A prediction method for high-risk areas of water-injection induced earthquakes

Abstract

The present invention relates to the technical field of earthquake research, and discloses a method for predicting high-risk areas of injection-induced earthquakes. S1: Calculate the Coulomb failure stress and poroelastic solution on the fault plane in the injection-induced earthquake danger area to obtain the specific fault state, and construct a prediction model based on the fault state; S2: Visualize the three-dimensional network of the fault plane; use a stress projection map to display the Coulomb stress at different positions near the injection well; in the polar coordinate diagram, the radial direction represents the dip angle, and the polar angle represents the equivalent azimuth angle, which is defined as a e = θ - az, where θ and az are the strike and azimuth angles respectively; for a specific injection well distance and movement direction, calculate the value of ΔS(δ, a e ), where 0° ≤ δ ≤ 90° and 0° ≤ a e ≤ 360°, and normalize the result to [-1, 1]. The present invention provides a simple prediction model based on the normalized Coulomb stress distribution, which can quickly and efficiently locate the potential high-risk areas of injection-induced earthquakes by identifying the relative position and orientation of the faults.

Description

Technical Field

[0001] The present invention relates to the technical field of earthquake research, and particularly relates to a method for predicting high-risk areas of water injection-induced earthquakes. Background Art

[0002] Fluid injection, as a common industrial activity such as hydraulic fracturing, geothermal development, and wastewater reinjection, plays a significant role in improving energy development efficiency and reducing environmental pollution. However, in recent years, more and more research and practices have shown that such activities may trigger earthquakes under certain conditions, especially by inducing fault instability, leading to a series of safety and environmental problems. These induced earthquakes have not only attracted extensive public attention but also posed higher risk management requirements for policymakers and industrial operators (Ellsworth, 2013, Reference [1]).

[0003] Currently, the risk management strategy for fluid injection-induced earthquakes mainly adopts the "traffic light system" (TLS), which adjusts injection operations by real-time monitoring of seismic activities. However, this method has obvious limitations. Its core problem is that it is reactive and often issues warnings when seismic activities have already occurred and may cause harm (Kao et al., 2018, Reference [2]; McGarr et al., 2015, Reference [3]). During this process, the activated faults may have released a large amount of strain energy, causing serious impacts on industrial facilities, public safety, and environmental protection. In addition, the existing TLS system has limited research on the spatial distribution characteristics of induced earthquakes and is difficult to provide an accurate high-risk area identification scheme (Alghannam & Juanes, 2020, Reference [4]).

[0004] The research on the mechanism of fluid injection-induced earthquakes has long been mainly focused on the diffusion effect of pore pressure. Existing research has shown that the increase in pore pressure will reduce the effective normal stress of the fault, thereby promoting Coulomb stress changes and triggering fault slip (Chen et al., 2018, Reference [5]; Deng et al., 2020, Reference [6]). However, the effect of pore pressure is usually limited to a small area near the injection point, and the induced seismic events are relatively small in scale and have low destructiveness (Thomas H.W. Goebel & Brodsky, 2018). In contrast, large destructive earthquakes often occur on faults far from the injection point, and the stress changes in these areas may be determined by more complex poroelastic effects and fault geometry characteristics. The existing theoretical models and practical methods in this field are not yet perfect (T.H.W. Goebel et al., 2017, Reference [8]).

[0005] Another challenge is that most current earthquake risk prediction methods rely on complex numerical simulations or large-scale computations, which not only pose high requirements for data integrity and computing resources but also limit their application in actual industrial scenarios (Segall & Lu, 2015, Reference [9]). The complex geological conditions and fault network distributions further increase the uncertainty of prediction, making it difficult to widely promote existing methods (Rudnicki, 1986, Reference

[10] ).

[0006] To address these issues, some earthquake risk assessment methods based on Coulomb stress distribution have emerged in recent years. These methods judge whether a fault is close to the rupture state by calculating the changes in shear stress and normal stress on the fault plane. However, these methods usually require specific geometric parameters of the fault to be known and have limited ability to visually identify high-risk areas (McNamara et al., 2015; Baisch et al., 2006, Reference

[11] ). In some complex geological conditions, such as areas with drastic changes in fault orientation or dense fault networks, existing methods may not be effectively applied.

