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Evaluation of the current in situ stress in the middle Permian Maokou Formation in the Longnüsi area of the central Sichuan Basin, China

  • Tianbiao Zhao , Qirong Qin , Hu Li EMAIL logo , Shilin Wang and Xingyu Mou
Published/Copyright: August 29, 2023
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Open Geosciences
From the journal Open Geosciences Volume 15 Issue 1

Abstract

The middle Permian Maokou Formation in the Longnüsi area in the central Sichuan Basin is currently a key formation for exploration and development. The evaluation of the current in situ stress in this area is of great significance for fracture prediction, well pattern deployment, drilling and construction, and fracturing stimulation. This study clarifies the current direction and magnitude distributions of the in situ stress by evaluating the Maokou Formation in the Longnüsi area using finite-element numerical simulation, acoustic emission experiments, and logging data (including data from imaging logging, array acoustic logging, conventional logging, and cross-dipole acoustic logging). Specifically, the current maximum horizontal stress of the Maokou Formation in the Longnüsi area is mainly in the NW‒SE direction, and the stress direction is greatly affected by the local fault zone. The current minimum horizontal stress magnitude of the Maokou Formation obtained by acoustic emission experiments is between 96.29 and 114.36 MPa, the current maximum horizontal stress magnitude is between 126.01 and 145.10 MPa, and the current horizontal stress difference is between 25.59 and 32.58 MPa. The current minimum and maximum horizontal stress magnitudes both decrease from north to south. The current horizontal stress parameters calculated by Huang’s model are not significantly different from those experimentally measured: there is a difference of less than 8% in the current minimum horizontal stress magnitude, a difference of less than 9% in the maximum horizontal stress magnitude, and a difference of less than 15% in the current horizontal stress difference. Therefore, Huang’s model has good applicability in terms of calculating the current horizontal stresses in the Longnüsi area. The current horizontal stress parameters, which are numerically simulated with the finite-element method, are also not much different from those experimentally measured: there is a difference of less than 11% in the current minimum horizontal stress magnitude, a difference of less than 10% in the maximum horizontal stress magnitude, and a difference of less than 20% in the current horizontal stress difference. The numerically simulated current horizontal stress also decreases from north to south. Therefore, the simulated results are highly accurate. This study clarifies the directions and magnitudes of the current in situ stress state of the Maokou Formation in the Longnüsi area of the central Sichuan Basin and provides a basis for the formulation of exploration and development plans for the Maokou Formation reservoir in the study area.

Keywords: current in situ stress; imaging logging; acoustic logging; acoustic emission experiment; numerical simulation; Longnüsi area

1 Introduction

The current in situ stress state refers to the natural forces that exist in a crustal rock mass and have not been disturbed by engineering activities; it is also known as the far-field stress state and is mainly composed of gravitational stress, tectonic stress, pore pressure, thermal stress, and residual stress [1]. Current in situ stress is one of the important parameters that control many factors, including the distribution of oil- and gas-rich areas, the distribution of reservoir fractures, formation fracture pressure, and collapse pressure. Current in situ stress must be considered in engineering design during oil and gas reservoir exploration and development, deployment of production well patterns, prediction of natural gas-rich areas, determination of perforation plans, the design of gas well fracturing, the problem of sand production in gas wells during production, deformation of the drilling casing, and stability of the well wall [2,3,4,5]. Therefore, obtaining accurate in situ stress field information has remained a focus of geophysicists [6].

The current in situ stress state is usually described by a vertical principal stress ( S v ) and two horizontal principal stresses, namely, the current maximum horizontal stress ( S H ) and the current minimum horizontal stress ( S h ); these three stresses are perpendicular to each other [7]. Various methods have been developed to determine current in situ stress. According to different approaches to implementation, these methods are categorized into measurement methods, calculation methods, and numerical simulation methods. The measurement methods mainly include the hydraulic fracturing method [8], the acoustic emission method (Kaiser effect) [9,10,11], and the earthquake mechanism analysis method [12]. Although measurement methods can obtain highly accurate data about the current in situ stress, they have shortcomings, such as high workloads, poor data continuity, and high measurement cost. Therefore, these methods are not suitable for regional stress measurement. In contrast, the calculation methods generate more accurate results and are becoming more applicable due to the increasingly comprehensive consideration of various factors. There is not much controversy about the calculation of the vertical principal stress, which is regarded as equal to the gravity of the overlying rock mass, and the latter can be obtained by integrating the density curve from the surface to the target depth. There are many calculation models for the horizontal principal stresses. They mainly include the uniaxial strain model, Mohr‒Coulomb failure model, Coulomb–Navier failure model, combined spring model, Huang’s model (a calculation model proposed by Rongzun Huang), and Ge’s model [13,14,15]. Among them, Huang’s model is currently the most popular calculation method. At present, the finite-element numerical simulation method is also widely used in the prediction of current in situ stress due to its high adaptability, high computational efficiency, and ability to directly represent the continuous stress field distribution [16,17,18]. Since any single method for evaluating the current in situ stress has limitations, the best way to evaluate a region’s stress state is the combined use of multiple methods [19].

