Method for calculating spatial three-dimensional natural fracture wall face internal friction coefficient

Abstract

The application discloses a method for calculating the inner friction coefficient of a three-dimensional natural fracture wall surface in space, which comprises the following steps: determining the strike of the natural fracture and the included angle between the natural fracture and the horizontal plane; determining the horizontal maximum principal stress direction; determining the in-situ three-directional principal stress; determining the poroelastic constant and the formation fluid pressure; determining the natural fracture approaching angle; determining the unit normal vector of the three-dimensional natural fracture surface; determining the normal stress and the shear stress of the three-dimensional natural fracture surface; determining the effective stress; and determining the inner friction coefficient of the spatial natural fracture. The application considers that the natural fracture in the underground reservoir is spatially distributed, and is kept in static mechanical balance under the joint action of the in-situ stress field and the formation fluid. The application obtains the calculation method of the inner friction angle of the three-dimensional natural fracture in space in the rock mass containing the natural fracture medium by using a mathematical method, fills the blank of the method for obtaining the inner friction coefficient of the three-dimensional natural fracture in space, and can show the influence of the strike and the dip angle of the natural fracture on the inner friction coefficient of the fracture surface.

Description

TECHNICAL FIELD

[0001] The application relates to a method for calculating the friction coefficient of a three-dimensional natural fracture wall surface in space, and belongs to the technical field of unconventional oil and gas reservoir volume fracturing exploration and development. BACKGROUND

[0002] Rock mass mechanical parameters and strength parameters have very important applications in the engineering technical field. In the hydraulic fracturing stimulation and reconstruction technology involved in the oil and gas exploration and development field, the target reservoir is usually regarded as an isotropic homogeneous continuous linear elastic body, and the first strength theory (or the maximum tensile stress criterion) is mainly used to determine the initiation and extension of the hydraulic fracture (Li Yingchuan: Production Engineering. Beijing, Petroleum Industry Press, 2008; Wan Renpu: Production Technology Manual. Beijing, Petroleum Industry Press, 1998; Zeng Fanhui et al.: Fracturing open hole well breakdown pressure prediction model considering seepage effect. Natural Gas Geoscience, 2019;). The main tensile strength is determined according to the Brazilian fracture experiment or calculated by using an empirical formula.

[0003] Since the “shale gas revolution”, the network volume fracturing reconstruction of unconventional oil and gas reservoirs with a large number of natural fracture structural weak surfaces has achieved great success. The industry has recognized through indoor experiments, theoretical analysis and field summary that “the wide existence of natural fractures and other structural weak surfaces in rock mass” is one of the most important key elements affecting the network fracturing reconstruction (Hu Yongquan et al.: Network fracturing control condition research. Journal of Southwest Petroleum University, 2013). Due to the fracture mechanics mechanism of the natural fracture-matrix rock mass medium, the mutual restriction condition of the hydraulic fracture-artificial fracture restricts the network fracture expansion and evolution behavior and the stimulation and reconstruction volume (Liu Yuanshuang et al.: Research on the opening mechanics condition of volume fracturing complex fractures. China and Foreign Energy, 2015; Li Yalong et al.: Research progress of shale reservoir fracturing network simulation, Petroleum Geophysical Prospecting, 2019), which promotes the engineering technical field to pay high attention to the properties of the natural fracture structural weak surface.

[0004] The experimental determination of the shear parameters (cohesion and internal friction angle) of the continuous medium is widely carried out according to GB / T 50266-2013 “Engineering rock mass test method standard”, mainly by using triaxial compression test and direct shear test. The patent “Rock structural plane shear test method and implementation device” (201210223787) of Liu Jianfeng and Xie Heping and the patent “Rock shear strength test method and process” (201710937345) of Xu Rongchao are all improvements on the shear test device and method of the continuous uniform medium, and the obtained mechanical parameters such as the internal friction coefficient of the continuous medium are still. These devices and methods are not suitable for the shear parameter test of the three-dimensional natural fracture surface under the action of the in-situ stress field loading and the formation pore fluid pressure. At present, there is no method for obtaining the friction coefficient of the natural fracture. SUMMARY

[0005] In order to overcome the problems in the prior art, the present application provides a method for calculating the friction coefficient of a three-dimensional natural fracture wall surface in space.

