Damage evolution characteristics of heterogeneous fractured sandstone reservoir under different fracturing fluids

To investigate the coupling effect of in situ stress and fluid pore pressure and the propagation law of damaged area during hydraulic fracturing and gas fracturing in heterogeneous fractured reservoirs, according to the effective stress principle and the smooth Rankine stress criterion, this paper establishes a coupled fluid–solid‐damage mathematical model of heterogeneous rock layers and carries out numerical simulations on the characteristic field changes of rock layers under water and nitrogen fracturing. The results show that the continuous injection of nitrogen or water can cause an increase in pore pressure in natural fractures and rock matrices, leading to rock damage and an increase in porosity. Under the same parameters, the damage area and length of the rock mass during nitrogen fracturing are larger than those of hydraulic fracturing, and the changes in pore pressure, permeability, and porosity are consistent with the damage area. The pore pressure near the connected natural fractures is relatively high, resulting in tensile strain; the pore pressure at isolated fractures is relatively low, and some even produce compressive strain. During nitrogen fracturing, the damage evolution is less affected by the in situ stress and the matrix permeability, while hydraulic fracturing is more affected by them. The damage area is the smallest when the horizontal in situ stress is equal. When the initial permeability of the matrix is low, the damaged area mainly follows the natural fractures and is distributed in a strip shape. As the permeability of the matrix increases, the fracturing fluid can enter the matrix, and the damaged area is in the shape of a block.


| INTRODUCTION
With the progress of human science and technology and the rapid development of the economy, the increasing demand for energy, the decreasing nonrenewable resources such as oil and coal, and the environmental problems brought by it, people have to pay attention to the active exploitation of clean energy such as natural gas, coalbed methane, and geothermal energy in underground rock reservoirs. 1,2The development and utilization of natural gas will bring major changes to China's energy utilization and environmental protection. 3,4However, compared with shallow conventional natural gas, the development of deep and unconventional natural gas is very difficult, the porosity of the reservoir rock layer is generally not higher than 10%, and the permeability is only about 1 × 10 −18 m 2 . 5Extraction from natural cracks alone is difficult, slow, and inefficient.Therefore, to effectively extract gas from low-permeability rock formations, it is necessary to adopt the method of artificially fracturing and increasing the permeability of rock formations to achieve large-scale commercial exploitation of oil and gas resources.
7][8] With the development of industrial technology in recent years, the combination of hydraulic fracturing and horizontal well drilling has become an effective means for unconventional energy development. 9The activation of existing natural fractures or new fractures generated by high-pressure water can greatly improve the permeability of reservoirs, which has obvious effects on improving the production of single wells. 10Wang et al. 11 investigated the distribution of water injection pressure and permeability in coal seam under fluid-solid interaction and obtained the relationship between water injection pressure, water injection time, and coal permeability.Feng et al. 12 studied the generation and evolution mechanism of the hydraulic failure area in faults and closed roofs during the hydraulic fracturing process, and analyzed the fluid migration and diffusion mechanism along the hyperpermeability channel.Fan et al. 13 established a unified mathematical model for coal seam fracturing and extraction including damage field, stress field, and seepage field, and simulated the effects of drilling hole spacing, water injection pressure, coal elastic modulus, and in situ stress on hydraulic fracturing and gas extraction process.Zhang et al. 14 established a numerical model of particle flow stress-fluid pressure coupling, carried out the numerical simulation of pore overpressure and hydraulic fracturing based on the discrete element method, and explored the coupling between formation stress and fluid pressure and the law of artificial fracture growth during hydraulic fracturing in shale reservoirs.Over the past few decades, several waterless fracturing technologies have been developed and applied in engineering practice, including oil-based fracturing, explosive fracturing, and gas fracturing. 15,16At present, gas fracturing has gradually attracted the attention of scholars.Wang et al. 17 conducted a detailed analysis of the effect of liquid nitrogen on enhancing fracture initiation and propagation in concrete samples, shale, and sandstone rocks, and demonstrated the ability and applicability of liquid nitrogen low-temperature fracturing through experiments.Lin, 18 through laboratory experiments, theoretical analysis, and numerical simulation, systematically studied the difference of fracture initiation when fracturing by water or gas, analyzed the effects of water pressure and gas pressure loading rate, reservoir permeability, fracture length, and in situ stress at different depths on water or gas fracturing, and found that gas fracturing has obvious advantages under different conditions.Zhang 19 developed a coupled fluid-solid-damage model and studied the anisotropic failure characteristics of layered shale, the movement law of permeability boundary, the evolution law of fracture pressure and permeability area, and the evolution difference of water/gas fracturing damage.
1][22] Therefore, in this paper, a numerical model for fluid-solid-damage of heterogeneous rock formations containing natural fractures under hydraulic and gas fracturing was established, and the damage and failure process, pore pressure changes, and porosity changes of injected water/nitrogen rock formations were simulated and analyzed.

