Strain energy density distribution of a tight gas sandstone reservoir in a low-amplitude tectonic zone and its effect on gas well productivity: A 3D FEM study

Journal of Petroleum Science and Engineering 170 (2018) 89–104

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Strain energy density distribution of a tight gas sandstone reservoir in a lowamplitude tectonic zone and its effect on gas well productivity: A 3D FEM study

T

Shuai Yina,∗, Jingzhou Zhaoa, Zhonghu Wub,∗∗, Wenlong Dingc a

School of Earth Science and Engineering, Xi'an Shiyou University, Xi'an, 710065, China College of Civil Engineering, Guizhou University, Guiyang, 550025, China c School of Energy Resources, China University of Geosciences, Beijing, 100083, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Strain energy density Tight gas sandstone Paleotectonic stress field Productivity

The tight gas sandstone reservoirs in the Paleozoic of the Sulige gas field in China are highly heterogeneous, and fractures are key factors for stable reservoir production. Low-amplitude folds or nose-like structures are widely developed in the Upper Paleozoic strata in this area. To effectively predict gas well productivity, in this paper, a 3D FEM numerical simulation based on the deformation and energy variation of the rock mass was used to predict the "sweet spots" of gas well productivity in a tight gas sandstone reservoir using the He8 segment of the Middle Permian Xiashihezi Formation in the Central Sulige block as an example. The paleotectonic stress field of the study area during the maximum episode of compression in the Yanshanian movement was restored, and the two rupture parameters of the integrated rupture rate (IF) and strain energy density (U) were constructed. The strain energy density distribution has a high correlation with gas well productivity, indicating that it can better predict the rock rupture degree in low-amplitude tectonic zones. A complex relationship exists between the strain energy density distribution and low-amplitude folds. The high strain energy density zones are mainly distributed among the high positions and wing areas of the low-amplitude fold zone, but the top area of the lowamplitude fold does not necessarily have a high strain energy density. Portions of the high strain energy density zones are located in the gentle tectonic zone, located near but outside the low-amplitude fold zone. The strain energy in these gentle tectonic zones with a high strain energy density value is relatively high, and the rock mass is prone to rupture. This study is of great value in enriching the prediction of "sweet spots" in tight gas sandstone reservoirs in low-amplitude tectonic zones worldwide.

1. Introduction The Sulige gas field is located in the northwestern portion of the Yishan slope in the Ordos Basin, China, and is a large-scale inland tight gas sandstone reservoir developed in Paleozoic clastic rocks (Cao., 2012; Lai et al., 2018; Zou et al., 2012). By the end of 2015, the accumulated proven geological reserves of the Sulige gas field exceeded 4 × 1012 m3 to become the largest natural gas field in China (Lai et al., 2018). The source rocks of this gas reservoir are coal and mudstone of the Upper Carboniferous Benxi Formation and the Lower Permian Taiyuan and Shanxi Formations (Cheng et al., 2016; Zou et al., 2009). The main gas-bearing intervals are the Permian He8 segment of the Xiashihezi Formation and the Shan1 segment of the Shanxi Formation. Previous studies have substantially examined the controlling factors

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and distribution characteristics of the effective tight sandstone reservoirs by studying the spatial distribution of hydrocarbon source rocks, hydrocarbon generation intensity, reservoir sedimentary microfacies and diagenesis (Cao, 2012; Cheng et al., 2016; Ding et al., 2016a; Farrokhrouz et al., 2014; Gong et al., 2018; Lai et al., 2018; Li et al., 2018; Wessling et al., 2013; Zou et al., 2012, 2014). Because of the effects of the paleotectonic stress field, many scholars have recently found that natural fractures are highly developed in the tight sandstone reservoirs of the Upper Paleozoic of the Sulige gas field. These fractures include core-scale fractures and microfractures (Lai et al., 2018). Core-scale fractures can be observed with the naked eye, and their fracture lengths are generally less than a meter. Microfractures are usually observed only under the microscope, their length is generally less than 0.05 mm, and their opening degree is generally

Corresponding author. Corresponding author. E-mail addresses: [email protected] (S. Yin), [email protected] (Z. Wu), [email protected] (W. Ding).

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https://doi.org/10.1016/j.petrol.2018.06.057 Received 10 March 2018; Received in revised form 19 May 2018; Accepted 18 June 2018 Available online 19 June 2018 0920-4105/ © 2018 Elsevier B.V. All rights reserved.

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Fig. 1. Location and tectonic features of the study area. Notes: (a) Location of the Sulige gas field; (b) tectonic features and well of the central Sulige well block; (c) tectonic features of the bottom of the Middle Permian Xiashihezi Formation.

less than 40 μm (Zeng et al., 2010). The core-scale fractures developed in the Upper Paleozoic sandstone of the Sulige gas field are primarily vertical fractures, whereas the microfractures are mainly grain-edge microfractures and grain-penetrating microfractures (Lai et al., 2018; Zou et al., 2012). Hydraulic fracturing in the core-scale fracture or microfracture zone can significantly improve the effect of reservoir development, which is important to increasing the stable production time of the Sulige gas field (Bose et al., 2015; Zhao et al., 2015; Zou et al., 2012). According to previous studies, these fractures were formed in a regional compressive-stress environment during the main episode of the Yanshanian movement, i.e., Late Jurassic-Early Cretaceous (Wan et al., 2010, 2013; Zhao et al., 2016; Zhou et al., 2006). For the prediction of fractures in tight sandstone reservoirs, certain techniques have been adopted by previous researchers, including geological and log analysis methods, structural curvature analysis methods, seismic prediction methods and FEM (finite element method) (Eltom et al., 2016; English., 2012; Farrell et al., 2014; Hardy et al., 1973; Hooker et al., 2013; Lai et al., 2016, 2017; Laubach, 1997; Lv et al., 2017; Maystrenko et al., 2018; Yin et al., 2016a; Zeng et al., 2012). The geological and log analysis methods are limited by single well data, and their prediction effects have apparent limitations. The structural curvature analysis methods show defects in analyzing the deformation and rupture characteristics of different lithological strata. The resolution of seismic prediction methods generally cannot reach the level of corescale or smaller fractures. The FEM tectonic stress field simulation is based on the principle of stress and strain transfer, which can produce better predictions of fractures at different scales. However, for different tectonic zones and rock mass types, it is difficult to determine which fracture calculation method is most effective (Eyal et al., 2001; Yin et al., 2017a). Many theoretical and technical difficulties still exist in predicting small-scale and microscale natural fractures or ruptures worldwide. Microscale ruptures or microfractures have poor development rules in space, and additionally, the scale of such fractures is relatively small, and they are difficult to identify quantitatively (Jamison., 2016; John., 1969; Laubach., 1997; Misra and Gupta., 2014; Price., 1966; Vishal et al., 2013a, 2013b; Yin et al., 2018a, 2018b; Zhao et al., 2016, 2017). For the development of tight gas sandstone reservoirs in the Sulige gas field, researchers are beginning to focus on the microscale ruptures or microfractures because they are important factors in determining whether tight sandstone reservoirs can achieve a stable and long-term production cycle (Jamison, 1983; Lai et al., 2018). Currently, few studies are available on the quantitative simulation

