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НАУЧНО-ТЕХНИЧЕСКИЙ ВЕСТНИК ИНФОРМАЦИОННЫХ ТЕХНОЛОГИЙ, МЕХАНИКИ И ОПТИКИ май-июнь 2023 Том 23 № 3 http://ntv.ifmo.ru/
I/ITMO SCIENTIFIC AND TECHNICAL JOURNAL OF INFORMATION TECHNOLOGIES, MECHANICS AND OPTICS ИНФОРМАЦИОННЫХ ТЕХНОЛОГИЙ, МЕХАНИКИ И ОПТИКИ
May-June 2023 Vol. 23 No 3 http://ntv.ifmo.ru/en/
ISSN 2226-1494 (print) ISSN 2500-0373 (online)
doi: 10.17586/2226-1494-2023-23-3-659-667
Method of type-C liquefied natural gas tank modeling based on volume optimization for future "milk-run" exploitation
Lev V. Ivanov1®, Alexander Yu. Baranov2, Anna V. Novitskaya3
U.3 ITMO University, Saint Petersburg, 197101, Russian Federation 2 R&D KRION LLC, Saint Petersburg, 197375, Russian Federation
1 levladiv@mail.ru», https://orcid.org/0000-0002-6916-7154
2 abaranov@itmo.ru, https://orcid.org/0000-0002-9263-8153
3 vasilenok_anna@itmo.ru, https://orcid.org/0000-0001-7100-6635
Abstract
Common practice methods of tank design for transportation of liquefied natural gas don't take into account the specifics of the gas carriers operation under the condition of partial filling of cryogenic tanks. A new method for designing of type-C tank is proposed. Method is based on solving the problem of increasing the volume of transported liquefied natural gas by small-scale inland carriers. The method is based on usage of a number of limiting parameters: minimal allowable ventless operation time, allowable values of the ship's draft, and the actual duration of voyages between neighboring consumers. The method allows optimizing type, shape, wall thickness, and heat insulation thickness of cryogenic tank. The proposed method is aimed at enlargement of usage of the ship's hull dimensions. This is achieved by changing the diameter, the distance between centers of the bi-lobe tank, the thickness of the insulation, and the maximum allowable working pressure. An increase in the volume of the tank is achieved by coordination such parameters as the maximum allowable draft of the vessel, the minimum time of ventless storage, and the time of ventless operation under partial filling conditions. The calculation of the ventless operation time is determined by the operating conditions of type-C tanks. The calculation of the heat ingress into the tank takes into account the contact area of liquefied gas and its vapors with the metal wall of the tank. The calculations do not take into account the assumption of thermal equilibrium between the liquid and vapor fractions, which leads to the need to take into account heat transfer from vapor to liquid. The implementation of the method is shown on the example of the modeling of the two-way river-sea type vessel. It is shown that optimization of tank parameters in accordance with proposed criteria can lead to an increase in the volume of transported natural gas by more than 4 %. The method can be used in the development of new and modernization of existing vessel projects to transportation of liquefied natural gas operating in water basins of Lena and Yenisei rivers in the East Siberian region. The described method can also be used in the design of road and rail tanks as well as small-scale bullet tanks for liquefied natural gas. Keywords
cryogenic tank design, type-C tank, partial filling, tank optimization, inland carrier, small-scale tanker, liquiefied natural gas, ventless operation
For citation: Ivanov L.V., Baranov A.Yu., Novitskaya A.V. Method of type-C liquified natural gas tank modeling based on volume optimization for future "milk-run" exploitation. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2023, vol. 23, no. 3, pp. 659-667. doi: 10.17586/2226-1494-2023-23-3-659-667
© Ivanov L.V., Baranov A.Yu., Novitskaya A.V., 2023
УДК 621.642.86
Метод моделирования резервуаров сжиженного природного газа типа С
