Characterization of the incipient smoke point for steam-/air-assisted and nonassisted flares

ABSTRACT

Flares are important safety devices for pressure relief; at the same time, flares are a significant point source for soot and highly reactive volatile organic compounds (HRVOCs). Currently, simple guidelines for flare operations to maintain high combustion efficiency (CE) remain elusive. This paper fills the gap by investigating the characteristics of the incipient smoke point (ISP), which is widely recognized as the condition for good combustion. This study characterizes the ISP in terms of 100–% combustion inefficiency (CE), percent opacity, absorbance, air assist, steam assist, air equivalence ratio, steam equivalence ratio, exit velocity, vent gas net heating value, and combustion zone net heating value. Flame lengths were calculated for buoyant and momentum-dominated plumes under calm and windy conditions at stable and neutral atmosphere. Opacity was calculated using the Beer–Lambert law based on soot concentration, flame diameter, and mass-specific extinction cross section of soot. The calculated opacity and absorbance were found to be lognormally distributed. Linear relations were established for soot yield versus absorptivity with R² > 0.99 and power-law relations for opacity versus soot emission rate with R² ≥ 0.97 for steam-assisted, air-assisted, and nonassisted flares. The characterized steam/air assists, combustion zone/vent gas heating values, exit velocity, steam, and air equivalence ratios for the incipient smoke point will serve as a useful guideline for efficient flare operations.

Implications: A Recent EPA rule requires an evaluation of visible emissions in terms of opacity in compliance with the standards. In this paper, visible emissions such as soot particles are characterized in terms of opacity at ISP. Since ISP is widely recognized as most efficient flare operation for high combustion efficiency (CE)/destruction efficiency (DE) with initial soot particles formed in the flame, this characterization provides a useful guideline for flare operators in the refinery, oil and gas, and chemical industries to sustain smokeless and high combustion efficiency flaring in compliance with recent EPA regulations, in addition to protecting the environment.

Introduction

Flares are an important mechanical device used for combustion and destruction of volatile organic compounds, toxic compounds, and other undesirable pollutants at refineries, oil/gas industries, and chemical plants (U.S. EPA 2012). They are also used as safety devices to relieve pressure, especially during startup, shutdown, and malfunction (SSM) situations (Singh et al. 2012, 2014; U.S. EPA and OAQPS 2012). Flares also burn waste gases generated by sewage digesters, coal gasification units, rocket engine testing, nuclear power plants with sodium/water heat exchangers, heavy water plants, and ammonia fertilizer manufacturing plants (US Environmental Protection Agency 2009). Russia leads the top 30 flaring countries (24k mcm in 2016), while the United States ranks sixth, flaring 8900 mcm in 2016 according to World Bank satellite data (Korppoo 2018; World Bank 2018). Flaring is considered to be one of the most controversial environmental issues that the energy industry has to deal with (Zolfaghari, Pirouzfar, and Sakhaeinia 2017). Flare emissions may consist of unburned fuel (methane and unburned volatile organic compounds [VOCs]) and combustion by-products like soot, CO, CO₂, oxides of nitrogen, and sulfur (Singh et al. 2012; 2014; US Environmental Protection Agency 2009). These emissions have direct health impacts associated with exposure and indirect health impacts like the resulting ozone formation. Flares account for nearly 61% of highly reactive volatile organic compounds (HRVOCs) emissions based on the 2007 HRVOC special emissions inventory. HRVOCs act as the precursors for ozone formation (ENVIRON 2008; TCEQ 2016). Emissions from flaring, such as unburned hydrocarbons, black carbon (BC), and CO₂, increase the greenhouse effect of the atmosphere (Rahimpour and Jokar 2012; Stohl et al. 2013). Control of smoke in the form of soot and VOC emissions from flaring are important issues from the environmental standpoint. The presence of smoke is an indication of incomplete combustion of hydrocarbons (U.S. EPA 2012). Destruction efficiency (DE) and combustion efficiency (CE) are common indicators of flare performance, in addition to smoke generation (Schwartz, White, and Bussman 2001).

Current EPA regulations (40 CFR 60.18) require smokeless flaring, which motivates flare operators to oversteam or over-air to suppress smoke at the expense of CE. A recent EPA rule (40 CFR parts 60 and 63) finalized the minimum combustion zone net heating value (NHV_cz) operating limit as 270 BTU/scf and the dilution parameter NHV_dil ≥ 22 BTU/ft² during any 15-min average period for flares subject to Petroleum Refinery Maximum Achievable Control Technology standards to ensure 98% DE (or 96.5% CE) or higher at all times (U.S. EPA 2015). Still, there is no guarantee that CE will be ≥96.5% (Fry et al. 2012). Allen and Torres reported that most efficient flare operation (high DE and CE) was achieved at the incipient smoke point (ISP) (Allen and Torres 2011a, 2011b). Cade and Evans reported that small carbon soot particles formed within the flame zone are oxidized and disappear upon complete combustion (Cade and Evans 2010). Linteris and Rafferty correlated incipient smoke point to flame radiation losses (Linteris and Rafferty 2008).

