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Test and analysis on the permeability of induced fractures in shale reservoirs
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ScienceDirect Natural Gas Industry B 5 (2018) 513e522 www.elsevier.com/locate/ngib
Research Article
Test and analysis on the permeability of induced fractures in shale reservoirs*,** Yin Congbin Downhole Operation Company, CNPC Chuanqing Drilling Engineering Company Limited, Chengdu, Sichuan 610052, China Received 11 January 2018; accepted 25 March 2018 Available online 19 September 2018
Abstract In order to improve the effectiveness of shale gas stimulated reservoir volume (SRV), it is necessary to evaluate and study the permeability of different types of induced fractures in shale and its influential factors. In this paper, the mineral composition characteristics, reservoir pore and fracture characteristics of shale were investigated, and the permeability of three types of induced fractures in shale (i.e., in-situ closed type, shear self-propped type and single-layer propped type) was tested. Besides, the effects of fracture type, fracture surface roughness, carbonate content, shale bedding and confining pressure on the permeability of induced fractures in shale reservoirs were studied systematically. The following research results were obtained. First, the permeabilityepressure relationship of in-situ closed fracture is in accordance with the Walsh theory. The permeability decreases with the increase of confining pressure and it is in the range of 0.13e16.75 mD. In-situ closed fracture plays the same role in increasing the productivity of shale gas reservoirs with or without proppant filling or dislocation. Second, compared with in-situ closed fracture permeability, the shear self-propped fracture permeability is 1e2 orders of magnitude (7.53e88.48 mD) higher, and single-layer propped fracture permeability is 2e3 orders of magnitude (9.98e771.82 mD) higher. Third, the larger the fracture surface roughness, the higher the fracture permeability. And there is a better positive correlation between the fractal dimension and the fracture permeability. Fourth, the permeabilityepressure relationship of shear self-propped fracture and single-layer propped fracture is, to some extent, deviated from the Walsh theory, which reflects the influence of self-propped point crushing, proppant embedding and crushing. In conclusion, the experimental results can be used as the reference for the selection of shale fracturing technologies and the optimization of parameters. © 2018 Sichuan Petroleum Administration. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Keywords: Shale gas; Stimulated reservoir volume (SRV); Fracture permeability; Roughness; In-situ closed fracture; Shear self-propped fracture; Laboratory test
1. Introduction Shale usually acts as the effective cap rock for a reservoir due to its extremely low permeability. Although the developed natural fractures or bedding fractures in shale can improve the local permeability to some extent [1e4], they are still not * Project supported by National Major Science and Technology Project “Horizontal well fracturing design optimization system” (No. 2016ZX05023-001). ** This is the English version of the originally published article in Natural Gas Industry (in Chinese), which can be found at https://doi.org/10.3787/j.issn. 1000-0976.2018.03.007. E-mail address: [email protected]. Peer review under responsibility of Sichuan Petroleum Administration.
enough to supply the effective flow paths during shale gas production. In order to achieve the commercial exploitation of shale gas, it is required that hydraulic fracturing technology be used to form a large-scale fracture network, which is called volume fracturing [5e8]. So far, the mechanism of volume fracturing in production increase is still not clear, such as the contributions of the abundant closed fractures, shear microfractures and filling fractures to the permeability after hydraulic fracturing, and the influence of treatments on the permeability of these micro-fractures [9]. The success of volume fracturing is largely based on the experience in oil fields, so a series of experiments are needed to study these influence factors and to improve the effectiveness of volume fracturing.
https://doi.org/10.1016/j.ngib.2018.03.006 2352-8540/© 2018 Sichuan Petroleum Administration. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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The characteristics of fracture permeability have been described by some researchers. Kranzz et al. [10] studied the influence of effective stress and fracture surface roughness on the fracture permeability in granite, and he discovered that the fractured rock is more sensitive to pressure than the whole rock and considered that the slab model to describe the fracture surface is not sufficient. Tasng and Witherspoon [11] considered the fracture mismatch reduces the nonlinear characteristic in a stress-fracture closure behavior. Meanwhile, they recognized the importance of roughness because flow decreases with the increase of shear displacement when the large-scale wavy surface exists and simultaneously the shear displacement is higher than half of the large-scale wavelength. Gangi [12] thought that the relationship between a fracture and its dependence on differential pressure can be better described by “second-order comb function model”. In this paper, the Walsh model [13] is selected to explain the relationship between fracture permeability and pressure because it is the simplest model to link permeability and confining pressure. Some literatures reported the influence factors on fracture conductivity and proppant-filling permeability. The importance of fracture displacement, fracture surface roughness, mechanical properties, and closure stress on conductivity has been demonstrated in the absence of proppant, [14e16]. When proppant exists, the strength and concentration of proppant and closure stress all would have an important influence [17,18]. However, all of these experiments were conducted using slab rocks. Fredd et al. [9] used split rocks to study the influence of fracture properties on the conductivity at low sanding concentration and discussed the effect of proppant and surface roughness on conductivity, but he did not deal with the relationship between the shear displacement and permeability and the influence of proppant placement for different kinds of shales. In this paper, the shales in Lujiaping Fm of Lower Cambrian, Wufeng Fm of Upper Ordovician, Longmaxi Fm of Lower Silurian, and Xujiahe Fm of Upper Triassic in the
Sichuan Basin were taken as the object to systematically study the influences of shale fracture types (in-situ closed type, shear self-propped type and single-layer propped type), fracture surface roughness, carbonate content, shale bedding and confining pressure on fracture permeability using the fracture permeability testing and CT scanning method, in order to provide reference for the selection of shale fracturing technologies and the optimization of parameters. 2. Characteristics of shale in different formations 2.1. Mineral composition and characteristics In order to identify the influences of the mineral composition and natural or bedding fractures on fracture permeability, we took 8 pieces of shale samples, including 4 samples with bedding parallel, symboled as H1, H2, H3 and H4, and 4 samples with bedding perpendicular, symboled as V1, V2, V3 and V4, respectively from Lujiaping, Wufeng, Longmaxi, and Xujiahe Fms in the Sichuan Basin (Fig. 1). The following results have been obtained. For the Lujiaping Fm, the proportions of clay, carbonate, and quartz are 22.5%, 25% and 40.5%, respectively. For the Wufeng Fm, the proportions of clay, carbonate, and quartz are 14.5%, 2% and 68.1%, respectively. For the Longmaxi Fm, the proportions of clay, carbonate, and quartz are 31%, 15% and 43.3%, respectively. For the Xujiahe Fm, the proportions of clay, carbonate, and quartz are 40.6%, 10% and 44.3%, respectively. It is also observed from the rock appearance that there are many highangle natural fractures and bedding fractures in the Wufeng and Longmaxi Fms while there are hardly any natural fractures in the Lujiaping and Xujiahe Fms. In the experiment, different kinds of induced fractures (in-situ closed type, shear self-propped type and single-layer propped type) in rock samples for every formation were created using the splitting method to test and evaluate permeability.
