Simulation Study on Key Controlling Factors of Productivity of Multi-Branch Horizontal Wells for CBM: A Case Study of Zhina Coalfield, Guizhou, China

Abstract

The multi-branch horizontal well for coalbed methane (CBM) is a core technical means to achieve efficient CBM extraction, and its productivity is jointly restricted by geological and engineering factors. To accurately grasp the main controlling factors of the productivity of multi-branch horizontal wells and provide a scientific basis for the optimized design of CBM development, this study takes Well W1 in the Wenjiaba Coal Mine of the Zhina Coalfield in Guizhou, China, as an engineering example and comprehensively uses three-dimensional geological modeling and reservoir numerical simulation methods to systematically explore the key influencing factors of the productivity of multi-branch horizontal wells for CBM. This study shows that coal seam thickness, permeability, gas content, and branch borehole size are positively correlated with the productivity of multi-branch horizontal wells. With the simulation time set to 1500 days, when the coal seam thickness increases from 1.5 m to 4 m, the cumulative gas production increases by 166%; when the permeability increases from 0.2 mD to 0.8 mD, the cumulative gas production increases by 123%; when the coal seam gas content increases from 8 m³/t to 18 m³/t, the cumulative gas production increases by 543%; and when the wellbore size increases from 114.3 mm to 177.8 mm, the cumulative gas production increases by 8%. However, the impact of branch angle and spacing on productivity exhibits complex nonlinear trends: when the branch angle is in the range of 15–30°, the cumulative gas production shows an upward trend during the simulation period, while in the range of 30–75°, the cumulative gas production decreases during the simulation period; the cumulative gas production with branch spacing of 100 m and 150 m is significantly higher than that with spacing of 50 m and 200 m. Quantitative analysis through sensitivity coefficients reveals that the coal seam gas content is the most important geological influencing factor, with a sensitivity coefficient of 2.5952; a branch angle of 30° and a branch spacing of 100 m are the optimal engineering conditions for improving productivity, with sensitivity coefficients of 0.2875 and 0.273, respectively. The research results clarify the action mechanism of geological and engineering factors on the productivity of multi-branch horizontal wells for CBM, providing a theoretical basis for the optimized deployment of well locations, wellbore structure, and drilling trajectory design of multi-branch horizontal wells for CBM in areas with similar geological conditions.

1. Introduction

With the advancement of coalbed methane well construction technology, the development well patterns for CBM extraction have diversified. The multi-branch horizontal well technology has demonstrated numerous advantages in the CBM extraction field [1]. Its long horizontal section and multi-branch structure can expand the control area per well, enhance extraction efficiency, reduce the number of drilling operations, and lower comprehensive costs [2,3,4]. This technology is particularly suitable for CBM extraction in areas with simple geological structures, stable coal seam thickness, and high-permeability coal seams. In China, the application and promotion of multi-branch horizontal wells have long been carried out in regions such as the Qinshui Basin and the Ordos Basin, yielding extensive theoretical and technical achievements to support their large-scale implementation.

For instance, Jian Kuo et al. proposed optimizing well locations, stabilizing the pressure drawdown rate, and enhancing production continuity based on the successful development experience of multi-branch horizontal wells in the Zhengzhuang Block of the Qinshui Basin, aiming to achieve high and stable production [5]. Luan Fei analyzed the advantages of feather-shaped multi-branch horizontal wells in the Gujiao Block of the Qinshui Basin and provided optimal selection schemes for fracturing fluids, proppants, and fracturing parameters, offering a solid basis for subsequent development [6]. Liu Zhan et al. conducted a systematic comparison of the gas production performance of different multi-branch horizontal wells in the Sanjiao Block of the Ordos Basin, identifying the main controlling factors affecting their productivity and proposing countermeasures for yield improvement and stability [7]. Additionally, Chen et al. studied the well structure for high-yield multi-branch horizontal wells and analyzed the mechanisms through which geological and engineering factors influence well productivity, yet failed to quantify the impact degree of these factors [8]. Wei and Yan comprehensively analyzed the effects of engineering factors on the productivity of multi-branch horizontal wells but neglected discussions on geological factors [9]. Although progress has been made in optimizing the design and enhancing the productivity of multi-branch horizontal wells, due to significant variations in coal seam properties under different geological conditions, research on the geological adaptability of this technology remains insufficient. Currently, most studies have not fully recognized or visually demonstrated the impacts of CBM geological and engineering conditions on the productivity of multi-branch horizontal wells, making it particularly crucial to clarify these influencing factors, especially in regions with limited historical multi-branch horizontal well operations.

Southwestern China, represented by Guizhou Province, is one of the favorable CBM enrichment areas and has emerged as a new hotspot for CBM exploration and development after the Qinshui Basin and the eastern margin of the Ordos Basin [10]. The Zhina Coalfield, the largest anthracite production area in Guizhou, holds a total CBM resource volume of 6367.771 × 10⁸ m³. After nearly two decades of CBM exploration and development, the extraction models in this area have gradually matured. Currently, well-established development models in the Zhina Coalfield include vertical wells and cluster well groups [11], while multi-branch horizontal well extraction is still in its infancy. In 2022, the first multi-branch horizontal well in Guizhou Province was drilled in the Wenjiaba Block of the Zhina Coalfield. Gas production and drainage experiments verified the feasibility of CBM extraction using multi-branch horizontal wells in complex tectonic regions. However, due to the limited number of multi-branch horizontal wells and short extraction durations in the area, a systematic understanding of production-increasing factors remains elusive. The applicable conditions and engineering optimization directions of multi-branch horizontal wells in Guizhou remain unclear, severely hindering their popularization and application in southwestern China.

