Fluid Accumulation Prevention Method in Gas Wellbore Based on Drift Model

Abstract

Wellbore liquid loading is a major issue in the later stages of gas well development, particularly for low-permeability gas fields such as shale gas and tight gas, severely affecting the normal production of gas wells. Accurately predicting the onset of wellbore liquid loading and implementing preventive measures are crucial for ensuring the normal production of gas fields. Therefore, based on the gas–liquid-carrying mechanism in gas wellbores and the flow patterns of gas–liquid two-phase flow in inclined wells, the criterion for gas critical liquid-carrying is determined by the shear stress between the liquid film and the pipe wall being zero. By considering the relative velocity between gas and liquid phases, porosity, and the distribution of velocity across the cross-section through the gas–liquid momentum balance equations, a gas critical liquid-carrying velocity model based on the drift model is established. Field data are used to compare the proposed model with four existing liquid-loading prediction models using the misjudgment rate, mean relative percentage error, and mean absolute percentage error as evaluation metrics for model accuracy. The results show that the proposed model outperforms the other models, with a misjudgment rate of 2.99%, mean relative percentage error of 3.83%, and mean absolute percentage error of 4.12%.

1. Introduction

During natural gas extraction, free water and hydrocarbon condensate continuously separate from the formation, forming liquid droplets dispersed in the gas flow and liquid films on the inner walls of the wellbore. In the early stages of production, high gas well production and formation pressure ensure strong liquid-carrying capacity, allowing liquid droplets and films to be carried to the wellhead. As formation pressure and gas production decline, the liquid-carrying capacity of the gas flow significantly weakens, unable to overcome the gravity of liquid droplets and the friction of liquid films, leading to the accumulation of liquid droplets and films in the wellbore, eventually forming wellbore liquid loading, which severely affects normal production. Therefore, accurately calculating the gas critical liquid-carrying velocity is crucial for preventing wellbore liquid loading.

Existing research on gas critical liquid-carrying primarily uses liquid droplet fallback or liquid film reversal as criteria for calculating the gas critical liquid-carrying velocity. The droplet model, first proposed by Turner, studies spherical droplets and derives a gas critical liquid-carrying velocity model under vertical well and laminar flow conditions [1]. Subsequent scholars have improved the Turner model by considering the droplet deformation [2,3,4,5], drag coefficient [6], critical Weber number [7], and interfacial tension [8], enhancing the accuracy of gas critical liquid-carrying velocity calculations. The liquid film model, first proposed by Wallis, uses dimensionless gas velocity as a criterion for calculating the gas critical liquid-carrying velocity [9]. Based on Wallis’s flooding correlation, subsequent scholars have analyzed liquid film distribution and forces, considering factors such as the inclination angle, pipe diameter, and friction coefficient between the wellbore and liquid film, establishing gas critical liquid-carrying flow rate models [10,11,12,13,14,15].

To further enhance the understanding of gas wellbore liquid loading and its prevention, it is important to note that the complexities of gas–liquid two-phase flow in inclined wells are not fully captured by traditional models. In particular, the assumption of a uniform gas flow velocity or the neglect of phase interactions in existing models can lead to significant discrepancies in the prediction of liquid carryover. This is especially problematic for inclined wells, where the gravitational component acting on the liquid phase becomes more pronounced. In these wells, the liquid phase experiences a combination of gravitational forces and frictional resistance from the wellbore walls, which complicates the prediction of liquid accumulation.

While previous models focused on either droplets or liquid films, they did not fully integrate the dynamic behavior of the gas and liquid phases in varying well conditions, particularly in the inclined section. The relative velocity between the gas and liquid phases plays a critical role in determining whether the liquid phase will be carried by the gas flow or will accumulate due to gravity. Additionally, wellbore inclination adds another layer of complexity by influencing the distribution of liquid in the flow cross-section and altering the flow dynamics. For instance, the gas phase is more likely to carry liquid in the upper part of the inclined section, while liquid accumulation becomes more likely in the lower regions where gravity has a stronger influence [16,17,18,19].

