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Scientific Reports volume 14, Article number: 23580 (2024 ) Cite this article Psi Plunger Pump For Washing
In the production of oil and natural gas, excessive clearance volume is an important factor affecting the normal operation of oil-gas multiphase pump. Currently, little research has been conducted on the effect of clearance volume on the output characteristics of multiphase pump at home and abroad, leading to extremely low efficiency in the field application of multiphase pump. Therefore, this study conducted numerical calculations on the internal flow characteristics and output performance of multiphase pump under different clearance volumes using FLUENT software. Results show that pressure and fluid velocity gradually decrease as the clearance volume increases. Simultaneously, the number and intensity of vortex flow gradually increase, media pressurization speed becomes slower, and the lag angle of the discharge valve opening becomes larger. Moreover, under conditions with a higher gas volume fraction, multiphase pump with larger clearance volumes experiences gas locking. Furthermore, this study provides a theoretical basis for the reasonable design of clearance volume for multiphase pump by drawing a relationship curve between gas volume fraction and clearance volume. These research findings can provide theoretical support for the performance optimization and design improvement of multiphase pumps.
Since the 21st century, the problem of energy shortage has become increasingly severe, and many countries have realized that energy security is a strategic issue related to their economic and social development. As a result, the development and construction of offshore oil and gas fields have become a hotspot for research and investment. Given the distance of offshore oil and gas fields from the target users, the produced oil well fluids (e.g., oil and natural gas) need to be transported to users after centralized external transmission and processing, a process known as oil-gas multiphase transportation1,2,3 . In the oil-gas multiphase transportation system, the most important equipment is the oil-gas multiphase pump.
The oil-gas multiphase reciprocating pump belongs to piston pumps, with the advantages of high efficiency, strong self-priming ability, and adaptation to high gas volume fraction and high compression ratio conditions. However, given the unstable proportion of natural gas components in well fluids, the gas volume proportion distribution range is extremely large4,5,6,7 (i.e., 0–100%). Therefore, the effect of gas compressibility on the pump’s performance must be considered. In view of the design and manufacturing process of the oil-gas multiphase pump, a certain clearance volume is present inside the piston cylinder, known as the clearance volume8 . The existence position (circled part) of the clearance volume in the oil-gas multiphase reciprocating pump is shown in Fig. 1. Given that a large amount of gas in the medium transported by the oil-gas multiphase pump, in addition to the suction and discharge working processes, the multiphase pump also adds expansion and compression processes. The expansion process will cause a decrease in the suction flow rate. If the clearance volume is extremely large, then it can cause serious gas lock phenomenon, leading to the failure of the multiphase pump to work normally. Therefore, the effect of the clearance volume on the internal flow characteristics and discharge performance of the oil-gas multiphase reciprocating pump must be investigated.
Existing position of clearance volume.
Wang9 analyzed the effects of clearance volume and compression ratio on compressor power from the perspective of energy efficiency. The results indicated that the power is directly proportional to the compression ratio, whereas the power is inversely proportional to the clearance volume.
With constant inlet pressure, power decreases with the increase of clearance volume. Jiang10 investigated the influence of clearance volume on the performance within the linear refrigeration compressor. The research indicated a negative correlation between the clearance volume and volumetric efficiency, leading to the conclusion that the clearance volume should be minimized as much as possible. Lasvignottes11 conducted experimental and simulation studies on the compression process of compressors, pointing out that an increase in clearance volume significantly affects the compression process and volumetric efficiency of the compressor. Zhang12 discussed the influence of clearance volume on the pressure rise and the opening lag angle of the discharge valve within the multiphase pump chamber. They found that the clearance volume results in the extension of the pressure rise process, leading to delayed discharge, suggesting that the clearance volume should be reduced.
Based on the analysis above, the research has mainly focused on the effect of clearance volume on compressor characteristics. Although there have been some studies on the characteristics of the clearance volume in multiphase pumps, there is little in-depth exploration of the relationship between the clearance volume and gas volume fraction from practical operating conditions, and determining the reasonable range of the clearance volume at specific gas volume fractions.
