Determination of Fracture Initiation Locations during Cross-Measure Drilling for Hydraulic Fracturing of Coal Seams

Yiyu Lu 1,2, Yugang Cheng 1,2,*, Zhaolong Ge 1,2,*, Liang Cheng 1,2, Shaojie Zuo 1,2 and Jianyu Zhong 1,2 1 State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400044, China; luyiyu@cqu.edu.cn (Y.L.); chengliang@cqu.edu.cn (L.C.); 20142002027@cqu.edu.cn (S.Z.); 20152002005t@cqu.edu.cn (J.Z.) 2 National & Local Joint Engineering Laboratory of Gas Drainage in Complex Coal Seam, Chongqing University, Chongqing 400044, China * Correspondence: chengyugang@cqu.edu.cn (Y.C.); gezhaolong@cqu.edu.cn (Z.G.); Tel./Fax: +86-23-6510-6640 (Y.C. & Z.G.)


Introduction
At present, to enhance gas drainage efficiency in a low-permeability coal seam, hydraulic fracturing (HF) is used as a standard practice [1][2][3].It achieves good results draining coal bed methane in most coal mines.However when using HF, most commonly the focus is on changes in the initiation pressure or fracture extension and the influence of where the fractures are initiated on increasing the seam permeability is neglected [4][5][6][7].In most cases, HF is usually carried out by cross-seam drilling because of the difficulty of in-seam sealing.However, the physical and mechanical differences between the roof, the floor, and the coal seam result in multiple compositional interfaces in the interval being drilled.In addition, coal seams can have two or more layers including soft and hard coal layers as well as rock bands and seams like this are especially common in Southwestern China.The coal-rock mass and its internal interfaces have a significant influence on where fractures are initiated when seams are drilled for HF.The fracture initiation location will have an effect on both the direction in which Energies 2016, 9, 358 2 of 13 fractures extend and fracture development.Therefore, it is essential to know whether the initiation location is in the coal seam or in the interface when undertaking cross-measure HF drilling.This paper investigates what determines fracture initiation location for drilling across layered coal-rock seams.
Many scholars have studied hydraulic fracture initiation pressure and crack extension direction but the mechanisms controlling the initiation location need further study.Through theoretical analysis, Huang et al. [8,9] found that changes in the inclined shaft angle influenced the crack orientation under the different stress conditions.Feng and Kang [10] analyzed the relationship between azimuth and borehole tilt angle and initiation location for different stress fields.Zhao and Chen [11] studied the extension of hydraulic fractures where the fracture reaches a formation interface.Li et al. [12] proposed a novel stimulation technique to study horizontal well fracturing through interlayers to a coal seam, a study focused on fracture propagation.Li's study, however, was not relevant to cross-measure HF drilling and the relationships between the coal seam and crustal stress were not considered.Zhang et al. [13] studied cross-drilling fracture initiation location theory through plane problem analysis.Zhang et al. [13] hypothesized that (a) initiation location in the axial direction is controlled by the weakest interface, and (b) that initiation location in the radial direction is controlled by minimum tensile strength of the coal and the vertical side stress coefficient.
Currently, most studies on cross-drilling HF fracture initiation have been confined to the two-dimensional problem and have not considered the three-dimensional stress state.Additionally, fracture simulation testing has largely been performed only on coal or on simulated coal material, and the effect of the occurrence of coal interlayered with rock on fracture initiation has not been studied.Due to these two limitations, our knowledge concerning fracture initiation is incomplete and so this paper is aimed at studying the location of cross-drilling HF fracture initiation in coal + rock by comparing the positions of pressure differences.Ranjith et al. [14][15][16], Lockner [17] think that acoustic emission (AE) technology is an effective tool in the study of rock fracture.It can monitor the internal defect of rock by receipting stress wave.AE technology plays an important role in this paper to monitor the initiation location precisely.The different initiation locations are obtained using a DISP acoustic emission positioning system (PAC Inc., Princeton, NJ, USA).

Fracture Initiation Location
There are two locations where fractures are initiated when performing cross-measure HF.One is in the coal seam, the other is in the coal-rock interface.There are essential differences between the mechanisms that control fracture initiation at these two locations.The following sections present a mathematical analysis of the two initiation locations.In order to simplify the analysis, in the mathematical model the coal and rock near borehole will be considered to be homogeneous elastic bodies [18][19][20][21].In addition, the filtration effect of the layers and the changes in pore water pressure will not be taken into account in the modeling.