of rock mass rupture in the tight sandstone reservoirs of the He8 segment in the Ordos Basin, which has restricted effective exploration and development of the tight sandstone reservoirs. Previously, researchers focused mainly on the stress environment of the formation of tight sandstone fractures in the He8 segment, including uniaxial stress (horizontal principal stress) evaluation, differential stress evaluation based on basin boundary deformation, tectonic trace stress inversion and layer erosion thickness recovery, etc. (Lai et al., 2018; Wan., 1993; Zhang et al., 2006). In this paper, 3D FEM was used to simulate the rupture parameters of the rock mass using the He8 segment of the Middle Permian Xiashihezi Formation in the Central Sulige well block as an example. The paleotectonic stress field of the study area for the maximum episode of compression during the Yanshanian movement was restored, and, the two rupture parameters of the integrated rupture rate (IF) and strain energy density (U) were constructed (Hardy et al., 1973; Ju et al., 2014; Ju and Sun., 2016). These parameters represent the probability of ruptures inside the rock mass. The reliability of different numerical simulation methods was verified by comparing their results with the gas well productivity. 2. Geological background The Ordos Basin is a composite basin located at the junction of multiple blocks (Cao, 2012), and its internal structural units were divided into the Yimeng uplift, west margin thrust belt, Tianhuan depression, Yishan slope, Jinxi flexure belt and Weibei uplift (Fig. 1a). The study area is the central Sulige well block, which is located in the central portion of the Sulige gas field, Ordos Basin (Fig. 1). The structure of the study area is shown in Fig. 1b–c. Low-amplitude structures are developed, and no faults appear in this area. The fold activities were mainly affected by the Yanshanian tectonic movement and were finally shaped during the Himalayan tectonic movement (Cao, 2012). The lowamplitude folds are characterized by broad, gentle folds and nose-like structures (Wu., 2017). The Upper Paleozoic Carboniferous-Permian strata are the key exploration layers in the study area. Previous studies have made full use of marker layer control, lithofacies tracing, sedimentary cycles and lithologic assemblage to divide the Upper Paleozoic stratigraphic units (Fig. 2) (Cao, 2012; Cheng et al., 2016; Wu, 2017). Multiple sets of gasbearing layers are developed in the Upper Paleozoic tight sandstone in this area. Among these layers, the Shan1 segment in the Lower Permian Shanxi Formation and the He8 segment in the Middle Permian Xiashihezi Formation are the gas-bearing strata with the highest potential, 90

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Fig. 2. Stratigraphic column of the Upper Paleozoic strata in the Ordos Basin.

density and rock mechanics parameters (including Young's modulus, Poisson's ratio, cohesion, and internal friction angle), and the output parameters include each principal stress, i.e., the maximum horizontal stress, minimum horizontal stress, vertical stress and shear stress, etc. The input parameters are the statically corrected logging interpretation results and are therefore reliable.

and their reservoir sand bodies consist mostly of distributary channel sediments of delta plain subfacies and underwater distributary channel sediments of delta frontier subfacies (Cheng et al., 2016). 3. A brief introduction to 3D FEM The finite element method (FEM) is a highly effective and commonly used tectonic stress field simulation method, and a large number of related studies have been conducted by previous researchers (Ding et al., 2012; Ju et al., 2017, 2018; Soloveichik et al., 2018; Ouraga et al., 2018; Yin et al., 2018c). The FEM calculations are based on the variational principle and discrete approximation interpolation (Yin et al., 2018c). First, the variational principle is used to transform the “variability problem” to be solved into the corresponding “variational problem”. The continuous geological body is divided into a series of units, and the discrete cells are linked together by nodes. Finally, the tectonic stress distribution is obtained through boundary stress loading (Cundall and Hart., 1985). The technology roadmap of the 3D geological model in this paper is shown in Fig. 3. In this paper, the tectonic stress field distributions of each subsegment in the Middle Permian He8 segment were predicted using 3D FEM, and the software selected for this application is ANSYS14.0. The input parameters of the 3D FEM simulation include the spatial distribution data of the formation, rock

4. 3D FEM simulation and analysis 4.1. Paleotectonic stress field recovery 4.1.1. Model building The planar tectonic features of the He8 segment in the study area are shown in Fig. 4. Based on the tectonic features of the four subsegments, the 3D finite element model of the He8 segment was constructed. This modeling technique is based on the shape function and trend surface analysis theory (Eyal et al., 2001). The model was completed from bottom to top (Fig. 5). In the modeling process, the 3D spatial coordinates of the key points were determined based on the structural form data of the geological body. A spline curve was constructed in ANSYS through the command flows, and the corresponding curved surface was generated. Finally, a 3D model that conforms to the actual geological body was produced by Fig. 3. Technology roadmap of 3D FEM geological modeling.

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Fig. 4. Planar tectonic features of the He8 segment in the study well block. Notes: The Middle Permian He8 segment can be divided into 4 subsegments, which are the (a) Upper He8-1 segment, (b) Upper He8-2 segment, (c) Lower He8-1 segment and (d) Lower He8-2 segment from top to bottom.

of tetrahedrons, and for the areas with complex structures, pentahedron and hexahedron units were applied (Fig. 7). A summary of the unit types and numbers of the finite element model is shown in Table 1. In this paper, fine meshing was performed on the established finite element model. The grid density was high, and its recognition accuracy was 20 m.

combining the continuous and closed curved surfaces (Camac and Hunt., 2009). For the different tectonic areas, several separate solid models were divided for meshing, and Boolean operations were used to connect the individual entities together. To achieve the desired effect, we used the spatial surface interpolation method in this step (Eyal et al., 2001). The model contained a total of 4750 key points, 1182 lines, 1020 areas and 288 vol units. The established 3D geological model of the target layer contains a four-layer structure, which can be divided from top to bottom into the Upper He8-1 segment, Upper He8-2 segment, Lower He8-1 segment and Lower He8-2 segment. The low-amplitude structures can be easily observed in the model (Fig. 6). The average formation thicknesses of the four layers are 14.99 m, 15.27 m, 17.04 m and 18.29 m from top to bottom. The Lower He8-2 segment at the bottom has the greatest exploration potential and gas production capacity, and its average sandstone ratio is also the highest at 52.64%. The sandstone ratio is the ratio of the sandstone thickness to the total formation thickness (Gross et al., 1995). The sandstone ratios of the other three layers from top to bottom are 23.41%, 24.49% and 42.81%.

4.1.3. Mechanical parameter assignments During the assignment of different units, the influence of the sandstone ratio (SMR) on rock mechanical parameters was sufficiently considered. For determination of the SMR, we made a comprehensive judgment based on the core observations and log curves. For example, as shown in Fig. 8, a thick layer of sandstone and a thin layer of mudstone are developed in the Lower He8-2 segment of Well S14 with an SMR of 87.23%. The observation of the cores shows that the sandstone in the He8 segment of the study area is primarily composed of quartz sandstone, and the quartz content is notably high, generally greater than 70%. The sandstone and mudstone sections can also be clearly distinguished from the GR log curve in Fig. 8. In fact, the sandstone and mudstone are interbedded in the He8 target layer. Compared with the entire Sulige gas field, the study area is highly localized, and the values of the rock mechanics parameters of the target layer show little variation. The Young's modulus of the rock is distributed from 23 GPa to 38 GPa, and the Poisson's ratio of the rock is distributed from 0.23 to 0.29. The histograms of the Young's modulus

4.1.2. Unit division Meshing is required because the established geometric models cannot be directly used in computational analysis (Ding et al., 2012). After meshing, the geometric model is known as the “finite element model.” The 3D geological model was meshed using a primary grid unit

Fig. 5. Finite element model of the target layer. 92

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Fig. 6. Low-amplitude structures of the finite element model of the target layer.