Therefore, this study starts from the actual field conditions, assuming the normal operation of the oil-gas multiphase pump, to investigate the effect of the clearance volume on the internal flow characteristics and output performance of the multiphase pump. The results of this study can provide theoretical support for the performance optimization and design improvement of multiphase pumps.
The oil-gas multiphase reciprocating pump consists of the power end (i.e., crankshaft, connecting rod, and crosshead) and the hydraulic end (i.e., piston assembly, piston cylinder, pump head body, packing box, suction valve, and discharge valve). The hydraulic end operates by driving the piston to reciprocate in the piston cylinder to cause periodic changes in the working chamber volume, thereby changing the pressure inside the chamber. The specific working process is when the chamber pressure is less than or equal to the opening pressure of the suction valve, the suction valve opens, allowing fluid to flow from the outside of the pump to the inside. When the chamber pressure is greater than or equal to the opening pressure of the discharge valve, the discharge valve opens, allowing the pressurized fluid to be discharged from the inside to the outside of the pump. Figure 2 shows the schematic of the structure of the oil-gas multiphase pump, and the working parameters are listed in Table 1.
The schematic of the structure of the oil-gas multiphase pump.
To analyze the effect of clearance volume on the flow and discharge characteristics inside the multiphase pump, a thermodynamic model of the working chamber must be established, the internal flow and pressure variation inside the chamber should be investigated, the transient characteristics of the pressure of the multiphase pump with respect to the angle of rotation should be obtained, and the discharge characteristics of the multiphase pump must then be solved.
According to the state equation of ideal gas, the state equation of the gas–liquid two-phase mixed medium can be obtained as follows13 :
where V represents the total volume of the multiphase medium, V0 is the total volume of the multiphase medium in the initial state, β0 denotes the gas holdup at the initial state, mg is the mass of the gas, ml is the mass of the liquid, and m is the total mass of the multiphase medium.
Given that the heat exchange between the multiphase pump and the external environment is not considered, the entire system is adiabatic. Therefore, the energy conservation equation is14 :
where cvg represents the specific heat at a constant volume for gas, cl represents the specific heat capacity for liquid, and cg represents the specific heat capacity for gas.
The state equation for the adiabatic compression process of gas–liquid two-phase mixed media can be obtained by combining and integrating Eqs. (1) and (2), as shown as follows:
where p0 is the total pressure at the initial state, and a is the process index of adiabatic compression, \(a=\frac{{{m_g}R}}{{{m_g}{c_{vg}}+({m_l} - {m_g}){c_l}}}\) .
Given the presence of clearance volume, the working process of the multiphase pump increases to include the suction, expansion, compression, and discharge processes. From the perspective of engineering applications, the size of the clearance volume must be controlled within a reasonable range. If the clearance volume is less than the minimum value of the reasonable range, then the piston will affect the pump head at the end of the stroke, leading to piston seizure and damage to components, which will affect the normal operation and service life of the multiphase pump. When the clearance volume exceeds the maximum value of the reasonable range, then suction flow rate will decrease or air lock will occur, thereby seriously reducing the volumetric efficiency of the multiphase pump.
Figure 3 shows the p–V diagram of the entire working process of the multiphase pump. In the figure, 1–2, 2–3, 3–4, and 4 − 1 represent the compression, discharge, expansion, and suction processes. Given the existence of the clearance volume V0, when the piston finishes the discharge process and returns, the suction valve cannot open immediately. The suction process can only proceed when the high-pressure gas in the clearance volume V0 expands from V3 to V4 and the pressure drops from p2 to p1, the opening pressure of the suction valve.
When the clearance volume increases to V0′, the expansion process continues to lengthen, and the slope of the 3–4 curve increases to 3′-4′, causing the compression process to increase and resulting in a reduction in suction and discharge time, thereby seriously affecting the pump’s efficiency.
The p–V diagram of the entire working process of the multiphase pump.
The kinematic diagram of the mechanism is shown in Fig. 4. On the basis of the structural form of the multiphase pump, the approximate equation for the piston displacement in one revolution of the crankshaft is obtained.
The kinematic diagram of the mechanism.
Assuming the x-axis as the negative direction, the approximate equation for the piston displacement is:
where \(\lambda\) is the connecting rod ratio, \(\lambda =\frac{r}{l}\) .