на основе оптимизации объема для будущей эксплуатации
в режиме частичного заполнения
Лев Владимирович Иванов1 Александр Юрьевич Баранов2, Анна Владимировна Новицкая3
1,2,з Университет ИТМО, Санкт-Петербург, 197101, Российская Федерация
2 Научно-производственное предприятие «КРИОН», Санкт-Петербург, 197375, Российская Федерация
1 levladiv@mail.ruEi, https://orcid.org/0000-0002-6916-7154
2 abaranov@itmo.ru, https://orcid.org/0000-0002-9263-8153
3 vasilenok_anna@itmo.ru, https://orcid.org/0000-0001-7100-6635
Аннотация
Введение. Распространенные на практике методы проектирования танков для транспортировки сжиженного природного газа не учитывают специфики эксплуатации танкеров-газовозов при частичном заполнении криогенных резервуаров. Предложен новый метод проектирования судовых танков типа С, основанный на решении задачи увеличения объема перевозимого сжиженного природного газа речными малотоннажными речными танкерами. Метод основан на применении ряда ограничительных параметров: минимального допустимого времени бездренажного хранения криопродукта, допустимых значений осадки судна и реальной продолжительности переходов между соседними потребителями. Выполнена оптимизация типа, формы, толщины стенок и теплового ограждения криогенного танка. Метод. Предложенный метод направлен на увеличение использования габаритов корпуса судна. Это достигается изменением диаметра, расстояния между центрами двудольного танка, толщины изоляции и максимально допустимого давления. Увеличение объема танка обеспечено согласованием таких параметров, как максимально допустимая осадка судна, минимальное время бездренажного хранения и время бездренажного хранения при различном начальном уровне заполнения. Расчет времени бездренажного хранения определен условиями эксплуатации резервуаров типа С. Расчет подвода тепла к резервуару учитывает площадь контакта сжиженного газа и его паров со металлическими стенками резервуара. В расчетах не принимается допущение о тепловом равновесии между жидкой и паровой фракциями, что приводит к необходимости учета теплопередачи от пара к жидкости. Основные результаты. Реализация метода показана на примере расчета танков для судов типа река-море. Показано, что оптимизации параметров резервуаров в соответствии с предложенными критериями может привести к увеличению объема перевозимого природного сжиженного газа более чем на 4 %. Обсуждение. Метод может найти применение при разработке новых и модернизации существующих проектов судов для перевозки сжиженного природного газа, работающих в водных бассейнах рек Лена и Енисей Восточно-Сибирского региона. Описанный метод может быть использован при проектировании автомобильных и железнодорожных цистерн, а также стационарных малогабаритных цилиндрических цистерн для транспортировки и хранения сжиженного природного газа. Ключевые слова
проектирование криогенного танка, танки типа С, частичное заполнение, оптимизация танка, речной газовоз, малотоннажный газовоз, сжиженный природный газ, бездренажное хранение
Ссылка для цитирования: Иванов Л.В., Баранов А.Ю., Новицкая А.В. Метод моделирования резервуаров сжиженного природного газа типа С на основе оптимизации объема для будущей эксплуатации в режиме частичного заполнения // Научно-технический вестник информационных технологий, механики и оптики. 2023. Т. 23, № 3. С. 592-600 (на англ. яз.). doi: 10.17586/2226-1494-2023-23-3-592-600
Introduction
Liquefied Natural Gas (LNG) has become a new major clean energy source1 [1]. Distant settlements are in need of fuel supply. Fuel supply chain in North-Eastern Siberia has name "Northern delivery". Due to logistic problems, the fuel price transportation fee may be up to 70 % of total price [2]. Since in such places usually there are no developed railways or roads, the only reliable way of LNG transportation is naval one: by sea or river.
