## 1. Introduction

Coalbed methane (CBM) is a clean and efficient energy source. The efficient development of CBM could not only increase the clean energy supply but also improve the safety of coal mine production and reduce greenhouse gas emissions. In China, the CBM reserves above 2000 m are estimated at 36.81 trillion m

^{3}, which is equivalent to the amount of reserved conventional natural gas, ranking in third place globally after Russia and Canada [

1]. However, CBM reserves are characterized by their low saturation, low permeability, low reservoir pressure, and relatively high metamorphic grade. In most mining areas, the coal seam permeability is 10

^{−4}–10

^{−3} mD, which is 3–4 orders of magnitude lower than that in the United States and Australia [

2,

3,

4]. Moreover, 44% of coal mines in China are high gas and outburst mines and prone to coal and gas outburst accidents during coal extraction [

5]. Therefore, to effectively extract coalbed methane and ensure mining safety, effective measures must be taken to improve the coal seam permeability and control the risk of gas disasters.

In coal seams, high-pressure water jet slotting is an effective method of improving the coal seam permeability [

6,

7,

8,

9]. As shown in

Figure 1, this technology can form a disc slot in the coal seam by using a high-pressure water jet, which effectively increases the area of exposed coal. Additionally, the pressure in the coal seam surrounding the slot is fully relieved, which results in the deformation of coal and the formation of cracks. This increases the gas flow channels and improves the flow conditions, which in turn accelerate the gas desorption and discharge, to result in permeability improvement [

10,

11]. Therefore, it can be seen that the slotting depth directly affects the pressure relief range and determines the gas drainage effect. Many studies have investigated water jet slotting. However, most existing studies have focused on improving the permeability mechanism [

12,

13,

14] and rock-breaking capability of the water jet [

15], optimizing and improving the slotting system [

16,

17], and so on. A few studies have investigated the effects of hydraulic parameters and operational parameters on the slotting depth, but there is no applicable theoretical model for determining the slotting depth in water jet slotting applications. This leads to the operational parameters and borehole layout being unknown when applying high-pressure water jet slotting technology.

This study investigated the effects of hydraulic parameters (nozzle diameter and jet pressure) and operational parameters (rotation speed and slotting time) on the slotting depth. Based on the rock-cutting model of a water jet, a model for calculating the water jet slotting depth was established. Water jet slotting experiments were conducted under different operational conditions to verify the calculation model. Additionally, water jet slotting field tests were conducted, and the slotting depths were investigated. The results of this study can be useful as guidelines for selecting the hydraulic parameters of water jet slotting and optimizing the layout of coal gas drainage boreholes in coal seams.

## 4. Model for Calculating Water Jet Slotting Depth

By comprehensively considering the influence of the jet pressure, translation speed, and cutting times on the total cutting depth, the cutting depth can be expressed as follows:

where

h is the total cutting depth and

k is the proportionality coefficient.

By combining Equations (9) and (10), the model for calculating the slotting depth caused by a high-pressure water jet in a coal seam is expressed as follows:

As expressed in Equation (14), the rotation speed has a significant effect on the slotting depth under fixed slotting time. As the rotation speed increases, the slotting depth becomes smaller each time but increases with the slotting repetition. Therefore, there exists an optimal rotation speed for the water jet slotting. This study conducted rotary slotting experiments to determine the relevant parameters in Equation (14) and obtain the optimal rotation speed. As shown in

Figure 9, the experimental system mainly was comprised of a high-pressure pump, hydraulic drilling rig, and the sample. The drilling rig, with a rated torque of 1250 N∙m, was used to control the rotation speed in the water jet slotting. The slotting sample was shaped coal with a ratio of coal particle:cement:water = 1:0.5:1, size of 1 × 1 × 1 m, f coefficient of 0.21, and tensile strength of approximately 0.08 MPa.

The experimental procedures are as follows: first, the nozzle diameter and initial standoff distance were set to 3 and 12.5 mm, and the jet pressure was controlled at 10 MPa. Then, the rotation speeds were set to 30, 40, 50, and 60 r/min, respectively. Additionally, the shaped coal sample rotary slotted by a high-pressure water jet and the slotting time was 0.5 min every time. Subsequently, the slotting depth was measured and a slot sample was taken again under the same slotting conditions until the slotting depth did not change. Finally, the rotation speed was changed and the abovementioned process was repeated.

The results are presented in

Figure 10. At the same rotation speed, the slotting depth increased with the slotting time, but the growth rate gradually decreased, then tended to be stable, and finally reached a certain limit value. As the rotation speed increased, the slotting depth became greater at the initial period and the limit depth was reached faster. Hence, the slotting depth was the combined result of rotation speed and slotting frequency. Although the relative moving speed was higher at a higher rotation speed, the slotting frequency per time increased, which resulted in deeper slotting depth at the initial period. Moreover, in the process of rotary slotting by the high-pressure water jet, the action mode of the water jet on the coal body changed. Similar to the oscillation effect of the pulsed water jet, the coal body is influenced by the water hammer pressure with periodic frequency, and thus the rock-breaking efficiency improves. In contrast, at lower rotation speed, the impact time of the single slotting coal becomes longer, and the hindrance of the water cushion becomes more severe. Therefore, in the early stages of slotting, the influence of slotting repetitions on the slotting depth is greater than that of a single impact. Increasing the rotation speed contributes to the improvement of the slotting efficiency and slotting depth. However, as the rotation speed increases, the limit slotting depth first increases and then decreases. This indicates that the influence of a single impact on the slotting depth is greater than that of numerous slotting repetitions at the later stages of jet slotting. This is attributed to the fact that the coal body is mainly destroyed by the quasi-static pressure of the water jet.

To verify the proposed slotting depth model, the experimental data were fitted based on Equation (14). The special fitting parameters were given in Equation (15). The fitting degree reached 86%, which indicates that the model established for calculating the slotting depth can be used to describe the relationship between the parameters and the slotting depth. Based on the fitting parameters, the effects of the jet pressure, rotation speed, and slotting time on the slotting depth can be obtained.

Figure 11 shows the fitting curves between the slotting depths and slotting time under the different rotation speeds at the jet pressure of 10 MPa. Thus, to improve the jet slotting depth, the rotation speed should be adopted according to the slotting time. Specifically, when the slotting times are 0–5, 5–10, and 10–15 min, the optimized rotation speeds should be 60, 50, and 40 r/min, respectively. Moreover, as shown in Equation (15), the jet pressure and the threshold rock-breaking pressure of the coal are proportional to the slotting depth. In other words, the jet pressure and threshold pressure only affect the slotting depth magnitude, and have no effect on its changing trend. Therefore, when the jet pressure changes, the relationships between the slotting depth and the rotation speed and slotting time do not change.

According to the abovementioned analysis, the slotting depths under different jet pressures and threshold rock-breaking pressures can be obtained. The tensile strength of coal is typically 0.28–2.25 MPa [

32].

Figure 12 shows the predicted slotting depths under the jet pressure of 25 MPa with a tensile strength of 0.5 MPa. The other parameters were as follows: nozzle diameter of 3 mm and initial standoff distance of 12.5 mm. Therefore, the optimized slotting parameters were obtained as follows: when the slotting time was 0–5 min, the optimized rotation speed was 60 r/min; when the slotting time was 5–10 min, the optimized rotation speed was 50 r/min; when the slotting time was 10–15 min, the optimized rotation speed was 40 r/min; when the slotting time was 15–20 min, the optimized rotation speed was 30 r/min and the slotting depth reached 1.9 m.