Initiation Location in a Coal Seam
The spatial relationship between a cross-measure HF borehole and a coal seam is shown in Figure 1.Due to the relative orientations of the coal seam and the mine workings, there may be an acute angle between the fracturing borehole and the direction normal to the coal seam (γ in Figure 1).In a vertical section, the relationship between the coal seam dip angle, the angle between the axis of the borehole and the vertical direction, and the angle between the borehole axis and the angle normal to the coal seam is given by Equation (1): where α is the angle between the axis of the borehole and vertical direction ( ˝); ϕ is the coal seam dip angle ( ˝); γ is the angle between the borehole axis and the angle normal to the coal seam ( ˝).When the borehole is perpendicular to the coal seam, γ = 0 and the stress state of the borehole and the coal seam are as is shown in Figure 2. The stress state on the borehole wall can be obtained by converting the Cartesian coordinates of the in situ rock stress [18], as shown in Equation ( 2): Where σx, σy, σz, τxy, τyz, and τzx are the normal and shear stresses in the local coordinate system (x,y,z); σv is the vertical principal stress (MPa); σH and σh are the major and minor horizontal principal stresses (MPa); and β is the azimuth of the major principle stress (°).In the cylindrical-coordinate system of the borehole, the stress state of a specific point around the borehole wall can be described by Equation (3): When the borehole is perpendicular to the coal seam, γ = 0 and the stress state of the borehole and the coal seam are as is shown in Figure 2. The stress state on the borehole wall can be obtained by converting the Cartesian coordinates of the in situ rock stress [18], as shown in Equation ( 2): where σ x , σ y , σ z , τ xy , τ yz , and τ zx are the normal and shear stresses in the local coordinate system (x,y,z); σ v is the vertical principal stress (MPa); σ H and σ h are the major and minor horizontal principal stresses (MPa); and β is the azimuth of the major principle stress ( ˝).When the borehole is perpendicular to the coal seam, γ = 0 and the stress state of the borehole and the coal seam are as is shown in Figure 2. The stress state on the borehole wall can be obtained by converting the Cartesian coordinates of the in situ rock stress [18], as shown in Equation ( 2): Where σx, σy, σz, τxy, τyz, and τzx are the normal and shear stresses in the local coordinate system (x,y,z); σv is the vertical principal stress (MPa); σH and σh are the major and minor horizontal principal stresses (MPa); and β is the azimuth of the major principle stress (°).In the cylindrical-coordinate system of the borehole, the stress state of a specific point around the borehole wall can be described by Equation (3): In the cylindrical-coordinate system of the borehole, the stress state of a specific point around the borehole wall can be described by Equation (3): where p is the water pressure in the borehole and σ r , σ θ , σ zz , τ rθ , τ θz , and τ zr are the radial, tangential, and axial components of the normal and shear stresses (MPa) at the borehole wall inclined at an angle of θ with σ y , respectively.In general, any point at the borehole wall is considered to be in tensile failure [19,20].Since the tensile strength of coal is less than that of rock, the maximum tangential stress σ θ reaches the tensile strength of coal first.When the stress state satisfies Equation ( 4), the borehole starts to split.R t is the strength of extension of coal seam.ˇˇˇˇp σ x `σy q ´2pσ x ´σy qcos2θ Equations ( 2)-( 4) can be combined to obtain Equation ( 5) to solve for the initiation pressure when the initiation location is in the coal seam (P f1 ).
Substituting Equation (1) into Equation (5) can return the initiation pressure.When the borehole is not completely perpendicular to coal seam, γ ‰ 0 ˝.

Initiation Location in the Coal-Rock Interface
According to the interfacial tension failure criterion, the water pressure in the interface must be high enough to overcome the resistance of the interface normal stress and the bonding force, C, for a fracture to form.Resolving the in situ rock stress in the interface normal direction can obtain the initiation pressure in the coal-rock interface, as shown in Equation ( 6): where P f2 is the initiation pressure in the coal-rock interface and C is the bonding force.

Model to Determine the Initiation Location
The initiation location, F, will be where the initiation pressure in the coal seam or the coal-rock interface is lowest.To compare the values of the two initiation pressures, determine F = P f1 ´Pf2 .This allows Equation (7) to be written as: Equation (7) shows that F is a function of the in-situ rock stresses (σ H , σ h , σ v ), the angle between the axis of borehole and the vertical, and the azimuth of the major principle stress.The ranges for the values of the parameters are: α P (0, π/2), β P (0, π) and θ P (0, 2π).Since θ is changing, F still has a minimum value F min when the other parameters are defined.
When F min < 0, P f1 < P f2 meaning the initiation location is in the coal seam.When F min > 0, P f1 > P f2 meaning the initiation location is in the coal-rock interface.

Analysis of Initiation Location Parameters
Generally, in situ rock stress is a combination of stress from the overlying strata due to gravity and tectonic stresses.The vertical principal stress is in almost all cases relatively constant.However, the horizontal maximum and minimum stresses show great variability near different kinds of faults.Normal faults, reverse faults, and strike-slip faults have different principle stress states, as shown in Figure 3.

