Buried Natural Gas Pipe Line Leakage – Quantifying Methane Release and Dispersion Estimations

1. Process Safety and Environmental Protection 146 (2021) 552–563 Contents lists available at ScienceDirect Process Safety and Environmental Protection journal homepage: www.elsevier.com/locate/psep Quantifying methane release and dispersion estimations for buried natural gas pipeline leakages Cuiwei Liu∗ , Yihan Liao, Jie Liang, Zhaoxue Cui, Yuxing Li College of Pipeline and Civil Engineering in China University of Petroleum (East China), Qingdao 266580, China a r t i c l e i n f o Article history: Received 15 May 2020 Received in revised form 3 October 2020 Accepted 19 November 2020 Available online 26 November 2020 Keywords: Natural gas pipelines Quantifying estimation Leakage rate Diffusion range Soil a b s t r a c t The methane into the soil from buried natural gas pipelines due to small leakages, changes the soil properties, posing potential risks to humans and the environment. It is essential to estimate the leakage rate and monitor the methane diffusion range outside the pipeline, which is challengeable due to the presence of soil. The main contribution of this work is to bridge the gap between estimating the leakage rate of underground pipelines and predicting the diffusion behaviors through calculating the gas concentration in the soil. The quantified leakage rate estimation model for air was firstly established by experimental results and validated by the numerical results, which was further modified by the methane with the numerical simulations. The methane diffusion model in the soil was then performed, through which, the influencing factors were explained and validated. In addition, the methane release and dispersion results in the soil could be used as the boundary conditions of gas diffusion model in the air. The results show that the quantifying estimation correlations can predict the leakage rate and dispersion range in the soil accurately, with errors less than 7.2 % and 15 %, respectively. Moreover, the quantified relations have been validated by the full-field experiments. And, the dispersion behaviors in the air could be portrayed instead of being regarded as a jet flow. © 2020 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. 1. Introduction Pipelines are used extensively all over the world for the transportation and distribution of natural gas (NG), including long distance pipelines and local distribution pipelines (Robert et al., 2014). NG leakage from either an above- or an under-ground pipeline will result in environmental and financial consequences. Because most local distribution pipelines, working under low pressure, are paved under the ground, it is difficult to measure the diffusion of leaked NG. Once leakage occurs, the leaked gas will pose significant threats to public safety (Morgan et al., 2015; Lelieveld et al., 2005), especially when it comes to background leakages (Haghighi et al., 2012). A background leakage is regarded as occur- ring when the ratio of the leakage orifice diameter to the pipe diameter is small or the working pressure is low (European Gas Pipeline Incident Group, 2015). Hendrick et al. reported a survey on fugitive methane emissions from leak-prone NG distribution infrastructure in urban environments, which revealed that small leakages posed larger potential hazards (Hendrick et al., 2016). ∗ Corresponding author. E-mail addresses: chuyun lcw@163.com (C. Liu), lyx13370809333@163.com (Y. Li). Although there are many methods (Batzias et al., 2011; Bagajewicz and Valtinson, 2014; Zhou et al., 2016; Kim et al., 2019; El-Zahab et al., 2018) available to detect and locate leakages, at the beginning, few of them are concerned with the estimation of the leakage rate and the diffusion range, which are two key points that determine the emergency response for the leakage management. Background leakage is more difficult to detect and locate due to the slow formation process and gradual low-pressure decline. There- after, much NG will build up in the soil or air at the leakage point, performing toxic diffusion, and even fire and explosions before a response is carried out, leading to severe damage to the environment, the city or people (Anifowose and Odubela, 2015; Balcombe et al., 2018; Van Fan et al., 2018). In China, the length of the city pipelines is more than 600, 000 km. Leakages always occur, up to several times a day (Ji et al., 2017; Chen et al., 2016). To prevent cities from severe damage, it is extremely important to understand that the NG leakage rate and diffusion range of above- or underground pipelines is a fundamental factor to be considered in the design and maintenance of safe pipelines for emergency response. Nowadays, leakage and dispersion estimation for buried NG pipelines has been attracting significant interests, mainly in relation to the physical process by which the leaked gas diffuses in the soil or air. Many experimental and numerical studies have been conducted focusing on this topic, with theoretical and empirical https://doi.org/10.1016/j.psep.2020.11.031 0957-5820/© 2020 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

