Method for determining the rock failure surface during drilling

Abstract

This invention discloses a method for determining the rock failure surface during drilling, comprising the following steps: 1) simulating and determining the drilling force model, and determining the relationship between the components in the model; 2) calculating the maximum shear stress at which the rock structure undergoes plastic failure; 3) determining the shape of the failure surface and the maximum shear stress τ in the shear zone determined in step 2) according to the maximum shear stress criterion. max This is related to predicting the failure surface; 4) Based on the maximum shear stress criterion, the iterative method is used to solve the force acting on the cutting surface, and the function of the failure surface is determined by inputting the basic drilling parameters, quantitatively presenting the failure surface morphology. The method of this invention introduces the Michel solution of elastoplastic mechanics to solve the stress state of the rock shear zone during drilling, and derives a specific response function of rock properties to drilling parameters based on the stress characteristics of the drill bit; referring to the maximum shear stress criterion, the shear stress of the unit body is compared with the shear strength of the rock to determine whether the rock is broken.

Description

Technical Field

[0001] This invention belongs to the field of underground space and tunnel engineering technology, and relates to a method for determining the rock failure surface during drilling. Background Technology

[0002] Digital drilling technology has become an effective means of evaluating rock properties in the field. This measurement-while-drilling (MWD) method is of practical significance for improving drilling efficiency and reducing tool wear. During drilling, the mechanical rate of penetration (ROP) is an important indicator of drilling efficiency. An effective combination of bit weight (BWT) and rotational speed (SSD) is key to improving ROP. Furthermore, as the borehole depth increases, confining pressure negatively impacts ROP, which is related to tool wear. Therefore, understanding the rock-breaking behavior of tools under constrained conditions is crucial for reducing tool wear. In fact, there is a quantitative relationship between rock properties and the required cutting force, which is related to the shape and material of the drill bit. To optimize drilling efficiency, it is necessary to elucidate the combined effect of tool wear and in-situ stress on the cutting force.

[0003] During drilling, the thrust (normal) and cutting force (tangential) provided by the drilling rig work together to break down the rock. When drilling into rough rock, friction with abrasive minerals causes mechanical wear on the diamond cutter in the form of scratches. To achieve sufficient contact with the rock, additional forces are concentrated at the initial scratch location to break down the rock, creating a strong stress concentration that accelerates the frictional wear of the tool. Wear plateau zone The evolution with cutting depth confirms that this phenomenon consists of three stages. Correspondingly, changes in tool geometry lead to nonlinear propagation of the failure surface. This conclusion is inconsistent with the assumption of a linear failure surface in most drilling models. Furthermore, in-situ stress has a significant impact on drilling parameters, especially in deep rock drilling. Under stress conditions during drilling, the rock undergoes plastic deformation leading to crack propagation.

[0004] However, in existing models, rock is usually considered an elastic body, which makes the reliability, scientific rigor, and accuracy of predicting the shape of the failure surface insufficient to meet the technical requirements of construction. Summary of the Invention

[0005] The purpose of this invention is to provide a method for determining the rock failure surface during drilling, which solves the problem that the reliability, scientificity, and accuracy of the prediction of the failure surface shape in existing digital drilling technologies cannot be guaranteed.

[0006] The technical solution adopted in this invention is a method for determining the rock failure surface during drilling, which is implemented according to the following steps:

[0007] Step 1: Simulate and determine the drilling force model, and determine the relationship between the components in the model;

[0008] Step 2: Calculate the maximum shear stress at which the rock structure undergoes plastic failure;

[0009] Step 3: Based on the maximum shear stress criterion, the shape of the failure surface and the maximum shear stress in the shear zone determined in Step 2 are compared. This is relevant, and can be used to predict the extent of damage;

[0010] Step 4: Based on the maximum shear stress criterion, the force acting on the cutting surface is solved using an iterative method. The function of the failure surface is determined by inputting the basic drilling parameters, and the morphology of the failure surface is quantitatively presented.

[0011] The beneficial effects of the present invention include the following aspects:

[0012] 1) This invention treats the rock as a semi-infinite elastoplastic planar body. Based on the frictional contact and cutting during drilling, the rock failure zone is divided into a fracture zone and a shear zone, as shown in Figure 2. The fracture zone experiences both cutting and compression. Based on this, the typical Mohr-Coulomb (MC) criterion is used to describe the rock fracture in the fracture zone. The cutting force shears the rock along the failure surface through the fracture zone, causing plastic failure. Therefore, the maximum shear stress criterion is considered in the shear zone. The Michell solution from elastoplastic mechanics is introduced to solve the stress state of the rock shear zone during drilling. Furthermore, the cross-sectional shape of the failure surface is determined as the distribution of the maximum shear stress point.

[0013] 2) Based on the stress characteristics of the drill bit, this invention derives a specific response function of rock properties to drilling parameters. On this basis, several analytical models for predicting rock mechanical and physical properties are established, such as permeability, brittleness, strength parameters, elastic modulus, and cohesion. The model proposed by Seliami is the first to consider the influence of in-situ stress on the mechanical drilling rate. The above models share similar assumptions, namely, that the cutting tool is ideally sharp and the failure surface is a straight line. These simplifications facilitate modeling but can lead to deviations from field results. Furthermore, rock failure behavior in the borehole is divided into brittle and ductile types, which are related to in-situ stress. With increasing hydrostatic stress, the mechanical drilling rate decreases, and the size of the resulting rock cuttings becomes smaller. Although numerical and experimental results have shown that cutting force and MSE (mechanical specific energy) are affected by the stress state in the borehole, the development of analytical models still lacks consideration of confining pressure. In addition, tool wear is also caused by the increase in in-situ stress, which is considered the main cause of friction. Since friction consumes the load provided by the drilling rig, thus reducing drilling efficiency, the combined effect of tool wear and in-situ stress should be studied in modeling and experimentation.

