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Estimation of the design pressure of a prismatic LNG storage vessel
Ocean Engineering 101 (2015) 40–46
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Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng
Estimation of the design pressure of a prismatic LNG storage vessel Unheon Choi, Daejun Chang n, Choonghee Jo Division of Ocean System Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, South Korea
art ic l e i nf o
a b s t r a c t
Article history: Received 16 June 2014 Accepted 5 April 2015
This study proposed a method of estimating to design pressure in a prismatic storage vessel for liquefied natural gas. The estimation of the design pressure refers to the IGC Code that provides the international standards for storage of liquefied gases in bulk. The estimation of the design pressure was a basic step to scheme a storage vessel. The design pressure resulted from the vapor pressure and the maximum liquid pressure. The liquid pressure was calculated from the effect of gravity and the acceleration applied to the center of gravity of the liquid. Loading conditions of up to 98% were considered in the calculation of the maximum liquid height. The heat ingress warmed the LNG, which caused it to exceed its boiling temperature. Calculation of the vapor pressure was described by the material and energy balance equations. Dynamic simulation about the pressure behavior was conducted by commercial software. The vapor pressure affected by heat ingress from surrounding conditions was calculated with time variations. & 2015 Elsevier Ltd. All rights reserved.
Keywords: LNG Design pressure Prismatic storage vessel Vapor pressure Liquid pressure
1. Introduction LNG is usually carried by ships that are specially designed to store cryogenic cargo ( 160 1C) and protected to prevent LNG leakage even in the case of an accident. On these ships, LNG is stored in specific containment systems. Over the last twenty years, there have been many attempts to develop better means of transportation for LNG (Kumar et al., 2011). Two types of vessels are mainly used as gas carriers. The first type of vessel is the MOSS type vessel, which is a spherical, self-supporting vessel. The other type of vessel is the membrane type vessel. The use of MOSS type vessels is gradually decreasing while the use of membrane type vessels is increasing. The reason of this shift is in the superior volume efficiency of the membrane type vessel that is more economical to transport cargo in limited space available on ships. The storage vessel can theoretically be constructed in any shape, however spheres and cylinders are the most commonly used shapes. More complicated shapes as prismatic type are far more difficult to design to ensure safety and are even harder to construct. The ASME Boiler and Pressure Vessel Code (ASME, 2010) provides design rules for rectangular vessels. These rules cover some common noncircular type vessels but are limited in terms of the design regulations. According to IMO IGC code (IMO, 2008), LNG fuel vessels must be selected from ‘Independent Types A, B, or C’. For LNG-fuelled
n
Corresponding author. Tel.: þ 82 10 4801 0172; fax: þ 82 42 350 1553. E-mail address: [email protected] (D. Chang).
http://dx.doi.org/10.1016/j.oceaneng.2015.04.018 0029-8018/& 2015 Elsevier Ltd. All rights reserved.
carriers, there are several options on installing the LNG tank. LNG carriers are typically equipped with membrane-type vessels or type B vessels. Small ships may be equipped with type C vessels. Type B prismatic vessels describe that are adjustable to hull shape and partial secondary barrier. Although this shape is to require BOG handling by propulsion engines, boilers or reliquefaction and complex fuel system and high costs, it has space efficiency in terms of storage of LNG compared to circular type vessels. Spherical tank made with partial secondary barrier also requires BOG handling and complex fuel system (Itoyama et al., 1989). In this study, design pressures for a prismatic vessel defined by Type B vessel are estimated. Design pressure of pressure vessels is a key factor on the vessel design because it influences on the vessel thickness and manufacturing. The design pressure is determined by summing up the liquid pressure and the vapor pressure. In the previous methods, liquid pressures are estimated by rules and international codes, and the vapor pressure is usually adapted as 0.7 barg based on the regulation (Senjanović et al., 2005). Thus, the commonly used formulas for the design pressure in the storage vessel are overestimated, and there is little consideration for chemical phenomena between the liquid and vapor. In the original international standard and code, hydrostatic pressure and vapor pressure are added after the separate estimation of them. Also, the continually generated boil-off gas affects the design of the LNG cargo vessels due to the pressure increase. The LNG cargo vessels should have acceptable ranges of the vessel pressure in order to resist the pressure increase by the boil-off gas in a constant volume. According to the rules (Det Norske, 2011), the
U. Choi et al. / Ocean Engineering 101 (2015) 40–46
Nomenclature A a0 ax ay az aα aβ aβy aβz B BWL CB E FD g GM h L m _ m Pi P0 P gd q_ q_ 1 q_ 2
infinitesimal area over which the liquid pressure is applied basic acceleration dimensionless acceleration in the longitudinal direction dimensionless acceleration in the transverse direction dimensionless acceleration in the vertical direction relative acceleration in x z plane relative acceleration in y z plane component of aβ in the y direction component of aβ in the z direction molded breadth molded breadth measured amidships at the scantling draught waterline. block coefficient of the ship modulus of elasticity dynamic force acceleration of gravity metacentric height mass specific enthalpy molded length mass of the water column above the area A mass flow rate internal pressure vapor pressure liquid pressure total heat input heat input by thermal conduction heat input by thermal convection
vapor pressure of Type B vessel should not exceed 0.7 barg, which is required to prevent the potential release of BOG in the event of tank failure. The vapor pressure is inherently increasing from the environmental condition; however the equation in IGC Code does not reflect the pressure behavior with time variations. In this study, in order to estimate the reasonable design pressure, a method that simultaneously considering the vapor pressure and the
41
Re Rm t T T sc U V x
specified minimum yield stress specified minimum tensile strength time (s or day) temperature scantling draught overall heat transfer coefficient service speed of ship longitudinal distance from amidships to the center of gravity of the tank xðiÞ mass fraction for component z vertical distance from the ship's actual waterline to the center of gravity of tank zβ maximum liquid height zβ 2 maximum zβ at point 2 α heeling angle in x z coordinate αmax maximum heeling angle in x z coordinate β heeling angle in y z coordinate βmax maximum heeling angle in y z coordinate ρ density of liquid ∇ displacement of ship σm equivalent primary general membrane stress σL equivalent primary local membrane stress σb equivalent primary bending stress ν Poisson's ratio ASME American society of mechanical engineers BOG boil-off gas IGC Code international code for the construction and equipment of ships carrying liquefied gases in bulk IMO international maritime organization LNG liquefied natural gas
liquid pressure in dynamic condition is presented; where in influence of processing components is considered. Fig. 1 shows the process flow diagram for LNG carrier that has cargo vessels. The LNG cargo systems control the cargo vessel pressure in consuming the generated boil-off gas due to the heat ingress. The LNG cargo systems consist of the LNG cargo vessels, LNG forcing vaporizer, gas header, fuel gas conditioning units and generator engine.
