Pseudo-source parameters for flares: Derivation, implementation, and comparison

ABSTRACT

The United States Environmental Protection Agency (US EPA) flare pseudo-source parameters are over 30 years old and few dispersion modellers understand their basis and underlying assumptions. The calculation of plume rise from the user inputs of pseudo-stack diameter, temperature and velocity have the most influence on air dispersion model predictions of ground-level concentrations. Regulatory jurisdictions across Canada, the United States and around the world have adopted their own approach to pseudo-source parameters for flares; all relate buoyancy flux to the heat release rate, none consider momentum flux and flare tip downwash as adopted by the Alberta Energy Regulator (AER). This paper derives the plume buoyancy flux for flares burning a gas in terms of combustion variables readily known or calculated without simplifying assumptions. Dispersion model prediction sensitivity to flared gas composition, temperature and velocity, and ambient conditions are now correctly handled by the AER approach. The AER flare pseudo-source parameters are based on both the buoyancy and momentum flux, thus conserving energy and momentum. The AER approach to calculate the effective source height for flares during varying wind speeds is compared to the US EPA approach. Instead of a constant source for all meteorological conditions, multiple co-located sources with varying effective stack height and diameter are used. AERMOD is run with the no stack tip downwash option as flare stack tip downwash is accounted for in the effective stack height rather than the AERMOD model calculating the downwash incorrectly using the pseudo-source parameters. The modelling approaches are compared for an example flare. Maximum ground level predictions change, generally increasing near the source and decreasing further away, with the AER flare pseudo-source parameters. It's time to update how we model flares.

Implications: What are the implications of continuing to model flare source parameters using the overly simplified US EPA approach? First, the regulators perpetuate the myths that the flare source height, temperature, diameter and velocity are constant for all wind speeds and ambient temperatures. Second, that it is acceptable to make simplifying assumptions that violate the conservation of momentum and energy principles for the sake of convenience. Finally, regulatory decisions based on simplified source modelling result in predictions that are not conservative (or realistic). The AER regulatory approach for flare source parameters overcomes all of these shortcomings. AERflare is a publicly available spreadsheet that provides the “correct” inputs to AERMOD.

Introduction

The Alberta Energy Regulator (AER) regulates Alberta’s oil and gas industry and has done extensive development of un-combusted and combusted sour gas release dispersion models with spreadsheet interfaces. Sour gas contains hydrogen sulfide (H₂S) that is converted to sulfur dioxide (SO₂) during combustion. The Energy Resources Conservation Board (ERCB), the predecessor of the AER, developed ERCBH2S to calculate emergency response and planning zones for accidental, un-combusted releases of H₂S (ERCB 2010) using SLAB. AERflare-incin is a regulatory tool for permitting routine and non-routine operations of sour gas flares and incinerators (AER 2014) using the atmospheric dispersion modeling system known as AERMOD developed by the American Meteorological Society and United States Environmental Protection Agency (US EPA) Regulatory Model Improvement Committee.

Flaring of sour gas is associated with sour oil and gas well tests, production, and processing; and upgrading of bitumen and the refining of oil. Sour gas is found in the foothills of the Rocky Mountains and flaring often resulted in predicted exceedances of air quality objectives on the elevated terrain using regulatory modeling approaches adopted from the US EPA. AER required operators to implement an air quality management plan that involved mobile and fixed monitoring in areas of predicted exceedances. Elevated concentrations of SO₂ were seldom measured during flare monitoring. Were they monitoring in the right locations based on the meteorology and dispersion modeling? Field observations of flare flame angles and heights during varying wind speeds and flaring rates lead the AER to question the validity of source modeling based on a constant effective source height. Flame models developed for assessing ground-level thermal radiation from flares were initially used to estimate the effective stack height at average wind speed and ambient temperature conditions for input into screening dispersion models. The AERMOD model allows for both multiple sources and time-varying emissions, thus allowing variations in physical heights and diameters and emissions parameters. The effective stack height depends on the flared gas momentum relative to the momentum of the wind and will be higher at low wind speeds and lower at high wind speeds. The AER effective stack height changes result in more realistic flare source modeling.

