Structural Optimization and Numerical Simulation Research of Anti-Air Lock Variable-Diameter Oil Pump

Abstract

Under the condition of gas–liquid two-phase flow, traditional sucker rod pumps are prone to gas locking due to the high compressibility of gas, and their volumetric efficiency is usually less than 30%, which seriously restricts the exploitation benefits of oil wells. To solve this difficult problem, this study proposes a variable-diameter tube pump structure that adopts an optimized cone angle of the pump cylinder. The results of computational fluid dynamics simulations using dynamic mesh modeling indicate that the stepped change in the pump barrel diameter can enhance the gas–liquid separation effect caused by vortices, while the flow-guiding grooves on the valve seat can reduce the response delay. Comparative calculations and analyses show that compared with the traditional design, its head increases to 13.89 m, and the hydraulic power rises to 1431.01 W, respectively, representing an increase of 17%. This is attributed to the reduction in the gas retention time during piston reciprocation and the stability of the flow field. This structural innovation effectively alleviates the gas lock problem and provides a feasible approach for improving energy efficiency in oil wells prone to vaporization, which is of great significance in oilfield development operations.

1. Introduction

Underground deep well pumping oil technology bears the strategic responsibility of ensuring energy supply. The “World Energy Outlook” released by the International Energy Agency (IEA) and the “Sustainable Energy Development Directive” issued by the European Union, which both clearly state that major oil companies should enhance energy utilization efficiency in deep well oil extraction projects and promote the green and sustainable development of the industry [1,2]. As the core equipment for mechanical oil extraction, the energy consumption of sucker rod pump oil extraction equipment has accounted for more than 30% of total energy consumption in the oilfield. The performance of its core component, the oil pump, directly affects the efficiency and stability of the entire extraction system [3].

Under the high-gas–liquid-ratio conditions of traditional oil pumps, during the reciprocating motion of the pump cylinder, due to gas compression, the pressure inside the cylinder lags behind, and the slide valve or fixed valve cannot open in time, resulting in insufficient suction and discharge of the medium. This leads to frequent gas locking and aggravates flow separation, significantly reducing the efficiency of the oil pump (its volumetric efficiency is less than 30%). To solve this problem, many scholars have developed various anti-air lock oil pump structures [4,5,6].

G.H. Lu et al. [7] designed a magnetic forced opening air-proof pump by using magnetic assistance to force the opening and closing of the valve ball, fundamentally solving the problem of the air lock. Field experiments showed that the pump efficiency of the magnetic forced-opening air-proof pump was 11.5% higher than that of the conventional oil extraction pump. W.W. Wang et al. [8] designed an upper-exchange air-proof oil pump by opening a unique ventilation groove structure on the upper part of the pump cylinder. In oil wells with a high gas–oil ratio, the one-time pumping rate of the upper-exchange air-proof oil pump reached 100%. Compared with ordinary oil pumps, the average pumping efficiency of the upper-exchange air-proof oil pump increased by 7.3%. Y.M. Lu et al. [9] designed an upper-exchange gas-proof oil pump and an exhaust channel for the liquid in the lower layer to address the gas lock problem in multi-layer mining, which provided a solution to the influence of gas on the pump’s operating conditions. Y. Gao et al. [10] optimized the structural design of the anti-gas oil pump through numerical simulation and opened pressure-guiding holes on the plunger to prevent gas locking. It is applicable to various gas–liquid ratios and ensures the stable operation of the entire system. J. Saponja et al. [11] have engineered a new ideal tubing anchor for 5.5-inch casing specifically to address the production challenges in horizontal wells and allow for full production maximization through the use of packerless gas separators. For the various existing anti-air lock oil pump technologies mentioned above, although they can provide an anti-air lock effect, there are still certain problems in practical applications, such as adaptability limitations, different requirements for complex working conditions, and high manufacturing and maintenance costs due to their complex structures. Therefore, in response to the above problems, this paper designs a variable-diameter anti-air lock oil pump. It has a simple structure, is suitable for most working conditions, has strong adaptability, and can effectively improve pump efficiency.

