Research progress on the calculation model of critical liquid carrying flow of gas well

The accumulation of liquid in gas wells has become a prevalent problem in the middle and later stages of gas well development with different wellbore structures, which seriously affects the production efficiency of gas wells. To precisely forecast the generation time of liquid accumulation in gas wells and timely adopt drainage gas production technology, the literatures on gas critical liquid‐carrying flow calculation models for vertical wells, inclined wells and horizontal wells were analyzed and summarized. The results show that the research on the calculation models for gas critical liquid‐carrying flow rate in vertical and inclined wells is relatively mature. However, because of the unique wellbore structure of horizontal wells, the gas‐liquid two‐phase flow pattern and distribution of droplets and liquid‐film are complex, leading to a lack of understanding of gas liquid carrying mechanism throughout the whole wellbore of existing horizontal wells, and we established a calculation model of gas critical liquid‐carrying flow rate in horizontal wells considers single factors. Based on the above summary and analysis, the research direction of the calculation model for gas critical liquid‐carrying flow rate in the entire wellbore of horizontal wells is pointed out. Combining the gas liquid‐carrying test of entire wellbore of the horizontal well, considering the distribution form of droplets and liquid‐film, the aggregation and fission between droplets, and the energy exchange between gas and liquid, the gas liquid‐carrying mechanism of the entire wellbore of horizontal well is revealed, clarifying the most easy to liquid‐accumulating well sections in the whole horizontal well, and a calculation model of gas critical liquid‐carrying flow rate of horizontal well considering multiple factors is established, providing crucial theoretical foundation and technical support for the drainage and gas recovery of a horizontal well.

theoretical foundation and technical support for the drainage and gas recovery of a horizontal well.

K E Y W O R D S
gas critical liquid-carrying, gas well, research progress, wellbore fluid accumulation

| INTRODUCTION
Gas output and formation pressure steadily decline as natural gas is exploited.The natural gas flow is not enough to overcome the gravity of droplets and frictional force of liquid-film, which brings them to the wellhead.The droplets and liquid-film stay and accumulate in the wellbore, gradually forming a liquid.As the amount of liquid in the wellbore rises, back pressure is generated, which inhibits natural gas production and causes the occurrence of crushing, resulting in the gas well to be shut down. 1,2Consequently, it is crucial to correctly forecast the generation time of liquid in the gas wells for timely adoption of drainage and gas production processes. 3t present, there are many different opinions on the study of gas-liquid accumulation.It is mainly through the droplet fallback or liquid film inversion as the judgment basis of gas-critical liquid carrying.However, the calculation values among different gas liquid accumulation prediction models have large deviations and poor generalization.Especially in horizontal wells, there is insufficient understanding of the gas critical liquid-carrying mechanism, and the established gas critical liquid-carrying flow rate calculation model considers a single factor.In 1969, Turner assumed that the droplets were spherical and derived from the droplet model for the first time under vertical well and laminar flow conditions. 46][7] However, for gas wells with low pressure and low production, such as the Sulige Gas Field, the on-site gas phase is mostly in a turbulent state, and the calculation using the Turner model has a large deviation. 8,9In the low-permeability waterproducing gas reservoir in the Daniudi gas field, widely used models such as the Turner model and the Min Li model have an average accuracy rate of predicting liquid accumulation in gas wells below 70%. 10 In the gas wells of the Zhongjiang gas field, condensate water is the main source and the water vapor is low, so it is difficult to use the Turner model. 11In 1969, Wallis first proposed liquid film inversion as a criterion for the critical liquidcarrying capacity of gas. 12Later, most scholars established a gas critical liquid-carrying flow calculation model based on Wallis' empirical formula for liquid flooding. 13,14In 1986, Barnea determined the reversal point and critical liquid-carrying flow rate of the liquid film based on the liquid film thickness, which was widely used in existing gas field sites, 15,16 such as the highproductivity gas wells in Changqing Gas Field.However, in horizontal wells, the liquid film at the bottom of the inclined section is unevenly distributed, and the calculation using the Barnea model has a large deviation. 17owever, in horizontal wells, the liquid film at the bottom of the inclined section is unevenly distributed, and the deviation of gas critical liquid-carrying flow rate calculated using the Barnea model is large.Therefore, the references on critical liquid-carrying flow calculation models for horizontal, inclined, and vertical wells are summarized and analyzed.It is pointed out that the existing critical liquid-carrying flow calculation models are insufficient, and clarifies the research development trend of critical liquid-carrying flow in the horizontal wells.

