LNG Tanker Research Articles

EN Methods for managing the energy efficiency of a reliquefaction plant operating on the reverse brighton cycle of a LNG tanker

LNG is transported over long sea and ocean distances only by tankers, called LNG carriers, in large on-board tanks at a temperature of -163ºC. Although these tanks are well insulated, some of the LNG evaporates under the external factors influence, and boil-off-gas gas (BOG) is formed. The main method of dealing with BOG is the reliquefaction of LNG. Many LNG carriers use technology based on the reverse Brighton cycle (RBC) for reliquefaction. The study has been carried out by thermodynamic analysis methods of the actual parameters and characteristics of the BOG reliquefaction plant based on the data obtained during the operation of the LNG carrier “UMM AL AMAD”. Energy and entropy-statistical methods of thermodynamic analysis have been used in the research. The reliquefaction plant operation has been evaluated based on the specific compression work consumption and the value of the effectiveness of a thermodynamic cycle. The analysis of the results showed that the investigated system operating according to the Brighton cycle has low energy efficiency values. The most energy-intensive loop is the nitrogen loop. It accounts for over 90% of the work overspending in the reliquefaction plant. The expander work partially compensates for the overexpenditure of compressor work. Irreversibility in the expander is 7.7%, and the N2 compressor is approximately 48.7% of the total irreversibility of the liquefaction process. In the BOG/LNG loop, the main contribution to the processes’ irreversibility is made by the BOG compressor (~3.7%) and the precooler (~1.55%) of the total irreversibility of the liquefaction process. The cryogenic heat exchanger is a component of both loops and its negative impact is estimated at 36.4% of the total irreversibility of the liquefaction process. The application of reliquefaction plants operating on the Brighton cycle is currently inefficient due to low energy efficiency and huge losses in the nitrogen loop, which does not meet IMO requirements for gas carriers

Algerian gas to strengthen energy security of the European Union: Policy, capacity and strategy

The last decade has seen relative stability in the global gas market, with European countries benefiting from access to abundant and inexpensive gas supplies, primarily from Russia. However, the onset of the Russo-Ukrainian war has exposed Europe's energy vulnerabilities, given its heavy reliance on Russian gas. In response, Algeria has emerged as a key alternative, drawing increased diplomatic engagement from the European Union. Algeria's significance stems not only from its considerable gas reserves and potential for production expansion but also from its geographical proximity to Europe and its robust gas infrastructure, including LNG tankers and a comprehensive pipeline network. This paper seeks to delve into Algeria's potential to bolster the European Union's energy security. Through a detailed examination of Algeria's resource capabilities and insights drawn from the experiences of Spain and Italy—countries that have navigated political tensions and competition with Russian gas respectively—the study aims to provide a nuanced analysis of how Algeria can play a pivotal role in ensuring a stable and secure energy supply for Europe.

Application of Biogas and Biomethane as Maritime Fuels: A Review of Research, Technology Development, Innovation Proposals, and Market Potentials

This review paper examines the applicability of biogas and biomethane as potential maritime fuels and examines issues of these fuels from a supply chain perspective (from production to end use). The objectives are to identify: (1) the latest research, development, and innovation activities; (2) issues and key barriers related to the technology readiness to bring biogas/biomethane to market; and (3) commercialisation issues, including cost parity with natural gas (the main competitor). A survey of the literature was carried out based on research articles and grey literature. The PESTEL and SWOT analyses identified opportunities for these fuels due to the relevant regulations (e.g., Fit for 55; the recent inclusion of the Mediterranean Sea as a SECA and PM control area; MPEC 79), market-based measures, and environmental, social, and governance strategies. The potential of biomass feedstock is estimated to have a substantial value that can satisfy the energy needs of the maritime industry. However, production costs of biomethane are high; estimated to be 2–4 times higher compared to natural gas. The market is moving in the direction of alternative drop-in fuels, including liquefied and compressed biomethane (LBM and CBM) and biogas. In terms of potential market penetration, LBM can be used as a marine drop-in fuel for the existing fleet that already combust LNG and LPG due to similar handling. Currently, these vessels are LNG and LPG tankers. However, in newly built vessels, LBM can be also supplied to container ships, vehicle carriers, and bulk carriers (about 20% of newly built vessels). Provided that compressed natural gas infrastructure exists, CBM can be exploited in vessels with low energy needs and low space requirements and shore-side electrification, because investments in retrofits are lower compared to constructing new infrastructure.