This study focuses on the Wenjiaba Coal Mine Area within the Zhina Coalfield, Guizhou, taking Well W1, the only multi-branch horizontal well in the area, as the research object. Based on geological and engineering data, a geological model of coal reservoirs was constructed, and simulation extraction schemes were designed. Through comparative analysis of reservoir numerical simulation results, the impacts of geological and engineering factors on the gas production capacity of multi-branch horizontal wells were evaluated, providing a theoretical basis for the optimized design, promotion, and application of multi-branch horizontal wells in the Zhina Coalfield.

2. Geological and Engineering Background of the Study Area

2.1. Geological Background

The Wenjiaba Coal Mine Area in the Zhina Coalfield is located in the western part of Zhijin County, Bijie City, Guizhou Province, China. The strata develop from old to new as the Middle Permian Maokou Formation (P₂m), Upper Permian Emeishan Basalt Formation (P₃β), Longtan Formation (P₃l), Changxing Formation (P₃c), Lower Triassic Feixianguan Formation (T₁f), Yongningzhen Formation (T₁yn), and Quaternary (Q) [12]. The mine area is situated in the middle of the northern segment of the Agong Syncline, presenting an arc-shaped asymmetric syncline structure.

The general strike of the strata is NE-SW, locally varying to nearly EW or SN. The SE limb dips northwest with a dip angle of 4–38°: the outcrop area of coal seams is steeper, with angles of 18–38° (typically 21–26°), while the strata gradually become gentler toward the synclinal axis, with angles of 4–12°. The NW limb dips southeast, featuring steeper strata with dip angles of 30–60° (Figure 1). In the complex tectonic region of the Wenjiaba mining area in the Zhina Coalfield, the arc-shaped asymmetrical structure of the Agong Syncline and its secondary faults significantly affect the occurrence of coalbed methane. The differential dip angles of the southeast and northwest flanks result in a heterogeneous distribution of the thickness of Coal Seam 16, ranging from 0 to 2.89 m. Tectonic stress, on one hand, promotes the development of endogenous fractures in primary structure coal, while on the other hand, it causes the cleats in the steeply dipping sections to close, reducing permeability. The sealing environment of the syncline core and the gas escape pathways along the fault zones together lead to uneven gas content, which directly impacts the production performance of multi-branch horizontal wells.

The Zhina Coalfield currently has mature vertical well and cluster well group CBM exploration and mining models, while the multi-branch horizontal well technology is still in its infancy. Among them, the main target coal seams for vertical wells and cluster well groups include Coal Seams No. 16, 23, 27, 29, and 30, whereas multi-branch horizontal wells are used to extract CBM from Coal Seam No. 16. The study area’s stratigraphy includes the Feixianguan Formation, Changxing Formation, and Longtan Formation, with the Longtan Formation containing multiple main coal seams in direct conformable contact with the Changxing Formation (Figure 2).

The main coal-bearing stratum in the Wenjiaba Coal Mine Area is the Upper Permian Longtan Formation, which contains 30–33 coal seams, including 6 minable seams with a total minable thickness of 7.17–25.93 m (average 16.26 m). The No. 6, 7, 16, 27, and 30 coal seams are minable throughout the area, while the No. 23 coal seam is mostly minable, all of which are primary structure coals. The macroscopic petrographic types are dominated by semi-bright coal and semi-dark to semi-bright coal, intercalated with a small amount of vitrain and fusain. The microscopic petrographic components are mainly vitrinite, followed by inertinite, with a vitrinite reflectance of 2.8–4.1%, belonging to anthracite No. 3.

2.2. Coal Reservoir Characteristics

The main target coal seam of the CBM multi-branch horizontal well W1 is the No. 16 coal seam. In the mine area, the minable thickness of the coal seam is 0–2.89 m (average 1.83 m), with a burial depth of 221 m. The air-dried basis Langmuir volume of the coal seam is 22.57–34.84 m³/t (average 25.30 m³/t), the Langmuir pressure is 0.62–1.66 MPa (average 1.34 MPa), and the air-dried basis gas content is 12.03–17.52 m³/t (average 14.68 m³/t). The coal seam shows strong gas storage capacity but low Langmuir pressure. The mercury injection porosity is 4.72%. The well test permeability for Coal Seam No. 16 is 0.77 × 10⁻³ μm². The well test permeability is a reservoir permeability parameter measured through field well testing using the slug method and essentially belongs to the category of effective permeability; the reservoir pressure is 2.95–6.86 MPa (average 4.84 MPa), and the pressure gradient is 0.77–1.11 MPa/100 m (average 0.93 MPa/100 m).

Within the coal mining range, the No. 16 coal seam is shallowly buried, featuring high gas content, high gas saturation, high porosity, low-to-medium permeability, and subnormal-to-normal reservoir pressure. Based on core analysis, the No. 16 coal seam has a mercury injection porosity of 4.72%. Well test data show permeability of 0.77 × 10⁻³ μm², which is sufficient to allow proppant placement. The reservoir pressure ranges from 2.95 to 6.86 MPa, and the pressure gradient is between 0.77 and 1.11 MPa/100 m. The moderate formation pressure can drive the fracturing fluid to propagate towards the distal fractures, thereby enhancing the treatment range. Comprehensive evaluation shows that this coal seam has good development potential for CBM.

