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Artificially fracturing coal-rock mass serves to form break lines therein, which is related to the distribution of cracked boreholes. For this reason, we use physical experiments and numerical simulations to study the crack initiation and propagation characteristics of dense linear multihole drilling of fractured coal-rock mass. The results indicate that only in the area between the first and last boreholes can hydraulic fracturing be controlled by dense linear multihole expansion along the direction of the borehole line; in addition, no directional fracturing occurs outside the drilling section. Upon increasing parameters such as the included angle _{1} direction, the drilling spacing _{3}), and cracking perpendicular to _{3}. Five propagation modes also appear in sequence: propagating along borehole line, step-like propagation, S-shaped propagation, bidirectional propagation (along the borehole line and perpendicular to _{3}), and propagation perpendicular to _{3}. Based on these results, we report the typical characteristics of three-dimensional crack propagation and discuss the influence of the gradient of pore water pressure. The results show clearly that crack initiation and propagation are affected by both the geostress field and the pore water pressure. The pore water pressure will exhibit a circular-local contact-to-integral process during crack initiation and expansion. When multiple cracks approach, the superposition of pore water pressure at the tip of the two cracks increases the damage to the coal rock, which causes crack reorientation and intersection.

Coal mining often encounters technical problems such as hard roofs, hard thick top coal, rock bursts, coal and gas outburst, etc. Hydraulic fracturing technology can transform coal-rock mass, form fracture lines in hard coal-rock mass, improve the permeability of coal seams [

At present, directional hydraulic fracturing controlled by dense linear multihole drilling is used mainly to improve the directionality of hydraulic fracturing of radial perforations, enhance the penetration of cracks, and increase the production of petroleum [_{1}, and the principal stress difference on fracture propagation law of dense linear multihole drilling controlled directional hydraulic fracturing is studied in this paper.

Because directional hydraulic fracturing controlled by dense linear multihole drilling is not widely applied in coal mines, the behavior and mechanism of crack propagation are also less known. To redress this situation, this paper analyzes the crack initiation and propagation in directional hydraulic fracturing controlled by dense linear multihole drilling based on the effect of pore water pressure gradient. A model of typical crack initiation and propagation is analyzed, thereby providing a robust theoretical basis for application in the field.

Figure _{1}, _{2}, and _{3}, with _{1} being the maximum principal stress, _{2} being the intermediate principal stress, _{3} being the minimum principal stresses, and _{1} > _{2} > _{3}. Figure _{3} and the tensile strength of the rock, the hydraulic fractures will expand perpendicular to the minimum principal stress. Figure

Principle and technology of directional hydraulic fracturing controlled by dense linear multihole drilling. (a) Traditional principle of directional hydraulic fracturing. (b) Principle of directional hydraulic fracturing controlled by dense linear multihole drilling. (c) Technology of directional hydraulic fracturing controlled by dense linear multihole drilling.

Such an approach not only cuts off hard-top coal and the roof of a working face in the vertical direction, reduces the probability of rock burst, increases top-coal recovery, and enhances gas permeability but also cuts the roof off of pillarless roadways in certain directions to relieve pressure while retaining the roadway.

Based on the previous study [

The 4000 kN true triaxial hydraulic fracturing experiment system is employed (Figure ^{3} and 500 × 500 × 500 mm^{3}, is realized through 6 flat jacks to produce the circumstances of crustal stress.

The true triaxial hydraulic fracturing experiment system. (a) Block diagram. (b) Physical photo.

The compressive pressure and hydraulic pressure can be controlled by the 4-channel electrohydraulic servo controlling system with high precision satisfying the experimental requirement. 3 channels are assigned to produce compressive pressure. Every hole is injected with water by the corresponding oil cylinder with the oil and water conversion supercharger. 63 MPa is the top limit of hydraulic pressure applied to the boreholes. During the experiment, the plot of triaxial compressive pressure and hydraulic pressure can be visualized and recorded on the software screen.

The specimens are made of the No. 32.5 cement and filtered fine sand with the matching ratio of 3.5 : 1 : 0.3 (sand : cement : water). The specific parameters about specimens are shown in Table

Physical and mechanical parameters of the cement mortar.

