Study on Improving Liquid Carrying Performance of Horizontal Wells With Swirl Jet Composite Device

Abstract

ABSTRACT

In the later stages of horizontal gas well development, due to insufficient formation energy, the stratified flow of gas and liquid in the horizontal section generates a decrease in the well's liquid‐carrying capacity, accumulating liquid in the wellbore. Since the flow pattern of gas–liquid two‐phase flow in horizontal wells is significantly different from that in vertical wells, existing vertical well liquid removal and gas production technologies cannot be directly applied to address the liquid accumulation issues in horizontal wells. This paper presents a swirl jet composite device that, through the combination of a spiral guide belt and an internal flow channel, effectively integrates the jet and vortex effects, capable of transforming the stratified flow in the horizontal section into an annular flow, thereby enhancing the gas well's liquid‐carrying capacity. This study applies a combination of theoretical, experimental, and simulation methods to conduct computational fluid dynamics analysis on the device's ability to improve the gas well's liquid‐carrying capacity. It deeply investigates the flow characteristics of the gas–liquid two‐phase flow within the device. The results indicate that the device can not only achieve gas–liquid separation by transforming the flow regime from laminar to an orderly annular flow but also increase the axial velocity to extend the effective distance of the swirling section. Compared with the case without the device installed, the liquid phase volume fraction at the bottom of the well is reduced by 85.9%, and the liquid holdup is reduced by 38%. This demonstrates that compared to traditional technologies such as gas‐lift dewatering and gas production, the device can enhance the liquid‐carrying capacity of horizontal wells and effectively address the issue of liquid accumulation in horizontal wells. It provides theoretical guidance and a practical basis for future research on applying swirl jet composite devices to improve the liquid‐carrying capacity of horizontal wells.

Introduction

In developing low-permeability gas fields, horizontal wells have the advantages of increasing the gas drainage area, enhancing single-well production, and significantly improving economic viability. Horizontal well development, as an effective means of increasing the degree of reserve utilization, is now being applied more and more widely in significant gas fields [1, 2]. With the widespread application of horizontal gas wells, insufficient formation energy and edge-bottom water invasion lead to the accumulation of liquid in gas wells; due to the limitations of the unique structure of horizontal wells, it becomes challenging to remove liquid in the later stages of well development, the accumulation of liquid in the wellbore severely affects the efficiency of gas well development, and continuous accumulation can even lead to water flooding and well shutdown, reducing the lifespan and ultimate recovery rate of the gas well. Due to the complexity of the two-phase flow of gas and liquid in horizontal wells, conventional vertical well pipe flow theory cannot accurately describe the water production and gas–water two-phase flow patterns in horizontal wells; accumulation of liquid in horizontal wells has become a significant issue in gas reservoir development [3–6]. An in-depth analysis and research on the gas–liquid flow patterns in horizontal wellbores and the mechanisms of liquid accumulation, as well as the exploration of effective dewatering and gas production process measures to stabilize the production of gas wells with liquid accumulation, is an urgent issue that needs to be addressed in the current development of horizontal gas wells.

The liquid-carrying capacity of horizontal wells is only about 1/3 to 1/2 of that of vertical wells; stratified flow in the well's horizontal section is one of the main factors leading to the decrease in the liquid-carrying capacity of horizontal wells [7, 8]. The flow pattern of gas–liquid two-phase flow is different from that in vertical wells; when the formation pressure is sufficient and the fluid velocity in the wellbore is high, the liquid phase is dispersed by the gas flow, existing in the form of droplets or mist, as shown in Figure 1a. As the formation pressure decreases and the fluid velocity reduces, the liquid phase content also becomes relatively lower. At this point, part of the liquid phase forms a continuous liquid film along the wellbore wall, while the gas carries droplets and flows rapidly through the center of the pipe, forming an annular flow, as shown in Figure 1b. When the formation pressure further decreases, the gas velocity is insufficient to press the liquid phase against the wellbore to form a continuous liquid film. The gas phase compresses the liquid film into a crescent shape, as shown in Figure 2a. As the fluid velocity decreases, the shear force of the gas phase on the liquid phase decreases, and the cross-sectional area of the liquid phase further thickens, reducing the crescent curvature as shown in Figure 2b. When the gas velocity is insufficient to carry the liquid phase, the liquid film shape completely changes to a horizontal state, as shown in Figure 2c. Laminar flow in horizontal wells exhibits a thicker and more uneven liquid film compared to other flow states. The increased liquid film thickness causes the gas phase to overcome greater resistance. Moreover, the stratification phenomenon reduces the contact area between the gas and liquid phases, weakening the shear force exerted by the gas phase on the liquid phase. Consequently, this diminishes the gas-carrying capacity for liquids in a well, resulting in decreased transport efficiency. Reduced liquid holding capacity exacerbates the liquid accumulation problem in horizontal wells. After 3 years of continuous production, the daily gas production in the S block of the Sulige area has decreased by about 39% compared to before the liquid accumulation. Currently, it is known that the horizontal sections of gas wells in the Sulige and Daniudi areas are basically between 800 and 1000 m, where the problem of liquid phase deposition is more severe [9, 10].

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Banerjee et al. were among the pioneers in researching gas–liquid two-phase flow within helical tubes [11, 12]. When a gas–liquid two-phase fluid flows through a helical pipe, the centrifugal force acting on the liquid is typically greater than that on the gas due to the significant difference in density between the two phases. As a result, the liquid film is expected to be positioned on the outer side of the helical pipe, away from its axis. Additionally, they found that the amount of liquid droplets carried by the gas core is reduced in annular flow. In 1980, Whilley et al. conducted experimental studies on stratified and annular flow patterns in air–water two-phase flow within helical pipes [13]. Their research focused on liquid film thickness distribution in stratified and annular flows and the transition between these flow patterns. Due to the effect of centrifugal force, the proportion of liquid phase carried by droplet entrainment in helical pipe annular flow is relatively small.

Vortex tools can transform the flow state of the fluid into an annular flow without changing the inlet velocity and flow rate, thanks to their inherent swirling capability, which can effectively improve the flow state of the gas well and enhance the gas well's liquid-carrying efficiency. Since the U.S. Department of Energy (DOE) demonstrated through experiments that vortex tools can change the flow state of the fluid, thereby reducing the critical liquid-carrying velocity of the fluid and reducing the pressure loss in the pipeline by 17%, vortex tools have been widely applied [14, 15]. Cazan and Aidun conducted experimental research on the flow state of gas−liquid two-phase flow under the influence of helical guide vanes. They found that the gas phase flows at the center of the low-pressure vortex, resulting in stratified flow between the gas and liquid phases. Cazan and colleagues conducted an experimental investigation into the flow dynamics of gas−liquid two-phase flow, explicitly focusing on the effects of helical guide vanes. Their findings indicated that the gas phase predominantly occupies the core of the low-pressure vortex, leading to a stratified flow regime between the gas and liquid phases [16]. This phenomenon reasonably explains the results of the experimental simulation by Bose and Vortex companies. After using the vortex tool, the liquid discharge rate of the gas well is significantly higher than when the vortex tool is not used, and parameters such as the bottom hole flowing pressure and fluid velocity inside the pipe have been improved to varying degrees. The simulation results are consistent with the experimental results, and theoretically, it has been proven that the vortex tool can help with gas well liquid discharge and gas extraction [17, 18]. China National Petroleum Corporation (CNPC) took the lead in introducing vortex tools and applying them to numerous oil fields in China. In the Sulige Gas Field, Sichuan Gas Field, and the old gas fields in Eastern Sichuan, it has been proven that vortex tools can improve the production conditions of gas wells, enhance liquid carrying capacity, reduce pressure drop in the pipeline, and increase recovery rates, all of which have a significant effect on achieving increased production. Moreover, they have successfully restored the H11 gas well, which had been flooded for over 5 months [19–21]. Ren et al. [22] used numerical simulation methods to verify that different structural parameters significantly impact the swirl intensity and effective swirl length of the fluid. The results indicate that optimizing the structural parameters can further enhance the vortex tools' production effect, proving that the numerical simulation method is feasible and reliable.