Fig. 1. LNG cargo handling system.
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U. Choi et al. / Ocean Engineering 101 (2015) 40–46
sloshing for full-loaded cargo tank. It is given by
2. Design pressure The estimation of the design pressure is a basic step to scheme a storage vessel. The calculated design pressure is used to obtain the total pressure of the storage vessel including the vapor pressure. The dimensions of the storage vessel and the ship particulars are shown in Table 1 and Fig. 2. In the IMO IGC code (IMO, 2008), the allowable stresses should not exceed specific values for type B independent vessels listed below.
σm r f σ L r1:5f σ b r 1:5F σ L þ σ b r1:5F σ m þ σ b r 1:5F σ m is the equivalent primary general membrane stress, σ L is the equivalent primary local membrane stress, σ b is the equivalent primary bending stress, f is the the lesser of Rm =A or Re =B, F is the the lesser of Rm =C or Re =D Re and Rm are specified minimum yield stress and tensile strength at room temperature, respectively. 9% Ni steel (material ASTM specification number A553) is a commonly used cryogenic material in natural gas containment systems. This material has a yield stress (Re ) of 515 MPa and a tensile strength (Rm ) of 690 MPa. The modulus of elasticity (E) and Poisson's ratio (ν) are 185 GPa and 0.3, respectively. For nickel steels and carbon-manganese steels, parameters A, B, C, and D should have at least A¼ 3, B ¼2, C ¼3, and D¼ 1.5, respectively. In consequence, the allowable total stress should not exceed the smaller values for f and F, such that¼ 230 MPa. 2.1. Internal pressure The internal pressure results from the vapor pressure and the internal liquid pressure but does not include the effect of liquid
P i ¼ P o þ P gd
ð1Þ
here p0 is the vapor pressure, and pgd is the liquid pressure. The vapor pressure (p0 ) is the maximum pressure at the top of the vessel. 2.2. Liquid pressure The liquid pressure in the vessel results from the effect of gravity and the acceleration applied to the center of gravity of the liquid. As the ship moves, the liquid inside the vessel shifts with a heeling angle (β) as shown in Fig. 3. Typically, the liquid pressure is checked at the three points indicated in Fig. 3, and the largest liquid height (zβ ) above the point where the pressure is to be determined is measured from the vessel shell in the β direction, as illustrated in the Fig. 3. When fully loaded, the liquid surface can extend outside of the vessel. The liquid pressure at the vessel surface is calculated by the following procedure. When the dynamic force (F D ) from acceleration is applied to the liquid, the liquid pressure at the tank surface is expressed as pgd ¼
FD A
ð2Þ
where A is an infinitesimal area over which the liquid pressure is applied. The force has the form F ¼ maβ , and the mass (m) represents the mass of the water column above the area (A). The force is expressed by F D ¼ ðρzβ AÞaβ
ð3Þ
pgd ¼ ρzβ aβ
ð4Þ
where ρ is the density of the liquid. In Eq. (4) aβ is the relative acceleration. Thus, P gd is expressed by the acceleration of gravity (g) as follows: pgd ¼ ρzβ ðaβ gÞ
Table 1 Ship and vessel parameters. Parameter
ð5Þ
Simplifying Eq. (5), the liquid pressure at the vessel surface, excluding sloshing, is expressed as follows: Value
pgd ¼
Ship Length over all (LOA) Length between perpendiculars (LBP) Breadth, molded Depth to main deck, molded Design draft Scantling draft Displacement (∇) Service speed
50 m 27 m 12 m 13.6 m 136,000 m3 19.5 knots
Vessel Breadth Height Length Volume
30 m 30 m 40 m 36,000 m3
315 m 303 m
ρzβ aβ
The dimensionless relative acceleration (aβ ) of the liquid due to the gravitational and dynamic loads acts perpendicular to the liquid surface. 2.3. Determination of acceleration The maximum dimensionless accelerations ax , ay , and az in the longitudinal, transverse and vertical directions, respectively, act on the center of gravity of the vessel. The values of ax , ay , and az depend on the ship characteristics and the coordinates of the chosen point. The value of az does not include the effect of the static weight. The value of ay includes the effect of the static weight in the transverse direction due to rolling. The value of ax includes the effect of the static weight in the longitudinal direction due to pitching. Eqs. (7)– (9) are used to determine the components of accelerations due to ship's motions in the North Atlantic (Det Norske, 2011). The longitudinal acceleration due to surges and pitches, including the gravity component of pitch, is expressed as follows (Lloyd, 2008). ax ¼ 7 a0
Fig. 2. Dimensions and orientation of prismatic vessel.
ð6Þ
1:02 104
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0:06 þ A2 0:25A
with
A ¼ 0:7
L z 0:6 þ5 1200 L CB ð7Þ
U. Choi et al. / Ocean Engineering 101 (2015) 40–46
43
Fig. 3. Direction of acceleration and liquid height under fully loaded conditions (a) and partially loaded conditions (b).
The transverse acceleration due to swaying, yawing, and rolling including the gravity component of rolling is expressed as follow: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x 2 κ Uz2 ay ¼ 7 a0 0:6 þ 2:5 þ 0:05 þ κ 1 þ 0:6 ð8Þ L B
Table 2 Metacentric height.
