Dynamic Control Simulation Research on Multibranch Horizontal Well Gas Extraction System

Abstract

This study uses COMSOL and Ventsim software to establish a multibranch horizontal well extraction system model that considers coal body deformation and gas seepage. It investigates the effects of valve opening variations on the negative pressure ratio and system extraction efficiency. The results indicate that when establishing a dynamic control mechanism, the pumping weights of each branch should be considered. When the drilling hole with the highest extraction efficiency is slowly closed, the negative pressure of other drilling holes will significantly decrease in a “double peak” pattern. When the non main extraction source is slowly closed, the increase in negative pressure of the drilling hole is inversely proportional to the extraction capacity; The flow increments of the three sets of dual valve joint control are 1 m³/s, 1.2 m³/s, and 1.8 m³/s, respectively. The highest extraction efficiency is achieved when the valve opening is 45%, 42%, and 55%.

1. Introduction

The technology of coal seam gas predrainage uses the negative pressure generated by a drainage pump to extract high-concentration gas stored in the coal seam to be mined through boreholes and pipelines to the surface. , This technology still faces issues such as low drainage efficiency, high costs, and difficult management. , With the development of drilling technology, the number of borehole branches and total length have continuously increased. − In the oil drainage field, multibranch horizontal wells have long been designed based on the theory that multistage branching is the most efficient material transport structure. In the gas drainage field, a gas drainage system has also been designed based on surface multibranch horizontal wells with in-seam well layout. However, the drainage efficiency of different boreholes varies significantly, and the “pathological” operation phenomenon of mismatched negative pressure and flow rate in the system still exists. , Therefore, studying the dynamic regulation mechanism of the drainage system is of great significance for improving drainage efficiency.

Current theoretical research and applications on dynamic regulation of gas drainage systems are already quite mature. − Theoretical research generally involves establishing a mathematical model of the drainage pipeline network through simulation or emulation, clarifying the pipeline network structure and negative pressure distribution rules, and then achieving flow field calculation in the pipeline network. In fluid simulation within pipelines, the most widely used turbulence model is the Standard k–ε model. Peng et al. used this model to study the influence of valve opening on the flow rectification characteristics behind the valve body. Field applications involve installing gas parameter monitors in drainage pipelines to monitor the variation laws of feedback parameters such as drainage negative pressure, flow velocity, and gas concentration, analyzing the drainage data of each monitoring point, and adjusting through electronically controlled valves. , Most current drainage regulation strategies are based on feedback control: ideal curves are obtained by processing historical drainage data, and then model predictive control algorithms and PLC (programmable logic controller) are used to adjust valve opening to correct drainage parameters, making them infinitely approach the ideal curves and achieve adaptive regulation of the drainage process. , During regulation, the instantaneous values of drainage parameters on both sides of the valve body during valve closure are recorded at a fixed action frequency, and dynamic curves are plotted. , The ideal curves of negative pressure-flow rate changes obtained by changing valve opening provide an intuitive evaluation of the actual effect of the dynamic regulation mechanism.

The gas drainage system for multibranch horizontal wells consists of wellbores, drainage pipelines in roadways, and coal seam drainage boreholes, which can more effectively predrain coal seam gas. Coal seam boreholes are arranged in a multibranch horizontal well configuration, including main drainage holes and branch holes, with main structural parameters including the number of branches, total length, and borehole spacing. Both the structural parameters of multibranch horizontal wells and the drainage time are important causes of unreasonable negative pressure distribution at borehole openings, − and an effective measure to solve this problem is to reallocate the drainage negative pressure of each branch using valves. Deng et al. built a gas drainage negative pressure control system based on fuzzy PID and proved that this method is more stable and accurate than traditional control algorithms; Zan et al. developed a teaching system for gas drainage regulation with valves, using single-chip microcomputers to adjust the valve openings in each area to explore the variation laws of drainage parameters. Du et al. developed a reliability framework diagram based on the operational system schematic of gas extraction pumps and quantitatively calculated the precision of the gas extraction pump system under different operating modes. In gas extraction systems, the extraction vacuum pressure measures the capacity of gas extraction pump stations and determines extraction effectiveness. , Therefore, gas extraction systems must control the start/stop operations of extraction pumps and valves within extraction pipelines, while also monitoring and regulating various relevant parameters within the pipelines.

Although much progress has been made in the research on drainage system regulation, most current regulation strategies for drainage systems focus on individual drainage boreholes, with less research on hierarchical regulation of multibranch boreholes and overall linkage control between coal seam drainage boreholes and roadway drainage pipelines. Multibranch horizontal wells have fewer borehole openings, with high negative pressure, large flow rate, and high gas concentration in the pipes, making the influence of valve regulation on the system non-negligible. This paper investigates the influence of dynamic valve regulation in multibranch horizontal wells on drainage efficiency through compressible flow pipeline network flow field calculation, establishes a dynamic regulation mechanism for the drainage system composed of hierarchical automatic control and overall combined control, and lays a theoretical foundation for intelligent regulation of drainage systems in multibranch horizontal wells.

