Introduction

The increase in global fossil energy consumption has driven the vigorous development of unconventional oil and gas1,2. Shale oil is a promising oil and gas resource that exists in shale in a free or adsorbed state, integrating source and storage3,4,5,6. Continental shale oil is currently one of the hotspots in the field of unconventional oil and gas development, and has become an important replacement resource7,8. Continental shale oil reservoirs have the characteristics of self generation and self storage, with tight lithology, permeability usually between 0.001 ~ 0.1mD, and porosity between 2%~15%. They need to be extracted through the “horizontal well + volume fracturing” method, which highly relies on the mechanical properties of shale9,10,11,12. During the process of volume fracturing, rock mechanics parameters have a significant impact on the initiation and propagation of hydraulic fracturing fractures.

In-situ stress is the fundamental force that causes deformation and failure in geotechnical engineering, and the magnitude and direction of in-situ stress have a direct impact on the initiation and propagation of cracks13,14. The commonly used methods for measuring in-situ stress include hydraulic fracturing to determine the magnitude of in-situ stress, micro-seismic monitoring of the maximum horizontal principal stress direction during hydraulic fracturing, acoustic imaging logging15,16, paleomagnetic testing of the maximum horizontal principal stress direction, and Kaiser acoustic emission method for determining in-situ stress. The Kaiser acoustic emission method can be measured indoors, so it is widely used. The magnitude and direction of in-situ stress control the direction and propagation of hydraulic fracturing fractures in landing phase shale oil reservoirs 17. Gupta et al.18,19 believe that changes in stress field are related to reservoir development, and propose that the smaller the horizontal principal stress difference of the reservoir, the more favorable it is for stress reversal to occur. The two parameters of horizontal principal stress difference and horizontal principal stress difference coefficient comprehensively determine whether hydraulic fractures and natural fractures can form a beneficial seepage fracture network system20.

The Ordos Basin has abundant unconventional oil and gas resources. The Chang 7 reservoir is the main source rock of the Yanchang Formation 21. A 1 billion ton Qingcheng shale oil field has been discovered in the Chang 7 reservoir of the Yanchang Formation in the Ordos Basin, with a cumulative submitted proven geological reserve of 11.53 × 108t22. “Horizontal well + volume fracturing “is an effective stimulation measure that has been widely applied 23,24,25. Hydraulic fracturing generates fractures in reservoirs and improves the flow channels of the reservoir. The direction of cracks is mainly controlled by in-situ stress26,27,28. So it is very important to test the magnitude and direction of the in-situ stress in this block. There are static and dynamic methods for in-situ stress testing. The static method is a method tested through indoor Kaiser acoustic emission experiments, which is usually difficult to core, expensive, and has the characteristics of discontinuous samples29,30,31. The dynamic method calculates rock mechanics parameters by establishing a mathematical model based on well logging data during the drilling process. The disadvantage of this method is that it requires high model requirements, and not all blocks are suitable for the same model, requiring model correction. Logging data can be used to calculate rock mechanics parameters such as porosity, oil saturation, water saturation, elastic modulus, Poisson’s ratio, maximum horizontal principal stress, minimum horizontal principal stress, and overlying rock pressure of shale reservoirs. It can also characterize oil and gas potential, evaluate reservoirs, and determine lithology32. Establishing a reasonable mathematical model using logging data can predict rock mechanics parameters. Establishing the relationship between dynamic and static geomechanics avoids the limitations of individual methods and ensures continuous and reliable results33,34,35,36. At present, the widely used models for calculating in-situ stress include the Eaton model, Anderson model, and Newberry model, as well as the “65 models " and “75 models” proposed by Huang Rongzun37.

The measurement of ground stress has an important impact on understanding the deformation and failure of underground reservoir rocks. The magnitude and direction of ground stress affect the initiation direction and propagation mode of hydraulic fractures. Kaiser acoustic emission experiment is a method for three-dimensional testing of ground stress. Based on the rock mechanics characteristics of stress memory, Kaiser point is the point where new cracks appear, which can accurately test the magnitude and direction of ground stress38,38.

This article aims to understand the geological characteristics of the Chang 7 shale oil reservoir in the Y block of the M oilfield in the Ordos Basin. The Kaiser acoustic emission experiment was used to test the rock in-situ stress, calculate the maximum and minimum horizontal principal stress gradients, and the vertical principal stress gradient. The dynamic rock mechanics parameters were calculated using logging data and compared with laboratory measured rock mechanics parameters to establish the relationship between dynamic and static parameters. The dynamic parameters were calculated using logging data to obtain static parameters, which is of great significance for the efficient development of shale oil reservoirs in this area.