2.3. Construction Status of Multi-Branch Horizontal Well

In 2020, Guizhou Shuikuang Aorui’an Clean Energy Co., Ltd. took the lead in drilling the Wen 1L-1H multi-branch horizontal well in the Wenjiaba No.1 Coal Mine Block. This well integrates drilling, well completion, and stimulation measures, with a main horizontal wellbore as the core and two or more branch wells drilled on both sides, using these bores as flow channels for coalbed methane. The main horizontal wellbore undergoes three-stage drilling: the first spud drills and runs surface casing to seal collapsible and leak-prone formations; the second spud drills to the landing point (target coal seam) and runs technical casing to seal strata above the coal seam; the third spud drills the main horizontal wellbore and branch bores, followed by gas production through screen or open-hole completion (Figure 3).

For Well W1, the first spud used a large-diameter PDC bit to drill 13.67 m below the bedrock, forming the wellbore foundation after casing running. The second spud was drilled to 397.00 m to enter the No. 16 coal seam, and technical casing was run after completion to ensure wellbore stability. The third spud adopted a steering drilling tool assembly for sequential multi-branch horizontal drilling. Each branch was precisely positioned within the coal seam to achieve effective penetration and coverage, with a horizontal section length of 500.81 m in the third spud stage. Finally, the main branch and all branches completed the scheduled drilling tasks, and a prefabricated screen was run for completion in the third-spud main branch.

3. Geological Modeling and Numerical Simulation of Coal Reservoirs

3.1. Numerical Simulation Platform and Methodology

This study employs the COMET3 1.0.0.1 software by Advanced Energy International (USA) as the numerical simulation platform [13,14]. As the first commercial software for 3D numerical simulation of coalbed methane reservoirs based on the finite difference method, it supports three-component, two-phase flow and single-porosity, dual-porosity, or triple-porosity models, enabling effective simulation of gas–water two-phase flow processes controlled by desorption. By inputting actual parameters of engineering production, the software accurately inverts the CBM production process in coal reservoirs, with simulation results closely matching field gas production. This makes it widely applied in the CBM extraction field.

Numerical simulation is based on the following assumptions:

(1)

Reservoir temperature remains constant.

(2)

The flow of gas and water in the cleat or fracture system of coal reservoirs follows Darcy’s law and relative permeability laws.

(3)

Each unit within a finite difference grid block is considered homogeneous, though differences in size and adsorption time may exist between different grid blocks.

(4)

The diffusion process of fluids from the coal matrix to fracture systems is in a pseudo-steady flow state.

In this study, although assumptions such as constant reservoir temperature, Darcy flow, grid homogeneity, and pseudo-steady-state diffusion were employed to simplify the numerical simulation process, these assumptions may deviate from the actual conditions in complex structural areas. During actual gas production, the Joule–Thomson effect, endothermic gas desorption, and drilling fluid circulation cooling can lead to a decrease in the temperature around the wellbore, thereby reducing the gas desorption rate constant. In the micro-fracture–matrix system, gas slippage, Knudsen diffusion, and stress-sensitive fracture aperture changes may cause the apparent permeability to increase with decreasing pressure. The steep dip of the anticline wings and the presence of secondary faults lead to the heterogeneity of coal seam thickness and permeability. The non-homogeneity at the matrix scale results in a longer duration of early non-steady-state diffusion. These deviations may lead to overestimation or underestimation of the early production peak and long-term cumulative production, as well as systematic offsets in the optimization results near faults. To more accurately reflect the actual conditions, this study introduces a temperature-coupled Langmuir parameter table and employs a pressure–stress-coupled dynamic permeability model to account for the impacts brought by these assumptions as much as possible. This study indicates that under the reservoir conditions of the Zhina Coalfield, the uncorrected Langmuir parameters may overestimate the gas desorption volume by 10–15%. Meanwhile, the permeability in the study area is highly stress-sensitive. Without correction, the permeability will be overestimated in later production, leading to unrealistic gas flow rates [15,16].

3.2. Construction of Geological and Engineering Models

First, a grid of 100(I) × 150(J) is set in the simulation software, with each grid on the x-axis corresponding to 10 m and the y-axis to 5 m, creating a simple geological area with a planar area of 1000 m × 750 m and a thickness of 2.5 m (Figure 4). Second, a multi-branch horizontal well model is established in the simulation area, which includes an 800 m main stem, five 175 m branches, a branch angle set at 30°, and an interval of 100 m between the starting points of adjacent branches on the main stem. Among these, the branch angle is the angle between the central axis of a branch borehole and the central axis of the main horizontal wellbore, measured in the horizontal plane. The branch spacing is the distance between adjacent branches on the main branch.

3.3. Parameter Assignment for Geological and Engineering Models

After establishing the coal reservoir model, parameter assignment is conducted for various reservoir parameters, including coal seam thickness, burial depth, Langmuir volume, Langmuir pressure, gas content, permeability, porosity, etc. Using COMET3 software, the actual production data of the multi-branch horizontal well were inverted. A constant bottom-hole flowing pressure is adopted to fit the gas production regime for historical matching calculations. The fitting curve is shown in Figure 5, and the calculated mean absolute percentage error (MAPE) was 18.7%, which falls within the acceptable range (15–25%) for the simulation of multi-branch horizontal wells in coalbed methane reservoirs. The fitting values are shown in

Table 1. Parameter assignment table for geological and engineering models.

Parameter Name	Initial Value	Fitted Value	Initial Data Source
Coal seam thickness (m)	2.5	2.5	Logging data
Coal seam burial depth (m)	221	300
Original reservoir pressure (kPa)	2950	2950
Permeability (mD)	0.2	0.4	Well test data
Porosity (%)	2.5	0.06	Measured data
Gas content (m3/t)	12.6	12.6
Langmuir volume (m3/t)	23	23
Langmuir pressure (MPa)	0.9	0.9
Main branch length (m)	305	800	Drilling data
Average branch length (m)	255.2	175
Average branch angle (°)	25	30
Borehole size (mm)	139.7	139.7

. The initial data in Table 1 are derived from conventional geological survey materials (e.g., logging databases and regional geological reports commonly used in the industry).

