Experimental and OLGA Modeling Investigation for Slugging in Underwater Compressed Gas Energy Storage Systems

Abstract

Underwater compressed gas energy storage (UW-CGES) holds significant promise as a nascent and viable energy storage solution for a diverse range of coastal and offshore facilities. However, liquid accumulation in underwater gas pipelines poses a significant challenge, as it can lead to pipeline blockages and energy transmission interruptions and adversely impact pipeline operation. In this paper, experimental and Oil and Gas Assays (OLGA) simulation studies have been conducted on the formation process of slug flow in pipelines. Firstly, experiments are conducted to capture high-speed camera images of slug flow under various liquid accumulation volumes and inclination angles. Subsequently, an OLGA model is developed to verify the experimentally observed flow regime, pressure, and slugging speed. Therefore, the flow regime verification results exhibit substantial consistency, and pressure variations display uniform trends, with an average slugging velocity error of 6.42%. The results indicate that the formation of slug flow involves three distinct stages: slug flow growth, ejection, and backflow. By analyzing slug flow, it can gain insights into the relationship between pressure and slug flow formation, exposing the sensitivity of this phenomenon to pressure fluctuations. These results further enhance recognition of the operational status of UW-CGES pipelines and provide support for safe operation.

1. Introduction

Underwater compressed gas energy storage (UW-CGES) is a novel technology that compresses and stores gases, such as air, natural gas, hydrogen, etc., underwater for energy storage. This technology involves delivering pressurized gas into underwater storage tanks where it is stored. Upon demand, the compressed gas can be conveyed through pipelines to power plants or other equipment for electricity production or other applications [1,2,3]. UW-CGES is accomplished through two distinct methods, cavern-style and tank-style, as displayed in Figure 1. Cavern-style involves utilizing natural underwater caverns or mines to store and manage energy. However, this approach requires specific geological conditions, reducing its applicability.

Conversely, tank-style employs submerged tanks for storing compressed gas [4,5,6,7]. The process involves compressing the gas, treating the tank for anti-corrosion and insulation, and transporting the compressed gas via pipelines to power plants or other facilities for energy release. Tank-style storage has advantages such as affordable construction, widespread commercialization, and mature technological development.

In underwater compressed gas energy storage pipelines, a liquid accumulation may form due to gas supersaturation, temperature changes, water presence, and high gas flow rates [8,9,10,11]. The specific reasons can be elucidated as follows:

• Supersaturation of the gas inside the pipeline causes liquefaction and the formation of a liquid layer at the bottom.
• Temperature changes lead to the cooling of gas inside the pipeline, causing partial liquefaction and accumulation.
• Water is transported gas may react with cooled gas at the bottom of the pipeline, causing a liquid layer to form.
• High gas flow rates induce unstable gas movement, promoting localized pressure changes and the consequent liquefaction and accumulation of some gas at the pipeline bottom.

The occurrence of liquid accumulation in pipelines may generate local blockage, which elevates pressure and friction within the pipeline, ultimately leading to a more profound issue of slug flow [12,13,14]. The motion of slug flow in pipelines presents complex regimes that can engender erosion and wall damage, contributing to further corrosion and wear. Additionally, slug flow may give rise to acutely sharp pressure waves within pipelines that lead to violent gas-liquid media oscillations and consequential noise and vibration. Failure to promptly maintain and clean pipelines can lead to grave incidents such as blockages and explosions caused by slug flow [15,16,17,18].

Currently, significant progress has been made in investigating the flow characteristics, motion laws, influencing factors, and other aspects of slug flow through numerical simulation [19,20,21], laboratory testing [22,23,24], and field observation [25,26,27]. Furthermore, some studies are dedicated to developing innovative technologies and devices for preventing and mitigating slug flow, which can enhance the effectiveness and safety of transport pipelines. Laboratory testing is a valuable tool for investigating the flow characteristics and motion laws of slug flow. However, it is essential to concede its potential limitations. For instance, reproducing the complex and dynamic environmental factors in field settings is challenging.