Comments: The Stark Realities of Energy Supply

Natural gas is considered the transition fossil fuel to move the world toward a meaningful reduction in global greenhouse-gas emissions. But the clampdown of Russia’s natural gas supplies shifted the market’s dynamics, and the repercussions are being experienced around the world. Europe is one of the hardest hit by this disruption in natural gas supplies. In a commentary posted on 18 July, Fatih Birol, executive director of the International Energy Agency, called for coordinated actions across Europe to prepare for the coming winter months and for worst-case scenarios of a complete shutoff of Russian gas and limited availability from other sources. Although Russia resumed a reduced flow of gas to Germany via the Nord Stream pipeline on 21 July, there is no certainty about the fluctuations or duration of the flow. Birol wrote, “Europe is now forced to operate in a constant state of uncertainty over Russian gas supplies, and we can’t rule out a complete cutoff.” The start of Europe’s winter heating season is 1 October. Birol called for action to fill European gas storage to adequate levels by reducing current gas consumption and to put that conserved gas into storage. High natural gas prices have led to gas conservation to some extent, but more efforts are required. He wrote that the gas required to be saved over the next 3 months “is in the order of 12 billion cubic metres—enough to fill about 130 LNG tankers,” equivalent to 424 Bcf. To lend some perspective to this, consider that US LNG exports averaged 10.1 Bcf/D in June. This reflects a 1.5 Bcf/D decrease from May because of a fire on 8 June that shut down Freeport LNG in Texas, according to the US Energy Information Administration (EIA). The agency expects US LNG exports to remain below average at 10.5 Bcf/D in the second half of this year. The Freeport LNG shutdown, and the resulting lower demand for LNG export gas, decreased the US benchmark Henry Hub natural gas spot price. It fell by $1.27/MMBtu to $8.16/MMBtu on 9 June and averaged $7.70/MMBtu in June. EIA expects the spot price to continue to decline to an average of $5.97/MMBtu in the second half of this year. European imports of LNG rose by more than 50% in the first 5 months of 2022 compared with the period a year earlier, according to Bernstein, a Wall Street research firm. Although a wide range of shippers have sent fuel to Europe, the major increases in its LNG imports have come from gas produced from US shale. The increased European demand also increased the price of its imported LNG to nearly nine times what it was about 2 years ago, and those higher prices enticed LNG shippers away from Asia. European futures prices have been around $40/MMBtu. The Wall Street Journal compared that to more than $200/bbl for oil, about twice the price for Brent crude, the international benchmark, as of 22 July. In most years, China, Japan, and South Korea have been the major markets for LNG. During the first 5 months of 2022, Asian imports fell by 8%—in part because of slowing demand from China caused by COVID-19 lockdowns. Birol’s commentary began with this sentence: “The world is experiencing the first truly global energy crisis in history.” For Europe, the Russian invasion of Ukraine also sparked a cost-of-living crisis when oil and gas prices soared. Crises, by definition, require immediate and effective actions.

Modeling the symmetric relation between Baltic Exchange indexes

PurposeThis research provides some evidence by the vine copula approach, suggesting the significant and symmetric causal relation between subsections of Baltic Exchange and hence concluding that investing in different indexes, which is currently a risk diversification system, is not a correct risk reduction strategy.Design/methodology/approachThe daily observations of Baltic Capesize Index (BCI), Baltic Handysize Index (BHSI), Baltic Dirty Tanker Index (BDTI) and Baltic LNG Tanker Index (BLNG) over an eight-year period have been used. After collecting data, calculating the return and estimating the marginal distribution of return rates for each of the indexes applying asymmetric power generalized autoregressive conditional heteroskedasticity and autoregressive moving average (APGARCH-ARMA), and with the assumption of skew student's t-distribution, the dependence of Baltic indexes was modeled based on Vine-R structures.FindingsA positive and symmetrical correlation was observed between the study groups. High and low tail dependence is observed between all four indexes. In other words, the sector business groups associated with each of these indexes react similarly to the extreme events of other groups. The BHSI has a pivotal role in examining the dependency structure of Baltic Exchange indexes. That is, in addition to the direct dependence of Baltic groups, the dependence of each group on the BHSI can transmit accidents and shocks to other groups.Practical implicationsSince the Baltic Exchange indexes are tradable, these findings have implications for portfolio design and hedging strategies for investors in shipping markets.Originality/valueVine copula structures proves the causal relationship between different Baltic Exchange indexes, which are derived from different types of markets.

