TY - JOUR
AU - Liang,, Hao
AB - Abstract In the Xu5 formation the sandstone reservoir and the shale reservoir are interbedded with each other. The average thickness of each formation is about 8 m, which increases the difficulty of the hydraulic fracturing treatment. The shale thickness ratio (the ratio of shale thickness to formation thickness) is 55–62.5%. The reservoir is characterized by ultra-low porosity and permeability. The brittleness index of sandstone is 0.5–0.8, and the brittleness index of shale is 0.3–0.8. Natural fractures are poorly developed and are mainly horizontal and at a low angle. The formation strength is medium and the reservoir is of the hybrid strike-slip fault and reverse fault stress regime. The difference between the minimum principal stress and the vertical stress is small, and the maximum horizontal principal stress is 20 MPa higher than the minimum horizontal principal stress and vertical stress. A mechanical model of a hydraulic fracture encountering natural fractures is built according to geological characteristics. Fracture mechanics theory is then used to establish a hydraulic fracturing model coupling the seepage–stress–damage model to simulate the initiation and propagation of a fracture. The hydraulic fracture geometry is mainly I-shaped and T-shaped, horizontal propagation dominates the extension, and vertical propagation is limited. There is a two to three meter stress diversion area around a single hydraulic fracture. The stress diversion between a hydraulic fracture and a natural fracture is advantageous in forming a complex fracture. The research results can provide theoretical guidance for tight reservoir fracturing design. sand-shale interbed, engineering geological characteristics, fracture propagation, strike-slip fault stress regime, reverse fault stress regime 1. Introduction With the aggressive exploitation of conventional oil and gas resources, it has been difficult for this conventional energy to meet the needs of industrial development. As typical unconventional energy, shale gas and tight sandstone gas has attracted more and more attention (Guo and Zhao 2012). The Upper Triassic Xu5 group is a sand and shale interbedded reservoir with ultra-low porosity and ultra-low permeability, which can be classified into three types of formation by the mud it contains: mud-rich type, sand-rich type and sand-shale interbedded type. This field has huge proven reserves and is an important block for Sinopec Southwest Oil and Gas Company. The effect of multistage fracturing performed previously in this field was not positive and there was serious production decline and severe water production due to improper fracturing design without clear understanding of the reservoir characteristics and fracture geometry. The key questions regarding the Xu5 formation are as follows. (i) What is the propagation mechanism and the penetration of fracture in sand-shale interbedded formation, and will the fracture be able to penetrate the shale? (ii) What is the fracture geometry and will it be able to form a complex fracture network? (iii) What is the stress interference between fracture networks if it is possible to form the fracture network? Daneshy (1978) carried out experimental research on fracture propagation in layered formations. He found that the distribution of the formation cannot completely restrict the height of a fracture (Daneshy 1978). Lu and Erdogan (1979) studied the influence of the fracture strength factor and the modulus of elasticity on fracture propagation in a layered formation based on fracture mechanics theory (Lu and Erdogan 1979). Warpinski et al (1982) pointed out that in situ stress is the predominant factor affecting fracture geometry. The fracture is difficult to extend when the stress intensity factor of the fracture tip is close to zero, according to fracture mechanics theory. The stress intensity factor is reduced when the fracture penetrates from a formation with a high elastic modulus to a formation with a lower elastic modulus, and the expansion of the fracture would be blocked (Lu and Erdogan 1979, Leguillon et al2000). It was found that the hydraulic fracture would penetrate and extend to the formation with the higher elastic modulus, based on laboratory experiments and field hydraulic fracturing phenomena (Daneshy 1978, Shaffer et al1980, Warpinski et al1982, Teufel and Clark 1984). The stress intensity factor increases when the fracture propagates from the formation with the low elastic modulus into the formation with the higher one, and the fracture would penetrate into the formation with the higher elastic modulus via the contacting surface (Thiercelin et al1989). Smith et al (2001) found that the top and bottom widths of the fracture narrowed when passing through hard formation (Smith et al2001). Gu and Siebrits (2008) studied hydraulic fracture propagation in layered formations of different elastic modulus with 3D hydraulic fracturing simulation software (Gu and Siebrits 2008). All the researchers studied fracture extension geometry in the adjacent two or three layers based on the formation elastic modulus and in situ stresses. The characteristics of the Xu5 formation cannot be fully reflected and natural fractures are not taken into account. The commonly used hydraulic fracturing design software is built on the basis of simple plane fracture models like PKN and KGD. These software packages cannot reflect the physical nature of fracture propagation because they are unable to take the spatially flexural propagation process of fracture into account and the consideration of interactional mechanics of the hydraulic fracture and natural fracture is insufficient (Hossain et al2000, King 2010, Meyer and Bazan 2011, Weng et al2011). A numerical simulation method combining the stress field with the intensity factor at the fracture tip can effectively solve the complex mechanical problems of the hydraulic fracture propagation together with the natural fracture. As for hydraulic fracture simulation, many scholars have put forward various numerical methods, such as the finite element method (Rahman et al2009, Nassir et al2010), the finite difference method (Nagel et al2013), the boundary element method (Rahman et al2002, Hossain and Rahman 2008), the displacement discontinuity method (DDM) (Zhang et al2007, 2009, Kresse et al2013), the discrete element method (DEM) (Nagel et al2011a, 2011b) and the extended finite element method (Taleghani 2009). The existing hydraulic fracturing calculation software includes FLAC3D (Rahman et al2002), RFPA (Tang et al2002, Yang et al2004), Abaqus (Chen et al2009, Zhang et al2010, Wang and Dahi Taleghani 2012), U/3DEC (Nagel et al2011a, 2012) and so on. FLAC3D is a professional geotechnical analysis software using the finite difference method to simulate rock mass strength size/time effect and fields coupling (water-temperature-force coupling), but the operability of the software interface is not strong. The software RFPA2D/3D, developed by Tang Chunan from Northeastern University, China, is for rock failure process analysis in hydraulic fracturing, based on the flow–stress–damage coupling model (FSD model) (Tang et al2002, Wang et al2009), but the material constitutive model adopted is too simplified. U/3DEC is software based on the discrete element method, which has a certain advantage in hydraulic fracturing in a naturally fractured shale gas reservoir, but it is not suitable for sand-shale interbedded formation reservoirs like the Xu5 formation (Nagel et al2012). The hydraulic fracturing module, Abaqus, based on the linear elastic fracture mechanics theory, simulates the hydraulic fracture initiation and extension as well as tangential flow and normal filtration of fracturing fluid in the hydraulic fracture by adopting the cohesive element damage model. Chen et al (2009) simulated the 2D fracture radial initiation and extension using a cohesive pore pressure unit and the simulation results and the K-vertex analytical solutions matched perfectly (Chen et al2009). Yao et al (2010) simulated hydraulic fracturing in plastic formation using a cohesive unit and found that the result from Abaqus is closer to the analytical solution than the P3D model or the PKN model in plastic formation (Yao et al2010). Yuan et al (2013a, 2013b), using the Abaqus fluid-structure coupling module, studied stress and pore pressure distribution in the process of fracturing, aimed at a tight reservoir in midwest Sichuan, but the dynamic extension process of hydraulic fracture and natural fracture, and the interference between multiple hydraulic fractures, were not considered. On the basis of the characteristics of the sand-shale interbedded formation reservoir in the Xu5 formation, a propagation model of a hydraulic fracture encountering a low angle natural fracture is established. Then the cohesive damage pore pressure unit of the Abaqus software is used to simulate a hydraulic fracture and a natural fracture; the seepage–stress–damage model of hydraulic fracture propagation is proposed. And a further study of the mechanical mechanisms of fracture propagation, fracture geometry and the mutual interference mechanism of multi-fracture is carried out, which can provide a theoretical basis to the development of tight sandstone gas in the Xu5 formation. 