Rock Mech Rock Eng DOI 10.1007/s00603-017-1213-3

ORIGINAL PAPER

Hydraulic Fracture Propagation Through an Orthogonal Discontinuity: A Laboratory, Analytical and Numerical Study Ella Marı´a Llanos1 • Robert G. Jeffrey2 • Richard Hillis1,3 • Xi Zhang4

Received: 25 April 2016 / Accepted: 27 March 2017  Springer-Verlag Wien 2017

Abstract Rocks are naturally fractured, and lack of knowledge of hydraulic fracture growth through the preexisting discontinuities in rocks has impeded enhancing hydrocarbon extraction. This paper presents experimental results from uniaxial and biaxial tests, combined with numerical and analytical modelling results to develop a criterion for predicting whether a hydraulic fracture will cross a discontinuity, represented at the laboratory by unbonded machined frictional interfaces. The experimental results provide the first evidence for the impact of viscous fluid flow on the orthogonal fracture crossing. The fracture elliptical footprint also reflects the importance of both the applied loading stress and the viscosity in fracture propagation. The hydraulic fractures extend both in the direction of maximum compressive stress and in the direction with discontinuities that are arranged to be normal to the maximum compressive stress. The modelling results of fracture growth across discontinuities are obtained for the locations of slip starting points in initiating fracture crossing. Our analysis, in contrast to previous work on the prediction of frictional crossing, includes the non-singular stresses generated by the finite pressurised hydraulic fracture. Experimental and theoretical outcomes herein suggest that hydraulic fracture growth through an orthogonal

& Ella Marı´a Llanos [email protected] 1

The University of Adelaide, Adelaide, SA, Australia

2

Strata Control Technology (SCT), Bendigo, VIC, Australia

3

Deep Exploration Technologies CRC (DET-CRC), Adelaide, SA, Australia

4

Commonwealth Scientific and Industrial Research Organization (CSIRO), Clayton, VIC, Australia

discontinuity does not depend primarily on the interface friction coefficient. Keywords Hydraulic fracturing  Numerical modelling  Laboratory experiments  Naturally fractured reservoirs

1 Introduction Although natural fractures (NFs) have been studied for a long time (Pollard and Aydin 1988), the understanding of their impact on hydraulic fracture (HF) growth remains a scientific challenge and has been addressed in the past by means of field (Jeffrey et al. 1992, 1993; van As and Jeffrey 2002), laboratory (Warpinski and Teufel 1987; Bahorich et al. 2012; Bunger et al. 2015), and numerical and analytical (Zhang et al. 2004, 2005a, b; Dahi Taleghani and Olson 2014; Lavrov et al. 2016) studies. The possible interactions between a HF and a NF can be classified as crossing, opening or arresting (Blanton 1982). There are several methods for detecting and characterising HF–NF interaction in the subsurface which range from extrapolation of surface observations to sophisticated seismic and electromagnetic geophysical measurements (Long et al. 1996). Real-time microseismic data have been used to monitor the propagation of HFs in petroleum and geothermal wells (Maxwell et al. 2002; Hasting et al. 2011; McMahon and Baisch 2013) and are an important tool to characterise the HF shape that develops. Llanos et al. (2015) used the areal extent of the seismic cloud to define the area of stimulated porosity and permeability and used the permeability anisotropy ratio (Holl and Barton 2015) as input in the simulation model of the Habanero geothermal field in Australia. The results of this type of modelling feed into financial models when making decisions about future

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large-scale commercial development. Extremely sensitive tiltmeters can also be placed on the surface of the ground to monitor the dip, dip direction and volume of HFs (Lecampion et al. 2005). These monitoring methods in interpreting HF shapes also require detailed study of HF–NF interaction. In the design of a hydraulic fracturing treatment, it is important to know the conditions at which the abovementioned fracture interaction behaviours could occur so that precautions can be taken or the treatment design altered. Criteria to predict whether a HF will cross a pre-existing discontinuity have been developed [e.g. Renshaw and Pollard (R&P) 1995; Blanton 1986; Gu and Weng (G&W) 2010; Sarmadivaleh and Rasouli (S&R) 2013]. However, these criteria do not consider the effects of fluid viscosity and finite HF size. In building a parametric model for understanding the problem of fracture interaction, the effects of stresses, geometry and fracture properties need to be included (Chuprakov et al. 2010). These initial efforts lead to the development of an analytical model called OpenT (Chuprakov et al. 2013a, b), which is sensitive to fracture parameters such as width, length, height and opening. OpenT also takes account of how the conditions of fluid injection such as pump rate and viscosity influence the interaction and has been integrated into Schlumberger’s unconventional fracturing design model (UFM), which is capable of simulating complex fracture network propagation in a NF environment (Kresse et al. 2013). When applied to HFs, the R&P (1995) criterion suggests that HFs can grow through NFs if the slippage can be prevented on the cohesionless NF before a new fracture can be initiated on the other side of the interface. G&W (2010) and S&R (2013) extended the R&P (1995) criterion to include HF crossing of frictional interfaces with cohesion at non-orthogonal intersection angles. R&P (1995) required that the tensile stress acting parallel to the interface, hence producing a new fracture perpendicular to the interface, matches the tensile strength of the rock. However, G&W (2010) required that the maximum tensile principal stress must equal the rock tensile strength for a new fracture to initiate on the opposite side of the interface. This tensile stress may not be perpendicular to the interface. The difference in the fracture initiation angle is reflected in the results, which suggest that for orthogonal cases a lower stress ratio (as defined by R&P (1995) in Sect. 3) is required for crossing to occur according to the G&W (2010) criterion when compared to the R&P (1995) criterion. On the other hand, Blanton (1986) developed a model to evaluate fracture nucleation along a partially opened NF under the shear stress loading conditions. His analysis does not include the stress change caused by the interaction between a HF and a NF, as the HF is not present.