CE measurements based on unique hyperspectral or multispectral infrared images and a smoke index indicating the smoke level in the flare plume were adjusted to optimize the flare performance (Zeng, Morris, and Dombrowski 2016). Based on heat release rate, gas temperature, and soot mass fractions, soot formation from ethanol and heptane flames was compared for different models (Yuen et al. 2017). Smoke points were examined empirically and experimentally using the mass fractions of different fuel–fuel and fuel–inert mixtures based on scaling laws relating the smoke points of fuel mixtures (Li and Sunderland 2013). Incipient soot particles were characterized with respect to oxygen mole fractions in oxidizer streams, soot zone structure, and degree of carbonization for ethane in inverse diffusion flames (Jung et al. 2012). Studies reported the light extinction efficiency of exhaust gas from the diesel engine (Lapuerta, Martos, and Cárdenas 2005) and light absorption coefficient for diesel soot, spark-generated carbon particles, and mixtures of soot particles based on the Beer–Lambert law (Weingartner et al. 2003). The optical properties of soot produced from combustion of petrol, diesel, fuel oil, paraffin, butane, and wood were studied and specific extinction coefficients were reported (Colbeck, Atkinson, and Johar 1997). Although the ISP is a good indicator for efficient combustion, the phenomenon is still not well understood; as a result, a clear characterization and clarification are needed.

Very few studies were performed earlier to characterize the incipient smoke point for flares based on soot yield, opacity, and other operating variables. This study aims at characterizing the ISP for steam-assisted, air-assisted, and nonassisted flares in terms of operable parameters such as steam assist (S) or air assist (A), exit velocity (V), air equivalence ratio (AER), steam equivalence ratio (SER), carbon number (CN) to represent vent gas species, net heating value of vent gas (NHV_vg), net heating value of combustion zone (NHV_cz), and in terms of performance variables such as 100–%CE, opacity, and absorbance. From propane and methane steam reforming/water gas shift reactions, C₁–C₃ compounds are assumed to undergo steam hydrocarbon reforming/water gas shift reactions with assisted steam in the combustion zone to produce carbon dioxide and hydrogen, thereby minimizing the production of soot and carbon monoxide. Therefore, the molar ratio of actual steam to that of steam required for completing steam reforming/water gas shift reactions is designated the steam equivalence ratio (SER). Likewise, the ratio of the actual fuel/air ratio to that of stoichiometric fuel/air ratio is designated as air equivalence ratio (AER). ISP characterization in terms of SER and AER identifies the range of steam and air required for lean and efficient combustion at ISP. Opacity calculations follow the Beer–Lambert law, assuming the flame shape to be vertically oriented at stable and a neutral atmosphere with calm and windy conditions and the optical path length at the widest diameter of the visible flame.

Methodology

Data sources

Test data identified as incipient smoke point in 1984 EPA (Pohl, Payne, and Lee 1984), a 2010 TCEQ flare study report and appendices (Allen and Torres 2011a; 2011b), and 2014 Carleton University (CU) flare study data (Corbin and Johnson 2014a; 2014b) were used to quantify the smoke produced at the ISP and to characterize the ISP. Test cases 94 and 105 reported little smoke with orange flame and were identified as ISP test cases in the 1984 EPA study. These sets of data with propane–nitrogen mixtures as fuel are highly complementary, as the 1984 EPA data include high NHV_vg and V data typical in SSM flare operations. Flare flames were not enclosed and are subjected to variations in wind velocity with screens to reduce the effect of natural wind. This study was performed to simulate the important features of commercial flare heads with 3 inch to 12 inch diameter and produced flames under a range of operating conditions representing the commercial flare flames. A 2010 flare study (12 data points for steam-assisted and 16 data points for air-assisted) includes low NHV_vg/low V data typical in normal operations (standby mode). S1.5.1, S4.1 (3 runs), S5.1 (3 runs), S6.1 (4 runs), and S8.3.1 were the test cases reported as the incipient smoke points for 2010 Tulsa campaign steam-assisted flares (36-inch tip diameter), and A1.1.1, A2.1 (2 runs), A3.1 (3 runs), A4.1 (3 runs), A5.1 (4 runs), and A6.1 (3 runs) were reported as ISP test cases for 2010 Tulsa campaign air-assisted flares (24-inch flare tip diameter). 2010 TCEQ flare study results were most directly applicable to industrial flare operations, as the field tests were conducted on full-scale industrial design flares in an uncontrolled ambient condition, representing a large number of flare models in the field. Tests were conducted to assess the performance of industrial flares with low vent gas flow rates with low NHV_vg. The CU flare study reported soot yield from a turbulent diffusion non-premixed flame burning hydrocarbon mixtures pertinent to low-momentum flares prevalent in oil and gas industry (Corbin and Johnson 2014a; 2014b). This study was performed at a lab-scale flare facility with burners of 1.5 to 3 inches diameter burning vent gas composition (methane-based average 6-mix and heavy 4-mix) relevant to flares burning light methane solution gas, a typical flare gas composition in the upstream oil and gas industry. From previous studies, which reported low soot concentration (Allen and Torres 2011a; 2011b) and orange flame with some dark areas as flame rating 5 for ISP (Cade and Evans 2010), CU data were identified as ISP test cases based on reported flame images and were included as nonassisted flares, as they were mainly for low carbon to hydrogen ratio in vent gas methane. As the minimum pipe size is 3 inches for the flare combustion efficiency to scale up to larger flares based on the “3 inch rule,” 10 data points from CU flare study with 3-inch diameter burning average 6-mix and heavy 4-mix methane-based mixtures were included in this study (Gogolek et al. 2010; U.S. EPA and OAQPS 2012). The reported CE data from the 2010 TCEQ flare study were corrected for soot emissions (maximum 0.6%) based on revised data provided by Aerodyne Research, Inc. (Aerodyne Research, Inc. 2010; Fortner et al. 2012).