By taking the time derivative of Eq. (4), the approximate equation for the piston velocity is obtained as follows:
Section 3D modeling, grid generation, and dynamic mesh setup will focus on utilizing this information to develop a program for the user-defined function (UDF) control module in dynamic mesh settings.
The working processes of Working Chambers I and II in the multiphase pump are completely the same, with only differences in the chamber volume. Thus, the modeling and analysis were only be conducted for Working Chamber II. The 3D full flow passage model is shown in Fig. 5.
The 3D full flow passage model.
The flow passage was partitioned into unstructured meshes using the Mesh module of Workbench. A tetrahedral mesh was generated for the piston chamber section using a sweeping method, whereas a hexahedral mesh was generated for the remaining passages using local refinement.
As the number of mesh divisions increases, the computed results will be closer to the actual conditions15 .Therefore, to ensure computational accuracy while considering computational speed, mesh independency verification was performed. When the clearance volume is 5% and the gas volume fraction is 10%, the results of the independency verification are shown in Fig. 6. From the figure, when the mesh count exceeds 678,975, the average flow rate stabilizes at a constant value, demonstrating that the mesh count no longer affects the simulation results. Therefore, the mesh count of 678,975 was selected for the calculation mesh. The mesh partitioning effect is shown in Fig. 7.
The results of the independency verification.
Due to the changing shape of the flow field over time according to the movement of the piston, a dynamic mesh model must be established to simulate this motion and variation.
The motion boundary was defined by a UDF, and the piston motion procedure was obtained according to Eq. (5):
The results of the independence of the time step size verification.
On the basis of the independence of the time step size verification (as shown in Fig. 8), when the time step sizes are 0.007 s and 0.008 s, the medium’s average pressure increases to a certain value before fluctuating at a minimum. Therefore, the time step size has little effect on the simulation results. To improve computational speed, 0.008s was selected as the step size for each step.
Combining the actual operating characteristics of the multiphase pump, the physical property parameters of the fluid inside the multiphase pump were set. Given that the transported medium is a two-phase mixture of gas and liquid, the first phase was set as the liquid phase of crude oil, and the second phase was set as the gas phase of natural gas. The detailed parameters of the medium are shown in Table 2.
In addition, a pressure-based solver was selected, and the solution methods utilize the pressure-velocity coupling of the PISO algorithm. The y + value in this paper is between 20 and 50, which satisfies the requirements of the \(k - \varepsilon\) turbulence model in the near-wall region. Therefore, the turbulence model is the standard \(k - \varepsilon\) turbulence model. The inlet and outlet boundary conditions were set as pressure boundaries, the inlet pressure set to 0.2 MPa, the outlet pressure set to 0.8 MPa, and the wall conditions were set as adiabatic conditions. Given the fact that the gas volume fraction transported by the multiphase pump would continuously change with different oil wells or development cycles, and the interaction between gas phase and liquid phase inside the pump was currently unclear, a mixture model that does not require explicit interaction between various parameters was selected for the solution.
The theoretical instantaneous flow rate expression for oil-gas multiphase pump is:
After the construction of the simulation model for the multiphase pump, simulation of the multiphase pump with a clearance volume of 7% was performed and compared with the theoretical value. The comparative results are shown in Fig. 9. The theoretical and simulated values show good overall consistency in trend, verifying the rationality and accuracy of the model built. Given that the liquid is incompressible, ideally, the gas volume fraction should be 0, and the opening angle of the discharge valve should be 180°; however, in the simulation data, it is 192.96°. The reason is that the simulation was set up for the first intake and discharge process of the pump, and before this, no medium was present inside the pump. Given the presence of the clearance volume, the medium inside the pump could not be completely discharged to the outside of the pump. Therefore, the simulated data show that the opening angle of the discharge valve is 12.96° higher than the theoretical value, which is the angle through which the pump overcomes the clearance volume.
The comparative results between theoretical value and simulated value.
This study adopts the method of controlling variables. Gas volume fraction is an irrelevant variable; clearance volume is the independent variable; and pressure, streamlines, and velocity vectors are the dependent variables.