2. C.Liuetal. Process Safety and Environmental Protection 146 (2021) 552–563 equations being determined. However, the mathematical models currently available for carrying out these predictions show a major gap in the range of conditions over which they can be applied with a reasonable degree of accuracy, due to a range of simplifications and assumptions. In 1998, Montiel et al. established a mathematical model of accidental gas release from pipelines as a combination of the classical ‘hole’ and ‘pipe’ models, for the calculation of gas releases in distribution systems at medium and low pressures, without taking surrounding soil into consideration (Montiel et al., 1998). Based on this model, many efforts have been carried out to predict NG leakage and dispersion from above-ground pipelines. To derive the equations for a buried pipeline, Nithiarasu established a finite element model for a leaking substance migration from a heat leakage source buried in the soil. The results showed that the leaking hole size had a significant effect on migration of the third component into the porous medium (Nithiarasu, 1999). Xiong et al. designed a mathematical model for NG porous flow in soil after a small leakage in an underground pipeline, based on theories of single-phase porous flow and high-speed non-Darcy porous flow. The errors between the gas dispersion model and the experimental results were as large as 100 % (Xiong et al., 2012). Because there are so many influencing factors, it is difficult to establish precise analytical equations to predict the gas dispersion. To improve the mathematical model, experiments were carried out to establish an empirical model by determining different coefficients, in particular the discharge coefficient for leakage rate and dispersion coefficient for dispersion. Jo and Ahn developed a simple and definite model, based on the Fanning equation with the addition of a gas discharge rate, to calculate the amount of leaked gas from a hole in high-pressure gas pipelines. Their proposed model showed that the gas discharge rate was slightly higher than that of the theoretical model (Jo and Ahn, 2003). Kostowski and Skorek proposed a discharge coefficient to design a method of accounting for a leakage by means of a reference flow equation. The dependency of the discharge coefficient on pressure was demonstrated with both data from other studies and the authors’ experimental results (Kostowski and Skorek, 2012). Hikoji and Toshisuke developed a concentration equation in soil for predicting gas leakage based on a convention-diffusion equation. The predicted and measured concentrations of leaked propane were found to coincide only when a diffusion coefficient was assumed much larger than the commonly used molecular diffusion results (Hikoji and Toshisuke, 1991). Okamoto and Gomi performed an empirical study on diffusion behavior of leaked gas, using full-scale gas leakage experiments to simulate real underground pipeline leakages. However, the diffusion range and time and the impact on the surrounding area were not clear, requiring further study (Okamoto and Gomi, 2011). Xie et al. accomplished multiple full-scale leakage tests on middle-low pressure buried pipelines to examine the influencing range of leakage and diffusion. The results revealed the influence of pressure and flow on the leakage rate and diffusion consequences, indicating that the relationship between the time taken for the NG to diffuse from the leakage point to the detection point and the distance between the two points approximately followed a power exponent curve (Xie et al., 2015). Yan et al. carried out an experimental study of methane diffusion in soil for an underground gas pipe leakage, which measured the gas concentration in the soil with different leakage rates. The results showed that the methane concentration increased as the leakage rate became larger (Yan et al., 2015). Deborah et al. performed nearly full-scale experiments, simulating light gas accidental releases on a 1-m depth buried pipeline. A 12-mm breach scenario was studied for several pressure levels and leakage orientations in sandy and clayed soils, and the influences of these factors on the gas release were investigated (Deborah et al., 2018). Bonnaud et al. also carried out experimental study and modelling of the consequences of small leakages on buried gas transmission pipeline. Release outcomes were influenced by the soil parameters, leakage diameter, pressure, and pipeline depth (Bonnaud et al., 2018). Although these experiments can help improve the mathematical model, only the main influencing factors can be taken into consideration. Simulations are able to consider a range of influencing factors. Parvini and Gharagouzlou established near-field and far-field models to predict the consequence of gas leakage for buried pipelines. The near-field model was related to soil while the far-field model was a gas dispersion model in atmosphere. The consequence of the near-field model was the boundary condition for the far-field model. However, the leakage rate calculation was neglected. There was also a gap between the two models which should be bridged in order to decrease the errors (Parvini and Gharagouzlou, 2015). Ebrahimi-Moghadam et al. developed a two-dimensional numerical method to investigate leakages in the above-ground and buried urban distribution NG pipelines. Two equations were developed to estimate the leakage by considering the impact of various parameters such as the pipeline and hole diameters. The volumetric flow rate of leaked gas had a linear relation, second order relation and fourth order relation with the pressure, hole diameter, and ratio of the hole diameter to the pipe diameter, respectively. The permeation depth of gas into soil for small diameter holes was larger than that for large holes but the volumetric rate of leaked gas was lower. Results showed that the relative errors between simulation results and correlation values decreased (Ebrahimi- Moghadam et al., 2016). Moreover, to improve the leakage rate estimation model, Ebrahimi-Moghadam et al. developed precise gas leakage calculator equations for low- and medium-pressure buried pipelines, using three-dimensional models. The correlations developed were functions of the pipe diameter, hole diameter, and pressure. The results indicated that a two-dimensional model was not precise enough for estimating the gas leakage from an underground pipeline, due to the soil resistance in three dimensions. In addition, the linear, second order and fourth order relations were observed between the amount of gas leakage and the three effective parameters, namely the pipe pressure, hole diameter, and ratio of the hole diameter to the pipe diameter, respectively. The results indicated that the relative difference between the results of the simulation and those given by the developed correlations was within a range of ±7 % for all cases (Ebrahimi-Moghadam et al., 2018). The leakage rate estimation model could be applied in the field, since the errors had been effectively minimized. However, the hole diameter was always unknown, which left the leakage rate calculation still unsolved. In previous investigations, many experimental and numerical studies have been conducted, with both theoretical and empirical equations being proposed. However, most present studies focus on either of leakage rate estimation or diffusion range estimation in the soil. Moreover, the mathematical models currently available for performing leakage estimation and dispersion concentration prediction show a major gap in the range of conditions over which they can be applied with a reasonable degree of accuracy. The NG dispersion process from the soil to the air has also been neglected. Hence, calculation of the gas leakage rate from a buried pipeline, based on experiments and simulations, which determines the gas dispersion in the soil and air, may be a remarkable contribution to present studies. This study presents two equations calculating the leakage rate and gas concentration in the soil for background leakages under the low pressure, which are regarded as the initial and boundary conditions, respectively, to portray two gas concentration estimations in the air. The empirical leakage rate estimation model was firstly established by experimental results using air as medium, which was validated by the numerical model with air and further modified by the numerical model with methane. The diffusion model 553

3. C.Liuetal. Process Safety and Environmental Protection 146 (2021) 552–563 Fig. 1. Leakage process into the air. in the soil was then calculated using methane as medium. The influencing factors on NG leakage and diffusion process, including the pressure, leakage hole shape and diameter, pipeline depth, soil characteristics, and temperature, were investigated, through which the methane concentration equation was fitted by the simulation results. In addition, when the methane diffusion in the soil became stable, the concentration distribution and leakage rate of methane were used as the inlet boundary conditions for the methane diffusion model in the air. During the experiments and simulations, as the methane is dangerous, air was used as the medium in the laboratory, by which the influencing factors on the leakage rate model were concluded. Moreover, air was used as the medium to conduct the simulations for leakage rate prediction model, by which the relations concluded by the experiments were validated. After the numerical model or method was verified, it was further applied to study the leakage rate and diffusion models, using methane as the medium. Finally, the leakage rate model, diffusion model in the soil were validated by the full-scale experiments. 2. Methodology 2.1. Theory The equations of the leakage rate and dispersion range are first derived. 2.1.1. Leakage rate equation When background leakage occurs, the valves located at both ends of the pipeline remain open. The leakage flow will reach a steady state as shown in Fig. 1. When the gas is released to the air, Lu et al. derived a mathematical model to calculate the leakage rate, as shown in Eq. (1) (Lu et al., 2014). Q = A3p2 2 RT2 − 1 pa p2 2 − pa p2 +1 (1) where pa/p2 CPR, pa is the atmosphere pressure, p2 is the absolute pressure at the leakage point, Pa; Q is the leakage rate, kg/s; A3 is the leakage hole area, m2; is the heat capacity ratio; R is gas constant, J/(kg·K); T2 is the temperature, K; CPR = 2 +1 −1 is the critical pressure ratio. Taking the soil into consideration, Tang et al. developed a com- putation model to calculate the leakage rate by introducing a leakage flow coefficient and a modification coefficient, as shown in Eq. (2) (Tang et al., 2009). Q = ˛CgA3p2 · 2 RT2 · − 1 pa p2 2 − pa p2 +1 (2) where pa/p2 ˇ; ˇ is the ratio of leakage orifice diameter to the pipe diameter; ˛ is the modification coefficient; Cg is the leakage flow coefficient. Besides the theoretical equations, Ebrahimi-Moghadam et al. derived two equations by fitting the two-dimensional simulation results (Ebrahimi-Moghadam et al., 2016). Eq. (3) was used for above ground pipelines while Eq. (4) was used when the soil was considered. Q = 0.748 1 + ˇ4

