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Theoretical and experimental analysis of the heating operation for cargo oil
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DOI: 10.1080/17445302.2022.2109352

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Theoretical and experimental analysis of the

heating operation for cargo oil shipped on an
actual voyage

Yu Wu, Leyang Dai, Ankang Kan, Chao Yang, Fang Wang & Gangshe Zhang

To cite this article: Yu Wu, Leyang Dai, Ankang Kan, Chao Yang, Fang Wang & Gangshe Zhang
(2022): Theoretical and experimental analysis of the heating operation for cargo oil shipped on an
actual voyage, Ships and Offshore Structures, DOI: 10.1080/17445302.2022.2109352

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SHIPS AND OFFSHORE STRUCTURES
https://doi.org/10.1080/17445302.2022.2109352

Theoretical and experimental analysis of the heating operation for cargo oil shipped on
an actual voyage
a
Yu Wu , Leyang Daib,c, Ankang Kand, Chao Yangd, Fang Wanga and Gangshe Zhange
a
Shanghai Engineering Research Center of Marine Renewable Energy, College of Engineering Science and Technology, Shanghai Ocean University,
Shanghai, People’s Republic of China; bFujian Provincial Key Laboratory of Naval Architecture and Ocean Engineering, School of Marine Engineering,
Jimei University, Xiamen, People’s Republic of China; cXiamen Key Laboratory of Marine Corrosion and Smart Protective Materials, Xiamen, People’s
Republic of China; dShanghai Frontiers Science Center of “Full penetration” far-reaching offshore ocean energy and power, Merchant Marine College,
Shanghai Maritime University, Shanghai, People’s Republic of China; eShanghai Jianqiao University, Shanghai, People’s Republic of China

ABSTRACT ARTICLE HISTORY

Cargo oil should be kept at a particular temperature to prevent transport difficulties caused by the high Received 14 March 2022
viscosity and pour point during shipping. Optimisation of the heating/insulation scheme on cargo oil Accepted 1 August 2022
must be investigated by studying the heat transfer mechanism of cargo oil, associated with the voyage
KEYWORDS
and hydrometeorological conditions. In this study, a theoretical model is developed to predict the heat Oil tanker; heating and
transfer of cargo oil in an oil tanker. The heating/insulation data are also measured in two voyages and thermal insulation; heat
compared with the predicted results. The relative errors of the temperature between the voyage and transfer; cargo oil tanks;
predicted results range from 9∼15% and 4∼6% without and with consideration of the voyage data
hydrometeorological conditions, respectively. The largest relative error of 15.1% is observed in the front
cargo tank (1C) affected by the wave/wind conditions. A steam flow rate of 1000∼4000 kg/h is
appropriated to optimise the heating/insulation scheme.

1. Introduction
behaviour of waxy crude oil in a double-plate floating roof oil
Shipping is one of the most important methods for crude oil trans- tank on the cooling process.
portation worldwide. Crude oil with high viscosity must be heated Some work was implemented to model and predict the heating
during transportation to prevent gelatinisation and ensure low flow and cooling processes for the oil in a cargo tank. For instance, Gar-
resistance for unloading. The heating operation of cargo oil is still cia (Martin et al. 2019) modelled the cooling process of cargo oil for
based on the long-term working experience of operators in general, a 10-°C temperature decrease on both the centre and wall of a cargo
but this is neither efficient nor economical. The high-temperature tank. Wei (Wei et al. 2016) investigated the effects of the geometry
steam produced by the fuel boiler is provided to heat the oil in of the cargo tank on the heat transfer mechanism by modelling the
cargo tanks, and optimisation of the heating and thermal insulation static cooling process of the waxy crude oil in the oil tanker. Farza-
scheme is beneficial to reduce fuel consumption, which is expected neh-Gord (Zhang et al. 2018; Farzaneh-Gord et al. 2020; Veloso
to further decrease energy losses and pollution emissions (Zhao et al. 2021) predicted the wax precipitation and temperature distri-
et al. 2019; Zhao et al. 2020). bution for crude oil in a cargo tank by modelling and experimental
The mechanism of the heat transfer process was studied by validation, and heat radiation was considered in particular. Zhao
both theoretical and experimental approaches to optimise the (Shen et al. 2017; Liu et al. 2019) proposed a wavelet finite element
heating/insulation scheme of crude oil as follows: Shadi (Rostami method to predict the cooling process of crude oil in a cargo tank
et al. 2018) improved the fluidity of crude oil by reducing the vis- with both experiments and simulations at liquid levels of 6.5 and
cosity with different methods and investigated the effects of the 11.5 m, respectively, to address the temperature distribution invol-
shear rate, temperature and light oil concentration on the oil vis- ving the cooling mechanism of crude oil in the cargo tank. They
cosity. Joao (Bassane et al. 2016) investigated the effects of temp- also (Zhao et al. 2014) studied the transient natural convection pro-
erature and gas condensate oil additives on oil viscosity to reduce cess and temperature distribution and pointed out that the evol-
the density and viscosity of oil. The heat and mass transfer pro- ution of the temperature field was assumed to be the local
cesses were also modelled and illustrated in the simulation cooling, integral cooling, thermal stratification and heat conduction
work. Sun (Sun et al. 2018; Sun et al. 2019) proposed a model processes. Akagi (Brkic and Praks 2021) evaluated the efficiency of
work to predict the heating process of a large floating roof tank the steam heating coil and the heat loss of the cargo oil based on the
coil; several conditions including the ambient temperature, solar heat transfer model for the steam coil.
radiation, heating steam pressure and physical properties of the Other work was focused on experimental measurements and
crude oil were considered in the simulated model. Zhou (Zhou analysis as follows: Kato (Yu et al. 2019) proposed a heat transfer
and Guo 2009) predicted the heating processes of steam coils in coefficient on the outer surface of the oil tank, which is positively
crude oil tanks, including the temperature distribution and energy correlated to the rolling effect based on the experimental measure-
consumption. Wang (Wang et al. 2017) developed a model to ment and empirical formula. Suhara (Magazinovic 2019) measured
evaluate the effect of wax precipitation and non-Newtonian the heat loss of a 33000 DWT oil tanker during the heating

