Computational Fluid Dynamics Simulation of Combustion Efficiency for Full-Size Upstream Flare Experiments

Abstract

Methane emissions from oil and gas production can occur throughout the value chain, but for many producers, one of the most significant sources is flaring. Understanding the influence of the operating conditions and the environmental factors the combustion efficiency and destruction and removal efficiency (CE/DRE) of flares is essential if their role in methane emissions, a potent but short-lived greenhouse gas, is to be better understood and mitigated. An industry-scale experimental study was focused on the emissions of un-assisted flares commonly encountered in upstream oil and gas production. This paper simulates two un-assisted flare tips combustions by using the commercial computational fluid dynamics (CFD) software package Fluent 21R2 to augment the physical experimental testing. Two three-dimensional (3D) flare tips models are built, and the k-omega SST turbulence model and flamelet generated manifold (FGM) combustion model are applied to simulate flaring combustion. The CFD model is first validated against full-scale industry flare tests that use extractive sampling of the combustion plume. CFD results are in good agreement with measured results when the vent gas net heating value (NHV) is greater than 300 BTU/SCF. Greater uncertainty exists for both CFD results and measured data if the NHV is less than 300 BTU/SCF. Then, the CFD model is extended to include high crosswind states up to 50 m/s that cannot be readily or safely examined empirically. The results emphasize the critical role of the vent gas net heating value (NHV) on flare combustion and crosswind in reducing the CE. The comparison helps pave the way for further use of CFD simulation to improve flare designs and modes of operation and supports the use of parametric models to track and report methane losses from flaring.

1. Introduction

A flare is a combustion device used to burn off excess or unwanted gases in a safe and controlled way. Flares are found across the oil and gas industry, including upstream (oil and gas production), midstream (transportation and storage, LNG facilities), and downstream (refining and distribution), and may also be found in other settings such as biogas facilities. As such, the size and design of flares varies significantly from simple pipe flares, where the gas pressure alone maintains combustion, to highly sophisticated flares that incorporate assist gases (air, steam) and advanced flare-tip geometries intended to optimize combustion whilst suppressing unwanted visible impacts of flaring such as soot formation [1]. Also, for unassisted flares such as those commonly encountered in upstream oil and gas production, information remains scarce due to the complexity of conducting full-scale tests. The composition of flare gas depends on its source and may include natural gas, inflammable gases such as carbon dioxide and nitrogen, and toxic gases such as hydrogen sulfide. Methane is the primary component of natural gas and is often present in flare gas from upstream production.

Since the industrial revolution, atmospheric methane concentrations have more than doubled, accounting for 25% of anthropogenic global warming [2]. Methane from oil and gas production and usage accounts for approximately a third of those emissions and is widely seen as the most accessible opportunity for achieving emissions reductions. The World Bank estimates that over 138,000 million m³ of gas is flared annually, of which the majority (around 80%) is methane [3]. However, unlike some other key sources of fossil fuel emissions, such as fugitives or the use of pneumatic devices, the flare is an integral part of the design and safe operation of many existing oil and gas facilities with limited alternatives for replacement or removal. Therefore, whilst initiatives such as the World Bank zero routine flaring by 2030 initiative has led to pledges and reductions in gas flared routinely during production, the use of flares to maintain safe operations (safety flaring, which includes low level flaring to maintain a lit flare in case of emergency) and during plant upset and maintenance (non-routine flaring) is likely to persist well into the energy transition.

Quantifying flare combustion uses two closely related values: combustion efficiency (CE) and destruction and removal efficiency (DRE). CE is a measure of the conversion of hydrocarbons to CO₂, whereas (DRE) also accounts for the incomplete combustion products of CO and soot. There is a convention that assumes 2% of all flared natural gas in upstream oil and gas production operations escapes to the atmosphere as unburnt hydrocarbons (often referred to as 98% DRE). However, this generalization is coming under increased scrutiny with a focus on climate change and the risk that flaring poses to meeting methane emission targets. For example, recent studies including those by Plant et al. (2022) have shown that flares operating in an onshore oil production setting can vary from <70 to >99% efficiency, including those which are unlit [4]. By contrast, measurements taken in the offshore setting of the Norwegian North Sea by Shaw et al. yielded a much narrower range in efficiency, with an average of 98.4% [5]. Fabrizio et al. conducted methane emissions measurement for the onshore LNG industry using fully traceable differential absorption LiDAR (DIAL). The measurement approach was to quantify emissions, determine emissions factors to enable accurate inventory reporting, and targeted maintenance and repair [6]. If emissions from flares are to be better understood and measurements made available to mitigate them, then these differences need to be better measured and tracked.

Previous research has demonstrated that flaring is a complex process which involves numerous factors that contribute to the CE/DRE. These parameters include compositional factors such as the lower flammability limit (LFL) and net heating value of the combustion zone gas (NHVcz) as well as the way that the flared gas mixes in the air, including the stoichiometric air ratio (SR), momentum flux ratio (MFR), and flare tip velocity [7].

Among the different environmental factors that can affect a flare, the most significant is crosswinds. Exploration of the modifying effects of crosswinds have relied primarily upon the use of scaled experiments [8] demonstrating that flare performance can be reduced under high winds that can strip unburnt hydrocarbons from the combustion zone. However, such tests are complex to perform and may encounter scaling problems when applied to some of the more advanced designs of flare. Seebold et al. (2004) stated that CE may be adversely impacted in the wake-dominated mixing regime due to fuel stripping, where unburned hydrocarbons detected downwind in a wake-dominated flare burn with a crosswind velocity of 8 m per second (m/s), or approximately 18 mph [9].