The Kelvin–Helmholtz (K-H) instability theory for horizontal pipe flow states that when pressure fluctuations within a horizontal pipe generate a sufficient suction force acting on the interfacial waves, if this suction force can overcome the effect of gravity on the stability of the interfacial waves, it may trigger the K-H instability effect [23]. As the gas velocity continues to increase, the interfacial instability waves will keep growing, and this growth will eventually lead to the formation of droplets and the continuous entrainment of liquid in the pipeline. In the annular mist flow experiments conducted by C.A.M. Veeken and Belfroid [24], researchers observed that the critical Weber number of the largest droplets was below 10. Theoretically, the diameter of these droplets should exceed 7.6 mm. However, no droplets with a diameter reaching or exceeding this size were found during the experimental process. The experimental results indicate that the essence of the gas well liquid accumulation phenomenon is not caused by the fallback of droplets but rather due to the reverse flow of the liquid film. This finding supports the applicability and accuracy of the liquid film model in describing the gas well liquid-carrying process. Compared to the traditional droplet model, the liquid film model can more accurately capture the dynamic characteristics of droplet carrying in gas wells. Xiao, Li, and Yu [25] conducted an in-depth force analysis on the droplets and liquid films within the gas well casing, and they established a critical liquid-carrying velocity model that includes the effect of well inclination angle. It considers the impact of the casing inclination angle on the liquid-carrying process, thereby providing a more accurate description of the liquid-carrying phenomenon in gas wells. In water-accumulated horizontal gas wells, the gas–liquid flow pattern is primarily stratified, and liquid film entrainment is the main liquid-carrying mechanism.

Based on the particle theory model of droplets in gas, for droplets to flow continuously in a horizontal wellbore, they must at least be able to remain suspended in the gas. Compared to laminar flow, in annular flow, the liquid phase forms a stable film along the wall, while the gas phase forms a columnar flow at the center of the wellbore, which can increase the central gas velocity. Once the droplets are entrained to the center of the gas phase, they can increase the gas–liquid contact area, which helps to improve the mass transfer efficiency between the two phases, reduce pressure drop, and thereby enhance the gas well's liquid-carrying capacity [26].

Among various two-phase flow combinations, gas-liquid two-phase flow is the most complex due to the compressibility of the fluids and the variability of the interfaces, making the gas–liquid two-phase flow an extremely complex evolutionary process [27]. However, the current applications of vortex tools and associated research predominantly concentrate on vertical well scenarios. There is a notable deficiency in studies concerning the transition mechanism and the factors that influence the shift from laminar to annular flow within the context of horizontal well conditions. Traditional liquid removal and gas production techniques such as foam liquid removal, plunger lift gas production, gas-lift liquid removal, and electric submersible pump liquid removal are costly [28], operationally complex, and unsuitable for direct application in horizontal well sections [29, 30]. The actual production process of horizontal wells, as well as experimental and simulation results, have demonstrated that among the gas collection routes of horizontal wells (horizontal section, inclined section, and vertical section), the inclined section has the poorest liquid-carry capacity. Furthermore, in the later stages of extraction, reservoir energy decays, the gas flow rate gradually decreases, and flow velocity is reduced. The inclined well section cannot carry liquid continuously, leading to a retreat of the liquid phase, which causes periodic changes in the liquid flow velocity of the horizontal pipe section: At the beginning of a cycle, the two-phase gas–liquid flow in the horizontal pipe is stratified. Due to the retreat of the liquid phase in the inclined pipe section, the flow area for the gas phase is reduced, causing some gas to accumulate in the horizontal pipe section, increasing the pressure inside the pipe and gradually increasing the energy of the gas phase. When the accumulated gas energy is sufficiently large, the speed at which the gas phase pushes the liquid phase forward also gradually increases. At this point, the gas phase pushes the liquid phase from the horizontal pipe section into the inclined pipe section, which is finally expelled through the inclined pipe section.

Therefore, the accumulation of liquid in horizontal wells is mainly caused by the fallback of droplets in the inclined section, and the initial accumulation in the horizontal section occurs near the inclined section. The purpose of this paper is to design and verify a swirling jet device that can increase the gas phase flow rate in the horizontal section, change the laminar flow state, lift the liquid phase through the horizontal section to the inclined section, and discharge to improve the liquid carrying capacity of the gas well. The device has a similar overall structure size to a standard horizontal well oil pipe and can be flexibly installed at different positions along the horizontal well as needed. Compared to traditional vortex tools, the swirl jet composite device, which replaces the central body of the vortex tool with an internal flow path design, has successfully integrated swirling and jet flow efficiently while reducing device energy consumption. The working principle of the device in the horizontal well is shown in Figure 3.

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This paper employs a combination of theoretical analysis, experimental studies, and numerical simulation to investigate the characteristics and patterns of the gas–liquid two-phase flow field after applying a new composite device in horizontal wells for liquid removal and gas production. Computational Fluid Dynamics (CFD) simulation analysis and verification were conducted, demonstrating the feasibility and effectiveness of using the swirl jet composite device to address liquid accumulation issues in horizontal wells.