CONTACT Chao Yang yc9316@163.com Shanghai Frontiers Science Center of “Full penetration” far-reaching offshore ocean energy and power, Merchant Marine
College, Shanghai Maritime University, Shanghai, 201306, People’s Republic of China; Gangshe Zhang 19252@gench.edu.cn Shanghai Jianqiao University,
Shanghai, 201306, People’s Republic of China
© 2022 Informa UK Limited, trading as Taylor & Francis Group
2 Y. WU ET AL.

procedure by arranging the sensors on the sidewall of the 1200-m3 Heat conduction and convection are considered for gaseous, ballast
cargo tank. Chen (Chen et al. 2022) measured the temperature of water and solid structures between the inner and outer hulls.
30,000 DWT FSO high-viscosity crude oil stored in an oil tank, Accordingly, the heat transfer process is defined based on the
and the heat losses, fuel consumption and thermal load were further energy conservation law as follows:
investigated in the heating process. Lin (Lin et al. 2021) built a test
∂t ∂t
rig to determine the controlling strategy on cargo oil heating. This ro vi,o co + rg vi,g cg = Ki,v Ai,v (tv − t) − Ki,u Ai,u t − ta
was appropriated to overcome the limitation of the heating method ∂t ∂t
3
(1)
of controlling the oil temperature but is unable to reflect the charac-
teristics of heat convection for the oil. Ivanov (Ivanov 2015) devel- − Ki,b Ai,b t − tsea − Ki,s Ai,s t − tsea − S Ki,j Ai,j (t − tj )
j=1
oped a code based on the heating transfer mechanism to guide the
heating procedures by setting the target temperature and uploading where ρo and ρd are the densities of the cargo oil and inert gas νi,o
the controlling parameters online. and νi,d are the volumes of the cargo oil and inert gas in cargo tank i,
As outlined above, heat transfer processes were investigated to respectively; co and cd are the specific heat capacities of the cargo oil
predict the heating and thermal insulation procedures for the and inert gas, respectively; Ki,v, Ki,u, Ki,b and Ki,s are the heat trans-
cargo oil. However, most of them were based on small-scale or fer coefficients of steam pipes, upper deck, bilge and side of the
local tank devices, and theoretical prediction or experimental cargo tank, respectively; Ki,1, Ki,2 and Ki,3 are the heat transfer
analysis/validation have been less investigated using actual data coefficients between the target tank and three adjacent cargo
of the operating procedures on board. The complex hydrome- tanks, respectively; tj is the cargo temperature of the adjacent
teorological conditions that appear during a voyage were seldom tank; Ai,1, Ai,2 and Ai,3 are the heat transfer surfaces with three adja-
considered in the open literature. In this study, both experimen- cent tanks; and τ is time.
tal and modelling methods are implemented to predict the heat- Equation 1 can be expressed as
ing and cooling processes of cargo oil on an actual voyage. The dt
effects of the hydrometeorological conditions (e.g. rain and + Mt = N (2)
dt
waves) and steam flow rate are investigated. The simulated
model is validated and proposed as an operating code to provide where
guidelines to optimise the heating and thermal insulation scheme 3
for cargo oil. Ki,v Ai,v + Ki,u Ai,u + Ki,s Ai,s + Ki,b Ai,b + S Ki,j Ai,j
j=1
M=
ro vi,o co + rg vi,g cg
2. Theoretical analysis of heat transfer process 3
Ki,v Ai,v tv + Ki,u Ai,u ta + Ki,b Ai,b tsea + Ki,s Ai,s tsea + S Ki,j Ai,j tj
The typical cross profile of the oil tank is shown in Figure 1. j=1
N=
The double hull structure is employed in the cargo tank, and ro vi,o co + rg vi,g cg
the side and bottom ballast tanks are allocated between the (3)
two hulls to ensure stability and buoyancy. The steam coil is
located in the bottom of the cargo tanks. The inert gas is also According to the initial conditions τ = 0 and t = t0, the
filled in the cargo tanks to prevent fire/explosion and volatiliz- expression of the heating time τ is expressed as
ation of the cargo oil. In addition, a single hull is designed on N
the top deck side, which is different from the hull structure on 1 to − M
the other sides. t = ln (4)
M N
It is assumed that the temperature of the cargo oil is the same as t−
M
that of the inert gas. The internal heat source is equal to zero in the
cargo oil (no reaction heat considered), and the latent heat of the Note that there is no heat source (steam in the heating coils) in
phase transition for the crude oil (e.g. solidification and vapouriza- the insulation process, and the heat source Ki,vAi,v(tv-t) in Equation
tion) and paraffin in the boundary layer are also not considered. 1 corresponds to zero in the thermal insulation (cooling) process.
The transfer processes occurring in the steam coil and oil tank
are addressed to clarify the heat transfer coefficients in Equation
4. As shown in Figure 2, five types of heat transfer processes are
considered in the steam coil and oil tank.