Regulatory jurisdictions across Canada, the United States, and around the world have adopted their own approach to pseudo-source parameters for flares; all relate buoyancy flux to the heat release rate, and none consider momentum flux and flare tip downwash as adopted by the AER. This article examines the inputs to dispersion models starting with the buoyancy and momentum flux and the assumptions made to simplify the calculations. It then discusses the effective stack height and pseudo-source parameters for flares that allow for combustion as the gas exits the flare tip. Implementing multiple pseudo-sources for a flare is described. A comparison is then made between the current US EPA and the AER approach on pseudo-source inputs and predicted concentrations using AERMOD Version 18081.

Source buoyancy flux

Briggs (1984) developed the volume flux of buoyant acceleration F_bs for a density difference at the source:

(1) $F_{bs}\equiv \frac{g}{\pi }\left(\frac{{\rho }_a-{\rho }_s}{{\rho }_a}\right)Q_s=\frac{g}{\pi }\left(1-\frac{T_a{M}_s}{T_s{M}_a}\right)Q_s\approx \frac{g}{4}{D}_s^2{V}_s\left(\frac{T_s-T_a}{T_s}\right),$(1)

where F_bs (m⁴/sec³) is the source buoyancy flux, g (9.806 m/sec²) is the gravitational constant, ρ_a (kg/m³) is the ambient air density, ρ_s (kg/m³) is the source gas density, Q_s (m³/sec) is the source volume flow rate, T_a (K) is the ambient temperature, T_s (K) is the source temperature, M_s (kg/kmol) is the source molar mass, M_a (kg/kmol) is the air molar mass, D_s (m) is the source diameter, and V_s (m/sec) is the source velocity---all at flowing conditions. The assumption made in the approximate equation used within AERMOD (US EPA 2017) is that M_s = M_a, which may be a reasonable approximation for hot stack gases with excess air.

For flares, the flowing conditions are at T_s and P_s (kPa), with P_s = P_a the atmospheric pressure. F_bs does not change with P_a since it cancels out of the density ratio, but it is sensitive to the temperature ratio. Note that V_s is referenced to P_a. By definition, this is the buoyancy flux at the source that will change as air is entrained, as shown later.

For a flare, the temperature, velocity and diameter of the combusted gases are not readily available. However, we know the energy of the hot plume, as shown by Briggs (1969) and Beychok (2005):

(2) $H_a={\dot{m}}_s{C}_{ps}(T_s-T_a)\approx \left({\dot{m}}_{f}NH{V}_f^o{\eta }_{plume}\right),$(2)

where the new variables are: H_a (J/sec) is the source enthalpy rate of the combusted flare gas relative to the air temperature, ṁ_s (kg/sec) is the source mass flow rate, and C_ps (J/(kg∙K)) is the source average specific heat from T_s to T_a on a mass basis. The heat of the plume is approximated using the product of ṁ_f (kg/sec) the un-combusted flare gas mass flow rate, NHV°_f (J/kg) the net heating value on a mass basis of the flare gas relative to reference conditions (15°C and 101.325 kPa in the oil and gas industry), and η_plume the fraction of heat released to the plume. Note that η_plume is equal to the (combustion efficiency*(1-radiation heat loss)). The US EPA (1986) uses a value of 45% (55% of the heat that could be released is lost due to incomplete combustion and radiation losses) based on a study done in Alberta where oil was injected into a sour gas flare to make the black smoky plume visible to measure the plume rise (Leahey and Davies 1984). Further manipulation of Equations 1 and 2 and introducing the ideal gas law leads to the equation used by US EPA (1986) for modeling flares:

(3) $F_{bs}\approx \frac{g}{\pi }\left(\frac{T_s-T_a}{T_s}\right)\frac{{\dot{m}}_s}{{\rho }_s}\approx H_a\left(\frac{g{R}_U}{\pi C_{ps}{M}_a{P}_a}\right)\approx \left({\dot{m}}_{f}NH{V}_f^o{\eta }_{plume}\right)\left(\frac{g{R}_U}{\pi C_{pa}{M}_a{P}_a}\right),$(3)

where the new variable is R_u (8.3145 (kPa m³)/(K∙kmol)) the universal gas constant. The simplifying assumptions made are that M_s = M_a, C_ps = C_pa and that NHV°_f is used to approximate the plume enthalpy relative to ambient conditions. At ambient temperature, C_ps ≈ C_pa, but the average C_ps increases with temperature. F_bs now changes with P_a, but it is not too sensitive to T_a, as will be shown later. Note the ambient pressure affects the buoyancy but is set to the reference pressure in the US EPA approach, probably to match NHV°_f, which is at reference conditions. Since buoyancy is on a volume basis, F_bs will increase as the atmospheric pressure decreases. When used with Equation 1 for F_bs in the dispersion model, T_a is allowed to vary hour-by-hour, which changes buoyancy flux and thus the rise. To define H_a without simplifying assumptions, a combustion energy balance must be done.

