# The Role of Fluid Overpressure on the Fracture Slip Mechanism Based on Laboratory Tests That Stimulating Reservoir-Induced Seismicity

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Setup and Sample Preparation

^{3}with a Young’s modulus of 84 GPa and a Poisson’s ratio of 0.25. A cylinder sample, with 100 mm height and 50 mm diameter, is separated smoothly along the surface with a 30° inclination to the vertical axis to simulate a pre-existing fracture. Then the fracture is refined with sandpaper with particles of 18.3 μm. Two boreholes are drilled parallel to the vertical axis near the fracture surface, allowing the fluid to be distributed in the fracture during the tests.

#### 2.2. Experimental Procedure

## 3. Results

#### 3.1. Roughness Alteration

#### 3.2. Mechanic Behavior of Fracture While Water Pressurization

_{n}) of the fracture are determined by the axial stress (σ

_{1}) and confining pressure (σ

_{3}):

_{c}) and the effective normal stress (σ

_{n}− p). r

_{τ}is defined as the ratio between the shear stress and shear strength of the fracture while under water pressurization [12].

_{0}to describe the energy released while sliding. M

_{0}is the product of the fracture area (A), shear displacement (D) and shear modulus (G), determined by the Young’s modulus and Poisson ratio.

_{τ}is 98%. The outlet pressure rises at a nonlinear incremental rate, depending on the water pressure diffusion along the fracture. There are 23 seismic events during the process.

_{τ}. This happens when the outlet pressure reaches this level, meaning that the distribution of the pore pressure on the whole fault surface is over 5.2 MPa.

## 4. Discussion

#### 4.1. Overpressure in Fracture Reactivation

_{p}is the shear strength acquired from the displacement-driven shear test. r

_{c}is the ratio between shear stress (τ) and shear strength (τ

_{p}), which is used to describe the critical state of the fault. The understress is evolved as 1 − r

_{c}. The fault is assumed to be critically stressed if the understress decreases to zero. On the contrary, the shear stress is 0 if the understress is equal to one. The increasing water pressure monitored by the system is defined as Δp and Δp and is normalized by the fault-effective normal stress. σneff (Δp/σ

_{neff}) is defined to describe the overpressure of the fracture.

_{n}< 1 − r

_{c}, the increased pressure and shear stress cannot induce slip; if Δp/σ

_{n}> 1 − r

_{c}, the fault is transitioning from the stable state to unstable state and an aseismic slip or seismic slip might happen. In our test, the overpressure is a dynamic oscillating state rather than a quasi-static state. Due to the heterogeneity of the pressure distribution and low permeability, the change in outlet pressure is delayed compared to the inlet pressure. Therefore, the inlet pressure and outlet pressure corresponding to every slip are analyzed in Figure 8, showing that the unstable slip occurs with the accumulation of pressure. The whole process is divided into three stages according to the inlet pressure (6 MPa, 7 MPa and 8 MPa). For each stage, the overpressure increases in both the inlet and outlet pressure. Every initiation of reactivation of the fault requires a higher pressure in both the inlet and outlet. Therefore, a higher pressure along the fault surface is a necessary condition for inducing a dynamic slip. And when a new balance between the inlet and outlet pressure has formed, the pressure-controlled stick-slip will turn into a stable sliding state. This phenomenon is consistent with the experiment investigated by Scuderi [24]. Finally, when the outlet and inlet pressure remains equal, the maximum injected energy by the rising water pressure remains constant and there is no more dynamic slip during pressure oscillation. Referring to the theory for describing the criterion of fault stability by combining the elastic dislocation theory with the rate-and-state-friction (RSF) constitutive, a relationship between fault stiffness (k

_{c}) and effective normal stress (σ

_{neff}) is defined as Equation (5). D

_{c}is the critical slip distance for the friction of the fracture surface changing from static friction to dynamical friction. Parameter a is the fracture friction at velocity V

_{1}. Parameter b is the fracture friction at velocity V

_{2}. σ

_{neff}is the effective normal stress on the fracture. All the parameters can be measured in the rate and state law friction test.

_{c}is the friction weakening rate parameter [27,28]. Equation (5) shows that increasing the pressure inside the fault can reduce k

_{c}and promote stable sliding, rather than an earthquake slip. But seismological observations contrast with this prediction. The dynamic slip instabilities are determined by the fluid pressurization exceeding the critical stress state for reactivation. This process is driven by energy unbalance due to the decrease in effective normal stress [24].

