Multiphase simulation of LNG vapour dispersion with effect of fog formation

Applied Thermal Engineering xxx (xxxx) xxxx

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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Multiphase simulation of LNG vapour dispersion with effect of fog formation ⁎

Biao Suna,b, , Joshua Wonga, Divyamaan Wadnerkara, Ranjeet P. Utikara, Vishnu K. Pareeka, Kaihua Guob a b

WA School of Mines: Mineral, Energy and Chemical Engineering, Curtin University, GPO Box U1987, Perth, WA 6845, Australia SYSU-BP LNG Center, Sun Yat-Sen University, Guangzhou, China

H I GH L IG H T S

process of mixing LNG vapour with humid air is investigated. • Dynamic model is developed to study LNG vapour dispersion with fog formation. • Multiphase formation can reduce the dense gas effect during LNG vapour dispersion. • Fog • Fog formation can enlarge the affected area of LNG vapour dispersion.

A R T I C LE I N FO

A B S T R A C T

Keywords: Multiphase model LNG vapour dispersion Fog formation Dense gas effect Relative humidity

LNG vapour dispersion known as dense gas dispersion is one of the main hazards from accidental LNG spill and is of critical importance in risk assessment. Most of the previous studies on this topic were conducted in the singlephase framework which is incapable of considering the effect of fog formation. LNG importing and exporting terminals are typically located at coastal areas where there is a high chance of fog formation. In this study, a multiphase CFD model has been developed to investigate the dynamic mixing of cryogenic LNG vapour cloud and ambient air. The effect of fog formation on LNG vapour dispersion was studied. The model was validated by historical experiments conducted by LLNL, upon which good agreements were achieved. Case studies of different relative humidity were performed in order to investigate the LNG vapour dispersion behaviour affected by different fog concentrations. It was found that the affected area of the vapour dispersion is enlarged if the air relative humidity is increased. The findings in this study could improve the understanding of the mechanism of LNG vapour dispersion in humid environments, and help to provide more reliable risk assessments for LNG plants.

1. Introduction Liquefied natural gas (LNG) has become one of the most important strategic energy resources all over the world. LNG is cleaner than conventional fossil fuels, such as oil and liquefied petroleum gas (LPG), and can reduce emissions of greenhouse and polluting gases (e.g., CO2, NOx and SOx). Besides household gas and power generation, the use of LNG as an alternative fuel for automobile and shipping has increased rapidly. Due to the hazardous nature of LNG, it is of critical importance to obtain an in-depth understanding of its hazards and to reduce the potential risks posed to LNG plants and nearby communities. In order to protect the public from hazards of accidental LNG release, safety exclusion (or hazard) zone around LNG operations is usually established at a boundary where the concentration of natural gas reduces to half of

⁎

the Lower Flammability Limit (LFL). However, the exclusive distance can be very debatable between the project investors and the public communities, as it defines the land area occupied by LNG plants and associates with the capital expenditure. Thus, detailed risk assessments by using valid numerical models are usually conducted before the commencement of each LNG project. LNG vapour is around 1.5 times heavier than ambient air and thus is recognised as a dense gas or heavy gas. LNG vapour dispersion is particularly important as it affects the largest area due to the transport of flammable vapour by convection. The dispersion behaviour of LNG vapour cloud is complex as the density of the vapour cloud varies due to significant heat and mass transfer. The dispersion is initially dominated by gravity (gravity-induced dispersion) and then driven by buoyancy (passive dispersion) when the density of the LNG vapour cloud becomes

Corresponding author. E-mail address: [email protected] (B. Sun).

https://doi.org/10.1016/j.applthermaleng.2019.114671 Received 14 April 2019; Received in revised form 5 November 2019; Accepted 10 November 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: Biao Sun, et al., Applied Thermal Engineering, https://doi.org/10.1016/j.applthermaleng.2019.114671

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Nomenclature

Sc Sct Sh Shq Si SMq Sq T U0 → up , → uq U (z ) vis Yi Yk ,Yω z0

CD Drag coefficient Clocal , Csat Local and saturated mass concentration of water vapour (kg/m3) Cv _fog Volume fraction of fog Diameter of droplets of phase q (m) dq Di, m Mass diffusion coefficient Thermal diffusion coefficient DT , i Mass diffusivity (m2/s) Dυ Cross-diffusion term Dω → Fpq Interphase drag force of phase p and q → g Gravitational acceleration (m/s2) Gk , Gω Generation of k and ω Gr Grashoff number Mass transfer coefficient (m/s) hm Enthalpy of phase q (J/kg) hq → Ji Mass diffusion term Turbulence kinetic energy (m2/s2) k l Characteristic length (m) Liquid water content (g/m3) LWC ṁ Mass transfer rate (kg/s) Pressure (Pa) p Psat Saturation pressure of water vapour Re Reynolds number RH Relative humidity Rim Modified Richardson number