Additionally, the experimental apparatus used can impact the fluid, introducing errors in the experimental results. Given that liquid slug flow’s formation, evolution, and motion processes are highly intricate, precise experimental parameter design and measurement method adjustment are necessary to obtain accurate and reliable data. Hu et al. [28] performed within a small-scale air-water test circuit, observing three distinct stages: slug formation, gas blowout, and transition. The research revealed a strong correlation between the spatiotemporal dynamics of flexible catenary risers and the severity of slug flow stages, liquid slug length, and liquid accumulation along the riser. Some scholars have established a mapping relationship between pressure and slug flow. Zhu et al. [29] performed a non-invasive analysis of slug flow vibration in a curved flexible riser. Notably, the researchers identified that the primary source of vibration induced by the slug flow was localized to the curved surface of the flexible riser. The dynamic response of the riser was influenced by fluctuations in slug flow pressure within the pipeline. Kim and Kim [30] examined pressure drop in slug flow using air and low-viscosity mineral oil in a 4 cm inner diameter pipe. They merged visual observations and pressure drop oscillation time analysis into a theoretical slug flow model for total pressure gradient prediction. AL-Dogail et al. [31] studied slug flow pressure with air and water. Pressure sensors distributed along the pipeline enabled statistical and regression analysis, revealing slug flow behavior traits.

On this basis, the investigation of slug flow commonly involves a combination of numerical simulation and visualization experiments [32,33,34]. Specifically, some studies quantify the movement speed and acceleration characteristic values of micro-scale gas-liquid interfaces under pulsating conditions. Comparison of experimental results with simulation models enables validation of model accuracy. Jiang et al. [35] analyzed the gas-liquid slug flow in a honeycomb micro-channel reactor using computational fluid dynamics (CFD) and micro-particle image velocimetry (micro-PIV). Liquid slug breakups caused non-uniform pressure and gas velocity, increased turbulence and altered residence time distribution. Cao et al. [36] investigated the effect of an elbow on slug flow at different velocities using experiments and CFD simulations. The results showed that higher liquid and gas velocities increased the number of bubbles in the elbow and film velocity. Sergeev et al. [37] proposed a pipeline solution for transitioning the two-phase flow regime using a streamlined mesh partition, achieving lower pressure drop and increased safety with minimal energy costs.

CFD simulation using Reynolds-averaged Navier-Stokes equations and k-ε models supported the feasibility of the proposed solution. However, the CFD model relied heavily on limited experimental data on fluid properties and operating conditions or ineffective assumptions, diminishing accuracy. Based on this, Valdés et al. [38] used a 3D-CFD model with Star-CCM+ software to assess non-complex drift velocity correlations, proving the accuracy with an average absolute relative error of only 6%, including highly viscous fluids. For the establishment of drift flux models, Pugliese et al. [39] implemented OpenFOAM CFD software to derive model parameters for drift flux, enabling the creation of constitutive equations for various scenarios. The CFD modeling accurately simulated slug flow in pipelines when validated against experimental data. Several scholars mentioned above have developed CFD models to enhance the simulation of slug flow in pipelines. It is worth noting that CFD has advantages in simulating slug flow in small pipelines, including multiphase flow simulation, complex geometry modeling, flow and pressure field computation and analysis, prediction of vortices and turbulence, and visualization of flow parameters. However, CFD simulation has limitations when applied to long-distance gas and energy storage pipelines. For instance, the high computational power issues caused by complex structures, model accuracy issues due to possible inaccurate data, problems of assumptions made in CFD models and reliability assessment issues.