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Blanton’s model provides an alternative to consider new fracture initiation after R&P (1995) criterion is not met. However, neither R&P (1995) nor Blanton (1986) considered fluid viscosity effects on crossing behaviour and the interface, curvature and roughness, which could result in a stress concentration and promote or retard crossing. van As and Jeffrey (2002) compared their results from the study in Northparkes E26 mine (Australia) to the R&P (1995) crossing criterion which predicts the HF would cross the NFs oriented perpendicular to the maximum principal stress and would be arrested by the NFs oriented perpendicular to the intermediate principal stress. At the mine site, crossing occurred in both directions and observations of the mapped fracture may have been circular or elliptical in plan view. Having a clear understanding of the effect of the stress field on the obtained HF shape is important for the design of borehole layout for preconditioning treatments (van As and Jeffrey 2002). The results by Chuprakov et al. (2013a, b) agree with experiments by Blanton (1986), Warpinski and Teufel (1987) and Gu et al. (2011). OpenT considers re-initiation and offsetting to occur at the end of the opened zone of the interface. While Blanton (1986) assumed re-initiation would always occur in the sliding zone. It must be remembered that the HF is absent in Blanton’s model. Chuprakov and Prioul (2015) developed the FracT and LamiFrac models. The former is an improved version of OpenT as it considers non-uniform opening of the HF. Like OpenT, FracT considered a pressurised HF that has grown into a NF to form an approximate T-shape geometry. Chuprakov and Prioul (2015) found that both the size of the slip zone and the HF width increase with the net pressure. Lamifrac allows numerical simulations of the 3D planar HF propagation through several weak bonded discontinuities. This paper reports experimental and numerical results to extend R&P’s (1995) work. Consideration is limited to orthogonal crossing. A comparison to works by Blanton (1986), G&W (2010), Chuprakov et al. (2010) and OpenT (Chuprakov et al. 2013a, b) is also presented. The effects of applied stress, fluid viscosity and slippage are considered with regard to the interaction between HFs and NFs. Following Detournay (2004), the work was done by carrying out experiments for conditions where the energy to propagate the HF was dominated either by fracture growth (toughness dominated, TD) or by viscous dissipation (viscosity dominated, VD). This work considers how the features of NFs may influence fracture crossing. The attention is also paid to what happens in the experiments where HFs in a naturally fractured rock tend to be more elongated in the maximum principal stress direction. The slip initiation prior

Hydraulic Fracture Propagation Through an Orthogonal Discontinuity: A Laboratory, Analytical… Table 1 Physical properties of the Donnybrook sandstone and of the fracturing fluid Donybrook sandstone

Fracturing fluid

Porosity / (%)

15

Density q (gm cm-3)

Poisson’s ratio m

0.28

Viscosity l (Pa s)*At

Young’s modulus E (GPa)

7.0

Injection rate Q (ml s-1)

0.0158 20.0

Permeability K (mD) Discontinuity friction coefficient (m)*From Tensile strength (T0)*From

Brazilian tests

Fracture toughness (KIC)*From

triaxial tests

(MPa)

Lim’s method

(MPa Hm)

1.42 20 C

1; 100

5–50

Fluid temperature T (C)

0.4–0.6

Injection volume/uniaxial test (ml)

12.5

4.40

Injection volume/biaxial test (ml)

25.0, 40.0

0.58

Fluid behaviour

Newtonian

to fracture crossing is studied using numerical and analytical methods. The experiments were conducted at the Hydraulic Fracturing Laboratory at CSIRO, and the numerical modelling was done by using CSIRO’s 2D HF modelling code called MineHF2D.

2 Laboratory Method 2.1 Material Properties and Preparation Uniaxial and biaxial tests were carried out using a honey-based fluid of different viscosities as the injection fluid for fracturing stacks of sandstone plates subjected to different stress conditions. The material properties are summarised in Table 1. A blue dye added to the injection fluid helped identifying the post-test fracture propagation path. It was found that local imperfections on the plate surface could produce stress concentrations and affect crossing. Therefore, before testing, the slabs were ground flat to less than 0.02 of a millimetre across each face.

Fig. 1 From left to right a crossing case—lateral view; b noncrossing case—lateral view

2.2 Sample Dimensions During the preliminary testing phase, five 12 9 12 9 4 cm plates were used in uniaxial tests (Fig. 1), but stress concentrations around the borehole affected the crossing behaviour. Therefore, an initial biaxial test was carried out using a set of nine 36 9 40 9 4 cm thick plates. The central and two neighbouring plates were cemented together to simulate a monolithic thicker central layer (Fig. 2). Significant fluid loss into the cement was observed after testing. In order to avoid any stress disturbance from the hole affecting the stress on the first interface, the final testing phase consisted of uniaxial tests that were run using a set of six 20 9 20 9 4 cm slabs with a 10-cm-thick central slab (Fig. 3). Likewise, the final test block configuration for the biaxial tests consisted of six 36 9 40 9 4 cm plates and a 12-cm-thick central slab.

Fig. 2 Intial testing configuration and borehole details for biaxial setup

The results presented in this paper correspond only to the experiments conducted with the geometry configuration for the final testing phase.

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Fig. 3 Central slab and borehole details as designed for uniaxial setup

2.3 Borehole Details A 22-mm hole was drilled in each central slab and cased with a 20-mm polyvinyl chloride (PVC) tube glued with epoxy and sealed at the bottom with a rubber cap (Fig. 3). A notch required for HF initiation was afterwards created and its final depth into the cased borehole wall varied between 3 and 5 mm. To initiate a HF in the stacked slabs, pressurised fluid must be supplied specifically at the interval containing the borehole notch. This is achieved by means of an o-ring straddle injection tool that isolates the outlets of the fluid injection system (Fig. 4). For the biaxial tests, two notches were machined at 15 and 25 cm below the top of the borehole (Fig. 2), which allowed two fracture tests to be carried out in each block. For the uniaxial tests, each wellbore contained one machined circumferential notch located at 6 cm below the top of the borehole (Fig. 3). 2.4 Laboratory Setup and Procedure The setup as depicted in Fig. 5 consisted of a positive displacement pump connected to a cylindrical fluid separation vessel, containing water on the pump side and the fracturing fluid on the injection tool side. The tool was placed in the borehole, and then the sample was axially compressed in a computer-controlled load frame. Stainless steel tubes were used as connectors between the pump, the

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Fig. 4 Fracturing fluid injection tool

vessel and the injection tool. Transducers were used for monitoring pressure and temperature. Uniaxial experiments were conducted using a 150 kN servo-controlled compression frame (Fig. 6) which consists of a movable bottom plate pushing towards a fixed top steel plate. The biaxial experiments were carried out in a polyaxial frame with a safe working load of 4000 kN in each direction. The small gap between the rock sample for the biaxial tests and the metal plates was filled with flat jacks, i.e. two stainless steel sheets with their edges welded together. Flat jacks have two fluid filling points which allow initial filling of the jack via one port while bleeding air from the other. Teflon sheets between the sample and the steel plates or flat jacks minimised induced frictional shear stress between the platens and the rock. The plane of the notches caused the fractures to initiate in the x–z plane and ry was zero. The procedure started with the use of the R&P (1995) criterion for estimating the rx stress required for crossing to occur (Fig. 1a or b) in the uniaxial setup. The estimated stress required for crossing to occur was then used to establish initial stress conditions for these tests and later for the biaxial tests. After completion, the blocks were carefully cut to measure fracture shape and extent (Fig. 7).