The central Sichuan Basin has always been a key area for oil and gas exploration and development [20,21,22,23]. The discovery of high-yield industrial gas flow in Wells NC1 and JT1 in the Maokou Formation has set off a wave of exploration and development in the central Sichuan Basin. Based on laboratory drilling data, Tian et al. classified the sedimentary facies of the Maokou Formation’s first member in the central Sichuan Basin [24]. Xiao et al. studied the formation mechanism of the dolomite reservoir in the Maokou Formation, which is in the Bajiaochang structure in the central and northern Sichuan Basin [25]. Long et al. predicted a favorable area for reservoir development in the Maokou Formation in the Longnüsi area of the central Sichuan Basin [26]. Relevant studies have also deepened the understanding of the reservoirs in the Maokou Formation in the central Sichuan Basin mainly from the perspective of exploration but have not evaluated the reservoirs’ current in situ stress [27,28,29,30,31,32]. This article comprehensively evaluates the current in situ stress of the Maokou Formation in the Longnüsi area based on conventional logging, imaging logging, acoustic logging, and other data combined with acoustic emission experiments and finite-element numerical simulation, thus providing a basis for the formulation of exploration and development plans.

2 Geological setting

The Sichuan Basin is a NE-trending rhombus-shaped geomorphologic basin located on the western margin of the Yangtze Plate, and it has the attributes of both a sedimentary basin and a tectonic basin [33,34,35]. The basin is bounded by the Micangshan thrust belt in the north, the Dabashan thrust belt in the northeast, the Longmenshan thrust belt and the Songpan-Ganzi fold belt in the west, the Daliangshan fault belt in the south, and the Xuefeng intracontinental tectonic system in the southeast. According to the current structural features of the Sinian System, the current structural features and deposition in the basin, and the current situations of basin deposition and structure, and oil and gas exploration, the interior of the Sichuan Basin is divided into the central Sichuan uplift belt, the southern Sichuan low-steep fold belt, the eastern Sichuan high-steep fold belt, and the northern Sichuan low-gentle fold belt [36], as shown in Figure 1a.

Figure 1 Comprehensive histogram of the regional geological setting and stratigraphy in the Longnusi area in the central Sichuan Basin: (a) study area, (b) top structure of the Maokou Formation, and (c) stratigraphic characteristics.
Figure 1

Comprehensive histogram of the regional geological setting and stratigraphy in the Longnusi area in the central Sichuan Basin: (a) study area, (b) top structure of the Maokou Formation, and (c) stratigraphic characteristics.

The study area is mainly in the central Sichuan Basin and is structurally located in the eastern part of the central Sichuan uplift belt, including part of the southern Sichuan low-steep fold belt and the eastern Sichuan high-steep fold belt. The tectonic-sedimentary evolution process in the study area is completely controlled by the tectonic-sedimentary evolution process of the central Sichuan paleo-uplift. The faults in the study area are less developed, the folds are gentle, and the terrain has the characteristics of being high slopes in the south and low in the north. As shown in the structural map of the top of the Maokou Formation in the study area, the region is overall low in the north and high in the south with a relatively gentle structure, and several near-E–W-trending faults are developed in the region, as shown in Figure 1b.

The Maokou period inherited the sedimentary pattern of the Qixia period. In the early Maokou period, the sedimentary landform was relatively stable with gentle slope facies as the main sediments; in the middle and late Maokou period, open platform sediments were the main sediments; and in the late Maokou period, the magma pushed up against the crust, and local tension and subsidence occurred, forming a rift basin. At the end of the Maokou period, volcanic activity and uplift reached their peak, and the whole middle and upper Yangtze region uplifted above sea level and suffered regional erosion, forming a parallel unconformity between the middle and upper Permian strata [37]. The overall thickness of the Maokou Formation in the study area is 120–360 m, and it is composed of the first, second, third, and fourth members from bottom to top. The bottom of the first member of the Maokou Formation developed medium- to thin-layered dark gray argillaceous limestone intercalated with thin-layered argillaceous strips, forming eyelid-shaped structures, and the upper part of the first member of the Maokou Formation developed thick dark gray argillaceous limestone. The lithologies of the second member of the Maokou Formation are mainly gray limestone, light gray biolimestone, and dolomite with some flint clusters or nodules. The third member of the Maokou Formation mainly developed light gray or grayish-white bioclastic sparitic limestone, as shown in Figure 1c. Influenced by the Dongwu movement at the end of the Maokou period, the fourth member of the Maokou Formation in the basin was uplifted and denuded to varying degrees, so this member is rarely encountered in boreholes [38,39].

3 Samples and methods

3.1 Samples

The samples and data used in this study were all from the Longnüsi area in the central Sichuan Basin. This study mainly combined logging data analysis, core experiments, and numerical simulation. The logging data mainly included imaging logging data, cross-dipole acoustic logging data, conventional logging data, and array acoustic logging data. The core experiments included acoustic emission experiments and triaxial compression experiments. Details about the samples and data used in this study are shown in Table 1.