Full-scale tests have focused on the performance of air- and steam-assisted flares, and until recently, the impact of localized environmental effects such as visible soot formation have been the primary concern. Such flares are most often encountered in the downstream (refinery) sector [10,11]. The heightened focus on methane emissions has increased the interest in the performance of unassisted flares, which are commonplace in production settings and account for the bulk of global flaring. The amount of publicly available data on the performance of these flares is limited. To help redress that problem, Evans et al. [12] conducted further experiments on the unassisted flares of different designs that were used by Chong et al. [13] to verify a parametric model capable of near real-time tracking of flare combustion. Such experiments are, however, limited by their capacity to measure the modifying influence of crosswinds on flare combustion. Besides the challenge of needing consistent and predictable wind speeds, it would be unsafe to use extractive systems during high wind speed events as well as extremely challenging to position the extractive system over the combustion plume in a reproducible way. This is a significant shortfall, as many flares operate in extremely harsh environments, including offshore, where high wind speeds are frequently encountered.

Recent advances in the availability of advanced computing facilities and software have improved the viability of using computational fluid dynamics (CFD) to augment understanding of flare combustion. CFD simulation is an important tool for understanding and optimizing the combustion process, as it allows us to analyze the complex interactions between different factors, such as fuel properties, mixing, ignition, flame propagation, and heat transfer. The main challenge in simulating an industrial flare is the accurate representation of the flow dynamics and gas combustion.

Pitsch et al. [14] applied large eddy simulation (LES) to simulate a premixed methane/air diffusion flame (Sandia flame D). Flame D is one of a suite of highly studied reference flame data sets and fulfils the role of a de facto reference standard for simulation studies. Jaravel et al. [15] performed LES with direct integration of reduced chemical kinetics including nitrogen monoxide chemistry on flame D. Jones [16] simulated the Sandia Flame Series (D–F) with augmented reduced mechanism (ARM) and demonstrated the ability of the method in capturing extinction and re-ignition in turbulent flames. Castiñeira et al. [17] conducted CFD simulation studies of steam-assisted and air-assisted flares to study the thermochemistry effects of steam and air on CE. Kanwar Devesh. Singh et al. [18] modeled industrial steam- and air-assisted flaring and compared it to full-scale empirical tests conducted by Allen et al. [19]. Wang et al. developed a reduced C1-C4 combustion mechanism called Vsoot and performed CFD models with Vsoot to simulate flaring events [20].

CFD studies of crosswinds have concentrated on laboratory-scale flame simulations. Castiñeira et al. conducted a CFD simulation of wind tunnel experiments. Inefficient combustion was observed at high crosswinds. The CE of low-momentum flares were higher than expected due to recirculating zone results from crosswind [21]. David et al. applied the eddy dissipation concept (EDC) to study the effects of crosswind on Flame D and found that high-momentum flames are more sensitive to crosswind problems as the jet velocity increases [22]. Priere. et al. applied LES to investigate the performance of mixing devices in jets subjected to crossflow conditions and successfully validated their predictions against experimental data [23]. CFD simulation was used by Kermani et al. to explore wind effects on temperature distribution, air–fuel mixing, and combustion efficiency for gas refinery flares [24].

Despite these advances, there have been limited examples in which a CFD model is verified against reference data before being compared to full-sale empirical data and used to investigate the impacts of crosswinds. Such a full value chain assessment is necessary if CFD is to be accepted as an alternative to the empirical testing of flares and accelerate the development of new flare designs and measurement systems used to track flare combustion in a trusted way. This work was designed to fulfil that need when applied to unassisted flares and, in doing so, reduce the risks associated with quantifying the emissions of methane from flaring.

2. Methods

All of the CFD simulations in this work were conducted using ANSYS Fluent 21R2 software at the BP High Performance Computing facility (HPC) in Houston, TX. The HPC enables partitioning of the computational mesh and distribution of the solver workload across multiple processors, thereby compressing the overall wall clock time for the simulations. Each simulation case was run using 5 nodes of 96 cores each (i.e., a total of 480 CPUs) on an Intel Cascade Lake cluster. Inter-node communication was facilitated by InfiniBand Interconnect and Intel MPI (message passing interface). Typical run time per simulation case was 8 h.

A two-step process was employed for assembling, validating, and applying the model as follows: (1) The model was compared to full-scale empirical data published by Evans et al. [12] to ensure that the model accuracy was scale independent; (2) the model was applied to explore the effect of crosswinds.

2.1. Simulation Methodology

The main challenge in simulating industrial flares is the accurate representation of the flow dynamics and gas combustion. Industrial flares are turbulent in nature and encompass a wide range of time and length scales. The governing transport equations for flares typically include the conservation equations for mass, momentum, and energy, as well as species and radiation transport equations. These are the typical equations used in the ANSYS Fluent Software package. A discrete ordinates (DO) radiation model is applied in combustion simulation, and the weighted sum of gray gases model (WSGGM) is used for the absorption coefficient. Angular discretization was set up with theta divisions (N_θ) of 3, phi divisions (N_Φ) of 3, theta pixels of 2, and phi pixels of 2. Turbulence was modelled using the k-omega SST model. The SST-k-omega model is designed for a wide range of Reynolds numbers—covering transition to highly turbulent flows—and different scenarios: shear, buoyancy, or rotational turbulence [25].

Combustion chemistry and its interaction with turbulent structures was modelled using a reduced-order technique called flamelet-generated manifold (FGM) [25]. FGM is a partially premixed combustion model that is based on a non-premixed combustion model and a premixed combustion model. In fast chemistry scenarios (such as hydrocarbon flames), the FGM approach is valid and enables the problem to be solved efficiently. In this approach, a representative 1-D flame is simulated a priori, and the generated chemical information is tabulated against a reduced number of control variables, thereby creating a low-dimensional manifold. Density weighted mean scalars (such as species fractions and temperature), denoted by Φ, are calculated from the probability density function (PDF) of f and c as in Equation (1):

$$\mathsf{\Phi }={\int }_0^1{\int }_0^1\mathsf{\Phi }\left(\mathrm{f},\mathrm{c}\right)\mathrm{p}\left(\mathrm{f},\mathrm{c}\right)\mathrm{d}\mathrm{f}\mathrm{d}\mathrm{c}$$

(1)

where:

c = reaction progress variable defined as reduced product mass fraction.

f = Mixture fraction, which tracks the variation of air-to-fuel ratio; air and fuel are not fully mixed.