Calculation of soot concentration

Opacity is a function of soot concentration and optical path length (Pilat and Ensor 1970). Soot concentration is expressed as

(1) $c=M/{Q_{cz}}^{\prime }$(1)

(2) ${Q_{cz}}^{\prime }={Q_{vg}}^{\prime }+{Q_S}^{\prime }+{Q_A}^{\prime }+{Q_{AR}}^{\prime }$(2)

where c is the soot concentration (lb/ft³), M is the mass flow rate of soot in the plume (lb/hr), Q_cz' is the combustion zone volumetric flow rate (ft³/hr), Q_vg' is the vent gas volumetric flow rate (ft³/hr), Q_S' is the steam assist volumetric flow rate (ft³/hr), Q_A' is 2% of the air assist volumetric flow rate (ft³/hr), and Q_AR' is the actual air volumetric flow rate (ft³/hr), assuming 125% excess air. Combustion zone gas flow rate was calculated at a flame temperature (T_f). Flame temperature (T_f) was calculated at 125% excess air using the heat balance equation (McAllister, Chen, and Fernandez-Pello 2011) shown as eq 3, accounting for heat loss due to radiation consistent with the heat loss calculated in sensible heat by TCEQ as shown in eq 5 (Ruggeri 2004):

(3) $\begin{array}{rl}& -{Q^{\ast }}_{rxn,P}=\sum {N_i}_{,R}(\mathrm{\Delta }{h}_i{{ }_{,R}}^{\circ }+{h_{si}}_{,R})\\ & -\sum {N_i}_{,P}(\mathrm{\Delta }{h}_i{{ }_{,P}}^{\circ }+{h_{si}}_{,P})\end{array}$(3)

where –Q*_{rxn, P} is the total enthalpy (kJ), N_i is the number of moles of component i, Δh° is the heat of formation (kJ/kmol), and Δh_si is the sensible enthalpy at flame temperature (kJ/kmol-K) for reactants R and products P.

Calculation of optical length

Flame volume has been correlated with heat release rate in the previous studies (Bubbico, Dusserre, and Mazzarotta 2016; Linteris and Rafferty 2008; Xin 2014; Zhang et al. 2015). Flame volume was correlated to the heat output (Q_n) in the range of 0.02–2.8 MW (Rashbash et al. 2004) with constant volumetric heat release rate 1200–1900 KW/m³ for turbulent flames burning propane, methane, and other hydrocarbons by the relation

(4) $\left(V_f\right)=1.21{\left(Q_n\right)}^{1.18}$(4)

Net heat output is assumed equivalent to sensible heat released by the vent gas and calculated according to the relation by TCEQ (Ruggeri 2004):

(5) $Q_n=q\left[1-0.048{\left(mw\right)}^{1/2}\right]$(5)

The average Q_n values for propene–Tulsa natural gas (TNG)–N₂ mix air-assisted and nonassisted flares were 0.9 and 0.09 MW, respectively. Q_n values for tests A1.1.1, S1.5.1, S6.1.A with 100% propene, propene–TNG–N₂ mix from 2010 TCEQ flare study and cases 94 and 105 with 100% propane from a 1984 EPA study are between 3 and 9.3 MW, beyond the applicable range of eq 4. Combustion intensity decreases as the heat output increases when eq 4 is applied over a wider heat output range, mainly if heat output is corrected for incomplete combustion by the fractional completeness of combustion (χ_c = 1 for complete combustion) (Orloff and De Ris 1982; Rashbash et al. 2004). Since measured CE values for the cases just described are greater than 96.5% (Allen and Torres, 2011a; Corbin and Johnson 2014a; Pohl, Payne, and Lee 1984), there is not much decrease in combustion intensity as the heat output remains almost the same since χ_c is >0.965 for those cases. Therefore, no correction for heat output was required and the flame volume was estimated for those cases by eq 4. To validate the flame volume, residence time of flame in the combustion zone was calculated. The average residence times for the steam- assisted, air- assisted, and nonassisted flames in the combustion zone are 0.41 sec, 0.32 sec, and 0.23 sec, respectively, and were in close agreement with the values reported in the literature (U.S. EPA 2002; LSC 2011).