In summary, research on gas critical liquid-carrying velocity models has focused on droplets or liquid films, using droplet fallback or liquid film reversal as criteria. However, studies on gas–liquid two-phase flow in vertical, inclined, and horizontal wells have not considered the interaction between gas and liquid phases during liquid-carrying. Additionally, the most challenging liquid-carrying section in horizontal wells is the inclined section, which is more complex than vertical wells [15,16,17,18]. Therefore, a gas critical liquid-carrying velocity prediction model for inclined wells based on the drift model is proposed, considering the relative velocity between gas and liquid phases, porosity, and the distribution of velocity across the cross-section.

2. Model Development

In gas–liquid two-phase flow within inclined wells, the liquid phase predominantly exists as droplets within the gas core and as films along the pipe walls. The droplets are subject to a combination of gravitational, buoyant, and drag forces, resulting in uneven horizontal forces that drive droplet accumulation towards the pipe walls. The liquid films, on the other hand, are driven by their own gravity, the gas–liquid interfacial shear stress, and the shear stress between the liquid film and the pipe wall. Due to gravity, liquid films are distributed unevenly around the inclined pipe wall, with a thicker accumulation at the bottom of the pipe compared to the top. As the gas velocity decreases, reverse flow is observed initially in the lower section where the film thickness is greatest.

When gas velocity is high, the liquid film is completely carried to the wellhead by the gas flow, and the shear stress between the pipe wall and liquid film is greater than zero. As gas velocity decreases, the gas–liquid interfacial shear stress decreases, reducing the liquid film velocity. When the shear stress between the liquid film and pipe wall decreases to zero, the liquid film reaches a critical state, and the gas velocity at this point is the gas critical liquid-carrying velocity. Further reduction in gas velocity results in negative shear stress between the liquid film and pipe wall, causing the liquid film to reverse flow under gravity, leading to liquid accumulation at the well bottom. The gas–liquid two-phase flow in the wellbore transitions to churn flow or slug flow, and liquid loading gradually begins. Figure 1 shows the schematic of gas–liquid-carrying in the inclined section of a horizontal well at different gas superficial velocities. Figure 2 shows the flowchart of the model establishment.

2.1. Momentum Balance Equation

In the gas–liquid two-phase flow in inclined gas wells, the momentum balance equation between the liquid film and gas core is

$$-{\tau }_{\mathrm{wf}}{\displaystyle \frac{S_{\mathrm{f}}}{A_{\mathrm{f}}}}+{\tau }_{\mathrm{i}}{\displaystyle \frac{S_{\mathrm{i}}}{A_{\mathrm{f}}}}-{\left({\displaystyle \frac{\mathrm{d}p}{\mathrm{d}L}}\right)}_{\mathrm{f}}-{\rho }_{\mathrm{l}}g\sin \theta =0$$

(1)

$$-{\tau }_{\mathrm{i}}{\displaystyle \frac{S_{\mathrm{i}}}{A_{\mathrm{c}}}}+-{\left({\displaystyle \frac{\mathrm{d}p}{\mathrm{d}L}}\right)}_{\mathrm{c}}-{\rho }_{\mathrm{c}}g\sin \theta =0$$

(2)

In the gas–liquid two-phase flow, the pressure gradients of the gas and liquid phases are approximately equal:

$${\left({\displaystyle \frac{\mathrm{d}p}{\mathrm{d}L}}\right)}_{\mathrm{c}}={\left({\displaystyle \frac{\mathrm{d}p}{\mathrm{d}L}}\right)}_{\mathrm{f}}=\left({\displaystyle \frac{\mathrm{d}p}{\mathrm{d}L}}\right)$$

(3)

Subtracting Equation (1) from Equation (2) gives

$${\tau }_{\mathrm{wf}}{\displaystyle \frac{S_{\mathrm{f}}}{A_{\mathrm{f}}}}-{\tau }_{\mathrm{i}}{S}_{\mathrm{i}}\left({\displaystyle \frac{1}{A_{\mathrm{c}}}}+{\displaystyle \frac{1}{A_{\mathrm{f}}}}\right)+\left({\rho }_{\mathrm{l}}-{\rho }_{\mathrm{c}}\right)g\sin \theta =0$$

(4)

where τ_wf—shear stress between the liquid film and pipe wall, Pa; τ_i—shear stress between the gas core and liquid film, Pa; S_f—wetted perimeter of the liquid film, m; S_i—wetted perimeter of the gas core, m; A_f—cross-sectional area of the liquid film, m²; A_c—cross-sectional area of the gas core, m²; ρ_i—density of the liquid phase, kg/m³; ρ_c—density of the gas core, kg/m³; and θ—inclination angle of the pipe, °.