In recent years, scholars have conducted relatively few numerical simulation studies on the pumping units of oil extraction pumps. L C Li et al. [12] used dynamic mesh technology and UDF programming to simulate the process of fluid entering the pump during the upward stroke, obtaining the distribution of the flow field, pressure changes, and the movement characteristics of the valve ball inside the pump and thus providing a reference for the design of the pump flow path and the study of working conditions. W D Ye. [13] observed the flow characteristics of the two-phase medium in the pump cylinder based on the theory of gas–liquid two-phase flow and dynamic mesh technology and obtained the design parameters for three types of anti-gas pumps that affect volumetric efficiency and stroke loss under different conditions, providing a methodological theory for the discrimination of oil extraction pump performance. N Liang et al. [14] optimized the parameters of pressure-guiding holes by changing the internal structure of the anti-gas oil extraction pump and using CFD technology, effectively improving the efficiency of gas–liquid separation and avoiding the occurrence of gas lock. L Liu et al. [15] clarified the influence of different stroke lengths and pump efficiency on the bottom hole pressure within the pump cylinder of an ultra-long-stroke oil extraction pump based on relevant calculation models and improved the flow conditions of the fluid in the wellbore through the simulation of fluid properties. Jalikop et al. [16] simulated the dynamic behavior of the traveling valve and standing valve throughout the entire pump cycle using the Finite Element Method (FEM) coupled with dynamic meshing techniques, serving as a highly valuable simulation methodology and design philosophy for this research. In addition, Newton C. H et al. [17] building upon existing research, have conducted innovative explorations into methods for enhancing the volumetric efficiency of oil recovery pumps. Carvalho et al. [18] explored the influence of water content, fluid viscosity, and gap on fluid slip and pump efficiency and determined the viscosity of the emulsion in the sucker rod pump. Utemissova, L et al. conducted an in-depth analysis of historical failure data from downhole pumping equipment and incorporated these data into algorithms to calculate the operational status of downhole equipment [19]. Ma, B et al., taking into account the coupling between the longitudinal vibration of the sucker–rod string and the wellbore flow, established the Comprehensive Mathematical Model of the Sucker-Rod Pumping System (CMSRS) and a mathematical model for downhole energy-efficiency parameters [20]. Despite these efforts, comprehensive numerical studies focusing on variable-diameter pump designs and their impact on gas–liquid separation and volumetric efficiency remain limited.

To address the gap between existing anti-gas lock solutions and the need for adaptable, cost-effective designs, this study proposes a variable-diameter oil pump structure with an optimized conical pump barrel. Through CFD simulations using dynamic meshing, we analyze the flow field, pressure distribution, and gas content variations during pump operation. The designed structure enhances gas–liquid separation through vortex-induced effects and reduces valve response delay via guided flow channels. This research aims to provide a robust, efficiency-driven pump design suitable for diverse and challenging well conditions, contributing to sustainable and energy-efficient oilfield operations.

2. Establishment of the Theoretical Model of the Oil Pumping Unit

The theoretical model of the oil pumping unit focuses on its core operational contradictions. By quantifying the pressure lag caused by gas compression and the delay in valve opening and closing in the gas–liquid two-phase flow, it accurately calculates the critical conditions of gas lock and the attenuation law of volumetric efficiency. This provides data support for subsequent fluid simulation and targeted improvement of valve structure and optimization of stroke and stroke rate parameters, effectively solving the technical bottleneck caused by the low efficiency of traditional oil pumping units under complex working conditions.

2.1. Internal Structural Construction of the Oil Pumping Unit

2.1.1. The Internal Structure of the Traditional Oil Well Pump

The structure of the traditional oil pumping pump is mainly composed of the pump barrel and the piston and is equipped with a moving valve (upper valve) and fixed valve (lower valve) as the core components. A schematic diagram of its working principle is shown in Figure 1.

The working logic of traditional oil pumping pumps is based on the reciprocating motion of the plunger to achieve the oil pumping cycle. During the upward stroke, as the plunger moves upward, a negative-pressure environment is formed inside the pump cylinder. The fixed valve is driven to open by pressure from the oil layer, and the mixed fluid of crude oil and gas enters the pump cylinder from the oil layer. At this time, the traveling valve remains closed due to the pressure of the upper liquid column, preventing liquid backflow. During the downward stroke, as the plunger moves downward, the pressure inside the pump cylinder suddenly increases. The fixed valve closes under pressure, and the traveling valve opens. The mixed fluid is pushed by the traveling valve to the upper part of the plunger, completing the drainage process. In the case of two-phase gas–liquid flow, the compression characteristics of the gas cause the pressure change inside the pump cylinder to lag, resulting in delayed valve opening and closing, which is very likely to trigger the gas lock phenomenon. This phenomenon will significantly reduce the volumetric efficiency of the pumping pump, and in actual operation, it often drops below 30%.