2. Engineering geological characteristics of the Xu5 formation 2.1. Basic geological characteristics Xu5 can be further divided into three submembers: the upper, middle and lower submembers (figure 1). The yellow stripes represent the sandstone and the other colored stripes represent carbonate-rich shales (calcarenite) and coaly shales. For the upper submember, the average thickness is 180 m; the thickness of the sand is greater as it’s getting closer to the top boundary, its average thickness being 10–30 m. The sand is mainly made of fine grain sandstone. The environment of this submember includes an underwater distributary’s channel and an estuary dam in the delta frontier. The average thickness of shale is 112 m, and the shale thickness ratio is 62.5%. For the middle submember, the average thickness is 200 m. The sandstone layer is thin and limey (muddy); its thickness is about 0.5–5 m and its shape is lenticular. This submember is mainly lacustrine shale deposition (condensation section); the average thickness of the shale is 155 m, and the shale thickness ratio is 76.8%. For the lower submember, the average thickness is 130 m. It includes lacustrine shale with a delta front underwater distributary channel and mouth bar deposition. The sand is relatively continuous; the closer to the bottom boundary, the greater the thickness of the sandstone body. The stratigraphic distribution is comparatively stable, and is an interbedded formation, of non-uniform thickness, of gray, dark gray, and black gray shale and gray and dark gray powder—fine sandstones. The shale thickness ratio is 55.4%. The seismic waves primarily reflect that the sand is continuous and the reflection is strong. This submember is a typical sand-shale interbedded formation reservoir. Figure 1. Open in new tabDownload slide Geologic model of the Xu5 formation. The shale thickness ratio of upper, middle and lower submember is 62.5%, 76.8% and 55.4%, respectively. Sandstone and shale are shown by yellow and blue, respectively (Gan et al2009). Figure 1. Open in new tabDownload slide Geologic model of the Xu5 formation. The shale thickness ratio of upper, middle and lower submember is 62.5%, 76.8% and 55.4%, respectively. Sandstone and shale are shown by yellow and blue, respectively (Gan et al2009). The Xu5 formation can be divided into three geological types by the mud content: mud-rich type, sand-shale interbedded type and sand-rich type. The mud-rich type formation occurs mainly in the middle submember. The maximum thickness of single sand is less than 6 m, so the mud-rich type formation can be simplified into a 6 m sandstone and 9 m shale interbed geologic model. For sand-rich formation, the maximum thickness of single sand is greater than or equal to 10 m, so it can be simplified into a 10 m sandstone and 6.7 m shale interbed geological model. Sand-shale interbedded formation occurs mainly in the lower submember; the thickness of single sand is 6–10 m, so the sand-shale interbedded type can be simplified into a 8 m sandstone and 8 m shale interbed geologic model. Figures 2 is a sand-shale interbedded formation outcrop of the Lianhua profile (located in Dujiangyan city, Sichuan province). The lithology of the outcrop is gray powder—a fine sandstone and black gray shale interbed with non-uniform thicknesses, whose thickness is 3–5 m. Figure 2. Open in new tabDownload slide Lotus section outcrop of sand-shale interbedded formation. Figure 2. Open in new tabDownload slide Lotus section outcrop of sand-shale interbedded formation. 2.2. Reservoir lithology characteristic We carry out x-ray diffraction quantitative analysis on rock samples of the sand-shale interbedded formation reservoir using an x-ray diffractometer (D/MAX 2500) (Zhu et al2012). The average percentage of clay in the eight gray sandstone samples is 19.86%, quartz is 48.73%, feldspar is 2.96%, carbonate is 21.81% and the brittleness mineral is 73.5%. The average percentage of clay in the seven black shale samples is 44.37%, quartz is 28.66%, feldspar is 4.42%, carbonate is 18.2% and the brittleness mineral content is 51.3%. The percentage of brittle mineral in gray sandstone is greater than in black shale, and the compressibility is also greater (figure 3). According to the Rickman et al (2008) method of calculating the brittleness index based on mineral components (Rickman et al2008), the brittleness index of sandstone is 0.5–0.8, with an average of 0.65. The brittleness index of the shale is 0.3–0.8, with an average of 0.57; higher than American Barnet shale (Sone 2012, Jin et al2014). Figure 3. Open in new tabDownload slide Mineral constituent triangular chart for HF-2 well. Figure 3. Open in new tabDownload slide Mineral constituent triangular chart for HF-2 well. Eight gray sandstone samples are analyzed using x-ray diffraction. The average percentage of chlorite is 9.75%, illite 38.13%, kaolinite 13.50% and illite/smectite mixed layer 38.63%. There are seven black shale samples and the results show that the average percentage of chlorite is 9.71%, illite 31.14%, and illite/smectite mixed layer 38%. The average percentage of chlorite in gray shale is 29%, illite 36.6%, kaolinite 8.87% and illite/smectite layer 50.34%. We can see that the clay composition in black shale, gray shale and gray sandstone is nearly the same except for the illite/smectite mixed layer. 2.3. Physical properties of the reservoir The porosity of gray sandstone is 1.79–3.04% and the average is 2.50%; the porosity of black shale is 2.215–3.807% and the average is 3.08%. Overall, the porosity of sandstone and shale is similar in the Xujiahe dense formation. The permeability of gray sandstone is 0.006–0.0975 mD and the average is 0.0152 mD; the permeability of black shale is 0.002–0.2398 mD and the average is 0.0655 mD. Nano–micro level organic matter pores in shale are well developed, the aperture is less than 200 nm, and 1.2 µm at the most. Nano CT scanning porosity is 4.85%. The aperture of the intergranular pore and the organic pore developed in black gray siltstone is 0.05–0.4 µm, and the porosity is 4.17% (figure 4). The total organic carbon (TOC) content is 2.35%. Vitrinite reflectance is 1.13%. Overall, the permeability of black shale is better than that of gray tight sandstone. The overall characteristics of the reservoir are ultra-low porosity and ultra-low permeability. Figure 4. Open in new tabDownload slide Nano CT scan result of black gray shale at a well depth of 3290.31 m in the XC28 well. Figure 4. Open in new tabDownload slide Nano CT scan result of black gray shale at a well depth of 3290.31 m in the XC28 well. 2.4. Characteristics of natural fractures The term ‘horizontal fracture’ means the angle between the fracture and the horizontal direction is less than 5°; a ‘low angle fracture’ means the angle is greater than 5° and less than 45°; a ‘high angle fracture’ means the angle is greater than 45° and less than 85°; a ‘vertical fracture’ means the angle is greater than 85°. From the 161 fractures observed in cores, there are nine vertical fractures (about 5.6%), 24 high angle fractures (about 14.9%), 95 low angle fractures (about 59.0%), and 33 horizontal fractures (about 20.5%) (figure 5). It can be seen that the fractures are mainly low angle and horizontal. The fractures are mainly developed in shale and fine sandstone, accounting for 37.9% and 53.4% of the total fractures respectively. Horizontal fractures and low angle fractures are mainly filling fractures, while vertical fractures and high angle fractures are mainly non-filled. The core fracture fillings are mainly carbonaceous (about 45.3% of total fractures), followed by the carbon and calcite filling (about 23.6%). In addition, there are calcite fillings or half fillings (about 7.4%). The width of the fractures are uniform; about 65.8% of the fractures have a width of 0–0.5 mm, and the greatest width is 1 cm. Figure 5. Open in new tabDownload slide Distribution characteristics of natural fractures. (a) A horizontal natural fracture exists in gray fine sandstone in a well depth of 3048.97–3049.47 m at the HF-1 well; the fracture is filled with carbonaceous material and calcite; (b) a 25° natural fracture exists in argillaceous siltstone in a well depth of 3295.53–43295.74 m at the XC28 well; the fracture is also filled with carbonaceous material and calcite; (c) a 65° natural fracture exists in gray argillaceous siltstone in a well depth of 3354.1–43354.56 m at the XC33 well; the fracture is an open and non-filled fracture; (d) a vertical natural fracture exists in black shale in a well depth of 3043.87–3043.98 m of the HF-1 well; the fracture is also an open and non-filled fracture. Figure 