Hydraulic Fracture Propagation Through an Orthogonal Discontinuity: A Laboratory, Analytical…

Fig. 5 Laboratory setup

Fig. 6 From left to right Uniaxial and biaxial experimental setup, respectively

Fig. 7 Fracture growth through discontinuities: biaxial test

3 Laboratory Results The R&P (1995) crossing criterion is (rx/ (T0 ? ry) [ (m ? 1)/3m) with the left-hand side of this expression providing a ‘‘crossing stress ratio’’ (CSR), which predicts crossing to occur when the inequality is

correct. The coefficient of friction of the interface is given by m in this expression. In the laboratory, ry = 0 was used for all tests. For the uniaxial tests, using the sandstone material properties, crossing was expected if the CSR was greater than 0.9, which is predicted to represent a condition where slip does not occur on the interface before the tensile strength (T0) of the rock is exceeded on the far side of the interface. The results as summarised in Tables 2 and 3 report which interface was crossed based on the post-test visual inspection along the plane x–z. Referring to Fig. 8, if the fracture was contained in the central slab (with its midplane numbered as 4) the result was reported as noncrossing (labelled by ‘‘none’’ in the table). The dotted red ellipse shows the third interface being crossed (3 in the table) while the fuchsia coloured line (dash) represents a case where the fracture grew further and extended to the second plate (2, 3 in the table). The solid thin blue ellipse depicts a case where growth was observed through interfaces 3 and 5.

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E. M. Llanos et al. Table 2 Summary of experimental data: uniaxial tests for fluid with 1 and 100 Pa s viscosity Experiment (with 1 Pa s)

rx (MPa)

CSR

Interface crossed

Experiment (with 100 Pa s)

rx (MPa)

CSR

Interface crossed

D1

5

1.14

None

D7

5.0

1.14

None

D2

6

1.36

None

D8

5.5

1.25

2, 3

D3

7

1.59

None

D9

6.0

1.36

2, 3

D10

8.0

1.82

2, 3

D4

8

1.82

3

D5

10

2.27

2, 3

D6

12

2.73

2, 3

Table 3 Summary of experimental data: biaxial tests with 1 and 100 Pa s viscosity

Experiment D11

l (Pa.s) 1

rx (MPa)

rz (MPa)

CSR

Notch depth (cm)

Interface crossed

12.0

12.0

2.73

15

3, 5

D12

1

8.0

8.0

1.82

25

3, 5

D13

100

4.0

4.0

0.91

15

3, 5

D14

100

8.0

8.0

1.82

25

3, 5

Fig. 8 Interface crossing cases observed

3.1 Fluid Viscosity Effect Savitski and Detournay (2002) and Detournay (2004) presented the solutions for a penny-shaped HF that grows either in the regime dominated by fluid viscous dissipation or by rock fracture toughness. For a penny-shaped fracture, the value of the dimensionless toughness K can be used to identify the fracture regime for the conditions used, given by K = (t/tmk)1/9, where  1=2 tmk ¼ l05 Q30 E013 =K 018 ; l0 ¼ 12l; ð1Þ   0 2 0 E ¼ E= 1  m ; K ¼ ð32=pÞ1=2 KIC where l is fluid dynamic viscosity; E is Young’s modulus; m is Poisson’s ratio; KIC is fracture toughness; Q0 is volumetric injection rate. When K is larger than about 3, valid when the time t is significantly larger than the characteristic time tmk, the propagation occurs in the TD regime. When K is smaller than about 0.5 (t  tmk), the propagation is in the VD regime. Clearly, the dimensionless

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toughness varies with time for a penny-shaped HF. It is found that the experiment results using the fluid viscosity of 1.0 Pa s were just in the TD regime while using the fluid viscosity of 100 Pa s were in the VD regime, when the time is sufficiently large. The biaxial experiments required 25 ml to reach the VD regime while at least 40 ml was injected for reaching the TD regime. Figure 9a shows one side of the central slab used for experiments D11 and D12 and illustrates the amount of leakoff that occurred. Garagash and Detournay (2000) concluded fluid lag is not relevant for TD fractures. However, fluid lag became significant for the VD cases tested (partly because ry is zero) as shown in Fig. 9b (experiments D13 and D14). Both HFs grew all the way to the left-side edges of the sample while stopped at the rightside boundary where the two vertical red lines are marked. The D13 HF has extended further than the D14 HF. This observation suggests that the HF growth may have been affected by local variation in the sample permeability. However, the larger of the two HFs broke through to the left-side edge of the block. This portion of the HF is believed to be affected by a boundary effect rather than a fluid lag effect, beyond the scope of this study. The size of the HF produced in experiment D13 also became large compared with the distance of the HF to the top of the sample (Fig. 9c) and the interaction with the traction-free surface was attributed to a slight curvature of the HF towards the surface of the block (Bunger 2005). 3.2 Hydraulic Fracture Geometry Observations on the x–z planes showed that a HF provided it interacts with and crosses a same number of NFs in either direction, will tend to grow farther in the direction of the

Hydraulic Fracture Propagation Through an Orthogonal Discontinuity: A Laboratory, Analytical…

Fig. 9 From left to right a fluid leakoff; b lag zone extension with no fluid penetration; c convex surface curvature (looking in -y direction)

Fig. 10 Effect of stress on HF geometry

maximum stress and in the direction with no discontinuities. As the normal stress acting on the interfaces was increased, the ultimate HF extent in that stress direction became larger. A shorter growth extent was observed in the direction associated with HF propagation through discontinuities. This preference in growth resulted in an elliptical HF. A few cases used by the experimental setup regarding the effect of the applied stress on the final geometry (green ellipse) are summarised in Fig. 10 as: •