The vertical acceleration due to heaves and pitches is expressed as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 0:61:5 45 2 x þ 0:05 az ¼ 7 a0 1 þ 5:3 ð9Þ L L CB where L is the molded length, and B is the molded breadth. The basic acceleration is denoted by a0 , which is expressed as V 34 600=L a0 ¼ 0:2pffiffiffi þ L L
ð10Þ
where V is the service speed in knots. The longitudinal distance is denoted by x from amidships to the center of gravity of the tank with content (m) where x is positive forward of amidships, and negative aft of amidships. The vertical distance is denoted by z from the ship's actual waterline to the center of gravity of tank with content (m) where z is positive above the waterline and negative below the waterline. In addition,
κ¼
13GM ðκ Z 1:0Þ B
Generally; κ ¼ 1:0
ð11Þ
where κ generally has a value of 1.0, and GM is the metacentric height. For specific loading conditions and hull forms, it may be necessary to determine κ from the formula. The block coefficient of the ship is expressed as CB ¼
∇ LBWL T sc
ð12Þ
where T sc is the scantling draught, and BWL is the molded breadth measured amidships at the scantling draught waterline. The value of ay is sensitive to the metacentric height. The metacentric height is determined according to the three draught conditions as shown in Table 2. The dimensions of LNG carrier and the parameters used for the calculation of the accelerations in Eqs. (7)–(9) are listed in Table 2. When the same scantling draught is applied for three draught conditions, the acceleration components are calculated as shown in Table 3. There are no differences in the vertical accelerations and longitudinal accelerations for the three draught conditions because the same scantling draught is used for all of the draught conditions. To calculate the relative acceleration, the acceleration components ax , ay , and az are considered to act separately. Thus, the design acceleration is described by an ellipsoidal envelope of the three acceleration components ax , ay , and az . The ellipsoid surface represents the assumed worst simultaneous combinations of the
Draught condition
GM
Loaded at deep draught Loaded on reduced draught In ballast
0.12 B 0.24 B 0.33 B
Table 3 Accelerations acting on vessels. Draught condition (acceleration)
Vertical, az (g)
Transverse, ay (g)
Longitudinal, ax (g)
Loaded at deep draught Loaded on reduced draught In ballast
7 0.347 7 0.347 7 0.347
7 0.507 7 0.720 7 0.875
7 0.135 7 0.135 7 0.135
acceleration components at an arbitrary heeling angle. The liquid pressure at a given point is obtained by multiplication of the acceleration and the liquid height. The acceleration ellipses in the y z plane and x z plane are used for the sake of the simplification of calculation. Fig. 4 corresponds to the cross sections of ellipsoid at the middle of the ellipse in y z and x z coordinates. When acceleration ellipsoid is described by the combined angles α and β , the governing acceleration vectors aβ and aα corresponding to the angles for a given location of the vessel can be determined within the ranges 0 r β r β max and 0r α r αmax where the maximum angles βmax and αmax are defined as shown in Fig. 4. The resulting acceleration in an arbitrary direction is determined along the perimeter line in Fig. 4 in which the acceleration includes both the static and dynamic components. In Fig. 4, the magnitude 1.0 in the vertical direction represents the acceleration of gravity with units of g. Thus, the intersection of the acceleration ellipse and a straight line with angles β or α is defined as the resulting acceleration. On the ellipse in the y-z plane, the value of β in an arbitrary direction β is described as follows: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi aβ ¼ aβy 2 þ ð1 þ aβz Þ2 ð13Þ The relationship between aβy and aβz is expressed by aβz ¼ aβy tan ðπ =2 β Þ 1
ð14Þ
where aβy is again expressed with ay and az using the following equation for the ellipse: aβy 2 aβz 2 þ 2 ¼1 ay 2 az
ð15Þ
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U. Choi et al. / Ocean Engineering 101 (2015) 40–46
2.4. Liquid pressure with maximum liquid height The maximum liquid height, zβ , occurs at the corner of the bottom surface of the prismatic vessel (point 2 in Fig. 3). For a full load condition, the maximum zβ at point 2 is expressed as ð20Þ zβ2 ¼ h þ l tan β cos β In reality, loading conditions of up to 98% are considered in the calculation of zβ and, the equation for the liquid height at point 2, zβ2 can be obtained. The heeling angles where the liquid pressures are maximized are listed in Table 4.
3. Vapor pressure The vapor pressure should not normally exceed 0.25 barg. However, if the cargo containment system is designed for a higher vapor pressure, it can be increased to such higher value. Nevertheless, the vapor pressure should not exceed 0.7 barg if the storage vessel is supported by the inner hull. The calculated liquid pressures are used to obtain the internal pressure of the vessel, including the vapor pressure. In this study, the dimensions of the prismatic LNG storage vessel are 40 m 40 m 30 m. The LNG is a cryogenic fluid stored at low temperatures ( 162 1C). The LNG is influenced by the inherent heat ingress of the vessel under environmental conditions. The heat ingress warms the LNG, which causes it to exceed its boiling temperature. Calculation of the vapor pressure is described by the material and energy balance equations (Henley and Rosen, 1969): X X ∂m X _ in xðiÞin Þ _ out_liq xðiÞout_liq Þ _ out_vap xðiÞout_vap Þ ¼ ðm ðm ðm ∂t ð21Þ Fig. 4. Acceleration ellipse in transverse (y z plane) direction (a) and longitudinal (x z plane) direction (b).
Letting k denotes tan ðπ =2 βÞ, Eq. (15) is changed to aβy 2 ðaβy k 1Þ2 þ ¼1 ay 2 az 2
ð16Þ
kay aβ y ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 7 k ay 4 ay 2 az 2 þ k ay 2 1 az 2 2
az 2 þ k ay 2
q_ 1 ¼ kcond A ð17Þ
Thus, aβ from Eq. (13) can be expressed as a function of β , ay , and az as follows: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h i2 aβ ¼ aβy 2 þ aβy tan ðπ =2 β Þ
aβ y ¼
2
az 2 þ k ay 2
ay
1 az 2
q_ 2 ¼ kconv A∂T
ð23Þ
where q_ 1 is thermal conduction and q_ 2 is thermal convection. It is expressed by q_ ¼ U A ∂T
ð24Þ
The overall heat transfer coefficient U is estimated by heat transfer analysis related to the insulation layer. Table 4 Heeling angle for maximum liquid pressure.
ð18Þ
The maximum heeling angle (βmax ) is obtained by manipulating the equations of the ellipse and the tangent line as follows.
π 1 az 2 ffi βmax ¼ tan 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi
∂T ∂l
with
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 kay 2 7 k ay 4 ay 2 az 2 þ k ay 2 1 az 2
2
ð22Þ
_ is mass flow rate, xðiÞ is mass fraction for component, h is where m mass specific enthalpy, and q_ is heat input. It is assumed that heat is mainly transferred by thermal conduction and convection. The heat input (q_ in ) caused by the temperature difference between the LNG and environmental temperature is expressed as q_ ¼ q_ 1 þ q_ 2
and solving for aβy , we get 2
X X ∂H X _ in hin Þ _ out_liq hout_liq Þ _ out_vap hout_vap Þ þ q_ in ¼ ðm ðm ðm ∂t
ð19Þ
The values for zβ are determined according to Fig. 3, perpendicular from the point at the tank shell to the liquid level.
Liquid level (%)
Heeling angle (deg.)
98 90 80 70 60 50 40 30 20 10
38 36 34 34 34 36 38 38 38 38
U. Choi et al. / Ocean Engineering 101 (2015) 40–46
45
Table 6 LNG composition (Salehpour and Nasrifar, 2008). Component
Mole fraction
Methane Ethane Propane Butane Nitrogen
0.94 0.047 0.008 0.002 0.003
Fig. 5. Pressure behavior according to various Insulation thickness (PUF).