Schmidt number Turbulent Schmidt number Sherwood number Energy source term of phase q Source term in species equation Momentum source term of phase q (N/m3) Mass source term of phase q (kg/m3·S) Temperature (oC) Wind velocity at reference height Velocity of phase p and q (m/s) Wind velocity at height z Visibility (km) Mass fraction of speciesi Turbulence dissipation of k and ω Reference height

Greek letters

αq , αq Γk , Γω λ

μt ρq ρw Ì¿

τ ω

Volume fraction of phase p and q Effective diffusivities of k and ω Dimensionless parameter depending upon the atmospheric stability Turbulent viscosity (Pa·S) Density of phase q (kg/m3) Density of liquid water (kg/m3) Stress tensor (kg/(m·s2) Specific dissipation rate

which can easily supersaturate the air (i.e., RH > 100%) in the mixing process. Fog is formed due to condensation of excess water vapour. If the relative humidity in ambient air is very low (e.g., RH 12% in Case #2), there is very little chance of fog formation (assuming the mixing process is adiabatic). However, if such dry and warm air mixes with low-temperature effluent (e.g., −30 °C in Case #3), it can still lead to fog formation in a low degree of mixing (i.e., the volume fraction of ambient air is less than 20% as shown in Fig. 2b). Numerical simulation of LNG vapour dispersion has gained momentum since the last two decades. Majority of the numerical studies on LNG vapour dispersion [9–14] were focused on single-phase simulation which treated the LNG vapour as one species diluted and dissipated by air convection. Fog formation has been investigated broadly

less than that of ambient air. The dimensionless number Richardson number [1] can be used to evaluate the effect of dense gas dispersion. LNG vapour dispersion has been extensively studied both numerically and experimentally. After the global trade of LNG imports and exports started, extensive experiments particularly large-scale field trials of LNG vapour dispersion, such as ESSO [2], Maplin [3], Burro [4], Coyote [5], Falcon [6], etc., were performed in order to understand the hazardous consequence of LNG and obtain a comprehensive database for the numerical studies in the later stages. The experiments were conducted under a broad range of conditions for different spill rates, pool sizes, and terrains. However, most of the experiments were carried out in desert areas where the weather conditions were warm and dry (temperature > 30 °C and RH < 30%). One critical factor omitted by the experiments was the humidity ratio which can potentially affect LNG vapour dispersion. LNG shipping and receiving terminals are normally located in coastal areas where the ambient air is usually very humid (RH > 50%) [7]. The likelihood of fog formation after accidental LNG release in these areas is significantly high. The fog cloud which mixes with LNG vapour is commonly mistaken as the footprint of the LNG vapour cloud. The experimental study conducted by Cormier et al. [8] suggested that the visible cloud (fog) captured by normal camera and the LNG vapour cloud captured by infrared hydrocarbon camera were of different sizes (shown in Fig. 1). The actual size of LNG vapour cloud (represented by green contour) was much larger than the fog cloud (represented by visible cloud), which implied that the affected area of the flammable gas was beyond the visible cloud. Essentially, fog is an aerosol consisting of airborne water droplets or ice crystals when water vapour condenses or solidifies due to low temperatures. In this study, fog is treated as liquid water droplets only. The process of ice formation is not considered, as the predominant temperature during LNG vapour dispersion in large and open areas is usually above the freezing point. Fig. 2 showed the conditions at which fog forms due to the mixing of cold effluent with warm ambient air. In general, such fog tends to form in air where ambient air has relatively higher temperature and humidity (e.g., Case #1). Such air carries relatively more water vapour

LNG vapour cloud (1% v/v) o

Ambient temperature 31 C RH 32.6%

Infrared camera

Normal camera

VisibleNormal cloud (fog) camera

Fig. 1. The comparison of vapour clouds captured by hydrocarbon camera and normal camera [8]. 2

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Region of fog formation

120 80%

#3 50% RH80%

12% -30

-20

2000

#1

-10

Vapour Pressure (Pa)

4000

Relative humidity (%)

Saturation line

Saturation line

100

#1 #3

80

o

o

#1: E(0 C, RH100%) - A(31 C, 80%) o o #2: E(0 C, RH100%) - A(31 C, 12%) o o #3: E(-30 C, RH100%) - A(31 C, 12%)

60

#2 E - Effluent A - Ambient air

40

RH50%

20

#2 #3

RH12%

0

0 0.0

-30-20-100102030

0.2

0.4

0.6

0.8

1.0

o

Temperature ( C)

Degree of mixing (or volume fraction of ambient air)

(a)

(b)

Fig. 2. Psychrometric chart to show fog formation (a) and variation of RH with the degree of mixing (b).