Fig. 7. Grid model of the target layer.

parameters from the logging interpretation, we found that a highly positive correlation exists between the Young's modulus and SMR of the rock, whereas a highly negative correlation exists between Poisson's ratio and the SMR of the rock. Therefore, in this paper, we assigned the Young's modulus and Poisson's ratio of the formation using the sandstone ratio as a constraint (Ding et al., 2013; Thiercelin and Roegiers., 2000). The relationship among the Young's modulus, Poisson's ratio and SMR of the He8 target layer is shown in Eqs. (1) and (2). Equation (1) has an R2 = 0.793 and RMSE = 1.96, and Equation (2) has an R2 = 0.606 and RMSE = 0.01 (R is the correlation coefficient and RMSE is the root-mean-square error):

Table 1 Summary of the finite element model. Formation

Upper Upper Lower Lower

He8-1 He8-2 He8-1 He8-2

Number of units Nodes

Elements

110 661 117 117 155 613 166 752

502 622 542 448 768 586 843 206

and Poisson's ratio of the He8 segment in the study area are shown in Fig. 9. The rock mechanics parameters of individual wells were obtained through logging interpretation, and these rock mechanics parameters were statically corrected (Fig. 8). Based on the rock mechanics parameter values at each well point, a simple kriging interpolation cannot accurately reflect the distribution of each rock mechanics parameter (Liu et al., 2017). Sedimentary facies (or SMR) is an important factor in controlling the distribution of rock mechanics parameters. Therefore, in this paper, the principle of sedimentary facies control was used to constrain the distribution of rock mechanics parameters. Based on the statistics of the sandstone ratio and the rock mechanics

E = 0.158⋅SMR + 21.37

(1)

ν = −0.0005⋅SMR + 0.275

(2)

where E is Young's modulus in GPa, ν is Poisson's ratio, and the SMR is the sandstone ratio. The sedimentary facies of the He8 segment of the study area consist of the primary distributary bay and distributary channel. The sedimentary facies of the He8 segment is divided by the SMR. When the SMR is less than 20%, the sedimentary facies is the distributary bay. When the SMR is ≥ 80%, the sedimentary facies is the distributary channel. In the process of assigning the rock mechanics parameters, we 93

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Fig. 8. Well logging interpretation results of the rock mechanics parameters for Well S14. Notes: GR — natural gamma; DEN — density; Δtp — compressional wave time difference; Δts — shear wave time difference; Ed — dynamic Young's modulus; Es — static Young's modulus; νd — dynamic Poisson's ratio; νs — static Poisson's ratio; C — cohesion; φ — internal friction angle; Vsh — shale content.

Fig. 9. Histograms of Young's modulus and Poisson's ratio of the He8 segment for wells in the study area.

fully considered the variations of these sedimentary facies. For other parameters, we still used the assignment method with the SMR as a constraint, and the result is shown in Table 2.

Table 2 Assignment of rock mechanics parameters. Formation

Sedimentary facies

SMR

Ρ (g·cm−3)

C (MPa)

Φ (°)

He8 segment

Distributary bay Distributary channel Distributary channel Distributary channel Distributary channel

SMR＜20% 20% ≤ SMR＜ 40% 40% ≤ SMR＜ 60% 60% ≤ SMR＜ 80% SMR≥80%

2.57 2.56

11.34 12.42

40.13 41.24

2.60

14.69

40.38

2.62

16.13

41.26

2.54

16.27

41.37

4.1.4. Loading scheme According to previous studies, the maximum episode of compressive tectonic stress during the Yanshanian period has the most important impact on the formation of fractures in the Xiashihezi Formation (Ren et al., 2002; Wan et al., 2010, 2013; Zhao et al., 2016; Zhou et al., 2006). In this period, the direction of the maximum horizontal principal stress was N45°W (Zhou et al., 2006). According to previous studies, the maximum principal stress of this area during the Yanshanian period was approximately 100 MPa, and the ratio of the maximum horizontal principal stress to the minimum horizontal principal stress was between 1.6 and 1.7 (Ding et al., 2016a; Wan et al., 2017; Zhou et al., 2006). The stress environment that we simulated is the paleotectonic stress field in the Yanshanian period. Prior to this stress activity, the studied Sulige area was in a period of calm tectonic activity, and its tectonic

Notes: SMR — sandstone ratio; ρ — density; C — cohesion; φ — internal friction angle.

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Fig. 10. Stress loading scheme for the finite element simulation. Notes: (a) Orthogonal stress mode for a single element, where L1, L2, and L3 are the element lengths, and θ is the rupture angle of rock, and (b) transection perpendicular to σ2 (or the σ1-σ3 plane) (Liu et al., 2017).

folds, the stress displays a diffusion and zoning characteristic. The rock of the target layer is tight and hard, and for different portions of the low-amplitude folds, distributions of both high- and low-stress areas occur. Fractures always have the tendency to rupture along the direction with the lowest rock strength. Especially during the intense hydrocarbon generation period, the rocks were prone to undergo vertical ruptures when the formation pressure was higher than the minimum horizontal principal stress (Yin et al., 2017b). Therefore, for regions where the formation pressure was higher than the minimum horizontal stress, the vertical fractures are generally much more developed (English, 2012). In the Upper He8-1 segment, the vertical stress has a small distribution range, which is distributed between 60 and 62 MPa (Fig. 11c), mainly due to the buried depth and the change in lithology. The shear stress of the Upper He8-1 segment is mostly distributed between 15 and 60 MPa (Fig. 11d). Similar to the horizontal principal stresses, under the influence of the local low-amplitude structures, the shear stress is higher in the western region and lower in the northeastern region and simultaneously has a stress diffusion characteristic. For the Upper He8-2 segment, the maximum horizontal principal stress is distributed between 90 and 138 MPa (Fig. 12a), and the minimum horizontal principal stress is distributed between 54 and 90 MPa (Fig. 12b). Similarly, the values of the maximum and minimum horizontal principal stresses increase from the eastern region to the western region, which is primarily due to the influence of the burial depth of the strata and the local tectonics. For the low-amplitude fold zone, the stress has a diffusion and zoning characteristic. The vertical principal stress has a small distribution range of 60.5–62.5 MPa (Fig. 12c). The shear stress of the Upper He8-2 segment is distributed between 16.5 and 60.5 MPa (Fig. 12d). The shear stress is higher in the western region and lower in the northeastern region and simultaneously has a stress diffusion characteristic. For the Lower He8-1 segment, the maximum horizontal principal stress is distributed between 90 and 139 MPa (Fig. 13a), and the minimum horizontal principal stress is distributed between 54 and 90 MPa (Fig. 13b). Similarly, the values of the maximum and minimum horizontal principal stresses increase from the eastern region to the western region. The vertical principal stress has a small distribution range of 60.5–63.5 MPa (Fig. 13c). The shear stress is distributed between 16.5 and 60.5 MPa (Fig. 13d), and it has an obvious stress diffusion characteristic. For the Lower He8-2 segment, the maximum horizontal principal stress is distributed between 90 and 139 MPa (Fig. 14a), and the minimum horizontal principal stress is distributed between 54 and 90 MPa (Fig. 14b). The values of the maximum and minimum horizontal principal stresses increase from the eastern region to the western region. The vertical principal stress has a small distribution range of 61–64 MPa (Fig. 14c), and the shear stress is distributed between 15