Analysis of Initiation Location Parameters
Generally, in situ rock stress is a combination of stress from the overlying strata due to gravity and tectonic stresses.The vertical principal stress is in almost all cases relatively constant.However, the horizontal maximum and minimum stresses show great variability near different kinds of faults.Normal faults, reverse faults, and strike-slip faults have different principle stress states, as shown in Figure 3. Equation (7) shows that the initiation location of cross-measure HF is determined by multiple parameters.In order to analyze the main parameters affecting the initiation location, we neglect the minor factors and make the following assumptions: 1. Since the strength of extension of coal and the coal bonding force are constant and they both inhibit the initiation pressure, it is assumed that their values are equal; 2. The borehole is perpendicular to coal seam; 3. The coal seam depth of burial is 500 m.The ratios of the principle stresses of a normal fault are v H h σ : σ : σ 3: 2 :1  , those for a reverse fault are v H h σ : σ : σ 1: 3: 2  , and stress ratios for a strike-slip fault are v H h σ : σ : σ 2 : 3 :1  .
The calculated variations for Fmin with different α's and β's is as shown in Figure 4. Equation (7) shows that the initiation location of cross-measure HF is determined by multiple parameters.In order to analyze the main parameters affecting the initiation location, we neglect the minor factors and make the following assumptions: 1. Since the strength of extension of coal and the coal bonding force are constant and they both inhibit the initiation pressure, it is assumed that their values are equal; 2. The borehole is perpendicular to coal seam; 3. The coal seam depth of burial is 500 m.The ratios of the principle stresses of a normal fault are σ v : σ H : σ h " 3 : 2 : 1, those for a reverse fault are σ v : σ H : σ h " 1 : 3 : 2, and stress ratios for a strike-slip fault are σ v : σ H : σ h " 2 : 3 : 1.
According to the statistics on the stress state in the shallow crust in China reported by Jing et al. [22], the three principle stresses conform to the rules shown in Equation (8).Based on the assumptions above, the variation of F min can be computed using MATLAB R2013a software (MathWorks Inc., Natick, MA, USA), for α = 0 ˝, 30 ˝, 45 ˝, 60 ˝, and 90 ˝and β = 0 ˝, 45 ˝, 90 ˝, 135 ˝, and 180 The calculated variations for F min with different α's and β's is as shown in Figure 4.  Considering the physical meaning of Fmin, Figure 4a shows that with the angle between the borehole axis and the vertical increasing near a normal fault, Fmin mainly decreases.This means that the initiation location tends to be in the coal-rock interface.Figure 4c shows that Fmin mainly increases near reverse faults, therefore the initiation location tends to be in the coal seam.Figure 4e shows that Fmin does not have a specific variation tendency near strike-slip faults, therefore the initiation location is determined by the value of α for that particular drill hole.
Figure 4b,d,f shows that with β increasing, Fmin changes in a similar fashion for the three types of faults.The values of Fmin follow a "valley-peak-valley" pattern.This pattern shows that the initiation location conforms to a similar pattern; "initiation location in coal seam-initiation location in coal-rock interface-initiation location in coal seam" as the direction of the principal stress changes.
Although the analysis above is an example of one analysis based on calculations performed under specific conditions, the variations in Fmin demonstrated can provide a reference for applying Considering the physical meaning of F min , Figure 4a shows that with the angle between the borehole axis and the vertical increasing near a normal fault, F min mainly decreases.This means that the initiation location tends to be in the coal-rock interface.Figure 4c shows that F min mainly increases near reverse faults, therefore the initiation location tends to be in the coal seam.Figure 4e shows that F min does not have a specific variation tendency near strike-slip faults, therefore the initiation location is determined by the value of α for that particular drill hole.
Figure 4b,d,f shows that with β increasing, F min changes in a similar fashion for the three types of faults.The values of F min follow a "valley-peak-valley" pattern.This pattern shows that the initiation location conforms to a similar pattern; "initiation location in coal seam-initiation location in coal-rock interface-initiation location in coal seam" as the direction of the principal stress changes.
Energies 2016, 9, 358 7 of 13 Although the analysis above is an example of one analysis based on calculations performed under specific conditions, the variations in F min demonstrated can provide a reference for applying the assessment criteria.The actual initiation location in any specific location should be computed by using the parameters at that locality.

Test System
In order to verify the validity of the initiation location determination criteria for different coal seams, we conducted some tests in the laboratory.These tests were similar to typical HF tests for coal seams.The purpose of the tests was to obtain the relationship between the actual crack pressure and the initiation location of the crack in relation to the dip of the coal seam.The tests used a three-axis HF simulation test system made up of four main parts: the pump system, the pressure flow system, stress loading system, and DISP acoustic emission test system.The pump system uses a 31.5 L/min, 20 MPa high-pressure water pump, the pressure flow measurement system is composed of a 500 kN electrohydraulic servo three axis test machine, an electromagnetic flowmeter, and a signal receiving apparatus, and the stress loading system uses self-designed hydraulic pressure loading devices.System connections are shown in Figure 5.
Energies 2016, 9, 358 7 the assessment criteria.The actual initiation location in any specific location should be computed by using the parameters at that locality.

Test System
In order to verify the validity of the initiation location determination criteria for different coal seams, we conducted some tests in the laboratory.These tests were similar to typical HF tests for coal seams.The purpose of the tests was to obtain the relationship between the actual crack pressure and the initiation location of the crack in relation to the dip of the coal seam.The tests used a three-axis HF simulation test system made up of four main parts: the pump system, the pressure flow system, stress loading system, and DISP acoustic emission test system.The pump system uses a 31.5 L/min, 20 MPa high-pressure water pump, the pressure flow measurement system is composed of a 500 kN electrohydraulic servo three axis test machine, an electromagnetic flowmeter, and a signal receiving apparatus, and the stress loading system uses self-designed hydraulic pressure loading devices.System connections are shown in Figure 5.

Sample Preparation and Stress Loading
Test samples were manufactured to resemble coal and rock from the Tonghua coal mine in the Songzao Mining Area, Chongqing, China.In order to decide on the appropriate mix of constituents for the samples, six sets of preliminary samples were prepared to compare their compressive strength to that of samples collected in the field [23,24].The test samples, 7 cm cubes as shown in Figure 6, were prepared according to Chinese national standards in procedures for "Method for determining the physical and mechanical properties of coal and rock" (GB/T23561.1-2009) and "Standard for test method of basic properties of construction mortar" (JGJ/T70-2009).Strength tests were performed using an AG-I electronic precision material testing machine.Based on the results of those tests, a ratio of cement: river sand of 1:6.38 was chosen for the simulated rock material and a coal: cement: gypsum ratio of 3:1:1 was deemed most appropriate for the simulated coal material.The test results are shown in Table 1.