| ANALYSIS OF THE CURRENT SITUATION OF GAS CRITICAL LIQUID CARRYING FLOW CALCULATION MODELS IN VERTICAL WELLS
The liquid in vertical wells is mainly dispersed on the gas core and inner wall of wellbore in the form of droplets and liquid-film, and droplet fallback or liquid-film reversal is usually used as the basis for judging the critical liquid carrying flow rate of gas.Therefore, the critical liquid carrying flow rate is analyzed from the droplet model and liquid-film model respectively.

| Droplet model
The droplet theoretical model mainly takes the droplet as a research object, taking the gas flow rate when the droplets fall back as gas critical liquid carrying flow rate, and determines whether the accumulation of liquid is generated by gas critical carrying flow rate calculation model.
In the process of gas carrying liquid, the droplets are affected by airflow and exhibit irregular shape, Turner et al. 4 were the first to propose a droplet model, assuming the droplet as a sphere as shown in Figure 1.They analyzed the force on the droplet and established a gas critical liquid carrying flow rate calculation model.By comparing and analyzing with field experimental data, the predicted critical liquid carrying flow rate was increased by 20% to increase the model's prediction accuracy, which is suitable for gas wells with high gasliquid ratios.Coleman et al. 18 studied the prediction of liquid accumulation in low-pressure gas wells, and verified that the Turner model's critical liquid carrying flow did not increase by 20%, which was more consistent with field experimental data through the field experimental data.
Based on Turner's model, 4 Li et al., 19 Peng et al., 20 and Wang et al. 21have established a model for calculating the gas critical liquid-carrying flow rate, respectively.The model considers the force deformation of the droplet during the gas-carrying process, and regards the droplet as flat shape, elliptical shape and ball-cap shaped respectively, as shown in Figures 2 and 3.
Figure 4 shows the gas critical liquid carrying flow rate at the wellhead for four droplet shape models. 20urner's model 4 assumes that the droplet has a spherical shape and approximates the drag force coefficient to 0.44.Li's model 19 assumes the droplet shape to be flat and approximates the drag force coefficient to 1.0, and its gas critical liquid-carrying flow rate is about 38% of that of Turner's model.Peng's model 20 assumes that the droplets are ellipsoids with an aspect ratio close to 0.9, and the gas critical liquid-carrying flow rate is about 69% of that of Turner's model.According to the droplet morphology diagram summarized by Grace through a large number of experiments, Wang's model 21 believes that the droplet shape is dominated by the ball-cap shaped in the gas well liquid-carrying process.The model approximates the drag force coefficient as 1.17, and takes 25% of the safety coefficient in combination with the actual production data at the gas well site to obtain the gas critical liquidcarrying flow rate.Four different droplet models are  compared with experimental measurements, respectively.The result shows that assuming the droplets to be elliptical is more consistent with the gas liquidcarrying process.