Physical Models and Meshing

The structure of the swirl jet composite device is shown in Figure 4, with Figure 4a being the three-dimensional model and Figure 4b, its schematic diagram. The model is established along the z-axis, with the y-direction representing the vertical direction of the device, mainly composed of an internal flow channel, nozzle, helical guide vane, liquid discharge hole, and so on. In this study, a pipeline diameter of 60 mm was selected based on the actual engineering conditions. A single-factor variable method was used to determine the optimal size of the composite device, with the optimal parameters selected while keeping other variables constant. The design of traditional vortex tools mainly relies on the vortex effect, with the optimal range for the helix angle usually being between 40° and 45°, and the helix angle should not exceed 60°. When the helix angle exceeds 60°, the effective swirling distance decreases significantly, and the pressure drop increases. The tangential velocity is insufficient when the helix angle is below 40°, decreasing separation efficiency. However, when the helix angle exceeds 45°, although the separation efficiency is higher, the energy loss increases, and the effective action distance of the vortex section is shortened [31, 32]. The new device effectively combines the jet and vortex effects. Combining the internal flow path with the nozzle can provide an axial velocity to maintain the effective distance of the swirling section, thus allowing for the design of a larger swirling angle to increase the separation capability within the device. After comprehensive consideration, the swirling angle is determined to be 52.5°, corresponding to a pitch L_p of 60 mm. The total length of the device is mainly determined by the number of turns of the spiral guide and the pitch. When the number of turns of the spiral guide is too few, its separation capability is insufficient, and it cannot achieve continuous separation of the liquid phase along the tube wall, thereby affecting the overall separation effect. However, increasing the number of turns of the spiral guide can improve the liquid phase separation capability, but it will also lead to increased energy consumption of the device, affecting its economic and feasibility in practical engineering applications. Therefore, after comprehensive consideration, the number of turns of the spiral guide was determined to be 8. The inner flow channel diameter is a key parameter affecting the fluid distribution effect within the device. When D_i is greater than 25 mm, the flow rate in the spiral channel decreases with increasing diameter. Since the fluid in the inner flow channel is mainly used to provide axial velocity rather than tangential velocity, too much fluid passing through the inner flow channel will reduce the device's separation capability. Conversely, when D_i is less than 25 mm, the flow rate in the inner flow channel decreases, leading to a reduction in axial velocity, which in turn reduces the effective working distance of the swirling section. Therefore, after comprehensive consideration, the inner flow channel diameter was determined to be 25 mm. When designing the ratio of the nozzle to the inner flow channel diameter, an excessively large ratio can lead to an increased fluid flow area, thereby reducing the axial velocity and increasing the fluid diffusion area, which interferes with the normal operation of the swirling section. Conversely, a too small ratio will increase the device's energy consumption. Based on these considerations, the ratio of the nozzle to the inner flow channel diameter was determined to be 1:3. The main function of the drain hole is to discharge the deposited liquid phase from the bottom of the inner flow channel into the spiral channel, preventing the accumulation of liquid within the inner flow channel. When D_h is less than 5 mm, its area is too small to completely discharge the deposited liquid phase within the inner flow channel. However, when D_h is greater than 5 mm, although it can completely discharge the accumulated liquid, an excessively large opening area will weaken the jet effect, affect the acceleration effect of the fluid in the spiral channel, and lead to a reduction in the axial velocity provided by the nozzle. Therefore, the drain hole diameter was determined to be 5 mm. Table 1 presents the structural dimensions of the composite device. To more clearly express the flow characteristics of the gas−liquid two-phase flow within the device, the characteristic surfaces are defined as shown in the figure: Z₁ represents the entrance of the composite device (Z₁ = 15 m); Z₂ is the point before passing through the liquid discharge hole (Z₂ = 15.08 m); Z₃ is the point after passing through the first liquid discharge hole (Z₃ = 15.26 m); Z₄ is the point after passing through both the first and second liquid discharge holes (Z₄ = 1₅.44 m); Z₅ is the exit of the device (Z₅ = 15.5 m); see Figure 4b.

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Table 1 Structure size of the new cyclone atomizer.

Structure parameter	Value	Structure parameter	Value
Total length of plant L	500 mm	Spiral guide band pitch Lp	60 mm
Internal flow path diameter Di	25 mm	Nozzle diameter to internal flow path diameter eratio	1: 3
Liquid discharge hole diameter Dh	10 mm	Coil number of spiral guide tape	8
Nozzle angle α	120°	Wellbore diameter D0	60 mm
Internal flow path wall thickness	1 mm	Thickness of spiral guide blade	2 mm

The mesh quality is crucial for the reliability and accuracy of computational results. This paper employs an unstructured mesh for the overall discretization and refines the mesh around the atomizing nozzle and liquid discharge holes to maximize the reliability of the simulation results. Figure 5 illustrates the differences in liquid volume fraction at the outlet of the swirl jet composite device under various mesh refinement levels. Without mesh refinement, as shown in Figure 5a, the aggregation of the liquid phase near the wall is significantly reduced, affecting the judgment of the maximum liquid volume fraction at the outlet, while a local mesh refinement of 5 mm around the nozzle, as shown in Figure 5b, provides some alleviation of the liquid aggregation issue near the wall. When the mesh around the nozzle is refined to 1 mm, as shown in Figure 5c, the aggregation of the liquid phase is pronounced. The transition of the liquid volume fraction is smooth, meeting the accuracy requirements for simulation results. Further, reducing the mesh refinement size does not change the liquid volume fraction but increases the simulation time and storage requirements. Therefore, a local mesh refinement size of 1 mm is applied to areas such as the atomizing nozzle and liquid discharge holes.

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The number of grid cells affects numerical simulations' accuracy and computational speed. Therefore, ensuring computational accuracy and improving computational speed is essential. Therefore, a grid independence verification is required for the swirl jet composite device. Numerical simulations were conducted on the swirl jet composite device in this paper using grid counts of 564133, 874361, 1263545, 1860254, 2213654, 2656391, 3065792, and 3421769, obtaining the maximum liquid volume fraction at the outlet of the swirl jet composite device as shown in Figure 6, the simulation results become stable when the grid count exceeds 2.2 million, and further increasing the grid count has a negligible effect on the simulation results. Therefore, the grid count is determined to be around 2.2 million.

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Mathematical Models

The following assumptions were made in this paper when studying the gas–liquid two-phase flow problem:

• 1.

  It is assumed that the entire flow process within the swirling device is adiabatic, and the effect of temperature on the gas–liquid two-phase flow is not considered. The gas–liquid two-phase flow is treated as a continuous medium without phase change, and the pressure and velocity are solved through the conservation equations of mass and momentum for both phases.

• 2.

  It is assumed that the density of each gas–liquid phase remains constant; thus, the two-phase flow is considered incompressible.

Multiphase Model

The gas–liquid two-phase flow within the composite device is complex with flow pattern transitions. Compared to other models, the Eulerian model considers the flow field as a continuous medium that fills the entire medium, considering the interactions between phases, using local conservation equations, and solving the continuity, momentum, and turbulence control equations for each phase, respectively. The computational results of the Eulerian model are more accurate, and the simulation results are closer to the experimental results [33, 34]. In horizontal pipelines, the liquid phase mainly exists in the form of laminar flow, which is different from the situation in vertical well sections where droplets mainly exist in a discrete form within the high-speed flowing gas core; in the laminar flow state, most of the liquid phase gathers at the bottom of the pipeline, existing in the form of liquid films, among other forms. When the fluid passes through the composite tool for diversion, the flow state transitions from laminar to droplets flowing along the inner wall of the wellbore, while the gas core is located at the center of the wellbore, forming an annular flow. On the micro-element cross-section in any direction of the wellbore flow, both liquid films and gas cores coexist, with the liquid phase being closer to a continuous phase. Considering the actual well conditions, the volume fraction of the liquid phase is set to 10%. When the volume fraction of the liquid phase is below 10%, the discrete phase model is more suitable. However, when the volume fraction of the liquid phase is greater than or equal to 10%, the applicability of the Eulerian model is higher. This paper aims to study the separation effect of gas–liquid two-phase fluids through the composite device and the improvement of the laminar flow state through simulation calculations. Therefore, we pay more attention to the changes in the overall flow state. In this case, the liquid phase defaults to a continuous phase, and the Eulerian model is used for simulation, which can more comprehensively capture the complexity of the gas–liquid two-phase flow and more accurately reflect the impact of the composite device on the gas–liquid two-phase flow. Based on the above analysis, the Eulerian model is chosen as the multiphase flow model for this study.