The FGM model assumes that the thermochemical states in a turbulent flame are like the states in a laminar flame and parameterize these by mixture fraction and reaction progress. Within the laminar flame, reaction progress increases from c = 0 in the unburnt reactants to c = 1 in the burnt products, over a nonzero flame thickness. A point within the turbulent flame brush with 0 < c < 1 has contributions from both fluctuating flame fronts, also intermediate reaction progress [25]. Since equilibrium assumption is not made, it is expected that species like CO and OH can be predicted more accurately. Assumed probability density functions account for the turbulence–chemistry interaction. Thus, this model assumes that the fundamental nature of the flame structure is unaltered by the turbulent eddies, but the turbulent flame brush is made up of an ensemble of laminar flamelets. The widely used combustion mechanism developed by the Gas Research Institute (University of California, Berkeley), GRI-Mech 3.0, is employed to simulate the representative 1-D flame. The mechanism consists of 53 species and 325 elementary reactions and is optimized for methane combustion but also includes ethane and propane combustion chemistry [26]. Previous studies using a similar methodology simulated Sandia Flame D and validated the approach by comparing the predicted species and temperature profiles against the measurements.

A steady-state RANS (Reynolds averaged Navier–Stokes) solver is selected for this study to predict the mean flame behavior. While a transient solver may capture the flame dynamics better, it would require a prohibitively high computational cost for simulating the selected range of operating scenarios. CE was calculated by averaging the species mass fluxes at the outlet using the following Equation (2). DRE is calculated as the mass percentage of hydrocarbon destroyed relative to the quantity entering the flare using Equation (3).

$$CE\left(\mathrm{\%}\right)=\frac{\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s} \mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w} \mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{c}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n} \mathrm{i}\mathrm{n} \mathrm{C}{\mathrm{O}}_2 \mathrm{p}\mathrm{r}\mathrm{o}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{f}\mathrm{l}\mathrm{a}\mathrm{m}\mathrm{e}}{mass flow rate of carbon in C_x{H}_y in the vent gas}\times 100$$

(2)

$$DRE\left(\mathrm{\%}\right)=(1-\frac{\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s} \mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w} \mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{e}\mathrm{x}\mathrm{h}\mathrm{a}\mathrm{u}\mathrm{s}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l} \mathrm{h}\mathrm{y}\mathrm{d}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}}{mass flow rate of total hydrocarbon in the vent gas})\times 100$$

(3)

The equation requires the mass flow rates of various species entering and exiting the domain. A surface integral of the speciated flow rate was constructed over the gas inlet/outlet surfaces to determine the net fuel flow rate. A similar surface integral is implemented over all the pressure outlet surfaces to calculate the net fluxes of the combustion products. The mass flow of each species was calculated as shown below in Equation (4).

$$m_i={\sum }_{faces}\rho x_{i }v A$$

(4)

where $m_i$ is the mass flow rate of species i through a boundary, $\rho$ is density, $x_i$ is mass fraction, $v$ is velocity vector, and $A$ is area projections over the faces of zone.

Carbon mass balance is used as an additional measure to verify proper convergence of the species fields to a steady-state solution. Net carbon flux is calculated by multiplying the mass flux of each species across all the boundaries with its carbon mass fraction and summing it over all the modelled species. Net carbon flux is maintained within a tight error tolerance to ensure solution accuracy.

2.2. Simulation Flare Design

Simulation models were built to replicate the design of two test flares used by Evans et al. [12]. The first design, hereafter referred to as the utility flare, is of a straight pipe design with an outer diameter of 14” and a wall thickness of 0.322”. The effective diameter is 11 inches (95.03 in²). It represents some of the simplest flare designs found routinely in oil and gas facilities. The second design, hereafter referred to as sonic flare, is a single arm, pressure-assisted flare tip with an 8” outer diameter and 0.322” wall thickness. Pressure at the tip is raised by forcing the flow through the fixed inside gas discharge slot, which is a metal cone creating an effective cross-sectional area of 21.7 in². Flares of this design increase the exit velocity of the gas to facilitate turbulent mixing with the air. There are many further designs of flare tip adopting an array of multi-arm designs that split the flared gas over multiple paths. However, when measuring CE/DRE using field laboratory methods, Evans et al. concluded that at the current levels of measurement uncertainty, the impact of these modifications was not possible to discern.

For utility flares, there is a slight restriction at the exit due to the flame stabilizer tab. Additionally, small holes in each flame tab around the pipe exit and the void between each flame tab were not considered. Figure 1 and Figure 2 show the developed 3-dimensional models and the corresponding base (initial) computational mesh. A finer mesh was employed around the exit of the flare tip where the combustion reactions are expected to improve the accuracy. Base mesh size is approximately 850K cells. Solution-based dynamic adaptive meshing is used to further improve the accuracy. As a result, final mesh size increased to about 8 million cells during the simulation.

In empirical tests, a 2-inch flare pilot burning Tulsa natural gas (TNG) was used to ignite the flare and keep it lit for low NHV gas. Pilots operate at effectively 100% CE/DRE, and their design and operation are not a main part of this study. To replicate this, in the model, the ignition source for the flare gas exiting the flare tip is provided numerically. This is achieved by setting the combustion progress variable to 1 in a small region directly above the flare tip. This simplified approach eliminates the need for explicit modelling of the pilot lines in the simulation.

The addition of a fully simulated pilot within the experiment would substantially increase computation time. To further investigate pilot effects, extra studies were performed using the sonic flare tip with a pilot model under a range of conditions. Pilot effects were proven to be more sensitive to high wind condition with the same NHV cases. This pilot effects study will be included in our future publications.

