Research on the engineering application of leakage diffusion theory based on finite volume method in LNG pipeline

In order to provide theoretical reference for the volume design of the terminal sump, this paper analyses the physical process of leakage and evaporation at the LNG terminal using. Combined with the theory of orifice leakage and evaporation diffusion and the actual project scenario, the corresponding mathematical model is given. From qualitative analysis, the main factors affecting LNG leakage and evaporation diffusion are given. The mathematical model is applied to engineering practice, and a large number of calculations are carried out to give the quantitative relationship between leakage, evaporation and diffusion and various influencing factors. Through research, it is found that the leakage of LNG is far greater than the evaporation on the wharf. When designing the volume of the sump, the evaporation of LNG on the wharf can be ignored. According to the leakage model of the pipeline orifice, the credible leakage volume in line with the actual project can be obtained.


Introduction
During the loading and unloading process of LNG (Liquefied Natural Gas) terminal, there may be leakage at the interface between the loading arm and the ship and the valve flange at the rear of the loading arm.In order to collect the leaked LNG, it is necessary to set up a sump behind the working platform of the wharf.At present, the design ideas for the volume of the LNG terminal sump are not uniform, the design schemes are diverse, and there is still a lack of detailed theoretical research and discussion [1,2].The designers lack the calculation methods and research conclusions with reference value in the design of the LNG terminal.
A combination approach of the physical process of orifice leakage and evaporation and diffusion of LNG terminal and the knowledge of engineering fluid mechanics and heat transfer is adopted to derive a complete calculation model in this paper.This model is used to carry out qualitative analysis and quantitative calculation of orifice leakage and evaporation of LNG terminal.Based on the case of LNG terminal engineering, this paper verifies the accuracy of the calculation model and provides conclusions with engineering application value.

Physical process of leakage evaporation in LNG terminal
Due to improper docking between the loading arm and the ship interface, uneven shrinkage of the upper and lower parts of the pipeline due to excessive precooling speed, poor airtightness, rust and other reasons, there is a lack of sealing at the connection between the loading and unloading arm and the ship interface, as well as at the valve flange behind the loading and unloading arm.When LNG flows at high pressure and high speed flows through the weak points, it may cause orifice leakage.The leaked low-temperature LNG falls into the collection tray or wharf surface below, and flows into the wharf sump through the collection pipe or guide ditch.The collected LNG is covered by high expansion foam in the sump to make it volatilize slowly until it is completely volatilized.Therefore, the volume of the terminal sump should meet the credible collection volume that may flow into a single operation.This leakage collection volume is not only related to the total leakage during the terminal operation, but also to the volatilization of leaked LNG in the collecting tray, guide ditch or collection pipe.
After a continuous leakage of LNG, it falls into a collection tray to form a liquid pool.The larger the leakage diameter, the longer the leakage time, the larger the total leakage volume and the larger the pool liquid area [3][4][5].After being exposed to air, low-temperature LNG quickly absorbs the ambient temperature and then completes phase transition, and undergoes gasification [6,7].The gasification diffusion process includes two stages: heavy gas diffusion and passive diffusion [8].The partially gasified LNG ultimately flows into the terminal sump.
From the above, it can be seen that the amount of LNG flowing into the terminal sump is related to the leakage diameter, leakage duration, pressure and flow rate inside the pipeline, environmental temperature, and the flow time from the leakage point to the sump.

