Impact of Hydrogen-Methane Blending on Industrial Flare Stacks: Modeling of Thermal Radiation Levels and Carbon Dioxide Intensity

Abstract

Regulatory changes related to the policy of reducing CO₂ emissions from natural gas are leading to an increase in the share of hydrogen in gas transmission and utilization systems. In this context, the impact of the change in composition on thermal radiation zones should be assessed for flaring during startups, scheduled shutdowns, maintenance, and emergency operations. Most existing models are calibrated for hydrocarbon flare gases. This study assesses how the CH₄–H₂ blends affect thermal radiation zones using a developed solver based on the Brzustowski–Sommer methodology with composition-dependent fraction of heat radiated (F) and range-dependent atmospheric transmissivity. Five blends, 0–50% (v/v) H₂, were analyzed for a 90 m stack at wind speeds of 3 and 5 m·s⁻¹. Comparisons were performed at constant molar (standard volumetric) throughput to isolate composition effects. Adding H2 contracted the radiation zones and reduced peak ground loads. Superposition analysis for a multi-flare layout indicated that replacing one 100% (v/v) CH₄ flare with a 10% (v/v) H₂ blend reduced peak ground radiation. Emission-factor analysis (energy basis) showed reductions of 3.24/3.45% at 10% (v/v) H₂ and 7.01/7.44% at 20% (v/v) H₂ (LHV/HHV); at 50% (v/v) H₂, the decrease reached 22.18/24.32%. Hydrogen blending provides coupled safety and emissions co-benefits, and the developed framework supports screening of flare designs and operating strategies as blends become more prevalent.

1. Introduction

A climate–neutral economy requires both the reduction of absolute CO₂ emissions and the maintenance of process safety in situations where gas flaring remains essential–such as during startups, scheduled shutdowns, maintenance, or emergency operations.

In May 2024, the Hydrogen and Decarbonized Gas Market Package was adopted, and the legal acts—Directive (EU) 2024/1788 and Regulation (EU) 2024/1789—set a target limit of ≤2% (v/v) hydrogen in cross-border gas interconnections [1,2]. At the distribution level, pilot programs are currently testing 10–20% (v/v) hydrogen–natural gas blends. As an example, the UK HyDeploy program demonstrated that domestic gas appliances can operate safely with a 20% (v/v) H₂–natural gas blend, with no adverse impact on performance or safety [3,4]. Other European initiatives are exploring blends of 5–20% (v/v) H₂, and up to~30% (v/v) in industrial clusters [5,6,7,8].

Flare systems (widely used in oil and gas production, LNG plants, refineries, and chemical processing facilities) are typically designed for flare gases dominated by methane (CH₄). Additionally, flare flames must be maintained continuously, as the flare stack must remain in a ready-to-ignite state to handle emergency gas releases from the process installation at any time [9,10]. Hydrogen blending affects the thermal radiation characteristics of flare flames, a critical factor for process safety and hazard-zone determination [11,12,13,14,15]. The addition of hydrogen modifies flame structure, combustion kinetics, and radiative output. The adiabatic flame temperature of pure hydrogen (approximately 2403 K) is slightly higher than that of methane (approximately 2200 K), while the fraction of heat radiated (F) decreases markedly [14]. API Standard 521 (7th Edition, 2023) defines F as the proportion of the total chemical heat-release rate emitted as thermal radiation—a key input for calculating safe thermal-radiation distances on the ground [15]. For methane-rich flare gases, typical F values range from 0.15 to 0.32, whereas for hydrogen-rich blends near 80% (v/v) H₂, F can drop to 0.10–0.11 [12,13,16]. This reduction is primarily due to (i) the absence of soot formation and associated continuum radiation, (ii) the relatively weak molecular emission of water vapor (H₂O) in the infrared, and (iii) strong self-absorption of H₂O radiation in the flame. Lower F values translate into smaller thermal-hazard zones for the same total heat-release rate; however, the higher flame temperature of hydrogen can increase local thermal radiation near the flare tip, which must be considered in tip design and material selection [13,16]. These policy and physics trends together motivate composition-aware assessment of flare-radiation levels and related carbon-intensity outcomes for CH₄/H₂ blends.

The literature on CH₄/H₂ flare radiation establishes key trends in emissivity, transmissivity, flame geometry, and resulting hazard distances, while also underscoring the limits of hydrocarbon-calibrated models when applied to CH₄/H₂ blends. Using a weighted multi-point source model, Zhang et al. quantified the influence of orifice diameter and pressure on H₂ jet-fire radiation and demonstrated that the flame extends and widens as pressure and leak diameter rise [17]. Zhou et al. [18] developed a model for CH₄/H₂ mixtures and examined how H₂ admixture alters thermal radiation, reporting an increase in effective emissivity with distance from the source. Miller et al. [19] emphasize that most thermal radiation models were calibrated for hydrocarbon flares and are routinely applied to hydrogen beyond their strict validity. Rossiello et al. [20] performed CFD analyses of flare gases and pure hydrogen on heavy-duty burners, and He et al. [21] proposed hydrogen-specific flare-radiation models for hazard-distance assessment; both lines of work indicate material differences in flame geometry and radiation fields between hydrocarbon and hydrogen releases. Benard et al. [22] compared point-source and solid-flame formulations for H₂ flares and showed that, near the base of the stack, solid-flame approaches are more reliable for sizing and layout. Li et al. [23] modified solid-flame models tailored to CH₄/H₂ jet fires and found that, for identical operating conditions, safe distances for CH₄/H₂ can be lower than for pure CH₄. Further confirmation that hydrogen-specific radiation models yield hazard distances distinct from hydrocarbon analogues is provided by He et al. [12].

Lévai and Bereczky [24] reported, from flame-optic tests, that adding hydrogen shortens flame height in a nonlinear fashion with composition. With higher H₂ content, both adiabatic flame temperature and laminar burning velocity increase, as shown by Sorgulu et al. [25], consistent with classic scaling in which flame length grows with total mass flow and nozzle diameter [26] and with turbulence–chemistry interactions that differentiate pure H₂ from CH₄/H₂ flames [27]. In diffusion flames, the flare tip mixes air and fuel at velocities, turbulence levels, and concentrations required for reliable ignition and stable combustion; small H₂ additions broaden the stability envelope because liftoff velocity rises faster than flashback propensity in the near-tip region, in line with diffusion–flame practice.

Baird et al. [28] provided a comprehensive safety assessment of hydrogen blending with natural gas and concluded that jet-fire heat-flux patterns for CH₄/H₂ can resemble those for 100% CH₄ under certain regimes. Most tools used to assess thermal radiation around flare stacks were calibrated on hydrocarbon data and, in the absence of hydrogen-specific models, are frequently extrapolated to H₂, as noted by Miller et al. [19] and Willoughby et al. [29]. More recent CFD and field-validated modeling for natural gas with hydrogen admixture demonstrate improved predictive fidelity for H₂-enriched flames and provide case-study validation at scale [20,30]. In horizontal jet-fire scenarios, H₂ flares exhibit lower fatality levels than natural-gas analogues in QRA settings [31]. Correlations for the fraction of heat radiated, F, have been generalized across H₂, CH₄, and C₃H₈, offering composition-aware inputs to radiation models [32]. Consistently, dispersion/safety zoning around pipelines transporting CH₄/H₂ tends to be smaller than for pipelines carrying pure CH₄ at the same operating conditions [33].