Safety evaluation of using ammonia as marine fuel by analysing gas dispersion in a ship engine room using CFD

ABSTRACT This paper seeks to address the question that each stakeholder in the maritime industry has about ammonia’s potential as a marine fuel, How safe is it to use ammonia as a fuel onboard vessel ? The principle aim of this paper is to quantify the exposure limits to which crew working onboard can get subjected to in a confined space onboard a vessel. It was achieved by simulating gas leaks at different locations inside an engine room of a hypothetical ammonia fuelled carrier similar to a 114,000 GWT LNG tanker using CFD. The transient nature of dispersion is analysed and compared for various scenarios. The results are promising and prove that ammonia does have a high risk due to its toxicity but a low risk in terms of flammability. Research findings also demonstrate that the gas dispersion depends on numerous factors such as position, area of leak, direction of leak, pressure and temperature of ammonia gas, obstruction due to placement of machinery and decks, ventilation, and the temperature gradient of surrounding material. The novelty of the paper lies in the problem it addresses and will contribute to the industry in a better understanding of the risk involved in operating an ammonia-fuelled vessel.

Concurrent 19. Presentation for: Viral mutations, vaccine effectiveness and rapid tests – COVID-19 risk management in the two largest LNG producing countries, Qatar and Australia

Presented on Wednesday 18 May: Session 19 The SARS-CoV-2 pandemic created challenges for the oil and gas industry. Qatar experienced three significant waves during the pandemic that disproportionately affected the workers in shared accommodation. In Australia, the public health measures limited the spread of SARS-CoV-2 in the industry until the Omicron wave. Anti-SARS-CoV-2 seropositivity was assessed in five oil and gas subcontractors and five hospital subcontractors in Qatar between 21 June and 9 September 2020. Vaccine effectiveness was assessed in Qatar. Vaccine effectiveness in an LNG tanker crew off Gladstone was calculated. The initial study in Qatar included 4970 craft manual workers (CMWs) who were mostly men (95.0%). Infection positivity (antibody and/or polymerase chain reaction (PCR) positive) ranged from 62.5% (95% CI: 58.3–66.7%) to 83.8% (95% CI: 79.1–87.7%). Only five infections were severe and one was critical – an infection severity rate of 0.2% (95% CI: 0.1–0.4%). Rapid antibody tests (RATs) were effective in diagnosis of the SARS-CoV-2 virus infections. Vaccine effectiveness against severe, critical or fatal infections were above 90% in both the Qatar and Australian studies, but protection against infection waned significantly after 6 months. In Qatar and Australia, the industry implemented effective control measures including the use of RATs, PCR tests, test, trace, isolation, quarantine (TTIQ) and vaccination. In both countries, the LNG industry collaborated with public health experts and other experts and was involved in research to assess and manage the risk of COVID-19. Production of LNG was not affected. Participation in public health research in both countries contributed to important scientific publications and protected the industry. COVID-19 may become endemic. To access the presentation click the link on the right. To read the full paper click here

Обоснование количества судов-бункеровщиков сжиженным природным газом для морского порта

Object and purpose of research. The paper considers specialist vessels for re-fueling gas-engined ships, so-called LNG bunkering tankers (LNG bunkering ship as per the Russian Maritime Register of Shipping). The purpose is to formulate recommendations regarding the bunkering tanker fleet configuration for a marine port taking into consideration their functioning model and projected demand for natural gas motor fuel. Materials and methods. Operational experience of the ship type under consideration as well as the performance factors have been generalized and analyzed. Statistics of bunkering companies operating on the St. Petersburg port market have been collected and systematized enabling us to give recommendations for the projected fuel demand. Main results. Operational characteristics of bunkering tankers in the port bunkering infrastructure have been generalized. An approach is suggested for justifying the required number of LNG re-fueling tankers based on the game theory. The main factors defining the volumes of LNG fuel required in port are highlighted. A case study is given for validation of the bunkering tanker demand in numbers for the port of St. Petersburg. Conclusion. Bunkering tankers are a key link in the bunkering infrastructure of any harbor. LNG tankers are growing in numbers every year, which is related to more stringent requirements for environment pollution and reduced discharges from vessels in operation. This study enables justification of bunkering tanker numbers early in the design of a port bunkering infrastructure.