∂ (αq ρq ) + ∇ ·(αq ρq → uq) = Sq ∂t

particularly in the area of meteorology and climatology [15,16] in order to forecast fog formation in various weather conditions and predict the visibility in atmosphere [17,18]. In LNG industry, fog formation is usually associated with the LNG regasification process which uses ambient air vaporisers (AAVs). Fog can be formed when cold effluents mix with ambient air, which can cause significant problems to the onsite visibility and affect human activities. Gavelli [19] proposed a single-phase CFD model based on the psychrometric equation to predict the fog formation and dissipation around AAVs. In his modelling approach, the dynamic mixing process of cold effluents and ambient air was not detailed. Wadnerkar et al. [20] developed a multiphase CFD model of fog formation and dissipation around AAVs by considering the processes of thermodynamic mixing, and heat and mass transfer. Very few numerical studies were reported to investigate the interactions between LNG vapour dispersion and fog clouds. Zhang et al. [21] conducted a multiphase simulation of LNG dispersion by applying the modified Hertz-Knudsen correlation to determine the fog formation rate. Luo et al. [22] explored the LNG vapour dispersion and fog formation by using the VOF multiphase model. Liu et al. [23] studied the dispersion of liquid hydrogen vapour affected by water phase change. However, the interphase forces, such as drag force between gas phase and liquid phase, were not detailed in these studies, as drag force can give hydrodynamic resistance between phases, which will impact LNG dispersion behaviour and fog formation. Because the VOF model only uses one set of governing equations for all phases, it is not ideal for characterising two dispersed phases (e.g., LNG vapour and fog) which can penetrate and diffuse into each other. In the current study, the effect of fog formation on LNG vapour dispersion is investigated. The behaviour of fog formation and dissipation is considered in a numerical mass transfer model. A detailed multiphase model is developed to investigate the dynamic mixing of cold vapour cloud and ambient air.

(1)

Momentum equation Ì¿ → ∂ (αq ρq → uq) + ∇ ·(αq ρq → uq → uq) = −αq ∇p + ∇ ·τq + αq ρq→ g + Fpq + SMq ∂t

(2)

→ where Fpq is the interphase drag force which is expressed as.: αp αq |→ up − → uq |2 → 3 Fpq = CD 4 dq

(3)

where CD is the drag coefficient which is accounted for by Schiller and Naumann [25] model: 0.687

CD =

) ⎧ (24 + 3.6Re Re ≤ 1000 Re ⎨ 0.44Re > 1000 ⎩

(4)

Energy equation Ì¿ ∂p ∂ (αq ρq hq) + ∇·(αq ρq → uq − ∇q¯q + Shq uq h q ) = − α q + τq: ∇→ ∂t ∂t

(5)

Turbulence equation The k-ω SST model allows accurate modelling of the gradients of temperature, velocity, and species near the ground surface and obstacles, and the free stream in obstacle-free fields. The model is given as:

∂ (ρkuj ) ∂ (ρk ) ∂ ⎛ ∂k ⎞ = + ⎜Γk ⎟ + Gk − Yk ∂x j ∂x j ⎝ ∂x j ⎠ ∂t

(6)

2. Methodology

∂ (ρωuj ) ∂ (ρω) ∂ ⎛ ∂ω ⎞ = + ⎜Γω ⎟ + Gω − Yω + Dω ∂x j ∂x j ⎝ ∂x j ⎠ ∂t

(7)

2.1. Governing equations

μt = α∗

In this study, the multiphase Eulerian model is selected, as it provides comprehensive sets of governing equations for different phases and correlations for phase interactions. Two phases, namely, air and fog, are treated as an interpenetrating continuum represented by volume fraction in the multiphase model. The Reynolds-average NavierStokes (RANS) equations are solved for each phase [24]. The governing equations are given below. Continuity equation

Species equation The species transport equations are included to account for the LNG vapour dispersion, and water vapour condensation and regeneration due to fog formation and dissipation. The model equation is expressed as:

ρk ω

→ ∂ (ρYi ) + ∇ ·(ρ→ v Yi ) = −∇ · Ji + Si ∂x 3

(8)

(9)

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μ → ∇T Ji = −⎛ρDi, m + t ⎞ ∇Yi − DT , i Sct ⎠ T ⎝ ⎜

the ideal gas law and vapour partial pressure. Psat and Patm are the saturation pressure of water vapour and atmospheric pressure, respectively. The saturation pressure Psat is calculated using Eq. (17).

