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Simulating on rollover phenomenon in LNG storage tanks and determination of the rollover threshold
Journal of Loss Prevention in the Process Industries 37 (2015) 132e142
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Journal of Loss Prevention in the Process Industries journal homepage: www.elsevier.com/locate/jlp
Simulating on rollover phenomenon in LNG storage tanks and determination of the rollover threshold Yuxing Li a, *, Zhenglong Li a, b, Wuchang Wang a a b
College of Pipeline and Civil Engineering, China University of Petroleum, Qingdao, Shandong, 266580, China China Petroleum Pipeline Research Institute, Langfang, Hebei, 065000, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 7 January 2015 Received in revised form 3 July 2015 Accepted 25 July 2015 Available online 1 August 2015
Rollover is a potential risk to the safety of LNG storage tanks during the LNG storage process, so study of its prevention method is very important. In this paper, rollover phenomenon in a liquefied natural gas (LNG) storage tank is modeled physically and mathematically. Its evolution is simulated using FLUENT™ software from the breakdown of stratification to the occurrence of rollover. Results show that the evolution consists of three phases: the initial phase where rollover occurs near the side wall of the storage tank; the turbulent phase where rollover transfers to the center of the tank; and the final phase where new layers evolve. Based on these phases, rollovers in 160,000, 30,000, and 5000 m3 LNG storage tanks are simulated at varying initial density differences, and a rollover coefficient is defined to describe rollover intensity. The simulations show that the rollover coefficient initially increases within a small scope and then increases rapidly with the increment of initial density difference. This turning point is chosen to be the rollover threshold, which is regarded as the critical density difference in this study. The critical density differences obtained from the simulation results of the 160,000, 30,000, and 5000 m3 LNG storage tanks are 3, 5, and 7 kg/m3, respectively, which can be used as their rollover criteria to ensure the safety of LNG storage tanks. © 2015 Elsevier Ltd. All rights reserved.
Keywords: LNG storage tank Rollover Rollover threshold Critical density difference Numerical simulation
1. Introduction Natural gas is becoming an increasingly important energy source. In the past decades, the global consumption of natural gas has increased by 28%, with natural gas accounting for nearly 24% of primary global energy demand (BP, 2013). As an important part of the natural gas industry, the liquefied natural gas (LNG) industry is experiencing a high-speed development stage. By the end of 2012, 98 regasification terminals existed worldwide, with a total regasification capacity of 649 million tons per annum. By the end of 2013, regasification terminals had over 44 million m3 of combined LNG storage capacity worldwide (World LNF Report, 2013). LNG imported to the receiving terminals generally come from different gas fields in different compositions. When LNG is injected to the tank and mixed with the residual LNG, stratification will happen. Stratification may also be attributed to the prior evaporation of N2 from LNG, which has a high content of it (Chatterjee and Geist, 1976). After stratification, the LNG layers in the tank become
* Corresponding author. Tel.: þ86 0532 86981818; fax: þ86 0532 86981822. E-mail address: [email protected] (Y. Li). http://dx.doi.org/10.1016/j.jlp.2015.07.007 0950-4230/© 2015 Elsevier Ltd. All rights reserved.
relatively stable, and natural convection circulates in each liquid layer because of the heat leaking into the tank, where LNG is stored at a low temperature of 160 C (Flower et al., 2002). The liquid in the upper layer tends to become dense after light components in the LNG evaporate because of the heat leak gained by the tank. However, the hydrostatic pressure at the upper layer prevents the evaporation of the lower layer, which allows the liquid to superheat and becomes less dense. When the densities of the layers approach equality, the interface between the two becomes unstable and mixes rapidly. This process is known as the rollover phenomenon. A sudden release of large amounts of boil-off gas, which causes a rapid increase in tank pressure and sometimes damage to the tank, accompanies this phenomenon. This event presents a considerable risk to the LNG terminal and enormous economic loss for the LNG company (Acton and Van Meerbeke, 1972). There were two well-known rollover accidents occurred in the Snam LNG storage and distribution station in La Spezia, Italy (1971) (Sarten, 1972) and the Partington LNG pitch peak station of the BG Company in the United Kingdom (1993) (Baker and Creed, 1996). These events made people aware of the damages caused by LNG rollover, and thus, many researchers have spent time studying this
Y. Li et al. / Journal of Loss Prevention in the Process Industries 37 (2015) 132e142
Nomenclature DAB S Fi ui
n nt r
T
t Gr g
b DT h
n sk sε
Mass diffusivity [m2/s] Mass fraction of each LNG component Fluid body force on the unit direction [N] Velocity of every direction [m/s] Kinematic viscosity coefficient of laminar flow [m2/s] Kinematic viscosity coefficient of turbulent flow [m2/s] Density [kg/m3] Temperature [K] Time [s] Grashof threshold Acceleration of gravity [m/s2] Expansion factor of fluid [1/K] Temperature difference of the fluid [K] Characteristic length of the container [m] Kinematic viscosity coefficient [m2/s] Turbulence Pr number of the k equation, sk ¼ 1.0 Turbulence Pr number of the ε equation, sε ¼ 1.3
phenomenon and have proposed their own rollover prediction models. Chatterjee and Geist (1972) were the first to propose a rollover model (i.e., the CeG model) (Chatterjee and Geist, 1972). Since then, a series of rollover models (Chatterjee and Geist, 1976; Germeles, 1975; Heesatand et al., 1983) (two-phase models that consist of a mass and heat transfer phase and a mixture phase) have been proposed using double-diffusive convection theory and the assumption of a stationary interface between the layers, which are basically based on the CeG model, until Shi (1993) (Shi et al., 1993) found the migrating interface from experiments. After the rollover accident in the United Kingdom, Bates and Morrison (1997) published the first three-phase model (i.e., the BateseMorrison model), in which rollover evolution consists of three phases: a stationary interface phase, a migrating interface phase, and a rollover phase. In China, Gu (2003) (Lu et al., 2003) extended the BateseMorrison model into four phases: a stationary interface phase, a second phase where the liquid in the lower layer is carried into the upper layer, a third phase where the interface of the layers is penetrated by a jet stream, and a rollover phase. The influence of evaporation on density, which improves accuracy, was also considered in this model. Other researchers have also investigated the rollover phenomenon, but their studies are mostly based on previous research (Bashiri and Fatehnejad, 2006; Roh et al., 2013; Lukaszewski et al., 2013; Roh and Son, 2012). The aforementioned rollover models explain the evolution from stratification formation to rollover occurrence. However, no model has ever proposed a threshold to judge an LNG rollover. Thus, the judgment of a rollover in LNG storage tanks is basically empirical and only a few basic measurements are available to prevent rollover from occurring in large storage tanks, such as separating the storage of LNG from different gas fields, selecting filling modes, and monitoring nitrogen content (An zhong, 2006). Therefore, research on rollover threshold can predict rollover accurately and ensure the security of LNG storage tanks. 2. Development of rollover CFD model and analysis on simulation results 2.1. Description of the rollover physical model In a storage tank, LNG typically evolves into many layers after
133
Gk,Gb
Turbulent kinetic energy. The former is generated from the velocity gradient of laminar flow, whereas the latter is buoyancy. 2 mt Turbulence viscosity coefficient, mt ¼ rCm kε C1ε, C2ε, C3ε, Cm Constant numbers, C1ε ¼ 1.44, C2ε ¼ 1.92, Cm ¼ 0.09 t0 Starting time of rollover, the time when the densities of the monitoring points begin to change [s]. tf Ending time of rollover, the time when the densities of the monitoring points stop changing [s]. Dt Rollover time, equal to the difference value between t0 and tf [s]. Dr0 Initial density difference, the density difference between the upper and lower layers after initialization [kg/m3]. Drmax Maximum density difference, the difference between the maximum and minimum densities in rollover evolution [kg/m3]. V Capacity of the LNG storage tank [m3]. DT C Critical temperature difference [K].
stratification, and rollover generally occurs between the two adjacent layers. Some studies indicate that heat leaking into the tank results in a density change in LNG, and that density difference among LNG at different depths leads to stratification and rollover. Thus, a 2D LNG storage tank model is developed based on the following assumptions and simplifications, as shown in Fig. 1. (1) LNG is an incompressible Newtonian fluid in this model. (2) All layers have the same depth (1 m) and are mixed uniformly at the beginning. Two adjacent layers are chosen as an object. (3) The LNG in the tank is assumed to be at the transition point between stratification and rollover; thus, stratification evolution can be omitted from the simulation. Meanwhile, nine monitoring points are set on the model to record LNG density change during rollover evolution (monitoring points 2, 4, 5, 6, and 8 are located at the midpoint).