stress was notably weak. This is a typical feature of the low-amplitude tectonic area. To overcome the boundary effect and to better apply the boundary stress, we extended the peripheral region of the model (study area), as shown in Fig. 10. The strain boundary condition of the loading scheme fixes the bottom left and right sides of the model and applies boundary stress to the upper left and upper right of the model. Before the Yanshanian stress loading, according to the Gold nick model (Yin et al., 2017c) and assuming that the horizontal stress is completely induced by vertical stress, the horizontal stress is approximately 20 MPa. Therefore, before applying the Yanshanian stress, we first applied an initial stress of 20 MPa to the N45°W and N45°E directions of the model. At this point, the displacement of the model as a whole is approximately 10 m. This displacement is quite small, and the displacement on a single finite element is also notably small; thus, it can be ignored. When the Yanshanian stress is applied, the displacement of the model as a whole is approximately 30 m. At this time, the displacement acting on a single finite element is also notably small and can also be ignored. Based on this valid information, the stress loading scheme for the finite element simulation is shown in Fig. 10. The applied maximum and minimum horizontal compressive stresses are 100 MPa and 60 MPa, respectively. For the deformation problems during stress loading, the target layer in the study area was under a strong compression environment during the Yanshanian period, and a slight contraction was present in the entire stratum. After the Yanshanian period, with the erosion of the strata and the unloading of stress, the strata expanded to a certain degree and eventually formed the current structural form. Overall, the displacement of the study low-amplitude structural area in each stage is quite small. Under the stress loading condition in the Yanshanian period, the total displacement of the target layer is 30 m. For the entire study area, this displacement amount can be ignored. Because the 3D FEM simulation primarily analyzes the distribution trend of the tectonic stress field, relevant research in the study area is relatively lacking. Currently, we believe that the simulation results are reliable and also feasible for fracture prediction. The computation time of the simulation was 60 min.

4.1.5. Paleotectonic stress field The paleotectonic stress field of the Upper He8-1 segment is shown in Fig. 11, including the maximum, minimum and vertical principal stresses and shear stress. For the Upper He8-1 segment, the maximum horizontal principal stress is distributed between 90 and 138 MPa (Fig. 11a), and the minimum horizontal principal stress is distributed between 55 and 95 MPa (Fig. 11b). The values of the maximum and minimum horizontal principal stresses increase from the eastern region to the western region, which is due to the influence of the burial depth of the strata and the local tectonics. Because it is affected by local low-amplitude 95

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Fig. 11. Planar distribution of the paleotectonic stress of the Upper He8-1 segment. Notes: (a) Maximum horizontal principal stress; (b) minimum horizontal principal stress; (c) vertical principal stress; and (d) shear stress.

and 60 MPa (Fig. 14d). The shear stress has an obvious stress diffusion characteristic.

4.2. Distribution of rupture parameters The simulated rupture parameters in this paper include the integrated rupture rate (IF) and the strain energy density (U) (Hardy et al., 1973; Ju et al., 2014; Wang et al., 2004), and they both represent the

Fig. 12. Planar distribution of the paleotectonic stress of the Upper He8-2 segment. Notes: (a) Maximum horizontal principal stress; (b) minimum horizontal principal stress; (c) vertical principal stress; and (d) shear stress. 96

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Fig. 13. Planar distribution of the paleotectonic stress of the Lower He8-1 segment. Notes: (a) Maximum horizontal principal stress; (b) minimum horizontal principal stress; (c) vertical principal stress; and (d) shear stress.

methods cannot effectively predict its occurrence (Wang et al., 2004).

probability of rock rupture. The rupture mode includes the core-scale ruptures (core-scale fractures) and selected microscale ruptures (microfractures). Both of these rupture types can have a significant impact on the productivity of tight sandstone gas wells. The microscale rupture has random distribution characteristics, and conventional research

4.2.1. Integrated rupture rate (IF) Tensile and shear ruptures are the two most common rupture types in the study of the He8 tight sandstone reservoir (Cao, 2012; Zou et al.,

Fig. 14. Planar distribution of the paleotectonic stress of the Lower He8-2 segment. Notes: (a) Maximum horizontal principal stress; (b) minimum horizontal principal stress; (c) vertical principal stress; and (d) shear stress. 97

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generally has good correlation with the core-scale fractures (Yin et al., 2018c; Zeng et al., 2013). Depending on the order of rock failure, during the stress loading process, microfractures are always preferentially generated within the rock, followed by core-scale (or medium-scale) fractures, and largescale fractures or faults are eventually generated (John, 1969). The study area belongs to a weak tectonic zone in which selected low-amplitude folds were developed and no faults occur. The main fracture types in the He8 tight gas reservoirs are core-scale fractures and microfractures (Wu, 2017). A microfracture represents an important type of rupture, and its high development degree can ensure the stable production of natural gas for a longer cycle (Yin et al., 2018b). Therefore, if the rupture parameter ignores the microscale rupture type, its productivity prediction for gas wells is less effective.

2012). The integrated rupture rate (IF) considers these two types of ruptures by combining the Griffith rupture criterion (tensile rupture criterion) and the Mohr-Coulomb criterion (shear rupture criterion) (Yin et al., 2018c). The IF parameter is defined as follows:

IF = aη + bR

(3)

where a is the proportion of tensile ruptures or tensile fractures, b is the proportion of shear ruptures or shear fractures, η is the tensile rupture rate, and R is the shear rupture rate. The parameters η and R can be characterized by the various principal stresses obtained from the 3D FEM simulation (Yin et al., 2018c). This parameter IF was used to describe the rupture characteristics of the rock. If IF is less than or equal to 1, ruptures are caused inside the rock. For an IF greater than 1, the greater the value of IF, the higher the degree of rock rupture will be. The distribution trend of IF can aid in judging the single well productivity of the He8 tight sandstone reservoir. The fractures of the He8 tight sandstone reservoir have shearing or tensile-shearing properties (Wan et al., 2013; Zhou et al., 2006). Shear rupture and tensile rupture are both important rupture forms in the He8 segment. However, shear failure is the most common rupture form for the initial rupture of rocks in a strong extrusion stress environment (Wang et al., 2004; Zhou et al., 2006). The ratio of shear rupture to tensile rupture of the target layer is 3:1. The ratio of shear rupture to tensile rupture of the target layer in the study area is based on the statistical results of the core-scale fracture observations. Fig. 13 shows that the IF value is generally distributed between 0.13 and 2.44 (Fig. 15). We can identify certain similar features of IF from its plane distribution (Fig. 15). The southeastern region of the four studied layers is generally a high-rupture region with an IF value greater than 1.5 (Fig. 15). The northern portion of the study area is the second highrupture region with an IF value greater than 1.5 (Fig. 15). This method can predict only the probability of rock rupture from the perspective of rock deformation. Previous studies have shown that this method is suitable for the prediction of tight reservoir fractures in highly deformed zones with highly developed faults, and this parameter

4.2.2. Strain energy density (U) Plastic deformation and other non-elastic deformations occur during rock deformation. Microscale ruptures primarily occur in the tight sandstone of the He8 segment in the study area. For deformed rock masses with microscale ruptures, the strain energy stored in the rock is essentially equivalent to the elastic energy (Salamon., 1984). Therefore, according to the principle of energy conservation, the work performed by external forces acting on the deformed rock mass is equal to the strain energy within the rock mass (Jaeger and Cook., 1976). The work can be obtained using the displacement of the single unit node in the direction of the force (Ju et al., 2014). The strain energy method can effectively predict the strain energy density of a geologic body under certain tectonic stresses (Ju et al., 2014). During the propagation process of stress in the rock mass, strain energy continuously accumulates, and transformation of strain energy occurs (Cook et al., 2015; Han et al., 2015). The particles experience significant deformation and bending at the “stress concentration” area, and finally, the rocks break (Far et al., 2014; Heidari et al., 2013). The better the sorting of the rocks and the finer the particle size, the more prone the tight rocks are to have microscale ruptures between particles

Fig. 15. Planar distribution of IF of the He8 segment in the Xiashihezi Formation. Notes: (a) Upper He8-1 segment; (b) Upper He8-2 segment; (c) Lower He8-1 segment; and (d) Lower He8-2 segment. 98