[0006] The technical solution provided by the present application to solve the above technical problems is: a method for calculating the friction coefficient of a three-dimensional natural fracture wall surface in space, comprising:

[0007] determining the strike of the natural fracture and the angle between the natural fracture and the horizontal plane according to imaging logging data of the natural fracture or microscopic observation of directional coring;

[0008] determining the horizontal maximum principal stress direction according to micro-seismic fracture monitoring or core testing;

[0009] determining the in-situ three-dimensional principal stress according to a test fracturing method or a core testing method such as Kaiser effect;

[0010] determining the pore elastic constant and the formation fluid pressure according to a core experiment testing method;

[0011] determining the approach angle of the natural fracture according to the horizontal maximum principal stress direction and the strike of the natural fracture;

[0012] determining the unit normal vector of the three-dimensional natural fracture surface according to the angle between the natural fracture and the horizontal plane and the approach angle of the natural fracture;

[0013] determining the normal stress and shear stress of the three-dimensional natural fracture surface according to the unit normal vector of the three-dimensional natural fracture surface and the in-situ three-dimensional principal stress;

[0014] determining the effective stress acting on the natural fracture in space according to the normal stress and shear stress of the three-dimensional natural fracture surface, the pore elastic constant and the formation fluid pressure;

[0015] determining the friction coefficient of the natural fracture in space according to the effective stress acting on the natural fracture in space.

[0016] Further technical solutions are that the in-situ three-dimensional principal stress includes a vertical principal stress σ z , a horizontal maximum principal stress σ y , and a horizontal minimum principal stress σ x .

[0017] Further technical solutions are that the calculation formula of the unit normal vector of the three-dimensional natural fracture surface is as follows:

[0018]

[0019] wherein:

[0020]

[0021]

[0022] wherein: is the unit normal vector; n x is the unit normal vector x-direction component; n y is the unit normal vector y-direction component; n z is the unit normal vector z-direction component; θ is the natural fracture approach angle; is the angle between the natural fracture and the horizontal plane.

[0023] A further technical solution is that the formula for calculating the normal stress of the three-dimensional natural fracture surface is as follows:

[0024] p n = σ x n x n x + σ y n y n y + σ z n z n z

[0025] wherein: n x is the unit normal vector x-direction component; n y is the unit normal vector y-direction component; n z is the unit normal vector z-direction component; σ z is the vertical principal stress; σ y is the horizontal maximum principal stress; σ x is the horizontal minimum principal stress; p n is the normal stress of the three-dimensional natural fracture surface.

[0026] A further technical solution is that the formula for calculating the shear stress of the three-dimensional natural fracture surface is as follows:

[0027]

[0028] wherein: p n is the normal stress of the three-dimensional natural fracture surface; is the force acting on the natural fracture wall; n x is the unit normal vector x-direction component; n y is the unit normal vector y-direction component; n z is the unit normal vector z-direction component; σ z is the vertical principal stress; σ y is the horizontal maximum principal stress; σ x is the horizontal minimum principal stress; p τ is the shear stress of the three-dimensional natural fracture surface.

[0029] Further technical solutions are that the effective stress acting on the space natural fracture includes effective normal stress and effective shear stress.

[0030] Further technical solutions are that the calculation formula of the effective normal stress is as follows:

[0031] p n,e = p n - αp s

[0032] In the formula, p n is normal stress of a three-dimensional natural fracture surface; α is a poroelastic constant; p s is formation fluid pressure; p n,e is effective normal stress.

