Analysis of leaked LNG flow and consequent thermal effect for safety in LNG cargo containment system

Ocean Engineering 113 (2016) 276–294

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Analysis of leaked LNG flow and consequent thermal effect for safety in LNG cargo containment system Sung Woong Choi a, Han Sang Kim b,n, Woo Il Lee c,nn a

Korea Institute of Machinery and Materials, LNG Cryogenic Technology Center, Gimhae-si, Gyeongsangnam-do 621-842, Republic of Korea Department of Mechanical Engineering, Gachon University, Gyeonggi-do 461-701, Republic of Korea c School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-742, Republic of Korea b

art ic l e i nf o

a b s t r a c t

Article history: Received 9 September 2015 Accepted 27 December 2015

As the large liquefied natural gas (LNG) carrier has emerged as an important LNG transportation, rigorous safety analysis of the carrier is required to achieve reliable technological solutions for safely transporting LNG. The present study uses numerical simulation (conjugate thermal analysis) to investigate LNG leakage and the consequent temperature change of the hull's steel plate in a LNG cargo containment system (CCS). To validate the numerical approach used in the study, experimental investigation on the temperature behavior of the hull's plate was conducted. The experimentally determined ductile-tobrittle transition temperature (DBTT) was used as the index of critical temperature for the hull's plate. A numerical simulation was used to estimate the behavior of cryogenic liquid in a porous structure in an LNG CCS and the resulting temperature change of the hull's plate due to LNG leakage under any filling conditions (various inlet pressures of leaking LNG and defect sizes). According to the numerical study, the thermal safety of the hull's plate is guaranteed in case where the LNG leakage hole is 2 mm in diameter. The critical leakage hole size where temperature of hull's plate did not reach a DBTT lies between 2 mm and 5 mm under the leakage conditions. & 2016 Elsevier Ltd. All rights reserved.

Keywords: Conjugate thermal analysis Hull's steel plate Ductile to brittle transition temperature (DBTT) Cryogenic liquid Liquefied natural gas (LNG)

1. Introduction Liquefied natural gas (LNG) has been an important global energy source for the past 30 years, and it is expected that this trend will continue over the next several decades in order to improve energy security and diversity. As the demand for natural gas increases, super-sized LNG carriers (such as Adam LNG, built in 2014 with a 162,000 m3 capacity) have emerged as one of the most efficient forms of long-distance transportation of LNG. Furthermore, the offshore production of LNG—such as LNG Floating Production Storage Offloading (FPSO)—will grow along with the trend of enlarging LNG storage system. LNG carriers have usually operated either fully loaded or with a minimum of cargo during the ballast voyage. The LNG tank is typically filled at more than 95% of the tank height under fully loaded condition or less than 10% under ballast condition. A number of incidents, caused by minor damages at the insulation system, were reported mostly for fully loaded tanks in the 1980s. However, recent demands for n

Corresponding author. Corresponding author. E-mail addresses: [email protected] (S.W. Choi), [email protected] (H.S. Kim), [email protected] (W.I. Lee). nn

http://dx.doi.org/10.1016/j.oceaneng.2015.12.046 0029-8018/& 2016 Elsevier Ltd. All rights reserved.

safety considerations have indicated a need for LNG carrier designs that require LNG carriers to be stable in any operating conditions under partially loaded and fully loaded conditions. LNG FPSO/ FSRUs and their shuttle vessels must also be able to operate under partially loaded condition (Shin et al., 2003). This requires that these LNG carriers with large CCS operate under various filling level condition, for which the risk of CCS should carefully be considered. Assessment of the possible risk associated with partial loading at any filling level is a new technological challenge and draws increasing attention in the LNG industry (Lee et al., 2007). To address these issues, several researchers have performed safety analyses of large-sized LNG storage and designs of cargo system, to ensure reliable technological solutions for the safe operation of these systems. Lee (2006) carried out a comparative risk assessment for KOGAS LNG tank designs using a quantitative fault tree methodology and found out the expected frequencies of an external LNG leakage. Bae et al. studied the structure of LNG CCS, using two- and three-dimensional models of LNG leakage in Mark III system LNG carriers, and evaluated CCS safety according to the international gas code standard. Among safety issues in LNG-related facilities, a major concern is the reliability of a LNG CCS for LNG carriers. Lots of research have been carried out to develop new type of LNG CCS with larger capacities and higher

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Nomenclature Cij Dij Ea ECVN g ! F h H k kp M _ bc m NuL Pr p R Ra Si t T

Inertia loss term viscous loss term energy [J/s] energy absorbed in a CVN impact test [J] acceleration due to gravity body force [N] convection coefficient [W=m2 K] sensible enthalpy [kJ/kg] thermal conductivity [W=mK] permeability [m2] mass of the hammer [kg] mass change from b phase to c phase [kg/s] Nusselt number Prandtl number pressure [Pa] length of the specimen Rayleigh number Source term for the i-th (x, y, or z) momentum conservation equation Time Temperature

thermal performance, as Bergan et al. (2009) report. Studies of damage in development of LNG CCS are significant because LNG CCS is subjected to various harsh conditions. These conditions may include thermal stresses due to the temperature differences between the LNG and the ambient environment, as well as internal and external mechanical loads such as an LNG sloshing load during LNG carrier voyages because of heavy weather or ballast voyages (Kontovas and Psaraftis, 2009). LNG leakage due to CCS damage or failure can have dangerous effects on the carrier's structure, including hull's damage. Han et al. (2011) addressed the structural safety of LNG carriers that were affected by cryogenic LNG. They examined the structural behavior of the inner hull's structure following the deformation under cryogenic conditions due to an applied load. In this study, we conduct a conjugate heat transfer analysis of LNG leakage in CCS. Assuming that leaked LNG mostly flows through a flat joint made of porous media, it is essential to investigate cryogenic liquid behavior in porous media so as to characterize LNG leakage in CCS. In order to explain the behavior of cryogenic liquids in porous structures, it is essential to understand the flow phenomena of cryogenic liquids subjected to evaporation. The micro-structure and material properties of the porous media significantly affect flow behavior in porous media, and lots of researchers (Klinkenberg, 1941; Marmoret et al., 1912; Ladd, 1960; Olsen, 1965; Langfelder et al., 1900) have investigated various characteristics of the permeability of porous media over the past few decades. Especially, Marmoret et al. (1912) demonstrated the permeability of a material to a gas and anisotropic glass to air for the anisotropic factors, and attempted to determine how air permeability changes with fluid contents for compacted media. Meanwhile, various researchers performed analysis of conjugate heat and mass transfer with involving natural convection. Serrano-Arellano et al. (2014) conducted numerical study of the double diffusive convection phenomena in a closed cavity with turbulent flow. The result showed that contaminant point sources located near bottom wall decrease as the Rayleigh number increases; Nusselt number was directly affected by the contaminant source location. Kuznetsov and Sheremet (2011)