| Droplet deformation
During the process of gas carrying liquid, droplets were deformed by the airflow.The physical model and force analysis are shown in Figure 5. Based on the Turner model, Guozhen Li et al. 22 established a gas critical liquid carrying flow calculation model, introducing characteristic parameters and taking into account droplet deformation, droplet size and droplet liquid volume.Xiaohua Tan et al. 23 established a gas critical liquid carrying flow rate calculation model considering droplet diameter, based on the equality between total free energy of droplet surface and turbulent kinetic energy of gas flow.The comparison and analysis of the gas critical liquid-carrying flow of this model with Turner's model, 4 Coleman's model, 18 and Li's model 19 are shown in Figure 6. 23The model is close to Li's model at high gas-liquid ratios and Coleman's model at low gas-liquid ratios, and has a wide range of applicability.Jie Pan et al. 24 examined how droplet deformation affected the surface area and surface free energy of the droplets, developed a formula for determining the maximum droplet diameter facing the airflow, took into account how droplet deformation affected the drag force on the droplet, and proposed a gas critical liquid carrying flow calculation model for ellipsoidal droplets.Zhibing Wang et al. 25 showed through experiments that droplets changed from spherical to elliptical in annular mist flow.According to the theory of droplet particle force balance, considering the influence of droplet deformation and maximum droplet size on liquid carrying capacity, characteristic parameters were introduced.Based on the principle of energy conservation, the relationship between droplet deformation degree and critical Weber number function was derived, then a model for calculating gas critical liquid carrying capacity was established.Through example calculation, the model is suitable for gas critical liquid-carrying in high and low pressure gas wells, and has good comprehensive performance.According to the theory of droplet particle force balance, Yu Xiong 26 took into account the impact of droplet deformation and droplet size on the gas critical liquid carrying flow rate, and comprehensively compared the functional relationship between drag coefficient, droplet deformation parameters, and critical Weber number to establish a model for calculating the gas critical liquid carrying flow rate.Using actual data from the Sourig gas field with low porosity, low permeability, low production, and low abundance for liquid accumulation prediction comparison, the accuracy of Turner's model, Li's model, and Wang's model were 64%, 84%, and 86%, respectively, while the accuracy of the Xiong's model reached 91%.Heng Xiao et al. 27 obtained the maximum diameter of elliptic droplet on a microscopic level by using the droplet breaking principle.The critical droplet entrainment rate was determined using droplet force balance theory, and the influence of droplet deformation on the resistance coefficient was determined.To develop a calculation model for the gas critical liquid carrying flow rate, the effects of pressure, temperature, and pipe diameter on the frictional resistance and surface tension of gas-liquid two-phase were taken into account.Through theoretical study, Zhennan Zhang et al. 28 were able to determine the wellbore's gasliquid two-phase flow pattern and transition criterion.The maximum size of droplets in the gas core depended on the droplet fragmentation process under co-flow circulation conditions and the droplet entrainment process under stirring circulation conditions.
To summarize the literature, considering the deformation of droplet in the airflow, the maximum droplet diameter was calculated by different methods, and the gas critical liquid-carrying flow calculation model was established.
The droplet deformation directly affects the parameters that express the characteristics of droplets.Surendra Kumar Soni et al. 29 experimentally studied the deformation and rupture of droplets under oblique continuous airflow.The motion trajectory and topological change of different droplets were recorded by high-speed imaging system, studying different fragmentation modes by changing droplet size, nozzle direction and fluid properties, so as to analyze the influence of droplet breaking on the critical Weber number.Daokuan Jiao et al. 30 simulated gas-liquid two-phase flow by combining direct numerical simulation with fluid volume function.By changing the integral length of turbulence, different inlet velocities were obtained, and the effects of turbulence and droplet deformation on the critical Weber number were analyzed.Zhennan Zhang et al. 31 used high-speed cameras and Doppler anemometers to carry out gasliquid two-phase vertical pipeline flow experiments, studied the characteristics of entrained droplets in mixed flow and annular flow, and showed that the droplet size distribution is to a certain extent determines the momentum exchange between the gas and the entrained droplets.Therefore, it is important to improve the accuracy of model for calculating a gas critical liquidcarrying flow rate by taking into account the effect of droplet deformation.