Fig. 1. Rock samples from typical formations.
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2.2. Microscopic pore and fracture characteristics According to the observation of rock samples, there are natural fractures in Wufeng and Longmaxi Fms and these fractures pass through the whole sample; in Lujiaping Fm, there is only one fracture which is filled with white cementitious material and does not pass through the whole sample. CT scanning for fracture and pore analysis shows that in the shales in Wufeng and Longmaxi Fms there are natural fractures which go through the whole rock; The rest of the matrix is so tight that large pore throat is hard to see. CT scanning of a small rock sample with a diameter of 2 mm from Lujiaping Fm shows (the green area means the matrix and the red area means the pore in Fig. 2) that there are only a few dispersed pores in the rock sample and the rest in the sample is the tight matrix, but there are more unconnected pores on the surface in the fracture which does not go through the whole rock. 2.3. Fracture surface roughness The rock sample was first scanned by a three-dimensional laser scanner. Based on the scanning data, the fracture surface morphology was imaged by Surfer (as shown in Fig. 3). The fracture surface roughness can be characterized by the surface fractal dimension [19]. In this study, 16 groups of fracture surface fractal dimension were calculated using the cubic covering method [20e22]. The results show that the fracture surfaces are different in shape. The surface roughness can be quantitatively described by fractal dimension. The higher fractal dimension corresponds to a higher roughness of fracture surface. The fracture dimensions of rocks in these 4 formations range from 2.0351 to 2.1091. The relationship
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between fractal dimension and carbonate mineral content is then described by averaging the fracture dimensions in parallel and vertical beddings for each formation, respectively (Fig. 4). The following results can be concluded from Fig. 3. First, for the rocks in each formation (the mineral composition is similar), the surface roughness of the fracture vertical to bedding is higher than that of the fracture parallel to bedding. Second, the fractal dimension basically increases with the increase in carbonate content, because the carbonate particle has bigger size and lower roundness. The locally concentrated cementation may result in higher fracture surface roughness when the carbonate content increases. 3. Permeability test of shale induced fractures 3.1. In-situ closed fracture The closure of the double fracture surface without displacement or any filling after fracturing will form in-situ closed fractures. The production data and reservoir properties in Weiyuan shallow target reservoir can be taken as a reference. The depth of this reservoir is about 1525 m and the minimum horizontal principal stress is about 29 MPa. At the early stage of production, gas and water were produced together and the bottom hole pressure ranged from 12 MPa to 14 MPa. At the later stage of production, gas was only produced and the bottom hole pressure ranged from 9 MPa to 10 MPa. The effective closure stress on proppant at different stages of production in this reservoir ranges from 17 MPa to 20 MPa, so a confining pressure from 3 MPa to 20 MPa was applied on the shale samples to test the permeability. As shown in Fig. 5, the permeability of the in-situ closed fractures in the 32 rock samples tested ranges from 0.15 mD to
Fig. 2. CT scanning results of shale samples.
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Fig. 3. Fracture surface morphologies for rock samples.
16.75 mD. The specific characteristics of in-situ closed fractures in each formation are described below. 3.1.1. Wufeng Fm The formations are greatly different in the permeability of rock samples, with the largest difference up to 8.40 mD when the confining pressure is 3 MPa. Generally, with the increase of the confining pressure, the difference of permeability in rock samples gradually decreases. However, the permeability in each rock sample is variably sensitive to the confining pressure, in a range from 60.78% to 94.92%. Typically, the permeability of samples with parallel bedding #1 and vertical bedding #3 changes little with the confining pressure, because the fracture surface in these two rock samples is not much damaged after the splitting, resulting in a low permeability of the in-situ closed fracture under a low confining pressure.
3.1.2. Xujiahe Fm The samples are consistent in the variation of permeability with the confining pressure. However, the permeability of rock samples is greatly variable at 3 MPa e up to 13.7 mD. With the confining pressure increasing, the permeability difference rapidly decreases. When the confining pressure is 20 MPa, the permeability mainly ranges from 0.20 mD to 0.44 mD, and reflects a small difference. 3.1.3. Longmaxi Fm The permeability is greatly different under confining pressures, with the largest difference up to 15.72 mD. However, for each rock sample, the permeability changes little with the confining pressure no matter what the permeability is at the initial confining pressure (3 MPa) or the high confining pressure (20 MPa). This is mainly because the rock samples in
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Fig. 4. Relationships between the fracture surface fractal dimension, carbonate content and bedding lamination.
Longmaxi Fm have large hardness, in the uplift of the wall surface of the in-situ closed fracture will hardly be damaged even with the increase of confining pressure. 3.1.4. Lujiaping Fm The samples reflect a consistency in the variation of permeability with confining pressure, except the Sample H1. The permeabilities under different confining pressures of each rock sample also change little, and the largest permeability difference is only 3.48 mD. For the Sample H1, the fracture surface roughness is high and the convex structures on the surface are hard. When the confining pressure is lower than 15 MPa, these convex structures on the surface can prop the fracture, but these convex structures break down under high confining pressure (higher than 15 MPa), which results in a
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tighter closure for the fracture surfaces and low permeability finally. From the rock samples in 4 formations, the relationship between the in-situ closed fracture permeability and the confining pressure conforms to the classic Walsh theory. The relationship between permeability and surface fractal dimension is shown in Fig. 6. It can be seen that there is a good correlation between the fracture surface roughness and fracture permeability. The permeability increases with the increase of roughness. Since the fracture permeability is mainly controlled by the surface shape or roughness, references [8,18] indicate that the classic relationship between flow rate and fracture aperture can be described by the following equation when the slab model is used. Q¼
h3 dp 12m dx
ð1Þ
where Q is the flow rate in the parallel smooth slab, m3/s; similarly, h: the distance between the parallel smooth slabs (i.e. fracture aperture), m; m: the fluid viscosity, mPa$s; p is: the pressure difference, Pa; x: the length of the parallel smooth slabs, m. According to Eq. (1), the fracture aperture controls the fracture permeability. For a in-situ closed fracture, its surface is not smooth; the larger surface roughness corresponds to more convex structures, leading to larger fracture aperture, thus the permeability of in-situ closed fractures is higher. A lot
Fig. 5. Tested in-situ closed fracture permeability of rock samples.