2.1. Steam coil

High-temperature steam is transferred through the heating coil
located in the bottom of the cargo tank, as shown in Figure 1.
The heat is transferred from the steam flow to the cargo oil as fol-
lows:
d2
ln
1 1 d1 1
= + + (5)
Kv Av hvi Avi 2pll hvo Avo
where hvi and hvo are heat convection coefficients of the steam
inside and outside the coil, respectively, d1 and d2 are the inner
Figure 1. The typical cross profile of oil tank. and outer diameters of the coil and l is the characteristic length.
 SHIPS AND OFFSHORE STRUCTURES 3

Figure 2. Heat transfer boundary conditions in oil tank (a is ballast water height in side ballast tank, b is oil height in tank).

2.2. Top side transfer process can be expressed as:

As shown in Figure 2(a), the heat is transferred from the oil tank to 1 di 1 d′o 1
the air side, which can be expressed as = + + + (7)
Ki,bottom Ai,bottom lm Awn2 KA lm Awo2 hsea Asea o2
1 1 dm,top 1
= + + (6) where hsea is the heat convection coefficient of the sea water outside,
Ki,top Ai,top hinert Ai,top lm Ai,top hair Ai,top and δi and δo are the thicknesses of the inner and outer tank hulls,
where hinert and hair are the heat convection coefficients of the inert respectively. KA denotes the transfer process in the ballast tank,
gas and air, respectively, and δ and λm are the thickness and con- including the heat conductivity of the stiffness ribs and the heat
ductivity of the top wall, respectively. convection of the ballast water:
1 dk 1
= + (8)
KA lm A′k + la A′a2 hwy Awo2
2.3. Bottom side
where λm is the thermal conductivity of the stiffener, A’k is the
The heat is also transferred from the oil to the sea water on the bot- cross section of the stiffener, λa is the thermal conductivity of
tom side. As shown in Figure 2(b), the double-hulled tank is the air, A’a2= Awn2- A’k is the horizontal cross-sectional area with-
employed at the bottom side mentioned above, and ballast water out the stiffener, hwy is the heat transfer coefficient of the ballast
is stored at the bottom ballast tank. It is assumed that there is no water and Awo2 and Awn2 are the outer and inner hull areas,
temperature difference between the oil and hull. Then, the heat respectively.
4 Y. WU ET AL.