Table 1

Analytical items and samples

Analytical item Analytical purpose Research content Sample name Sample number
Stress direction Maximum horizontal stress direction Orientation of drilling-induced fractures Imaging logging data 8
Minimum horizontal stress direction Azimuth of borehole breakouts 8
Maximum horizontal stress direction Stratigraphic anisotropy Cross-dipole acoustic logging data 6
Stress magnitude Magnitude of horizontal stress Acoustic emission experiment Core 14
Magnitude of vertical stress Stratigraphic density Conventional logging data 7
Magnitude of horizontal stress Longitudinal and shear wave velocities Array acoustic logging data 7
Numerical simulation Rock mechanics parameters Triaxial compression experiment Core 4

3.2 Analytical method for determining the in situ stress directions

3.2.1 Imaging logging

During the drilling process, as the borehole core is removed, the stress concentration at the borehole under the action of confining pressure causes the development of drilling-induced fractures. When the concentrated stress exceeds the fracture strength of the rock around the borehole, borehole breakouts occur [40]. The orientation of drilling-induced fractures often indicates the direction of the current maximum horizontal stress, while the azimuth of borehole breakouts is generally perpendicular to the direction of the current maximum horizontal stress; that is, the azimuth of borehole breakouts indicates the direction of the current minimum horizontal stress [41]. The orientations of the drilling-induced fractures and the azimuths of the borehole breakouts can be judged from the imaging logging data. Borehole breakouts in the imaging logging appear as wide dark bands with an interval of 180°, while the drilling-induced fractures appear as narrow dark bands perpendicular to the azimuths of the borehole breakouts in the imaging logging [42]. Hence, we can judge the directions of the current maximum horizontal stress and the current minimum horizontal stress by identifying the orientations of the drilling-induced fractures and the azimuths of the borehole breakouts on the imaging logging data.

3.2.2 Cross-dipole acoustic logging

The cross-dipole acoustic logging instrument has two orthogonal dipole emitters that emit pressure pulses to the formation in two mutually perpendicular directions. The anisotropy of the formation can be judged by the time difference and phase difference of the two received waveforms. In the azimuthally anisotropic formations caused by the current horizontal stress difference, the fast and slow flexural waves of the cross-dipole acoustic logging show dispersive crossover, which can be used to distinguish the causes of formation anisotropy and then identify the presence of heterogeneous in situ stress. Specifically, the orientation of the fast shear wave is the same as the direction of the current maximum horizontal stress [43]. Therefore, we can use the predominant orientation of the propagation of fast shear waves in in situ stress-induced anisotropic formations to determine the direction of the current maximum horizontal stress.

3.3 Calculation method for determining the in situ stress magnitudes

3.3.1 Acoustic emission experiment

Two full-sized and complete core samples with a length of 20 cm were taken from each of 7 wells, including Wells MX56, HS4, HS3, and L1, totaling 14 samples [44,45]. In the laboratory, three small samples (diameter × height: Ф25 mm × 50 mm) were drilled from each core sample at an interval angle of 45° from the horizontal direction according to the Specification for Measurement of Rock Acoustic Properties in Laboratory (SY/T6351-2012). Uniaxial compression experiments were carried out on the samples taken from different directions, and the acoustic emission signal of the sample during the loading process was measured by a comprehensive rock acoustic experiment system (model SDS-1). The magnitude of the horizontal stress was calculated using the elastic planar stress formula [46]:

(1) S H = σ x + σ y 2 + 2 2 ( σ x − σ xy ) 2 + ( σ xy − σ y ) 2 , S h = σ x + σ y 2 − 2 2 ( σ x − σ xy ) 2 + ( σ xy − σ y ) 2 tan ( 2 θ ) = σ x + σ y − 2 σ xy σ x − σ y , ,

where σ x is the magnitude of the core’s stress at the Kaiser point in the 0° direction, σ xy is the magnitude of the core’s stress at the Kaiser point in the 45° direction, σ y is the magnitude of the core’s stress at the Kaiser point in the 90° direction, and θ is the azimuth of the maximum horizontal principal stress.

3.3.2 Value of vertical in situ stress magnitude

The vertical principal stress is also the overlying formation pressure, which refers to the pressure caused by the total weight of the rock overlying the formation and the fluid in the rock’s pores. The vertical principal stress is calculated by [2]:

(2) S v = ρ 0 × g × H 0 + ∫ H 0 H ρ b × g × dh × 10 − 3 ,

where S v is the vertical stress magnitude, MPa; ρ b is the formation density varying with depth and the value of this parameter comes from conventional logging data, g/cm3; ρ 0 denotes the mean formation density from the top boundary of the study well section to the wellhead, which is generally 2.3 g/cm3 in the study area; H 0 is the depth of the study well section’s top boundary, m; and H is the depth of the study well section’s bottom boundary, m.

3.3.3 Huang’s model

Array acoustic logging can provide longitudinal wave, shear wave, Stoneley wave, and full wave information. Huang’s model can be used to calculate the magnitudes of the current minimum and maximum horizontal stresses, and it is defined in the following equation [47]:

(3) S h = μ 1 − μ ( S v − α P p ) + K h ( S v − α P p ) + α P p S H = μ 1 − μ ( S v − α P p ) + K H ( S v − α P p ) + α P p ,

where S h and S H are the magnitudes of the current minimum and maximum horizontal stresses, respectively, MPa; S v is the vertical stress, MPa; K h and K H are the tectonic stress coefficients in the directions of the current minimum and maximum horizontal stresses, respectively; P p is the formation pressure, MPa; μ is Poisson’s ratio of the rock; and α is the effective stress coefficient. μ is calculated by the longitudinal and shear wave speeds. K h , K H , and α are inversely calculated by the measured current in situ stress results. P p is obtained through measurements, and S v is calculated based on conventional logging data.