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Fig. 16. Planar distribution of the strain energy density of the He8 segment in the Xiashihezi Formation. Notes: (a) Upper He8-1 segment; (b) Upper He8-2 segment; (c) Lower He8-1 segment; and (d) Lower He8-2 segment.

where E is Young's modulus (GPa); ν is Poisson's ratio; σX, σY and σZ are the three principal stresses (MPa); and τXY, τYZ and τZX are the shear stress components of the three principal stress directions (MPa). All of these parameters can be obtained from the 3D FEM simulation. According to the operation results, the U-value of the target layer is distributed in the range of 0.10–0.34 (Fig. 16). Overall, the regions with high U-values among the four study layers are mostly distributed in the southeastern region, which is consistent with the IF value distribution. For the Upper He8-1 and He8-2 segments (Fig. 16a–b), the range of the high U-value zones (U ≥ 0.24 J m−3) is substantially lower than that for the Lower He8-1 and He8-2 segments (Fig. 16c–d). This observation is related to the lower sandstone ratio of the upper two layers. The higher mud content gives the formation a relatively higher toughness, and thus, rupture is less likely to occur during stress loading. For the Lower He8-1 and He8-2 segments, the regions with high Uvalues have similar distributions, which are primarily distributed among the three regions circled in Fig. 16c–d. The high U-value region in the southeastern portion of the study area is similar to the aforementioned high IF value region. However, the other two high U-value regions are different from the aforementioned high IF value region. Additionally, a high U-value is not observed in the northern portion of the study area, which is substantially different from the aforementioned northern high IF value region.

Table 3 Single well productivity and simulated rupture parameters. Well name

Su1 Su4 Su8 Su10 Su11 Su12 Su19 Su20 Su31 Su33 Su34 Su37 Su38 Su39 Su40 Su41 Su42 Su43 Su44 Su45 Su46

Daily gas production ( × 104 m3) Maximum volume

Minimum volume

Average volume

1.1 1.2 1.1 0.9 0.8 0.7 1.7 2.0 1.0 3.2 2.0 1.1 0.8 1.3 2.0 1.2 1.0 2.1 2.2 1.3 1.5

0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.3 0.2 0.4 0.3 0.2 0.2 0.2 0.3 0.2 0.2 0.3 0.3 0.2 0.2

0.472 0.825 0.764 0.531 0.366 0.404 1.135 1.027 0.582 2.209 1.038 0.603 0.464 0.897 1.310 0.661 0.591 1.166 1.364 0.823 0.879

IF

U (J·m−3)

0.80 1.35 1.52 1.23 1.23 0.80 0.94 1.25 1.05 2.18 1.78 1.40 1.59 1.79 1.55 1.49 1.26 1.18 1.13 1.55 1.32

0.22 0.26 0.23 0.21 0.15 0.19 0.27 0.27 0.24 0.30 0.25 0.24 0.21 0.23 0.24 0.23 0.22 0.24 0.28 0.23 0.27

4.3. Relationship between rupture parameters and single well productivity (Ding et al., 2016a; Yin et al., 2016b). This method can better consider the probability of microscale ruptures. The higher the strain energy density of the rocks, the higher the degree of rock failure will be. The strain energy density of a rock mass under tectonic stress can be expressed as follows (Ju et al., 2014):

U=

1 [(σX2 + σY2 + σZ2) − 2ν (σX σY + σY σZ + σZ σX )] 2E 2 2 2 2(1 + ν )(τXY ) + τYZ + τZX + 2E

The Middle Permian He8 segment in the study area is a “low-efficiency reservoir” because of the relatively lower gas production (Ding et al., 2016b). To compare the consistency of the rupture parameters with the productivity of gas wells, we compared the relationship between rupture parameters and single-well productivity for wells with a stable capacity (Table 3 and Fig. 17). All of the wells have high drilling and completion quality with a stable production time of more than 3 years, and the production layer is located in the Lower He8-2 segment. Fig. 17 shows that the gas wells with high productivity (daily gas

(4) 99

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Fig. 17. Relationship between the rupture parameters and single well productivity. Notes: (a) Distribution of integrated rupture rate (IF) and (b) distribution of strain energy density (U).

production > 1 × 104 m3) are mostly located in the southeastern portion of the study area, which is consistent with the distribution of IF and U-values. The productivity of the gas wells in the northern area is generally low, which agrees well with the U-value distribution but largely differs from the IF value distribution. The relevance between the rupture parameters and the single well productivity is shown in Fig. 18. The productivity of Well Su33 is outside of the 99% prediction interval, and therefore, the productivity data of this well was excluded from regression analysis. The correlation of the single well productivity with the U-value is significantly better than that with the IF value. The U values are positively correlated with single well productivity, but the IF values are weakly positively correlated with single well productivity. This result indicates that the strain energy method is much more reliable in predicting the gas well production for the tight sandstone reservoirs of this study.

4.4. Discussion Fig. 19 shows the main high IF value distribution areas (region A and region B, IF ≥ 1.5) and the main high U-value distribution areas (region C, region D and region E, U ≥ 0.24 J m−3). According to the research in this paper, the strain energy method can predict the productivity of a tight gas sandstone reservoir more accurately than the comprehensive rupture rate method. The predictions of these two methods have certain similarities, but certain large differences remain. The integrated rupture rate method predicts the degree of rock mass ruptures from the perspective of macroscopic ruptures caused by the deformation of rocks (Zeng et al., 2013). However, the strain energy method predicts the degree of rock mass ruptures from the perspective of energy accumulation during the deformation of rocks (Wang et al., 2004). For weak tectonic or low-amplitude tectonic zones, the integrated rupture rate ignores the microscale ruptures and could also

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Fig. 18. Relationship between the rupture parameters and single well productivity. Notes: RMSE—root-mean-square error.

Fig. 19. Relationship among the rupture parameter distribution, low-amplitude structures and gas well productivity. 101

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studied. This study is of great value to enriching the prediction of “sweet spots” in tight gas sandstone reservoirs in low-amplitude tectonic zones worldwide.

overestimate the rock rupture degree (Fig. 19a), which might be the main reason for the large difference between the IF distribution and the gas well productivity. The strain energy density distribution has a high coincidence with gas well productivity (Fig. 18), indicating that it can better predict the rock rupture degree in low-amplitude tectonic zones. Because the prediction result of the strain energy method is the most reliable, we compared the relationship among the distribution of the high U-value region, the low-amplitude tectonic zone and its culmination or high position (Fig. 19b). Fig. 19b shows that a large proportion of the high U-value areas, such as in the northern portion of “Region E” and the southern portion of “Region F”, are distributed in the lowamplitude tectonic zone (green line range in Fig. 19). However, certain large high U-value areas are not distributed in the low-amplitude tectonic zone, such as “Region D”, the southern portion of “Region E” and the northern portion of “Region F” (Fig. 19b). The occurrence of the formation outside the low-amplitude tectonic zone is relatively limited, and is known as the “gentle tectonic zone” (Ding et al., 2016b). The tectonic activity in these areas was weak, and thus, microfracture is an important type of rupture. At this point, the advantages of the strain energy method are obvious. Seven distinct high positions are found in this low-amplitude tectonic zone (Fig. 19b, green five-pointed star). Three of the high points are located in the high U-value regions, and these areas represent the top and the wing areas of the low-amplitude folds with a high rock rupture degree. The other four high positions are not located in the high U-value regions, indicating that no higher rupture degree occurs for the rocks in the top portion of these low-amplitude fold areas. The deformation degree of these low-amplitude folds is not sufficient to cause a large-scale rock failure. However, the wing areas of these low-amplitude folds are located close to the high U-value region, indicating that the wing areas of the low-amplitude folds are also areas with high rock rupture. According to the prediction results of the strain energy method, the relationship between the high U-value region and the low-amplitude folds is rather complicated. These high U-value regions might be distributed outside or within the low-amplitude fold zone. The high Uvalue areas distributed outside the low-amplitude fold zone are mainly distributed in the vicinity of the low-amplitude fold zone, ensuring sufficient energy for rupture. The high U-value regions distributed within the low-amplitude fold zone are mostly distributed in the high position or wing area of the low-amplitude fold. The study found that not all structural highs are high U-value zones (or areas of high rock rupture). For the low-amplitude folds in the study area, only 43% of the top positions belong to the high U-value areas (Fig. 19b). The influencing factor of gas production analyzed in this paper is strain energy density based on the geomechanical theory. The principle of this geomechanical theory is based on rock mass deformation, energy aggregation and rupture probability. The areas with high U-values are relatively better for enriching natural gas. In fact, the factors affecting the gas production of tight sandstone reservoirs also include gas-inplace, reservoir properties, preservation conditions and production techniques. Therefore, for “sweet spot” prediction in the He8 tight sandstone reservoir, various geological and engineering factors and Uvalue distributions should all be comprehensively considered. The tight sandstone gas enrichment zone is the result of the coupling of these various factors. The study in this paper showed that the microfracture development area represented by the U-value distribution has an important influence on the distribution of tight sandstone gas. This study is simply a 3D finite element simulation study based on single factor of microfractures. In the exploration of a specific tight gas sandstone, other geological and engineering factors should also be considered. In this paper, an FEM numerical simulation based on the deformation and energy variation of the rock mass was used to predict the tight gas sandstone reservoir productivity, and a good evaluation result was obtained. The relationship among the strain energy distribution, the low-amplitude structures and gas well productivity was systematically

