Numerical Study and Optimization of Speed Control Unit for Submarine Natural Gas Pipeline Pig

Abstract

The speed control of a pipeline inspection gauge (PIG) directly affects the quality of the comprehensive inspection of submarine pipelines. However, the mechanism of the gas flow behavior in a pipeline under the influence of a pig speed control valve is not well understood. In this study, the driving differential pressure of a pig was modeled based on the building block method and numerical simulations. For the first time, the influence of the pressure and flow rate of the gas in a pipeline on the torque of the speed control valve opening process was studied. The results show that when the opening angle of the speed control valve increased from 4.5° to 22°, the gas differential pressure reduced from 1325 to 73 kPa, realizing a 94.5% pressure reduction. In addition, the torque of the bypass valve increased from 7.7 to 2470 Nm during the closing process. The pressure and flow rate increases were directly correlated with increased torque. The established experimental system for torque measurement confirmed the numerical analysis results. By clarifying the law of torque variation, this study provides theoretical guidance for the structural design and control scheme of a pig speed control unit.

1. Introduction

Submarines contain large amounts of natural gas. With the rapid development of deep-sea oil and gas, the scale of subsea gas extraction and transportation is increasing rapidly, creating several special subsea production challenges [1]. Pipelines are the most important means of transportation in the oil and gas industry and link production to the processing. Long-distance pipelines require regular cleaning and comprehensive inspections to ensure safe pipeline operation [2]. The maintenance, cleaning, and inspection of pipelines are usually performed using a cylindrical or spherical pipe cleaning device. The Dutch-Shell Group of Companies was the first to successfully develop a pipe-cleaning machine with an inspection function that allowed simple pipe inspection and cleaning [3]. As an important means of maintenance in oil and gas pipeline transportation, intelligent pipeline inspection gauges (PIGs) equipped with non-destructive testing (NDT) technology are of considerable significance for pipeline safety [4]. A pig with a detection function is also an important part of an intelligent submarine pipeline system and is an important means of guaranteeing the safe operation of submarine pipelines [5]. This in-line inspection method is highly regarded for its accuracy and ability to provide comprehensive health assessments with minimal disruption to pipeline operations. [6]. For pipeline in-line inspection operations, the most important condition for obtaining accurate and effective measurement results is ensuring that the traveling speed of the pig is stable. The ideal traveling speed for conventional inspection techniques is relatively stable in the range of 0.5–4 m/s [7]. Although the range of fluid flow rates in pipelines is extremely variable, natural gas pipelines often contain gas flow rate variations ranging from 0 to 15 m/s. This causes operational problems such as excessive pig velocity and oscillation [8,9]. A pig traveling too fast can damage the pipe or itself, thereby introducing a significant safety risk [10]. In addition, the unstable speed invalidates the data collected from pipe inspection, failing to comprehensively check for defects. The impact of pipeline leakage or pig blockage accidents is extremely serious, and the economic losses and hazards caused by such accidents are significant [11]. The stable operation of a pig plays a crucial role in the safety of pipe-pigging operations and the validity of in-line pipeline inspection data. Therefore, conducting research on pig speed control is important to ensure the safe operation of submarine pipelines [12].

Conventional pig designs are usually larger in diameter than the inside wall of the pipe and are constructed of either a polyurethane cup or a foam rubber cylinder. A pig is usually a tight fit between the pipe wall and the pipe, making it impossible for fluids to pass through [13]. The pig travels under the pressure of the transport fluid and moves at the same speed as the fluid in the pipeline. The speed of this completely sealed pig is difficult to control and is directly affected by the flow rate of the transport fluid. In gas pipelines, constant-speed oscillations and speed excursions occur in pigs owing to changes in gas compressibility and friction non-uniformity [14,15]. The flow velocity of the fluid transported by pipelines often exceeds the ideal preset velocity for internal inspection. Nieckele et al. (2001) were the first to investigate a bypass pig designed with a bypass hole in the center for conditions where the flow velocity was much greater than the ideal operating velocity [16]. This fixed bypass pig allows fluid to flow in the direction of the bypass hole, and fluid will flow from the end of the pig to the front [17]. The kinetic mechanism of such a pig changes, and the isolation of the front and back fluids no longer creates the differential pressure driving the pig. Instead, the bypass hole reduces the differential pressure between the front and back of the pig, and the pig velocity is lower than the fluid velocity. This fixed bypass hole relatively reduces the speed of the pig when the flow rate is too high.