| Stress-strain and damage evolution of rocks
Based on the theory of elasticity, the mechanical equilibrium of porous medium rock is controlled by the following factors: where σ is the stress tensor and f is the volumetric force.The stress-strain relationship of rock materials conforms to the law of linear pore elasticity and combines isotropic damage models 23 αp where σ′ is the effective stress tensor, α is the Biot coefficient, p is the fluid pressure in the rock pores, D is the scalar damage parameter, C is the elastic stiffness matrix, I is the unit matrix, and ε is the rock strain tensor, defining the tensile strain to be positive and the compressive strain to be negative.
The isotropic damage model is used to simulate the failure process of rock materials, and the control equation under the load-unloading conditions is 23 where ε eq is the equivalent strain, u is the rock displacement in all directions, and F is the internal variable that records the maximum equivalent strain.
Based on the smoothed Rankine stress criterion, we define the equivalent tensile strain and compressive strain as follows 23 : where E is the elastic modulus of the rock, and then the damage parameters for tensile and compressive are derived by assuming the elastic brittle constitutive behavior, denoted as D t and D c , respectively, 24 where are the ultimate elastic tensile strain and compressive strain of rocks, respectively.f t0 and f c0 are tensile strength and compressive strength, respectively.f ηf = tr t0 and f ηf = cr c0 are residual tensile strength and compressive strength, respectively.η is the residual strength ratio.κ t and κ c are internal variables under tensile and compression conditions, respectively.
Finally, the stress-strain equation of the reservoir rock can be obtained as where It should be noted that the heterogeneous rocks studied in this article mainly refer to rocks containing natural cracks.It is composed of rock matrix and natural fractures.For rock matrix, the mechanical parameters of each region are the same and can be considered as isotropic media.For natural fractures, they can also be regarded as isotropic media, but their strength and elastic modulus are much lower than those of rock matrix, while their porosity and permeability are much higher.Therefore, rocks can be simplified as isotropic media for calculation.

| Fluid flow in natural fractures and rock matrices
Assuming that there is only a single-phase fluid in the internal pores of rocks, the continuity equation for single-phase fluid in porous rocks is where ρ l is the fluid density and ϕ is the porosity of rocks (the porosity of rock matrices and fractures are ϕ m and ϕ f , respectively), t is the injection time,  v l is the fluid velocity, Q is the source term, ε v is the volumetric strain of rock-solid skeleton.
The motion of fluids follows Darcy's law where k is the permeability of rocks (the permeability of rock matrices and fractures are k m and k f , respectively), μ l is the dynamic viscosity of fluids, and p l is the fluid pressure.Since the rock is a porous elastic medium, its water storage model is 24 For natural fractures in rock, the relationship between the fracture permeability k f and the fracture opening b f according to the cube's law is 25 The equivalent water storage coefficient of rock fractures is where K l is the bulk modulus of the fluid and K n is the normal stiffness of the fracture.For rock matrix, its porosity can be calculated as 24 where ϕ m0 is the initial porosity of the matrix, ϕ r is the residual porosity, σ ¯′ is the effective mean stress.The stress-related porosity coefficient is The matrix permeability is 24 where ζ is the permeability coefficient associated with damage, with a value of 0.5 in this paper.
The equivalent water storage coefficient of the rock matrix is where the bulk modulus of the rock is The fluid-solid-damage interaction in fractured reservoirs among multiphysical fields in the model is shown in Figure 1.