T amb U eff va jvj ! v dr;a ! vm

277

ambient temperature

effective thermal conductivity [W/mK] velocity for phase a [m/s] magnitude of velocity [m/s] drift velocity for phase a [m/s] mass-averaged velocity [m/s]

Greek symbols

α ρ μ φ ϕ

Volume fraction Density of the material [kg=m3 ] Viscosity [Pa s] angle of fall angle at the end of the swing

Subscript a, b, c, p phase m mixture dr drift L length of flat plate

performed a numerical study of conjugated heat and mass transfer by natural convection in an enclosure. The configuration consisted of a three-dimensional enclosure with solid wall of finite thickness and conductivity; a heat and mass source on the bottom of the cavity with constant temperature and concentration were used. In the results, Nusselt and Sherwood number data were mainly presented with Rayleigh and dimensionless time, buoyancy ratio. In addition, the effect of the mass source size on the heat and mass transfer regime was investigated. In addition, the conjugate heat transfer phenomena in a porous media was introduced. Al-Farhany and Turan (2011) conducted the steady conjugate double-diffusive natural convective heat and mass transfer in a two-dimensional variable porosity layer sandwiched between two walls using a concentration variable in a non-Darcy model. They found the heat transfer rate increased when the Rayleigh number increased, while it decreased when the thermal conductivity ratio and the wall thickness increased. The present numerical study is for the conjugate heat and mass transfer involved with the cryogenic multiphase flow behavior (Xu et al., 2004; Van Sciver, 2005; Chen et al., 2004) that various researchers have investigated. Among them, Chen et al. (2004) conducted analyses of temperature and pressure changes in LNG tanks. Kumazawa and Whitcomb (2008) numerically analyzed the spread of natural gas in the atmosphere following the accidental release of LNG from a tank ship in an open area. Kuznetsov and Sheremet also (Kuznetsov and Sheremet, 2009) performed a conjugate heat transfer analysis containing two-dimensional laminar convective-conduction heat transfers in a rectangular enclosure, under condition of mass transfer within a cavity with local heat sources. However, most numerical studies for the flow behavior of cryogenic liquid were conducted without considering the effect of evaporation; therefore, the validity of the results remained uncertain. Lee et al. (2011) demonstrated a numerical method for a conjugate heat transfer analysis of leaked LNG, similar to the present study. However, their study did not consider experimentally validated properties, such as the unsaturated permeability and thermophysical properties of porous media, which vary with applied pressures and environmental temperatures. Moreover, their investigation of CCS control volume was limited in

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the flat joint area of the secondary insulation panel, while the present study includes the flow effect through the flat joint in the primary and secondary panels of CCS structure. As noted above, to successfully design safe LNG CCS, it is necessary to understand LNG behavior in porous media. Permeability is a key parameter for LNG flow behavior in porous media, and it is crucial to incorporate the thermophysical properties of LNG CCS composition materials in a heat transfer analysis, in order to predict and describe the behavior of LNG. In our previous work (Choi et al., 2015), we developed experimental and numerical approaches to analyze cryogenic liquid behavior in porous media, based on experimentally determined properties such as permeability and thermophysical material properties. The present paper reports LNG leakage flow and consequent temperature change of hull's plate in CCS, based on experimentally determined the ductile-to-brittle transition temperature (DBTT) of material of the hull's plate. Experimental investigations are discussed, and the simulation results are compared with experiment to validate the numerical approach developed in this study. The numerical simulation method is explained, and parametric simulation analysis is performed for various LNG leakage conditions.

2. Problem description 2.1. Background 2.1.1. Description of the cargo containment system (CCS) LNG carriers are classified as either Moss-type or Membranetype carriers, and the CCS for Membrane-type carriers is classified into NO 96 or Mark III systems, designed by Gaz Transport and Technigaz (GTT), France (Kim and Lee, 2005). This is shown in Fig. 1. NO 96 system has a cryogenic liner made of two identical metallic membranes and two independent insulation layers. The primary and secondary membranes are made of invar, a 36% nickel-steel alloy, which is 0.7 mm thick. The primary membrane contains the LNG cargo while the secondary membrane, identical to the primary, ensures redundancy in case of leakage. Each of the 500-mm-wide invar strakes is continuously spread along the tank walls and is evenly supported by the primary and the secondary insulation layers. The primary and secondary insulation layers consist of a load-bearing system made of prefabricated plywood boxes and filled with expanded perlite. The thickness of the primary layer is adjustable from 170 mm to 250 mm, so as to meet any boil-off gas (BOG) requirement; the typical thickness of the secondary layer is 300 mm. The primary layer is secured by means of the primary couplers, themselves fixed to the secondary coupler

assembly. The secondary layer is laid and evenly supported by the inner hull through load-bearing resin ropes, and fixed by means of the secondary couplers anchored to the inner hull (Deybach and Gavory, 2008). A Mark III system has a cryogenic liner composed of a primary metallic membrane that is positioned on top of a prefabricated insulation panel, including a complete secondary membrane. The primary membrane is made of corrugated stainless steel (304 L, 1.2 mm thickness). It contains the LNG cargo and is directly supported by and attached to the insulation system. The secondary membrane is made of a composite laminated material: a thin sheet of aluminum between the two insulation layers. The insulation consists of a load-bearing system made of prefabricated panels in reinforced polyurethane foam, including both primary and secondary insulation layers and the secondary membrane. The thickness of the insulation is adjustable from 250 mm to fulfill any BOG requirement. The panels are secured to the inner hull by means of resin ropes, which serve a double purpose of anchoring the insulation and evenly spreading the loads (Deybach and Gavory, 2008). Regarding the two CCS types, in the present study, LNG leakage could be a more serious issue for the Mark III system than for the NO 96 system because of structural differences: the NO 96 system consists of plywood boxes, while the Mark III system has a flat joint inside the panel. A cryogenic LNG would leak into a porous medium, such as glass wool, which is susceptible to leakage problems in the Mark III system. 2.1.2. Failure mode and effect analysis (FMEA) study for the hull's structure In the LNG CCS, CCS can be damaged depending on the various accident scenarios. Various risk scenarios regarding the cargo itself and the hull's structure of Mark III system can be estimated quantitatively by means of a failure mode and effect analysis (FMEA) study. As listed in Table 1, the damage or failure may occur in the process of manufacturing, mitigation, and compensation (Bae et al.). 2.2. General remarks about problem definition and assumptions The purpose of the present analysis is to discern if the LNG leakage creates a brittle state in the hull's plate. The Mark III CCS consists of two separate spaces that are filled with insulation materials to keep higher thermal efficiency. Fig. 2 shows the description of the Mark III system used for the present analysis. Among the complicated structural components in Mark III CCS, the function of the liquid-tight secondary barrier is to prevent further LNG leakage in case of primary barrier's damage. Once the