Sample Preparation and Stress Loading
Test samples were manufactured to resemble coal and rock from the Tonghua coal mine in the Songzao Mining Area, Chongqing, China.In order to decide on the appropriate mix of constituents for the samples, six sets of preliminary samples were prepared to compare their compressive strength to that of samples collected in the field [23,24].The test samples, 7 cm cubes as shown in Figure 6, were prepared according to Chinese national standards in procedures for "Method for determining the physical and mechanical properties of coal and rock" (GB/T23561.and "Standard for test method of basic properties of construction mortar" (JGJ/T70-2009).Strength tests were performed using an AG-I electronic precision material testing machine.Based on the results of those tests, a ratio of cement: river sand of 1:6.38 was chosen for the simulated rock material and a coal: cement: gypsum ratio of 3:1:1 was deemed most appropriate for the simulated coal material.The test results are shown in Table 1.The specimens are made in a 300 mm × 300 mm × 300 mm die.By changing the height of the four pivot points of the die to control the coal rock strata.After mixing the material with water, it is placed in the die in order by layer using a steel rule to measure and control the thickness of the coal seam.The fracturing pipe to connect with hydraulic line is set into the specimen and 110 mm long by 3 mm diameter hole simulation fractures are drilled at the lower end of the fracturing pipe.It is very important to cement the samples at the interface during the test.In order to avoid the presence of strength defects in the coal-rock interface, the die should be shaken many times to prevent natural fractures existing in the coal-rock interface.Natural fractures in the coal seam would influence the initiation location of the crack.After the specimen is made, the relationship between the fracture tube and the stress loading position cannot be changed (α = 0°).All samples were made with φ = 20° and β = 0°, 30°, 45°, 60°, 90°, as shown in Figure 7.When HF is carried out, preexisting stresses play a major role in the initiation and expansion of cracks.Therefore, setting the stress environment to match those that would exist in the natural environment is very important for the tests.We use the in situ stress measurement result in Tonghua coal mine to simulate stresses, as shown in Table 2 [25].The sample is under triaxial simulate stresses to match the in situ stresses.The three directions of the sample all have a surface under displacement constraints, and the opposite surface is under stresses constraints, as shown in Figure 8.The specimens are made in a 300 mm ˆ300 mm ˆ300 mm die.By changing the height of the four pivot points of the die to control the coal rock strata.After mixing the material with water, it is placed in the die in order by layer using a steel rule to measure and control the thickness of the coal seam.The fracturing pipe to connect with hydraulic line is set into the specimen and 110 mm long by 3 mm diameter hole simulation fractures are drilled at the lower end of the fracturing pipe.It is very important to cement the samples at the interface during the test.In order to avoid the presence of strength defects in the coal-rock interface, the die should be shaken many times to prevent natural fractures existing in the coal-rock interface.Natural fractures in the coal seam would influence the initiation location of the crack.After the specimen is made, the relationship between the fracture tube and the stress loading position cannot be changed (α = 0 ˝).All samples were made with ϕ = 20 ˝and β = 0 ˝, 30 ˝, 45 ˝, 60 ˝, 90 ˝, as shown in Figure 7.The specimens are made in a 300 mm × 300 mm × 300 mm die.By changing the height of the four pivot points of the die to control the coal rock strata.After mixing the material with water, it is placed in the die in order by layer using a steel rule to measure and control the thickness of the coal seam.The fracturing pipe to connect with hydraulic line is set into the specimen and 110 mm long by 3 mm diameter hole simulation fractures are drilled at the lower end of the fracturing pipe.It is very important to cement the samples at the interface during the test.In order to avoid the presence of strength defects in the coal-rock interface, the die should be shaken many times to prevent natural fractures existing in the coal-rock interface.Natural fractures in the coal seam would influence the initiation location of the crack.After the specimen is made, the relationship between the fracture tube and the stress loading position cannot be changed (α = 0°).All samples were made with φ = 20° and β = 0°, 30°, 45°, 60°, 90°, as shown in Figure 7.When HF is carried out, preexisting stresses play a major role in the initiation and expansion of cracks.Therefore, setting the stress environment to match those that would exist in the natural environment is very important for the tests.We use the in situ stress measurement result in Tonghua coal mine to simulate stresses, as shown in Table 2 [25].The sample is under triaxial simulate stresses to match the in situ stresses.The three directions of the sample all have a surface under displacement constraints, and the opposite surface is under stresses constraints, as shown in Figure 8.When HF is carried out, preexisting stresses play a major role in the initiation and expansion of cracks.Therefore, setting the stress environment to match those that would exist in the natural environment is very important for the tests.We use the in situ stress measurement result in Tonghua coal mine to simulate stresses, as shown in Table 2 [25].The sample is under triaxial simulate stresses to match the in situ stresses.The three directions of the sample all have a surface under displacement constraints, and the opposite surface is under stresses constraints, as shown in Figure 8.According to reference [23], the tests are in general similar to the geometry, the unit weight, the strength of extension and the stress field that would be present in a real-world HF situation.Comparing the test specimens and test conditions with those that might pertain in a working coal mine, the simulated coal seam thickness: real coal seam thickness ratio is 1:10, the bulk density similarity ratio is 1.22:1, the strength of extension similarity ratio is 0.79:1, and the experimental stress: the actual site stress ratio is 1:10.Therefore, the triaxial simulate stresses are 2.37 MPa (the major horizontal principal stresses), 0.99 MPa (the minor horizontal principal stresses), 0.45 MPa (the vertical principal stresses).