2.2. Development of the rollover mathematical model 2.2.1. Governing equations (1) Continuous equations
vux vuy þ ¼ 0: vx vy
(1)
(2) Momentum equations
d ux þ uy 1 vp vp þ þ ðn þ nt ÞV2 ux þ uy þ Fx þ Fy : ¼ r vx vy dt Among these;
Fx ¼ 0 : Fy ¼ g
(2) (3)
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Y. Li et al. / Journal of Loss Prevention in the Process Industries 37 (2015) 132e142 Table 1 Flow state discrimination of the natural convection by Grashof number.
Fig. 1. Simplified model and monitoring points for rollover (160,000 m3 LNG storage tank).
(3) Composition equation
! vS v2 S v2 S ¼ DAB þ : vt vx2 vy2
(4)
2.2.2. Discrimination of the rollover flow model Natural convection is caused by the uneven temperature field of fluid itself. The uneven temperature field results in the uneven density field, which produces the buoyancy lift to be the power of nature convection. As rollover is caused by the uneven density field in the LNG storage tank, it is typical natural convection. And the flow state of natural convection characterize by Grashof number (Gr ¼ gbDTh3/n2) as in Table 1 (Shiming and Wenquan, 2006; Guofa, 2007). In this paper, rollover in three type of LNG storage tanks with different capacity are researched. Their parameters are showed in Table 3, with the property parameters of LNG showing in Table 2, Grashof numbers can be calculated and the flow state of rollover can be characterize to be turbulent flow as it showed in Table 3. Thus, a turbulent model should be selected to simulate rollover evolution in the LNG storage tank. Among the existing turbulent models, kε model is suitable to this situation, and it is widely used by its commonality and economy and reasonable accuracy, so the kε equation is selected to simulate rollover evolution in the LNG storage tank.
Flow state
Grashof number
Laminar flow Turbulent flow
1.43 104~3 109 >2 1010
The boundary conditions for S (mass fraction of LNG component) and k equation are vS/vy ¼ 0 and vk/vy ¼ 0, and the dissipation rate of k is assumed to be equal in the wall-adjacent control volume. The grid of the model is generated using the geometry preprocessor of the gambit program and a structured grids is adopted with fine mesh next to the wall surfaces. The total number of grid cells amounted to over 1.6 104 for the 160,000 m3 tank, 8 103 for the 30,000 m3 tank and 4 103 for the 5000 m3 tank (Fig. 3). As the density difference between the LNG layers leads to rollover, the upper layer in the model (Fig. 1) is initialized with a larger density than the lower layer. And the initial velocity of the 2D model is set to be ux ¼ 0, uy ¼ 0. The simulations are regarded as being convergent when the residuals of continuity, velocity, turbulent kinetic energy (k), and turbulent diffusion rate (epsilon) all decreased to below 1 103 (Fig. 4).
2.3. Analysis on the simulation results In this section, the rollover evolution in a 160,000 m3 tank with a diameter of 80 m is simulated using FLUENT™ software. Moreover, a mixture model, kε equation, and wall boundary conditions are selected. A structured grid generates a mesh in the computational domain. The liquid in the upper layer is given at 424 kg/m3, which is 1 kg/m3 greater than the liquid in the lower layer. The density contours shown in Fig. 5 reflect the rollover evolution in the 160,000 m3 tank. The contours observed in this study are shown as the left half of the physical model because rollover occurs symmetrically in the tank. The following information can be derived from Fig. 5.
(1) Turbulent kinetic energy equation (k equation):
v v v ðrkÞ þ ðrkui Þ ¼ vt vxi vxj
" mþ
# mt vk þ Gk þ Gb rε: sk vxj
(5)
(2) Turbulent diffusion equation (ε equation):
v v v ðrεÞ þ ðrεui Þ ¼ vt vxi vxj
"
# m vε ε mþ t þ C1ε ðGk þ C3ε Gb Þ k sε vxj
C2ε r
ε2 : k (6)
2.2.3. Boundary and initial conditions Fig. 2 is the domain and boundaries of the LNG storage tank model. The model domain is fluid domain and a no-slip boundary condition was applied to the walls. Besides, a Standard Wall Function is selected in the simulation as a supplement to the kε equation.
(1) At 100 s, the interface closed to the tank wall begins to migrate down to the lower layer, which results in a mixture of the two layers and vortices emerging at the interface. (2) At 150 s, the interface of the two layers becomes tortuous, which makes the layers unstable. (3) At 200 s, the stratification in the tank is broken down, which results in rapid mixing of the two layers and the formation of numerous vortices. Meanwhile, the rollover near the side wall slows down and the mixture is nearly completed. It can be observed that vortices appear and transfer on the interface between the layers. Given that monitoring points 4, 5, and 6 are located on the interface, the variations of vortex magnitudes on these points (Fig. 6) can reflect vortex evolution. As shown in Fig. 6, the vortex magnitudes of monitoring points 4 and 6 (near the side wall of the storage tank) increase rapidly from 50 s to 100 s, which indicates the formation of vortices and the rollover of LNG near the side wall. However, the vortex magnitude of monitoring point 5 (at the center of the tank) is maintained in this period, which indicates a stable center in the storage tank. Between 100 s and 200 s, the vortex magnitudes of monitoring points 4 and 6 decline rapidly, whereas that of monitoring point 5 increases rapidly. These results can be attributed to the LNG
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Table 2 Physical property parameters of LNG. Name
Density rkg/m3
Height h/m
Temperature T/K
Environment temperature/K
Dynamic viscosity n/(kg/m.s)
Value
424
80
112
298
1.179e-04
Table 3 Parameters of LNG storage tanks and the flow state discrimination. Capacity/m3 Diameter/m Height/m Grashof number Flow state
160,000 80 32 2.1 1013 Turbulent flow
30,000 42 22 6.8 1012 Turbulent flow
5000 22 13 1.4 1012 Turbulent flow
Fig. 2. Domain and boundaries of the tank model.
mixture being nearly complete close to the side wall while only beginning at the center during this period. After 200 s, the vortex magnitudes of all monitoring points become smooth and steady. The rollover in the entire tank ends gradually with the finished mixture of the two layers and the
Fig. 5. Density contours of the model during the rollover evolution.
evolution of new layers. The preceding analysis shows that the density difference in the LNG storage tank causes the rollover, which leads to an unstable LNG and rollover evolution from the side wall to the center of the storage tank. The simulation results also show that the rollover evolution consists of three phases. Phase 1: Rollover occurs near the side wall of the storage tank. During this phase, the dense liquid in the upper layer begins to migrate down to the lower layer because of the unstable interface near the side wall. The extruding liquid in the lower layer moves into the upper layer, and thus, the velocity magnitude and vortex magnitude near the side wall of the tank increase. Phase 2: Rollover transfers to the center of the tank. During this phase, the interface between the layers begins to twist under the disturbance of the rollover near the side wall, which allows the rollover to transfer to the center of the tank. Meanwhile, the mixture of the layers, the velocity magnitude, and the vortex magnitude in the tank are enhanced. Phase 3: Evolution of new layers. Rollover evolution ends with
Fig. 3. Part of the fine mesh of 160,000 m3 tank.