Continuity equation for gas–liquid two-phase flow [35, 36]: 1$<math altimg="urn:x-wiley:20500505:media:ese32060:ese32060-math-0001" display="block" wiley:location="equation/ese32060-math-0001.png" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mfrac><mrow><mo>\unicode{x02202}</mo><mo>(</mo><msub><mi>\unicode{x003B1}</mi><mi>n</mi></msub><msub><mi>\unicode{x003C1}</mi><mi>n</mi></msub><mo>)</mo></mrow><mrow><mo>\unicode{x02202}</mo><mi>t</mi></mrow></mfrac><mo>\unicode{x0002B}</mo><mo>\unicode{x02207}</mo><mo>\unicode{x022C5}</mo><mo>(</mo><msub><mi>\unicode{x003B1}</mi><mi>n</mi></msub><msub><mi>\unicode{x003C1}</mi><mi>n</mi></msub><msub><mi mathvariant="bold-italic">u</mi><mi>n</mi></msub><mo>)</mo><mo>\unicode{x0003D}</mo><mn>0</mn><mo>.</mo></mrow></mrow></math>$

Momentum equation [37]: 2$<math altimg="urn:x-wiley:20500505:media:ese32060:ese32060-math-0002" display="block" wiley:location="equation/ese32060-math-0002.png" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mfrac><mrow><mo>\unicode{x02202}</mo><mo>(</mo><msub><mi>\unicode{x003B1}</mi><mi>n</mi></msub><msub><mi>\unicode{x003C1}</mi><mi>n</mi></msub><mo>)</mo></mrow><mrow><mo>\unicode{x02202}</mo><mi>t</mi></mrow></mfrac><mo>\unicode{x0002B}</mo><mo>\unicode{x02207}</mo><mo>\unicode{x022C5}</mo><mrow><mo>(</mo><msub><mi>\unicode{x003B1}</mi><mi>n</mi></msub><msub><mi>\unicode{x003C1}</mi><mi>n</mi></msub><msub><mi mathvariant="bold-italic">u</mi><mi>n</mi></msub><msub><mi mathvariant="bold-italic">u</mi><mi>n</mi></msub><mo>)</mo></mrow><mo>\unicode{x0003D}</mo><mo>\unicode{x02212}</mo><msub><mi>\unicode{x003B1}</mi><mi>n</mi></msub><mo>\unicode{x02207}</mo><msub><mi>\unicode{x003C1}</mi><mi>n</mi></msub><mo>\unicode{x0002B}</mo><mo>\unicode{x02207}</mo><mfenced close="]" open="["><mrow><msub><mi>\unicode{x003B1}</mi><mi>n</mi></msub><msub><mi>\unicode{x003BC}</mi><mi>n</mi></msub><mfenced><mrow><mo>\unicode{x02207}</mo><msub><mi mathvariant="bold-italic">u</mi><mi>n</mi></msub><mo>\unicode{x0002B}</mo><mo>\unicode{x02207}</mo><msubsup><mi mathvariant="bold-italic">u</mi><mi>n</mi><mi>T</mi></msubsup></mrow></mfenced></mrow></mfenced><mo>\unicode{x0002B}</mo><msub><mi>\unicode{x003B1}</mi><mi>n</mi></msub><msub><mi>\unicode{x003C1}</mi><mi>n</mi></msub><mi mathvariant="bold-italic">g</mi><mo>\unicode{x0002B}</mo><mi mathvariant="bold-italic">F</mi><mo mathvariant="bold">.</mo><mspace width="1em"/></mrow></mrow></math>$

In the equation, $<math altimg="urn:x-wiley:20500505:media:ese32060:ese32060-math-0003" wiley:location="equation/ese32060-math-0003.png" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mi>n</mi></mrow></mrow></math>$ represents the phase ($<math altimg="urn:x-wiley:20500505:media:ese32060:ese32060-math-0004" wiley:location="equation/ese32060-math-0004.png" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mi>n</mi><mi>g</mi></mrow></mrow></math>$ represents the gas phase, $<math altimg="urn:x-wiley:20500505:media:ese32060:ese32060-math-0005" wiley:location="equation/ese32060-math-0005.png" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mi>n</mi><mi>l</mi></mrow></mrow></math>$ represents the liquid phase, $<math altimg="urn:x-wiley:20500505:media:ese32060:ese32060-math-0006" wiley:location="equation/ese32060-math-0006.png" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mi>n</mi><mi>m</mi></mrow></mrow></math>$ represents the mixture of gas and liquid); $<math altimg="urn:x-wiley:20500505:media:ese32060:ese32060-math-0007" wiley:location="equation/ese32060-math-0007.png" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mi>\unicode{x003B1}</mi><mi>n</mi></msub></mrow></mrow></math>$ is the volume fraction of each phase; $<math altimg="urn:x-wiley:20500505:media:ese32060:ese32060-math-0008" wiley:location="equation/ese32060-math-0008.png" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mi mathvariant="bold-italic">u</mi><mi>n</mi></msub></mrow></mrow></math>$ is the velocity of each phase, with units in meters per second, m/s; $<math altimg="urn:x-wiley:20500505:media:ese32060:ese32060-math-0009" wiley:location="equation/ese32060-math-0009.png" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mi>\unicode{x003C1}</mi><mi>n</mi></msub></mrow></mrow></math>$ is the density of each phase, with units in kilograms per cubic meter, kg/m³; $<math altimg="urn:x-wiley:20500505:media:ese32060:ese32060-math-0010" wiley:location="equation/ese32060-math-0010.png" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mi>p</mi><mi>n</mi></msub></mrow></mrow></math>$ is the pressure of each phase, with units in pascals, Pa; $<math altimg="urn:x-wiley:20500505:media:ese32060:ese32060-math-0011" wiley:location="equation/ese32060-math-0011.png" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mi>\unicode{x003BC}</mi><mi>n</mi></msub></mrow></mrow></math>$ is the dynamic viscosity coefficient; g is the acceleration due to gravity, with units in meters per second squared, m/s²; F represents the external body force.