Orifice leakage model
The leakage of unloading pipelines of LNG terminal is usually thin-walled orifice leakage.According to the Bernoulli equation of fluid mechanics, the velocity of LNG flowing out of the orifice is: Where, V2 is the leakage flow rate at the orifice, m/s;  is the local resistance coefficient at the orifice; V1 is the fluid velocity inside the pipeline, m/s; P1 is the internal pressure of the pipeline, kPa; P2 is the external environmental pressure of the pipeline, kPa;  is the LNG density, kg/m 3 ; G is the gravitational acceleration, taken as 9.8m/s 2 . Let, Substitute it into the above formula to get: Where, C is the liquid leakage coefficient, which is a function of Reynolds number and hole diameter.For LNG pipeline orifice leakage, the liquid leakage coefficient C can be taken according to the semi-empirical data in fluid mechanics [9]: 1) Turbulent state: for sharp leakage orifice and when Reynolds number is greater than 30000, the liquid leakage coefficient C is approximately 0.61.
2) Laminar flow state: for a smooth leakage orifice or when the Reynolds number is less than 30000, the liquid leakage coefficient C can be approximately taken as 1.
Generally, during the loading and unloading process of LNG terminal, the number of pumps and the opening of regulating valve remain unchanged, that is, the flow velocity V1 and the pressure P1 in the pipe IOP Publishing doi:10.1088/1742-6596/2599/1/0120193 remain unchanged, and the leakage flow velocity V2 at the orifice also basically remains unchanged, so the leakage volume M at the orifice can be expressed as: In the formula, M is the leakage amount at the orifice, kg; T is the duration of leakage at the orifice, s; D is the leakage diameter, mm.

Evaporation diffusion model
According to the principle of heat transfer, the mechanism of liquid evaporation can be divided into three types: flash evaporation, heat evaporation and mass evaporation [10].Flash evaporation is the evaporation of a liquid using its own heat.Heat evaporation is the evaporation of liquid that flows to the ground and absorbs heat from the ground and air.Mass evaporation is caused by the movement of airflow above the surface of pool liquid.Due to the low temperature and short exposure time of the leaked LNG, the flash evaporation and mass evaporation of LNG terminal are small, and the main reason for evaporation is the heat evaporation caused by absorbing the heat from the ground and the surrounding environment.For heat evaporation, according to Fourier Law: Where: q is the thermal conductivity rate in the y direction, J/s; A is the thermal conductivity area perpendicular to the y direction, m 2 ; K is the coefficient of thermal conductivity of material, J/ (mꞏsꞏK); is the temperature gradient in the y direction, K/m.The LNG evaporation rate caused by heat absorption is: Where, q1 is evaporation rate, kg/s; K is the coefficient of thermal conductivity of the material, J/ (mꞏsꞏK); A is the area of sump, m 2 ; T is the ambient temperature, K; T0 is the boiling point of liquid, K; H is the liquid evaporation heat, J/kg;  is the thermal diffusion coefficient, m 2 /s; T1 is the evaporation time, s.
The evaporation of LNG in the wharf, liquid guide ditch/collection pipe is: Where, Q1 is evaporation capacity, kg.It can be seen from the above formula [11] that the evaporation of leaked LNG is directly proportional to the ambient temperature, and is directly proportional to the 0.5 power of the evaporation time (the flow time between the leakage point and the sump).

Numerical calculation results and quantitative analysis of LNG terminal leakage
In the existing LNG terminals in China, there are three common sizes of unloading manifold pipe: 38 ", 40" and 42 ".The unloading pressure in the pipe is generally between 0.28 MPa and 0.33 MPa, which is related to the pump opening scheme and the opening of the regulating valve.The flow rate in the pipe is generally between 3.0 m/s and 5.3m/s, which is related to the unloading pipe diameter and the unloading flow rate.The flow rate of the pipe is generally between 10000 m 3 /h and 1400 m 3 /h.
According to the distances between the sump and the front edge of the various wharfs in China, it can be seen that the flow time of LNG in the liquid guide ditch/collecting pipe is about 0~3min.The local temperature FMIA-2023 Journal of Physics: Conference Series 2599 (2023) 012019 of LNG terminals along the coast of China is about 5 ℃~35 ℃.In this study, the leakage diameter is considered to be 0~100mm and the leakage duration is considered to be 0~15min.