⎟

(10)

In this study, three species are considered, namely, water vapour, dry air, and methane (assuming LNG vapour is 100% methane). The source term Si is applied to the species of water vapour to account for fog formation, while the other source term opposite to Si is added to the continuity equation of fog phase. The SIMPLE algorithm is applied to account for pressure-velocity coupling.

Csat = ρair ·

ωsat ωsat + 1

ωsat = 0.622

Psat Patm − Psat

Psat = 610.5 × 2.2. Modelling of fog formation and dissipation

Psat = The principle of mass transfer of fog formation/dissipation was expressed in Eq. (11) [26,27] where ṁ rate is the mass transfer rate (kg/ s); Clocal and Csat are the mass concentrations of local and saturated water vapour (kg/m3), respectively; hm is the mass transfer coefficient (m/s); A is the area of mass transfer (the surface area of the mesh cell, m2). If the local vapour concentration (Clocal ) is higher than the saturation concentration (Csat ) which implies the local relative humidity is greater than 100% (shown in Fig. 2a), then fog is formed by indicating a positive mass transfer rate (ṁ rate ). On the contrary, when ṁ rate is negative, fog dissipation occurs as the mixed air is not saturated with water vapour. When the cold LNG vapour cloud dissipates (or passes by) and the local temperature increases, the local air becomes unsaturated resulting in local fog dissipation.

ṁ = A·hm ·(Clocal − Csat ) hm =

Dυ = 2.26 × 10−5·

if T≥ 0 °C.

5723.27 e (9.55 − T + 3.53lnT − 0.0073T ),

if T< 0 °C.

(17)

The experimental results of Falcon series field test were used to validate the multiphase model in this study. The test was conducted by Lawrence Livermore National Laboratory (LLNL) in 1987. In the test, LNG was released onto the water surface of a rectangular water pond (40 m × 60 m), shown in Fig. 3a. In order to provide uniform LNG distribution on top of water, a distributor called spill spider with four exits was used. Water was recycled in order to evaporate LNG rapidly. Therefore, the evaporation rate of LNG could be assumed to be equal to the LNG spill rate. A billboard with a width 17.1 m and height 13.3 m stood in front of the water pond, which was to generate turbulence comparable to a typical LNG storage tank [6]. The fence behaved as a vapour barrier aimed at containing the LNG vapour cloud and reducing the hazard distance. In the downwind direction, a total number of 21 sensor stations (shown in Fig. 3b) were placed in three parallel arrays (50 m, 150 m, and 250 m) in order to record the temporal vapour concentration and track the movement of LNG vapour clouds. Each station had sensors at four different heights (1 m, 5 m, 11 m and 17 m). Operating conditions of different tests are listed in Table 1. In this study, Falcon 4 is selected as the base case because it had the maximum spill duration and relatively higher relative humidity. As discussed in Fig. 2, fog could still be formed if the local temperature is low enough when mixing with ambient air of low relative humidity. Based on that, the test of Falcon 4 still had the chance of fog formation.

(13) (14)

Sh = 2 + 0.6Gr 0.25Sc 0.33

(16)

3. Falcon series of LNG spill tests

(12)

T + 273.15 273.15

17.27T e 237.7 + T ,

Eqs. (11)–(17) to account for fog formation and dissipation were implemented in a user-defined function (UDF) which was embedded in the multiphase CFD model. Besides the mass source terms in both air phase and fog phase, other source terms for energy and momentum based on the mass exchange between phases were also taken into consideration.

(11)

Sh·Dυ l

(15)

The mass transfer coefficient hm (Eq. (12)) is calculated by using the Sherwood number (Sh). The characteristic length (l, m) is usually taken as the hydraulic diameter of the local mesh cell; the mass diffusivity (Dυ , m2/s) is the function of local temperature (Eq. (13)). Sherwood number is a function of Schmidt number (Sc) and Grashoff number (Gr) and expressed by the Ranz-Marshall correlation (Eq. (14)) [28] which is preferable to calculate the evaporation rate of tiny water drops at low Reynolds number. The saturation concentration of vapour Csat (Eq. (15)) is calculated by using the saturated humidity ratio ωsat ( Eq. (16)) and the density of humid air, while the local vapour concentration Clocal is calculated using

140 120 100 80

Crosswind (m)

40

G20

G12

G19

G04

G11

G18

G03

G10

G17

G05

0

-40

G13

G06

Fence

20

-20

G21

G14 G07

60

Billboard Water pond

G02

-60

G09

G01

G16

G08

-80

G15

-100 -120 -140 -150

-100

-50

0

50

100

Downwind (m)

(a)

(b) Fig. 3. Computational domain and mesh (a) and sensor station array in Falcon test (b). 4

150

200

250

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4. Results and discussion

Table 1 Conditions of Falcon series field test.