Fig. 4. Residual of 160,000 m3 tank simulation.
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time during this phase, and new layers are formed under the effect of gravity. The LNG in the storage tank becomes stable again. 3. Rollover threshold for LNG storage tanks Rollover studies aim to prevent rollover and ensure safety in LNG storage tanks. Previous studies have indicated that the cause of stratification and rollover is density difference. Density and temperature differences in varying depths are observed when stratification occurs in a tank. Given that temperature difference results in density difference, a series of initial density differences between layers is provided to the rollover model for FLUENT™ simulation. Based on the simulation results of rollover evolution, a rollover threshold can be determined to judge if rollover is occurring in the LNG storage tank. Three types of tanks with volumes of 160,000, 30,000, and 5000 m3, and diameters of 80, 42, and 22 m, respectively, are simulated in this section. 3.1. Rollover threshold for the 160,000 m3 LNG storage tank In this section, rollover evolution under varying density differences is simulated to determine a rollover threshold. The study that used the 160,000 m3 LNG storage tank is taken as an example. 3.1.1. Determining rollover time Simulation result of the 160,000 m3 tank shown in Fig. 7 (the diameter is 80 m and the initial density difference is 1 kg/m3) is chosen as an example to explain the density-changing trend of each monitoring point. As shown in Fig. 7, the densities at monitoring points 1, 2, and 3 (at the bottom of the storage tank) increase from the initial density to the maximum density, whereas the densities at monitoring points 7, 8, and 9 (at the top of the storage tank) change inversely. However, the densities at monitoring points 4, 5, and 6 (on the interface between the layers) exhibit rapid fluctuations during rollover evolution and share the same mediate density at the starting and finishing times of rollover. Thus, the difference value between the average density of monitoring points 1, 2, 3, 7, 8, and 9 and the average density of monitoring points 4, 5, and 6 can reflect density fluctuation in rollover evolution. The variation of density fluctuation with time is shown in Fig. 8. The time when density fluctuation starts is defined as the beginning time of rollover, and the time when density fluctuation
stops is defined as the finishing time of rollover. The value between them is defined as the rollover time.
3.1.2. The influence of density difference on rollover 1) Analysis on the density contours The density contours shown in Fig. 9 are obtained from the simulation results (in the 160,000 m3 LNG storage tank with a diameter of 80 m) under a series of initial density differences (0.5, 1, 3, 5, and 7 kg/m3) at 100 s. The density contours in Fig. 9 can be divided into the following types. (1) When the initial density differences are 0.5 kg/m3 and 1 kg/ 3 m , rollover occurs near the side wall of the storage tank (Phase 1 in Section 2.3). (2) When the initial density differences are 5 kg/m3 and 7 kg/m3, rollover nearly evolves to the end (Phase 3 in Section 2.3). The velocity magnitudes of points 1, 2, 3, 7, 8, and 9 (at the bottom and top of the storage tank) and the vortex magnitudes of points 4, 5, and 6 (on the interface between layers) are recorded during rollover evolution to compare the rollover intensity under different initial density difference. 2) Analysis on the velocity magnitude The velocity magnitudes that changed with time under a series of initial density differences (1, 3, 4, 5, and 6 kg/m3) are shown in Fig. 10. As shown in Fig. 10, velocity magnitudes with initial density differences of 4, 5, and 6 kg/m3 are significantly larger than others during rollover evolution. The value difference among them is obvious. 3) Analysis on the vortex magnitude The vortex magnitudes that changed with time under a series of initial density differences (1, 3, 4, 5, and 6 kg/m3) are shown in Fig. 11. As shown in Fig. 11, vortices with bigger magnitudes emerge near the side wall of the storage tank (monitoring points 4 and 6) at an early time (approximately 50 s) when the initial density difference is over 3 kg/m3. These vortices transfer rapidly to the center of the tank, which allows the vortex magnitude at the center (monitoring point 5) to rapidly reach a high value (at approximately 100 s). Under this situation, the vortex magnitude of the entire storage tank peaks and decreases sharply within a short time, which result in a violent rollover in the LNG storage tank. By contrast, vortices emerge at a later time (at approximately 100 s or 200 s) with smaller vortex magnitudes and slower transfer speeds when the initial density difference is less than 3 kg/m3, and the vortex magnitude of the entire storage tank fluctuates for a long time, which results in a steady rollover in the LNG storage tank. 4) Summary
Fig. 6. Variations of vortex magnitudes with time.
From the preceding analysis, the rollover in the 160,000 m3 LNG storage tank can be divided into two types based on intensity. When the initial density difference is less than 3 kg/m3, rollover occurs late and lasts long. Velocity and vortex magnitudes are small, which makes rollover relatively steady. However, rollover occurs early and finishes within a short time when the initial density difference is over 3 kg/m3. Velocity and vortex magnitudes are large, which makes rollover violent.
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Fig. 7. Density variations with time at nine monitoring points.
Fig. 9. Comparison of the density contours with different initial density differences at the time of 100s.
Fig. 8. Variation of density fluctuation with time.
3.1.3. Definition of the rollover coefficient Initial density difference (Dr0) is proven to be the main cause of rollover through simulation results. Moreover, it is the key parameter to determine rollover time (Dt) and maximum density difference during rollover evolution (Drmax). Rollover can be
divided into four types (Table 4), which combines the two aforementioned parameters. The relationships among maximum density difference, rollover time, and initial density difference are shown in Fig. 12. As shown in Fig. 12, a linear relationship exists between maximum density difference and initial density difference. Thus, density fluctuation and rollover intensity increase with initial density difference. However, rollover time initially decreases rapidly and becomes stable after an initial density difference of 4 kg/m3. Thus, rollover under a small initial density difference lasts longer time. Therefore, as initial density difference increases, rollover type transforms from type 4 to type 3 in Table 4, and rollover intensity turns from steady to violent.
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Fig. 10. Velocity magnitude variations with time.
A rollover coefficient f, the unit is kg/(m3$s)] is defined. It combines the two parameters Drmax and Dt because these parameters cannot reflect rollover intensity individually.
f ¼
jDrmax Dr0 j Dt
(7)
In Equation (7), jDrmaxDr0j reflects the absolute density fluctuation between density difference in rollover evolution and initial density difference. Thus, the rollover coefficient reflects this fluctuation per unit time and can be used to describe rollover intensity in the LNG storage tank. Equation (7) indicates that the rollover coefficient increases with the increase in initial density difference. Therefore, rollover intensity increases with the increase in the rollover coefficient. So
rollover coefficient can be used to determine the critical density difference for the LNG tank rollover. 3.1.4. Rollover threshold for the 160,000 m3 LNG storage tank The relationships between the rollover coefficient and the initial density difference of the 160,000 m3 LNG storage tank are shown in Fig. 13. As shown in Fig. 13, the rollover coefficient changes gradually within a small scope when the initial density difference is smaller than 3 kg/m3, but increases rapidly afterward. The transition point (3 kg/m3) at the curve reflects a sudden variation of rollover intensity. Rollover is steady and poses minimal threat to the storage tank before this point but it becomes violent and harmful afterward. Thus, a density difference of 3 kg/m3 is proposed to be the
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Fig. 11. Vortex magnitude variations with time.