[0033] Further technical solutions are that the calculation formula of the effective shear stress is as follows:

[0034] τ e = p τ

[0035] In the formula, p τ is shear stress of a three-dimensional natural fracture surface; τ e is effective shear stress.

[0036] Further technical solutions are that the calculation formula of the space natural fracture internal friction coefficient is as follows:

[0037] μ = τ e / p n,e

[0038] In the formula, p n,e is effective normal stress; τ e is effective shear stress; and μ is the space natural fracture internal friction coefficient.

[0039] The present application has the following beneficial effects: the present application considers that the natural fracture in the underground reservoir is spatially distributed, and is kept in static mechanical balance under the joint action of the in-situ stress field and the formation fluid. The mechanical principle and the strength criterion are applied, and the calculation method of the space three-dimensional natural fracture internal friction angle in the rock mass containing the natural fracture medium is obtained through the mathematical method. The present application fills the blank of the method for obtaining the space three-dimensional natural fracture internal friction coefficient, and can show the influence of the natural fracture strike and the dip angle on the internal friction coefficient of the fracture surface. BRIEF DESCRIPTION OF DRAWINGS

[0040] Figure 1 is the spatial force decomposition of the natural fracture wall surface;

[0041] Figure 2 is the natural fracture dominant strike map interpreted by the imaging logging.

[0042] Figure 3 Natural fracture dip angle map for imaging logging interpretation;

[0043] Figure 4 Horizontal maximum principal stress orientation map for micro-seismic test to determine target area;

[0044] Figure 5 Natural fracture internal friction coefficient versus approach angle map. DETAILED DESCRIPTION

[0045] The technical solutions of the present application will be described clearly and completely below in conjunction with the drawings. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0046] A method for calculating the spatial three-dimensional natural fracture wall internal friction coefficient, comprising the following steps:

[0047] (1) Using imaging logging or microscopic observation of directional coring to obtain the natural fracture strike and the angle between the natural fracture and the horizontal plane;

[0048] (2) Using micro-seismic monitoring, core testing and other methods to obtain the horizontal maximum principal stress orientation;

[0049] (3) Using testing fracturing method or Kaiser effect and other core testing methods to determine the in-situ three-dimensional principal stress;

[0050] (4) Using core experiment testing or other methods to obtain the pore elastic constant and the formation fluid pressure;

[0051] (5) According to the horizontal maximum principal stress orientation and the natural fracture strike to determine the natural fracture approach angle;

[0052] (6) Calculating the unit normal vector of the spatial distribution natural fracture;

[0053] The spatial natural fracture formed in the process of oil and gas reservoir accumulation is shown in the Cartesian coordinate system as shown in the accompanying drawings. Let the unit normal vector of the natural fracture be: Figure 1

[0054]

[0055] Wherein:

[0056]

[0057] ​

[0058] where: is the unit normal vector; n x is the unit normal vector x-direction component; n y is the unit normal vector y-direction component; n z is the unit normal vector z-direction component; θ is the natural fracture approach angle; is the angle between the natural fracture and the horizontal plane;

[0059] (7) Calculate the normal stress and shear stress of the spatial distribution natural fracture surface;

[0060] At this time, the force acting on the natural fracture surface is:

[0061]

[0062] According to the stress decomposition principle in the theory of elasticity, the normal stress and shear stress calculation formula of the natural fracture surface in the rock mass medium containing natural fractures can be derived.