Flame length is calculated as (Datta 2008)

(6) ${\mathrm{L}}_{\mathrm{f}}=\mathrm{e}\mathrm{x}\mathrm{p}\left(0.4562{ }^{\ast }\mathrm{l}\mathrm{n}\left(\mathrm{Q}\right)-5.3603\right)$(6)

Steam-assisted flames were assumed to be vertically oriented in the shape of two symmetrical cones of equal volume with the bases attached to one another, as shown in Figure 1. Flame shapes for air-assisted and nonassisted flares are discussed in the supplemental information. Initial soot particles were observed along the optical path length (L) located at the widest part of the flame, that is, the diameter of the conical part. From the flame volume and the flame length, radius (r_f) of the flame and optical path length (L) were calculated as given here:

(7) ${\mathrm{r}}_{\mathrm{f}}=[\left(3{\mathrm{V}}_{\mathrm{f}}\right)/(\pi {\mathrm{L}}_{\mathrm{f}}){]}^{1/2}$(7)

(8) $\mathrm{O}\mathrm{p}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{h},\mathrm{L}=2^{\ast }{\mathrm{r}}_{\mathrm{f}}$(8)

Figure 1. Schematic view of an assumed plume forced upward, showing radius r_f, flame height (L_f), the height of the bottom portion of flame (L₁), and plume rise Δh.

Calculation of opacity

According to the Beer–Lambert law, absorbance is expressed as

(9) $\mathrm{A}\mathrm{b}\mathrm{s}\mathrm{o}\mathrm{r}\mathrm{b}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}={\alpha }_{\mathrm{e}\mathrm{x}\mathrm{t}}{ }^{\ast }\mathrm{L}{ }^{\ast }\mathrm{c}$(9)

where α_ext (= α_abs + α_sca) is the mass-specific extinction coefficient (m²/g).

Since scattering function is negligible compared to absorption, mass specific extinction coefficient (α_ext) is considered equivalent to mass-specific absorption coefficient (α_abs). According to the Marathon Petroleum Flare study (Cade and Evans 2010), orange flames were observed at an incipient smoke point which corresponds to wavelength 600 nm. Soot aggregates formed by internal mixing with a nonabsorbing organic layer around the core BC have α_abs in the range of 1–25 m²/g (Optical Properties 2018). Fuller et al. reported α_abs ≥ 10 m²/g for internally mixed soot and 4 to >20 m²/g for different composition of soot aggregates at 550 nm (Fuller and Kreidenweis 1999). Likewise, soot aggregates formed by external mixing have α_abs in the range of 1–10 m²/g (Lazaridis 2010; Optical Properties 2018) and isolated spheres of light absorbing carbon have α_abs < 10 m²/g (Fuller and Kreidenweis 1999). The mode mobility diameter of primary particles for steam-assisted flares at high DE (90 nm) is larger compared to air-assisted flares (70 nm), while the particle number concentrations for steam-assisted flares were smaller than that for air-assisted flares (Aerodyne Research Inc 2010; Fortner et al. 2012). Based on the mode particle size and soot concentration in the sample for test series S5.1, absorption cross section was calculated to be 12.1 m²/g (α_abs calculation for a steam-assisted flare test case S5.1.2 is shown in supplemental information). Due to limited availability of particle size data for all cases of steam-assisted, air-assisted, and nonassisted flares, the intermediate value 12 m²/g is assumed for internally mixed soot from steam-assisted flares, 4.5 m²/g for air-assisted flares, and 5.8 m²/g (Coderre et al. 2011) for nonassisted flares at 600 nm at the ISP conditions.

Transmittance is

(10) $\mathrm{T}={\mathrm{e}}^{-\mathrm{A}\mathrm{b}\mathrm{s}}$(10)

(11) $\mathrm{O}\mathrm{p}\mathrm{a}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}=1-\mathrm{T}$(11)

Transmittance is also expressed as (Beer’s Law 2017; Gallik 2011)

(12) $\mathrm{T}=\mathrm{I}/{\mathrm{I}}_0$(12)

(13) $\begin{array}{rl}& \mathrm{A}\mathrm{b}\mathrm{s}=\mathrm{l}\mathrm{o}{\mathrm{g}}_{10}1mu\left({\mathrm{I}}_0/\mathrm{I}\right)\\ & =1mu2-\mathrm{l}\mathrm{o}{\mathrm{g}}_{10}1mu\mathrm{\%}\mathrm{T}\end{array}$(13)