Plume buoyancy flux

In the earlier AER work on un-combusted H₂S dispersion, the plume buoyancy flux equation was derived from the conservation principles to determine the buoyancy flux of cold, high-velocity releases from sour gas well blow-outs and pipeline ruptures that contain aerosols (Wilson 2010). In the limit, as infinite ambient air is added to the source, the plume buoyancy flux is

(4) $F_{bp}=\frac{g{\dot{m}}_s}{\pi {\rho }_a}\left[\frac{C_{ps}}{C_{pa}}\frac{T_s}{T_a}-\frac{C_{ps}}{C_{pa}}+\frac{M_a}{M_s}-1\right]=\frac{g{R}_U{\dot{m}}_s}{\pi M_a{P}_a}\left[\frac{C_{ps}}{C_{pa}}\left(T_s-T_a\right)+\left(\frac{M_a}{M_s}-1\right)T_a\right],$(4)

where the new variable is F_bp (m⁴/sec³) the plume buoyancy flux. The source mass flow rate includes excess air if this was a traditional stack exit or the end of a flame. Average specific heats between T_s and T_a must be used. T_s is the effective stagnation source temperature (static temperature plus temperature increase due to kinetic energy minus temperature reduction for vaporizing the aerosol fraction). This equation can be shown to be equivalent to Briggs (1975) early work where T_s is defined as the total temperature (which includes the kinetic energy). If it is assumed that M_s = M_a and C_ps = C_pa, then the plume buoyancy (Equation 4) reduces to the source buoyancy (Equation 1). It can be shown that buoyancy flux does change from the source to downwind in the plume, but only by a few percentage points.

The following expression for F_bp was derived by the lead author starting from Equation 4 to eliminate T_s by doing an energy balance (AER 2011). It is dependent on the flare flow rate divided by the site atmospheric pressure times a constant and the sum of five terms:

(5) $\begin{array}{r}{F}_{bp}=\frac{{\dot{m}}_f}{P_a}\frac{g{R}_U}{\pi M_a}\left[\begin{array}{c}\frac{NH{V}_f^0{\eta }_{plume}}{C_{pa}}+\frac{C_{pf}\left(T_f-T_0\right)}{C_{pa}}+R_{s/f}\left(\frac{M_a}{M_{stoich}}-1\right)T_a\\ -R_{s/f}\left(\frac{C_{pstoich}}{C_{pa}}-1\right)\left(T_a-T_0\right)-\left(T_a-T_0\right)\end{array}\right],\end{array}$(5)

where the new variables are: C_pf (J/(kg∙K)) is the mass-specific heat of the flare gas, R_s/f is the stoichiometric exhaust to fuel mass ratio, M_stoich (kg/kmol) is the stoichiometric molar mass of the exhaust products, C_pstoich (J/(kg∙K)) is the stoichiometric mass specific heat of the exhaust products, and T₀ (K) is the reference temperature for the net heating value.

This solution for the buoyancy flux of a combustion source is applicable to a flare or a stack exit. Notice that F_bp is independent of the excess air and only the stoichiometric combustion properties are required. This equation confirms that one cannot increase the buoyancy of a hot stream relative to the ambient air by adding excess air through entrainment. Equations 4 and 5 give the same result for F_bp if the calculations are done correctly.

The first term in the bracket is F_bs given by Equation 3 when multiplied by the common unit term. It represents the energy released to the plume by the fuel relative to reference conditions with the process and radiation losses accounted for. The AER sets η_plume for a flare based on a literature review that recommended 25% radiation losses for flare dispersion modeling (AENV 2000) in Alberta, but the user can override the default. AERflare also includes the flare combustion efficiency due to incomplete conversion (Kostiuk, Johnson, and Thomas 2004). The first term is the dominant contributor to buoyancy. Four of the five terms are relative to T₀ used to define NHV°_f. The last four terms change F_bp about 1% from F_bs for typical methane flare exhaust products but should not be ignored, because of their dependence on T_a.

