Liquefied natural gas tanker truck-to-tank transfer for on-road transportation

Applied Thermal Engineering 162 (2019) 114313

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Liquefied natural gas tanker truck-to-tank transfer for on-road transportation Amir Sharafian, Paul Blomerus, Walter Mérida

T

⁎

Clean Energy Research Centre, The University of British Columbia, 2360 East Mall, Vancouver, BC V6T 1Z3, Canada

HIGHLIGHTS

liquefied natural gas tanker offloading methods for on-road transportation are studied. • Six transfer via pressure buildup units has the largest methane emissions. • Fuel transfer via pumping and controlled pressure buildup units provides the best performance. • Fuel delivery pipe diameter and insulation are key factors in the fuel offloading process. • Fuel • Vacuum jacketed pipes can be replaced with rigid foam insulation. ARTICLE INFO

ABSTRACT

Keywords: Liquefied natural gas Tank-to-tank transfer Methane emissions Refueling station

Fugitive methane emissions from the liquefied natural gas (LNG) supply chain have revealed uncertainty in the overall greenhouse gas emissions reduction associated with the use of LNG in heavy-duty vehicles and marine shipping. Methane is the main constituent of natural gas and a potent greenhouse gas. Recent measurements have shown that the LNG offloading process had the largest contribution to methane emissions in the refueling portion of the supply chain. However, there are limited studies analyzing the LNG offloading process for smallscale applications. This study investigates six methods used to offload LNG from a tanker truck to an LNG refueling station and their contribution to methane emissions. A verified thermodynamic model is created by comparing numerical results with the experimental data collected from an LNG offloading process in a refueling station. The modeling results show that the LNG transfer by using a pressure buildup unit causes methane emissions as high as 104 g/kg LNG. In contrast, LNG transfer by using a pump and controlled pressure buildup unit provides the lowest risk of methane venting. Also, the results of parametric study indicate that rigid foam insulation can be considered as an economical alternative to vacuum jacketed pipes in LNG refueling stations.

1. Introduction

gaseous natural gas at the atmospheric pressure. The volumetric energy density of LNG at 100 kPa is about 22.2 MJ/L which is 60% of that of diesel. This property makes LNG an attractive fuel for heavy-duty trucks and ships, where fuels with high energy densities are required. Natural gas is liquefied at −162 °C and 100 kPa. Due to the large temperature gradient between LNG and the environment, heat transfer to LNG facilities causes the evaporation of LNG, generation of boil-off gas (BOG), and an increase in the operating pressure [4]. For safety reasons and maintaining LNG at low pressures, the extra BOG should be released to the atmosphere [5], flared [6–8] or re-liquefied [9]. Methane is the main constituent of natural gas [10] and a potent GHG. Methane leakage from equipment [11,12], such as pneumatic valves, pressure relief valves, seals, etc., and misuse of facilities, such as improper refueling procedure [13], are other sources of emissions.

The global demand for alternative fuels in the transportation sector has continuously increased in response to the rising price of oil and a desire to combat greenhouse gas (GHG) and air pollutant emissions. Heavy-duty vehicles and ships, used in the transportation of heavy freight, account for 7.9% (3.0 Gt CO2e) and 2.5–3.5% (0.9–1.3 Gt CO2e) of global GHG emissions, respectively [1–3]. Scenarios developed by the International Maritime Organization (IMO) indicated that the emissions from ships will grow between 50% and 250% by 2050 [3] because of the growing demand for shipping to support international trade. Liquefied natural gas (LNG) has been proposed as an alternative fuel in heavy-duty vehicles and ships. LNG is about 600 times denser than ⁎

Corresponding author. E-mail address: [email protected] (W. Mérida).

https://doi.org/10.1016/j.applthermaleng.2019.114313 Received 18 April 2019; Received in revised form 9 August 2019; Accepted 27 August 2019 Available online 27 August 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature A BOG BP CNG c0 cp D EPA f FPSO GHG GWP HPDI IEA L LNG m MAWP

NOx NPSH PBU PM PR PRV Q RFP ρ t U UA V VJP

Area (m2) Boil-off gas Bare pipeline Compressed natural gas Constant pressure drop coefficient, (N·s2/kg·m5) Specific heat capacity (J/Kg·K) Diameter (m) Environmental Protection Agency Friction factor Floating, production, storage, and offloading Greenhouse gas Global warming potential Higher pressure direct injection International Energy Agency Length (m) Liquefied natural gas Mass (kg) Maximum allowable working pressure (kPa)

Nitrogen oxides Net positive suction head Pressure buildup unit Particulate matter Peng-Robinson Pressure relief valve Volume flow rate (m3/s) Rigid foam pipeline Density (kg/m3) Thickness (m) Overall heat transfer coefficient (W/m2·K) Thermal conductance of tank (W/K) Gross volume (m3) Vacuum jacketed pipeline

Subscription i insulate o

Despite significant potential to reduce air pollutants, such as nitrogen oxides (NOx) and particulate matter (PM), recent studies have revealed uncertainty in the overall GHG emissions reduction associated with the natural gas use [14–20]. The major concern is related to methane emissions from the natural gas supply chain. Carbon dioxide (CO2) and methane emissions account for 92% of the global GHG emissions [21]. Methane has a higher global warming potential (GWP) than CO2 due to its higher radiative forcing [22,23]. The GWPs of methane are 85 and 30 times as high as those of CO2 in 20- and 100year horizons, respectively [24]. The LNG well-to-tank supply chain is comprised of production, gathering, processing, liquefaction, and storage and distribution. Alvarez et al. [25] summarized the results of methane emissions measurements from the US oil and gas supply chain in 2015 and showed that about 23g/kg of gross US gas production was emitted to the atmosphere across the natural gas supply chain; this is 60% higher than the GHG inventory reported by the US Environmental Protection Agency (EPA). According to Alvarez et al. [25], production (58%), gathering (20%), and storage and distribution (17%), in order, had the main contributions in the methane emissions. With the growing market of LNG as a fuel for heavy-duty vehicles and marine shipping, methane emissions abatement from the downstream of LNG supply chain, i.e., storage and distribution, becomes crucial. Sharafian et al. [26] investigated the use of LNG in Canada’s heavyduty trucks and indicated that LNG has the potential to reduce GHG emissions by up to 22% by 2050 in comparison with heavy-duty diesel trucks if the well-to-wheel methane emissions from the natural gas supply chain is maintained below 1g/kgLNG . However, under current methane emissions of 26.4g/kgLNG in Canada, LNG heavy-duty trucks emit 24% (GHG-20) and 1.7% (GHG-100) more GHGs than their diesel counterparts. Sharafian et al. [26] concluded that stringent methane abatement regulations and supporting methane emissions measurement campaigns would assist to control and reduce methane emissions. Clark et al. [13] measured the methane emissions from six LNG refueling stations and 16 LNG heavy-duty trucks with high pressure direct injection (HPDI) engines (Fig. 1). Their measurements showed that the cumulative methane emissions from LNG offloading from a tanker truck to a station and dispensing to a vehicle were about 4.48g/kgLNG .