Boundary conditions were defined as follows. The left side of the domain was designated as the wind inlet with a specified velocity condition, while the right side served as the outlet subjected to the atmospheric pressure conditions. The flare gas inlet was situated at the bottom of the flare tip. The flare pipe surfaces were assumed to be adiabatic, no-slip walls, while the atmospheric domain boundaries (except for the wind inlet and outlet) were assumed to be adiabatic, shear-free walls. A sufficiently large atmospheric domain was modelled so that the flame was unconfined for all practical purposes. The temperature measurements used in the simulation replicated those recorded during empirical testing.

2.3. Validation Experimental Design

The net heating value of vent gas (NHV) is critical to flare ignition and sustained burning. This is normally expressed for unassisted flares in BTU/SCF, with alternate equations available for air- and steam-assisted flares to account for the role of these additional gases. Turbulent mixing of the vented gas and ambient air dictates whether the mixture attains flammable conditions to maintain a high CE/DRE. Mixing characteristics are, in turn, a function of the gas flow rate, the speed at which it exits the flare tip, and ambient air conditions and crosswinds. MFR (momentum flux ratio) is a parameter used in flare combustion studies to quantify the momentum transfer from the gas to the surrounding atmosphere that includes consideration of crosswinds. A high MFR indicates a strong momentum transfer and better mixing of the combustion products with the surrounding air, which can improve combustion efficiency and reduce emissions. As the MFR increases, the behavior of the flare flame can be classified into three distinct regimes: wake-dominated, buoyancy-dominated, and inertia-dominated [27]. MFR is defined as:

$$MFR=\frac{{\rho }_{vg\times {V_{vg}}^2}}{{\rho }_{air}\times {V_{wind}}^2}$$

(5)

where MFR is the calculated momentum flux ratio, unitless; ${\rho }_{vg}$ is the density of flare waste gas, lb/scf; $V_{vg}$ is the flare vent gas velocity, ft/s; ${\rho }_{air}$ is the density of air, lb/scf; and $V_{wind}$ is the wind velocity, ft/s.

Validation relative to empirical data was conducted by simulating conditions tested by Evans et al. Seven single-pipe utility flare tip cases with NHV values ranging from 200 BTU/SCF to 930 BTU/SCF and jet velocities ranging from 0.2 m/s to 5 m/s were investigated as shown in

Table 1. Utility flare tip experiment test conditions.

Test No.	Flare Type	TNG Flowrate (SCFH)	N2 Flowrate SCFH)	NHV (BTU/SCF)	Vjet (m/s)	U (m/s)	MFR
1	Utility	8666	30,313	213	4.93	3.57	1.7240
2	Utility	341	1216	214	0.19	4.92	0.0014
3	Utility	1272	3476	253	0.60	1.79	0.0975
4	Utility	10,542	28,402	260	4.92	5.36	0.7498
5	Utility	12,661	25,628	305	4.84	3.13	2.1606
6	Utility	3080	1648	559	0.59	4.02	0.0164
7	Utility	39,267	0	929	4.96	2.68	2.0531

. Five sonic flare tip cases with NHV values ranging from 170 BTU/SCF to 600 BTU/SCF and jet velocities ranging from 0.5 m/s to 2 m/s were investigated as shown in

Table 2. Sonic flare tip experiment test conditions.

Test No.	Flare Type	TNG Flowrate (SCFH)	N2 Flowrate SCFH)	NHV (BTU/SCF)	Vjet (m/s)	U (m/s)	MFR
1	Sonic	366	1753	170	1.19	7.15	0.0255
2	Sonic	234	809	201	0.58	1.34	0.177
3	Sonic	570	1519	240	1.17	1.34	0.698
4	Sonic	1393	2861	290	2.39	4.47	0.244
5	Sonic	682	371	513	0.59	4.92	0.011

. Gas composition replicated the same gases used by Evans et al., in which a range of NHV values were formulated by mixing TNG with nitrogen. These tables show, for each case, the gas composition, net heating value of vent gas (NHV), jet velocity (V_jet), crosswind velocity (U), and momentum flux ratio (MFR).

2.4. Investigation of Crosswind

In order to assess the effect of high crosswind speed on CE and DRE, the MFR range considered was varied from 10⁻⁴ to 10³, covering the different combustion regimes as defined by Seebold et al. [27]. Four flare tip velocities (0.6 m/s, 1.2 m/s, 2.4 m/s, and 5 m/s) were designed to cover the range of operating flow rates of gas in keeping with previous empirical studies. The NHV varied from 100 to 920 BTU/SCF. The input conditions for 24 utility flare corner (UC) cases and 24 sonic flare corner (SC) cases are listed in

Table A1. Input Conditions for 24 Single pipe Utility Flare Corner (UC) cases.