Due to multiple unique factors specific to North Siberia region, existing methods of technical analysis and optimization of LNG tanks are not effective. Such specific factors include: long distances between each point of LNG consumption, shallow draft on majority of waterways,
1 GIIGNL. Annual Report. 2020 URL: https://giignl.org/ document/giignl-2020-annual-report/ (accessed: 08.12.2021).
and lack a single large consumers [3]. Based on analytical papers [4-6], the conception of "milk-run" delivery is the most rational solution. Milk Run concept means that LNG carrier moves along the distribution route and unloads parts of LNG. Afterwards, vessel continues movement with partial filled tanks. The main problem with partial filling is faster self-pressurization. When inner pressure reaches peak number of Maximum Allowable Working Pressure (MAWP) safety valve opens and Boil-Off Gas (BOG) is released. Discharge of BOG is a big problem that harms economic efficiency of LNG transportation and causes environmental damage.
Different method of modeling of small-scale LNG tank was developed. Paper [7] described an original method of projecting inland small-scale LNG carrier based on usage of standard ISO insulated LNG containers. Boundary conditions are selected by specific of a waterway of river Danube: ship's length, breadth and draft. Maximum
allowable draft defines maximum weight of cargo. Different variants of vessel hulls were analyzed to find the best one.
Although standard ISO1 containers are reliable way of LNG storage, the coefficient of effective displacement usage is lower than any other Cargo Containment System (CCS). That's why this method cannot be used to design LNG carriers for main rivers. Also described method does not suit for reconstruction and modernization projects.
LNG carriers on Lena and Yenisei will be exploited in "milk-run" based logistics supply chain. By that reason the CCS for these vessels must be designed in view of this feature. Different models were already designed: for small pressurized vessels and large ones. For example, in [8] model, the case has been presented without phase-equilibrium between LNG and its vapor. Separated heat ingress is calculated towards vapor phase and liquid phase: vapor overheat in large LNG reservoir reaches up to 10 K. Heat transfer from vapor to liquid phase has been calculated by integrating the heat flux from the vapor phase to the vapor-liquid interface. The main mechanism of heat transfer is conduction. LNG is presented as multicomponent liquid. Although this method is reliable for the full-scale LNG reservoirs — for the small-scale ones it needs to be adjusted.
In paper [9], evaporation rate under different loading condition is calculated with ANSYS Fluent software. With assumption of different initial filling, the authors did not consider the change of the liquid level due to change in density of LNG due to the increase of temperature.
Lee et al. [10] present experimental data from nitrogen tank self-pressurization. This paper stated that equivalent thermal conductivity is a convenient calculation method of heat ingress through the wall to BOG and from BOG to LNG (if sloshing effect is neglected).
Ferrin et al. [11] calculated convective heat ingress under different filling conditions. The modeling object in this paper is small vertical cylinder tank. Although the described method of heat transfer calculation is accurate, it's hard to apply Computational Fluid Dynamics (CFD) calculations for the full-scale tank holding time calculation due to the necessity of high-performance computer.
Paper [12] presents the whole algorithm of calculation LNG evaporation from a reservoir. Heat transfer coefficient between BOG and LNG is presented as a steady number. Heat ingress rate is a steady number as well. REFPROP wrapper was used to perform the modeling. With static number of heat transfer coefficient, it is not reliable for the calculations with constant change in thermodynamic parameters of LNG and its vapor.
All the methods described above cannot be utilized effective enough under specific conditions that require taking into consideration partial filling of tank. Described methods include simplifications making obtainable data unusable in such conditions. Presented method is based on the usage of ship's hull parameters and drainfree operation time under different filling conditions, so it may be implemented in development of new ship and modernization of the existing ones. Method allows
1 ISO VAC 40 LNG: 40 ft LNG Iso Container. URL: https:// wessingtoncryogenics.com/products/liquefied-natural-gas-containers/iso-vac-40-lng/ (accessed: 27.01.2023).
adjusting tank dimensions, volume, thickness of tank walls, and thermal insulation. Proposed method allows achieving enlargement of LNG volume and prevent LNG loss due to BOG discharge under any specific conditions of tank exploitation.
Model development
The enlargement of LNG tanks is achieved by optimization parameters of tank: its shape, length, diameter, thickness of wall, and insulation. Volume enlargement is achieved when following parameters are matched:
— Draft of the fully loaded vessel matches with maximum allowable draft for the unique waterway.