(14) $\mathrm{A}\mathrm{b}\mathrm{s}=2-\mathrm{l}\mathrm{o}{\mathrm{g}}_{10}\left(100-\mathrm{\%}\mathrm{O}\mathrm{p}\mathrm{a}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}\right)$(14)

Results and discussion

Effect of steam on combustion efficiency and soot emissions near the ISP

CE remains relatively constant for test cases S1.6.1, S1.7.1 from test series S1 and S6.3, and S6.5 from test series S6 at steam assists (94–114 lb/MMBTU) higher than that required for ISPs (94 and 84 lb/MMBTU for S1.5.1 and S6.1 respectively) and then decreases at increased steam assists >140 lb/MMBTU, while some of the S4 and S8 show higher CEs at lower steam assists (30–70 lb/MMBTU) compared to steam required for ISP (84 lb/MMBTU for S8.3.1 and 101 lb/MMBTU for S4.1). All other test cases in test series S1, S5, and S9 show a gradual decrease in CE with an increase in steam from ISP toward snuff point, as shown in Figure 2a. Soot yield decreases with an increase in steam for test series S1, S5, S6, and S9, as shown in Figure 2b (Allen and Torres 2011a; 2011b). Test series S4 and S8 were conducted at steam assist less than that required for ISP, while S4 produced relatively low soot yield with less steam compared to other test cases. Low soot yield in S4 may be due to a higher exit velocity that caused better combustion of low NHV vent gases. It is noteworthy that test case S4.2 produced low soot with a high CE at a lower steam assist compared to ISP. This suggests understeaming may be advantageous compared to ISP, as suggested in 2010 TCEQ test series S4 and S8 (Figure 3).

Figure 2. (a) CE vs. steam assists for steam-assisted cases from 2010 TCEQ flare study data. (b) Soot yield vs. steam assists for steam-assisted cases from 2010 TCEQ Flare study data.

Figure 3. (a) CE vs. steam assist for 2010 test series S4 and S8 compared to ISP. (b) Soot yield vs. steam assist for test series S4 and S8 compared to ISP (Allen and Torres 2011a; 2011b).

Effect of airflow on combustion efficiency and soot emissions near the ISP

When assist air increases from the ISP to the snuff point, CE decreases for all test cases. No tests were conducted at lower air assists compared to the ISP. It is clear that soot decreases with increases in assist air for all test cases, while CE decreases with assist air from the ISP to the snuff point due to an increase in unburned hydrocarbon emissions, as shown in Figure 4 (Allen and Torres 2011a; 2011b). Hence, it is clear that most efficient combustion is still observed at the ISP for all air-assist flare test cases.

Figure 4. Unburned hydrocarbons vs. CE for air-assisted flares (Allen and Torres 2011a; 2011b).

Characterization of the incipient smoke point

The incipient smoke point is characterized in terms of performance variables 100–%CE, %opacity, and absorbance distributions for steam-assisted, air-assisted, and nonassisted flares. Performance variables 100–%CE and %opacity were lognormally distributed (figures in supplemental information). These variables following lognormal distribution were categorized by geometric mean and one geometric standard deviation (σ_g) above and below the geometric mean, that is, 84.1% and 15.9% of the distribution (Cooper and Alley 2002). Table 1 summarizes the 100–%CE, %opacity, and absorbance distributions for steam-assisted, air-assisted, and nonassisted flares at the ISP. Of opacity data for steam- and air-assisted flares, 84.1% were below 7.4%. All calculated opacity values were less than the legal limit of 20% opacity. At 20% opacity corresponding to Ringelmann number 1, emissions were visible with distinct edges, as the smoke blocks adequate background (U.S. EPA 2017; UNL 2008).

Table 1. x_15.9, x₅₀, and x_84.1 values for lognormal distribution of 100–%CE, %opacity, and absorbance data for steam-assisted, air-assisted, and nonassisted flares at the ISP.

	Steam-assisted^a				Air-assisted^b				Nonassisted^c
	x15.9^d	x50^e	x84.1^f	x̅^g	x15.9^d	x50^e	x84.1^f	x̅^g	x15.9^d	x50^e	x84.1^f	x̅^g
100–%CE	0.33	1.30	5.10	2.43	1.52	2.58	4.37	2.90	0.11	0.19	0.34	0.22
%Opacity	0.27	1.41	7.38	2.95	1.9	3.04	4.86	3.39	0.79	1.33	2.24	1.49
Absorbance	1 × 10^−3	6 × 10^−3	0.03	0.01	8 × 10^−3	0.013	0.02	0.02	3 × 10^−3	6 × 10^−3	1 × 10^−2	6 × 10^−3

Note. ^a For 14 data points for steam-assisted flares.

^b For 16 data points for air-assisted flares.

^c For 10 data points for nonassisted flares.

^d x_15.9 represents 1 standard deviation below the geometric mean at 15.9% cumulative probability level.