The second term represents the sensible energy due to the fuel. This term is zero when T_f = T₀. The AER default value for T_f is T_a, but T_f can be set by the user. The third term allows for the difference in molar mass of the stoichiometric exhaust stream and the air. For methane combustion, R_s/f is about 18.2 and (M_a/M_stoich – 1) is about 0.044 so the product is about 0.81, which is then multiplied by T_a. For extremely sour gas or acid gas flaring, the buoyancy can be reduced by this term if the sulfur dioxide and/or carbon dioxide concentration are high enough such that M_stoich > M_a. The fourth term allows for the difference in specific heats between T₀ and T_a. Average specific heats on a mass basis between T_stoich and T₀ for the source and between T_a and T₀ for the air must be used. For methane combustion, R_s/f is about 18.2 and (C_pstoich/C_pa – 1) is about 0.22, so the product is about 3.9, which is then multiplied by (T_a – T₀). The fifth term is the difference in temperature between T_a and T₀ and if they are equal it is zero.

For a flare or other combustion device that uses ambient air, we can see that by assuming M_a = M_stoich, C_pa = C_pstoich, and T_f = T₀, F_bp is a very weak function of ambient temperature T_a given by the fifth term as the first term is very much larger and only changes slightly with C_pa. With T_a = T₀, Equation 5 for F_bp is the same as Equation 4 for F_bs.

To illustrate using the AERflare spreadsheet, say F_b is 100 for a reference and ambient temperature of 15°C for the combustion of methane with 55% heat loss. The simplified US EPA approach yields an F_bs of 105.2 at −40°C ambient and 97.6 at 40°C ambient with constant T_s of 1000°C. The refined approach yields F_bp of 100.5 at −40°C ambient with a calculated T_s of 538°C and F_bp of 99.7 at 40°C ambient with a calculated T_s of 608°C. F_bp is essentially constant with ambient temperature for the refined approach. Also note the difference in temperatures between the source and ambient varies only 10°C from 578 to 568°C using the refined approach compared to 80°C from 1,040 to 960°C for the simplified approach for ambient temperatures of −40 to 40°C, respectively. The energy balance confirms that a flare ingesting air at −40°C will not be as hot as one ingesting air at 40°C, assuming a constant heat loss fraction.

First, the US EPA assumed source temperature of 1,000°C is too high for a methane flare with such high heat losses. T_s is estimated for any flared gas composition assuming constant air properties in the AERflare spreadsheet (635°C in this example) as a starting guess for the iterative solution of the temperature. Second, for flares or other combustion device that consume ambient air and do not have an exit temperature controller, the modeled source temperature should not be held constant as the ambient temperature changes. As demonstrated in the previous paragraph, a better approximation is holding the difference between the source and ambient temperature constant, rather than the source temperature constant.

Source momentum flux

Briggs (1969) defines F_ms (m⁴/sec²) as the source momentum flux:

(6) $F_{ms}=\frac{V_s{Q}_s{\rho }_s}{\pi {\rho }_a}=\frac{V_s{\dot{m}}_s}{\pi {\rho }_a}=\frac{M_s{T}_a}{M_a{T}_s}{V_s}^2\frac{{D_s}^2}{4}\approx \frac{T_a}{T_s}{V_s}^2\frac{{D_s}^2}{4},$(6)

where the variables have been previously defined. The last term of Equation 6 is an approximation assuming M_s = M_a and is used within AERMOD (US EPA 2017). Note that F_ms varies directly with the temperature ratio.

The momentum of a flare starts with the un-combusted source gas exiting the flare tip. As air is entrained the mixture velocity decreases to conserve momentum, flare gas burns and the density of the mixture of combustion products and un-combusted flare gas decreases as the temperature increases until all of the flared gas is burned. To be conservative, this increase in momentum due to the hot gases is ignored in the current AER approach and the flare gas momentum is conserved from the flare tip to the end of the combustion zone. The flare gas momentum flux F_mf (m⁴/sec²) is

(7) $F_{mf}=\frac{V_f{Q}_f{\rho }_f}{\pi {\rho }_a}=\frac{V_f{\dot{m}}_f}{\pi {\rho }_a}=\frac{M_f{T}_a}{M_a{T}_f}{V_f}^2\frac{{D_f}^2}{4},$(7)

where the new variables are: V_f (m/sec) is the flare gas exit velocity, Q_f (m³/sec) is the flare volume flow rate, ρ_f (kg/m³) is the flare gas density all at flowing conditions, ρ_a (kg/m³) is the density of the ambient air, M_f (kg/kmol) is the flare gas molar mass, and D_f (m) is the flare tip diameter. Note that F_mf varies directly with the temperature ratio which is set by the user. With the AER default of T_f = T_a the ratio is one.