3.2. Rollover threshold for the 30,000 m3 and 5000 m3 LNG storage tanks
Table 4 Four situations of the rollover process. Category Maximum density difference Rollover time Rollover intensity
1 Large Large Uncertain
2 Small Small Steady
3 Large Small Violent
4 Small Large Steady
rollover threshold for the 160,000 m3 LNG storage tank (diameter: 80 m). Measures should be taken to ensure the safety of the LNG tank when the density difference in the tank becomes larger than the critical density difference.
Fig. 12. Maximum density difference and rollover time change with initial density difference.
Initial density differences of 0.5 kg/m3 and 1.0 kg/m3 to 9.0 kg/ m (with an interval of 1.0 kg/m3) are provided for the 30,000 m3 (diameter: 42 m) and the 5000 m3 (diameter: 22 m) LNG tanks, respectively, for rollover simulation. Based on the simulation results, the relationships between the rollover coefficient and initial density difference are shown in 3
Fig. 13. The rollover coefficient changes with the initial density difference (160,000 m3).
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Curve in Fig. 16 can be described by logarithmic function (The red curve (in the web version)). And the fitting function is Equation (9).
DTC ¼ 0:855 lnðVÞ þ 12:48
(9)
In the La Spezia LNG rollover accident, the LNG storage tank has a capacity of 50,000 m3 and a diameter of 49.1 m. The temperature difference between the injected LNG and the residual LNG is 4.53 K (Sarten, 1972). As the critical temperature difference of the 50,000 m3 LNG storage tank can be figured out to be 3.23 K using Equation (9), which is less than the rollover temperature difference, the simulation results are verified to be right. Thus the rollover thresholds could help warn the operators to take measures to prevent rollover at an early time. 4. Influencing factor analysis of the rollover threshold Fig. 14. The rollover coefficient changes with initial density difference (30,000 m3).
In previous sections, the rollover threshold of the LNG storage tanks are proposed through rollover simulations based on a twolayer model with a constant layer depth. However, LNG layer depths are different when stratification occurs, and volume storage tanks can also have different diameters. Thus, rollover evolution with different tank diameters and layer depths are simulated in this section. 4.1. Influence of tank diameter
Fig. 15. The rollover coefficient changes with initial density difference (5000 m3).
Fig. 14 (30,000 m3) and 15 (5000 m3). As shown in Figs. 14 and 15, the rollover coefficient exhibits the same variation trend as shown in Fig. 13. Critical density differences of 5 kg/m3 and 7 kg/m3 can also be proposed for the 30,000 m3 and 5000 m3 LNG storage tanks, respectively. 3.3. Verification of simulation results The density of LNG has a liner relationship with its temperature (The State Administration, 2003), which is shown in Equation (8).
r ¼ 1:35T
(8)
So the critical density differences could be converted into critical temperature difference using the equation. The result is shown in Table 5 and Fig. 16 (The black curve).
To study the influence of tank diameter, diameter changes from 79 m to 83 m (for every 1 m) are set for the 160,000 m3 tank, from 38 m to 42 m (for every 1 m) for the 30,000 m3 tank, and from 20 m to 24 m (for every 1 m) for the 5000 m3 tank. Based on the simulations, the relationships between the rollover coefficient and the initial density differences of the 160,000, 30,000, and 5000 m3 LNG storage tanks are shown in Figs. 17e19 respectively. As shown in Figs. 17e19, the critical density differences of the 160,000, 30,000, and 5000 m3 LNG storage tanks can be proposed to remain between 2 and 4, 4e6, and 6e8 kg/m3, respectively. Small changes to the tank diameter have minimal effect on the critical density difference. 4.2. Influence of layer depth To study the influence of layer depth, layer depths of 1, 1.5, and 2 m are set for the 160,000 m3 LNG storage tank (diameter: 80 m) for rollover simulation. The results are shown in Fig. 20. As shown in Fig. 20, the critical density difference of the 160,000 m3 LNG storage tank can be proposed to be approximately 3, 4, and 5 kg/m3 when the layer depth values are 1, 1.5, and 2 m, respectively. Critical density difference increases with layer depth. The contact area between the liquid layers and the tank wall enhances the stability of the interface and delays rollover evolution because contact area increases as layer depth increases.
Table 5 Critical temperature difference of the LNG storage tanks. Tank capacity (m3)
Critical density differences (kg/m3)
Critical temperature differences (K)
160,000 30,000 5000
3 5 7
2.22 3.70 5.18
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Fig. 16. Critical temperature difference changes with the tank capacity and its fitted curve. Fig. 19. Diameter influence results for the 5000 m3 LNG storage tank.
Fig. 17. Diameter influence results for the 160,000 m3 LNG storage tank. Fig. 20. Simulation results of different layer depths.
5. Conclusions Early research on rollover was aimed at its cause and evolution and lacked a rollover threshold. Through the development of a rollover evolution model and rollover simulations in LNG storage tanks, the conclusions drawn from this study can be summarized as follows. (1) Rollover intensities under varying initial density differences are dissimilar. Rollover occurs much earlier and violent at a bigger initial density difference. (2) A rollover coefficient is defined to describe rollover intensity in the LNG storage tank. Its transition point varying with the initial density difference is proposed to be the rollover threshold which is shown as critical density difference. Density difference in the LNG storage tanks should not exceed the threshold. (3) The critical density differences for the 160,000, 30,000, and 5000 m3 LNG storage tanks are 3, 5, and 7 kg/m3, respectively. Fig. 18. Diameter influence results for the 30,000 m3 LNG storage tank.
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(4) Small diameter changes in storage tanks with a certain volume have little effect on the critical density difference. Furthermore, critical density difference increases with increasing layer depth. Acknowledgments The paper is supported by the National Science and Technology Major Project of China (2011ZX 05026-006-07). This work is also supported by the CNOOC Shandong Chemical Engineering Co., Ltd Grant No. E-0810C011. Thank for the permission to publish this paper. References Acton, A., Van Meerbeke, R.C., 1972. Rollover in LNG storage e an industry view. In: LNG8 Conference, LA, U.S.A.,, pp. 738e742. An zhong, Gu, 2006. Liquefied Natural Gas (LNG) Technology. China Machine Press, Beijing (in Chinese) 2:235. Baker, N., Creed, M., 1996. Stratification and rollover in liquefied natural gas storage tanks. Process Saf. Environ. Prot. 74 (B1), 25L 30. Bashiri, A., Fatehnejad, L., 2006. Modeling and Simulation of Rollover in LNG Storage Tanks (Ph.D. thesis). International Gas Union. Bates, S., Morrison, D.S., 1997. Modeling the behavior of stratified liquid natural gas in storage tanks: a study of the rollover phenomenon. Int. J. Heat Mass Transf. 40 (R), 1875e1884. BP, 2013. BP Statistical Review of World Energy 2013. BP, London. Chatterjee, N., Geist, J.M., 1972. The effects of stratification on boil-off rates in LNG tanks. Pipeline Gas. J. 199 (40).