3.4 Finite-element simulation of current in situ stress

3.4.1 Process

The basic idea of the finite-element numerical simulation method is as follows: First, the geological body is discretized into several finite elements connected by nodes, and the corresponding rock mechanics parameters are assigned to the corresponding elements. The basic physical fields in the study area include displacement, stress, and strain. According to the boundary force conditions and node balance conditions, the solution to the equation system with the node displacement as the unknown quantity and the overall stiffness matrix as the coefficient is obtained. The displacement of each node is calculated, and then, the stress and strain within each element can be calculated. The finite-element solution problem can usually be divided into the following steps: (1) pretreatment, (2) solution, and (3) posttreatment. The specific solution process is shown in Figure 2.

Figure 2 Flow chart of the finite-element numerical simulation.
Figure 2

Flow chart of the finite-element numerical simulation.

3.4.2 Triaxial experiment

One core sample was collected from the middle Permian Maokou Formation in Wells MX56, HS4, TT1, and L1, totaling four core samples. The collected core samples were processed and prepared into standard cylindrical samples (diameter × height: Ф50 mm × 100 mm) in the laboratory. The processing accuracy met the experimental specifications recommended by the International Society for Rock Mechanics and the American Society for Experimenting and Materials. The loading device used in the experiment was a GCTS RTR-2000 electrohydraulic servo high-temperature and high-pressure dynamic rock triaxial experiment system produced in the United States. The main parameters obtained from the triaxial experiments included compressive strength, Young’s modulus, and Poisson’s ratio.

4 Results and discussion

4.1 Current in situ stress directions

4.1.1 Identification of imaging logging

The orientation of the drilling-induced fractures in the imaging logging data indicates the direction of the maximum horizontal stress, and the azimuth of the borehole breakouts indicates the direction of the current minimum horizontal stress. Therefore, in the same drilling well, if the directions of in situ stress identified by the two methods are perpendicular to each other, it indicates that the method is effective. As an example, Figure 3 shows the identification method and results of imaging data for two wells.

Figure 3 Current in situ stress direction analysis diagrams of the Maokou Formation in the study area: (a) drilling-induced fractures of Well MX151, (b) drilling-induced fractures of Well MX56, (c) borehole breakouts of Well MX151, and (d) borehole breakouts of Well MX56.
Figure 3

Current in situ stress direction analysis diagrams of the Maokou Formation in the study area: (a) drilling-induced fractures of Well MX151, (b) drilling-induced fractures of Well MX56, (c) borehole breakouts of Well MX151, and (d) borehole breakouts of Well MX56.

Figure 3a shows the orientations of the drilling-induced fractures in Well MX151. The predominant orientations of the drilling-induced fractures at this depth range are 125° ± 5° and 305° ± 5°, which indicates that the current maximum horizontal stress at this depth range is in the NW‒SE direction. Figure 3c shows the azimuths of borehole breakouts in Well MX151. The predominant azimuths of the borehole breakouts at this depth range are 30° ± 5° and 210° ± 5°, which indicates that the current minimum horizontal stress at this depth range is in the NE‒SW direction. The direction of maximum horizontal stress and minimum horizontal stress obtained in well MX151 are perpendicular.

Figure 3b shows the orientations of the drilling-induced fractures in Well MX56. The predominant orientations of the drilling-induced fractures at this depth range are 115° ± 5° and 295° ± 5°, which indicates that the current maximum horizontal stress at this depth range is in the NW‒SE direction. Figure 3d shows the azimuths of the borehole breakouts in Well X56. The predominant azimuths of the borehole breakouts at this depth range are 25° ± 5° and 205° ± 5°, which suggests that the current minimum horizontal stress at this depth range is in the NE‒SW direction. The direction of maximum horizontal stress and minimum horizontal stress obtained in well MX56 are perpendicular.

We identified the orientations of the drilling-induced fractures and the azimuths of the borehole breakouts for eight wells (including Wells MX39, MX42, MX56, etc.) in the study area and determined the directions of their current maximum horizontal stress and current minimum horizontal stress (Table 2). The direction of maximum horizontal stress and minimum horizontal stress obtained in Well MX56 is perpendicular.

Table 2

Statistics of the interpretation results of drilling-induced fractures and borehole breakouts

Well Dominant azimuth of drilling-induced fractures Current max horizontal in situ stress direction Dominant azimuth of borehole breakout Current min horizontal in situ stress direction
MX39 125° ± 5° and 305° ± 5° NW‒SE 35° ± 5° and 215° ± 5° NE‒SW
MX42 95° ± 5° and 275° ± 5° Near E‒W 5° ± 5° and 185° ± 5° Nearly S‒N
MX56 115° ± 5° and 295° ± 5° NW‒SE 25° ± 5° and 205° ± 5° NE‒SW
MX151 125° ± 5° and 305° ± 5° NW‒SE 35° ± 5° and 215° ± 5° NE‒SW
MX208 95° ± 5° and 275° ± 5° Near E‒W 5° ± 5° and 185° ± 5° Nearly S‒N
TS13 125° ± 5° and 305° ± 5° NW‒SE 35° ± 5° and 215° ± 5° NE‒SW
GS113 125° ± 5° and 305° ± 5° NW‒SE 35° ± 5° and 215° ± 5° NE‒SW
GS129 125° ± 5° and 305° ± 5° NW‒SE 35° ± 5° and 215° ± 5° NE‒SW