Based on the assumption of a steady-state flow of gases, the pressure drop coefficient is the most important parameter for analyzing the dynamics of a fixed bypass pig whose motion behavior in the pipe is influenced by the fluid [9]. The relationship between the pressure drop across the pig and the flow rate in the bypass hole is used to study the movement of the pig [18]. Several studies have been conducted on the pressure drop coefficient of a pig bypass. Hendrix et al. (2016) established a mathematical model of the pressure drop coefficient of a pig using the building block approach [19]. Chen developed a CFD numerical simulation to prove that it is an effective method for studying the variation law of differential pressure in a pig [20]. In addition, a study on the change characteristics of the liquid load during submarine pipeline pigging found that the bypass effectively eliminated the segment-plugging phenomenon generated by pigging [21]. Liu et al. (2020) initiated an optimization study of the structural parameters of an underwater jet pig. They applied a bypass pigging strategy to alleviate the severe segmental plugging problem in offshore riser systems, which had been difficult to solve [3]. This significantly extended the range of pigging applications in subsea pipeline systems.

Thomas found that the maximum velocity reduction capacity of a pig depends on the bypass system area. Based on this, a controlled-speed pig was proposed to adjust the bypass area. This bypass rotary valve, which allows the bypass area to be changed, can reduce the distance traveled at high speeds compared with pigs with non-adjustable bypass areas [22]. Phodapol et al. (2021) proposed the MC-Pig method based on a closed-loop control algorithm. A proportional–integral control valve was used to regulate the shape of the bypass and, thus, the flow rate through the pig. In a 16-inch pipe with a gas flow velocity of 4.38 m/s, the pig velocity could be adjusted from 0.59 to 3.88 m/s [23]. Zhu et al. (2014) established a test platform for bypass valves and conducted torque tests at a fixed gas pressure level [24]. When bypass valves operate in pipelines, they usually encounter different pipeline conditions, and different gas flow rates significantly impact the torque of the bypass valves. For bypass valves with adjustable leakage areas, an accurate understanding of the dynamic opening characteristics of the valve is crucial for opening and closing the valve as well as effectively controlling its speed. Adapting to different pipeline conditions to achieve stable speed control is a challenge in this field.

In this study, the torque variation during the opening process of speed control valves in high-pressure gas pipelines was analyzed for the first time using the CFD method under different working conditions. The relationship of the bypass valve torque corresponding to different valve openings at different bypass flow velocities and pressures was investigated. The influence of structural parameters of different bypass valves on the driving differential pressure of pigs was explored. Most existing studies on pipe cleaning focus on the study of the pressure drop coefficient. This study further reveals the mechanism of the influence on pig velocity under the change in pipeline conditions and the coupling effect of the bypass valve. This provides a comprehensive direction for designing the speed control unit and control scheme for pig velocity, which is significant for the stable operation of intelligent pigging in pipelines.

2. Model of the Speed Control Unit

2.1. Structure of the Speed Control Unit

The speed-controlled pig shown in Figure 1 comprises a speed control unit, cup, defect detection system, data processing system, and mileage wheels. The speed control unit shown in Figure 2 comprises a rotatable inner valve, a fixed outer valve, a motor that drives the valve to rotate, and an odometer wheel that collects and calculates the pig velocity. The inner and outer valves are assembled using concentric shafts. The rotary valve has a fixed groove inside that connects to the motor axis, and the motor drives the rotary valve to rotate. In the pipeline, gas flows through the internal flow channel of the pig skeleton and exits the rotary speed control valve. When the rotary valve is fully closed, the pig isolates the gas in front and behind it, and the gas creates a pressure differential, driving the unit forward. The pig velocity exceeds the ideal range when the pipeline gas flow is high. The speed at which a pig travels can be monitored by mileage wheels. At this time, the speed control valve of the controllable speed control pig operates. The fixed outer valve and the rotating inner valve have interlocking openings that regulate the flow when the valve is adjusted. In this study, the valve body had eight circumferentially distributed openings, and the valve could be rotated from 0° to 22.5°. The internal valve body was rotated using a motor drive to form a leakage channel with a fixed external valve. The gas flowed out of the leakage channel, changing the differential pressure between the front and back of the pig. A change in the bypass area directly affected the gas flow behavior through the pig. Changes in flow behavior directly determine the two most important factors for pig speed control: the driving differential pressure built up by the gas in front of and behind the pig and the torque generated at the speed control valve.

2.2. Modeling of Differential Pressure for Speed Control Valves

To better understand the effect of the speed control valve on the pig velocity operating behavior and improve the efficiency of the speed control valve for velocity adjustment, the first step is to analyze the gas flow behavior in the pig and speed control valve. The pressure drop generated from the front and back of the gas flow through the pig was the driving differential pressure of the pig traveling inside the pipe. The differential pressure is defined as follows [7]:

$$∆P=P_{tail}-P_{nose}={\displaystyle \frac{K_p\rho }{2}}\left[{\left({\displaystyle \frac{A}{A_d}}\right)}^2{\left(V_{gas}-V_{pig}\right)}^2\right]$$

(1)

where ∆P is the differential pressure between the PIG tail and PIG nose, Pa; P_tail is the pressure at the PIG tail, Pa; P_nose is the pressure at the PIG nose, Pa; K_p is the pressure drop coefficient; A is the area of the inner pipe cross-section, m²; A_d is the area of the skeleton cross-section, m²; V_gas is the gas velocity, m/s and V_pig are the PIG velocity, m/s.