Fig. 1. Two types of cargo containment systems (a: Mark III system, b: NO 96 system).

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Table 1 FMEA study of barrier damage (Bae et al.). Process

System failure

Cause

Effect

Panel installation

Panel capsizing

Binding imperfection

Clash with forklift

Careless driving

Jig and tool falling

Handle without care

NH3 Test for LNG cargo

Remaining of inspection material Paraphernalia falling

Unskilled workman Management without care

Membrane installation

Jig and clamp falling

Unskilled workman

Fault construction by dust Fire by electric leakage

Insufficient removal of dust by cutting works Electric leakage

Carriage falling

Leaving broken gear behind

Member damage Replacement of broken Member damage Replacement of broken Worker injury Replacement of broken Inspection error Falling items broken Replacement of broken Delay of schedule Replacement of broken Seam error Hole re-formation Delay of schedule Replacement of broken Delay of schedule Replacement of broken Replacement of broken Replacement of broken

Welding

Pump tower installation

Moving membrane falling Member falling when pump tower turnover Scaffolding install/Removal Install and removal members falling Clash with forklift Scaffolding collapse

Binding imperfection Binding imperfection Absence of bottom plywood Careless driving Arbitrary scaffolding demount

panel panel panel

panel panel

panel panel panel panel

Replacement of broken panel Replacement of broken panel Scaffolding damage Replacement of broken panel

Fig. 2. The assembly description of the Mark III system.

secondary barrier is damaged, however, it is likely that the leaked LNG flows through the secondary insulation layer and reaches the inner hull's plate in the carrier. Damage to the inner hull's plate of the LNG carrier will eventually lead to damage of the entire hull's structure. The present study assumes the most severe conditions, in which both primary and secondary barriers are damaged. Under these circumstances, LNG leaks through the primary and secondary barrier in the damaged CCS. To be more specific, the triplex located between the primary and secondary barriers was assumed to be damaged. It was also assumed that the flat joint and hull's plate were in direct contact with each other, because the mastic resin adhesive layer between the secondary insulation layer and hull's plate was assumed to be damaged in the modeling. The LNG at  162 °C would flow through the porous material (glass wool), located in the gap between the pieces of the primary and secondary insulation layers. Because the temperature of the medium is higher than the cryogenic temperature of the LNG, most of the leaked LNG could quickly evaporate while it flows through the flat joint. The multiphase flow mixed with LNG and NG is considered

where LNG is subjected to evaporation in a flat joint of the porous structure. LNG carriers must comply with all relevant local and international regulatory requirements, including those of the International Maritime Organization (IMO), International Gas Carriers Code (IGC), and the US Coast Guard (USCG) (Vanem et al., 2008). It was determined that an LNG leakage must be able to be contained by a barrier for 15 days, based on the IGC Code stipulations.

3. Experiments 3.1. Determining the DBTT of the hull's steel plate material 3.1.1. Theory The Charpy impact test, also known as the Charpy V-notch (CVN) test, is a standardized high strain-rate impact test that determines the amount of energy a material absorbs during fracture (Tvergaard and Needleman, 1988). The absorbed energy (also called the impact energy, the energy needed to fracture a material)

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40 case 1 case 2 case 3

35

Impact energy [J]

30 25 20 15 10

Fig. 3. CVN impact test diagram.

5 0

Table 2 Chemical composition and mechanical properties of a mild steel specimen.

-200

-150

-125

-100

-75

-50

-25

0

25

Temperature [ C]

Chemical composition (wt%)

Fig. 4. CVN impact tests on mild steel.

Materials

C

Cr

Ni

Mn

S

P

Si

Case 1 Case 2 Case 3

0.15 0.16 0.14

0.05 0.06 0.04

0.06 0.08 0.03

0.45 0.30 0.35

0.025 0.030 0.020

0.015 0.017 0.013

0.15 0.18 0.12

Mechanical properties Yield strength (MPa) 240 Tensile strength (MPa) 460 Elongation (%) 25

determined by a CVN impact test is calculated as follows: ECVN ¼ MRð cos φ  cos ϕÞg;

-175

ð1Þ

where ECVN is energy absorbed in a CVN impact test (vertical load on a column), M is the mass of the hammer, R is the length of the specimen, φ is the angle of fall, ϕ is the angle at the end of the swing, and g is the acceleration due to gravity, as shown in Fig. 3, respectively. The measured absorbed energy from a CVN impact test can indicate the toughness of the material. The DBTT can be determined from the temperature at which the energy needed to fracture the material drastically changes. 3.1.2. Materials and experimental conditions CVN impact tests were conducted using a pendulum-type impact machine with a maximum capacity of 300 J. Test samples were fabricated in accordance with ASTM E23, which is a standard method of testing notched-bar impact of metallic materials, used to obtain the absorbed energy. The specimens of the investigated materials used in this study comprise a 10  10 mm2 section, with a length of 55 mm. The notches in the specimens were formed with a central 45° V-notch, with a depth of 2 mm and a root radius of 0.25 mm. The chemical compositions and mechanical properties of the investigated materials are listed in Table 2. To obtain DBTT, the CVN impact test was conducted using a custom-built cryogenic chamber to investigate the effect of low temperatures on the energy absorption of each material in fracture. The experimental temperature ranged from the ambient temperature (25 °C) to the liquid nitrogen temperature (  196 °C) to generate complete absorbed energy. The temperature inside the chamber was controlled by changing the amount of liquid nitrogen. In order to maintain the thermal equilibrium state, all of the specimens were pre-cooled at the temperature at which they were to be tested for approximately 40–50 min. Finally, fractography analyses of the fracture surfaces for the tested specimens were conducted using a scanning electron microscope (SEM) (S-4800, Hitachi, Inc., Japan).