In Wells MX39, MX151, TS13, GS113, and GS129, the predominant orientations of the drilling-induced fractures are 125° ± 5° and 305° ± 5°, so the current maximum horizontal stress for these five wells is in the NW‒SE direction; the predominant azimuths of the borehole breakouts are 35° ± 5° and 215° ± 5°, so the minimum horizontal stress is in the NE‒SW direction. In Well MX56, the predominant orientations of the drilling-induced fractures are 115° ± 5° and 295° ± 5°, so the current maximum horizontal stress is in the NW‒SE direction, and the predominant azimuths of the borehole breakouts are 25° ± 5° and 205° ± 5°. In Wells MX42 and MX208, the predominant orientations of the drilling-induced fractures are 95° ± 5° and 275° ± 5°, so the current maximum horizontal stress is in the near-E‒W direction; the predominant orientations of the drilling-induced fractures are 5° ± 5° and 185° ± 5°, so the current minimum horizontal stress is the near-N‒S direction. By interpreting these results, the current directions of the maximum horizontal stress in the study area are perpendicular to the corresponding directions of the minimum horizontal stress, which is consistent with the distribution pattern of horizontal stress in the formation.

4.1.2 Analysis of cross-dipole acoustic logging

The anisotropy caused by the heterogeneous stress can be obtained by processing the cross-dipole acoustic logging data, and the azimuth of the fast shear wave is the same as the direction of the current maximum horizontal stress.

Figure 4 shows the processed cross-dipole acoustic logging data and the identified current maximum horizontal stress direction in Well MX146. The anisotropy caused by the heterogeneous stress in the formation is strong, and the predominant azimuth of the fast shear wave was 125° ± 5°, so the direction of the current maximum horizontal stress in the formation at this depth is NW‒SE.

Figure 4 Analysis of the current in situ stress directions of the Maokou Formation in Well MX146 in the study area.
Figure 4

Analysis of the current in situ stress directions of the Maokou Formation in Well MX146 in the study area.

We analyzed the cross-dipole acoustic logging data from six wells (including Wells MX145, MX146, and MX202) in the study area and identified the stress anisotropy and the predominant orientations of fast shear wave propagation to determine the corresponding directions of the current maximum horizontal stress (Table 3). The predominant orientation of fast shear wave propagation in the Maokou Formation in Wells MX145, MX146, HS7, and L1 is 125° ± 5°, so the current maximum horizontal stress in these wells is in the NW‒SE direction. The predominant azimuth of fast shear wave propagation in the Maokou Formation in Well MX202 is 145° ± 5°, so the current maximum horizontal stress in this well is in the NW‒SE direction. The predominant orientation of fast shear wave propagation in the Maokou Formation in Well HS5 is 135° ± 5°, so the current maximum horizontal stress is in the NW‒SE direction.

Table 3

Statistics of the interpretation results of cross-couple level acoustic logging data

Well Dominant azimuth of fast shear wave propagation Current max horizontal in situ stress direction
MX145 125° ± 5° NW‒SE
MX146 125° ± 5° NW‒SE
MX202 145° ± 5° NW‒SE
HS5 135° ± 5° NW‒SE
HS7 125° ± 5° NW‒SE
L1 125° ± 5° NW‒SE

4.1.3 Characteristics

Using imaging logging data and cross-dipole acoustic logging data, we analyzed the in situ stress direction in the Maokou Formation in each of the 14 wells in the Longnüsi area. According to the in situ stress direction of MX145, MX146, HS7, L1, MX39, MX151, TS13, GS113, and GS129 (these wells are far away from fault), the direction of in situ stress obtained by the two research methods is consistent, which can explain the reliability of two research methods to a certain extent.

Figure 5 shows that 12 wells in the study area have the same current maximum horizontal stress direction (NW‒SE) but different current maximum horizontal stress azimuths. Among them, the current maximum horizontal stress azimuths of Wells MX39, MX145, MX146, MX151, HS7, GS113, GS129, TS13, and L1 are all 125° ± 5°; the current maximum horizontal stress azimuth of Well MX56 is 115° ± 5°; the current maximum horizontal stress azimuth in Well MX202 is 145° ± 5°; and the current maximum horizontal stress azimuth in Well HS5 is 135° ± 5°. The current maximum horizontal stresses of Wells MX42 and MX208 are both in the near E‒W direction, 95° ± 5°.

Figure 5 Direction of current maximum horizontal stress in the Maokou Formation in each studied well in the Longnüsi area.
Figure 5

Direction of current maximum horizontal stress in the Maokou Formation in each studied well in the Longnüsi area.

The complex causes of the various current in situ stress directions are the focus of current research and discussion in relevant fields. Existing studies have shown that (1) the in situ stress directions are restricted and influenced by factors such as boundary shape, external boundary force, fractures, and folds. Among these factors, fractures have a great influence on the direction of in situ stress directions. (2) The larger the fault size and the greater the widths of the fracture zone and the drilling-induced fracture zone, the greater the deflection range of the induced in situ stress direction is; the farther the strata are from the fracture, the closer the directions are to the regional in situ stress directions, and the smaller the in situ stress deflection is.