2.2. Geometric Relationship of Gas–Liquid Phase Distribution

Assuming the pipe’s inner diameter is d and the liquid film thickness is δ, then the pipe’s cross-sectional area A is

$$A={\displaystyle \frac{\pi d^2}{4}}$$

(5)

Cross-sectional area of the gas core A_c:

$$A_{\mathrm{c}}={\left(1-2{\displaystyle \frac{\mathsf{\delta }}{d}}\right)}^{2}A$$

(6)

Cross-sectional area of the liquid film A_f:

$$A_{\mathrm{f}}=4{\displaystyle \frac{\delta }{d}}{\left(1-{\displaystyle \frac{\delta }{d}}\right)}^{2}A$$

(7)

Interfacial perimeter between the gas core and liquid film S_i:

$$S_{\mathrm{i}}=\pi d\left(1-2{\displaystyle \frac{\delta }{d}}\right)$$

(8)

Wetted perimeter of the liquid film S_f:

$$S_{\mathrm{f}}=\pi d$$

(9)

2.3. Shear Stress

The interfacial shear stress τi in annular flow:

$${\tau }_{\mathrm{i}}={\displaystyle \frac{1}{2}}{f}_{\mathrm{i}}{\rho }_{\mathrm{c}}{\displaystyle \frac{\left(v_{\mathrm{c}}-v_{\mathrm{f}}\right)\left|v_{\mathrm{c}}-v_{\mathrm{f}}\right|}{2}}$$

(10)

where fi is the interfacial friction coefficient, selected as fi = 0.005 (1 + 380δ/d), based on Wallis’s correlation [9].

2.4. Gas Core and Liquid Film Velocities

Based on the mass balance equation, the velocities of the gas core and liquid film, and the average density of the gas core, can be calculated as follows:

Gas core velocity v_c:

$$v_{\mathrm{c}}={\displaystyle \frac{\left(v_{\mathrm{sg}}+v_{\mathrm{sl}}FE\right)d^2}{{\left(d-2\delta \right)}^2}}$$

(11)

where v_sg—gas superficial velocity, m/s; v_sl—liquid superficial velocity, m/s.

Liquid film velocity v_f:

$$v_{\mathrm{f}}=v_{\mathrm{sl}}{\displaystyle \frac{\left(1-FE\right)d^2}{4\delta \left(d-\delta \right)}}$$

(12)

Density of the gas core ρ_c:

$${\rho }_{\mathrm{c}}={\rho }_{\mathrm{g}}\varphi +{\rho }_{\mathrm{l}}\left(1-\varphi \right)$$

(13)

where ϕ—porosity.

2.5. Liquid Droplet Entrainment in the Gas Core

In the gas–liquid two-phase flow in pipes, liquid primarily exists as droplets in the gas core and as films on the pipe walls in a dynamic equilibrium. High gas velocity causes the liquid film to break into droplets entrained in the gas core; low gas velocity causes droplets in the gas core to settle into the liquid film. The distribution of droplets and films with gas core velocity directly affects the gas core density and liquid film superficial velocity. Therefore, this model considers liquid droplet entrainment in the gas core using Wallis’s correlation [9] to calculate the entrainment fraction FE:

$$FE=1-e^{\left[-0.125\left(\mathit{\Psi }-1.5\right)\right]}$$

(14)

$$\mathit{\Psi }=10^4{\displaystyle \frac{v_{\mathrm{sg}}{\mu }_{\mathrm{g}}}{\sigma }}{\left({\displaystyle \frac{{\rho }_{\mathrm{g}}}{{\rho }_{\mathrm{l}}}}\right)}^{0.5}$$

(15)