[0063] p n = n k e k .σ ij n j e j = n i σ ij n j

[0064] = σ xx n x n x + σ xy n y n x + σ xz n z n x + σ xy n x n y + σ yy n y n y

[0065] + σ yz n z n y + σ xz n x n z + σ yz n y n z + σ zz n z n z

[0066]

[0067] (8) Calculate the effective stress acting on the space natural fracture;

[0068] The reservoir is usually full of formation fluid, and the corresponding formation fluid pressure is denoted as p s ; Since rock mass failure is induced by effective stress, the effective normal stress and effective shear stress of structural weak surface under formation fluid pressure are calculated according to the Terzaghi principle, and the expression is:

[0069] p n,e = p n - αp s

[0070] τ e = p τ

[0071] In the formula: p n is the normal stress of the three-dimensional natural fracture surface; α is the pore elastic constant; p s is the formation fluid pressure; p n,e is the effective normal stress; p τ is the shear stress of the three-dimensional natural fracture surface; τ e is the effective shear stress;

[0072] (9) Determine the friction coefficient in the space natural fracture;

[0073] Consider that the natural fracture in the rock mass under the original formation condition does not produce a new fracture surface, that is, the space natural fracture is in a state of static mechanical equilibrium. The natural fracture wall surface should satisfy the Coulomb shear strength theory, that is, when the shear force of the fracture surface is greater than the shear strength, the fracture occurs shear failure. The strength condition expression of its failure is:

[0074] τ e = c + μp n,e

[0075] The internal friction coefficient of the natural fracture wall surface can be expressed as

[0076] μ = (τ e - c) / p n,e

[0077] For the opening natural fracture, the cohesion is approximately zero. Therefore:

[0078] μ = τ e / p n,e

[0079] In the formula: p n,e is the effective normal stress; τ eμ is the internal friction coefficient of the natural fracture in space; and c is the cohesion of the natural fracture surface.

[0080] Embodiment

[0081] The natural fractures of a reservoir in a well section of 691.0-713.0 m of KL-B509 in an oilfield in the west are developed, imaging logging is performed in the process of well construction, in-situ stress field is tested by core experiment, and fracturing microseismic monitoring is performed.

[0082] The internal friction coefficient of the natural fracture is calculated by using the method of the present application in the field, and the steps are as follows:

[0083] A, the parameters of the natural fracture strike, the direction of the horizontal maximum principal stress, the horizontal three-direction principal stress, the pore elastic constant and the like of the natural fractured reservoir are collected;

[0084] ① 44 high-conductance natural fractures in the well section of 691.0-713.0 m are interpreted by using the original interpretation of the imaging logging, the dominant strike of the natural fractures is NE0-10° and NE30-40°, and the dip angle is 24-28° (as shown in Figure 2 and 3 );

[0085] The average value is taken in the example: the dominant strike is 10° and the dip angle is 25°;

[0086] ② The horizontal maximum principal stress direction is NE45° (as shown in Figure 4 ) in the example by using the microseismic fracturing fracture monitoring;

[0087] ③ The in-situ three-direction principal stresses are obtained by using the core testing method based on the Kaiser effect in the example, and the vertical principal stress σ z is 15.0 MPa, the horizontal maximum principal stress σ y is 13.5 MPa, and the horizontal minimum principal stress σ x is 11.0 MPa.

[0088] ④ The pore elastic constant α is 0.7, and the formation fluid pressure is 6.8 MPa by experiment testing;

[0089] B, the normal stress and the shear stress of the natural fracture surface are calculated;

[0090] ① The dominant natural fracture strike is NE10°, and the horizontal maximum principal stress direction is NE45°; then

[0091] the natural fracture approach angle is θ=NE45-NE10=35°;

[0092] ② The dip angle is obtained according to the imaging logging data

[0093] ③ the unit normal vector is calculated

[0094]

[0095] IV. Calculate the normal stress and shear stress on the natural fracture surface

[0096] p n = 13.5 x 0.3462 2 + 11.0 x 0.2424 2 + 15 x 0.9063 2 = 14.585 MPa

[0097]

[0098] C. Calculate the effective stress in the natural fracture;

[0099] p n,e = 14.585 - 0.7 x 6.8 = 9.825 MPa

[0100] τ e = 1.019 MPa

[0101] G. Determine the friction coefficient in the natural fracture;

[0102] μ = 1.019 / 9.825 = 0.1037

[0103] Assuming that the in-situ stress field, formation pressure and pore elastic constant remain constant, similar calculations can be made to obtain the relationship between the friction coefficient on the natural fracture wall and the approaching angle when the dominant direction of the natural fracture changes. The relationship is shown in the attached figure. Figure 5 .