Preparation of experimental samples and experimental methods

The Y block of the M oilfield is located in the northwest of the Ordos Basin. The Yanchang Formation Chang 7 oil reservoirs is rich in oil and gas resources, with an average daily oil production of 0.21 tons per conventional well and 8.45 tons per horizontal well in the Chang 7 oil well. There is a significant difference in production between conventional and horizontal wells. In-situ stress is the natural stress that exists in the geological strata without engineering disturbance, also known as the initial stress, absolute stress, or original rock stress of the rock mass. Studying the in-situ stress in this area is helpful for evaluating the fracturability of shale oil reservoirs. The magnitude and direction of in-situ stress have a significant impact.

Purpose of acoustic emission experiment

Rock acoustic emission (AE) refers to the transient elastic acoustic wave phenomenon produced by the generation, propagation, and penetration of microcracks in rocks during the process of deformation and failure under stress.

Acoustic Emission (AE) is the elastic wave generated when the strain energy stored inside a material is rapidly released. Acoustic emission method is an experimental method that uses elastic waves emitted by rocks to investigate their internal state and mechanical properties. By utilizing the Kaiser effect of rocks and observing the changes in acoustic signals emitted by the rock sample during loading, the in-situ stress experienced by the rock sample underground can be measured.

The purpose of this experiment is to use acoustic emission (Kaiser effect) method to measure the value of in-situ stress. If combined with paleomagnetic orientation method (for non oriented rock cores), the direction of initial in-situ stress can be determined. The magnitude and direction of the measured ground stress have a significant impact on the initiation and propagation of fractures during the horizontal well volume fracturing process. Therefore, in the design of horizontal well volume fracturing, the magnitude and direction of ground stress are very important. Generally, the trajectory direction of the horizontal well is consistent with the direction of the minimum horizontal principal stress, which can generate multiple artificial fractures perpendicular to the wellbore and greatly improve productivity.

Acoustic emission experimental equipment

The Kaiser effect testing system for rocks mainly includes: rock pressure testing machine, pressure sensor, acoustic emission instrument, acoustic emission probe, dynamic resistance strain gauge, and computer data acquisition system.

The framework diagram of the testing system is shown in Fig. 1. If the core is buried deep, the in-situ stress level will exceed the uniaxial compressive strength. At this time, the experiment should be conducted in a three-axis high-pressure reactor. The core sampling location for this experiment is the Chang 71 reservoir in Block Y of the M oilfield in the Ordos Basin, with a depth ranging from 2200 m to 2500 m. The experiments were all triaxial compression tests, with a confining pressure of 30 MPa and a temperature of 65 ℃.

Fig. 1
Fig. 1The alternative text for this image may have been generated using AI.
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Framework diagram of acoustic emission experimental testing system.

Principle of acoustic emission experiment

Acoustic emission (AE) is a phenomenon in which internal or potential defects in rocks change their state and automatically produce sound under external conditions. The most important characteristic of AE is that when the external load does not exceed the maximum load that the rock has ever experienced, AE signals are not observable or very rare, but when the load exceeds, AE activity suddenly increases.

During testing, first perform parallelism treatment on both ends of the specimen, then use a loading device to compress the specimen axially, and simultaneously activate the AET testing system (acoustic emission instrument) to detect the signal. When the test piece is subjected to force and generates an acoustic emission signal, the probe on the surface of the test piece receives and converts it into an electrical signal. After filtering, pre amplification, and identification, it enters the AET host to generate events that characterize the acoustic emission characteristics, such as ringing, amplitude, energy, and other parameters. These data and results can be recorded by a computer data acquisition system.

If measuring the in-situ stress of a certain depth layer, at least 4 core samples should be prepared in 4 directions (1 vertical direction, 3 horizontal directions separated by 45 ° each) as required, and then the acoustic emission curve of each core sample should be tested. The sampling requirements for Kaiser AE core are shown in Fig. 2. By finding the normal stress corresponding to Kaiser point from the acoustic emission curve of each core and substituting it into the following equation, the three principal stresses experienced by the sample underground can be obtained.

Preparation requirements for rock samples for acoustic emission experiments: In order to determine the three principal stresses (1 vertical direction and 2 horizontal directions) that the rock sample experiences underground, the rock sample should be centered in different directions before conducting acoustic emission experiments. To determine three principal stresses, at least four core samples should be taken in four directions (one vertical direction and three horizontal directions separated by 45 ° each), all of which are cylindrical bodies with a diameter of 25 mm and a length of approximately 40–60 mm. The schematic diagram of horizontal coring in Fig. 2 shows that the angle between each block is 45 °, and the axis of the experimental sample is perpendicular to the axis of the large rock core. When preparing, pay attention to keeping the two end faces of the rock sample parallel to avoid bias pressure. The diameter difference of the entire height of the rock column should not exceed 0.2 mm, and the cylindrical surface should be smooth to prevent surface stress concentration.