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Fig. 6. Relationship between the permeability and fractal dimension of rock samples.
of in-situ closed fractures with rough surfaces are created during shale volume fracturing, which can effectively improve reservoir productivity even without proppant filling or dislocation. 3.2. Shear self-propped fracture A fracture can be propped by the displaced convex structures when one of the fracture surfaces moves gently to the left or to the right. This kind of fracture is called shear selfpropped fracture. In this experiment, the shear self-propped fracture is created by pasting copper foil gasket at the
opposite sections of the rock sample. The fracture permeability test was conducted at a confining pressure of 3e20 MPa, and the results are shown in Fig. 7. The tested permeability of self-propped fractures ranges from 7.53 mD to 88.48 mD, 1e2 orders of magnitude higher than those of in-situ closed fractures. The tests results in all formations are described as follows. (1) In the Wufeng Fm, compared with in-situ closed fractures, the permeability of self-propped fractures is much higher and reaches up to 88.48 mD which is 14.22 times that of in-situ closed fractures. In general, the difference
Fig. 7. Tested shear self-propped fracture permeability of rock samples.
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Fig. 8. Relationship between the shear self-propped fracture permeability and fractal dimension of rock samples.
in the shear self-propped fracture permeability of rock samples drastically reduces, and the permeability of each rock sample drops greatly with the confining pressure. (2) In the Xujiahe Fm, the permeability of shear selfpropped fractures is much higher than that of in-situ closed fractures at a confining pressure lower than 10 MPa, but slightly higher at a confining pressure higher than 10 MPa. Moreover, the permeability of shear self-propped fractures decreases quickly with the increase of confining pressure.
(3) Im the Longmaxi Fm, the permeability of shear selfpopped fractures is very different in different samples. The permeability of shear self-popped fractures in parallel bedding almost remains unchanged with the variation of confining pressure, while the permeability of shear self-popped fractures in vertical bedding changes significantly with the variation of confining pressure. (4) In the Lujiaping Fm, the permeability of shear selfpropped fractures in all rock samples are high, and changes little with the increase of confining pressure.
Fig. 9. Tested single-layer propped fracture permeability of rock samples.
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pffiffiffi 3 2h p K 1 bðp p0 Þ ¼ 1 ln a0 K0 p0 1 þ bðp p0 Þ
The relationship between shear self-popped fracture permeability and fracture surface fractal dimension is illustrated in Fig. 8. It can be seen that shear self-popped fracture permeability has a positive correlation with fracture surface roughness in rock samples from the same formation. However, high fracture surface roughness does not represent high fracture permeability in rock samples from different formations, because the surface roughness affected by the mineral composition in different formations is not the same. The hardness of convex structure on fracture surface is different under different mineral compositions, resulting in different degrees of breaking on fracture surface under different confining pressures. Therefore, both the mineral composition and surface roughness can significantly affect the fracture permeability.
where K is the transient fracture permeability, D; similarly, K0: the initial fracture permeability, D; h: the height of surface roughness, m; a0: the initial fracture aperture, m; p: the transient pressure, MPa; p0: the initial pressure, MPa; b: the variation of the ratio of the contact area to the fracture area with the pressure, dimensionless. When b equals to 0, the surface roughness hardly changes with the variation of pressure. Then Eq. (2) can be simplified as pffiffiffi 13 2h p K ¼1 ln ð3Þ a0 K0 p0
3.3. Single-layer propped fracture
Eq. (3) shows that there is a linear relationship between (K/ pffiffiffi K0)1/3 and ln( p/p0) with a slope of ð 2h=a0 Þ. If the initial
ð2Þ
Based on the above rock samples with shear self-dropped fractures, single-layer propped fracture are created by uniformly injecting 40e70 mesh ceramists at the sanding concentration of 0.25 kg/m2. The permeability of single-layer propped fractures in all rock samples can be seen from Fig. 9. The tested permeability of single-layer propped fractures ranges from 9.98 mD to 771.82 mD, 2e3 orders of magnitude higher than that of in-situ closed fractures. Thus, the permeability is improved obviously. (1) In the Wufeng Fm, the permeability is improved to the greatest extent. The permeability of rock sample with parallel bedding #2 is up to 771.82 mD when the confining pressure is 3 MPa, 2 orders of magnitude higher than that of in-situ closed fractures. On the whole, the permeability does not change greatly in the samples from the same formation, and shows a consistent tendency with the confining pressure. (2) In the Xujiahe Fm, the permeability changes little in the samples and shows a consistent tendency with the confining pressure. (3) In the Longmaxi Fm, the permeability in all rock samples, except that with parallel bedding #1, changes little with the variation of confining pressure, but it is very different in samples with parallel bedding and vertical bedding. (4) In the Lujiaping Fm, the permeability remains identical in all rock samples, and consistent with the confining pressure. 4. Variation law in fracture permeability The dependence of fracture permeability on pressure controls the final production increase. In this study, the experimental results were analyzed using the Walsh theoretical model which can describe the relationship between the pressure and the permeability of a fracture with two rough surfaces.
Fig. 10. Relationship between the fracture permeability and pressure in shale samples from Lujiaping Fm.