Case No.	Flare Type	Exit Velocity (m/s)	Flow Rate (SCFH)	NHV (BTU/SCF)	Gas Composition	Wind Speed (m/s)	MFR	CE	DRE	CE Error (%)
UC1	Utility	0.6	4700	270	29% TNG + 71% N2	24.89	0.0005	85.76%	94.43%	−0.18
UC2	Utility	0.2	1560	250	27% TNG + 73% N2	6.80	0.00075	95.56%	97.53%	−0.31
UC3	Utility	0.2	1560	200	22% TNG + 78% N2	5.96	0.001	93.17%	96.42%	−0.44
UC4	Utility	0.2	1560	600	65% TNG + 35% N2	4.25	0.0016	98.83%	98.90%	−0.2
UC5	Utility	0.6	4700	250	27% TNG + 73% N2	11.92	0.0022	95.20%	97.44%	−0.42
UC6	Utility	0.6	4700	155	17% TNG + 83% N2	10.79	0.0028	78.48%	88.64%	−0.89
UC7	Utility	0.6	4700	300	33% TNG + 67% N2	9.46	0.0034	98.32%	98.46%	−0.28
UC8	Utility	0.6	4700	200	22% TNG + 78% N2	8.93	0.004	94.15%	96.05%	−0.5
UC9	Utility	0.2	1560	300	33% TNG + 67% N2	2.60	0.005	98.67%	98.70%	−0.2
UC10	Utility	0.2	1560	270	29% TNG + 71% N2	2.48	0.0056	98.31%	98.58%	−0.21
UC11	Utility	0.6	4700	270	29% TNG + 71% N2	7.07	0.0062	98.59%	98.80%	−0.3
UC12	Utility	0.2	1560	250	27% TNG + 73% N2	2.26	0.0068	97.49%	98.24%	−0.3
UC13	Utility	0.2	1560	200	22% TNG + 78% N2	2.19	0.0074	97.45%	98.47%	−0.25
UC14	Utility	0.6	4700	155	17% TNG + 83% N2	6.38	0.008	91.19%	94.98%	−0.26
UC15	Utility	0.6	4700	600	65% TNG + 35% N2	5.50	0.0086	98.88%	98.90%	−0.19
UC16	Utility	5	39,000	300	33% TNG + 67% N2	47.92	0.0092	90.86%	93.59%	−0.46
UC17	Utility	0.6	4700	920	pure TNG	4.61	0.01	99.55%	99.57%	−0.52
UC18	Utility	5	39,000	920	pure TNG	22.19	0.03	98.12%	99.48%	−1.2
UC19	Utility	5	39,000	250	27% TNG + 73% N2	19.02	0.06	96.55%	96.82%	−2
UC20	Utility	5	39,000	200	22% TNG + 78% N2	14.89	0.1	95.53%	95.98%	−2.23
UC21	Utility	0.6	4700	250	27% TNG + 73% N2	0.25	5	95.82%	97.01%	−0.32
UC22	Utility	5	39,000	155	17% TNG + 83% N2	1.50	10	90.68%	94.16%	−0.02
UC23	Utility	5	39,000	270	29% TNG + 71% N2	0.46	100	98.07%	98.12%	−1.81
UC24	Utility	0.2	1560	100	11% TNG + 89% N2	0.01	1000	No Flame

and

Table A2. Input Conditions for 24 SONIC Corner Cases (SC).

Case No.	Flare Type	Exit Velocity (m/s)	Flow Rate (SCFH)	NHV (BTU/SCF)	Gas Composition	Wind Speed (m/s)	MFR	CE	DRE	CE Error (%)
SC1	SONIC	1.2	2100	270	29% TNG + 71% N2	49.78	0.0005	41.10%	61.80%	2.86
SC2	SONIC	0.6	1050	250	27% TNG + 73% N2	20.41	0.00075	69.20%	86.60%	1.16
SC3	SONIC	0.6	1050	200	22% TNG + 78% N2	17.87	0.001	60.79%	77.83%	−1.22
SC4	SONIC	0.6	1050	600	65% TNG + 35% N2	12.76	0.0016	99.23%	99.57%	−0.52
SC5	SONIC	1.2	2100	250	27% TNG + 73% N2	23.84	0.0022	75.76%	88.74%	−0.84
SC7	SONIC	1.2	2100	155	17% TNG + 83% N2	21.58	0.0028	91.52%	95.72%	−0.51
SC8	SONIC	1.2	2100	300	33% TNG + 67% N2	18.92	0.0034	71.06%	85.28%	−1.15
SC9	SONIC	1.2	2100	200	22% TNG + 78% N2	17.87	0.004	96.63%	97.99%	−0.48
SC10	SONIC	0.6	1050	300	33% TNG + 67% N2	7.80	0.005	95.37%	97.31%	−0.47
SC11	SONIC	0.6	1050	270	29% TNG + 71% N2	7.44	0.0056	92.98%	96.12%	−0.52
SC12	SONIC	1.2	2100	270	29% TNG + 71% N2	14.14	0.0062	93.93%	96.42%	−0.54
SC13	SONIC	0.6	1050	250	27% TNG + 73% N2	6.78	0.0068	89.18%	93.40%	−0.68
SC14	SONIC	0.6	1050	200	22% TNG + 78% N2	6.57	0.0074	42.12%	52.63%	−1.33
SC15	SONIC	1.2	2100	155	17% TNG + 83% N2	12.77	0.008	98.73%	99.12%	−0.39
SC16	SONIC	2.4	4200	600	65% TNG + 35% N2	22.02	0.0086	59.76%	73.07%	−0.93
SC17	SONIC	5	8700	300	33% TNG + 67% N2	47.92	0.0092	99.79%	99.82%	−0.72
SC18	SONIC	2.4	4200	920	pure TNG	18.45	0.01	99.17%	99.23%	−0.25
SC19	SONIC	5	8700	920	pure TNG	22.19	0.03	88.97%	91.22%	−0.94
SC20	SONIC	5	8700	250	27% TNG + 73% N2	19.02	0.06	84.24%	87.21%	−0.7
SC21	SONIC	5	8700	200	22% TNG + 78% N2	14.89	0.1	99.54%	99.83%	−0.22
SC22	SONIC	1.2	2100	250	27% TNG + 73% N2	0.50	5	90.83%	94.32%	−0.05
SC23	SONIC	5	8700	155	17% TNG + 83% N2	1.50	10	97.01%	97.47%	−0.26
SC24	SONIC	5	8700	270	29% TNG + 71% N2	0.46	100	No Flame
SC6	SONIC	0.6	1050	100	11% TNG + 89% N2	0.02	1000	No Flame

in the Appendix A.

3. Results

3.1. Model Verification against Physical Test Data

Figure 3 and Figure 4 compare the CE results between experiment and simulation techniques. All the CE results are summarized in

Table A3. Single Pipe Utility flare tip CE validation Results.