The working mechanism of the speed control valves was established based on the momentum theorem. The pressure drop generated by the gas flow through the pig was almost dependent on the geometry of the pig for certain pipe flow parameters. Nguyen et al. (2001) found the building block approach to be a simple and effective solution for the pressure drop generated by a change in the flow cross-section in the pipe [25]. The building block approach considers the sudden contraction flow at the tail end of the pig, straight pipe flow inside the pig, and sudden expansion flow at the pig’s front end as standard flow behaviors. This type of analysis decomposes the pressure drop based on the geometry of the pig. Each standard element of the decomposition individually corresponds to the contribution of the geometric structural features to pressure drop, describing the overall pressure drop as a linear combination of several standard elements. The building block approach has been proven to be an effective evaluation method in studies related to pigs [26]. As shown in Figure 3, the structure of the pig in this study can be divided into three elements according to the building block approach. The sudden contraction produced by the combination of the tail cup and skeleton restricts the flow. The straight pipe flows in the cylinder inside the skeleton, and the sudden expansion of the flow channel is formed by the outflow fixed valve and rotary valve. The pressure drop coefficients for sudden contraction and straight pipe flow can be constructed based on the Idelchik correlation equation [27].

$$K_{sp}=0.5{\left(1-{\displaystyle \frac{A_d}{A}}\right)}^{0.75}+{\displaystyle \frac{4f{L}_{\mathrm{pig}}}{d}}$$

(2)

where K_sp is the pressure drop coefficient of the tail and skeleton; L_pig is the length of the pig, m; f is the coefficient of friction and d is the skeleton diameter, m.

The analysis assumes steady-state flow conditions, where the pressure drop coefficients remain constant over time and do not vary with transient effects. We assumed ideal flow conditions with negligible effects of non-idealities such as compressibility and turbulence. It was assumed that the flow distribution across the components is uniform. Fluid properties such as viscosity and density were assumed to be constant within the range of operating conditions.

For a speed-controlled pig, various valve structures directly affect the sudden expansion flow behavior. This valve-altered flow behavior is no longer considered, having expanded suddenly. Hendrix et al. (2016) conducted a study of disc valves installed at the front ends of a pig [28]. The pressure drop coefficient of the pig is related to H, d, and h. H is the diameter of the valve, m; h is opening length of the valve, m. The pressure drop coefficients for this speed control valve structure were established as follows:

$$K_d={\displaystyle \frac{2H}{d}}+{\displaystyle \frac{0.155d^2}{h^2}}-1.85$$

(3)

However, the effective application of its limitations was as follows:

$$0.1<{\displaystyle \frac{h}{d}}<0.25$$

(4)

$$1.2<{\displaystyle \frac{H}{d}}<1.5$$

(5)

For the rotary speed control valve structure in this study, the angle of valve rotation directly determined the leakage channel formed by the inner and outer valves, changing the leakage area. The pressure drop term resulting from this change in valve body rotation can be defined as follows:

$$K_{cn}=0.5{\left(1-{\displaystyle \frac{A_d}{A}}\right)}^{0.75}+{\displaystyle \frac{4f{L}_{\mathrm{pig}}}{d}}+\left({\displaystyle \frac{2H}{d}}+{\displaystyle \frac{0.155d^2}{h_{eqv}^2}}-1.85\right)$$

(6)

$$h_{eqv}=H^{\times }{\displaystyle \frac{h}{d}}{\displaystyle \frac{n\omega }{360}}$$

(7)

K_cn is the pressure drop loss coefficient of the nose cup clearance flow leakage; h_eqv is the equivalent disk-to-pig distance, m; w is rotary valve rotation angle, ° and n is the number of opening areas. The building block approach to pressure drop resolution significantly simplifies pressure drop prediction for different construction features and allows for preliminary assessment at the early stages of pig design. For the speed-controlled pig, the use of the building block method allows for a quick analysis of the effect of structural parameters on pressure drop in different parts, which greatly improves efficiency in engineering design and manufacturing. However, based on the assumption that the flow patterns are uncorrelated in the building blocks, this linear combination does not allow for the prediction of the resulting interaction effects of the individual building blocks. The CFD numerical simulation method is widely used to further correct the pressure drop coefficients of the pig.

2.3. Torque Variation of Speed Control Valve

The pig was powered by a motor that controlled the rotation of the bypass valve. However, in natural gas pipelines, the shear force generated by the gas flowing through the valve body creates an additional torque on the rotatable inner valve. Typically, natural gas pipelines have high flow rates and pressures, and the torque affected by these factors can significantly influence the operation of motor-controlled actuators. The radial cross-section of the speed control valve is shown in Figure 4. As the fluid flows through the speed control valve, the structural constraints between the outer and inner valves change the flow behavior of the fluid. A fluid force is generated on the radial wall of the rotating inner valve opening, causing the inner valve to rotate. This study utilized computational fluid dynamics (CFD) methods to analyze the variation in rotational torque of the valve at different rotation angles and pipeline flow parameters. Additionally, it investigates the rotational forces generated by the fluid on the valve during the dynamics of opening and closing.