Despite this progress, three practical gaps remain for engineering design and operations. First, many zoning workflows still pair F values calibrated for hydrocarbons with transmissivity assumed constant with range, even though the literature reports composition-dependent F and attenuation that varies with humidity and distance [12,19,21,22,23]. Integrated, lightweight implementations suitable for CH₄/H₂ blends remain rare. Second, CH₄/H₂ comparisons are often inconsistent because results are reported at different throughputs, which confounds composition effects with simple scaling. Third, interaction among flares is underrepresented, even though the superposition of ground-level radiation from nearby flares is directly relevant to layout decisions.

In this study, we implement a Brzustowski–Sommer–based solver with composition-dependent F and range-dependent atmospheric transmissivity, perform constant-molar-throughput comparisons across 0–50% (v/v) H₂ for single- and multi-flare configurations with superposition, and quantify associated CO₂-emission reductions via composition-adjusted emission factors, with external model cross-checks to support design-grade application.

2. Methodology

The methodology adopted in this work includes the calculation framework, underlying assumptions, and analytical tools used to estimate the thermal radiation envelopes for single- and multi-flare stacks operating with hydrogen blends ranging from 0–50% (v/v), as well as the corresponding reductions in CO₂ emissions. To support early-stage layout screening, an engineering correlation framework based on the Brzustowski–Sommer methodology was adopted. The approach is well established in flare radiation design and is computationally efficient, while allowing inclusion of a composition-dependent fraction of heat radiated F and a range-dependent atmospheric transmissivity.

2.1. Combustion of Hydrogen–Natural Gas Blends

In CH₄/H₂ systems, combustion bifurcates into two parallel reactions: CH₄ undergoes oxidation to CO₂ and H₂O, whereas hydrogen oxidizes exclusively to H₂O [34]. A hydrogen flame typically appears nearly invisible, especially when burned in pure oxygen, producing only water vapor [34,35]. In atmospheric combustion, additional species from air are present in the flare gas. The morphology of the flame, including length and shape, is also modified: hydrogen enhances the laminar combustion speed and molecular diffusion, promoting faster mixing with air. Empirical jet–flame studies demonstrate that flame height decreases with increasing hydrogen content, up to approximately 60% (v/v) H₂ by volume [36,37,38]. A comparison of key design–relevant parameters for hydrogen and natural gas is presented in

Table 1. Selected Physical and Flammability Parameters of CH₄ and H₂ Relevant to Flare System Design.

Parameter (298 K, 1 bar)	Unit	CH4	H2
Lower Heating Value (LHV) 1	(MJ·kg–1)	35.8	120
Higher Heating Value (HHV) 1	(MJ·kg–1)	55.5	142
Density 2	(kg·m–3)	0.717	0.0899
Laminar Combustion Speed 3	(m·s–1)	0.4	2.9
Stoichiometric flame temperature 4	(K)	2497 (burning with air); 3083 (burning with pure oxygen)	2673
Lower and Upper Explosive Limit (LEL, UEL) 5	(%)	5–15	4–75
Minimum Ignition Energy (MIE) 6	(mJ)	0.28–0.30	0.017–0.02
Fraction of Heat Radiated 7	(–)	0.15–0.25	0.05–0.15

¹ [39], ² [39,40], ³ [41], ⁴ [14], ⁵ [7,39], ⁶ [12,16], ⁷ [12,15,16].

.

Experimental studies on large-scale flares utilizing H₂/CH₄ blends indicate that for hydrogen concentrations up to approximately 20% (v/v), the radiation zone greater than 4 (kW·m^–2) remains comparable to that observed for pure CH₄ [36]. However, when the hydrogen content exceeds 50% (v/v), this zone is significantly reduced. The maximum flame temperature increases with the hydrogen content at constant burner power. Hydrogen promotes the formation of a greater number of reactive radicals and enhances air–fuel mixing intensity, which tends to shorten the flame length. However, this effect is counterbalanced by the higher flame temperature and increased jet velocity, both of which contribute to flame elongation.

In the study by Zhao et al., it was demonstrated that increasing the hydrogen content in a non-premixed CH₄/H₂ jet introduces two opposing influences on flame height [38]. The enhanced diffusivity of the fuel blend, the elevated concentration of reactive intermediates, and the intensified air entrainment contribute to a shorter flame. Conversely, higher adiabatic flame temperatures and increased jet exit velocity, especially under low Reynolds number conditions, tend to elongate the flame.

2.2. Thermal Radiation Assessment for Existing Industrial Flare Systems

Flare stacks, as defined in API Standard 521, are designed to safely dispose of excess gases during emergency depressurizations and plant startups or shutdowns [15]. The discharged gases are most often hydrocarbons, which undergo combustion to form CO₂, H₂O, and trace species determined by the composition of the flare gas. Steam injection is frequently used to promote atomization, enabling smokeless combustion and maintaining required flame temperatures. The introduction of steam enhances turbulent mixing with ambient air and creates an induced draft, increasing air entrainment into the flare tip and improving combustion stability. Nitrogen is commonly supplied to displace flammable mixtures upward, preventing flashback and combustion within the flare riser or tip. Continuous readiness is ensured by maintaining a pilot flame supplied with high-pressure fuel gas, typically at 8–15 (m³·h^–1) [10].

Various approaches exist to estimate thermal radiation zones. The available methods differ in terms of their level of detail and fidelity in representing real conditions. A comparative summary of selected methodologies is presented in

Table 2. Overview of Thermal Radiation Estimation Methods for Flare Systems.

Method	Authors/Name	Typical Applications 1	Advantages 1	Limitations 1
Simple point source approach	Simple Approach (API Std 521, Annex C) 2	Preliminary stack height selection	Instant calculations, minimal data required	Conservative; does not account for flame shape or wind
Semi-Empirical Model B&R	Brzustowski & Sommer 3	Refineries, gas processing facilities	Includes wind, jet direction, flammability class; still in use	Requires charts/tables; calibration needed
Line-Surface Model Chamberlain	Chamberlain 4	High flares onshore/offshore	Improved accuracy for luminous flares; widely used in British standards	Underestimates radiation for low luminosity gases
Extended “Low Luminosity” Model	Miller et al., He et al. 5	H2-rich flaring, multi–tip ground flares	Validated via full-scale tests, 0–100 (%) H2; supports low-luminosity flames	Greater number of parameters

¹ [14,42,43], ² [15], ³ [44], ⁴ [15,45,46], ⁵ [11,12].