Viral mutations, vaccine effectiveness and rapid tests – COVID-19 risk management in the two largest LNG producing countries, Qatar and Australia

The SARS-CoV-2 pandemic created challenges for the oil and gas industry. Qatar experienced three significant waves during the pandemic that disproportionately affected the workers in shared accommodation. In Australia, the public health measures limited the spread of SARS-CoV-2 in the industry until the Omicron wave. Anti-SARS-CoV-2 seropositivity was assessed in five oil and gas subcontractors and five hospital subcontractors in Qatar between 21 June and 9 September 2020. Vaccine effectiveness was assessed in Qatar. Vaccine effectiveness in an LNG tanker crew off Gladstone was calculated. The initial study in Qatar included 4970 craft manual workers (CMWs) who were mostly men (95.0%). Infection positivity (antibody and/or polymerase chain reaction (PCR) positive) ranged from 62.5% (95% CI: 58.3–66.7%) to 83.8% (95% CI: 79.1–87.7%). Only five infections were severe and one was critical – an infection severity rate of 0.2% (95% CI: 0.1–0.4%). Rapid antibody tests (RATs) were effective in diagnosis of the SARS-CoV-2 virus infections. Vaccine effectiveness against severe, critical or fatal infections were above 90% in both the Qatar and Australian studies, but protection against infection waned significantly after 6 months. In Qatar and Australia, the industry implemented effective control measures including the use of RATs, PCR tests, test, trace, isolation, quarantine (TTIQ) and vaccination. In both countries, the LNG industry collaborated with public health experts and other experts and was involved in research to assess and manage the risk of COVID-19. Production of LNG was not affected. Participation in public health research in both countries contributed to important scientific publications and protected the industry. COVID-19 may become endemic.

Using DBN and evidence-based reasoning to develop a risk performance model to interfere ship navigation process safety in Arctic waters

Risk performance reasoning strategy for LNG ships navigating in Arctic waters is proposed in this paper. Many uncertainties exist in the reasoning of ship navigation risk in Arctic waters, which are influenced by multi-source risk causing events. As a result of the aforementioned concerns, the dynamic Bayesian network (DBN) structure is offered as a solution for an uncertain risk assessment model. The DBN network can benefit from a strategy for solving ambiguous data information based on Dempster–Shafer (D–S) evidence theory and a cloud model. Additionally, a risk performance reasoning technique for LNG tanker collision accidents in Arctic waters is developed. Besides, the marine meteorological reanalysis data, data from ship-borne sensor monitoring, and expert knowledge in the suggested risk performance reasoning method are incorporated. A case study confirmed that the risk performance reasoning of accidents was needed revealed that the main risk in Arctic summer waters is posed by obstacles in the channel that are difficult to detect, such as icebergs and reefs.

Floating on air

Retrofitting Shell’s Patricia Camila LNG tanker with air lubrication led to significant fuel and emissions savings for the giant vessel

Implementing 3D Model LNG Tanker Ship Cargo Handling System Equipment for Training Using Augmented Reality

The learning system of the vessel is very important for a marine engineer to understand the characteristic of machinery system. This can be conducted by looking at the block diagram and seeing the 3D picture or directly observing the system on a vessel in order to get a complete understanding. It is difficult to do direct observation due to safety regulations and company confidentiality, especially for LNG tanker ship. To overcome this restriction, this study will propose a 3D drawing for training that can represent the real operational condition of cargo handling system equipment of an LNG tanker vessel. Augmented Reality 3D is used to recreate the system and put necessary information about the object along with the 3D drawing. The augmented reality 3D object and information showing with the android application by scanning the object augmented reality marker. In this research, the user is satisfied with the experience and interface based on user data collected from the questionnaire method with aspect of attractiveness, uses ability, effectiveness, user interface experience, and measure the understanding about the application with questionnaire value measurement.

Propulsion system shaft line analysis of a 70.000 dwt LNG tanker

In the presented project, a study was made on the propulsion installation on board the LNG tanker with a load capacity of 70,000 dwt. In this regard, all the steps regarding the calculation and design of the main elements of this type of installation were followed, such as the propulsion engine, the propeller and the shaft lines. At the end of the shaft sizing stage, a simulation was performed in a specialized software to analyse and verify the evolution of the component elements in an operation scenario.