Inner Insulation Outer

According to their analysis, fuel delivery by a tanker truck had the largest contribution to the methane emissions (29%) followed by venting the BOG from vehicles’ onboard tanks to the atmosphere prior to the refueling process (22%). In a later study, Clark et al. [27] showed that the current methane emissions from the US LNG and compressed natural gas (CNG) refueling stations, and natural gas-fueled vehicles can be reduced from 13.2 g/kgLNG to 1.5 g/kgLNG by 2035 under rapid technology development, an increase in natural gas vehicles market, and adoption of best practices to abate methane emissions. In the LNG storage and distribution subsector, methane can be emitted during pipeline purging, pump priming (if the pump is located outside the tanker truck or in a sump tank), precooling process of equipment, and inerting the system at the end of LNG offloading. Table 1 shows a summary of studies on LNG transfer at a large scale between terminals and ships. While LNG loading and offloading processes were studied in largescale applications, such as LNG export and receiving terminals, there are limited studies on the LNG transfer for small-scale applications, such as LNG delivery to refueling stations. LNG storage tanks in largescale applications are usually atmospheric tanks with a constant pressure during loading and offloading processes [28–31], whereas LNG storage tanks in small-scale applications are pressurized tanks and their vent Vehicle manualual vent 1.09 g/kgLNG

Vehicle fuel tank 1.0 g/kg LNG ank Fueling nozzle 0.11 g/kgLNG

Fuel delivery to station 1.28 g/kgLNG

Station tank boil-off gas Statio 1.0 g/kg LNG

Fig. 1. Methane emissions from LNG delivery to a station, LNG station operation, and fuel dispensing to LNG heavy-duty trucks [13].

2

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Table 1 Pertinent literature to large-scale LNG transfer between ships and terminals. Reference

Scope of research

Yan and Gu [28]

Studied the LNG transfer from a floating, production, storage, and offloading (FPSO) facility to an LNG cargo ship under steady-state assumption, and source and receiver tanks at constant pressures of 100 and 250 kPa, respectively.

Sriknath et al. [7]

Studied the offloading of LNG and liquid propane from ships to storage terminals under constant liquid flow rate

to the long distances between ships and storage terminals (12–20 km), • Due excessive amounts of BOG were generated during the offloading of LNG

Modeled the LNG loading and BOG management in LNG export terminals under steady and unsteady conditions

the BOG as a fuel for power generation was the most efficient • Consuming method to manage the pressure of LNG terminals. However, this method

Kurle et al. [29,30]

Findings

optimum flow rate could be achieved to balance the cost of pump • An discharge head and minimize the amount of BOG generation. the optimum flow rate was highly dependent on the design of the • Reaching LNG transfer pipeline and it could be impossible to be changed in already built facilities.

and liquid propane.

the offloading flow rate might not be possible in an actual • Manipulating operation. was a tradeoff between the precooling process of equipment and • There offloading process to minimize the amount of BOG generation and decrease the LNG offloading cost.

• Li et al. [31]

Analyzed the BOG generation during LNG offloading from a ship to a receiving terminal by using a dynamic simulation

• •

reduced the terminals’ revenues and was subject to the availability of demand for electricity. Re-liquefaction of BOG on a ship or at the shore was suggested in which less than 20% of the BOG energy was used to power the liquefier, increasing revenue, and preventing flaring of the BOG. The pressure difference between the LNG carrier and the receiving terminal had a significant impact on the BOG generation. If the pressure of the receiving terminal was increased by 1 kPa from that of the LNG carrier, the BOG generation rate decreased by 3,900 kg/h.

is the simplest method to transfer LNG with the lowest capital cost. However, in this method, a portion of fuel is evaporated and cannot be used again. In addition, as a result of building a high pressure in the source tank or having a high pressure in the receiver tank, there is a higher chance of BOG release to the atmosphere. To resolve the issue of the high-pressure buildup in the tank, a pump can replace the PBU. Using a pump shortens the LNG transfer time as the transfer process can be started right after the priming the pump and the precooling process. In this architecture, the pressure of the source tank gradually decreases due to the LNG displacement. If the pressure of the source tank drops below the net positive suction head (NPSH) of the pump, the LNG evaporation in the suction line of the pump damages the pump (known as cavitation phenomenon). The third architecture (Fig. 2c) has a pump and a PBU to overcome the limitations of previously mentioned architectures. Using a pump and PBU assists to build up enough pressure in the source tank, prevent cavitation in the pump, and shorten the fuel transfer time. In this architecture, a portion of LNG is evaporated in the source tank. Only sufficient LNG should be evaporated to maintain the pressure of the tank above the NPSH of the pump. Therefore, proper sizing of the PBU and controlling its operation become important. A vapor return pipeline (shown with a dashed line in Fig. 2) can be added to these three architectures to transfer the extra vapor in the receiver tank to the source tank, and reduce the pressure of the receiver tank before starting the LNG offloading process. Accepting the vapor from the receiver tank decreases the pressure difference between the source and receiver tanks. This is specifically important in LNG tank-totank transfer by using a PBU that only relies on the pressure gradient of the source and receiver tanks for LNG transfer. If the pressure of the receiver tank is near its maximum allowable working pressure (MAWP), the LNG transfer process cannot be started as the pump and/or PBU may not be capable of creating a high enough discharge head to overcome the receiver tank pressure. In such circumstances, the extra vapor in the receiver tank should be returned to the source tank or released to the atmosphere before starting the LNG offloading process.

pressure changes over time. In pressurized LNG storage tanks, the pressure may gradually decrease because of BOG condensation in contact with the new load of LNG or increase because of excessive BOG generation along the delivery pipeline. Besides, centrifugal pumps, which are commonly used for offloading LNG in refueling stations located in North America, have a specific characteristic curve (head vs. flow rate). Changes in the pressure of LNG source and receiver tanks during the LNG offloading process cause the discharge head of the pump and the LNG flow rate to be affected. This study investigates the performance of methods used to offload LNG from a tanker truck (the source tank) to an LNG storage tank (the receiver tank) in a refueling station. Six LNG tank-to-tank transfer methods– the first five methods are currently in use in industry and the last one is our suggested method– are modeled. Key criteria in evaluating the LNG tank-to-tank transfer processes are introduced. The numerical results are validated against the experimental data collected from a refueling station located in British Columbia, Canada. Next, a comprehensive parametric study is conducted to determine critical design parameters in the LNG tank-to-tank transfer process. The findings of this study can be deployed in other applications such as LNG transfer from a tanker truck to LNG-fueled ships. 2. LNG tank-to-tank transfer architectures The LNG tank-to-tank transfer process is affected by the initial pressure of the source and receiver tanks, the pressure drop due to piping, and the LNG flow rate. Fig. 2 shows three possible LNG tank-totank transfer architectures which are currently in use. LNG is transferred by using: (1) a pressure buildup unit (PBU) only, (2) a pump, and (3) a pump and PBU. In the first architecture (Fig. 2a), a portion of LNG in the source tank is sent to the PBU where LNG is evaporated in a naturally air-heated heat exchanger. When a portion of LNG is evaporated, the pressurized gaseous natural gas is sent to the top of the source tank to create a high-pressure vapor space (also known as a false head) to push the LNG from the source tank to the receiver tank. This method

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Fig. 2. Architectures of LNG tank-to-tank transfer with/without vapor return by using (a) a PBU, (b) a pump, and (c) a pump and PBU.