| Experimental verification
To verify the correctness of the fluid-solid-damage coupling model in the previous section, hydraulic and nitrogen fracturing tests were conducted on sandstone samples.The sandstone specimen is processed into a cylinder with a diameter of 50 mm and a height of 100 mm, and a circular hole with a diameter of 10 mm and a depth of 60 mm is drilled in the center of one end of the specimen, as shown in Figure 2A.In the experiment, the two ends of the sandstone sample are first sealed with vulcanized silicone glass adhesive, and then water or nitrogen is injected into the sandstone sample borehole through a pressure loading system.During the loading process, the injection pressure is recorded in real-time and acoustic emission (AE) signals are collected.
Figure 2B,C shows the changes in water injection pressure and nitrogen injection pressure over time, respectively.At the beginning of a period of time (about 400 s of water injection and about 60 s of nitrogen injection), the fluid injection pressure increases slowly, and then it continues to increase over time.When the injection pressure reaches 7.54 MPa (water pressure) and 4.70 MPa (nitrogen pressure), the sample ruptures and macroscopic cracks occur.Afterward, the fluid injection pressure rapidly decreases, and the test ends.During the hydraulic fracturing process, there are almost no AE counts before the peak injection pressure.When macroscopic cracks occur, the number of AE counts increases sharply.In nitrogen fracturing, the AE signal appears earlier, and the number of AE counts is higher when the rock sample is damaged.
The coupling model mentioned above was used to simulate this experiment.In the solid deformation field of rock, all boundaries are not constrained and the rock does not have rigid displacement.In the seepage field, increasing fluid injection pressure is applied to the inner boundary of the model, and the pore pressure on the outer boundary is set as the initial formation pressure.
The number of damaged units is the number of units that meet the failure criteria during the numerical simulation process, which can be compared to the number of AE counts.During the simulation process, the injection pressure curves of water and nitrogen maintain almost the same path as the test load, and the change in the number of damaged units over time is similar to the number of AE counts, as shown in Figure 2B,C.These analyses indicate that the mathematical model proposed in this article can effectively simulate the damage evolution of sandstone during hydraulic and nitrogen fracturing processes.

| Establishment of the numerical calculation model
In petroleum engineering, in situ stress can be calculated from logging curves, and the occurrence of natural fractures can be obtained from seismic data inversion.According to the stress conditions and the distribution of internal natural fractures of a certain target reservoir in the Tarim Basin, China, a rock formation model with geometric dimensions of 50 m × 50 m is established, as shown in Figure 3.In this paper, the Comsol Multiphysics finite element software is used for numerical simulation.The injection point is ( The physical and mechanical parameters of rock matrix and natural fractures, as well as fluid injection parameters, are seen in Table 1, and the physical parameters of fracturing fluids (water and nitrogen) are seen in Table 2.In the modeling, there are great differences between water and nitrogen in terms of dynamic viscosity, fluid density, compression coefficient, and other fluid properties.For example, the dynamic viscosity of water is greater than that of nitrogen, and after injection into the rock, its flow in the rock is slower under the influence of shear stress.The compressibility coefficient of water is smaller than that of nitrogen, and its compression effect in pores is different due to the influence of the bulk modulus of the rock.As seen in Figure 4, when injecting water for 3 h, the changes in damage and porosity of the rock are not obvious, the pore pressure near the injection point increases rapidly to 12 MPa due to low permeability and porosity, while the pore pressure in the connected natural fracture is stable at about 9 MPa, and it is basically 0 in rock matrices.It indicates that water flows mostly in natural fractures and is in the stage of filling cracks.As the water continues to be injected for 5 h, obvious damage begins to occur in the rock layer, the porosity of the rock matrix near the injection point increases to 25%, and the pore pressure at the injection point increases to 15 MPa, while it reaches 13 MPa in the fracture.At this point, it is in the initial stage of damage development, and damage occurs in the stress concentration area near the injection point and connected natural fractures.After 7 h of water injection, the rock damage area doubled, the pore pressure of the rock fractures reaches 15 MPa, and the higher pore pressure is mainly distributed in a strip shape along the natural fractures.This is a stable stage of damage development, and the water pressure in the fracture is still less than that at the injection point.At the end of 9 h of water injection, the rock damage doubled again compared to that at the seventh hour, and the pore pressure in the fracture reached 18 MPa, which is basically consistent with that at the injection point, and the distribution shape of the rock porosity is basically consistent with the damage area, remaining at about 30%, and could even reach 35% at the tip of the fracture.
The evolution process of reservoir damage is very different under gas fracturing compared to hydraulic fracturing.As seen in Figure 5, when injecting gas for 1 h, the damage and porosity of the rock begin to change, but it is not obvious, the pore fluid pressure at the injection point increases to 13 MPa, and it reaches 10 MPa in the natural fractures, which is almost equal to that for 3 h in hydraulic fracturing.After 3 h of gas injection, the rock formation is rapidly damaged, and its expansion shape and range are basically consistent with that at the seventh hour in hydraulic fracturing, and the pore pressure in fractures is 15 MPa, but the pore pressure near the injection point is only 17 MPa.It shows that the gas injection has a faster propagation speed along the fracture and matrix, which is more likely to invade the rock matrix, resulting in faster pressure attenuation.After 5 h of gas injection, the length of the damage zone reached an extreme value, and the damage area doubled, while it basically followed the natural fracture strip.When gas is injected for 7 h, the length of the damage zone no longer changes, the damaged area is connected from strip shape to block shape, the pore pressure in the damaged area increases to more than 25 MPa, and the pore pressure of the natural crack in the undamaged area also reaches about 10 MPa, while it is basically maintained at the original pore pressure of 5 MPa in hydraulic fracturing.At the end of 9 h of gas injection, the damaged area is basically fully connected with the damage area of one-third of the entire rock formation, and the porosity distribution is basically consistent with the damage area.The variation of von Mises stress is similar to that in hydraulic fracturing.
According to the above analysis, the continuous injection of nitrogen and water can cause an increase in pore pressure in natural fractures and rock matrices, leading to rock damage and increased porosity, increasing reservoir permeability and promoting oil and gas recovery.However, due to the lower density and dynamic viscosity of nitrogen compared to water, it expands faster along the fracture and matrix during injection, and the gas is easier to penetrate into the rock matrix, resulting in a faster increase in pore pressure.Under higher pore pressure, the rock is more prone to tensile damage, with a larger damage area and higher permeability enhancement.Fluid dynamic viscosity is the main factor that causes differences between hydraulic fracturing and gas fracturing.