3.1.3. Results and discussion Fig. 4 shows the CVN impact-test results of mild steels in the experimental temperature ranged from ambient to cryogenic temperature. In order to ascertain the repeatability of the test results, tests were performed at least four times for each case, and results were shown with an error bars which mean standard deviation. According to this result, the absorbed energy decreased gradually, and the decrease in test temperature exhibiting characteristic phases: an upper-shelf energy region, a lower-shelf energy region, and a transition region. In the upper-shelf energy region, the phase showed very little decrease in impact energy. And it subsequently exhibited a sudden drop in the absorbed energy, indicating the DBTT. After that, the lower-shelf energy region showed little decrease in impact energy. The result suggests that mild steel retained adequate ductility for ambient temperatures to 25 °C, and exhibited a significant energy drop, and brittle characteristics at temperatures below  100 °C. It was determined that the DBTT for each case are  58,  60, and  62 °C, respectively. An SEM was used to examine the microscopic fracture features of the specimens, in order to investigate the DBTT and observe the fracture features of the mild steel specimens. Fig. 5 shows the typical fracture surfaces for a mild steel specimen tested at different temperatures. Each figure shows the fracture surfaces in different temperature ranges from 25 °C to 196 °C. As the temperature decreased, a gradual transition occurred from ductile to brittle characteristics in their failure modes. The mild steel exhibited adequate ductile fracture above  25 °C. In this temperature region, the fracture surface was characterized by many wide, dimple-like structures found in the depression. On the other hand, in the lower-shelf energy region, at temperatures below  100 °C, this material exhibited brittle fracture behavior, as indicated by the flat and fragile features of fractured grain with large, brittle fracture surfaces. Numerous sharp-edge grains and coarse grains can be observed. It can be inferred that from a microstructural perspective, much more energy per unit area is required to generate small dimples (Benedetti et al., 2005). Based on the above experimental and fractography results, the DBTT of mild steel can be estimated at around  60 °C. 3.2. Experiments for validation of numerical analysis 3.2.1. Experimental apparatus To investigate the temperature change of the hull's steel plate during LNG leakage from the damaged Mark III system, we used the experimental apparatus resembling Mark III LNG insulation system. The present experiment investigates the cryogenic flow in

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281

Fig. 5. SEM fractured surface: (a) 25, (b)  25, (c)  50, (d)  75, (e)  100 and (f)  150 °C.

Fig. 6. A schematic illustration of the cryogenic liquid flow experimental system.

Fig. 7. Schematic illustrations of the experimental apparatus (all dimensions in mm).

porous media where cryogenic liquid was injected into an experimental apparatus. Figs. 6 and 7 respectively show the schematic illustration of the cryogenic liquid flow experimental system and apparatus. The experimental mold had open lateral sides, and mild steel was placed in the end flange at the opposite end of the injection side so that the flow exited through those two lateral sides, a process which imitated the Mark III LNG insulation system. The dimensions of the experimental mold were 300 mm  300 mm  30 mm, made of a 15-mm-thick acrylic material. Glass wool made of E-type glass fibers (KGM-24, KCC, Korea) was placed in the mold at the flat joint and the bulk density of glass wool is 24 kg/m3. Prior to the experiment, the entire experimental apparatus (including the pipe and valves but excluding the experimental mold) was pre-cooled to a liquid nitrogen temperature of about 110 K. Liquid nitrogen, controlled by a cryogenic fluid pressure regulator (Series CR, Generant, US), was injected at a constant pressure into the 6-mm inlet gate valve, which opened and closed manually. To investigate the effect of cryogenic liquid on the hull's plate, T-type thermocouples were installed in the hull's plate. Prior to the installation, all the thermocouples were calibrated by a manufacture's calibration system with an accuracy of about 70.1 K. The output collected from the thermocouples was recorded by a data logger and stored in a laboratory computer. 3.2.2. Experimental results and discussion Under different inlet pressures of 0.02–0.06 MPa, liquid nitrogen was injected continuously for 5000 s into a flat joint of glass wool. Fig. 8 shows temperature profiles at different locations under different inlet pressures of 0.02–0.06 MPa: temperature sensor positions 1, 2, and 3 were located in the middle of a mild steel plate, 50 mm from the middle, and 100 mm from the middle, respectively. We observed that the temperature in the hull's plate reached around  40–50 °C at 5000 s for the temperature sensor position 1 at all inlet pressures, which are mostly influenced by cryogenic liquid flow. The liquid phase of liquid nitrogen could not be maintained in the glass wool and most of it vaporized because of the difference between its temperature and that of the

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30

30

20

20 10

Temperature [ oC]

Temperature [ oC]

10

0

-10

-20

0 -10 -20 -30

position 1 position 2 position 3

-30

position 1 position 2 position 3

-40

-40

-50 0

1000

2000

3000

4000

5000

0

1000

2000

time [s]

3000

4000

5000

time [s] 40

Temperature [ oC]

20

0

-20

position 1 position 2 position 3

-40

-60 0

1000

2000

3000

4000

5000

time [s] Fig. 8. Temperature profile of mild steel for different locations under different inlet pressures of cryogenic liquid (a) 0.02 MPa, (b) 0.04 MPa, (c) 0.06 MPa.

environment. The vaporized nitrogen exited through the two open lateral sides of the mold. The result for the experiment shows that temperature drops more rapidly with increasing inlet pressure. This was because higher injection pressure led to higher flow rates, allowing the temperature to drop more rapidly. Regarding the temperature behavior between sensor positions, the temperature difference between sensors decreased as inlet pressure increased. As the inlet pressure increased, larger liquid-phase area formed near the inlet area and then expanded and propagated radially from the inlet area toward the lateral side with increasing flow rate, according to our previous studies (Choi et al., 2015). The heat transferred between glass wool and hull's plate with continuous flow of cryogenic liquid, and radially propagated liquid nitrogen from the inlet area caused the heat transfer area to expand radially to hull's plate. With increasing flow rate, the expanded heat transfer area led to a decrease in temperature difference between them.

experiment and the simulation, in the middle position of the mild steel plate. The overall comparison yields a reasonable alignment, with few differences between experiment and simulation. The slight discrepancy between the two cases may be due to the adoption of the convection coefficient, which results in minor inconsistency. However, the temperature change tendencies for the simulation and experimental results were shown to be quantitatively similar for the mild steel plate. Hence, we find that the simulation results agree closely with the experimental results. This finding suggests that the computational method can be applied to studying transient cryogenic liquid flow behavior reflecting the evaporation effect.