OLGA demonstrates distinct advantages in simulating long-distance pipelines and energy storage pipelines. Specifically, it offers a methodology to optimize the design and evaluate system performance by considering crucial factors such as storage medium type, pipeline length and height, and pressure. OLGA can simulate diverse fluid behaviors, including single-phase, multi-phase flow, and sediment transport. Moreover, OLGA features fast computation and precise forecasting of complex flows, dynamic changes, and transient responses inside the pipeline. Mesa et al. [40] used OLGA software to simulate experiments and predict vibration caused by slug flow in risers and subsea pipelines. OLGA and experimental data were compared using OrcaFlex for vibration analysis, revealing differences in bubble density and flow field. Kim et al. [41] evaluated corrosion inhibition severity by random forest (RF) predicting maximum slug lengths (MSL) with OLGA pipeline simulation and shale gas field well geometry. The MSL was projected onto a 3D map as the output of RF and had satisfactory results in trained RF. He et al. [42] used OLGA7.0 to study gas-liquid flow regimes in hilly terrain pipelines, identifying four regimes. OLGA7.0 accurately predicted severe slugging and stable flow but had poor accuracy for dual-peak slug and oscillating flow with insufficient sensitivity to gas changes. Ganat and Hrairi [43] utilized an OLGA simulator to predict the flow regimes in vertical pipes of 35 oil wells, and the results showed good consistency between the predicted and measured oil flow rates. The impact of flow regime changes on accuracy was minimal, and the possible variations between oil rate measurements were emphasized. Vandrangi et al. [44] tested pipeline leak detection with OLGA software, and leaks ranging from 0–50%. Large leaks caused the pressure/mass flow rate to decrease, while temperature initially dropped and rose after 25%. OLGA has extensive applications in long-distance and storage pipelines, exhibiting efficacy in flow regime identification, slug flow characteristics analysis, pipeline corrosion, and leakage detection.

The present study aims to model and analyze the dynamic process of slug flow formation in pipelines by combining experiments and OLGA software. Initially, high-speed camera experiments are performed to observe slug flow formations under various liquid accumulation volumes and incline angles. Then, an OLGA model is constructed to confirm the observed flow regime, pressure, and velocity. Finally, the formation stages of slug flow are investigated, and the sensitivity of slug flow to pressure fluctuations is analyzed. The contribution of the article is summarized as follows. Firstly, an experimental setup is established to simulate energy storage gas transmission pipelines, enabling the collection of pipeline pressure data that elucidates the genesis of slug flow. This allows for the categorization of slug flow stages based on pressure dynamics. Subsequently, OLGA software is employed to simulate the energy storage gas transmission pipeline, facilitating an analysis of slug flow formation. A meticulous comparison and scrutiny of flow regimes, pressure variations, and slugging velocities against experimental results are carried out, resulting in a notable alignment between the two. Ultimately, the synergistic integration of the OLGA model and experimental findings effectively elucidate the intricate progression of liquid accumulation in energy storage gas transmission pipelines. This comprehensive approach supplements research into compressed gas energy storage systems, contributing substantively to the field.

This paper is structured as follows. Section 2 introduces the test rig and outlines the experimental procedure. Section 3 describes the OLGA model used in this study. Section 4 presents the experimental results and provides a comprehensive analysis of the data obtained from the OLGA simulation. Finally, the conclusions and expectations are provided in Section 5.

2. Experiment

2.1. Test Setup and Instrumentation

The slug flow experimental investigation is examined in a pipeline situated in hilly terrain, as represented in Figure 2. The experimental arrangement consists of a test section, an air supply pipeline, an image acquisition device, and a data acquisition system, as displayed in the figure. The test pipe is constructed from organic glass and possesses dimensions of 26 mm inner diameter, 32 mm outer diameter, and a length of 6600 mm. Aluminum pipe clamps are employed to support the horizontally and inclined pipes, which are connected with organic elbows at angles of 5°, 10°, 15°, and 20° within the test section. This configuration simulates a section of low-lying resembling a hilly terrain.

For the test, the compressed air flow is furnished by an Atlas Copco air compressor and tank with a 1.5 m³ capacity. Monitoring of the gas flow rate is done using the FESTO-565406 sensor, which possesses ±0.3% accuracy. To regulate the inlet velocity in the pipeline, a pressure-reducing valve (IR3020-03) is employed. This valve offers a range of 0.01 to 0.8 MPa and a sensitivity of 0.2%. Moreover, pressure is measured using the MPM489 sensor, with an accuracy of ±0.5%, installed at P1, P2, P3, and P4, as demonstrated in Figure 2.

The sensors in this study are linked to a data acquisition instrument and a computer system consisting of an Advantech industrial computer IPC-610L and an acquisition card PCI-1710U. For visualizing the movement of slug flow under optimal lighting conditions, an imaging system is employed, which incorporates a high-speed camera with a 50 mm f/1.8D lens. This camera possesses a resolution of 1920 × 1020 pixels and a capture rate of 1500 frames per second. The ambient temperature of the laboratory is maintained at approximately 25 °C, and the physical properties of the experimental fluid, including density and viscosity, are unaffected by the prevailing temperature and humidity. A summary of the fluid parameters is provided in

Table 1. Physical parameters of fluids.