2.1.2. The Internal Structure of the Designed Variable-Diameter Pumping Unit

The variable-diameter oil pumping pump designed in this paper adopts a variable cross-sectional pump cylinder structure. Through the stepwise change in the inner diameter of the pump cylinder, a non-equal diameter direct passage is formed, as shown in Figure 2.

The variable-diameter structure generates an eddy current effect through a sudden change in cross-sectional area, promoting gas–liquid separation; the design of the guide channel reduces the lag in valve opening and closing and lowers the flow resistance. The design is based on the principles of gas–liquid two-phase flow dynamics. It utilizes the local pressure gradient generated by the abrupt change in cross-section to promote the aggregation and separation of gases, and from the perspective of the flow channel structure, it inhibits the gas lock effect of traditional pumping units when the gas–liquid mixture is transported.

Table 1. Geometric dimensions and parameters.

Pump Barrel Inside Diameter	Traveling Valve Bore	Reduced End Diameter	Length of the Tapered Section
44 mm	32 mm	64 mm	150 mm

presents the specific geometric parameters of several tapered sucker rod pumps. Compared with the traditional equal-diameter pump cylinder, the variable-diameter structure can reduce the gas content in the pump cylinder and optimize the velocity field and pressure field distribution in the pump cylinder during the reciprocating motion of the plunger. When the plunger moves upward to the large-diameter conical section, the liquid at the bottom of the oil pipe will rapidly enter the pump cylinder, causing the pressure inside the pump cylinder to increase and the gas content of the plunger section to drop significantly, thereby avoiding the occurrence of the gas lock phenomenon. Meanwhile, the retention time of the gas in the pump cylinder is shortened, and the aggregation efficiency of the dispersed bubbles is significantly improved. In addition, the streamlined chamfering treatment in the variable-diameter transition area helps to reduce fluid separation losses. This structural innovation changes the flow boundary conditions of the fluid within the pump cylinder, fundamentally optimizing the trajectory of the two-phase gas-liquid flow. It provides a new technical path for solving the problems of low volumetric efficiency.

2.2. Establishment of the Calculation Model

Based on the multiphase flow dynamics theory, a mathematical model describing the gas–liquid two-phase flow within the pumping unit was constructed by coupling continuity, momentum conservation and state equations. The derivation aims to reveal the evolution laws of pressure distribution, velocity field and phase distribution within the pump barrel at the theoretical level, providing a physical basis for subsequent numerical simulations and ultimately predicting key performance indicators such as pump efficiency through the model to guide the structural optimization of variable-diameter pumping units.

Derivation of the Physical Equation

Based on the law of conservation of mass, continuous equations for the liquid phase and the gas phase are respectively established.

The liquid-phase continuity equation is as follows:

$${\displaystyle \frac{\partial \left({\alpha }_l{\rho }_l\right)}{\partial t}}+\nabla \cdot \left({\alpha }_l{\rho }_l\overrightarrow{v_l}\right)=0$$

(1)

$${\displaystyle \frac{\partial \left({\alpha }_g{\rho }_g\right)}{\partial t}}+\nabla \cdot \left({\alpha }_g{\rho }_g\overrightarrow{v_g}\right)=0$$

(2)

Here, ${\alpha }_l$ represents the liquid-phase volume fraction; ${\alpha }_g$ represents the gas-phase volume fraction; ${\rho }_l$, ${\rho }_g$ represent the corresponding densities; and $\overrightarrow{v_l}$, $\overrightarrow{v_g}$ represent the velocity vectors. This equation describes the mass conservation characteristic of the gas–liquid two-phase medium flowing within the pump barrel, taking into account the changes in phase volume fractions over time and space.

Based on Newton’s second law, the momentum equation for the mixed phase is established:

$${\displaystyle \frac{\partial \left({\rho }_m\overrightarrow{v_m}\right)}{\partial t}}+\nabla \cdot \left({\rho }_m\overrightarrow{v_m{v}_m}\right)=-\nabla p+\left(u_m\nabla \overrightarrow{v_m}\right)+{\rho }_m\overrightarrow{g}+\overrightarrow{F_{\mathrm{int}}}$$

(3)

Here, ${\rho }_m={\alpha }_l{\rho }_l+{\alpha }_g{\rho }_g$ represents the mixed density, ${\mu }_m$ represents the mixed density, $\overrightarrow{v_m}$ represents the mixed-phase velocity, $p$ represents the pressure, $\overrightarrow{g}$ represents the gravitational acceleration, and $\overrightarrow{F_{\mathrm{int}}}$ represents the inter-phase force between gas and liquid (such as drag force, lift force, etc.). This equation takes into account the effects of inertial force, pressure gradient, viscous force, gravity, and inter-phase coupling on fluid motion and is used to describe the momentum transfer law of the flow field within the pump barrel.

