure.................................................................................................................................... 2 Alabama procedure............................................................................................................................... 3 Iowa procedure ..................................................................................................................................... 3 Ohio procedure ..................................................................................................................................... 5 New Jersey procedure .......................................................................................................................... 6 North Dakota procedure ....................................................................................................................... 7

Overview There is no flare source type in the AERMOD, ISCST3 and ISC-Prime models. Flares are modeled as point sources in these models, so they are entered as point sources in BEEST. The input parameters (such as temperature and stack diameter) are calculated according to a regulatory agency’s published procedure. This document describes several commonly used procedures.

SCREEN3 procedure The SCREEN3 model calculates plume rise for flares based on an effective buoyancy flux parameter. An ambient temperature of 293K is assumed in this calculation and therefore none is input by the user. It is assumed that 55 percent of the total heat is lost due to radiation. Plume rise is calculated from the top of the flame, assuming that the flame is bent 45 degrees from the vertical. SCREEN3 calculates and prints out the effective release height for the flare. SCREEN3 provides the same options for flares as for point sources, including building downwash, complex and/or simple terrain, fumigation, and the automated and/or discrete distances. 1

While building downwash is included as an option for flare releases, it should be noted that SCREEN3 assumes an effective stack gas exit velocity (VS) of 20 m/s and an effective stack gas exit temperature (TS) of 1,273K, and calculates an effective stack diameter based on the heat release rate. These effective stack parameters are somewhat arbitrary, but the resulting buoyancy flux estimate is expected to give reasonable final plume rise estimates for flares. However, since building downwash estimates depend on transitional momentum plume rise and transitional buoyant plume rise calculations, the selection of effective stack parameters could influence the estimates. Therefore, building downwash estimates should be used with extra caution for flare releases. If more realistic stack parameters can be determined, then the estimate could alternatively be made with the point source option of SCREEN3. In doing so, care should be taken to account for the vertical height of the flame in specifying the release height.

Texas procedure Flares are a special type of elevated source that may be modeled as a point source. The technique to calculate buoyancy flux for flares generally follows the technique described in the SCREEN3 Model User’s Guide (EPA, 1995b). Use the following parameters: •

Effective stack exit velocity = 20 meters per second

•

Effective stack exit temperature = 1,273 Kelvin

•

GEP stack height = 65 meters

•

Effective stack diameter

The effective stack diameter (in meters) is calculated using the following equations: DS =

q n * 10 −6

qn = q * (1 − 0.048 * MW ) qn = net heat release in cal/s q = gross heat release in cal/s MW = mean molecular weight of the gas going to the flare 2

Alabama procedure Stack Height = Flare stack height (or GEP stack height if actual height > 65 meters) Exit Velocity = 20 meters per second Exit Temperature = 1,273 Kelvin Compute an effective diameter as follows: DS = (9.88 *10 −4 ) * 0.45 * H H = gross heat release in cal/s Building downwash should be considered if there are any buildings near the flare that have a height greater than or equal to the flare stack height.

Iowa procedure Flare sources can be treated in a similar way as point sources, except that there are buoyancy flux adjustments associated with radiative heat and heat losses. The thermal effects of the flame with its lift and expansion of the plume require an effective stack height and effective stack diameter to be calculated. Effective stack height Due to the high temperature associated with flares, the effective release height of the plume (in meters) can be calculated as follows: HSL = H S + (4.56 * 10 -3 ) * ((

H R 0.478 ) ) 4.1868

HSL = effective flare release height (m) HS = stack height above ground (m) HR = net heat release rate (J/s) = (1 − F ) * H (for a single gas) H = total heat (sensible + radiated) release rate (J/s) F = radiative loss factor (%) The value of the radiative heat loss factor depends on the burning conditions of the flare. If there is information specific to the flare, it should be used. SCREEN3 recommends a default radiative heat loss factor of 55%. This is very conservative as most gases have values about half of that. 3

Gathering the constants together and converting from meters to feet, the effective release height of the plume (in feet) can be calculated as follows: HSL = H S + (7.54 * 10 -3 ) * ( H R

0.478

)

Effective stack diameter The idea here is to adjust the stack diameter (holding other stack parameters constant, including the exit velocity) so that the point source (a virtual flare) will yield the same predicted ambient pollutant concentrations as a flare (modeled as a flare). The effective stack diameter can be determined by equating the buoyancy flux from the flare (hot source—Brigg’s equation 4.20) to the general buoyancy flux equation. Equivalently, this is making the flare plume height equal to that associated with a conventional stack. The buoyancy flux from the flare is: F=

g *HR H = (2.59 * 10 −3 ) * R π * ρ *T * CP T

g = acceleration due to gravity = 9.81 m/s2 ρ = density of air = 1.2 kg/m3 T = air temperature (K) CP = specific heat of dry air constant = 1,004 J/(kg*K) The buoyancy flux for stack releases is: 2

F = g * VS * RS *

TS − T TS

VS = exit velocity (m/s) RS = stack inner radius (m) TS = stack exit temperature (K) Setting these two equations equal, solving for the stack diameter (2*RS), substituting the above values for the constants, and converting from meters to feet, the effective stack diameter (in feet) is: DS = 0.1066 *