Flare pseudo-source parameters

Dispersion models require the input of the stack source T_s, V_s, D_s, and the height h_s. For a flare, pseudo-source parameters (V_s^*, D_s^*, T_s^*, and h_s*) are used. AERMOD calculates the buoyancy flux using Equation 1 and the momentum flux using Equation 6 based on the input V_s^*, D_s^*, and T_s^* along with h_s* to determine the initial plume trajectory and the final plume rise. T_a is known and varies hourly. Pseudo-parameters should not be used for stack tip downwash adjustments.

The US EPA approach for flares uses the buoyancy flux F_bs defined by Equation 3. With one equation and three unknown variables, two of the variables must be specified, and then the third one can be solved. The US EPA (1986) assumes T_s^* of 1,273 K and V_s^* of 20 m/sec, then calculates D_s^* based on Equation 1 from:

(8) $D_s^{\ast }=2\sqrt{\frac{F_{bs}}{g{V}_s^{\ast }}\left(\frac{T_s^{\ast }}{T_s^{\ast }-T_a}\right)},$(8)

Since momentum flux is not considered by the US EPA approach, it is not conserved. With older US EPA dispersion models, this did not matter as the plume was placed at the final rise which was the maximum plume rise due to buoyancy or momentum, and buoyancy rise dominates for flares.

The AER approach considers both buoyancy flux using F_bp defined by Equation 5 and momentum flux F_mf defined by Equation 7. With these two equations and three unknown variables, one of the variables must be specified and then the other two can be solved for. The AER calculates T_s^* for each T_a, then calculates V_s^* from:

(9) $V_s^{\ast }=\frac{g{F}_{mf}}{F_{bp}}\left(\frac{T_s^{\ast }-T_a}{T_a}\right).$(9)

Notice that both momentum and buoyancy are considered. Similar to Equation 8, D_s^* is then calculated from:

(10) $D_s^{\ast }=2\sqrt{\frac{F_{bp}}{g{V}_s^{\ast }}\left(\frac{T_s^{\ast }}{T_s^{\ast }-T_a}\right)}.$(10)

To illustrate momentum conservation, flaring pure methane results in an exhaust to fuel mass ratio of about 35 that is about 3 times hotter than the ambient temperature. To conserve momentum as the plume mass increases and heats up due to combustion, the stack velocity V_s^* decreases to about (V_f/35) x 3, or about 1/10 of the flare tip exit velocity V_f. With V_s^* being 10% of the flare tip velocity, the required diameter D_s^* is very large to allow for the entrained air but conserves mass, momentum and energy.

The AER is often asked by modelers how realistic these inputs are in comparison to the US EPA inputs? First, the US EPA inputs are assumed to have some real physical meaning, but they too are pseudo-parameters! AER pseudo-parameters are calculated from energy and momentum balances for the sole purpose of calculating F_b and F_m correctly within the dispersion model. These are not real values, they are pseudo-source parameters that the dispersion model needs to conserve buoyancy and momentum: picture them as a horizontal slice across a flame tip to represent a vertical stack exit. Ideally, regulators should modify the dispersion model to allow flare sources at random angles to the horizontal with much smaller diameters and larger velocities representing reality, to avoid the need of using pseudo-parameters.

Effective stack height and stack tip downwash

The current flare flame length is based on the total heat released assuming complete combustion and no losses (US EPA 1986). The effective height from Beychok (2005) and US EPA (1995) assumes the midpoint of a flame angled at 45 degrees from horizontal and is independent of flare tip exit velocity and wind speed at the flare tip. Stack tip downwash is then calculated based on the ratio of the assumed pseudo-velocity V_s^* (20 m/sec) and wind speed U_a at the stack height h_s, and the calculated pseudo-diameter D_s^*. This stack tip downwash adjustment has no physical basis, but fortunately, it is only invoked when the wind speed exceeds V_s^*/1.5 (20/1.5 ~ 13.3 m/sec) and does not approach the maximum correction of 3 times the pseudo-diameter D_s^*.