Fig. 2
Fig. 2The alternative text for this image may have been generated using AI.
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Schematic diagram of acoustic emission core sampling.

Acoustic emission signals are generated by micro fractures in the internal structure of rocks under load, which are controlled by the effective stress acting on the rocks. Therefore, the stress at the Kaiser point and the incompletely recorded point are the effective stresses (effective in-situ stress) that rocks experience underground. According to the theory of pore elasticity:

$$\sigma ={\sigma _1}+\sigma {P_p}$$
(1)

Among them, σ is the normal stress corresponding to the Kaiser point, MPa; σ1 To achieve effective in-situ stress, MPa; Pp For pore pressure, MPa; α The Biot coefficient.

Finally, by substituting the normal stress corresponding to the Kaiser point into formula (2)–(5), the maximum and minimum horizontal principal stresses at the depth of the rock formation can be calculated.

$${\sigma _{\text{v}}}={\sigma _ \bot }+\alpha {P_{\text{p}}}$$
(2)
$$\sigma _{H} = \frac{{\sigma _{{0^{^\circ } }} + \sigma _{{90^{^\circ } }} }}{2} + \frac{{\sigma _{{0^{^\circ } }} - \sigma _{{90^{^\circ } }} }}{2}(1 + \tan ^{2} 2\theta )^{{\frac{1}{2}}} + \alpha P_{{\text{p}}}$$
(3)
$$\sigma _{{\text{h}}} = \frac{{\sigma _{{0^{^\circ } }} + \sigma _{{90^{^\circ } }} }}{2} - \frac{{\sigma _{{0^{^\circ } }} - \sigma _{{90^{^\circ } }} }}{2}(1 + \tan ^{2} 2\theta )^{{\frac{1}{2}}} + \alpha P_{{\text{p}}}$$
(4)
$$\tan 2\theta = \frac{{\sigma _{{0^{^\circ } }} + \sigma _{{90^{^\circ } }} - \sigma _{{45^{^\circ } }} }}{{\sigma _{{0^{^\circ } }} + \sigma _{{90^{^\circ } }} }}$$
(5)

Among them, \({\sigma _{0^\circ }}\), \({\sigma _{45^\circ }}\), \({\sigma _{90^\circ }}\) are the normal stresses corresponding to the Kaiser points of the 0 °, 45 °, and 90 ° rock cores that are radially spaced 45 ° apart from each other, MPa; σ⊥ Corresponding to the normal stress at the Kaiser point of the axial core; σH, σh They are the maximum and minimum horizontal principal stresses, respectively, MPa; σv For the stress of the overlying strata, MPa; PP is pore pressure, MPa; θ is the angle between \({\sigma _{0^\circ }}\) and the minimum horizontal principal stress direction the marker line. Based on this value, combined with the sampling location (the relationship between the angle and the marker line), the angle between the minimum horizontal principal stress and the marker line can be obtained. Furthermore, based on the geomagnetic orientation results, the stress direction of the rock core underground can be obtained.

By utilizing the Kaiser effect of rocks and observing the changes in acoustic signals emitted by the rock sample during loading, the in-situ stress experienced by the rock sample underground can be measured. It is sometimes difficult to distinguish the Kaiser point on the stress acoustic emission signal curve of natural rock cores taken from underground when reloading indoors. Through experiments, it was found that rocks not only exhibit Kaiser effect, but also exhibit an isolated and significant abrupt change in acoustic emission signal at the Kaiser point of the first loading test when subjected to the second loading of the sample. This phenomenon is called acoustic emission incomplete recording phenomenon. Usually, the phenomenon of incomplete recording of acoustic emissions is more pronounced and easier to distinguish than the Kaiser effect. By comparing the acoustic emission curves of two loads, the Kaiser point can be obtained more accurately.

If the sample is a directional core, the direction of the maximum and minimum horizontal principal stresses can also be obtained through experiments. However, the core of this experiment is a non directional core, and the acoustic emission method alone can only obtain the stress direction on the core (relative to the marker line), and cannot determine the direction of the underground rock stress.

Acoustic emission experiment steps

The experimental steps for acoustic emission in this study are as follows:

  1. (1)

    Extract drilling core samples from the site as required to prepare experimental rock samples. Each group of samples should include at least 4 specimens, with 1 taken from the vertical direction (parallel to the wellbore axis) and the other 3 taken from 3 directions that form a 45 ° angle with each other in the horizontal plane. To ensure more accurate and reliable test results, several sets of samples can be taken simultaneously in the same oilfield block for experimentation.