| Drag coefficient, Weber number and interfacial tension
In the flow of gas-liquid two-phase in a wellbore, the fluid force on the liquid droplet is usually represented by drag coefficient, the contraction force acting on the unit length of fluid interface is the interfacial tension and the ratio of inertial force to surface tension is the Weber number.The interfacial tension, critical Weber number and drag coefficient represent the force acting on liquid and its motion, directly affecting the accuracy of liquid accumulation prediction model.Yuansheng Li et al. 32 established a formula for interfacial tension by piecewise fitting the experimental data on interfacial tension.It is possible to calculate the flow of gas critical liquid while taking interfacial tension and droplet deformation into account.The model can more accurately predict the critical liquidcarrying flow rate under different droplet sizes.Zhiping Li et al. 33 calculated the actual interfacial tension according to the temperature and pressure of gas wellbore.By introducing the actual interfacial tension, Turner's model, 4 Li's model 19 and Wang's model 21 were modified to obtain the gas critical liquid-carrying flow rate calculation model considering the actual interfacial tension.The corrected models were compared to the gas critical liquid-carrying flow rate of condensate wells, and the accuracy of Turner's model could reach 90%.Zhibin Wang et al. 34,35 simulated droplet dynamic characteristics by using fluid volume function approach and direct numerical simulation method, studied the influence of Reynolds number and Weber number on the deformation and resistance of droplets was studied.A formula for calculating the gas critical liquid-carrying flow rate was developed based on the outcomes of the numerical simulations and the droplet force balance principle.The model is suitable for gas wells with low fluid production.Based on Min Li et al., 19 Gang Liu et al. 36 established a calculation model of gas critical liquid-carrying flow rate by taking into account the effects of temperature and pressure on interfacial tension.Yufa He et al. 37 used global fitting method to modify the drag coefficient by Reynolds number to obtain a calculated correlation equation.A calculation model of gas critical liquid-carrying flow with changed parameters is constructed by calculating the high precision natural gas physical property parameters suitable for deepwater gas well circumstances.
In summary, the drag coefficient, critical Weber number and interfacial tension are subject to the influence of liquid-carrying factors such as droplet shape and size, fluid properties, wellbore temperature and pressure, so setting them as a fixed value will affect the accuracy of a calculation model of gas critical liquidcarrying flow rate.
A portion of liquid in the vertical wellbore sticks to the inner wall of the wellbore in the form of liquid film, and the reversal of liquid film is usually used as the basis for judging wellbore fluid accumulation.The distribution and force analysis of liquid film in the vertical wellbore are shown in Figure 7. Wallis 12 first proposed that dimensionless airflow can be used as a criterion for judging liquid film reversal, and the model does not consider the impact that fluid volume and properties on the critical volume of liquid carrying.Barnea 16 proposed that the liquid film reversal point and critical gas flow rate can be derived from the infection point of dimensionless shear force curve calculated with different liquid film thicknesses.Zabaras et al. 38 studied the stability criterion of liquid film in vertical pipeline annular flow, and believed that the reverse flow of liquid film under the action of low-speed airflow is the main reason for liquid accumulation.Guner et al., 39 Li et al. 40 proposed a piecewise equation for the circumferential distribution of liquid film based on the experimental findings， and used the interface friction factor proposed by Andritsos 41 to determine the critical liquid carrying flow of gas.Based on the liquid film hypothesis, Jie Pan et al. 42 established a gas critical liquid-carrying flow rate calculation model by analyzing the force balance of gasliquid two-phase, take into account the dynamic effects of liquid film atomization and droplet deposition.
In summary, the calculation model of gas critical liquid-carrying flow rate in vertical wells is relatively mature, which mainly takes droplet fall as the critical point of calculating gas critical liquid-carrying flow rate.The gas's crucial liquid-carrying characteristics, including interfacial tension, drag coefficient, critical Weber number, and droplet shape and deformation.However, the existing models often ignore the fission and polymerization after droplet-to-droplet collision, and the momentum exchange between droplet and air is not considered, which leads to the inaccurate value of the gas critical liquid-carrying flow rate.

| ANALYSIS OF THE CURRENT SITUATION OF GAS CRITICAL LIQUID CARRYING FLOW CALCULATION MODELS IN INCLINED WELLS
Compared with the vertical well, the structure of inclined well is different, the force and distribution of liquid droplets and film in the inclined well are more complicated.The current calculation models are summarized and analyzed to more correctly anticipate the gas critical liquid-carrying flow rate in inclined wells.

