Research on the Application of Double-Tube Gas Lift Drainage Recovery in Coalbed Methane Wells: A Case Study of the Hancheng Block, China

Chen Li; Yongsheng An; Yanning Yang; Wenbo Jiang; Long Peng; Yongzan Liu

doi:10.2113/2022/9886330

Abstract

The key point in coalbed methane (CBM) wells is to pump out the confined water to produce gas. Traditional drainage coalbed methane recovery methods have different limitations and characteristics. A new drainage gas recovery method called double-tube gas lift is applied in the Hancheng block for CBM production. The working mechanism of double-tube gas lift technology is to insert a hollow sucker rod into the original production pipe string to assist CBM production. What is more, the gas production channel and the drainage channel can be distinguished by this method. An improved measure is designed to overcome the double-tube gas lift’s shortcomings by adjusting the entry depth of the smaller tubing to expose the coal seam. In this way, the two-phase liquid of injected gas and produced liquid can be discharged from the annulus between the tubing and the smaller tubing. The produced gas is directly discharged from the annulus between the external tubing and the casing. The analysis of influence factors shows that the gas injection volume, water production, smaller-diameter tubing size, and the well entry depth have a significant influence on the production of the double-tube gas lift technology. The improved double-tube gas lift method has been applied in the Hancheng CBM wells to prove that this method has great production results and has the potential to get more applications in other CBM fields.

1. Introduction

Coalbed methane (CBM) has arisen as one of the clean natural gas resources to supplement the demand for conventional hydrocarbons. A total of more than 17,000 wells were in production, and the estimated recoverable resource of CBM came to $4.96 \times 10^{12} m^{3}$ in China [1]. Therefore, the development prospect of CBM is very broad. CBM fields have some notable characteristics: small output, low wellhead pressure, and high investments in unit capacity. Gas production from CBM reservoirs differs from conventional gas wells because the CBM is stored by adsorption in the coal matrix [2]. CBM wells are usually exploited by tubing drainage and casing production [3]. The artificial lifting system is applied to drain the lamination water from the coal seam to reduce the pressure [4]. In this way, the adsorbed methane can be desorbed from the pores of the coal seam. Therefore, it is crucial to pump out the confined water in the formation to reduce the pressure of the coal seam. Main drainage coalbed methane recovery methods contain the electric submersible pump, sucker rod pump, jet pump, foam, gas lift, and progressive cavity pump. Each drainage recovery method has its limitations and characteristics [5]. The rod pump is a commonly used technology in the production of CBM. This method is durable and has a low failure rate and low cost. However, it needs to continuously adjust the drainage system based on the liquid production volume [6, 7]. An electric submersible pump (ESP) is wildly applied in the strong drainage of the gas reservoir, but it requires a high-quality electric power supply. Moreover, the application of ESP for drain recovery is rare due to the voltage of the CBM discharge site being hard to keep stable [8, 9]. The progressive cavity pump (PCP) also is one of the lifting methods in CBM wells. The operation of PCP often fails, resulting in production interruption and huge economic loss [10]. Gas lift is another drainage method, whose advantages include high lifting height, low production cost, and random well types. The traditional single-tube gas lift method is suitable for strong liquid drainage at the early stage of CBM exploitation [11]. However, the gas lift drainage recovery is limited, while the formation water volume decreases drastically in the later stage of production [12]. In the exploitation of China’s CBM field, a beam pump unit with a tubing pump is the primary drainage method [13]. The failure of the stuck pump is the main reason for pump inspection in the CBM production [14]. New gas lift drainage recovery technology with double tube has the potential to improve the recovery factor in the CBM wells. In 2017, some CBM wells in the Hancheng block in China started to utilize the double-tube gas lift method for trial production. As a new drainage gas recovery technology type, the double-tube gas lift is still in the field experiment stage [15, 16]. The research on optimizing this new double-tube gas lift and its adaptability to CBM wells is at the initial stage of large-scale field application. The purpose of this study is to process a new idea of applying the improved double-tube gas lift technology to CBM wells based on the actual field trial production experiments in the Hancheng block. The optimal design of the double-tube gas lift and its influence factors have been discussed to improve the oilfield application of this new technology.

