Study on mechanical properties and microscopic damage mechanism of tight sandstone reservoir under uniaxial compression

Abstract

Due to the characteristics of low porosity, low permeability and serious anisotropy in tight reservoirs, it is difficult for conventional hydraulic fracturing theory to accurately guide the efficient exploitation of tight reservoirs. It has been shown that the reservoir rock mechanical properties are the key factor impacting the fracturing effect, but the current research on the damage properties of tight reservoir rocks is not comprehensive enough. Therefore, in order to improve the fracturing theory of tight reservoirs, this paper first explores the evolution mechanism of rock fractures through uniaxial compression experiments. Secondly, based on the particle discrete element method, the damage and failure process of tight sandstone under uniaxial compression is simulated from the microscopic scale. The test results show that the rock failure mainly includes tensile failure, shear failure, and tensile-shear failure; Internal micro-fractures will interconnect during rock destruction to form primary fractures through the rock mass, while secondary micro-fractures will also be generated. The numerical simulation results show that when the rock is subjected to tensile-shear failure, with the increase of load, tensile micro-fractures are mainly produced in the specimen, accompanied by a few shear fractures. Under the joint action of shear failure and tensile failure, V-shaped cracks are easily formed in rock. The tensile strength of rock is mainly affected by the microscopic tensile strength, and the cohesive force, modulus, stiffness ratio, friction coefficient and friction angle have significant effects on the compressive strength of rock. Therefore, a reasonable choice of microscopic parameters can realistically simulate the compression-tensile strength ratio of the rock. The research results of this paper can provide the theoretical basis of rock mechanics for the efficient exploitation of tight reservoirs.

1 Introduction

Oil and natural gas as an important energy to promote the rapid development of the world, the demand is increasing year by year (He et al., 2023; Huang et al., 2022). With the depletion of conventional oil and gas resources, the effective development of unconventional reservoirs such as tight oil and tight gas is becoming a global trend (Huang et al., 2018; Huang et al., 2023; Zhang et al., 2022). Under the action of sedimentation, diagenesis and tectonic movement, the interior of this kind of low permeability reservoir is composed of irregularly shaped skeleton particles and cemented fill, accompanied by a large number of micro-fractures, so its interior presents typical characteristics such as discontinuity, anisotropy and heterogeneity (Bai et al., 2023; Huang et al., 2019; S; Huang et al., 2018; Li et al., 2022; Wang et al., 2022). Basic production capacity is basically not available after drilling, and it is necessary to achieve commercial development standards through hydraulic fracturing (Tan et al., 2021; Tan et al., 2017; Zhang et al., 2019). Hydraulic fracturing is a technical method to pump high pressure liquid into the rock to break the rock and increase the permeability of low permeability reservoir (Zhang et al., 2017; Huang et al., 2020; Dontsov, 2022). The effect of its reconstruction is influenced by many factors (Tan et al., 2020; Luo et al., 2022; Zheng et al., 2022). Previous studies have shown that the mechanical properties of reservoir rocks are the key to determining the fracturing effect except fracturing parameters and reservoir temperature (Detournay et al., 2022; Ji et al., 2015). Therefore, clarifying the mechanical properties of reservoir rock is the key to perfecting hydraulic fracturing technology.

The laboratory test can obtain the uniaxial tensile strength, uniaxial compressive strength and triaxial compressive strength of the rock. The stress-strain curve can be calculated to get the modulus of elasticity, Poisson’s ratio, friction coefficient, as well as the cohesion of the rock and the angle of internal friction and other macro-mechanical parameters of the rock (Huang et al., 2022; Du et al., 2022). Previous studies have shown that the macroscopic mechanical parameters of rocks have an important influence on the study of rock mechanical properties. However, they cannot explain the internal fracture initiation, fracture extension and anisotropy characteristics of rocks, so it is essential to further study the characteristics of rocks from the micro-scale or mesoscale (Tian et al., 2022; Zhang et al., 2023). Microscale studies are not applicable to reservoirs in meters and kilometers (Liu et al., 2021). While the meso scale (micron to millimeter range) is the statistical performance of the mechanical properties at the micro scale, which can be better linked with the macro scale. Moreover, the particle size range of most rocks belongs to the mesoscale range, so studying the mechanical properties of rocks on the mesoscale can better reflect the complex mechanical characteristics of rocks and provide a basis for the macroscopic mechanical properties of rocks (Lai et al., 2023). In this paper, the evolution process of rock fractures is explored on the basis of uniaxial compression test, and flat-joint damage model is established based on particle discrete element method, which can effectively describe rock mesoscopic damage. The damage process of rock is studied from the mesoscale, and the sensitivity analysis of rock mesoscopic parameters is carried out.