Sensor Arrangement and Acoustic Emission (AE) Sensor Verification
In order to monitor the initiation location and fracture shape during the HF experiments, eight DISP acoustic emission (AE) sensors were attached on the outside of the specimen along the coal seam [26].Two sides of the specimen had four sensors each, and the sensors were placed 5 cm away from the edges, as shown in Figure 9a.To verify that the sensors were recording the correct location of the fractures, a tracer was introduced into the fracturing fluid so that the tracer material would attach itself to the fracture surface when the fracturing fluid entered the cracks.The goal was to see whether the AE events faithfully represented the fracture initiation locations and fracture shape.After this experiment, we cut the specimen apart to expose the tracer-coated fracture surface.As shown in Figure 9b, the AE-recorded fracture sites agree well with the sites impregnated with tracer material site, verifying the validity of the AE events.Table 2. Test result of in-situ stress in Tonghua coalmine [25].
Principle stress/MPa 23.7 9.9 4.5 θ x (The angle between principal stress and x)/ ˝39.0 94.6 51.1 θ y (The angle between principal stress and y)/ ˝129.1 87.8 38.9 θ z (The angle between principal stress and z)/ ˝86.8 3.4 88.4 According to reference [23], the tests are in general similar to the geometry, the unit weight, the strength of extension and the stress field that would be present in a real-world HF situation.Comparing the test specimens and test conditions with those that might pertain in a working coal mine, the simulated coal seam thickness: real coal seam thickness ratio is 1:10, the bulk density similarity ratio is 1.22:1, the strength of extension similarity ratio is 0.79:1, and the experimental stress: the actual site stress ratio is 1:10.Therefore, the triaxial simulate stresses are 2.37 MPa (the major horizontal principal stresses), 0.99 MPa (the minor horizontal principal stresses), 0.45 MPa (the vertical principal stresses).

Sensor Arrangement and Acoustic Emission (AE) Sensor Verification
In order to monitor the initiation location and fracture shape during the HF experiments, eight DISP acoustic emission (AE) sensors were attached on the outside of the specimen along the coal seam [26].Two sides of the specimen had four sensors each, and the sensors were placed 5 cm away from the edges, as shown in Figure 9a.To verify that the sensors were recording the correct location of the fractures, a tracer was introduced into the fracturing fluid so that the tracer material would attach itself to the fracture surface when the fracturing fluid entered the cracks.The goal was to see whether the AE events faithfully represented the fracture initiation locations and fracture shape.After this experiment, we cut the specimen apart to expose the tracer-coated fracture surface.As shown in Figure 9b, the AE-recorded fracture sites agree well with the sites impregnated with tracer material site, verifying the validity of the AE events.showing AE-recorded event sites and a photograph of a fracture surface in the tested specimen.A tracer was introduced into the fracturing fluid and the presence of the tracer material (light brown in the photograph) on the fracture surface verifies that the AE events recorded the fracture initiation sites and fracture shape well.

Fracture Initiation Location Verification
The mathematical model is aimed at forecasting the fracture initiation location during cross-measure drilling for HF, and the article verifies the model through comparing the initiation location of the experiment with the forecast result of the mathematical model.To verify the validity of the mathematical model, there are four steps of the initiation location verification.
Firstly, we can obtain the variation of Fmin by substituting every parameter into the mathematical model, as shown in Equation (7).The tensile strength of the simulated coal seam material is just 0.23 MPa and the bonding force of coal-rock interface cannot be simulated quantitatively.However, because these two values have less effect than the other parameters on where fractures initiate, it is assumed that these values are equal for the purpose of verifying the initiation location model.Calculation results show that Fmin is negative when β is between 7° and 41°, which means that for those values of β, fractures will initiate in the coal seam.Conversely, Fmin is positive when β is less than 7 or greater than 41, which means fracture initiation will be in the coal-rock interface.Therefore, the initiation location variation with β can be described as shown in Figure 10.Secondly, the initiation location of sample can be monitored by the DISP AE system during the experiment.The experiment just described shows that the initiation locations and the shape of the fracture can be estimated by the sequence of AE events.Figure 11 shows the AE events in two A tracer was introduced into the fracturing fluid and the presence of the tracer material (light brown in the photograph) on the fracture surface verifies that the AE events recorded the fracture initiation sites and fracture shape well.

Fracture Initiation Location Verification
The mathematical model is aimed at forecasting the fracture initiation location during cross-measure drilling for HF, and the article verifies the model through comparing the initiation location of the experiment with the forecast result of the mathematical model.To verify the validity of the mathematical model, there are four steps of the initiation location verification.
Firstly, we can obtain the variation of F min by substituting every parameter into the mathematical model, as shown in Equation (7).The tensile strength of the simulated coal seam material is just 0.23 MPa and the bonding force of coal-rock interface cannot be simulated quantitatively.However, because these two values have less effect than the other parameters on where fractures initiate, it is assumed that these values are equal for the purpose of verifying the initiation location model.Calculation results show that F min is negative when β is between 7 ˝and 41 ˝, which means that for those values of β, fractures will initiate in the coal seam.Conversely, F min is positive when β is less than 7 ˝or greater than 41 ˝, which means fracture initiation will be in the coal-rock interface.Therefore, the initiation location variation with β can be described as shown in Figure 10.showing AE-recorded event sites and a photograph of a fracture surface in the tested specimen.A tracer was introduced into the fracturing fluid and the presence of the tracer material (light brown in the photograph) on the fracture surface verifies that the AE events recorded the fracture initiation sites and fracture shape well.