4. d2 p1 (3) Q = 0.44 1 + ˇ4

5. d2 p1 (4) where Q is the volumetric leakage rate under the standard condition, Nm3/h; p1 is the pipe pressure at the initial point, in bar. Ebrahimi-Moghadam et al. (2018) derived an additional two equations by ﬁtting the three-dimensional simulation results. When the pressure of the pipe was between 3 and 5 bar, Eq. (5) was used without soil while Eq. (6) was used with soil. Q = 0.808 1 + ˇ4

6. d2 p1 (5) Q = 0.117 1 + ˇ4

7. d2 p1 (6) Thereafter, the leakage rate can be calculated through the empirical equations fitted by the simulation results. 2.1.2. Diffusion equation in the soil Tang et al. and Zhang and Chengestablisheda three-dimensional steady-state model for gas diffusion in soil (Tang et al., 2009; Zhang and Cheng, 2014). Taking the leakage point as the coordinate origin point, the xoz plane was parallel to the ground, and the y-axis was perpendicular to the ground. When the leakage time was t s, the diffusion concentration of NG at a distance of r m from the leakage point was obtained by Eq. (7): c (r, t) = q 4Dmr 1 − erf r 2 √ Dmt (7) where q was the leakage rate, m3/s; Dm was the diffusion coefficient, m2/s; erf was the Gaussian error function. 2.2. Experiments for leakage rate model 2.2.1. Experimental setup A low-pressure gas pipeline loop was designed and established after a similarity analysis with actual NG transportation pipelines which varied from 0 to 50 kPa, as shown in Fig. 2. The experimental system consisted of a buried pipeline section with leakages in a box full of soil, a metering section including two flowmeters, two pressure sensors, a data acquisition section and a pressure stabilizing section. The working pressure of the pipeline was varied between 10 and 50 kPa by the steady valve and reducing valve. Flowmeters 1 and 2 were used to record the flows. The pressure sensors were applied to measure the pressures. The data acquisition system included the PCS1800 distributed control system. Air was used in the experiments instead of NG. The actual experimental facilities were shown in Fig. 3. Fig. 3 showed that the physical loop was composed of the main pipe and the branch pipe, both of which were buried in the soil in a box. A ball valve was located on the branch, which was used to control the leakage in case it occurred. Behind the valve was an orifice plate, which was used to control the leakage orifice shape and diameter. When the valve was opened and the gas flowed through the plate, leakage occurred. The diameter of the main pipe was 42 mm and the orifice diameter was variable from 1 to 4, mm, as seen in Fig. 4. When the soil was taken into consideration, parameters including the particle diameter and porosity were important, especially 554

8. C.Liuetal. Process Safety and Environmental Protection 146 (2021) 552–563 Fig. 2. Buried gas pipeline experimental setup with leakages. Fig. 3. Buried gas pipeline leakage experimental loop. Fig. 4. Physical diagram of leak holes with 1–4, mm. for setting the parameters of porous media in the numerical simulation to calculate the viscous resistance and internal resistance. A Bettersize2000 laser particle size distribution meter was used to measure the diameter of solid particles. The soil used in the experiments was from the Huangdao District of Qingdao, and was mainly brown loam. Three soil samples were studied, of which the distribution range of soil particle size was about 1∼500 ␮m. The average value of the peak of particle size distribution curve in three groups of soil samples was 198 ␮m, which was close to the value of 209 ␮m measured by Xie et al. for the brown loam (Xie et al., 2015). The average bulk density of the soil was measured as 1311.3 kg/m3. The soil porosity was 0.6. 2.2.2. Experimental scenarios The influencing factors on gas leakage rate were the working pressure, pipe diameter, leakage hole diameter, temperature and soil depth (Ebrahimi-Moghadam et al., 2018). From the experimental (Bonnaud et al., 2018) and numerical simulation results (Ebrahimi-Moghadam et al., 2018) in the literature, the pipeline working pressure, soil depth and leakage hole diameter had the greatest influence on the leakage rate. As background leakage occurred under low pressure, the leaked gas would not break through the soil. The soil depths were set to 0, 20, 30, 40, 50, and 60 cm. The pressures were set to 10, 20, 30, 40, and 50 kPa. The leakage hole diameters used were 1–4 mm. A total of 120 sets of experiments were carried out to include all combinations of values. Since the gas leaked would form channels in the soil to reduce the resistance of gas release in subsequent experiments, the soil was processed and refilled after each experiment to ensure its unifor- mity. Each experiment was repeated three times, and the average values were recorded. 2.3. Numerical simulation 2.3.1. Leakage rate model The FLUENT numerical simulation software was used to establish the leakage and diffusion model of a buried gas pipeline. The 555