| Fracture aperture
The fracture aperture at different monitoring points caused by hydraulic fracturing and nitrogen fracturing are comparatively analyzed, as seen in Figure 6.The value of initial fracture aperture is 5 mm, and the maximum fracture aperture after hydraulic fracturing is 6.59 mm, while it reaches 6.65 mm after gas fracturing, which shows that nitrogen has a better fracturing effect than water.The distribution pattern of fracture aperture variation is basically similar in hydraulic fracturing and gas fracturing.For the same crack, the aperture in the middle is greater than that in the tip.The aperture of connected fractures within the damage area is relatively large, while the aperture of isolated fractures that are not connected to the injection point changes very little and is basically not within the damage area.

| Pore pressure
Figure 7 analyzes and compares the pore pressure at eight monitoring points in the rock layer, and it is found that when the fracturing fluid is injected at a constant mass flow rate, the pore pressure of the rock layer steadily increases in hydraulic fracturing, with little | 3453 change in the rate of increase.However, in the initial stage of nitrogen fracturing, the rate of increase in pore pressure is faster, and then it decreases to a certain extent.This is because nitrogen basically connects the natural fractures near the injection point, and the gas diffuses outward at higher pressures.Monitoring point 2 is closest to the injection point, but within 1.5 h, the pore pressure is lower than the initial pressure of 5 MPa.This phenomenon is more obvious in gas fracturing, because the injection of fracturing fluid breaks the balance between the original rock stress and pore pressure, causing a sharp increase in pore pressure at the injection point.The pore pressure at monitoring point 2 decreases due to the compression of high pore pressure at the injection point.When the rock at point 2 is damaged, the fluid pore pressure gradually recovers and rapidly increases.
Monitoring points 6 and 8 are located far away from the injection point and in isolated fractures.Their pore pressure remains almost unchanged in the early stage of hydraulic fracturing and begins to rise after 7 h, while it begins to rise significantly after 5 h in nitrogen fracturing.This is because the damaged fractures are already connected at this time, and the fracturing fluid pressure rises, which can also be seen in Figures 4 and 5.
Monitoring points 1 and 7 are located far away from the injection point and in the rock matrix, but the pore pressure at monitoring point 7 is much greater than that at monitoring point 1.At the end of 9 h, the pore pressure at point 7 is about 15 MPa under hydraulic fracturing, and it is only 6 MPa at point 1, about 40% of that at point 7.Under nitrogen pressure fracturing, it reaches 23 MPa at point 7, close to that at the injection point, while it is only 12 MPa at point 1.This is because monitoring point  7 is close to the natural fractures connected to the injection point, and the number of fractures is relatively dense, while monitoring point 1 is close to an isolated fracture, where fluid can only flow through the matrix, resulting in a slow increase in pore pressure.Moreover, the maximum horizontal principal stress and natural fractures jointly control the expansion direction of the damage area, and point 7 happens to be in the damage area.
Monitoring points 3, 4, and 5 are closer to the injection point, and their pore pressure is basically consistent with the variation of pore pressure at the injection point over time, ultimately reaching the maximum value of pore pressure.