Table 5 Thermal properties in vessel surfaces. No
Layer
Properties
Unit
Value
1 2
LNG 9% Nickel Steel
3
Polyurethane
4
Air
Temperature Thickness Thermal conductivity Thickness Thermal conductivity Convection coefficient
K m W/m K m W/m K W/m2 K
111.5 0.026 21 0.350 0.023 318.5
Overall heat transfer coefficient
W/m2 K
0.0655
Fig. 7. Design pressure of storage vessel.
layer is not enough for the protection of the heat ingress from the ambient temperature. It results in the increase of the vessel pressure. The vapor pressure of the storage vessel is defined as below 0.7 barg in IGC code. The vapor pressure of the storage vessel is 0.7 barg as an end vapor pressure after bunkering operations of storage vessels. To design the appropriate thickness of insulation layer, heat transfer study should be conducted. The temperature of environment is 45 1C that is the upper ambient design temperature with the cargoes to be carried for normal service. That temperature is a severe temperature during the LNG storage vessel voyage. Fig. 5 shows the pressure behavior according to various insulation thicknesses. In this study, 350 mm thick polyurethane insulation layer was obtained to satisfy the pressure criteria for up to 30 days of navigation. The thermal properties of the materials used in this study are listed in Table 5.
Fig. 6. LNG height during boil-off gas generation, LVF 98%.
3.1. Insulation layer The heat flow rate can be obtained from a heat transfer analysis of the LNG storage vessel. For a storage vessel with a constant volume, the pressure increase results from the generated boil-off gas. To maintain the acceptable pressure range, an adequate insulation layer is needed to protect the heat ingress. The thick insulation layer sufficiently protects the heat ingress from ambient temperature. However, that causes the cost increase for LNG cargo vessel and occupies the space in the ship, which is related to the cost about the cargo space. On the other hand, the thin thickness
3.2. Dynamic simulation The increase of vapor pressures can be somewhat offset by the decrease of the maximum liquid pressure during 30 days voyage. The LNG height is decreasing from generating the boil-off gas by the heat ingress. The decrease of the liquid volume influenced by the boil-off gas is shown in Fig. 6. Some studies for the influence of BOG on the pressure of LNG tanks were reported (Adom et al., 2010; Gorla, 2010). In this study, for the determination of the vapor pressures considering BOG, a dynamic simulation is conducted using a commercial software gPROMS developed by PSE. The LNG composition used for the calculation of the vapor pressure is shown in Table 6. As indicated in Fig. 7, the vapor pressure increases while the liquid pressure decreases with time.
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U. Choi et al. / Ocean Engineering 101 (2015) 40–46
Table 7 Design pressure by conventional method.
po pgd pi pd
Properties
Storage vessel (barg)
Design vapor pressure Internal liquid pressure Internal pressure Design pressure
0.7 2.56 3.26 3.26
Acknowledgement
Table 8 Design pressure.
po pgd pi pd
vapor pressure (0.67 barg) and the liquid pressure (2.39 barg) in 30 days. As indicated in Fig. 7, the maximum design pressure is the pressure after 30 days summed by the decreased internal liquid pressure and the increased vapor pressure. It considers phase change of liquid to vapor based on heat ingress from outside. In conclusion, the design pressure should be defined by the maximum pressure in the LNG cargo operation, considering the liquid pressure and vapor pressure.
Properties
Storage vessel (barg)
Vapor pressure in 30 days Liquid pressure in 30 days Internal pressure Design pressure
0.67 2.39 3.06 3.06
4. Conclusion and discussions This study proposes a method for the estimation of design pressure that consists of the vapor pressure and the internal liquid pressure in a prismatic type B vessel. The procedure for estimating the design pressure of the prismatic storage vessel is given. In the case of the conventional method (Senjanović et al., 2005), the design pressure of the prismatic storage vessel is about 3.26 barg as shown in Table 7. In this method, the design vapor pressure is fixed at 0.7 barg as limited upper value during voyage and the internal liquid pressure 2.56 barg is calculated by the same equation used the proposed method. However, the conventional method for internal liquid pressure does not consider the decreasing of LNG height, which has an effect on liquid pressure in terms of dynamic force. This method does not reflect the pressure behavior arising from the change of vapor pressure and internal liquid pressure by time variation. The design pressure 3.06 barg in Table 8 was estimated by the proposed method, which is the equivalent of the maximum internal pressure obtained from the
This research was supported by a grant from the LNG Plant R&D Center funded by the Ministry of Land, Trasportation and Maritime Affairs (MLTM) of the Korean government. References Adom, E., Islam, S.Z., Ji, X., 2010. Modeling of boil off gas in LNG tanks: a case study. Int. J. Eng. Technol. 2, 292–296. ASME, 2010. ASME Boiler and Pressure Vessel Code: Section VIII Division 2, New York, pp. 139 196. Det Norske Veritas, 2011. Rules for Classification of Ships: Liquefied Gas Carriers, Oslo. Germanischer Lloyd, 2008. Rules for Classification and construction: Ship Technology, Hamburg, pp. 7 12. Gorla, R.S.R., 2010. Rapid calculation procedure to determine the pressurizing period for stored cryogenic fluid. Appl. Therm. Eng. 30, 1997–2002. Henley, E.J., Rosen, E.M., 1969. Material and Energy Balance Computations. John Wiley & Sons, Houston. IMO, 2008. International Code for the Construction and Equipment of Ships Carrying Liquefied Gasses in Bulk, London, pp. 38 53. Itoyama, N., Yuasa, K., Miyazawa, M. 1989. A new generation of spherical tank LNG carriers. In: Proceedings of the 9th International Conference on Liquefied Natural Gas, Nice, France. Kumar, S., Kwon, H.-T., Choi, K.-H., Lim, W., Cho, J.H, Tak, K., Moon, I., 2011. LNG: an eco-friendly cryogenic fuel for sustainable development. Appl. Energy 88, 4264–4273. Salehpour, A., Nasrifar, K., 2008. Predicting the liquid density of gas condensate and LNG mixtures form equations of state. J. Fac. Eng. 42 (2), 257–268. Senjanović, I., Slapničar, V., Mravak, Z., Rudan, S., Ljuština, A.M. 2005. Structure design of cargo tanks in liquefied gas carriers. In: Proceedings of the International Congress of Marine Research and Transpiration, ICMRT'05, Ischia, Naples, Italy.