Average wind speed (m/s) @2m Ambient temperature (oC) Relative humidity (%) LNG Spill rate (m3/s) Spill duration (s)

Falcon 1

Falcon 2

Falcon 3

Falcon 4

Falcon 5

1.7

4.7

4.1

5.2

2.8

33.3 No data 28.7 131

31.5 No data 15.9 78

34.8 4.0 18.9 54

31.4 12.0 8.7 301

32.3 13.7 30.3 78

4.1. Model validation In this study, both single-phase and multiphase simulations have been conducted to compare with experimental results. In the singlephase simulation, only two species (air & methane) were involved. While in the multiphase phase simulation, the species of water vapour was added to the air phase to account for fog formation and dissipation. Simulation results of downwind temperature and gas concentration were compared with the experimental data, shown in Figs. 4 and 5. Both single-phase and multiphase models demonstrated the trends compared to the experimental data. Gas concentration was compared at four different locations, namely, 1 m and 5 m heights at 50 m and 150 m downwind distances, respectively. In the test of Falcon 4, LNG release stopped at 301 s. At a relatively shorter distance (e.g., 50 m), the gas concentration kept increasing with time, with the peak concentration around 3.0% observed at 320 s. While at a further distance of 150 m, the vapour concentration peaked at a later stage (at 340 s). It was observed that the LNG vapour concentration calculated by the multiphase model was around 20% higher than that of the single-phase model. The multiphase model accounted for the latent heat released during fog formation. This released heat increased the local temperature of LNG vapour cloud, which could decrease the density of the vapour cloud and reduce the dense gas effect. As a result, the LNG vapour cloud was lifted and transported more easily by air convection compared to the single-phase model. One challenge related to analysing fog is to define proper criteria to characterise visible fog. An empirical correlation [17] was used to analyse the relationship between visibility (vis , km) and liquid water content (LWC, g/m3) calculated in Eqs. (19) and (20) where ρw is the density of water and Cv _fog is the volume fraction of fog.

In order to minimise the impact of the boundaries, the computational domain in CFD simulation was enlarged intentionally with all three dimensions almost ten times larger compared to the fenced area. The wind was in the positive direction of X-axis. The computational domain was 1000 m long in X-axis (parallel to wind direction), 500 m wide (perpendicular to wind direction) and 50 m high (gravitational direction). As the geometry was symmetrical with the XZ plane, the simulations were conducted by using only half of the actual domain in order to reduce the computational cost. The upwind boundary in Xdirection was defined as the velocity inlet. Vertical velocity profile was calculated in Eq. (18).

z U (z ) = U0 ⎛ ⎞ z ⎝ 0⎠ ⎜

λ

⎟

(18)

where U0 is the wind velocity at the reference height z 0 (U0 = 5.2 m/s, z 0 = 2 m in this study); U (z ) is the wind velocity at a given height z; λ is the dimensionless parameter depending on the atmospheric stability and surface roughness [29] (λ = 0.2 in this study). The downwind boundary in X-direction was defined as an outlet. The boundary condition of mass flow inlet was applied at the water pond surface. A steady-state wind field without LNG vapour was applied as the initial conditions to the multiphase simulation. The mass flow of LNG vapour was turned on at 0 sec in transient simulations. Both mesh and time-step independence have been tested in this study. A mesh of 179,520 cells was used for subsequent simulations. A time step of 0.1 s was selected to run transient simulations. All the cases were conducted on a supercomputing system with computer processors of Intel Xeon E5-2690V3 and 2.6 GHz frequency. One typical case simulation was conducted using 144 processors and completed in around four hours.

vis = 0.027·LWC −0.88

(19)

LWC = ρw ·Cv _fog

(20)

The visibility in a foggy atmosphere generally ranges from metres to kilometres [17]; thus the range of fog volume fraction is between 10−5 and 10−8. In this study, an iso-surface of fog volume fraction 10−6 is selected to represent the visible fog. Fig. 6 showed the relationship of fog contour with profiles of temperature, and water vapour concentration at the run time of 300 s when the affected area of LNG vapour dispersion was almost maximum. Relatively denser fog was observed inside the fenced area, shown in Fig. 6a, which was because the lowest temperature was present and the difference of water vapour concentration was significant, thus providing the maximum driving force for fog formation. Water vapour concentration in this area 32

32.0 30

30.0

Temperature ( C)

150m downwwind, 11m high

28

o

o

Temperature ( C)