9. C.Liuetal. Process Safety and Environmental Protection 146 (2021) 552–563 Fig. 5. Geometric model. Fig. 6. Meshing of the model. model area was 4 × 0.8 × 4 m. The leakage hole was located at the center of the bottom, and the origin point of the xyz coordinates was set at a corner of the bottom. The center of the leakage point was (2, 0, −2), m, as shown in Fig. 5. The governing equations were the continuity equation, momen- tum equation and energy equation, with the component transport model, as seen in literature (Ebrahimi-Moghadam et al., 2018). The standard k − ε two-equation model was chosen as the turbulence equation. The soil could be viewed as a geometry substance composed of soil particles with pores between the particles. It was assumed that the soil was an isotropic porous medium with a uniform particle size. Because the leakage hole diameter was relatively small with 1–4 mm, the mesh near the leakage point should be refined, and the generated mesh was as shown in Fig. 6. The leakage hole which was on the bottom was set as the pressure-inlet boundary condition, the yellow ground side was set as the pressure-outlet boundary condition, the fluid domain was set as the porous medium, and the fluid medium was set as air, firstly. After the leakage rate model of air was validated by the experimental results, the leakage rate o predicted by the established model in Fig. 5 could be used to study the leakage rate and diffusion model of methane. To analyze the mesh independence, the number of grid cells was varied from 67,800 to 376,000, then to 1,029,000, and the results with leakage hole diameters of 2 mm and 4 mm are shown in Fig. 7. Different grid cell numbers had little influence on the calculated gas leakage rate, in addition on the gas diffusion. Based on the calculation time and the precision of the results, a model with 376,000 grid cells was selected for further simulations. 2.3.2. Diffusion model in the soil The gas diffusion model established by Eq. (7) was complex, and difficult to be applied in the field. It is, however, of great significance in establishing an empirical model through simulation. The content of methane in NG is generally more than 95 %, and pure methane is assumed as the composition of NG for these studies. The concentration lines in the soil after NG leakages should be calculated. The explosion limit of methane concentration is 5 %–15 %. The concentration of the first-level alarm line is 1.25 %, and that of the second-level alarm line is 2.5 %. The diffusion ranges between these two concentration lines are of primary interest in this paper, as detection within this range leaves enough time to deal with the leakage situation. After the numerical method was validated by the leakage rate model obtained by the experimental and numerical results, the numerical method was further applied to study the leakage and dispersion behaviors, using methane as the medium. For these calculations, the soil porosity was 0.6, the diameter of soil particle was 0.198 mm, the temperature was 300 K, the soil depth was 0.8 m, the hole was circular and the leakage direction was upward. Six monitoring points a–f were set in the model to analyze the methane diffusion behaviors, of which the coordinates were (1.4, 0.8, −2), (1.7, 0.4, −2), (1.85, 0.2, −2), (1.925, 0.1, −2), (2, 0.2, −1.85), (2.2, 0.15, −2) m, respectively. As the leakage point was located at (2, 0, −2), points a, b, c, d were in the same plane, and were used to study the methane diffusion behavior at different distances which were 1, 0.5, 0.25, and 0.125, m, respectively away from the leakage hole, and points c, e, f were used to study the methane diffusion behaviors in different planes with the same distance which was 0.25 m away from the leakage hole. 2.3.3. Atmospheric diffusion model In the previous section, the relations for calculating the leakage rate and dispersion concentration of methane in the soil have been established, which could be used as the initial and boundary conditions for the atmospheric diffusion model. The geometry region for the diffusion model was 50 × 50 × 50 m, having a circular entrance shape at the center of the bottom, as shown in Fig. 8. The mesh independence was also conducted, by which the number of grid cells was selected as 7783668. As the gas diffused from the soil and reached the ground before diffusing into the air, the distribution of NG was approximately a circular area, in which the concentration and diffusing speed into the air of NG were different. However, when the leakage from the pipe and diffusion of NG in the soil reached a steady state, the mass flow rate at the leakage hole would be equal to that at the entrance area diffusing into the air. Therefore, the leakage rate was selected as the inlet boundary condition of the atmospheric diffusion model. The boundary type was mass-flow-inlet, the direction was along the y-axis, the ground was the wall boundary type, and the other surfaces were the pressure-outlet boundary conditions. 2.4. Full-scale experiments Although the leakage rate relations could be obtained with experiments in 2.2.1, the air was set as the medium rather than the methane. To validate the above laboratory and numerical models, full-scale experiments with NG were carried out under the pressure of 0–500 kPa, using the facilities in Fig. 9. The gas mixture was discharged from a NG reservoir through a pressure-reducing valve to the pipe in the 4 × 4 × 2 m soil tank. The volumetric flow rates were read by a flow meter. A pressure transmitter was placed in the pipe near the leakage point. Gas concentrations were measured by detectors for methane, of which the 556

10. C.Liuetal. Process Safety and Environmental Protection 146 (2021) 552–563 Fig. 7. Mesh independence analysis. Fig. 8. Geometric model of gas diffusion in the atmosphere. locations were distributed averagely according to the numerical model. A vacuum pump was used to initially remove the air from the pipe to eliminate the concentration changes. 3. Results and discussion 3.1. Leakage rate model for air 3.1.1. Experimental results When the leakage hole diameter was 4 mm, the soil depth was 50 cm, and the pressure was 40 kPa, the flow fluctuations were measured by flowmeter 1 and 2 and used to calculate the leakage flow, as shown in Fig. 10. In Fig. 10, when the leakage occurred at 80 s, the flow rate measured by flowmeter 1 slightly increased while that measured by flowmeter 2 decreased greatly, and the leakage rate increased from 0 to 2.8 Nm3/h rapidly, and quickly reached a steady state. After the leakage stopped, the flow rates of the two flowmeters returned to be the same and the leakage rate returned to zero. The leakage rate in this study refers to the value after the leakage reached the steady state. For a leakage hole diameter of 2 mm, a pressure of 30 kPa, a soil depth of 60 cm, the relationships between the leakage rate and the soil depth, the leakage hole diameter, and the pressure level were shown in Figs. 11–13, respectively. Fig. 9. Full-scale experiments. 557