[0007] In summary, there are significant deficiencies in the existing technologies in accurately identifying high-risk areas, reducing computational complexity, and improving real-time performance.

[0008] References mentioned or involved in this application:

[0009] [1] Ellsworth, W. L. (2013). Injection-Induced Earthquakes. Science, 341(6142). doi:10.1126 / science.1225942

[0010] [2] Kao, H., Visser, R., Smith, B., & Venables, S. (2018). Performance assessment of the induced seismicity traffic light protocol for northeastern British Columbia and western Alberta. The Leading Edge, 37(2), 117 - 126. doi:10.1190 / tle37020117.1

[0011] [3]McGarr,A.,Bekins,B.,Burkardt,N.,Dewey,J.,Earle,P.,Ellsworth,W.,...Sheehan,A.(2015).Coping with earthquakes induced by fluid injection.Science,347(6224),830 - 831.doi:10.1126 / science.aaa0494

[0012] [4]Alghannam,M.,&Juanes,R.(2020).Understanding rate effects in injection - induced earthquakes.Nature Communications,11(1).doi:10.1038 / s41467 - 020 - 16860 - y

[0013] [5]Chen,X.,Haffener,J.,Goebel,T.H.W.,Meng,X.,Peng,Z.,&Chang,J.C.(2018).Temporal Correlation Between Seismic Moment and Injection Volume for an Induced Earthquake Sequence in Central Oklahoma.Journal of Geophysical Research:Solid Earth,123(4),3047 - 3064.doi:10.1002 / 2017jb014694

[0014] [6]Deng,K.,Liu,Y.,&Chen,X.(2020).Correlation Between Poroelastic Stress Perturbation and Multidisposal Wells Induced Earthquake Sequence in Cushing,Oklahoma.Geophysical Research Letters,47(20).doi:10.1029 / 2020gl089366

[0015] [7]Goebel, T. H. W., & Brodsky, E. E. (2018). The spatial footprint of injection wells in a global compilation of induced earthquake sequences. Science, 361(6405), 899 - 904. doi:10.1126 / science.aat5449

[0016] [8]Goebel, T. H. W., Weingarten, M., Chen, X., Haffener, J., & Brodsky, E. E. (2017). The 2016 Mw5.1 Fairview, Oklahoma earthquakes: Evidence for long - range poroelastic triggering at >40km from fluid disposal wells. Earth and Planetary Science Letters, 472, 50 - 61. doi:10.1016 / j.epsl.2017.05.011

[0017] [9]Segall, P., & Lu, S. (2015). Injection - induced seismicity: Poroelastic and earthquake nucleation effects. Journal of Geophysical Research: Solid Earth, 120(7), 5082 - 5103. doi:10.1002 / 2015jb012060

[0018]

[10] Rudnicki, J. W. J. M. o. m. (1986). Fluid mass sources and point forces in linear elastic diffusive solids. 5(4), 383 - 393.

[0019]

[11] McNamara,D.E.,Hayes,G.P.,Benz,H.M.,Williams,R.A.,McMahon,N.D.,Aster,R.C.,...Earle,P.(2015).Reactivated faulting near Cushing,Oklahoma:Increased potential for a triggered earthquake in an area of United States strategic infrastructure.Geophysical Research Letters,42(20),8328-8332.doi:10.1002 / 2015gl064669

[0020]

[12] Baisch,S.,Weidler,R.,Voros,R.,Wyborn,D.,&de Graaf,L.(2006).Induced seismicity during the stimulation of a geothermal HFR reservoir in the Cooper Basin,Australia.Bulletin of the Seismological Society of America,96(6),2242-2256.doi:10.1785 / 0120050255 Summary of the Invention

[0021] In order to overcome or alleviate one or more of the above technical problems, including the insufficient positioning accuracy of existing prediction methods for high-risk areas, the poor real-time performance of monitoring and risk assessment, and the fact that risk management means mainly rely on reactive measures after an earthquake occurs. There is an urgent need for a prediction method that can combine actual geological conditions to quickly and efficiently identify high-risk areas of fluid injection-induced earthquakes.