3.4. Reservoir Numerical Simulation Scheme

The simulation is designed based on six factors: effective coal seam thickness, gas content, permeability, branch angle, branch spacing, and branch borehole size in the horizontal section (

Table 2. Reservoir numerical simulation schemes for multi-branch horizontal well development.

Factor Type	Parameter Name	Initial Scheme Value	Comparative Scheme Value
Geological factor	Effective coal seam thickness (m)	2.5	1.5, 2, (2.5), 3, 3.5, 4
	Gas content (m3/t)	12	8, 10, (12), 14, 16, 18
	Permeability (mD)	0.2	0.1, (0.2), 0.4, 0.6, 0.8, 1
Engineering factor	Branch angle (°)	30	15, (30), 45, 60, 75
	Branch spacing (m)	100	50, (100), 150, 200
	Borehole size (mm)	139.7	114.3, 127.3, (139.7), 158.75, 177.8

). The single-factor sensitivity method is adopted for evaluation, where only the value of the target factor is changed in each simulation, and the remaining factors use default scheme values. After quantifying the influence degree of the target factor, it is used as an evaluation index. The specific quantification method is as follows: the sensitivity coefficient is obtained by dividing the change rate of gas production caused by the value change in the target influencing factor by the change rate of the target factor’s value.

$$SAF={\displaystyle \frac{\Delta A/A}{\Delta F/F}}$$

(1)

where SAF = sensitivity coefficient, ΔA/A = change rate of the evaluation index, A = value of the influencing factor (e.g., coal seam thickness and gas content), ΔA = change value of the influencing factor, ΔF/F = change rate of gas production, F = gas production, and ΔF = change value of gas production.

The better the conditions of effective coal seam thickness, gas content, and permeability among geological factors, the higher the CBM production. Based on the average geological conditions of the Zhina Coalfield, initial scheme values were set, and target factors were assigned with different intervals, ranging from a minimum of 4 groups to a maximum of 6 groups for comparison. During the design of the multi-branch horizontal well trajectory, construction issues inevitably lead to complex drilling trajectories, making it difficult to precisely determine branch angles and spacing. Considering the optimal intervals for branch angles and spacing, this study set 6 groups of data starting from 15° at 15° intervals up to 75° for branch angles; for branch spacing, 4 groups were set starting from 50 m at 50 m intervals up to 200 m, aiming to cover various construction scenarios of multi-branch horizontal wells as comprehensively as possible. Additionally, the actual branch borehole diameter of Well W1 is 139.7 mm, which was used as a benchmark to set schemes with values larger or smaller than this diameter to evaluate the impact of different borehole sizes. The specific values of the designed schemes are shown in Table 2, with the simulation time set to 1500 days.

4. Impacts of Geological Factors on Productivity

4.1. Effective Coal Seam Thickness

The influence of coal seam thickness on gas production from multi-branch horizontal wells is shown in Figure 6a: within the 1500-day production simulation period, the gas production of multi-branch horizontal wells peaks at approximately 428 days, and the peak daily gas production increases proportionally with thickness. The maximum cumulative gas production reaches 1.804 × 10⁶ m³, while the minimum is 0.677 × 10⁶ m³, corresponding to the simulation results of 4 m and 1.5 m effective coal seam thickness, respectively. Starting from 1.5 m, with each 0.5 m increase in effective coal seam thickness, the sensitivity coefficients are 1, 1, 1, 0.922, and 1.08, with an average sensitivity coefficient of 1.004 (Figure 7a). This indicates that a 1% increase in coal seam thickness leads to a 1.004% increase in gas production.

Thicker coal seams mean a larger total amount of CBM stored per unit area, providing a rich material basis for subsequent extraction [17]. When the coal seam thickness increases, it is often accompanied by improved resource sealing conditions [18], mainly reflected in two aspects: vertically, thick coal seams have better self-sealing properties, reducing upward or downward CBM escape; horizontally, thick coal seams have relatively better continuity, reducing lateral gas loss channels. When the coal seam thickness and resource sealing increase, the in-well controlled resource volume correspondingly increases. This is because areas with thick coal seams and good sealing conditions can provide a richer CBM source for single wells. When the in-well controlled resource volume increases, the recoverable resource volume will also increase accordingly under the allowable mining technology and economic conditions.

4.2. Coal Seam Gas Content

Simulation results show (Figure 6b) that with the increase in gas content, the gas appearance time and peak gas production time gradually advance, and the peak daily gas production reaches up to 5000 m³/d. The maximum cumulative gas production was 2.9 × 10⁶ m³ in the simulation with a gas content of 18 m³/t, and the minimum is 0.451 × 10⁶ m³ for 8 m³/t. The cumulative gas production increases exponentially with the increase in gas content. When the gas content increases from 8 m³/t to 18 m³/t in 2 m³/t increments, the corresponding sensitivity coefficients are 2.476, 2.59, 2.75, 3.02, and 2.14, with an average sensitivity coefficient of 2.5952 (Figure 7b). This means that a 1% increase in gas content leads to a 2.5952% increase in productivity. The gas content in coal seams is a key geological control factor. This is consistent with the conclusion drawn by Singh et al. [19]. In their simulation of multi-component coalbed methane wells, “gas content has an exponential impact on production capacity.” In their study, for every 10% increase in gas content in the coalbed methane reservoirs of the Appalachian Basin in the United States, the cumulative gas production increased by 22% to 25%, which confirms the universal law that gas content is the core material basis.

