Experimental Study on the Leakage Temperature Field of Buried CO 2 Pipelines

In view of the fact that the leakage of small holes in the buried CO 2 pipeline is not easy to be detected, which leads to the problem of inability to accurately trace the source of the pipeline repair in the later stage. This paper designs and establishes a buried CO 2 pipeline leak simulation experiment system and conducts experiments on small-hole leaks in buried CO 2 pipelines to investigate the changes in soil temperature around the CO 2 pipeline leaks. The results showed that the type of movement of CO 2 in porous media after it is released from the leak is "funneling". At a distance of about 50 mm from the horizontal, the temperature difference in the horizontal surface is smallest at the 50 cm closest to the vertical distance of the leak, while at a distance of 225 mm from the horizontal, the temperature difference in the horizontal surface is largest at the 70 cm farthest from the vertical distance of the leak. The research results can provide a theoretical basis for the later development of technologies that can quickly locate the leakage points of buried CO 2 pipelines and accurately determine their leakage status.


Introduction
In recent years, the global average temperature has been rising, and warm winters have occurred in many places and regions.The global greenhouse effect is becoming increasingly serious and has seriously affected the survival of human beings and the development of society (Li et al.2018;Ozturk et al.2016; Kolb et al.2021).Among various greenhouse gases, CO 2 is considered to be the main culprit of global warming, therefore, reducing CO 2 emissions and stopping global warming are important issues that need to be addressed by various countries (Li et al.2022; Andersona et al.2016; Machado et al.2021).As one of the options for climate change mitigation, carbon capture and storage (CCS) technology has received special attention from the international community, especially from developed countries, among which, CO 2 enhanced oil recovery(CO 2 -EOR) is the most pro table, mature, promising and widely used technology among CO 2 storage technologies (Alphen et al.2010;Huijgen et al.2006;Sanna et al.2012).
Since Whorton (Whorton et al. 1952)obtained the rst patent for the use of CO 2 recovery technology in 1952, the development and application of CO 2 drive for enhanced oil recovery has continued to develop.
Currently, CO 2 -EOR projects are in good use in countries such as the United States, Canada and China (Watheq et al.2019; Bruce et al.2020; Thornea et al.2020).Although CCS technology can achieve economic bene ts and improve the environmental problems of people's lives, in the actual production process of CCS, buried CO 2 pipelines cause CO 2 leakage due to local failure of the pipe due to corrosion and mechanical strikes, which has a serious impact on the surrounding ecological environment, and the high concentration of CO 2 can also cause asphyxiation hazards to people and livestock in the surrounding area.Since the pipeline is buried underground and not easily detected, it cannot achieve the effect of oil repelling and also creates a great safety hazard (Xing et  Ahmad et al (2015) conducted a large-scale experimental study of pipeline rupture by high-pressure CO 2 gas, explored the concentration and temperature distribution within the gas cloud after CO 2 release, and determined the maximum jet height and the farthest distance of diffusion.Wang et al (2019).investigated the diffusion behavior of CO 2 in a high-pressure pipeline after leakage by constructing a 14.85 m long pipe with 15 mm inner diameter in the laboratory, and studied the temperature change and the motion of dry ice particles in the far eld, and proposed an improved model to analyze the anomalous low-temperature zone formed during the leakage of CO 2 .Liu et al (2019).conducted an experimental and numerical simulation study of the diffusion behavior of CO 2 after a leak occurs, and the results showed that when the wind speed is below 10 m/s, CO 2 is discharged from the high-pressure pipe at a very low temperature after an accidental release due to the Joule-Thompson effect.Although the CO 2 cloud is gradually heated by the warm air, when it disperses, it creates a relatively low temperature zone in the atmosphere.Simulation results show that for a 400 mm ID pipe break, the temperature in the area within 600 m from the center of the leak can be reduced by 10°C.Hill et al (2008).decomposed the model of CO 2 diffusion after sublimation of dry ice into two parts and calculated the sublimation diffusion leakage rate of dry ice blocks through the energy balance equation and Gaussian heavy gas diffusion model, respectively.Liu et al (2015).conducted an in-depth study on the impact force and its in uencing factors in the event of leakage in CO 2 transport pipeline in conjunction with the CO 2 pipeline transport process under the actual working conditions of CCS.
Although domestic and foreign scholars have paid much attention to CO 2 pipeline leakage, there is a lack of research on the diffusion behavior of CO 2 under small-hole leakage conditions, and the accurate traceability of leakage points is of great practical signi cance for risk reduction and loss mitigation.In order to develop techniques for quickly locating leaks in buried CO 2 pipelines and accurately determining their leak status, it is indispensable to study the temperature eld distribution patterns of leaks in buried CO 2 transport pipelines and conduct experiments on buried CO 2 transport pipeline leaks.Therefore, this paper designs an experimental device to study the leakage law of buried CO 2 pipeline, and conducts experimental research on the leakage diffusion phenomenon which is not easily detected and monitored in production.By analyzing the changes of typical parameters in the experimental process, the temperature variation law in the process of buried CO 2 pipeline leakage is obtained.