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fracture aperture is constant, the change of the slope only depends on the surface roughness. This condition would occur when the convex structures start to contact under the action of pressure. Taking the rock samples from Lujiaping Fm as an example, the relationship between fracture permeability and pressure was analyzed using the above method. The results are shown in Fig. 10. For in-situ closed fractures, the permeability change is linear when the pressure ranges from 3 MPa to 20 MPa, and the relationship between permeability and pressure is in agreement with the Walsh theory. For shear self-propped fractures, the permeability change in parallel bedding #1 is linear when the pressure ranges from 5 MPa to 15 MPa, mainly because the fracture surface toughness is constructed by the convex structures and there are certain stages for the breaking in convex structures. When the confining pressure is low, some parts of the convex structures are broken, but the others still have certain strength. When the pressure ranges from 5 MPa to 15 MPa, the convex structures no longer break. When the confining pressure is higher than 15 MPa, the convex structures would further break and change the fracture surface roughness, resulting in a change in the fracture permeability finally. The permeability of other 3 rock samples show a linear variation when the pressure ranges from 10 MPa to 20 MPa, because the convex structures continuously break down when the pressure is lower than 10 MPa but there is no breaking when the pressure is higher than 10 MPa. For singlelayer propped fractures, the permeability change in vertical bedding #1 is linear when the pressure ranges from 5 MPa to 15 MPa, but it is not linear whether the pressure is lower or higher than this range. Essentially, the fracture closes or the proppant rearrange under the low pressure and proppant is embedded into rock or partially broken under the high pressure. The permeability of other 3 rock samples shows a linear change when the pressure ranges from 10 MPa to 20 MPa, because the proppant is stable and will no longer migrate when the pressure is higher than 10 MPa, resulting in the stabilization in fracture surface roughness and fracture permeability. 5. Conclusions In this study, the permeability was tested of different kinds of induced fractures under the conditions referring to the depth, geo-stress, and post-frac production pressure of the Weiyuan shallow shale. The conclusions have a guiding significance for hydraulic fracturing design of shallow shale about 1500 m. (1) The fracture surface roughness in vertical bedding is higher than that in parallel bedding in the rock samples from the same formation. Moreover, it increases with the increase of carbonate content. (2) The permeability of in-situ closed fractures ranges from 0.13 mD to 16.75 mD. For the rock samples from same formation, the relationship between the permeability of in-situ closed fractures and the surface roughness is positively correlated on the whole. For the rock samples from different formations, the decline of fracture
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permeability with the increase of confining pressure are different due to the difference in the physical and mechanical properties of rocks and there is permeability difference in the same formation. A lot of in-situ closed fractures with high roughness are created during shale volume fracturing, which can also effectively improve the reservoir productivity even without proppants filling or dislocation. (3) The permeability of shear self-propped fractures ranges from 7.53 mD to 88.48 mD, 1e2 orders of magnitude higher than that of in-situ closed fractures. It would be high if the fracture surface roughness is high in the rock samples from the same formation. But there is no such rule for permeability in the rock samples from different formations due to the mineral composition difference. (4) The permeability of sing-layer propped fractures ranges from 9.98 mD to 771.82 mD, 2e3 orders of magnitude higher than that of in-situ closed fractures. This shows that it can effectively improve permeability. (5) The relationship between the permeability of in-site closed fractures and the confining pressure is in agreement with the Walsh theory, but only under a certain pressure range the permeabilities in shear self-propped and single-layer propped fractures change with the confining pressure followed by the Walsh theory. The deviation reflects the unstable arrangement, embedding, and crushing of proppant, self-propped point crushing, and particle migration, which is in line with the constant change in permeability.
References [1] Bowker KA. Barnett shale gas production, fort worth basin: issues and discussion. AAPG Bull 2007;91(4):523e33. [2] Gale JFW, Reed RM & Holder J. Natural fractures in the Barnett shale and their importance for hydraulic fracture treatments. AAPG Bull 2007;91(4):603e22. [3] Jiang Zaixing, Zhang Wenzhao, Liang Chao, Wang Yongshi, Liu Huimin & Chen Xiang. Characteristics and evaluation elements of shale oil reservoir. Acta Petrol Sin 2014;35(1):184e96. [4] Liu Yuzhang, Xiu Nailing, Ding Yunhong, Wang Xin, Lu Yongjun, Dou Jingjing, et al. Multi-factor coupling of hydraulic fracture network in a shale gas reservoir. Nat Gas Ind 2015;35(1):61e6. [5] Yin Congbin, Li Yanchao, Wang Subing, Xiong Yuran, He Feng & Qin Li. Methodology of hydraulic fracture network prediction in shale reservoirs and its application. Nat Gas Ind 2017;37(4):60e8. [6] Martineau DF. History of the Newark East field and the barnett shale as a gas reservoir. AAPG Bull 2007;91(4):399e403. [7] Cipolla CL, Weng Xiaowei, Mack MG, Ganguly U, Gu Hongren, Kresse O, et al. Integrating microseismic mapping and complex fracture modeling to characterize hydraulic fracture complexity. In: Paper 140185-MS presented at the SPE hydraulic fracturing technology conference. Texas, USA: The Woodlands; 24e26 January 2011. https://doi.org/10.2118/140185-MS. [8] Zeng Shunpeng, Zhang Guoqiang, Han Jiaxin, Yuan Bin, Wang Yanpeng & Ji Zheng. Model of multi-fracture stress shadow effect and optimization design for staged fracturing of horizontal wells. Nat Gas Ind 2015;35(3):55e9. [9] Fredd CN, McConnell SB, Boney CL & England KW. Experimental study of fracture conductivity for water-fracturing and conventional fracturing applications. SPE J 2001;6(3):288e98.
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Yin CB. / Natural Gas Industry B 5 (2018) 513e522
[10] Kranzz RL, Frankel AD, Engelder T & Scholz CH. The permeability of whole and jointed Barre Granite. Int J Rock Mech Min Sci Geomech Abstr 1979;16(4):225e34. [11] Tsang YW & Witherspoon PA. The dependence of fracture mechanical and fluid flow properties on fracture roughness and sample size. J Geophys Res 1983;88(B3):2359e66. [12] Gangi AF. Variation of whole and fractured porous rock permeability with confining pressure. Int J Rock Mech Min Sci Geomech Abstr 1978;15(5):249e57. [13] Walsh JB. Effect of pore pressure and confining pressure on fracture permeability. Int J Rock Mech Min Sci Geomech Abstr 1981;18(5):429e35. [14] Tang Ying, Xing Yun, Li Lezhong, Zhang Binhai & Jiang Shixin. Influence factors and evaluation methods of the gas shale fracability. Earth Sci Front 2012;19(5):356e63. [15] Barton N, Bandis S & Bakhtar K. Strength, deformation and conductivity coupling of rock joints. Int J Rock Mech Min Sci Geomech Abstr 1985;22(3):121e40. [16] Makurat A, Gutierrez M & Backer L. Fracture flow and fracture cross flow experiments, vol. 7. Norwegian Petroleum Society Special Publications; 1996. p. 139e48.
[17] Guo Tiankui, Zhang Shicheng, Liu Weilai & Lai Wenxu. Initiation pressure of multi-stage fracking for perforated horizontal wells of shale gas reservoirs. Nat Gas Ind 2013;33(12):87e93. [18] Penny GS. An evaluation of the effects of environmental conditions and fracturing fluids upon the Long-term conductivity of proppants. In: Paper 16900-MS presented at the SPE annual technical conference and exhibition; 27e30 September 1987. https://doi.org/10.2118/16900-MS. Dallas, Texas, USA. [19] Brown SR. Fluid flow through rock joints: the effect of surface roughness. J Geophys Res 1987;92(B2):1337e48. [20] Zhou HW & Xie H. Direct estimation of the fractal dimensions of a fracture surface of rock. Surf Rev Lett 2003;10(5):751e62. [21] Zhang Yaheng, Zhou Hongwei & Xie Heping. Improved cubic covering method for fractal dimensions of a fracture surface of rock. Chin J Rock Mech Eng 2005;24(17):3192e6. [22] Guo Tianku, Zhang Shicheng, Gao Jun, Zhang Jingchen & Yu Haiqing. Experimental study of fracture permeability for Stimulated Reservoir Volume (SRV) in shale formation. Transport Porous Media 2013;98(3): 525e42.