| Droplet model
The force of a droplet in an inclined well changes depending on the angle of inclination and differs from that in a vertical well.The distribution and force analysis of liquid droplets in the inclined wellbore are shown in Figure 8.By revising the coefficient while taking into account the impact of the pipe wall on droplet friction and well inclination well, Li et al. 43  | 4779 interfacial tension based on gas well temperature and pressure data, taking into account the variation of drag coefficient with Reynolds number, and established a calculation model for the critical liquid carrying flow rate of inclined well gas.Shejiao Du et al. 45 considered the internal flow of droplet and the impact of droplet deformation, and derived a functional relationship between the critical Weber number and droplet deformation parameters based on energy conservation equation.Based on the force balance analysis of droplets, a gas critical liquid-carrying flow calculation model was constructed taking into account the impacts of droplet deformation and wellbore inclination angle.Wenming Yang et al. 46 established a calculation model of gas critical liquid-carrying flow rate with high gas-liquid ratio in directional gas wells based on the relationship between well deviation angle, drag coefficient and Reynolds number.Ruiqing Ming et al. 47 considered the influence of directional well inclination angle and Reynolds number on gas liquid carrying, and established a calculation model of gas critical liquid-carrying flow rate for continuous liquid carrying in transitional and turbulent flow.
As shown in Figure 9, Li's model, 43 He's model, 44 Du's model, 45 and Yang's model 46 are used to calculate the gas critical liquid-carrying flow rate by taking the actual gas well in the offshore oil field as an example.By analyzing and comparing Yang's model and Du's model, the gas critical liquid-carrying flow rate is obviously smaller.The accuracy of Li's model and He's model is 61.9% and 95.12%, respectively.
In summary, most of the gas critical liquid-carrying models studied in inclined wells based on droplet models are established on the basis of vertical wells, and gas critical liquid carrying flow calculation models are established considering wellbore inclination angle.

| Liquid film model
In inclined wells, the liquid film is distributed extremely unevenly in the circumferential direction due to gasliquid separation caused by gravity.To clarity how the inclination angle affects the gas critical liquid-carrying flow rate, the force analysis of liquid film is shown in Figure 10.On the basis of Turner's model, 4 Belfroid et al. 48added the angle correction item and believed that the root cause of liquid film inversion into fluid accumulation.Based on experimental results of the distribution of liquid film thickness in the inclined tube annular flow, Xiaoxu Liu et al. 49 proposed a relationship between the liquid film thickness at the bottom of inclined tube and the average thickness of liquid film in the vertical tube annular flow, determined the empirical relationship between the average thickness of liquid film in the vertical tube and the interface friction coefficient, and established a calculation model of gas critical liquidcarrying flow rate with high gradient and high liquid gas ratio.The model is applicable to gas well with a wide range of gas-liquid ratio and liquid flow rate.Jinchao Li et al. 50considered the uneven distribution of liquid film in the wellbore of inclined wells and the influence of gas core droplet entrainment, and established a calculation model for the critical liquid carrying flow rate of fully inclined gas suitable for different pipe diameters and liquid phase flow rates, which is suitable for lowpermeability gas wells.Wujie Wang et al. 51  the impact of wettability and surface tension on the circumferential distribution of liquid film along the inner wall of the wellbore based on the assumption of gasliquid two-phase stratified flow in inclined gas wells.By examining the influence of changes in gas-liquid interface shape on the potential energy, kinetic energy and surface-free energy of gas-liquid two-phase system per unit pipe length, established a model for calculating the phase interface friction factor and finally closed control equations.According to the field production data of Yanchang gas field, the misjudgment rate of the model is 2.38%.Shu Luo et al. 52 found through experiments that the distribution of liquid film thickness is only related to the inclination angle and circumferential position of pipeline, and is independent of liquid velocity.On the basis of liquid film inversion, considering that the liquid film inversion is not easy to be observed during the experiment, the gas critical liquid-carrying flow rate is calculated by calculating the residual gradient pressure.Dechun Chen et al. 53 divided wellbore fluid into droplets in the gas core and a liquid film near the pipe wall, constructed a mechanical balance between liquid film and whole fluid.A calculating model for the gas critical liquid-carrying flow rate was developed using the tube diameter and inclination angle.Ayush Rastogi et al. 54 conducted an experiment on gas liquid accumulation in inclined pipelines.A calculation model for the gas critical liquid-carrying flow rate was developed based on the liquid film reversal principle, taking into account the inclination angle, liquid flow rate, gas-liquid density, viscosity, and pipe diameter.The model improves the accuracy of large diameter inclined well predictions.S. Shekhar et al. 55 established a calculation model of gas critical liquid-carrying flow rate based on the theory of liquid-film inversion theory, taking into account the influence of gas well diameter and inclination angle.Arnold Landjobo Pagou et al. 56 established a gas critical liquid-carrying flow rate calculation model based on the liquid film inversion theory, taking into account the impacts of gas-liquid volume change, tube diameter, inclination angle, and circumferential angle.Yilin Fan et al. 57 believed through experiments that liquid film reversal is the primary reason for wellbore liquid accumulation.Based on stratified flow, a gas critical liquid-carrying flow calculation model was established considering inclination angle and liquid flow rate, which revealed the influence of fluid properties on gas liquidcarrying flow under the flow condition.Wenqi Ke et al. 58 used the minimal liquid interface shear force to determine the critical point of liquid film reversal based on Newton's law of internal friction and gas-liquid twophase force equilibrium.Considering the influence of tilt angles and liquid film thickness, a gas critical liquid-carrying flow calculation model based on liquidfilm reversal was established.Zhibing Wang et al. 59 established a force balance analysis model of inclined tube bottom film on the basis of studying the thickness of inclined tube bottom film and the friction coefficient of liquid interface, revealing the mechanism of liquid accumulation caused by the inclined tube bottom film.Dechun Chen et al. 60 analyzed the force on the liquidfilm in the directional wellbore, considering the shear force between gas core and liquid-film, the shear force between liquid-film and pipe wall, the fluid gravity and pressure difference before and after liquid film, and established a prediction model for the gas critical liquidcarrying flow rate in directional gas well.The correction coefficient of the prediction model relative to the Turner model was derived, which is mainly related to the inner diameter of tubing and the inclination angle of well, and is less affected by the friction coefficient of tubing wall.Yuru Liang et al. 61 based on the theory of liquid-film reversal, considered operating pressure, wellhead temperature, water content, and pipeline inclination angle, studied the effect of maximum inclination angle and total elevation on the critical liquid-carrying flow rate, and established a calculation model for gas critical liquidcarrying flow rate in the upward inclined pipeline section.Weiwei Shen et al. 62 considered the uneven circumferential distribution of liquid film and the entrainment of liquid droplets in the gas-phase core in inclined well, established a gas critical liquid-carrying flow rate calculation model suitable for different pipe diameters and inclination angles.
In summary, the calculation models of gas critical liquid-carrying flow rate in inclined well mainly include droplet model and liquid-film model.Among them, the liquid-film model is more consistent with the actual condition of gas-carrying fluid in inclined wells.Existing liquid-film models are based on the analysis of the force of liquid film, considering factors such as inclination angle, pipe diameter, friction coefficient between wellbore and liquid-film, and so forth, to establish the calculation model of gas critical liquid-carrying flow.