Fracture Initiation Location Verification
The mathematical model is aimed at forecasting the fracture initiation location during cross-measure drilling for HF, and the article verifies the model through comparing the initiation location of the experiment with the forecast result of the mathematical model.To verify the validity of the mathematical model, there are four steps of the initiation location verification.
Firstly, we can obtain the variation of Fmin by substituting every parameter into the mathematical model, as shown in Equation (7).The tensile strength of the simulated coal seam material is just 0.23 MPa and the bonding force of coal-rock interface cannot be simulated quantitatively.However, because these two values have less effect than the other parameters on where fractures initiate, it is assumed that these values are equal for the purpose of verifying the initiation location model.Calculation results show that Fmin is negative when β is between 7° and 41°, which means that for those values of β, fractures will initiate in the coal seam.Conversely, Fmin is positive when β is less than 7 or greater than 41, which means fracture initiation will be in the coal-rock interface.Therefore, the initiation location variation with β can be described as shown in Figure 10.Secondly, the initiation location of sample can be monitored by the DISP AE system during the experiment.The experiment just described shows that the initiation locations and the shape of the fracture can be estimated by the sequence of AE events.Figure 11 shows the AE events in two Secondly, the initiation location of sample can be monitored by the DISP AE system during the experiment.The experiment just described shows that the initiation locations and the shape of the fracture can be estimated by the sequence of AE events.Figure 11  Thirdly, the tracer material in the samples can be observed for judging the initiation location.The initiation location conditions for the five types of samples are shown in Table 3.The experiment results show that initiation location is in the coal seam only when α = 0 and β = 30 (Sample 2), indicating that Fmin is negative, whereas the initiation location is in the coal-rock interface when α = 0 and β = 0, 45, 60, 90 (Sample 1, 3, 4, 5) indicating that Fmin is positive.
Finally, by comparing the monitor initiation location, the observed initiation location with the variation in mathematical model, we can verify the validity of the mathematical model.Table 3 shows that the experimental results correspond with the theoretical calculations, indicating that the three-dimensional initiation location model for cross-measure HF can be applied in engineering.According to the experiments, the crack will extend along the interface forming a single main fracture plane when the initiation location is in the coal-rock interface.Additionally, the crack will preferentially propagate in the coal seam before crossing the coal-rock interface when the initiation Thirdly, the tracer material in the samples can be observed for judging the initiation location.The initiation location conditions for the five types of samples are shown in Table 3.The experiment results show that initiation location is in the coal seam only when α = 0 ˝and β = 30 ˝(Sample 2), indicating that F min is negative, whereas the initiation location is in the coal-rock interface when α = 0 and β = 0 ˝, 45 ˝, 60 ˝, 90 ˝(Sample 1, 3, 4, 5) indicating that F min is positive.Thirdly, the tracer material in the samples can be observed for judging the initiation location.The initiation location conditions for the five types of samples are shown in Table 3.The experiment results show that initiation location is in the coal seam only when α = 0° and β = 30° (Sample 2), indicating that Fmin is negative, whereas the initiation location is in the coal-rock interface when α = 0° and β = 0°, 45°, 60°, 90° (Sample 1, 3, 4, 5) indicating that Fmin is positive.
Finally, by comparing the monitor initiation location, the observed initiation location with the variation in mathematical model, we can verify the validity of the mathematical model.Table 3 shows that the experimental results correspond with the theoretical calculations, indicating that the three-dimensional initiation location model for cross-measure HF can be applied in engineering.Thirdly, the tracer material in the samples can be observed for judging the initiation location.The initiation location conditions for the five types of samples are shown in Table 3.The experiment results show that initiation location is in the coal seam only when α = 0° and β = 30° (Sample 2), indicating that Fmin is negative, whereas the initiation location is in the coal-rock interface when α = 0° and β = 0°, 45°, 60°, 90° (Sample 1, 3, 4, 5) indicating that Fmin is positive.
Finally, by comparing the monitor initiation location, the observed initiation location with the variation in mathematical model, we can verify the validity of the mathematical model.Table 3 shows that the experimental results correspond with the theoretical calculations, indicating that the three-dimensional initiation location model for cross-measure HF can be applied in engineering.Thirdly, the tracer material in the samples can be observed for judging the initiation location.The initiation location conditions for the five types of samples are shown in Table 3.The experiment results show that initiation location is in the coal seam only when α = 0° and β = 30° (Sample 2), indicating that Fmin is negative, whereas the initiation location is in the coal-rock interface when α = 0° and β = 0°, 45°, 60°, 90° (Sample 1, 3, 4, 5) indicating that Fmin is positive.
Finally, by comparing the monitor initiation location, the observed initiation location with the variation in mathematical model, we can verify the validity of the mathematical model.Table 3 shows that the experimental results correspond with the theoretical calculations, indicating that the three-dimensional initiation location model for cross-measure HF can be applied in engineering.Thirdly, the tracer material in the samples can be observed for judging the initiation location.The initiation location conditions for the five types of samples are shown in Table 3.The experiment results show that initiation location is in the coal seam only when α = 0° and β = 30° (Sample 2), indicating that Fmin is negative, whereas the initiation location is in the coal-rock interface when α = 0° and β = 0°, 45°, 60°, 90° (Sample 1, 3, 4, 5) indicating that Fmin is positive.
Finally, by comparing the monitor initiation location, the observed initiation location with the variation in mathematical model, we can verify the validity of the mathematical model.Table 3 shows that the experimental results correspond with the theoretical calculations, indicating that the three-dimensional initiation location model for cross-measure HF can be applied in engineering.Thirdly, the tracer material in the samples can be observed for judging the initiation location.The initiation location conditions for the five types of samples are shown in Table 3.The experiment results show that initiation location is in the coal seam only when α = 0° and β = 30° (Sample 2), indicating that Fmin is negative, whereas the initiation location is in the coal-rock interface when α = 0° and β = 0°, 45°, 60°, 90° (Sample 1, 3, 4, 5) indicating that Fmin is positive.
Finally, by comparing the monitor initiation location, the observed initiation location with the variation in mathematical model, we can verify the validity of the mathematical model.Table 3 shows that the experimental results correspond with the theoretical calculations, indicating that the three-dimensional initiation location model for cross-measure HF can be applied in engineering.Finally, by comparing the monitor initiation location, the observed initiation location with the variation in mathematical model, we can verify the validity of the mathematical model.Table 3 shows that the experimental results correspond with the theoretical calculations, indicating that the three-dimensional initiation location model for cross-measure HF can be applied in engineering.