2. Gas Drainage System of Multi-Branch Horizontal Wells

This paper takes the gas predrainage of multibranch horizontal wells in Shaqu No.1 mine as an example to study the dynamic regulation mechanism of the gas drainage system.

2.1. Gas Drainage System of Multi-Branch Horizontal Wells in Shaqu No.1 mine

To complete the gas predrainage of the 3 + 4# coal seam and 5# coal seam in Shaqu No.1 mine, a multibranch horizontal well gas drainage system shown in Figure is constructed. This system was created using Cinema 4D software to illustrate the spatial relationship between the 3 + 4# coal seam, the 5# coal seam, and the surface well site. Each horizontal main well can connect to multiple branch wells, with the main well terminus linked to the extraction main pipeline via a connecting pipe. Within the entire extraction system, the extraction main pipeline constitutes the primary level, connecting pipelines the secondary level, horizontal main wells the tertiary level, and branch wells the quaternary level. The 3 + 4# coal seam is 305 m deep with an average thickness of 4.1 m, featuring two parallel horizontal main holes with a spacing of 180 m. One of the main holes has two branch holes. The 5# coal seam is approximately 5 m vertically below the 3 + 4# coal seam, with an average thickness of 3.3 m and only one horizontal main hole containing four branch holes. The horizontal distance between the connection points and the main roadway pipeline is 45 m, the angle between branch holes and the main hole is 38°, the spacing between adjacent branches is 300 m, and the inner diameters of both the boreholes and connection pipes are 0.1524 m. The inner diameter of the main drainage pipeline in the horizontal return air roadway and return air shaft is 0.63 m. The horizontal main holes are connected to the underground drainage pipeline, and the wellbore is sealed to ensure gas flows only within the boreholes and pipelines.

1.

Multibranch horizontal wells gas drainage system in Shaqu No.1 mine.

2.2. Modeling and Parameter Setting of the Gas Drainage System in Ventsim

Ventsim, a ventilation simulation system software, enables 3D ventilation design, air network calculation, and dynamic simulation of ventilation processes, simulating the rationality and economy of ventilation methods in a 3D visual environment. The software’s advantages include a true 3D visual interface for simple operation, and intuitive results through color-coding of key data after dynamic airflow simulation. Since negative pressure and gas flow rate are also critical parameters for evaluating pipeline operation in multibranch horizontal wells, this paper uses the compressible fluid network calculation module in Ventsim to study the flow field calculation of the multibranch horizontal well pipeline network in Shaqu No.1 mine, aiming to improve the unreasonable negative pressure distribution in the gas drainage system of multibranch horizontal wells. Multiple horizontal wells consist of a main branch and branch boreholes used for gas drainage. It is important to note that a fully dynamic, two-way coupling between the COMSOL reservoir model and the Ventsim pipeline model is computationally complex due to their distinct time scales. The gas desorption and seepage in the coal seam respond slowly (days to weeks), whereas the gas flow dynamics in the pipeline respond to valve adjustments almost instantaneously (seconds to minutes). Therefore, this study adopts a staged approach. We extract the steady-state flow rate calculated by COMSOL at the 90th day under a 50 kPa negative pressure as the boundary condition for Ventsim. The study assume that during the brief operational time frame of valve adjustments, the secondary reaction effect of negative pressure fluctuations on the actual gas emission rate from the coal matrix is negligible.

Based on a fluid–solid coupling model, COMSOL multiphysics software was used to simulate gas extraction from a coal seam with multiple horizontal wells. The governing equations for the numerical model are as follows.

• 1)Dual-porosity medium gas migration model

During the extraction process, the negative pressure generated by the extraction pump accelerates the gas migration rate. The gas migration rate in the seepage pores and fractures of the coal seam is higher than that in the coal matrix pores, resulting in a lower gas pressure in the seepage pores and fractures of the coal seam compared to that in the coal matrix. The gas in the coal matrix system can be regarded as a uniformly distributed mass source for the seepage pore-fracture system of the coal seam. During the extraction period, driven by the concentration gradient, the desorption of gas molecules in the coal matrix is induced. ,

$$Q_{\mathrm{m}}=-\frac{c{\rho }_{\mathrm{c}\mathrm{h}4}{\epsilon }_{\mathrm{L}}{p}_{\mathrm{L}}}{{(p_{\mathrm{L}}+p)}^2}\mathrm{d}t$$ 1

in the formula, Q _m represents the gas desorption rate, with the unit of kg/(m³·s); c represents the apparent density of coal, with the unit of kg/m³;ε_L represents the Langmuir volume constant, with the unit of m³/kg; p _L represents the Langmuir pressure constant, with the unit of Pa; p represents the gas pressure, with the unit of Pa; and t represents the extraction time, with the unit of s.

The migration of free gas in the pores of coal matrix is a diffusion process along the direction of concentration difference, and its migration to seepage pores conforms to Fick’s Diffusion Law −

$$q_{\mathrm{f}}=-D_{\mathrm{f}}\frac{\partial C}{\partial l}$$ 2

in the formula, q _f represents the diffusion flux, with the unit of g/s; D _f represents the diffusion coefficient, with the unit of m²/s; ∂C/∂l represents the concentration gradient, with the unit of g/m².