Chatterjee, N., Geist, J.M., 1976. Spontaneous stratification in LNG tanks containing nitrogen, paper 76-WA/PID-6. In: ENG, A.S.O.M. (Ed.). ASME Winter Annual Meeting, New York, 5 December. Flower, A., et al., 2002. Natural Gas in Asia: the Challenges of Growth in China, India, Japan and Korea. Oxford University Press, pp. 200e231. Germeles, A.E., 1975. A model for LNG tank rollover. Adv. Cryog. Eng. 21, 326e336. Guofa, Qiao, 2007. The Study on the Influential Factors of Evaporation Rate of the Liquefied Natural Gas Tank. China Doctor Dissertation of China. University of Petroleum, East China, p. 5. Heesatand, J., Shipman, C.W., Meader, J.W., 1983. A predictive model for rollover in stratified LNG tanks. AICHE J. 29 (2), 199e207. Lu, X.S., Lin, W.S., Gu, A.Z., Qin, Z.H., 2003. Numerical modeling of stratification and rollover in LNG and the improvements to Bates-Morrison Model. In: Proceedings of the 6th ASME-JSME Thermal Engineering Joint Conference, Kohala Coast, Hawaii. Paper TED-AJ03e606. Lukaszewski, M.W., Zimmerman, W.B.J., Tennant, M.T., et al., 2013. Application of inverse methods based algorithms to Liquefied Natural Gas (LNG) storage management. Chem. Eng. Res. Des. 91 (3), 457e463. Roh, S., Son, G., 2012. Numerical study of natural convection in a liquefied natural gas tank. J. Mech. Sci. Technol. 26 (10), 3133e3140. Roh, S., Son, G., Song, G., et al., 2013. Numerical study of transient natural convection in a pressurized LNG storage tank. Appl. Therm. Eng. 52 (1), 209e220. Sarten, 1972. LNG stratification and rollover. Pipe Gas J. 199. Shi, J.Q., Beduz, C., Scurlock, R.G., 1993. Numerical modelling and flow visualization of mixing of stratified layers and rollover in LNG. Cryogenics 33 (No.12), 1116e1124, 3(12). Shiming, Yang, Wenquan, Tao, 2006. Heat Transfer, fourth ed. Higher Education Press, p. 8 (in Chinese). The State Administration of Quality Supervision, Inspection and Quarantine of the People's Republic of China. GB/T19204. General Characteristics of Liquefied Natural Gas [S], 2003. Diss. World LNG Report e 2013 ed., International Gas Union (IGU), 2013.
Contents lists available at ScienceDirect
Journal of Loss Prevention in the Process Industries journal homepage: www.elsevier.com/locate/jlp
Simulating on rollover phenomenon in LNG storage tanks and determination of the rollover threshold Yuxing Li a, *, Zhenglong Li a, b, Wuchang Wang a a b
College of Pipeline and Civil Engineering, China University of Petroleum, Qingdao, Shandong, 266580, China China Petroleum Pipeline Research Institute, Langfang, Hebei, 065000, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 7 January 2015 Received in revised form 3 July 2015 Accepted 25 July 2015 Available online 1 August 2015
Rollover is a potential risk to the safety of LNG storage tanks during the LNG storage process, so study of its prevention method is very important. In this paper, rollover phenomenon in a liquefied natural gas (LNG) storage tank is modeled physically and mathematically. Its evolution is simulated using FLUENT™ software from the breakdown of stratification to the occurrence of rollover. Results show that the evolution consists of three phases: the initial phase where rollover occurs near the side wall of the storage tank; the turbulent phase where rollover transfers to the center of the tank; and the final phase where new layers evolve. Based on these phases, rollovers in 160,000, 30,000, and 5000 m3 LNG storage tanks are simulated at varying initial density differences, and a rollover coefficient is defined to describe rollover intensity. The simulations show that the rollover coefficient initially increases within a small scope and then increases rapidly with the increment of initial density difference. This turning point is chosen to be the rollover threshold, which is regarded as the critical density difference in this study. The critical density differences obtained from the simulation results of the 160,000, 30,000, and 5000 m3 LNG storage tanks are 3, 5, and 7 kg/m3, respectively, which can be used as their rollover criteria to ensure the safety of LNG storage tanks. © 2015 Elsevier Ltd. All rights reserved.
Keywords: LNG storage tank Rollover Rollover threshold Critical density difference Numerical simulation
1. Introduction Natural gas is becoming an increasingly important energy source. In the past decades, the global consumption of natural gas has increased by 28%, with natural gas accounting for nearly 24% of primary global energy demand (BP, 2013). As an important part of the natural gas industry, the liquefied natural gas (LNG) industry is experiencing a high-speed development stage. By the end of 2012, 98 regasification terminals existed worldwide, with a total regasification capacity of 649 million tons per annum. By the end of 2013, regasification terminals had over 44 million m3 of combined LNG storage capacity worldwide (World LNF Report, 2013). LNG imported to the receiving terminals generally come from different gas fields in different compositions. When LNG is injected to the tank and mixed with the residual LNG, stratification will happen. Stratification may also be attributed to the prior evaporation of N2 from LNG, which has a high content of it (Chatterjee and Geist, 1976). After stratification, the LNG layers in the tank become
* Corresponding author. Tel.: þ86 0532 86981818; fax: þ86 0532 86981822. E-mail address: [email protected] (Y. Li). http://dx.doi.org/10.1016/j.jlp.2015.07.007 0950-4230/© 2015 Elsevier Ltd. All rights reserved.
relatively stable, and natural convection circulates in each liquid layer because of the heat leaking into the tank, where LNG is stored at a low temperature of 160 C (Flower et al., 2002). The liquid in the upper layer tends to become dense after light components in the LNG evaporate because of the heat leak gained by the tank. However, the hydrostatic pressure at the upper layer prevents the evaporation of the lower layer, which allows the liquid to superheat and becomes less dense. When the densities of the layers approach equality, the interface between the two becomes unstable and mixes rapidly. This process is known as the rollover phenomenon. A sudden release of large amounts of boil-off gas, which causes a rapid increase in tank pressure and sometimes damage to the tank, accompanies this phenomenon. This event presents a considerable risk to the LNG terminal and enormous economic loss for the LNG company (Acton and Van Meerbeke, 1972). There were two well-known rollover accidents occurred in the Snam LNG storage and distribution station in La Spezia, Italy (1971) (Sarten, 1972) and the Partington LNG pitch peak station of the BG Company in the United Kingdom (1993) (Baker and Creed, 1996). These events made people aware of the damages caused by LNG rollover, and thus, many researchers have spent time studying this
Y. Li et al. / Journal of Loss Prevention in the Process Industries 37 (2015) 132e142
Nomenclature DAB S Fi ui
n nt r
T
t Gr g
b DT h
n sk sε
Mass diffusivity [m2/s] Mass fraction of each LNG component Fluid body force on the unit direction [N] Velocity of every direction [m/s] Kinematic viscosity coefficient of laminar flow [m2/s] Kinematic viscosity coefficient of turbulent flow [m2/s] Density [kg/m3] Temperature [K] Time [s] Grashof threshold Acceleration of gravity [m/s2] Expansion factor of fluid [1/K] Temperature difference of the fluid [K] Characteristic length of the container [m] Kinematic viscosity coefficient [m2/s] Turbulence Pr number of the k equation, sk ¼ 1.0 Turbulence Pr number of the ε equation, sε ¼ 1.3
phenomenon and have proposed their own rollover prediction models. Chatterjee and Geist (1972) were the first to propose a rollover model (i.e., the CeG model) (Chatterjee and Geist, 1972). Since then, a series of rollover models (Chatterjee and Geist, 1976; Germeles, 1975; Heesatand et al., 1983) (two-phase models that consist of a mass and heat transfer phase and a mixture phase) have been proposed using double-diffusive convection theory and the assumption of a stationary interface between the layers, which are basically based on the CeG model, until Shi (1993) (Shi et al., 1993) found the migrating interface from experiments. After the rollover accident in the United Kingdom, Bates and Morrison (1997) published the first three-phase model (i.e., the BateseMorrison model), in which rollover evolution consists of three phases: a stationary interface phase, a migrating interface phase, and a rollover phase. In China, Gu (2003) (Lu et al., 2003) extended the BateseMorrison model into four phases: a stationary interface phase, a second phase where the liquid in the lower layer is carried into the upper layer, a third phase where the interface of the layers is penetrated by a jet stream, and a rollover phase. The influence of evaporation on density, which improves accuracy, was also considered in this model. Other researchers have also investigated the rollover phenomenon, but their studies are mostly based on previous research (Bashiri and Fatehnejad, 2006; Roh et al., 2013; Lukaszewski et al., 2013; Roh and Son, 2012). The aforementioned rollover models explain the evolution from stratification formation to rollover occurrence. However, no model has ever proposed a threshold to judge an LNG rollover. Thus, the judgment of a rollover in LNG storage tanks is basically empirical and only a few basic measurements are available to prevent rollover from occurring in large storage tanks, such as separating the storage of LNG from different gas fields, selecting filling modes, and monitoring nitrogen content (An zhong, 2006). Therefore, research on rollover threshold can predict rollover accurately and ensure the security of LNG storage tanks. 2. Development of rollover CFD model and analysis on simulation results 2.1. Description of the rollover physical model In a storage tank, LNG typically evolves into many layers after
133
Gk,Gb
Turbulent kinetic energy. The former is generated from the velocity gradient of laminar flow, whereas the latter is buoyancy. 2 mt Turbulence viscosity coefficient, mt ¼ rCm kε C1ε, C2ε, C3ε, Cm Constant numbers, C1ε ¼ 1.44, C2ε ¼ 1.92, Cm ¼ 0.09 t0 Starting time of rollover, the time when the densities of the monitoring points begin to change [s]. tf Ending time of rollover, the time when the densities of the monitoring points stop changing [s]. Dt Rollover time, equal to the difference value between t0 and tf [s]. Dr0 Initial density difference, the density difference between the upper and lower layers after initialization [kg/m3]. Drmax Maximum density difference, the difference between the maximum and minimum densities in rollover evolution [kg/m3]. V Capacity of the LNG storage tank [m3]. DT C Critical temperature difference [K].