^e x₅₀ represents geometric mean.

^f x_84.1 represents 1 standard deviation above the geometric mean at 84.1% cumulative probability level.

^g x̅ represents the arithmetic mean.

Nonassisted flares burning methane-based 6-mix and heavy 4-mix have lower opacity (1.3%) compared to steam- and air-assisted flares. Lower opacity of 6-mix flares (0.9%) is due to high methane concentration compared to heavy 4-mix flares (2%). The mean opacity value for steam-assisted propylene flares (1.3%) is lower compared to air-assisted flares (3%) due to the steam assist, which improves mixing of air and fuel by increasing turbulence and provides more oxygen for combustion compared to air-assisted flares (Castiñeira and Edgar 2006). Steam-assisted propane flares even with low steam assist have a lower opacity compared to propylene-based steam- and air-assisted flares. This high absorption of propylene is due to high electron density caused by the π-bonding in propylene (Jäger et al. 1999). The mode mobility diameter of primary particles for steam-assisted flares at high DE (90 nm) is larger compared to air-assisted flares (70 nm), while the particle number concentrations for steam-assisted flares were smaller than those for air-assisted flares (Aerodyne Research, Inc. 2010; Fortner et al. 2012). Particles of size equal to that of light may cause more scattering and increases in opacity, as extinction is a function of absorption and scattering. Moreover, smaller particles lead to a higher opacity than larger particles at a given emission rate (ETA 2013). Since the particle size is larger (more opacity) and the number of particles is less (less opacity) for steam-assisted flares (Fortner et al. 2012), these two effects will likely cancel each other. Volatile fractions like formaldehyde, acetaldehyde, butene, and acrolein were higher than air-assisted flares in comparative studies of test series S1.5 and A3.1 (Knighton et al. 2012). Since soot formed from steam-assisted flares was assumed to be internally mixed, there is absorption enhancement compared to externally mixed soot from air-assisted flares (Chou et al. 2005; Khalizov et al. 2009; Schnaiter et al. 2005). Though steam-assisted flares efficiently reduced soot concentration, volatile fractions might have formed an organic layer around the primary soot particle to increase the size of aggregates with low density and high absorption cross section, which makes it more visible at lower concentration (Fuller and Kreidenweis 1999; Lazaridis 2010; Optical Properties 2018).

Operating parameters A, S, V, CN, NHV_cz, NHV_vg, SER, and AER for air-assisted, steam-assisted, and nonassisted flares were assumed to follow the lognormal distribution and the incipient smoke point was characterized in terms of operating parameters as shown in Table 2. Table 2 shows the range of operating parameters for the incipient smoke operation of steam-assisted, air-assisted, and nonassisted flares.

Table 2. x_15.9, x₅₀, and x_84.1 values for lognormal distribution of S, A, AER, SER, V, NHV_cz, and NHV_vg for steam-assisted, air-assisted, and nonassisted data at ISP.

	Steam-assisted^a				Air-assisted^b				Nonassisted^c
	x15.9^d	x50^e	x84.1^f	x̅^g	x15.9^d	x50^e	x84.1^f	x̅^g	x15.9^d	x50^e	x84.1^f	x̅^g
Assist (S or A)^h	16	57	211	83	4431	6176	8609	6536
Equivalence ratio^i	0.13	0.45	1.62	0.64	0.10	0.12	0.16	0.13
V^j	0.5	3.1	19	31	0.63	1.05	1.77	1.2	0.61	1.54	3.93	2.2
NHVcz^k	159	347	757	521	228	270	320	274	1003	1093	1191	1097
NHVvg^k	342	686	1374	890	297	586	1157	763	1003	1093	1191	1097
CN	0.47	0.93	1.84	1.2	0.40	0.81	1.62	1.1	1.15	1.27	1.40	1.3

Note. ^a For 14 data points for steam-assisted flares.

^b For 16 data points for air-assisted flares.

^c For 10 data points for nonassisted flares.

^d x_15.9 represents 1 standard deviation below the geometric mean at 15.9% cumulative probability level.

^e x₅₀ represents geometric mean.

^f x_84.1 represents 1 standard deviation above the geometric mean at 84.1% cumulative probability level.

^g x̅ represents the arithmetic mean.

^h S or A expressed in lb/MMBTU.

ⁱ Equivalence ratio is either SER or AER.

^j V expressed in ft/sec.

^k NHV_cz and NHV_vg are expressed in BTU/scf.

Soot yield versus absorptivity

ISP data are collected over a wide range of flare diameters and exit velocities for propylene-, propane-, ethylene-, and methane-based flares, leading to different flame diameters. At low opacity with low soot concentration c (as in the case of the ISP),

(15) $\mathrm{T}=\mathrm{e}\mathrm{x}\mathrm{p}\left(-\mathrm{A}\mathrm{b}\mathrm{s}\right)\cong 1-\mathrm{A}\mathrm{b}\mathrm{s}$(15)

Therefore, opacity = 1 – T ≅ Abs = α_abs${ }^{\ast }{L}^{\ast }c={{\alpha }_{abs}}^{\ast }\mathrm{o}\mathrm{p}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{h}$${ }^{\ast }c.$

As a result, opacity/optical length = absorptivity ≅ α_abs ${ }^{\ast }$ c, and c is proportional to soot yield.