2 Uniaxial compression experiment

2.1 Experimental method

In order to study the fracture evolution process of low permeability sandstone, uniaxial compression test combined with non-contact three-dimensional deformation measurement system is used to track the deformation and strain conditions of rock specimen surface, obtain the stress-strain curve of rock and analyze the fracture evolution of rock sample during deformation and failure. This uniaxial compression experiment adopts a microcomputer controlled electro-hydraulic servo universal testing machine (Figure 1A), which can exert a maximum pressure of 1,000 kN. The Aramis system (Figure 1B) is used to measure strain and deformation failure of the rock sample during uniaxial loading. The Aramis system consists of two high-resolution cameras (resolution: 2,448 × 2050 pixels, acquisition speed: 15 Hz), graphics workstation, controller and display. It has the advantages of high measurement accuracy, wide range and intuitive results, and can synchronize time, pictures and analog signals accurately. The sample size can be measured from 1 mm to 1,000 mm, the accuracy is 0.01%, and the measurement range is 0.01%–500%.

FIGURE 1

2.2 Analysis of experimental results

The rock samples used in this experiment are taken from the low permeability tight sandstone reservoir of Chang 6, Zhenying area, Ordos Basin. The rock samples in this area are mainly lithic feldspar sandstone and feldspar lithic sandstone. A total of 9 standard cores with a height of 50 mm and a diameter of 25 mm are taken from the low permeability tight sandstone reservoir at a depth of 900–1,600 m, and the loading rate is 0.01 mm/s during the experiment. Three representative cores with numbers A3, A6 and A7 are selected for results analysis in those experimental results.

Figure 2 and Figure 3 show the stress-strain curve and failure process of core A3. Corresponding feature points such as A, B, C and D can be found in the curve in Figure 2. The curve can be divided into four stages, namely, OA stage, AB stage, BC stage and CD stage. The OA stage is the pore and fracture compaction stage. The micro-fractures and structural planes in the core will gradually close under the action of external pressure. The deformation in this stage is nonlinear, showing an upward concave trend, and the stiffness of the sample will gradually increase. Phase AB is a linear elastic process, and the stress-strain curve is approximately straight line. It can be find that the stiffness of the specimen is basically kept constant. The BC stage is the unstable development stage of the fracture. With the increase of the external load of the rock, the stress concentration at the fractures and pores inside the rock becomes more and more obvious. The fracture changes from stable expansion to unstable expansion, and the energy inside the rock gathers rapidly. When it extends to the critical energy release point, the fracture develops rapidly into a macroscopic fracture. When it develops to a certain stage, the stress will reach the peak strength of 52.01 MPa, that is, point C. In the BC stage, shear fractures are formed at the end of the core and extended rapidly. With the increase of stress, new shear fractures are formed and quickly connected with the previous shear fractures. At this time, the surface of the sample remained intact and do not collapse, as shown in Figure 3. The CD stage is the post-rupture stage. Under the action of macroscopic cracks, the internal structure of the core is destroyed and continues to load. The macroscopic cracks penetrate through each other and form the macroscopic fracture surface.

FIGURE 2

FIGURE 3

Figure 4 and Figure 5 show the stress-strain curve and core failure process of A6 core. The stress-strain curve follows the O-A-B-C process, which is similar to the process of A3 core, including pore and fracture compaction stage, linear elastic stage and fracture unstable development stage. After the peak stress point C, the rock still has some residual strength, which is due to the core failure in the BC stage is split failure, in other words, a tensile fracture is produced. After the peak stress, there are new shear fractures and tensile fractures generated, when the internal fractures of the core have not yet penetrated the whole core. Following the redistribution of stresses within the core, the sample showed a certain increase in stress at point D and finally fell to point E. At this time, a number of tensile fractures and shear fractures occurred in the sample, and the internal structure of the sample is damaged, as shown in Figure 5.

FIGURE 4

FIGURE 5

Figure 6 shows the stress-strain curve of core A7, which has a double peak stress intensity, and the uniaxial compression process stage before point C is similar to that of core A3 and A6.

FIGURE 6

The first peak strength (29.07 MPa) at point C is due to shear fractures appearing at the top of the core with the increase of stress and strain in section BC, resulting in local fractures in the core. Local instability leads to the reduction of the core bearing capacity, but the overall structure of the core is not damaged, as shown in Figure 7. When the stress drops to a certain extent, the internal stress of the core is redistributed, and the ability of the core to withstand external loads increases. At the same time, the core cracked under the combined action of tension and shear, which expanded rapidly and the stress reached the second peak strength (28.94 MPa) at point D. Continuing to apply the load, the fracture penetrates the entire specimen, and the interior of the core is damaged, so that the stress falls rapidly to the E point, while the opening of the fracture increases.