Figure 1 .
Figure 1.Diagram showing the relative positions of a hydraulic fracture borehole and a coal seam.(a) Graph showing a 3D view of hydraulic fracture; (b) graph showing a profile view of hydraulic fracture borehole from the seam inclination direction.

Figure 2 .
Figure 2. Diagram showing the stress state in a hydraulic fracture borehole wall when the borehole is perpendicular to the coal seam.

Figure 1 .
Figure 1.Diagram showing the relative positions of a hydraulic fracture borehole and a coal seam.(a) Graph showing a 3D view of hydraulic fracture; (b) graph showing a profile view of hydraulic fracture borehole from the seam inclination direction.

Figure 1 .
Figure 1.Diagram showing the relative positions of a hydraulic fracture borehole and a coal seam.(a) Graph showing a 3D view of hydraulic fracture; (b) graph showing a profile view of hydraulic fracture borehole from the seam inclination direction.

Figure 2 .
Figure 2. Diagram showing the stress state in a hydraulic fracture borehole wall when the borehole is perpendicular to the coal seam.

Figure 2 .
Figure 2. Diagram showing the stress state in a hydraulic fracture borehole wall when the borehole is perpendicular to the coal seam.

Figure 3 .
Figure 3. Schematic block diagrams showing the principle stress states of normal, reverse, and strike-slip faults.σH and σh are the major and minor horizontal principal stresses, σv is the vertical principal stress.

Figure 3 .
Figure 3. Schematic block diagrams showing the principle stress states of normal, reverse, and strike-slip faults.σ H and σ h are the major and minor horizontal principal stresses, σ v is the vertical principal stress.

Figure 4 .
Figure 4. Graph showing Fmin variation in three different faults.(a) Graph showing Fmin variation with α in a normal fault; (b) graph showing Fmin variation with β in a normal fault; (c) graph showing Fmin variation with α in a reverse fault; (d) graph showing Fmin variation with β in a reverse fault; (e) graph showing Fmin variation with α in a strike-slip fault; and (f) graph showing Fmin variation with β in a strike-slip fault.

Figure 4 .
Figure 4. Graph showing F min variation in three different faults.(a) Graph showing F min variation with α in a normal fault; (b) graph showing F min variation with β in a normal fault; graph showing F min variation with α in a reverse fault; (d) graph showing F min variation with β in a reverse fault; (e) graph showing F min variation with α in a strike-slip fault; and (f) graph showing F min variation with β in a strike-slip fault.

Figure 6 .
Figure 6.Photograph of 7 cm cubes of coal seam simulation material.The numbers on the cubes represent the different coal: cement; gypsum ratios used to manufacture the test cubes.

Figure 7 .
Figure 7. Photograph of five specimens used for hydraulic fracture testing.The specimens are 300 mm cubes and each has a fracturing pipe protruding from the top.The specimens were all made with the simulated coal seam dipping at 20° but each specimen was tested under a different principal stress (the "β = x" number shown for each specimen).

Figure 6 .
Figure 6.Photograph of 7 cm cubes of coal seam simulation material.The numbers on the cubes represent the different coal: cement; gypsum ratios used to manufacture the test cubes.

Energies 2016, 9 , 358 Figure 6 .
Figure 6.Photograph of 7 cm cubes of coal seam simulation material.The numbers on the cubes represent the different coal: cement; gypsum ratios used to manufacture the test cubes.

Figure 7 .
Figure 7. Photograph of five specimens used for hydraulic fracture testing.The specimens are 300 mm cubes and each has a fracturing pipe protruding from the top.The specimens were all made with the simulated coal seam dipping at 20° but each specimen was tested under a different principal stress (the "β = x" number shown for each specimen).

Figure 7 .
Figure 7. Photograph of five specimens used for hydraulic fracture testing.The specimens are 300 mm cubes and each has a fracturing pipe protruding from the top.The specimens were all made with the simulated coal seam dipping at 20 ˝but each specimen was tested under a different principal stress (the "β = x" number shown for each specimen).

Figure 9 .
Figure 9. Location of acoustic emission (AE) sensors on the HF test sample (a) and block diagrams (b)showing AE-recorded event sites and a photograph of a fracture surface in the tested specimen.A tracer was introduced into the fracturing fluid and the presence of the tracer material (light brown in the photograph) on the fracture surface verifies that the AE events recorded the fracture initiation sites and fracture shape well.

Figure 10 .
Figure 10.Graph showing the variation in theoretical fracture initiation location.For values of β between 7° and 41°, Fmin is negative and fractures will initiate in the coal seam.For all other values of β, Fmin is positive and fractures initiate in the coal-rock interface.

Figure 9 .
Figure 9. Location of acoustic emission (AE) sensors on the HF test sample (a) and block diagrams (b) showing AE-recorded event sites and a photograph of a fracture surface in the tested specimen.A tracer was introduced into the fracturing fluid and the presence of the tracer material (light brown in the photograph) on the fracture surface verifies that the AE events recorded the fracture initiation sites and fracture shape well.