  2. (2)

    During the experiment, there is a rubber sheet with a diameter of 25 mm and a thickness of about 2 mm between the sample end face and the upper and lower cushion blocks to reduce end face friction and mechanical noise, and ensure good contact between the rock sample end face and the cushion blocks. Keep both ends of the rock sample parallel.

  3. (3)

    Preliminary estimation of the overlying rock pressure based on burial depth, and comparison with 70% of the uniaxial compressive strength of the rock. If the overlying rock pressure is greater than this value, acoustic emission tests under triaxial conditions will be conducted; If the overlying rock pressure is lower than this value, a uniaxial acoustic emission test can be conducted.

  4. (4)

    Perform repeated loading experiments on the processed samples indoors to measure the variation curve of acoustic emission signals with load during the loading process of the rock sample.

  5. (5)

    On the second loading of the acoustic emission load curve, identify the point where the acoustic emission cannot be recorded completely, refer to the load value of the point where the acoustic emission cannot be recorded completely, and determine the Kaiser point in the first loading of the acoustic emission load curve.

  6. (6)

    The average value of the load at the Kaiser point and the unrecorded point is the maximum normal stress that the rock core experiences underground. By substituting the measured normal stress values of the three horizontal rock samples with the previous equation, the maximum and minimum horizontal principal stress and overlying formation pressure that the rock sample experiences underground can be obtained as the Kaiser point stress of the vertical rock sample.

Experimental results and analysis

Acoustic emission experiment results

This test conducted acoustic emission stress testing on 44 core samples from Chang 7, Group 11 experiments of the Triassic Yanchang Formation in Block Y of the M oilfield in the northwest of the Ordos Basin. The test confining pressure is 30 MPa and the temperature is 65 ℃.

The acoustic emission test results of the first group of 1 # rock core (horizontal direction 0 °) are shown in Fig. 3, where Fig. 3 (a) shows the stress-strain curve during triaxial compression. The ringing count and cumulative ringing count in the acoustic emission signal measured simultaneously during the testing process are shown in Fig. 3 (b), and the energy and cumulative energy are shown in Fig. 3 (c). Based on the cumulative ringing count and cumulative energy of the sound emission, the time at which the Kaiser sound emission inflection point occurs is determined. Then, the differential stress corresponding to the Kaiser sound emission inflection point during the triaxial compression process is determined according to the time, which is the Kaiser point stress value of 46.42 MPa at 0 ° in the horizontal direction of the first set of experiments. The time for Kaiser point of core 1 is determined to be 40.995s.

Fig. 3
Fig. 3The alternative text for this image may have been generated using AI.
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Stress strain curve and acoustic emission signal of core 1 # under a confining pressure of 30 MPa.

The acoustic emission test results of the first group of 2 # rock cores (horizontal direction 45 °) are shown in Fig. 4, where Fig. 4 (a) shows the stress-strain curve during triaxial compression. The ringing count and cumulative ringing count in the acoustic emission signal measured simultaneously during the testing process are shown in Fig. 4 (b), and the energy and cumulative energy are shown in Fig. 4 (c). Based on the cumulative ringing count and cumulative energy of the sound emission, the time at which the Kaiser acoustic emission inflection point occurs is determined. Then, the differential stress corresponding to the Kaiser acoustic emission inflection point during the triaxial compression process is determined according to the time, which is the Kaiser point stress value of 39.35 MPa at 45 ° in the horizontal direction of the first set of experiments. The time for Kaiser point of core 2 is determined to be 51.835s.

Fig. 4
Fig. 4The alternative text for this image may have been generated using AI.
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Stress strain curve and acoustic emission signal of core 2 # under a confining pressure of 30 MPa.

The acoustic emission test results of the first group of 3 # rock cores (90 ° horizontal direction) are shown in Fig. 5, where Fig. 5 (a) shows the stress-strain curve during triaxial compression. The ringing count and cumulative ringing count in the acoustic emission signals measured simultaneously during the testing process are shown in Fig. 5 (b), and the energy and cumulative energy are shown in Fig. 5 (c). Based on the cumulative ringing count and cumulative energy of the acoustic emission, the time at which the Kaiser acoustic emission inflection point occurs is determined. Then, the differential stress corresponding to the Kaiser acoustic emission inflection point during the triaxial compression process is determined according to the time, which is the Kaiser point stress value of 33.57 MPa at 90 ° in the horizontal direction of the first set of experiments. The time for Kaiser point of core 3 is determined to be 31.31s.

Fig. 5
Fig. 5The alternative text for this image may have been generated using AI.
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Stress strain curve and acoustic emission signal of core 3 # under a confining pressure of 30 MPa.