[0104] The above description is not intended to limit the present application in any form, although the present application has been disclosed by the above examples, however, it is not intended to limit the present application, any skilled person in the art, without departing from the technical solution of the present application, can make some changes or modifications to the equivalent examples of equivalent changes by using the above disclosed technical content, as long as it does not deviate from the technical solution of the present application, according to the technical essence of the present application, any simple modification, equivalent change and modification of the above examples, still belongs to the scope of the technical solution of the present application.

Claims

1. A method of calculating spatial three-dimensional natural fracture wall face internal friction coefficients, characterized in that, The method comprises the following steps: determining the strike of natural fractures and the angle between the natural fractures and the horizontal plane according to imaging logging data of natural fractures or microscopic observation of directional coring; determining the horizontal maximum principal stress direction according to microseismic fracture monitoring or core testing; determining the in-situ three-directional principal stress according to a test fracturing method or a Kaiser effect core testing method; determining the pore elastic constant and the formation fluid pressure according to a core experimental testing method; determining the natural fracture approach angle according to the horizontal maximum principal stress direction and the strike of natural fractures; determining the unit normal vector of the three-dimensional natural fracture surface according to the angle between the natural fractures and the horizontal plane and the natural fracture approach angle; determining the normal normal stress and shear stress of the three-dimensional natural fracture surface according to the unit normal vector of the three-dimensional natural fracture surface and the in-situ three-directional principal stress; determining the effective stress acting in the spatial natural fracture according to the normal normal stress and shear stress of the three-dimensional natural fracture surface, the pore elastic constant and the formation fluid pressure; the effective stress acting in the spatial natural fracture comprises effective normal stress and effective shear stress; the calculation formula of the effective normal stress is as follows: where: is the normal stress on a three-dimensional natural fracture face; is the poroelastic constant; is the formation fluid pressure; is the effective normal stress; the calculation formula of the effective shear stress is as follows: wherein: is the shear stress of the three-dimensional natural fracture plane; is the effective shear stress; determining the spatial natural fracture internal friction coefficient according to the effective stress acting in the spatial natural fracture; the calculation formula of the spatial natural fracture internal friction coefficient is as follows: where: is the effective normal stress; is the effective shear stress; is the spatial natural fracture internal friction coefficient.

2. The method of claim 1, wherein, The in-situ three principal stresses include a vertical principal stress , a horizontal maximum principal stress , a horizontal minimum principal stress .

3. The method of claim 2, wherein, the calculation formula of the unit normal vector of the three-dimensional natural fracture surface is as follows: wherein: where: is the unit normal vector; is the unit normal vector x is the directional component; is the unit normal vector y is the directional component; is the unit normal vector z is the directional component; is the natural fracture approach angle; is the natural fracture angle with the horizontal.

4. The method of claim 2, wherein, the calculation formula of the normal normal stress of the three-dimensional natural fracture surface is as follows: where: is the unit normal vector x is the directional component; is the unit normal vector y is the directional component; is the unit normal vector z is the directional component; is the vertical principal stress; is the horizontal maximum principal stress; is the horizontal minimum principal stress; is the normal stress on the three-dimensional natural fracture surface.

5. The method of claim 2, wherein, the calculation formula of the shear stress of the three-dimensional natural fracture surface is as follows: wherein: is the normal stress of the three-dimensional natural fracture surface; is the force acting on the natural fracture wall surface; is the unit normal vector x is the directional component; is the unit normal vector y is the directional component; is the unit normal vector z is the directional component; is the vertical principal stress; is the horizontal maximum principal stress; is the horizontal minimum principal stress; is the shear stress of the three-dimensional natural fracture surface.

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