.

Single-source models assume that the entire flame can be represented by a single point or spherical energy source [15]. Although computationally simple, they neglect the effects of wind and flame geometry. In semi-empirical models, the flame center of gravity and flame length are determined using dimensionless correlations, while the thermal radiation is still estimated using a point source equation. Line and surface source models represent the flame as a linear segment or an elongated cylinder and apply wind-dependent shape factors to improve the accuracy of the lateral distribution [15,42].

The most accurate representation is achieved through full CFD–RTE simulations (Computational Fluid Dynamics with Radiative Transfer Equation), which are performed using specialized software such as ANSYS Fluent or OpenFOAM. These models incorporate combustion chemistry, turbulence, and spectral gas absorption. However, such simulations are time-intensive and highly complex to execute [47].

A classical approach to flare system design is the Brzustowski–Sommer method, which belongs to the family of point-source-based empirical correlations. It was developed based on full-scale flame radiation measurements conducted in crosswind conditions and remains one of the calculation methods referenced in API Standard 521 [15].

Given the gas flow rate, the geometry of the flare stack and the wind velocity, the method aims to sequentially determine (i) the location of the flame center and its total length; (ii) the thermal radiation at any ground level observation point, and (iii) the critical distances corresponding to standard thermal radiation thresholds, as listed in

Table 3. Recommended Design Thermal Radiation Exposure Levels [15].

Recommended Thermal Radiation Level (kW·m–2)	Conditions
9.46	Maximum limit for urgent emergency actions. Personnel with proper protective clothing (e.g., fire suits) can tolerate this level only for a few seconds.
6.31	Suitable for short-duration emergency tasks, ≤30 (s) without shielding, provided appropriate clothing is worn.
4.73	Acceptable for emergency actions lasting 2–3 min with appropriate clothing but no shielding.
1.58	Continuous exposure level for personnel wearing proper work clothing.

.

Based on the flare gas flow parameters specified, including the mass flow rate $\dot{\mathrm{m}}$ (kg·h⁻¹), molecular weight MW (kg·kmol⁻¹), gas temperature T (K), flare tip diameter D (m), and lower heating value LHV (kJ·kg⁻¹), the following quantities are determined sequentially [15,44]. First, the normal volumetric flow rate $\dot{\mathrm{W}}$ (Nm³·s^–1) is calculated from the mass flow rate under standard conditions according to Equation (1):

$$\dot{\mathrm{W}}={\displaystyle \frac{\dot{\mathrm{m}}}{3600}}·{\displaystyle \frac{22.4}{\mathrm{M}\mathrm{W}}}·{\displaystyle \frac{\mathrm{T}}{273}}$$

(1)

The thermal power Q (kW) released by the flare, as given by Equation (2), is determined from the lower heating value LHV (kJ·kg⁻¹) of the gas:

$$\mathrm{Q}={\displaystyle \frac{\dot{\mathrm{m}}}{3600}}·{\displaystyle \frac{\mathrm{L}\mathrm{H}\mathrm{V}}{1000}}$$

(2)

Using the volumetric flow rate, the gas exit velocity U_j (m·s^–1) at the flare tip is then calculated, as defined in Equation (3):

$${\mathrm{U}}_{\mathrm{j}}={\displaystyle \frac{\mathrm{W}}{\mathsf{\pi }·\frac{{\mathrm{D}}^2}{4}}}$$

(3)

The reference speed of sound ${\mathrm{a}}_{\mathrm{i}\mathrm{s}\mathrm{o}}$ (m·s^–1), is obtained using the empirical correlation given in Equation (4):

$${\mathrm{a}}_{\mathrm{i}\mathrm{s}\mathrm{o}}=91.2·\sqrt{{\displaystyle \frac{\mathrm{T}}{\mathrm{M}\mathrm{W}}}}$$

(4)

The Mach number M (–) is calculated as the ratio of jet velocity to isentropic speed of sound, as shown in Equation (5):

$$\mathrm{M}={\displaystyle \frac{{\mathrm{U}}_{\mathrm{j}}}{{\mathrm{a}}_{\mathrm{i}\mathrm{s}\mathrm{o}}}}$$

(5)

Brzustowski and Sommer developed a correlation that relates two dimensionless numbers to the normalized coordinates (x_c, y_c) of the flame center: CL_av (–), which describes ability of the fuel jet to dilute below the lower explosive limit, LEL (%), and dj·R (–), which reflects the ratio of jet momentum to wind (a higher value indicates a longer flame) –as expressed in Equations (6) and (7) [44].

$$\mathrm{C}{\mathrm{L}}_{\mathrm{a}\mathrm{v}}={\displaystyle \frac{\mathrm{L}\mathrm{E}\mathrm{L}}{100}}·{\displaystyle \frac{\mathrm{M}·{\mathrm{a}}_{\mathrm{i}\mathrm{s}\mathrm{o}}}{\mathrm{U}}}·{\displaystyle \frac{\mathrm{M}\mathrm{W}}{\mathrm{M}{\mathrm{W}}_{\mathrm{a}\mathrm{i}\mathrm{r}}}}$$

(6)

$$\mathrm{d}\mathrm{j}·\mathrm{R}=\mathrm{D}·{\displaystyle \frac{{\mathrm{U}}_{\mathrm{j}}}{\mathrm{U}}}·\sqrt{{\displaystyle \frac{{\mathrm{T}}_{\mathrm{a}\mathrm{i}\mathrm{r}}·\mathrm{M}\mathrm{W}}{\mathrm{T}·\mathrm{M}{\mathrm{W}}_{\mathrm{a}\mathrm{i}\mathrm{r}}}}}$$

(7)

The total flame length (m) is determined using the following Equation (8):

$$\mathrm{L}=2·\sqrt{{\mathrm{x}}_{\mathrm{c}}^2+{\mathrm{y}}_{\mathrm{c}}^2}$$

(8)

Once the center of gravity of the flame and the total length have been established, it is essential to evaluate the thermal radiation zones by estimating the radiation impact distances corresponding to the standard exposure thresholds. This process requires careful consideration of the fraction of heat radiated (F), which expresses the proportion of the total chemical heat release of the flare that is converted into thermal radiation [15].

The value of F is highly dependent on the fuel composition. When hydrogen is blended into natural gas, this fraction decreases as a result of reduced soot formation and lower infrared emissivity of hydrogen flames [12,13,15,16]. To account for this behavior, the correlation shown in Equation (9) is applied for H₂/NG blends:

$$\mathrm{F}\left({\mathrm{H}}_2\right)=\left\{\begin{array}{c}0.19\\ 0.19·(1-0.80·\left({\displaystyle \frac{\mathrm{y}-0.20}{0.30}}\right)\\ 0.10\end{array}\right.\begin{array}{c}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{y}\le 0.20\\ \mathrm{f}\mathrm{o}\mathrm{r} 0.20\le \mathrm{y}<0.50\\ \mathrm{f}\mathrm{o}\mathrm{r}\ge 0.50\end{array}$$

(9)

where F denotes the fraction of heat radiated (dimensionless), and y is the molar fraction of hydrogen in the gas blend on a v/v basis.