The acoustic emission test results of the first group of 4 # rock cores (vertical direction) are shown in Fig. 6, where Fig. 6 (a) shows the stress-strain curve during triaxial compression. The ringing count and cumulative ringing count in the acoustic emission signal measured simultaneously during the testing process are shown in Fig. 6 (b), and the energy and cumulative energy are shown in Fig. 6 (c). Based on the cumulative ringing count and cumulative energy of the sound emission, the time at which the Kaiser acoustic emission inflection point occurs is determined. Then, the differential stress corresponding to the Kaiser acoustic emission inflection point during the triaxial compression process is determined according to the time, which is the Kaiser point stress value of 45.21 MPa in the vertical direction of the first set of experiments. The time for Kaiser point of core 4 is determined to be 128.358s.

Fig. 6
Fig. 6The alternative text for this image may have been generated using AI.
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Stress strain curve and acoustic emission signal of core 4 # under a confining pressure of 30 MPa.

Calculate the maximum horizontal principal stress = 69.37 MPa, minimum horizontal principal stress = 56.38 MPa, and vertical principal stress = 50.63 MPa in the first set of experiments using formulas (1)–(5). The experimental methods and calculation processes of the other groups are similar to those of the first group.

Table 1 tests the rock mechanics parameters of the core, including elastic modulus, Poisson’s ratio, differential stress, residual stress, residual elastic modulus, and other mechanical properties. Table 2 presents the results of acoustic emission tests under confining pressure of 30 MPa and temperature of 65 ℃. By applying the previous formula, the in-situ stress results of each group of rock cores can be obtained. In the calculation process, the Biot coefficient of mudstone is taken as 0.50, the Biot coefficient of sandy mudstone is taken as 0.55, the Biot coefficient of mudstone is taken as 0.6, and the Biot coefficient of tight sandstone is taken as 0.65. Further processing was performed on the horizontal geostress results in Table 2 to obtain the geostress gradient of each experimental point, and the geostress values in the vertical direction are shown in Table 3.

Table 1 Acoustic emission test results.
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Table 2 Calculation results of horizontal ground stress.
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Table 3 Calculation results of vertical ground stress.
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Ground stress characteristics: The methods commonly used to determine the direction of current ground stress include microseismic monitoring and rock acoustic emission experiments. The current geostress direction within the Chang 7 shale oil reservoir in this block is dominated by the NE-SW direction. When the horizontal principal stress difference is greater than 3 MPa, the artificial fractures generated by volume fracturing directly propagate along natural fractures without forming a fracture network, which cannot form an effective reservoir transformation volume and leads to poor fracturing effect.

Based on the data tested in Table 4, it can be concluded that the vertical principal stress distribution of the Chang 7 this block is between 49.72 ~ 61.13 MPa, the maximum horizontal principal stress distribution is between 59.04 ~ 75.4 MPa, and the minimum horizontal principal stress distribution is between 46.75 ~ 56.38 MPa. The horizontal stress difference is between 10.16 ~ 21.67 MPa, and the horizontal stress difference coefficient is between 0.21 ~ 0.42. Therefore, conventional horizontal well volume fracturing is not easy to form complex fracture networks, and it is necessary to carry out dense cutting fracturing technology to transform the reservoir, form complex fracture networks, and achieve efficient development of shale oil reservoirs.

Table 4 Ground stress test results of Chang 7 acoustic emission in block Y of M oilfield.
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The influence of in-situ stress on the morphology of the fracture network is mainly reflected in the magnitude of the horizontal principal stress difference, which is determined by the horizontal stress difference coefficient 40:

$${K_{\text{h}}}=\frac{{{\sigma _H} - {\sigma _{\text{h}}}}}{{{\sigma _{\text{h}}}}}$$
(6)

In the formula: \({K_{\text{h}}}\) is the coefficient of horizontal stress difference;\({\sigma _H}\), \({\sigma _{\text{h}}}\) They are the maximum and minimum horizontal principal stresses, respectively, MPa.

When the coefficient of horizontal stress difference is small, it is conducive to the formation of a complex crack network When the coefficient of horizontal stress difference is less than K h<0.25, microcracks are developed in the reservoir, and hydraulic fractures are more likely to communicate with microcracks, which is conducive to the formation of complex networks in hydraulic fracturing. Among the 11 sets of in-situ stress tests, 2 sets had K h<0.25, accounting for 18.18% of the total number of sets. ② When the coefficient of horizontal stress difference is 0.25 < Kh<0.35, the development of microcracks in the reservoir is average, and hydraulic fractures are difficult or not connected to microcracks. Among the 11 sets of in-situ stress tests, there are 6 sets with 0.25 < Kh<0.35, accounting for 54.55% of the total number of sets. ③ When the horizontal stress difference coefficient Kh>0.35, there are no fractures in the reservoir, and hydraulic fractures also exist in the form of single fractures. Among the 11 sets of in-situ stress tests, 3 sets had Kh>0.35, accounting for 27.27% of the total number of sets.