Experimental Setup
A CO 2 pipeline leakage simulation experimental system is designed and built in this paper, as shown in Fig. 1.The system includes pressure-bearing device, pressure relief device, CO 2 injection device, chamber, experimental parameter measurement system and data acquisition system.The maximum working pressure of the whole experimental platform can reach 30 MPa, and the pressure relief system is easy to install and replace.

Experimental Program
In order to accurately simulate the actual conditions of buried CO 2 pipeline leakage, a 150 mm diameter pressure-bearing device with the same diameter as the buried CO 2 pipeline was used to test the buried CO 2 pipeline leakage temperature eld using two pressure cases of 10 MPa and 15 MPa and two leakage diameters of 3 mm and 5 mm.A total of 62 PT100 temperature sensors were arranged in the space of this experimental device, distributed on 8 measuring rods, numbered from left to right as No. 1 to No. 8 measuring rods, sensor rod numbers and corresponding positions are shown in Fig. 2, and the horizontal distance between each measuring rod and the leakage port is shown in Table 1.

Typical experimental phenomena and results
The raw data of buried CO 2 pipeline leakage temperature eld experiments are shown in Tables 2 ~ 3.  Note: The symbol "-" in the table means that the data set does not have this measurement point; the meaning of the experiment number is "pressure -caliber -measuring rod number" The experiment with a leak diameter of 3 mm and a leak pressure of 15 MPa is used as an example to illustrate the whole process of temperature change of buried CO 2 pipeline leak.The rupture disc speci cation is Pm = 15 MPa, D m =3 mm, and the ambient temperature is 21℃.The high-pressure pump continuously pressurizes the CO 2 injected into the pressure vessel until the rupture disc ruptures, and then the pressure inside the vessel decreases rapidly, and CO 2 is ejected from the top of the pressure vessel at high speed.As shown in Fig. 4, the pressure inside the vessel at the time of rupture of the rupture disc in the experiment occurred in time △t for 4.375 s.The pressure difference was △P for a sudden drop of 15.39 MPa.
During the process of CO 2 release, the temperature around the leak port plummets due to a dramatic phase change in the pressure-bearing device, which absorbs a large amount of external heat.Since the soil contains a considerable portion of moisture, the soil area in the direction of the leak vent will condense a part of the ice and dry ice mixture area in a period of time (as shown in Fig. 5).The time of the release is about 30 s.After the end of the injection process, a large amount of solid dry ice precipitates at the bottom of the container, and as the temperature inside the container gradually increases due to the absorption of heat from the outside air in the pressure vessel, the dry ice will then sublimate and dissipate in the air.
The change of temperature around the leak is the most signi cant feature of this physical explosion process.Figure 6 shows the curve of the change of ambient temperature around the pressure-bearing device after the rupture of the rupture disc and the release of CO 2 .As can be seen from the curve, the highest pressure Pmax in the vessel reached 15.9 MPa during the whole experiment.During the process of leakage, CO 2 underwent a violent phase change and absorbed a large amount of heat from the surrounding area, which caused the temperature in the soil medium to drop abruptly; after the complete release of CO 2 , it rose back to the surrounding ambient temperature.The whole process lasts about 600 s, and the maximum cooling rate ε max is about 9.4 K/s.
1) Stage 1: Temperature plunge stage.In this stage, due to the sudden release of dense-phase liquid or supercritical-phase CO 2 from the pressure-bearing device, a large amount of heat is absorbed from the surrounding area, and the rate of heat absorption from CO 2 leakage to the surrounding area is much higher than the rate of heat absorption from the soil to the surrounding environment.At the same time, the CO 2 heat absorption causes the surrounding soil temperature to plummet to -20~-40°C.Most of the liquid water medium in the soil condenses into solid ice, and the thermal conductivity of the soil is greatly reduced.Thus, the cooling rate ε H is much larger than the heating rate ε T in this stage, and the soil temperature plunges in this stage.
2) Second stage: Temperature decreases slowly.In this stage, the pressure in the pressure-bearing device decreases, the release of CO 2 is nearly completed, and the rate of heat absorption into the surrounding environment is gradually weakened, resulting in a slower temperature drop.
3) The third stage: The reheating stage.In this stage, CO 2 is completely released and no longer absorbs heat from the surrounding environment, and the soil only exchanges heat with the surrounding environment.Although the increase of water content in the soil due to the increase of temperature will lead to the increase of soil thermal conductivity, but from Fig. 6, the trend of the return temperature stage curve slowdown can be seen, compared to the reduction of temperature difference for ε T inhibition effect is more obvious.