[0022] The object of the present invention is to provide a prediction method for high-risk areas of water injection-induced earthquakes, and to provide a simple prediction model based on the normalized Coulomb stress distribution. By identifying the relative positions and orientations of faults, it can quickly and efficiently locate potential high-risk areas of injection-induced earthquakes. The ultimate goal of this model is to reduce earthquake-induced risks, avoid potential disasters caused by fault activation, and optimize the safety and industrial efficiency of injection operations. At the same time, it provides theoretical support and technical means for real-time risk management and more accurate earthquake monitoring.

[0023] The present invention is mainly based on the Coulomb stress change theory and the linear poroelastic model. By analytically calculating the stress field distribution caused by fluid injection and combining the fault geometric characteristics, it identifies high-seismic-risk regions. The present invention proposes a low-cost, easy-to-operate and widely applicable solution to address this technical problem through a prediction model based on the normalized Coulomb stress distribution.

[0024] The present invention provides the following technical solutions:

[0025] A method for predicting high-risk regions of water-injection-induced earthquakes, which includes the following steps:

[0026] S1: Calculate the Coulomb failure stress and the poroelastic solution on the fault plane in the high-risk region of water-injection-induced earthquakes to obtain the specific fault state, and build a prediction model based on this.

[0027] Specifically, when the shear stress between the fault planes exceeds the frictional strength (the frictional strength is proportional to the effective normal stress), the fault will slip. It is usually difficult to directly determine the absolute stress state on the fault, but the influence of external disturbances on fault slip (promoting or inhibiting fault rupture) is usually expressed in the form of changes in the Coulomb instability stress:

[0028] ΔS = τ d + μ(τ n + p) (1)

[0029] Where τ d and τ n are respectively the changes in the shear stress and the normal stress decomposed onto the fault plane; p is the perturbation of the pore fluid pressure, and μ is the friction coefficient; Td is the shear stress along the slip direction; an increase in the shear stress, pore pressure, or tensile normal stress will cause ΔS to become positive, thus making the fault closer to rupture.

[0030] For a fault plane characterized by the unit normal vector n and the slip direction d, if the stress tensor acting on the fault plane is σ, then the tangential force on the fault plane is:

[0031] T = σ·n 2)

[0032] The perturbations of the normal and shear stresses are:

[0033] τ n = T·n, τ d = T·d (3)

[0034] Use the linear poroelastic theory to calculate the stress tensor and pore pressure caused by fluid injection, and its control equation is:

[0035]

[0036]

[0037] where \(u\) is the displacement vector, \(p\) is the excess pore pressure, \(\lambda\) and \(\mu\) are the Lame constants, \(\alpha\) is the dimensionless coefficient of effective stress, \(M\) -1 is the volume compressibility proposed by Biot (1941), \(\kappa\) is the permeability, \(\eta\) is the hydrodynamic viscosity of the fluid, and \(Q\) is the fluid source density.

[0038] For a point source starting at \(t = 0\), if the injection rate \(q(x,t)\) is constant, i.e., \(Q(x,t)=q\delta(x)H(t)\), then the solution in a homogeneous infinite space is:[[]]

[0039]

[0040] where denotes the distance to the source point, and the functions \(\xi\) and \(g\) are defined as:[[]]

[0041]

[0042] S2: Perform stereonet visualization of the fault plane;

[0043] Use a stress projection map to show the Coulomb stress at different positions near the injection well; in the polar coordinate plot, the radial direction represents the dip angle, and the polar angle represents the equivalent azimuth angle, which is defined as \(a\) e =\(\theta - a_z\), where \(\theta\) and \(a_z\) are the strike and azimuth angles respectively; for a specific injection well distance and movement direction, calculate the value of \(\Delta S(\delta,a\) e ), where \(0^{\circ}\leq\delta\leq90^{\circ}\) and \(0^{\circ}\leq a\) e \(\leq360^{\circ}\), and normalize the result to \([-1,1]\).