3. Governing equations and assumptions

to determine the best method(s) for LNG tank-to-tank transfer. The LNG tank-to-tank architectures are initially modeled to be solved under the steady-state assumption. Then, the models are exported to the dynamic mode to be initialized at predefined conditions as given in Tables 2–5

Six thermodynamic models are developed by using the 2018 version of a commercial software (Aspen Plus and Aspen Plus Dynamics [32])

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Table 2 Specifications of LNG source and receiver tanks and their initial operating conditions. Parameter

Value

Description

LNG source tank Tank positioning Gross volume, VSource tank Length of inner tank, LSource tank Outer diameter, Do, Source tank Inner diameter, Di, Source tank Insulation thickness, tinsulate, Source tank Mass of storage tank (empty), mSource tank Specific heat capacity of storage tank, cp, Source tank Surface area of inner tank, ASource tank Overall heat transfer coefficient of tank, USource tank

– 48.075 m3 14.217 m 2.489 m 2.075 m 0.207 m 11,430 kg 477 J/kg·K 99.44 m2 0.0163 W/m2·K

A horizontal tank LNG transport trailer (Model # ST-12700) [33] Calculated from the length of outer tank [33] Calculated from the net capacity of the tank Calculated from the tank inner and outer diameters [33] Assumed for stainless steel 304 at 25 °C [34] Calculated from inner tank geometry Calculated from BOG generation rate of 0.4%/day for nitrogen at −195.8 °C and 101.325 kPa [35]

Thermal conductance of tank, (UA) Source tank Maximum allowable working pressure of tank, MAWPSource Initial LNG volume percentage in tank Initial LNG temperature in tank Initial LNG pressure in tank

tank

LNG receiver tank Tank positioning Gross volume, VReceiver tank Length of inner tank, LReceiver tank Outer diameter, Do, Receiver tank Inner diameter, Di, Receiver tank Insulation thickness, tinsulate, Receiver tank Mass of storage tank (empty), mReceiver tank Specific heat capacity of storage tank, cp, Receiver tank Surface area of inner tank, AReceiver tank Overall heat transfer coefficient of tank, UReceiver tank Thermal conductance of tank, (UA)Receiver tank Maximum allowable working pressure of tank, MAWPReceiver Initial LNG volume percentage in tank Initial LNG temperature in tank Initial LNG pressure in tank

1.62 W/K 584 kPa 80% −146 °C 300 kPa – 68.137 m3 11.356 m 3.404 m 2.764 m 0.320 m 21,491 kg 477 J/kg·K 110.61 m2 0.012 W/m2·K

tank

1.33 W/K 1,300 kPa 20% −127 °C 865 kPa

[33] Assumed Calculated from saturation pressure of methane Assumed A vertical tank A vertical double-wall storage tank with a vacuum insulation between two walls [36] Calculated from the length of outer tank [36] Calculated from the net capacity of the tank Calculated from the tank inner and outer diameters [36] Assumed for stainless steel 304 at 25 °C [34] Calculated from inner tank geometry Calculated from BOG generation rate of 0.15%/day for methane at −162 °C and 101.325 kPa [36] [36] Assumed Assumed Assumed

and solved under the transient assumption. In this study, pure methane is considered as the representation of LNG. Methane is the main constituent of LNG and has a lower heat capacity, and saturation temperature and pressure than other hydrocarbons in the LNG mixture such as ethane, propane, n-butane, etc. This causes methane to be evaporated faster than heavier hydrocarbons and the pressure be dictated by the methane pressure. Therefore, using pure methane leads to a conservative design of LNG facilities. In the case of having high concentration of nitrogen in the LNG mixture (e.g., more than 1%), the analysis should account for the presence of nitrogen due to having a lower saturation temperature than methane at a constant pressure. The governing equations are time-dependent conservation of mass and energy, and the equation of state. The LNG and vapor are assumed to be in thermal equilibrium. The densities of the liquid and vapor phases are calculated by using the Peng-Robinson (PR) equation of state embedded in the software. For this study, a source tank volume of 48.0-m3 is chosen to correspond to commonly used tanker trucks in North America. The tanker is assumed to be initially filled to 80% of its volume and its pressure is at 300 kPa when it reaches the refueling station. The receiver tank is a vertical 68.0-m3 vacuum jacketed tank installed in a refueling station. The initial LNG level and pressure of the receive tank are set at 20% and 865 kPa. These values are within the actual operating ranges of LNG refueling stations in British Columbia, Canada. In real applications, the storage tanks installed in refueling stations have a higher MAWP than the tanker truck. This is because the storage tanks at stations have

thicker walls and insulation to hold LNG for several days whereas, tanker trucks are only in charge of delivering fuel. A vacuum jacketed pipeline connects the source and receiver tanks for LNG delivery. In this study, an equivalent length of the pipeline is used to take into account the effects of bending, changes in the diameter and elevation of pipelines, and friction losses. The LNG delivery pipeline is a 29-m long vacuum jacketed pipe with an inner diameter of 0.057 m. The vapor return pipeline is a 25-m long bare pipe with an inner diameter of 0.02786 m. The PBU is an air-heated heat exchanger with a heat transfer conductance of 600 W/K. The pump is a centrifugal type with a maximum discharge rate of 46.6 m3/h. Pressure relief valves (PRVs) installed on the LNG source and receiver tanks are assumed to be pop open-pop close PRVs. The activation pressure of the PRVs is set at the MAWP of the source and receiver tanks. These parameters are selected based on our observations from in operation LNG refueling stations. Further details on the specs of the components and their operating ranges are summarized in Tables 2–5. 4. LNG tank-to-tank transfer operating procedures In this study, six operating procedures for LNG offloading process are considered:

• LNG transfer by using a PBU with vapor return, • LNG transfer by using a PBU without vapor return, • LNG transfer by using a pump with vapor return,

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Table 3 Specifications of LNG delivery and vapor return pipelines, and pressure buildup unit. Parameter LNG delivery pipeline Equivalent length, Leq., LNG Pipe Outer diameter of inner pipe, Do, Inner pipe Inner diameter of inner pipe, Di, Inner pipe Outer diameter of jacket pipe, Do, Jacket pipe Inner diameter of jacket pipe, Di, Jacket pipe Insulation thickness, tinsulation, Pipe Mass of pipe, mPipe Specific heat capacity of pipe, cp, Pipe Heat transfer leak rate to inner pipe Inner surface area of the inner pipe, AInner pipe Overall heat transfer coefficient of pipe, UPipe Thermal conductance of pipe, (UA)Pipe