The AER effective height of the flare source is determined by calculating the flame vertical height using the Brzustowski (1974) flame model. As documented in AER (2011), Brzustowski uses a dimensionless lower flammability limit to determine the flame tip position along a dimensionless jet axis and then converts to the vertical and downwind distances using the ratio of flare-tip to cross-wind momentum and the flare tip diameter. The effective height of the flare source h_s* (m) is calculated from: the physical height of the flare stack h_s; the vertical flame height z_L, and the US EPA (2017) stack tip downwash based on the actual flare diameter D_f and ratio of V_f and U_a:

(11) $h_s^{\ast }=h_s+z_L+2min\left(D_f\left(\frac{V_f}{U_a}-1.5\right),0\right).$(11)

Since we are accounting for the flare tip stack downwash outside the model, AERMOD is run with the no stack tip downwash (NOSTD) option in AERflare to prevent false downwash corrections based on the pseudo-diameter and pseudo-velocity.

AERflare multi-source hour-by-hour implementation in AERMOD

The AERflare source calculations cannot be implemented directly within the current version of AERMOD because the variable emission file only varies the emission variables (velocity, temperature, and emissions) and not the physical variables (stack height and diameter). However, AERMOD allows for both multiple sources and time-varying emissions, thus allowing variations in physical heights and diameters and emissions variables. Because meteorology affects both the emission and physical variables leading to flare pseudo-parameters, some simplifications are adopted to implement the AERflare source model in the AERMOD modeling framework.

In principle, the methodology is to represent multiple co-located sources with a single source having an emission for each hour. Instead of trying to model hour-by-hour sources, two simplifications are used. First, the meteorological dataset is reduced by using wind speed increments of 0.5 m/sec and integer temperature increments. This reduces the meteorological variations from 8,760 for a year to a few thousand site-specific unique combinations. Because the spreadsheet is used as the source calculation engine and is relatively slow compared to a coded implementation of the calculations, the reduced meteorological dataset reduces the number of spreadsheet re-calculations. Second, the number of pseudo-sources is reduced by dividing the range of effective stack heights into a convenient number and using the average pseudo-value for each stack height and diameter combination.

The AERflare default number of sources is nine, but it can be changed by the user. The choice of nine sources was determined by observing when the predictions change less while the overall methodology could still be applied relatively computationally quickly.

Comparison of US EPA and AERflare modeling approaches

The effect of the pseudo-source parameters and multiple emission sources is demonstrated in this section. Table 1 provides the comparison cases that were run through AERflare using the AERSCREEN option. Flat terrain was used in all cases. Land use in the surrounding area is a coniferous forest for the screening meteorology. The elevation was set to sea level to allow the atmospheric pressure to be the reference value (101.325 kPa) in the US EPA approach and to 1,000 m for Alberta (89.877 kPa). Radiation heat loss is set to 55% for the US EPA approach. AERflare predicts the flare conversion efficiency based on the wind speed, flare exit velocity, diameter, and the heating value of the flared gas, and 25% radiation heat loss from the combusted portion to calculate the heat to the plume. The US EPA pseudo-source parameters are based on an ambient temperature of 20°C. The hour-by-hour temperature is used in the dispersion modeling. In Alberta, the screening ambient temperatures vary from −53°C to + 39°C with an average of 5°C.

Table 1. Comparison cases.

Case	Radiation Heat Loss (%)	Site Elevation (m)	Pseudo-Source Parameter Modeling
EPA55-0-Constant	55	0	Constant height, diameter, velocity and temperature ^a
EPA55-0-DeltaT	55	0	Constant height, diameter and velocity with temperature set at 980°C above ambient ^a
AER55-1000-HBH	55	1,000	Variable height, diameter, velocity and temperature ^b
AER25-1000-HBH	25	1,000	Variable height, diameter, velocity and temperature

Notes. ^a 20°C assumed for flare gas and ambient temperature and reference pressure to determine buoyancy flux and pseudo-source parameters.

^b Hour-by-hour ambient temperature used for flare gas and site pressure to determine buoyancy and momentum flux and source temperature. Hour-by-hour wind speed and ambient temperature and site pressure used for effective height.

The US EPA approach pseudo-parameters are held constant for all hours of meteorology. The delta temperature (DeltaT) mode uses a feature in AERMOD that adjusts the source temperature to a constant delta above the ambient temperature by inputting a negative value (−980) but otherwise use constant pseudo-parameters. The AERflare hour-by-hour mode uses nine different source height and diameter bins that have a null emission rate unless the modeled hour of meteorology is within the bin limits as described in the previous section: then the pollutant emission rate is used with a calculated temperature and pseudo-velocity and pseudo-diameter for that hour of meteorology.