Test No.	Flare Type	TNG Flowrate (SCFH)	N2 Flowrate (SCFH)	NHV (BTU/SCF)	Vjet (m/s)	U (m/s)	MFR	CEexp	CEcfd
1	Utility	8666	30,313	213	4.93	3.57	1.7240	95.19%	97.69%
2	Utility	341	1216	214	0.19	4.92	0.0014	96.81%	95.08%
3	Utility	1272	3476	253	0.60	1.79	0.0975	92.47%	95.50%
4	Utility	10,542	28,402	260	4.92	5.36	0.7498	97.38%	98.52%
5	Utility	12,661	25,628	305	4.84	3.13	2.1606	99.12%	98.00%
6	Utility	3080	1648	559	0.59	4.02	0.0164	99.16%	99.93%
7	Utility	39,267	0	929	4.96	2.68	2.0531	99.92%	100.00%

and

Table A4. Sonic flare tip CE validation Results.

Test No.	Flare Type	TNG Flowrate (SCFH)	N2 Flowrate (SCFH)	NHV (BTU/SCF)	Vjet (m/s)	U (m/s)	MFR	CEexp	CEcfd
1	Sonic	1483	7231	157	1.19	7.15	0.0255	89.30%	90.00%
2	Sonic	234	809	201	0.58	1.34	0.177	88.10%	97.04%
3	Sonic	570	1519	240	1.17	1.34	0.698	97.48%	97.43%
4	Sonic	1395	2859	291	2.39	4.47	0.244	96.87%	96.70%
5	Sonic	682	371	513	0.59	4.92	0.011	99.64%	99.44%

in the Appendix A. In both cases, as NHV increases, so does CE. Uncertainty analyses are summarized in the Section 3.3. Figure 5 and Figure 6 show the temperature contour plots for utility cases 3, 5, and 7 and sonic case 3, 4, and 5. Flame length and peak flame temperature are a strong function of the flare gas NHV, the flow rate, and the wind speed. Crosswinds shift the fuel–air mixing zone to the downwind side, which results in the observed flame downwash. Higher crosswinds also create higher shear in the flame region, increasing the risk of local flame quenching. However, high crosswinds do not always lead to low CE, as the standing vortex developed on the lee-ward side of the flare tip can anchor and stabilize the flame [7].

3.2. Uncertainty Analysis of CFD Validation Results

Uncertainty in the combustion simulations arises from several sources. Numerical uncertainties are due to the limitations of the numerical methods used to solve the transport equations. Modeling uncertainties are due to the simplifications and assumptions made in the mathematical models used to describe the fluid flow (e.g., turbulence model or inflow profiles). The turbulence–chemistry interaction model is another important source of uncertainty. Manifold methods, such as the FGM model used in this work, rely on the presumed shape of the probability density function (PDF) and a 1D flame for tabulation. More detailed methods such as composition-transported PDF or the eddy dissipation concept using a detailed chemical mechanism can be more accurate; however, they require significantly higher computational costs. Geometric uncertainties are due to simplifications made to the geometry of the flare tip system being simulated. For example, pilots are not explicitly modeled, and the flame stabilization tabs around the tip of the utility flare and the sonic tip internal connectors are simplified to manage the model complexity. All of the above uncertainties contribute to the total model systemic error.

The uncertainty of the measurements was estimated in accordance with the “Guide to Expression of Uncertainty in Measurement”, often referred to as the GUM [28]. The empirical testing (JZ) results are reported with an estimate of uncertainty by the vendor using the error propagation method. The JZ CE/DRE measurement uncertainties were mainly introduced by instrument errors and testing variabilities, such as sample extraction variations. Peter et al. [12] gave a detailed discussion on the experimental system uncertainties (eCE-sys) and demonstrated that they increase as the NHV decreases.

Model uncertainty (Dif) is calculated as a percentage of deviation between CE_cfd and CE_exp.

Table 3. Uncertainty results for utility flare tip validation cases.

Test No.	Flare Type	NHV (BTU/SCF)	CEexp	CEcfd	Dif(%)	eCE-sys
1	Utility	213	95.19%	97.69%	2.63%	1.78%
2	Utility	214	96.81%	95.08%	−1.78%	1.49%
3	Utility	253	92.47%	95.50%	3.27%	2.12%
4	Utility	260	97.38%	98.52%	1.17%	1.22%
5	Utility	305	99.12%	98.00%	−1.13%	0.58%
6	Utility	559	99.16%	99.93%	0.77%	0.27%
7	Utility	929	99.92%	100.00%	0.08%	0.03%

and

Table 4. Uncertainty results for sonic flare tip validation cases.

Test No.	Flare Type	NHV (BTU/SCF)	CEexp	CEcfd	Dif(%)	eCE-sys
1	Sonic	157	89.30%	90.00%	0.78%	5.31%
2	Sonic	201	88.10%	97.04%	10.15%	2.64%
3	Sonic	240	97.48%	97.43%	0.05%	1.11%
4	Sonic	290	96.87%	96.70%	0.17%	0.09%
5	Sonic	513	99.64%	99.44%	0.20%	0.11%

are uncertainty results for the single-pipe utility flare tip and sonic flare tip. Dif decreases as NHV increases for both flare tips, which is consistent with eCE-sys. For the utility flare tip in Table 3, when NHV values are less than 250 BTU/SCF, the CFD predicts around 1.83% higher CE than the experimental results and 3% higher CE than experimental CE for the sonic flare tip in Table 4. When NHV values are greater than 250 BTU/SCF, the difference between the experimental and CFD model outputs for both the utility flare tip and sonic flare tip is smaller, with an average difference of 1% for the utility flare tip in Table 3 and 0.18% for the sonic flare tip in Table 4. eCE-sys rapidly increases when NHV is less than 300 BTU/SCF. This low NHV operating regime poses challenges to both CFD models and experimental measurements due to flame instability and local extinction. Uncertainty should be taken into consideration when analyzing flare performance.