The equation of state for the gaseous phase follows the ideal gas law:

$$p={\displaystyle \frac{{\rho }_{g}RT}{M_g}}$$

(4)

Here, $R$ represents the gas constant, $T$ represents the temperature, and $M_g$ represents the molar mass of the gas. This is used to describe the relationship between gas-phase pressure and density. The liquid-phase state equation takes into account the volume compressibility of crude oil and water and characterizes the influence of pressure changes on the liquid-phase density through the state equation in order to adapt to the pressure fluctuations caused by the reciprocating motion within the pump cylinder.

The formula for the volumetric efficiency of the oil pump is

$${\eta }_v={\displaystyle \frac{Q_{actual}}{Q_{theoretical}}}\times 100\%$$

(5)

Among them, $Q_{theoretical}$ represents the theoretical displacement, which is directly determined by the piston diameter, stroke length and stroke frequency; $Q_{actual}$ represents the actual displacement, which needs to account for the effects of gas compression, valve leakage, fluid leakage, etc. The core principle lies in solving the actual filling and discharging volumes within the pump cylinder through the gas–liquid two-phase flow equation.

The above equation is based on the multiphase flow dynamics theory. By coupling continuity, momentum conservation and state equations, it constructs a mathematical model to describe the gas–liquid two-phase flow within the pumping unit. Its derivation aims to reveal the evolution laws of pressure distribution, velocity field, and phase distribution within the pump barrel at the theoretical level. This provides a physical basis for subsequent numerical simulations and ultimately predicts key performance indicators such as pump efficiency through the model, guiding the structural optimization of variable-diameter pumping units.

Combining fluid mechanics and multiphase flow theory, we can establish the relationship equation between diameter variation and separation efficiency.

According to the ascending speed of Stokes gas,

$$V_b={\displaystyle \frac{g{d}_b^2({\rho }_l-{\rho }_g)}{18{\mu }_l}}$$

(6)

Among them, ${\rho }_l$ and ${\rho }_g$ represent the densities of liquids and gases, respectively; ${\mu }_l$ represents the viscosity of liquids; and $d_b$ indicates the diameter of bubbles.

Whether a bubble is separated is determined by its vertical velocity. If the upward velocity of the bubble carried by the liquid is $V_{f\left(z\right)}$ less than the upward velocity of the buoyancy itself, $V_b$, and separation can be achieved, then the critical diameter is

$$D_{crit}(z)=\sqrt{{\displaystyle \frac{4Q_l}{\pi V_b}}}$$

(7)

Here, $Q_l$ represents the volume flow rate of the liquid. At the given flow rate, the diameter of the pump cylinder must be greater than the critical value.

The fluid shifts from $z=0$ motion to $z=L$ required residence time and $t_{res}$ integral:

$$t_{res}={\int }_0^L{\displaystyle \frac{1}{v_f\left(z\right)}}dz={\int }_0^L{\displaystyle \frac{A\left(z\right)}{Q_1}}dz={\displaystyle \frac{\pi }{4Q_l}}{\int }_0^L{D\left(z\right)}^{2}dz$$

(8)

$A\left(z\right)$ represents the cross-sectional area of the conical segment at position $z (0\le z\le L)$, and $D\left(z\right)$ is defined as the function describing the variation in the conical segment’s diameter with position $z$.

The separation efficiency $\mathrm{ղ}$ is expected to be positively correlated with the ratio ${t_{res}/t}_{trap}$, as this condition ensures that the escape time $t_{trap}\approx D_{max}/2V_b$ (the time taken for gas to reach the top wall) is less than the fluid’s residence time $t_{trap}<t_{res}$, allowing complete separation before the fluid exits.

$$\mathrm{ղ}\propto {\displaystyle \frac{(\frac{\pi }{4Q_l}{\int }_0^L{D\left(z\right)}^{2}dz)}{(\frac{D_{max}}{2V_b})}}={\displaystyle \frac{\pi V_b}{2Q_l{D}_{max}}}{\int }_0^L{D\left(z\right)}^{2}dz$$