Table 2 provides the example flaring parameters, dispersion model inputs, and calculated values for the comparison cases. The AERflare default Alberta average wind speed of 3.5 m/sec and ambient temperature of 5°C are used for demonstrating the AER pseudo-parameters in the table. The AER flare temperature is calculated with excess air added so the un-combusted mixture is at the lower flammable limit, which corresponds to the flame model. The US EPA momentum flux is much larger and can be several orders of magnitude larger than reality for flares with exit velocities less than the assumed 20 m/sec.

Table 2. Example flare modeling parameters, inputs, and values for each case.

Flaring Parameter	Value
Flare stack exit height	30.5 m
Flare stack exit diameter	305 mm
Flare gas flow rate	100 10^3m^3/day
Flare gas composition	30% H2S and 70% CH4
Complete combustion net heat release rate	3.51 × 10^7 J/sec (8.39 × 10^6 cal/sec)
SO2 emission rate	940.8 g/sec
Dispersion Model Input Parameter	EPA55-0- Constant & DeltaT	AER55-1000- Hour-by-hour	AER25-1000- Hour-by-hour
Pseudo-Temperature (K)	1273 & −980	775.30	1075.64
Pseudo-Velocity (m/sec)	20.000	0.570	0.551
Pseudo-Diameter (m)	1.919	13.228	16.130
Effective Stack Height (m)	39.799	35.102^a	35.102^a
Assumed Ambient (K)	293^b	278.15	278.15^c
Calculated Values
Flared Gas Exit Velocity (m/sec)	Not considered	17.240	17.240
Flame Angle from Horizontal (°)	45.0 (constant)	17.9^a	17.9^a
Buoyancy Flux (m^4/sec^3)	139.05	156.59	260.76
Momentum Flux (m^4/sec^2)	84.79	5.11	5.11

Notes. ^a At site average wind speed of 3.5 m/sec.

^b Assumed ambient and flare gas temperature and reference pressure for pseudo-parameters presented above that are held constant within model except for ambient temperature.

^c Assumed ambient and flare gas temperature and site pressure for pseudo-parameters presented above that all change hour-by-hour within the model and for calculated values below.

Figure 1 compares how the momentum and buoyancy fluxes for the example flare vary with ambient temperature. The US EPA momentum is arbitrarily set with no regard for conserving momentum while the AER method uses the momentum of the un-combusted gas at the flare tip which is very much less than the US EPA. The EPA55-0-Constant and DeltaT case buoyancy fluxes are about 13% less than the AER55-1000-HBH at 20°C due to the ambient pressure reduction. The buoyancy flux increases in the AER25-1000-HBH case due to the reduced plume heat loss. The irregularities in the AER buoyancy flux lines are due to combustion inefficiency that varies from 99.6% at low wind speeds to 97.5% at high wind speeds. Notice how the EPA fluxes crossover at the assumed reference temperature of 20°C and are sensitive to ambient temperature. The DeltaT approach slightly reduces this sensitivity to the ambient temperature but the high assumed source temperature of 1,273 K dominates the temperature ratios used in the flux calculations.

Figure 1. Comparison of modeled flux changes with ambient temperature.

Figure 2 compares how the effective stack height including downwash effects varies with the 10 m reference height wind speed. The 30.5 m high flare stack has a higher, upright flame at low wind speeds and a lower, almost horizontal flame at higher wind speeds. The EPA effective height is constant at 39.8 m until a wind speed of 13.3 m/sec where pseudo-downwash effects are implemented.

Figure 2. Comparison of modeled effective stack heights including stack tip downwash.

Figure 3 compares the maximum predicted ground level concentrations of SO₂ as a function of downwind distance from the example flare. The EPA cases predict lower maximum values near field (< 600 m) due to the higher momentum flux than the AER cases, resulting in a more upright initial trajectory. Mid-field (> 600 m and < 3,800 m), the EPA cases predict similar values to the AER55 case even though there is less buoyant rise. The AER25 case has higher buoyancy resulting in lower predictions. Near-field the hour-by-hour approach predicts higher due to lower effective stack heights at high wind speeds and in the mid-field it predicts lower due to higher effective stack heights at low wind speeds. In the far-field (> 3,800 m) the AER55 case predicts lower concentrations due to the higher buoyancy and plume rise but predictions converge due to the common SO₂ mass emission rate and thorough mixing in the surface layer. The maximum concentration predictions are used for stack height design and would increase when the AER approach that does not make simplifying assumptions is used.