	Water	Air
Density	997.05 kg∙m−3	1.184 kg∙m−3
Kinetic Viscosity	8.9008 × 10−4 Pa∙s	1.849 × 10−5 Pa∙s
Surface Tension	Air/Water = 0.07197 N∙m−1

.

2.2. Experimental Process

During the experimental investigation, water volumes of 50 mL, 80 mL, 100 mL, 200 mL, and 300 mL were injected into the pipe. The water is dyed blue to enhance the visibility of liquid slug movements. The compressor is activated to regulate the pipeline pressure, followed by a gas injection to capture the formation and movement of slug flow while recording pressure variations. The high-speed camera also monitors the slug flow formation at different inlet gas velocities, liquid volumes, and pipe inclination angles. Cleaning the pipeline and recycling the used liquid concluded the experiment, which gained insight into pressure oscillations during liquid accumulation in the concave pipe, leading to the formation of slug flow.

3. OLGA Modeling

This study employed the OLGA 2020.1.0 software to simulate multiphase flow within experimental pipelines. To enhance the accuracy of predictions, this version of OLGA utilizes a comprehensive slug tracking model to simulate the erratic behavior of slugs over an extended period. The concrete procedures of OLGA software modeling are illustrated as follows.

3.1. Pipeline Model

The system configuration, as depicted in Figure 3, is composed of an inlet (closed node), a source (fluid source), a flow path (pipeline), and an outlet (pressure node). During the experiment process, stable fluid within the pipeline is directly modeled via the implementation of a fluid source within OLGA. The geometric construction of the experimental pipeline is exemplified in Figure 4, consisting of five delineated sections with dimensions consistent with the experimentally established pipeline. For a comprehensive exploration of fluid flow within the pipeline, each section is subdivided into nodes, represented through flow paths within OLGA’s interface. Integration of a recovery device facilitates the collection and subsequent utilization of accumulated liquid, with the removal of this feature within the simulation process having a negligible impact on the analysis of slug flow characteristics in the pipeline. In consideration of enhancing OLGA’s simulation efficiency, this section with a single outlet node is implemented.

3.2. Fluids PVT Description

In the context of simulation utilizing OLGA, it is critical to construct a fluid property file that precisely encompasses the properties of the experimental medium under examination. This process necessitates the use of PVTsim19.2, which offers the demanded fluid property parameter values, contingent upon both temperature and pressure, as single-valued functions. Throughout the simulation, the essential parameter values are obtained through an interpolation scheme, which leverages the temperature and pressure of individual data points. To ensure accuracy and prevent errors on the pressure and volume temperature (PVT) tables, the pressure and temperature ranges were expanded while inputting data to the PVT tables. Specifically, the pressure range was set to 0–20 bar, while the temperature range was set to −20 to 100 °C. The composition of the air is detailed in

Table 2. PVTsim physical parameters of gas.

Component	Mole Fraction (%)	Density (kg∙m−3)
N2	78.126	1.184
O2	20.907
Ar	0.934
CO2	0.033

.

3.3. Boundary Conditions

Table 3. The default value of simulation in OLGA.

	Flow Model	Setting
Overall setting	TEMPERATURE	WALL
	STEADYSTATE	ON
	MASSEQCHEME	1STORDER
	COMPOSITIONAL	OFF
	NOSLIP	OFF
	PHASE	THREE
	HYDSLUG	ON
	SLUGVOID	AIR
	TABLETOLERANCE	ON
	FLASHMODEL	WATER
Integration	Simulation start time	0 s
	Simulation stop time	30 min
	Minimum time step	0.001 s
	Maximum time step	0.5 s

illustrates the default settings of the OLGA simulation model. The TEMPERATURE model relies on ‘WALL’ selection for temperature calculation, whereas the STEADYSTATE preprocessor necessitates temperature calculation (ON). MASSEQCHEME mass equation numerical discretization employs ‘1STORDER’. The COMPONENTAL component tracking model invokes PVT tables for calculation and does not track during simulation. Minimization of simulation errors is enabled by setting NOSLIP to ‘OFF’ to account for sliding between air and water in the pipeline. OLGA restricts fluid phases in the tube to single-phase or three-phase only, with this model set to three-phase and a zero-volume fraction for the third phase (with no impact on simulation). Due to slug flow in the pipe, the simulation adopts ‘ON’ for HYDSLUG. The bubble porosity phase relationship model is set to ‘AIR’, whilst FLASHMODE provides a mass transfer model for air and water, with ‘WATER’ selection indicating mass transfer between the two. TABLETOLERANCE is set to ‘ON’ during PVT table operations to prevent exceeding temperature and pressure limits established within the simulation’s PVT file.