Figure 10 shows the gas volume fraction β at 40%, with clearance volumes VC ranging from 5%, 10%, 15%, to 20%. The piston is at the same crank angle (φ = 220°), displaying the pressure distribution contour maps during the compression process of the pump.
The pressure distribution contour maps at different clearance volumes.
From the figure, for flow channels with different clearance volumes, the pressure from the piston position to the exhaust valve shows a gradual decrease. At the same time, with the increase of the clearance volume, the average pressure inside the flow channel gradually decreases. The reason is that the increase in the independent variable leads to more residual gas in the chamber, thereby prolonging the compression process. Moreover, the clearance volume has a lagging effect on pressure increase, which will cause the delayed opening time of the exhaust valve.
Figure 11 shows the gas volume fraction β at 40%, with clearance volumes VC ranging from 5%, 10%, 15%, to 20%. The piston is at the same crank angle (φ = 220°), displaying the streamline distribution contour maps during the compression process of the pump.
The streamline distribution contour maps at different clearance volumes.
The diagram shows that for flow channels with different clearance volumes, the velocity distribution exhibits a gradual decrease from the piston to the outlet. Despite the difference in clearance volumes, the distribution of streamlines has not undergone significant changes. A minor turbulent phenomenon appears at the far right of Working Chamber II when the clearance volume is 20%. Turbulent flow lines will cause a certain degree of energy loss. Therefore, the larger the clearance volume is, the more fluid energy loss will occur, leading to a decrease in head and flow rate16 . The clearance volume only significantly affects the flow velocity, and its influence on the distribution of streamlines can be neglected.
Figure 12 shows the gas volume fraction β at 40%, with clearance volumes VC ranging from 5%, 10%, 15%, to 20%. The piston is at the same crank angle (φ = 300°), displaying the velocity vector distribution during the discharge process of the pump.
The velocity vector distribution at different clearance volumes.
The figure shows that for flow passages with different clearance volumes, different degrees of vortex flow occur, and with the increase of clearance volume, the area of vortex flow also gradually expands. The generation of vortex flow will cause a decrease in discharge flow rate, leading to cavitation, noise, and other problems. Therefore, in the structural design, the size of the clearance volume should be carefully controlled to avoid its excessive adverse effects.
The analysis in Section Analysis of the effect of clearance volume on the internal flow field indicates that the existence of clearance volume will have a certain effect on the pressure rise and discharge flow rate of the working chamber. Therefore, this section focuses on the specific numerical changes caused by the clearance volume in the pressure rise process and flow characteristics.
Figure 13 shows the curve of medium pressure change with crank angle when the gas volume fraction is constant and the clearance volume VC is 5%, 10%, 15%, and 20%.
The curve of medium pressure change at different clearance volumes.
The figure shows that the larger the clearance volume is, the slower the pressure rise will be, that is, the crank angle–pressure curve is flat. Specifically, when the clearance volume is 5%, the crank angle needs to rotate 273.73° as the working chamber pressure increases from 0.2 MPa to 1 MPa. However, when the clearance volume increases to 10%, the same pressure increase process requires the crank angle to rotate 282.19°; as the clearance volume continues to increase to 15%, the crank angle further increases to 292.94°; and when the clearance volume reaches 20%, this value becomes 302.91°, representing a 10.66% increase in time compared with the 5% clearance volume. At the same time, if a further increase in the chamber pressure is required, the lag effect of the clearance volume on the pressure rise process will become significant, further prolonging the compression time. Therefore, the clearance volume has a significant effect on the pressure rise process due to the increasing amount of gas remaining in the flow path after the discharge process, leading to a higher gas volume fraction in the next working cycle and thus an increase in the pressure rise process.
The increase in clearance volume leads to a lengthening of the pressure rise process, resulting in a delayed opening time of the discharge valve, which, in turn, affects the suction volume of the multiphase pump. Therefore, the specific effect of the clearance volume on the delayed opening angle of the discharge valve should be studied in detail.
Lag angle of discharge valve opening at different clearance volumes.