Turbulence Model

Liu Wen et al. [38] conducted experiments and simulation studies on the gas–liquid two-phase swirling flow field induced by a spiral guide vane inside a circular pipe at high Reynolds numbers, comparing the RNG k−ε and RSM, two commonly used turbulence models for describing three-dimensional swirling flow, and found that the RSM model is better at capturing the characteristics of spiral vortices, with simulation results more closely matching the experimental outcomes. Under the working conditions of a swirling device, there is also a gas–liquid two-phase swirling flow field caused by the spiral guide vane inside the circular pipe, which corresponds to the scenario tested by Liu Wen, where the gas–liquid two-phase flow exhibits a swirling flow pattern, the influence of the fluid's rotating streamline curvature leads to rapid changes in the stress tensor, the RSM model takes into account the effects of Reynolds stresses and is suitable for flows with high swirling intensity, and can account for the anisotropy of the flow field. The transport equation for the RSM model [39] is calculated as follows: 3$<math altimg="urn:x-wiley:20500505:media:ese32060:ese32060-math-0012" display="block" wiley:location="equation/ese32060-math-0012.png" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mfrac><mo>\unicode{x02202}</mo><mrow><mo>\unicode{x02202}</mo><mi>t</mi></mrow></mfrac><mo stretchy="false">(</mo><mspace width="0.05em"/><mi>\unicode{x003C1}</mi><mover accent="true"><msub><mi>u</mi><mi>i</mi></msub><mi mathvariant="normal">\unicode{x000AF}</mi></mover><mover accent="true"><msub><mi>u</mi><mi>j</mi></msub><mi mathvariant="normal">\unicode{x000AF}</mi></mover><mo stretchy="false">)</mo><mo>\unicode{x0002B}</mo><msub><mi>C</mi><mi mathvariant="italic">ij</mi></msub><mo>\unicode{x0003D}</mo><msubsup><mi>D</mi><mi mathvariant="italic">ij</mi><mi>T</mi></msubsup><mo>\unicode{x0002B}</mo><msubsup><mi>D</mi><mi mathvariant="italic">ij</mi><mi>L</mi></msubsup><mo>\unicode{x0002B}</mo><msub><mi>P</mi><mi mathvariant="italic">ij</mi></msub><mo>\unicode{x0002B}</mo><msubsup><mi>G</mi><mi mathvariant="italic">ij</mi><mi>T</mi></msubsup><mo>\unicode{x0002B}</mo><msub><mi>\unicode{x003D5}</mi><mi mathvariant="italic">ij</mi></msub><mo>\unicode{x0002B}</mo><msub><mi>\unicode{x003B5}</mi><mi mathvariant="italic">ij</mi></msub><mo>\unicode{x0002B}</mo><msub><mi>F</mi><mi mathvariant="italic">ij</mi></msub><mo>\unicode{x0002B}</mo><msub><mi>S</mi><mi>user</mi></msub><mo>.</mo></mrow></mrow></math>$

In the equation: C_ij is the convective term, D^T_ij is the turbulent diffusion term, D^L_ij is the molecular viscous diffusion term, P_ij is the term of shear stress generation, G^T_ij is the buoyancy generation term, Φ_ij is the pressure strain term, ε_ij is the viscous dissipation term, F_ij is the system rotation generation term, S_user is the source item.

Solve Control Parameter Settings

The physical properties of the gas-liquid two-phase fluid for the new type of swirl jet composite device are shown in Table 2.

Table 2 Physical properties of the gas–liquid two-phase fluid.

Materials	Density (kg/m3)	Viscosity (Pa•s)
Nature gas	0.6679	1.087 × 10−5
Water	998.2	1.003 × 10−3

The initial operating parameters are consistent with the actual conditions of a horizontal gas well in a certain gas field, as shown in Table 3.

Table 3 Gas well engineering parameters.

Pressure(MPa)	Gas production rate qgs(m3/d)	Liquid production rate ql(m3/d)
5.74	0.89 × 104	1.08

Utilizing FLUENT 2022 for Computational Fluid Dynamics (CFD) calculations on the device, the multiphase flow model employs the Eulerian model, the turbulence model selects the Reynolds Stress Model (RSM), standard wall functions are used, the SIMPLE algorithm is employed for pressure-velocity coupling, the pressure interpolation format is PRESTO!, the QUICK scheme is used for the interpolation calculations of the momentum equation and liquid volume fraction in the control equation set, the rest are second-order upwind schemes. To accurately set the simulation boundary conditions, it is necessary to calculate the actual flow velocity of the subsurface fluid, solving for the subsurface natural gas density as shown in Equation (4): 4$<math altimg="urn:x-wiley:20500505:media:ese32060:ese32060-math-0013" display="block" wiley:location="equation/ese32060-math-0013.png" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mi>\unicode{x003C1}</mi><mi>g</mi></msub><mo>\unicode{x0003D}</mo><mfrac><mrow><mn>3484</mn><msub><mi>\unicode{x003C1}</mi><mn>0</mn></msub><mi>P</mi></mrow><mi mathvariant="italic">ZT</mi></mfrac><mo>.</mo></mrow></mrow></math>$

In the equation: $<math altimg="urn:x-wiley:20500505:media:ese32060:ese32060-math-0014" wiley:location="equation/ese32060-math-0014.png" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mi>\unicode{x003C1}</mi><mn>0</mn></msub></mrow></mrow></math>$ is the relative density of natural gas, kg/m³; $<math altimg="urn:x-wiley:20500505:media:ese32060:ese32060-math-0015" wiley:location="equation/ese32060-math-0015.png" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mi>P</mi></mrow></mrow></math>$ is pressure, Pa; $<math altimg="urn:x-wiley:20500505:media:ese32060:ese32060-math-0016" wiley:location="equation/ese32060-math-0016.png" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mi mathvariant="italic">Z</mi></mrow></mrow></math>$ is the compression coefficient of gas; $<math altimg="urn:x-wiley:20500505:media:ese32060:ese32060-math-0017" wiley:location="equation/ese32060-math-0017.png" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mi mathvariant="italic">T</mi></mrow></mrow></math>$ is temperature, K.

The volume factor refers to the ratio of the actual gas volume underground to the volume of gas at standard temperature and pressure, and the dimensionless volume factor is shown in Equation (5): 5$<math altimg="urn:x-wiley:20500505:media:ese32060:ese32060-math-0018" display="block" wiley:location="equation/ese32060-math-0018.png" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mi>B</mi><mi>g</mi></msub><mo>\unicode{x0003D}</mo><mfrac><mrow><mi mathvariant="italic">ZT</mi><msub><mi>P</mi><mi>s</mi></msub></mrow><mrow><msub><mi>Z</mi><mi>s</mi></msub><msub><mi>T</mi><mi>s</mi></msub><mi>P</mi></mrow></mfrac><mo>.</mo></mrow></mrow></math>$

In the equation: $<math altimg="urn:x-wiley:20500505:media:ese32060:ese32060-math-0019" wiley:location="equation/ese32060-math-0019.png" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mi>Z</mi><mi>s</mi></msub></mrow></mrow></math>$ is the compression coefficient of gas at normal temperature and pressure; $<math altimg="urn:x-wiley:20500505:media:ese32060:ese32060-math-0020" wiley:location="equation/ese32060-math-0020.png" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mi>P</mi><mi>s</mi></msub></mrow></mrow></math>$ is the standard atmosphere, Pa; $<math altimg="urn:x-wiley:20500505:media:ese32060:ese32060-math-0021" wiley:location="equation/ese32060-math-0021.png" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mi>T</mi><mi>s</mi></msub></mrow></mrow></math>$ is the temperature in the standard state, K.

Actual underground gas flow rate: 6$<math altimg="urn:x-wiley:20500505:media:ese32060:ese32060-math-0022" display="block" wiley:location="equation/ese32060-math-0022.png" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mi>q</mi><mi>g</mi></msub><mo>\unicode{x0003D}</mo><msub><mi>q</mi><mi mathvariant="italic">gs</mi></msub><mo>\unicode{x022C5}</mo><msub><mi>B</mi><mi>g</mi></msub><mo>.</mo></mrow></mrow></math>$

Based on the actual operating parameters of the horizontal well, the boundary conditions are determined as follows: gravitational acceleration of 9.81 m/s², liquid volume fraction of 0.1; the gas–liquid mixture inlet is set as a velocity inlet at 1 m/s; the outlet is set as a pressure outlet. The fluid state is calculated as transient, with various residual control settings at 1e⁻⁴; the results are considered to have converged when all residual values are below and the monitored values are stable. The time step is 0.001 s, and the relaxation factor is set to the default value, with Pressure at 0.3, Density at 1, Body Force at 1, Momentum at 0.7, Volume Fraction at 0.5, Turbulent Kinetic Energy at 0.8, Turbulent Dissipation Rate at 0.8, Turbulent Viscosity at 1.