50m downwind, 11m high 28.0

Single phase Multiphase Experimental value

26.0

24.0

Falcon 4 Test

24

Falcon 4 Test Sensor G11

Sensor G04

22.0

Single phase Multiphase Experimental value

26

22

20.0

20

0

100

200

300

400

500

600

700

800

900

1000

0

Time (s)

100

200

300

400

500

Time (s)

Fig. 4. Comparison of temperatures at 50 m and 150 m downwind distances. 5

600

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900

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4.0

Single phase model Multiphase model Exprimental value

Concentration (mol%)

3.0

3.0

2.5

Sensor G04 50m downwind, 1m height

2.0

Falcon 4 Test

1.5

Single phase model Multiphase model Exprimental value

3.5

Concentration (mol%)

3.5

1.0 0.5

2.5

Sensor G04 50m downwind, 5m high

2.0 1.5

Falcon 4 Test 1.0 0.5

0.0

0.0 0

100

200

300

400

500

600

700

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900

0

100

200

300

400

Time (s)

500

2.0

700

800

900

2.0

Single phase model Multiphase model Exprimental value

Single phase model Multiphase model Exprimental value Concentration (mol%)

1.5

Sensor G11 150m downwind, 1m high

1.0

0.5

0.0

1.5

Sensor G11 150m downwind, 5m high

1.0

0.5

0.0 100

200

300

400

500

600

700

800

900

0

100

200

300

400

Time (s)

500

600

Time (s)

Fig. 5. Comparison of gas concentration at 50 m and 150 m downwind distances. Fog volume fraction (v/v) 3.0e-06

1.5e-06

o

30 Height (m)

0

Air flow (5.2m/s, 31.4 C, RH12%) o

30 C

20

o

20 C

10

o

0C

o

10 C

Billboard

0 0

0

20

Fenced area

40

60

80

100

120

140

Downwind distance (m)

(a) 40

Water vapour (mol%) 5.43e-01

2.72e-01

20 Wind

t = 300s Billboard

10 0 -20

2.60e-04

Fog profile (volume fraction 1e-06, grey contour)

30 Height (m)

Concentration (mol%)

600

Time (s)

0

20

40

60

80

100

120

140

160

Downwind distance (m)

(b) Fig. 6. Fog volume fraction and temperature profile (a) and water vapour concentration and fog cloud (b). 6

700

800

900

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80

320m 60

CH4 (mol%)

60m

10 Crosswind distance (m)

40

5.0

20

Fog cloud

0

2.5%

1.0%

-20 -40

Fenced area

1.0

-60 -80 0

50

100

150

200

250

300

350

400

Downwind distance (m)

(a) Height (m)

30

Fenced area 20

1.0%

10

5.0%

0 0

Fog cloud

50

100

2.5% 150 200 Downwind distance (m)

250

300

(b) Fig. 7. Methane contours and fog cloud (at run time 300 s) of top view (a) and front view (b). 0.050

0.030

0.045

12% RH 30% RH 50% RH 80% RH

Mole concentration of CH4

0.035

0.025

Mole concentration of CH4

80%

0.040 50%

0.030

30%

0.025

G04 @ 50m downwind 1m high

12%

0.020 0.015

LNG spill duration 301s

0.010

12% RH 30% RH 50% RH 80% RH

80%

0.020

50% 30%

G11 @ 150m downwind 1m high

0.015 12%

0.010

LNG spill duration 301s 0.005

0.005 0.000

0.000 0

100

200

300

400

500

600

0

100

200

Run time (s)

300

400

500

600

Run time (s)

Fig. 8. Comparison of LNG vapour concentration of the cases with different relative humidity.

direction, while the LNG vapour cloud (characterised by methane mole fraction 1.0%) reached a distance at around 320 m (Fig. 7a). The maximum height of the LNG vapour cloud was around 17.4 m which was about 2 m higher on average than that of fog (Fig. 7b). The findings from multiphase simulation agreed with the observation from the experiment conducted by and Cormier et al. [8] where the size of LNG vapour cloud was larger than that of the visible fog cloud.

decreased significantly, as the local water vapour was condensed into fog and LNG vapour expanded to replace space (Fig. 6b). As moving away from the cold zone, the fog volume fraction decreased while the local temperature increased. Even in a relatively higher temperature range (20–30 °C), the fog could still be formed by condensing the local excess water vapour from air. Fig. 7 showed the LNG vapour concentration profile. The fog cloud was superimposed with the dark grey contour. Fog was observed only in the vicinity of the fenced area and did not travel as far as the LNG vapour. In locations where fog was present, the methane concentration was between 2.5% and 5.0%. Fog travelled 60 m in 300 s in downwind

4.2. Effect of relative humidity The effect of humidity ratio was studied to further investigate the 7

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Fog volume fraction (v/v) 1.0e-05

5.0e-05

Crosswind (m)

Fig. 9. Downwind profiles of LNG vapour concentration (a) and temperature (b) of different RH cases.