Under normal circumstances, the migration of gas in the seepage fracture system occurs in the form of linear seepage, and the seepage process conforms to Darcy’s Law

$$v=-\frac{K}{\mu }\mathrm{\nabla }{P}_{\mathrm{f}}$$ 3

in the formula, K represents the coal permeability, with the unit of mD; μ represents the dynamic viscosity coefficient of gas, 1.84 × 10^–5 Pa·s; P _f represents the fracture gas pressure, with the unit of Pa.

• 2)Control equation of coal seam deformation

In the direction perpendicular to the coal seam, the coal seam is subjected to vertical stress from the overlying strata. Additionally, since the pore-fracture space of the coal seam contains high-pressure gas, stress transfer also occurs: the gas pressure in the coal seam exerts a certain load on the inner surface of the coal seam’s pores and fractures, which can cause the coal matrix to shrink. On the other hand, the adsorption of gas molecules by the inner surface of coal pores can induce the expansion of the coal matrix.

In the coal mass, the diffusion process of adsorbed gas conforms to Fick’s Law, and the seepage law of gas in the coal seam conforms to Darcy’s Law. In deep, soft coal seams with low permeability, the deformation and failure characteristics of the coal mass around gas drainage boreholes affect the predrainage effect of coal seam gas. For simulations of multibranch horizontal wells, casing is used to support the boreholes, which achieves a certain degree of control over borehole deformation: both the maximum vertical displacement and maximum horizontal displacement are significantly reduced, and the distance from the location of the maximum vertical stress to the borehole, as well as the stress concentration factor, are also decreased.

In this regard, based on the condition of an inhomogeneous stress field, a mechanical model of the coal mass disturbed by boreholes was established. Furthermore, based on geometric equations, force equilibrium equations, and constitutive equations, and considering adsorption–desorption characteristics and adsorption-induced deformation, the control equations for coal seam deformation can be summarized as shown in eq . −

$$\{\begin{array}{l}G{u}_{i,jj}+\frac{G}{1-2\upsilon }{u}_{j,ji}-[\beta +\frac{K{\epsilon }_{\mathrm{L}}{p}_{\mathrm{L}}}{{(p_{\mathrm{L}}+p)}^2}]p_i+f_i=0\\ G=\frac{E}{2(1+\upsilon )}\\ K=\frac{E}{3(1-2\upsilon )}\\ \alpha =1-\frac{K_{\mathrm{C}}}{K_{\mathrm{S}}}\\ K_{\mathrm{S}}=\frac{2K_{\mathrm{m}}(1-2\upsilon )}{2(1-2\upsilon )-3{\varphi }_0(1-\upsilon )}\\ F_{vx}=-[\alpha +\frac{ad·K_{\mathrm{C}}·p_{\mathrm{L}}}{{(p_{\mathrm{L}}+p)}^2}]p\mathrm{d}x\\ F_{vy}=-[\alpha +\frac{ad·K_{\mathrm{C}}·p_{\mathrm{L}}}{{(p_{\mathrm{L}}+p)}^2}]p\mathrm{d}y\end{array}$$ 4

in the formula, G represents the shear modulus, with the unit of Pa; K represents the bulk modulus, with the unit of Pa; β represents the Biot coefficient; ν represents the Poisson’s ratio; u represents the displacement, with the unit of m; E represents the elastic modulus, with the unit of Pa; α represents the effective stress coefficient of coal seam fractures; K _C represents the bulk modulus of coal, with the unit of Pa; K _S represents the bulk modulus of the coal mass skeleton, with the unit of Pa; K _m represents the bulk modulus of the coal matrix, with the unit of Pa; ϕ₀ represents the initial fracture porosity of the coal seam; F _vx and F _vy represent the body loads on the coal mass in the x and y directions, respectively, with the unit of N/m³; ad represents the adsorption deformation coefficient of coal; The remaining parameters are the same as above.

• 3)Permeability variation equation

The permeability and fracture porosity of coal seams are key factors affecting the fluid migration rate in coal seams, and they are crucial for the prediction of bionic gas drainage and the evaluation of drainage effectiveness. Permeability is highly sensitive to changes in the stress state and fracture porosity of coal seams.

The volumetric strain of the coal matrix can be considered as the combined effect of four components: the strain caused by coal seam pore pressure, the strain induced by gas adsorption–desorption, the thermal expansion strain, and the strain caused by in situ stress.

Considering elastic strain and adsorption–desorption, and based on the cubic law, the equation for fracture porosity variation and the expressions for coal seam permeability in the strike and dip directions are shown in eq . ,

$$\{\begin{array}{l}\varphi ={\varphi }_0+\frac{p-p_0}{M}+(\frac{K_{\mathrm{C}}}{M}-1)(\frac{ad·p}{p_{\mathrm{L}}+p}-\frac{ad·p_0}{p_{\mathrm{L}}+p_0})\\ M=\frac{E(1-\upsilon )}{(1+\upsilon )(1-2\upsilon )}\\ k_x=k_{x0}{\left(\frac{\varphi }{{\varphi }_0}\right)}^3\\ k_y=k_{y0}{\left(\frac{\varphi }{{\varphi }_0}\right)}^3\end{array}$$ 5

in the formula, p ₀ represents the initial gas pressure of the coal seam, with the unit of Pa; M represents the axial constraint modulus, with the unit of Pa; the remaining parameters are the same as above.