3.2.3. Comparison with the numerical results Numerical simulation was performed using the same set of physical condition as in the experiments to compare with experimental results. By performing the simulation for the experimental studies, the validity of numerical simulation was examined by comparing its results with experimental results (Choi et al., 2015). Fig. 9 compares temperature distribution from the

LNG is an odorless, colorless, and noncorrosive cryogenic liquid at normal atmospheric pressure. The properties of LNG vary with its composition, which depends on the reservoir source of the original gas. While LNG is predominately methane (about 87– 99 mol%), it also includes hydrocarbons, nitrogen, sulfur, and CO2 (Mokhatab et al., 2014). Knowledge of the LNG phase behavior and thermodynamic properties is required for rigorous numerical

4. Numerical analysis 4.1. Material properties for numerical calculation

S.W. Choi et al. / Ocean Engineering 113 (2016) 276–294

30

30

20

20 10

Temperature [ oC]

10

Temperature [ oC]

283

0

-10

-20

0 -10 -20 -30

experiment simulation

-30

experiment simulation

-40

-40

-50 0

1000

2000

3000

4000

5000

0

1000

2000

time [s]

3000

4000

5000

time [s]

40

Temperature [ oC]

20

0

-20

-40 experiment simulation -60 0

1000

2000

3000

4000

5000

time [s] Fig. 9. Temperature profile of mild steel, for numerical validation. (a) 0.02 MPa, (b) 0.04 MPa, (c) 0.06 MPa.

For the properties of natural gas (NG), boiling temperature, density, and molecular weight were considered, as shown in Table 4 (Mokhatab et al., 2014).

Table 3 Thermodynamic properties of LNG. Mechanical properties  160 to  162  16 to  19 425–485 2.2–3.7 0.11–0.18 511

Boiling point (°C) Molecular weight (g/mol) Density (kg/m3) Specific heat capacity (kJ/kg/°C) Viscosity (mPa s) Vaporization latent heat (kJ/kg)

Table 4 Properties of NG. Component

Boiling point (°C)

Liquid density (kg/ m3)

Molecular weight

Methane (CH4) Ethane (C2H6) Propane (C3H8) Hydrocarbons (C4 þ ) Nitrogen (N2)

 161.5  89.0  42.1  11.7  195.8

425 546.7 583 595 815

16.04 30.07 44.10 58.12 28.01

calculations. The representative properties such as boiling point and density of LNG vary with its composition: typically  162 °C and between 425–485 kg/m3, respectively, as shown in Table 3.

4.2. Numerical method In the present study, a flow model for a single fluid mixture was used for multiphase flow. The mixture model (a multiphase model used for flows containing several phases moving at different velocities) solves for the continuity, momentum, energy equations, and volume fraction equations for each phase. The equation of mass continuity for a mixture can be expressed as follows:
 ∂ ρm ! ð2Þ þ ∇ ρm v m ¼ 0; ∂t n P

! v m¼a¼1

α a ρa ! va ρm

;

ρm ¼

n X

α a ρa ;

ð3Þ

a¼1

where vm ¼the mass-averaged velocity, ρm ¼the mixture density, and αa ¼the volume fraction for phase a. The momentum conservation equation for the mixture can be obtained by summing the individual momentum conservation equations for all phases. The momentum conservation equation

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can be expressed as follows:   
 ∂
!  ! ! ! T ρm v m þ ∇ U ρm ! v m v m ¼  ∇p þ∇ U μm ∇ v m þ ∇ v m ∂t ! þ ρm g þ F ; ð4Þ where the mixture viscosity for the given phase can also be obtained from n X

μm ¼

α a μa :

ð5Þ

a¼1

The equation of energy conservation for the mixture is: n  n h X  i  ∂ X α a ρa E a þ ∇ U αa ! v a ρa Ea þ p ¼ ∇ U U ef f ∇T þ Si ; ∂t a ¼ 1 a¼1

j¼1

ð6Þ

where Ueff is the effective thermal conductivity, obtained from U ef f ¼

n X

α a ka :

NG was incorporated into commercial CFD software by implementing a user-defined function code that represents the mass transfer by using the latent heat for the energy equation and mass transfer for the volume fraction equation. The flow model in the flat joint of porous media was established by adding a source term to the momentum conservation equation. The source term is composed of a viscous loss term and an inertial loss term. The corresponding source term takes the following form: 2 3 3 3 X X ð9Þ Dij μvj þ C ij ρjvjvj 5: Si ¼  4

ð7Þ

a¼1

The parameter Si includes all other volumetric heat sources. From the continuity equation for secondary phase b, the volume fraction equation is calculated from the following equation: n

 X ∂ ! _ cb  m _ bc Þ; α b ρb þ ∇ U α b ρb ! v m ¼ ∇ U αb ρb v dr;b þ ðm ∂t c¼1

ð8Þ where the dot over the variable represents partial derivatives with respect to time. The final term on the right-hand side represents the mass transfer due to evaporation. The evaporation of LNG to

j¼1

In Eq. (9), the values of each Dij in the viscous loss term comprise a diagonal matrix with coefficients K1p , and Cij in the inertial loss term is also a diagonal matrix. It should be noted that pressure drop is proportional to fluid velocity, which was measured in the permeability experiment carried out in our previous work (Choi et al., 2015). Cij can be calculated in the Kozeny–Carman equation (Zhong et al., 2002). For the heat transfer in the hull's plate, the energy transport equation is;   ∂ , ρH þ ∇ U ρHv ¼ ∇ U ðk∇T Þ þ Si ; ð10Þ ∂t where the terms on the right side of the equation represent heat flux due to conduction and the volumetric heat sources in the energy transport region, respectively. All the governing equations, together with the boundary conditions, were solved using the finite volume method in the commercial CFD package Fluent (ANSYS Fluent, version 13.0). 4.3. Physical model and calculation conditions The present parametric study identifies the amount of time leakage was retained in the flat joint and the temperature distribution of the hull's plate for the leaked LNG. The numerical Table 5 Time-step size and grid dependence test. Position 1 ε grid (Coarse–Medium) ε grid (Medium–Fine) ε time step size (Large– Medium) ε time step size (Medium– Small)

Position 2 3

2.54  10 1.25  10  3 0.121  10  3

Position 3 3

3.12  10 5.23  10  3 2.51  10  3 4.52  10  3 0.213  10  3 0.254  10  3

0.0821  10  3 0.0912  10  3

Fig. 10. The physical model used in the numerical simulation.