Changes in temperature distribution in sandy soil leaking from buried pipelines
Since the temperature change in the experiments stabilized and slowly rebounded at the end of the leakage process, the third phase described in Section 4.1.2was not studied, so the analysis of the temperature change over time for each sensor in each group of experiments focused on the phase where the temperature plummeted after the leakage occurred.
In this group of experiments, the experimental data in different experimental parameters are reproducible.In this section, the temperature distribution is analyzed from the point of view of comparison with each measurement point of the same measuring rod and comparison with each measurement point of the same height level, using a leak diameter of 5 mm and a leak pressure of 15 MPa as the research object.

Analysis of the temperature change pattern of each measuring rod measurement point
This subsection is analyzed with each measuring rod as an independent individual, analyzing the temperature variation with time for different vertical distances of the measuring points on the same rod and the minimum temperature variation with vertical distance for each measuring point.
The measuring rod No. 3 in the axial region is located directly above the leakage port and is the rod with the largest temperature drop among all the measuring rods.As can be seen from Fig. 7, the maximum temperature difference measured in the experiment reached 42.8℃, and the temperature difference of most measurement points on the No. 3 rod decreased with the increasing distance from the leak, but the largest temperature difference occurred at the 20 cm vertical distance from the leak rather than at the 10 cm nearest to the leak.The reason is that the CO 2 jet at the vertical distance of 20 cm from the leak is in the most intense phase change state and absorbs a large amount of heat from the surrounding soil environment, making the temperature difference at this location the largest.At the location below 20 cm, the temperature at the location below 20 cm is slightly higher than that at 20 cm because the CO 2 jet energy is larger, so that a large amount of CO 2 does not phase change at the lower location.The temperature at the other locations of the measurement point becomes less energy absorbed as the distance increases, so the temperature difference becomes smaller.
The temperature change of each measurement point on the No. 3 pole with time is shown in Fig. 8, the temperature change is " rst drop and then rise" phenomenon, and the time point of temperature drop are relatively close, if the time is extended inde nitely, the temperature will be the same as the ambient temperature.
The temperature of the measurement points on the No.3 measuring rod from the vertical distance of 10 cm to 50 cm from the leakage port have a common feature, that is, the temperature curve has a roughly similar trend of ups and downs, there is a "sudden drop -rapid recovery -and then drop" phenomenon, and marked in Fig. 8.The main reasons for this phenomenon are as follows.
1) The soil medium around the leakage port was blown away by the huge impact.After the rupture of the rupture disc, the pressure-bearing device instantly released pressure and produced a CO 2 jet.According to the experimental results of the literature [114] , the impact force out of 0.25 m from the leakage port was 1500 N or even higher, and under the action of the powerful jet impact, the soil medium near the measurement point of the lower part of the No. 3 measuring rod was instantly blown away to the surrounding, making instantaneous in ux of air in the surrounding environment.Because the thermal conductivity of air is much smaller than the thermal conductivity of soil media (air thermal conductivity 0.023 W•(m•K) −1 , industrial sand thermal conductivity 0.27 W•(m•K) −1 ), resulting in the temperature of the air in the region is higher than the soil media, making the temperature curve will appear a short time back up; and then under the action of gravity, the lower temperature of the soil media back down under the action of gravity, so that the temperature again decreased.so that the temperature drops again.
2) Dry ice accumulation.After the leak of the pressure-bearing device, the pressure inside the device is instantaneously reduced, and the violent phase change of CO 2 leads to the accumulation of a little dry ice condensed into CO 2 at the leak, which hinders the release of CO 2 and makes the state of CO 2 release unstable, which leads to the incoherent leakage of low-temperature gas and a brief recovery of temperature.
The horizontal distance between the No.2 measuring rod and the leakage port is 2 cm, taking the No. 2 measuring rod as an example to analyze the law of temperature change in the near eld, as can be seen from Fig. 9, the temperature change on the No. 2 measuring rod has two phenomena.
1) Closer to the leak of the two vertical distance of the lower measurement points (10 cm at 20 cm) temperature trends are in line with the measurement points in the No. 3 pole "plunge -rapid recovery -and then fall" changes, the reason is the same as the No. 3 pole.
2)The remaining ve points of temperature in the value of the existence of a large drop, the location of the lower two points of the temperature river amplitude is smaller.