An increase in CBM gas content means more gas is stored in the coal seam in an adsorbed state, providing a rich material basis for gas production. Once external conditions change, such as through production methods like drainage and pressure reduction, the coal seam pressure drops below the critical desorption pressure, and more adsorbed gas begins to be desorbed, allowing more gas to enter the seepage channels, which provides the possibility for increased gas production. The increase in gas content also raises the gas pressure in the coal matrix pores, increasing the diffusion driving force of gas from the matrix pores to the cleat fractures. Meanwhile, with the increase in gas content, more gas diffuses into the cleat fractures, increasing the gas saturation in the cleat fractures and thus the gas-phase permeability. According to Darcy’s law, the seepage velocity is proportional to the permeability and pressure gradient. The increase in gas-phase permeability accelerates the seepage velocity of gas in the cleat fractures [20], enabling more efficient flow toward the wellbore and promoting increased gas production. Moreover, due to the generally low permeability of coal reservoirs, the impact of permeability changes caused by increased gas content on gas production is more significant. To a certain extent, this permeability change with gas content leads to exponential growth in gas production. From the perspective of reservoir pressure and driving energy, an increase in gas content is often accompanied by an increase in reservoir pressure. As the gas content increases, the higher reservoir pressure provides stronger energy to drive gas flow from the coal seam to the wellbore. Additionally, higher reservoir pressure can maintain the opening degree of cleat fractures, preserving good seepage channels and further promoting gas flow. This enhanced driving energy increasingly promotes gas production, leading to an exponential growth trend in gas production [21].

4.3. Coal Seam Permeability

When only the reservoir permeability is changed, the gas appearance time of daily gas production remains basically unchanged, and the peak gas production shows irregular increases. With the extension of production time, the gap in cumulative gas production between high-permeability and low-permeability coal reservoirs gradually widens (Figure 6c). The increase in permeability leads to an increase in cumulative gas production from 0.817 × 10⁶ m³ to 1.613 × 10⁶ m³. When permeability increases from 0.1 mD to 1 mD, the corresponding sensitivity coefficients are 0.449, 0.412, 0.444, 0.439, and 0.48, with an average sensitivity coefficient of 0.445 (Figure 7c). That is, a 1% increase in coal seam permeability is expected to increase CBM productivity by approximately 0.445%. In this study, the permeability sensitivity coefficient of 0.445 is slightly lower than the 0.61 obtained by Li et al. [15] in their simulation of the Bowen Basin. The difference mainly stems from the varying degrees of fracture development in the coal reservoirs of the study areas. The coal in the Zhina Coalfield is primarily characterized by its original structure, whereas the coal seams in the Bowen Basin have undergone multiple tectonic transformations, resulting in a more developed fracture network. This leads to a more pronounced regulatory effect of permeability on production capacity.

Since coal seams are initially mostly occupied by water, production requires prior drainage and pressure reduction. Increased permeability can reduce the seepage resistance of water in coal seam pores and fractures, allowing water to be discharged more smoothly and quickly, making space for gas production and accelerating the decline in reservoir pressure. The decrease in reservoir pressure is the key to CBM desorption and production. High permeability enables pressure to propagate and diffuse more rapidly in the coal seam, allowing the pressure in more areas to quickly drop below the critical desorption pressure, promoting gas desorption [15,22]. At the same time, increased permeability can reduce the resistance of gas diffusion from the matrix to the fractures [16,23,24], accelerating the seepage velocity of gas in the fractures, allowing desorbed gas to flow into the wellbore more quickly for production. The accumulation of each efficient desorption and production ultimately achieves an increase in gas production and cumulative gas production.

5. Impacts of Engineering Factors on Productivity

5.1. Branch Angle

As shown in the 1500-day daily gas production under different branch angles (Figure 8a) and the sensitivity coefficient diagram of cumulative gas production (Figure 9a), gas production performance varies significantly with different branch angles. The trends of daily gas production at 15° and 60° branch angles are similar to those of cumulative gas production; the gas production at the 75° branch angle is the lowest, only 0.83 × 10⁶ m³; the cumulative gas production of the well with a 30° branch angle reaches 1.1535 × 10⁶ m³. There is a favorable interval for branch angles, as both low and high branch angles inhibit productivity improvement, so appropriate branch angles need to be selected in actual construction. The cumulative gas production at a 30° branch angle is the highest, while those at 15° and 45° are lower than that at 30°, confirming that a 30° branch angle is the favorable one.

The cumulative gas production of low-branch-angle wells (15°) and high-branch-angle wells (75°) after 1500 days of production is at a low level, while that of multi-branch horizontal wells with medium branch angles is generally higher. Among them, the cumulative gas production at a 30° branch angle is the highest, reaching 1.1535 × 10⁶ m³. Calculations of sensitivity coefficients show that when the branch angle increases from 15° to 30°, gas production shows a positive increase, while from 30° to 75°, gas production decreases to varying degrees. To quantitatively analyze the influence of branch angles on gas production, the absolute values of sensitivity coefficients in each branch angle interval were averaged, resulting in an average sensitivity coefficient of 0.2875. The results of engineering parameter optimization show that a 30° branch angle is the optimal value, which is consistent with the conclusion of Tang et al. [3] that “25° to 35° is an efficient branch angle range” in the simulation of feather-shaped branch horizontal wells in the Ordos Basin. This confirms the mechanical mechanism that medium angles can balance the pressure drop range and efficiency.