Value

Description

29 m 60.3 mm 57.0 mm 114.3 mm 110.0 mm 24.85 mm 8.6 kg/m 477 J/kg·K 0.72 W/m 5.2 m2

Includes the effects of pipe, valves, fittings, etc. Stainless steel pipe, schedule 5 [37] Stainless steel pipe, schedule 5 [37] Stainless steel pipe, schedule 5 [37] Stainless steel pipe, schedule 5 [37] Calculated from (Di, Jacket pipe - Do, Inner pipe)/2 [37] Assumed for stainless steel 304 at 25 °C [34] [37] Calculated from inner diameter of the inner pipe

0.0215 W/m2·K

Calculated from (UA)Pipe and AInner

0.112 W/K 5

2

5

pipe

Calculated from the heat transfer rate of 0.72 W/m [37], and ambient and LNG temperatures of 25 °C and −162 °C, respectively. c0 = 8 × f × Leq., LNG Pipe/(π2 × Di,5 Inner pipe )

Constant pressure drop coefficient in LNG pipeline, c0

7.50 × 10 N·s /kg·m

Initial wall temperature

25 °C

ΔP = c0 × ρ×Q Assumed

25 m 33.4 mm 27.86 mm 2.09 kg/m 477 J/kg·K 2.2 m2

Includes the effects of pipe, valves, fittings, etc. Stainless steel pipe, schedule 10 [13] Stainless steel pipe, schedule 10 [13] [13] Assumed for stainless steel 304 at 25 °C [34] Calculated from inner diameter of the pipe

Vapor return pipeline Equivalent length, Leq., Vapor return line Outer diameter of inner pipe, Do, Inner pipe Inner diameter of inner pipe, Di, Inner pipe Mass of pipe, mPipe Specific heat capacity of pipe, cp, Pipe Inner surface area of the inner pipe, AInner pipe Overall heat transfer coefficient of pipe, UPipe Thermal conductance of pipe, (UA)Pipe

35.0 W/m2·K 76.6 W/K

Constant pressure drop coefficient in LNG pipeline, c0

3.06 × 107N·s2/kg·m5

Calculated from internal, external and wall thermal resistances [38] and assuming gaseous natural gas and ambient temperatures of −162 °C and 25 °C, respectively. c0 = 8 × f × Leq., LNG Pipe /(π2 × Di,5 Inner pipe )

Initial wall temperature

25 °C

ΔP = c0 × ρ×Q Assumed

Pressure buildup unit (PBU) Thermal conductance of PBU, (UA)PBU

600 W/K

Virtual pump power consumption

15 W

Estimated for a 66-m long air-to-liquid heat exchanger with a heat transfer surface area of 2.16 m2/m. The thermal conductance of the PBU includes the internal and external convective heat transfer resistances and conductive thermal resistance of the PBU walls. Used in the model to pump LNG from the source tank to the PBU

When using a PBU with vapor return process, the vapor return valves between the receiver and source tanks (V4 and V5 in Fig. 2a) are opened and the vapor is transferred from the receiver tank at a higher pressure to the source tank at a lower pressure. When the pressure difference between the two tanks reaches less than 50 kPa, the PBU is run by opening V6 and V7 as shown in Fig. 2a. Also, the extra vapor in the receiver tank should be vented to atmosphere to reduce the receiver tank pressure by opening the manual vent valve (not shown) in order to make the fuel offloading process possible. As the PBU evaporates LNG in the source tank, the pressure difference between the source and receiver tanks gradually decreases. When the pressure of the source tank is increased by 0.1 kPa higher than that of the receiver tank, the valves on the LNG delivery pipeline (V1, V2, and V3) are opened. The PBU continuously evaporates a portion of LNG and increases the pressure of the source tank to maintain a positive pressure difference between the two tanks and push the LNG to the receiver tank. This process is continued until the LNG volume in the source tank reaches 2% of the tank volume. At this stage, the valves between the two tanks are closed and the process terminates. When using a PBU without vapor return process, valves V6 and V7 (shown in Fig. 2a) are opened and LNG is sent to the PBU and is

Table 4 Pump characteristic curve at 60 Hz [39]. Pump type

Centrifugal pump, Model TC-34 1.5 × 2.5 × 6–2 Stage

Shaft speed

Discharge head (m)

Volumetric flow rate (m3/h)

60 Hz (3600 rpm)

254.0 247.1 233.4 213.0 182.3 147.9* 93.0* 59.7* 0.0*

0.0 9.7 16.3 22.2 28.0 33.0 39.0 42.0 46.6

* These values are extrapolated from the pump characteristic curve data for modeling purposes.

• LNG transfer by using a pump without vapor return, • LNG transfer by using a pump and PBU without vapor return, and • LNG transfer by using a pump and controlled PBU without vapor return.

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Table 5 Specifications of primary PRVs installed on the LNG source and receiver tanks. Parameter

PRV installed on

Non-dimensional LNG volume in receiver tank

Model Inlet diameter of PRV (mm) Throat diameter of PRV (mm) Outlet diameter of PRV (mm) Activation set pressure (kPa) Full lift pressure, opening (kPa) Reseating pressure (kPa) Full lift pressure, closing (kPa) Leak rate

Description

Source tank

Receiver tank

– 38.1 23.0 63.5 584 584 550 550 0%

– 38.1 23.0 63.5 1300 1300 1270 1270 0%

HEROSE #06388.2314.6040 (size:1–1/2″ MPT × 2″ FPT) [40] [40] [40] [40] Based on MAWP of tanks [33,36] Set for a pop open-pop close PRV Assumed Set for a pop open-pop close PRV Assumed to be fully sealed.

the receiver tank to reduce its pressure by releasing the extra vapor to the atmosphere, and then start the LNG transfer process. This causes an increase in methane emissions from the refueling station. A similar procedure is followed for the LNG transfer by using a pump with and without vapor return process (Fig. 2b). The only difference is that instead of controlling the PBU, the pump should be energized. The LNG flow rate are adjusted based on the pump discharge head and the pump curve given in Table 4. The pump discharge head is determined based on the pressure difference between the two tanks and the pressure drop along the LNG delivery pipeline. If the pressure difference between the source and receiver tanks exceeds the maximum pump’s discharge head, the LNG tank-to-tank transfer by using a pump without vapor return process fails to operate. In such circumstances, the vapor in the receiver tank should be vented to the atmosphere before starting the LNG transfer process and that significantly increases the methane emissions from the process. The LNG tank-to-tank transfer by using a pump and PBU without vapor return process starts by running the PBU and turning the pump on (Fig. 2c). The LNG transfer process continues until the LNG volume in the source tank reaches 2% of the tank volume. The limitations of this mechanism are similar to the LNG tank-to-tank transfer by using a pump without vapor return process. However, as the PBU builds up the pressure in the source tank, the cavitation phenomenon in the pump is prevented. To further improve the performance of the LNG tank-to-tank transfer by using the pump and PBU without vapor return, the LNG flow rate sent to the PBU can be controlled by using an on-off pneumatic valve to maintain the pressure of the source tank at about 300 kPa and well-below the tank MAWP. Operating the LNG transfer by the pump and controlled PBU without vapor return is similar to the operation of LNG transfer by the pump and PBU without vapor return. However, the controlled PBU generates lower amounts of BOG in the source tank. In analyzing the results, the following parameters are desired:

1 0.8 0.6 0.4 0.2 0

Maximum relative difference = 22% Average relative difference = 10% 0

0.2

0.4

0.6

0.8

1

Non-dimensional time

Receiver tank non-dimensional pressure

(a)

1

Maximum relative difference = 27% Average relative difference = 8%

0.8 0.6 0.4 0.2 0

0

0.2

0.4

0.6

0.8

1

Non-dimensional time

(b)

Fig. 3. Comparison of numerical results and the experimental data collected from an LNG offloading process by using a pump and PBU without vapor return: (a) Non-dimensional LNG volume and (b) non-dimensional pressure of the receiver tank.

• Short fuel transfer process time, • Long source tank holding time after LNG offload, • Low pressure in the receiver tank, and • Low pressure in the source tank but above the NPSH of a pump

evaporated. Also, the vapor in the receiver tank is vented to the atmosphere to reduce the tank pressure. When the pressure of the source tank exceeds that of the receiver tank by 0.1 kPa, valves V1, V2 and V3 are opened and the LNG is transferred to the receiver tank. This process is continued until the LNG volume in the receiver tank reaches 2% of the tank volume. The MAWP of the source tank is 584 kPa (as given in Table 2). In circumstances that the initial pressure of the receiver tank is higher than the MAWP of the source tank, the LNG tank-to-tank transfer by using a PBU without vapor return process fails to operate. In practice, the refueling station operator should open the manual vent of

5. Results and discussions 5.1. Model validation The accuracy of the thermodynamic models was compared against

7

LNG offlloading process time (min)

140 120

140

LNG offloading process time

120

Source tank holding time after LNG offload

100

100

80

80

60

60

40

40

20

20

0

PBU with vapor return

PBU without vapor return

Pump with vapor Pump without return vapor return

Tank final pressure (kPa)

(a)

Pump + PBU without vapor return

Pump + controlled PBU without vapor return

0

Source tank holding time after LNG offloading process (hr)

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1200 Source Tank

1000

Receiver Tank

800 600 400 200 0

PBU with vapor return

PBU without vapor return

Pump with vapor Pump without return vapor return

(b)

Pump + PBU without vapor return

Pump + controlled PBU without vapor return

Fig. 4. Comparison of different LNG offloading processes. The hatched columns in (a) show the LNG offloading processes with methane emissions. The initial pressures of the source and receiver tanks are shown by dash symbols in (b). Table 6 Characteristics of LNG delivery pipeline with different inner diameters [37]. Parameter

Outer diameter of inner pipe, Do, Inner pipe, (mm) Outer diameter of jacket pipe, Do, Jacket pipe, (mm) Inner diameter of jacket pipe, Di, Jacket pipe, (mm) Insulation thickness, tinsulation, Pipe, (mm) Equivalent length, Leq., LNG Pipe, (m) Mass of pipe, mPipe, (kg/m) Heat transfer leak rate to inner pipe, (W/m) Inner surface area of the inner pipe, AInner pipe, (m2) Overall heat transfer coefficient of pipe, UPipe, (W/m2·K) Thermal conductance of pipe, (UA)Pipe, (W/K) Constant pressure drop coefficient in LNG pipeline, c0, (N·s2/kg·m5)

Inner diameter of inner pipe, Di,

Inner pipe,

(mm)

30.1

45.0

84.65

135.46

33.4 88.9 84.65 25.625 25.21 6.2 0.43 2.4 0.0243 0.058 1.86 × 107

48.3 101.6 97.38 25.45 27.30 7.4 0.54 3.9 0.0204 0.079 2.44 × 106

88.9 141.3 135.46 23.28 32.85 14.6 0.94 8.7 0.0189 0.165 1.07 × 105

114.3 168.3 162.76 24.23 39.96 17.9 1.23 17.0 0.0155 0.263 1.12 × 104

the experimental data collected from an LNG refueling station in British Columbia, Canada. A tanker truck equipped with a pump and PBU delivers LNG to the refueling station. The exact amount of LNG offloaded to the refueling station was determined by weighing the tanker truck before and after the LNG offloading process. The refueling station is equipped with a pressure transducer which has a 100–2,000 kPa range and accuracy of ± 1.1 kPa. A differential pressure transducer, which has a 1–100 kPa range and accuracy of ± 0.065 kPa, measures the LNG level in the receiver tank. Using the LNG level, the control

system at the station calculates the LNG volume in the storage tank. The real-time pressure and LNG volume in the receiver tank are logged by the control system of the refueling station. Fig. 3 shows a comparison between the numerical and experimental data of LNG offloading process by using a pump and PBU without vapor return. Due to confidentiality considerations, the LNG volume and pressure of the receiver tank are non-dimensionalized. It can be seen that the thermodynamic model predicts the LNG volume and pressure of the tank with average relative difference of 10% and 8%, respectively.

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(b) Fig. 5. Effects of LNG delivery pipe diameter on the LNG tank-to-tank process. The specs of LNG delivery pipeline are provided in Table 6 (other parameters are as given in Tables 2–5). The initial pressures of the source and receiver tanks are shown by dash symbols in (b). Table 7 Characteristics of LNG delivery pipeline at different lengths. Parameter

Outer diameter of inner pipe, Do, Inner pipe, (mm) Inner diameter of inner pipe, Di, Inner pipe, (mm) Outer diameter of jacket pipe, Do, Jacket pipe, (mm) Inner diameter of jacket pipe, Di, Jacket pipe, (mm) Insulation thickness, tinsulation, Pipe, (m) Mass of pipe, mPipe, (kg/m) Heat transfer leak rate to inner pipe, (W/m) Inner surface area of the inner pipe, AInner pipe, (m2) Overall heat transfer coefficient of pipe, UPipe, (W/m2·K) Thermal conductance of pipe, (UA)Pipe, (W/K) Constant pressure drop coefficient in LNG pipeline, c0, (N·s2/kg·m5)

Equivalent length, Leq.,

LNG Pipe,

(m)

18

38

48

58

60.3 57.0 114.3 110.0 24.85 8.6 0.72 3.2 0.0215 0.069 4.66 × 105

60.3 57.0 114.3 110.0 24.85 8.6 0.72 6.8 0.0215 0.146 9.83 × 105

60.3 57.0 114.3 110.0 24.85 8.6 0.72 8.6 0.0215 0.185 1.24 × 106

60.3 57.0 114.3 110.0 24.85 8.6 0.72 10.4 0.0215 0.223 1.50 × 106

For the model validation, the exact amount of LNG offloaded by the tanker truck is included in the model (in kg). However, the final LNG volume in the receiver tank is 6% higher than the experimental data

which is attributed to the remainder of LNG in the sump pump tank and piping in the refueling station, and a lower density of pure methane than that of actual LNG mixture used in the numerical modeling.