Contents lists available at ScienceDirect
Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng
Estimation of the design pressure of a prismatic LNG storage vessel Unheon Choi, Daejun Chang n, Choonghee Jo Division of Ocean System Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, South Korea
art ic l e i nf o
a b s t r a c t
Article history: Received 16 June 2014 Accepted 5 April 2015
This study proposed a method of estimating to design pressure in a prismatic storage vessel for liquefied natural gas. The estimation of the design pressure refers to the IGC Code that provides the international standards for storage of liquefied gases in bulk. The estimation of the design pressure was a basic step to scheme a storage vessel. The design pressure resulted from the vapor pressure and the maximum liquid pressure. The liquid pressure was calculated from the effect of gravity and the acceleration applied to the center of gravity of the liquid. Loading conditions of up to 98% were considered in the calculation of the maximum liquid height. The heat ingress warmed the LNG, which caused it to exceed its boiling temperature. Calculation of the vapor pressure was described by the material and energy balance equations. Dynamic simulation about the pressure behavior was conducted by commercial software. The vapor pressure affected by heat ingress from surrounding conditions was calculated with time variations. & 2015 Elsevier Ltd. All rights reserved.
Keywords: LNG Design pressure Prismatic storage vessel Vapor pressure Liquid pressure
1. Introduction LNG is usually carried by ships that are specially designed to store cryogenic cargo ( 160 1C) and protected to prevent LNG leakage even in the case of an accident. On these ships, LNG is stored in specific containment systems. Over the last twenty years, there have been many attempts to develop better means of transportation for LNG (Kumar et al., 2011). Two types of vessels are mainly used as gas carriers. The first type of vessel is the MOSS type vessel, which is a spherical, self-supporting vessel. The other type of vessel is the membrane type vessel. The use of MOSS type vessels is gradually decreasing while the use of membrane type vessels is increasing. The reason of this shift is in the superior volume efficiency of the membrane type vessel that is more economical to transport cargo in limited space available on ships. The storage vessel can theoretically be constructed in any shape, however spheres and cylinders are the most commonly used shapes. More complicated shapes as prismatic type are far more difficult to design to ensure safety and are even harder to construct. The ASME Boiler and Pressure Vessel Code (ASME, 2010) provides design rules for rectangular vessels. These rules cover some common noncircular type vessels but are limited in terms of the design regulations. According to IMO IGC code (IMO, 2008), LNG fuel vessels must be selected from ‘Independent Types A, B, or C’. For LNG-fuelled
n
Corresponding author. Tel.: þ 82 10 4801 0172; fax: þ 82 42 350 1553. E-mail address: [email protected] (D. Chang).
http://dx.doi.org/10.1016/j.oceaneng.2015.04.018 0029-8018/& 2015 Elsevier Ltd. All rights reserved.
carriers, there are several options on installing the LNG tank. LNG carriers are typically equipped with membrane-type vessels or type B vessels. Small ships may be equipped with type C vessels. Type B prismatic vessels describe that are adjustable to hull shape and partial secondary barrier. Although this shape is to require BOG handling by propulsion engines, boilers or reliquefaction and complex fuel system and high costs, it has space efficiency in terms of storage of LNG compared to circular type vessels. Spherical tank made with partial secondary barrier also requires BOG handling and complex fuel system (Itoyama et al., 1989). In this study, design pressures for a prismatic vessel defined by Type B vessel are estimated. Design pressure of pressure vessels is a key factor on the vessel design because it influences on the vessel thickness and manufacturing. The design pressure is determined by summing up the liquid pressure and the vapor pressure. In the previous methods, liquid pressures are estimated by rules and international codes, and the vapor pressure is usually adapted as 0.7 barg based on the regulation (Senjanović et al., 2005). Thus, the commonly used formulas for the design pressure in the storage vessel are overestimated, and there is little consideration for chemical phenomena between the liquid and vapor. In the original international standard and code, hydrostatic pressure and vapor pressure are added after the separate estimation of them. Also, the continually generated boil-off gas affects the design of the LNG cargo vessels due to the pressure increase. The LNG cargo vessels should have acceptable ranges of the vessel pressure in order to resist the pressure increase by the boil-off gas in a constant volume. According to the rules (Det Norske, 2011), the
U. Choi et al. / Ocean Engineering 101 (2015) 40–46
Nomenclature A a0 ax ay az aα aβ aβy aβz B BWL CB E FD g GM h L m _ m Pi P0 P gd q_ q_ 1 q_ 2
infinitesimal area over which the liquid pressure is applied basic acceleration dimensionless acceleration in the longitudinal direction dimensionless acceleration in the transverse direction dimensionless acceleration in the vertical direction relative acceleration in x z plane relative acceleration in y z plane component of aβ in the y direction component of aβ in the z direction molded breadth molded breadth measured amidships at the scantling draught waterline. block coefficient of the ship modulus of elasticity dynamic force acceleration of gravity metacentric height mass specific enthalpy molded length mass of the water column above the area A mass flow rate internal pressure vapor pressure liquid pressure total heat input heat input by thermal conduction heat input by thermal convection
vapor pressure of Type B vessel should not exceed 0.7 barg, which is required to prevent the potential release of BOG in the event of tank failure. The vapor pressure is inherently increasing from the environmental condition; however the equation in IGC Code does not reflect the pressure behavior with time variations. In this study, in order to estimate the reasonable design pressure, a method that simultaneously considering the vapor pressure and the
41
Re Rm t T T sc U V x
specified minimum yield stress specified minimum tensile strength time (s or day) temperature scantling draught overall heat transfer coefficient service speed of ship longitudinal distance from amidships to the center of gravity of the tank xðiÞ mass fraction for component z vertical distance from the ship's actual waterline to the center of gravity of tank zβ maximum liquid height zβ 2 maximum zβ at point 2 α heeling angle in x z coordinate αmax maximum heeling angle in x z coordinate β heeling angle in y z coordinate βmax maximum heeling angle in y z coordinate ρ density of liquid ∇ displacement of ship σm equivalent primary general membrane stress σL equivalent primary local membrane stress σb equivalent primary bending stress ν Poisson's ratio ASME American society of mechanical engineers BOG boil-off gas IGC Code international code for the construction and equipment of ships carrying liquefied gases in bulk IMO international maritime organization LNG liquefied natural gas
liquid pressure in dynamic condition is presented; where in influence of processing components is considered. Fig. 1 shows the process flow diagram for LNG carrier that has cargo vessels. The LNG cargo systems control the cargo vessel pressure in consuming the generated boil-off gas due to the heat ingress. The LNG cargo systems consist of the LNG cargo vessels, LNG forcing vaporizer, gas header, fuel gas conditioning units and generator engine.