— Ventless operation holding time under maximum filling condition matches 15 days.
— Ventless operation holding time under partial filling condition is more than time set by operational conditions.
Current draft of vessel is determined by weight of the CCS. Weight is determined by volume of tanks and wall thickness. Type and shape of tank are determined by the available space in the ship's hull. Total weight of CCS is limited by maximum allowable draft:
Draft = fWtotai, L, B, H) < Maximum allowable draft,
where Wtotal — total weight of CCS; L — length of the ship; B — breadth; H—vessel's board height. Total weight of CCS:
Wtotal = WLNG + Wtanb
where WLNG — mass of LNG; Wtank — mass of tanks.
Wlng = AY, Fl, n); Wtank = fV, n, Wall, Ins),
where V — volume of tank; Fl — filling limit; n — number of tanks; Wall — thickness of the tank walls; Ins
— thickness of the tank insulation. Volume of tank:
V = fDmax, l, Wall, Ins),
where Dmax — overall diameter of the tank; lt — tank's length.
MAWP is determined by the thickness of tank walls and volume of a tank. Ventless operation holding time is determined by MAWP, surface area of tank, and thickness of heat insulation. Second parameter of optimization determines thickness of heat insulation. If holding time is more than required 15 days, insulation thickness gets diminished, volume of tank increases, and thickness of tank walls gets calculated again. Holding time is limited by minimal ventless operation time and maximal time of voyage under partial filling conditions (MTPFC).
Holding time = f(V, Wall, Ins, MAWP, Fl) > required time.
Maximum allowable filling limit is 0.98. Maximum filling limit is one under which maximal ventless holding
time is reached. For maximum filling level minimal required time is 15 days.
When second optimization parameter is matched, thickness of heat insulation is adjusted for partial filling conditions when minimal time is determined by the future of exploitation conditions.
Optimization of tank volume is achieved when all the following conditions are matched:
Holding time > 15 days
whatever
Holding time under partial filling > MTPFC[ comes
) first
Draft = Maximum allowable draft
Overall algorithm of tank optimization is based on maximization of volume of LNG carried by the vessel. This algorithm is presented in Fig. 1.
A method for specifying the type-C tank shape was chosen based on paper [13]. Accessible space is determined by IGC and DNVGL codes regulation1. Upper-deck part of
1 The International Code of the Construction and Equipment of Ships Carrying Liquefied Gases in Bulk (IGC Code). URL: https://www.imo.org/en/OurWork/Environment/Pages/IGCCode. aspx (accessed: 27.01.2023).
tank cannot be higher than 3 meters above the upper deck (or tank radius, whatever number is smaller). For bi-lobe tanks distance between cylinders centers is 0.35 r to 0.75 r [14].
Maximum diameter of type-C LNG tanks is the sum of below-deck space height (Hb) and upper (Hu) deck space height.
Dmax = Hb + Hu.
Hence, tank shape is chosen by the following conditions:
В
Dr
■ < 1.35 — cylinder shape of the tank;
В
1.35 < —— <1.8 — bi-lobe shape;
В
Dr
1.8 — multi-lobe shape.
Maximum tank length:
lmax < 0.2L.
С End
Fig. 1. Modeling algorithm
Hence, number of tanks:
n = -
^max
where Lh — length of the vessel's hull.
The number of tanks is obtained by rounding this number up. Tank length:
_Lh-2lcoff
lt = , n
where lcof — length of cofferdam.
Type-C tanks work under high pressure. MAWP is a function of tanks walls thickness. Therefore, maximum thickness of tanks walls is limited by maximum allowable weight of CCS. Weight of CCS is a sum of metal parts weight, insulation layer weight, and LNG stored in the tanks with maximum allowable filling. Tanks wall thickness is calculated by GNVGL guideline1. Sloshing effect is neglected due to the high thickness of the walls that cannot be damaged by LNG sloshing. Sloshing is taken under consideration only when dealing with membrane tanks.