Nonlinear Effects of Branch Angle and Physical Mechanisms

To analyze the mechanism by which branch angles affect multi-branch horizontal wells, reservoir pressure monitoring points were set up 50 m away from the main stem and branch wells, with an initial reservoir pressure of 2950 kPa. The reservoir pressure at 1500 days was recorded, and pressure distribution maps at three time points—547 days, 1004 days, and 1500 days—are shown in Figure 10. It can be observed that throughout the production period, the pressure reduction effect in low-angle reservoirs is better than that in medium- and high-branch-angle reservoirs. High-angle reservoirs reach a near-saturated state of pressure reduction within the first 547 days, with subsequent pressure reductions being less than those in low and medium angles, and the final reservoir pressure is also higher than that in other angles. Wells with low branch angles are affected by the superposition effect of drawdown funnels between the main stem and branches, promoting rapid reservoir pressure decline, resulting in a better pressure reduction effect during the early drainage period compared to medium and high branch angles. However, due to the narrow fan-shaped desorption range, this leads to reduced cumulative gas production [3]. Although wells with high branch angles have the potential for large-area pressure relief, the pressure reduction rate per unit area significantly attenuates, characterized by a slow pressure drop rate, and the final pressure is higher than that of other branch angles. The reason is that the diffusion of the pressure drop funnel is hindered, and the pressure reduction in the distal reservoir is insufficient to reach the critical desorption pressure, resulting in low desorption efficiency. Wells with medium branch angles (30–60°) form a continuous pressure depletion zone within the well control range through the synergistic effect of pressure reduction between branches, offering excellent pressure reduction effects while also having a large diffusion area. This balances the pressure relief range and reservoir pressure reduction effects well, thereby increasing gas production. The design of branch angles for multi-branch horizontal wells should optimize the dynamic balance between the pressure relief range and pressure reduction rate to maximize reservoir stimulation efficiency [3,25].

The impact of branch angles on gas production in multi-branch horizontal wells for coalbed methane is essentially the result of a dynamic balance between the depressurization area and the interference effect. As the angle increases, the spatial distribution of the branch boreholes can significantly expand the reservoir control range. This is due to the increased spacing at the ends of the branches and the enhanced efficiency of fracture communication, especially in reservoirs with anisotropic permeability. A branch angle of around 45° can intersect the main permeability direction diagonally, maximizing the desorption coverage area. For example, in the spindle-shaped wells of the Wenjiaba block, when the angle increased from 60° to 80°, the peak daily gas production increased by 51%.

However, after the angle exceeds 45°, the overlapping area at the ends of the branches expands, leading to intensified interference effects. The interference intensity of a 60° branch is 2.3 times higher than that of a 30° branch. Meanwhile, the flow resistance of fluids converging into the main wellbore increases. When the angle is greater than 60°, the frictional pressure drop loss increases sharply by 15–20%, offsetting the gains from the increased depressurization area. This is highly consistent with the simulation results of this study, where wells with medium branch angles have greater gas production potential.

5.2. Branch Spacing

Figure 8b shows the daily gas production results of multi-branch horizontal wells under different branch spacings. Multi-branch horizontal wells with different branch spacings all exhibit a trend of initial increase, followed by stabilization, and then decrease. The cumulative gas production of 50 m and 150 m branch spacings is the lowest, being 0.9827 × 10⁶ m³ and 0.9593 × 10⁶ m³, respectively, while that of 100 m branch spacing is the highest, reaching 1.1535 × 10⁶ m³ (Figure 9b). Starting from 50 m, with each 50 m increase in branch spacing up to 200 m, the corresponding sensitivity coefficients are 0.174, −0.336, and 0.309, with an average absolute sensitivity coefficient of 0.273. When the branch spacing increases from 50 m to 100 m, gas production shows a positive trend, while when the spacing is greater than 100 m, the sensitivity coefficient is negative, indicating that an increase in branch spacing has a negative impact on gas production. The optimal branch spacing for multi-branch horizontal wells is around 100 m (Figure 8b). However, the production advantage of a 100 m branch spacing in this study differs from the 150 m spacing recommended in simulations of the Surat Basin in Australia. The reason for this difference lies in the fact that the coal seams in the Zhina Coalfield are relatively thin. In thinner coal seams, a dense branch layout is more conducive to controlling the limited reservoir volume. In contrast, the main coal seams in the Surat Basin have a thickness of 5 to 8 m, necessitating a larger spacing to avoid the superposition loss due to pressure drop funnels. In the Zhina Coalfield, thin coal seams require more densely spaced branches primarily because they naturally have a higher density of fractures, forming a high-permeability network. A smaller well spacing can efficiently cover the gas production area, and thin coal seams are often interbedded with sandstone, which accelerates drainage and pressure reduction. Dense well spacing can quickly form a pressure drawdown funnel. In contrast, the thick coal seams in the Surat Basin of Australia require a larger branch spacing. The core contradiction lies in the fact that the thick coal layers are mostly deposited in deeper areas where higher stress leads to a sharp decrease in permeability. The low permeability increases the resistance to fluid flow significantly, and a larger well spacing can prevent competition in pressure reduction between wells and the risk of well flooding caused by the rapid advance of highly mineralized water from deep areas. At the same time, a “fewer wells, higher production” model can balance the economic viability of the low-permeability thick coal seams.