[0044] In the above embodiments, in the above embodiments, step S1 accurately solved the stress state of the fault, laying a solid foundation for the construction of the prediction model.

[0045] As mentioned in step S2, the stress projection map (stereonet) is used to show the Coulomb stress at different positions near the injection well. The equivalent azimuth angle is introduced because the point injection problem has rotational symmetry, see appendix Figure 1 . For example, if two faults with the same movement direction have the same strike - azimuth angle value, then the injection will bring the same perturbation (\(\tau\) d , \(\tau\) n ) to the two faults.

[0046] Appendix Figure 3Shows an example of a stress spherical projection map, which is designed for a right-lateral strike-slip fault located 1 km away from the injection source and at the same depth as the injection source. The normalized Coulomb stress ΔS is represented in color. Red and blue represent positive and negative Coulomb stress values respectively, corresponding to high and low seismic risks. For example, at the same depth as the injection source, if the equivalent azimuth angle is between 30° and 120° or between 210° and 300°, the right-lateral strike-slip fault will be stable, otherwise the fault may be at risk.

[0047] According to some embodiments, the normalized Coulomb stress values are represented by different color codings in step S2.

[0048] In the above embodiments, users will quickly and intuitively identify the high-seismic-risk areas around the injection point and their corresponding fault geometric features.

[0049] Compared with the prior art, the present invention has the following beneficial effects:

[0050] Compared with traditional methods, the method for predicting high-risk areas of injection-induced earthquakes disclosed by the present invention provides a prediction model. Through the three-dimensional network visualization of this prediction model and the fault plane, the accuracy and efficiency of seismic risk prediction are significantly improved. Its prediction model based on Coulomb stress distribution does not need to rely on complex numerical simulation tools and can directly use existing geological and geophysical data for rapid analysis. This not only reduces the calculation cost but also enables risk assessment to play an important role in real-time monitoring. By introducing the three-dimensional network visualization technology, the model provided by the present invention has obvious advantages in the intuitiveness of fault geometric parameters and the identification ability of risk areas. In addition, the versatility and flexibility of the model enable it to adapt to different geological conditions and industrial scenarios, providing an important guarantee for the optimization of injection operations and the improvement of public safety. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a three-dimensional network visualization schematic diagram provided by an embodiment of the present invention.

[0052] Figure 2 It is a schematic diagram of the normalized Coulomb stress distribution provided by an embodiment of the present invention (cluster earthquake area).

[0053] Figure 3 It is a schematic diagram of the normalized Coulomb stress distribution provided by an embodiment of the present invention (non-cluster earthquake area). DETAILED DESCRIPTION OF THE EMBODIMENTS

[0054] APPENDIX Figures 1-3 Intuitively shows the core content of the technical solution of the present invention, covering the visualization technology of Coulomb stress distribution and the identification of high-risk areas of injection-induced earthquakes.

[0055] Appendix Figure 1 The visualization scheme of the Coulomb stress distribution is shown through the projection map. In the figure, the polar radius represents the dip angle of the fault, the polar angle represents the equivalent azimuth angle, and the color coding represents the normalized Coulomb stress value. The red area is the location of high-risk faults, and the blue area is the location of low-risk faults. The appendix provides a concise and intuitive way to identify high-risk faults and their geometric features. The method for predicting high-risk areas of water injection-induced earthquakes provided by the present invention greatly improves the efficiency and usability of high-risk area identification, and provides important support for real-time monitoring and dynamic adjustment.

[0056] Using the data of induced earthquake cases in different regions, including water injection data and the location and focal mechanism information of earthquakes, based on the above calculations, the spatial hazard results of water injection-induced earthquakes in Cushing, San Ardo, Prague, etc. are obtained, as shown in the appendix Figures 2-3 shown below.