The magnitude and direction of ground stress affect the shape and direction of cracks. The relationship between vertical principal stress and horizontal principal stress can be classified into three types: the first type is σH > σv > σh; The second type is σH > σh > σv; The third type is σv > σH > σh, and the total number of groups for these three types is 11. The first type has 8 groups, accounting for 72.73% of the total number of groups, the second type has 2 groups, accounting for 18.18% of the total number of groups, and the third type has 1 group, accounting for 9.09% of the total number of groups. This will affect the direction of crack formation, as cracks are always perpendicular to the direction of minimum principal stress.

Some basic laws of ground stress distribution

Through theoretical research, geological surveys, and extensive analysis of in-situ stress data, some basic laws of in-situ stress distribution have been preliminarily recognized.

  1. (1)

    From Tables 2 and 3, it can be calculated that the average maximum horizontal stress gradient is 2.534 MPa/100m, the average minimum horizontal stress gradient is 1.891 MPa/100m, and the average vertical stress gradient is 2.051 MPa/100m. The principal stresses in three directions can be calculated through the gradient of in-situ stress, as shown in formulas (7) to (9):

    $${\text{Formula for maximum horizontal principal stress:}}\quad {\text{y}}=2.534{\text{x}}$$
    (7)
    $${\text{Formula for minimum horizontal principal stress:}}\quad {\text{y}}=1.891{\text{x}}$$
    (8)
    $${\text{Vertical principal stress formula:}}\quad {\text{y}}=2.051{\text{x}}$$
    (9)

    In the formula: x is the depth of the formation/100, m; y is the main stress, MPa.

    The experimental results in Table 4 are plotted as the relationship between in-situ stress and depth, as shown in Fig. 7. And by linearly fitting the maximum horizontal stress, minimum horizontal stress, and vertical stress, it can be concluded that the stress at a depth of 2200 m ~ 2500 m in Block Y of M oilfield increases linearly with depth. The slope of the fitted horizontal maximum principal stress line is 0.0279 MPa/m, which means the horizontal maximum principal stress gradient is 2.79 MPa/100m. The slope of the horizontal minimum principal stress line is 0.0215 MPa/m, which means the horizontal minimum principal stress gradient is 2.15 MPa/100m. The slope of the vertical principal stress line is 0.0229 MPa/m, which means the vertical principal stress gradient is 2.29 MPa/100m.

    The in-situ stress parameters of other wells in the Chang 7 shale oil reservoir of Block Y in the northwest of the Ordos Basin can be calculated based on the fitted formula (10) to formula (12), which are only applicable to the Chang 7 shale oil reservoir in this block. The in-situ stress parameters of other blocks can refer to this formula.

    $${\text{Formula for maximum horizontal principal stress:}}\quad {\text{y}}=0.0279{\text{x}}$$
    (10)
    $${\text{Formula for minimum horizontal principal stress:}}\quad {\text{y}}=0.0215{\text{x}}$$
    (11)
    $${\text{Vertical principal stress formula:}}\quad {\text{y}}=0.0229{\text{x}}$$
    (12)

    In the formula: x is the depth of the formation, m; y is the main stress, MPa.

    The average vertical stress gradient of the formation is 0.0229 MPa/m, which is derived from the self weight of the formation.

    Fig. 7
    Fig. 7The alternative text for this image may have been generated using AI.
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    Map of ground stress variation with depth at 2200–2500 m depth in block Y of M oilfield.

  2. (2)

    In most regions, the maximum horizontal principal stress is often greater than the vertical stress, and the ratio of the two horizontal principal stresses often reaches 1.3 or more. The average ratio of the maximum horizontal principal stress to the minimum horizontal principal stress of the Yanchang Formation 7 shale oil reservoir in the Y block of the M oilfield in the northwest of the Ordos Basin is 1.30, which means that the minimum principal stress value in this block is 77% of the maximum horizontal principal stress value. The vertical principal stress value of this block is 83% of the maximum horizontal principal stress value.

Calculate rock mechanics parameters based on logging data

In the process of mining application, there will be logging data during the drilling of a horizontal well, and the cost of closed coring is relatively high. Not every well is coring, so in order to understand the rock mechanics characteristics of underground reservoirs, it is necessary to establish the relationship between the dynamic data calculated from logging data and the static data tested through indoor triaxial mechanics experiments after closed coring. By converting the relationship between dynamic and static rock mechanics parameters, static rock mechanics parameters can be calculated from well logging data. Therefore, the establishment of dynamic and static rock mechanics parameter models is crucial.

Establishment of rock mechanics parameter model based on logging data calculation

The rock mechanics parameters of the reservoir can be obtained through logging curves, providing engineering parameters for the next step of fracturing.