Using COMSOL based on a fluid–solid coupling model, the gas drainage effects of No.5, No.41, and No.42 multibranch horizontal wells were simulated under an orifice negative pressure of 50 kPa. The gas extraction model for the 3 + 4# and 5# coal seams was constructed using COMSOL software. The entire model was divided into 158,682 elements via a triangular mesh, with a maximum element size of 30 m and a minimum element size of 0.1524 m. The maximum element growth curvature was 1.8, and the curvature factor was 0.7. The friction resistance coefficients of boreholes in Ventsim are adjusted according to the gas flow rate ratio at the connection points to simulate drainage resistance. To bridge the gap between microscopic seepage in the coal seam and macroscopic flow in the pipeline network, an equivalent resistance model was adopted. The friction resistance coefficients of boreholes in Ventsim were not merely geometric parameters; they integrated the nonlinear seepage resistance derived from the fluid–solid coupling simulation in COMSOL. Based on the fluid–solid coupling eqs –, the variation curves of gas flow rate with depth and time during the extraction process of the 3 + 4# coal seam and 5# coal seam multibranch horizontal wells were simulated (Figure ). As shown in Figure a,b, at Day 90 of drainage, the gas flow rates at the orifices of boreholes No.5, No.41, and No.42 are 1.8, 1.4, and 0.6 m/s, respectively, with a drainage efficiency ratio of 9:7:3. The friction resistance coefficients of the three boreholes in the Ventsim drainage pipeline model are adjusted to match this ratio with the simulated orifice gas flow rates. Although the gas flow rate ratio should be recalculated in the late drainage stage, the valve adjustment time is very short, and this paper focuses on the influence of dynamic valve adjustment on drainage efficiency during the high-efficiency drainage period. Therefore, changes in friction resistance coefficients are not considered.

2.

Gas flow rate variation curve with depth and time. (a)­5 # main hole; (b)­41 # & 42 # main hole.

Figure shows the gas extraction pipeline network structure of Shaqu No. 1 mine, created using Ventsim software. By dynamically controlling the gas flow rate, velocity, and pressure in the main extraction pipeline and connecting pipes within the coal seam, the gas extraction parameters can be dynamically adjusted. The surface pump station is modeled as a pipeline section for easy adjustment of the negative pressure at the drainage outlet, and this section does not participate in the calculation. Boreholes are simplified as a single pipeline. As shown in the figure, the pipeline network structure has a total of 4 boundary points (yellow icons): the drainage outlet, the bottom of No.41 borehole, the bottom of No.5 borehole, and the bottom of No.42 borehole, all set to communicate with the surface. Among them, the surface pump station is set as a negative pressure outlet (red icon) to ensure the negative pressure at the drainage outlet is the predetermined −50 kPa, while the other 3 borehole bottoms are set as gas inlets (green icons) with a composition and proportion of 80% CH₄, 5% H₂O, 3% O₂, and 12% N₂. It is worth noting that in the drainage pipeline network model constructed by Ventsim for development roadways, gas enters from the bottom of the borehole. In contrast, the gas inflow direction within the multibranch horizontal wells deployed in the coal seam is toward the screen holes in the main branch or branches.

3.

Drainage pipeline network structure of Shaqu No.1 mine in Ventsim.

There are 7 nodes (gray icons) in total: the orifice of No.41 borehole, the orifice of No.5 borehole, the orifice of No.42 borehole, the No.41 branch, the No.5 branch, the No.42 branch, and the inflection point of the main underground pipeline, with a local resistance set to 0.0005. On the premise of constant fluid properties, a smaller pipe diameter leads to higher flow velocity, greater viscous resistance, and more energy loss. During simulation, different degrees of energy loss are simulated by setting different friction resistance coefficients: the main drainage pipes in the roadway and vertical shaft are set to 0.0013, and the 3 butt pipes are set to 0.0029. After successful calculation, information such as gas volume flow rate, flow velocity, mass flow rate, and pressure of each pipeline and node can be intuitively viewed.

2.3. Hierarchical Automatic Control and Overall Joint Regulation Mechanism

Hierarchical automatic control of the gas drainage system refers to small-diameter electric control valves installed in the orifice pipelines automatically adjust based on the changing trends of gas concentration and pure flow rate in their respective branches, following system-set algorithms to continuously meet the safety and economic requirements of the branch drainage, without considering impacts on other branches or the overall system. If the control results meet expectations, no manual intervention is needed; if the requirements are not met after a certain period, overall joint regulation intervention is required.