5. Open in new tabDownload slide Distribution characteristics of natural fractures. (a) A horizontal natural fracture exists in gray fine sandstone in a well depth of 3048.97–3049.47 m at the HF-1 well; the fracture is filled with carbonaceous material and calcite; (b) a 25° natural fracture exists in argillaceous siltstone in a well depth of 3295.53–43295.74 m at the XC28 well; the fracture is also filled with carbonaceous material and calcite; (c) a 65° natural fracture exists in gray argillaceous siltstone in a well depth of 3354.1–43354.56 m at the XC33 well; the fracture is an open and non-filled fracture; (d) a vertical natural fracture exists in black shale in a well depth of 3043.87–3043.98 m of the HF-1 well; the fracture is also an open and non-filled fracture. The electron microscope scanning result shows that there is intergranular fracture in the shale formation and the width ranges from 0.6 to 25 µm (figure 6). According to logging interpretation, the number of natural fractures is less than 0.2 per meter, on average, in the mud-rich formation, there are 0.2–0.35 natural fractures per meter, on average, in the sand-shale interlayered formation, and more than 0.35 natural fractures per meter in the sand-rich reservoir. Figure 6. Open in new tabDownload slide Intergranular fracture in shale. Figure 6. Open in new tabDownload slide Intergranular fracture in shale. 2.5. Rock mechanical characteristics 2.5.1. Compressive strength. Twelve cores from the 3045–3360 m sand-shale interlayered formation section of Xu5 were processed into samples with a length/diameter ratio of 1.8–2.0. The test equipment being used is the RTR-1000 triaxial rock mechanics testing system and the experimental results are shown in table 1. According to the change rule of axial strain and the radial strain rule along the axial load, the stress–strain curve is obtained (figure 7). The difference in the stress–strain characteristics of sand and shale is clear, the elastic deformation stage of sandstone and the plastic deformation of shale is evident, and the plasticity of shale is significantly stronger than sandstone. The yield stress and yield strain increase with the increase in confining pressure. The yield stress order of different stone is: quartz and lithic sandstone > siltstone > shale. Under geological conditions, the difference in yield stress is nearly three times, and the difference in yield strain is four times. The plastic strain of sandstone is less than for shale. The plasticity of shale is strong under geological conditions. Table 1. Experimental results of rock mechanics parameters. Well . Lithology . Depth (m) . Effective confining pressure (MPa) . Compressive strength (MPa) . Elasticity modulus (GPa) . Poisson’s ratio . Cohesion MPa . φ (°) . XC28 Siltstone 3293.73  0  39.49 13.72 0.412 14.53 38.19 3293.98 12 160.27 38.74 0.331 3293.30 22 118.97 19.39 0.279 3293.27 32 200.32 42.12 0.086 XC33 Shale 3353.68  0  11.76 11.29 0.285 5.19 27.77 3355.03 12  67.98 22.61 0.298 3355.03 22  59.32 14.51 0.294 3355.08 32 110.91 17.69 0.310 HF-2 Quartz and lithic sandstone 3063.02  0  40.61 39.65 0.208  5.34 45.96 3063.20 12  86.03 38.94 0.211 3063.80 22 142.85 41.60 0.269 3063.35 32 239.56 37.88 0.487 Well . Lithology . Depth (m) . Effective confining pressure (MPa) . Compressive strength (MPa) . Elasticity modulus (GPa) . Poisson’s ratio . Cohesion MPa . φ (°) . XC28 Siltstone 3293.73  0  39.49 13.72 0.412 14.53 38.19 3293.98 12 160.27 38.74 0.331 3293.30 22 118.97 19.39 0.279 3293.27 32 200.32 42.12 0.086 XC33 Shale 3353.68  0  11.76 11.29 0.285 5.19 27.77 3355.03 12  67.98 22.61 0.298 3355.03 22  59.32 14.51 0.294 3355.08 32 110.91 17.69 0.310 HF-2 Quartz and lithic sandstone 3063.02  0  40.61 39.65 0.208  5.34 45.96 3063.20 12  86.03 38.94 0.211 3063.80 22 142.85 41.60 0.269 3063.35 32 239.56 37.88 0.487 Open in new tab Table 1. Experimental results of rock mechanics parameters. Well . Lithology . Depth (m) . Effective confining pressure (MPa) . Compressive strength (MPa) . Elasticity modulus (GPa) . Poisson’s ratio . Cohesion MPa . φ (°) . XC28 Siltstone 3293.73  0  39.49 13.72 0.412 14.53 38.19 3293.98 12 160.27 38.74 0.331 3293.30 22 118.97 19.39 0.279 3293.27 32 200.32 42.12 0.086 XC33 Shale 3353.68  0  11.76 11.29 0.285 5.19 27.77 3355.03 12  67.98 22.61 0.298 3355.03 22  59.32 14.51 0.294 3355.08 32 110.91 17.69 0.310 HF-2 Quartz and lithic sandstone 3063.02  0  40.61 39.65 0.208  5.34 45.96 3063.20 12  86.03 38.94 0.211 3063.80 22 142.85 41.60 0.269 3063.35 32 239.56 37.88 0.487 Well . Lithology . Depth (m) . Effective confining pressure (MPa) . Compressive strength (MPa) . Elasticity modulus (GPa) . Poisson’s ratio . Cohesion MPa . φ (°) . XC28 Siltstone 3293.73  0  39.49 13.72 0.412 14.53 38.19 3293.98 12 160.27 38.74 0.331 3293.30 22 118.97 19.39 0.279 3293.27 32 200.32 42.12 0.086 XC33 Shale 3353.68  0  11.76 11.29 0.285 5.19 27.77 3355.03 12  67.98 22.61 0.298 3355.03 22  59.32 14.51 0.294 3355.08 32 110.91 17.69 0.310 HF-2 Quartz and lithic sandstone 3063.02  0  40.61 39.65 0.208  5.34 45.96 3063.20 12  86.03 38.94 0.211 3063.80 22 142.85 41.60 0.269 3063.35 32 239.56 37.88 0.487 Open in new tab Figure 7. Open in new tabDownload slide Stress–strain curve of shale in sand-shale interbedded formation. Figure 7. Open in new tabDownload slide Stress–strain curve of shale in sand-shale interbedded formation. The breaking strength under different confining pressures can be obtained by a tri-axial compressive strength test. We can obtain the internal friction angle and cohesion by regressing the experimental data based on the Mohr–Coulomb criterion. The Mohr–Coulomb criterion is expressed in terms of principal stress: σ1=σ3ctg2(45°-ϕ2)+2Cctg(45° -ϕ2),1 where C is cohesive force (MPa), φ is the internal friction angle (degrees), σ1 is the maximum principal stress (MPa), and σ3 is the minimum principal stress (MPa). In general, the internal friction of rock can be determined by two or more triaxial compression strength experiments under different confining pressure. 2.5.2. Shear strength. The shear test apparatus and the theory of the sand-shale reservoir is shown in figure 8 (Yan et al2014). The shear test results are shown in table 2. Rock shear strength is smaller than its compressive strength. For the sand-shale interbedded formation reservoir, the average shear strength of sandstone is 14.74 MPa and the internal friction angle is 42.91°. The average shear strength of shale is 5.19 MPa and the internal friction angle is 27.77°. Table 2. Direct shear strength test results. Well . Lithology . Depth (m) . Volume density (g cm-3) . Normal stress σ (MPa) . Top shear stress τ (MPa) . Top shear strength . C (MPa) . ϕ (°) . XC33 sandstone 3355.42–3355.90 2.64  6.76 22.99 16.34 44.17 2.70  8.73 24.14 2.88 18.03 34.40 2.64 22.68 39.81 2.62 26.89 41.10 HF-2 sandstone 3081.17–3081.61 2.67  9.05 31.05 22.74 43.30 2.66 13.49 37.75 2.67 18.05 37.57 2.67 22.63 42.26 2.67 26.82 49.93 Well . Lithology . Depth (m) . Volume density (g cm-3) . Normal stress σ (MPa) . Top shear stress τ (MPa) . Top shear strength . C (MPa) . ϕ (°) . XC33 sandstone 3355.42–3355.90 2.64  6.76 22.99 16.34 44.17 2.70  8.73 24.14 2.88 18.03 34.40 2.64 22.68 39.81 2.62 26.89 41.10 HF-2 sandstone 3081.17–3081.61 2.67  9.05 31.05 22.74 43.30 2.66 13.49 37.75 2.67 18.05 37.57 2.67 22.63 42.26 2.67 26.82 49.93 Open in new tab Table 2. Direct shear strength test results. Well . Lithology . Depth (m) . Volume density (g cm-3) . Normal stress σ (MPa) . Top shear stress τ (MPa) . Top shear strength . C (MPa) . ϕ (°) . XC33 sandstone 3355.42–3355.90 2.64  6.76 22.99 16.34 44.17 2.70  8.73 24.14 2.88 18.03 34.40 2.64 22.68 39.81 2.62 26.89 41.10 HF-2 sandstone 3081.17–3081.61 2.67  9.05 31.05 22.74 43.30 2.66 13.49 37.75 2.67 18.05 37.57 2.67 22.63 42.26 2.67 26.82 49.93 Well . Lithology . Depth (m) . Volume density (g cm-3) . Normal stress σ (MPa) . Top shear stress τ (MPa) . Top shear strength . C (MPa) . ϕ (°) . XC33 sandstone 3355.42–3355.90 2.64  6.76 22.99 16.34 44.17 2.70  8.73 24.14 2.88 18.03 34.40 2.64 22.68 39.81 2.62 26.89 41.10 HF-2 sandstone 3081.17–3081.61 2.67  9.05 31.05 22.74 43.30 2.66 13.49 37.75 2.67 18.05 37.57 2.67 22.63 42.26 2.67 26.82 49.93 Open in new tab Figure 8. Open in new tabDownload slide Principle of direct shear experiment. 1. Positioning bolt hole. 2. Immobile indenter. 3. Mobile indenter. 4. Piston connected with hand-held pump. 5. Mobile indenter connected with the jack. 6. Core sample. 7. Base frame. Figure 8. Open in new tabDownload slide Principle of direct shear experiment. 1. Positioning bolt hole. 2. Immobile indenter. 3. Mobile indenter. 4. Piston connected with hand-held pump. 5. Mobile indenter connected with the jack. 6. Core sample. 7. Base frame. 