Validity Verification

The composite device is installed at the starting position of the inclined pipe section, and the synergistic effect of swirl and jet is used to adjust the flow state in the pipe. As shown in Figure 7, after the installation of the composite device, the liquid accumulation in S₁–S₂ sections has a significant slowing effect. When the composite device is not installed, the average liquid phase volume fraction of the S₂ section is 0.204. The average liquid phase volume fraction of the same S₂ section is reduced to 0.101, a decrease of 50.5%. At the same time, after the installation of the composite device, the maximum liquid phase volume fraction of the outer wall can be reduced from 0.507 to 0.107 so that the liquid phase originally deposited in the lower part of the pipe wall can be evenly distributed throughout the pipe through the effect of swirling flow. While solving the problem of liquid deposition falling back in the S₁–S₃ segment, the gas–liquid two-phase flow can be evenly mixed when entering the vertical segment, which improves the efficiency of the liquid phase carrying by the gas phase and avoids the problem of liquid phase falling back in the vertical segment.

[IMAGE OMITTED. SEE PDF]

To gain a deeper understanding of the phase transition mechanism of the gas–liquid two-phase flow within the device, the fluid streamlines at the inlet and outlet of the device are analyzed, as shown in Figure 8. It can be observed from Figure 8b that after entering the internal flow path, a portion of the fluid moves along the axial direction. At the same time, most liquid deposited at the bottom of the wellbore is guided into the spiral channel and moves in a spiral motion under the influence of the spiral guide vane. As the gas–liquid two-phase flow exits the device (refer to Figure 8a), it exhibits an orderly spiral motion pattern within the wellbore. Due to the nozzle's constraining effect, the fluid's diffusion area within the internal flow path is reduced; this does not hinder the fluid from maintaining its spiral motion characteristics. On the contrary, this design provides the fluid with a higher axial velocity, thereby effectively enhancing the gas well's liquid-carrying capacity.

[IMAGE OMITTED. SEE PDF]

This paper analyzes the fluid velocity, flow pattern transformation, and other characteristics in the swirling passage, internal flow path, and liquid discharge holes of the composite device, providing an in-depth dissection of the device's mechanism and effectiveness in liquid removal for horizontal wells.

The velocity contour map of the new type of swirl jet composite device is shown in Figure 9. After the mixed fluid enters the device, the fluid velocity in the internal flow path increases rapidly due to the reduction in the cross-sectional area of the flow path; when the fluid reaches the Z₂ position, the velocity in this area can reach 2.56 m/s, which is 2.56 times the velocity of 1 m/s at the inlet Z₁, indicating a significant acceleration effect of the fluid within the device.

[IMAGE OMITTED. SEE PDF]

Because drain holes 1 and 2 are located at the lower part of the inner channel, when the fluid flows into the spiral channel through the drain hole, the jet acceleration effect they produce on the fluid promotes the separation efficiency of the fluid in the spiral channel due to the small diameter of the drain holes. Particularly, liquid discharge hole 2 has a superior acceleration effect compared to hole 1 due to its proximity to the nozzle, which is clearly demonstrated in the axial velocity contour plots a and b of Figure 9 of the device. Although the fluid in the internal flow path experiences a decrease in velocity after passing through the discharge holes, at the device's outlet, the nozzle of the internal flow path re-accelerates the internal gas, effectively balancing the velocity reduction caused by the discharge holes. The average fluid velocity at the Z₅ cross-section is 2.74 m/s, significantly increasing from the inlet velocity of 1 m/s. By comparing the velocity distribution at the Z₅ interface, it can be observed that due to the action of the nozzle, the velocity increase at the axis of rotation is particularly evident. The orderly decrease in velocity gradient from the wellbore center to the edge indicates the stability of the fluid flow state.

As shown in Figure 10, the gas-liquid two-phase flow exhibits distinct stratification before entering the device, with the liquid phase primarily settling at the bottom of the wellbore due to gravity, and as the fluid enters the device and undergoes spiral motion, under the influence of centrifugal force, the denser liquid is separated to the periphery of the outer wall, forming a continuous liquid film, the less dense gas phase is mainly distributed around the outer wall of the internal flow path, creating a distinct step-like pattern of the liquid phase on the outer wall of the wellbore. As the distance increases, the step-like distribution of the liquid phase volume fraction becomes increasingly apparent. Additionally, the presence of liquid discharge holes in the intervals Z₂—Z₃ and Z₃—Z₄ has a significant accelerating effect on the fluid; as the velocity increases, the separation capability of the device is also enhanced, and the liquid film formed on the outer wall of the casing becomes more pronounced; after passing through the device, a continuous and uniform liquid film has been formed at the device outlet, completing the transition from stratified flow to annular flow; compared to stratified flow, annular flow offers a significant advantage in terms of the expanded gas–liquid contact area, which allows for more thorough contact between the gas and liquid, increasing the shear force of the gas on the liquid phase; this not only promotes the mixing of gas and liquid but also more effectively carries the liquid flow, thereby improving the liquid-carrying efficiency and mixing effect of the fluid.

[IMAGE OMITTED. SEE PDF]

We can better understand the dynamic characteristics of the gas–liquid two-phase flow within the device by observing Figure 11. Due to the laminar flow effect, some of the liquid phase does not fully enter the spiral channel. Instead, it deposits in the internal flow path, causing a buildup of fluid within the internal flow path, a problem effectively mitigated by the design of liquid discharge holes 1 and 2. As shown in Figure 11a, the deposited liquid phase at the bottom of the internal flow path is redirected into the spiral channel by the action of the discharge holes. After treatment by discharge hole 1, the amount of deposited liquid at the bottom is significantly reduced, and the fluid accumulation in the internal flow path is markedly alleviated. The liquid discharge from hole 2 is slightly less than from hole 1, as shown in Figure 11b. After the two-step liquid discharge process, the amount of fluid accumulation in the internal flow path is significantly reduced, and no significant fluid accumulation is observed in areas prone to buildup, such as the nozzle exit.

[IMAGE OMITTED. SEE PDF]

To better quantify the liquid discharge performance of the discharge holes, comparing Figure 12, we can observe a significant improvement in the stratification phenomenon at the Z₃ and Z₄ cross-sections after passing through the discharge holes, and compared to the Z₂ cross-section without passing through the discharge holes, the liquid holdup at the Z₃ cross-section after passing through discharge hole 1 has decreased by 20%. Furthermore, the liquid holdup at the Z₄ cross-section after passing through discharge holes 1 and 2 has decreased by 12.2% compared to the Z₃ cross-section, ultimately resulting in a 29.8% reduction in liquid holdup within the internal flow path. It can be concluded that the design of the discharge holes can facilitate the deposition of the liquid phase within the internal flow path and enhance the separation efficiency of the device segment.