11. C.Liuetal. Process Safety and Environmental Protection 146 (2021) 552–563 Fig. 10. Fluctuations of the measured flow and the calculated leakage flow. Fig. 11. Relationship between the leakage rate and the soil depth, leakage hole diameter = 2 mm. Fig. 12. Relationship between the leakage rate and the leakage hole diameter, pressure = 30 kPa. These relations could be verified based on the results reported in literature (Ebrahimi-Moghadam et al., 2016; 2018). It should be noted that compared to the leakage hole diameter and the pressure, the soil depth had a smaller influence on the leakage rate. When either the pressure or the leakage hole diameter was zero, the leakage rate would be 0 Nm3/h. The leakage rate could be expressed by a formula where one influencing factor was mul- tiplied by the others. Therefore, according to Eqs. (1), (4) and (6), nonlinear fitting of the experimental data was carried out to obtain an empirical correlation between the leakage rate and the soil Fig. 13. Relationship between the leakage rate and the pressure level, soil depth =60 cm. Fig. 14. Errors between the fitted and experimental results. depth, leakage hole diameter and pressure, of which the exponents could be roughly determined by Figs. 11–13. Q = 0.567 (h + 139.592) −0.1 − 0.542 · d1.5 · p0.7 (8) where Q is the leakage rate, Nm3/h; h is the soil depth, cm; d is the leakage hole diameter, mm; p is the pressure level, kPa. Eq. (8) had the same form as Eq. (6), although the exponents were different. The errors between the leakage rates obtained by the fitted equation and those measured by the experiments were shown in Fig. 14. When the leakage rate was small, the fitted results were close to those obtained by the experiments, and the errors increased when the leakage rate became large, of which the root mean squared error was 0.19 and the coefficient of determination was 0.94. The errors were between 15 % and 25 %. To reduce the errors, a coefficient ˛ was introduced after comparing the leakage rate with soil to that without soil. Background leakage occurred in the experiments, in which the leakage hole diameter and the working pressure satisfied conditions to generate subsonic flow. In comparing Eq. (4) to Eq. (3), the leakage rate calculated with soil was 58.8 % of that calculated without soil. This indicated that the ratio of the leakage rate calculated with soil to that without soil may be constant which was validated by Han (2014). He experimentally measured the leakage rate in non-buried and buried NG pipelines, and found that the ratio between them to be 75 %–80 %. In the experiments carried out for this study, the ratio was 65 %–75 %. 558

12. C.Liuetal. Process Safety and Environmental Protection 146 (2021) 552–563 Fig. 15. Contours of methane concentration in soil with time with 4 mm leakage hole at 300 kPa. The maximum experimental pressure was 50 kPa, under which pa/p2 CPR was satisfied. The theoretical leakage rate can be calculated by Eq. (1). When h was 0 in Eq. (8), the coefficient ˛ was introduced: Q = 0.567˛ (h + 139.592) −0.1 − 0.542 · d1.5 · p0.7 (9) The coefficient ˛ is a function calculated by fitting the experimental results: ˛ = 4.209d0.5 · (p + 10.456)−0.3 (10) When the leakage hole diameter was 10 or 20 mm, and the pressure was 0–90 kPa, the results, as calculated by Eqs. (9) and (1), were shown in Table 1. From Table 1, the errors were −2.2 %–1.1 %, and the accuracy satisfied the leakage rate calculation. Therefore, when the leakage hole diameter, pressure, and soil depth were known, the gas leakage rate could be easily predicted. However, in actual situations, the size of the leakage hole was always unknown. To solve this problem, a solution was proposed based on a Bayesian network (BN) model, which was used to predict the leakage hole diameter. Through the BN model, for the diameters in this study, the most likely corresponding orifice diameter could be predicted with an accuracy of more than 90 % (Liu et al., 2020). Therefore, when leakage occurred in a gas pipeline, after the pressure and flow rate were measured, the leakage hole diameter could be predicted by the proposed BN model, and then Eqs. (9) and (10) could be applied to calculate the leakage rate. 3.1.2. Numerical model validation To validate the numerical model, the buried depth was set as 60 cm, the leakage hole diameter was 2 mm or 4 mm, and the results were compared to those of the experiments in Section 2.3 by chang- ing the working pressure. The errors were between −26.018 % and 6.937 %, as seen in Table 2. The source of the errors mainly resulted from the soil being regarded as an isotropic porous medium with uniform particle size distribution, and the structure of the porous medium did not change during the numerical simulation. Although the soil was processed and refilled for each experiment, the gas would still form fixed channels in the soil, which reduced the resistance of the soil during the gas leakage and dispersion. Therefore, the leakage rate measured in the experiment was generally larger than that obtained by numerical simulation under the same condition. Although these errors existed, the numerical model was validated to be effective. In the future, the errors of the established Fig. 16. Methane concentrations at the monitored points with 4 mm leakage hole at 300 kPa. models should be minimized by improving the soil porous media model with a non-isotropic porous medium containing different particle sizes, by considering more parameters in the fitted relations, especially the moisture content, and by establishing full-scale experimental facilities. 3.2. Methane diffusion model in the soil When the air was used as the medium for the experiments and simulations, as the pressure was limited by the experimental facilities, 0–50 kPa was selected. To make the established equations useful in a wide range of pressure, 0–500 kPa was set in the following simulations and full-experiments. When the leakage hole diameter was 4 mm and the pressure was 300 kPa, a cross section XOY, parallel to the xoy plane and passing through the center of the leakage hole, was chosen, for which the methane concentration contours were shown in Fig. 15. Due to the resistance of the soil, the methane concentration distribution was approximately circular before the methane reached the surface. The simulated methane concentrations of the monitored points were shown in Fig. 16. The concentrations at points c, e, and f at the same time were almost the same. For each of points a, b, c, and d, the concentration increased with time. The increase process can be divided into three stages: an initial stage, a rapid growth stage, and a slow growth 559