[0057] Appendix Figure 1 shows the Coulomb stress distribution and earthquake distribution in a typical clustered earthquake region (such as the Cushing area). The color coding represents the normalized Coulomb stress value. The red area represents high Coulomb stress values (high-risk areas), and the blue area represents low Coulomb stress values (low-risk areas). Earthquake events are marked with white dots, clearly showing the spatial consistency between the actual earthquake events and the high-risk areas predicted by the model. The appendix indicates that the prediction model of the present invention can accurately identify high-risk areas and effectively support the seismic risk assessment around the injection point.

[0058] Appendix Figure 2 shows the Coulomb stress distribution in a non-clustered earthquake region, such as the Prague and St. Gallen areas. Compared with the clustered earthquake region, the high-risk areas of non-clustered earthquakes are usually more dispersed and may occur at positions farther from the injection point. The white dots in the appendix represent the actual earthquake events, and the color gradient shows the stress distribution state. Through this figure, the accuracy of the model in predicting high-risk areas of large earthquakes at long distances can be observed, further verifying the wide applicability of the model.

[0059] The present invention will be described in detail below in conjunction with embodiments and the appendix. However, it should be understood that the embodiments and the appendix are only used for exemplary description of the present invention and do not constitute any limitation to the protection scope of the present invention. All reasonable transformations and combinations within the scope of the inventive concept of the present invention fall within the protection scope of the present invention.

[0060] To verify the accuracy and applicability of the prediction model provided by the present invention, multiple typical cases of fluid simulation-induced seismicity were selected, including the Cushing area (Oklahoma), San Ardo area (California), and Prague area (Oklahoma) in the United States. These cases cover a variety of geological conditions and fault characteristics, and can fully demonstrate the application effects and technical advantages of the present invention in different scenarios.

[0061] Example 1

[0062] Application in the Cushing area

[0063] The Cushing area has become a key area for induced seismicity research due to its rich oil and gas resources and frequent injection activities. The fault distribution in this area is complex, and the induced earthquakes mostly show clustered small earthquake events. In this example, first, the fault geometric parameters, injection point locations, and regional stress field data in the Cushing area were collected, and then the Coulomb stress distribution was calculated using the prediction model provided by the present invention.

[0064] The calculation results of the prediction model are as shown in Appendix Figure 2 and 3 They jointly show that the high-risk areas in the Cushing area are mainly distributed on the faults within 5 kilometers of the injection point, and the fault dips and strikes in these areas are consistent with the main directions of the regional stress field. By comparing historical earthquake data, it is found that the actually occurred small earthquake events highly coincide with the high-risk areas predicted by the model. This result verifies the effectiveness of the prediction model in the identification of clustered earthquake risks.

[0065] In addition, the prediction model also shows the prediction ability for unrecorded earthquake areas. Near some injection points in Cushing, although no earthquakes have occurred yet, the high-risk areas predicted by the prediction model provide a scientific basis for targeted enhanced monitoring. This provides theoretical support for laying out monitoring networks in advance and reducing potential risks.

[0066] Example 2

[0067] Application in the San Ardo area

[0068] The geological conditions in the San Ardo area are relatively special. Its fault network is complex, and the induced earthquake events show greater randomness. The application of the prediction model in this area focuses on identifying the fault slip trend and potential high-risk areas.

[0069] In the application in San Ardo, the prediction model reveals two main risk areas around the injection point through the Coulomb stress distribution, and the specific distribution is as shown in Appendix Figure 2As shown. On the one hand, high-risk areas are concentrated in faults with smaller dips near the injection point, which is related to the local effect of pore pressure diffusion. On the other hand, the model also identifies a high-risk area farther away from the injection point, where the fault has a larger dip and is relatively perpendicular to the regional principal stress direction. Actual seismic data show that although seismic events in these distant high-risk areas are fewer, they often have larger magnitudes, demonstrating the model's predictive ability for large earthquake risks.

[0070] Another major advantage of the prediction model's prediction results is its ability to exclude low-risk areas. In some fault areas where no earthquakes have occurred, the ΔS calculated by the model shows a negative value, which provides an important basis for judging the safe operation of the injection point, thereby reducing unnecessary operating costs.