2.4. Inner side boundary between tanks the insert gas/oil in the cargo tank, respectively:
The heat transfer processes between different oil tanks are shown 1 1 dm 1 dn 1
= + + + + (12)
in Figure 2 (c) and can be divided into three parts of the tank K1 A1 hinert Awn1 lm Awn1 K1′ A′1 ln Awo1 hsea Awo1
wall as h1, h2 and h3. Then, the heat transfer in Equation 1 can be
addressed as 1 1 dm 1 dn
= + + +
K2 A2 hoil/inert Awn2 lm Awn2 K2′ A′2 ln Awo2
q = (K1 A1 + K2 A2 + K3 A3 )(t − tj ) (9) 1
+ (13)
where K1A1, K2A2 and K3A3 denote the heat transfer processes at h1, hsea Awo2
h2 and h3, respectively. K1A1 denotes the heat transfer between the 1 1 dm 1 dn 1
inert gas through the h1 part of the tank wall. Similarly, K2A2 and = + + + + (14)
K3 A3 hoil Awn3 lm Awn3 K3′ A′3 ln Awo3 hsea Awo3
K3A3 denote the heat transfer between the oil and inert gas of differ-
ent tanks in the h2 part and between the oil of different tanks in h3, where hinert and hsea are the heat convection coefficients of the
respectively. For example, the heat transfer coefficient of K2A2 can inert gas and sea water, respectively; δm and λm are the thick-
be expressed as ness and heat conductivity of the outside wall of the cargo
tank, respectively; and δn and λm are the thickness and heat
1 1 di 1 conductivity of the inside wall of the cargo tank, respectively.
= + + (10)
K2 A2 hoil A2 lm A2 hinert A2 K’1A’1, K’2A’3 and K’3A’3 denote the heat transfer processes in
the ballast tank in consideration of the ballast water, stiffening
where hinert and hoil are the heat convection coefficients of rib and air, which are associated with the heights of the ballast
the inert gas and oil, respectively, and δ and λm are the thick- water and cargo oil, as shown in Figure 2(d)-(f). Notably, Eq. 13
ness and conductivity of the wall, respectively. Notably, the is equal to 0 when the height of the ballast water is identical to
heat transfer process at h2 is considered as three cases: the the height of the cargo oil in Figure 2(e).
height of the oil on the left side is higher, equal to and lower
than the height of the oil on the right side, which will be
illustrated later. 2.6. convection coefficients and dimensionless numbers
The transfer coefficients of the heat convection are addressed
according to the mechanism of heat transfer processes in different
2.5. Outside boundary between tank and sea working conditions. For example, the convection coefficient can be
The heat transfer processes between the cargo oil and sea water expressed as
are shown in Figure 2(d)-(f). The height of the sea water is l
higher than the oil height in most draft conditions of the h = Nu (15)
l
oil tanker, but there are ballast tanks with the sea water on
the outside of the cargo tank, which may affect the heat trans- where λ is the heat conductivity of the material, l is the character-
fer process between the oil and sea water. Accordingly, the istic length (or inner/outer diameters for the heating coil) and Nu
heat transfer process is divided into three different parts h1, is the Nusselt number to evaluate the heat convection, which
h2 and h3 [similar to the inner side boundary in Figure 2(c)] depends on the working conditions. In this study, two types of
between the ballast water and the cargo oil. These are calculated heat convection are considered in the model: (1) Natural convec-
as follows: tion in the finite space is introduced for heat convection in the
oil tank or ballast tank, e.g. the heat convection of the inert gas
q = Kside Aside (t − tw ) = (K1 A1 + K2 A2 + K3 A3 )(t − tw ) (11) on the top region of the cargo tank. (2) Forced convection over
the steam coil, flat plane or outside wall, e.g. the heat convection
where K1A1, K2A3 and K3A3 denote the heat transfer processes of air or sea water outside the wall. Then, the Nusselt number is
at h1, h2 and h3 between the air/water in the ballast tank and introduced as follows.
For natural convection in finite space:
Nud = CGrPrn (16)
Table 1. Convection coefficients of heat transfer boundaries in oil tank model.
Wall Convection Nusselt number with different convection g bl3 (tw − t1 )
conditions coefficient: mechanism: Gr = (17)
l g2
hd = Nud
l For forced convection:
Heating coil Steam side: hvi Re<5×104: Nuvapor = 5.03Re1/3 1/3
vapor Prvapor
4/5
Re≥5×10 : Nuvapor = 0.0265Revapor Pr1/3
4
Nuair = CRem n
air Prair (18)
vapor
Oil side: hvo Nuoil = 0.48(Groil Proil )1/4
Top Air side: ha Nuair = 0.037Re4/5
air Prair
1/3
ul
Inert gas: hinert Nud = 0.061(GrPr) 1/3 Re = (19)
g
Bottom Ballast water: hwater Nuair = 0.13(GrPr)0.3
Sea water: hsea Nusea = 0.037Re4/5 1/3 For the steam velocity inside the heat coil:
sea Prsea
Inner wall Oil: hoil Nud = 0.1(GrPr) 1/3
Ge
Inert gas: hinert u= p (20)
Outside wall Oli: hoil Nud = 0.1(GrPr) 1/3
r l2
Inert gas: hinert 4
Ballast water: hballast Nuw = 0.046(GrPr)1/3 where Gr, Pr and Re are the dimensionless numbers; β is the volume
Sea water: hsea Nusea = 0.037Re4/5 1/3
sea Prsea expansion coefficient, t is the temperature; and γ and u are the
 SHIPS AND OFFSHORE STRUCTURES 5