| Volumetric strain
The changes in volumetric strain of rock at different monitoring points after fracturing is shown in Figure 8.The volume strain at the eight monitoring points and the injection point generally increases with the injection of fracturing fluid, resulting from tensile expansion due to increasing pore pressure.The peak volumetric strain under hydraulic fracturing can reach 4.5 × 10 −4 , while it can reach 6.5 × 10 −4 under nitrogen fracturing.
The volume strain at monitoring point 8 is quite special.Although it also increases over time, its initial value is −3 × 10 −4 , then increases to −2 × 10 −4 and 5 × 10 −5 under hydraulic fracturing and nitrogen fracturing after 9 h, respectively.This is because monitoring point 8 is located at the tip of the natural fracture on the edge of the rock stratum, which is strongly compressed by the in situ stress.With the increase of fracture pore pressure, its volume strain begins to increase.In addition, similar to monitoring point 8, the volumetric strain at monitoring point 6 is also significantly lower than other monitoring points, which is also due to the significant compression effect at the crack tip on the edge of the rock layer.

| Effect of in situ stresses on damage evolution
For different initial in situ stress states, the damage effect of different fracturing fluid injection would be different, so it is necessary to study the sensitivity of water and nitrogen injection damage to initial in situ stress, which is of great significance to actual engineering projects in different regions.On the basis of the present numerical model, we set three cases where the in situ stresses in the x and y directions are 2:1, 1:1, and 1:2, respectively.
Figure 9 shows the damage distribution of rock formations under different initial in situ stresses, when the in situ stress ratio is 1:1 under hydraulic fracturing, the fracturing damage area is the smallest, only one-fifth of the rock formation, and the damage area is mainly concentrated near the injection point and the tips of the natural fractures.When the in situ stress ratio is 2:1, the damage area is the largest, which is roughly distributed along the diagonal from bottom left to top right, and there are some undamaged rock matrices within the damaged zone.When the in situ stress ratio is 1:2, the trend of the damage area extending along the diagonal from bottom left to top right is suppressed, but it expands along the y direction (σ y is larger), and there are almost no undamaged rock matrices within the damaged zone.Under nitrogen fracturing, there is almost no difference in the shape and range of the damage zone, and the damage area is the smallest when the in situ stress ratio is 1:1, but the shape is generally the same, so it seems that the in situ stress has no obvious effect on nitrogen fracturing.Under the same in situ stresses, nitrogen fracturing is much larger than hydraulic fracturing in terms of damage area.We note that the final damage area is basically consistent with the connected natural fracture area, which indicates that the hydraulic fracturing damage area is greatly affected by both in situ stresses and natural fractures, while the gas fracturing damage area is mainly affected by natural fractures.
Figure 10 shows the equivalent stress (von Mises stress) on the monitoring line from coordinates (0,25) to (50,25) in rock formation under different in situ stresses.In general, the equivalent stress is the largest when the in situ stress ratio is 1:2, followed by 2:1, and the smallest when 1:1.Therefore, the minimum equivalent stress when the in situ stress ratio is 1:1 may be easier to make the rock formation reach the equilibrium state, leading to smaller damage areas.The maximum and minimum equivalent stresses under hydraulic fracturing are about 2 and 18 MPa, respectively, with the maximum values located near the injection point.However, it is significantly different than the maximum and minimum equivalent stress values during nitrogen fracturing are around 1 and 22 MPa, respectively, with the maximum values located at the edge of the model and little variation near the injection point.This is because the density and dynamic viscosity of nitrogen gas are lower than those of water, resulting in a faster expansion rate along the fractures and matrix during injection, and the gas is easier to penetrate into the rock matrix and conduct to the edge of the model.