| ANALYSIS OF THE CURRENT SITUATION OF GAS CRITICAL LIQUID CARRYING FLOW CALCULATION MODELS IN HORIZONTAL WELLS
Horizontal wells are more complex than vertical wells and inclined wells, including horizontal section, inclined section and vertical section, and the schematic diagram of droplet and liquid-film distribution in horizontal wells | 4781 is shown in Figure 11.Distinct wells have distinct droplet and liquid-film movement patterns, distribution forms, and gas-liquid two-phase flow patterns when it comes to the process of gas carrying liquid.To comprehensively understand the gas-carrying mechanism of whole wellbore of horizontal wells and accurately forecast the gas critical liquid-carrying flow rate, the existing models for calculating gas critical liquid-carrying flow rate of horizontal wells are summarized and analyzed.

| Droplet model
The gas-liquid two-phase flow patterns in different sections of horizontal wells are different, and the distribution and carrying form of liquid droplets are different.Dengsheng et al. 63 based on particle theory calculations, and based on the conversion criterion of mist flow and annular flow, introduced the gas-liquid two-phase flow state in horizontal pipes into the calculation of the minimum gas critical liquid-carrying flow rate, and established the gas critical liquid-carrying flow rate calculation model.Chao Zhou et al. 64 determined the length of long axis of maximum stable deformation droplet and selected the drag coefficient and surface tension formula suitable for shale gas horizontal wells based on the energy balance relationship of maximum stable deformation droplet.The Mukherjee-Brill two-phase flow model is chosen to determine the wellbore pressure distribution of horizontal shale gas wells based on the error analysis.A model of the gas critical liquid-carrying flow rate in the whole wellbore of shale gas wells is constructed taking into account the drop energy loss caused by wellbore liquid production, drop deformation, and slope rate variation.Juntai Shi et al. 65 conducted continuous liquid-carrying experiments in horizontal wells, studied the droplet size and shape variation law, established a gas critical liquidcarrying flow rate calculation model, and clarified the relationship between gas critical liquid-carrying flow rate calculation model and maximum diameter of droplet as a function.