kinematic viscosity and velocity of the fluid material, respectively. L unloading. Major operating parameters on voyage 077 are listed
is the characteristic length (which denotes the diameter of the steam in Table 3 as follows:
coil), and Ge is the mass flux of the steam flow (kg/s). C, m, n and p As shown in Table 3, the loading temperature at Ulsan port
are the effective parameters associated with the different heat con- ranges from 64–65 °C, the required heating temperature is 56–57
vection conditions and are listed in Table 1. °C, the required thermal insulation temperature is higher than
57.2 °C and the unloading temperature at Huangpu port ranges
from 58–60 °C. Twenty-four hours are required for heating the
3. Experimental measurement on actual voyage
cargo oil in tank 1C, and 5 h are required to heating the cargo oil
The actual heating and thermal insulation data on board are tested for other cargo tanks. Four days are cost in voyage 077, which is
on the voyages of a 72000 DWT oil tanker ‘LIAN AN HU’ (Dalian much shorter than that of 15 days in voyage 076. Therefore,
Ocean Shipping Company, China). There are 11 cargo tanks named cargo tank 1C is heated for one day, while the other cargo tanks
1C, 2P/S, 3P/S, 4P/S, 5P/S and 6P/S from the bow to the stern in are heated for only 5 h before unloading. The fuel consumption
Figure 3. The cargo oil heating system is also shown in Figure 3: of the boiler is approximately 7–8 MT in voyage 077. The heating
the high-pressure steam is produced by the fuel boiler in the engine operation was started at 16:00 on 1st April for cargo tank 1C and
room and is sent to the cargo tanks through the main steam pipe was started at 9:45 on 2nd April until unloaded at Huangpu port.
allocated on the top side (deck) of the oil tanker. The steam is
further distributed through the branching pipes and is transported
4. Modelling prediction and discussion
down to the steam coils in the bottom of the cargo tank to heat the
oil. After that, the returning steam/water is sent back from the cargo The heat transfer models in the oil tanker are built to predict the
tank to the water tank in the engine room for cycling. The pressure heating and thermal insulation procedures for the cargo oil in
and flow rate of the steam are measured and controlled by the con- Voyages 076 and 077 presented above. The geometric parameters
trolling system. The oil temperature is also monitored by several of the cargo tanks in the LIAN AN HU oil tanker, the operating
temperature sensors distributed in the cargo tank. As shown in and temperature-dependent parameters including the density, vis-
Figure 4, five sensors are allocated in one monitoring plane, and cosity, thermal conductivity, specific heat at constant pressure, ther-
four planes are allocated in the tank (the on plane is located on mal expansion coefficient, etc., are collected on voyages 076 and 077
the steam coil). The average temperature of the cargo oil in the for the cargo oil, steam, air, inert gas and sea water. The theoretical
tanks is obtained. model is also coded based on Visual Studio in the C language. The
predicted results are compared with the onboard data from voyages
076 and 077 for validation. The effects of the hydrometeorological
3.1. Voyage 076
and steam flow rates are investigated to improve the accuracy of the
The general information of voyage 076 is listed below: the oil tanker predicted results compared with the onboard data.
‘LIAN AN HU’ (72000 DWT) with 81223.9 m3 SRFO cargo oil
departed from Singapore Port on March 10th and arrived at Kawa-
4.1. Results of standard model vs. voyage data
saki Port on March 21st and to Osaka Port on March 24th for
unloading. Major operating parameters on voyage 076 are listed The predicted results are compared with the on-board data for
in Table 2 as follows: different cargo tanks on voyage 076, as shown in Figure 5. The pre-
where Pl is the loading steam pressure, Pu is the loading pressure, dicted temperature is higher than the measured temperature, which
Tl is the required heating temperature, Th is the required heat insu- indicates that the heat transfer model employed in this study is still
lation temperature, Ti is the required heat insulation temperature, ‘ideal’ because some heat loss mechanisms have not yet been con-
Tu is the unloading temperature and τh and τi are the heating sidered. The oil temperature first decreases from 45 °C to 38 °C
and insulation times, respectively. for most cargo tanks because the cargo oil is cooled down for 3
As shown in Table 2, the loading temperature at the Singapore days, as mentioned above. As shown in Figure 5(a), the temperature
port ranges from 41–42 °C, and the required heating and insulation differences between the predicted and measured data in the front
temperatures are at least 42 °C. The unloading temperature in cargo tanks (1C, 2P/S, 3P/S) range from 2.3∼7 °C. It is clear that
Kawasaki and Osaka ports ranges from 51–53 °C. Partial cargo the errors are no more than 3 °C from March 15th ∼ 20th for all
oil was unloaded at Kawasaki port, and the others were unloaded of the cargo tanks, while they are up to 5∼7.5 °C on March 16th
at Osaka port. The heating time is 163 h for cargo tanks 1C, 2P/ and approximately 5.5∼9.2 °C on March 20th. According to the
S, 4P/S and 6P/S and 216.5 h for cargo tanks 2P/S, 3P/S and 5P/ voyage record, there is a large amount of rain on 16 March when
S. Because half the oil in cargo tanks 2P/S is unloaded at Kawasaki the oil tanker is sailing in the Philippine Sea, leading to an obvious
port. The heat insulation time is 98.5 h, while the fuel consumption temperature decrease in the oil in all of the cargo tanks. Similarly,
is 61.7 MT in total for the heating process. The cargo oil was natu- the predicted temperature also decreases with the decrease in the
rally cooled for three days and then heated until unloading. It is surrounding temperature from 22 °C to 18 °C, but the forced con-
noted that the cargo tanks 1C, 4P/S and 6P/S are empty during vection and other heat transfer mechanisms caused by rain are not
the voyage from Kawasaki to Osaka, which increases the heat losses considered in the theoretical model, leading to the underestimation
of the cargo oil tank adjacent to the empty tank. To ensure that the of the heat losses on the cargo tanks, particularly on the top deck
cargo oil is above 50 °C (the required unloading temperature for the side.
cargo oil), the heating procedure is implemented in the voyage from Similarly, a high difference in the oil temperature is achieved on
Kawasaki to Osaka. 20 March, e.g. a maximum error of 15.1% (8.9 °C) is achieved
between the predicted and measured temperatures in the No. 1C
cargo tank. Because there is a storm with a large wave when the
3.2. Voyage 077
ship is sailing from Kawasaki to Osaka, the wave is up to the
The general information of voyage 077 is listed below: 81,223.9 m3 deck frequently under a large wind for more than one day. Consid-
of cargo oil FO 180CST was uploaded and departed from Ulsan ering the full-load condition, the heat transfer process in the front
port on 29 March and arrived at Huangpu port on 2 April for oil cargo tanks (e.g. 1C, 2P/S) is obviously affected by the wave (16 °
6 Y. WU ET AL.

Figure 3. Schematic diagram of cargo oil heating system.