Firstly, research was conducted on the calculation methods of transverse and longitudinal waves41, and empirical formulas for calculating transverse and longitudinal waves were obtained, as shown in formula (13);

$$\Delta {t_{\text{s}}}=\frac{{\Delta {t_{\text{p}}}}}{{{{\left( {1 - 1.15\frac{{1/{\rho _{\text{b}}}+1/\rho _{{\text{b}}}^{3}}}{{{e^{1/{\rho _{\text{b}}}}}}}} \right)}^{1.5}}}}$$
(13)

In the formula, △t p represents the time difference of longitudinal waves in rocks (referred to as acoustic time difference), µs·m− 1;

△t s represents time difference of rock transverse waves, µs·m− 1;

\({\rho _b}\) - formation bulk density, g·cm− 3, Calculated by formula (14);

$${\rho _{\text{b}}}=0.31/D{T^{{\text{0}}{\text{0.25}}}}$$
(14)

Secondly, calculate the dynamic Young’s modulus and dynamic Poisson’s ratio.

  1. (1)

    Determination of dynamic Young’s modulus: Through research, it is necessary to use empirical formulas for predicting transverse and longitudinal waves to regress and obtain the calculation formula for dynamic Young’s modulus42, as shown in formula (15):

    $${E_{\text{d}}}=\frac{{{\rho _{\text{b}}}\left( {3\Delta t_{{\text{s}}}^{2} - 4\Delta t_{{\text{p}}}^{2}} \right)}}{{\Delta t_{{\text{s}}}^{2}\left( {\Delta t_{{\text{s}}}^{2} - \Delta t_{{\text{p}}}^{2}} \right)}} \times {10^9}$$
    (15)

    In the formula, E d - dynamic Young’s modulus, MPa;△t p - Rock longitudinal wave time difference (referred to as acoustic time difference), µs/m; △t s - Time difference of rock transverse waves, µs/m; \({\rho _b}\) - Formation bulk density, g/cm3。.

  2. (2)

    Determination of dynamic Poisson’s ratio: Using the calculation results of transverse and longitudinal waves, calculate the dynamic Poisson’s ratio according to empirical formulas, as shown in formula (16):

    $${\mu _d}=\frac{{\Delta t_{s}^{2} - 2\Delta t_{p}^{2}}}{{2\left( {\Delta t_{s}^{2} - \Delta t_{p}^{2}} \right)}}$$
    (16)

Establishment of dynamic and static rock mechanics parameter conversion model

By using longitudinal and transverse wave time difference and density logging data, as well as the calculation formulas listed in formula (15) and formula (16), dynamic rock mechanics parameters can be obtained, while rock mechanics testing can obtain static rock mechanics parameters. The deformation and failure of underground rocks are closer to the experimental conditions of indoor rock mechanics. Therefore, it is necessary to know the relationship between the dynamic and static parameters of rocks. By using well logging data, dynamic parameters can be obtained, and then the required static parameters can be determined.

Establish a conversion relationship chart between the static Poisson’s ratio and static Young’s modulus measured in the experiment and the dynamic Poisson’s ratio and dynamic Young’s modulus calculated from logging data, as shown in Figs. 8 and 9. According to Figs. 8 and 9, the conversion relationship between the dynamic and static Poisson’s ratio and the dynamic and static Young’s modulus of the Chang 7 shale oil reservoir in this block is as follows:

$${E_s}= - 0.365{E_d}+35.199$$
(17)
$${\mu _s}=0.5827{\mu _d} - 0.0175$$
(18)
Fig. 8
Fig. 8The alternative text for this image may have been generated using AI.
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Study on the conversion relationship between dynamic and static Young’s modulus of Chang 7 shale oil reservoir.

Fig. 9
Fig. 9The alternative text for this image may have been generated using AI.
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Study on the conversion relationship between dynamic and static Poisson’s ratios in the Chang-7 shale oil reservoir.

Research on the establishment of a new model for calculating ground stress

The magnitude of the horizontal principal stress difference has a direct impact on whether a complex fracture network can be formed. The smaller the horizontal principal stress difference, the less resistance the fracture experiences during the advancement process, and the better the fracture ductility. The more complex the fracture system formed during volume fracturing, the more crucial it is for reservoir transformation and development. Through research, the minimum and maximum horizontal principal stresses can be obtained using formula (19) (Huang Rongzun, hydraulic fracturing method) and formula (20) (Huang Rongzun, drilling collapse method), respectively.

$${\sigma _h}=\frac{{{\nu _{\text{s}}}}}{{1 - {\nu _s}}}({\sigma _\nu } - \alpha {P_p})+{\beta _1}({\sigma _\nu } - \alpha {P_p})+\alpha {P_p}$$
(19)
$${\sigma _H}=\frac{{{\nu _{\text{s}}}}}{{1 - {\nu _s}}}({\sigma _\nu } - \alpha {P_p})+{\beta _2}({\sigma _\nu } - \alpha {P_p})+\alpha {P_p}$$
(20)

In the formula, σ h - minimum horizontal principal stress, MPa; σ H - maximum horizontal principal stress, MPa; β 1- the structural stress coefficient in the direction of the minimum horizontal principal stress (taken as 0.45 in this article); β2- the structural stress coefficient in the direction of the maximum horizontal principal stress (taken as 0.75 in this article).