•

•

Case A The HF crossed interfaces in the r1A direction but grew more quickly along the z axis because there were no interfaces for the HF to cross in that direction. It was elliptical in shape with the shorter dimension along the x axis parallel to r1A. Case B The HF crossed the interfaces perpendicular to r1B more easily, due to the higher stress in this direction. The x axis dimension of the fracture was larger in this ellipse, compared to case A. Case C For the biaxial experiments carried out for this work, two horizontal stresses were identical (i.e. r1C = r2C) while the vertical stress was nil. Although

there is no measured result for a case where r1C > r2C and if discontinuities parallel to r1C are present, from the observations in cases A and B it is concluded that the HF will grow more easily in the direction of larger stress, r1C. It will grow to become elliptical in shape with its long axis parallel to r1C. Figure 11 is a zoomed view of a central plate and two neighbouring plates contained in the sample. The figure compares a circular geometry with the measured elliptical shape. The HF extent was measured and is shown as a solid black line. The circular shape (dashed) is predicted by theory for a HF growing in a homogeneous material. The laboratory HFs are expected to be initially circular in their plan view shape (Bunger et al. 2005). The elliptical shape results from the interaction of the HF with the frictional interfaces. Recent work (Jeffrey et al. 2015) measured the delay associated with hydraulic fractures crossing frictional interfaces, further confirming this result. In the biaxial experiments, the TD HF exhibited an elliptical shape while a more circular shape was apparent in the VD cases.

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figures using black and red solid lines, respectively, showing that both fractures as defined by the leading edge positions, are elliptical in shape. 3.3 Crossing Criteria Comparison

Fig. 11 Fracture circular geometry versus measured elliptical shape in central plate and two boundaries

Figure 12 shows the HF grew further in the z direction than in the x direction when two interfaces were penetrated. The HF propagating in the TD regime required a larger volume of fluid to generate fracture crossing, suggesting a significant portion of the initial 25 ml injected was lost into the interfaces and the rock matrix. This fluid loss into interfaces could be an explanation for the reduced fluid penetration size observed along the interface between slabs 3 and 4. This is more noticeable in experiment D12 (especially at the bottom left side) and may also explain why the HF was not as close to reaching the lower interface (towards 2) compared to the growth of the other end of the ellipse where the HF was near to interface 6. The experiments run under VD conditions show the applied stress had two distinctly different effects on the HF geometry (Fig. 13). For a lower stress, the HF shape is less circular (experiment D13) while for cases under higher compression (experiment D14), the fracture grew more circular. If higher compression had been applied, the HF would have grew further in the x direction, i.e. it would have crossed more interfaces. The ultimate extent of the HF growth without and with fluid lag is presented in both Fig. 12 Experiments using 1.0 Pa s fluid: D11 (left) and D12 (right)

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The results of the experiments are plotted following the R&P (1995), G&W (2010) and Blanton’s (1986) criteria (Figs. 14, 15, 16). Each test is represented by a dot in these figures where red or green dots symbolise non-crossing and crossing cases, respectively. None of the criteria were in agreement with the data obtained from these tests; except for the results from the uniaxial tests run under VD conditions, which seem to fit the R&P (1995) criterion well. The test data suggest a higher normal stress is needed to generate a crossing condition than what is predicted by the criteria. The laboratory testing undertaken for this work produced four findings: 1.

2.

The higher the normal stress acting across the interfaces is the more likely the HF will cross the interface, consistent with theoretical analyses (for example, R&P 1995). Although more complicated to carry out, the experiments that include a nonzero minimum stress would allow minimising fluid lag and reduce the free surface effect when using a high-viscosity fracturing fluid. The results support the existence of a viscosity effect. Contrary to R&P (1995), the VD HFs crossed the NFs more easily than the TD fractures. A HF propagating in a TD regime is more likely to result in fluid entering and pressurising a NF during the interaction, which serves to reduce the shear strength of the NF and its ability to transmit shear stress into the rock on the other side. A VD fracture is more likely to cross a NF because the fluid is less likely to enter into a discontinuity. This is an important finding of this work and features regarding the interface permeability and its interaction with the injected fluid viscosity need to be accounted for in any crossing criterion. A similar suggestion has been published by Chuprakov et al. (2013a, b) and Bunger et al. (2015).

Hydraulic Fracture Propagation Through an Orthogonal Discontinuity: A Laboratory, Analytical…

σ

σ

σ

σ

Fig. 13 Experiments using 100 Pa s fluid: D13 (left) and D14 (right): ultimate extent of fracture without and with fluid lag (black and red lines, respectively) (colour figure online)

Fig. 14 Uniaxial tests results for fluid with 1 Pa s (left) and 100 Pa s (right) viscosity compared to R&P (1995) and G&W (2010) criteria

Fig. 15 Uniaxial tests results for fluid with 1 Pa s (left) and 100 Pa s (right) viscosity compared to Blanton’s (1986) criterion

3.

The effect of discontinuities on HF propagation was observed as a retarded but stress-dependent growth process. The HF grew further for cases where a higher

normal stress was applied across the discontinuity direction. As normal stress acting on the discontinuities was increased, the ultimate HF length in that

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σ

σ

E. M. Llanos et al.

Fig. 16 Biaxial tests results presented compared to R&P (1995) and G&W (2010) (left) and to Blanton (right)

4.

stress direction becomes larger. The biaxial experiments proved most useful in studying HF growth and shape as affected by the crossing interactions. The R&P (1995) criterion predicts crossing to occur for cases where arresting was the result obtained by uniaxial experiments carried out as part of the testing series completed for this work. Additionally, consistency between crossing and non-crossing cases was not observed in light of these proposed criteria when comparing the uniaxial and the biaxial tests. The biaxial tests showed that crossing occurred for all stress conditions even though the criteria predict a noncrossing case.

•

The interpretation of these findings leads to the following conclusions: •

•

•

The measured HF geometry suggests that: For HF growth, the data from these experiments support the conclusion that an elliptical fracture shape develops as a result of the interaction. Crossing of NFs was enhanced under VD conditions, in part because the high-viscosity fluids were not lost or able to enter into the discontinuity as easily as lowviscosity fluids. However, the VD HF exhibited fluid lag. A lower fluid viscosity was used for the TD tests, but high leakoff of fluid into the moderately permeable sandstone made use of a fluid with less than 1 Pa s viscosity impractical. The crossing conditions derived by R&P (1995) were based on plane-strain assumption with no internal pressure and are applicable to cross-sections of an elliptical HF. The results presented in this paper suggest that the intermediate principal stress in the direction out of the cross-section plays a significant role in the crossing interaction. Hence, a study that includes the effect of 3-D stress states should be carried out.