C of the local sea water temperature) and wind. This leads to a sig- for 5 h in other cargo tanks since March 29th in voyage 077.
nificant decrease in the oil temperature in the 1C and 2P/S cargos. Then, the cargo oil was under the heat insulation conditions (natu-
The forced convection mechanism of the wave and wind on the top ral cooling) until it arrived at Huangpu portas on April 2nd, as illus-
side of the cargo tanks is not considered in the theoretical model, trated in Section 3. It is clear that the temperature of the cargo oil
leading to large errors in the temperature differences between the decreases slowly in the thermal insulation processes, while the
predicted and measured results in the 1C and 2P/S cargos on 20 decrease in the oil temperature is larger in cargo tank 1C due to
March. the larger outer heating transfer surfaces on the ship bow region
As shown in Figure 5(b), the differences in the cargo oil temp- than in the other cargo tanks. In contrast with the results in voyage
erature on the back cargo tanks (No. 4P/S∼6P/S) are also high 076, the differences in the temperature between the measured and
(approximately 4.8∼6.2 °C) on March 16th because the forced predicted data are no more than 5% because there was no bad
heat transfer process was underestimated in heavy rain. While the weather, such as rain/snow or large winds/waves, in voyage 077,
temperature differences between the measured data and predicted and the heat losses are not underestimated in the modelling
results (2.8∼5.5 °C) for the back cargo tanks in the wave condition work. Accordingly, the predicted results of the heating and cooling
are not as high as those in the front cargo tanks in Figure 5(a), this processes are sufficiently accurate under clear weather conditions.
indicates that the effects of the wave are not obvious for cargo tanks As shown in Figure 7, the relative errors of the oil temperature
4P/S∼6P/S in the back regions. In addition, partial cargo oil in the are outlined between the measured and predicted results for the
1C and 4P/S tanks was unloaded at Kawasaki on March 19th, and different hydrometeorological conditions including the clear
the inert gas was filled in the empty cargo tanks with a 22∼26 °C weather, wave/wind, and rain conditions that appeared in voyages
decrease in the temperature, which is also a negative effect on the 076 and 077. It is clear that large relative errors are achieved
thermal insulation of the cargo tanks near the empty one. This between the voyage and predicted results, e.g. 5∼15% of the relative
leads to decreases in the oil temperature in the 2P/S∼5P/S cargo errors in the wave/wind conditions and 9∼12% of the relative errors
tanks after March 21 in both the measured and predicted results. in the rain conditions. Because the hydrometeorological conditions
As shown in Figure 6, another type of cargo oil (FO 180 CST) are not considered in the theoretical model, a strong heat transfer
was loaded at Ulsan port and heated for 1 d in carge tank 1C and mechanism such as force convection located on the topside/deck

Figure 4. Schematic diagram of sensor layout in cargo tanks.

