Thermal radiation assessment of flaring gas in floating LNG bunkering terminal

3. 1 Combustion and Radiation Models

The flare radiation simulations were conducted using FDS software [13] and the results were visualized using Smokeview [14], which is a product of an international collaborative effort led by the National Institute of Standards and Technology and the VTT Technical Research Centre of Finland. The software package is widely used in the fire engineering community and provides comprehensive verification and validation [15].

Based on the largeeddy simulation technique in FDS, the Favrefiltered transport equations of mass, momentum, energy, and species, combined with the equation of state for an ideal gas, have been summarized in a previous dispersion study [16]. To model combustion and radiation for the flare radiation study, the source terms of $$ {\dot{q}}^{\text{'}\text{'}\text{'}}$$ and $$ {\dot{q_{\mathrm{r}}}}^{\text{'}\text{'}\text{'}}$$ were activated in the energy transport equation. More details regarding the model are described in [15][16]. A brief background of the model is summarized below.

For a one-step global mechanism, the stoichiometric oxidation of methane fuel, assumed as a flaring gas, can be expressed as

Here, the chemical species are grouped by the mole fraction into lumped species, Z, such as fuel (F, CH₄), air (A, composed of 21% O₂ and 79% N₂ by volume), and products (P, composed of 9.5% CO₂, 19% H₂O, and 71.5% N₂ by volume).

Based on the mixing-limited, infinitely fast reaction of lumped species, the combustion model determines the mass production rate of species i per unit volume, $$ {\dot{m}}_{\mathrm{i}}^{\text{'}\text{'}\text{'}}$$, in the species transport equation. When the fuel and oxidizer are initially non-premixed, the mean chemical source term for the fuel is modeled using the eddy dissipation concept, where the rate of fuel consumption is proportional to both the local limiting reactant concentration and local rate of mixing [15].

Here, Y_F and Y_A indicate the lumped mass fractions of fuel and air, respectively, and stoi indicates the mass stoichiometric ratio of air. The characteristic time scale for mixing, 𝜏_mix, is generally assumed as the fastest of the three time scales for diffusion, subgrid-scale advection, and buoyant acceleration specific to the cell size (filter width) [15].

Once $$ {\dot{m}}_i^{\text{'}\text{'}\text{'}}$$ for species i has been determined, the heat release rate per unit volume, $$ {\dot{q}}^{\text{'}\text{'}\text{'}}$$, is calculated by summing the mass production rates for each species times their respective heats of formation.

where Δℎ_f,i is the heat of formation of species i. This indicates that the faster the reactants are mixed, the more heat is released.

Meanwhile, the gas-phase thermal radiation is contained in the divergence of the heat flux vector, $$ \nabla \cdot {\dot{\mathit{q}}}^{\mathit{\text{'}}\mathit{\text{'}}}$$, in the energy equation [15][16]. The radiative source term is defined by the net contribution to the radiative loss term, as follows:

where $$ {\dot{\mathit{q}}}_{\mathbf{r}}^{\mathit{\text{'}}\mathit{\text{'}}}$$ is the radiant heat flux vector.

3. 2 Heat Flux Model

The net heat flux is the sum of the radiative and convective heat fluxes at a solid surface, without considering the heat source generated by the pyrolysis at the surface boundary [15].

The radiative heat flux is the net radiative heat flux, composed of incoming and outgoing heat fluxes.

The incoming radiative heat flux is a component absorbed within an infinitely thin layer at the solid surface from the surrounding gases, where 𝜀 indicates emissivity and $$ {\dot{q}}_{\mathrm{i}\mathrm{n}\mathrm{c},\mathrm{r}\mathrm{a}\mathrm{d}}^{\text{'}\text{'}}$$ indicates the incident radiative heat flux based on the integrated radiation intensity at a measuring device. The outgoing radiative heat flux is the component emitted at the solid surface, where 𝑇_s is the surface temperature. The convective heat flux is calculated as follows:

where h is the convective heat-transfer coefficient and 𝑇_g is the gas temperature in the vicinity of the wall. In the present study, the wall was modeled as a 0.01-m-thick steel surface. A constant value of h = 10 W/m²∙K was used to calculate the wall-surface temperature. The thermal properties of the steel were fixed as follows: density of 7,500 kg/m³, specific heat of 0.5 kJ/kg∙K, conductivity of 50 W/m∙K, emissivity of 0.9, and mean absorption coefficient of 5 × 10⁴ 1/m.

When the net heat flux was zero, the adiabatic surface temperature was calculated using an analytical solution.

where 𝑇_AST is the adiabatic surface temperature.