ScienceDirect Natural Gas Industry B 5 (2018) 513e522 www.elsevier.com/locate/ngib
Research Article
Test and analysis on the permeability of induced fractures in shale reservoirs*,** Yin Congbin Downhole Operation Company, CNPC Chuanqing Drilling Engineering Company Limited, Chengdu, Sichuan 610052, China Received 11 January 2018; accepted 25 March 2018 Available online 19 September 2018
Abstract In order to improve the effectiveness of shale gas stimulated reservoir volume (SRV), it is necessary to evaluate and study the permeability of different types of induced fractures in shale and its influential factors. In this paper, the mineral composition characteristics, reservoir pore and fracture characteristics of shale were investigated, and the permeability of three types of induced fractures in shale (i.e., in-situ closed type, shear self-propped type and single-layer propped type) was tested. Besides, the effects of fracture type, fracture surface roughness, carbonate content, shale bedding and confining pressure on the permeability of induced fractures in shale reservoirs were studied systematically. The following research results were obtained. First, the permeabilityepressure relationship of in-situ closed fracture is in accordance with the Walsh theory. The permeability decreases with the increase of confining pressure and it is in the range of 0.13e16.75 mD. In-situ closed fracture plays the same role in increasing the productivity of shale gas reservoirs with or without proppant filling or dislocation. Second, compared with in-situ closed fracture permeability, the shear self-propped fracture permeability is 1e2 orders of magnitude (7.53e88.48 mD) higher, and single-layer propped fracture permeability is 2e3 orders of magnitude (9.98e771.82 mD) higher. Third, the larger the fracture surface roughness, the higher the fracture permeability. And there is a better positive correlation between the fractal dimension and the fracture permeability. Fourth, the permeabilityepressure relationship of shear self-propped fracture and single-layer propped fracture is, to some extent, deviated from the Walsh theory, which reflects the influence of self-propped point crushing, proppant embedding and crushing. In conclusion, the experimental results can be used as the reference for the selection of shale fracturing technologies and the optimization of parameters. © 2018 Sichuan Petroleum Administration. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Keywords: Shale gas; Stimulated reservoir volume (SRV); Fracture permeability; Roughness; In-situ closed fracture; Shear self-propped fracture; Laboratory test
1. Introduction Shale usually acts as the effective cap rock for a reservoir due to its extremely low permeability. Although the developed natural fractures or bedding fractures in shale can improve the local permeability to some extent [1e4], they are still not * Project supported by National Major Science and Technology Project “Horizontal well fracturing design optimization system” (No. 2016ZX05023-001). ** This is the English version of the originally published article in Natural Gas Industry (in Chinese), which can be found at https://doi.org/10.3787/j.issn. 1000-0976.2018.03.007. E-mail address: [email protected]. Peer review under responsibility of Sichuan Petroleum Administration.
enough to supply the effective flow paths during shale gas production. In order to achieve the commercial exploitation of shale gas, it is required that hydraulic fracturing technology be used to form a large-scale fracture network, which is called volume fracturing [5e8]. So far, the mechanism of volume fracturing in production increase is still not clear, such as the contributions of the abundant closed fractures, shear microfractures and filling fractures to the permeability after hydraulic fracturing, and the influence of treatments on the permeability of these micro-fractures [9]. The success of volume fracturing is largely based on the experience in oil fields, so a series of experiments are needed to study these influence factors and to improve the effectiveness of volume fracturing.
https://doi.org/10.1016/j.ngib.2018.03.006 2352-8540/© 2018 Sichuan Petroleum Administration. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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The characteristics of fracture permeability have been described by some researchers. Kranzz et al. [10] studied the influence of effective stress and fracture surface roughness on the fracture permeability in granite, and he discovered that the fractured rock is more sensitive to pressure than the whole rock and considered that the slab model to describe the fracture surface is not sufficient. Tasng and Witherspoon [11] considered the fracture mismatch reduces the nonlinear characteristic in a stress-fracture closure behavior. Meanwhile, they recognized the importance of roughness because flow decreases with the increase of shear displacement when the large-scale wavy surface exists and simultaneously the shear displacement is higher than half of the large-scale wavelength. Gangi [12] thought that the relationship between a fracture and its dependence on differential pressure can be better described by “second-order comb function model”. In this paper, the Walsh model [13] is selected to explain the relationship between fracture permeability and pressure because it is the simplest model to link permeability and confining pressure. Some literatures reported the influence factors on fracture conductivity and proppant-filling permeability. The importance of fracture displacement, fracture surface roughness, mechanical properties, and closure stress on conductivity has been demonstrated in the absence of proppant, [14e16]. When proppant exists, the strength and concentration of proppant and closure stress all would have an important influence [17,18]. However, all of these experiments were conducted using slab rocks. Fredd et al. [9] used split rocks to study the influence of fracture properties on the conductivity at low sanding concentration and discussed the effect of proppant and surface roughness on conductivity, but he did not deal with the relationship between the shear displacement and permeability and the influence of proppant placement for different kinds of shales. In this paper, the shales in Lujiaping Fm of Lower Cambrian, Wufeng Fm of Upper Ordovician, Longmaxi Fm of Lower Silurian, and Xujiahe Fm of Upper Triassic in the
Sichuan Basin were taken as the object to systematically study the influences of shale fracture types (in-situ closed type, shear self-propped type and single-layer propped type), fracture surface roughness, carbonate content, shale bedding and confining pressure on fracture permeability using the fracture permeability testing and CT scanning method, in order to provide reference for the selection of shale fracturing technologies and the optimization of parameters. 2. Characteristics of shale in different formations 2.1. Mineral composition and characteristics In order to identify the influences of the mineral composition and natural or bedding fractures on fracture permeability, we took 8 pieces of shale samples, including 4 samples with bedding parallel, symboled as H1, H2, H3 and H4, and 4 samples with bedding perpendicular, symboled as V1, V2, V3 and V4, respectively from Lujiaping, Wufeng, Longmaxi, and Xujiahe Fms in the Sichuan Basin (Fig. 1). The following results have been obtained. For the Lujiaping Fm, the proportions of clay, carbonate, and quartz are 22.5%, 25% and 40.5%, respectively. For the Wufeng Fm, the proportions of clay, carbonate, and quartz are 14.5%, 2% and 68.1%, respectively. For the Longmaxi Fm, the proportions of clay, carbonate, and quartz are 31%, 15% and 43.3%, respectively. For the Xujiahe Fm, the proportions of clay, carbonate, and quartz are 40.6%, 10% and 44.3%, respectively. It is also observed from the rock appearance that there are many highangle natural fractures and bedding fractures in the Wufeng and Longmaxi Fms while there are hardly any natural fractures in the Lujiaping and Xujiahe Fms. In the experiment, different kinds of induced fractures (in-situ closed type, shear self-propped type and single-layer propped type) in rock samples for every formation were created using the splitting method to test and evaluate permeability.