Fig. 11. Different set of grids for the mesh independence study: mesh with (a) coarse grid, (b) medium grid, (c) finer grid.

0.121  10  3

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Fig. 12. Phase contours of leaked LNG in the flat joint for different inlet pressures for a leakage hole with a 2-mm diameter (a: 0.2 bar inlet pressure, b: 0.7 bar inlet pressure, c: 1.3 bar inlet pressure).

approach developed in our previous work (Choi et al., 2015) was specially designed to study the behavior of a cryogenic liquid in porous structures. Adding to that existing approach, in the present study we performed a conjugate heat transfer analysis of LNG leakage in CCS to investigate the phase change and heat transfer when a LNG leakage occurs. The physical model used in the numerical simulation is the Mark III LNG CCS consisting of two insulation barriers, the flat joint between insulation materials, as shown in Fig. 10. The 4-mm and 30-mm flat joints are located in the primary and secondary insulation layer between insulation materials of polyurethane foam, respectively. The conduction heat transfer was considered between the flat joint and insulation materials of polyurethane foam. At the bottom part, 18 mm of hull's plate is placed adjacent to the flat joint.

The same dimensions as for the experimental apparatus were used for the numerical model. 270-mm height for the flat joint used for primary and secondary insulation and 100 mm  300 mm  18 mm in length (L)  width (W)  thickness (T) for the hull's plate were used according to the LNG carrier data (Deybach and Gavory, 2008). For the LNG inlet condition, 0.2–1.3 bar inlet pressure was used for each parametric study case. For the LNG properties, thermodynamic properties and the phase behavior of LNG were considered to change with temperature, referring to the LNG database (Mokhatab et al., 2014) for the calculation. The experimentally determined properties such as thermophysical properties of reinforced polyurethane foam, glass wool, and permeability of flat joint, was considered in the numerical calculation from our previous works (Choi et al., 2012, 2015). Heat flux due to heat convection was applied to the bottom hull's plate with empirical correlation expression for external convection flow at the lower surface of the heated plate (Eqs. (12) and (13)). For the flow

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Fig. 13. Phase contours of leaked LNG in the flat joint for different inlet pressures, for a leakage hole with a 5-mm diameter (a: 0.2 bar inlet pressure, b: 0.7 bar inlet pressure, c: 1.3 bar inlet pressure).

analysis of LNG in the flat joint of glass wool, permeability of flat joint was also employed corresponding to our previous experimental data (Choi et al., 2015). The boundary condition for the LNG inlet was specified as the hydrostatic pressure condition. The hydrostatic pressure was estimated based on the filling level of LNG cargo containment, where the filling level condition was defined by the volume of LNG

to the volume of the cargo containment for the 30-m height tank. Accordingly, the inlet pressure of the LNG ranged from 0.2 bar to 1.3 bar. Diameters of leakage hole for the inlet boundary condition were assumed to be in the range of 2–8 mm. The turbulence intensity of 5% and free stream velocity components were set on the inlet boundary. As for the outlet boundary, ambient pressure (zero gauge pressure) was imposed. On the lateral side, opened

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Fig. 14. Phase contours of leaked LNG in the flat joint for different inlet pressures, for a leakage hole with an 8-mm diameter (a: 0.2 bar inlet pressure, b: 0.7 bar inlet pressure, c: 1.3 bar inlet pressure).

outlet boundary condition was assigned on the both lateral sides, so the fluid flowed through a flat joint made of porous media to the lateral directions. The LNG leaking area in the flat joint is in contact with a cryogenic LNG at  162 °C, and the bottom surface area of the inner hull's part that was exposed to the air was set to 0 °C (Choi

et al., 2012). The airflow on the bottom surface of the hull's plate induces free convection heat transfer due to free convection flow. Therefore, the Neumann boundary condition is applied at the bottom surface of the hull's plate. ∂T  k ¼ hðTðtÞ  T amb ðtÞÞ; for t Z 0: ð11Þ ∂n

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Fig. 15. Temperature contours of leaked LNG and hull's steel plate in the flat joint for different inlet pressures, for a leakage hole with an 2-mm diameter (a: 0.2 bar inlet pressure, b: 0.7 bar inlet pressure, c: 1.3 bar inlet pressure).

The convection coefficient in the hull's plate was set equal to the value determined empirically, which is for external convection flow at the lower surface of the heated plate (Eq. (12)). From the

Nusselt number of the empirical correlation expression, the convection coefficient can be obtained by means of Eqs. (12) and (13). Liquid and vapor phases were treated as interpenetrating continua

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Fig. 16. Temperature contours of leaked LNG and hull's steel plate in the flat joint for different inlet pressures, for a leakage hole with an 8-mm diameter (a: 0.2 bar inlet pressure, b: 0.7 bar inlet pressure, c: 1.3 bar inlet pressure).

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0

Temperature [ oC]

Temperature [ oC]

0

-10

30 min 120 min 5h 10 h 1 day 3 days 5 days 8 days 12 days 15 days

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6

9

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-20

-30

21

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6

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Lengh of hull [mm]

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0

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30 min 120 min 5h 10 h 1 day 3 days 5 days 8 days 12 days 15 days

-20

-30

0

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6

9

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18

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Lengh of hull [mm] Fig. 17. Temperature distribution in an 18-mm-thick hull's plate along the hull's thickness for different inlet pressures, for a leakage hole with a 2-mm diameter (a: 0.2 bar inlet pressure, b: 0.7 bar inlet pressure, c: 1.3 bar inlet pressure).

for the numerical simulation (Lakehal et al., 2002). 2 32 0:387RaL 1=6 6 7 Nu L ¼ 40:825 þ h i8=27 5 ; 9=16 1 þð0:492=PrÞ 1=4

Nu L ¼ 0:27RaL ;