Figure 5 shows that a linear relation (eq 16) is established between soot yield (lb/MMBTU) and absorptivity (1/ft) for steam-assisted, air-assisted, and nassisted flares.

Figure 5. Soot yield vs. absorptivity for (a) steam-assisted flares, (b) air-assisted flares, and (c) nonassisted flares at ISP.

(16) $\mathrm{S}\mathrm{o}\mathrm{o}\mathrm{t}\mathrm{y}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d}=\omega { }^{\ast }\mathrm{A}\mathrm{b}\mathrm{s}\mathrm{o}\mathrm{r}\mathrm{p}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{i}\mathrm{t}\mathrm{y}$(16)

where ω = 1.8, 4.6, and 3.4 for steam-assisted, air-assisted, and nonassisted flares respectively.

The high coefficients of determination (R² > 0.99) provide that absorptivity is a good indicator of soot yield.

Opacity*c_vg versus soot emission rate

Figure 6 shows the effect of soot emission rate on opacity for steam-assisted, air-assisted, and nonassisted flares with R² ≥ 0.97. It was observed that %Opacity * C_vg (flow rate of combustibles in the vent gas, lb/hr) increases with soot emission rate, as shown in eq 17. Five percent opacity (or 95% transmittance) corresponds to the Ringelmann number of 0.25; 10% opacity (or 90% transmittance) corresponds to the Ringelmann number of 0.5, and 20% opacity to the Ringelmann number of 1 (ETA 2013; Stockham and Betz 1971). Hence, the Ringelmann number may also be correlated to the soot emission rate (lb/hr) from eq 17,

Figure 6. %Opacity * C_vg (combustibles in vent gas [lb/hr]) vs. soot emission rate (lb/hr)/at ISP for (a) steam-assisted flares, (b) air-assisted flares, and (c) nonassisted flares.

(17) $\mathrm{\%}\mathrm{O}\mathrm{p}\mathrm{a}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}{ }^{\ast }{\mathrm{C}}_{\mathrm{v}\mathrm{g}}=\eta \mathrm{x}\mathrm{s}\mathrm{o}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{m}\mathrm{i}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{o}{\mathrm{n}}^{\delta }$(17)

where η = 19223, 1953, and 8014; δ = 1.0, 1.3, and 1.3 for steam-assisted, air-assisted, and nonassisted flares, respectively.

Relation between exit velocity at the ISP and the combustion zone net heating value

The combustion zone net heating value NHV_cz for the steam-assisted flares at the ISP showed a logarithmic relation with V_ISP with R² = 0.95, as shown in Figure 7a. Log V_ISP can also be expressed in terms of vent gas net heating value NHV_vg with R² = 0.93, as shown in Figure 7b (S1.5.1 data point removed as an outlier).

Figure 7. (a) Exit velocity vs. combustion zone net heating value for steam-assisted flares at the ISP. (b) Plot of V_max per 40CFR60.18 and V_ISP as a function of NHV_vg for steam-assisted flares reveals V_max/V_ISP ≈ 65 (1.81 orders of magnitude).

The relation between the logarithmic maximum allowable velocity (log V_max) calculated as per 40CFR 60.18f(5) (U.S. EPA 2015) for NHV_vg values at the ISP is also shown in Figure 7b. It can be seen that the ratio of V_max/V_ISP is approximately 65 (1.81 orders of magnitude). These correlations between V_ISP, V_max, NHV_cz, and NHV_vg are summarized in Table 3.

Table 3. Equations representing relations between V_ISP, V_max, NHV_cz, and NHV_vg based on 40 CFR 60.18(f)(5) and the ISP conditions.

NHVcz^a = 329.9 ln (VISP) + 130.6

log VISP^a = 1.2 × 10^−3 NHVcz – 0.112

log VISP^a = 1.1 × 10^−3 NHVvg – 0.383

log Vmax^a = 1.1 × 10^−3 NHVcz – 1.8882

log Vmax^a,b = 1.2 × 10^−3 NHVvg + 1.426

Note. ^aSteam-assisted flares.

^b Nonassisted flares.

Conclusion

Incipient smoke points reported in the 1984 EPA, 2010 TCEQ study and test cases in the 2014 Carleton University flare study, which was identified as ISP, were analyzed in this study. Reported CE was corrected for soot emissions based on revised soot data provided by Aerodyne Research, Inc. The major conclusions of this study are as follows:

• The steam-assist, air-assist, combustion zone/vent gas heating value, exit velocity, absorbance, 100–%CE, and %opacity for steam-assisted, air-assisted, and nonassisted flares are characterized in the form of x_15.9, x₅₀, and x_84.1 at the incipient smoke point. These characterized values will serve as a useful guideline for efficient flare operations.