stratification, and rollover generally occurs between the two adjacent layers. Some studies indicate that heat leaking into the tank results in a density change in LNG, and that density difference among LNG at different depths leads to stratification and rollover. Thus, a 2D LNG storage tank model is developed based on the following assumptions and simplifications, as shown in Fig. 1. (1) LNG is an incompressible Newtonian fluid in this model. (2) All layers have the same depth (1 m) and are mixed uniformly at the beginning. Two adjacent layers are chosen as an object. (3) The LNG in the tank is assumed to be at the transition point between stratification and rollover; thus, stratification evolution can be omitted from the simulation. Meanwhile, nine monitoring points are set on the model to record LNG density change during rollover evolution (monitoring points 2, 4, 5, 6, and 8 are located at the midpoint).
2.2. Development of the rollover mathematical model 2.2.1. Governing equations (1) Continuous equations
vux vuy þ ¼ 0: vx vy
(1)
(2) Momentum equations
d ux þ uy 1 vp vp þ þ ðn þ nt ÞV2 ux þ uy þ Fx þ Fy : ¼ r vx vy dt Among these;
Fx ¼ 0 : Fy ¼ g
(2) (3)
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Y. Li et al. / Journal of Loss Prevention in the Process Industries 37 (2015) 132e142 Table 1 Flow state discrimination of the natural convection by Grashof number.
Fig. 1. Simplified model and monitoring points for rollover (160,000 m3 LNG storage tank).
(3) Composition equation
! vS v2 S v2 S ¼ DAB þ : vt vx2 vy2
(4)
2.2.2. Discrimination of the rollover flow model Natural convection is caused by the uneven temperature field of fluid itself. The uneven temperature field results in the uneven density field, which produces the buoyancy lift to be the power of nature convection. As rollover is caused by the uneven density field in the LNG storage tank, it is typical natural convection. And the flow state of natural convection characterize by Grashof number (Gr ¼ gbDTh3/n2) as in Table 1 (Shiming and Wenquan, 2006; Guofa, 2007). In this paper, rollover in three type of LNG storage tanks with different capacity are researched. Their parameters are showed in Table 3, with the property parameters of LNG showing in Table 2, Grashof numbers can be calculated and the flow state of rollover can be characterize to be turbulent flow as it showed in Table 3. Thus, a turbulent model should be selected to simulate rollover evolution in the LNG storage tank. Among the existing turbulent models, kε model is suitable to this situation, and it is widely used by its commonality and economy and reasonable accuracy, so the kε equation is selected to simulate rollover evolution in the LNG storage tank.
Flow state
Grashof number
Laminar flow Turbulent flow
1.43 104~3 109 >2 1010
The boundary conditions for S (mass fraction of LNG component) and k equation are vS/vy ¼ 0 and vk/vy ¼ 0, and the dissipation rate of k is assumed to be equal in the wall-adjacent control volume. The grid of the model is generated using the geometry preprocessor of the gambit program and a structured grids is adopted with fine mesh next to the wall surfaces. The total number of grid cells amounted to over 1.6 104 for the 160,000 m3 tank, 8 103 for the 30,000 m3 tank and 4 103 for the 5000 m3 tank (Fig. 3). As the density difference between the LNG layers leads to rollover, the upper layer in the model (Fig. 1) is initialized with a larger density than the lower layer. And the initial velocity of the 2D model is set to be ux ¼ 0, uy ¼ 0. The simulations are regarded as being convergent when the residuals of continuity, velocity, turbulent kinetic energy (k), and turbulent diffusion rate (epsilon) all decreased to below 1 103 (Fig. 4).
2.3. Analysis on the simulation results In this section, the rollover evolution in a 160,000 m3 tank with a diameter of 80 m is simulated using FLUENT™ software. Moreover, a mixture model, kε equation, and wall boundary conditions are selected. A structured grid generates a mesh in the computational domain. The liquid in the upper layer is given at 424 kg/m3, which is 1 kg/m3 greater than the liquid in the lower layer. The density contours shown in Fig. 5 reflect the rollover evolution in the 160,000 m3 tank. The contours observed in this study are shown as the left half of the physical model because rollover occurs symmetrically in the tank. The following information can be derived from Fig. 5.
(1) Turbulent kinetic energy equation (k equation):
v v v ðrkÞ þ ðrkui Þ ¼ vt vxi vxj
" mþ
# mt vk þ Gk þ Gb rε: sk vxj
(5)
(2) Turbulent diffusion equation (ε equation):
v v v ðrεÞ þ ðrεui Þ ¼ vt vxi vxj
"
# m vε ε mþ t þ C1ε ðGk þ C3ε Gb Þ k sε vxj
C2ε r
ε2 : k (6)
2.2.3. Boundary and initial conditions Fig. 2 is the domain and boundaries of the LNG storage tank model. The model domain is fluid domain and a no-slip boundary condition was applied to the walls. Besides, a Standard Wall Function is selected in the simulation as a supplement to the kε equation.