3. 3 Wind Model

The atmospheric boundary layer in FDS was modeled using the Monin–Obukhov similarity theory [15]. The wind profile, u, and potential temperature are functions of height, z:

where 𝑢_∗ is the friction velocity; k = 0.41 is the Von Kármán constant; and Z₀ = 0.03 m is the aerodynamic roughness length for an open space, based on the Davenport–Wieringa classification. In addition, 𝜃_∗ is the scaling potential temperature; 𝜃₀ is the ground-level potential temperature; and L is the Obukhov length, which characterizes the thermal stability of the atmosphere. Furthermore, the similarity functions proposed by Dyer are used in 𝜓_m and 𝜓_h. Note that a neutrally stratified atmosphere has an infinite Obukhov length; however, unstable atmospheres are considerably affected by buoyancy-induced turbulence, resulting in enhanced mixing because of a decrease in temperature with height. In contrast, the stable atmospheres suppress the turbulence mixing because of an increase in temperature with height.

4. 1 Flaring Condition and Modeling

The mass flow rate of the flare gas was determined as the maximum release rate considering the Boil-Off Gas (BOG) rates, according to the loading condition presented in Table 2. As shown in Figure 3, the flare gas replaced with methane gas was assumed to be injected vertically upward on a 2 m × 2 m surface. The flare exit was positioned 123 m above the tip of the flare tower. The volume flow rate was set to 5.63 m³/s by assuming a releasing methane temperature of −160 ℃. An air flow with a specific velocity of 15 m/s, which is similar value to that of the exit velocity of the fuel, was supplied around the flare exit to shield the initial methane from flowing across the ambient wind flow. The initial velocity profiles of the central fuel and co-flow air were used as a top hat. From the flare burner modeling, a flare image with heat release and smoke emission was obtained, as shown in Figure 4.

Figure 3:

Flare model

Table 2:

Mass flow rate of BOG generation based on the operation modes

Figure 4:

Representative 3D rendering image

For comparison, the intensity of solar radiation ranged 0.79–1.04 kW/m² depending on the geographical location and time of year. Solar radiation can be a factor for some locations; however, its effect added to flare radiation imposes only a minor effect on the acceptable exposure time. In this study, a solar radiation of 1.0 kW/m² was considered for the radiation calculations.

4. 2 Grid Refinement

A three-dimensional 400 m × 140 m × 200 m domain was established in multisized meshes with the smallest finite volume of 0.5 m × 0.5 m × 0.5 m. A total of 11,861,500 cells were used after a grid independence analysis, and the cell size ratio was unified to 1 in the Cartesian coordinate system. The grid cell size affects the run time and result accuracy. The FDS software [13] suggests performing a mesh sensitivity study in which a model is first executed with a relatively coarse mesh, followed by gradually decreasing the cell size until the difference in the results becomes insignificant. To select an appropriate grid resolution, FDS recommends calculating the following sion expression:

which should range between 4 and 16 according to the validation study sponsored by the U.S. Nuclear Regulatory Commission [15]. 𝛿x is the nominal size of a mesh cell and 𝐷∗ is the characteristic flare diameter:

where $$ \dot{Q}$$ is the total heat-release rate of the flare [kW/m²], 𝜌_∞ is the air density (=1.2 kg/m³), C_p is the air thermal capacity (=1.0 kJ/kgK), T_∞ is the ambient air temperature (=293 K), and g is the gravitational acceleration (=9.81 m/s²). According to the selected flaring condition, the grid resolution around the flare tip location was determined as 0.05 m. Here, the nondimensional value was calculated as $$ \raisebox{1ex}{$D^{\mathrm{*}}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{\delta }\mathrm{x}$}\right.=5.8$$, specific tothe heat release rate of 49.75 kW for pure methane.

4. 3 Ambient Condition

Assuming that realistic meteorological conditions were disregarded, the initial wind profiles were artificially generated using the reference velocity of u_ref = 5, 10, 20, and 30 m/s at 𝑧_ref = 122.0 m and the neutral Obukhov length (L = 1000000). The initial wind was set to a direction of 270° and blew toward the positive direction of the x-axis, as shown in Figure 5. The initial temperature of the ambient air was set at 20 °C, with a relative humidity of 40%. An adiabatic property was generated at the bottom-surface boundary condition, and the other boundary conditions were set to open, which enabled a typical inflow/outflow condition.