During valve rotation, the rotation angle directly determines the bypass area between the standing and rotary valves. The flow behavior determined by the bypass area was defined as orifice flow. For example, in Figure 4, the vector of the flow flowing into the rotary valve from the interior of the pig was defined as v₁, and the vector of the flow flowing out of the rotary valve into the open space of the pipeline was defined as v₂. α represents the incident angle, °. The difference in the momentum generated by the inflow and outflow of this fluid domain was the fluid force acting on the rotary valve. The difference in the fluid force between the left and right radial walls of the rotary valve opening was the rotary force. To control the rotation of the valve using the motor, the load torque of the motor should match the rotary force of the fluid acting on the rotary valve wall in different situations.

According to the momentum theorem, it can be established that the fluid flow into the rotary valve generates a fluid force at the wall as follows:

$$F_r=\rho Q{v}_2\mathit{cos}{\alpha }_2-\rho Q{v}_1\mathit{cos}{\alpha }_1$$

(8)

The steady-state fluid torque acting on the rotary valve as a whole is as follows [24]:

$$T_s=8∆P_{\mathrm{v}}{A}_{w}r\left(c_{\mathrm{d}2}{c}_{\mathrm{v}2}\mathit{cos}{\alpha }_2-c_{\mathrm{d}1}{c}_{\mathrm{v}1}\mathit{cos}{\alpha }_1\right)$$

(9)

The transient hydraulic torque as the rotary valve rotates is as follows:

$$T_t=-\rho {\int }_{\tau }\iint {\displaystyle \frac{\partial vr}{\partial t}}d\tau =-J{\displaystyle \frac{d\omega }{dt}}-{\displaystyle \frac{d{w}_u}{dt}}{\int }_{\tau }\iint \rho rd\tau$$

(10)

where Q is the flow rate, m³/s; ΔP_v is the differential pressure between the front and back of the valve, Pa; A_w is the rotary and standing valves constituting the bypass area of the flow channel, m²; r is the radius of valve, m; C_v represents the velocity coefficients of inflow and outflow; C_d is the discharge coefficients of inflow and outflow; J is the rotary valve basin fluid relative to the motor rotary axis of inertia, kg·m²; and w_u is the spool basin fluid relative velocity of the circumferential component, m/s. The torque equation responds to parameters that affect the change in torque. However, the angles of fluid inflow and outflow, as well as the flow rate, are difficult to determine, and the variation law of torque in the pipeline under the coupled influence of fluid pressure, flow rate, and other parameters is unclear. Therefore, further simulations and experimental studies are required.

3. Numerical Simulation of the Speed Control Unit

3.1. Numerical Modeling of a Pig in the Pipeline

In engineering practice, the structure of a smart pig is complex. To ensure the accuracy and computational efficiency of the numerical analysis, the structural characteristics of the pig must be simplified to establish a model. The model should highlight the structural features that contribute significantly to the change in flow behavior and simplify complex structural features with small contributions. This ensures an effective analysis of the change in flow behavior and reduces the difficulty of the computational solution. A model of the speed-controlled pig in the subsea gas pipeline was established, as shown in Figure 5. The structural features of the model used in this study included the internal cylindrical skeleton of the pig, a speed control valve comprising a rotary valve spool, and a standing valve. In this study, different models were established by considering three main parameters: the rotation angle of the rotary valve, the opening length of the rotary valve bypass hole, and the inner diameter of the skeleton. The flow domain, which consisted of the pig and fluid inside the pipe, was simplified and extracted.

In the equilibrium state, based on the assumption that the gas flow rate is stable with respect to the traveling speed of the pig, the flow behavior of the gas inside the pipeline through the pig can be regarded as relative motion behavior [29,30]. This study assumes that the pig is stationary and that the inlet flow velocity is the relative velocity difference between the pig and gas. The influence of different structural characteristic parameters on the flow behavior when the pig was in equilibrium with the pipe was investigated according to the typical application conditions for smart pigs with common sizes. The model utilized the boundary conditions of a 3 m/s velocity inlet and an 8 MPa pressure outlet. The length of the pipe upstream of the pig was set to 5D and downstream to 15D to ensure flow fully developed. The model sets three varying parameters: the rotation angle of the rotary valve, the opening length of the rotary valve bypass hole, and the inner diameter of the skeleton, as listed in

Table 1. Model parameter settings.

Parameter	h (m)	d (m)	θ (°)
1	0.04	0.2	22
2	0.06	0.3	18
3	0.08	0.35	13.5
4	0.10	0.4	9
5	0.12	0.45	4.5

.