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As found by Bunger et al. (2015), the crossing of HF through orthogonal discontinuities is not strongly dependant on the friction coefficient of the interface under some circumstances. This finding contradicts several current criteria in which interface friction plays a key role for understanding the HF–NF crossing interaction. Here, this phenomenon is explained by the following consideration. Let us suggest that a new fracture exists on the far side of the closed NF opposite to the HF. The necessary conditions for its existence must satisfy that (1) along the new fracture the net pressure (P - R22) is larger than the tensile strength (T0) and (2) the interface is still fully closed even while the fluid penetrates the interface to exclude the maximum opening stress associated with the OpenT theory. Thus, we have P  R22 [ T0

ð2Þ

P\R11

ð3Þ

Combining the above two inequalities, we find that crossing can occur if the value of CSR is larger than one as given below R11 [ 1; R22 þ T0 •

ð4Þ

which is independent of the coefficient of friction. R&P (1995) and G&W (2010) do not allow for crossing after slip and/or opening has occurred and fluid invasion of the interface has begun, but the laboratory results obtained here show that the HF can cross discontinuities after some fluid penetration into the interface. Some slip is likely to have occurred in such cases although no direct measurements of slip on interfaces were made. This result creates the need for additional studies of the mechanics surrounding frictional crossing interactions with permeable discontinuities.

Hydraulic Fracture Propagation Through an Orthogonal Discontinuity: A Laboratory, Analytical…

4 Mathematical Model and Scaling R&P (1995) assume HF re-initiation is not possible after the occurrence of slip along the NF. However, even though a NF is in a partially sliding stage, tensile stress parallel to the NF at some points can be generated. Indeed, this is the mechanism that the Blanton’s (1986) criterion uses to test for the occurrence of crossing. Only after the entire NF is in slip, will the stress concentration disappear, as studied by Dollar and Steif (1988). Hence, there is potential for fracture re-initiation between the start of slip and the full sliding of the NF. Also, a flaw may exist in the rock on the far side of the NF, which would allow a HF to re-initiate without requiring generation of a tensile stress equal to the tensile strength of the intact rock. Such a variation of tensile strength is not considered in this work, but it must be recognised as a factor that can influence laboratory and field scale results on fracture crossing and interaction. In developing the linear elastic fracture mechanics (LEFM) model, it is assumed that no plastic deformation or energy absorption takes place at the fracture tip. Instead, the material is elastic and energy is used either to elastically deform the material all around the fracture or break the material at the tip. A restriction to the validity of LEFM is the requirement that any plastic deformation be confined to a small process zone at the tip that is encompassed by the region dominated by the elastic stress singularity zone near the fracture tip, although the process zone cannot be neglected in some cases (Papanastasiou 1997). R&P (1995) employed the LEFM-based solutions for the associated singular near-tip elastic stress fields, to calculate the stress at a point on the interface for checking the sliding condition. Hence, many geometric lengths such as finite HF length are not included in their criterion. The associated simplification can certainly cause some mismatch between the predictions and the experimental and field scale results, where the fracture length is constrained. Alternatively, Blanton (1986) has not included the stress induced by the HF itself and assumed that a simplified shear stress distribution exists on the NF in the absence of the HF. Blanton’s (1986) criterion is possibly more correct for fracture initiation from a fault, where slip is remote from any pressurised HF. The effect of fluid viscosity on the stress field around a HF has been shown to be significant as revealed by Lecampion and Zhang (L&Z) (2005) who indicated that a HF propagating in the VD regime would induce slip on the NF more easily than a HF in the TD regime. This conclusion suggests that crossing, according to R&P (1995), should be more difficult for VD HFs. This prediction is not supported by results from the experiments undertaken for this work (Llanos et al. 2006). Therefore, the effect of

viscosity on the crossing interaction is more complicated and cannot be predicted based only on whether or not slip occurs on the NF before the HF intersects it. However, in order to understand the mechanics of HFs crossing NFs, the effect of slip prior to and after intersection should be investigated, especially for the finite-length fracture geometry. In this section, the incipient point of frictional slip is determined by first reformulating the problem and grouping some parameters to form dimensionless terms so as to reduce the number of parameters in the analysis. 4.1 Scaling A uniformly pressurised finite-length fracture approaching perpendicularly to a frictional interface is considered (Fig. 17). A uniform pressure distribution in a HF is equivalent to injecting an inviscid fluid. This pressure distribution is used here because it allows use of a closed-form analytical solution for stresses around the pressurised fracture. Let H and L denote the distance between the closest and furthest tip of the HF from the NF, respectively. H is considered as fixed, and L is increased to study the effect of fracture size. This process generates stresses on the NF that are identical to those produced by moving the near-tip closer to the NF. When the fracture tip moves closer, the stress levels on the NF increase. Or in other words, the length of the NF is considered to be infinite so that incipient slip can occur at any distance to the HF plane. To meet the failure criterion, the pressure in the HF is adjusted to ensure the fracture is always in critical equilibrium at both tips, i.e. the internal pressure Pf is computed so that KI = KIC is satisfied. The parameters used for the problem under the planestrain conditions are therefore: Geometry (H and L); Discontinuity (m friction coefficient); Stress (R11 and R22); Rock properties (E0 Young modulus; m Poisson ratio) and KIC (critical stress intensity factor). Evolution is considered in terms of the change in geometry, namely H is adopted as the evolution parameter. Time is not a parameter of the problem, but the evolution in time can be readily computed a posteriori by dividing the fracture volume by any given constant injection rate Q0. Besides the stress and

Fig. 17 Geometry for the scaling problem definition

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displacement fields (U, V), the solution S of the problem consists in particular of: net fracture pressure (P = Pf - R22); slip initiation point (Y) and maximum tensile stress RImax (or maximum KI) along the other side of the discontinuity, where RI is the most tensile principal stress. Thus the solution is of the form S ¼ F ðH; L; E0 ; m; KIC ; m; R11 ; R22 Þ

ð5Þ

Following the scaling used by Detournay (2004) and Bunger et al. (2005), it is convenient to introduce the following characteristics quantities, namely scaling length (L ) and scaling stress (S ): pffiffiffiffi L ¼ H and R ¼ ðKIC = H Þ ð6Þ Hence, the scaled quantities are:

ð8Þ 

ry ¼ rA ½rc =2r    2 cosðh  hC Þ  2 sin hC sin h  þ sin hR sinðh þ hR  hC Þ þ sin hL sinðh þ hL  hC Þ