Wells MX39, MX145, MX146, MX151, HS7, GS113, GA129, TS13, and L1 in the study area are far from the fault zone, so the current horizontal stress directions of these nine wells are not affected by the fault zone. These stress directions represent the main regional in situ stress directions. In other words, the current maximum horizontal stress direction in the study area is the same as the maximum horizontal stress direction of these nine wells, which is NW‒SE. Wells MX56, MX202, HS5, MX42, and MX208 are very close to or in the fault zone, so the current in situ stress states there are greatly affected by the fault. The stress directions of these wells do not represent the current regional in situ stress direction. Hence, the fault zone has a significant influence on the direction of current horizontal in situ stress in the study area.

4.2 Current in situ stress magnitudes

4.2.1 Experimental results

We conducted acoustic emission experiments on the Maokou Formation cores from seven wells (including Wells MX56, HS4, and HS3) and obtained the magnitudes of the current horizontal stress magnitudes for each well, as shown in Table 4. Table 4 shows that the magnitude of the Maokou Formation’s current minimum horizontal stress in the study area is between 96.29 and 114.36 MPa, the magnitude of the current maximum horizontal stress magnitude is between 126.01 and 145.10 MPa, and the current horizontal stress difference is between 25.59 and 32.58 MPa.

Table 4

Statistics of the results of acoustic emission experiment

Well Depth (m) S h (MPa) S H (MPa) S H ‒ S h (MPa)
Experimental value Average value Experimental value Average value Experimental value Average value
MX56 4509.4–4509.6 113.25 114.36 140.65 141.86 27.40 27.50
4573.2–4573.4 115.47 143.07 27.60
HS4 4337.1–4337.3 104.26 106.23 133.21 131.82 28.95 25.59
4348.5–4348.7 108.20 130.43 22.23
HS3 4128.6–4128.8 98.11 97.21 126.20 126.01 28.09 28.80
4131.1–4131.3 96.31 125.82 29.51
TT1 4163.3–4163.5 103.00 103.52 130.27 130.87 27.27 27.35
4168.2–4168.4 104.04 131.47 27.43
T4 4150.9–4151.1 100.29 101.29 127.39 129.10 27.10 26.81
4185.1–4185.3 102.29 128.81 26.52
H12 4502.0–4502.2 94.19 95.23 124.01 123.11 29.82 27.88
4503.1–4503.3 96.27 122.21 25.94
L1 4079.9–4080.1 98.21 96.29 127.95 128.53 29.74 32.24
4122.5–4122.7 94.37 129.11 34.74

According to the magnitudes of the single-well stress obtained by the acoustic emission experiment and the well locations in the study area, the numerical distribution of the in situ stress in the study area was clarified, as shown in Figure 6. The maximum horizontal stress of Well MX56 in the northern part of the study area is 141.86 MPa, which is the largest among the seven wells. The maximum horizontal stress of Well H12 in the southern part of the study area is 123.11 MPa, which is the smallest among the seven wells. Wells TT1, HS4, T4, L1, and HS3 run from north to south in the central part of the study area, and they have maximum horizontal stresses of 130.87, 131.82, 129.10, 128.53, and 126.01 MPa, respectively. The maximum horizontal stresses of these seven wells tend to decrease gradually from north to south.

Figure 6 Distribution characteristic maps of the magnitudes of the horizontal stresses in the Maokou Formation in the Longnüsi area.
Figure 6

Distribution characteristic maps of the magnitudes of the horizontal stresses in the Maokou Formation in the Longnüsi area.

The minimum horizontal stress of Well MX56 in the northern part of the study area is 114.36 MPa, which is the largest among the seven wells. The minimum horizontal stress magnitude of Well H12 in the southern part of the study area is 96.23 MPa, which is the smallest among the seven wells. Wells TT1, HS4, T4, L1, and HS3 run from north to south in the central part of the study area and have minimum horizontal stresses of 103.52, 106.23, 101.29, 96.29, and 97.21 MPa, respectively. The minimum horizontal stresses of the seven wells in the study area also tend to decrease gradually from north to south. There is no obvious pattern in the stress differences of the seven wells in the study area.

4.2.2 Calculated results

The magnitudes of the vertical and horizontal stresses of the Maokou Formation in seven wells (including Wells MX56, HS4, and HS3) were calculated using conventional logging data and array acoustic logging data. The corresponding calculation results are shown in Table 5. The calculated vertical principal stress is between 103.37 and 115.12 MPa, the current minimum horizontal stress is between 93.91 and 105.45 MPa, the current maximum horizontal stress is between 119.07 and 136.44 MPa, and the current horizontal stress difference is between 23.61 and 32.81 MPa.

Table 5

Statistics of calculated in situ stress magnitudes

Well Depth (m) S v (MPa) S h (MPa) S H (MPa) S H ‒ S h (MPa)
MX56 4,573 115.12 105.45 136.27 30.82
HS4 4,349 112.21 101.36 128.66 27.30
HS3 4,131 103.71 103.73 136.54 32.81
TT1 4,169 105.59 105.08 136.44 31.36
T4 4,186 105.74 95.46 119.07 23.61
H12 4,504 113.17 99.28 124.69 25.41
L1 4,123 103.37 93.91 122.42 28.51

4.2.3 Evaluation of the calculated methods

Acoustic emission experiments and logging data calculations were carried out for seven wells in the study area, and the magnitudes of the horizontal stresses in these wells were obtained. To clarify the applicability of Huang’s model in this area, the magnitudes of the horizontal stress calculated by Huang’s model were compared with the results obtained by the acoustic emission experiments. Based on the magnitudes of the stress obtained from the acoustic emission experiments, the accuracy of the values calculated by Huang’s model was analyzed. The comparison results are shown in Table 6.