| Effect of initial permeability on damage evolution
The initial permeability of different reservoir rocks varies greatly, which may have a significant impact on the distribution of damage zones under hydraulic and nitrogen fracturing.On the basis of the present numerical model, we set three cases where the initial permeability of rock formations are 1 × 10 −18 , 5 × 10 −18 , 1 × 10 −17 , and 5 × 10 −17 m 2 , respectively.
Figure 11 shows the damage distribution of rock formations under different initial permeability after hydraulic and nitrogen fracturing.Under hydraulic fracturing, the area of the damage zone generally increases with the increase of initial permeability.But if the initial permeability reaches a certain value, the area and length of the damage zone would decrease.This is because after water is injected into the rock layer, it can not only flow rapidly along natural fractures but also enter the matrix due to the high permeability of the reservoir, which would not form high pore pressure, thus reducing the degree of damage to the rock.For nitrogen fracturing, the damage area of the rock formation is much larger than that of hydraulic fracturing at the same initial permeability.The damage area and length also increase with the increase of initial permeability, but the rate of increase significantly decreases.This is because the dynamic viscosity of nitrogen is relatively low.When the permeability is high, the gas enters the rock matrix driven by the pore pressure difference, causing damage to the fracture and matrix.Regarding the shape of the damage zone, when the initial permeability is low, the damage zone is distributed in a strip shape along natural fractures.This is because the initial permeability of the reservoir is too small, making it difficult for fluids to enter the rock matrix and can only flow along natural fractures.Pore pressure causes tensile damage within the fractures.When the initial permeability of the reservoir is high, the fluid will enter the rock matrix, and the gradually increasing pore pressure with injection will cause damage to the matrix.This will gradually connect the discretely distributed damage areas into a block shape.
The variation of pore pressure at a certain location is closely related to its damage evolution.We selected two monitoring points with significant changes in pore pressure, injection point, and monitoring point 4, and present the changes in pore pressure with injection time during hydraulic fracturing and gas fracturing under different initial permeability, as shown in Figure 12.
From Figure 12A, it can be seen that regardless of hydraulic fracturing or nitrogen fracturing, the pore pressure at the injection point decreases with the increase of the initial permeability of the reservoir.The maximum pore pressure under nitrogen fracturing is 34.3, 26.8, 24.6, and 19.9 MPa, corresponding to the four cases of initial permeability, which decrease by 21.9%, 8.2%, and 19.1%, respectively.The maximum pore pressure under hydraulic fracturing is 23, 19, 17.9, and 14.9 MPa, respectively, reducing by 17.3%, 5.7%, and 16.8%.From Figure 12B, it can be seen that the pore pressure at monitoring point 4 ultimately reaches the maximum injection pressure, indicating that the monitoring point 4 has been damaged due to injection.However, there are significant differences in the changes in pore pressure over time.Under nitrogen cracking, the pore pressure remains almost unchanged within 1 h when the initial permeability is 5 × 10 −18 and 1 × 10 −17 m 2 , then it rapidly increases from 1 to 2 h, and after 2 h, the change pattern is consistent with the injection point, indicating that monitoring point 4 undergoes damage between 1 and 2 h.In contrast, the pore pressure under hydraulic fracturing only increases rapidly after 3 h, and even takes 5 h when the initial permeability is 1 × 10 −18 m 2 .This is because the density and dynamic viscosity of water is higher than that of nitrogen, and the lower the initial permeability of the reservoir, the lower its flow velocity in natural fractures and rock matrices, resulting in longer fracturing time and lower efficiency.continuous injection of nitrogen and water can cause an increase in pore pressure in natural fractures and rock matrices, leading to rock damage and an increase in porosity.Due to the lower density and dynamic viscosity of nitrogen compared to water, it expands faster along cracks and matrix during injection, resulting in faster increase in pore pressure and larger damage areas.After injecting fracturing fluid with the same mass flow rate for 9 h, the effect of nitrogen fracturing is significantly higher than that of hydraulic fracturing.The damage zone under nitrogen fracturing is in a block shape, with an area of one-third of the entire rock formation, while the damage zone under hydraulic fracturing is generally in a strip shape, with an area of only one-fifth of the rock formation.2. The aperture in the middle of the fracture is greater than that in the tip.The aperture of connected fractures within the damage area is relatively large, while the aperture of isolated fractures that are not connected to the injection point changes very little and is basically not within the damage area.The increase in pore pressure and volumetric strain is significant at the connected fractures, while it is relatively small at isolated fractures, and volumetric strain is even negative compressive strain.3.Under hydraulic fracturing, the damage evolution of reservoir rock is greatly affected by in situ stress, initial permeability, and natural fractures, while it is mainly affected by the distribution of natural fractures under gas fracturing.The damage area is the smallest when the horizontal in situ stress is equal.When the initial permeability of the matrix is low, the damaged area mainly follows the natural fractures and is distributed in a strip shape.As the initial permeability of the matrix increases, the fracturing fluid can enter the matrix, and the damaged area is in the shape of a block.
25 m, 25 m) and the diameter is 25 cm.The left and bottom sides of the model are applied to normal displacement constraints, with the minimum horizontal stress on the upper side and the maximum horizontal stress on the right.Considering the relative position with natural fractures, eight monitoring points were set up as the result investigation: point 1 (18 m, 30 m), point 2 (23 m, 26 m), point 3 (21 m, 20 m), point 4 (24 m, 14 m), point 5 (27 m, 20 m), point 6 (36 m, 38 m), point 7 (33 m, 30 m), and point 8 (38 m, 5 m).