Analysis of the reasons for the generation of two temperature changes.The initial form of CO 2 jet forming is vertical upward, so that it has less ripple for the surrounding measurement points at lower locations; with the upward injection of CO 2 gas, turbulence occurs under the action of the pore resistance of porous media, making the gas in the porous media seepage trajectory changes, most of the seepage CO 2 acts on the position between 40 cm and 50 cm of the No. 2 measuring rod, resulting in a vertical distance from the leak The temperature drop at 10 cm and 20 cm is much smaller than the temperature drop at 40 cm and 50 cm of the leak.
Since the temperature drop measured at the near measurement point is mainly from the CO 2 jet, and the temperature drop measured at the far measurement point is mainly from the seepage of CO 2 in the soil medium and heat transfer, the temperature drop rate at the near measurement point is signi cantly higher than the temperature drop rate at the far measurement point.
The whole process can be divided into three regions according to the trend of curve changes in Fig. 10.
The rst region is located at the measurement points closer to the leak (at 10 cm and 20 cm), and the temperature difference between them is very small, only about 6℃.This indicates that these two measurement points are not affected by the diffusion of CO 2 gas at low temperature, because the initial shape of the CO 2 jet is vertical upward, so that these two points are not affected by the CO 2 jet and phase change heat absorption, but only by the heat transfer, which makes the temperature of the two places decrease.
The second region is located slightly further away from the measurement points 20 cm, 30 cm, 40 cm and 50 cm from the part of the measurement point.Unlike the case of measurement rod No. 3, the temperature drop in this region increases with the vertical distance and reaches a maximum temperature difference of 15.6℃ at 50 cm.The temperature drop at the measurement point in this distance interval is the most obvious, because the CO 2 jet is turbulent under the action of the pore resistance of the soil medium, which makes the gas percolation trajectory in the porous medium change, and most of the percolating CO 2 acts on the position between 40 cm and 50 cm of measurement rod No.2.The temperature drop of each measurement point of measurement rod No. 2 is the largest at 40-50 cm.
The third region is located at the top 50 cm, 60 cm and 70 cm of the measuring point part of the No. 2 measuring rod, the temperature drop in this region decreases with the increase of vertical distance, the law is consistent with the characteristics of heat transfer, indicating that this region is not affected by the jet action wave.were in a symmetrical position.And the CO 2 jet pattern is not completely symmetrical due to the accumulation of dry ice at the leakage port caused by the CO 2 release.A similar description of the morphology of the CO 2 jet is given in the literature [114] .Due to the violent phase change in the pressurebearing device during the rapid CO 2 release, the jet pattern of the CO 2 release is highly random and unpredictable.This is one of the main reasons why the data from the two measurement rods are not completely symmetrical.
Based on the good agreement between the data of measuring rod 1 and measuring rod 4, the deployment scheme can be simpli ed.Ignoring the small differences in temperature, it is assumed that the soil medium is homogeneous and that the properties are independent of location and orientation.Therefore, the temperature sensors can be placed in one direction only.
As shown in Fig. 12, by comparing the data of these two measuring rods it can be concluded that the measurement points of the two rods have a good consistency in the temperature difference trend, as well as the characteristics of the temperature in each region.The temperature drop of the measurement point in the top region increases with the increase of the vertical height.On the contrary, the temperature of the three sensors at 0, 10 cm and 20 cm, which are closer to the leak, has almost no change.The remaining measurement points satisfy the rule that the larger the vertical distance, the larger the temperature difference.
Since the initial shape of CO 2 jet is vertical upward, the measurement points at the lower part of measuring rod No. 1 and No. 4 are not affected by CO 2 jet and phase change heat absorption, but only by heat transfer, so there is almost no temperature change at the measurement points at the lower part of measuring rod No. 1 and No. 4; due to the existence of pore resistance of soil medium, CO 2 kinetic energy is gradually dissipated and the movement of CO 2 changes from jet to percolation diffusion of porous medium.Due to the existence of the pore resistance of the soil medium, the kinetic energy of CO 2 is gradually dissipated, and the movement of CO 2 changes from jet ow to percolation diffusion in the pores of the porous medium.
As can be seen from Fig. 13, the closer the measuring rod from 5 to 8 is to the leak, the greater the maximum temperature difference obtained from the measuring point on the rod.At the same time, the temperature difference also tends to increase as the vertical distance from the leak is larger.Combined with Fig. 13 and Table 4, the time required to reach the minimum temperature at the measurement points on different rods was also different, and the time required to reach the minimum temperature was longer as the distance of the measurement rods from the leakage port was farther.After being obstructed by the pore resistance of the porous medium, the jet form changed at a distance of about 40 cm from the leakage port, and the trajectory of CO 2 gradually changed from vertical upward to seepage around.