Table 6

Comparative analysis of calculated results and experimental results

Well S h S H SH ‒ Sh
Experimental value (MPa) Calculated value (MPa) Difference (%) Experimental value (MPa) Calculated value (MPa) Difference (%) Experimental value Calculated value (MPa) Difference (%)
MX56 114.36 105.45 −7.79 141.86 136.27 −3.94 27.50 30.82 12.07
HS4 106.23 101.36 −4.58 131.82 128.66 −2.40 25.59 27.30 6.68
HS3 97.21 103.73 6.71 126.01 136.54 8.36 28.80 32.81 13.92
TT1 103.52 105.08 1.51 130.87 136.44 4.26 27.35 31.36 14.66
T4 101.29 95.46 −5.76 128.10 119.07 −7.05 26.81 23.61 −11.94
H12 95.23 99.28 4.25 123.11 124.69 1.28 27.88 25.41 −8.86
L1 96.29 93.91 −2.47 128.53 122.42 −4.75 32.24 28.51 −11.57

The magnitudes of the current minimum horizontal stress calculated by Huang’s model were different from those obtained by the acoustic emission experiments, with the smallest difference (only 1.51%) observed for Well TT1 and the largest difference observed for Well MX56 (7.79%). Therefore, the overall difference in the current minimum horizontal stress obtained by the two methods is relatively small (below 8% in all wells). The magnitudes of the current maximum horizontal stress calculated by Huang’s model are also different from those obtained from the acoustic emission experiment, with the smallest difference (only 1.28%) observed for Well H12 and the largest difference observed for Well HS3 (8.36%). Therefore, the overall difference in the current maximum horizontal stress obtained by the two methods is relatively small (below 9% in all wells). The difference between the stress differences obtained by the two methods is between 6.68% and 14.66%, with the smallest difference observed for Well HS4 (6.68%) and the largest difference observed for Well TT1 (14.66%). Therefore, the overall difference between the stress differences obtained by the two methods is small (below 15% in all wells). Hence, Huang’s model has good applicability in terms of calculating the magnitudes of the horizontal stresses in the Maokou Formation in the Longnüsi area.

The magnitudes of the horizontal stresses calculated by Huang’s model were further analyzed. The correlations between the calculated results and the experimental results were also analyzed, and the relationships between the experimental data and the calculated data for the minimum horizontal stress (Figure 7) and for the maximum horizontal stress magnitude (Figure 8) were obtained. The R 2 values of both formulas are very low, which indicates that the correlation between the two sets of data is low.

Figure 7 Relationship between the experimental data and the calculated data for the minimum horizontal stress.
Figure 7

Relationship between the experimental data and the calculated data for the minimum horizontal stress.

Figure 8 Relationship between the experimental data and calculated data for the maximum horizontal stress.
Figure 8

Relationship between the experimental data and calculated data for the maximum horizontal stress.

4.3 Simulation results and evaluation

4.3.1 Selection of parameters

During the modeling process, the parameters of the geological model were obtained through rock mechanics experiments [48–50]. The rock mechanics experimental conditions and results for Wells MX56, HS4, TT1, and L1 are shown in Figure 9 and Table 7. The mean values of the experimental results were selected as the values of the rock mechanics parameters in the geological model.

Figure 9 Rock mechanics experimental results: (a) Well MX56, (b) Well HS4, (c) Well TT1, and (d) Well L1.
Figure 9

Rock mechanics experimental results: (a) Well MX56, (b) Well HS4, (c) Well TT1, and (d) Well L1.

Table 7

Statistics of rock mechanics parameters

Well Depth (m) ρ b (g/cm3) Conditions Results
T (℃) P 0 (MPa) P (MPa) P f (MPa) σ (MPa) E (104 MPa) μ
MX56 4573.42–4573.66 2.65 119.79 115 120.7 67.23 457.29 4.667 0.268
HS4 4337.93–4338.16 2.63 113.61 105 120.7 66.56 442.78 4.589 0.245
TT1 4164.01–4164.23 2.65 108.43 112 120.7 62.89 448.91 4.614 0.258
L1 4123.58–4123.80 2.66 108.02 103 120.7 63.12 456.41 4.629 0.265
Mean value 2.65 — — — — 451.35 4.62 0.26

4.3.2 Simulated results

The distributions of the magnitudes of the current maximum and minimum horizontal stresses in the study area were simulated with ABAQUS software [51–53] (Figures 10 and 11). The simulation results show the following: (1) The current maximum horizontal stress in the study area is between 131 and 155 MPa, decreasing from north to south. (2) The current minimum horizontal stress magnitude in the study area is between 102 and 122 MPa, decreasing from north to south.

Figure 10 Distribution of the magnitudes of the maximum horizontal stress magnitude in the Longnüsi area in central Sichuan.
Figure 10

Distribution of the magnitudes of the maximum horizontal stress magnitude in the Longnüsi area in central Sichuan.

Figure 11 Distribution of the magnitudes of the minimum horizontal stress magnitude in the Longnüsi area in central Sichuan.
Figure 11

Distribution of the magnitudes of the minimum horizontal stress magnitude in the Longnüsi area in central Sichuan.