13. C.Liuetal. Process Safety and Environmental Protection 146 (2021) 552–563 Table 1 Prediction results of leakage rate and errors. Leakage hole diameter /mm Leakage pressure /kPa Calculated leakage rate /Nm3 /h Errors % Eq. (9) Eq. (1) 10 10 33.012 33.404 −1.174 20 47.593 47.075 1.100 30 58.051 57.453 1.040 40 66.449 66.113 0.509 50 73.581 73.665 −0.114 60 79.845 80.427 −0.723 70 85.471 86.586 −1.288 80 90.605 92.267 −1.801 90 95.345 97.555 −2.266 20 10 132.049 133.617 −1.174 20 190.370 188.299 1.100 30 232.204 229.813 1.040 40 265.796 264.451 0.509 50 294.325 294.662 −0.114 60 319.382 321.708 −0.723 70 341.886 346.346 −1.288 80 362.419 369.068 −1.801 90 381.379 390.221 −2.266 Table 2 Errors of numerical and experimental results. Leakage hole diameter /mm Leakage pressure/kPa Leakage rate/kg/h Relative error % Simulation results Experimental results 2 10 0.453 0.463 −2.183 20 0.683 0.787 −13.204 30 0.876 0.917 −4.491 40 1.050 1.285 −18.278 50 1.213 1.640 −26.018 4 10 1.345 1.258 6.937 20 2.021 2.163 −6.579 30 2.582 2.508 2.960 40 3.081 3.231 −4.656 50 3.547 4.519 −21.507 stage. The closer the monitored point was to the leakage hole, the larger the concentration was. Methane is flammable and explosive. There are no ignition sources in the soil. However, when methane diffuses from the soil to the ground and is mixed with the air, the explosion limit can be reached. To describe the dangerous situation above the surface of the ground, a projection to the ground of the distance between the monitored points and the leakage hole was carried out, in which the line with 1.5 % concentration was defined as the first-level alarm radius. Likewise, the second-level alarm radius was defined as the 2.5 % concentration line. The line between the XOY plane and the ground surface was chosen to be the monitored line, for which the methane concentrations were shown in Fig. 17. The methane concentrations were symmetrically distributed with x = 2 m as the symmetric axis, with the largest concentration in the middle and decreasing values distributed on both sides. The two alarm radii were also obtained as shown in Fig. 18. The methane diffusion ranges gradually increased with time, and the speed of increase gradually lessened. The difference between the first-level and second-level dangerous radii was almost unchanged. 3.3. Influencing factors on leakage rate and diffusion model for methane The leakage rate of gas in soil was studied experimentally as outlined in Section 3.1.1. The influencing factors were found to be pressure, leakage hole diameter, and buried depth, as shown in Eq. (8). Besides these three factors, the other influencing factors on the Fig. 17. Methane concentrations on the monitored line with 4 mm leakage hole at 300 kPa. leakage rate, including the soil properties, temperature, and leakage hole shape could be researched by simulations. Likewise, the influencing factors on diffusion model in soil could be researched by simulations. Both could be seen in S1 of Supporting Information (SI) section. From the numerical simulation results, the main factors influencing the leakage rate were pressure, leakage hole diameter, soil particle diameter and porosity, through which the leakage rate calculation equation was modified and determined. The concentration distribution of methane in soil was mainly affected by diffusion time, distance from leakage hole, pressure, leakage hole diameter 560

14. C.Liuetal. Process Safety and Environmental Protection 146 (2021) 552–563 Fig. 18. Dangerous radius on the ground with time with 4 mm leakage hole at 300 kPa. and soil properties. The temperature, soil depth and leakage hole shape had little influence on leakage rate and gas diffusion process. 3.4. Quantitative relations for NG leakage and diffusion in the soil As the influencing factors on leakage rate and diffusion model were revealed. The quantitative relations were then established. 3.4.1. Leakage rate prediction When any one of the parameters, pressure, leakage hole diameter, or soil porosity, was 0, the gas leakage rate would be 0. According to the relations shown in Figs. S1, S4, S7, and S10, the numerical simulation results were used to fit the relationship between the leakage rate and pressure, leakage hole diameter, soil porosity and soil particle diameter, nonlinearly, which were based on the relations shown in the empirical Eq. (6): Q = 1.808 (ds + 0.405) −0.1 − 0.906 · ϕ3 · d1.5 · p0.75 (11) where ds is the soil particle diameter, mm; ϕ is the soil porosity. The values of the exponents of pressure and leakage hole diameter were validated by Eq. (9). In comparing Eq. (11) to Eq. (9), the influence of soil on the leakage rate for the background leakages was determined by the soil particle size and soil porosity, instead of the soil depth. When the temperature was 300 K, the soil depth was 0.8 m, the hole shape was circular, the soil porosity was 0.6, the soil particle diameter was 0.198 mm, the results of numerical simulation and fitted relationship of leakage rate with different pressures under different leakage hole diameters were shown in Fig. 19. The errors in Fig. 19 were less than 7.2 %, which validated the established leakage rate model, as shown in Eq. (11). 3.4.2. Gas concentration prediction When the leakage time was 0 s or the leakage rate was 0 kg/h, the methane concentration was taken as 0. When the distance from the leakage hole was 0 m, the methane concentration was taken as 1. The methane concentration calculation relation followed Eq. (12): C = kQmrntt r / = 0 1 r = 0 (12) where C is the concentration of methane, %; k is the diffusion coefficient; Q is the leakage rate, m3/s; r is the distance from the leakage hole, m; t is the leakage time, s. When the soil porosity was 0.6, the soil particle diameter was 0.198 mm, the temperature was 300 K, the soil depth was 0.8 m and the leakage hole was circular with the leakage direction upwards, Fig. 19. Results of numerical simulation and fitted relation of leakage rate with pressures. Fig. 20. Methane concentrations with distance from leakage hole. Fig. 21. Methane concentrations at each monitored point with different leakage rates. the leakage hole diameter was 4 mm and the pressure was 300 kPa, respectively, the methane concentrations with the distance r from the leakage hole were shown in Fig. 20. At a given time, the methane concentration decreased with the increase of the distance, and the curve followed a power exponen- tial law with a negative exponent. When the leakage hole diameter was 4 mm, and the leakage time was 50 s, the methane concentrations with different leakage rates at different monitored points were shown in Fig. 21. 561