Vessel lightweight (LWT) is calculated by the following formula [7]:
mLWT = -4.44-10-6(LBH)2 + 0.195LBH. Deadweight (DWT) of vessel:
mDWT = 1.2(mt + ^NOI
where mLNG — mass of LNG stored in tanks; mt — total mass of the tank; 1.2 is a coefficient that includes weight of the fuel, water supply, weight of the ship's crew, etc. Therefore, total displacement of the vessel:
A = mLWT + mDWT.
Loaded draft of the vessel:
Draft = A(LBQpw)-1,
where CB — is cubic coefficient of vessels hull; pw — relative density of water.
Second limiting parameter is minimum allowable holding time. This parameter is set by IGC code and equal to 15 days.
Assumption is made that LNG is pure methane. Heat ingress into the tank calculated as conduction only. Insulation is made from sprayed polyurethane foam (PUF). Density of PUF is 40 kg/m3. Thermal conductivity is a function of temperature:
lPUF = -0.0003 TPUF2 + 0.1908TPUF - 4.2758.
This equation is based on experimental parameters [15], in range from 95 to 220 K. Mean deviation of
1 DNVGL-CG-0135 Liquified gas carriers with independent cylindrical tank of type C. 2016. URL: https://rules.dnvgl.com/ docs/pdf/DNVGL/CG/2016-02/DNVGL-CG-0135.pdf (accessed: 08.12.2021).
presented polynomial equation from experimental results is R2 = 0.9983. PUF temperature is average temperature between cold LNG side and warm outer side.
Type-C tank is made from 304L stainless steel. Since thermal conductivity does not change much, lm = 24.21 W/(m-K) is a constant.
Insulation layer is covered by a thin layer of coating that prevents water contact with PUF. Thickness of this layer is 5 mm and thermal conductivity is lcoat = 0.5 W/(m-K).
Metal in contact with LNG assumed to have temperature of LNG. Metal in contact with BOG assumed to have temperature of BOG.
Fourier's law calculates heat ingress Q through insulation.
Q = -
T -T
■*■ nut irv
\rFm
\PIIFFI
•PUFrPUF.av
^coatFи
where dm, dins, dcoat — thickness of metal layer, PUF insulation and primer coating; Fmav — mean contact surface between liquid and outer side of walls; FPUKav — mean contact surface between outer surface of metal and outer surface of the heat insulation; Fcoat — mean contact surface between outer surface of the heat insulation and outer surface of coating; Tout—temperature outside of the tank; Tins — temperature inside the tank.
Heat ingress is calculated separately towards vapor phase and liquid phase. To calculate mean surface for cylinder tank body and hemisphere tank head following formulas were used:
F,
Ft + Fm
av.cil
F = iIf F
av.hs t-* m
where Ft — surface area of contact inside the tank; Fm — surface area of wall outside the tank.
Heat ingress to vapor and liquid phase are calculated separately since there is no equilibrium state and vapor phase is overheated.
Surface area is a variable parameter. Heat ingress towards liquid and vapor are different and based on the area of contact between fluid and tank wall. Since shape of a tank is not an ordinary vertical cylinder, contact surface calculation is a complicated task. Height of the interface between liquid and vapor allow calculating area of contact between liquid and tank wall. LNG and BOG liquid (pL) and vapor (pV) densities are functions of temperature and pressure:
Pl = f(P, Tl);
Pv=f(P, Tv).
Height of the interface is a function of liquid density:
hmt = fPL) -f(P, Tl).
Hence, area of contact between wall and liquid:
Fl = Ahmt) -f(PL) -fP, Tl);
F = F - Fl
1 V 1 total 1 ■
Evaporation heat is also a function of pressure and temperature:
HVaP = fP, Tl).
Saturation temperature of liquid methane is a function of pressure:
Tat = fP).
Heat transfer from overheated BOG to liquid LNG is assumed by mechanism of conduction since convection part in negligible [9].
qvl = fvl^v~
dz
z=0
8TX
where — — temperature gradient in the stratified vapor
zone.
dz
Vapor-liquid interface area is function of height of interface if sloshing effect is neglected. For the cases of vertical cylinder reservoirs, FVL is constant.