3.3. Investigating the Impact of Crosswinds

The CE for all the simulated cases is plotted as a function of NHV and is color-coded into three different MFR categories, as shown in Figure 7. All of the simulated CE results are summarized in Table A1 and Table A2 in the Appendix A. In accordance with the reported trends in the literature, CE increases with NHV. CE also increases with MFR when NHV is maintained at a constant value. When NHV is greater than 300 BTU/SCF, CE exceeds 98.5%.

Flame extinction was observed for cases UC24 (NHV = 100 BTU/SCF, U_wind = 0.01 m/s) and SC6 (NHV = 155 BTU/SCF, U_wind = 21.58 m/s). In both cases, the NHV of the flare gas is quite low, while SC6 is also subjected to high crosswind. In contrast, a weak flame with a CE of 42.12% was observed for SC 14, despite having the same low NHV as SC6 but being subjected to a lower wind speed (resulting in a higher MFR). This demonstrates that the flame is significantly more sensitive to crosswind at lower NHV.

4. Discussion

4.1. MFR (Wind Effects) Study

A steady-state solver was chosen over an unsteady solver to sweep through the flare operating conditional space more efficiently. An initial validation and verification exercise indicated that the CE can be predicted with sufficient accuracy. Calculated temperature profiles were used to estimate the overall flame shape and structure. The results demonstrate reasonable trends, indicating a longer hot gas plume with higher NHV and gas flow rates, while higher crosswinds bend the flame toward the downwind side. At high crosswinds, tip wake region plays an important role, and a good computational mesh resolution must be maintained. A solution-based dynamic adaptive mesh strategy was used to track the evolving flame trajectory and efficiently cluster the grid points into the regions of interest.

Figure 8 explores the relationship between CE and MFR. CE increases for cases with the same NHV but increasing MFR, which helps to quantitively understand the impact of MFR on flare performance. Sonic and utility flare tips are designed differently and exhibit different combustion performance. Therefore, it is meaningful to compare the CE results of these two flare tips. It shows that the CE for utility flare tips were generally higher than sonic tips. For the same NHV, UC CE is higher than SC CE when MFR is comparable. More scatter in the results for the sonic flare tip compared to the single-pipe utility flare tip can be attributed to the difference in their design and flow dynamics. The sonic tip has a constricted opening at the tip exit, resulting in a complex ring flow pattern and significantly higher flow speed and shear. The utility flare tip has a simpler design with a flame stabilizer at the exit, leading to a more stable flow and combustion behavior. Therefore, increased scatter in the sonic tip results indicates that the combustion in this type of design is more sensitive to variations in operating conditions and environmental factors. The same MFR achieved by higher gas jet speed and lower wind speed decreases CE less than that with lower jet speed and higher windspeed [6]. This observation suggests that MFR alone is not sufficient to fully understand the crosswind effects, and further investigation is needed to establish a proper relationship between CE and MFR.

4.2. Comparison Study with Numerical Parametric Model

A numerical parametric model was developed for calculating flare CE and DRE and was verified against available physical test data. The parametric model considers key variables influencing flare performance, including flare vent gas net heating value, flare design, flow rate, exist velocity, and inert gas composition as well as the environmental factor of crosswind speed, with each effect characterized using a parametric model [13]. Unlike the computationally intensive CFD models, parametric models have the advantage of running in real time, making them ideal digital twins deployable on operating assets for flare performance monitoring in real time. Physical tests were conducted on three full-scale industrial flares, including non-assisted, single-arm pressure-assisted, and multi-arm pressure-assisted flare designs, and CE/DRE were reported based on an extractive sampling method [12]. In this work, the parametric model was further tested against the validated CFD model and applied to additional cases that are not covered under the physical testing program. These cases, referred to as UC and SC, were designed to explore extreme operating conditions that are generally hard to achieve and measure in a controlled test environment but can be encountered on an actual operating asset. This not only allowed us to expand on the available data in the operating space but also to explore the critical boundary regions more thoroughly. For example, the CFD model was used to simulate scenarios with wind speeds of more than 20 m/s, conditions which have previously been reported as the point at which wind begins to significantly affect DRE.

Figure 9 and Figure 10 are the CE comparison results of CFD simulation and numerical parametric models. All comparison results are summarized in

Table A5. Input Conditions for 24 Single pipe Utility Flare Corner (UC) cases.

Case No.	Flare Type	NHV (BTU/SCF)	MFR	CE	DRE	CE-Parametric Model	DRE-Parametric Model
UC1	Utility	270	0.0005	85.76%	94.43%	58.93%	64.68%
UC2	Utility	250	0.00075	95.56%	97.53%	85.18%	88.24%
UC3	Utility	200	0.001	93.17%	96.42%	70.28%	75.07%
UC4	Utility	600	0.0016	98.83%	98.90%	99.20%	100.00%
UC5	Utility	250	0.0022	95.20%	97.44%	73.52%	77.97%
UC7	Utility	155	0.0028	78.48%	88.64%	45.26%	51.76%
UC8	Utility	300	0.0034	98.32%	98.46%	89.64%	92.07%
UC9	Utility	200	0.004	94.15%	96.05%	59.52%	65.23%
UC10	Utility	300	0.005	98.67%	98.70%	95.28%	96.86%
UC11	Utility	270	0.0056	98.31%	98.58%	93.14%	95.05%
UC12	Utility	270	0.0062	98.59%	98.80%	88.59%	91.17%
UC13	Utility	250	0.0068	97.49%	98.24%	91.12%	93.34%
UC14	Utility	200	0.0074	97.45%	98.47%	79.89%	83.62%
UC15	Utility	155	0.008	91.19%	94.98%	45.26%	51.76%
UC16	Utility	600	0.0086	98.88%	98.90%	99.14%	100.00%
UC17	Utility	300	0.0092	90.86%	93.59%	59.31%	65.03%
UC18	Utility	920	0.01	99.55%	99.57%	99.46%	100.00%
UC19	Utility	920	0.03	98.12%	99.48%	99.06%	100.00%
UC20	Utility	250	0.06	96.55%	96.82%	58.36%	64.15%
UC21	Utility	200	0.1	95.53%	95.98%	54.89%	60.90%
UC22	Utility	250	5	95.82%	97.01%	92.81%	94.77%
UC22	Utility	155	10	90.68%	94.16%	54.93%	60.94%
UC23	Utility	270	100	98.07%	98.12%	94.49%	96.20%
UC24	Utility	100	1000	No Flame		12.36%	12.36%

and

Table A6. Input Conditions for 24 SONIC Corner Cases (SC).