 SHIPS AND OFFSHORE STRUCTURES 7

Table 2. Ooperating parameters of heating/insulation scheme in voyage 076. = 0 denotes clear weather. Similarly, the effect of the wave is
No. Pl/MPa Pu/MPa Tl/°C Th/°C Ti/°C Tu/°C τh/h τi/h defined as
1C 0.35 0.2 41 50 >42 51 163 98.5
uwave l
2P 0.35 0.2/0.35 41 50 >42 52 163/216.5 98.5 Rewave = (23)
2S 0.35 0.2/0.35 42 50 >42 52 163/216.5 98.5 gwave
3P 0.35 0.35 41 50 >42 53 216.5 98.5
3S 0.35 0.35 42 50 >42 53 216.5 98.5 hJ = C × 0.037Rewave
4/5 1/3
Prwave + (1 − C) × 0.037Re4/5 1/3
air Prair (24)
4P 0.35 0.2 42 50 >42 53 163 98.5
4S 0.35 0.2 42 50 >42 53 163 98.5 where uwave and rwave are the velocity and kinetic viscosity of the
5P 0.35 0.35 42 50 >42 52 216.5 98.5
5S 0.35 0.35 41 50 >42 52 216.5 98.5 sea water, respectively. Similarly, C is the effective parameter
6P 0.35 0.2 41 50 >42 53 163 98.5 between 0 and 1 to denote the wave condition, e.g. C = 1 and 0
6S 0.35 0.2 42 50 >42 52 163 98.5 denote a large wave and no wave, respectively.
As shown in Figure 8, the temperature of the cargo oil measured
of the cargo tanks is underestimated in rain/wave/wind weather onboard for voyages 076 and 077 are compared with the predicted
conditions. Furthermore, the relative error in cargo tank 1C results by the revised model in consideration of the hydrometeoro-
(15.1%) is the largest and decreases obviously for other cargo logical conditions. It is clear that the temperature differences
tanks. In particular, the relative errors are less than 5% in cargo between the measured and predicted values are remarkably reduced
tank 6P/S, which indicates that the effects of the wave can be in voyage 076 in Figure 8(a). For instance, the temperature differ-
omitted in the back cargo tanks, as presented above. Comparatively, ences range from 2.3∼4.1 °C on March 16th, which is lower than
large relative errors are achieved for all cargo tanks in the rain con- the 5∼7.5 °C differences in the previous model, indicating that
dition due to the estimation of the forced heat convection on the the heat losses caused by heavy rain are predicted more accurately
deck. In contrast, the relative errors are no more than 5% for the in this model. Similarly, the temperature differences range from
clear weather conditions in voyages 076 and 077, indicating that 2.5∼4.8 °C on March 20th, which is smaller than 5.5∼9.2 °C in
the predicted results are accurate enough without severe weather Figure 5, which indicates that the heat losses caused by the large
conditions appearing in the voyage. wave are also considered correctly in the revised model.
As shown in Figure 8(c), the relative errors of the oil tempera-
ture are presented between the measured and predicted results
4.2. Results of theoretical model with hydrometeorological for different hydrometeorological conditions. The relative errors
conditions vs. voyage data decrease remarkably when the hydrometeorological conditions
are considered in the theoretical model. For instance, the relative
As discussed in Section 4.1, the hydrometeorological conditions are errors are 4.4∼5.6% in Figure 8(c) vs. 5∼15% in Figure 7 under
not considered in the modelling work above. High differences in the wave/wind conditions and 4.2∼4.8% in Figure 8(c) vs. 9∼12% in
oil temperature appeared between the predicted and measured Figure 7 under rain conditions. In other words, the relative errors
results, which may be related to the underestimation of the hydro- of the oil temperature are decreased significantly by considering
meteorological conditions. Accordingly, the bad weather and waves the hydrometeorological conditions in the heat transfer model. In
occurring in the voyage are considered in the following model for addition, the errors (4%∼5.5%) are not obviously changed in the
prediction. The effects of the hydrometeor conditions are defined clear weather conditions in voyages 076 and 077, i.e. the modelling
in the heat convection of air on the top side of the oil tank (deck work is not improved significantly in good weather conditions.
region) in Figure 1. As mentioned in Equations (18)-(19), force
convection is assumed to occur between the air side and the flat
plane outside the cargo tanks. When the weather is not good, the
4.3. Effects of steam parameters on cargo oil heating
local Reynolds number is defined as
The cargo oil is heated with the high-pressure steam provided by the
u l
Rerain = rain (21) steam boiler in the engine room, as presented in Figure 2. The
grain steam is supplied continuously or intermittently to ensure that the vis-
where urain and rrain are the velocity and kinetics viscosity of the cosity of the cargo oil is not too high (or solidified), which is difficult to
rain (or snow). Then, the convection coefficient can be evaluated as deliver through the oil pipe, while the fuel consumption of the steam
boiler is also considered in consideration of the economic and pol-
hJ = C × 0.037Re4/5 1/3 4/5 1/3
rain Prrain + (1 − C) × 0.037Reair Prair (22) lution issues. This is not only associated with the heat transfer (losses)
model for the cargo tank presented above but also referred to as the
where C is the effective parameter between 0 and 1 to denote the steam (heat sources) supplied into the cargo tank. Accordingly, the
weather condition, e.g. C = 1 denotes heavy rain or snow, and C heat transfer coefficients and heating time are investigated with various
steam flow rates under several steam pressure conditions (0.4, 0.6 and
Table 3. Operating parameters of heating/insulation scheme in voyage 077.
0.8 MPa) and hydrometeorological conditions (sun, rain and waves).
As shown in Figure 9(a), the heating time decreases with
No. Pu/MPa Tl/°C Th/°C Ti/°C Tu/°C τh/h τi/h
increasing steam flow rate. The heating time decreases obviously
1C 0.3 64 56–57 >57.2 58 24 74
2P 0.3 64 56–57 >57.2 58 5 93 from 1000∼4000 kg/h, indicating the strong heating effects on the
2S 0.3 65 56–57 >57.2 59 5 93 cargo oil. On the other hand, the heating time decreases smoothly
3P 0.3 65 56–57 >57.2 59 5 93 when the steam flow rate is higher than 4000 kg/h, which indicates
3S 0.3 64 56–57 >57.2 59 5 93 that the heating effects are reduced under the high steam flow con-
4P 0.3 65 56–57 >57.2 60 5 93
4S 0.3 65 56–57 >57.2 59 5 93
dition, which may be attributed to the higher heat losses occurring
5P 0.3 65 56–57 >57.2 60 5 93 in the high temperature condition. The increase in the steam flow is
5S 0.3 65 56–57 >57.2 59 5 93 not economic above 4000 kg/h if the heat insulation is not
6P 0.3 64 56–57 >57.2 59 5 93 improved, i.e. the steam flow rate of 4000 kg/h is the optimised
6S 0.3 65 56–57 >57.2 59 5 93 point for the heating scheme. Similar phenomena are observed
8 Y. WU ET AL.

Figure 5. Predicted and measured temperatures of cargo oil with time in voyage 076.

Figure 6. Predicted and measured temperatures of cargo oil with time in voyage 077.
 SHIPS AND OFFSHORE STRUCTURES 9

Figure 7. Relative error of oil temperature between predicted and measured results
in various cargo tanks without considering hydrometeorological conditions in
model.