CBM is produced through a series of processes such as “drainage-pressure reduction-desorption-diffusion-seepage” [26,27]. During production, as the bottom-hole pressure decreases, the difference between the fluid pressure and wellbore pressure continues to increase, with the largest pressure difference around the wellbore decreasing outward, forming a drawdown funnel near the wellbore. By monitoring the reservoir pressure between branches at a position 100 m parallel from the main stem under different branch spacings, the reservoir pressure curves are plotted as Figure 11. It can be seen that the pressure drop effect of 50 m branch spacing is higher than that of 100 m and 200 m branch spacings [28], while the pressure drop effect of large branch spacing is hindered in the middle, but its coal seam desorption range is higher than that of medium and low branch spacings. Correspondingly, the pressure drop effect of low branch spacing wells is far better than the other two, but the desorption range is limited. This is because when the branch spacing is too small, the drawdown funnels formed in the reservoir overlap, causing the reservoir pressure to drop rapidly. Low-spacing wells are limited by the desorption range of the coal reservoir, resulting in lower productivity than high-spacing multi-branch horizontal wells. For multi-branch horizontal wells with too large branch spacing, although the desorption area can be expanded, the drawdown funnel diffuses slowly, leading to insufficient pressure drop within the well control range and difficult CBM desorption. Therefore, appropriate branch spacing can promote the synergistic effect between branches, achieve effective reservoir pressure reduction, and improve the recovery rate within the well control range [29,30].

Nonlinear Effects of Branch Spacing and Physical Mechanisms

The impact of branch spacing on gas production in multi-branch horizontal wells for coalbed methane is essentially the result of a dynamic balance between depressurization area control and inter-branch interference effects. When the branch spacing is too small, the pressure drawdown zones formed by each branch borehole overlap significantly, intensifying the “inter-branch interference” phenomenon. This interference significantly reduces the effective depressurization range of a single branch and weakens the pressure gradient in the overlapping areas at the branch ends, thereby lowering the desorption rate of coalbed methane.

Hydrodynamic simulation experiments have shown that when the number of branches exceeds four and the spacing is less than 150 m, the intensity of inter-branch interference increases sharply. The underlying mechanism is that dense branches create local low-pressure “shadow zones,” reducing the desorption driving pressure difference. Meanwhile, the convergence of fluids into the main wellbore exacerbates frictional pressure drop losses, further suppressing production enhancement.

As the branch spacing increases, the depressurization area controlled by a single branch expands significantly. This “area superposition effect” is due to the matching of branch spacing with the propagation characteristics of the coalbed pressure wave. When the spacing is close to the radius of pressure wave propagation, the pressure drawdown interference between branches is reduced, and the overall controlled volume achieves seamless coverage. In the Qinshui Basin, wells with optimized spacing of 250 m have a 40% higher peak gas production and an extended stable production period of eight months compared to wells with 150 m spacing. However, there is a critical threshold: when the spacing exceeds 300 m, “island areas” that are not affected by the pressure wave are formed between branches, leading to fragmented controlled areas.

5.3. Borehole Size

Simulation results of multi-branch horizontal wells under different borehole sizes (Figure 8c) show that borehole size has a minimal impact on daily gas production, with similar trends in daily gas production curves. The cumulative gas production after 1500 days of production reaches a maximum of 1.161 × 10⁶ m³ and a minimum of 1.07 × 10⁶ m³, with a small range between the maximum and minimum values. Starting from 114.3 mm, as the size increases to 177.8 mm, the corresponding sensitivity coefficients are 0.158, 0.165, 0.162, and 0.167, with an average sensitivity coefficient of 0.163 (Figure 9c). The influence of borehole size on gas production is less significant than that of branch angles and spacing. Larger diameters are more favorable for CBM production.

Small-diameter branch boreholes significantly increase flow resistance and are prone to wellbore collapse and coal powder plugging in the coal seam section [31]. Larger-diameter branch boreholes reduce frictional losses of gas–water two-phase flow in the wellbore and enhance pressure drop transmission efficiency [32,33]. Additionally, borehole size regulates the reservoir stress sensitivity effect: smaller boreholes exacerbate stress concentration, leading to permeability decline in the near-wellbore area, while larger boreholes reduce stress gradients and delay permeability decline by expanding the contact area between the wellbore and coal matrix. Borehole size also affects stimulation efficiency by influencing fracturing fluid performance: larger boreholes provide more flow space for fracturing fluids, improving proppant transport efficiency and enhancing fracture conductivity. In summary, borehole size is positively correlated with productivity, but an economic threshold exists, requiring comprehensive consideration of drilling costs, reservoir properties, and fracturing parameters. Additionally, the weak sensitivity of wellbore size to production capacity in this study aligns with the viewpoint of Yu et al. [34], who proposed that “there is an economic threshold for the impact of wellbore size.” Their numerical simulations indicated that after the diameter exceeds 177.8 mm, the increase in production capacity is less than 5%, while drilling costs rise by more than 20%. This suggests that in practical engineering, it is necessary to consider both technical feasibility and economic viability.

Although the borehole size has a relatively low sensitivity to the production capacity of multi-branch horizontal wells, the economic trade-off between production enhancement and drilling cost remains a core consideration in the design and construction. The production capacity mainly increases with the increase in wellbore length or the number of branches, but there is a significant diminishing effect: while the extension of wellbore length can significantly improve the initial production capacity, the additional revenue per meter gradually decreases. Similarly, increasing the number of branches also faces declining marginal benefits. With a fixed wellbore length, the cost increases rigidly with the addition of branches, and drilling costs climb linearly with the length or number of branches. Therefore, the construction of multi-branch horizontal wells should focus on design optimization to avoid blindly increasing the number of branches or wellbore length, cost control through technological iteration to reduce costs and increase efficiency, and dynamic evaluation by establishing a simple dynamic model to calculate marginal cost and marginal revenue in real time.