The function applies a piecewise linear decrease from F = 0.19 (–) down to F = 0.10 (–) as the H₂ content increases from 20% (v/v) to 50% (v/v). For hydrogen concentrations above 50% (v/v), the radiative fraction is fixed at F = 0.10 (–), which reflects pure H₂ combustion behavior.

In the presented methodology, atmospheric transmissivity is not assumed to be constant but is treated as a variable dependent on the distance from the flame center [15,44]. This approach allows for a more accurate representation of infrared attenuation under real atmospheric conditions, particularly for long-distance radiation calculations. The transmissivity coefficient $\mathsf{\tau }$ should be calculated based on the API Standard 521, and incorporates the effect of ambient humidity RH (%) as well as the line-of-sight distance r between the flame and the ground-level observation point [15]. This ensures that the reduction of radiative intensity due to water vapor absorption is properly accounted for across the entire radiation field. By dynamically adjusting transmissivity at each location, as expressed in Equation (10), the method improves the accuracy of predicted thermal radiation intensities and resulting safety distances.

$$\mathsf{\tau }\left(\mathrm{R}\mathrm{H},\mathrm{r}\right)=0.79·{\left({\displaystyle \frac{3000}{\mathrm{R}\mathrm{H}·\mathrm{r}}}\right)}^{{\displaystyle \frac{1}{16}}}$$

(10)

where RH (%) denotes the ambient relative humidity, and r (m) is the distance from the flame center to the observation point.

The location of the flame center can be expressed as the coordinate pair (x_c, H + y_c), where H (m) denotes the height of the flare stack, x_c (m) represents the horizontal displacement of the flame center from the axis of the stack in the wind direction, and y_c (m) is the vertical displacement from the center of the flame above the flare stack tip. For a point at ground level located along the wind axis at horizontal coordinate r, the distance from the center of the flame is calculated as r(x) (kW·m^–2) using Equation (11) [15]:

$$\mathrm{r}\left(\mathrm{x}\right)=\sqrt{{\displaystyle \frac{\mathrm{F}·\mathrm{Q}}{4·\mathsf{\pi }·\mathrm{r}·{\mathrm{x}}^2}}}·\mathsf{\tau }\left(\mathrm{R}\mathrm{H},\mathrm{r}\right)$$

(11)

This formulation accounts for both geometric attenuation due to the inverse square law and the spectral absorption of infrared radiation by atmospheric constituents.

To determine the critical distance from the flame at which the thermal radiation level considered falls below a predefined threshold R_k (kW·m^–2), a two-step approach is used. An initial estimate of the distance, obtained without neglecting atmospheric absorption, is calculated using Equation (12):

$${\mathrm{d}}_{\mathrm{r}\mathrm{a}\mathrm{d}}\left({\mathrm{R}}_{\mathrm{k}}\right)=\sqrt{{\displaystyle \frac{\mathrm{F}·\mathrm{Q}·1000}{4·\mathsf{\pi }·{\mathrm{R}}_{\mathrm{k}}}}}$$

(12)

The critical radiation distance d_rad(R_k) (m) corresponds to the minimum separation between the flame center and a ground–level location at which the incident thermal radiation flux does not exceed a predefined threshold R_k (m).

2.3. Indicators for Assessing CO₂ Emissions from Combustion

Despite ongoing mitigation efforts, routine and emergency flaring continues to generate substantial direct CO₂ emissions worldwide. Figure 1 presents direct CO₂ emissions resulting from flaring natural gas and the flaring intensity, defined as the annual ratio of natural gas flared to total oil production for the years 2010–2030, according to the International Energy Agency (IEA) [48].

When combusting hydrogen-enriched natural gas blends, an important environmental aspect is the resulting CO₂ emissions. Since hydrogen does not contain carbon, the blend of H₂ with natural gas (NG) reduces the carbon intensity of the fuel and consequently reduces CO₂ emissions during combustion [49].

Carbon accounting and sustainability reporting frameworks typically rely on predefined emission factors (carbon intensity expressed in kgCO₂ per unit of energy, (kgCO₂·GJ⁻¹) or (kgCO₂·MJ⁻¹)) along with oxidation factors. Any reduction in the carbon content of the fuel mix directly decreases reportable CO₂ emissions [49]. This is particularly relevant in regulatory and financial contexts, where such reductions can translate into compliance benefits or cost savings.

For example, a 10% (v/v) hydrogen admixture to methane results in approximately a 3 (%) reduction in CO₂ emissions, while a 20% (v/v) H₂ blend leads to a 7–10 (%) decrease in the CO₂ mass emitted per unit of chemical energy [4,7].

One of the primary metrics for assessing the climate impact of different fuels is carbon intensity. For pure CH₄, a typical reference value is approximately 50.1 (kgCO₂·GJ⁻¹) (based on LHV) (Figure 2) [50].

With the growing prevalence of hydrogen blending in gas distribution and industrial applications, the reduction in CO₂ intensity becomes a measurable and predictable parameter, provided that the blend composition is known and stable. In addition to lowering CO₂ emissions, national inventories and compliance schemes (such as the IPCC Guidelines for National Greenhouse Gas Inventories, the EU Emissions Trading System (EU ETS), and the US EPA Greenhouse Gas Reporting Program) require operators to account for CO₂ released during fuel combustion [51]. Two broad methodological approaches are permitted: Tier 1, in which a single conservatively high emission factor (EF) is taken from regulatory tables, and Tier 2/Tier 3 (based on analysis), in which EF is derived from laboratory gas composition analysis or continuous gas quality measurements [49].

In almost all scenarios, the mass of CO₂ is calculated rather than measured directly by multiplying activity data (fuel quantity) by a chain of emission-related coefficients. The generic Tier 1 formula adopted by the IPCC (2006) is shown in Equation (13) [49]:

$$\mathrm{C}{{\mathrm{O}}_2}_{\mathrm{E}\mathrm{M}}=\mathrm{A}\mathrm{D}·\mathrm{N}\mathrm{C}\mathrm{V}·\mathrm{E}\mathrm{F}·\mathrm{O}\mathrm{F}$$

(13)

where AD denotes the amount of fuel combusted (Nm³) of gas; NCV is the net calorific value (lower heating value) of the fuel; EF represents the emission factor (kgCO₂·MJ⁻¹); and OF is the oxidation factor (−), defined as the fraction of carbon oxidized to CO₂, which for high efficiency burners is typically assumed to be 1.0 (−).