15. C.Liuetal. Process Safety and Environmental Protection 146 (2021) 552–563 Table 3 Predicted and calculated leakage rate results. Leakage pressure/kPa Leakage rate/(kg/h) Predicted error/% Calculated error/% Predicted results by Eq. (11) Calculated results by Eq. (14) Experimental results 10 0.785 0.346 0.801 −2.038 −56.865 30 1.789 1.043 1.725 3.747 −39.496 50 2.624 1.571 2.542 3.229 −38.225 100 4.414 3.512 4.609 −4.232 −23.788 200 7.423 5.125 7.178 3.416 −28.605 300 10.061 8.646 10.458 −3.794 −17.329 The methane concentration increased approximately linearly with the increase of the leakage rate. The exponents of variables in Eq. (12) could be roughly determined by Figs. 16, 20, and 21, for which the ranges were set as 0.5≤m≤1.2, −1.2≤n≤−0.5 and 0.1≤j≤0.5, respectively. The sum of absolute relative differences between the fitted and numerical concentrations was defined as S. The relations between the concentration and the influencing factors could be fitted, nonlinearly. The initial state was set as k1 = 0.2, m1 = 0.5, n1=−1.2, j1 = 0.1, which was input into the following equation: S = 388 i=1 abs (Ci − Ci) /Ci (13) Giving a value of S1 = 127.233. Next, the iteration steps of m, n, and j were set to 0.05 and the iteration calculation was carried out to find out the parameters for the optimal non-linear fitting results, which could calculate the minimum sum. The values S = 69.177, m = 0.7, n=-0.8, j = 0.35, k = 0.2431 were obtained. Thereafter, the relation in Eq. (14) was expressed as follows: C = ⎧ ⎨ ⎩ 0.2431 Q0.7t0.35 r0.8 r / = 0 1 r = 0 (14) The fitted gas diffusion concentrations of Eq. (14) were close to the simulation results under different conditions, for which the errors were −14 %–15 %. Although Eq. (14) satisfied the accuracy in the engineering application process, it should be a topic of further study in the future to minimize the errors. 3.4.3. Validation of quantitative relations with full-experimental results As shown in Eq. (14), if the methane concentration could be measured, the leakage rate could also be calculated. The actual, predicted and calculated leakage rate could be seen in Table 3, which were obtained by the full-scale experiments. The errors of the predicted leakage rates by Eq. (11) were between −4.232 % and 3.747 %, and those of the calculated leakage rates by Eq. (14) were −56.865∼−17.329 %. As the pressure increased from 10 kPa to 300 kPa, the errors of the calculated leakage rates by Eq. (14) decreased. The errors mainly resulted from that when full-field experiments were carried out, the leaked gas from the pipe not only diffused in the soil above the pipeline but also in the soil below the pipeline. In the future, the relations could be modified or improved considering the gas dispersion in the soil below the pipeline. 3.4.4. Gas diffusion in the air A gas diffusion model in the air was established, regarding the concentration distribution and leakage rate of methane calculated by the two quantitative relations as the initial and inlet boundary conditions, respectively. The dispersion behaviors in the air could be portrayed and shown to be different to a jet flow, as shown in S2 of SI section. The influencing range of the established atmospheric diffusion model was larger than that of the present model, especially near the ground, which was closer to the actual situation. Definitely, the gas diffusion behaviors of NG in the air needed to be validated by the experiments in the future. 4. Conclusions In this study, a leakage rate estimation model and a methane concentration prediction model were established for buried gas pipelines using experimental and numerical simulation methods, by which two quantitative relations were developed. The following conclusions were drawn: (1) An empirical leakage rate estimation model with air as the medium was established by experimental results, which was validated and modified by the numerical simulation. This model could be applied when the leakage hole diameter, pressure, and soil depth were known, and the errors were −2.2 %–1.1 %. (2) The empirical leakage rate estimation model was improved and modified with the methane as the medium through the numerical simulation results, which were used to fit the relationship between the leakage rate and pressure, leakage hole diameter, soil porosity and soil particle diameter, nonlinearly. (3) A gas diffusion model in the soil was developed by numerical simulation, through which, the influencing factors were explained, including the pressure, orifice diameter and config- uration, soil depth, soil characteristics, and temperature. (4) Quantitative relations for NG leakage and diffusion in the soil were fitted by the numerical results. The errors of the leakage rate predication relation were less than 7.2 %, and the errors of the fitted gas diffusion concentration relation were −14 %–15 %. (5) A gas diffusion model in the air was established, regarding the concentration distribution and leakage rate of methane calculated by the two quantitative relations as the initial and inlet boundary conditions, respectively. The dispersion behaviors in the air could be portrayed and shown to be different to a jet flow. (6) In the future, the established relations should be modified and validated with more experiments with full-scale experimental facilities. (7) If the duration time between the leakage detection and management is known, the leaked gas cloud could be predicted to broadcast a warning of any possible explosion. Declaration of Competing Interest The authors report no declarations of interest. Acknowledgements This work was supported by the National Natural Science Foundation of China [grant numbers 51704317]; the Shandong Provincial Key R D Program [grant number 2019GSF111026]; 562