2. Mechanism and Challenges

2.1. Working Mechanism

The principal of the double-tube gas lift drainage gas recovery technology is to insert a hollow sucker rod into the original production pipe string to assist CBM production based on the single-tube gas lift drainage recovery technology. Due to the smaller inner diameter of the gas injection and liquid discharge channel and no downhole tools, the double-tube gas lift technology has the characteristic of lower starting pressure, smaller gas injection volume, and a longer pump inspection cycle. Moreover, the gas production channel and the drainage channel can be distinguished by this method. Therefore, the double-tube gas lift drainage recovery method is particularly suitable for the production of CBM wells. Figure 1 represents the schematic diagram of the double-tube gas lift device. It can be seen in Figure 1 that three flow systems are operating in a CBM production well [17–19]. The first is the inflow performance system from the reservoir to the wellbore, the second is the gas injection system from the wellhead to the bottom of the well, and the third is the production system from the wellbore. When CBM wells are in operation with a double tube, the infused gas can be injected through a smaller oil tubing to the coal reservoir and the coalbed methane and production liquid will be lifted out from the annulus between the two oil tubings, which is called a “positive lift.” Meanwhile, the injected gas can also be poured into the annulus of oil tubings. The coalbed methane and production liquid will be lifted out from the smaller tubing, which is called a “reversed lift.”

2.2. Present Challenges

The case reported in well Hancheng #1 illustrates the successful application of double-tube gas lift drainage recovery technology to achieve daily gas production of 4874 m³. Up to November 2021, double-tube gas lift drainage technology has been applied in several CBM wells in Hancheng Block, China. Previous trial production of CBM wells proved that the double-tube gas lift had the following four characteristics:

(1)
Lower starting pressure and a lower requirement on air compressor
(2)
Smaller gas injection volume and compressors can meet the requirements of lifting multiple wells
(3)
No downhole tool and easy to implement
(4)
High-cost performance and good return on investment

However, the trial production experiments showed that a total length of 80-100 m liquid loading between the annulus of oil tubing and casing always existed. The consequence of the double-tube gas lift method performed worse when the well depth increased. Also, no other downhole tools could be interjected after inserting a smaller tubing for double-tube gas lifting. Two crucial problems that existed in the Hancheng block were listed below:

(1)
Liquid production in the initial stage of coalbed methane drainage is large. The gas lift method is advantageous for substantial liquid drainage, and the liquid level can be well controlled. However, the double-tube gas lift technology is restricted when the formation water volume decreases in the late drainage stage. How to distinguish the gas production channel and liquid production channel to ensure that the process of gas injection will not affect the gas production, which is the most important point for gas production of coalbed methane
(2)
The domestic and foreign single-tube oil production theory is mature. However, the optimal design method of the double-tube gas lift technology needs further consideration. It is necessary to form the gas lift parameter optimization design scheme to provide technical guidance for the production of CBM wells with the double-tube gas lift drainage recovery technology

3. Double-Tube Gas Lift Process Design

3.1. Improvement of Double-Tube Gas Lift

The production system of the double-tube gas lift is relatively complicated. The injected fluid is pure gas and the outflow liquid is a mixed fluid of injected gas, produced gas, and produced liquid. To overcome the shortcomings of the existing double-tube gas lift drainage recovery technology, the improved measure is executed by adjusting the entry depth of the oil tubing. The improved double-tube gas lift schematic diagram is depicted in Figure 2. It can be drawn from Figure 2 that the entry depth of both the external tubing and the smaller internal tubing is below the depth of the target coal seam. The purpose of this improved design is to reduce the pressure of the coal seam by lowering the liquid level. Moreover, the gas production channel and the liquid production channel can be distinguished to ensure that the injected gas will not affect coalbed methane production. Taking positive lift as an example, after increasing the entry depth of the external tubing and the smaller internal tubing, the two-phase liquid of injected gas and produced liquid will be discharged from the annulus between the tubing and the smaller tubing. The produced gas is directly discharged from the annulus between the external tubing and the casing.