The present simulation incorporates variable time steps, ranging from 0.001 to 0.5 s, determined by assigning the minimum value to secure actual simulation time and the maximum value to prohibit probable errors attributable to PVT tables. Initialization data is acquired to secure computational convergence during the simulation’s preliminary stages. The simulation runs for a total period of 30 min.

The flowchart of this study is shown in Figure 5, from which the structure and method of this article can be clearly understood.

4. Results and Discussion

4.1. Experimental Results

Pressure fluctuation can be used to predict the initiation mechanism of slug flow. In this study, pressure fluctuation measurement is used to verify the characteristics of slug flow. The flow process of slug flow can be rigorously divided into three distinct stages, viz., the generation of slug flow, the eruption of slug flow, and the flow back of slug flow, as eloquently demonstrated in Figure 6. The initial phase of slug flow generation is also precisely illustrated in Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13 and Figure 14, as shown in green and purple boxes in Figure 6. The subsequent slug eruption process can be visually perceived in Figure 15, Figure 16, Figure 17 and Figure 18, as displayed in the orange box in Figure 6. Ultimately, the process of slug flow back has been elucidated meticulously in Figure 19, Figure 20, Figure 21 and Figure 22, as presented in the black box in Figure 6.

Figure 7 and Figure 8 represent the pressure fluctuation of liquid accumulation initiation movement in the tube. The case corresponds to gas velocity (V_GS) = 5.08 m/s, liquid accumulation of 200 mL, and angle θ = 20°. When the gas is introduced, and the liquid accumulation in the pipe begins to move, its pressure fluctuates without any regularity, showing a saw-tooth fluctuation signal, as displayed in Figure 7 and Figure 8. Observing the figures, it can be inferred that the pressure peak at P3 is higher than at P1 and P2. It is attributed to P3 being located at the elbow connection, with the horizontal pipe section on the left and the inclined section on the right, as shown in Figure 9. As gas flows through the pipe, the static liquid accumulation surface experiences a progressive destabilization, leading to small amplitude waves (indicated by the red ellipse in Figure 9). This wave formation leads to a gradual increase in the volume of liquid accumulation at P3. Consequently, the reduced gas flow area results in higher pressure at P3 compared to pressures at P1 and P2. The cause of P1 being slightly larger than P2 is due to P1 being closer to the gas inlet and P2 being farther away, with the same flow cross-sections of the two places, the gas has a slight pressure loss at P2.

Comparing Figure 7 and Figure 8, the pressure of P4 is less than P1, P2, and P3. It is because P4 is in the middle of the inclined pipe section, and no liquid slug appeared in this section, as shown in Figure 10. Due to the narrowing of the gas flow section at P3, P4 has a smaller gas volume and a larger cross-section in the pipe than P1 and P2, so its pressure is less than P1 and P2.

Figure 11 shows the pressure fluctuations at liquid accumulation initiation. As gas ingress persists, the liquid in the pipe blocks the elbow, causing the pressure at P3 to increase sharply, and then the pressures at P1 and P2 also increase, as shown in Figure 11. It shows that the pressure fluctuation changes of P1, P2, and P3 are similar in Figure 11. The cause of the liquid level at the elbow rising and touching the top of the pipe is the inclined pipe blocks the downstream movement of the liquid slug, as can be seen from the red ellipse in Figure 13. With a fixed cross-section, the increase of gas velocity leads to increasing pressure, and the blockage at the elbow enhances this pressure rise. However, the pressure loss in the pipeline is also enlarged, which can be inferred by comparing P1 and P2 in Figure 7 and Figure 11. There is an increase in average pressure for liquid accumulate initiation compared to initiation movement. It can be seen from Figure 11 and Figure 12 that with the continuous influx of gas, the amplitude and frequency of pressure fluctuation in the pipeline increase. Similar to liquid accumulate initiation, the fluctuation of initiation movement is also an irregular saw-tooth wave.