Figure 3. Comparison of maximum predicted SO₂ concentrations.

Using the DeltaT source temperature approach with the EPA pseudo-parameters result in almost the same maximum predictions as the constant source temperature approach at elevated ambient temperatures. This is because the assumed source temperature is too high for the assumed heat losses and dominates the temperature ratio, but the colder season predictions did increase.

Figure 4 compares the average predicted ground level concentration of SO₂ as a function of downwind distance from the example flare. The EPA55-0-Constant case predicts lower average values near field (< 600 m) than the EPA55-0-DeltaT and AER55 case. Beyond 600 m the average predictions are very similar. The AER25 case has higher buoyancy resulting in lower predictions. All predictions converge far downwind due to the common SO₂ mass emission rate and thorough mixing in the surface layer. The average concentration predictions are used for long term air quality assessments and increase slightly with the AER55 approach compared to the EPA55-0-Constant approach but are almost the same as the EPA55-0-DeltaT approach.

Figure 4. Comparison of average predicted SO₂ concentrations.

Summary

Prediction sensitivity to flared gas composition and temperature, and ambient temperature and pressure are correctly handled by the AER approach. The derived plume buoyancy flux formulation in combustion terms for flares will result in greater flux than simplified source buoyancy flux formulations mainly due to using the atmospheric pressure rather than the reference pressure. The derived formula accounts for the plume energy and molar mass of stoichiometric combustion products. The algorithms reduce to the classical Briggs buoyancy flux used by US EPA when the simplifying assumptions of the plume having the same molar mass and specific heat of the ambient air are made.

The US EPA approach results in the buoyancy and momentum flux calculated in the model being overly sensitive to the ambient temperature. This study shows that for flares or another combustion device that consume ambient air and does not have an exit temperature controller, the modeled source temperature should not be held constant as the ambient temperature changes, rather assuming the difference between the source and ambient temperature is held constant is a better approximation. The US EPA momentum flux needs to be related to the actual flare exit velocity rather than being arbitrarily set.

An attempt was made to adjust the US EPA modeling approach by using a feature in AERMOD that adjusts the source temperature to a constant delta above the ambient temperature by inputting a negative value. This only slightly reduced the buoyancy and momentum flux sensitivity to ambient temperature because the assumed source temperature of 1,273 K is much too high for the assumed heat losses and dominates the ambient to source temperature ratio used in the flux calculations.

The AERflare pseudo parameters are based on conservation of both buoyancy and momentum flux. This approach conserves momentum rather than the US EPA approach of arbitrarily assigning the flare a velocity and thus momentum flux. The effective stack height changes with wind speed based on flare flame models. The AER approach is best applied using an hour-by-hour variation of stack height and stack diameter source parameters and is implemented in AERflare using AERMOD with hourly pseudo-source and emission parameters. The source is characterized by a pseudo-height that takes into account stack tip downwash using the flare tip diameter and exit velocity. AERMOD is, therefore, configured with NOSTD control option when modeling flares using this new method.

Modeling predictions using the AER hour-by-hour method can show increases in predicted ground level maximums near-field due to the more realistic, lower effective stack height at high wind speeds, and lower source momentum that reduces the initial trajectory of the plume, compared to the US EPA approach. AER hour-by-hour mid-field predictions are typically lower than US EPA method predictions because the realistic higher effective stack height at low wind speeds is accounted for. It is time to update the regulatory approach to modeling flares.

The focus of this article is on a flare source model; the authors plan to work on a comparison of predicted to observed flaring concentrations in the near future for publication.

Acknowledgments

This work was done with the support of the Alberta Energy Regulator, Zelt Professional Services Inc. and the Petroleum Technology Alliance Canada--Alberta Upstream Petroleum Research Fund.

Additional information

Notes on contributors

Michael J. Zelensky

Michael J. Zelensky is an air quality advisor in the Science and Evaluation Branch of the Alberta Energy Regulator in Calgary AB, who derived the equations and developed the concepts of the AERflare-incin regulatory tool.

Brian W. Zelt

Brian W. Zelt is the principal of Zelt Professional Services Inc. in Okotoks AB, who coded the equations and calculation routines to run AERMOD and process the output within the AERflare-incin spreadsheet tool.