Fvl = Af(hmt)) ^HPl) ^HP, TL).
Evaporation condition calculation algorithm follows. If at the beginning of a time step TL < Tsat, evaporation on this time step does not occur. Change of the masses of liquid and vapor are 0.
Temperature and density of liquid on the next time step:
T,_T (QL + QVLW
T L — Tl + ;
CPLmL
PL — HTl', P).
Volume of liquid on the next time step: mL
VL — —.
PL
Volume of vapor on the next time step:
Vy — Vtotal - Vl'. Temperature and density of vapor on next time step:
_ {QV-QvlW
TV — TV + CP yffly ;
mv
V/
Enthalpy of vapor:
hymy+iQv-Qv^At
PV
hV — -
mv
New pressure at the end of a time step:
P — f(Py', hV).
If at the beginning of time step TL > Tsat, evaporation occurs. Changes of masses on the next step:
Am =
(Ql + Qvl)&
H.
vap
Enthalpy of liquid and vapor:
(hLmL + (Ql + Qy£)At - AmHvap)
mL - Am (hymv+ (Qr-QvlW + A mHvap)
hL —
hV —
mr+ Am
If enthalpy of liquid on the next step is more than enthalpy of saturated liquid hL' > hsat:
Am =
(h' - hsat)mL
Я,
vap
And enthalpy and temperature of liquid on the next step is:
hL = hsa^ TL = Tsat.
Density of liquid on the next time step: mL - Am
Pl
VL
Therefore, volume of liquid and vapor:
VL = (mL - Am)pL';
Vv = Vtotal - Vl'.
Hence, density of vapor:
Pv
my+ Am Vv' .
Pressure on the next time step: P = fpv', hV).
Calculation algorithm is based on one used in paper [12]. The main difference is calculation of changed surface area of tank contact with LNG and BOG and interface area between vapor and liquid phase.
Maximal holding time is obtained from calculated data under different initial filling level. The graph of changes in holding time dependent of filling limit is presented in Fig. 2.
Graph from the Fig. 2 repeats the pattern for self-pressurized cryogenic reservoirs from the book [16].
However, "milk-run" transportation requires partial filling conditions. Since holding time of partially filled tank is much lower than fully filled, it is necessary to calculate drainless time under partial filling conditions. Such conditions depend on logistics: future area of work of the vessel. To prevent LNG loss by BOG discharge, such modes of operation must be taken into account.
Results and discussion
As an example of this method usage, vessel RSD62 was set as a case. RSD62 is small-scale inland oil carrier
40
Filling level, % Fig. 2. Holding time under different filling conditions
В
0.3 0.26 0.22 ! 0.18 0.14 0.1
/
Max ■ 50 % •30% 15 days 4 days 3 days
0 100 200 300 Holding time, horns
400
Fig. 3. Pressure build-up under different filling conditions
Table. Parameters of CCS
Step Tank Volume, V, m3 Total Volume, Vtotab m3 Wall thickness, Wall, mm Insulation thickness, Ins, mm MAWP, MPa Holding time, days
Fl, % Ventless operation time, days
1 1769.1 7Q76.5 31.94 3QQ Q.34 91.8 24.46
5Q 19.12
3Q 12.87
2 1826.6 73Q6.5 29.43 2QQ Q.29 92.8 17.46
5Q 11.50
3Q 7.62
3 188Q.8 7523.4 25.43 Ш Q.25 93.6 6.46
5Q 5.17
3Q 3.33
4 1837.7 735Q.8 27.68 Ш Q.28 93 16.17
5Q 10.17
3Q 6.75
5 1845.9 7383.9 27.16 165 Q.27 93.2 15.29
5Q 9.12
3Q 6.04
used for northern delivery in North-Eastern Siberia. Main dimensions of this vessel are L — 141 m, B — 16,92 m, H — 6,3 m, Lh — 100 m, Draft — 3,5 m1.