Calculation results and quantitative analysis of orifice leakage model
The above orifice leakage model is used to calculate the total leakage of LNG terminal, and the results are shown in Figure 1~Figure 4 below:   The above calculation results are analyzed as follows: 1) When the leakage duration is relatively short, the leakage amount has little to do with the leakage aperture.However, when the leakage duration is longer, the total leakage significantly increases with the increase of the leakage aperture.If the leakage duration exceeds 5 minutes, the leakage amount is closely related to the leakage diameter.When calculating the leakage amount, the selection of leakage diameter should be carefully considered; On the contrary, it is not necessary to consider the impact of difference in leakage aperture.
2) When the leakage aperture is small, the relationship between the leakage amount and the leakage duration is not significant; However, when the leakage aperture is large, the total leakage increases significantly with the increase of leakage duration.If the leakage aperture is greater than 25mm, the leakage amount is closely related to the leakage duration.When calculating the leakage amount, the selection of leakage duration should be emphasized.Otherwise, the impact of the difference in leakage duration does not need to be considered.
3) As the pressure inside the pipe at the leakage point increases, the total leakage at the terminal also increases, but this increase is not significant, that is, the pressure has no significant impact on the total leakage.When calculating the leakage rate, the change of pressure in the pipe may not be considered.
4) With the increase of the flow rate in the pipe at the leakage point, the total leakage of LNG from the terminal will also increase, but this increase is not obvious, that is, the flow rate has no significant impact on the total leakage.When calculating the leakage rate, the difference of flow velocity in the pipe may not be considered.

Calculation results and quantitative analysis of evaporation diffusion model
The above evaporation diffusion model is used to calculate the evaporation of leaked LNG, and the results are shown in Figure 5 and Figure 6: The above calculation results are analyzed as follows: 1) The higher the ambient temperature, the greater the evaporation of LNG on the wharf.But this correlation is not significant.The difference of ambient temperature may not be taken into account when calculating the evaporation.
2) With the increase of evaporation duration (the time from the leakage point to the terminal sump, which is related to the location of the sump), the LNG evaporation capacity of the terminal will also increase, and this increase is very significant.When calculating the evaporation, the difference of evaporation duration should be taken into account, that is, the location of the sump has a significant impact on the evaporation after LNG leakage.
3) By comparing the data of LNG leakage and evaporation at the wharf, it can be seen that the leakage is far greater than the evaporation.When designing the volume of the LNG terminal sump, it is important to consider the leakage rate.The evaporation capacity has little influence on the volume setting of the sump, so it can be ignored.

Conclusion
The following conclusions are drawn through qualitative analysis and quantitative calculation: 1) The amount of leakage at the wharf of LNG terminal is proportional to the square of the leakage aperture.This proportional relationship is especially obvious when the leakage duration is greater than 5 minutes.Therefore, when the selected emergency cut-off valve has a long shutdown time, special consideration should be given to the impact of this factor on the volume design of the LNG terminal sump.
2) The amount of orifice leakage is directly proportional to the leakage duration.This proportional relationship is especially obvious when the leakage diameter is greater than 25mm.Therefore, when considering large aperture leakage, special attention should be paid to the influence of leakage duration on the volume design of the terminal sump.
3) The orifice leakage amount of the LNG terminal is proportional to the 0.5 power of the pressure in the pipe and directly proportional to the flow rate in the pipe, but this proportional relationship is not significant.When designing the volume of the sump, the difference of the pressure and flow velocity in the pipe may not be considered.
4) The evaporation of the sump is proportional to the ambient temperature, but the direct relationship is not obvious.The difference of ambient temperature may not be taken into account in the volume design of LNG terminal sump.5) The evaporation of the sump is proportional to the 0.5 power of the evaporation duration (the flow time from the leakage point to the sump), which is relatively significant.Therefore, when designing the volume of the terminal sump, the distance between the sump and the front edge of the LNG terminal should be comprehensively considered, as this distance is more sensitive to the volume design of the LNG terminal sump.
6) The evaporation is far less than the leakage, so the evaporation may not be considered when designing the volume of the sump.

Figure 1 .
Figure 1.Relationship between leakage diameter and leakage amount

Figure 2 .Figure 3 .
Figure 2. Relationship between leakage duration and leakage amount

Figure 4 .
Figure 4. Relationship between flow rate and leakage amount in the pipe at the leakage point

Figure 5 .Figure 6 .
Figure 5. Relationship between LNG evaporation capacity at the wharf and ambient temperature