| Liquid-film model
The distribution of liquid-film varies in different well sections.Ruiqing Ming et al. 66 conducted a force analysis on the liquid-film and center airflow in the wellbore of horizontal wells, and established a gas critical liquidcarrying flow rate prediction model by comprehensively considering the stable existence of liquid-film and continuous liquid carrying.Zhibin Wang et al. 67 studied the liquid-film thickness at the bottom and friction coefficient under annular flow conditions for liquid carrying in horizontal wells, revealing the impact of fluid properties such as pipe diameter, flow rate and pressure on gas critical liquid carrying.

| Experimental study
The gas-liquid two-phase flow pattern varies depending on the amount of liquid carried by gas.To clarify the gas-liquid two-phase flow pattern in different well sections and further improve the accuracy of calculation model for the gas critical liquid-carrying flow rate in the entire wellbore of horizontal wells, many scholars have carried out gas-liquid carrying simulation tests in the entire wellbore of horizontal wells.The schematic diagram of full wellbore gas carrying liquid simulation test in the horizontal well is shown in Figure 12.An experimental research on continuous liquid-carrying in horizontal gas wells was conducted by Gaojing Xiao et al. 68 The findings indicate that the liquid in horizontal sections of gas reservoirs is mostly transported by liquid film, and the closer vertical section is to the wellhead, the more droplets are carried.Li Li et al. 69 conducted an experiment on a gas-liquid two-phase prediction model in the horizontal wellbore.The findings demonstrate that the gas-liquid two phase flow pattern in a horizontal wellbore typically exhibits stratified flow, intermittent flow, and mist flow, and that the pipe diameter and inclination angle clearly affect this pattern.Qi Wang et al. 70 simulated a gas-liquid two-phase flow in horizontal wells by using the visualized gas-liquid twophase wellbore pipe flow simulation experimental device.According to the findings, inclined sections have the worst liquid carrying capacities and the highest critical liquid carrying flow rates, which can be utilized to determine the critical liquid-carrying flow rates for horizontal gas wells.Feng Qin et al. 71 carried out visual liquid-carrying simulation experiment in the whole wellbore of horizontal wells.The results show that the inclined pipe section is the starting position of liquid accumulation in horizontal wells.However, it is not necessary to simply look at whether the liquid is falling back in a certain section, but to comprehensively judge the beginning of liquid accumulation according to whether the liquid volume of whole wellbore increases and the degree of liquid falling back in each section.Xu Wang et al. 72 conducted a simulation experiment on the rule of fluid accumulation in horizontal wells.The findings demonstrate that the gas critical liquid-carrying flow rate in the inclination section decreases with the increase of the well inclination angle, and the maximum gas critical liquid-carrying flow rate is achieved at 40°.Yonghui Liu et al. 73 conducted a visualization simulation experimental device for horizontal wells, using highdefinition cameras to capture the reversal of liquid-film as the start of liquid accumulation, and developed a gas critical liquid-carrying flow rate model at various angles, tubing inner diameter and liquid apparent flow rate.Zhejun Zhao et al. 74 conducted experimental research on the actual production status of low-pressure and lowproduction wells based on the principle of similarity, indicting that low-pressure and low-production gas wells actually have a mixed state of upper mist flow and lower slug flow.The upper mist flow liquid-carrying meet the calculation results of droplet model, while the lower slug flow is judged based on the gas phase velocity.Zilong Liu et al. 75 conducted a gas carrying experiment in the horizontal wells under different angles, pressures and liquid volume, and obtained the relationship between gas critical liquid-carrying and angle.Based on the analysis of force acting on liquid-film on the wellbore of inclined gas wells, a calculation model for gas critical liquidcarrying flow rate in horizontal wells was established.
In summary, there are relatively few models for calculating the gas critical liquid-carrying flow rate in horizontal wells based on the droplet model and liquidfilm model.They mainly analyze the mutual influence between different well sections through the continuous liquid carrying experiment of gas-liquid two-phase in horizontal wells, and further establish a gas critical liquid carrying flow rate calculation model.However, the existing model does not consider the small angle inclination of horizontal sections of horizontal wells and has insufficient understanding of gas liquid-carrying mechanism of the whole wellbore of horizontal wells.It is difficult to accurately judge the gas liquid-carrying state in different well sections under different working conditions, and it is impossible to accurately judge the position where liquid accumulation is most likely to occur.It cannot effectively guide the drainage and gas production of horizontal wells.Liquid accumulation is a prevalent issue in the middle and later phases of gas well development.To increase the precision of predicting the generation time of liquid accumulation, domestic and foreign literatures on gas critical liquid-carrying flow calculation models in vertical wells, inclined wells and horizontal wells were analyzed and summarized.The main analysis findings are listed below.First, the research on gas critical liquid-carrying in vertical and inclined wells is relatively mature, mainly using droplet falling and liquid-film reversal as the critical points for gas liquid-carrying respectively, the force analysis of droplets and liquid-film is carried out, and a calculation model of gas critical liquid-carrying is constructed.Second, because of the special well structure, the gas-liquid two-phase flow pattern as well as distribution of droplets and liquid-film in horizontal wells are complex.The primary method is to conduct gas critical liquid-carrying simulation experiments throughout the wellbore of horizontal wells to examine how various well sections interact with one another, clarify the most easy to liquid-accumulating well sections in the whole horizontal well, and create a calculation model for the gas critical liquid-carrying flow rate.Based on the above summary and analysis, the research direction of the calculation model for gas critical liquid-carrying flow rate in the entire wellbore of horizontal wells is pointed out.Combining the gas liquid-carrying test of whole wellbore of the horizontal well, considering the distribution form of droplets and liquid-film, the aggregation and fission between droplets, and the energy exchange between gas and liquid, the gas liquid-carrying mechanism of the entire wellbore of horizontal well is revealed, clarifying the most easy to liquid-accumulating well sections in the whole horizontal well, and a calculation model of gas critical liquid-carrying flow rate of horizontal well considering multiple factors is established, providing a crucial theoretical foundation and technical support for the drainage and gas recovery of a horizontal well.