Energies 2016, 9 , 358 10 Figure 9 .
Figure 9. Location of acoustic emission (AE) sensors on the HF test sample (a) and block diagrams (b)showing AE-recorded event sites and a photograph of a fracture surface in the tested specimen.A tracer was introduced into the fracturing fluid and the presence of the tracer material (light brown in the photograph) on the fracture surface verifies that the AE events recorded the fracture initiation sites and fracture shape well.

Figure 10 .
Figure 10.Graph showing the variation in theoretical fracture initiation location.For values of β between 7° and 41°, Fmin is negative and fractures will initiate in the coal seam.For all other values of β, Fmin is positive and fractures initiate in the coal-rock interface.

Figure 10 .
Figure 10.Graph showing the variation in theoretical fracture initiation location.For values of β between 7 ˝and 41 ˝, F min is negative and fractures will initiate in the coal seam.For all other values of β, F min is positive and fractures initiate in the coal-rock interface.

Figure 11 .
Figure 11.Block diagrams showing acoustic emission event time sequences.The block diagrams in (a) represent time progressions during the experimental run from T = 50 s on the left to T = 56 s on the right and (b) from T = 64 s on the left to T = 70 s on the right.Figure11ashows events for a samples with φ = 20°, β = 30°, and the locations of the AE events indicate that the fractures initiated in the coal seam.Figure11bshows a sample with φ = 20°, β = 90°, and for this sample the fractures initiated in the coal-rock interface.The green numbered dots are the locations of the AE sensors.

Figure 11 .
Figure 11.Block diagrams showing acoustic emission event time sequences.The block diagrams in (a) represent time progressions during the experimental run from T = 50 s on the left to T = 56 s on the right and (b) from T = 64 s on the left to T = 70 s on the right.Figure11ashows events for a samples with ϕ = 20 ˝, β = 30 ˝, and the locations of the AE events indicate that the fractures initiated in the coal seam.Figure11bshows a sample with ϕ = 20 ˝, β = 90 ˝, and for this sample the fractures initiated in the coal-rock interface.The green numbered dots are the locations of the AE sensors.

Figure 11 .
Figure 11.Block diagrams showing acoustic emission event time sequences.The block diagrams in (a) represent time progressions during the experimental run from T = 50 s on the left to T = 56 s on the right and (b) from T = 64 s on the left to T = 70 s on the right.Figure11ashows events for a samples with φ = 20°, β = 30°, and the locations of the AE events indicate that the fractures initiated in the coal seam.Figure11bshows a sample with φ = 20°, β = 90°, and for this sample the fractures initiated in the coal-rock interface.The green numbered dots are the locations of the AE sensors.

11 EnergiesFigure 11 .
Figure 11.Block diagrams showing acoustic emission event time sequences.The block diagrams in (a) represent time progressions during the experimental run from T = 50 s on the left to T = 56 s on the right and (b) from T = 64 s on the left to T = 70 s on the right.Figure11ashows events for a samples with φ = 20°, β = 30°, and the locations of the AE events indicate that the fractures initiated in the coal seam.Figure11bshows a sample with φ = 20°, β = 90°, and for this sample the fractures initiated in the coal-rock interface.The green numbered dots are the locations of the AE sensors.

11 EnergiesFigure 11 .
Figure 11.Block diagrams showing acoustic emission event time sequences.The block diagrams in (a) represent time progressions during the experimental run from T = 50 s on the left to T = 56 s on the right and (b) from T = 64 s on the left to T = 70 s on the right.Figure11ashows events for a samples with φ = 20°, β = 30°, and the locations of the AE events indicate that the fractures initiated in the coal seam.Figure11bshows a sample with φ = 20°, β = 90°, and for this sample the fractures initiated in the coal-rock interface.The green numbered dots are the locations of the AE sensors.

11 EnergiesFigure 11 .
Figure 11.Block diagrams showing acoustic emission event time sequences.The block diagrams in (a) represent time progressions during the experimental run from T = 50 s on the left to T = 56 s on the right and (b) from T = 64 s on the left to T = 70 s on the right.Figure11ashows events for a samples with φ = 20°, β = 30°, and the locations of the AE events indicate that the fractures initiated in the coal seam.Figure11bshows a sample with φ = 20°, β = 90°, and for this sample the fractures initiated in the coal-rock interface.The green numbered dots are the locations of the AE sensors.

11 EnergiesFigure 11 .
Figure 11.Block diagrams showing acoustic emission event time sequences.The block diagrams in (a) represent time progressions during the experimental run from T = 50 s on the left to T = 56 s on the right and (b) from T = 64 s on the left to T = 70 s on the right.Figure11ashows events for a samples with φ = 20°, β = 30°, and the locations of the AE events indicate that the fractures initiated in the coal seam.Figure11bshows a sample with φ = 20°, β = 90°, and for this sample the fractures initiated in the coal-rock interface.The green numbered dots are the locations of the AE sensors.

Table 1 .
Basic mechanical parameters of the samples used in the HF tests.

Table 1 .
Basic mechanical parameters of the samples used in the HF tests.

Table 1 .
Basic mechanical parameters of the samples used in the HF tests.

Table 3 .
Monitor results for initiation locations.

Table 3 .
Monitor results for initiation locations.

Table 3 .
Monitor results for initiation locations.

Table 3 .
Monitor results for initiation locations.

Table 3 .
Monitor results for initiation locations.

Table 3 .
Monitor results for initiation locations.

Table 3 .
Monitor results for initiation locations.