The following steps were followed to perform the gas dispersion analysis, executed through Kameleon FireEX (KFX). The first step involves the conversion of the model file for KFX simulation. To define the structural system, involving geometry information and boundary conditions, the DGN-file structure as a three-dimensional (3D) computer-aided design (CAD) model was translated to the KFX file format by using the KFX software. The vent mast dispersion scenarios involve various parameters related to release location, direction, and flow rate, along with wind speed and direction. In order to conduct a KFX simulation, an appropriate KFX model file was manipulated with the dataset of the selected scenario. The specific control parameters were appropriately chosen by considering the simulation time and reliability of analysis. The probabilistic analysis was not incorporated in this work. In general, the probabilistic calculations in the total risk assessment may consider thousands of scenarios, combining different release rates, release locations, wind conditions, release volumes, etc., while only very limited number of scenarios can be operated with CFD-codes. Thus, the results from the simulations should not be used directly during design, but as support for QRA in the front-end engineering and design (FEED) package.

The system of equations is solved by applying a low-pass filter using the large-eddy simulation technique, in which the small-scale eddies that pass through the grid are modeled, and the large-scale eddies are computed, respectively. The low-pass filter width is taken as the cube root of cell volume. KFX is based on the finite difference method, which implements a predictor–corrector scheme explicitly with second-order accuracy in space and time. It is not suitable for complex-shaped geometries, as it uses rectilinear meshing, but it helps in faster computation. More details on the physical concepts are given in the KFX user & theory manuals [10][11].

According to the conversion procedure of the DGN file to a KFX file for the topside and hull structure, the files have been translated to KFX geometry format using the KFX tool. An overview of the KFX model is shown in Figure 1. For the KFX geometry, the calculation domain for the dispersion simulation of unignited flare gas was 480 m × 120 m × 285 m, and ~5 × 105 cells were used, with the smallest control volume of 0.0423 m × 0.001 m × 0.001 m. The smallest grid cell was used with the cell size growing outwards in all directions from the release cell. Hence, the mesh geometry was well represented in Figure 2, while larger grid sizes, placed far away from the release cell, were coarser and had less accuracy. Because the minimum control volumes for each calculation were automatically determined from the expanded jet diameter for choked flow, they tended to generate grids with a very large aspect ratio for control volumes far away from the release point. However, the optimized grid resolution was chosen by the KFX built-in wizard to obtain a result of sufficiently accurate and efficient simulations [10][11].

Figure 1: 
3D KFX model of LNG-FPSO geometry

Figure 2: 
3D grid system of the geometry

The governing equations were solved using partial differential equations (PDEs) to describe the transient behavior of different field variables in space. The PDEs describing fluid flow are commonly referred to as transport equations and are comprised of transient, convective, diffusion, and source equations. In this non-reacting gas-dispersion simulation, the source term and radiative heat flux were ignored. The equations representing mass, momentum, energy, and species are shown below with the ideal gas equation.

▪　 Conservation of mass:

▪　 Conservation of momentum:

▪　 Conservation of energy:

▪　 Conservation of species:

▪　 The Equation of state:

where ρ is the density, u is the velocity vector, p is the pressure, τ is the viscous stress tensor, g is the gravitational acceleration, h_s is the sensible enthalpy, q˙" is the heat flux, Y_i is the mass fraction of species i, J_i is the diffusive flux, R is the universal gas constant, T is the temperature, and W_i is the molecular weight of species i.

Based on the previous data of the flare radiation study [12], in this study, four release scenarios and the gas compositions for all the release scenarios were selected as below:

▪　 Scenario 01: High Pressure (HP) Warm Flare,
▪　 Scenario 02: High Pressure (HP) Cold Flare,
▪　 Scenario 03: Low Pressure (LP) Warm Flare, and
▪　 Scenario 04: Low Pressure (LP) Cold Flare.

The HP Warm flare was composed of hydrocarbon vapors, amines, water, and liquid hydrocarbons from various high-pressure sources in the process. The HP Cold flare was composed of hydrocarbon vapors and liquid hydrocarbons from various high-pressure sources in the liquefaction system. The LP Warm flare was composed of hydrocarbon vapors from various low-pressure sources in the process, and the LP Cold flare was composed of hydrocarbon vapors and liquid hydrocarbons from various low-pressure sources from the liquefaction, refrigerant, and boil-off gas (BOG) systems. These flares relieve the pressure resulting from the combination of any single safety system with any possible process failure.