The values of default emission factors for natural gas are typically expressed on a lower heating value (LHV) basis and are intended for use in national greenhouse gas inventories, compliance reporting, and carbon accounting. Although the EU Monitoring & Reporting Regulation (MRR) and the IPCC Guidelines adopt an identical factor of 56.1 (kgCO₂·GJ⁻¹) for commercial natural gas regardless of hydrogen content, the US EIA provides separate coefficients based on higher heating value (HHV) with conversion to LHV, applicable specifically to dry pipeline gas without accounting for hydrogen blending (

Table 4. Reference CO₂ Emission Factors for Natural Gas Used in Inventories and Compliance Reporting.

Regulatory	Basis	$\mathbf{Default}\mathbf{E}{\mathbf{F}}_{\mathbf{C}{\mathbf{H}}_4}$
EU Monitoring & Reporting Regulation (MRR) 2018/2066, Annex VI; IPCC Guidelines 2006, Vol 2 [49]	LHV	56.1 (kgCO2·GJ−1)
US EIA “Carbon Dioxide Emission Coefficients“ [50]	HHV → LHV	52.9 (kgCO2·GJ−1)

) [50,51].

When composition data are available, a Tier 2/3 factor can be calculated by mass balance. Assuming ideal gas behavior and complete oxidation of CH₄ to one mole of CO₂, the net emission factor on a LHV or HHV basis, EF_mix,LHV; EF_mix,HHV (kgCO₂·GJ⁻¹) for a CH₄–H₂ blend can be expressed by the following equations (Equations (14) and (15)) [51,52]:

$${\mathrm{F}}_{\mathrm{m}\mathrm{i}\mathrm{x},\mathrm{L}\mathrm{H}\mathrm{V}}={\displaystyle \frac{\left(1-{\mathrm{y}}_{{\mathrm{H}}_2}\right)·{\mathrm{m}}_{\mathrm{C}\mathrm{O}2}}{\left(1-{\mathrm{y}}_{{\mathrm{H}}_2}\right)·\mathrm{L}\mathrm{H}{\mathrm{V}}_{\mathrm{C}{\mathrm{H}}_4}+{\mathrm{y}}_{{\mathrm{H}}_2}·\mathrm{L}\mathrm{H}{\mathrm{V}}_{{\mathrm{H}}_2}}}$$

(14)

$$\mathrm{E}{\mathrm{F}}_{\mathrm{m}\mathrm{i}\mathrm{x},\mathrm{H}\mathrm{H}\mathrm{V}}={\displaystyle \frac{\left(1-{\mathrm{y}}_{{\mathrm{H}}_2}\right)·{\mathrm{m}}_{\mathrm{C}\mathrm{O}2}}{\left(1-{\mathrm{y}}_{{\mathrm{H}}_2}\right)·\mathrm{H}\mathrm{H}{\mathrm{V}}_{\mathrm{C}{\mathrm{H}}_4}+{\mathrm{y}}_{{\mathrm{H}}_2}·\mathrm{H}\mathrm{H}{\mathrm{V}}_{{\mathrm{H}}_2}}}$$

(15)

The ${\mathrm{y}}_{{\mathrm{H}}_2}$ parameter represents the volumetric fraction of hydrogen in the blend. The $\mathrm{L}\mathrm{H}{\mathrm{V}}_{\mathrm{C}{\mathrm{H}}_4}$ denotes the lower heating value of CH₄, 802 (kJ·mol⁻¹), while $\mathrm{H}\mathrm{H}{\mathrm{V}}_{\mathrm{C}{\mathrm{H}}_4}$ is the higher heating value of CH₄, 890 (kJ·mol⁻¹ [52]). $\mathrm{L}\mathrm{H}{\mathrm{V}}_{{\mathrm{H}}_2}$ corresponds to the lower heating value LHV of hydrogen, 242 (kJ·mol⁻¹) and $\mathrm{H}\mathrm{H}{\mathrm{V}}_{{\mathrm{H}}_2}$ is its higher heating value, 286 (kJ·mol⁻¹) [52]. The ${\mathrm{m}}_{\mathrm{C}{\mathrm{O}}_2}$ denotes the molar mass of carbon dioxide, 44 (g·mol⁻¹).

3. Case Study

A dedicated computational framework was developed for the calculation of thermal radiation and the modeling of flame behavior, and subsequently applied to CH₄/H₂ blends to investigate the influence of hydrogen enrichment on key operational parameters of elevated flare stacks.

A constant set of environmental conditions was assumed. Pasquill stability class D; wind speed: 3 (m·s⁻¹) and 5 (m·s⁻¹); ambient relative humidity RH = 60 (%); ambient temperature T_∞ = 289 (K). Flare stack geometry was fixed as stack height H = 90 (m), flare–tip internal diameter D_tip = 0.70 (m), and static pressure at the tip p₂ = 104 (kPa). Design ground-level thermal radiation thresholds followed API Std 521: 1.58, 4.73, 6.31, and 9.46 (kW·m⁻²) [15]. Blend properties used by the solver were obtained from the following correlations (

Table 5. Composition-Weighted Formulas for CH₄/H₂ Blends Used for Calculations.

Correlation	Equation
Molecular weight (−)	${\sum }_{\mathrm{i}}{\mathrm{z}}_{\mathrm{i}}·\mathrm{M}{\mathrm{W}}_{\mathrm{i}}$
Molar lower/higher heating value (kJ·kg−1)	${\sum }_{\mathrm{i}}{\mathrm{z}}_{\mathrm{i}}·\mathrm{L}\mathrm{H}{\mathrm{V}}_{\mathrm{i}}$ ${\sum }_{\mathrm{i}}{\mathrm{z}}_{\mathrm{i}}·\mathrm{H}\mathrm{H}{\mathrm{V}}_{\mathrm{i}}$
Mass–based lower heating value (kJ·mol−1)	${\displaystyle \frac{\mathrm{L}\mathrm{H}{\mathrm{V}}_{\mathrm{m}\mathrm{i}\mathrm{x},\mathrm{m}\mathrm{o}\mathrm{l}}}{\mathrm{M}{\mathrm{W}}_{\mathrm{m}\mathrm{i}\mathrm{x}}}}$
Hourly mass rate (kg·h−1) 1	$\dot{\mathrm{m}}={\displaystyle \frac{\mathrm{Q}\left(\mathrm{k}\mathrm{W}\right)·3600}{\mathrm{L}\mathrm{H}{\mathrm{V}}_{\mathrm{m}\mathrm{i}\mathrm{x},\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}}\left(\mathrm{k}\mathrm{J}·{\mathrm{k}\mathrm{g}}^{-1}\right)}}$

¹ [15,44].

).

Calculations were performed for a single elevated flare stack that handled CH₄/H₂ blends, with the base scenario defined as a pure CH₄ mass flow rate of 150,000 (kg·h⁻¹). The molar masses adopted for CH₄ and H₂ were 16.043 (kg·kmol⁻¹) and 2.016 (kg·kmol⁻¹), respectively. This corresponds to a reference molar flow rate of 9,349.872 (kmol·h⁻¹) for pure CH₄. In subsequent scenarios, the total molar flow rate was kept constant to isolate composition effects, with a specified fraction of the CH₄ molar flow replaced mole–for–mole by hydrogen.