5. Conclusions (1) In this paper, using the He8 segment of the Middle Permian Xiashihezi Formation in the Central Sulige block as an example, an FEM numerical simulation based on the deformation and energy variation of the rock mass was used to predict tight gas sandstone reservoir productivity. (2) The paleotectonic stress field of the study area during the maximum episode of compression of the Yanshanian movement was restored. The tectonic stress had a diffusive distribution characteristic, and its distribution was affected by the combined effects of the burial depth of the stratum and the low-amplitude tectonics. (3) The two rupture parameters of integrated rupture rate (IF) and strain energy density (U) were constructed. For weak tectonic or low-amplitude zones, the integrated rupture rate ignores the microscale ruptures and might also overestimate the rock rupture degree. The strain energy density distribution has a high coincidence with gas well productivity, indicating that it can better predict the rock rupture degree in low-amplitude tectonic zones. (4) A complex relationship exists between the strain energy density distribution and the low-amplitude folds. The high strain energy density zones are primarily distributed among the high positions and wings of the low-amplitude fold zone, but the top of the lowamplitude folds does not necessarily have a high strain energy density. Portions of the high strain energy density zones are located near but outside the low-amplitude fold zone. The energy of these zones is relatively high, and the rock mass is prone to rupture. Acknowledgements This research was supported by the National Science and Technology Major Project of China (2016ZX05050) and the Open Foundation of Shandong Provincial Laboratory of Depositional Mineralization & Sedimentary Mineral, Shandong University of Science and Technology (Grant Nos. DMSM2017081). References Bose, C.C., Fairchild, B., Jones, T., Gul, A., Ghahfarokhi, R.B., 2015. Application of nanoproppants for fracture conductivity improvement by reducing fluid loss and packing of micro-fractures. J. Nat. Gas Sci. Eng. 27, 424–431. Camac, B.A., Hunt, S.P., 2009. Predicting the regional distribution of fracture networks using the distinct element numerical method. AAPG (Am. Assoc. Pet. Geol.) Bull. 93 (11), 1571–1583. Cao, B.D., 2012. Controlling Factors of Gas Accumulation in the Yuxi Gas Field in Western Shanxi Fold belt in Ordos Basin. Changan University in Chinese with English abstract). Cheng, J.H., Li, R.X., Qin, X., Li, D., Zhao, B., 2016. Impact of diagenetic facies on mechanical properties of sandstone rock in low-permeability reservoirs: a case study of the Upper Paleozoic has reservoir in east Ordos Basin. Acta Pet. Sin. 37 (10), 1256–1262 in Chinese with English abstract). Cook, J.E., Goodwin, L.B., Boutt, D.F., Tobin, H.J., 2015. The effect of systematic diagenetic changes on the mechanical behavior of a quartz-cemented sandstone. Geophysics 80 (2), D145–D160. Cundall, P.A., Hart, R.D., 1985. Development of generalized 2-D and 3-D distinct element programs for modeling jointed rock. Miscellaneous Paper SL-85–1. Itasca Consulting Group, US Army Corps of Engineers. Ding, W.L., Dai, P., Zhu, D.W., Zhang, Y.Q., He, J.H., Li, A., Wang, R.Y., 2016a. Fractures in continental shale reservoirs: a case study of the Upper Triassic strata in the SE Ordos Basin, Central China. Geological Magzine 154 (4), 663–680. Ding, W.L., Fan, T.L., Yu, B.S., Huang, X.B., Liu, C., 2012. Ordovician carbonate reservoir fracture characteristics and fracture distribution forecasting in the Tazhong area of Tarim Basin, Northwest China. J. Petrol. Sci. Eng. 86–87, 62–70. Ding, W.L., Zhu, D.W., Cai, J.J., Gong, M.L., Chen, F.Y., 2013. Analysis of the developmental characteristics and major regulating factors of fractures in marine-continental transitional shale-gas reservoirs: a case study of the Carboniferous-Permian strata in the southeastern Ordos Basin, central China. Mar. Petrol. Geol. 45, 121–133. Ding, X.Q., Yang, P., Han, M.M., Chen, Y., Zhang, S.Y., Zhang, S.N., Liu, X., Gong, Y.M., Nechval, A.M., 2016b. Characteristics of gas accumulation in a less efficient tight-gas