 105 r RaL r 1010 :

ð12Þ

ð13Þ

Spatial discretization for the convective and diffusion terms was performed using the second-order upwind and central differencing schemes, respectively. The QUICK scheme (Versteeg and Malalasekera, 2007) was used to determine convective terms in the volume fraction equation, and the Euler backward scheme was used to carry out time integration. The SIMPLE type algorithm (Murthy and Mathur, 1997) was used for pressure-velocity coupling. The calculation was repeated until the convergence was achieved. The accuracy of the numerical results was verified through mesh independence study. The mesh independence study was carried out for a 0.2 bar inlet pressure condition with 2 mm diameter of leakage hole case. The three sets of grids were tested: a coarse grid with 100,000 cells, a fine grid with 250,000 cells, and a medium grid with 200,000 cells as shown in Fig. 11. The base time-step size was 0.05 s. For the assessment of the time-step size dependence, two more time-step sizes were tested, a larger one, 0.1 s and a smaller one, 0.01 s. The results were represented with ε

(difference between the calculated values using different grid and time-step size) which were accumulation of root-mean-square values of the calculated temperatures at three locations (Lee et al., 2011) using Eq. (14) every 5 min, where N is the total number of calculation. Table 5 showed that the values of ε were quite small and the solutions were independent of the grids and time-step sizes in the tested range. To achieve smooth convergence, convergence for each time step was based on the residual for velocity below 10  4 and the residual for mass and energy balance below 10  6. 0sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1  2 N   1 X @ T coarser;n  T f iner;n  A ð14Þ ε¼   N T n¼1

f iner;n

A structured uniform hexahedral grid with 200,000-cell was generated by conformal mapping methods (Bern and Eppstein, 1992) for the flow domain and solid domain which was corresponding to the flat porous medium region and the inner hull steel plate. 4.4. Results and discussion A numerical parametric study was carried out to investigate LNG leakage in damaged LNG CCS. Various scenarios were considered for a period of 15 days under any filling conditions and defect sizes, where the inlet pressure of the leaked LNG varied for

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0

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-20

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temperature [ oC]

temperature [ oC]

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-40 30 min 1h 5h 10 h 1 day 5 days 8 days 12 days 15 days

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-80

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-100 0

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lengh of hull [mm]

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lengh of hull [mm]

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lengh of hull [mm] Fig. 18. Temperature distribution in an 18-mm-thick hull's plate along the hull's thickness for different inlet pressures, for a leakage hole with a 5-mm diameter (a: 0.2 bar inlet pressure, b: 0.7 bar inlet pressure, c: 1.3 bar inlet pressure).

different LNG levels condition in the CCS. The physical model calculated in present numerical simulation is Mark III LNG insulation system, and the result are shown the contour in the flat joint of glass wool with both the primary and secondary insulation layers combined. Figs. 12–14 show the phase contours of leaked LNG for different inlet pressures and diameters of leakage hole: specifically 0.2– 1.3 bar and 2–8 mm, respectively. The LNG phase contours clearly show the behavior of the leaked LNG flow in the LNG CCS, indicating that liquid-phase area forms near the inlet area and then expands and propagates from the leaked area toward the lateral side, where vaporized NG exits. This behavior is mainly due to the flow of the leaked LNG and evaporation of LNG. The LNG flow formed the liquid-phase area and led to proceed to the hull's plate, depending on the inlet pressure and the size of the leakage hole. For a leakage hole that is 2 mm in diameter, the liquid-phase area did not reach the hull's plate under any LNG inlet pressure conditions. However, for the 5-mm-diameter leakage hole, the liquid-phase area reached the hull's plate under the condition of 0.7 bar inlet. For the 8-mm-diameter leakage hole under 0.2 bar inlet condition, the liquid-phase area reached the hull's plate in the eight days. Therefore, whether the leaked LNG proceeds to the hull's plate depends upon the LNG filling condition and the size of the leakage hole. Figs. 15, 16 present temperature contours of leaked LNG, for a leakage hole with a diameter of 2 mm and 8 mm for different inlet

pressures. The temperature contours of the leaked LNG flowing through the porous media of the flat joint show quite different patterns depending on the inlet pressure and the diameter of the leakage hole. These factors affect the flow rate and affect the resulting temperature change rate of the porous media. For example, high inlet pressure and large diameter lead to an increase in the flow rate of the leaked LNG such as for the 8-mmdiameter leakage hole under 1.3 bar inlet condition, and the temperature of the porous media will decrease faster. With porous structure of flat joint of glass wool along with cryogenic liquid evaporation, pressure distribution of LNG flow in the flat joint of glass wool showed a nonlinear profile since the flow is two phase (gas and liquid) flow (Choi et al., 2015). Therefore, it takes relatively long time for the leaked LNG flow in the liquid phase of cryogenic state to reach the hull's plate, which means the thermal effect of LNG leakage could be limited in case of the lower inlet pressure. However, with the higher inlet pressures and larger diameters of leakage hole, the LNG leakage flow has higher flow rates. The higher flow rates allow the temperature of the flat joint to drop below the temperature of liquefaction ( 162 °C) more rapidly. This leads to the increased liquid phase of LNG, and the leaked LNG reaches the hull's plate in shorter time compared to the case of the lower inter pressure, which affects the temperature distribution of hull's plate. With LNG's flow propagation, the temperature of the LNG leak dominates CCS of the leak area from the leaking part in the porous

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20 0

0

temperature [ oC]

temperature [ oC]

-20 -20

-40 30 min 1h 5h 10 h 1 day 5 days 8 days 12 days 15 days

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30 min 1h 5h 10 h 1 day 5 days 8 days 12 days 15 days

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lengh of hull [mm] Fig. 19. Temperature distribution in an 18-mm-thick hull's plate along the hull's thickness for different inlet pressures, for a leakage hole with an 8-mm diameter (a: 0.2 bar inlet pressure, b: 0.7 bar inlet pressure, c: 1.3 bar inlet pressure).

Fig. 20. Thermal penetration depth whose temperature is below DBTT (a) and the time at which the temperature of the hull's steel plate drops below DBTT (b).