FIGURE 7

3 Basic theory of particle discrete element method

FIGURE 8

Potyondy, 2012).

The force-displacement equation describes the direct relationship between the contact force and the relative displacement at the contact point between particles. Assuming that the normal contact force at the contact is F_n N) and the relative displacement is u_n m), the tangential force at the contact is described by increment, that is, the tangential force increment at the contact is ∆F_s N) and the relative displacement is u_s m). The normal force and tangential forces-displacement equation at the contact is expressed by the following formula:

In the discrete element method, the particle is assumed to be a rigid body, and the contact force exists between the particle and the particle. Under the action of external forces, the particles are in an unbalanced state, which will cause the particles to generate acceleration and velocity. At this time, the particles will produce rotation and dynamic behavior, and the contact force will be updated with the change of particle force and displacement. Assuming that at time t s), the resultant force of particles in the direction i is F_i, the bending moment is M_i (Nm), the mass of particles is m (kg), and the moment of inertia is I_i (kgm²), then the translational acceleration ü_i (m/s²) and rotational acceleration _I (s^-2) of particles in the direction i are respectively as follows:

At t+∆t/2, the translational velocity and rotational velocity of the particle in the direction i are as follows:where is the translational velocity (m/s) of the particle in direction i at the moment t-∆t/2, with ∆t being the calculated time step, and is the rotation velocity (s^-1) of this particle in the i direction at the moment t-∆t/2.

In the particle discrete element method, the constitutive model of the material is defined by assigning the contact model to the contact between particles. It mainly includes four models: linear parallel bond model (Wu et al., 2021), flat-joint model (Potyondy, 2012), smooth-joint model (Fener et al., 2005)and soft-bond model (Huang et al., 2023). The flat-joint model is composed of rigid grains, and the grains are bonded by the contact of the flat-joint. The grains are composed of circular (2D) or spherical (3D) particles and notional surfaces. A grain surface can have multiple abstract surface units, and the abstract surface unit is rigidly connected with the corresponding grain. Therefore, the effective contact between the grains becomes the contact between the abstract surfaces. Flat-joint contact describes the behavior of the intermediate contact surface between abstract surfaces, as shown in Figure 9. In the two-dimensional model, the contact is a straight-line segment that can be discretized into several small units of equal length. In the three-dimensional model, the contact is a disc with a certain thickness, which can be discretized into a number of small units of equal volume from the radial and circular directions. Each element may be bonded, non-bonded with friction, so that the mechanism behavior of the intermediate contact surface may be bonded, non-bonded friction type, or vary along the contact surface. Compared with the linear parallel bonding model, this model can solve the problems such as low compression-tensile strength ratio, small internal friction angle and linear strength envelope. Compared with the linear parallel bond model, this model can solve problems such as low compression-tensile strength ratio, small internal friction angle, linear strength envelope and so on. The element failure at the bond adopts the constitutive relation curve of Figure 10. Since the contact in the flat-joint model contains multiple elements, the failure of each element remains independent, so the model can characterize the damage process in the failure of the specimen.

FIGURE 9

Potyondy, 2012).

FIGURE 10

4 Numerical simulation of microscopic damage

4.1 Numerical model

The flat-joint model can well simulate the microscopic damage of rock, so this paper adopts the model to investigate the microscopic parameters and damage process of rock. Some scholars have carried out sensitivity analysis on the microscopic parameters such as modulus (E_c) stiffness ratio (K_n/K_s), tensile strength (σ_t), bond strength (C)l, friction coefficient μ) and friction angle Φ) in the flat-joint model, and proposed a fast parameter calibration method (Wu and Xu, 2016). Therefore, this chapter does not reiterate the parameter calibration method. The physical parameters of tight sandstone, shale and coal rock in low permeability reservoirs are quite different. On the basis of previous studies, this paper selects the relevant macro parameters, and calibrates the meso parameters for rock uniaxial compression experiment and numerical calculation. The macro and meso parameters of rock are shown in Table 1. The sample used for numerical simulation is 100 mm in height and 50 mm in width. The contact between particles contains two abstract surface elements. The maximum particle radius is 0.6 mm, while the ratio of maximum radius to minimum radius is 1.8, and the particle density ρ) is 2,500 kg/m³.

The particle contact in the plane joint model can be divided into several abstract surface units, each of which can break separately. Therefore, it is assumed that the contact is broken only when the last broken abstract surface unit at the contact between particles is broken, and microcracks appear at this time. The abstract surface units that are broken before the contact are the damage of the contact. This model is defined in this paper as the flat-joint damage model. In the ordinary flat-joint model, if the abstract surface element at the contact is broken, there will be a micro-fracture. Hence, the results of the flat-joint damage model are consistent with those of the flat-joint model, but the number of micro-fractures produced is inconsistent.