Overall joint regulation of the gas drainage system involves: optimizing through particle swarm algorithm based on real-time feedback of drainage parameters from all system nodes, including gas concentration/pure flow rate, drainage gas pressure/temperature/flow rate/density, etc. Regulation schemes for all branches that meet drainage safety or economic requirements are uploaded to a cloud platform for operators to select or intervene manually. In case of conflicts between overall joint regulation and hierarchical automatic control results, overall joint regulation takes precedence. The regulation schematic of overall joint control is shown in Figure .

4.

Schematic diagram of gas extraction system overall joint regulation in Shaqu No.1 mine.

The overall coordinated regulation aims to find the optimal combination of valve openings to maximize the system’s extraction efficiency. This can be formulated as a mathematical optimization problem. The decision variables are the valve openings of each branch, defined as the vector V = [v ₁, v ₂, ..., v _n ], where n is the number of branch valves. The primary objective is to maximize the total pure gas flow rate of the extraction system, which can be expressed as

$$\max f(V)=\sum _{i=1}^n{Q}_i(V)\times C_i(V)$$ 6

where Q _i (V) is the mixed gas mixture flow rate of branch i; and C _i (V) is the gas concentration of branch i. Both are dynamic functions of the global valve opening vector V.

Constraints, Valve opening limit: 0 ≤ v _i ≤ 100%; negative pressure safety limits: P _min ≤ P _i ≤ P _max, where P _i (V) is the negative pressure at the orifice of branch i, P _min is the minimum negative pressure required to ensure gas discharge (to prevent gas accumulation), and P _max is the upper limit provided by the surface pumping station. Although advanced heuristic algorithms (such as reverse calibration swarm optimization) can solve this system of nonlinear equations in practical deployed systems, this study mapped the solution space of the objective function through systematic steady-state parameter sweeps to reveal the fundamental patterns of valve regulation.

3. Influence Law of Automatic Control on Orifice Negative Pressure

3.1. Influence of Valve 42 Regulation on Orifice Negative Pressure

As shown in Figure , the valve opening range can be divided into an ineffective section, slow section, and rapid section according to the change rate of the orifice negative pressure in the branch where the valve is located: Ineffective section (100%–70% opening): The negative pressure reduction rate at the 42# orifice is very small, decreasing only by 555 Pa (approximately 1.43% of the initial value). Slow section (70%–20% opening): The negative pressure reduction rate accelerates, with a total decrease of 21,752 Pa (56.23% of the initial value). This section can be further subdivided: 70%–50% opening: The average reduction rate is 266.55 Pa per 1% opening decrease. 50%–20% opening: The average reduction rate increases to 547.37 Pa per 1% opening decrease. Rapid section (20%–0% opening): the negative pressure reduction rate is the highest, particularly in the 20%–8% opening range, where a 14,801 Pa decrease occurs (1233.42 Pa per 1% opening decrease). The reduction slows down in the 8%–0% range. For the other two branches, the trends are nearly identical: In the ineffective section, the negative pressure increase rate is minimal. In the slow section, the increase rate accelerates, with a higher rate in the 50%–20% range than in the 70%–50% range. In the rapid section, the highest increase rate occurs at 20%–8% opening, slowing down at 8%–0% opening. The negative pressures at the 5# and 41# borehole orifices increased by 667 and 1018 Pa, respectively.

5.

Influence of valve 42 opening changing on negative pressure of 3 groups of boreholes.

The conclusion shows that for the 42# borehole (the second-highest producer among the three groups and located at the end of the main pipeline), gradually reducing the valve opening in its branch leads to a continuous increase in the negative pressure at the other two borehole orifices, with the overall growth rate accelerating.

3.2. Influence of Valve 5 Regulation on Orifice Negative Pressure

As shown in Figure , when regulating the valve 5, the variation pattern of the orifice negative pressure in its branch is completely consistent with the analysis in Section : Ineffective section: the negative pressure reduction rate at the 5# orifice is minimal, decreasing by only 773 Pa (approximately 2.44% of the initial value). Slow section: the total negative pressure reduction is 22,040 Pa (69.64% of the initial value), with two subsections: 70%–50% opening: average reduction of 337.95 Pa per 1% opening decrease. 50%–20% opening: average reduction increases to 509.37 Pa per 1% opening decrease. Rapid section (20%–8% opening): a total reduction of 8174 Pa occurs, with an average of 681.16 Pa per 1% opening decrease; the reduction slows in the 8%–0% range. For the other two branches, while the trend is nearly identical, the specific patterns differ from Section : in the ineffective section, the negative pressure increase rate is minimal. In the 70%–40% opening range, the increase rate accelerates significant reduction occurs in the 35%–16% opening range (for 42# borehole) and 30%–16% range (for 41# borehole). The negative pressure increases slightly at 16%–4% opening, then decreases rapidly at 4%–0% opening. The negative pressures at the 42# and 41# borehole orifices decreased by 3343 and 3685 Pa, respectively.

6.

Influence of valve 5 opening changing on negative pressure of 3 groups of boreholes.