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18

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58

18

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Pump + PBU without vapor return Pump + controlled PBU without vapor return LNG delivery pipeline Length (m)

(b) Fig. 6. Effects of LNG delivery pipeline length on the LNG tank-to-tank process. The specs of LNG delivery pipeline are provided in Table 7 (other parameters are as given in Tables 2–5). The initial pressures of the source and receiver tanks are shown by dash symbols in (b).

5.2. Base-case model analysis

Fig. 4a illustrates that the LNG tank-to-tank transfer by using a pump without vapor return, a pump and PBU without vapor return, and a pump and controlled PBU without vapor return provide the shortest fuel offloading process time (57–59 min). Also, Fig. 4a shows that the source tank holding time after LNG offloading process is highly affected by the LNG tank-to-tank transfer methods. A longer holding time of the source tank (a tanker truck) after a LNG offloading process minimizes the chance of methane emissions to the atmosphere from the tank on its return journey to a liquefaction plant. The vapor in the source tank is returned to the liquefaction plant to be re-liquefied before filling the source tank. As shown in Fig. 4a, the maximum LNG holding time of the source tank belongs to the LNG tank-to-tank transfer by using a pump without vapor return, however, during the fuel offloading process, the source tank pressure decreases (Fig. 4b). This is not desired as the low pressure in the source tank increases the chance of cavitation in the pump. The second longest LNG holding time of the source tank belongs to the LNG tank-to-tank transfer by using a pump and controlled PBU without vapor return (99 hrs) which is 2.8 times longer than the LNG

Fig. 4 shows the performance of six LNG offloading processes at the base conditions given in Tables 2–5. The LNG offloading process times displayed by the hatched columns correspond to processes with methane emissions to the atmosphere. The methane emissions in this study is attributed only to the LNG offloading processes and do not consider emissions from valves, fittings, and connection and disconnection of LNG delivery pipeline. The results of our analysis indicate that to transfer LNG by using the PBU with and without vapor return, 782 and 1,546 kg of methane should be vented from the receiver tank, respectively, to reduce the receiver tank pressure. These amounts of methane emissions correspond to 49 and 104 g/kgLNG for fuel transfer by using a PBU with and without vapor return, respectively. This finding highlights that the LNG transfer by using a PBU only causes high methane emissions. This method is regularly used in some countries and this amount of methane emissions should be included in the life cycle assessment of LNG as a fuel for transportation.

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This LNG transfer method is similar to that by using a pump and PBU without vapor return. However, it controls the amount of LNG evaporated in the source tank to maintain the tank pressure within a certain range. Therefore, it reduces BOG generation in the source tank. Besides, this method increases the LNG holding time of the source tank by 2.8 times more than that by using a pump and PBU without vapor return at the base-case conditions.

Table 8 Characteristics of LNG delivery pipeline with different insulation materials. Parameter

Outer diameter, Do, Pipe, (mm) Inner diameter, Di, Pipe, (mm) Outer diameter of jacket pipe, Do, Jacket pipe, (mm) Inner diameter of jacket pipe, Di, Jacket pipe, (mm) Insulation thickness, tinsulation, (mm) Length, LPipe, (m) Mass of pipe, mPipe, (kg/m) Inner surface area of pipe, APipe, (m2) Overall heat transfer coefficient of pipe, UPipe, (W/m2·K) Thermal conductance of pipe, (UA)Pipe, (W/K) Constant pressure drop coefficient in LNG pipeline, c0, (N·s2/kg·m5)

Pipe insulation material BP‡

RFP†

VJP*

60.3 57.0 –

60.3 57.0 161.9

60.3 57.0 114.3

–

60.3

110.0

– 29 3.93 5.2 53.21

50.8 29 4.5 5.2 0.74

24.85 29 8.6 5.2 0.0215

276.69

3.85 5

7.50 × 10

7.50 × 10

5.3. Parametric study 5.3.1. Effect of LNG delivery pipe diameter The LNG delivery pipeline causes the pressure drop and heat transfer to the LNG during the LNG offloading process. Table 6 shows the specification of LNG delivery pipelines with inner diameters ranging from 30.1 mm to 135.46 mm. These dimensions are determined based on standard vacuum jacketed pipelines available in the market, such as pipelines given in Ref. [37]. Fig. 5a shows that the LNG pipeline with 30.1 mm inner diameter causes the longest fuel offloading process time. For example, when using a LNG delivery pipeline with 30.1 mm diameter, and a pump with vapor return, the fuel offloading process takes about 122 min whereas, using LNG delivery pipelines with 57–135.46 mm diameter decreases the fuel offloading process to 98 min. It should be noted that as the pipe diameter increases, it becomes more expensive. Therefore, the pipe size should be selected with respect to the pump discharge head and flow rate. As noted in Table 4, the pump has the maximum discharge head and volumetric flow rate of 254 m and 46.6 m3/h, respectively. To this end, the pipe with inner diameter of 57 mm is the best choice compared with pipes with inner diameter of 84.65 and 135.46 mm to achieve a short fuel offloading process time while the pump discharge volumetric flow rate reaches its maximum capacity. Also, Fig. 5a demonstrate that using a pump and controlled PBU without vapor return leads to the highest source tank holding time after LNG offloading process (99 hrs). Fig. 5b displays the effect of LNG delivery pipelines with 30.1–135.46 mm inner diameter on the final pressure of the source and receiver tanks. It can be seen that the three LNG transfer methods keep the final pressure of the source tank always equal or higher than its initial pressure to protect the pump. Moreover, Fig. 5b indicates that the lowest final pressure of the receiver tank is achieved by using a pump with vapor return followed by a pump and controlled PBU without vapor return. The results displayed in Fig. 5 suggest that the LNG transfer by using a pump and controlled PBU without vapor return equipped with an LNG delivery pipeline with 57 mm inner diameter provides the best performance in terms of LNG offloading process time, source tank holding time after LNG offload, and final pressures in the source and receiver tanks.