Porosity |
Permeability |
Uniaxial compressive strength |
Modulus of elasticity |
Fracture toughness |
---|---|---|---|---|

12.7885 | 1.1339 | 6.2747 | 0.7208 | 13.2300 |

In this experiment, the cubic specimen of 500 × 500 × 500 mm^{3} is simulated as the real coal and rock matrix. The hole packer, which is 18 mm in outer radius, 8 mm in inner radius, and 220 mm in length, is sealed with the specimens by integrated pouring to ensure the tightness. And there is a 100 mm length naked hole extending from the end of the hole packer. This section of naked hole is spared to simulate the true situation of hydraulic fracturing. In one specimen, 2 or 3 linear layout boreholes can be installed. Limited by the production equipment of the cubic specimen, only two types of specimens containing multiple water-injection holes can be produced at present. One is a specimen with two water-injection holes and is used in the experiment of synchronous water injection into two boreholes, and the other is a specimen with three water-injection holes and is used for the experiment of synchronous water injection into three boreholes (Figure _{1} is 15 degrees two holes with 282 mm interval and 114 mm away from the edge of the sample are installed (Figure

The manufacture of specimens and loading (_{1} > _{2} > _{3}). (a) Cubic mode. (b) The shape of the specimen. (c) Place in the loading frame.

On the one hand, in situ stress conditions are intricate and the changes in crustal stress have a considerable impact on the extension of hydraulic fractures. On the other hand, the adaption in the holes’ space is usually an effective way to alternate the shape of fractures. So, the crustal distribution and the holes’ space are considered to find the typical propagation behavior of hydraulic cracks controlled by dense linear multiholes (Table

Experimental scheme.

No. | Principal stress (MPa) | Borehole spacing |
Arrangement angle of boreholes |
---|---|---|---|

A |
_{1} = 6, _{2} = 5, _{3} = 4 |
141 | 15 |

B |
_{1} = 6, _{2} = 5, _{3} = 2 |
141 | 15 |

C |
_{1} = 6, _{2} = 5, _{3} = 2 |
282 | 15 |

With specimen put into the loading frame shown in Figure

Figure _{1} is the water-injection and pressure-increase stage, X_{1}-X_{2} is the crack-initiation stage, X_{2}-X_{3} is the stable expansion stage, and X_{3}-X_{4} is the pressure-relief stage. In the crack-initiation stage, the first rupture occurred in the sample, and the water pressure dropped suddenly. During the steady expansion stage, the water pressure fluctuated continuously. This result is attributed to the high-pressure water that entered after the hydraulic crack opened, causing the crack to expand. The expansion of the crack reduces the water pressure. Once water-injection ceases, the water pressure decreases.

Water pressure during hydraulic fracturing.

Comparing test block A and test block B, the water pressure required for cracking of test block B is lower than that of test block A. It can be seen that the lower the minimum principal stress _{3} is, the lower the water pressure required to crack the test block. Comparing specimen B with specimen C shows that the water pressure required to crack specimen C is greater than that for specimen B. It can be seen that the larger the distance of the drilled holes is, the larger the water pressure required for the cracking of the test block.

With holes marked with K_{1}, K_{2}, and K_{3} from left to right, the fractured specimen A, in the stress environment where _{1} is 6 MPa, _{2} is 5 MPa, and _{3} is 4 MPa, is demonstrated in Figure _{1}–K_{3} basically begins and goes along the direction of ligature of the holes, which is apparently directional. Outside the fractured section of K_{1}–K_{3}, fractures begin and go along the direction of _{1}. All the holes lie in the smooth hydraulic failure plane which is orientational and not biforked or layered.

Crack propagation of directional hydraulic fracturing controlled by dense linear multihole drilling. (a) Crack along ligature of holes (specimen A). (b) Hydraulic cracks along ligature of holes and σ_{1} (specimen B). (c) Hydraulic cracks totally along σ_{1} (specimen C).

The distinct directional behavior within the section K_{1}–K_{3} results from the high level of stress concentration induced by the superposition of stress between two holes. This stress concentration provides a priority to the tensile strength of samples, finally cracking initially along the ligature of holes. As the pressurized water increases, the fractures are forced to open to going closer to each other and consequently intersecting smoothly. Outside the stretch of K_{1}–K_{3}, the failure plane almost perpendicular to the minimum principal stress has an undesirable directional effect because the area of stress superimposition between holes has very limited impact on the fractures as they move away where the stress field dominates the propagation. All these factors demonstrate that good directional effect is often obtained within the span of different boreholes. The results show that only in the area between the first and last boreholes can the hydraulic cracks expand along the direction of the borehole line, causing the coal-rock mass to fracture along the borehole line and thereby causing directional fracture. In areas outside the drilling section, the hydraulic fracturing is mainly perpendicular to the minimum principal stress expansion and no directional fracturing occurs.