Figure 9. Heat transfer coefficient and heating time related to steam vapour flow
rate under different (a) steam pressure and (b) hydrometeorological conditions.

for the heat transfer coefficients. In addition, shorter heating times

are achieved when the steam pressure is higher. In contrast, the heat
transfer coefficients of the cargo oil model are not changed signifi-
cantly by the steam presumption.
As shown in Figure 9(b), the effects of the different hydrome-
teorological conditions mentioned in Section 4.2 are also compared.
It is found that higher heating time and heat transfer coefficients are
achieved for the wave and rain conditions. The changes in the heat
transfer coefficients are more remarkable under the hydrometeoro-
logical conditions in Figure 9(b) than under the steam pressure
conditions in Figure 9 (a). The forced heat convection is improved
significantly by rain or waves on the top side of the cargo tank, as
illustrated in Section 4.2. Accordingly, more heat losses of the
cargo oil are achieved to increase the heating time in rainy or
wave conditions. In addition, improvements in the heat transfer
are higher in the rain case than in the wave case because the forced
heat convection by the wave is only located on the front cargo tanks
such as 1C and 2P/S, as mentioned above. In contrast, the effects of
rain are located on the whole deck of the cargo tanks.

5. Conclusion
Optimisation of the heating and thermal insulation for cargo oil is
beneficial to reduce fuel consumption and pollution emissions for
Figure 8. Oil temperature obtained from measured and predicted results consider- oil tankers. The optimised operating scheme is highly related to
ing hydrometeorological conditions in (a) voyages 076 and (c) 077; (c) relative error the accurate prediction of the cargo oil temperature involving the
of oil temperature between predicted and measured results. theoretical analysis of the heat transfer processes in the cargo
10 Y. WU ET AL.

tank. In this study, a heat transfer model was proposed to address Brkic D, Praks P. 2021. Probability analysis and prevention of offshore oil and
the heating and cooling processes in cargo oil tanks. The operating gas accidents: fire as a cause and a consequence. Fire-Switzerland. 4:71.
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and condition data, including the steam parameters and heating/ ing high oil-absorption resin for storage facility and fuel pipelines. Prog Org
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conditions such as wave and rain weather and the steam flow rate Selecting best painting colour for crude oil storage tanks exterior surface.
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were also investigated. Major conclusions are outlined as follows:
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considered on the top side of the cargo tanks. The relative errors of based heating control strategy for cargo oil in tanker. Journal of Jimei
the oil temperature between the measured and predicted results University (Natural Science). 26:453–458.
Liu JY, Zhao J, Si ML, Dong H, Zhao WQ. 2019. The effect of periodic change of
range from 9∼15% without considering the rain/wind/wave con- external temperature on the temperature field of crude oil. Case Studies in
ditions and from 4∼6% considering the hydrometeorological con- Thermal Engineering. 15:100526.
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are obvious in the front cargos (including 1C, 2P/S) of the oil tanker. ing. International Journal of Naval Architecture and Ocean Engineering.
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The largest relative error is 15.1% between the predicted and measured
Martin S, Jensen JO, Li Q, Garcia-Ybarra PL, Castillo JL. 2019. Feasibility of
results in cargo tank 1C due to underestimating the meteorological ultra-low Pt loading electrodes for high temperature proton exchange mem-
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are appropriated to increase the heating rate efficiently and optimise Rostami A, Shokrollahi A, Ghazanfari MH. 2018. New method for predicting n-
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Acknowledgement Sun W, Cheng QL, Li ZD, Wang ZH, Gan YF, Liu Y, Shao S. 2019. Study on coil
This work is supported by the National Natural Science Foundation of China optimization on the basis of heating effect and effective energy evaluation
(No.52101320 and No.52071203); the Startup Foundation for Young Teachers during oil storage process. Energy. 185:505–520.
of Shanghai Ocean University (A2-2006-21-200325); the support of Fishery Sun W, Cheng QL, Zheng AB, Gan YF, Gao W, Liu Y. 2018. Heat flow coupling
Engineering and Equipment Innovation Team of Shanghai High-level Local characteristics analysis and heating effect evaluation study of crude oil in the
University; And the authors would like to express their gratitude for the support storage tank different structure coil heating processes. Int J Heat Mass
of Fishery Engineering and Equipment Innovation Team of Shanghai High-level Transfer. 127:89–101.
Local University. The authors would also like to thank the support from the Veloso RC, Souza A, Maia J, Ramos NMM, Ventura J. 2021. Nanomaterials with
high solar reflectance as an emerging path towards energy-efficient envelope
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Disclosure statement Wei S, Qinglin C, Xi Y. 2016. Research on the variation law of heating tempera-
No potential conflict of interest was reported by the author(s). ture field and the effective energy utilization rate of a steam coil for the float-
ing roof tank. Numerical Heat Transfer Part A-Applications. 70:1345–1355.
Yu GJ, Jia S, Geng YT. 2019. Numerical investigation into the two-phase convec-
Funding tive heat transfer within the hold of an oil tanker subjected to a rolling
motion. Journal of Marine Science and Engineering. 7:94.
This work was supported by National Natural Science Foundation of China: Zhang ZY, Li LH, Zhang JS, Ma C, Wu X. 2018. Solidification of oily sludge. Pet
[Grant Number 52101320]. Sci Technol. 36:273–279.
Zhao J, Liu JY, Qu DJ, Dong H, Zhao WQ. 2019. Effect of physical properties on
the heat transfer characteristics of waxy crude oil during its static cooling
ORCID process. Int J Heat Mass Transfer. 137:242–262.
Yu Wu http://orcid.org/0000-0001-9619-1654 Zhao J, Liu JY, Qu DJ, Dong H, Zhao WQ. 2020. Effect of geometry of tank on
the thermal characteristics of waxy crude oil during its static cooling. Case
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