ð9Þ sxy ¼ rA ½rc =2r     sin hR cosðh þ hR  hC Þ  þ sin hL cosðh þ hL  hC Þ  2 sin hC cos h ð10Þ where the net pressure is defined as rA ¼ pf  R22 , p  fhC ; hL ; hR ; h g  p and other terms are given by:

2H Xj R Rjj ; xj ¼ ; e ¼ 0 ; rjj ¼ ; HþL H E R RImax P Ys U ; rImax ¼ ; p¼ ; ys ¼ ; u ¼ R eH R H V t¼ eH

h¼

pffiffiffiffiffiffiffiffiffi rL rR ; pffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2 þ y2 ; rC ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rL ¼ ðx þ aÞ2 þ y2 ; qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rR ¼ ðx  aÞ2 þ y2 ;

r ¼

So that fys ; p; rImax g ¼ Uðh; e; r11 ; r22 ; m; mÞ:

rx ¼ rA þ rA ½rc =2r     2 cosðh  hC Þ þ 2 sin hC sin h   sin hR sinðh þ hR  hC Þ  sin hL sinðh þ hL  hC Þ

ð7Þ

It is possible to see a reduction in the number of controlling parameters by 2 after comparing Eqs. 5 and 7. The effect of r22 is expected to enter only via its influence on the net pressure and in the computation of rImax. The evolving non-dimensional parameter in Eq. 7 is h to highlight how close the fracture tip is from the discontinuity. In addition, the effect of m is not significant, as it is only included in the plane-strain modulus E0 . The end of the elastic regime corresponds either to the onset of slip or opening on the discontinuity and it is the part of solution, as was done by L&Z (2005), but is recast using the dimensionless formalism presented above to provide a full picture. The elastic regime corresponds to the range for the evolving parameter hp \ h \ 1 where the elastic limit is of the form hp = hp(r11, m). The subscript p when applied to h stands for the onset of frictional slip on the natural fracture. In this work only the onset of slip is evaluated, and therefore the method is valid if m \ ms (r11) (initial slip regime).

1 h ¼ ðhL þ hR Þ; 2 hC ¼ tan1 ½y=x; hL ¼ tan1 ½y=ðx þ aÞ;

ð11Þ

hR ¼ tan1 ½y=ðx  aÞ;

In order to find the incipient slip location, the effective normal stress and the corresponding net frictional stress are calculated based on Coulomb’s frictional law at any position y along the discontinuity in terms of Eqs. 12 and 13, Effective normal stress :

fx ðrA ; R11 ; a; yÞ ¼ rx  R11 ð12Þ

Net frictional stress : gðrA ; R11 ; a; y; mÞ ¼ sxy  mfx ðrA ; R11 ; a; yÞ

ð13Þ

where rx and sxy are known from Eqs. 8 and 10 and a ¼ ðLHÞ 2 . However, Eq. 13 contains two variables ( a, y) and can only be solved numerically at a given H. An alternative way is to find the location of the maximum in net frictional stress along the discontinuity. The slip should occur first at this location. Therefore, the incipient slip location can be found numerically. In particular, this approach leads to

4.2 Analytical Solution Method The onset of slip is estimated analytically using the geometry illustrated in Fig. 18. The stress components for a uniformly pressurised fracture are considered (Eqs. 8–10; Weertman 1996). These equations are valid for a mode I fracture in an infinite linear elastic solid, or when there is no relative displacement along the NF. The subscripts L and R refer to the left and right hand HF tip, respectively, while the C stands for the centre of the HF.

123

Fig. 18 Geometry of the problem for the analytical calculation of hp

Hydraulic Fracture Propagation Through an Orthogonal Discontinuity: A Laboratory, Analytical…

hðrA ; R11 ; a; y; mÞ ¼ oy gðrA ; R11 ; a; y; mÞ ¼ 0

ð14Þ

Additionally, the stress field depends on the net pressure in the HF. Based on the failure criterion, the net pressure can be calculated using Eq. 15. Moreover, the solutions on y are only dependent on the stress ratio R11/rA. The dimensionless parameter, S, is introduced as an alternative for this stress ratio and is defined in Eq. 16. KIC rA ¼ pffiffiffiffiffiffi p a sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R11 2H S¼ rA pðL  HÞ

ð15Þ

ð16Þ

4.3 Numerical Solution Method The analytical results obtained from the model described in Sect. 4.2 are validated and compared to results obtained using the fully coupled numerical hydraulic fracture model MineHF2D in the following. The numerical model can calculate the onset of slippage on the NF as a HF grows towards it based on the slip magnitude at the middle of an element. In particular, MineHF2D uses an algorithm based on a fixed grid with constant displacement discontinuities to solve the elastic equations coupled to a finite difference scheme for the fluid flow within the fracture. The model checks the slippage condition based on Coulomb’s friction law. Explicitly, if the shear stress at a point reaches the critical value that is equal to the product of the coefficient of friction and the effective normal stress equal to the difference of the normal stress and fluid pressure, a sliding mode is present at that point on the natural fracture. The shear strength thus varies with the normal stress at each position, since the normal stress is dependent on the hydraulic and natural fracture interaction. For the numerical simulations, the material properties and the boundary conditions imposed were chosen to represent those as used in the laboratory. To comply with the assumptions used in analytical solutions, the fluid flow in the fractures is based on the uniform pressure assumption in MineHF2D. And the propagation criterion KI = KIC is satisfied by adjusting the pressure. By satisfying this condition, the HF is maintained in a propagating state, which would be the case for a fracture approaching a NF.