2.5.3. Tensile strength. Cut about 25–45 mm of the core, flatten both ends of the core and around the outside. In the center of the sample with a diameter of 100 mm, drill a round hole with a diameter of 16 mm, and then make a prefracture of about 2 mm parallel to the central axis of the hole, along the radial direction of hole wall, so as to make the initial fracture length in the stable extension area (Chen and Zhang 2004, Zhao and Chen 2006). The experimental procedure is similar to the Brazilian disc test; the sample is loaded under nonconfining pressure until its failure. The tensile strength of sandstone is obviously higher than that of shale, as is shown in table 3. The experimental tensile strength of sandstone varies from 4.00– to 7.08 MPa, and the average value is 5.54 MPa. The experimental tensile strength of mudstone varies from 1.20– to 2.32 MPa, and the average value is 1.68 MPa. Table 3. Tensile strength test results. Lithology . Well number . Thickness (mm) . Diameter (mm) . Load (KN) . Tensile strength (MPa) . Average tensile strength (MPa) . Shale 1 23.67 99.30 5.6260 1.52 1.68 2 25.10 98.20 8.9860 2.32 3 43.80 99.16 8.1720 1.20 Sandstone 1 17.92 25.30 8.49 7.08 5.54 2 17.65 25.30 5.76 4.00 Lithology . Well number . Thickness (mm) . Diameter (mm) . Load (KN) . Tensile strength (MPa) . Average tensile strength (MPa) . Shale 1 23.67 99.30 5.6260 1.52 1.68 2 25.10 98.20 8.9860 2.32 3 43.80 99.16 8.1720 1.20 Sandstone 1 17.92 25.30 8.49 7.08 5.54 2 17.65 25.30 5.76 4.00 Open in new tab Table 3. Tensile strength test results. Lithology . Well number . Thickness (mm) . Diameter (mm) . Load (KN) . Tensile strength (MPa) . Average tensile strength (MPa) . Shale 1 23.67 99.30 5.6260 1.52 1.68 2 25.10 98.20 8.9860 2.32 3 43.80 99.16 8.1720 1.20 Sandstone 1 17.92 25.30 8.49 7.08 5.54 2 17.65 25.30 5.76 4.00 Lithology . Well number . Thickness (mm) . Diameter (mm) . Load (KN) . Tensile strength (MPa) . Average tensile strength (MPa) . Shale 1 23.67 99.30 5.6260 1.52 1.68 2 25.10 98.20 8.9860 2.32 3 43.80 99.16 8.1720 1.20 Sandstone 1 17.92 25.30 8.49 7.08 5.54 2 17.65 25.30 5.76 4.00 Open in new tab 2.6. In situ stress distribution characteristics The maximum horizontal in situ stress direction of the HF-1 and HF-2 wells is almost east-west, and its azimuth angle is about 103 ± 6°, according to the transverse wave and imaging log interpretation. The in situ stresses of the sand-shale interbedded formation reservoir are tested by the Kaiser effect tests. Results show that the in situ stress pattern of the Xu5 formation is the coexistence of the strike-slip fault stress regime and the reverse fault stress regime, and the extrusion stress is high (table 4). Table 4. Test results of in situ stresses. Lithology . Well depth (m) . Vertical stress (MPa) . Maximum horizontal principal stress (MPa) . Minimum horizontal principal stress (MPa) . Shale 3059.11 63.06  99.35 55.67 Shale 3060.35 62.35  95.09 55.77 Sand 3050.89 62.71 121.7 67.85 Lithology . Well depth (m) . Vertical stress (MPa) . Maximum horizontal principal stress (MPa) . Minimum horizontal principal stress (MPa) . Shale 3059.11 63.06  99.35 55.67 Shale 3060.35 62.35  95.09 55.77 Sand 3050.89 62.71 121.7 67.85 Open in new tab Table 4. Test results of in situ stresses. Lithology . Well depth (m) . Vertical stress (MPa) . Maximum horizontal principal stress (MPa) . Minimum horizontal principal stress (MPa) . Shale 3059.11 63.06  99.35 55.67 Shale 3060.35 62.35  95.09 55.77 Sand 3050.89 62.71 121.7 67.85 Lithology . Well depth (m) . Vertical stress (MPa) . Maximum horizontal principal stress (MPa) . Minimum horizontal principal stress (MPa) . Shale 3059.11 63.06  99.35 55.67 Shale 3060.35 62.35  95.09 55.77 Sand 3050.89 62.71 121.7 67.85 Open in new tab Tectonic movement and anisotropy of the shale only affect the frame stress and do not affect the pore pressure, according to effective stress theory in porous media (except for abnormally high pressure caused by tectonic movement). The above two factors and the Biot coefficient are regarded as the weight numbers of effective stress and pore pressure in the calculation of the horizontal stress, combined with the inclination of the formation. The formula to calculate the principal stress of any inclined formation is as follows (Yuan et al2013a): {σv=∫0Dρ(z)gdzσH=[vvE(1−ν)Ev+A](σv−αPp)cos ψ+(σv−αPp)sin ψ cos (ω−ωo)+αPpσh=[vvE(1−ν)Ev+B](σv−αPp)cos ψ+(σv−αPp)sin ψ sin (ω−ωo)+αPp,2 where D is the well depth; A, B are tectonic stress coefficients; E, Ev, υ, vv are elastic parameters of transverse isotropic formation, respectively; ψ is dip angle; ω is the dip direction; wo is orientation of the maximum horizontal stress; σv is the vertical stress; σh is the minimum horizontal principal stress; σH is the maximum horizontal principal stress. According to conventional well logging curves like acoustic logging, density, porosity, and natural gamma ray, and combining the results of the indoor Kaiser experiment and the filler experiment, the longitudinal stress profile of the X26 well is shown in figure 9. The vertical stress gradient is 2.40–2.43 MPa/100 m, the maximum and minimum horizontal stress gradients are 2.58–3.33 MPa/100 m and 2.22–2.36 MPa/100 m respectively, the difference coefficient of horizontal stress is 0.21–0.34, with an average of 0.29. The conclusion can be draw that the mode of formation is the hybrid strike-slip and reverse fault stress regime. Yuan et al (2013b) also proved that the Xu5 formation is the hybrid strike-slip and reverse fault stress regime. Figure 9. Open in new tabDownload slide Longitudinal stresses profile of the XC26 well (GR represents the natural gamma ray). Figure 9. Open in new tabDownload slide Longitudinal stresses profile of the XC26 well (GR represents the natural gamma ray). 2.7. Discussion It can be seen from table 5 that, compared to other typical shale gas reservoirs, the thickness of the Xu5 formation is larger, has more layers in the vertical direction, and that sandstone and shale are interbedded. The reservoir properties are poor and the ground pressure coefficient is higher. The clay content is high in the Xu5 formation, so plasticity is especially strong in shale in in situ stress conditions and the question of whether hydraulic fractures can penetrate shale is unavoidable. As to the hybrid strike-slip and reverse fault stress regime, hydraulic fracture geometry is diverse and this would increase the difficulty of fracturing design. The Xu5 formation is quite different from pure shale and tight sandstone reservoirs in America. The American fracturing experience does not fit well. Table 5. Reservoir properties of Xinchang and typical shale (Curtis 2002. AAPG©(2002) reprinted with permission of the AAPG, whose permission is required for further use). Historic production area . Pike County, Kentucky . Wise County, Texas . Otsego County, Michigan . Harrison County, Indiana . San Juan and Rio Arriba Counties, New Mexico . Oklahoma . British Columbia, Alberta (Adams 2013) . Western Sichuan . Shale reservoir Ohio Barnett Antrim New Albany Lewis Woodford Montney Xu5 Sedimentary type Marine facies Marine facies Marine facies Marine facies M-L facies Marine facies Marine facies Land facies Depth (m) 610–1524 1981–2591 183–730 183–1494 914–1829 1829–3658 1200–3000 2100–3500 Net thickness (m) 9–31 15–60 21–37 15–30 61–91 — 0–300 100–430 TOC (%) 0–4.7 4.5 0.3–24 1–25 0.45–2.5 1–14 0.5–10 2.35 Vitrinite reflectance (% Ro) 0.4–1.3 0.6–1.6 0.4–0.6 0.4–1.0 1.6–1.9 — — 1.13 Brittle mineral (%) 35–50 76.5 45–60 54 50–75 20–40 (quartz, carbonate-free) — 30.2–60.3 Brittle mineral (%) — 23.5 — 35.5 — 25–45 — 35.7 Total porosity (%) 4.7 4–5 9 10–14 3–5.5 3–9 1–10 3.61 Gas content (m3 t-1) 1.68–2.83 8.5–9.9 1.1–2.8 1.1–2.3 0.4–1.3 — — 1.44 Pressure gradient (Kg m-3) 0.35–0.92 1.03 0.81 0.99 — 1.73–2.18 — 1.8–2.0 Historic production area . Pike County, Kentucky . Wise County, Texas . Otsego County, Michigan . Harrison County, Indiana . San Juan and Rio Arriba Counties, New Mexico . Oklahoma . British Columbia, Alberta (Adams 2013) . Western Sichuan . Shale reservoir Ohio Barnett Antrim New Albany Lewis Woodford Montney Xu5 Sedimentary type Marine facies Marine facies Marine facies Marine facies M-L facies Marine facies Marine facies Land facies Depth (m) 610–1524 1981–2591 183–730 183–1494 914–1829 1829–3658 1200–3000 2100–3500 Net thickness (m) 9–31 15–60 21–37 15–30 61–91 — 0–300 100–430 TOC (%) 0–4.7 4.5 0.3–24 1–25 0.45–2.5 1–14 0.5–10 2.35 Vitrinite reflectance (% Ro) 0.4–1.3 0.6–1.6 0.4–0.6 0.4–1.0 1.6–1.9 — — 1.13 Brittle mineral (%) 35–50 76.5 45–60 54 50–75 20–40 (quartz, carbonate-free) — 30.2–60.3 Brittle mineral (%) — 23.5 — 35.5 — 25–45 — 35.7 Total porosity (%) 4.7 4–5 9 10–14 3–5.5 3–9 1–10 3.61 Gas content (m3 t-1) 1.68–2.83 8.5–9.9 1.1–2.8 1.1–2.3 0.4–1.3 — — 1.44 Pressure gradient (Kg m-3) 0.35–0.92 1.03 0.81 0.99 — 1.73–2.18 — 1.8–2.0 Open in new tab Table 5. Reservoir properties of Xinchang and typical shale (Curtis 2002. AAPG©(2002) reprinted with permission of the AAPG, whose permission is required for further use). Historic production area . Pike County, Kentucky . Wise County, Texas . Otsego County, Michigan . Harrison County, Indiana . San Juan and Rio Arriba Counties, New Mexico . Oklahoma . British Columbia, Alberta (Adams 2013) . Western Sichuan . Shale reservoir Ohio Barnett Antrim New Albany Lewis Woodford Montney Xu5 Sedimentary type Marine facies Marine facies Marine facies Marine facies M-L facies Marine facies Marine facies Land facies Depth (m) 610–1524 1981–2591 183–730 183–1494 914–1829 1829–3658 1200–3000 2100–3500 Net thickness (m) 9–31 15–60 21–37 15–30 61–91 — 0–300 100–430 TOC (%) 0–4.7 4.5 0.3–24 1–25 0.45–2.5 1–14 0.5–10 2.35 Vitrinite reflectance (% Ro) 0.4–1.3 0.6–1.6 0.4–0.6 0.4–1.0 1.6–1.9 — — 1.13 Brittle mineral (%) 35–50 76.5 45–60 54 50–75 20–40 (quartz, carbonate-free) — 30.2–60.3 Brittle mineral (%) — 23.5 — 35.5 — 25–45 — 35.7 Total porosity (%) 4.7 4–5 9 10–14 3–5.5 3–9 1–10 3.61 Gas content (m3 t-1) 1.68–2.83 8.5–9.9 1.1–2.8 1.1–2.3 0.4–1.3 — — 1.44 Pressure gradient (Kg m-3) 0.35–0.92 1.03 0.81 0.99 — 1.73–2.18 — 1.8–2.0 Historic production area . Pike County, Kentucky . Wise County, Texas . Otsego County, Michigan . Harrison County, Indiana . San Juan and Rio Arriba Counties, New Mexico . Oklahoma . British Columbia, Alberta (Adams 2013) . Western Sichuan . Shale reservoir Ohio Barnett Antrim New Albany Lewis Woodford Montney Xu5 Sedimentary type Marine facies Marine facies Marine facies Marine facies M-L facies Marine facies Marine facies Land facies Depth (m) 610–1524 1981–2591 183–730 183–1494 914–1829 1829–3658 1200–3000 2100–3500 Net thickness (m) 9–31 15–60 21–37 15–30 61–91 — 0–300 100–430 TOC (%) 0–4.7 4.5 0.3–24 1–25 0.45–2.5 1–14 0.5–10 2.35 Vitrinite reflectance (% Ro) 0.4–1.3 0.6–1.6 0.4–0.6 0.4–1.0 1.6–1.9 — — 1.13 Brittle mineral (%) 35–50 76.5 45–60 54 50–75 20–40 (quartz, carbonate-free) — 30.2–60.3 Brittle mineral (%) — 23.5 — 35.5 — 25–45 — 35.7 Total porosity (%) 4.7 4–5 9 10–14 3–5.5 3–9 1–10 3.61 Gas content (m3 t-1) 1.68–2.83 8.5–9.9 1.1–2.8 1.1–2.3 0.4–1.3 — — 1.44 Pressure gradient (Kg m-3) 0.35–0.92 1.03 0.81 0.99 — 1.73–2.18 — 1.8–2.0 Open in new tab The stratigraphic model in the Xujiahe formation is in the hybrid strike-slip and reverse fault stress regime. The maximum horizontal stress is 20 MPa higher than the minimum horizontal stress or the vertical stress. According to the features of natural fractures described in section 2.4, natural fractures are mainly low angle and horizontal with an average of 20–35 fractures per 100 m of formation. The characteristics of sand-shale interbedded formation are obvious. Under these particular reservoir conditions, natural fracture geometry and stress patterns, the shape of the fractures are not the conventional two-wing fractures but complex fracture patterns. 3. Fracture propagation mechanism in sand-shale interbedded formation reservoir The natural fractures in the Xu5 formation are mainly horizontal or of a low angle. The destruction of natural fractures during hydraulic fracturing occurs in two situations (Rahman et al2009, Warpinski et al2009, Nagel et al2013): (i) the propagation of a hydraulic facture close to natural fractures causes the destruction of the natural factures. A large number of microseismic monitoring data show the presence of a lot of acoustic emission point near the major fracture, which indicates that the change in stress during hydraulic fracture propagation may cause the damage to the natural fractures, even though the natural fractures are not penetrated. (ii) When a hydraulic fracture intersects with a natural fracture, the stress at the face of the natural fracture will change, which urges the natural fracture to open or shear slip. There are three hydraulic fracture propagation modes. When the hydraulic fracture encounters a natural fracture (figure 10) (Keshavarzi et al2012, Kresse et al2013) (i) the hydraulic fracture continues to extend after penetrating through the natural fracture; (ii) the hydraulic fracture extends into the natural fracture to a certain distance and then breaks through the natural fracture to propagate; (iii) the hydraulic fracture propagates in the natural fracture as the natural fracture is squeezed open. Figure 10. Open in new tabDownload slide Interaction of hydraulic fracture and natural fracture. Figure 10. Open in new tabDownload slide Interaction of hydraulic fracture and natural fracture. As for the natural fractures which are going to intersect with the hydraulic fracture, the hydraulic fracture propagation path will be greatly influenced by the shear failure, dislocation and slippage of the nature fractures which are going to intersect with the hydraulic fracture. The main factors affecting the interaction response of the hydraulic fracture and the natural fractures are the stress differences and the natural fractures’ own conditions. As the main angle of the natural fractures are low and horizontal, it is rather difficult to penetrate the natural fractures. Hence the hydraulic fracture forms a horizontal fracture in the strike-slip fault and reverse fault stress conditions. A weak plane is ignorable in a typical sand-shale interlayered formation like the Xu5 formation. A hydraulic fracture which propagates along natural fractures or penetrates through them with low angle deviation still has a good chance to meet weak planes. The propagation feature might be greatly affected by weak planes. Therefore, what the propagation mechanism really is when natural fractures and weak planes are both considered needs further investigation. Shaffer et al (1980) and Leguillon et al (2000) pointed out that the fracture will slip or strip into stratification if the cementing strength of the interface is weak, and the height of the fracture will be restricted (Shaffer et al1980, Leguillon et al2000). Gu and Siebrits (2008) mapped four potential forms of cracks propagating at the interface: stripping, slipping through, diverting through and branching (figure 11), and they thought that slipping or stripping usually occurred in shallow formations where the overlying pressure was small and the cementing strength was weak (Gu and Siebrits 2008). As the in situ stress mode of the Xu5 formation is an interaction pattern where the strike-slip fault stress regime interacts with the reverse fault stress regime and the vertical principal stress is small, the hydraulic fracture at the interface will slip or strip into stratification. A numerical model considering both natural fractures and a weak plane condition might be too complex. A more straightforward method of numerical simulation is adopted next, with natural fractures and a weak plane considered, in order to study the propagation mechanism. Figure 11. Open in new tabDownload slide Fracture stripping (a); diverting (b); slipping (c); branching (d) (Gu and Siebrits 2008). Copyright 2008, Society of Petroleum Engineers Inc. Copyright 2008, SPE. Reproduced with permission of SPE. Further reproduction prohibited without permission. Figure 11. Open in new tabDownload slide Fracture stripping (a); diverting (b); slipping (c); branching (d) (Gu and Siebrits 2008). Copyright 2008, Society of Petroleum Engineers Inc. Copyright 2008, SPE. Reproduced with permission of SPE. Further reproduction prohibited without permission. 3.1. Seepage-stress–damage model of hydraulic and natural fractures 3.1.1. Geological model simplification. Natural fractures are mainly horizontal and low angle. Assume that the hydraulic fracture remains vertical after passing a natural fracture. Low and high angle natural fractures are made horizontal and vertical, respectively, in the model. The sand-shale interlayered formation was simplified into a model interlayered by only one sand layer and one shale layer. The sketch of the actual formation is shown in figure 12. The formation of shale and sand is shown by dark brown and light brown colors, respectively. Natural fractures are shown by white lines. Figure 12. Open in new tabDownload slide 2D sketch of sand-shale interlayered formation. Figure 12. Open in new tabDownload slide 2D sketch of sand-shale interlayered formation. 3.1.2. Hydraulic simulation model of the X5 sand and shale interbedded formation. The 2D seepage–stress–damage model of hydraulic and natural fractures propagation in sand-shale interlayered formation, based on the geological model of Xu5, is shown in figure 13. As can be seen in figure 13, the model is a vertical plane selected along the borehole axis. A vertical hydraulic fracture is preset throughout the model. A hydraulic fracture and a natural fracture are preset both in shale and sandstone, thus there are four horizontal fractures in the model. The interface between shale and sandstone is assumed to be a natural weak plane which is considered to be a horizontal natural fracture in the model. We assume that the width of the vertical fracture is constant and that the horizontal fracture width will not be affected by the fracture length. Five perforations are set at each intersection of borehole and horizontal fracture. Fracturing fluid is injected into the perforations simultaneously during the simulation. Figure 13. Open in new tabDownload slide 2D schematic diagram of the seepage–stress–damage model. The model is 100 m long and 16 m high with an 8 m shale upside and an 8 m sandstone downside. Figure 13. Open in new tabDownload slide 2D schematic diagram of the seepage–stress–damage model. The model is 100 m long and 16 m high with an 8 m shale upside and an 8 m sandstone downside. 