In specimen B (_{1} = 6 MPa, _{2} = 5 MPa, and _{3} = 2 MPa), K_{1} and K_{2} mainly crack along the _{1} direction, and the water pressure in the crack of the K_{2} borehole expands along the _{1} direction. Conversely, the branch cracks are connected to the hydraulic cracks of the K_{1} and K_{3} boreholes; in other words, the K_{2} borehole, which is in the middle, extends along both the _{1} direction and along the line connecting the boreholes. Moreover, on both sides, the range of expansion of the hydraulic cracks K_{1} and K_{3} is relatively small, and the undulation of the crack surface is relatively large, where the central hydraulic crack of K_{2} basically penetrates the entire surface of the sample. The expansion range is large and the crack surface is relatively flat (Figure

Compared with specimen B whose boreholes’ space is 141 mm, in specimen C whose boreholes’ space is 282 mm and loading condition is the same as specimen B, the fractures of K_{1} and K_{2} begin and continue, respectively, along the _{1} and are smooth and paralleled as shown in Figure

To study the crack initiation and propagation of directional hydraulic fracturing controlled by dense linear multihole drilling, we used RFPA^{2D}-flow to simulate the hydraulic fracturing controlled by dense linear multihole drilling under different conditions. RFPA^{2D}-flow is a real fracture process analysis system with the elastic mechanics as the stress analysis tool and elastic damage theory and its modified failure criterion as the medium deformation and failure analysis module [

The basic equations involved in the software are as follows:

Constitutive equation:

Seepage equation:

Seepage-stress relationship equation:

The numerical model is shown in Figure _{1}, K_{2}, and K_{3}. The borehole diameter _{1} is _{1} and _{3} (_{1} > _{3}) are applied around the model. Water pressure is applied simultaneously to the three boreholes. The water pressure starts at zero and increases in steps of 1 MPa until destruction.

Numerical model.

Material parameters of the model.

Mechanics and seepage parameter | Rock stratum |
---|---|

Homogeneous degree | 4 |

Mean of compressive strength _{0} (MPa) |
75 |

Mean of elastic modulus _{0} (GPa) |
30 |

Poisson ratio |
0.25 |

Internal friction angle |
30 |

Pressure-tension ratio | 10 |

Porosity ratio | 0.1 |

Seepage coefficient |
0.01 |

Pore water pressure (MPa) | 0.1 |

Coupling coefficient | 0.1 |

Damage mutation coefficient | 5 |

To study the crack initiation and propagation of directional hydraulic fracturing controlled by dense linear multihole drilling under the effect of various parameters, we use the parameter sets given in Table _{1} − _{3}).

Numerical simulation scheme.

No. | Principal stress (MPa) | Borehole spacing |
Angle _{1.} (°) |
---|---|---|---|

A1 |
_{1} = 11, _{3} = 9 |
225 | 15° |

A2 |
_{1} = 11, _{3} = 9 |
225 | 30° |

A3 |
_{1} = 11, _{3} = 9 |
225 | 45° |

A4 |
_{1} = 11, _{3} = 9 |
225 | 60° |

A5 |
_{1} = 11, _{3} = 9 |
225 | 75° |

B1 |
_{1} = 11, _{3} = 9 |
200 (5 |
40° |

B2 |
_{1} = 11, _{3} = 9 |
240 (6 |
40° |

B3 |
_{1} = 11, _{3} = 9 |
280 (7 |
40° |

B4 |
_{1} = 11, _{3} = 9 |
320 (8 |
40° |

B5 |
_{1} = 11, _{3} = 9 |
360 (9 |
40° |

C1 |
_{1} = 11, _{3} = 10 |
225 | 40° |

C2 |
_{1} = 11, _{3} = 8 |
225 | 40° |

C3 |
_{1} = 11, _{3} = 6 |
225 | 40° |

C4 |
_{1} = 11, _{3} = 4 |
225 | 40° |

C5 |
_{1} = 11, _{3} = 2 |
225 | 40° |

Figure _{3}; when _{3}; when _{3}.