TS H * R T * (TS − T ) VS

Thus, using an estimated stack gas exit temperature and the actual exit velocity to the flare, an effective stack diameter can be calculated. 4

NOTE 1: All parameters in the above equations are in mks units. NOTE 2: Another way of computing the net heat release from the total heat release is: HR = H * (1 − 0.048 * MW ) MW is the (mean) molecular weight of the flared gas. If the molecular weight is reasonably certain, this is an alternative method of determining the effective stack parameters. The Ideal Gas Law and emission rate determination One form of the Ideal Gas Law is: P=

ρ * R *T M

or ρ =

P*M R *T

ρ = mass density of gas (g/m3) P = pressure of gas = 101.325 kPa M = molecular weight of gas = 64.1 g/mole for SO2 R = gas constant = 8.314 J/(mole*K) T = temperature (K) The emission rate can thus be expressed as: Emission rate = gas flow rate * ρ NOTE 1: The gas flow rate is converted to metric units (m3/s), yielding an emission rate in g/s. This is subsequently converted to English units (lb/hr). NOTE 2: The gas flow and density should be expressed for the same standard temperature and pressure (STP) conditions. Herein, it is 70°F (294 K) and 1 atm (101.325 kPa).

Ohio procedure For screening purposes, the flare option in SCREEN3 or AERSCREEN is acceptable. For refined modeling, it is necessary to compute equivalent emission parameters, i.e., adjusted values of temperature and stack height and diameter. Several methods appear in the literature, none of which seems to be universally accepted. Ohio EPA/DAPC has used the following procedure, which is believed to be consistent with SCREEN3 and AERSCREEN. 5

1. Compute the adjustment to stack height as a function of heat release Q (in MMBtu/hr). Hequiv = Hactual + 0.944 * Q 0.478 The stack height H has units of meters. 2. Assume temperature of 1,273 Kelvin. 3. Assume exit velocity of 20 meters per second. 4. Assume the following buoyant flux: FB = 1.162 * Q 5. Back-calculate the stack diameter that corresponds to the above assumed parameters. Recall the definition of buoyant flux: FB = 3.12 * V *

Tstack − Tambient Tstack

V is the volumetric flow rate in actual m3/s. Substituting for FB and solving for the equivalent stack diameter Dequiv we get: Dequiv = 0.1755 * Q This method pertains to the “typical” flare, and will be more or less accurate depending on various parameters of the flare in question, such as heat content and molecular weight of the fuel, velocity of the uncombusted fuel/air mixture, presence of steam for soot control, etc. Hence, this method may not be applicable to every situation, and the applicant may submit their own properly documented method in a modeling protocol.

New Jersey procedure Unlike enclosed flares, open flares are unique point sources as they do not have a defined stack exit diameter. For modeling, it is necessary to compute equivalent emission parameters, i.e. adjusted values of temperature, stack height and "stack" inside diameter. SCREEN3 has a source category for flares, and makes these adjustments internally. AERMOD does not have a source category for flares and therefore need to have the adjustments made by the modeler. The approach consistent with SCREEN3 is as follows. 6

1. Compute the adjustment to stack height (H in meters) as a function of total heat release Q (in MMBtu/hr): Hequivalent = Hactual + 0.944 * Q 0.478 NOTE 1: some flares are rated in calories per second and the conversion factor is 14.3 Btu/hr for every cal/s. NOTE 2: the adjustment is to account for flame length and assumes the flame is tilted 45-degrees from the vertical. 2. Assume a temperature of 1,273 Kelvin. 3. Assume an exit velocity of 20 meters per second. 4. Assume an effective stack diameter Deff of: Deff = 0.1755 * Q Equivalent diameter is applicable for both vertical and horizontal flares since it is back calculated from a buoyancy flux assumption. Buoyancy flux is not a function of flare orientation. Therefore, the equation can be used for both horizontal and vertical flare orientations. This method pertains to the "typical" flare, and will be more or less accurate depending on various parameters of the flare in question, such as heat content and molecular weight of the fuel, velocity of the uncombusted fuel/air mixture, presence of steam for soot control, etc. Hence, this method may not be applicable to every situation; therefore, the applicant may submit their own properly documented method for review and approval.

North Dakota procedure 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. 7

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 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. The following procedure is now used to develop model input parameters for flares. 1. Set stack exit velocity to 40 meters per second and stack gas temperature to 1000 K. 2. Obtain the total flare heat release, QT (in cal/s), by summing the heat of combustion of the individual flared gas components, based on the volume flared in one second. 3. Obtain the net heat release, Q (in cal/s), by multiplying the value obtained in Step 2 by 0.45 (this accounts for 55 percent heat loss due to entrainment of ambient air). 4. Calculate the virtual stack diameter, DS, as follows: DS = (7.29 *10 −4 ) * Q DS is the stack diameter (m) Q is the net heat release from combustion of gas stream (cal/s) 5. Calculate the effective (model input) stack height, HSE, as follows: HSE = H S + H F HF = (4.56 * 10 −3 ) * QT

0.478

HSE is the effective stack height for model input (m) HS is the physical stack height (m) HF is the flame length (m) QT is the total heat release from the flare (cal/s)

8