0.1118 5

7.50 × 105

Tambient is assumed to remain constant at 25 °C and TLNG is at −162 °C. Heat transfer coefficient (hconvection) on the surface of the pipe is set at 10 W/ m2·K. ‡ BP: Bare pipe (Stainless steel 304 pipe with no insulation and k = 9.6 W/ m·K at −162 °C [34]). † RFP: Rigid foam pipe (Polyurethane foam with k = 0.021 W/m·K at 1 atm and density of 32 kg/m3 [41]). * VJP: Vacuum jacketed pipe (Heat transfer rate to the pipe is 0.72 W/m based on data reported in Ref. [37]).

holding time of the source tank by using a pump and PBU without vapor return. The final pressures of the source and receiver tanks are shown in Fig. 4b. The initial pressures of these tanks are shown by dash symbols. In LNG offloading processes by using a pump with vapor return, and a pump and PBU without vapor return, the final pressure of the source tank increases more than its initial pressure. This is desirable to prevent cavitation in the pump. Furthermore, Fig. 4b indicates that the pressure of the source tank is maintained constant by using the pump and controlled PBU without vapor return. According to the results shown in Fig. 4b, the final pressure of the receiver tank decreases due to the vapor return to the source tank and/ or the BOG condensation in contact with a new load of LNG. Using a pump with and without vapor return leads to the lowest final pressures in the receiver tank (475–485 kPa) followed by the LNG transfer by using a pump and controlled PBU without vapor return (510 kPa). The highest final pressure in the receiver tank belongs to the LNG transfer by using a pump and PBU without vapor return (570 kPa). Based on the results of the base-case study, the following LNG tankto-tank transfer methods are considered for further analysis:

• LNG transfer by using a pump with vapor return: While this method has

• •

5.3.2. Effect of LNG delivery pipeline length Table 7 shows the characteristics of 18–58 m-long LNG delivery pipelines. Fig. 6 shows that increasing the length of the LNG delivery pipeline from 18 to 58 m increases the fuel offloading process time by up to 3%, and does not affect the final pressures of the source and receiver tanks. This is due to the pump capability to overcome the pressure drop along the 18–58 m-long pipeline. Therefore, it can be concluded that the length of LNG pipeline is not a key factor in the design of LNG offloading systems from a tanker truck to a refueling station. However, a shorter length reduces the capital cost of LNG offloading systems.

the longest LNG offloading process time, it protects the pump from cavitation in comparison with the LNG tank-to-tank transfer by using a pump without vapor return. Also, in places where the usage of PBU is prohibited due to safety reasons (e.g., failure of PBU and LNG spill), this method is the most reliable option. LNG transfer by using a pump and PBU without vapor return: This method provides a short fuel offloading process time and prevents the pressure of the LNG source tank to drop, thereby it prevents the cavitation phenomenon in the pump. LNG transfer by using a pump and controlled PBU without vapor return:

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(a) Tank final pressure (kPa)

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RFP

VJP

Pump with vapor return

BP

RFP

VJP

BP

RFP

VJP

Pump + PBU without vapor return Pump + controlled PBU without vapor return LNG delivery pipeline insulation type

(b) Fig. 7. Effects of insulation of LNG delivery pipeline on the LNG tank-to-tank process. The specs of insulation of LNG delivery pipeline are provided in Table 8 (other parameters are as given in Tables 2–5). The initial pressures of the source and receiver tanks are shown by dash symbols in (b).

5.3.3. Effect of LNG delivery pipeline insulation type Insulation of the LNG delivery pipeline directly impacts the heat transfer rate to the LNG and the amount of BOG generation. In this study, two types of insulated pipelines are compared against a bare pipeline (BP), namely, rigid foam pipeline (RFP) and vacuum jacketed pipeline (VJP). These pipelines have identical inner diameters and lengths, as given in Table 8. However, the thermal conductance of the BP (905.16 W/K) and the RFP (12.58 W/K) is about 2,475 and 34 times as high as that of VJP (0.37 W/K), respectively. Fig. 7a shows that the BP, RFP and VJP do not affect the LNG offloading process time. However, Fig. 7b illustrates that using BP in comparison with VJP increases the final pressure of the receiver tank by 49–66 kPa due to the high heat transfer to the LNG from the environment. Fig. 7 also shows that using a pump and controlled PBU without vapor return provides a similar fuel offloading process time to the one with a pump and PBU without vapor return. Furthermore, it increases the source tank holding time after LNG offload by more than 2.8 times to 99 hrs. Finally, the results indicate that RFP can replace VJP in LNG tank-to-tank transfer because RFP is not as expensive as VJP and is

more flexible for installation in applications with limited space. 5.3.4. Effect of receiver tank initial pressure The initial pressure of the receiver tank is changed from 400 to 1200 kPa to study the performance of the LNG tank-to-tank transfer methods. In this section, the LNG tank-to-tank transfer by using a PBU with vapor return is also considered. The results shown in Fig. 8a indicate that the LNG tank-to-tank transfer by using a PBU with vapor return is directly affected by the initial pressure of the receiver tank. The amount of methane vented from the LNG transfer by using a PBU with vapor return varies from 600 to 930 kg for the receiver tank at the initial pressures of 400 and 1,200 kPa, respectively. These amounts of methane emissions correspond to 40–58 g/kgLNG . Fig. 8a illustrates that the LNG offloading process time by using a pump with vapor return increases from 63 to 108 min (a 71% increase) by increasing the receiver tank initial pressure from 400 kPa to 1200 kPa, respectively. The LNG transfer process time by using a pump and PBU without vapor return, and a pump and controlled PBU without vapor return increases from 52 to 69 min (a 33% increase) by increasing the receiver tank initial pressure from 400 kPa to 1200 kPa,

12

LNG offlloading process time (min)

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120 100

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80

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400 600 865 10001200 400 600 865 10001200 400 600 865 10001200 400 600 865 10001200 PBU with vapor return

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Receiver tank initial pressure (kPa)

(a) Tank final pressure (kPa)

1400 1200

Source Tank

Receiver Tank

1000 800 600 400 200 0

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Pump with vapor return

Pump + PBU without vapor return

Pump + controlled PBU without vapor return

Receiver tank initial pressure (kPa)

(b) Fig. 8. Effects of initial pressure of the receiver tank on the LNG tank-to-tank process (other parameters are as given in Tables 2–5). The hatched columns in (a) show the LNG offloading processes with methane emissions. The initial pressures of the source and receiver tanks are shown by dash symbols in (b).

respectively. This implies that these two methods are less sensitive to the receiver tank initial pressure compared with the LNG transfer by using a pump with vapor return. The results shown in Fig. 8a also indicates that the LNG transfer by using a pump and controlled PBU without vapor return leads to the longest source tank holding time after LNG offload (99 hrs) and independent from the receiver tank initial pressure.