This study selected a realizable KE turbulence model, and the near-wall region was treated using standard wall functions. Another important aspect of numerical modeling of the pig in natural gas pipelines is the mesh establishment of the model. Finding a suitable meshing method and ensuring the mesh quality for the simulation modeling of the pig in the pipeline is important. The results were compared for the value of the differential pressure between the pig and the rotational torque of the valve. The results for different mesh numbers are shown in Figure 6. The difference between the number of meshes 217,108 and 426,985 was less than 1%. No significant difference was observed between mesh3 and mesh5; therefore, mesh3 was chosen in this study to develop the simulation analysis of the pig.

3.2. Influence of Changes in Structural Parameters of the Speed Control Unit

The pressure field distributions for different valve opening lengths are shown in Figure 7. As the rotary valve opening length size decreased from 0.12 to 0.04 m, the area of the leakage channel gradually increased, and the flow velocity in the flow channel gradually decreased. The velocity contours are shown in Figure 8. As the rotary valve opening length h increased, the fluid flow path changed, and the angle of the jet from the inside of the rotary valve became increasingly larger.

The pressure distributions for different rotary valve opening lengths are shown in Figure 7. The differential pressure formed in the front and back of the pig decreased as the rotary valve opening height h increased. A larger leakage area reduced the pressure drop from the same inlet conditions. This implies that a longer valve length reduces the driving differential pressure on the pig. For high-pressure gas pipelines, reducing the pig-driving differential pressure and, thus, the pig velocity is common. Therefore, a larger rotary valve length has a better speed reduction effect, provided that the pig runs at stable friction.

Figure 9 shows the velocity distribution contours for different skeleton diameters. As the skeleton diameter decreased from 0.45 to 0.2 m, the average flow velocity of the gas inside the pig’s skeleton increased significantly, producing a region of high velocity inside the skeleton with the maximum flow velocity increasing from 43.7 to 106 m/s. This region is typical of the flow behavior of sudden contractions with sudden expansion. The generation of the pressure drop depended mainly on the degree of change in the cross-sectional area front and back the flow. Therefore, the law of influence of the change in skeleton diameter on the change in pressure drop is significant and apparent. In conjunction with the pressure distribution shown in Figure 10, increasing the inside skeleton diameter significantly reduced the differential pressure generated in the front and back of the pig. However, the ability of the pig to reduce pressure stabilized when the internal diameter exceeded 0.4 m. The differential pressure between the 0.45 and 0.4 m internal diameters was not significantly reduced. This is because the skeleton diameter is nearly equal to the valve body diameter, which determines the overall pressure drop capacity of the pig. Increasing the skeleton diameter did not reduce the pressure drop capacity of the pig and would have presented additional difficulties in the mounting and structural dimensioning of the internal parts of the pig. Therefore, this study used a skeleton diameter parameter of 0.4 m for subsequent studies and prototype manufacturing.

For the speed-controlled intelligent pig in a pipeline, the opening length of the rotary valve and the internal size of the skeleton cannot be changed during operation. Using this design, the bypass area can be changed, the differential pressure in the front and back of the pig can be adjusted, and the speed control unit can achieve speed control. From the distribution of the flow field in Figure 11, the change in the flow field from the inlet of the hole in the skeleton port to the inlet of the gas from the opening of the rotary valve was very drastic. The gas flow velocity in this region was high, and the generated fluid force was relatively complex. Therefore, the motor of the intelligent speed-controlled pig developed in this study was placed at the front end of the standing valve. This part of the flow field was relatively stable and less affected by the gas jet, which relatively reduced the motor’s susceptibility to damage.

Figure 12 shows the axial pressure distribution curve along the pipeline for different valve rotary angles when the rotation angle of the valve rotary valve was from 4.5° to 22°. As the rotation angle of the rotary valve increased, the differential pressure in the front and back of the pig decreased. The pressure decreased sharply after the gas flowed out of the rotary valve. When the cross-sectional area of the pipe was certain, the dynamic pressure between the front and back sections of the pig remained almost constant. The static pressure drop of the gas in the pipe after the flow restriction of the pig was the main contributor to the overall differential pressure. The velocity vectors in Figure 13 show that the fluid jets radially outward in the rotary valve region of the jet structure. In the region between the standing valve and pipe wall, the gas jet formed a recirculation zone located at the corner near the pipe wall. After the fluid separated from the pig, the jet flowed around the valve and rejoined downstream, and the fluid flow stabilized only after a certain distance along the pipe axis. The pressure distribution curve shows that the gas pressure distribution also stabilized.

The velocity vectors in Figure 13 show that the smaller the rotation angle, the farther the stabilization is returned. The difference between the pressure integrations performed on the stressed surfaces at the tail and nose of the pig was calculated as the gas pressure difference driving the force on the pig in the pipe. A comparison of the differential pressure values for the same flow conditions in Figure 12 revealed that when the rotation angle was 4.5°, the differential pressure between the tail and nose of the pig was 1.32 MPa, and when the rotation angle was 22°, the differential pressure between the front and rear of the pig was 0.07 MPa, which is a decrease of 94.7%. The results showed that a rotary valve opening angle of 0–20% significantly affected the variation in the differential pressure. The values of the differential pressure corresponding to different openings indicated that the differential pressure generated by the tail and nose of the pig could be significantly controlled by adjusting the rotation angle of the valve.