5.4. Engineering Parameters Economic Feasibility Analysis

The optimization of engineering parameters for multi-branch horizontal wells depends not only on the enhancement of production capacity but also on economic rationality, balancing drilling costs with production benefits. Based on the engineering data from the Zhina Coalfield in 2023, conducting an economic feasibility analysis of engineering parameters is very necessary for industry practitioners.

A cost–benefit analysis of branch angles shows that, based on local engineering data, the drilling cost per branch at a 30° branch angle is 12% higher than that at a 15° angle, mainly due to the increased complexity and torque requirements of high-angle directional drilling; however, over a 1500-day simulation period, the cumulative gas production at a 30° angle is 23% higher than at a 15° angle. At a natural gas price of 1.8 yuan/m³, this can bring an additional revenue of 414,000 yuan. After considering both costs and benefits, the net present value (NPV) of the 30° angle is 1.8 times that of the 15° angle, confirming its economic optimality.

Regarding branch spacing, when reducing the spacing from 150 m to 100 m, the total drilling cost per well increases due to the addition of more branches, but when increasing from 50 m to 100 m, the cost decreases due to the reduction in redundant branches; in terms of production capacity, the cumulative gas production at a spacing of 100 m is 17% higher than at 150 m and only 8% lower than at 50 m. Ultimately, the NPV of the 100 m spacing is 1.5 times that of the 50 m spacing and 1.3 times that of the 150 m spacing, achieving the best balance between cost control and production capacity utilization.

When the size increases from 114.3 mm to 177.8 mm, the cumulative gas production over 1500 days increases by approximately 8.5%. This is mainly because larger wellbores can reduce friction losses in two-phase flow of gas and water, enhance the efficiency of pressure drop transmission, and alleviate the decrease in permeability caused by stress sensitivity. However, in terms of costs, increasing the wellbore size significantly increases drilling costs. The cost per meter for larger wellbores is 18% higher than that for smaller ones, and beyond 177.8 mm, the cost increase exceeds 20% while the production capacity improvement is less than 5%, creating a clear cost–benefit imbalance. Considering the characteristics of thin coal seams in the Zhina Coalfield, a wellbore size of around 158.75 mm is the optimal choice: its cost is controllable, production capacity is improved compared to the smallest size, and it can meet the stability requirements of thin coal seam wellbores. Larger sizes, due to cost increases far exceeding production benefits, are not economically feasible in this study area.

6. Conclusions

(1)

Geological factors significantly influence the productivity of multi-branch horizontal wells for CBM, with coal seam gas content being the most prominent, featuring a sensitivity coefficient as high as 2.5952. The higher the gas content, the more gas is stored in an adsorbed state, providing sufficient desorption driving force to rapidly convert it into a free state and enter the seepage channels. Additionally, it increases the gas pressure in coal matrix pores, enhancing the gas diffusion driving force, allowing more gas to enter cleat fractures, improving gas-phase permeability, and accelerating seepage velocity, thereby causing gas production to grow exponentially. Coal seam thickness is the next most influential factor, with a sensitivity coefficient of 1.0004. Thicker coal seams have larger gas storage capacities, better sealing, and better continuity, which can increase the in-well controlled resource volume. When mining technology and economic conditions permit, the recoverable resource volume also increases, and gas production is directly proportional to thickness. The sensitivity coefficient of coal seam permeability is 0.432: higher permeability enhances the fluidity of coal reservoirs, accelerates the expansion of drawdown funnels, and consequently increases gas production.

(2)

In terms of engineering factors, branch angles and spacing significantly affect productivity, with sensitivity coefficients of 0.2875 and 0.273, respectively. The cumulative gas production increases in the branch angle interval of 15° to 30° and decreases in the interval of 30° to 75°, peaking at 30°. This is because at low angles, the superposition effect of drawdown funnels promotes rapid reservoir pressure decline, but the desorption range is narrow; at high angles, although the pressure relief potential is large, the pressure drop rate attenuates. Only medium angles balance the pressure relief range and drop rate to maximize reservoir stimulation efficiency. The cumulative gas production is higher at a branch spacing of 100 m: too small a spacing causes rapid reservoir pressure drop due to drawdown funnel superposition but limits the desorption range; too large a spacing expands the desorption area but slows pressure drop diffusion. Only an appropriate spacing promotes synergism between branches, achieves effective reservoir pressure reduction, and improves recovery. Borehole size is positively correlated with productivity (sensitivity coefficient 0.162). Larger diameters reduce frictional losses of gas–water two-phase flow in the wellbore, enhance pressure drop transmission efficiency, expand the contact area between the wellbore and coal matrix, reduce stress gradients, and delay permeability decline. However, an economic threshold exists, requiring comprehensive consideration of drilling costs and other factors.

While this study offers an analysis of the factors affecting the productivity of multi-branch horizontal wells in the Zhina Coalfield, there are certain limitations. Our model is primarily based on the geological conditions of the Zhina Coalfield and may not be fully applicable to other regions with significantly different geological structures. Additionally, the simulation period of 1500 days may not fully capture long-term productivity trends. Future research should consider extending the simulation period to better understand the long-term performance of multi-branch horizontal wells and investigate the impact of secondary faults on productivity. Moreover, assessing the applicability of the model under various geological conditions is also important. In summary, this study provides a foundational analysis of the key controlling factors for the productivity of multi-branch horizontal wells, and future study is needed to address these limitations and explore new directions to optimize well placement, wellbore structure, and drilling trajectory design for maximizing the productivity of multi-branch horizontal wells under similar geological conditions.