Fig. 1. LNG cargo handling system.
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U. Choi et al. / Ocean Engineering 101 (2015) 40–46
sloshing for full-loaded cargo tank. It is given by
2. Design pressure The estimation of the design pressure is a basic step to scheme a storage vessel. The calculated design pressure is used to obtain the total pressure of the storage vessel including the vapor pressure. The dimensions of the storage vessel and the ship particulars are shown in Table 1 and Fig. 2. In the IMO IGC code (IMO, 2008), the allowable stresses should not exceed specific values for type B independent vessels listed below.
σm r f σ L r1:5f σ b r 1:5F σ L þ σ b r1:5F σ m þ σ b r 1:5F σ m is the equivalent primary general membrane stress, σ L is the equivalent primary local membrane stress, σ b is the equivalent primary bending stress, f is the the lesser of Rm =A or Re =B, F is the the lesser of Rm =C or Re =D Re and Rm are specified minimum yield stress and tensile strength at room temperature, respectively. 9% Ni steel (material ASTM specification number A553) is a commonly used cryogenic material in natural gas containment systems. This material has a yield stress (Re ) of 515 MPa and a tensile strength (Rm ) of 690 MPa. The modulus of elasticity (E) and Poisson's ratio (ν) are 185 GPa and 0.3, respectively. For nickel steels and carbon-manganese steels, parameters A, B, C, and D should have at least A¼ 3, B ¼2, C ¼3, and D¼ 1.5, respectively. In consequence, the allowable total stress should not exceed the smaller values for f and F, such that¼ 230 MPa. 2.1. Internal pressure The internal pressure results from the vapor pressure and the internal liquid pressure but does not include the effect of liquid
P i ¼ P o þ P gd
ð1Þ
here p0 is the vapor pressure, and pgd is the liquid pressure. The vapor pressure (p0 ) is the maximum pressure at the top of the vessel. 2.2. Liquid pressure The liquid pressure in the vessel results from the effect of gravity and the acceleration applied to the center of gravity of the liquid. As the ship moves, the liquid inside the vessel shifts with a heeling angle (β) as shown in Fig. 3. Typically, the liquid pressure is checked at the three points indicated in Fig. 3, and the largest liquid height (zβ ) above the point where the pressure is to be determined is measured from the vessel shell in the β direction, as illustrated in the Fig. 3. When fully loaded, the liquid surface can extend outside of the vessel. The liquid pressure at the vessel surface is calculated by the following procedure. When the dynamic force (F D ) from acceleration is applied to the liquid, the liquid pressure at the tank surface is expressed as pgd ¼
FD A
ð2Þ
where A is an infinitesimal area over which the liquid pressure is applied. The force has the form F ¼ maβ , and the mass (m) represents the mass of the water column above the area (A). The force is expressed by F D ¼ ðρzβ AÞaβ
ð3Þ
pgd ¼ ρzβ aβ
ð4Þ
where ρ is the density of the liquid. In Eq. (4) aβ is the relative acceleration. Thus, P gd is expressed by the acceleration of gravity (g) as follows: pgd ¼ ρzβ ðaβ gÞ
Table 1 Ship and vessel parameters. Parameter
ð5Þ
Simplifying Eq. (5), the liquid pressure at the vessel surface, excluding sloshing, is expressed as follows: Value
pgd ¼
Ship Length over all (LOA) Length between perpendiculars (LBP) Breadth, molded Depth to main deck, molded Design draft Scantling draft Displacement (∇) Service speed
50 m 27 m 12 m 13.6 m 136,000 m3 19.5 knots
Vessel Breadth Height Length Volume
30 m 30 m 40 m 36,000 m3
315 m 303 m
ρzβ aβ
The dimensionless relative acceleration (aβ ) of the liquid due to the gravitational and dynamic loads acts perpendicular to the liquid surface. 2.3. Determination of acceleration The maximum dimensionless accelerations ax , ay , and az in the longitudinal, transverse and vertical directions, respectively, act on the center of gravity of the vessel. The values of ax , ay , and az depend on the ship characteristics and the coordinates of the chosen point. The value of az does not include the effect of the static weight. The value of ay includes the effect of the static weight in the transverse direction due to rolling. The value of ax includes the effect of the static weight in the longitudinal direction due to pitching. Eqs. (7)– (9) are used to determine the components of accelerations due to ship's motions in the North Atlantic (Det Norske, 2011). The longitudinal acceleration due to surges and pitches, including the gravity component of pitch, is expressed as follows (Lloyd, 2008). ax ¼ 7 a0
Fig. 2. Dimensions and orientation of prismatic vessel.
ð6Þ
1:02 104
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0:06 þ A2 0:25A
with
A ¼ 0:7
L z 0:6 þ5 1200 L CB ð7Þ
U. Choi et al. / Ocean Engineering 101 (2015) 40–46
43
Fig. 3. Direction of acceleration and liquid height under fully loaded conditions (a) and partially loaded conditions (b).
The transverse acceleration due to swaying, yawing, and rolling including the gravity component of rolling is expressed as follow: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x 2 κ Uz2 ay ¼ 7 a0 0:6 þ 2:5 þ 0:05 þ κ 1 þ 0:6 ð8Þ L B
Table 2 Metacentric height.