3.2. Process Design

The lowering of the liquid level in the annulus between the external tubing and the casing will expose the coal seam, which is conducive to the desorption of CBM. However, the conventional nodal analysis method cannot meet the design requirement of the double-tube gas lift drainage recovery technology. There is an urgent need to establish a new node analysis method to calculate the depth of the smaller-diameter tubing exceeding the coal seam. This new node analysis method must integrate the four flowing parts of tubing, the annulus between external tubing and smaller tubing, the annulus between external tubing and casing, and the reservoir to the wellbore.

Taking Hancheng #1 well as an example, according to the production allocation scheme of the CBM wells in the Hancheng block, the inflow performance relationship (IPR) curve can be calculated as shown in Figure 3. The IPR curves of CBM and water need to be separately calculated. By this means, under the condition of the flow pressure $P_{CBM}$ is known, the water production $Q_{w}$ and the gas production $Q_{g}$ corresponding to this flow pressure $P_{CBM}$ can be calculated.

Once the water production $Q_{w}$ and wellhead $P_{b}$ are determined, it is distinct to calculate the bottom hole flow pressure $P_{wf}$ at the penetration depth of the smaller-diameter tubing. Given the entry depth of the smaller tubing, the bottom hole pressure can be calculated under different gas injection rates based on the two-phase outflow curve of the annulus between the external tubing and the smaller-diameter tubing. Furthermore, to ensure that the entry depth of the smaller tubing is identical, the bottom hole pressure can be calculated according to the single-phase gas flow curve of the smaller tubing. A node analysis of bottom hole pressure is used to determine the accurate production coordination point by combining the pure gas injection inflow curve of the smaller tubing and the two-phase outflow curve of the annulus between external tubing and smaller-diameter tubing. As shown in Figure 4, the intersection point $P_{c}$ of the pure inflow curve and the gas-water outflow curve is the production coordination point, which is the best production time. The gas injection rate corresponding to the intersection point $P_{c}$ is the optimal gas injection rate $Q_{g}$ ⁠, and the bottom hole pressure $P_{wf}$ can be obtained. Providing that the entry depth of the smaller-diameter tubing is changed, the bottom hole pressure of different production coordination points also will change. Therefore, the relationship between the bottom hole pressure and the entry depth of the smaller tubing at the coordination points can be calculated.

Under the condition that the bottom hole is acquired, the height of the annulus liquid column also needs to be known to calculate the pressure of the coal seam. It is reasonable to prospect an appropriate development scheme to exactly exposing the coal seam. At this time, the height of the annulus between the external tubing and the smaller tubing is the same as the depth of the smaller tubing exceeding the coal seam. The pressure at the coal seam can be calculated as follows:

\begin{matrix} (1) & P = P_{w f} - ρ_{w} g h, \end{matrix}

where

P

is the pressure at the coal seam,

P_{w f}

is the bottom hole pressure at the coordination point,

ρ_{w}

is the liquid density in the annulus between the external tubing and the casing;

g

is the acceleration of gravity, generally taken as 9.8 m/s², and

h

is the liquid column in the annulus between the external tubing and the casing.