Fig. 1. Rock samples from typical formations.
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2.2. Microscopic pore and fracture characteristics According to the observation of rock samples, there are natural fractures in Wufeng and Longmaxi Fms and these fractures pass through the whole sample; in Lujiaping Fm, there is only one fracture which is filled with white cementitious material and does not pass through the whole sample. CT scanning for fracture and pore analysis shows that in the shales in Wufeng and Longmaxi Fms there are natural fractures which go through the whole rock; The rest of the matrix is so tight that large pore throat is hard to see. CT scanning of a small rock sample with a diameter of 2 mm from Lujiaping Fm shows (the green area means the matrix and the red area means the pore in Fig. 2) that there are only a few dispersed pores in the rock sample and the rest in the sample is the tight matrix, but there are more unconnected pores on the surface in the fracture which does not go through the whole rock. 2.3. Fracture surface roughness The rock sample was first scanned by a three-dimensional laser scanner. Based on the scanning data, the fracture surface morphology was imaged by Surfer (as shown in Fig. 3). The fracture surface roughness can be characterized by the surface fractal dimension [19]. In this study, 16 groups of fracture surface fractal dimension were calculated using the cubic covering method [20e22]. The results show that the fracture surfaces are different in shape. The surface roughness can be quantitatively described by fractal dimension. The higher fractal dimension corresponds to a higher roughness of fracture surface. The fracture dimensions of rocks in these 4 formations range from 2.0351 to 2.1091. The relationship
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between fractal dimension and carbonate mineral content is then described by averaging the fracture dimensions in parallel and vertical beddings for each formation, respectively (Fig. 4). The following results can be concluded from Fig. 3. First, for the rocks in each formation (the mineral composition is similar), the surface roughness of the fracture vertical to bedding is higher than that of the fracture parallel to bedding. Second, the fractal dimension basically increases with the increase in carbonate content, because the carbonate particle has bigger size and lower roundness. The locally concentrated cementation may result in higher fracture surface roughness when the carbonate content increases. 3. Permeability test of shale induced fractures 3.1. In-situ closed fracture The closure of the double fracture surface without displacement or any filling after fracturing will form in-situ closed fractures. The production data and reservoir properties in Weiyuan shallow target reservoir can be taken as a reference. The depth of this reservoir is about 1525 m and the minimum horizontal principal stress is about 29 MPa. At the early stage of production, gas and water were produced together and the bottom hole pressure ranged from 12 MPa to 14 MPa. At the later stage of production, gas was only produced and the bottom hole pressure ranged from 9 MPa to 10 MPa. The effective closure stress on proppant at different stages of production in this reservoir ranges from 17 MPa to 20 MPa, so a confining pressure from 3 MPa to 20 MPa was applied on the shale samples to test the permeability. As shown in Fig. 5, the permeability of the in-situ closed fractures in the 32 rock samples tested ranges from 0.15 mD to
Fig. 2. CT scanning results of shale samples.
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Fig. 3. Fracture surface morphologies for rock samples.
16.75 mD. The specific characteristics of in-situ closed fractures in each formation are described below. 3.1.1. Wufeng Fm The formations are greatly different in the permeability of rock samples, with the largest difference up to 8.40 mD when the confining pressure is 3 MPa. Generally, with the increase of the confining pressure, the difference of permeability in rock samples gradually decreases. However, the permeability in each rock sample is variably sensitive to the confining pressure, in a range from 60.78% to 94.92%. Typically, the permeability of samples with parallel bedding #1 and vertical bedding #3 changes little with the confining pressure, because the fracture surface in these two rock samples is not much damaged after the splitting, resulting in a low permeability of the in-situ closed fracture under a low confining pressure.
3.1.2. Xujiahe Fm The samples are consistent in the variation of permeability with the confining pressure. However, the permeability of rock samples is greatly variable at 3 MPa e up to 13.7 mD. With the confining pressure increasing, the permeability difference rapidly decreases. When the confining pressure is 20 MPa, the permeability mainly ranges from 0.20 mD to 0.44 mD, and reflects a small difference. 3.1.3. Longmaxi Fm The permeability is greatly different under confining pressures, with the largest difference up to 15.72 mD. However, for each rock sample, the permeability changes little with the confining pressure no matter what the permeability is at the initial confining pressure (3 MPa) or the high confining pressure (20 MPa). This is mainly because the rock samples in
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Fig. 4. Relationships between the fracture surface fractal dimension, carbonate content and bedding lamination.
Longmaxi Fm have large hardness, in the uplift of the wall surface of the in-situ closed fracture will hardly be damaged even with the increase of confining pressure. 3.1.4. Lujiaping Fm The samples reflect a consistency in the variation of permeability with confining pressure, except the Sample H1. The permeabilities under different confining pressures of each rock sample also change little, and the largest permeability difference is only 3.48 mD. For the Sample H1, the fracture surface roughness is high and the convex structures on the surface are hard. When the confining pressure is lower than 15 MPa, these convex structures on the surface can prop the fracture, but these convex structures break down under high confining pressure (higher than 15 MPa), which results in a
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tighter closure for the fracture surfaces and low permeability finally. From the rock samples in 4 formations, the relationship between the in-situ closed fracture permeability and the confining pressure conforms to the classic Walsh theory. The relationship between permeability and surface fractal dimension is shown in Fig. 6. It can be seen that there is a good correlation between the fracture surface roughness and fracture permeability. The permeability increases with the increase of roughness. Since the fracture permeability is mainly controlled by the surface shape or roughness, references [8,18] indicate that the classic relationship between flow rate and fracture aperture can be described by the following equation when the slab model is used. Q¼
h3 dp 12m dx
ð1Þ
where Q is the flow rate in the parallel smooth slab, m3/s; similarly, h: the distance between the parallel smooth slabs (i.e. fracture aperture), m; m: the fluid viscosity, mPa$s; p is: the pressure difference, Pa; x: the length of the parallel smooth slabs, m. According to Eq. (1), the fracture aperture controls the fracture permeability. For a in-situ closed fracture, its surface is not smooth; the larger surface roughness corresponds to more convex structures, leading to larger fracture aperture, thus the permeability of in-situ closed fractures is higher. A lot
Fig. 5. Tested in-situ closed fracture permeability of rock samples.