F I G U R E 1
Force analysis diagram of spherical droplets.F I G U R E 2 Force analysis diagram of elliptical droplets.

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I G U R E 3 Force analysis diagram of ball-cap shaped droplets.F I G U R E 4 Comparison curves of four critical liquid-carrying computational models with different droplet shapes and experimental data.

F I G U R E 5
Droplet physical model and force analysis diagram.(A) Physical model diagram of liquid droplets.(B) Deformation diagram of liquid droplet physical model.(C) Deformation diagram of liquid droplet physical model.d, droplet diameter; d 0 , droplet deformation diagram; A, airflow surface area.F I G U R E 6 Critical liquid-removal rate of gas wells for different gas-liquid ratio.
suggested a calculation model of gas critical liquid-carrying flow rate in inclined well based on the Turner model.Based on data on gas well temperature and pressure, Yingxu He et al. 44 calculated F I G U R E 7 Schematic diagram of liquid film distribution and force analysis in vertical wellbore.τ WL , shear stress between liquid film and shaft wall; τ, shear stress at gas-liquid interface; G, liquid film gravity, D, diameter of wellbore.F I G U R E 8 Schematic diagram of force analysis of droplets in inclined wells.θ, angle of inclination; G, gravity of droplet; Fr, buoyancy; F R , drag force.ZHENG ET AL.
investigated F I G U R E 9 Comparison of calculation results of Li'model, Yang'model, Du'model, and He'model.F I G U R E 10 Schematic diagram of force analysis on liquid film in inclined wells.f, friction between gas and liquid film; f WL , friction between the inner wall of wellbore and liquid film; G, gravity of liquid film.

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I G U R E 11 Schematic diagram of droplet and liquid-film distribution in horizontal wells.

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I G U R E 12 Schematic diagram of gas liquid carrying simulation test for the entire wellbore of horizontal well.DEVELOPMENT TRENDS