60 Fenced area 30 -6 Fog 1X10 0 -30 -60 Case: RH 12% 0

0

The exclusive distance increased with relative humidity from around 55 m (12% RH) to 125 m (80% RH), shown in Fig. 9a. The average temperature at a given downwind distance increased with relative humidity, shown in Fig. 9b. Although the average temperature rise was less than 1 °C, it provided localised heating for cold LNG vapour. The minor temperature increase did not change the mechanism of LNG vapour dispersion from gravity-induced to passive dispersion, but it reduced the dense gas effect by increasing the local temperature. The reduced dense gas effect was also reflected by an increased exclusive distance, shown in Fig. 9a. However, more consistent and systematic experimental and numerical studies are required in order to achieve indepth understandings. Fig. 10 compared the contours of fog volume fraction and LNG vapour concentration at 300 s under different relative humidity. In the base case (12% RH), the footprint of visible fog (volume fraction 1.0 × 10−06) was much smaller than the LNG vapour concentration (mole fraction 1.0%), shown in Fig. 10a. However, when the RH increased, the fog footprint encompassed the LNG vapour cloud (dash line), shown in Fig. 10b. Moreover, the maximum fog volume fraction observed at 80% RH was much higher than lower RH cases, which suggests a denser fog and lower visibility in high air RH scenarios. The development of both fog and LNG vapour cloud with time at different RH cases was shown in. The light grey, dark grey, and light blue contours represented fog volume fraction 10−06 (light fog), 5.0 × 10−6 (dense fog), and LNG vapour concentration (mole fraction 1.0%), respectively. Fog formation and LNG vapour dispersion occurred simultaneously. Both fog and LNG vapour concentration profiles had similar shapes, with both profiles shrinking in the central part (due to the effect of billboard and vapour barrier in the experiments). As shown in Tables 1 and 2, the processes of LNG vapour dispersion and fog formation were coupled and interacted with each other. At 12% RH case, a minimal amount of fog was observed, and the footprint of LNG vapour cloud was much larger than that of the fog. At 30% RH, the footprint of light fog and the pace of fog formation and dissipation were almost the same as the LNG vapour cloud. The dense fog was confined in the vicinity of the fenced area and did not spread with time. At higher relatively humidity (50% and 80%), the light fog spread more broadly than the LNG vapour cloud, and the dense fog travelled beyond the fenced area. Moreover, when increasing the relative humidity from 12% to 80%, the duration of LNG vapour dispersion prolonged, and the affected area of LNG vapour cloud was enlarged.

CH4 1%

50 100 150 200 250 300 350 400 Downwind distance (m)

(a)

200

-6

Fog 1x10

150 Fenced area

Crosswind (m)

100 50

-5

Fog 1x10

0

-6

Fog 5x10

-50 -100

CH4 1%

Case: RH 80%

-150 -200 0

200

400

600

800

Downwind distance (m)

(b) Fig. 10. LNG vapour concentration and fog volume fraction 12% RH (a) and 80% RH (b).

impact of fog formation on LNG vapour dispersion. By maintaining all the other conditions the same (e.g., LNG spill and ambient air conditions), cases of air relative humidity of 30%, 50%, and 80% were tested in the multiphase model. The humidity ratio of 80% RH was 6.7 times of the base case (12% RH). The methane concentration profiles were compared at 50 m and 150 m as shown in Fig. 8. The concentration at all times was increased with relative humidity at both distances 50 m and 150 m. The methane concentration in 80% RH was around double of that in 12% RH. The occurrence of peak concentration slightly delayed in the case of 80% RH compared to 12% RH (from 317 s to 327 s). According to the LNG industrial standard NFPA 59A, the exclusive safety distance related to LNG vapour dispersion should be defined at a point where the concentration is reduced to half of the lower flammable limit (LFL, 5% for natural gas). The average LNG vapour concentration and temperature were plotted against the downwind distance in Fig. 9.

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Table 2 Comparison of time-dependent footprints of fog and LNG vapour dispersion.

RH

100s

200s

300s

400s

12%

30%

50% Fog 5e-06

80%

Fog -6 5x10

CH4 1%

Fog -6 1x10

655m

5. Conclusion

3211101), the SYSU-BP LNG Centre (No. 99103-9390001).