Figure 14 shows the values of the differential pressure and pressure drop coefficient for different rotation angles of the valve and the pressure drop coefficient calculated using the building block approach. A comparison of the pressure drop coefficient showed that the pressure drop coefficient constructed by the building block approach had a very strong correlation with the results of the simulation value. The building block approach can characterize how changes in the valve rotation angle w, skeleton diameter d, and the opening length of the rotary valve ℎ affect the pressure drop coefficient. The average relative error was 14.5% at h/d < 0.25, which is highly relevant. When h/d < 0.25, the average relative error was 14.5%, indicating a strong correlation. However, when h/d > 0.25, the error increased and exceeded 22.9%. The building block approach for modeling the pressure drop of the rotary valve type appeared to have a large error. Therefore, the applicability of Equation (6) is limited, and correction terms should be added based on the fitting results from the numerical simulations.

Analysis of these three parameters, all of which have an extremely strong influence on the pressure drop, can be implemented to change the driving differential pressure of the pig. Therefore, it is very important to design the structural parameters of the speed-controlled pig at the design stage. The speed control of the pig is realized by controlling the rotation angle of the valve.

3.3. Influencing Factors and Variation Law of Torque

Pig models are developed for various openings, pressures, and gas flow rates. The effects of the variation in these parameters on the variation in the rotary valve torque were explored. Figure 15 shows the velocity vectors of the intelligent pig model in the radial section at different rotation angles. Under a certain differential pressure and inlet flow rate, the flow rate of the rotary valve opening jet changed with the rotation angle of the valve, and the angles of fluid inlet and exit also changed.

In combination with Figure 16, the pressure distribution in the rotary valve cross-section can be understood to be due to the structural limitations of the rotary and standing valves, and the gas flow behavior in this section is changed. The flow velocity increased on the outer side close to the rotary valve opening and decreased on the inner side of the rotary valve opening. Based on the fluid continuity principle, the pressure was lower on the outer wall surface and higher on the inner wall surface of the opening of the rotary valve. This differential pressure on the rotary valve wall due to the flow behavior is the reason for the torque generated by the speed control valve during pipeline operation. Through observation, the characteristics of this pressure distribution and the force’s direction on the rotary valve wall can make the rotary valve tend to close the state movement. This stabilized reverse rotary force enables the rotary valve to close stably during pipeline operation. This ensures that the speed control valve can be stably closed when it encounters special working conditions, such as an abnormal power supply or insufficient power. At this time, there is enough gas to re-establish a sufficient driving differential pressure to avoid pig blockage in the pipeline.

Figure 17 shows the pressure distribution acting on the radial wall of the rotary valve. The rotary valve torque along the axial direction of the pipe was also monitored in a simulation to obtain the rotary valve torque. The gas density ρ is determined by the pressure in the pipeline. Therefore, according to Equation (8), for the fluid rotational force of the valve, the torque will be directly related to the inlet flow rate and pipeline pressure. The torque values obtained from the simulation results for different flow rates and pressures were analyzed, and they were 50.3 Nm at 2 Mpa and 280.1 Nm at 10 Mpa, proving the correlation between torque and pipe pressure. The torque increased from 23.2 to 565.8 Nm when the inlet flow velocity varied from 1 to 5 m/s. The flow velocity affected the magnitude of the fluid pressure drop, indicating that the flow behavior directly affected the rotational torque.

When the rotary valve was at different rotation angles, it was analyzed using the velocity vectors shown in Figure 15. The angle of rotation affects torque in two main ways. First, the angle determines the leakage area of the opening. Different leakage areas change the flow velocity owing to structural limitations, resulting in a higher flow velocity and consequently affecting the rotational torque. Second, different rotation angles cause the angle of the opening cross-section of the inlet and outlet to differ, and the different angles of the velocity directly affect the magnitude of the rotary force, which changes the torque.

Based on the results obtained from numerical simulations at various angles, a torque variation curve for the rotary valve during its rotation can be fitted. The torque decreased as the rotation angle of the valve increased from 0° to 20°, corresponding to an increase in the open area of the valve from 0% to 100%. The rotary valve torque decreased from 2400 to 7.2 Nm for rotation angles ranging from 4.5° to 22°. For V_gas–V_pig of 3 m/s, the load torque in the start-up phase was too large. In engineering practice, no fluid flows out of the bypass hole during the start-up phase because the valve is closed. At this time, the pig velocity will be running at a velocity that tends to be close to the gas flow rate, and the value of the V_gas–V_pig velocity difference is small. In the low bypass flow rate state, the load torque is small, and the motor has sufficient power to operate properly. With a preset speed reduction target, it should be ensured that sufficient load torque can be provided at that speed difference V_gas–V_pig at that rotation angle.