(9)

Substituting the diameter variation function $D\left(z\right)=D_{min}+kz$ into the integration term (9), where $k=(D_{max}-D_{min})/L$ and the proportionality constant $C$ (which is experimentally determined and including all the modifications of the simplified assumptions), the relationship equation between the separation efficiency and the diameter is obtained:

$$\mathrm{ղ}={\displaystyle \frac{C\pi V_{b}L(D_{max}^3-D_{min}^3)}{6Q_l{D}_{max}(D_{max}-D_{min})}}$$

(10)

From the above equation, it can be seen that increasing the outlet diameter is an effective means of improving efficiency. It greatly reduces the outlet flow rate and provides a larger space for gas aggregation, which works in accordance with practical experience of the mine.

2.3. Pre-Processing Settings for Simulation

Precise simulation preprocessing is critical for capturing transient gas–liquid interactions in reciprocating pumps. Dynamic mesh settings enable accurate modeling of plunger motion and valve dynamics, while initial conditions directly govern flow field evolution. These configurations ensure physical fidelity of multiphase flow simulations, forming the foundation for subsequent performance analysis.

2.3.1. Initial Condition Settings

The model used was the standard $\mathrm{k}-\mathsf{\epsilon }$ turbulence model with a turbulence intensity set at 5%. The standard $\mathrm{k}-\mathsf{\epsilon }$ turbulence model can capture the mainstream velocity changes and vortex generation regions caused by diameter variation, which are precisely the macroscopic flow field characteristics that affect gas–liquid separation. The Eulerian multiphase flow model was selected, with crude oil and gas as the materials. The density of crude oil was set to 890 kg/m³. Based on the simulation software (Fluent 2022 R1), the initial flow field was set at the bottom dead center of the piston. A pressure inlet (2 MPa) was used to simulate reservoir inflow, while the discharge boundary was set as a pressure outlet with a gas content of 40% and a stroke length of 1.8 m.

2.3.2. Dynamic Mesh Settings

The grid adopts a tetrahedral grid, with an average size of 1 mm. The reciprocating motion of the plunger in the oil pump and the movement of the small ball in the fixed valve are simulated using layering method. Among them, the opening and closing of the standing valve and traveling valve inside the oil pump, as well as the reciprocating motion of the plunger, are implemented via UDF compilation to ensure adherence to normal operational patterns.

3. Numerical Simulation

The flow field inside the oil pump was numerically simulated using FLUENT software. The movement of the plunger in the oil pump was controlled by the UDF program. The variation cloud diagrams and data of the flow field inside the oil pump were thus obtained. The results of the numerical calculation were sorted and compared and analyzed to compare the performance of the traditional oil pump and the variable-diameter oil pump.

3.1. Performance Analysis of the Traditional Oil Pump

As shown in Figure 3, during the upstroke phase, as the plunger moves upward driven by the sucker rod, the standing valve gradually opens, allowing fluid to enter the pump barrel via the difference in pressure. Oil and gas separate, with gas accumulating at the lower end of the plunger. When the plunger reaches the top dead center, the gas content in the upper part of the pump barrel is at its highest. The increasing presence of gas in the pump chamber leads to a slower decrease in pressure, which may result in “gas lock” and significantly reduce oil production efficiency.

3.2. Performance Analysis of Variable-Diameter Pump

Figure 4 shows the pressure and gas content variation curves in the pump barrel of the gas-proof pump during one cycle. The simulation results indicate that during the upstroke phase, as the plunger continuously moves upward, the gas content in the pump barrel increases due to gas expansion, while the pressure inside decreases. When the pressure reaches the standing valve-opening pressure, the standing valve ball opens, allowing reservoir fluid to rapidly enter the pump barrel. Subsequently, the pressure in the pump barrel gradually stabilizes at 2 MPa.

Figure 5 shows the pressure and gas content rate variation curves of the variable-diameter oil pump within one cycle. When the plunger of the oil pump enters the variable-diameter section, due to the internal–external pressure difference, the pressure inside the pump barrel rapidly increases from 2 MPa to 8 MPa, causing the standing valve to close quickly and preventing reservoir fluid from entering the pump barrel. The pressure difference across the plunger changes from 6 MPa to 2 MPa. Simultaneously, crude oil from the tubing enters the pump barrel, significantly reducing the gas content inside and disrupting the gas–liquid phase stratification. At this stage, when the plunger moves downward during the downstroke, the traveling valve can open smoothly, preventing the occurrence of “gas lock”.