[IMAGE OMITTED. SEE PDF]

The previous discussion described the flow pattern transition of the gas–liquid two-phase flow within the device section. To provide a more comprehensive and in-depth analysis of the overall impact of the swirl jet composite device on the gas well's liquid-carrying capacity, it is necessary to consider the changes in the gas–liquid two-phase flow after the device section as well.

Therefore, by comparing Figure 13, we can observe that in the wellbore not equipped with the swirl jet composite device, the flow pattern has developed into stratified flow, whereas in the wellbore with the device installed, a continuous annular flow has been established. Within the Z₆—Z₈ interval, the annular flow is stably moving; as the distance increases, the device's separation capability for the fluid continuously weakens, significantly when the fluid flow position exceeds Z₈ = 16.5 m, due to the continuous decrease in tangential velocity the liquid film separated to the pipe wall gradually decreases. By observing the cross-sectional contour map at Z₉ = 17 m, it can be found that the center of the annular flow has shifted, as shown in Figure 13(a). Thus, the effective distance of the swirling section is 1.5 m. When the fluid flow exceeds this effective distance, the liquid film gradually peels off under the action of the shear force of the central gas and moves towards the central region, carried forward by the gas core in the form of droplets. At this point, the flow pattern gradually transitions from annular to mist flow. By comparing the liquid phase deposition at the bottom hole across the three cross-sections, Z₇, Z₈, and Z₉, we can quantify the device's ability to improve the gas well's liquid-carrying capacity: The bottom hole liquid phase volume fraction was reduced by 85.9%, 86.7%, and 88.2%, respectively. Reduced liquid phase deposition at the bottom hole increased the gas–liquid contact area. It decreased the resistance to the gas phase flow, thereby achieving the goal of enhancing the gas well's liquid-carrying capacity.

[IMAGE OMITTED. SEE PDF]

The liquid holdup (liquid phase volume fraction) is an important parameter in multiphase flow, as it directly reflects the spatial proportion of the liquid phase in the mixed fluid. As the liquid holdup increases, the proportion of the liquid phase in the gas–liquid two-phase flow per unit area also increases. This increase can reduce the gas's ability to carry droplets, which can cause droplet accumulation within the pipeline. Furthermore, since the viscosity of the liquid phase is typically higher than that of the gas phase, an increase in liquid holdup will correspondingly increase the overall medium's viscosity, leading to increased resistance to fluid flow, thereby affecting the production efficiency of the gas well. By comparing Figure 14, we can observe that, in the absence of specific devices, the liquid holdup continues to rise as the pipeline distance increases, and the accumulation phenomenon becomes more pronounced due to the stratified flow pattern. After the device is installed, the liquid holdup significantly decreases within the area affected by the device. At the cross-section Z₆ = 15.5 m, the liquid holdup was reduced from 0.158 without the device to 0.098 with the device installed, a reduction of 38%.

[IMAGE OMITTED. SEE PDF]

As the fluid flows past the Z₆ cross-section, the liquid holdup increases slightly due to the gradual weakening of the swirling effect. However, even so, its value remains significantly lower than the level when the device is not installed. The liquid holdup increases rapidly in the swirling section from 16.5 to 17 m as the swirling effect further diminishes. However, when the fluid flows into the area from 17 to 18.5 m, the flow pattern transitions to mist flow, and the liquid holdup remains essentially stable at this point. It is noteworthy that even after the swirling section has ended, at Z = 19 m, the liquid holdup is still 0.101, a 41% reduction compared to 0.171 without the device installed. This result confirms the effectiveness of the swirl jet composite device in reducing liquid holdup, thereby significantly enhancing the gas well's liquid-carrying capacity.

A comparison of the liquid holdup between the device with an internal flow path and the central body under the same size conditions was conducted to verify the effectiveness of the additional internal flow path device. According to the presentation in Figure 15, it can be observed that at the entrance of the device, after the addition of the internal flow path, the accumulation of liquid has significantly decreased. Throughout the entire device section, the liquid holdup remains continuously lower than that of the central body control group without an internal flow path installed. Since the fluid in the internal flow path has not undergone a swirling action at the device outlet, its liquid holdup is slightly higher than that of the central body control group. However, after the fluid passes through the Z₆ = 16 m cross-section, the liquid holdup of the composite device and the central body control group are essentially consistent. Based on the above results, we can conclude that the device with an additional internal flow path has advantages in reducing the accumulation of liquid at the entrance and maintaining a lower liquid holdup. Although the initial liquid holdup at the outlet is slightly higher, after the fluid has flowed a certain distance, its performance is comparable to that of the central body control group. This indicates that adding an internal flow path is an effective design improvement that enhances the device's overall performance.

[IMAGE OMITTED. SEE PDF]

When assessing equipment performance, it is necessary to consider both the device's beneficial effects and energy consumption comprehensively. The swirl jet composite device effectively reduces pressure drop and energy consumption by adopting an internal flow path instead of a traditional central body to achieve more efficient energy utilization. To further quantify the energy loss of the device, the energy consumption loss coefficient K_TP is commonly used for measurement in practical industrial applications, which is defined as the ratio of the energy loss produced after the gas–liquid two-phase fluid passes through the swirling flow device to the total kinetic energy of the fluid before entering the device. As shown in Equation (7): 7$<math altimg="urn:x-wiley:20500505:media:ese32060:ese32060-math-0023" display="block" wiley:location="equation/ese32060-math-0023.png" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mi>K</mi><mi>TP</mi></msub><mo>\unicode{x0003D}</mo><mfrac><mfrac><mrow><msub><mi>P</mi><mn>2</mn></msub><mo>\unicode{x02212}</mo><msub><mi>P</mi><mn>1</mn></msub></mrow><mrow><msub><mi>\unicode{x003C1}</mi><mi>TP</mi></msub><mi>g</mi></mrow></mfrac><mfrac><msubsup><mi>U</mi><mi>TP</mi><mn>2</mn></msubsup><mrow><mn>2</mn><mi>g</mi></mrow></mfrac></mfrac><mo>\unicode{x0003D}</mo><mfrac><mrow><mi mathvariant="normal">\unicode{x00394}</mi><msub><mi>P</mi><mi>TP</mi></msub></mrow><msub><mi>E</mi><mn>0</mn></msub></mfrac><mo>.</mo></mrow></mrow></math>$

In the equation: P_TP is the pressure drop in the test section, Pa; ρ_TP is the mixture density of two phases of inlet fluid, kg/m³; g is the gravitational acceleration, m/s²; U_TP is the mixing speed of the inlet fluid, m/s; and E₀ is the initial kinetic energy of the inlet fluid.

The energy consumption coefficient of the composite device is 51.33, and the central body control group is 34.59, effectively reducing the energy consumption by 32.66%.