Analysis of temperature change pattern of each horizontal measurement point
The analysis method in this subsection is to take the measurement points located on the same horizontal plane as the object of study and observe the temperature change of each measurement point in relation to the horizontal distance from the leakage point.
The relationship between the maximum temperature difference of each measurement point on the horizontal plane at a vertical distance of 10 cm and 20 cm from the leak and the distance from the leak is shown in Fig. 14.The temperature of the measurement points on these two horizontal planes only changed signi cantly at the measurement points of measuring rod No. 2 and measuring rod No. 3.That is, at these two heights, only the area within 20 mm from the leakage port has a signi cant temperature drop.
On the horizontal surface relatively close to the leak, the area of temperature drop is smaller and the lowest temperature is located directly above the leak.From the morphology of the jet based on the CO 2 injection, it is known that the closer to the leak, the smaller the radiation area of the jet; the area outside this range is not affected by the jet, and all heat transfer is carried out through heat transfer.
The maximum temperature difference between the vertical distance of 30 cm and 40 cm from the leak is similar to that between 10 cm and 20 cm, and the relationship between the maximum temperature difference and the horizontal distance from the leak is shown in Fig. 15.
The results show that the larger the horizontal distance from the leak port in the same plane, the smaller the maximum temperature difference.As the distance between the measurement point and the leakage port increases, its temperature in uence decreases and the temperature drop becomes atter.The gradient of temperature drop in each horizontal plane is different.
The relationship between the maximum temperature difference and the horizontal distance from the leak at the vertical height of 50 cm to 70 cm is shown in Fig. 16.The temperature change is also similar to the trend of the rest of the horizontal surface, and the overall trend shows that the smaller the horizontal distance between the measurement point and the leak, the greater the temperature difference.At the distance of about 50 mm from the horizontal distance, the order of the temperature difference between the horizontal surfaces changed.The temperature difference of the horizontal surface at 50 cm, which is the smallest vertical distance from the leak, is the smallest.In turn, at 225 mm, the temperature difference of the horizontal plane at 70 cm, which is the farthest from the vertical distance of the leak, is the largest, and as the horizontal distance between the measurement point and the leak increases, the larger the vertical distance, the larger the temperature drop of the plane.The two main reasons for the above phenomenon are as follows.
(1) Combined with the data from the previous planes, it can be seen that the movement of CO 2 in the porous medium after it is released from the leak is "funnel" type.
(2) The porosity of the soil medium at the bottom is larger than the porosity of the surface soil due to the gravitational effect of the soil, and thus its pore resistance is larger, so the CO 2 percolation in it is more di cult and the maximum temperature difference is smaller.
Figure 17 shows the temperature thermogram of each horizontal surface at the moment of 80 s using Matlab software.From the gure, it can be seen that the highest measuring point on each measuring rod has reached the lowest temperature, and the temperature distribution law of each horizontal surface at this time has the following characteristics.
(1) In each horizontal surface of the measurement point, the measurement point with the largest temperature difference is located directly above the leak, and the lowest temperature in the entire region appears in the vertical distance from the leak 20 cm horizontal surface.
(2) Each horizontal measurement point in the closer to the leak, the more rapid the temperature drop, the temperature drop with the rise of the horizontal surface and decrease.
(3) As the vertical height of the horizontal surface from the leak increases, the range of the low temperature region in the horizontal surface also gradually expands.
It can be seen that after the pipeline leaks in the sandy soil for a period of time, the temperature distribution in the soil medium is funnel-shaped due to the phase change of dense-phase liquid or supercritical CO 2 , heavy gas diffusion, pore resistance, uid percolation, and energy transfer.When the vertical distance from the leak is 10-20 cm, the temperature drop is more obvious only in the area directly above the leak, which is caused by the absorption of ambient heat by the phase change of dense-phase liquid or supercritical CO 2 , and the morphology of the high-pressure gas jet.The high-pressure jet of lowtemperature gas can maintain a relatively stable motion trajectory vertically upward at close range under the effect of initial kinetic energy.With the increase of injection height, the kinetic energy of CO 2 jet is lost due to the in uence of soil pore resistance and gravity, and the motion form of CO 2 in soil media is changed from seepage to percolation in soil media pores, and the motion trajectory is changed from vertical upward to diffusion to the surrounding environment.The low temperature gas gradually diffuses to the surroundings, the temperature difference gradually decreases, and the low temperature area gradually expands.