Conclusion: for the 5# borehole (highest gas production among the three groups, located between the other two branches), gradually reducing the valve opening in its branch causes the negative pressure at the other two boreholes first increases slowly in a “double-peak” pattern and then decreases rapidly, with an overall significant reduction. The reason is that 5# borehole accounts for about 50% of the system’s total gas production. Reducing its gas supply significantly impacts pipeline negative pressurethe sharp decrease in flow leads to reduced negative pressure. Recommendation: when forced to reduce the valve 5 opening, maintain it above 35% (if possible) to slightly increase the negative pressure at the other two boreholes.

3.3. Influence of Valve 41 Regulation on Orifice Negative Pressure

As shown in Figure , the variation pattern of the orifice negative pressure in the branch 41 is consistent with Sections and 2.2, with minor differences: ineffective section (100%–70% opening): The negative pressure reduction rate at the 41# orifice is extremely small, decreasing by only 140 Pa (approximately 0.3% of the initial value). Slow section (70%–20% opening): the total reduction is 10,298 Pa (22.35% of the initial value), with two subsections: 70%–50% opening: average reduction of 77.6 Pa per 1% opening decrease. 50%–20% opening: average reduction increases to 291.53 Pa per 1% opening decrease. Rapid section (20%–0% opening): the negative pressure reduction rate is the highest, with a total decrease of 35610.2 Pa (1780.51 Pa per 1% opening decrease in the 20%–2% range); the reduction slows in the 2%–0% range.

7.

Influence of valve 41 opening changing on negative pressure of 3 groups of boreholes.

For the other two branches, the trend aligns with Section , but with differences in specific growth rates: ineffective section (100%–70% opening): minimal negative pressure increase. Slow section (70%–20% opening): accelerated increase rate. Rapid section (20%–0% opening): sharpest increase rate. The negative pressures at the 42# and 5# borehole orifices increased by 377 and 302 Pa, respectively.

Conclusion: for the 41# borehole (lowest gas production, closest to the extraction port), gradually reducing the valve opening in its branch causes the negative pressure at the other two boreholes to first remain nearly unchanged, then increase slowly, and finally increase rapidly, with an overall upward trend.

4. Results and Discussion

4.1. Influence Law of Dual-Branch Joint Regulation on Negative Pressure Ratio and Extraction Efficiency

4.1.1. Influence of Valves 42 and 5 Joint Regulation on Negative Pressure and Efficiency

During the simulation in this section, the extraction negative pressure of the surface pump remains 50 kPa. Based on previous conclusions, the 100%–70% opening range is ineffective for valve regulation, so only the 70%–0% range is meaningful. The valve 42 is reduced from 70% to 0%, while the valve 5 is increased from 0% to 70%. The adjustment frequency is 5% per step in the slow zone and 2% per step in the fast zone, with the valve 41 kept fully open throughout. The regulation speed is tailored to sensitivity to protect equipment while accelerating adjustments. Figure a shows the variation in negative pressure at the three borehole orifices during joint regulation of the valve 42 and valve 5, with the horizontal axis representing the valve 5 opening (the valve 42 opening decreases synchronously).

8.

Influence of valves 5 opening changing on extraction parameters of boreholes. (a) Extraction pressure; (b) flow rate.

Key observations: the negative pressure at the 42# orifice decreases gradually, with a slowing reduction rate. The negative pressure at the 5# orifice increases gradually. The negative pressure at the 41# orifice first increases rapidly within the 10%–20% opening range of the valve 5, then stabilizes. Conclusion: when integrating a high-production branch into the extraction system, the fast zone of valve regulation has the most significant impact on other branches. This highlights the critical role of dynamic coordination between high-production branches in optimizing negative pressure distribution and extraction efficiency.

The influence of the regulation that the opening degree of valve 42 decreases and the opening degree of valve 5 increases on the gas flow rate in the main extraction pipeline in the roadway is shown in Figure b. During the regulation period, the gas flow is difficult to be stable. Therefore, the method of fitting the scatter plot with a curve is adopted to analyze the variation law of the gas flow rate. It can be seen from the figure that during the period when the opening degree of valve 5 increases (while the opening degree of valve 42 decreases synchronously), the gas flow rate in the main pipeline first increases and then decreases, and the maximum value appears when the opening degree of valve 5 is 45% (and the opening degree of valve 42 is 10%), that is, the extraction efficiency of the system is the highest at this time.

4.1.2. Influence of Valves 42 and 41 Joint Regulation on Negative Pressure and Efficiency

During the simulation in this section, the extraction negative pressure and the action frequency are consistent with those in the previous subsection. Valve 41 is adjusted from 70% to 0, while valve 42 is adjusted from 0 to 70%. Valve 5 remains fully open throughout the process. Figure a shows the changes in the negative pressure at the three borehole openings when valves 42 and 41 are jointly regulated. The abscissa represents the opening degree of valve 42 (the opening degree of valve 41 decreases synchronously).

9.

Influence of valves 42 opening changing on extraction parameters of boreholes. (a) Extraction pressure; (b) flow rate.

As can be seen from the figure, due to the gradual increase in valve opening, the negative pressure at the opening of borehole 42 continuously increases. The growth rate is the highest in the rapidchange range of 0–20%, medium in the range of 20%–50%, and slower in the range of 50%–70%. It first increases rapidly within a specific range and then remains stable. The range of rapid increase is from 10% to 20%.