Figure 12 represents the pressure fluctuation of P4 at liquid accumulation initiation. Compared with initiation movement, the pressure fluctuation of P4 at this moment decreases sharply. At this time, there is no liquid slug formed in the inclined pipe section, but some liquid exists at the bottom of this section, see Figure 14. The critical state of slug flow in the pipe is presented in Figure 14. The main reason for the decrease of pressure at P4 is that the liquid slug at P3 is blocked, resulting in a small amount of gas flowing up the inclined section, which reduces the pressure.

The gas continued to flow in so that the liquid accumulated at the elbow was sprayed upward in the form of a slug, and the pressure change of the horizontal pipe is shown in Figure 15. The pressures at P1, P2, and P3 are smaller than the corresponding pressure for the liquid accumulation initiation case, with multiple pressure peaks. Compared with P1 and P2, the pressure wave peak of P3 is higher, and so is the frequency. There is a gap at the top of the pipe at P3, the appearance of the gap reduces the pressure in the horizontal section, as highlighted by the red ellipse in Figure 17. Compared with the initial blockage, after some liquid slugs are discharged, the amount of liquid accumulation in the section decreases, and the blockage height is somewhat reduced.

The pressure fluctuation at P4 at the appearance of slug flow is presented in Figure 16. With the eruption of slug flow, a large slug occurs in the inclined section, as highlighted by the yellow ellipse in Figure 18. Due to a large amount of gas and liquid being mixed in the pipe, and the occurrence of slug flow, the pressure at P4 increases sharply. It can be observed that the pressure fluctuation at P4 shows periodic regularity in Figure 16. Compared with the fluctuation amplitude at P1, P2, and P3, the fluctuation amplitude at P4 is larger, and the frequency is smaller. The reason is that the liquid accumulation at the elbow compresses the air and stores a larger pressure to carry a larger gas pressure when it leaves. Thus, the liquid slug rushes into the up-dip pipe. Occupying the pipe flow area in a short time, when compressing the air again, increases the pressure in the pipe.

Following slug flow eruption, only a fraction of the slug exits the pipeline while the rest flows back, leading to a subsequent rise in pressure at P1, P2, and P3, as depicted in Figure 19. As can be seen from Figure 14 and Figure 18, the pressure fluctuations at P1, P2, and P3 in the eruption of slug flow are weaker than the flow back of slug flow. The liquid slug eruption causes a flow back, leading to accumulation at the elbow, represented by the red ellipse in Figure 21. Nonetheless, the level of accumulated liquid is lower compared to its previous state.

After part of the slug flows back, the pressure fluctuation at P4 is displayed in Figure 20. At this time, the accumulated liquid at the elbow in the pipe is not enough to make the slug rush out of the pipe section. Thus, the regular fluctuation in the pipe section persists, as depicted in Figure 20. Since there is still a small liquid slug in the inclined tube, the pressure at P4 is greater than that at P1, P2, and P3. However, compared to the case with the eruption of slug flow, the pressure fluctuating amplitude is lower and the frequency is smaller. Figure 22 shows the liquid slug leaving at P4 and the remaining liquid slug flow backs along the pipe as highlighted by a yellow ellipse.

Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17, Figure 18, Figure 19, Figure 20, Figure 21 and Figure 22 reveal that before the slug flow occurs, the pressures at P1, P2, and P3 increase and present an irregular saw-tooth wave. The pressure at P4 is decreased and presents an irregular saw-tooth wave. After the occurrence of slug flow, the pressures at P1, P2, and P3 gradually decrease, showing a mixture of saw-tooth waves and square waves. However, different from P1, P2, and P3, the pressure wave at P4 always shows regularities. After the formation of the first slug flow, the liquid accumulated at the elbow eventually reaches the top of the pipe, increasing the pressure at P1, P2, and P3 and a decrease in the pressure at P4. After some slugs flow out of the pipe section, the liquid level at the elbow can also cause slug flow without touching the top of the pipe, and the pressure at P1, P2, and P3 decreases, while the pressure at P4 only decreases slightly due to the presence of the small amount of slug in the pipe.