3.3. Pressure Drop Calculation in Double-Tube Gas Lift Wellbore

To calculate the whole wellbore pressure drop during the double-tube gas lift, a stable gas-liquid two-phase flow model must be continuous and differentiable over the entire computational range. This research applies the Hasan and Kabir model [20] to describe the flow mechanism of two-phase flow in the wellbore and annulus. This model is a drift-flux model and performs different calculation methods of the pressure gradient under different flow patterns. The advantages of the model lie in a wide range of multiphase flow applications and strong calculation continuity. Hasan and Kabir divided the flow patterns of gas-liquid two-phase flow in vertical or inclined tubes into four types according to the distribution state of gas-liquid two-phase, namely, bubble flow, slug flow, churning flow, and annular flow. Table 1 summarizes the discrimination criteria for four flow patterns.

For bubble flow, the terminal bubble-rise velocity of a Taylor bubble can be presented as follows:

\begin{matrix} (2) & v_{0 \infty} = 1.53 {[\frac{g (ρ_{l} - ρ_{g}) σ}{{ρ_{l}}^{2}}]}^{1 / 4}, \\ {v_{\infty}}_{T} = 0.35 {[\frac{g D (ρ_{L} - ρ_{g})}{ρ_{L}}]}^{1 / 2} . \end{matrix}

The critical flow velocity from slug flow to churning flow is expressed as

\begin{matrix} (3) & 2 v_{m s}^{1.2} {(\frac{ϕ}{2 D})}^{0.4} {(\frac{ρ_{l}}{σ})}^{0.6} \sqrt{\frac{0.4 σ}{g (ρ_{l} - ρ_{g})}} = 0.725 + 4.15 \sqrt{\frac{v_{s g}}{v_{m}}} . \end{matrix}

Hassan and Kabir believed that the pressure gradient calculation method of gas-liquid two-phase flow is similar to that of single-phase flow, and the total pressure gradient is composed of gravity pressure gradient, friction pressure gradient, and acceleration pressure gradient.

\begin{matrix} (4) & ‐ \frac{d p}{d z} = ρ_{m} g + \frac{f_{m} v_{m}^{2} ρ_{m}}{2 D} + ρ_{m} v_{m} \frac{{d v}_{m}}{d z}, \\ (5) & f_{m} = \frac{1}{{[4 \log (((ε / d) / 3.7065) - (7.149 / {Re}_{m}) \log (({(ε / d)}^{1.1098} / 2.8257) + {(7.149 / {Re}_{m})}^{0.8981}))]}^{2}}, \\ (6) & ρ_{m} = (1 - ϕ_{g}) ρ_{L} + ϕ_{g} ρ_{g}, \end{matrix}

where

f_{m}

is the Fanning friction factor for gas-liquid mixtures, dimensionless;

z

is the height, m; and

ρ_{m}

is the density of the gas-liquid mixture, kg/m³.

When calculating the gravity pressure gradient, friction pressure gradient, and acceleration pressure gradient, the mixture density is an indispensable parameter. The void ratio

ϕ

is used to calculate the mixture density

ρ_{m}

⁠. Based on the drift model, Hassan and Kabir derived the relationship between the void fraction

ϕ

and the diffusion coefficient

C_{0}

and the drift velocity

v_{d}

⁠. The diffusion coefficient

C_{0}

and drift velocity

v_{d}

corresponding to different flow patterns are shown in Table 2.

\begin{matrix} (7) & v_{\infty b} = 1.53 {[\frac{g (ρ_{L} - ρ_{g}) σ}{{ρ_{L}}^{2}}]}^{1 / 4}, \\ {\bar{v}}_{\infty} = v_{\infty b} (1 - e^{- 0.1 v_{g b} / (v_{s g} - v_{g b})}) + v_{\infty T} (e^{- 0.1 v_{g b} / (v_{s g} - v_{g b})}) . \end{matrix}

To make the transition of flow patterns smoother during calculation, Hassan and Kabir performed weighted average processing on the $C_{0}$ of two adjacent flow patterns.