The temperature at the flare tip was taken to be 289 (K). Lower Explosive Limit (LEL) values were determined using Le Chatelier’s rule, as expressed in Equation (16) [45,46,53]:

$${\displaystyle \frac{1}{\mathrm{L}\mathrm{E}{\mathrm{L}}_{\mathrm{m}\mathrm{i}\mathrm{x}}}}={\displaystyle \frac{{\mathrm{y}}_{{\mathrm{H}}_2}}{\mathrm{L}\mathrm{E}{\mathrm{L}}_{{\mathrm{H}}_2}}}+{\displaystyle \frac{1-{\mathrm{y}}_{{\mathrm{H}}_2}}{\mathrm{L}\mathrm{E}{\mathrm{L}}_{\mathrm{C}{\mathrm{H}}_4}}}$$

(16)

Calculations were performed for single elevated flare stacks and for the five compositions of CH₄/H₂ blends listed below. The resulting compositions, the molar and mass flow rates of CH₄ and H₂, the total H₂ total mass flow rates, and the total mass flow rates of H₂ with LEL_mix values are summarized in

Table 6. Parameters Adopted for Subsequent Calculations for CH₄ and H₂ Blends.

Parameter	Unit	Scenario 1	Scenario 2	Scenario 3	Scenario 4	Scenario 5
${\mathrm{H}}_2$ in CH4/H2 blend	% (v/v)	0	5	10	20	50
${\mathrm{T}}_{\mathrm{m}\mathrm{i}\mathrm{x}}$	(K)	289	289	289	289	289
${\dot{\mathrm{n}}}_{\mathrm{C}{\mathrm{H}}_4}$	$\left(\mathrm{k}\mathrm{m}\mathrm{o}\mathrm{l}·{\mathrm{h}}^{-1}\right)$	9349	8882	8414	7479	4674
${\dot{\mathrm{n}}}_{{\mathrm{H}}_2}$	$\left(\mathrm{k}\mathrm{m}\mathrm{o}\mathrm{l}·{\mathrm{h}}^{-1}\right)$	0	467	934	1869	4674
${\dot{\mathrm{m}}}_{\mathrm{C}{\mathrm{H}}_4}$	$\left(\mathrm{k}\mathrm{g}·{\mathrm{h}}^{-1}\right)$	150,000	142,500	135,000	120,000	75,000
${\dot{\mathrm{m}}}_{{\mathrm{H}}_2}$	$\left(\mathrm{k}\mathrm{g}·{\mathrm{h}}^{-1}\right)$	0	942	1884	3769	9424
${\dot{\mathrm{m}}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$	$\left(\mathrm{k}\mathrm{g}·{\mathrm{h}}^{-1}\right)$	150,000	143,442	136,884	123,769	84,424
$\mathrm{M}{\mathrm{W}}_{\mathrm{m}\mathrm{i}\mathrm{x}}$	$\left(\mathrm{k}\mathrm{g}·\mathrm{k}\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}\right)$	16.043	15.342	14.640	13.238	9.030
$\mathrm{L}\mathrm{E}{\mathrm{L}}_{\mathrm{m}\mathrm{i}\mathrm{x}}$	$\left(\mathrm{\%}\right)$	5.00	4.94	4.88	4.76	4.44
$\mathrm{L}\mathrm{H}{\mathrm{V}}_{\mathrm{m}\mathrm{i}\mathrm{x}}$	$\left(\mathrm{k}\mathrm{J}·{\mathrm{k}\mathrm{g}}^{-1}\right)$	50,000	50,450	50,956	52,122	57,813
$\mathrm{H}\mathrm{H}{\mathrm{V}}_{\mathrm{m}\mathrm{i}\mathrm{x}}$	$\left(\mathrm{k}\mathrm{J}·{\mathrm{k}\mathrm{g}}^{-1}\right)$	55,475	56,042	56,666	58,105	65,123

.

The five scenarios in Table 6 are composition cases for CH₄/H₂ blends at 0, 10, 20, 35, and 50% (v/v) H₂. They were selected to include the baseline (100% (v/v) CH₄), cover blends already trialed or discussed in European pilots and distribution studies (10–20% H₂), bracket higher-blend use cases considered in industrial clusters (≈30–35% H₂), and provide an upper-bound sensitivity at 50% H₂ to probe the transition to low-luminosity flames and its implications for radiation zoning. In all scenarios, flare geometry and operating conditions are held fixed; thus, Scenarios 1–5 are designed to isolate the effect of hydrogen on thermal-radiation behavior.

In this study, the fraction of heat radiated, F, for each $\mathrm{C}{\mathrm{H}}_4/{\mathrm{H}}_2$ scenario was determined using a hybrid approach that combines the Chamberlain correlation based on the velocity with a composition-dependent adjustment for flames rich in hydrogen and low luminosity [15,45,46]. For the CH₄–rich scenarios (0, 5, and 10% (v/v) H₂), the flames remain in the luminous, soot-forming regime; therefore, F was taken directly from the Chamberlain formula, as given in Equation (17) [45,46,53]:

$$\mathrm{F}=0.21{\mathrm{e}}^{-0.00323{\mathrm{U}}_{\mathrm{j}}}+0.11$$

(17)

The exit velocity for each CH₄/H₂ blend was calculated as shown in Equation (18) [15,49]:

$${\mathrm{U}}_{\mathrm{j}}={\displaystyle \frac{4·\dot{\mathrm{m}}}{\mathsf{\pi }·{\mathrm{D}}^2·\frac{\mathrm{P}·\mathrm{M}{\mathrm{W}}_{\mathrm{m}\mathrm{i}\mathrm{x}}}{\mathrm{R}·\mathrm{T}}}}$$

(18)

where $\dot{\mathrm{m}}$ is the total mass flow rate (kg·s⁻¹), D is the flare tip internal diameter (m), and ρ is the density at flare tip conditions (kg·m⁻³). The density was calculated from the molar composition, the molecular weight MW_mix (kg·kmol⁻¹), and the gas constant R.

At 20% (v/v) H₂, the system enters a transition region. Here, F was assigned as the lower of the Chamberlain value and the composition-dependent correlation $\mathrm{F}\left({\mathrm{y}}_{{\mathrm{H}}_2}\right)$ [12], both giving about 0.190 (−), reflecting the onset of reduced luminosity. For the hydrogen-rich scenario (50% (v/v) H₂), the flames exhibit low-luminosity behavior with negligible soot formation; in these conditions, F was assumed as 0.100 (−). This ensures that for luminous hydrocarbon flames, the radiative fraction is driven by exit velocity, whereas for low-luminosity hydrogen flames, it is governed by composition, in agreement with full–scale experimental observations.