The Fig. 14 shows a nearly linearly positive correlation between the opening lag angle of the exhaust valve and the clearance volume. When the clearance volume is 5%, the opening lag angle of the exhaust valve is 88.19°. When the clearance volume increases to 20%, the opening lag angle of the exhaust valve is 113.83°. In comparison with the 5% clearance volume, the opening of the exhaust valve is delayed by 0.066 s.
Figure 15 shows the curve of the instantaneous discharge flow rate with the crank angle at different clearance volumes. The figure shows that the larger the clearance volume is, the smaller the instantaneous discharge flow rate will be. The reason is that the clearance volume affects the start time of the discharge process, which can also be seen in the effect of the clearance volume on the lag angle in Section Effect of clearance volume on pressure rise rate. The larger the clearance volume is, the later the start time of the discharge process will be. At the same time, when the clearance volume is 20%, a backflow phenomenon occurs in the latter half of the discharge process. The reason for the difference between the theoretical and actual flow rates lies in the fact that the theoretical flow rate is based on the formula derived under the conditions of the pump in pure water medium with no clearance volume. However, in practical applications, the air content and clearance volume will have certain effects on the discharge flow rate.
The curve of the instantaneous discharge flow rate at different clearance volumes.
Figure 16 shows the maximum flow rate Qmax, average flow rate Qm, and minimum flow rate Qmin at different clearance volumes. From the figure, the presence of clearance volume affects the maximum flow rate Qmax, average flow rate Qm, and minimum flow rate Qmin. The larger the clearance volume is, the smaller the maximum flow rate Qmax, average flow rate Qm, and minimum flow rate Qmin will be. At the same time, with the increase in clearance volume, the decreasing trend of the maximum flow rate Qmax and average flow rate Qm is basically the same. The decrease in the minimum flow rate Qmin is particularly pronounced when the clearance volume increases from 5 to 10%, decreasing by approximately 3.75 m3/h.
The maximum flow rate Qmax, average flow rate Qm, and minimum flow rate Qmin at different clearance volumes.
Due to the characteristic of instantaneous flow rate not being constant for the piston pump, the situation of instantaneous flow rate pulsation must be evaluated using the pulsation rate of flow.
Figure 17 shows the upper flow rate pulsation rate δQ1 and the lower flow rate pulsation rate δQ2 under different clearance volumes. The figure shows that the upper and lower flow rate pulsation rates increase with the clearance volume, and the lower flow rate pulsation rate is always greater than the upper flow rate pulsation rate. The increasing trend of the upper flow rate pulsation rate is basically unchanged. When the clearance volume increases from 5 to 20%, the upper flow rate pulsation rate increases by about 41.87%. The response of the lower flow rate pulsation rate to the increase of clearance volume is quite different. When the clearance volume increases from 5 to 10%, the lower flow rate pulsation rate increases significantly, by about 30%. When the clearance volume increases from 10 to 15%, the increase of the lower flow rate pulsation rate is insignificant, only increasing by about 5.71%. Furthermore, when the clearance volume increases from 15 to 20%, the lower flow rate pulsation rate begins to increase dramatically, by about 25.39%. Flow pulsation can cause noise in the multiphase pump, and it can be transmitted through the pipeline to other components upstream and downstream, causing the other components to vibrate17,18 . Therefore, the clearance volume must be minimized as much as possible to eliminate the influences of vibration and noise as much as possible.
The upper flow rate pulsation rate δQ1 and the lower flow rate pulsation rate δQ2 under different clearance volumes.
Due to the compressibility of gases, the concept of gas volume fraction must be discussed when the pressure is equal. Based on this, the values of gas volume fraction presented in this paper are under standard atmospheric pressure. Furthermore, since the inlet pressure of the multiphase pump does not conform to standard atmospheric pressure, it is necessary to convert the gas volume fraction at the standard atmospheric pressure to the gas volume fraction at the inlet pressure before the simulation of the gas volume fraction as a variable. Gas volume fraction under different inlet pressures are shown in Table 3.
The relationship between the clearance volume, gas volume, and lag angle can be obtained through the relationship between the clearance volume and the lag angle and that between the gas volume and the lag angle19 .