4.2. Simulation Results and Comparisons

4.2.1. Flow Regime Analysis and Comparisons

The dynamic modeling steps of OLGA are described in Section 3. In Section 4, a comparative analysis of the entire process of slug flow formation in the experimental and OLGA models will be conducted. The figures presented in this section (i.e., Figure 23, Figure 24, Figure 25 and Figure 26) have been compared with Figure 9, Figure 10, Figure 13, Figure 14, Figure 17, Figure 18, Figure 21 and Figure 22, respectively. It is demonstrated that the OLGA software accurately replicates the formation of slug flow by undergoing three essential phases, slug generation, slug injection, and slug flow back, consistent with the experimental outcomes. In Figure 23, Figure 24, Figure 25 and Figure 26, the red dotted circle indicates the flow diagram at the pipeline’s elbow position (P3), while the yellow dotted circle specifies the flow diagram in the pipeline’s middle (P4) of the upwardly inclined pipe. Notably, the simulation diagram does not emphasize the detailed flow during the slug flow’s formation process, which relates to the node selection in the simulation software. Generally, an increase in the number of nodes arranged on the pipeline provides a more detailed description of the flow. However, this approach also leads to an increment in calculation time and a reduction in operational efficiency.

The flow regime (ID) diagram depicted in Figure 27 provides a comprehensive illustration of the slug flow formation process. The black dotted line represents the geometric model of the pipe, while the yellow line indicates the initiation movement of slug flow, wherein an ID of 1 is observed throughout the pipeline, suggesting a lack of slug flow. The blue line corresponds to the liquid accumulation stage, where a significant liquid slug is identified at the pipe elbow position (P3), with an ID of 3 at this location and an ID of 1 at other positions. The green line showcases the flow regime in the pipeline post slug flow occurrence. At this stage, the ID in the pipeline between P3 and P4 is observed to be 3, while an ID of 1 is noted in other positions. Lastly, the red line represents the flow regime of slug flow backflow in the pipe, with an ID of 3 observed in the upwardly inclined pipe and 1 in other positions.

4.2.2. Pressure Analysis and Comparisons

The pressure fluctuation signal at P3 in the pipeline is analyzed in Figure 28, presenting a comparative evaluation between the experimental and OLGA simulation results. The thick and solid blue lines represent the experimental results, while the thin and solid blue lines depict the OLGA simulation results. Furthermore, the red dotted lines display the experiment’s three stages of slug flow formation, while the red solid lines reveal the same stages in the OLGA simulation. The slug flow formation stage’s duration is comparable in the experiment and simulation. However, during the slug eruption and flow backstage, the experiment’s duration surpasses the simulation’s. As a result, the period from slug generation to discharge is lengthier in the experiment than in the OLGA simulation.

Moreover, the experiment’s pressure values are slightly higher than the simulation, and the formation pressure of each slug in the experiment is not entirely consistent. In contrast, the pressure fluctuations of each slug formation cycle in the simulation remain relatively consistent. It is crucial to highlight that the experimental and simulation results’ discrepancies may arise from installation errors, measurement errors, and environmental factors, but they may not potentially impact the slug flow formation stage analysis in this study.

4.2.3. Gas Velocity Analysis and Comparisons

The present study investigates the critical velocity of slug flow in a pipe, examining the effects of liquid accumulation volumes and pipe angles. Experimental results are presented in Figure 29, which displays the slugging speeds at different angles when the liquid accumulation volume is 50 mL, 80 mL, 100 mL, 200 mL, and 300 mL, represented by the blue, red, yellow, purple, and green dotted lines, respectively. It is revealed that an increase in the angle of the pipe leads to a higher slugging speed, as the inclined surface generates greater frictional forces that require an increased amount of kinetic energy from the slug. Additionally, a decrease in the critical velocity of slug flow is observed as the volume of liquid accumulation increases. This result can be attributed to the proximity of larger liquid volumes to the top of the pipe, increasing the likelihood of interface fluctuation touching the top of the pipe. Consequently, the accumulation of liquid at the elbow occurs when gas enters the pipe, and the fluctuation amplitude reaches the top of the pipe, triggering slug flow.