2.6. Porosity

In gas–liquid two-phase flow, the interaction between gas and liquid phases causes velocity differences. The drift model, which considers the relative velocity between gas and liquid phases, as well as the porosity and velocity distribution across the flow cross-section, is a primary method for studying gas–liquid two-phase flow patterns. Therefore, based on the drift model, the porosity ϕ is

$$\varphi ={\displaystyle \frac{v_{\mathrm{sg}}}{C_0\left(v_{\mathrm{sg}}+v_{\mathrm{sl}}\right)+v_{\mathrm{mg}}}}$$

(16)

where C₀—distribution coefficient; v_mg—drift velocity, m/s.

The distribution coefficient C₀ and drift velocity v_mg are important parameters characterizing gas–liquid two-phase flow patterns, considering the inclination angle and flow patterns in inclined wells [19].

$$C_0=1+0.16\left(1-{\displaystyle \frac{{\rho }_{\mathrm{g}}{v}_{\mathrm{sg}}}{{\rho }_{\mathrm{g}}{v}_{\mathrm{sg}}+{\rho }_{\mathrm{l}}{v}_{\mathrm{sl}}}}\right)$$

(17)

$$v_{\mathrm{mg}}=f\left(\theta \right){\left[g\sigma {\displaystyle \frac{\left({\rho }_{\mathrm{l}}-{\rho }_{\mathrm{g}}\right)}{{\rho }_{\mathrm{l}}^2}}\right]}^{1/4}$$

(18)

$$f\left(\theta \right)=a_1{v}_{\mathrm{sg}}^{a_2}\left(1+b_1\sin \theta +b_2{\sin }^2\theta +b_3{\sin }^3\theta \right)$$

(19)

Based on experimental data, the distribution coefficient C₀ and the function f(θ) considering the inclination angle are fitted using the simplex method and global optimization [20,21,22,23], yielding a₁ = −0.1124, a₂ = 0.9014, b₁ = 13.0455, b₂ = −5.1737, and b₃ = −17.6701.

3. Model Comparison and Case Validation

3.1. Fluid Property Parameters

Based on the geological conditions of the gas wellbore, the density of formation brine is 1074 kg/m³, the relative molecular weight is 18, the natural gas relative density is 0.6, and the wellhead temperature is 310 K.

(1)

Natural gas density:

$${\rho }_{\mathrm{g}}=3484.4{\displaystyle \frac{r_{\mathrm{g}}P}{ZT}}$$

(20)

where r_g—natural gas relative density, dimensionless; P—pressure, MPa; T—bottomhole temperature, K; and Z—compressibility factor at P and T.

(2)

Pseudo-critical temperature and pseudo-critical pressure of natural gas:

$$T_{\mathrm{c}}=a_0+a_1{r}_{\mathrm{g}}$$

(21)

$$p_{\mathrm{c}}=b_0+b_1{r}_{\mathrm{g}}$$

(22)

where a₀, a₁, b₀, and b₁ are coefficients related to natural gas properties. a₀ = 10.6, a₁ = 152.22, b₀ = 4778, and b₁ = −248.21 [24].

(3)

Compressibility factor

When 5.4 < p_r ≤ 15 and 1.05 ≤ T_r ≤ 3.0,

$$Z={\displaystyle \frac{p_{\mathrm{r}}}{{\left(3.66T_{\mathrm{r}}+0.711\right)}^{-1.4667}}}-{\displaystyle \frac{1.637}{0.319T_{\mathrm{r}}+0.522}}+2.071$$

(23)

When 0.2 < p_r ≤ 5.4,

$$Z=p_{\mathrm{r}}\left(A{T}_{\mathrm{r}}+B\right)+C{T}_{\mathrm{r}}+D$$

(24)

(4)

Natural gas viscosity

$${\mu }_{\mathrm{g}}=K\times {10}^{-3}{e}^{x{\rho }_{\mathrm{g}}^y}$$

(25)

$$K={\displaystyle \frac{\left(1.26+0.078r_{\mathrm{g}}\right)T^{1.5}}{116+306r_{\mathrm{g}}+T}}$$