Figure 18 shows the torque of the valve under the different parameters of pressure, flow velocity, and rotation angle. It can be seen from Figure 18 that the torque increased with an increase in the pipeline gas pressure, increased with an increase in the pipeline gas flow velocity, and decreased with an increase in the rotation angle. By analyzing the torque values for different pressures and flow velocities, the pressure and flow velocity of the pipeline were found to directly affect the magnitude of the torque value of the rotary valve under the working conditions. The increased pressure and flow velocity parameters directly correlated with increased torque. Therefore, in a high-pressure gas pipeline, the operating pressure of the torque range must be clearly calculated to avoid ignoring the high-pressure environment caused by the phenomenon of torque increase. Explicit parameters can be obtained for the dynamic load torque variation of the speed control valve in the pipeline. The speed control valve can be effectively controlled by adjusting the motor’s output torque and optimizing the control algorithm.

4. Experiment

4.1. Experiment System

Based on the numerical simulation results of this study on the design of the relevant structural parameters of the speed control valve, a prototype speed-controlled pig for high-pressure gas pipelines was developed. Figure 19 shows the states where the rotary valves are at different angles.

To verify the accuracy of the numerical analysis method for torque calculation, an experimental system for torque measurement of the speed control valve was developed based on the schematic diagram of the experimental system for torque measurement, as shown in Figure 20. The motor of the speed control valve was mounted with a torque sensor on the connecting axis of the valve, which recorded the torque of the rotary valve load under fluid action. The experiment system mainly comprised an air compressor, air tank, and Φ1016 steel pipe connection. Pressure sensors and flow meters were installed to record the pipeline pressure and flow rate. The outlet of the pipeline used in this study was at atmospheric pressure. Air was injected at a constant flow rate through an air compressor at the inlet end to simulate the variation in torque obtained by the rotary valve with respect to the rotation angle for specific inlet conditions. The actual image of the torque measurement test system is shown in Figure 21.

Before the experiment started, the torque sensor was installed on the motor shaft, and the torque data acquisition system was embedded in the Φ1016 pig. We set the initial state of the rotary valve to fully open. A position sensor was installed inside the valve body to record the angle of rotation. The pipeline was 36 m in length, and the integrated pig was dragged to a position 12 m from the pipeline entrance using a winch at the end of the pipeline. The external motor controller was connected to the rotary motor via cables and placed at the end of the pipe.

The inlet side of the pipeline was connected to the air compressor and the storage tank in that order. The system was powered by three air compressors, each with a capacity of 100 m³/min, which supplied the flowing gas. The compressors’ outlets were connected to the air tank to stabilize the output compressed air, eliminating or reducing the pulsation of the compressor’s output airflow pressure. The actual flow rate in the pipeline was monitored by a flow meter at the outlet of the air tank. When the gas enters the pipeline, the differential pressure of the pig was insufficient to drive the pig, rendering the pig completely stationary. Pressure sensors are installed in the front section of the pipeline.

By adjusting the compressor output flow rate, the gas flow rate in the pipeline changed. When the gas flow velocity stabilized at 2 m/s and the pressure remained constant for 1 min, the motor controller was used to gradually close the rotary valve from the fully open state. During this process, the torque variation of the motor was collected by the torque sensor and recorded in the data acquisition system. Subsequently, the rotary valve was returned to the fully open state using the controller. The compressor output flow rate was then increased. When the gas flow velocity stabilized at 4 m/s, the above experimental process was repeated. At the end of the experiment, the compressor was turned off and the pig was pulled out of the pipeline using a winch.

4.2. Analysis of Experimental Results

Figure 22 shows the torque values for inlet flow velocities of 2 and 4 m/s at different rotation angles. The torque variation curves obtained from the experimental measurements showed that the torque value decreased as the rotation angle increased under fixed inlet flow parameters. When the converted inlet flow velocity was 2 m/s, and the rotation angle was reduced from 22° to 4.5°, the torque increased from 0.37 to 41.92 Nm. When the converted inlet flow velocity was 4 m/s, and the rotation angle was reduced from 22° to 4.5°, the torque increased from 1.2 to 85.76 Nm. The experimentally measured torque reduction trend was consistent with the numerical simulation results. The potential reasons for the discrepancies between the numerical simulations and experimental values include the effects of flow patterns, model assumptions, geometric simplifications, measurement accuracy, and turbulence and compressibility. By comparing the torque changes at inlet flow velocities of 2 m/s and 4 m/s, it was observed that the load torque increased with the flow velocity. Consistent with the results of the numerical simulations, the flow velocity was directly correlated with the increase in torque. Therefore, pig operation in a pipeline first requires defining the speed reduction target. The load torque required to overcome the rotational force of the fluid in this range of speed reduction values was further determined to optimize the control algorithm.