The critical slug velocity of 200 mL of liquid accumulation at different angles using OLGA simulation, as depicted in Figure 30. The blue, red, yellow, and purple lines in the figure represent slugging speeds corresponding to pipe inclination angles of 5°, 10°, 15°, and 20°. The results indicate that the critical slug velocity increases as the pipe angle increases, owing to the increased friction in the inclined pipe, requiring greater kinetic energy from the slug to overcome it. The experimental slugging speeds of 200 mL of accumulated liquid at 5°, 10°, 15°, and 20° are 3.71 m/s, 4.26 m/s, 5.79 m/s, and 7.65 m/s, respectively. In contrast, the OLGA simulation slugging speeds for the same volume of accumulated liquid at 5°, 10°, 15°, and 20° are calculated as 3.423 m/s, 4.138 m/s, 6.85 m/s, and 9.404 m/s, respectively. The comparison of experimental and simulation results showed errors of 8.38%, 2.95%, 15.47%, and 18.65%, respectively.

Table 4. Comparison of slugging velocity.

Liquid Volume (mL)	Angle (°)	OLGA (m/s)	Experiment (m/s)	Error (%)
50	5	5.51	5.72	3.81
	10	6.29	6.11	2.86
	15	7.34	7.14	2.72
	20	9.73	10.65	9.45
80	5	3.95	4.31	9.11
	10	4.89	5.24	7.16
	15	7.09	6.88	2.96
	20	8.69	9.05	4.14
100	5	3.75	4.02	7.2
	10	4.61	4.98	8.03
	15	6.42	6.21	3.27
	20	7.89	8.13	3.04
200	5	3.423	3.71	8.38
	10	4.138	4.26	2.95
	15	6.85	5.79	15.47
	20	9.404	7.65	18.65
300	5	2.56	2.34	8.59
	10	3.04	2.91	4.28
	15	3.88	3.96	2.06
	20	4.91	5.12	4.27

represents the comparison results of the slug flow critical speed experiment and OLGA simulation for other types of liquid accumulations. Despite significant errors under individual fluid accumulation volume conditions, there are also instances where the errors are small. The analysis and comparison of the critical velocity of slug flow under five types of fluid accumulation volume and four pipe incline angles revealed an average error of 6.42%.

Overall, the comparison between the experimental and OLGA simulation results shows good agreement regarding slug flow formation and propagation. The simulation results also provide a more detailed understanding of the fluid dynamics and flow behavior during slug flow formation, which can be useful for optimizing production processes and designing pipelines.

OLGA’s precision in forecasting intricate slug flow dynamics can be compromised, particularly within scenarios characterized by severe slugging or abrupt alterations in flow regimes. In the context of lengthy subaqueous compressed gas energy storage pipelines, this can impede accurate slug flow prediction. Enhancing the OLGA model’s efficacy in underwater pipelines necessitates the incorporation of pragmatic instances of extensive gas transportation, thereby refining the model’s capacity to anticipate fluid behavior in this unique context.

5. Conclusions

To establish a mapping relationship between the formation process of slug flow in pipeline segments and the pressure inside the pipeline, a multi-faceted approach was taken in this study. Firstly, an experiment was constructed to investigate the slug flow formation process under different liquid accumulation volumes and inclination angles using air and water as flowing media. Secondly, OLGA simulation software was implemented to verify the flow regime, pressure, and slugging speed of the slug flow in the experiment, demonstrating a high level of agreement between the simulation and experiment. Finally, high-speed cameras were utilized to capture the formation process of slug flow and compared with the OLGA simulation. The experimental and simulation results indicate that the formation of slug flow was a complex process that involves three distinct stages: the growth of slug flow, the ejection of slug flow, and the flow back of slug flow. Through the analysis of the experimental and simulation studies, the relationship between the formation process of slug flow and pressure inside the pipeline was explained, revealing the sensitivity of the appearance of slug flow to pressure. Specifically, the findings allow for an enhanced understanding of the intricate relationship between the formation process of slug flow and pressure. These outcomes provide valuable theoretical support for identifying slug flow through pressure signals and improving our understanding of the safe operation of underwater compressed gas energy storage system pipelines.