Figure 18 shows that when the gas volume fraction is constant, an increase in clearance volume will lead to a corresponding increase in the lag angle, causing the relationship curve to exhibit a steeper trend. At the same time, when the clearance volume Vc is set to 5%, 10%, 15%, and 20%, and the gas volume is set to 20%, 40%, 60%, and 80%, data records show certain operating conditions where the exhaust valve opening lag angle is not reached. The reason for this phenomenon is that the gas volume fraction inside the pump remains at a relatively high level under these specific operating conditions. Therefore, even when the piston moves to the end of its stroke, the pressure of the medium inside the pump cannot reach the opening pressure of the exhaust valve, causing the exhaust valve to fail to open normally. As a result, the medium inside the pump only undergoes compression and expansion processes, causing the multiphase pump to remain in a gas-locked state. When the multiphase pump is in a gas-locked state, not only does it affect normal operation, but gas locking is often accompanied by hydraulic shocks, which may cause damage to the components of the mixing pump, thereby seriously affecting the reliability of the mixing pump. Therefore, when the gas volume fraction of the production fluid in the oil well is relatively high, designing oil-gas multiphase pumps with a large clearance volume should be avoided to ensure operational safety and reduce unnecessary risks.
The relationship between the clearance volume, gas volume, and lag angle.
On the basis of Fig. 18, when the gas volume fraction of the well is known, the corresponding range of the annular volume for normal operation of the multiphase pump can be obtained (as shown in Fig. 19). When the operating conditions meet the requirements below the curve, the oil-gas multiphase pump can operate normally. However, when the operating conditions are above the curve, the oil-gas multiphase pump will experience gas locking, thereby affecting its normal operation. At this point, adjusting the annular volume of the oil-gas multiphase pump to adapt to the field environment can ensure that it operates normally at the oil well site.
The relationship between the clearance volume and gas volume.
This paper adopts a numerical simulation method to investigate the effect of clearance volume on the internal flow characteristics and output performance of the oil-gas multiphase reciprocating pump. The following conclusions are drawn:
With the increase of clearance volume, the pressure and fluid velocity show a gradually decreasing trend, whereas the vortex flow increases in quantity and intensity.
With a constant gas volume fraction, as the clearance volume increases, the medium pressurization speed gradually slows down, and the lag angle of discharge valve opening gradually increases. In addition, the maximum, average, and minimum flow rates are negatively correlated with the clearance volume, whereas the upstream and downstream flow pulsation rates are positively correlated with the clearance volume.
The study identifies the range of clearance volume corresponding to the normal operation of the oil-gas multiphase pump when the gas volume fraction in the oil well is known. The gas volume fraction–clearance volume relationship curve is crucial for optimizing the design of the multiphase pump and improving its efficiency. It serves as an important basis for guiding and improving pump performance.
All data generated or analysed during this study are included in this published article.
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This work was funded by the Research Initiation Fund at Qingdao University of Technology (2005-20312011)and the Key Scientific Research Cultivation Project at Qingdao University of Technology(2005-203360003).
Department of Mechanical and Electrical Engineering, Qingdao University of Technology, Qingdao, 266520, China
Xuemin Jing, Yongqi Wang & Xuefeng Zhang
Weihai Yinxing Prestressed Wire Co., Ltd, Weihai, 264200, China
School of Mechanical, Electrical and Information Engineering, Shandong University, Weihai, 264200, China
School of Mechanical Engineering, Shandong University of Technology, Zibo, 255049, China
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Conceptualization, X. J. and X. Z.; Methodology, X. J. and X. W.; Software, X. J.; Investigation, X. J. and X. W.; Formal analysis, X. J.; Writing – original draft, X. J.; Writing – review & editing, X. W. and Y. W.; Funding acquisition, Y. W. and X. W.; Supervision, X. Z. All authors have read and agreed to the published version of the manuscript.
The authors declare no competing interests.
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Jing, X., Wang, Y., Zhang, X. et al. Effect of clearance volume on the internal flow characteristics and output performance of oil-gas multiphase reciprocating pump. Sci Rep 14, 23580 (2024). https://doi.org/10.1038/s41598-024-73442-4
DOI: https://doi.org/10.1038/s41598-024-73442-4
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