Conclusion
(1) The instantaneous release of CO 2 absorbed a large amount of heat from the surrounding area, which caused the soil temperature around the leak to plummet to -20~-40℃.Most of the water components in the soil condensed into solid ice, which greatly reduced the water content of the soil, which in turn greatly reduced the thermal conductivity of the soil, and the reduction of the soil thermal conductivity inhibited the recovery of the soil temperature.
(2) The analysis of the temperature change in the near eld shows that the temperature of the measurement points at a vertical distance of 10 cm ~ 50 cm from the leakage port have a common feature, that is, their temperature curves have similar trends, and there is a phenomenon of "sudden droprapid recovery -then drop".
(3) Analysis of the temperature change in the far eld shows that the temperature drop at the top area increases with the increase in vertical height.On the contrary, the temperature of the three sensors at 0, 10 cm and 20 cm, which are closer to the leak, has almost no change.The rest of the measurement points satisfy the law that the larger the vertical distance is, the larger the temperature difference is.
(4) During the leakage process of buried CO 2 pipeline, the temperature distribution in the soil medium is funnel-shaped, and the temperature distribution in each horizontal plane takes the measurement point on the axis of the leakage direction as the lowest temperature point, and due to the uniform nature of the soil medium, the isotherm radiates outward in an approximately circular shape.Among the measurement points in each horizontal plane, the measurement point with the largest temperature difference was located directly above the leak, and the lowest temperature in the whole area appeared in the horizontal plane 20 cm away from the leak vertically.

Declarations
Author statement Zhenyi Liu contributed to the conception of the study Zihao Xiu wrote the manuscript Yao Zhao performed the data analyses and wrote the manuscript Mingzhi Li guide the experiment Pengliang Li guide the experiment Peng Cai Check the full paper Yizhen Liang Check the full paper The authors declare that they have no known competing nancial interests or personal relationships that could have appeared to in uence the work reported in this paper.Relationship between ambient temperature difference and distance at each measurement point at 30 cm and 40 cm Relationship between ambient temperature difference and distance for each measurement point at 50 cm, 60 cm and 70 cm Three-dimensional diagram of the temperature distribution at each level at 80 s of leakage al.2014; Wee 2013).At present, domestic and foreign researchers have done a lot of research on the diffusion behavior and temperature distribution of CO 2 in pipelines after leakage, and have achieved certain results (Charlotte et al.2013; Lia et al.2019; Yan et al.2016; Hu et al.2022; Teng et al.2020; Xie et al.2014; Teng et al.2021;).

Take No. 1
and No. 4 measuring rod as an example to analyze the temperature change law in the middle and far eld, as shown in Fig. 11, the temperature change with time at each measuring point on No. 1 and No. 4 measuring rod is roughly the same, only the temperature change at the vertical distance of 40 cm and 50 cm measuring point is slightly different.The reason is that the sandy soil texture is not uniform enough.Although the soil environment laid in the experiment was uniform enough, it was still far from the ideal condition, which led to the difference between measuring rod No.1 and No.4 even though they

Figure 2 Top
Figure 2 Figure 3

Figure 14 Relationship
Figure 14

Table 1
The horizontal distance between each measuring rod and the leakage port and the number of sensors

Table 2
Note: The symbol "-" in the table means that the data set does not have this measurement point; the meaning of the experiment number is "pressure -caliber -measuring rod number"