Application of the Tail Equivalent Linearization Method to wave bending moment and comparison with experimental data

This paper estimates extreme midship wave bending moment of a ship in a specific sea state using First Order Reliability Method (FORM) and the Tail Equivalent Linearization Method (TELM). FORM and TELM are applied to the random vibration analysis of the nonlinear bending moment and results are compared and verified against experimental data obtained from model tests as well as numerical simulations. A case study of an LNG tanker is presented, demonstrating that the proposed methodology yields reasonable results and that the TELM approach provides a fast and computationally efficient way of analyzing nonlinear vertical bending moment of ships in stationary sea states.

Comparative study on analysis methods for added resistance of four ships in head and oblique waves

This paper presents a comparative study of wave-induced motion responses and the added resistance of a ship. Four representative types of ships are adopted as test models: LNG carrier, tanker, containership, and bulk carrier. Two experimental techniques—captive and free-running model tests—are conducted under regular head and oblique wave conditions to create benchmark data. Several numerical computation methods (asymptotic formula, 2D strip theory, 3D panel method, and CFD) are applied to perform the seakeeping analysis. The comparison results indicate that the accuracy and reliability of each analysis technique are validated, and its characteristics and limitations are investigated with respect to the physical aspects of the added resistance caused by a wave. The analysis results are compared based on how steady flow-induced coupling effects are considered. Further, the sensitivities of seakeeping quantities with respect to wave steepness were examined based on the results of linear and fully nonlinear computations. The overall tendency of the added resistance in accordance with the incident direction of a wave is discussed.

Post-combustion carbon capture for tank to propeller via process modeling and simulation

The International Maritime Organization (IMO) has issued a long-term sustainable strategy to gradually phase out the major ship-related sources of greenhouse gas emissions. While the post-combustion carbon capture has been well investigated for onshore plants, the maritime carbon capture system is still in an early stage due to its unique characteristics and design limitations. Aiming at providing a holistic way to find the most efficient and sustainable PCC solution for an LNG tanker, this work proposed a system of the tank to propeller post-combustion carbon capture which integrates ship engine process modeling with chemical absorption/desorption process modeling techniques. A rate-based aqueous monoethanolamine (MEA) process model was developed and validated, then scaled up and modified to capture CO2 from the flue gas. To increase the carbon capture efficiency and decrease the energy penalty, this work provided detailed steps for process model development covering innovative absorber/stripper design under variation of solvents, packed type, and liquid to gas ratio. This work also included a thorough sustainability evaluation based on emission reduction efficiency, energy penalty, and carbon cyclic capacity among two single aqueous amines, MEA and diisopropanolamine (DIPA), and one blended amine with a promoter, methyldiethanolamine (MDEA) with piperazine (PZ). Although DIPA presented a better performance on energy requirement for solvent regeneration, the blended amine was the optimal solvent to meet the requirement of the IMO carbon abatement strategy. Compared to the seven molality MEA, the MDEA-PZ option could capture more than 57 % CO2 while around 25 % specific reboiler duty can be saved.

Fuel cells for shipping: To meet on-board auxiliary demand and reduce emissions

The reduction of harmful emissions from the international shipping sector is necessary. On-board energy demand can be categorised as either: propulsion, or auxiliary services. Auxiliary services contribute a significant proportion of energy demand, with major loads including: compressors, pumps, and HVAC (heating, ventilation, and air-conditioning). Typically, this demand is met using the same fuel source as the main propulsion (i.e. fossil fuels). This study has analysed whether emissions from large scale ships could feasibly be reduced by meeting auxiliary demand by installing a hydrogen fuel cell, using data from an LNG tanker to develop a case study. Simulations have shown that for a capacity of 10 x 40ft containers of compressed hydrogen, the optimal fuel cell size would be 3 MW and this could save 10600 MWh of fossil fuel use, equivalent to 2343 t of CO2. Hence this could potentially decarbonise a significant proportion of shipping energy demand. Although there are some notable technical and commercial considerations, such as fuel cell lifetime and capital expenditure requirements. Results imply that if auxiliary loads could be managed to avoid peaks in demand, this could further increase the effectiveness of this concept.