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media of the flat joint, depending on the inlet pressures and size of the leakage hole. Figs. 17–19 show LNG leakage propagation and the consequent temperature distribution in an 18-mm-thick hull's plate along the hull's thickness for different inlet pressures and leakage diameters. These figures indicate the overall trend of temperature distribution for two dominant time stages: developing and equilibrium time stage to reach the cryogenic temperature. During the developing time stage, excessive heat was transferred between temperate liquefied LNG and the hull's plate due to the large temperature difference, resulting in a dramatic temperature decrease during that time. Due to continuous LNG flow and vaporization heat of the LNG, there is little temperature difference between CCS of the leaked area and the LNG. In this state, the temperature profile of the hull's plate shows the equilibrium time stage. The temperature distribution results for the hull's plate show that the hull's plate did not reach a DBTT of  60 °C for a leakage hole with a 2-mm diameter within the time duration. At 15 days, for a leakage hole with a 2-mm diameter, the temperature of the hull's plate reached about  23, 26, and  30 °C, for 0.2, 0.7, and 1.3 bar inlet pressure conditions of leaking LNG, respectively. However, when the leakage hole diameter was 5 mm or greater, the temperature of the hull's plate reached DBTT for all pressure conditions within the time duration. For a leakage hole with a 5mm diameter, the temperature of the hull's plate part drops below 60 °C at 15 h, 3 h, and 2 h, for 0.2, 0.7, and 1.3 bar inlet pressure conditions, respectively. Similarly, for the leakage hole with an 8mm diameter, the temperature of the hull's plate drops below 60 °C at 4 h, 2 h, 1 h, for 0.2, 0.7, and 1.3 bar inlet pressure condition, respectively. These results are mainly due to the fact that a liquid-phase area reached the hull's plate, as observed in the phase contour figures. The above results reveal that the critical size of the leakage hole where the temperature of the hull's plate do not reach a DBTT of 60 °C lies between 2 mm and 5 mm for the given leakage conditions. For a leakage hole with a 4-mm diameter, the temperature of the hull's plate reached about 54,  58, and  62 °C at 15 days, for 0.2, 0.7, and 1.3 bar inlet pressure condition, respectively. For the 1.3 bar inlet pressure condition, the temperature of the hull's plate reached DBTT in eight days. Even under the 0.2 bar and 0.7 bar inlet pressure conditions, the temperature of the hull's plate did not reach the DBTT within the time duration. Fig. 20 shows the time at which the temperature of the hull's plate drops below a DBTT of  60 °C and a thermal penetration depth whose temperature is below  60 °C. It is inferred that whether the temperature of the hull's plate reached DBTT was influenced by the size of the leakage hole and the inlet pressure of leaking LNG. However, the effect of the leakage hole size is greater than the inlet pressure of leaking LNG for time to reach DBTT. The results demonstrate that the thermal safety of the hull's plate is guaranteed for a leakage hole with a 2-mm diameter. For a leakage hole with a 4-mm diameter, thermal safety is guaranteed except under fully loaded condition. For a leakage hole with a diameter greater than 5 mm, thermal safety cannot be guaranteed for all filling conditions.

 The experimental investigation of the temperature behavior of

5. Concluding remarks

Al-Farhany, K., Turan, A., 2011. Non-darcy effects on conjugate double-diffusive natural convection in a variable porous layer sandwiched by finite thickness walls. Int. J. Heat Mass. Transf. 54 (13), 2868–2879. Bae, J., Joh, K. et al. Safety evaluation of Mark III type LNG carriers under barrier leakages. In: Proceedings of 15th International Conferences on Liquefied Natural Gas. Bergan, P. l G., Bakken, K. r, et al., 2009. A New Double Barrier Tank for Transportation and storage of LNG. Offshore and Arctic Engineering, American Society of Mechanical Engineers. Benedetti, M., Heidemann, J., et al., 2005. Influence of sharp microstructural gradients on the fatigue crack growth resistance of α þ β and near-α titanium alloys. Fatigue Fract. Eng. Mater. Struct. 28 (10), 909–922.

For large LNG carriers, the risk of damage to CSS should be carefully investigated to ensure rigorous safety design. In particular, LNG leakage in the CSS causes serious damage to the entire LNG carrier. A conjugate thermal analysis was used to investigate LNG leakage and the resulting temperature changes of the hull's steel plate obtained under various damage scenarios in LNG CCS. The main conclusions are as follows:









the hull's plate was presented, using an experimental apparatus resembling a Mark III LNG insulation system. Temperature in the hull's plate reached around from  40 to 50 °C in the experimental duration, because the liquid phase of liquid nitrogen could not be maintained in the glass wool and most of it vaporized due to the difference between its temperature and that of the environment. With increasing inlet pressure, temperature drops more rapidly, which is mainly due to higher flow rates. Hull's temperature difference between sensors decreased as inlet pressure increased. To validate the numerical approach developed in this study, we compared the simulation results with the experimental results, and found that the two results agreed well. The simulation results therefore effectively demonstrated the cryogenic liquid's behavior in porous media with respect to phase transitions. Parametric simulation studies were performed for the LNG leakage under various damage scenarios which are different inlet pressures and leakage hole diameters. From the experimentally obtained DBTT for the hull's plate material, the DBTT was used as the index of critical temperature for the numerical simulation. The numerical parametric studies estimated the temperature change of the hull's plate due to LNG leakage for various inlet pressures of leaking LNG and defect sizes of damaged LNG CCS within the time duration. The size of the leakage hole and inlet pressure of leaking LNG both affect whether the temperature of the hull's plate reached the DBTT of the hull's plate. The effect of the leakage hole size is greater than the inlet pressure of leaking LNG for time to reach DBTT. From these results, we concluded that thermal safety of the hull's plate is guaranteed for LNG leakage in cases where the leakage hole's diameter is 2 mm. When the diameter of the leakage hole exceeds 5 mm, thermal safety cannot be guaranteed under all filling conditions. In cases where a DBTT of 60 °C is not reached, the critical size of the leakage hole should lie between 2 mm and 5 mm for the given leakage conditions. For a leakage hole with a diameter of 4 mm, thermal safety is guaranteed except under fully loaded condition. The present numerical approach of this paper can be effectively used in future research regarding cryogenic LNG facilities and its applications such as thermal stratification, heat flow phenomena in LNG storage tank, flow analysis in cryogenic pipe, and BOG estimation in cryogenic storage tank.

Acknowledgment This work was supported by the Energy Efficiency & Resources Core Technology Program of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and received financial assistance from the Ministry of Trade, Industry & Energy of the Republic of Korea (No. 20132010500030).

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