The vertical acceleration due to heaves and pitches is expressed as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 0:61:5 45 2 x þ 0:05 az ¼ 7 a0 1 þ 5:3 ð9Þ L L CB where L is the molded length, and B is the molded breadth. The basic acceleration is denoted by a0 , which is expressed as V 34 600=L a0 ¼ 0:2pffiffiffi þ L L
ð10Þ
where V is the service speed in knots. The longitudinal distance is denoted by x from amidships to the center of gravity of the tank with content (m) where x is positive forward of amidships, and negative aft of amidships. The vertical distance is denoted by z from the ship's actual waterline to the center of gravity of tank with content (m) where z is positive above the waterline and negative below the waterline. In addition,
κ¼
13GM ðκ Z 1:0Þ B
Generally; κ ¼ 1:0
ð11Þ
where κ generally has a value of 1.0, and GM is the metacentric height. For specific loading conditions and hull forms, it may be necessary to determine κ from the formula. The block coefficient of the ship is expressed as CB ¼
∇ LBWL T sc
ð12Þ
where T sc is the scantling draught, and BWL is the molded breadth measured amidships at the scantling draught waterline. The value of ay is sensitive to the metacentric height. The metacentric height is determined according to the three draught conditions as shown in Table 2. The dimensions of LNG carrier and the parameters used for the calculation of the accelerations in Eqs. (7)–(9) are listed in Table 2. When the same scantling draught is applied for three draught conditions, the acceleration components are calculated as shown in Table 3. There are no differences in the vertical accelerations and longitudinal accelerations for the three draught conditions because the same scantling draught is used for all of the draught conditions. To calculate the relative acceleration, the acceleration components ax , ay , and az are considered to act separately. Thus, the design acceleration is described by an ellipsoidal envelope of the three acceleration components ax , ay , and az . The ellipsoid surface represents the assumed worst simultaneous combinations of the
Draught condition
GM
Loaded at deep draught Loaded on reduced draught In ballast
0.12 B 0.24 B 0.33 B
Table 3 Accelerations acting on vessels. Draught condition (acceleration)
Vertical, az (g)
Transverse, ay (g)
Longitudinal, ax (g)
Loaded at deep draught Loaded on reduced draught In ballast
7 0.347 7 0.347 7 0.347
7 0.507 7 0.720 7 0.875
7 0.135 7 0.135 7 0.135
acceleration components at an arbitrary heeling angle. The liquid pressure at a given point is obtained by multiplication of the acceleration and the liquid height. The acceleration ellipses in the y z plane and x z plane are used for the sake of the simplification of calculation. Fig. 4 corresponds to the cross sections of ellipsoid at the middle of the ellipse in y z and x z coordinates. When acceleration ellipsoid is described by the combined angles α and β , the governing acceleration vectors aβ and aα corresponding to the angles for a given location of the vessel can be determined within the ranges 0 r β r β max and 0r α r αmax where the maximum angles βmax and αmax are defined as shown in Fig. 4. The resulting acceleration in an arbitrary direction is determined along the perimeter line in Fig. 4 in which the acceleration includes both the static and dynamic components. In Fig. 4, the magnitude 1.0 in the vertical direction represents the acceleration of gravity with units of g. Thus, the intersection of the acceleration ellipse and a straight line with angles β or α is defined as the resulting acceleration. On the ellipse in the y-z plane, the value of β in an arbitrary direction β is described as follows: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi aβ ¼ aβy 2 þ ð1 þ aβz Þ2 ð13Þ The relationship between aβy and aβz is expressed by aβz ¼ aβy tan ðπ =2 β Þ 1
ð14Þ
where aβy is again expressed with ay and az using the following equation for the ellipse: aβy 2 aβz 2 þ 2 ¼1 ay 2 az
ð15Þ
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U. Choi et al. / Ocean Engineering 101 (2015) 40–46
2.4. Liquid pressure with maximum liquid height The maximum liquid height, zβ , occurs at the corner of the bottom surface of the prismatic vessel (point 2 in Fig. 3). For a full load condition, the maximum zβ at point 2 is expressed as ð20Þ zβ2 ¼ h þ l tan β cos β In reality, loading conditions of up to 98% are considered in the calculation of zβ and, the equation for the liquid height at point 2, zβ2 can be obtained. The heeling angles where the liquid pressures are maximized are listed in Table 4.
3. Vapor pressure The vapor pressure should not normally exceed 0.25 barg. However, if the cargo containment system is designed for a higher vapor pressure, it can be increased to such higher value. Nevertheless, the vapor pressure should not exceed 0.7 barg if the storage vessel is supported by the inner hull. The calculated liquid pressures are used to obtain the internal pressure of the vessel, including the vapor pressure. In this study, the dimensions of the prismatic LNG storage vessel are 40 m 40 m 30 m. The LNG is a cryogenic fluid stored at low temperatures ( 162 1C). The LNG is influenced by the inherent heat ingress of the vessel under environmental conditions. The heat ingress warms the LNG, which causes it to exceed its boiling temperature. Calculation of the vapor pressure is described by the material and energy balance equations (Henley and Rosen, 1969): X X ∂m X _ in xðiÞin Þ _ out_liq xðiÞout_liq Þ _ out_vap xðiÞout_vap Þ ¼ ðm ðm ðm ∂t ð21Þ Fig. 4. Acceleration ellipse in transverse (y z plane) direction (a) and longitudinal (x z plane) direction (b).
Letting k denotes tan ðπ =2 βÞ, Eq. (15) is changed to aβy 2 ðaβy k 1Þ2 þ ¼1 ay 2 az 2
ð16Þ
kay aβ y ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 7 k ay 4 ay 2 az 2 þ k ay 2 1 az 2 2
az 2 þ k ay 2
q_ 1 ¼ kcond A ð17Þ
Thus, aβ from Eq. (13) can be expressed as a function of β , ay , and az as follows: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h i2 aβ ¼ aβy 2 þ aβy tan ðπ =2 β Þ
aβ y ¼
2
az 2 þ k ay 2
ay
1 az 2
q_ 2 ¼ kconv A∂T
ð23Þ
where q_ 1 is thermal conduction and q_ 2 is thermal convection. It is expressed by q_ ¼ U A ∂T
ð24Þ
The overall heat transfer coefficient U is estimated by heat transfer analysis related to the insulation layer. Table 4 Heeling angle for maximum liquid pressure.
ð18Þ
The maximum heeling angle (βmax ) is obtained by manipulating the equations of the ellipse and the tangent line as follows.
π 1 az 2 ffi βmax ¼ tan 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi
∂T ∂l
with
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 kay 2 7 k ay 4 ay 2 az 2 þ k ay 2 1 az 2
2
ð22Þ
_ is mass flow rate, xðiÞ is mass fraction for component, h is where m mass specific enthalpy, and q_ is heat input. It is assumed that heat is mainly transferred by thermal conduction and convection. The heat input (q_ in ) caused by the temperature difference between the LNG and environmental temperature is expressed as q_ ¼ q_ 1 þ q_ 2
and solving for aβy , we get 2
X X ∂H X _ in hin Þ _ out_liq hout_liq Þ _ out_vap hout_vap Þ þ q_ in ¼ ðm ðm ðm ∂t
ð19Þ
The values for zβ are determined according to Fig. 3, perpendicular from the point at the tank shell to the liquid level.
Liquid level (%)
Heeling angle (deg.)
98 90 80 70 60 50 40 30 20 10
38 36 34 34 34 36 38 38 38 38
U. Choi et al. / Ocean Engineering 101 (2015) 40–46
45
Table 6 LNG composition (Salehpour and Nasrifar, 2008). Component
Mole fraction
Methane Ethane Propane Butane Nitrogen
0.94 0.047 0.008 0.002 0.003
Fig. 5. Pressure behavior according to various Insulation thickness (PUF).