16. C.Liuetal. Process Safety and Environmental Protection 146 (2021) 552–563 the PetroChina Innovation Foundation [grant number 2018D-5007- 0603]; the Fundamental Research Funds for the Central Universities [grant numbers 19CX07004A]. We are grateful for permission to publish this study. Appendix A. Supplementary data Supplementary material related to this article can be found, in the online version, at doi:https://doi.org/10.1016/j.psep.2020.11. 031. References Anifowose, B., Odubela, M., 2015. Methane emissions from oil and gas transport facilities–exploring innovative ways to mitigate environmental consequences. J. Clean. Prod. 92, 121–133. Bagajewicz, M., Valtinson, G., 2014. Leak detection in gas pipelines using accurate hydraulic models. Ind. Eng. Chem. Res. 53 (44), 16964–16972. Balcombe, P., Brandon, N.P., Hawkes, A.D., 2018. Characterising the distribution of methane and carbon dioxide emissions from the natural gas supply chain. J. Clean. Prod. 172, 2019–2032. Batzias, F.A., Siontorou, C.G., Spanidis, P.-M.P., 2011. Designing a reliable leak bio- detection system for natural gas pipelines. J. Hazard. Mater. 186 (1), 35–58. Bonnaud, C., Cluzel, V., Corcoles, P., Dubois, J.-P., Louvet, V., Maury, M.a., Narbonne, A., Orefice, H., Perez, A., Ranty, J., Salim, R., Zeller, L.-M., Foissac, A., Poenou, J., 2018. Experimental study and modelling of the consequences of small leaks on buried transmission gas pipeline. J. Loss Prev. Process Ind. 55, 303–312. Chen, C.-h., Sheen, Y.-N., Wang, H.-Y., 2016. Case analysis of catastrophic underground pipeline gas explosion in Taiwan. Eng. Fail. Anal. 65, 39–47. Deborah, H.-A., Gaël, B., David, M.C., Claire, S.-M., Renato, F.M., Didier, J., Maud, B., Arnaud, F., Thomas, L., 2018. Consequences of a 12-mm diameter high pressure gas release on a buried pipeline. Experimental setup and results. J. Loss Prev. Process Ind. 54, 183–189. Ebrahimi-Moghadam, A., Farzaneh-Gord, M., Deymi-Dashtebayaz, M., 2016. Corre- lations for estimating natural gas leakage from above-ground and buried urban distribution pipelines. J. Nat. Gas Sci. Eng. 34, 185–196. Ebrahimi-Moghadam, A., Farzaneh-Gord, M., Arabkoohsar, A., 2018. CFD analysis of natural gas emission from damaged pipelines: correlation development for leakage estimation. J. Clean. Prod. 199, 257–271. El-Zahab, S., Abdelkader, E.M., Zayed, T., 2018. An accelerometer-based leak detection system. Mech. Syst. Signal Process. 108, 276–291. European Gas Pipeline Incident Group, 2015. 9th Report of the European Gas Pipeline Incident. Haghighi, A., Covas, D., Ramos, H., 2012. Direct backward transient analysis for leak detection in pressurized pipelines: from theory to real application. J. Water Supply.: Res. Technol. 16 (3), 189–200. Han, G.J., 2014. Research on the Leakage of Buried Gas Pipeline and Diffusion Regu- larity. Chongqing University. Hendrick, M.F., Ackley, R., Sanaie-Movahed, B., Tang, X.J., Phillips, N.G., 2016. Fugitive methane emissions from leak-prone natural gas distribution infrastructure in urban environments. Environ. Pollut. 213, 710–716. Hikoji, W., Toshisuke, H., 1991. Diffusion of leaked flammable gas in soil. J. Loss Prev. Process Ind. 4 (4), 260–264. Ji, T., Qian, X., Yuan, M., Wang, D., He, J., Xu, W., You, Q., 2017. Case study of a natural gas explosion in Beijing, China. J. Loss Prev. Process Ind. 49, 401–410. Jo, Y.-D., Ahn, B.J., 2003. A simple model for the release rate of hazardous gas from a hole on high-pressure pipelines. J. Hazard. Mater. 97, 31–46. Kim, S.O., Park, J.S., Park, J.W., 2019. A leak detection and 3D source localization method on a plant piping system by using multiple cameras. Nucl. Eng. Technol. 51, 155–162. Kostowski, W.J., Skorek, J., 2012. Real gas flow simulation in damaged distribution pipelines. Energy 45 (1), 481–488. Lelieveld, J., Lechtenböhmer, S., Assonov, S.S., Brenninkmeijer, C.A.M., Dienst, C., Fischedick, M., Hanke, T., 2005. Greenhouse gases: low methane leakage from gas pipelines. Nature 434, 841–842. Liu, C., Wang, Y., Li, X., Li, Y., Khan, F., Cai, B., 2020. Quantitative assessment of leakage orifice based on Bayesian network for gas pipelines. Reliab. Eng. Syst. Safe., submitted. Lu, L., Zhang, X., Yan, Y., Li, J., 2014. Theoretical analysis of natural-gas leakage in urban medium-pressure pipelines. J. Environ. Hum. 1 (2), 71–86. Montiel, H., Vı́Lchez, J.A., Casal, J., Arnaldos, J., 1998. Mathematical modelling of accidental gas releases. J. Hazard. Mater. 59 (2–3), 211–233. Morgan, E.G., Adrian, D., Robert, C.A., Kaiguang, Z., Nathan, P., Robert, B.J., 2015. Natural gas pipeline replacement programs reduce methane leaks and improve consumer safety. Environ. Sci. Technol. Lett. 2, 286–291. Nithiarasu, P., 1999. Finite element modeling of a leaking third component migration from a heat source buried into a fluid saturated porous medium. Math. Comput. Model. 29 (4), 27–39. Okamoto, H., Gomi, Y., 2011. Empirical research on diffusion behavior of leaked gas in the ground. J. Loss Prev. Process Ind. 24 (5), 531–540. Parvini, M., Gharagouzlou, E., 2015. Gas leakage consequence modeling for buried gas pipelines. J. Loss Prev. Process Ind. 37, 110–118. Robert, B.J., Adrian, D., Nathan, G.P., Robert, C.A., Charles, W.C., Desiree, L.P., Kaiguang, Z., 2014. Natural gas pipeline leaks across Washington, DC. Environ. Sci. Technol. 48, 2051–2058. Tang, B.J., Tian, G.S., Zhang, Z.G., Xue, H.Q., 2009. Model for leakage and diffusion of buried gas pipeline. Gas and Heat 29 (5), 1–5. Van Fan, Y., Perry, S., Klemeš, J.J., Lee, C.T., 2018. A review on air emissions assessment: transportation. J. Clean. Prod. 194, 673–684. Xie, Y.S., Wang, T., Lv, L.H., Bai, Y.Q., Song, B.X., Zhang, X.F., 2015. Full-scale experiment of diffusion behaviors of city pipeline gas in soils. Nat. Gas Ind. B 35 (8), 106–113. Xiong, Z.H., Li, Z.L., Gong, J., Li, K., 2012. A model for underground pipeline small leakage and its numerical solution. Acta Petrol. Sin. 33 (3), 493–498. Yan, Y., Dong, X., Li, J., 2015. Experimental study of methane diffusion in soil for an underground gas pipe leak. J. Nat. Gas Sci. Eng. 27, 82–89. Zhang, P., Cheng, S.J., 2014. Study on small micropore leakage in buried gas pipeline. China Safe. Sci. J. 24 (2), 52–58. Zhou, X., Li, K., Tu, R., Yi, J., Xie, Q., Jiang, X., 2016. A modelling study of the multiphase leakage flow from pressurized CO2 pipeline. J. Hazard. Mater. 306, 286–294. 563

Buried Natural Gas Pipe Line Leakage – Quantifying Methane Release and Dispersion Estimations

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Similar to Buried Natural Gas Pipe Line Leakage – Quantifying Methane Release and Dispersion Estimations

Similar to Buried Natural Gas Pipe Line Leakage – Quantifying Methane Release and Dispersion Estimations (20)

Recently uploaded

Recently uploaded (20)

Buried Natural Gas Pipe Line Leakage – Quantifying Methane Release and Dispersion Estimations