To validate the reliability of the simulation results, a liquid holdup measurement experiment was designed and implemented for a novel swirl jet composite device; this paper mainly studies how to improve the liquid-carrying capacity of gas wells and the impact on the flow pattern of gas–liquid two-phase flow after adding a newly designed swirl jet device. However, the visualization method in direct measurement occupies a very important position in the measurement of liquid holding capacity, as the visualization measurement mainly relies on human judgment and requires good visualization performance of the pipeline, for example, pipelines with poor light transmittance or large refraction such as threaded pipelines have large errors when using the visualization method. This can lead to increased uncertainty in experimental results. In addition, due to the limitations of the working conditions in this paper and considering the safety of the experiment, this paper did not use the visualization measurement method to verify the simulated results of the liquid holding capacity. This paper uses the simplest and most effective quick shut-off valve method to test the gas phase liquid holding capacity; that is, by quickly closing the valves at both ends of the test section, the captured two-phase mixture inside is used to measure the liquid holding capacity. This method is widely used for the detection of gas-liquid two-phase flow content, and the gas content measurements by Godbole, Tang, and Ghajar [40], Qian and Hrnjak [41], and so on, were all obtained using this method. The flow chart of the liquid holdup test is shown in Figure 16:

[IMAGE OMITTED. SEE PDF]

The liquid holdup calculation formula is shown as Equation (8): 8$<math altimg="urn:x-wiley:20500505:media:ese32060:ese32060-math-0024" display="block" wiley:location="equation/ese32060-math-0024.png" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mi>h</mi><mi>l</mi></msub><mo>\unicode{x0003D}</mo><mfrac><mi>m</mi><mrow><msub><mi>\unicode{x003C1}</mi><mi>l</mi></msub><mo>\unicode{x02219}</mo><mi>v</mi></mrow></mfrac><mo>.</mo></mrow></mrow></math>$

In the equation: $<math altimg="urn:x-wiley:20500505:media:ese32060:ese32060-math-0025" wiley:location="equation/ese32060-math-0025.png" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mi>m</mi></mrow></mrow></math>$ is the mass of the retained liquid in the test section, kg; $<math altimg="urn:x-wiley:20500505:media:ese32060:ese32060-math-0026" wiley:location="equation/ese32060-math-0026.png" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mi>\unicode{x003C1}</mi><mi>l</mi></msub></mrow></mrow></math>$ is the liquid density, kg/m³; and $<math altimg="urn:x-wiley:20500505:media:ese32060:ese32060-math-0027" wiley:location="equation/ese32060-math-0027.png" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mi>v</mi></mrow></mrow></math>$ is the total pipeline volume of the test section, m³.

The equipment used in the test is shown in Table 4.

Table 4 Model table of experimental equipment.

Device name	Equipment type	Maximum range	Accuracy
Gas flow meter	D07-23FM	250SLM	±1.5%
Gas flow meter	D07-60B	2000SLM	±2%
Liquid flow meter	YYCL07	7SLM	±1%
Liquid flow meter	YYCL50	50SLM	±1%
Tachymeter	ZSX5	25 m/s	±1%
Electronic weighing meter	TD30002A	3000 g	±1%

It can be seen from the above formula that as long as the mass of the retained liquid in the test section, denoted as m, is measured, and the total volume of the fluid domain in the test section, denoted as V, is obtained, the liquid holding capacity of the test section can be calculated.

Before the experiment, static calibration measurement is required. There is a certain error between the mass of the liquid flowing out of the test section's drainage hole and the mass of the liquid inside the pipe; that is, the more fluid enclosed inside the pipe, the closer the discharge from the drainage hole is to the mass of the fluid inside the pipe. Multiple test results show that the residual liquid mass inside the empty pipe and the test section pipe with a swirl device is relatively stable, ranging from 0.011 to 0.022 kg. The impact on the experimental results is negligible and can be disregarded.

The circulation of the water circuit in the experimental process is provided by a magnetic pump; after the liquid phase, water passes through the magnetic pump, enters the Liquid flow meter, and then flows into the gas-liquid mixer. The power for the gas circuit part is provided by a gas compressor, stored in a fixed large-scale gas storage tank, passing through an air filter and a pressure-reducing valve, a gas flow meter with a different range according to the experimental conditions, and then enters the gas–liquid mixer through a check valve to mix with water. The speed after mixing is monitored by using a tachymeter; when the speed reaches the velocity of the numerical simulation conditions in this paper, and the velocity is stable, open the test section valve and let the fully mixed gas–liquid two-phase flow enter the empty pipe test section and the test section with a swirl jet composite device. After a period of stability, the solenoid valves are quickly closed at both ends of the experimental section; the fluid flows into the liquid collection vessel under gravity action, and the liquid phase weight is obtained through an electronic weighing instrument.

Based on the measured liquid mass m₁ and m₂ discharged from the empty pipe and the test section with the device, once the volume of the fluid domain is obtained, the liquid holding capacity of both can be determined and compared with the simulated values, as shown in the figure below.

It can be seen from the comparison graph of experimental results and simulated data in Figure 17 that the simulated and tested liquid holding capacities with the device are both less than that of the empty pipe; the trend of liquid holding capacity between experimental and simulated values is consistent with the change in inlet velocity. Although the liquid in the test section cannot be guaranteed to be completely drained, there are certain differences between the simulated and experimental conditions, leading to some deviation between the experimental data and the simulated results, with the simulated results being higher than the experimental values; the aforementioned experimental results can still fully demonstrate the effectiveness of the new swirl atomization device in enhancing the liquid-carrying capacity of gas wells.

[IMAGE OMITTED. SEE PDF]

Conclusion

This paper employs a combination of numerical simulation and experimental methods to address the structural characteristics of horizontal wells and the liquid accumulation issue in the later stages of gas well production, designing a novel swirl jet composite device and verifying its effectiveness in horizontal wells. Through an in-depth study of the flow pattern characteristics and energy consumption of the gas–liquid two-phase flow within the device, the following conclusions are drawn:

• 1.

  The swirl jet composite device can improve the flow pattern in horizontal wells, transforming stratified flow into orderly annular flow. Compared to the empty pipe control group, the liquid phase volume fraction at the bottom of the well is reduced by 85.9%, and the liquid holdup is reduced by 38%, proving that the device can effectively enhance the liquid-carrying capacity of gas wells and reduce liquid accumulation at the bottom of the well.

• 2.

  The design combines the internal flow path and the nozzle in the swirl jet composite device, which not only increases the axial velocity of the fluid but also reduces the device's energy consumption. The energy consumption coefficient of the swirl jet composite device is 51.33, compared to 34.59 for the central body control group, effectively reducing energy consumption by 32.66%, which is beneficial for subsequent liquid removal and gas extraction in gas wells.

• 3.

  The design of the liquid discharge holes in the swirl jet composite device effectively avoids the problem of liquid phase deposition within the internal flow path. The liquid holdup at the Z₃ cross-section after passing through the discharge hole 1 decreases by 20% compared to the Z₂ cross-section without passing through the discharge hole. The liquid holdup at the Z₄ cross-section after passing through both discharge holes 1 and 2 decreases by 12.2% compared to the Z₃ cross-section, ultimately reducing the liquid holdup within the internal flow path by 29.8%. Additionally, the discharge holes can accelerate the fluid in the spiral channel, improving the separation efficiency of the fluid.

In summary, this paper has successfully designed a new swirl jet composite device that can effectively improve the liquid accumulation problem in horizontal wells and verified its effectiveness in horizontal wells. This research has important theoretical and practical significance for improving liquid accumulation in horizontal gas wells and enhancing liquid-carrying capacity. In the future, further exploration of the impact of different device parameters and operating conditions on device performance can be conducted to optimize the design further and promote the device's application in practical engineering.

Acknowledgments

This work was supported by General program of Shandong Natural Science Foundation, Grant number: ZR2022MD033.

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