Table 5 Thermal properties in vessel surfaces. No
Layer
Properties
Unit
Value
1 2
LNG 9% Nickel Steel
3
Polyurethane
4
Air
Temperature Thickness Thermal conductivity Thickness Thermal conductivity Convection coefficient
K m W/m K m W/m K W/m2 K
111.5 0.026 21 0.350 0.023 318.5
Overall heat transfer coefficient
W/m2 K
0.0655
Fig. 7. Design pressure of storage vessel.
layer is not enough for the protection of the heat ingress from the ambient temperature. It results in the increase of the vessel pressure. The vapor pressure of the storage vessel is defined as below 0.7 barg in IGC code. The vapor pressure of the storage vessel is 0.7 barg as an end vapor pressure after bunkering operations of storage vessels. To design the appropriate thickness of insulation layer, heat transfer study should be conducted. The temperature of environment is 45 1C that is the upper ambient design temperature with the cargoes to be carried for normal service. That temperature is a severe temperature during the LNG storage vessel voyage. Fig. 5 shows the pressure behavior according to various insulation thicknesses. In this study, 350 mm thick polyurethane insulation layer was obtained to satisfy the pressure criteria for up to 30 days of navigation. The thermal properties of the materials used in this study are listed in Table 5.
Fig. 6. LNG height during boil-off gas generation, LVF 98%.
3.1. Insulation layer The heat flow rate can be obtained from a heat transfer analysis of the LNG storage vessel. For a storage vessel with a constant volume, the pressure increase results from the generated boil-off gas. To maintain the acceptable pressure range, an adequate insulation layer is needed to protect the heat ingress. The thick insulation layer sufficiently protects the heat ingress from ambient temperature. However, that causes the cost increase for LNG cargo vessel and occupies the space in the ship, which is related to the cost about the cargo space. On the other hand, the thin thickness
3.2. Dynamic simulation The increase of vapor pressures can be somewhat offset by the decrease of the maximum liquid pressure during 30 days voyage. The LNG height is decreasing from generating the boil-off gas by the heat ingress. The decrease of the liquid volume influenced by the boil-off gas is shown in Fig. 6. Some studies for the influence of BOG on the pressure of LNG tanks were reported (Adom et al., 2010; Gorla, 2010). In this study, for the determination of the vapor pressures considering BOG, a dynamic simulation is conducted using a commercial software gPROMS developed by PSE. The LNG composition used for the calculation of the vapor pressure is shown in Table 6. As indicated in Fig. 7, the vapor pressure increases while the liquid pressure decreases with time.
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U. Choi et al. / Ocean Engineering 101 (2015) 40–46
Table 7 Design pressure by conventional method.
po pgd pi pd
Properties
Storage vessel (barg)
Design vapor pressure Internal liquid pressure Internal pressure Design pressure
0.7 2.56 3.26 3.26
Acknowledgement
Table 8 Design pressure.
po pgd pi pd
vapor pressure (0.67 barg) and the liquid pressure (2.39 barg) in 30 days. As indicated in Fig. 7, the maximum design pressure is the pressure after 30 days summed by the decreased internal liquid pressure and the increased vapor pressure. It considers phase change of liquid to vapor based on heat ingress from outside. In conclusion, the design pressure should be defined by the maximum pressure in the LNG cargo operation, considering the liquid pressure and vapor pressure.
Properties
Storage vessel (barg)
Vapor pressure in 30 days Liquid pressure in 30 days Internal pressure Design pressure
0.67 2.39 3.06 3.06
4. Conclusion and discussions This study proposes a method for the estimation of design pressure that consists of the vapor pressure and the internal liquid pressure in a prismatic type B vessel. The procedure for estimating the design pressure of the prismatic storage vessel is given. In the case of the conventional method (Senjanović et al., 2005), the design pressure of the prismatic storage vessel is about 3.26 barg as shown in Table 7. In this method, the design vapor pressure is fixed at 0.7 barg as limited upper value during voyage and the internal liquid pressure 2.56 barg is calculated by the same equation used the proposed method. However, the conventional method for internal liquid pressure does not consider the decreasing of LNG height, which has an effect on liquid pressure in terms of dynamic force. This method does not reflect the pressure behavior arising from the change of vapor pressure and internal liquid pressure by time variation. The design pressure 3.06 barg in Table 8 was estimated by the proposed method, which is the equivalent of the maximum internal pressure obtained from the
This research was supported by a grant from the LNG Plant R&D Center funded by the Ministry of Land, Trasportation and Maritime Affairs (MLTM) of the Korean government. References Adom, E., Islam, S.Z., Ji, X., 2010. Modeling of boil off gas in LNG tanks: a case study. Int. J. Eng. Technol. 2, 292–296. ASME, 2010. ASME Boiler and Pressure Vessel Code: Section VIII Division 2, New York, pp. 139 196. Det Norske Veritas, 2011. Rules for Classification of Ships: Liquefied Gas Carriers, Oslo. Germanischer Lloyd, 2008. Rules for Classification and construction: Ship Technology, Hamburg, pp. 7 12. Gorla, R.S.R., 2010. Rapid calculation procedure to determine the pressurizing period for stored cryogenic fluid. Appl. Therm. Eng. 30, 1997–2002. Henley, E.J., Rosen, E.M., 1969. Material and Energy Balance Computations. John Wiley & Sons, Houston. IMO, 2008. International Code for the Construction and Equipment of Ships Carrying Liquefied Gasses in Bulk, London, pp. 38 53. Itoyama, N., Yuasa, K., Miyazawa, M. 1989. A new generation of spherical tank LNG carriers. In: Proceedings of the 9th International Conference on Liquefied Natural Gas, Nice, France. Kumar, S., Kwon, H.-T., Choi, K.-H., Lim, W., Cho, J.H, Tak, K., Moon, I., 2011. LNG: an eco-friendly cryogenic fuel for sustainable development. Appl. Energy 88, 4264–4273. Salehpour, A., Nasrifar, K., 2008. Predicting the liquid density of gas condensate and LNG mixtures form equations of state. J. Fac. Eng. 42 (2), 257–268. Senjanović, I., Slapničar, V., Mravak, Z., Rudan, S., Ljuština, A.M. 2005. Structure design of cargo tanks in liquefied gas carriers. In: Proceedings of the International Congress of Marine Research and Transpiration, ICMRT'05, Ischia, Naples, Italy.