For the initial cycle of tank modeling, volume of a tank is set as 1200 m3. Initial insulation thickness is set as 300 mm.
To obtain thermodynamic properties of liquid methane and its vapor, CoolProp wrapper for Python was utilized. All parts of the algorithm were realized with Python programming.
Initial conditions for modeling are: LNG temperature is 110 K and vapor temperature is 112 K. Before loading, LNG tank is cooled with methane vapor and after loading of LNG its vapor is slightly overheated. Environment temperature is 290 K.
Partially loaded tank conditions were analyzed. Longest trip with 50 % filling is 4 days. Longest trip with 30 % filling is 3 days.
After the modeling, the preferable tank shape appeared to be bi-lobe one. Maximal filling level is 93.2 %. All iterations of calculated CCS are presented in Table.
After modeling, it was investigated that optimal design is tank with insulation thickness of 165 mm. Fig. 3 shows pressure build-up inside the tank under different filling conditions of the tank after last iteration.
With presented method, on the first iteration total volume of LNG carried by vessel is 7076.5 m3. After volume optimization this number was increased to 7383.8 m3. Extra 307.3 m3 generate additional positive economic effect on whole vessel project.
1 Project RSD62. Dry-cargo vessel of river and mixed (river-sea) with a deadweight of 5640 tons URL: https://www.meb.com. ua/dry/RSD62.html (accessed: 12.10.2022).
Conclusion
This paper presented new method of type-C LNG tank modeling. Proposed method is easy to use and it may be
completely automated. New method is not only suitable for new vessel projects but also for reconstruction and modernization projects. Optimization is based on the maximal usage of allowable space in vessel's hull and a close approximation of draft of fully loaded vessel up to maximum allowable draft on the waterway. Heat insulation is modeled to match minimum requirement of holding
time according to IGC code, but also specific regimes of future exploitation were taken into account. With modeling of specific partially filling conditions of "milk-run" logistics, drainless operation mode on whole route of LNG distribution is preserved. This specific modeling prevents BOG discharge into the environment and economic losses due to loss of cargo.
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Литература
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Authors
Lev V. Ivanov — Engineer, ITMO University, Saint Petersburg, 197101, Russian Federation, sc 57216964617, https://orcid.org/0000-0002-6916-7154, levladiv@mail.ru
Alexander Yu. Baranov — D.Sc., Professor, Head of Research Department, R&D KRION LLC, Saint Petersburg, 197375, Russian Federation; Professor, ITMO University, Saint Petersburg, 197101, Russian Federation, sc 57191032604, https://orcid.org/0000-0002-9263-8153, abaranov@itmo.ru
Anna V. Novitskaya — PhD, Lecturer, ITMO University, Saint Petersburg, 197101, Russian Federation, sc 57211850010, https://orcid. org/0000-0001-7100-6635, vasilenok_anna@itmo.ru
Авторы
Иванов Лев Владимирович — инженер, Университет ИТМО, Санкт-Петербург, 197101, Российская Федерация, sc 57216964617, https://orcid.org/0000-0002-6916-7154, levladiv@mail.ru Баранов Александр Юрьевич — доктор технических наук, профессор, руководитель департамента, Научно-производственное предприятие «КРИОН», Санкт-Петербург, 197375, Российская Федерация; профессор, Университет ИТМО, Санкт-Петербург, 197101, Российская Федерация, sc 57191032604, https://orcid.org/0000-0002-9263-8153, abaranov@itmo.ru
Новицкая Анна Владимировна — кандидат технических наук, преподаватель, Университет ИТМО, Санкт-Петербург, 197101, Российская Федерация, sc 57211850010, https://orcid.org/0000-0001-7100-6635, vasilenok_anna@itmo.ru
Received 16.01.2023
Approved after reviewing 12.04.2023
Accepted 23.05.2023
Статья поступила в редакцию 16.01.2023 Одобрена после рецензирования 12.04.2023 Принята к печати 23.05.2023
Работа доступна по лицензии Creative Commons «Attribution-NonCommercial»