#### 4.2. Hydraulic Energy and Seismic Energy

_{H}is the injected hydraulic energy, defined as the product of the injection fluid pressure (P Pa/s) and the injection rate (Q m

^{3}/s) (Equation (7)) [29]. The injected volume and pressure change with time. Thus, the injection energy is calculated by integrating E

_{H}over the injection interval (t

_{1}− t

_{2}). ΔW is the potential elastic energy. E

_{f}is the frictional energy dissipated on the fault plane and is supposed to be equal to ΔW [30]. E

_{r}is radiated energy, which is also regarded as seismic energy. It is hard to monitor the radiated energy because of the limited knowledge of the radiation pattern and limited frequency band [31]. Thus this energy is calculated by establishing the relationship [32] with the seismic moment (Equation (8)). E

_{d}is deformation energy; l is energy loss, ignored in this experiment.

_{H}) and radiated energy (E

_{r}). The moment magnitude (M

_{w}) can be calculated according to Equation (8). Therefore, the seismic energy (M

_{0}) can be calculated according to Equation (4). Above this, the relationship between seismic energy and hydraulic energy is established. In Figure 9, the black line is the ratio between seismic energy and hydraulic energy. The 11 black lines represent the ratio of 100% to 0.00000001%, correspondingly. The triangles and circles in Figure 9 are data collected from several field experiments and laboratory experiments. Therefore, Figure 9 shows the relationship between seismic energy and hydraulic energy. The triangle symbols represent the triggered seismicity and the circle symbols represent the induced seismicity. The total input hydraulic energy is 2.52 J. The deformation energy, aiming to enlarge the fracture aperture, ranges from 88% to 93% of the injection energy. Fluid could flow along the aperture more smoothly after several slips. The ratio of seismic energy and hydraulic energy is defined as seismic efficiencies. For triggered seismicity, the seismic efficiency ranges from 0.1% to 10%, referencing the field tests and laboratory tests. But for the induced seismicity, this parameter ranges from 1 × 10

^{−7}% to 1 × 10

^{−3}%. According to Equation (7), we can deduce that the tectonic stress of a fracture and the fluid flow inside the fracture determines the released seismic energy. Therefore, seismic energy could be predicted using hydraulic energy.

## 5. Conclusions

_{n}and 1 − r

_{c}determine the sliding state. When Δp/σn < 1 − rc, the increased pressure and shear stress cannot induce slip. When Δp/σn > 1 − rc, the fault is transitioning from a stable state to an unstable state. Furthermore, hydraulic energy is adopted as another explanation as to why fluid overpressure can induce unstable sliding by establishing the relationship between the input energy and the released energy. Based on this, the seismic energy can be estimated from the input hydraulic energy, which is an effective method for evaluating reservoir-induced seismicity. Going forward, future work is required to determine why seismic turns to aseismic while the new balance is formed, which is also a complicated problem in predicting the magnitude of seismicity.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 5.**The contour of the roughness of the smooth fracture surface. (

**a**) before shearing; (

**b**) after shearing; (

**c**) shear surface.

**Figure 6.**The cyclic pressurization instability of a saw-cut fracture. (

**a**) The shear stress and shear displacement with shearing time; (

**b**) The inlet pressure and outlet pressure with shearing time.

**Figure 7.**The dynamic slip parameters with a seismic event. (

**a**) Pressure with a seismic event; (

**b**) Slip distance with a seismic event; (

**c**) Maximum slip rate with a seismic event; (

**d**) Stress drop with a seismic event.

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**MDPI and ACS Style**

Zhu, Y.; Xu, C.; Song, D.; Liu, X.; Wang, E.
The Role of Fluid Overpressure on the Fracture Slip Mechanism Based on Laboratory Tests That Stimulating Reservoir-Induced Seismicity. *Appl. Sci.* **2023**, *13*, 3382.
https://doi.org/10.3390/app13063382

**AMA Style**

Zhu Y, Xu C, Song D, Liu X, Wang E.
The Role of Fluid Overpressure on the Fracture Slip Mechanism Based on Laboratory Tests That Stimulating Reservoir-Induced Seismicity. *Applied Sciences*. 2023; 13(6):3382.
https://doi.org/10.3390/app13063382

**Chicago/Turabian Style**

Zhu, Yujie, Chen Xu, Danqing Song, Xiaoli Liu, and Enzhi Wang.
2023. "The Role of Fluid Overpressure on the Fracture Slip Mechanism Based on Laboratory Tests That Stimulating Reservoir-Induced Seismicity" *Applied Sciences* 13, no. 6: 3382.
https://doi.org/10.3390/app13063382