(26)

$$x=3.5+{\displaystyle \frac{548}{T}}+0.29r_{\mathrm{g}}$$

(27)

$$y=2.4-0.2x$$

(28)

(5)

Formation water viscosity

$${\mu }_{\mathrm{l}}=M\times e^{x{\rho }_{\mathrm{l}}^y}$$

(29)

$$N={\displaystyle \frac{\left(7.77+0.0063M\right)T^{1.5}}{122.4+12.9M+T}}$$

(30)

$$x=2.57+{\displaystyle \frac{1914.5}{T}}+0.0095M$$

(31)

$$y=1.11-0.04x$$

(32)

3.2. Data Validation

Based on the critical gas velocity data for the liquid-carrying capacity provided in Reference [25], the inclined section model and classical models for gas–liquid critical flow in inclined wells were employed to calculate the critical gas flow rate. By comparing the calculated critical gas flow rate with the actual gas production rate, the presence of liquid accumulation in the wellbore was assessed. The accuracy of these models was evaluated by comparing their predictions with the actual production status of the gas wells.

If the gas production rate in the wellbore exceeds the critical liquid-carrying flow rate, liquid accumulation will be prevented. If the gas production rate equals the critical liquid-carrying flow rate, the wellbore will be in a critical liquid accumulation state. Conversely, if the gas production rate is lower than the critical liquid-carrying flow rate, liquid accumulation is likely to occur. Since the actual field gas flow rate under critical conditions cannot be precisely determined, relying solely on the comparison between field gas rates and critical liquid-carrying flow rates to evaluate model accuracy is unreliable. Therefore, the misjudgment rate was introduced as a more robust measure to assess the validity of the mathematical models for critical gas–liquid flow.

$$\mathrm{Misjudgment} \mathrm{Rate}={\displaystyle \frac{\mathrm{Number} \mathrm{of} \mathrm{Misjudged} \mathrm{Wells}}{\mathrm{Total} \mathrm{Number} \mathrm{of} \mathrm{Gas} \mathrm{Wells}}}\times 100\%$$

As shown in Figure 3, Figure 4, Figure 5 and Figure 6, the numbers of misjudged wellheads for References [26,27,28,29] and detailed data can be found in

Table 1. Basic data of liquid accumulation in horizontal wells.