The negative pressure at the opening of borehole 5 fluctuates significantly at the beginning and shortly before the end of the regulation period, and remains almost constant at other times. Overall, the negative pressure hardly changes. Affected by the closing of the valve, the negative pressure at the opening of borehole 41 gradually decreases. Except for the rapid decrease in the range of 45%–50%, the decreasing rate is approximately constant.

Therefore, the mutual distribution of the negative pressure between borehole 41 and borehole 42 has little influence on borehole 5, which has the highest output.

The influence of the regulation where the opening of valve 41 decreases and the opening of valve 42 increases on the gas flow in the main extraction pipeline in the main roadway is shown in Figure b. Similarly, the method of curvefitting the scatter plot is used to analyze the variation law of the gas flow.

As can be seen from the figure, during the period when the opening of valve 42 increases (while the opening of valve 41 decreases synchronously), the variation law of the gas flow in the main pipeline is consistent with that in Figure . It first increases and then decreases. The maximum value appears when the opening of valve 42 is 42% (and the opening of valve 41 is 11%), indicating that the extraction efficiency of the system is the highest at this time.

4.1.3. Influence of Valves 5 and 41 Joint Regulation on Negative Pressure and Efficiency

Valve 41 is adjusted from 70% to 0, while valve 5 is adjusted from 0 to 70%. Valve 42 remains fully open throughout the process. Figure a shows the changes in the negative pressure at the three borehole openings when valve 5 and valve 41 are jointly regulated. The abscissa represents the valve 5 opening (valve 41 opening decreases synchronously).

10.

Influence of valves 5 opening changing on extraction parameters of boreholes. (a) Extraction pressure; (b) flow rate.

As can be seen from the figure, although the valve at the opening of borehole 42 remains fully open, at the initial stage of regulation, the negative pressure at the borehole opening is affected by the other two branches. When the opening degree of valve 5 is between 0 and 15%, the negative pressure at the opening of borehole 42 gradually decreases, and the decreasing rate gradually slows down. When valve 5 opening is between 15% and 40%, the negative pressure gradually increases, and the increasing rate gradually slows down. After valve 5 opening reaches 40%, the negative pressure hardly changes.

The change in the negative pressure at the opening of borehole 5 is completely consistent with the form and rate of the negativepressure increase of the branch with an increasing valve opening in the previous two subsections: the growth rate is the fastest in the rapidchange range of 0–20%, medium in the range of 20%–50%, and slower in the range of 50%–70%. The growth rate gradually increases in the first two intervals. Affected by the closing of the valve, the negative pressure at the opening of borehole 41 gradually decreases. Except for the rapid decrease in the range of 45%–50%, the decreasing rate is approximately constant.

It can be seen that the negative pressure at the opening of borehole 42 increases by a total of 4257 Pa before and after the regulation, indicating that when a branch with strong extraction capacity replaces a branch with weak extraction capacity, the negative pressure of other branches in the system will increase slightly.

The influence of the joint regulation where valve 41 opening decreases and valve 5 opening increases on the gas flow in the main extraction pipeline in the main roadway is shown in Figure b. As can be seen from the figure, during the period when valve 5 opening increases (while valve 41 opening decreases synchronously), the variation law of the gas flow in the main pipeline also shows an initial increase followed by a decrease. However, the maximum value appears when valve 5 opening is 55% (and valve 41 opening is 6%), indicating that the extraction efficiency of the system is the highest at this time. The time when the maximum value appears is slightly later than that in Figure b, which is related to the different extraction efficiencies of different leaf veinlike boreholes under the same negative pressure at the borehole opening.

4.2. Influence Law of Tri-Branch Joint Regulation on Negative Pressure Ratio and Extraction Efficiency

4.2.1. Integrated Control of Gas Extraction between Different Coal Seams

During the simulation in this section, the negative pressure of the ground pumping pump is still 50 kPa. The valves 41 and 42 of the 3 + 4# coal seam were reduced from 70% to 0, while the valve 5 of the 5# coal seam is increased from 0% to 70%. The operating frequency of the three valves is 5%/time in the slow zone and 2%/time in the fast zone. Figure a shows the changes in negative pressure at the three drilling holes during the overall control of the three branches, with the horizontal axis set as the opening of valve 5 (the opening of the other two branches decreases synchronously). As shown in the figure, in the two branches of the 3 + 4 # coal seam, the 41 # orifice is closest to the ground extraction pump, while the 42 # branch is farthest. Therefore, during the valve closing process, the negative pressure change of the 41 # orifice lags behind that of the 42 # borehole, but the change pattern of the two is basically the same: at the beginning of the regulation, the negative pressure slightly increases but the amplitude is small, and the negative pressure of the latter two decreases gradually at a slower rate, with 45%–50% of the negative pressure rapidly decreasing, consistent with the previous section. The increase pattern of negative pressure in borehole 5 # is consistent with that of dual valve regulation, and the increase process is also divided into three intervals: 0–20%, 20%–50%, and 50%–70%.