• The median opacity of propylene flares was higher than for propane- and methane-based flares, which may be due to high absorption efficiency caused by electron density of the π-bonding.

• Linearity between soot yield and absorptivity with R² > 0.99 and soot emission rate normalized with VG_cz mass flow rate and opacity with R² ≥ 0.97 for steam-assisted, air-assisted, and nonassisted flares.

• Flame length decreases exponentially with velocity ratio with R² > 0.95 for steam- and air-assisted buoyant flames at ISP, which may be likely due to fuel trapped into the immediate wake of the stack, and a large amount of fuel is consumed at higher cross-flow speeds.

• NHV_cz increased exponentially with V_ISP for the steam-assisted flares with the goodness of fit (R² = 95%).

• Analysis of steam-assisted flares indicated that there is room for understeaming (less than the steam assist required by the ISP) to increase CE based on 2010 TCEQ test data.

Nomenclature

A	=	Air assist (lb/MMBTU)
Abs	=	Absorbance
BTU	=	British thermal unit
BC	=	Black carbon or soot yield (lb/MMBTU)
c	=	Soot concentration (lb/ft3)
C	=	flow rate of combustibles, (lb/hr)
I0	=	Incident intensity (cd)
I	=	Transmitted intensity (cd)
k	=	Imaginary part (eqs 19–21 in supplemental information)
m	=	Refractive index function (eq 19 in supplemental information)
n	=	Real part (eqs 19–21 in supplemental information)
M	=	Mass flow rate of soot (lb/hr)
MMBTU	=	Millions of BTU
NHV	=	Net heating value (BTU/scf)
q	=	Gross heat release (cal/s)
Q'	=	Volumetric flow rate (ft3/hr)
S	=	Steam assist
scf	=	Standard cubic feet (at 68 °F and 1 atm)
T	=	Temperature (Kelvin)
T	=	Transmittance
u	=	Average cross-wind speed (ft/sec)
V	=	Flare tip exit velocity of vent gas includes center steam as per 40 CFR 60.18 (f) (4) (ft/s)
χc	=	Fractional completeness of combustion
Metric Units	=
d	=	Flare tip diameter (m)
DE	=	Destruction and removal efficiency (%)
Dp	=	Primary particle diameter (m)
L	=	Optical Path Length (m)
L1	=	Height of bottom portion of flame for steam-assisted flares (m)
Lf	=	Flame Length (m)
mw	=	Molecular weight (g/mol)
q'	=	Efficiency (eqs 23–26 in Supplemental Information)
Qn	=	Net heat output, MW
Q	=	Gross heat release (watt)
r	=	Radius, m
TNG	=	Tulsa natural gas
u	=	Average cross-wind speed (ft/s)
Vf	=	Flame volume (m3)
Vsample	=	Volume of sample (m3)
Greek Symbols	=
α	=	Mass specific coefficient (m2/g)
δ Constant	=
ε	=	Extinction coefficient (m−1)
λ	=	Wavelength (m)
η	=	Constant
ρ	=	Density (g/cm3)
σ	=	Cross sections
τ	=	Residence time (sec)
ω	=	Coefficient
Subscripts	=
A	=	Air-assist
a	=	Ambient
abs	=	Absorption
cz	=	Combustion zone
ext	=	Extinction
f	=	Flame
isp	=	Incipient smoke point
p	=	Products
Plume	=	Plume
R	=	Reactants
rxn	=	Reaction
s	=	Stack
si	=	Sensible
S	=	Steam-assist
sca	=	Scattering
AR	=	Actual air
vg	=	Vent gas

Acknowledgment

Special thanks are due to Ed Fortner and Scott Herndon of Aerodyne Research, Inc. (ARI), for providing numeric soot data for 2010 John Zink flare campaign. The authors also acknowledge the data contributed by Dr. Darcy Corbin and Dr. Matthew Johnson from their flare study at Carleton University in 2014. Valuable comments from Dr. Peyton Richmond and Dr. Helen Lou during the course of this study are also acknowledged.

Additional information

Funding

The authors gratefully acknowledge the financial support from TCEQ Grant for Activities Program (Project 582-10-94307-FY14-06), TCEQ Supplemental Environmental Program (SEP Agreement 2009-009), and the Texas Air Research Center (TARC Grant 079LUB0096A).

Notes on contributors

Daniel H. Chen

Daniel H. Chen, Ph.D., P.E., is University Professor & Scholar, Leland Best Distinguished Faculty Fellow at Lamar University, Beaumont, TX.

Arokiaraj Alphones

Arokiaraj Alphones is a Ph.D. candidate in the Dan F. Smith Department of Chemical Engineering at Lamar University, Beaumont, TX.