Vsg/(m·s−1)	Water Production Volume/(m3·d−1)	Relative Density of Natural Gas	Oil Pressure/MPa	Pipe Diameter (in)	Wellhead Temperature/°C	Well Inclined Angle/(°)	Belfroid Model/(m·s−1)	New Model/(m·s−1)
12.34	0.042	0.59	0.40	4.41	16	20	14.31	23.11
11.91	0.051	0.59	0.40	4.95	16	20	14.31	24.49
12.51	0.024	0.59	0.55	2.81	16	24	12.44	16.07
13.60	0.029	0.59	0.60	2.87	16	21	11.76	15.31
12.53	0.029	0.59	0.60	2.99	16	0	9.12	12.10
12.53	0.029	0.59	0.60	2.99	16	23	11.89	15.79
13.71	0.027	0.59	0.55	2.87	16	14	11.13	15.18
13.74	0.056	0.59	0.60	3.96	16	27	12.05	18.48
10.99	0.069	0.59	0.60	4.89	16	22	11.79	20.09
12.26	0.076	0.59	0.60	4.89	16	16	11.33	19.30
12.8	0.080	0.59	0.60	4.89	16	20	11.66	19.86
15.68	0.098	0.59	0.60	4.89	16	29	12.13	20.67
12.53	0.029	0.59	0.60	2.99	16	27	12.05	16.06
15.48	0.012	0.59	0.60	1.75	16	16	11.32	11.55
9.91	0.062	0.59	0.60	4.89	16	24	11.91	20.29
11.35	0.071	0.59	0.60	4.89	16	17	11.42	19.45
12.8	0.080	0.59	0.60	4.89	16	30	12.16	20.72
13.34	0.083	0.59	0.60	4.89	16	47	12.06	20.55
11.35	0.071	0.59	0.60	4.89	16	19	11.58	19.73
12.47	0.060	0.59	0.60	3.96	16	42	11.29	17.33
10.54	0.112	0.63	0.70	4.41	62	13	7.48	12.12
8.33	0.135	0.63	1.50	4.28	45	27	6.25	10.02
12.16	0.247	0.63	2.40	6.09	73	18	7.96	15.10
4.33	0.146	0.63	1.50	4.41	49	20	4.33	7.09
3.66	0.225	0.63	4.60	4.41	46	20	3.18	5.22
12.24	0.124	0.63	8.20	4.28	54	22	7.90	12.61
3.01	0.348	0.63	1.50	6.09	59	31	3.48	6.59
3.73	0.225	0.59	8.10	4.28	50	0	2.28	3.67
4.31	0.225	0.59	9.80	4.28	50	0	2.46	3.96
6.28	0.191	0.59	8.50	4.28	73	0	3.38	5.42
3.88	0.202	0.59	5.00	4.28	50	0	2.45	3.96
9.48	0.595	0.61	8.50	6.09	75	15	4.45	8.37
9.51	0.438	0.61	4.60	6.09	69	15	5.12	9.68
6.59	0.461	0.61	3.40	6.09	68	39	4.54	8.56
7.84	0.416	0.61	5.10	6.09	71	39	5.22	9.88
9.57	0.348	0.61	3.90	6.09	72	39	6.30	11.93
13.3	0.393	0.61	2.70	6.09	42	39	6.67	12.64
5.38	0.169	0.61	2.20	4.28	43	63	3.97	6.42
6.56	0.146	0.61	4.60	4.28	46	63	4.72	7.65
10.69	0.157	0.61	3.30	4.28	33	63	5.74	9.21
21.83	0.191	0.65	2.20	4.41	43	43	9.00	14.56
10.62	0.152	0.65	1.20	4.41	49	35	7.12	11.56
5.91	0.157	0.65	1.95	4.41	42	30	5.08	8.30
7.36	0.129	0.65	3.60	4.41	38	30	6.22	10.15
8.07	0.124	0.65	2.40	4.41	40	30	6.69	10.89
8.15	0.107	0.65	2.10	4.41	36	30	7.19	11.70
7.71	0.112	0.65	1.80	4.41	59	30	7.09	11.50
7.47	0.264	0.63	2.00	6.09	55.6	40	6.33	12.04
13.16	0.225	0.63	2.52	6.18	55	18	8.67	16.57
14.91	0.247	0.63	1.20	6.09	67	26	9.22	17.49
5.33	0.180	0.64	1.20	4.41	40	30	4.56	7.46
4.72	0.163	0.64	2.43	4.41	56	21	6.16	10.00
8.21	0.135	0.63	2.45	4.41	70	19	6.19	10.05
12.67	0.213	0.63	2.70	4.28	73	25	6.13	9.78
7.46	0.169	0.63	3.60	4.28	68	25	5.23	8.38
9.37	0.146	0.63	2.50	4.28	66	25	6.29	10.06
4.01	0.225	0.65	8.70	4.28	60	32	3.31	5.34
14.15	0.191	0.61	1.90	4.41	62.5	29	7.31	11.84
6.53	0.090	0.66	1.90	4.41	25	31	6.86	11.20
10.74	0.180	0.59	2.50	4.28	38	48	6.03	9.67
3.93	0.094	0.58	2.50	4.67	22	62	5.09	8.60
6.4	0.065	0.58	2.70	2.88	32	49	5.37	7.13
6.08	0.142	0.60	3.00	4.28	20	64	4.62	7.48
6.28	0.091	0.58	3.10	3.92	16	56	5.74	8.87
5.13	0.127	0.60	2.32	4.41	35	46	5.38	8.81
3.56	0.635	0.66	3.10	6.18	53	30	2.99	5.55
5.58	0.828	0.65	11.10	6.09	53	15	3.07	5.66

, and the proposed models are 4, 6, 5, 3, and 2, respectively. The corresponding misjudgment rates are 5.97%, 8.96%, 7.46%, 4.48%, and 2.99%. The proposed model exhibits the lowest misjudgment rate.