11.

Impact of simultaneous changes in valve opening on extraction parameters. (a) Extraction pressure; (b) flow rate.

The impact of the joint regulation of three branches in two coal seams on the gas flow inside the main drainage pipe in the roadway is shown in Figure b. After fitting the flow scatter plot with a polynomial curve, it can be seen from the graph that during the period when the opening of valve 5 increases (while the opening of valves 41 and 42 decreases synchronously), the gas flow rate in the main pipe also shows a trend of first increasing and then decreasing. The maximum value in the scatter plot occurs at valve 5 opening of 20% (valves 41 and 42 opening of 20%) and valve 5 opening of 45% (valves 41 and 42 opening of 10%), with a maximum flow rate of 2.8 m³/s. The maximum value of the fitted curve appears at valve 5 opening of 30% (valves 41 and 42 opening of 16%), which theoretically indicates that the system’s pumping efficiency is highest at this time.

4.2.2. Integrated Control of Gas Extraction in Drilling Groups with Different Efficiencies

The negative pressure for extraction is still set to 50 kPa. The valves 42 and 5 of the high extraction efficiency branch are increased from 0% to 70%, while the valve 41 of the low extraction efficiency branch is decreased from 70% to 0. The frequency of valve action is consistent with the previous text. Figure a shows the changes in negative pressure at the three drilling holes during the overall control of the three branches. The horizontal axis is set as the opening of valve 5 (the opening of valve 42 changes uniformly, while the opening of valve 41 decreases synchronously). As shown in the figure, the pressure rise curves of borehole 42 and borehole 5 with increased negative pressure are almost identical in form; Although the 5 # connecting pipe is closer to the ground pump station and has a negative pressure of 5 # > 42 # at the main branch, the gas flow rate of the 5 # connecting pipe is much higher than that of the 42 # connecting pipe, and the pressure loss inside the 5 # connecting pipe is much greater than that of the 42 # connecting pipe. Therefore, the negative pressure of the 5 # pumping at the orifice is lower than that of the 42 # connecting pipe. Due to the gradual closure of the valve, the negative pressure at the 41 # orifice showed an overall downward trend, with only slight upward fluctuations within the range of 0–20%. The reason for this phenomenon is that at this time, it is in a rapid zone of negative pressure changes in two high extraction rate boreholes, and the pressure inside the main pipe is extremely unstable; The negative pressure at the 41 # orifice also rapidly decreases within the range of 45%–50%, as it begins to enter the fast zone of the valve 41.

12.

Impact of simultaneous changes in valve opening on negative pressure at 3 boreholes. (a) Extraction pressure; (b) flow rate.

The impact of joint regulation of two coal seams and three branches with different extraction efficiencies on the gas flow inside the main extraction pipe in the roadway is shown in Figure b. During the period when the opening of valve 5 increases (with valve 42 having the same opening and valve 41 decreasing synchronously), the gas flow rate in the main pipe shows a trend of first increasing and then decreasing. The maximum value of the fitted curve occurs when the opening of valve 5 and valve 42 is 55% (valve 41 has an opening of 6%), theoretically indicating the highest pumping efficiency of the system.

The simulations conducted in this study are essentially steady-state parameter scans aimed at identifying the optimal valve opening configurations for varying extraction efficiencies. They do not reflect the transient dynamic response characteristics of a closed-loop control system (such as PID overshoot or settling time). Furthermore, the current model employs a decoupled approach between reservoir emission and pipeline transport. Future research will focus on establishing a mathematical transfer function between orifice negative pressure and coal seam gas emission to achieve real-time, bidirectional coupling, and simulating the transient dynamics of PLC-based PID control within the network.

5. Conclusions

• (1)The hierarchical self-control mechanism adjusts the valve opening of a single branch based on changes in its pumping parameters to maximize the pumping efficiency of the branch, while the overall linkage control considers the current pumping weight of each branch to maximize the overall efficiency of the system. This mechanism innovatively takes the state where the flow rate reaches the extreme value of the valve opening variation curve as the final result of regulation.
• (2)Under the graded self-control mechanism, the sensitivity range of the pressure at the borehole opening to changes in valve opening is invalid (100%–70%), slow (70%–20%), and fast (20%–0); When the main extraction source (5 #) is closed, the negative pressure of other branches’ extraction will decrease in a “double peak” pattern; after closing a branch, the more branches there are and the higher the extraction efficiency, the smaller the increase in negative pressure during drilling and extraction. These laws clarify the physical nature of pressure redistribution in complex extraction systems.
• (3)The boost curve is divided into three intervals: 0–20%, 20%–50%, and 50%–70%. The boost is fastest in 0–20%, and the decompression curve is fastest in 45%–50%. The impact of dual branch integrated control on the gas flow rate of the main pipeline is in a parabolic form, with the gas flow rate increasing first and then decreasing, and the system extraction efficiency is highest at 45%, 42%, and 55%, respectively; The system has the highest extraction efficiency when the flow rate is 30% and 55% respectively during the overall regulation of the three branches.

Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.

The authors declare no competing financial interest.