4.3. Calculation of Speed-Controlled Pig Speed Regulation Capacity

After launching the study of the pressure drop coefficient and torque, the application of the results of the study in practical operations became a complex problem, as pig operations in pipelines encounter changes in pressure, flow rate, and friction force.

$$m{\displaystyle \frac{dv}{dt}}=∆P\left(1-\phi \right)A-F_f-mg\mathit{sin}\theta +F_{\tau }$$

(11)

$${\mathrm{V}}_{\mathrm{p}\mathrm{i}\mathrm{g}}={\mathrm{V}}_{\mathrm{g}\mathrm{a}\mathrm{s}}-\mathsf{\phi }\sqrt{{\displaystyle \frac{{2(\mathrm{F}}_{\mathrm{f}}-\mathrm{m}\mathrm{g}\sin \mathsf{\theta })}{{\mathrm{K}}_p\mathsf{\rho }}}}$$

(12)

where m is the mass of the PIG, kg; θ is the incline angle of the pipe, °; φ is the bypass rate of the PIR; F_τ is the shear force of the gas flow, and N and F_f are the friction force between the pig and pipe. According to the dynamic equation of the pig, the speed of the pig is affected by many factors. Based on the calculation, the pressure drop coefficient of the pig was obtained at different rotation angles. The speed of the pig was also controlled. The relative velocity and speed reduction capability mainly depend on the pig contingent on the bypass rate φ, friction F_f, and pressure drop coefficient K_p. Therefore, this study proposed a design workflow for the speed-controlled pig based on the simulation study results. Based on the results of the numerical simulation, the relevant parameters of the pig can be reasonably designed by combining the actual working conditions of the pipeline. This allows the pig to operate in a pipe within an ideal velocity range.

Determining the speed reduction capacity is the most important aspect of speed control unit design [31]. The resultant parameters of this study were calculated by combining Equations (1) and (11), and the pipe flow parameters were based on the assumptions of a pressure of 8 MPa and a flow rate of 6 m/s. The optimization and design process for the parameters of the speed-controlled pig is illustrated in Figure 23. Figure 24 shows the operating velocity parameters of the speed-controlled pigs at different operating friction values. By adjusting the rotary valve angle, when the friction was 14 tf, the pig had a speed control ability of 1.21–5.13 m/s; when the friction was 6 tf, the pig had a speed control ability of 0.79–3.36 m/s. The larger the friction, the larger the range of speed control. In high-pressure pipelines, speed control benefits from an appropriate increase in the friction resistance of the pig.

A simulation analysis of the pig dynamics was developed based on the measurement results of the friction force. Based on the assumption of uniform friction, the speed reduction capability of the prototype was analyzed at different pressures. The maximum speed reduction capability was 8.67 m/s at 2 MPa and 3.88 m/s at 10 Mpa (Figure 25). The lower the pressure, the greater the speed range of the prototype. Based on the maximum speed control capacity for different pressures, combined with the actual flow rate of the pipeline, it was possible to assess whether the developed speed-controlled pig could satisfy the speed reduction target. Consequently, this ensures the operational quality of in-pipe inspection and guarantees the effective detection of pipeline defects.

5. Conclusions

In this study, the flow field of a speed-controlled pig in a pipe was modeled using a building block approach and a CFD numerical simulation. The effects of different pipeline gas flow and structural parameters of the pig speed control valve on the driving differential pressure and torque were studied.

(1)

Numerical simulation results showed that the gas differential pressure decreased from 425 to 93 kpa when the skeleton diameter increased from 0.2 to 0.4 m. When the skeleton diameter exceeded the diameter of the bypass valve, the differential pressure no longer decreased with the skeleton diameter. The gas differential pressure decreased from 571 to 69 kpa when the opening length of the valve increased from 0.04 to 0.12 m. When the valve rotation angle decreased from 22° to 4.5°, the gas differential pressure increased from 73 to 1325 kPa. The pressure drop coefficients calculated using the building block approach correlated well with the numerical simulation results, and the final outflow term of the building block approach was corrected based on the numerical simulation results.

(2)

As the pipeline pressure and flow rate increased, the rotational torque of the rotary valve due to the bypass gas increased continuously. The torque values were directly correlated with the pressure and flow rate parameters. When the rotary angle decreased from 22° to 4.5°, the torque increased from 7.7 to 2470 Nm. The variation law of the torque with the rotary angle has been clearly defined, which avoids the speed control failure caused by insufficient torque under different working conditions.

(3)

An experimental torque measurement system was established to validate the calculation of the rotary valve torque for speed-controlled bypass valves. The experimental results showed that with an increase in flow rate from 2 to 5 m/s, the bypass valve simultaneously exhibited a torque increase at different angles during the closing process, which was directly related to the gas flow velocity. During the gradual closing of the rotary valve, the torque increased slowly as the angle of rotation decreased from 22.5° to 10° and increased faster as the angle of rotation decreased from 10° to 0°.

(4)

This study investigates how the speed control valve responds to changes in torque under various pipeline conditions. Based on this result, motor- and speed control valve-related parameters can be designed to optimize the control algorithm to achieve stable pig speed control.