102

Journal of Petroleum Science and Engineering 170 (2018) 89–104

S. Yin et al. reservoir, He 8 interval, Sulige gas field, Ordos Basin, China. Russ. Geol. Geophys. 57, 1064–1077. Eltom, H.A., Abdullatif, O.M., Babalola, L.O., Bashari, M.A., Yassin, M., Osman, M.S., Abdulraziq, A.M., 2016. Integration of facies architecture, ooid granulometry and morphology for prediction of reservoir quality, Lower Triassic Khuff Formation, Saudi Arabia. Petrol. Geosci. 23 (2), 177–189. English, J.M., 2012. Thermomechanical origin of regional fracture systems. AAPG (Am. Assoc. Pet. Geol.) Bull. 96 (9), 1597–1625. Eyal, Y., Gross, M.R., Engelder, T., Becker, A., 2001. Joint development during fluctuation of the regional stress field in southern Israel. J. Struct. Geol. 23 (2–3), 279–296. Far, M.E., Hardage, B., Wagner, D., 2014. Fracture parameter inversion for Marcellus shale. Geophysics 79 (3), C55–C63. Farrell, N.J.C., Healy, D., Taylor, C.W., 2014. Anisotropy of permeability in faulted porous sandstones. J. Struct. Geol. 63, 50–67. Farrokhrouz, M., Aset, M.R., Kharrat, R., 2014. Empirical estimation of uniaxial compressive strength of shale formations. Geophysics 79 (4), D227–D233. Gong, F., Di, B.R., Wei, J.X., Ding, P.B., Shuai, D., 2018. Dynamic mechanical properties and anisotropy of synthetic shales with different clay minerals under confining pressure. Geophys. J. Int. 212 (3), 2003–2015. Gross, M.R., Fischer, M.P., Engelder, T., Greenfield, R.J., 1995. Factors controlling joint spacing in interbedded sedimentary rocks: integrating numerical models with field observation from the Monterey Formation, USA. In: In: Ameen, M.S. (Ed.), Fractography: Fracture Topography as a Tool in Fracture Mechanics and Stress Analysis. Geological Society Special Publication, vol 92. pp. 215–233. Han, T., Clennell, M.B., Josh, M., Pervukhina, M., 2015. Determination of effective grain geometry for electrical modeling of sedimentary rocks. Geophysics 80 (4), D319–D327. Hardy, M.P., Hudson, J.A., Fairhurst, C., 1973. The failure of rock beams: part I - theoretical studies. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 10, 53–67. Heidari, Z., Verdin, C.T., Pereeg, W.E., 2013. Improved estimation of mineral and fluid volumetric concentrations in thinly bedded carbonate formations. Geophysics 78 (4), 261–269. Hooker, J.N., Laubach, S.E., Marrett, R., 2013. Fracture-aperture-frequency, spatial distribution, and growth processes in strata-bounded and non-strata-bounded fractures, Cambrian Meson Group, NW Argetina. J. Petrol. Sci. Eng. 54, 54–71. Jaeger, J.C., Cook, N.G.W., 1976. Fundamentals of Rock Mechanics. Chapman and Hall, London, pp. 128–130. Jamison, W.L., 1983. Microcracks in rocks:a review. Tectonophysics 100, 449–480. Jamison, W.R., 2016. Fracture system evolution within the Cardium sandstone, central Alberta Foothills folds. AAPG (Am. Assoc. Pet. Geol.) Bull. 100 (7), 1099–1134. John, H., 1969. On the Coulomb–Mohr failure criterion. J. Geophys. Res. 74, 5343–5348. Ju, W., Hou, G.T., Feng, S.B., Zhao, W.T., Zhang, J.Z., You, Y., Zhan, Y., Yu, X., 2014. Quantitative prediction of the Yanchang formation Chang63 reservoir tectonic fracture in the Qingcheng-Heshui area, Ordos Basin. Earth Sci. Front. 21 (6), 310–320 in Chinese with English abstract). Ju, W., Sun, W.F., 2016. Tectonic fractures in the lower cretaceous Xiagou formation of Qingxi Oilfield, Jiuxi basin, NW China. Part two: numerical simulation of tectonic stress field and prediction of tectonic fractures. J. Petrol. Sci. Eng. 146, 626–636. Ju, W., Wu, C.F., Wang, K., Sun, W.F., Li, C., Chang, X.X., 2017. Prediction of tectonic fractures in low permeability sandstone reservoirs: a case study of the Es3m reservoir in the Block Shishen 100 and adjacent regions, Dongying Depression. J. Petrol. Sci. Eng. 156, 884–895. Ju, W., Yang, Z.B., Qin, Y., Yi, T.S., Zhang, Z.G., 2018. Characteristics of in-situ stress state and prediction of the permeability in the Upper Permian coalbed methane reservoir, western Guizhou region, SW China. J. Petrol. Sci. Eng. 165, 199–211. Lai, J., Wang, G., Ran, Y., Zhou, Z., Cui, Y., 2016. Impact of diagenesis on the petrophysical properties of tight oil reservoirs: the case of Upper Triassic Yanchang Formation Chang 7 oil layers in Ordos Basin, China. J. Petrol. Sci. Eng. 145, 54–65. Lai, J., Wang, G., Fan, Z., Wang, Z., Chen, J., Zhou, Z., Wang, S., Xiao, C., 2017. Fracture detection in oil-based drilling mud using a combination of borehole image and sonic logs. Mar. Petrol. Geol. 84, 195–214. Lai, J., Wang, G.W., Wang, Z.Y., Chen, J., Pang, X.J., Wang, S.C., Zhou, Z.L., He, Z.B., Qin, Z.Q., Fan, X.Q., 2018. A review on pore structure characterization in tight sandstones. Earth Sci. Rev. 177, 436–457. Laubach, S.E., 1997. A method to detect natural fracture strike in sandstones. AAPG (Am. Assoc. Pet. Geol.) Bull. 81 (4), 604–623. Li, D.Q., Wei, J.X., Di, B.R., Ding, P.B., Huang, S.Q., 2018. Experimental study and theoretical interpretation of saturation effect on ultrasonic velocity in tight sandstones under different pressure conditions. Geophys. J. Int. 212 (3), 2226–2237. Liu, J.S., Ding, W.L., Wang, R.Y., Yin, S., Yang, H.M., Gu, Y., 2017. Simulation of paleotectonic stress fields and quantitative prediction of multi-period fractures in shale reservoirs: a case study of the Niutitang Formation in the Lower Cambrian in the Cen'gong block, South China. Mar. Petrol. Geol. 84, 289–310. Lv, D.W., Wang, D.D., Li, Z.X., Liu, H.Y., Li, Y., 2017. Depositional environment, sequence stratigraphy and sedimentary mineralization mechanism in the coalbed- and oil shale-bearing succession: a case from the Paleogene Huangxian Basin of China. J. Petrol. Sci. Eng. 148, 32–51. Maystrenko, Y.P., Gernigon, L., Olesen, O., Ottesen, D., Rise, L., 2018. 3-D thermal effect of late Cenozoic erosion and deposition within the Lofoten–Vesterålen segment of the Mid- Norwegian continental margin. Geophys. J. Int. 213 (2), 885–918. Misra, S., Gupta, S., 2014. Superposed deformation and inherited structures in an ancient dilational step-over zone: post-mortem of the Rengali Province, India. J. Strul. Geol. 59, 1–17. Ouraga, Z., Guy, N., Pouya, A., 2018. Effect of hydro mechanical coupling on natural fracture network formation in sedimentary basins. Geophys. J. Int. 213 (2), 798–804. Price, N.J., 1966. Fault and Joint Development in Brittle and Semibrittle Rock. Pergamon