6. Conclusions In this study, the LNG transfer from a tanker truck to an LNG refueling station was modeled. Four criteria were introduced to compare the LNG offloading processes, namely, the fuel offloading process time, source tank holding time after LNG offload, and the final pressures of source and receiver tanks. Six LNG offloading processes were considered as the base-case study. The results of base-case study showed that the LNG transfer by using a PBU with and without vapor return caused the methane emissions of 49 and 104 g/kgLNG , respectively. At the base-case operating conditions, the LNG transfer by using a pump without vapor return, a pump and PBU without vapor return, and a pump and controlled PBU without vapor return provided the shortest LNG transfer process time. However, the LNG transfer by using a pump without vapor return decreased the source tank pressure which could cause the cavitation in the pump. Comparing six LNG offloading processes, it was concluded that using a pump and controlled PBU without vapor return (the proposed method in this study) was the best method which provided a short fuel transfer time, long source tank holding time after LNG offload, and low pressures in the source and receiver tanks at the end of the LNG offloading process. This conclusion was found to be independent of the LNG pipeline length, diameter and insulation type. The results of a parametric study indicated that in the design of LNG delivery pipeline and PBU, the pipe diameter and insulation had the

5.3.5. Effect of PBU size The PBU size has a direct impact on the LNG evaporation rate and pressure buildup in the source tank. In this study, the heat transfer conductance (UA = overall heat transfer coefficient × heat transfer surface area) of the PBU represents its size. Fig. 9a shows that using a PBU with the thermal conductance of 300–1200 W/K does not affect the fuel offloading process time as the LNG transfer is mainly controlled by the pump. However, when using a pump and PBU without vapor return, a larger PBU decreases the source tank holding time after LNG offload from 79 to 23 hrs due to the increase of the source tank final pressure as shown in Fig. 9b. In contrast, the LNG transfer by using a pump and controlled PBU is not significantly affected by the PBU size as shown in Fig. 9a. A controlled PBU adjusts the LNG evaporation rate independent from its size. Therefore, the final pressures of the source and receiver tanks are not affected by the PBU size as shown in Fig. 9b.

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(a)

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Source Tank

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800 600 400 200 0

300

600

900

1200

300

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600

900

1200

Pump + controlled PBU without vapor return

PBU heat transfer conductance, UA, (W/K)

(b) Fig. 9. Effects of heat transfer conductance of the PBU on the LNG tank-to-tank process (other parameters are as given in Tables 2–5). The initial pressures of the source and receiver tanks are shown by dash symbols in (b).

highest impacts on the LNG offloading process compared with other parameters, e.g., pipe length and the PUB size. Also, comparing the rigid foam and vacuum-jacked insulations for the LNG delivery pipeline showed that these insulations provided a similar performance. However, the rigid foam insulation was not as expensive as vacuum jacked pipes and it could reduce the capital cost of LNG offloading systems.

[6] A.R. Brandt, G.A. Heath, E.A. Kort, F. O’Sullivan, G. Pétron, S.M. Jordaan, et al., Methane leaks from north american natural gas systems, Science 343 (2014) 733–735, https://doi.org/10.1126/science.1247045. [7] A. Srikanth, S. Narasimhan, S. Narasimhan, Optimization of unloading operations in petroleum product storage terminals, Ind. Eng. Chem. Res. 53 (2014) 13728–13735, https://doi.org/10.1021/ie400389x. [8] M.S. Zakaria, K. Osman, A.A. Yusof, M.H.M. Hanafi, M.N.A. Saadun, M.Z.A. Manaf, Parametric analysis of boil-off gas rate inside liquefied natural gas storage tank, J. Mech. Eng. Sci. 6 (2015) 845–853, https://doi.org/10.1017/CBO9781107415324. 004. [9] D. Holden, Liquefied natural gas (LNG) bunkering study, DNV.GL (Report No.: PP087423-4, Rev 3), 2014. [10] Đ. Dobrota, B. Lalić, I. Komar, Problem of boil - off in LNG supply chain, Trans. Marit. Sci. 02 (2013) 91–100, https://doi.org/10.7225/toms.v02.n02.001. [11] D.T. Allen, A.P. Pacsi, D.W. Sullivan, D. Zavala-araiza, M. Harrison, K. Keen, et al., Methane emissions from process equipment at natural gas production sites in the United States: pneumatic controllers, Environ. Sci. Technol. 49 (2014) 630–640, https://doi.org/10.1021/es5040156. [12] D.R. Johnson, A.N. Covington, N.N. Clark, Methane emissions from leak and loss audits of natural gas compressor stations and storage facilities, Environ. Sci. Technol. 49 (2015) 8132–8138, https://doi.org/10.1021/es506163m. [13] N.N. Clark, D.L. McKain, D.R. Johnson, W.S. Wayne, H. Li, V. Akkerman, et al., Pump-to-wheels methane emissions from the heavy-duty transportation sector, Environ. Sci. Technol. 51 (2016) 968–976, https://doi.org/10.1021/acs.est. 5b06059. [14] H. McJeon, J. Edmonds, N. Bauer, L. Clarke, B. Fisher, B.P. Flannery, et al., Limited impact on decadal-scale climate change from increased use of natural gas, Nature 514 (2014) 482–485, https://doi.org/10.1038/nature13837. [15] R.A. Alvarez, S.W. Pacala, J.J. Winebrake, W.L. Chameides, S.P. Hamburg, Greater focus needed on methane leakage from natural gas infrastructure, Proc. Natl. Acad. Sci. U. S. A. 109 (2012) 6435–6440, https://doi.org/10.1073/pnas.1202407109. [16] R.W. Howarth, R. Santoro, A. Ingraffea, Methane and the greenhouse-gas footprint of natural gas from shale formations, Clim. Change 106 (2011) 679–690, https:// doi.org/10.1007/s10584-011-0061-5. [17] A. Venkatesh, P. Jaramillo, W.M. Griffin, H.S. Matthews, Uncertainty in life cycle greenhouse gas emissions from United States natural gas end-uses and its effects on policy, Environ. Sci. Technol. 45 (2011) 8182–8189, https://doi.org/10.1021/

Acknowledgement The authors gratefully acknowledge the financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC) and the MITACS Elevate Postdoctoral Fellowship program. References [1] Climate Change 2014: Mitigation of Climate Change (Vol. 3), Intergovernmental Panel on Climate Change, 2015. [2] N. Olmer, B. Comer, B. Roy, X. Mao, D. Rutherford, Greenhouse Gas Emissions From Global Shipping, 2013–2015, The International Council on Clean Transportation, 2017. https://www.theicct.org/publications/GHG-emissions-global-shipping-20132015. [3] T.W.P. Smith, J.P. Jalkanen, B.A. Anderson, J.J. Corbett, J. Faber, S. Hanayama, et al., Third IMO greenhouse gas study 2014, International Maritime Organization (IMO) (2014), https://doi.org/10.1007/s10584-013-0912-3. [4] Q.S. Chen, J. Wegrzyn, V. Prasad, Analysis of temperature and pressure changes in liquefied natural gas (LNG) cryogenic tanks, Cryogenics (Guildf) 44 (2004) 701–709, https://doi.org/10.1016/j.cryogenics.2004.03.020. [5] M. Miana, R. Legorburo, D. Díez, Y.H. Hwang, Calculation of boil-off rate of liquefied natural gas in Mark III tanks of ship carriers by numerical analysis, Appl. Therm. Eng. 93 (2015) 279–296, https://doi.org/10.1016/j.applthermaleng.2015. 09.112.

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