In this study, a multiphase model for simulating LNG vapour dispersion has been developed by integrating a detailed phenomenological model of fog formation. The multiphase model was validated using the experimental data and showed acceptable agreement. The case scenarios with different relative humidity were studied to investigate the effect of fog formation on LNG vapour dispersion. The following conclusions were drawn from this research work:

Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.applthermaleng.2019.114671. References [1] R.E. Britter, Atmospheric dispersion of dense gases, Annu. Rev. Fluid Mech. 21 (1989) 317–344. [2] G. Feldbauer, J. Heigl, W. McQueen, R. Whipp, W. May, Spills of LNG on waterVaporization and downwind drift of combustible mixtures, ESSO Research and Engineering Company Report No, EE61D-72 (Performed for the American Petroleum Inst.), (1972). [3] J.S. Puttock, D.R. Blackmore, G.W. Colenbrander, Field experiments on dense gas dispersion, J. Hazard. Mater. 6 (1982) 13–41. [4] J.B. R. P. Koopman, R. T. Cederwall, et al., Burro series data report-LLNL/NWC 1980 LNG spill tests (Volume 2), Lawrence Livermore Laboratory, (Dec. 1982). [5] F. Rigas, S. Sklavounos, Simulation of Coyote series trials–Part II: A computational approach to ignition and combustion of flammable vapor clouds, Chem. Eng. Sci. 61 (2006) 1444–1452. [6] T. Brown, R. Cederwall, S. Chan, D. Ermak, R. Koopman, K. Lamson, J. McClure, L. Morris, Falcon series data report: 1987 LNG vapor barrier verification field trials, Lawrence Livermore National Lab, CA (USA), 1990. [7] S. Mokhatab, J.Y. Mak, J.V. Valappil, D.A. Wood, Handbook of liquefied natural gas, Professional Publishing, Gulf, 2013. [8] B.R. Cormier, R. Qi, G. Yun, Y. Zhang, M. Sam Mannan, Application of computational fluid dynamics for LNG vapor dispersion modeling: A study of key parameters, J. Loss Prev. Process Ind. 22 (2009) 332–352. [9] B. Sun, K. Guo, V.K. Pareek, Hazardous consequence dynamic simulation of LNG spill on water for ship-to-ship bunkering, Process Saf. Environ. Prot. 107 (2017) 402–413. [10] F. Nazarpoura, J. Wen, S. Dembelea, I.D. Udechukwua, LNG Vapour Cloud Dispersion Modelling and Simulations with OpenFOAM, Chem. Eng. 48 (2016). [11] J. Fiates, R.R.C. Santos, F.F. Neto, A.Z. Francesconi, V. Simoes, S.S. Vianna, An alternative CFD tool for gas dispersion modelling of heavy gas, J. Loss Prev. Process Ind. 44 (2016) 583–593. [12] B. Sun, K. Guo, LNG accident dynamic simulation: Application for hazardous consequence reduction, J. Loss Prev. Process Ind. 26 (2013) 1246–1256. [13] Y. Tominaga, T. Stathopoulos, CFD simulations of near-field pollutant dispersion with different plume buoyancies, Build. Environ. 131 (2018) 128–139. [14] L. Dong, H. Zuo, L. Hu, B. Yang, L. Li, L. Wu, Simulation of heavy gas dispersion in a large indoor space using CFD model, J. Loss Prev. Process Ind. 46 (2017) 1–12. [15] I. Gultepe, B. Zhou, J. Milbrandt, A. Bott, Y. Li, A.J. Heymsfield, B. Ferrier, R. Ware, M. Pavolonis, T. Kuhn, A review on ice fog measurements and modeling, Atmos. Res. 151 (2015) 2–19. [16] M. Hrebtov, K. Hanjalić, Numerical study of winter diurnal convection over the city of Krasnoyarsk: Effects of non-freezing river, undulating fog and steam devils, Bound.-Layer Meteorol. 163 (2017) 469–495.

(1) The single-phase model of LNG vapour dispersion was valid if air relative humidity is low (e.g., RH < 30%). However, the model could underestimate the hazards, if the ambient conditions become humid. (2) At low air RH cases (e.g., RH < 30%), LNG vapour cloud travelled beyond the visible fog, which agreed with the observation in experiment. However, at high air RH scenarios (e.g., RH > 50%), fog cloud can overtake and dominate LNG vapour cloud. (3) Fog formation can reduce the dense gas effect of LNG vapour dispersion, which can enlarge the affected area and slow down the process of LNG vapour dissipation. These findings can improve understandings of the behaviour of LNG vapour dispersion, particularly in humid environments. It is of critical importance when assessing the risks in humid regions (e.g., LNG shipping and receiving terminals) and in different weather conditions. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This work is supported by resources provided by the Pawsey Supercomputing Centre with funding from the Australian Government and the Government of Western Australia. The authors also wish to acknowledge the support of the Key Laboratory of LNG Cryogenic Technology of Guangdong High Education Institute (No. 390009

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