Figure 11 shows the numerical simulation results of the sample. Figure 11A shows that rock failure is accompanied by the generation of multiple fragments. At this time, multiple shear fractures and tensile fractures appear in the rock macroeconomically, moreover, the shear fractures run through the entire sample. Figure 11B shows the stress-strain curve of the specimen. There is a certain fluctuation in the initial stress increase of the curve, which is due to the stress change caused by the decrease of the porosity of the sample under compression and the densification of the particle structure. While the stress continues to increase, the stress-strain curves show linear characteristics, and there are micro-fractures in the specimen. It can be seen from Figure 12 that the generated micro-fractures are mainly tensile failure micro-fractures. The number of tensile micro-fractures in the flat-joint damage model is significantly lower than that in the flat-joint model, that is, there are two failure modes between rock particles. With the increase of stress, the shear failure micro-fractures gradually appear in the sample. The comparison of tensile micro-fractures in two different models shows that the number of micro-fractures in contact damage and tensile failure continues to increase. When the stress reaches its peak, the shear failure micro-fractures increase rapidly, and the tensile failure micro-fractures increase linearly. When the strain exceeds the peak strength, the stress decreases, and the number of shear failure micro-fractures and tensile micro-fractures continues to increase. At this time, the rock sample is destroyed and a V-shaped shear fracture is formed. After stopping loading, a total of 6,265 micro-fractures are generated in the flat-joint damage model (including 4,968 tensile failure micro-fractures and 1,297 shear failure micro-fractures), and a total of 13,771 micro-fractures are generated in the flat-joint model (including 11,658 tensile failure micro-fractures and 2,113 shear failure micro-fractures). The number of tensile break micro-fractures in the flat-joint model is more than twice that of those in the flat-joint damage model. Therefore, in the process of core failure, there are two failure modes of shear failure and tensile failure at the contact, but the damage is mainly tensile failure. After reaching the peak stress, the shear micro-fractures appear rapidly and gradually form a V-shaped shear fracture throughout the whole specimen.

FIGURE 11

FIGURE 12

4.2 Influence of microscopic parameters on compression-tensile strength ratio and micro-fracture

FIGURE 13

FIGURE 14

FIGURE 15

FIGURE 16

FIGURE 17

FIGURE 18

Figure 19 shows the relationship between microscopic cohesion and strength. When the microscopic cohesion is within 5 MPa, the internal tensile strength of the sample is larger than the shear strength, so the micro-fractures of the sample are all shear micro-fractures (Figure 20). The tensile strength and compressive strength increase with the increase of microscopic cohesion, while the compression-tensile strength ratio decreases. When the microscopic cohesion is greater than 10 MPa, the compressive strength increases with the increase of the microscopic cohesion, the tensile strength remains unchanged, the compression-tensile strength ratio is consistent with the trend of the compressive strength, and the shear micro-fracture will decrease while the tensile micro-facture will increase.

FIGURE 19

FIGURE 20

5 Discussion

The microscopic parameters of rock are one of the important factors affecting the mechanical properties of rock. It is a key step to reveal the damage mechanism of rock by clarifying the change mechanism of rock properties under various parameters. The above research shows that, in addition to the tensile strength (microscopic), the rest of the rock meso-parameters change the ratio between the two micro-fractures by affecting the compressive strength of the rock. Under conventional conditions, the rock sample is squeezed from the height direction by uniaxial compression, and the two sides of the rock sample are continuously expanding outward under the action of internal force. Since the compressive strength of the rock is much greater than the tensile strength, the ability of the rock sample to withstand external expansion is much lower than the ability to withstand pressure. At this time, the inside of the rock sample slips downward while expanding to both sides, forming a large number of tensile micro-fractures, and the surface of the rock sample shows obvious V-shaped fractures. The compressive strength of the rock increases with the increase of rock microscopic parameters, but the tensile strength is almost unchanged. Compared with the normal condition, the vertical bearing capacity of the rock is greatly enhanced. Under the same pressure, the vertical displacement of the rock sample is smaller, but the outward expansion trend on both sides is almost unchanged, so it is difficult for the fracture to appear as a V-shape. However, the increase of pressure bearing capacity will inevitably lead to the accumulation of a large amount of pressure inside the rock, making the rock fracture more sudden and lack of buffer stage.

The absence of fracture buffer stage will make the rock fracture change from ductile failure to brittle failure, which is obviously unfavorable. In order to effectively identify the mechanism of rock failure, the ratio of compressive strength to tensile strength can be introduced to effectively predict the ratio of shear micro-fractures and tensile micro-fractures during rock failure, so as to determine the fracture mode of rock. However, how to accurately locate the transition point of rock fracture mechanism under compression-tensile strength ratio is still a difficult problem to be solved.

6 Conclusion

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