For bubble flow,

\begin{matrix} (8) & C_{0} = 1.2 . \end{matrix}

For slug flow,

\begin{matrix} (9) & C_{0} = 1.2 (1 - e^{- 0.1 v_{g b} / (v_{s g} - v_{g b})}) + 1.15 (e^{- 0.1 v_{g b} / (v_{s g} - v_{g b})}) . \end{matrix}

For churning flow,

\begin{matrix} (10) & C_{0} = 1.2 (1 - e^{- 0.1 v_{m s} / (v_{m} - v_{m s})}) + 1.15 (e^{- 0.1 v_{m s} / (v_{m} - v_{m s})}) . \end{matrix}

For annular flow,

\begin{matrix} (11) & C_{0} = 1.15 (1 - e^{- 0.1 v_{g c} / (v_{s g} - v_{g c})}) + 1.0 (e^{- 0.1 v_{g c} / (v_{s g} - v_{g c})}) . \end{matrix}

After $C_{0}$ and $v_{d}$ are determined, the void ratio $ϕ$ can be calculated. Moreover, the total pressure gradient can be obtained by bringing other parameters into the pressure gradient formula (4). The flow chart of the iterative calculation of the wellbore model is shown in Figure 5.

4. Double-Tube Gas Lift Application and Sensitivity Analysis

The Hancheng CBM field is located on the southeastern margin of the Ordos Basin. It is another key area for CBM production in China after the Quinnan CBM field. The main coal-bearing strata in the Hancheng block are composed of the Permian Taiyuan formation and the Shanxi Formation. The thickness of the coal seam is 12 meters with a total of 13 coal-bearing layers. The main features in the Hancheng block are low pressure, low permeability, and high gas content. Since 2017, more than 20 CBM wells with double-tube gas gift technology have been applied in the Hancheng block. The sensitivity analysis of influence factors is performed by taking the Hancheng #3 well as an example. The sensitivity analysis of the other CBM wells shows similar results as the Hancheng #3 well.

4.1. Field Application

The Hancheng #3 well was the typical CBM well; this well was put into production in November 2010 with a depth of 1100 m. The depth of the main coal seam layer is 752.75 meters and the bottom hole is 1.27 MPa. In the early stage of CBM production, the screw pump was used for drainage and gas production, and the gas production was stable at 1218.21 m³/d. However, after a production period, the screw pump appeared to be worn, stuck pump, and gas lock problems because of the produced sand and coal powder in the drainage process. Since March 2017, the Hancheng #3 well began to use the double-tube gas lift drainage recovery technology for gas production. The average gas production was 1107.35 m³/d, the average water production was 6.54 m³/d, and the gas production dropped 9.1%. The reason for the decline in gas production is that the traditional double-tube gas lift technology increased the pressure at the coal seam compared to the screw pump. Also, there existed a length of liquid unloading accumulation in the annulus between the external tubing and the casing, which affected the desorption of coalbed methane.

To overcome the shortcomings of the traditional double-tube gas lift drainage recovery technology, the process design method mentioned above was adopted to improve the CBM production. Table 3 details the pipe string equipped in the Hancheng #3 well.

It was planned to carry out the technical improvement according to the gas production of 1200 m³/d. Figure 6 shows the pressure at the coal seam that met the production allocation plan was 1.5 MPa. During this time, the water production was 6.54 m³/d.

Given the entry depth of the smaller-diameter tubing, calculate the two-phase outflow curve in the annulus between the smaller tubing and the external tubing. The bottom hole pressure varied with the gas injection volume under the condition that the water production of 6.54 m³/d was calculated. Moreover, the relationship between bottom hole pressure and the gas injection volume could be obtained by changing the gas injection volume. It could be observed in Figure 7 that the smaller tubing inflow curve and the outflow curve in the annulus between the external tubing and the smaller tubing formed an optimal production coordination point $P_{c}$ ⁠. The best gas injection volume was 3515.15 m³/d, where the bottom hole pressure was 2.96 MPa.