(1) At 100 s, the interface closed to the tank wall begins to migrate down to the lower layer, which results in a mixture of the two layers and vortices emerging at the interface. (2) At 150 s, the interface of the two layers becomes tortuous, which makes the layers unstable. (3) At 200 s, the stratification in the tank is broken down, which results in rapid mixing of the two layers and the formation of numerous vortices. Meanwhile, the rollover near the side wall slows down and the mixture is nearly completed. It can be observed that vortices appear and transfer on the interface between the layers. Given that monitoring points 4, 5, and 6 are located on the interface, the variations of vortex magnitudes on these points (Fig. 6) can reflect vortex evolution. As shown in Fig. 6, the vortex magnitudes of monitoring points 4 and 6 (near the side wall of the storage tank) increase rapidly from 50 s to 100 s, which indicates the formation of vortices and the rollover of LNG near the side wall. However, the vortex magnitude of monitoring point 5 (at the center of the tank) is maintained in this period, which indicates a stable center in the storage tank. Between 100 s and 200 s, the vortex magnitudes of monitoring points 4 and 6 decline rapidly, whereas that of monitoring point 5 increases rapidly. These results can be attributed to the LNG
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Table 2 Physical property parameters of LNG. Name
Density rkg/m3
Height h/m
Temperature T/K
Environment temperature/K
Dynamic viscosity n/(kg/m.s)
Value
424
80
112
298
1.179e-04
Table 3 Parameters of LNG storage tanks and the flow state discrimination. Capacity/m3 Diameter/m Height/m Grashof number Flow state
160,000 80 32 2.1 1013 Turbulent flow
30,000 42 22 6.8 1012 Turbulent flow
5000 22 13 1.4 1012 Turbulent flow
Fig. 2. Domain and boundaries of the tank model.
mixture being nearly complete close to the side wall while only beginning at the center during this period. After 200 s, the vortex magnitudes of all monitoring points become smooth and steady. The rollover in the entire tank ends gradually with the finished mixture of the two layers and the
Fig. 5. Density contours of the model during the rollover evolution.
evolution of new layers. The preceding analysis shows that the density difference in the LNG storage tank causes the rollover, which leads to an unstable LNG and rollover evolution from the side wall to the center of the storage tank. The simulation results also show that the rollover evolution consists of three phases. Phase 1: Rollover occurs near the side wall of the storage tank. During this phase, the dense liquid in the upper layer begins to migrate down to the lower layer because of the unstable interface near the side wall. The extruding liquid in the lower layer moves into the upper layer, and thus, the velocity magnitude and vortex magnitude near the side wall of the tank increase. Phase 2: Rollover transfers to the center of the tank. During this phase, the interface between the layers begins to twist under the disturbance of the rollover near the side wall, which allows the rollover to transfer to the center of the tank. Meanwhile, the mixture of the layers, the velocity magnitude, and the vortex magnitude in the tank are enhanced. Phase 3: Evolution of new layers. Rollover evolution ends with
Fig. 3. Part of the fine mesh of 160,000 m3 tank.
Fig. 4. Residual of 160,000 m3 tank simulation.
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time during this phase, and new layers are formed under the effect of gravity. The LNG in the storage tank becomes stable again. 3. Rollover threshold for LNG storage tanks Rollover studies aim to prevent rollover and ensure safety in LNG storage tanks. Previous studies have indicated that the cause of stratification and rollover is density difference. Density and temperature differences in varying depths are observed when stratification occurs in a tank. Given that temperature difference results in density difference, a series of initial density differences between layers is provided to the rollover model for FLUENT™ simulation. Based on the simulation results of rollover evolution, a rollover threshold can be determined to judge if rollover is occurring in the LNG storage tank. Three types of tanks with volumes of 160,000, 30,000, and 5000 m3, and diameters of 80, 42, and 22 m, respectively, are simulated in this section. 3.1. Rollover threshold for the 160,000 m3 LNG storage tank In this section, rollover evolution under varying density differences is simulated to determine a rollover threshold. The study that used the 160,000 m3 LNG storage tank is taken as an example. 3.1.1. Determining rollover time Simulation result of the 160,000 m3 tank shown in Fig. 7 (the diameter is 80 m and the initial density difference is 1 kg/m3) is chosen as an example to explain the density-changing trend of each monitoring point. As shown in Fig. 7, the densities at monitoring points 1, 2, and 3 (at the bottom of the storage tank) increase from the initial density to the maximum density, whereas the densities at monitoring points 7, 8, and 9 (at the top of the storage tank) change inversely. However, the densities at monitoring points 4, 5, and 6 (on the interface between the layers) exhibit rapid fluctuations during rollover evolution and share the same mediate density at the starting and finishing times of rollover. Thus, the difference value between the average density of monitoring points 1, 2, 3, 7, 8, and 9 and the average density of monitoring points 4, 5, and 6 can reflect density fluctuation in rollover evolution. The variation of density fluctuation with time is shown in Fig. 8. The time when density fluctuation starts is defined as the beginning time of rollover, and the time when density fluctuation
stops is defined as the finishing time of rollover. The value between them is defined as the rollover time.
3.1.2. The influence of density difference on rollover 1) Analysis on the density contours The density contours shown in Fig. 9 are obtained from the simulation results (in the 160,000 m3 LNG storage tank with a diameter of 80 m) under a series of initial density differences (0.5, 1, 3, 5, and 7 kg/m3) at 100 s. The density contours in Fig. 9 can be divided into the following types. (1) When the initial density differences are 0.5 kg/m3 and 1 kg/ 3 m , rollover occurs near the side wall of the storage tank (Phase 1 in Section 2.3). (2) When the initial density differences are 5 kg/m3 and 7 kg/m3, rollover nearly evolves to the end (Phase 3 in Section 2.3). The velocity magnitudes of points 1, 2, 3, 7, 8, and 9 (at the bottom and top of the storage tank) and the vortex magnitudes of points 4, 5, and 6 (on the interface between layers) are recorded during rollover evolution to compare the rollover intensity under different initial density difference. 2) Analysis on the velocity magnitude The velocity magnitudes that changed with time under a series of initial density differences (1, 3, 4, 5, and 6 kg/m3) are shown in Fig. 10. As shown in Fig. 10, velocity magnitudes with initial density differences of 4, 5, and 6 kg/m3 are significantly larger than others during rollover evolution. The value difference among them is obvious. 3) Analysis on the vortex magnitude The vortex magnitudes that changed with time under a series of initial density differences (1, 3, 4, 5, and 6 kg/m3) are shown in Fig. 11. As shown in Fig. 11, vortices with bigger magnitudes emerge near the side wall of the storage tank (monitoring points 4 and 6) at an early time (approximately 50 s) when the initial density difference is over 3 kg/m3. These vortices transfer rapidly to the center of the tank, which allows the vortex magnitude at the center (monitoring point 5) to rapidly reach a high value (at approximately 100 s). Under this situation, the vortex magnitude of the entire storage tank peaks and decreases sharply within a short time, which result in a violent rollover in the LNG storage tank. By contrast, vortices emerge at a later time (at approximately 100 s or 200 s) with smaller vortex magnitudes and slower transfer speeds when the initial density difference is less than 3 kg/m3, and the vortex magnitude of the entire storage tank fluctuates for a long time, which results in a steady rollover in the LNG storage tank. 4) Summary
Fig. 6. Variations of vortex magnitudes with time.
From the preceding analysis, the rollover in the 160,000 m3 LNG storage tank can be divided into two types based on intensity. When the initial density difference is less than 3 kg/m3, rollover occurs late and lasts long. Velocity and vortex magnitudes are small, which makes rollover relatively steady. However, rollover occurs early and finishes within a short time when the initial density difference is over 3 kg/m3. Velocity and vortex magnitudes are large, which makes rollover violent.
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Fig. 7. Density variations with time at nine monitoring points.
Fig. 9. Comparison of the density contours with different initial density differences at the time of 100s.
Fig. 8. Variation of density fluctuation with time.