Case No.	Flare Type	NHV (BTU/SCF)	MFR	CE	DRE	CE-Parametric Model	DRE-Parametric Model
SC1	SONIC	270	0.0005	41.10%	61.80%	58.93%	64.68%
SC2	SONIC	250	0.00075	69.20%	86.60%	58.40%	64.19%
SC3	SONIC	200	0.001	60.79%	77.83%	54.93%	60.95%
SC4	SONIC	600	0.0016	99.23%	99.57%	97.76%	98.94%
SC5	SONIC	250	0.0022	75.76%	88.74%	58.40%	64.18%
SC7	SONIC	155	0.0028	91.52%	95.72%	59.34%	65.06%
SC8	SONIC	300	0.0034	71.06%	85.28%	54.93%	60.94%
SC9	SONIC	200	0.004	96.63%	97.99%	88.96%	91.50%
SC10	SONIC	300	0.005	95.37%	97.31%	84.78%	87.89%
SC11	SONIC	270	0.0056	92.98%	96.12%	59.64%	65.33%
SC12	SONIC	270	0.0062	93.93%	96.42%	81.97%	85.44%
SC13	SONIC	250	0.0068	89.18%	93.40%	61.83%	67.37%
SC14	SONIC	200	0.0074	42.12%	52.63%	45.25%	51.75%
SC15	SONIC	155	0.008	98.73%	99.12%	93.49%	95.35%
SC16	SONIC	600	0.0086	59.76%	73.07%	59.31%	65.03%
SC17	SONIC	300	0.0092	99.79%	99.82%	98.93%	99.92%
SC18	SONIC	920	0.01	99.17%	99.23%	98.73%	99.75%
SC19	SONIC	920	0.03	88.97%	91.22%	58.36%	64.15%
SC20	SONIC	250	0.06	84.24%	87.21%	54.89%	60.90%
SC21	SONIC	200	0.1	99.54%	99.83%	92.53%	94.54%
SC22	SONIC	250	5	90.83%	94.32%	53.53%	59.63%
SC23	SONIC	155	10	97.01%	97.47%	94.43%	96.15%
SC24	SONIC	100	1000	No Flame		12.36%	18.81%
SC6	SONIC	155	0.0028	No Flame		12.36%	18.81%

in the Appendix A. The results indicate that when the gas NHV was greater than 300 BTU/SCF, the predictions from the CFD and parametric model aligned well. However, when the gas NHV was less than 300 BTU/SCF, the CFD model predicted a CE that is generally higher than the parametric model. The CFD model results suggested that the effect of wind speed (and MFR) on the flare performance in the 100–300 BTU/SCF region was less significant than predicted by the parametric model. With these CFD results, the parametric model can be optimized for the specific NHV region. Combining physical test and simulation test data yielded valuable information to predict methane emissions over a larger range of flare operating conditions.

5. Conclusions

Computational fluid dynamics methodology was used to simulate a 14” utility flare and an 8” pressure-assisted sonic flare. First, the model was benchmarked against the physical tests by replicating a range of test conditions. The CFD model-predicted CE matched reasonably well with the test-measured CE. When the gas NHV was greater than the critical threshold of 300 BTU/SCF, the simulation-predicted CE was within 1%. At lower NHV levels, there was greater departure between the CFD model-predicted and the measured values. However, it is important to note that higher uncertainties were also reported in the measured values for gas NHV levels < 300 BTU/SCF.

A DoE (design of experiments) with a total of 48 cases was created covering a wide range of gas heating values (100–920 BTU/SCF), gas exit velocities (0.2–5 m/s), and wind speeds (0–50 m/s). CE dependence on the flare gas NHV and the momentum flux ratio (MFR) was explored. The results confirmed that the CE remained high (>95%) above and fell steeply below a critical flare gas NHV near 300 BTU/SCF. The results also confirmed that the critical NHV where the transition occurred was a function of MFR. Generally, a low MFR moved the critical NHV to higher values. Further investigation using simulations and field tests will help in better understanding the multivariate dependencies of CE (for instance, on NHV, MFR, and flare tip design).

While the CFD models are derived from fundamental physical principles and, thus, are considered to be of higher rigor, the simulations are time intensive and cannot be used in real time as digital twins. Numerical parametric models, on the other hand, are lightweight and can be used for real-time flare monitoring. However, they must be tested against reliable flare data for proper benchmarking. Simulations performed in this work enabled us to further verify the numerical parametric model published earlier in more operating scenarios, including some extreme scenarios (high crosswinds, low NHV). The comparison demonstrated that the simulations predicted similar CE to the parametric model at NHV > 300 BTU/SCF, while simulations showed generally higher CE at NHV < 300 BTU/SCF. This work demonstrates the feasibility of detailed physics-based models not only in supporting the design and operation of flares but also to complement physical testing programs by simulating flare conditions that are hard to manage in controlled test environments.

A flare pilot was used to ignite the flare and keep it lit at low NHV gas levels. Its effect on the measured CE/DRE was accounted for in this upstream industry flare experiment study. However, in CFD simulations, pilot effects are not taken into consideration. More CFD studies are needed to quantify pilot effects on CE under different operating conditions. Moreover, more precise CFD studies, incorporating unsteady states with an LES turbulence model and the eddy dissipation concept with a detailed combustion mechanism, are essential to gain a deeper understanding of how the pilot system, wind speed, NHV, vent gas velocity, and their combination influence flare emissions.