[0071] Example 3

[0072] Application in the Prague area

[0073] The Prague area is famous for the large earthquakes that have occurred in its history and is an important case for studying the triggering of isolated large earthquakes by fluid injection. The application of the model of the present invention in this area aims to evaluate the risk distribution of distant faults near the injection point.

[0074] By calculating the Coulomb stress distribution, the prediction model identifies a high-risk fault about 10 kilometers away from the injection point. The strike of this fault is parallel to the direction of the regional stress field, as specifically shown in the appendix Figure 3 As shown. Actual seismic events show that this fault has experienced multiple isolated large earthquakes, which is highly consistent with the model's prediction results. In addition, the model also reveals a potential medium-risk area, where the fault geometry shows a trend of incomplete matching with the principal stress direction, but there is still a possibility of slip instability. This identification of the medium-risk area provides a direction for further earthquake risk research.

[0075] In the above three cases, the prediction model of the present invention all shows an accurate prediction ability for high-risk areas. By normalizing the calculation of the Coulomb stress distribution, the prediction model can not only accurately identify high-risk areas of clustered earthquakes but also effectively predict potential faults of isolated large earthquakes. This adaptability to different earthquake types makes the model highly versatile.

[0076] At the same time, the ability of the prediction model to exclude low-risk areas has also been verified in multiple cases. For example, in some fault areas of Cushing and San Ardo, the ΔS predicted by the prediction model shows a negative value, and in fact, no earthquakes have occurred in these areas. This result further shows that the prediction results of the prediction model are credible and have scientific guiding significance.

[0077] In addition, the fast calculation and visualization capabilities of this model give it significant advantages in practical industrial applications. Without relying on complex numerical simulations or expensive computing resources, users can quickly obtain the distribution map of high-risk areas by inputting simple geological parameters. This ease of operation provides a convenient tool for industrial operators and also provides effective support for researchers to further explore the mechanism of injection-induced earthquakes.

[0078] The above embodiments are only the preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the inventive concept belong to the protection scope of the present invention. It should be noted that for those of ordinary skill in the art, improvements and refinements made without departing from the principle of the present invention should also be regarded as within the protection scope of the present invention.

Claims

1. A method for predicting high-risk areas of water-injection induced earthquakes, characterized in that, It includes the following steps: S1: Obtain the Coulomb failure stress and poroelastic solution on the fault plane in the water injection-induced earthquake danger area, obtain the specific fault state, and construct a prediction model based on the fault state; Specifically, the promotion or inhibition of fault rupture by external interference on fault slip is expressed in the form of changes in Coulomb instability stress: （1） Among them, and are the changes in shear stress and normal stress decomposed onto the fault plane, respectively; is the perturbation of pore fluid pressure, is the friction coefficient; is the shear stress along the slip direction; For a fault plane characterized by a unit normal vector and a slip direction , if the stress tensor acting on the fault plane is , then the shear force on the fault plane is: （2） The perturbations of the normal and shear stresses are: （3） Use linear poroelastic theory to calculate the stress tensor and pore pressure caused by fluid injection, and its control equation is: （4） （5） wherein, is the displacement vector, is the excess pore pressure, and are the Lame constants, is the dimensionless coefficient of effective stress, is the volume compressibility, is the permeability, is the hydrodynamic viscosity, is the fluid source density; S2: Visualize the stereonet of the fault plane; The Coulomb stress at different positions near the injection well is shown using a stress projection map; in the polar coordinate plot, the radial direction represents the dip angle and the polar angle represents the equivalent azimuth angle, which is defined as , where and are the strike and azimuth angles respectively; for a specific injection well distance and movement direction, calculate the value of , where and , and normalize the result to .

2. The prediction method for high-risk areas of water-injection induced earthquakes according to claim 1, characterized in that, In step S1, for the point source starting at time if the injection rate is constant, i.e., then the solution in a homogeneous infinite space is: （6） Among them, represents the distance to the source point, and the functions and are defined as: （7）。 3. The prediction method for high-risk areas of water-injection induced earthquakes according to claim 1, characterized in that In step S2, the normalized Coulomb stress values are represented by different color codings.

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