3.3. Error Analysis

The Average Percentage Error (APE) and Average Absolute Percentage Error (AAPE) were used to evaluate the prediction errors of the models in References [26,27,28,29] and the proposed model, as shown in Figure 7. As illustrated in Figure 6, the model from Reference [26] exhibits the largest positive APE and AAPE values, indicating that its calculated critical gas flow rates are significantly higher than the actual production rates. The model from Reference [29] also shows relatively large positive APE and AAPE values, suggesting an overestimation of the critical gas flow rates. Additionally, the larger discrepancy between the APE and AAPE for Reference [29] reflects greater variability in its predictions. In contrast, the proposed model demonstrates the smallest positive APE and AAPE values, indicating that its calculated critical gas flow rates are slightly lower than the actual production rates. The minimal difference between APE and AAPE for the proposed model further confirms its stability and reliability [30].

3.4. Application

The primary application of liquid accumulation prediction models lies in the establishment of a monitoring system capable of providing early warnings for liquid loading. By integrating real-time data—including pressure, temperature, flow rate, and wellbore conditions—the model tracks when the gas flow rate begins to approach the critical gas velocity required to prevent liquid accumulation. Continuous monitoring enables operators to anticipate liquid loading before it reaches problematic levels, thereby facilitating proactive measures such as adjusting production parameters, optimizing gas rates, or initiating artificial lift systems.

The model’s prediction of critical gas velocity serves as a benchmark for optimizing natural gas production. By maintaining the gas flow rate above the critical velocity, operators can prevent liquid accumulation in the wellbore, thereby enhancing overall production efficiency. Should the model indicate that the gas flow rate approaches or falls below the critical velocity, operators can implement adjustments to mitigate risks. For instance, increasing the gas production rate helps prevent liquid accumulation by sustaining higher gas velocities, which enhances liquid transport. Concurrently, well control parameters—such as choke size or backpressure—can be optimized to regulate flow conditions and ensure that the gas velocity remains above the critical threshold.

4. Conclusions

To address liquid accumulation in inclined gas wellbores, a drift model-based critical gas velocity model for liquid removal was developed using the condition of zero shear stress between the liquid film and pipe wall as the criterion for critical liquid-carrying capacity. The model incorporates the relative velocity between the gas and liquid phases, porosity, and velocity distribution across the cross-section. Field data were used to compare the proposed model with four existing liquid accumulation prediction models using the misjudgment rate, APE, and AAPE as evaluation metrics. The results demonstrate that the proposed model outperforms others, with a misjudgment rate of 2.99%, APE of 2.83%, and AAPE of 3.12%. These metrics indicate high accuracy, with calculated critical gas flow rates being slightly lower yet more stable compared to actual production rates.

Although the critical gas velocity prediction model for gas well liquid transportation based on the drift model proposed in this study demonstrates good predictive capabilities, there are still some limitations. Firstly, it only considers the basic gas–liquid two-phase flow mechanism. This model mainly takes into account factors such as the relative velocity and porosity of the gas–liquid two-phase flow, but in practical applications, the accumulation of liquids in the wellbore is also affected by other factors such as gas quality, temperature fluctuations, and pipeline wear, which are not fully reflected in the model. Secondly, the field data used in this study is limited to a certain type of gas field. Although the results are excellent on this dataset, the generalization ability of the model still needs to be verified. In the actual application process, due to the uncertainty of the data and the assumptions of the model, the accuracy and stability of the numerical calculation may still be affected, especially in complex wellbore environments. Particularly, its applicability in different types of gas fields or extreme conditions remains to be verified.

Future research should take into account more complex factors in practical applications, such as the different components of gases, the changing patterns of liquids, and the temperature and pressure distribution inside the wellbore, to establish a more comprehensive multi-factor coupling model and improve the accuracy of predictions. Considering the dynamic changes in wellbore conditions, dynamic prediction models based on real-time data and machine learning can be explored. By monitoring the status of gas wells and fluid characteristics online, the critical gas velocity prediction can be adjusted in a timely manner to enhance the model’s response capability. Meanwhile, experiments and data collection should be conducted in more types of gas fields, at different development stages, and under various operating conditions to improve the model’s universality and accuracy.