3.1.3. Initial conditions and boundary conditions. The displacement constraints in the y direction are applied to the up and down sides of the model. Displacement of the left and right sides of the model in the x direction is also constrained. Initial conditions are adjusted based on the geological characteristics of Xu5 studied in chapter 1. The initial saturation of the model is set at 1, the initial pore pressure at 54.3 Mpa, the initial vertical in situ stress (σv) at 98.6 Mpa, the initial min. horizontal in situ stress (σh) at 76.2 Mpa, the initial overburden pressure at 74.3 Mpa, the initial void ratio in sandstone at 2.14% and in shale at 3.65%, the initial permeability in sandstone at 0.059 mD and in shale at 0.031 mD. The natural fracture and hydraulic fracture were set as the cohesive pore pressure unit in Abaqus. The fracture was meshed as COH2D in the cohesive unit and a layer of pore pressure nodes were set in the middle of the cohesive element in order to convert the cohesive unit into a cohesive pore pressure unit, which was divided into 2570 COH2D4P units. The common nodes method at the intersection of the horizontal and vertical fractures was adopted to realize the characteristics of flow horizontally and vertically at the same time. The sandstone and shale layers were meshed into 40 000 CPE4P units as a quadrilateral element coupled with the displacement and pore pressure. Because the expansion of the fracture around the wellbore is not a major aspect of the study, the effect of casing and cement sheath on fracture propagation can be ignored to simplify the model. 3.1.4. Definition of model parameters. The fracture propagation is modeled using the pore pressure and the stress cohesive element. The bilinear cohesive element traction-separation law, as shown in figure 14, is adopted in this study. The law assumes that the cohesive element is intact without any relative displacement. Damage initiates when the traction reaches the cohesive strength Tmax or the separation reaches the critical value δini. Beyond δini, the traction reduces linearly to 0 up to δfail where the cohesive element is completely damaged. The fracture energy GC which is equal to the area under the T–S curve can be defined by (Zuorong et al2009): GC=KC2E,3 where KC is the fracture toughness and E the Young’s modulus. Figure 14. Open in new tabDownload slide Bilinear cohesive element traction-separation law. Figure 14. Open in new tabDownload slide Bilinear cohesive element traction-separation law. The secondary stress crack criterion is used to judge fracture initiation. The criterion assumes that the cohesive pore pressure element will crack when the sum of the square of the ratios of the 3D stress of the element and the corresponding ultimate strength equals 1 (Camanho and Davila 2002). {〈tn〉tn0}2+{tsts0}2+{tttt0}2=1,4 where tn0 is the tensile strength of the pore pressure cohesive element, ts0 and tt0 are the shear strengths of two tangential directions, respectively. The damage evolution model of the cohesive pore pressure element is shown below: tn={(1-D)t¯n,    t¯n≥0t¯n,                    when cohesive element withstands stress,ts=(1-D)t¯stt=(1-D)t¯t5 where t¯n ⁠, t¯s and t¯t are the three directional stresses of the cohesive pore pressure unit, respectively, on the basis of elastic deformation at the no damage stage. The formula for the damage factor based on the linear displacement extension rule is as follows (Turon et al2006): D=dmf(dmmax−dm0)dmmax(dmf−dm0),6 where dmmax is the biggest displacement, dmf is the displacement when the element is open and dm0 is the displacement when the element begins to get damaged. The damage evolution for mixed mode failure criteria is defined based on the Benzeggagh–Kenane fracture criterion, when the critical fracture energies during deformation along the two shear directions are similar; when EsC=EtC ⁠, the criterion is represented as: EnC+(EsC-EnC)(ESET)η=EC,7 where the mixed-mode fracture energy EC=En+Es+Et ⁠. En, Es, and Et are the work done by the traction and its conjugate relative displacement in the normal, the first, and the second shear directions, respectively, EnC ⁠, EsC ⁠, and EtC are critical breakdown pressures, and η is a material parameter, ES=Es+Et ⁠, ET=En+ES ⁠. The cohesive element allows fluid flow in the fracture and fluid leak-off into the matrix. The equations of the coupling of seepage and stress are given by Zhang et al (2010). A dynamic evolution equation of rock permeability can be expressed as (Zhu et al2013): k=k0[(1n0)(1+εV)3−(1−n0n0)(1+εV)−1/3]3,8 where n0 is the initial porosity and k0 the initial permeability coefficient. The permeability evolution equation of rock was implemented by the second development function of the finite element software subroutine during the calculation. The user-defined subroutine can be compiled by the subroutine interface provided by the simulation software. Taking the dynamic evolvement of the reservoir porosity and permeability into consideration, and using the relationship between the permeability, porosity and the volumetric strain, the rock permeability and porosity can be obtained. They can be used as the initial physical parameters in the next analysis, and then the volumetric strain and rock physical parameters coupling is achieved. The fluid in the cohesive element is regarded as power-law fluid and the tangential volume flow rate can be calculated (Yao et al2010): qd= (2n′1+2n′)(1K′)1n′(d2)1+2n′n′|∇p|1-n′n′∇p,9 where γ˙ is the tangential strain rate, K′ is consistency, and n′ is the power law coefficient. The path along which the fluid normally flows in the cohesive pore pressure element acts as filtration on the upper and lower surface: {qt=ct(pi−pt)qb=cb(pi−pb),10 where qt, qb are the volume flow rates of the upper and lower surfaces, respectively, ct, cb are fluid loss coefficients, pt, pb are pore pressures, and pi is fluid pressure. The parameters of the rock mechanics, natural fracture and hydraulic fracture, acquired by average statistical data of the Xu5 formation, are shown in tables 6 and 7. The values of the elastic modulus and Poisson’s ratio for sand and shale in the model is obtained by weighted averages of the rock mechanics experimental results in table 1. Table 6. Rock mechanics parameters of play. Position . Lithology . E (GPa) . ν . K (mD) . φ (%) . Pp (MPa) . σv (MPa) . σH (MPa) . σh (MPa) . 3050 Sandstone 21.7 0.23 0.059 2.14 54.3 74.3 98.6 76.2 3050 Shale 23.5 0.19 0.031 3.65 54.3 74.3 98.6 76.2 Position . Lithology . E (GPa) . ν . K (mD) . φ (%) . Pp (MPa) . σv (MPa) . σH (MPa) . σh (MPa) . 3050 Sandstone 21.7 0.23 0.059 2.14 54.3 74.3 98.6 76.2 3050 Shale 23.5 0.19 0.031 3.65 54.3 74.3 98.6 76.2 Open in new tab Table 6. Rock mechanics parameters of play. Position . Lithology . E (GPa) . ν . K (mD) . φ (%) . Pp (MPa) . σv (MPa) . σH (MPa) . σh (MPa) . 3050 Sandstone 21.7 0.23 0.059 2.14 54.3 74.3 98.6 76.2 3050 Shale 23.5 0.19 0.031 3.65 54.3 74.3 98.6 76.2 Position . Lithology . E (GPa) . ν . K (mD) . φ (%) . Pp (MPa) . σv (MPa) . σH (MPa) . σh (MPa) . 3050 Sandstone 21.7 0.23 0.059 2.14 54.3 74.3 98.6 76.2 3050 Shale 23.5 0.19 0.031 3.65 54.3 74.3 98.6 76.2 Open in new tab Table 7. Parameters of cohesive pore pressure elements. Layer . En (GPa) . Es (GPa) . Et (GPa) . tn0 (MPa) . tto (MPa) . tso (MPa) . GC (Pa m) . η . ct/cb (m3 s-1) . Sandstone 214 214 214 2.5 2.5 2.5 73 2.84 1.3e-11 Shale 130 130 130 1.68 1.68 1.68 44 2.84 1.3e-11 Natural fracture 121 121 121 1 1 1 21 2.84 1.3e-11 Layer . En (GPa) . Es (GPa) . Et (GPa) . tn0 (MPa) . tto (MPa) . tso (MPa) . GC (Pa m) . η . ct/cb (m3 s-1) . Sandstone 214 214 214 2.5 2.5 2.5 73 2.84 1.3e-11 Shale 130 130 130 1.68 1.68 1.68 44 2.84 1.3e-11 Natural fracture 121 121 121 1 1 1 21 2.84 1.3e-11 Open in new tab Table 7. Parameters of cohesive pore pressure elements. Layer . En (GPa) . Es (GPa) . Et (GPa) . tn0 (MPa) . tto (MPa) . tso (MPa) . GC (Pa m) . η . ct/cb (m3 s-1) . Sandstone 214 214 214 2.5 2.5 2.5 73 2.84 1.3e-11 Shale 130 130 130 1.68 1.68 1.68 44 2.84 1.3e-11 Natural fracture 121 121 121 1 1 1 21 2.84 1.3e-11 Layer . En (GPa) . Es (GPa) . Et (GPa) . tn0 (MPa) . tto (MPa) . tso (MPa) . GC (Pa m) . η . ct/cb (m3 s-1) . Sandstone 214 214 214 2.5 2.5 2.5 73 2.84 1.3e-11 Shale 130 130 130 1.68 1.68 1.68 44 2.84 1.3e-11 Natural fracture 121 121 121 1 1 1 21 2.84 1.3e-11 Open in new tab 3.2. Model validation Taking the 3045–3115 m deep sand-shale interlayered formation called Xu5 as an example, the results of finite element numerical calculation were compared with the measured fracturing operation curve. The lithology combination of the fracturing section was that the upper