After determining the production coordination point, the relationship between the bottom hole pressure and the entry depth of the smaller tubing could be obtained by altering the smaller tubing’s entry depth. Combined with the liquid density $ρ_{w}$ in the annulus, the pressure at the coal seam could be calculated as a function of the liquid column $h$ in the annulus between the external tubing and the casing. Figure 8 represents the relationship between the entry depth of the smaller tubing and the bottom hole pressure and the pressure at the coal seam. Since the pressure at the coal seam of the production allocation plan was 1.5 MPa and the bottom hole pressure of the optimal production coordination point was 2.96 MPa, the calculated best entry depth of the smaller tubing was 1006.42 m.

In September 2018, the entry depth of the smaller tubing was adjusted according to the optimized design of the double-tube gas lift method. Figure 9 revealed the production curve of water and CBM of the Hancheng #3 well. It could be drawn from Figure 9 that the stable CBM production exceeded 2000 m³/d after a period of drainage, which meant the improved double-tube gas lift drainage recovery technology achieved a good field application.

A total of 20 CBM wells had been lifted with the double-tube gas lift drainage recovery method. These wells had achieved great productions results, most of which reached a CBM production of 2000 m³/d after a period of drainage.

4.2. Analysis of Influence Factors

To determine the influence factors of the double-tube gas lift technology, sensitive analysis experiments were carried out in the Hancheng #3 well. The deep of the coal seam was 800 m, the bottom hole temperature was 30°C, the formation pressure was 1.27 MPa, the wellhead oil pressure was 0.1 MPa, and the average water production was 2.4 m³/d.

4.2.1. Gas Injection Volume Analysis

Taking the gas injection volume of the gas well as a sensitive factor and keeping other conditions unchanged, the relationship between the bottom hole flow pressure and the gas injection volume of the gas well under different gas well production conditions is shown in Figure 10. It could be seen that the increase in gas injection volume would lead to the bottom hole flow pressure increasing linearly. Under the same gas injection volume, the higher the gas well production, the higher the bottom hole pressure. Furthermore, the essence of CBM well drainage was to reduce the bottom hole flow pressure through drainage, thereby reducing the fluid pressure in the reservoir. Therefore, in the case of ensuring liquid unloading, a smaller gas injection volume should be selected for production to reduce the bottom hole pressure and increase the production of CBM wells.

4.2.2. Water Production Analysis

Taking the water production volume as a sensitive factor and keeping other conditions unchanged, the relationship between the bottom hole flow pressure and water production volume is presented in Figure 11. What could be known was that the increase of water production in gas wells rapidly increased the bottom-hole pressure and critical gas flow volume required to lift the liquid, thus making it hard for gas lift. For these CBM wells with higher water production, to meet the lifting demand of the liquid, it was necessary to increase the gas injection volume. However, the rise of the gas injection would increase the bottom hole pressure and then affect the desorption of adsorbed CBM. Therefore, the disadvantage of this technology for CBM well drainage was that the gas well could be produced normally only after the bottom hole liquid was drained to a certain extent. It was a better choice to optimize the design of the drainage channel to obtain lower bottom hole pressure.

4.2.3. Smaller-Diameter Tubing Size Analysis

Taking the smaller-diameter tubing as a sensitivity factor, the change of the bottom-hole flow pressure with the smaller-diameter tubing is analyzed in Figure 12. Switching to a larger inner diameter pipe string could effectively reduce the bottom hole flow pressure. At the same time, it increased the critical gas flow volume. It was a great idea to design suitable smaller-diameter tubing according to the actual need of oilfield production and the rated pressure and rated displacement of the used compressor.

4.2.4. The Entry Depth of the Smaller-Diameter Tubing Analysis

Take the gas production volume of 1000 m³/d as an example. Assuming that there was a pure water column between the bottom of the well and the depth of the coal seam, the drainage and production characteristics of CBM wells with different depths are detailed in Figure 13. It was clear from Figure 13 that the increase in the well depth of the gas well would increase the bottom hole pressure. What is more, the corresponding coal seam pressure drops significantly when the bottom hole pressure was raised, which was beneficial to the desorption of coalbed methane.