4.3.3 Evaluation of simulated values

To evaluate the effect of numerical simulation, we compared the numerically simulated horizontal stress magnitudes of seven wells in the study area with the acoustic emission experimental results from these wells, as shown in Table 8. The magnitudes of the numerically simulated current horizontal stress parameters are different from those obtained by the acoustic emission experiments and have a difference of less than 11% in the current minimum horizontal stress, a difference of less than 10% in the current maximum horizontal stress magnitude, and a difference of less than 20% in the stress difference. Therefore, there is a small difference between the results obtained by the numerical simulations and those obtained by the acoustic emission experiments. Further comparison and analysis of the results obtained by the acoustic emission experiments (Figure 6) and the results obtained by the numerical simulation (Figures 10 and 11) show that the magnitudes of the horizontal stresses obtained by the two methods have similar planar distribution patterns; from north to south, the magnitudes of both the current maximum horizontal stress and the current minimum horizontal stress have decreasing trends. Hence, the numerical simulation results are accurate and have high reference values [54,55].

Table 8

Comparative analysis of simulated and experimental results

Well S h S H S H ‒ S h
Experimental value (MPa) Simulated value (MPa) Difference (%) Experimental value (MPa) Simulated value (MPa) Difference (%) Experimental value (MPa) Simulated value (MPa) Difference (%)
MX56 114.36 112.92 −1.26 141.86 144.76 2.04 27.50 31.84 15.78
HS4 106.23 104.72 −1.42 131.82 135.01 2.42 25.59 30.29 18.37
HS3 97.21 103.18 6.14 126.01 135.89 7.84 28.80 32.71 13.58
TT1 103.52 108.34 4.66 130.87 138.91 6.14 27.35 30.57 11.77
T4 101.29 109.49 8.10 128.10 140.01 9.30 26.81 30.52 13.84
H12 95.23 103.12 8.29 123.11 131.10 6.49 27.88 27.98 0.36
L1 96.29 105.93 10.01 128.53 134.95 4.99 32.24 29.02 −9.99

5 Conclusions and recommendations

Combined with theoretical calculation, numerical simulation, and other research means, the evaluation of the current in situ stress in the middle Permian Maokou Formation in the Longnü si area of the central Sichuan Basin is realized. The research results of this article provide ideas and methods for studying the current in situ stress of reservoirs, and the main conclusions are as follows.

  1. The current maximum horizontal stress of the Maokou Formation in the Longnüsi area is mainly in the NW‒SE direction. The stress direction is greatly affected by the fault zone.

  2. The minimum horizontal stress magnitude of the Maokou Formation in the Longnüsi area is between 96.29 and 114.36 MPa, the current maximum horizontal stress magnitude is between 126.01 and 145.10 MPa, and the current horizontal stress difference is between 25.59 and 32.58 MPa.

  3. The results calculated by Huang’s model were close to the results obtained by the acoustic emission experiment. Therefore, Huang’s model has good applicability in terms of calculating the magnitudes of the current horizontal stresses in the Longnüsi area.

  4. The error of the numerical simulation results is small. The simulated magnitude of the current horizontal stress also has a decreasing trend from north to south, similar to the results obtained from the experiments. Therefore, the simulation results have high accuracy.

  5. We have almost used the commonly used methods for determining in situ stress, we have comprehensively evaluated the magnitude, direction, and distribution of in situ stress, and providing ideas for the evaluation of current in situ stress in reservoirs. However, as the samples and data used for stress analysis are limited, we use two kinds of logging techniques to obtain logging data and stress analysis in order to obtain more effective drilling data and ensure that the research results better reflect the actual situation. But there are still some issues that need to be further studied. Specifically, we will pay more attention and research on the comparison between imaging logging and cross-dipole acoustic logging in determining the direction of current in situ stress in the future.

Acknowledgments

This study was financially supported by the Key R&D Projects of the Deyang Science and Technology Plan (Nos 2022SZ049 and 2021SZ002), Research Project of Sichuan College of Architectural Technology (No. 2023KJ14), and the Open funds of Natural Gas Geology Key Laboratory of Sichuan Province (No. 2021trqdz05).

  1. Conflict of interest: The authors declare no conflict of interest.

  2. Data availability statement: All data are included in the manuscript.

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Received: 2023-05-19
Revised: 2023-07-25
Accepted: 2023-08-04
Published Online: 2023-08-29

© 2023 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/geo-2022-0524
Keywords for this article
current in situ stress; imaging logging; acoustic logging; acoustic emission experiment; numerical simulation; Longnüsi area
Creative Commons
BY 4.0

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  119. Dynamic analysis of MSE wall subjected to surface vibration loading
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  131. Rapid Communication
  132. Branch fault discovered in Tangshan fault zone on the Kaiping-Guye boundary, North China
  133. Technical Note
  134. Introducing an intelligent multi-level retrieval method for mineral resource potential evaluation result data
  135. Erratum
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  137. Addendum
  138. The relationship between heat flow and seismicity in global tectonically active zones
  139. Commentary
  140. Improved entropy weight methods and their comparisons in evaluating the high-quality development of Qinghai, China
  141. Special Issue: Geoethics 2022 - Part II
  142. Loess and geotourism potential of the Braničevo District (NE Serbia): From overexploitation to paleoclimate interpretation
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