siltstone was folded with shale, and the lower shale was folded with sandstone. The thickness of the sandstone is 28.44 m and the thickness of the shale is 31.56 m, the total ratio of sand to shale is 47.4% and the ratio of the number of layers to thickness is 0.23 (figure 15). There are nine horizontal and low angle fractures and four high angle fractures, according to the logging interpretation. The average porosity of the sandstone is 7% and the average porosity of the interlayered section is 3.1%. Proppant concentration is 4.8%. The viscosity of the fracturing fluid is 0.03 Pa s. The fluid injection rate is 10 m3 min-1. Figure 15. Open in new tabDownload slide Parameter optimization for the XC32 well. GR represents the natural gamma ray, CAL1 and CAL2 represent the borehole diameter, RD represents the deep investigation double lateral resistivity log, RS represents the shallow investigation double lateral resistivity log, CNL represents the compensated neutron logging, AC represents the acoustic time, DEN represents the rock density, HFRI represents the horizontal natural fracture, VFRI represents the vertical natural fracture. Figure 15. Open in new tabDownload slide Parameter optimization for the XC32 well. GR represents the natural gamma ray, CAL1 and CAL2 represent the borehole diameter, RD represents the deep investigation double lateral resistivity log, RS represents the shallow investigation double lateral resistivity log, CNL represents the compensated neutron logging, AC represents the acoustic time, DEN represents the rock density, HFRI represents the horizontal natural fracture, VFRI represents the vertical natural fracture. The effects of the fracturing fluid and proppant on the fracturing operation are realized by using a subroutine of the finite element software (Barree and Conway 1994): μ=μ0(1−c0.65)−1.7,11 where μ is the viscosity of the fracturing fluid (Pa s) and c is the volumetric concentration of the proppant. The bottom hole pressure curve calculated by the finite element method and the actual fracturing operation curve measured during the hydraulic fracturing process are shown in figure 16. The fracture initiation pressure simulated by the finite element numerical method is 87.1 MPa while the actual measured pressure is 91.4 MPa. The difference between the simulated result and the actual one is only 4.7%. The fracture propagation pressure fits well with the treating pressure, which proves that the model is valid. The method of calculating the pressure at the end of the fracture based on the fracturing curve can be found in a document by Zhu et al (2013). The bottom hole pressure increases rapidly at the initial stage of the fracturing process during simulation, so the pressure will reach the initial breakdown pressure in 1–2 s, while it will take 2–3 min in reality. The reason for this is that the power of the fracturing pump needs some time to reach its maximum and unsaturated natural fractures may exist in the formation (Zhang et al2010). The result of FEM simulation may fluctuate while simulating the fracture propagation but the actual fracturing operation curve is relatively flat. The possibility of the fracture tip propagating to a surrounding formation is the same when isotropic formation is assumed in the simulation, which leads to the process of holding pressure and reducing pressure. Because the real formation is not always homogeneous and isotropic while fracturing, it is impossible for the fracture tip to propagate all around it at the same time and the pressure curve will be much more smooth. Figure 16. Open in new tabDownload slide Hydraulic fracturing curve of the XC32 well. Figure 16. Open in new tabDownload slide Hydraulic fracturing curve of the XC32 well. 3.3. Results and discussion 3.3.1. Fracture geometry in sand-shale interbedded formation with the strike-slip fault stress regime. Taking the parameters of the XC32 well as an example, the hydraulic fracture geometry was studied by changing the mutual magnitudes of stresses. Hydraulic fracturing led to horizontal fracture in the Xu5 formation. Vertical hydraulic fractures and horizontal natural fractures crisscrossed in I and T shapes (figure 17). The strength of the natural fracture was weak so that it was easy to initiate and propagate. It was hard for the horizontal hydraulic fracture to initiate and propagate in shale and sandstone. The difficulty of fracture propagation was greatest in natural fractures in shale, less difficult in natural fractures at the sand-shale interface, and less difficult again in natural fractures in sandstone. Though the stress intensity factor of the fracture tip in shale was smaller than that of sandstone, the fracture toughness of shale was far smaller than that of sandstone and the vertical hydraulic fracture in shale propagated more easily (figure 17(b)). With increasing vertical stress, horizontal fracture propagation was restricted and vertical propagation gradually had priority, so that the fracture geometry gradually turned from I-shaped to T-shaped (figure 17(c)). With decreasing vertical stress and getting close to the minimum horizontal principal stress, the propagation of the natural fracture was more significant. Figure 17. Open in new tabDownload slide Fracture geometry in strike-slip faults sand-shale interbedded formation. (a) σv–σh = 1.5 MPa, (b) σv–σh = 3 MPa and (c) σv–σh = 5 MPa. Figure 17. Open in new tabDownload slide Fracture geometry in strike-slip faults sand-shale interbedded formation. (a) σv–σh = 1.5 MPa, (b) σv–σh = 3 MPa and (c) σv–σh = 5 MPa. An indoor 3D physical simulation experiment was conducted by Athavale and Miskimins (2008) to investigate the fracture propagation feature. The laminated sample, as shown in figure 18, was constructed by using alternating layers of sandstone and cement to achieve the lamination effect. Each layer had unique mechanical properties. Some layers were bonded together using epoxy, some using a polyurethane based adhesive and some were kept unbonded, as shown in figure 18 (left) (Athavale and Miskimins 2008). The test results show that orthogonal fractures were formed in the laminated 3D sample. F1, F2, F3 and F4 are vertical. Horizontal fracture F5 initiates along the well-bonded interlayer, and the unbounded interface is also obviously opened. Tests reveal that a hydraulic fracture would also propagate along a well-bonded interface in normal slip fault stress conditions when the vertical stress is 17 MPa higher than the minimum horizontal principle stress. The test result of the 3D hydraulic fracture propagation simulation is much more complex, while the basic fracture propagation feature in interlayered formation can still be obtained using the 2D numerical model. The stress difference between vertical stress and the minimum horizontal principle stress of the Xu5 formation is smaller than that in the test. There is a good chance that horizontal fractures would form in interlayers under the stress conditions of the Xu5 formation and the 2D model predicts the fracture morphology well. Figure 18. Open in new tabDownload slide 3D laboratory-scaled hydraulic fracturing test model. Laminated block made of sandstone and cement (left) and one face of the block after the test (right). Test conditions: σv = 29 MPa, σH = 18.6 MPa, σh = 11.7 MPa, injection rate is 2 cc min-1. (Reproduced with permission from Athavale and Miskimins 2008). Figure 18. Open in new tabDownload slide 3D laboratory-scaled hydraulic fracturing test model. Laminated block made of sandstone and cement (left) and one face of the block after the test (right). Test conditions: σv = 29 MPa, σH = 18.6 MPa, σh = 11.7 MPa, injection rate is 2 cc min-1. (Reproduced with permission from Athavale and Miskimins 2008). According to the microseismic trace performed on the XC32 well, the maximum length of the plane was 1013 m, the maximum width was 519 m, the maximum vertical height was 309 m, and fracturing volume in total was about 84 924 700 m3 (figure 19). The length of the fracture was twice the width and three times the height. The fracture propagating around in the horizontal direction led to the larger width and the fracture distributed horizontally as a whole. According to the microseismic trace performed on the adjacent new 21-4H well, the maximum length in the plane was 550 m, the maximum width was 380 m, vertical height was 162 m, and fracturing volume in total was about 7 810 000 m3. The length of the fracture was similar to the width. According to the microseismic result of the XC29 well, the maximum length in the plane was 492 m, the maximum width was 444 m and fracture length and width were basically the same. These monitoring results further validated the special case of forming horizontal fractures in this area. Figure 19. Open in new tabDownload slide Microseismic test result for the XC32 well. Figure 19. Open in new tabDownload slide Microseismic test result for the XC32 well. 3.3.2. Fracture geometry in sand-shale interbedded formation with reverse fault stress regime. As shown in figure 20, most of the fractures were horizontal in the reverse fault stress regime and the vertical hydraulic fracture extension was limited. The fracture geometry was mainly I-shaped. The natural fractures were more likely to propagate in shale than in sandstone, and the sand-shale interface was the hardest part for the natural fracture to propagate in. When the injection rate was over 10 m3 min-1, the natural fracture in the sand-shale interface would propagate rapidly and eventually form fracture geometry of the shape double I. The preset horizontal hydraulic fractures in sandstone and shale did not initiate. Figure 20. Open in new tabDownload slide Fracture geometry in sand-shale interbedded formation with reverse fault stress regime. (a) Injection rate is 5 m3 min-1, (b) Injection rate is 10 m3 min-1. Figure 20. Open in new tabDownload slide Fracture geometry in sand-shale interbedded formation with reverse fault stress regime. (a) Injection rate is 5 m3 min-1, (b) Injection rate is 10 m3 min-1. 