5. Summary and Conclusions

This paper presented a new double-tube gas lift drainage coalbed methane recovery method to help improve the CBM production in the Hancheng block. Through experimental analyses, the following conclusions have been developed:

The traditional gas lift technology is limited as the formation water volume decreases in the late stage of drainage. Furthermore, it is hard to distinguish between the gas production channel and the liquid production channel.

The improved double-tube gas lift drainage recovery technology is designed to adjust the entry depth of smaller tubing to decrease the coal seam pressure and distinguish the gas production channel and liquid production channel.

The analysis of influence factors of the double-tube gas lift technology showed that the gas injection volume, water production, smaller-diameter tubing size, and well entry depth have a significant influence on the production of the double-tube gas lift technology. It was a better choice to design the double-tube gas lift considering these factors to fulfill the actual production needs.

The improved double-tube gas lift method has been proven to have great production results in the Hancheng block. This technology has the potential to obtain more applications in the CBM field.

Data Availability

The data used in this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no known competing financial interests or personal relationships reported in this paper.

Acknowledgments

The authors of this article would like to express their gratitude to the CNOOC (China) Co., Ltd. Zhanjiang Branch (Grant No. CCL2019ZJFN1147) for financial support.

Exclusive Licensee GeoScienceWorld. Distributed under a Creative Commons Attribution License (CC BY 4.0).

Flow pattern	Discrimination criteria
Bubble	$v_{s g} < 0.429 v_{s l} + 0.357 v_{0 \infty}$ and $v_{0 \infty} < v_{\infty T}$
Slug	$v_{s g} > 0.429 v_{s g} + 0.357 v_{0 \infty}$ and $v_{m} < v_{m s}$
Churning	$v_{s g} < 3.1 {[g (ρ_{L} - ρ_{g}) σ / {ρ_{g}}^{2}]}^{1 / 4}$ and $v_{m} > v_{m s}$
Annular	$ϕ_{g} > 0.7$ and $v_{s g} > 3.1 {[g (ρ_{L} - ρ_{g}) σ / {ρ_{g}}^{2}]}^{1 / 4}$

Flow pattern	Discrimination criteria
Bubble	$v_{s g} < 0.429 v_{s l} + 0.357 v_{0 \infty}$ and $v_{0 \infty} < v_{\infty T}$
Slug	$v_{s g} > 0.429 v_{s g} + 0.357 v_{0 \infty}$ and $v_{m} < v_{m s}$
Churning	$v_{s g} < 3.1 {[g (ρ_{L} - ρ_{g}) σ / {ρ_{g}}^{2}]}^{1 / 4}$ and $v_{m} > v_{m s}$
Annular	$ϕ_{g} > 0.7$ and $v_{s g} > 3.1 {[g (ρ_{L} - ρ_{g}) σ / {ρ_{g}}^{2}]}^{1 / 4}$

Flow pattern	Diffusion coefficient $C_{0}$	Drift velocity $v_{d}$
Bubble	1.2	$v_{\infty b}$
Slug	1.2	${\bar{v}}_{\infty}$
Churning	1.15	${\bar{v}}_{\infty}$
Annular	1.0	0

Flow pattern	Diffusion coefficient $C_{0}$	Drift velocity $v_{d}$
Bubble	1.2	$v_{\infty b}$
Slug	1.2	${\bar{v}}_{\infty}$
Churning	1.15	${\bar{v}}_{\infty}$
Annular	1.0	0

Pipe string	Size (in)	Inner diameter (mm)	Outer diameter (mm)
Smaller tubing	1	24	36
Tubing	2^7/8	62	73
Casing	5^1/2	127.3	139.7

Research on the Application of Double-Tube Gas Lift Drainage Recovery in Coalbed Methane Wells: A Case Study of the Hancheng Block, China

Abstract

1. Introduction