Performance Analysis of Combined Cycle with Air Breathing Derivative Gas Turbine, Heat Recovery Steam Generator, and Steam Turbine as LNG Tanker Main Engine Propulsion System

This study explains the performance analysis of a propulsion system engine of an LNG tanker using a combined cycle whose components are gas turbine, steam turbine, and heat recovery steam generator. The researches are to determine the total resistance of an LNG tanker with a capacity of 125,000 m3 by using the Maxsurf Resistance 20 software, as well as to design the propulsion system to meet the required power from the resistance by using the Cycle-Tempo 5.0 software. The simulation results indicate a maximum power of the system of about 28,122.23 kW with a fuel consumption of about 1.173 kg/s and a system efficiency of about 48.49% in fully loaded conditions. The ship speed can reach up to 20.67 knots.

Long-range role of natural gas in the EU green transition: analytical overview

Pan-European and national policy documents were reviewed that set the goals for the development of the European economy and energy. The objective of this paper is due to changes in European policy vision of the natural gas’s future prospects of in the context of establishing strict climatic requirements and the desire to achieve a carbon-neutral level of the European economy development. In previous periods, it was believed that until the 2040s-2050s we can expect the “Golden Age” of natural gas, which was due to the success of the revolution in the United States, significant expectations of a repeat of the US success of shale gas production in other parts of the world, increased transportation of natural gas by pipelines and LNG tankers; decreased growth rate of a nuclear energy and further cost reduction of a shale gas production. A change in the European energy policy towards the strengthening of environmental requirements, reduction of greenhouse gas emissions and emerging of EU's role in combating climate change causes uncertainties regarding prospects of natural gas as an energy resource in Europe. By choosing the European vector of development, Ukraine is interested in meeting requirements of EU policy within the framework of its international obligations and European integration ambitions. This makes it necessary to adapt national development programs and strategies to new conditions and challenges that arise in the EU. The analysis of the main EU policy documents on prospects for the natural and other synthetic gases development allows us to begin to reassess national development plans for adapting the internal developed gas infrastructure to new market opportunities, which will permit Ukraine to increase its competitiveness in the gas market further, and consumers will be able to receive energy resources at more competitive prices and an appropriate quality of service. The complex of problematic issues that arise in the EU member states regarding the formation of incentives for the introduction of synthetic, green gases, adoption of appropriate regulatory mechanisms, formation of effective financial mechanisms that would attract investment in the development of a new infrastructure or development of new technologies requires from Ukraine to define priorities of its economic development, to form a roadmap for the energy system transformation in accordance with new international requirements, internal needs and economic opportunities to implement corresponding technological transformations. The central government after consultations with interested participants in the energy market should form a nationwide vision of the vector for the energy sector development in Ukraine and the place of natural gas in the energy supply of Ukraine until 2050.

Microstructure and Mechanical Properties of Fe-36Ni and 304L Dissimilar Alloy Lap Joints by Pulsed Gas Tungsten Arc Welding.

High-quality joining of dissimilar alloys between Fe-36Ni alloy and 304L stainless steel is essential in the manufacturing of LNG tanker. In this study, lap joints of Fe-36Ni and 304L dissimilar alloys were fabricated by a pulsed gas tungsten arc welding (P-GTAW) process. The effects of low-frequency pulse on the appearance, microstructure and mechanical properties of the Fe-36Ni/304L lap joints was investigated. With the increase of frequency, the feature sizes of α (the transition angle of the upper surface of Fe-36Ni to the surface of the weld bead) and R (shortest distance between weld root and weld surface) exhibited downtrend and uptrend, respectively, while La (the maximum weld width of lower sheet) and P (the maximum weld penetration of lower sheet) changed in a smaller range. Fusion zone (FZ) is mainly composed of γ phase and M23C6 during solidification, and M23C6 particles are distributed on the grain boundaries of the cells, which reduced the mechanical properties of joint. The average hardness between 110 HV1 and 136 HV1 is lower than that of the base metals. Fractures of all joints located at the Fe-36Ni side near the weld, and a dimple fracture in all samples indicated a ductile fracture. This study found that the heat input values remain 198.86 J mm−1 and increased pulse frequency can improve the maximum tensile force. The average maximum tensile force of the lap weld is 11.95 kN when pulsed frequency is 15 Hz.