When the plunger enters the downstroke phase, the pressure inside the pump barrel stabilizes at the tubing pressure (8 MPa). As the traveling valve opens, the liquid in the pump barrel is discharged, leading to an increase in the gas content within the barrel. Since the pressure inside the pump barrel has already reached the opening pressure of the traveling valve before the downstroke begins, the variable-diameter pump experiences no stroke loss during the downstroke compared to conventional pumps.

3.3. Comparative Analysis of Oil Pump Performance

Compared with conventional oil pumps, the variable-diameter oil pump fundamentally eliminates the conditions for gas lock occurrence, ensuring continuous operation even under extremely high gas–liquid ratios. By achieving primary gas–liquid separation within the pump, it enhances the effective discharge volume per stroke, significantly increasing overall liquid production and operational efficiency.

Figure 6 shows the gas content variation curve in the pump barrel when the taper of the variable-diameter section is reduced. When the plunger enters the tapered section, the gas content in the pump barrel is significantly reduced to 40%. In contrast, as shown in Figure 4b, a large-taper variable-diameter pump can reduce the gas content to 15%. Therefore, increasing the taper of the variable-diameter section effectively lowers the gas content in the pump barrel, enhances the anti-gas locking performance, and ultimately improves pumping efficiency.

4. Experimental Verification

A field test was conducted in a well with a high gas–liquid ratio, where the submergence depth was 138 m and the dynamic fluid level was 764 m. Using identical polished rod speeds and identical theoretical displacements, the working efficiency of the conventional pumping unit was compared with that of the theoretical pumping unit.

Figure 7 illustrates the working condition of a conventional pumping unit. The right segment of the curve is inclined rather than vertical. This indicates that during the upstroke, the pump barrel was not completely filled with liquid. The plunger initially impacted and compressed the gas inside the pump before contacting the liquid level, resulting in a slow increase in the load. The left segment of the curve shows a pronounced concave shape. This is because during the downstroke, the opening of the standing valve (suction valve) was delayed. As a result, the sucker rods could not fully bear the weight during the descent, causing a rapid decrease in the polished rod load and leading to an abnormal load variation curve. This condition reduces pumping efficiency and decreases production. The pumping efficiency of this pump was 6.86%.

Figure 8 shows a field performance plot of the variable-diameter pumping unit. The curve is relatively full and regular, presenting an inclined parallelogram shape. This indicates a good degree of pump fillage and effective liquid lifting. At the beginning of the upstroke, the plunger first compresses the gas upward. Because the traveling valve is closed and the standing valve is open, the plunger instantly bears the full weight of the liquid column, causing a sharp load increase and a near-vertical rise in the curve. During the downstroke, the traveling valve opens promptly, releasing the pressure above the plunger and resulting in a rapid load drop. The pumping efficiency of this variable-diameter pump was 32.68%.

Based on the above situation comparison and analysis, under the same working conditions such as stroke, stroke count and submersion, the traditional oil pump and the variable diameter oil pump were tested. The variable diameter oil pump solved the air lock problem that occurred in the traditional oil pump, and the efficiency was increased by 25%, verifying the correctness and accuracy of the simulation.

5. Conclusions

Based on the structural design, numerical simulation, and experimental validation conducted in this study, the following conclusions can be drawn:

(1)

When the plunger of the variable-diameter pumping unit enters the tapered section, the pressure inside the pump barrel rapidly increases. Simultaneously, due to the inflow of liquid from the tubing, the gas content in the pump barrel decreases quickly, effectively preventing the difficulty of opening the traveling valve during the downstroke.

(2)

Compared to traditional pumping units, the variable-diameter pumping unit disrupts the separation of gas and liquid phases at the plunger during the downstroke. This significantly reduces the gas content while effectively avoiding gas lock, thereby improving pumping efficiency.

(3)

When the taper of the variable-diameter section is larger, the reduction in gas content as the plunger moves through this section becomes more pronounced. The mass flow rate of crude oil discharged from the pump barrel through the plunger increases, contributing to enhanced pumping unit efficiency.

(4)

Considering the complexity of the working environment of the oil pump and the limitations of time and other conditions, the geometric model optimization that affects the pump efficiency of the oil pump considered in this paper is still not perfect, with issues such as the taper size of the reducer section and the length of the reducer section remaining. In future research, a more complete geometric model should be established, multiple groups should be compared and analyzed, and the results should be optimized.