This study treats the elevated flare as a turbulent, mixing-controlled diffusion flame. Molecular species-diffusion fields are not explicitly resolved; instead, the influence of H₂ is represented by composition-dependent thermophysical/stoichiometric properties and a composition-dependent radiative heat fraction F (lower for H₂-rich, non-luminous flames). This approach captures the observed tendency of H₂ enrichment to shorten diffusion flames and enhance stability, which reduces predicted radiation footprints, while remaining within an API-type engineering framework.

4. Results and Discussion

4.1. Thermal Radiation Calculations

Five blends were analyzed for a common stack: 100% (v/v) CH₄ and CH₄ with 5, 10, 20, and 50% (v/v) H₂. Figure 3 shows, in a vertical side–view (Cross–section vs. Easting), the flame center and axis together with the ground–referenced isopleths for 9.46, 6.31, 4.73, and 1.58 (kW·m⁻²). Solid contours correspond to U = 3 (m·s⁻¹), while dashed contours correspond to U = 5 (m·s⁻¹).

For U = 3 (m·s⁻¹), increasing the hydrogen fraction causes a clear contraction of all radiation zones. The effect is already visible at 5–10% (v/v) H₂ and becomes pronounced for 20–50% (v/v) H₂, with the outer 1.58 (kW·m⁻²) contour receding the most. The flame axis shortens slightly and its center shifts modestly downwind with composition, but the dominant change is the reduction of the footprint radii for every threshold. This behavior is consistent with both the lower molar heat release of CH₄/H₂ blends and the lower luminous (radiative) fraction of hydrogen-rich flames. For U = (5 m·s⁻¹), the wind tilts “lays down” the flame, bringing the hot core closer to the ground on the lee side. The observed contraction with increasing H₂ is consistent with hydrogen-aware flare models and jet-flame experiments [19,21,23,32,36,38].

Figure 4 shows the corrected distance D_c for each thermal radiation threshold as a function of hydrogen content. The corrected distance denotes the distances evaluated after applying atmospheric transmissivity τ(R,RH) along the optical path (line of sight) from the flame to the ground receptor.

Within the algorithm used, a single D_c is obtained for each blend/threshold, common to both wind speeds, U = 3 (m·s⁻¹) and U = 5 (m·s⁻¹). The curves exhibit a nearly linear decrease in corrected distance Dc from pure CH₄ to 50% (v/v) H₂. All calculations were performed at a constant molar flow throughput at the flare tip for every blend. Holding the molar flow constant makes the comparison energy-based and composition-driven: as CH₄ is replaced by H₂, the total heat-release rate per mole and the radiative fraction both decrease, so the predicted distances contract systematically without confounding the trends with trivial scaling from different feed rates.

Figure 5 shows the ground-level thermal radiation profiles as a function of the horizontal distance from the stack. Each panel corresponds to one blend scenario (I: 100% (v/v) CH₄; II–V: CH₄ with 5, 10, 20, and 50% (v/v) H₂). Horizontal dash–dot lines mark the reference thresholds, 1.58; 4.73; 6.31; and 9.46 (kW·m⁻²); the red cross indicates the downwind location of the local maximum.

For U = 3 (m·s⁻¹), the curves peak slightly downwind and remain below 2 (kW·m⁻²) for CH₄, with a reduction of the peak as hydrogen is added. Increasing the wind to 5 (m·s⁻¹) tilts the flame and moves the peak further downwind with a modest increase in the local maximum relative to U = 3 (m·s⁻¹) for the same composition. By scenario IV (20% (v/v) H₂), the entire profile already falls below 1.58 (kW·m⁻²), and in scenario V (50% (v/v) H₂), the predicted ground-level load is at or below the adopted solar background, 0.8 (kW·m⁻²), only ambient solar irradiance is effectively perceived at the ground. This trend is consistent with existing studies that report lower radiative fractions and shorter diffusion flames for CH₄/H₂ blends (e.g., Miller et al. [19]; He et al. [12,21]; Li et al. [23]; Zhou et al. [32]; Zhao et al. [38]; and Kong et al. [36]). Figure 6 condenses Figure 5 into the maximum ground-level radiation attained for each fuel blend and wind speed.

To validate the computational algorithm, we reproduced the scenarios in DNV Phast using identical input data. Figure 7 overlays the side-view isopleths predicted by the Brzustowski–Sommer implementation (solid lines) with contours exported from DNV Phast using the Cone model (dashed lines)—an illustrative result for scenario I–100% (v/v) CH₄ at U = 3 (m·s⁻¹).

The agreement is strong across all thresholds. For the inner zones, 9.46, 6.31, and 4.73 (kW·m⁻²), the DNV Phast Cone model contours and calculated contours are nearly coincident, with only minor azimuthal offsets around the lee side where the flame tilt is most influential. The outer 1.58 (kW·m⁻²) boundary shows a slightly larger downwind radius in the Cone model, consistent with its treatment of flame lay-down and far-field attenuation. Using the Cone output as reference, a mean radial error (MRE) falls within 3–7 (%) for the three inner thresholds and 8–12 (%) for 1.58 (kW·m⁻²), with a small bias (mean signed difference) of the order of a few percent. Across all scenarios I–V and both wind speeds, the pooled average MRE is~7.8 (%), median~7.4 (%), with a small downwind-biased signed error of about~2 (%). The pooled mean radial error (MRE) values obtained for each scenario, relative to the DNV Phast Cone model, are presented in

Table 7. Pooled mean radial error (MRE) by scenario (relative to DNV Phast Cone model).

	Unit	Scenario 1 0% (v/v) H2; 100% (v/v) CH4	Scenario 2 10% (v/v) H2; 90% (v/v) CH4	Scenario 3 20% (v/v) H2; 80% (v/v) CH4	Scenario 4 30% (v/v) H2; 70% (v/v) CH4	Scenario 5 50% (v/v) H2; 50% (v/v) CH4
Pooled MRE–DNV Phast Cone model vs. developed solver	%	6.8	7.1	7.4	8.3	9.2

.

The observed trends align with existing literature, which documents a contraction of ground-level radiation footprints as H₂ content increases. This phenomenon reflects the transition to low-luminosity flames in methane/hydrogen (CH₄/H₂) mixtures [11,12,13], indicating significant safety and environmental benefits associated with H₂/CH₄ blending.

Figure 8 repeats the comparison of the calculated contours with the DNV Phast API radiation model. The contours of the API model exhibit a systematic outward shift for the low–intensity boundary, 1.58 (kW·m⁻²), while remaining close to the present solution for higher thresholds. This behavior reflects the API model’s more pronounced flame lay-down and effective radiative fraction in the far field; the jagged appearance of the plotted API curves stems from DNV Phast’s contour discretization, not from physical variability.

Compared to the DNV Phast API contours, the pooled MRE by scenario remains in the~7–10% band, with a mild upward drift at higher H₂ fractions (

Table 8. Pooled mean radial error (MRE) by scenario (relative to DNV Phast API model).