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Fig. 6. Relationship between the permeability and fractal dimension of rock samples.
of in-situ closed fractures with rough surfaces are created during shale volume fracturing, which can effectively improve reservoir productivity even without proppant filling or dislocation. 3.2. Shear self-propped fracture A fracture can be propped by the displaced convex structures when one of the fracture surfaces moves gently to the left or to the right. This kind of fracture is called shear selfpropped fracture. In this experiment, the shear self-propped fracture is created by pasting copper foil gasket at the
opposite sections of the rock sample. The fracture permeability test was conducted at a confining pressure of 3e20 MPa, and the results are shown in Fig. 7. The tested permeability of self-propped fractures ranges from 7.53 mD to 88.48 mD, 1e2 orders of magnitude higher than those of in-situ closed fractures. The tests results in all formations are described as follows. (1) In the Wufeng Fm, compared with in-situ closed fractures, the permeability of self-propped fractures is much higher and reaches up to 88.48 mD which is 14.22 times that of in-situ closed fractures. In general, the difference
Fig. 7. Tested shear self-propped fracture permeability of rock samples.
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Fig. 8. Relationship between the shear self-propped fracture permeability and fractal dimension of rock samples.
in the shear self-propped fracture permeability of rock samples drastically reduces, and the permeability of each rock sample drops greatly with the confining pressure. (2) In the Xujiahe Fm, the permeability of shear selfpropped fractures is much higher than that of in-situ closed fractures at a confining pressure lower than 10 MPa, but slightly higher at a confining pressure higher than 10 MPa. Moreover, the permeability of shear self-propped fractures decreases quickly with the increase of confining pressure.
(3) Im the Longmaxi Fm, the permeability of shear selfpopped fractures is very different in different samples. The permeability of shear self-popped fractures in parallel bedding almost remains unchanged with the variation of confining pressure, while the permeability of shear self-popped fractures in vertical bedding changes significantly with the variation of confining pressure. (4) In the Lujiaping Fm, the permeability of shear selfpropped fractures in all rock samples are high, and changes little with the increase of confining pressure.
Fig. 9. Tested single-layer propped fracture permeability of rock samples.
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pffiffiffi 3 2h p K 1 bðp p0 Þ ¼ 1 ln a0 K0 p0 1 þ bðp p0 Þ
The relationship between shear self-popped fracture permeability and fracture surface fractal dimension is illustrated in Fig. 8. It can be seen that shear self-popped fracture permeability has a positive correlation with fracture surface roughness in rock samples from the same formation. However, high fracture surface roughness does not represent high fracture permeability in rock samples from different formations, because the surface roughness affected by the mineral composition in different formations is not the same. The hardness of convex structure on fracture surface is different under different mineral compositions, resulting in different degrees of breaking on fracture surface under different confining pressures. Therefore, both the mineral composition and surface roughness can significantly affect the fracture permeability.
where K is the transient fracture permeability, D; similarly, K0: the initial fracture permeability, D; h: the height of surface roughness, m; a0: the initial fracture aperture, m; p: the transient pressure, MPa; p0: the initial pressure, MPa; b: the variation of the ratio of the contact area to the fracture area with the pressure, dimensionless. When b equals to 0, the surface roughness hardly changes with the variation of pressure. Then Eq. (2) can be simplified as pffiffiffi 13 2h p K ¼1 ln ð3Þ a0 K0 p0
3.3. Single-layer propped fracture
Eq. (3) shows that there is a linear relationship between (K/ pffiffiffi K0)1/3 and ln( p/p0) with a slope of ð 2h=a0 Þ. If the initial
ð2Þ
Based on the above rock samples with shear self-dropped fractures, single-layer propped fracture are created by uniformly injecting 40e70 mesh ceramists at the sanding concentration of 0.25 kg/m2. The permeability of single-layer propped fractures in all rock samples can be seen from Fig. 9. The tested permeability of single-layer propped fractures ranges from 9.98 mD to 771.82 mD, 2e3 orders of magnitude higher than that of in-situ closed fractures. Thus, the permeability is improved obviously. (1) In the Wufeng Fm, the permeability is improved to the greatest extent. The permeability of rock sample with parallel bedding #2 is up to 771.82 mD when the confining pressure is 3 MPa, 2 orders of magnitude higher than that of in-situ closed fractures. On the whole, the permeability does not change greatly in the samples from the same formation, and shows a consistent tendency with the confining pressure. (2) In the Xujiahe Fm, the permeability changes little in the samples and shows a consistent tendency with the confining pressure. (3) In the Longmaxi Fm, the permeability in all rock samples, except that with parallel bedding #1, changes little with the variation of confining pressure, but it is very different in samples with parallel bedding and vertical bedding. (4) In the Lujiaping Fm, the permeability remains identical in all rock samples, and consistent with the confining pressure. 4. Variation law in fracture permeability The dependence of fracture permeability on pressure controls the final production increase. In this study, the experimental results were analyzed using the Walsh theoretical model which can describe the relationship between the pressure and the permeability of a fracture with two rough surfaces.
Fig. 10. Relationship between the fracture permeability and pressure in shale samples from Lujiaping Fm.