Figure 5:

Wind direction

5. 1 Acceptance of Radiative Heat Flux

Equation 14 expresses the exposure times required for reaching the pain threshold, t_th, as a function of the radiation intensity, I_rad. The data were derived from tests conducted on people who were radiated on the forearm at room temperature. The data indicate that burns follow the pain threshold fairly quickly [17].

Because the allowable radiation level is a function of exposure length, factors involving reaction time and human mobility should be considered. In emergency releases, a reaction time of 3–5 s may be assumed. If 5 s have elapsed before an average individual seeks cover or departs from the area, then the total exposure period will range from 8 to 10 s. In evaluating the emergency procedures, an exposed individual becoming incapacitated during an attempt to exit the area may be considered.

Based on API 521 [17], the flare owner or operator shall determine the need for a solar-radiation-contribution adjustment to the values listed in Table 3. In this context, the maximum permissible design levels of radiation for the exposure of personnel at the maximum emergency flaring were assigned as follows:

Table 3:

Recommended Design Thermal Radiation for Personnel

• ● Continuous full-shift exposure: 1.6 kW/m²
• ● Operational blowdown (maximum 30 min): 3.2 kW/m²
• ● 60 s peak exposure: 4.7 kW/m²
• ● 29 s peak exposure: 6.3 kW/m²

This recommended practice is a more stringent requirement than API 521. In an emergency blowdown, 3.2 kW/m² will be applied as the radiation criterion, which is expected to occur with a maximum exposure duration of 30 min. The operators are assumed to be equipped with at least single-layer whole-body working clothing and a hard hat. The peak exposure times correspond to the time required to escape to a safe location.

5. 2 Simulation Results

Figure 6 shows the representative velocity and temperature fields on the x–z plane at y = 19 m, which is the center location of the flare tower for the wind velocities of 5, 10, 20, and 30 m/s when the emergency releasing gas is flaring. The chemically reacting flow of methane gas was calculated under all crosswind conditions, which blew identically toward the FLBT platform in the x-direction. Consequently, the radiation levels reaching the platform were investigated and the results were described based on specific locations.

Figure 6:

Representative velocity (left) and temperature (right) fields for wind velocities of (a) 5, (b) 10, (c) 20, and (d) 30 m/s

At a wind velocity of 5 m/s, the mean radiative heat flux was presented for the major facilities shown in Figure 7. The results are listed, with the standard deviations of the monitoring devices, in Table 4. The statistical values were obtained from the time average of 100 s after an unsteady period.

Table 4:

Time-averaged radiative heat flux on each monitoring device at the wind velocity of 5 m/s

Figure 7:

Wind velocity of 5 m/s: time-averaged radiative heat flux on each monitoring device

The maximum radiative heat flux did not exceed 0.9 kW/m² for the ① helicopter deck, ② living quarter, ③ turret, ④ manifold 2, ⑤ loading arm, ⑥ reliquefaction unit, and ⑦ manifold 1.Considering an initial solar radiation of 1.0 kW/m² with asurface emissivity of 0.9, it is reasonable to state that the effect of the radiative heat flux emitted from the heat release rate by the flaring was negligible. These results were similar to those obtained under other wind conditions. Hence, the radiative heat flux originating from the flaring system will not affect the personnel on the FLBT platform.

For the flare tower, however, the locations around the flaring gas exit, such as the ⑧ flare tip front and ⑨ flare tip back, can be significantly affected by the mean radiative heat flux of approximately 24–58 kW/m² in the steady state with respect to variations in the wind velocity of 5–30 m/s, as listed in Table 5. At the monitoring devices approximately 20 m below the flare tip, such as at the ⑩ flare tower front and ⑪ flare tower back, the maximum radiative heat flux on the beam surface reached up to approximately 1.6 kW/m². Hence, the detailed design of the flaring nozzle and beam structure around the flaring nozzle must protect the flaring assets.

Table 5:

Time-averaged radiative heat flux [kW/m2] on each monitoring device depending on the variation in wind velocity

Author Contributions

Conceptualization, B. C. Choi; methodology, B. C. Choi; Software, B. C. Choi; Formal Analysis, B. C. Choi; Investigation, I. C. Jung and H. Y. Lee; Resources, I. C. Jung and H. Y. Lee; Data curation, I. C. Jung and H. Y. Lee; Writing-Original Draft Preparation, I. C. Jung, H. J. Jo, and B. C. Choi; Writing-Review & Editing, I. C. Jung, H. J. Jo, and B. C. Choi; Visualization, B. C. Choi; Supervision, I. C. Jung, H. J. Jo, and B. C. Choi; Project Administration, D. H. Jung and H. G. Sung; Funding Acquisition, D. H. Jung and H. G. Sung.