5 Modelling Results In their results for large toughness cases, L&Z (2005) indicate that NFs that are oriented orthogonally with respect to the HF are more stable to induced shear and this increases the chances of crossing. L&Z (2005) also

investigated the governing parameters controlling the beginning of the interaction between a single pre-existing discontinuity and an approaching HF. The onset of the interaction was defined as the first occurrence of slip, i.e. frictional shear strength exceeded by shear stress at a point along the NF. L&Z (2005) do not consider displacement and stress conditions after sliding initiates. Fracture reinitiation may occur after the HF reaches the NF. The elastic limit corresponding to the onset of slip along the discontinuity is determined for TD conditions as per the dimensionless analysis described in the previous section. In order to verify the dependence on the evolving parameter, the analysis was carried out for several different fracture geometries. For the modelling carried out for this work, the definition of the onset of the interaction as described by L&Z (2005) is followed. This section reports on the numerical and analytical results for the onset of slip. The evolution parameter hp defining the beginning of the interaction is graphically presented as a function of two dimensionless parameters: the stress ratio and the discontinuity friction coefficient. A small hp value indicates that for slip to occur, the HF’s total length must be large compared to the distance from the closest tip to the discontinuity. As hp increases to 1 the HF’s length relative to H decreases to zero. Conversely, when hp = 0 the HF’s length can be considered to be infinite. Table 4 shows a range of values of L with regard to H and the corresponding scale quantity h. As expected, frictional slip occurs more easily for low stress values and for low values of m in which cases the HF does not need to grow much before slip occurs. As S, the dimensionless stress, increases, the likelihood for slip to develop decreases. The results in Fig. 19 also depict a region where the slope of the curves seems to be insensitive to the coefficient of friction. For the higher dimensionless stress down to S = 0.32, a hp value does not decrease further as m is increased after a critical point. This indicates that for S [ 0.32, hp does not depend on m provided m is [ 0.5. For values of S \ 0.32 and m [ 0.5, which are applicable to sandstones, granites and gneiss, the data vary slowly with m and fall nearly on straight lines indicating a more or less linear behaviour in the hp versus m curves. The independence of hp on m becomes more obvious when presenting the results with respect to the dimensionless stress for different values of friction, as in Fig. 20. For S higher than 0.4 and coefficients of friction Table 4 Values of h for different values of L with regard to H L

H

1.2H

1.5H

1.8H

2.5H

3H

4H

5H

8H

19H

h

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

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E. M. Llanos et al. Fig. 19 Evolution of hp with respect to m for different values of S. Comparison between analytical and numerical results

higher than 0.5, the results indicate slip is prevented by frictional strength developed under high loading conditions since hp is zero. Also, unless the values of m are very small, for values of S higher than 0.4 the chances for slipping occurring are small since H must be very small or L must be very large to produce a nearly zero hp. This implies that for these conditions incipient slip can only occur when the fracture tip is very close or touches on the NF. By using the analytical method, more data can be calculated and therefore smoother curves were obtained. By plotting together the numerical and analytical results, a reasonable match is observed, and the curves show a power–law relationship. The curves in Fig. 20 can be fitted by least squares methods. To reduce the computational burden, the universal curves for hp were fitted to curves. The universal curves can be obtained by using Eq. 17 which can be used for design of industrial HFs to predict potential for fracturing crossing, provided dimensionless friction (m) and stress (S) are given. The application of Eq. 17 assumes slip on the NF is an indicator of a non-crossing interaction, which will not always be the case. A crossing criterion needs to also include effects of opening and crossing after sliding occurs. For example, the lack of sliding of the interface as predicted by this analysis may prove to be sufficient to predict that crossing will occur, but sliding is not sufficient to predict a non-crossing interaction. The values of the fitting coefficients a, b, c, d, e and f are given in Table 5. Alternatively, Eq. 18 can be used to calculate the fitting coefficients. The fitting parameters X0, Y0, A and B are summarised in Table 6. hp ¼

ða þ bS þ cS2 Þ ð1 þ dS þ eS2 þ fS3 Þ

123

ð17Þ

A coefficientða; b; c; d; e; f Þ ¼ Y0 þ  B

1 þ Xm0

ð18Þ

The findings of the modelling undertaken in this work suggest a HF propagating in a TD regime does not need to grow to a large distance before easily inducing irreversible slip on the discontinuity with low coefficients of friction and under low stress loading conditions. As the stress increases a longer HF is required for slip to occur. Slip limited for discontinuities with friction coefficients higher than 0.5 and the crossing conditions tend to follow the condition proposed above independent of the coefficient of friction.

6 Discussion This section presents a comparison of the results found for each stage of the propagation of the HF with Chuprakov et al. (2010), i.e. approaching, contacting and infiltrating a discontinuity. The geometry of the problem addressed by Chuprakov et al. (2010) considers a HF propagating with a uniform inner pressure towards an initially closed NF in an impermeable elastic rock medium. The far field stresses, R11 and R33, act parallel and perpendicular to the HF, respectively. The angle of the HF and R11 with respect to the NF varied from 0 to 90. Similar to the geometry used in this work, the length of the NF was considered infinite. Contact occurs once the HF touches the NF, i.e. when the distance H becomes zero. OpenT considers the HF as semiinfinite. This work considers a finite-length HF and takes account of the stress generated by the entire pressurised HF in predicting slip.

Hydraulic Fracture Propagation Through an Orthogonal Discontinuity: A Laboratory, Analytical… Fig. 20 Evolution of hp with respect to S for different values of m. Comparison between analytical and numerical results

Table 5 Values of fitting coefficients for given values of m

m;

a

b

c

d

e

F

0

1

0

0

0

0

0

0.05

0.989500

-1.09520

0.298100

0.239400

-1.02830

0.504400

0.1

0.990112

-1.64810

0.649261

1.049084

-4.36092

0.2

0.981776

-2.56899

1.645566

1.705347

-9.55252

18.97925

0.3 0.4

0.984751 1.003887

-2.82950 -3.15526

1.967569 2.362533

3.045700 4.382706

-17.9869 -27.1852

52.34666 83.31532

0.5

0.985954

-3.19942

2.474528

4.247058

-25.1014

0.6

0.985585

-3.24377

2.546011

4.703988

-27.7665

114.0495

0.7

0.985366

-3.29767

2.631914

5.032807

-30.0283

129.9824

0.8

0.984056

-3.31565

2.665303

5.213019

-30.5647

139.3449

0.9

0.985049

-3.34779

2.713770

5.477470

-32.7733

152.5022

1.0

0.984991

-3.40850

2.809477

5.594832

-34.0346

159.1824

Table 6 Values of fitting parameters

a

B

C

A

0.0000001

3.564932

B

0.0000001

1.299716

X0

0.0000001

0.102898

Y0

0.9884000

-3.57958

6.1 HF Approaching a Discontinuity In this initial stage, Chuprakov et al. (2010) focused on opening and/or slippage along the NF. Chuprakov and Prioul (2015) offer an explicit formula for the length of the slip zone, which they calculate only after contact has occurred. Chuprakov et al. (2010) observed that once the NF slips the tensile stress on the opposite side of the interface quickly increases. Their model is able to predict

d 2.864705

-1.82130

e 6.082595

-1.83157

0.183256

0.299919

0.008881

0.060368

4.939399

94.07905

f 34.67183 2.171063 0.289484

-34.9528

196.0379 -2.06646 0.491851 -1.68097

the onset of a new tensile fracture, generated at the tips of the open zone along the NF (Chuprakov et al. 2010). This open zone requires fluid infiltration to occur before it can grow further. However, Chuprakov et al. (2010) assumed no fluid pressurisation in the discontinuity once it opens as the HF approaches it. The reason for this has to do with leakoff not being considered in the model. The issue of leakoff has been addressed by Chuprakov and Prioul (2015). As presented in Sect. 3, a HF propagating in a TD