3.3.3. Induced stress field of hydraulic fracture and natural fracture mutual interference. Fracture propagation will change the stress field around the borehole during hydraulic fracturing and the original in situ stress, pore pressure, number of fractures, fracture spacing, fracture length and the direction of fracture propagation are closely related to the change. If the original horizontal stress difference is small, stress diversion usually happens around the borehole and hydraulic fractures when more than one fracture are propagating at the same time. In the process of hydraulic fracture propagation, the diversion of the in situ stress direction will lead to new fractures being generated near the borehole and the hydraulic fracture. The advent of fractures is helpful in volumetric fracturing in an unconventional reservoir. Taking well XC32 as an example, the vertical stress was 73.2 MPa, the minimum horizontal stress was 76.2 MPa, and the stress difference was 3 MPa. During the process of hydraulic fracturing, the horizontal fractures in the sand-shale interbedded formation were susceptible to the interference phenomenon, which changed the in situ stress direction around the hole and fractures. It was easy to form a 2–3 m stress diversion area in the process of dynamic propagation of a vertical fracture (figure 21). In figure 21, the vertical vector was the original maximum principal stress and horizontal vector was the stress inversion vector caused by the fracture induced stress field. Figure 22 shows the induced stress field of the propagation of three horizontal natural fractures at the same time. The stress reversal area was larger, enveloping the whole multiple fracture zone, with multiple fracture interference, and the stress field was complex between two horizontal fractures, which included the stress reversal area, the transition area and the nondiversion area. Figure 21. Open in new tabDownload slide Single fracture induced stress field. Figure 21. Open in new tabDownload slide Single fracture induced stress field. Figure 22. Open in new tabDownload slide Multiple fractures induced stress field. Figure 22. Open in new tabDownload slide Multiple fractures induced stress field. Induced stress is defined as: Δσ¯min⁢ =|σ¯min|-|σ¯min0|, where Δσ¯min is the induced stress in the minimum horizontal stress direction, |σ¯min| the absolute value of the minimum horizontal rock skeleton stress and |σ¯min0| the absolute value of the initial minimum horizontal rock skeleton stress. Horizontal and vertical paths used to analyze the induced stress distribution feature were chosen based on figure 17(b). Pore pressure decreases and induced stress of the rock skeleton increases with increasing horizontal distance away from the vertical hydraulic fracture, as is shown in figure 23. In figure 24 there are peak values in the corresponding places where natural fractures are open. Because the effect of rock deformation in the face of the fracture is much stronger than the effect of pore pressure, the induced stress is positive and maximum near the fracture. The induced stress decreases with increasing distance away from the fracture horizontally and vertically. As the natural fracture propagated more easily, the strength of the induced stress field was relatively small when compared to the hydraulic fracture. Therefore, it is easy to produce a new diversion fracture between the two fractures beyond the fracture tip, which makes the final fracture geometry more complex and improves the overall effect of fracturing. This provides a theoretical basis for multiple fracturing significantly improving the effect of fracturing. Figure 23. Open in new tabDownload slide Horizontal induced stress of rock skeleton distribution when multifractures propagate simultaneously. Shale and sandstone are shown by dark brown and light brown colors in the lower right corner, respectively. Hydraulic fractures and natural fractures are shown by yellow and white lines, respectively. Dashed lines are studied stress paths in the horizontal direction. Figure 23. Open in new tabDownload slide Horizontal induced stress of rock skeleton distribution when multifractures propagate simultaneously. Shale and sandstone are shown by dark brown and light brown colors in the lower right corner, respectively. Hydraulic fractures and natural fractures are shown by yellow and white lines, respectively. Dashed lines are studied stress paths in the horizontal direction. Figure 24. Open in new tabDownload slide Vertical induced stress of rock skeleton distribution when multifractures propagate simultaneously. The white dash lines are studied stress paths. Figure 24. Open in new tabDownload slide Vertical induced stress of rock skeleton distribution when multifractures propagate simultaneously. The white dash lines are studied stress paths. 4. Conclusion In the Xu5 formation the average porosity of sandstone is 2.50% and average porosity of shale is 3.08%. The average permeability of sandstone is 0.0152 mD and of shale is 0.0655 mD. Organic matter of the nano–micro level in shale is rich in pore; rubricans siltstone develops intergranular pore and organic pore. The brittleness index of sandstone varies from 0.5 to 0.8, and the brittleness index of shale varies from 0.3 to 0.8; a complex fracture is easily formed by fracturing. Natural fractures are mainly composed of low angle fractures and horizontal fractures and the fractures are undeveloped, with 20–35 fractures per 100 m. The stratigraphic model is the hybrid strike-slip and reverse fault stress regime. The maximum horizontal principal stress is 20 MPa larger than the other two principal stresses, and the difference between vertical stress and the minimum principal stress is small. The uni-axial compressive strength and shear strength of the reservoir is medium, and the tensile strength is small. A mechanical model of a hydraulic fracture penetrating through a natural fracture was established. We found that the hydraulic fracture would propagate along the natural fracture easily when the approaching angle is less than 45°; the hydraulic fracture propagating direction after penetrating through the natural fracture is within 20° when the approaching angle is over 45°. According to the engineering geological characteristics of the sand-shale interbedded formation, the seepage–stress–damage coupling model of hydraulic fracturing was established based on the theory of continuous fracture mechanics. The model can simulate the mechanism of interactive propagation of a hydraulic fracture and a natural fracture and the stress interference characteristics of multiple fractures. In the sand-shale interbedded formation dominated by horizontal and low angle fractures, the fracture geometry is mainly I-shaped and T-shaped. The greater the vertical stress, the easier the T fracture is generated, and the smaller the vertical stress, the easier the I fracture is generated. When the vertical stress is greater than the minimum horizontal principal stress, the propagation of the vertical fracture has an advantage over the horizontal fracture and the horizontal fracture still occurs; when the vertical stress is less than the minimum horizontal principal stress, the propagation of the horizontal fracture has an advantage over the vertical fracture and vertical propagation is limited. The stress inversion phenomenon occurs around both horizontal and vertical fractures during hydraulic fracturing. 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TI - Engineering geological characteristics and the hydraulic fracture propagation mechanism of the sand-shale interbedded formation in the Xu5 reservoir
JF - Journal of Geophysics and Engineering
DO - 10.1088/1742-2132/12/3/321
DA - 2015-06-01
UR - https://www.deepdyve.com/lp/oxford-university-press/engineering-geological-characteristics-and-the-hydraulic-fracture-oC51MAvrrA
SP - 321
VL - 12
IS - 3
DP - DeepDyve
ER -