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fracture aperture is constant, the change of the slope only depends on the surface roughness. This condition would occur when the convex structures start to contact under the action of pressure. Taking the rock samples from Lujiaping Fm as an example, the relationship between fracture permeability and pressure was analyzed using the above method. The results are shown in Fig. 10. For in-situ closed fractures, the permeability change is linear when the pressure ranges from 3 MPa to 20 MPa, and the relationship between permeability and pressure is in agreement with the Walsh theory. For shear self-propped fractures, the permeability change in parallel bedding #1 is linear when the pressure ranges from 5 MPa to 15 MPa, mainly because the fracture surface toughness is constructed by the convex structures and there are certain stages for the breaking in convex structures. When the confining pressure is low, some parts of the convex structures are broken, but the others still have certain strength. When the pressure ranges from 5 MPa to 15 MPa, the convex structures no longer break. When the confining pressure is higher than 15 MPa, the convex structures would further break and change the fracture surface roughness, resulting in a change in the fracture permeability finally. The permeability of other 3 rock samples show a linear variation when the pressure ranges from 10 MPa to 20 MPa, because the convex structures continuously break down when the pressure is lower than 10 MPa but there is no breaking when the pressure is higher than 10 MPa. For singlelayer propped fractures, the permeability change in vertical bedding #1 is linear when the pressure ranges from 5 MPa to 15 MPa, but it is not linear whether the pressure is lower or higher than this range. Essentially, the fracture closes or the proppant rearrange under the low pressure and proppant is embedded into rock or partially broken under the high pressure. The permeability of other 3 rock samples shows a linear change when the pressure ranges from 10 MPa to 20 MPa, because the proppant is stable and will no longer migrate when the pressure is higher than 10 MPa, resulting in the stabilization in fracture surface roughness and fracture permeability. 5. Conclusions In this study, the permeability was tested of different kinds of induced fractures under the conditions referring to the depth, geo-stress, and post-frac production pressure of the Weiyuan shallow shale. The conclusions have a guiding significance for hydraulic fracturing design of shallow shale about 1500 m. (1) The fracture surface roughness in vertical bedding is higher than that in parallel bedding in the rock samples from the same formation. Moreover, it increases with the increase of carbonate content. (2) The permeability of in-situ closed fractures ranges from 0.13 mD to 16.75 mD. For the rock samples from same formation, the relationship between the permeability of in-situ closed fractures and the surface roughness is positively correlated on the whole. For the rock samples from different formations, the decline of fracture
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permeability with the increase of confining pressure are different due to the difference in the physical and mechanical properties of rocks and there is permeability difference in the same formation. A lot of in-situ closed fractures with high roughness are created during shale volume fracturing, which can also effectively improve the reservoir productivity even without proppants filling or dislocation. (3) The permeability of shear self-propped fractures ranges from 7.53 mD to 88.48 mD, 1e2 orders of magnitude higher than that of in-situ closed fractures. It would be high if the fracture surface roughness is high in the rock samples from the same formation. But there is no such rule for permeability in the rock samples from different formations due to the mineral composition difference. (4) The permeability of sing-layer propped fractures ranges from 9.98 mD to 771.82 mD, 2e3 orders of magnitude higher than that of in-situ closed fractures. This shows that it can effectively improve permeability. (5) The relationship between the permeability of in-site closed fractures and the confining pressure is in agreement with the Walsh theory, but only under a certain pressure range the permeabilities in shear self-propped and single-layer propped fractures change with the confining pressure followed by the Walsh theory. The deviation reflects the unstable arrangement, embedding, and crushing of proppant, self-propped point crushing, and particle migration, which is in line with the constant change in permeability.
References [1] Bowker KA. Barnett shale gas production, fort worth basin: issues and discussion. AAPG Bull 2007;91(4):523e33. [2] Gale JFW, Reed RM & Holder J. Natural fractures in the Barnett shale and their importance for hydraulic fracture treatments. AAPG Bull 2007;91(4):603e22. [3] Jiang Zaixing, Zhang Wenzhao, Liang Chao, Wang Yongshi, Liu Huimin & Chen Xiang. Characteristics and evaluation elements of shale oil reservoir. Acta Petrol Sin 2014;35(1):184e96. [4] Liu Yuzhang, Xiu Nailing, Ding Yunhong, Wang Xin, Lu Yongjun, Dou Jingjing, et al. Multi-factor coupling of hydraulic fracture network in a shale gas reservoir. Nat Gas Ind 2015;35(1):61e6. [5] Yin Congbin, Li Yanchao, Wang Subing, Xiong Yuran, He Feng & Qin Li. Methodology of hydraulic fracture network prediction in shale reservoirs and its application. Nat Gas Ind 2017;37(4):60e8. [6] Martineau DF. History of the Newark East field and the barnett shale as a gas reservoir. AAPG Bull 2007;91(4):399e403. [7] Cipolla CL, Weng Xiaowei, Mack MG, Ganguly U, Gu Hongren, Kresse O, et al. Integrating microseismic mapping and complex fracture modeling to characterize hydraulic fracture complexity. In: Paper 140185-MS presented at the SPE hydraulic fracturing technology conference. Texas, USA: The Woodlands; 24e26 January 2011. https://doi.org/10.2118/140185-MS. [8] Zeng Shunpeng, Zhang Guoqiang, Han Jiaxin, Yuan Bin, Wang Yanpeng & Ji Zheng. Model of multi-fracture stress shadow effect and optimization design for staged fracturing of horizontal wells. Nat Gas Ind 2015;35(3):55e9. [9] Fredd CN, McConnell SB, Boney CL & England KW. Experimental study of fracture conductivity for water-fracturing and conventional fracturing applications. SPE J 2001;6(3):288e98.
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Yin CB. / Natural Gas Industry B 5 (2018) 513e522
[10] Kranzz RL, Frankel AD, Engelder T & Scholz CH. The permeability of whole and jointed Barre Granite. Int J Rock Mech Min Sci Geomech Abstr 1979;16(4):225e34. [11] Tsang YW & Witherspoon PA. The dependence of fracture mechanical and fluid flow properties on fracture roughness and sample size. J Geophys Res 1983;88(B3):2359e66. [12] Gangi AF. Variation of whole and fractured porous rock permeability with confining pressure. Int J Rock Mech Min Sci Geomech Abstr 1978;15(5):249e57. [13] Walsh JB. Effect of pore pressure and confining pressure on fracture permeability. Int J Rock Mech Min Sci Geomech Abstr 1981;18(5):429e35. [14] Tang Ying, Xing Yun, Li Lezhong, Zhang Binhai & Jiang Shixin. Influence factors and evaluation methods of the gas shale fracability. Earth Sci Front 2012;19(5):356e63. [15] Barton N, Bandis S & Bakhtar K. Strength, deformation and conductivity coupling of rock joints. Int J Rock Mech Min Sci Geomech Abstr 1985;22(3):121e40. [16] Makurat A, Gutierrez M & Backer L. Fracture flow and fracture cross flow experiments, vol. 7. Norwegian Petroleum Society Special Publications; 1996. p. 139e48.
[17] Guo Tiankui, Zhang Shicheng, Liu Weilai & Lai Wenxu. Initiation pressure of multi-stage fracking for perforated horizontal wells of shale gas reservoirs. Nat Gas Ind 2013;33(12):87e93. [18] Penny GS. An evaluation of the effects of environmental conditions and fracturing fluids upon the Long-term conductivity of proppants. In: Paper 16900-MS presented at the SPE annual technical conference and exhibition; 27e30 September 1987. https://doi.org/10.2118/16900-MS. Dallas, Texas, USA. [19] Brown SR. Fluid flow through rock joints: the effect of surface roughness. J Geophys Res 1987;92(B2):1337e48. [20] Zhou HW & Xie H. Direct estimation of the fractal dimensions of a fracture surface of rock. Surf Rev Lett 2003;10(5):751e62. [21] Zhang Yaheng, Zhou Hongwei & Xie Heping. Improved cubic covering method for fractal dimensions of a fracture surface of rock. Chin J Rock Mech Eng 2005;24(17):3192e6. [22] Guo Tianku, Zhang Shicheng, Gao Jun, Zhang Jingchen & Yu Haiqing. Experimental study of fracture permeability for Stimulated Reservoir Volume (SRV) in shale formation. Transport Porous Media 2013;98(3): 525e42.