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E. M. Llanos et al.

regime is more likely to enter and pressurise a NF during this phase, which serves to reduce the shear strength of a NF and its ability to transmit shear stress into the rock on the other side. Similarly, Eq. 17 allows determining the initiation of slip away from the intersection point if desired. Such a crossing process would allow a potential offset to develop. The fracture re-initiation site must be found using a model such as MineHF2D or OpenT and assuming what conditions are favourable for the fracture to re-initiate and continue propagating in the original direction. Contrary to Blanton (1986), the study by Chuprakov et al. (2010) suggests the normal and shear stress profiles along the discontinuity during the interaction are more parabolic than linear. The same feature was observed in the numerical study carried out for this work, as presented in more detail in Llanos (2015).

6.3 HF Infiltrating a Discontinuity Chuprakov et al. (2010) studied two cases: fluid leaking into the fault with lag possible and secondly no fluid allowed into the NF. They found that at sufficiently small injection rates the HF is arrested for conditions that allow fluid to infiltrate into the discontinuity. For larger injection rates, the HF reinitiates at the NF after the contact. Additionally, Chuprakov et al. (2013a, b) found that both OpenT and MineHF2D predicted crossing for higher fracturing fluid viscosity with less sensitivity to the relative stress difference. The experimental results of this work confirm this and it is found that VD fractures seemed to cross NFs more easily than TD fractures especially as the loading stress increased. 6.4 Application

6.2 HF Contacting a Discontinuity Chuprakov et al. (2010) considered a uniformly pressurised HF, as has been done in this work. This enlarges the open zone and positions the tensile stress peak at the end of the open zone along the NF. At this point in the process, they found that the tangential stress reaches its maximum possible values. This point also corresponds to the most likely point for a tensile fracture to be created on the far side of the NF. They also assumed that at this stage, the HF touches the fault without crossing it directly. With regard to the coefficient of friction of the NF, Chuprakov et al. (2010) concluded that it plays a role on the fracture interaction problem only when it is low enough (less than 0.6) for a shear zone to develop ahead of the tensile zone. For values of coefficients of friction higher than 0.6 they concluded only a tensile fracture propagates and the fracture offset is small. According to OpenT, the chances of a NF with a coefficient of friction of 0.5 being crossed by a HF are directly proportional to the HF’s length and normal crack displacement (opening). Likewise, the shorter the HF’s length and opening at the contact with the discontinuity, the more difficult it will be for crossing to occur, even at 90 approach angle. The parameter ‘‘b’’ in Blanton’s (1986) criterion depends on the coefficient of friction and the lengths of the opening and slippage zones along the NF. The coefficient of friction is also highlighted in those models depending on slip initiation (for example, R&P 1995). The impact of the coefficient of friction, fracture length and stress on the interaction problem were analysed in the modelling undertaken in this work. The outcome indicates a TD HF does not need to grow much before inducing irreversible slip on a discontinuity with a coefficient of friction below 0.5 and under low normal loading conditions. The insensitive nature of fracture crossing on the coefficient of friction is also supported by our experimental results.

123

It is often assumed that in enhanced geothermal systems (EGS) stimulation occurs mainly through induced slip on discontinuities and that propagation of new fractures from a slipping NF plays a minor role. McClure and Horne (2013, 2014) refer to this concept as ‘‘pure shear stimulation’’ (PSS), which is possible if the fluid pressure is maintained below the minimum principal stress during the stimulation, for example, when the crack tip is far away from the wellbore. In order for PSS to happen, the discontinuity must have an adequate storativity and initial transmissivity and early-time tensile fracture growth is necessary to create a conductive channel for fluid flow by crossing and connecting natural fractures. This is very important for fracture propagation near the injection well surrounded by NFs (Zang et al., 2014). McClure and Horne (2013, 2014) found that high injection rates help the HFs propagate through the NF. They also concluded that as a result of high injection rates, the chances of PSS is higher in areas with thick faults like Soultz, Cooper Basin, Basel and Fjallbacka. This is consistent with our findings that the leakoff into the NF can be limited if the injection rate is increased. Reid et al. (2011) reported that the fracture treatment at the Paralana geothermal field was carried out at a pressure above the minimum principal stress and the HF formed by that stimulation had proppant placed into it.

7 Conclusions The more accurate prediction of HF interaction with a NF is an important area of research in hydraulic fracturing, especially since naturally fractures shale reservoirs use hydraulic fracture stimulation as a primary tool. The numerical and analytical analysis of slip initiation demonstrate some important concepts and lead to a set of

Hydraulic Fracture Propagation Through an Orthogonal Discontinuity: A Laboratory, Analytical…

universal curves for predicting initial interface slip. The experimental results have shown that frictional interfaces interacting with the in situ stress and the hydraulic fracture affect the overall fracture growth. The results show that use of a fluid with higher viscosity can promote a crossing interaction to occur. Further areas of research to be undertaken by extending the work presented in this paper include: experimental consideration to oblique intersection cases as well as to use triaxial rather than just biaxial stress conditions; further laboratory and numerical exploration of the impact of intermediate and vertical loading stresses on the fracture propagation with appropriate failure criteria applied accordingly; connection between sliding of the interface and the propensity for crossing and including the interface permeability as a parameter in the experiments. Thus, this work helps in understating some important concepts in the complex problem of the hydraulic/NF interaction as well as giving rise to opportunities for further research. Acknowledgements Ella Marı´a Llanos would like to thank the coauthors for their guidance and understanding during her PhD, summarised in this paper. Special thanks to CSIRO and Schlumberger Moscow for their financial support as well as to The Endeavour International Postgraduate Research and The University of Adelaide scholarships. Thanks as well to Leo Connelly, Nigel Smith, Anthony Coleman and all the staff at the Hydraulic Fracturing Laboratory at CSIRO.

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