Crack initiation of directional hydraulic fracturing controlled by dense linear multihole drilling with various parameter values. (a) Angle _{1}. (b) Borehole spacing

Figure _{3}; when _{3}; when _{3}.

Figure _{3}; when Δ_{3}.

Figure _{3} appear at borehole K_{3}. When _{3} appear at boreholes K_{1}–K_{3}, indicating that hydraulic cracks propagate both along the borehole line and perpendicular to _{3}. When _{3} and the interactions between cracks are weak so that the cracks propagate independently and in parallel. No obvious branch cracks or reorientation occurs.

Crack propagation of directional hydraulic fracturing controlled by dense linear multihole drilling with various parameter values. (a) Angle _{1}. (b) Borehole spacing

Figure _{3} at boreholes K_{1}–K_{3}, indicating that the cracks propagate both along the borehole line and perpendicular to _{3}. When _{3} and interactions between cracks are weak so that the cracks propagate independently and in parallel. No obvious branch cracks or reorientation occurs.

Figure _{3} at borehole K_{2}. When Δ_{2}, branch cracks propagate perpendicular to _{3}; when Δ_{3} and interactions between cracks are weak. They propagate independently and in parallel, and no obvious branch cracks or reorientation occurs.

The relationship between the water pressure _{0} required for the fracture in the hydraulic fracturing process and _{3}, and _{0} gradually decreases (Figure _{0} gradually increases (Figure _{3}, _{0} gradually increases (Figure _{3} is, the greater the principal stress difference is, the easier the coal-rock mass is cracked in the vertical _{1} direction, and the lower the water pressure required for fracturing.

Fracture water pressure under different influencing factors. (a) Angle _{1}. (b) Borehole spacing _{3}.

Taking the test block C3 as an example, the pore water pressure evolution of the porous single-row coupled directional hydraulic fracturing is shown in Figure

Pore water pressure and evolution of damage due to multicrack propagation. (a) Pore water pressure. (b) Pore water pressure for drilling connections. (c) Acoustic emission event.

The pore water pressure of the borehole connection during the hydraulic fracturing process is shown in Figure

The acoustic emission event during the hydraulic fracturing process is shown in Figure

Figure _{3}, and the rupture characteristics under different conditions result from the competitive relationship between these two directions.

Three-dimensional configuration of hydraulic cracks.

For small _{3}. After crack initiation, the cracks are deflected in the direction of the borehole line: large deflections form a ladder pattern of cracks, whereas slight deflections form an S-shaped pattern of cracks. Upon further increasing _{3}. Branch cracks appear upon subsequent propagation, and cracks propagate both along the borehole line and perpendicular to _{3}. When _{3}, with no branch cracks or rotational behavior.

By increasing _{3} (Figure _{3} (Figure _{3} (Figure _{3} (Figure

Crack initiation and propagation modes of directional hydraulic fracturing controlled by dense linear multihole drilling. (a) Three modes of crack initiation of directional hydraulic fracturing controlled by dense linear multihole drilling. (A) Initiation along the borehole line. (B) Bidirectional initiation. (C) Initiation perpendicular to _{3}. (b) Five modes of crack propagation of directional hydraulic fracturing controlled by dense linear multihole drilling. (A) Propagation along borehole line. (B) Propagation forming ladder pattern. (C) Propagation forming S-shaped pattern. (D) Bidirectional propagation. (E) Propagation perpendicular to

The directional propagation of hydraulic cracks in a borehole section is more evident than that outside the borehole section.

By increasing _{3}; and (c) initiation perpendicular to _{3}.

By increasing _{3}; and (e) propagation perpendicular to _{3}.

The initiation and propagation of hydraulic cracks are affected by both the geostress field and the pore water pressure. With the cracking expansion of the hydraulic crack, the pore water pressure field sequentially shows the process of circular-local contact-total connection, which gradually develops from the interval distribution to continuous high-stress strip. When multiple cracks approach each other, the pore water pressure fields at the tip of two cracks become superimposed on each other, which generates numerous microcracks between the two crack tips. This phenomenon damages the coal rock, which provides conditions for the reorientation and intersection of cracks.

Based on the crack initiation and propagation laws of directional hydraulic fracturing controlled by dense linear multihole drilling, we give the three-dimensional configuration of crack propagation by considering the effect of the pressure gradient of pore water.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This study was supported by the National Key R&D Program of China (2018YFC0604703) and the Natural Science Foundation of Jiangsu Province (BK20161184).