Pp - formation (pore) pressure, MPa, The calculation formula is shown in formula (21):

$${P_p}={\rho _{\text{w}}}g{\text{h}} \times {\text{a}} \times {10^{ - 3}}$$
(21)

In the formula, ρ w - density of water, g/cm3; a - Formation pressure coefficient, decimal, (value in this article is 0.7); h - vertical depth, m.

α - contribution coefficient of formation pore pressure (effective stress coefficient or Biot coefficient), with a value range of 0 < α < 1. The value of α in this article is 0.65.

σ v - vertical stress (overlying rock pressure), MPa, The specific calculation formula is shown in formula (22);

(22)

In the formula, H0 represents the starting vertical depth of the study well section, m; H represents the depth value in the middle of the target layer, m;

Finally, according to formula (19) and formula (20), the horizontal principal stress difference can be calculated. The specific calculation formula is shown in (23):

$$\Delta \sigma ={\sigma _H} - {\sigma _h}$$
(23)

The comparison between the static stress data calculated by indoor experiments and the dynamic stress data calculated by constructing a stress model using logging data is shown in Table 5. The maximum horizontal principal stress error is between 0.29% and 12.60%; The minimum horizontal principal stress error is between 0.87% and 14.53%; The vertical stress error is between 1.73% and 15.35%. The model can be modified by adjusting the construction stress coefficient to reduce errors.

Table 5 Error in dynamic rock mechanics parameters calculated from static data and logging curves of indoor experiments in block Y.
Full size table

Conclusions

  1. (1)

    This article takes the Y block of the M oilfield in the Ordos Basin as the research object, and uses the Kaiser acoustic emission experiment principle to conduct stress testing experiments on the Chang 71 rock samples in the study area. It can be found that the vertical principal stress distribution of the Chang 7 of the block is between 49.72 ~ 61.13 MPa, the maximum horizontal principal stress distribution is between 59.04 ~ 75.4 MPa, the minimum horizontal principal stress distribution is between 46.75 ~ 56.38 MPa, the horizontal stress difference is between 10.16 ~ 21.67 MPa, and the horizontal stress difference coefficient is between 0.21 ~ 0.42. Therefore, conventional horizontal well volume fracturing is not easy to form complex fracture networks, and dense cutting fracturing technology is needed to transform the reservoir, form complex fracture networks, and achieve efficient development of shale oil reservoirs.

  2. (2)

    Through theoretical research, geological surveys, and extensive analysis of ground stress data, some basic laws of ground stress distribution have been preliminarily recognized. The average horizontal maximum stress gradient of shale oil reservoir in Block Y of M oilfield is 2.534 MPa/100m, the average horizontal minimum stress gradient is 1.891 MPa/100m, and the average vertical stress gradient is 2.051 MPa/100m. The principal stresses in three directions at a certain depth of the formation can be calculated through the gradient of ground stress. The average ratio of the maximum horizontal principal stress to the minimum horizontal principal stress of the 7th shale oil reservoir in the Y block of the M oilfield in the northwest of the Ordos Basin is 1.30, which means that the minimum principal stress value in this block is 77% of the maximum horizontal principal stress value. The vertical principal stress value of this block is 83% of the maximum horizontal principal stress value.

  3. (3)

    Establishing a rock mechanics parameter calculation model based on well logging curves can yield formulas for dynamic Young’s modulus and dynamic Poisson’s ratio. Explore the relationship between static parameters measured in indoor experiments and dynamic parameters calculated from well logging curves, and establish a formula for converting dynamic and static rock mechanics parameters. Establishing a new model for calculating ground stress using well logging curves, comparing the static ground stress data obtained from indoor experiments with the dynamic ground stress data obtained from constructing a ground stress model using well logging data, the maximum horizontal principal stress error is between 0.29% and 12.60%; The minimum horizontal principal stress error is between 0.87% and 14.53%; The vertical stress error is between 1.73% and 15.35%. The model can be modified by adjusting the construction stress coefficient to reduce errors. The error between the two meets practical requirements and can be applied to mining practice.