The chemical compositions of each flare for different scenarios are given in Table 2. The pseudo-fuels are defined with respect to the scenarios in Table 3. A common location of the release points was then chosen with no obstruction in the initial development of the jet at the flare tower tip. Data for the reservoir, surroundings, and release rates were specified for the gas dispersion scenario as a calculation input. In addition, a release diameter was specified. Further, the equivalent release parameters, such as the initial release velocity and hole diameter, were estimated. The physical data applied for jet releases are listed in Table 4.

It is noted that, due to high pressure and corresponding small release diameter, the simulated releases in the process area resulted in a highly under-expanded jet with a shock structure, which would have required a compressible solver and extensive grid refinement to resolve. Thus, the KFX-tool “Jet boundary conditions calculator” was used to calculate the expanded jet conditions at the downstream of the original release point. Jet boundary conditions calculator is a tool in the KFX software that calculates inlet conditions for supersonic jet releases. The jet boundary condition method utilized ideal gas relations and conservation of mass, momentum, and energy to predict the downstream fluid state of the shock structure. Air entrainment into the highly turbulent jet was also taken into account using this method. When the high-pressure gas was discharged through an opening ejection point into an atmosphere, the released gas would expand very rapidly to the ambient pressure. The complex expansion process of high-pressure gas releases was modeled using the pseudo-source concept to reduce the computational costs for simulation cases of practical interest.

In addition, KFX uses the log-law wall boundary to enable reasonable calculations of shear stress, heat flux, and mass flux from a fluid to a solid wall in a relatively coarse grid. More details about the physical background for the methods used are given in the KFX theory manual [11].

Table 5 exhibits the logarithmic wind boundary profile set with the ambient temperature and atmospheric pressure for domain calculation. Considering the two reference wind conditions, eight simulations were carried out in total.

Long-term relief scenarios for any excess hydrocarbon gases from the process and utility systems during start-up, operational, and emergency conditions would be reasonable, in order to examine the dispersion distance of the ejected gas as a conservative investigation. Therefore, the simulations were calculated up to ~300 s in real time after saturation, i.e., until the fuel/carbon balance attained a steady state in the domain.

Important results depending on the purpose of each scenario and visualization of the gas concentration to demonstrate the flammable limits were presented and discussed in this chapter. The release point and release direction, as well as the wind direction, would be easily understood in the gas concentration plots. The pictures described in this paper are based on the human perception to an extent, with a fair representation of the appearance of gas dispersions.

As a result, the mole percent of unignited flare gas discharged from the flare tip into the ambient air was presented using the stepped ranges, as shown in Figure 3 for HP-warm, Figure 4 for HP-cold, Figure 5 for LP-warm, and Figure 6 for LP-cold, as an account of eight selected scenarios with respect to the gas releases and wind conditions. The gas dispersion results were investigated to assess the flammable limits for the following locations:

Figure 3: 
Flammable limits with the release rate of 177.67 kg/s

Figure 4: 
Flammable limits with the release rate of 319.81 kg/s

Figure 5: 
Flammable limits with the release rate of 11.84 kg/s

Figure 6: 
Flammable limits with the release rate of 33.84 kg/s

▪　 Helideck and helicopter approach and
▪　 All topside modules.

In this study, the maximum extension of the unignited flare gas in the ambient air was estimated with respect to the lower flammable limit (LFL), which is less than the mole percent of ~5.0%, 50% LFL (less than the mole percent of ~2.5%), 10% LFL (less than the mole percent of ~0.5%), and below that, as shown in Figure 3 ~ Figure 6. The maximum permissible concentration of hydrocarbon gas was set to 10% LFL. The analysis was focused on the flammable gas concentration on the helideck in order to meet the requirement, as per the CAP 437 Safety Regulation [13].

Reference [13] stated that the maximum permissible concentration of hydrocarbon gas within the helicopter operating area is 10% LFL. Concentrations above 10% LFL have the potential to cause helicopter engines to surge and/or flame out with the consequent risk to the helicopter and its passengers. It should also be appreciated that, in forming a potential source of ignition for flammable gas, the helicopter can pose a risk of the installation itself.”

As listed in Table 6, the selected scenarios showed that the mole percent of gas in the ambient air were below the acceptance criterion of 10% LFL for the target area, which includes the helideck (located on the top of the accommodation) and topside modules.