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I G U R E 2 Experimental and simulation results of the sandstone samples during hydraulic and nitrogen fracturing.(A) Sandstone samples, (B) Experimental and simulation data of hydraulic fracturing, and (C) Experimental and simulation data of nitrogen fracturing.AE, acoustic emission.NUMERICAL SIMULATION 4.1 | Evolution characteristics of the fractured reservoir under hydraulic and gas fracturing 4.1.1| Damage evolution

Figures 4
Figures4 and 5show the spatiotemporal changes of rock damage, pore pressure, equivalent stress (von Mises stress), and porosity during water and nitrogen injection processes, respectively.The rock formation system with natural fractures is basically in equilibrium in the early stage of fluid injection, and the damage is small.As the mass flow of the fluid increases, different degrees of damage begin to occur at different locations in the rock

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I G U R E 3 Numerical model and grid division of the fractured reservoirs for hydraulic or gas fracturing.(A) Numerical model, and (B) Model grid.

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I G U R E 4 Rock damage, pore pressure, equivalent stress, and porosity under hydraulic fracturing.(A) Damage, (B) Pore pressure, (C) Von mises stress, and (D) Porosity.F I G U R E 5 Rock damage, pore pressure, equivalent stress, and porosity under nitrogen fracturing.(A) Damage, (B) Pore pressure, (C) Von mises stress, and (D) Porosity.F I G U R E 6 Fracture aperture distribution under different injection fluids.(A) Hydraulic fracturing, and (B) Nitrogen fracturing.XU ET AL.

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I G U R E 7 Changes in pore pressure at different monitoring points.(A) Hydraulic fracturing, and (B) Nitrogen fracturing.

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I G U R E 8 Changes in volumetric strain of rock at different monitoring points.(A) Hydraulic fracturing, and (B) Nitrogen fracturing.F I G U R E 9 Damage distribution of rock formations under different initial in situ stresses.(A) Hydraulic fracturing, and (B) Nitrogen fracturing.

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I G U R E 10 Von mises stress on the monitoring line from coordinates (0,25) to (50,25) in rock formation under different in situ stresses.(A) Hydraulic fracturing, and (B) Nitrogen fracturing.F I G U R E 11 Damage distribution of rock formations under different initial permeability.(A) Hydraulic fracturing, and (B) Nitrogen fracturing.

5 | CONCLUSIONS 1 .
A fluid-solid-damage coupling mathematical model for fractured reservoirs is established, and the changes in characteristic fields of heterogeneous rock formation containing natural fractures under different injection fluids are numerically simulated.The

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I G U R E 12 Changes in pore pressure at different monitoring points under different initial permeability.(A) Injection point, and (B) Monitoring point 4.