	Unit	Scenario 1 0% (v/v) H2; 100% (v/v) CH4	Scenario 2 10% (v/v) H2; 90% (v/v) CH4	Scenario 3 20% (v/v) H2; 80% (v/v) CH4	Scenario 4 30% (v/v) H2; 70% (v/v) CH4	Scenario 5 50% (v/v) H2; 50% (v/v) CH4
Pooled MRE–DNV Phast API model vs. developed solver	%	7.2	7.8	8.6	9.6	10.3

). This is consistent with the API model’s systematic outward shift of the 1.58 kW·m⁻² boundary and its far-field treatment; signed bias remains modest (<±3%).

To assess mutual interaction between nearby flares, ground-level radiation fields from each flame were calculated and then superposed. The maps below (Figure 9 and Figure 10) compare the reference scenario with two identical 100% (v/v) CH₄ flares to a mixed scenario in which one flare burns a CH₄/H₂ blend (10% (v/v) H₂).

Replacing one of three 100% (v/v) CH₄ flare stacks with a 10% (v/v) H₂ blend reduced the area of radiation zones and decreased peak ground thermal radiation. With two CH₄ flare stacks, the 1.58 (kW·m⁻²) zones strongly overlap, producing a broad joint footprint. The global ground maximum occurs downwind and increases from 3.11 (kW·m⁻²) with U = 3 (m·s⁻¹) to 3.49 (kW·m⁻²) with U = 5 (m·s⁻¹) as stronger wind tilts the flames and lowers the clearance of the flame to the ground on the lee side.

Replacement of a CH₄ flare stack with the 10% (v/v) H₂ blend reduces the superposed field: the overlapping region above 1.58 (kW·m⁻²) contracts and the peak ground load drops to 3.07 (kW·m⁻²) for U = 3 (m·s⁻¹) and 3.31 (kW·m⁻²) for U = 5 (m·s⁻¹). This demonstrates the potential for improved safety management through hydrogen integration.

4.2. Emission Metrics

The blended fuel emission factor F_mix was evaluated for the five fuels (scenarios I–V) used in the thermal radiation study, on both LHV and HHV bases (Figure 11,

Table 9. Emission Factors From CH₄–H₂ Blend and Relative CO₂ Reduction (Constant Molar Flow).

Scenario	H2 % (v/v)	${\mathbf{F}}_{\mathbf{m}\mathbf{i}\mathbf{x},\mathbf{L}\mathbf{H}\mathbf{V}}$ (−)	${\mathbf{F}}_{\mathbf{m}\mathbf{i}\mathbf{x},\mathbf{H}\mathbf{H}\mathbf{V}}$ (−)	$∆\mathbf{C}{\mathbf{O}}_2\mathbf{v}\mathbf{s}\mathbf{C}{\mathbf{H}}_4$ $\left(\mathbf{L}\mathbf{H}\mathbf{V}\right)$	$∆\mathbf{C}{\mathbf{O}}_2\mathbf{v}\mathbf{s}\mathbf{C}{\mathbf{H}}_4$ $\left(\mathbf{H}\mathbf{H}\mathbf{V}\right)$
I	0	0.0549	0.0494	–	–
II	5	0.0540	0.0486	–1.56%	–1.66%
III	10	0.0531	0.0477	–3.24%	–3.45%
IV	20	0.0510	0.0458	–7.01%	–7.44%
V	50	0.0422	0.0374	–22.18%	–24.32%

). A constant molar throughput at the flare tip was assumed. The lower and higher heating values were assumed to be CH₄: 802/890 (kJ·mol⁻¹), which is equal to 50,030/55,540 (kJ·kg⁻¹), and H₂: 242/286 (kJ·mol⁻¹), which is equal to 120,770/142,550 (kJ·kg⁻¹).

Trends are summarized in Table 9 for the blend levels commonly considered in policy and pilot projects.

At constant molar throughput, replacing 50% (v/v) of CH₄ with H₂ lowers the CO₂ emission factor by 22.18 (%) (LHV) and 24.32 (%) (HHV), which should translate into proportionally lower emissions charges for the same duty. For blend levels relevant to gas distribution, 10–20% (v/v) H₂, the reduction is modest but material: 3.24 (%) (LHV)/3.45 (%) (HHV) at 10% (v/v) H₂, rising to 7.01 (%) (LHV)/7.44 (%) (HHV) at 20% (v/v) H₂. These findings are further supported by the assumptions mentioned in [51,52] and by the emission-factor formulations in the Guidelines for National Greenhouse Gas Inventories [49]. Taken together, these corroborate both the direction and the order of magnitude of the calculated CO₂-intensity reductions across 0–50% (v/v) H₂.

5. Conclusions

This study shows that, at constant molar throughput, increasing the hydrogen fraction from 0 to 50% (v/v) systematically contracts the 9.46, 6.31, 4.73, and 1.58 kW·m² thermal radiation envelopes and lowers peak ground radiation. The direction of this composition effect is robust across the examined operating cases.

Introducing a composition-dependent radiative fraction F together with a range-dependent atmospheric transmissivity materially changes the predicted envelope extents relative to the common pairing of hydrocarbon-calibrated F with range-invariant transmissivity. Accounting for humidity and distance effects at the screening stage improves the fidelity of layout estimates without sacrificing simplicity.

For a representative flare stack at wind speeds of 3 and 5 m·s⁻¹, wind primarily modulates flame geometry and envelope shape but does not reverse the composition trend. Hydrogen addition continues to reduce peak ground radiation as wind varies within this range.

In multiflare layouts, superposition of ground-level radiation can exceed any single flare case, underscoring the role of spacing and relative orientation. Partial substitution of CH₄ by H₂ at equal throughput reduces radiation peaks, offering a practical lever for layout refinement under hydrogen blending.

At the same time, the equivalent CO₂ emission rate decreases with hydrogen fraction, pairing smaller radiation footprints with lower emissions. This co-benefit is relevant for screening trade-offs between safety envelopes and environmental performance.

However, it is important to recognize that hydrogen addition can influence NO_x emissions because higher flame temperatures and increased combustion intensity may promote their formation. Where hydrogen blending is pursued, additional NO_x mitigation measures may be required to ensure compliance with environmental standards and safe operation.

The implemented solver, based on the Brzustowski–Sommer methodology, augmented with composition-aware F and range-dependent transmissivity, therefore provides a practical, low-cost tool for hydrogen-aware layout screening and option ranking in both single and multiflare contexts.

The approach is correlation-based and steady-state. Molecular diffusion and soot chemistry are not explicitly resolved, meteorology is represented by discrete wind cases, and geometry is fixed for screening. These choices are appropriate for early-stage design, but critical applications should be complemented by site-specific sensitivity studies, refined F and transmissivity calibration, broader validation across flare hardware, and, where warranted, higher fidelity modeling. Future work will couple the solver to site meteorological statistics and enable automated spacing optimization for multiflare arrays under hydrogen blending.