3.1.3. Definition of the rollover coefficient Initial density difference (Dr0) is proven to be the main cause of rollover through simulation results. Moreover, it is the key parameter to determine rollover time (Dt) and maximum density difference during rollover evolution (Drmax). Rollover can be
divided into four types (Table 4), which combines the two aforementioned parameters. The relationships among maximum density difference, rollover time, and initial density difference are shown in Fig. 12. As shown in Fig. 12, a linear relationship exists between maximum density difference and initial density difference. Thus, density fluctuation and rollover intensity increase with initial density difference. However, rollover time initially decreases rapidly and becomes stable after an initial density difference of 4 kg/m3. Thus, rollover under a small initial density difference lasts longer time. Therefore, as initial density difference increases, rollover type transforms from type 4 to type 3 in Table 4, and rollover intensity turns from steady to violent.
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Fig. 10. Velocity magnitude variations with time.
A rollover coefficient f, the unit is kg/(m3$s)] is defined. It combines the two parameters Drmax and Dt because these parameters cannot reflect rollover intensity individually.
f ¼
jDrmax Dr0 j Dt
(7)
In Equation (7), jDrmaxDr0j reflects the absolute density fluctuation between density difference in rollover evolution and initial density difference. Thus, the rollover coefficient reflects this fluctuation per unit time and can be used to describe rollover intensity in the LNG storage tank. Equation (7) indicates that the rollover coefficient increases with the increase in initial density difference. Therefore, rollover intensity increases with the increase in the rollover coefficient. So
rollover coefficient can be used to determine the critical density difference for the LNG tank rollover. 3.1.4. Rollover threshold for the 160,000 m3 LNG storage tank The relationships between the rollover coefficient and the initial density difference of the 160,000 m3 LNG storage tank are shown in Fig. 13. As shown in Fig. 13, the rollover coefficient changes gradually within a small scope when the initial density difference is smaller than 3 kg/m3, but increases rapidly afterward. The transition point (3 kg/m3) at the curve reflects a sudden variation of rollover intensity. Rollover is steady and poses minimal threat to the storage tank before this point but it becomes violent and harmful afterward. Thus, a density difference of 3 kg/m3 is proposed to be the
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139
Fig. 11. Vortex magnitude variations with time.
3.2. Rollover threshold for the 30,000 m3 and 5000 m3 LNG storage tanks
Table 4 Four situations of the rollover process. Category Maximum density difference Rollover time Rollover intensity
1 Large Large Uncertain
2 Small Small Steady
3 Large Small Violent
4 Small Large Steady
rollover threshold for the 160,000 m3 LNG storage tank (diameter: 80 m). Measures should be taken to ensure the safety of the LNG tank when the density difference in the tank becomes larger than the critical density difference.
Fig. 12. Maximum density difference and rollover time change with initial density difference.
Initial density differences of 0.5 kg/m3 and 1.0 kg/m3 to 9.0 kg/ m (with an interval of 1.0 kg/m3) are provided for the 30,000 m3 (diameter: 42 m) and the 5000 m3 (diameter: 22 m) LNG tanks, respectively, for rollover simulation. Based on the simulation results, the relationships between the rollover coefficient and initial density difference are shown in 3
Fig. 13. The rollover coefficient changes with the initial density difference (160,000 m3).
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Curve in Fig. 16 can be described by logarithmic function (The red curve (in the web version)). And the fitting function is Equation (9).
DTC ¼ 0:855 lnðVÞ þ 12:48
(9)
In the La Spezia LNG rollover accident, the LNG storage tank has a capacity of 50,000 m3 and a diameter of 49.1 m. The temperature difference between the injected LNG and the residual LNG is 4.53 K (Sarten, 1972). As the critical temperature difference of the 50,000 m3 LNG storage tank can be figured out to be 3.23 K using Equation (9), which is less than the rollover temperature difference, the simulation results are verified to be right. Thus the rollover thresholds could help warn the operators to take measures to prevent rollover at an early time. 4. Influencing factor analysis of the rollover threshold Fig. 14. The rollover coefficient changes with initial density difference (30,000 m3).
In previous sections, the rollover threshold of the LNG storage tanks are proposed through rollover simulations based on a twolayer model with a constant layer depth. However, LNG layer depths are different when stratification occurs, and volume storage tanks can also have different diameters. Thus, rollover evolution with different tank diameters and layer depths are simulated in this section. 4.1. Influence of tank diameter
Fig. 15. The rollover coefficient changes with initial density difference (5000 m3).
Fig. 14 (30,000 m3) and 15 (5000 m3). As shown in Figs. 14 and 15, the rollover coefficient exhibits the same variation trend as shown in Fig. 13. Critical density differences of 5 kg/m3 and 7 kg/m3 can also be proposed for the 30,000 m3 and 5000 m3 LNG storage tanks, respectively. 3.3. Verification of simulation results The density of LNG has a liner relationship with its temperature (The State Administration, 2003), which is shown in Equation (8).
r ¼ 1:35T
(8)
So the critical density differences could be converted into critical temperature difference using the equation. The result is shown in Table 5 and Fig. 16 (The black curve).
To study the influence of tank diameter, diameter changes from 79 m to 83 m (for every 1 m) are set for the 160,000 m3 tank, from 38 m to 42 m (for every 1 m) for the 30,000 m3 tank, and from 20 m to 24 m (for every 1 m) for the 5000 m3 tank. Based on the simulations, the relationships between the rollover coefficient and the initial density differences of the 160,000, 30,000, and 5000 m3 LNG storage tanks are shown in Figs. 17e19 respectively. As shown in Figs. 17e19, the critical density differences of the 160,000, 30,000, and 5000 m3 LNG storage tanks can be proposed to remain between 2 and 4, 4e6, and 6e8 kg/m3, respectively. Small changes to the tank diameter have minimal effect on the critical density difference. 4.2. Influence of layer depth To study the influence of layer depth, layer depths of 1, 1.5, and 2 m are set for the 160,000 m3 LNG storage tank (diameter: 80 m) for rollover simulation. The results are shown in Fig. 20. As shown in Fig. 20, the critical density difference of the 160,000 m3 LNG storage tank can be proposed to be approximately 3, 4, and 5 kg/m3 when the layer depth values are 1, 1.5, and 2 m, respectively. Critical density difference increases with layer depth. The contact area between the liquid layers and the tank wall enhances the stability of the interface and delays rollover evolution because contact area increases as layer depth increases.
Table 5 Critical temperature difference of the LNG storage tanks. Tank capacity (m3)
Critical density differences (kg/m3)
Critical temperature differences (K)
160,000 30,000 5000
3 5 7
2.22 3.70 5.18
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Fig. 16. Critical temperature difference changes with the tank capacity and its fitted curve. Fig. 19. Diameter influence results for the 5000 m3 LNG storage tank.
Fig. 17. Diameter influence results for the 160,000 m3 LNG storage tank. Fig. 20. Simulation results of different layer depths.
5. Conclusions Early research on rollover was aimed at its cause and evolution and lacked a rollover threshold. Through the development of a rollover evolution model and rollover simulations in LNG storage tanks, the conclusions drawn from this study can be summarized as follows. (1) Rollover intensities under varying initial density differences are dissimilar. Rollover occurs much earlier and violent at a bigger initial density difference. (2) A rollover coefficient is defined to describe rollover intensity in the LNG storage tank. Its transition point varying with the initial density difference is proposed to be the rollover threshold which is shown as critical density difference. Density difference in the LNG storage tanks should not exceed the threshold. (3) The critical density differences for the 160,000, 30,000, and 5000 m3 LNG storage tanks are 3, 5, and 7 kg/m3, respectively. Fig. 18. Diameter influence results for the 30,000 m3 LNG storage tank.
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