Press, United Kingdom. Ren, J.Y., Tamaki, K., Li, S.T., Zhang, J.X., 2002. Late Mesozoic and Cenozoic rifting and its dynamic setting in Eastern China and adjacent areas. Tectonophysics 344 (3–4), 175–205. Salamon, M.D.G., 1984. Energy considerations in rock mechanics: fundamental results. J. South Afr. Inst. Min. Metall. 84, 233–246. Soloveichik, Y.G., Persova, M.G., Domnikov, P.A., Koshkina, Y.I., Vagin, D.V., 2018. Finite-element solution to multidimensional multisource electromagnetic problems in the frequency domain using non-conforming meshes. Geophys. J. Int. 212 (3), 2159–2193. Thiercelin, M.J., Roegiers, J.C., 2000. In: Economides, M.J., Nolte, K.G. (Eds.), Formation Characterization: Rock Mechanics. Wiley Press, New York. Vishal, V., Ranjith, P.G., Singh, T.N., 2013a. CO2 permeability of Indian bituminous coals: implications for carbon sequestration. Int. J. Coal Geol. 105, 36–47. Vishal, V., Ranjith, P.G., Pradhan, S.P., Singh, T.N., 2013b. Permeability of sub-critical carbon dioxide in naturally fractured India bituminous coal at a down-hole stress conditions. Eng. Geol. 167, 148–156. Wan, T.F., 1993. Intraplate Deformation and its Uses in the Eastern China. Geological Publishing House, Beijing, pp. 79–84 in Chinese). Wan, Y.P., Li, H.L., Li, Y., Song, Z.J., Li, Y.Y., Qi, P.W., 2017. The field stress between late Jurassic and early cretaceous in the eastern Ordos Basin. Earth Sci. 42 (4), 499–556 in Chinese with English abstract). Wan, Y.P., Li, Y.Y., Liang, X., 2010. Fractures of reservoirs inferred from inclusions: a case study of the Upper Paleozoic of Northern Shanxi slope. Geology and Exploration 46 (4), 711–715 in Chinese with English abstract). Wan, Y.P., Wang, G.H., Gui, R., 2013. Fractures of the Upper Paleozoic in Northern Shanxi slope and its natural gas accumulation significance. J. Jilin Univ. (Earth Sci. Ed.) 43 (1), 28–38 in Chinese with English abstract). Wang, L.J., Wang, H.C., Wang, W., Sun, B.S., Qiao, Z.J., 2004. Relation among three dimensional tectonic stress field, fracture and migration of oil and gas in oil field, Chinese. J. Rock Mech. Eng 23, 4052–4057 (In Chinese with English abstract). Wessling, S., Bartetzko, A., Tesch, P., 2013. Quantification of uncertainty in a multistage/ multiparameter modeling workflow: pore pressure from geophysical well logs. Geophysics 78 (3), 101–112. Wu, Y.C., 2017. Characteristics and distribution of Carboniferous - Permian gas reservoirs in the southern Shanxi fold flex belt. Shandong University of Science and Technology in Chinese with English abstract). Yin, S., Ding, W.L., Zhou, W., Shan, Y.M., Wang, R.Y., Liu, J.J., Gu, Y., 2016a. Logging assessment of tight clastic rock reservoir fractures via the extraction of effective pore aspect ratios: a case study of lower Permian strata in the southern Qinshui Basin of eastern China. J. Nat. Gas Sci. Eng. 36, 597–616. Yin, S., Ding, W.L., Sun, Y.X., Wang, X.H., Zhang, M., Zhang, N.J., 2016b. Shale uniaxial compressive failure properties and the affecting factors of UCS. Earth Sci. Front. 23 (2), 75–95. Yin, S., Zhou, W., Shan, Y.M., Ding, W.L., Xie, R.C., Guo, C.H., 2017a. Assessment of the geostress field of deep-thick gypsum cap rocks: a case study of Paleogene Formation in the southwestern Tarim Basin, NW China. J. Petrol. Sci. Eng. 154, 76–90. Yin, S., Ding, W.L., Wang, F.Q., Cao, X.Y., Liu, J.J., Lu, X.J., 2017b. Stress mechanism of negative inversion structures and its implication for oil and gas in Southern Qinshui Basin, China. J. Chengdu Univ. Technol. (Sci. Technol. Ed.) 44 (6), 1–14 in Chinese with English abstract). Yin, S., Ding, W.L., Zhou, W., Shan, Y.M., Xie, R.C., Guo, C.H., Cao, X.Y., Wang, R.Y., Wang, X.H., 2017c. In situ stress field evaluation of deep marine tight sandstone oil reservoir: a case study of Silurian strata in northern Tazhong area, Tarim Basin, NW China. Mar. Petrol. Geol. 80 (1), 49–69 2017. Yin, S., Li, A.R., Jia, Q., Ding, W.L., Li, Y.X., 2018a. Numerical simulation of the in situ stress in a high-rank coal reservoir and its effect on coal-bed methane well productivity. Interpretation 6 (2), 1–11. Yin, S., Lv, D.W., Ding, W.L., 2018b. New method for assessing microfracture stress sensitivity in tight sandstone reservoirs based on acoustic experiments. Int. J. GeoMech. 18 (4), 1–16. Yin, S., Jia, Q., Ding, W.L., 2018c. 3D paleotectonic stress field simulations and fracture prediction for marine-continental transitional facies forming a tight-sandstone reservoir in a highly deformed area. J. Geophys. Eng. 18, 1–17. Zeng, L.B., Jiang, J.W., Yang, Y.L., 2010. Fractures in the low porosity and ultra-low permeability glutenite reservoirs: a case study of the late Eocene Hetaoyuan formation in the Anpeng Oil-field, Nanxiang Basin, China. Mar. Petrol. Geol. 27, 1 642–1 650. Zeng, L.B., Su, H., Tang, X.M., Peng, Y.M., Gong, L., 2012. Fractured tight sandstone oil and gas reservoir: a new play type in the Dongpu depression, Bohai Bay Basin, China. AAPG (Am. Assoc. Pet. Geol.) Bull. 97 (3), 363–377. Zeng, W.T., Ding, W.L., Zhang, J.C., Zhang, Y.Q., Guo, L., Jiu, K., Li, Y.F., 2013. Fracture development in Paleozoic shale of Chongqing area (South China). Part two: numerical simulation of tectonic stress field and prediction of fractures distribution. J. Asian Earth Sci. 75, 267–279. Zhang, Y.Q., Shi, W., Liao, C.Z., 2006. Fault kinematic analysis and change in Late Mesozoic tectonic stress regimes in the Peripheral zones of the Ordos Basin, North China. Acta Geol. Sin. 80 (5), 639–647 in Chinese with English abstract). Zhao, J.L., Tang, D.Z., Xu, Hao, Lv, Y.M., Tao, S., 2015. High production index and the key factors in coalbed methane production: a case in the Hancheng block, southeastern Ordos Basin, China. J. Petrol. Sci. Eng. 130, 55–67. Zhao, J.L., Xu, H., Tang, D.Z., Mathews, J.P., Li, S., Tao, S., 2016. Coal seam porosity and fracture heterogeneity of macrolithotypes in the Hancheng Block, eastern margin, Ordos Basin, China. Int. J. Coal Geol. 159, 18–29. Zhao, J.L., Tang, D.Z., Qin, Y., Xu, H., Lv, Y.M., Tao, S., Li, S., 2017. Evaluation of fracture system for coal marcolithotypes in the Hancheng Block, eastern margin of the Ordos

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Journal of Petroleum Science and Engineering 170 (2018) 89–104

S. Yin et al.

Zou, C.N., Zhu, R.K., Liu, K.Y., Su, L., Bai, B., Zhang, X.X., Yuan, X.J., Wang, J.H., 2012. Tight gas sandstone reservoir in China: characteristics and recognition criteria. J. Petrol. Sci. Eng. 88–89, 82–91. Zhao, W.T., Hou, G.T., Hari, K.R., 2016. Two episodes of structural fractures and their stress field modeling in the Ordos Block, Northern China. J. Geodyn. 97, 7–21. Zhou, W., Zhang, S.N., Li, L., Su, F.Y., 2006. The character of Upper Paleozoic reservoir fractures and the evaluation of their distribution in Tabamiao. J. Mineral Petrol. 26 (4), 54–61 in Chinese with English abstract).

Basin, China. J. Petrol. Sci. Eng. 159, 799–809. Zou, C.N., Tao, S.Z., Zhu, R.K., Yuan, X.J., Li, W., Zhang, G.Y., Zhang, X.X., Gao, X.H., Liu, L.H., Xu, C.C., Song, J.R., Li, G.H., 2009. Formation and distribution of “continuous” gas reservoirs nd their giant gas province: a case from the Upper riassic Xujiahe Formation giant gas province, Sichuan Basin. Petrol. Explor. Dev. 36 (3), 307–319. Zou, C.N., Yang, Z., Zhang, G.S., Hou, L.H., Zhu, R.K., Tao, S.Z., Yuan, X.J., Dong, D.Z., Wang, Q.G., Wang, L., Bi, H.B., Li, D.H., Wu, N., 2014. Conventional and unconventional petroleum "orderly accumulation": concept and practical significance. Petrol. Explor. Dev. 41 (1), 14–30.

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