[0014] 3) In this invention, the rock is assumed to be an elastoplastic planar body during drilling. Tool wear and in-situ stress are considered when establishing the drilling model. Then, the shear stress of each rock mass unit is calculated based on the modified model. Referring to the maximum shear stress criterion, the shear stress of the unit is compared with the shear strength of the rock to determine whether the rock will break. Drilling tests are conducted on rocks with different cohesion to obtain the magnitude of the shear stress on the rock cutting surface. Furthermore, to verify the correctness of the model, the maximum stress point is used as a curve to predict the failure surface, and the influence of several factors on the shape of the failure surface is analyzed. Finally, based on… Figure 1 By comparing the various failure surfaces, we can obtain the conclusions predicted by the model, which are related to the previous generation of internal cracks, pores, and defects in the rock. Attached Figure Description

[0015] Figure 1 In the wear flat area The variation law of cutting depth d;

[0016] Figure 2a It is an analysis of rock cutting forces in the fractured and sheared zones during drilling.

[0017] Figure 2b It is the dissection of the Michel wedge during the drilling process;

[0018] Figure 3 The method of this invention determines the shear failure surface based on the distribution of the maximum shear stress point;

[0019] Figure 4a The evolution of shear stress at different cutting depths using the method of the present invention;

[0020] Figure 4b The evolution of shear stress under different cutting forces according to the method of the present invention;

[0021] Figure 5a The relationship between the normal and tangential forces and the drilling depth when drilling through granite using the method of this invention;

[0022] Figure 5b The method of the present invention relates the drilling speed, wear angle, and rotational speed to the drilling time when drilling along granite.

[0023] Figure 6a Comparison between the model prediction of cutting force and experimental measurement using the method of this invention;

[0024] Figure 6b Comparison between the model prediction and experimental measurement of the wear angle using the method of this invention;

[0025] Figure 7 The method of this invention uses the cutting force measured by Akbari (2014) to validate the model and compares it with the cutting force prediction model of Cheng (2019);

[0026] Figure 8 This invention compares the morphology of typical granite fragments with predicted results.

[0027] Figure 9a This invention addresses the determination of the functional expression for the shape of the fracture surface, the coordinate system transformation of the fracture surface shape, and the fitting curve.

[0028] Figure 9b This invention relates to the determination of the functional expression for the shape of the failure surface of granite;

[0029] Figure 9c This invention relates to the determination of the functional expression for the shape of sandstone failure surfaces;

[0030] Figure 9d This invention relates to the determination of the functional expression for the failure surface shape of gneiss;

[0031] Figure 10 This invention considers the impact of internal defects in rocks on the failure plane comparison. Detailed Implementation

[0032] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0033] This invention relates to a method for determining the rock failure surface during drilling, which is implemented according to the following steps:

[0034] Step 1: Simulate and determine the drilling force model, and determine the relationships between the components in the model.

[0035] Reference Figure 1 Wear flattening zone through existing technology As the cutting depth evolves, it is confirmed that this phenomenon consists of three stages: running-in wear, stable wear, and severe wear. Model analysis is as follows: Figure 2a Pore ​​stress In-situ stress hydrostatic stress Normal stress N and shear stress S Acting on the rock respectively (by thrust) and torque (Provided), during the drilling process, the tangential and normal components of the frictional force on the wear surface are respectively expressed as: The parameters of the cutting tool include the cutting depth. d ,inclination α wear angle β The stress distribution expression for the wedge with tool width l is:

[0036] (1)

[0037] (2)

[0038] in, γ The apex angle of the rock wedge, The external stress of the wedge's x-axis in contact with the rock of the drill bit. P The included angle between them is something to note. The symbol is positive, and the symbol is in a clockwise direction. It is positive; A The rock-drill bit contact area is calculated using the following formula: A= ldcos α ; The area of ​​the wear zone is calculated using the following formula: =ldcos α sin β ;inclination α Fixed as wear angle β Friction is related to mechanical forces that cause wear; during drilling, friction is considered the primary cause of tool wear. β The range is 0~15°. Considered as a function of the drill bit's motion variables, the relationship is:

[0039] (3)

[0040] Where v and w represent the axial velocity and tangential velocity of the drill bit, respectively.

[0041] Step 2: Calculate the maximum shear stress at which the rock structure undergoes plastic failure.

[0042] Assuming the crushing zone is under a compressive stress state, the state of the shear zone satisfies and Based on the stress conditions, the normal stress in the crushing zone is determined through the following stress analysis. With shear stress The following relationships exist:

[0043] (4)

[0044] (5)

[0045] (6)

[0046] in, Let be the friction angle of the crushed zone, then the internal friction angle of the rock is... Friction angle with the crushing zone The expression is:

[0047] (7)

[0048] When shear stress is applied to the rockS When the stress state is such that the expression is:

[0049] (8)

[0050] In equation (8), the stress state of the shear zone is established in polar coordinates. The expression for equation (8) in rectangular coordinates is:

[0051] (9)

[0052] in, x, y These are the values ​​of the coordinates of the destruction point in rectangular coordinates.

[0053] Similarly, normal stress N The stress state expression in the shear zone is:

[0054] (10)

[0055] In-situ stress and hydrostatic stress With tilt angle α The direction of the stress acts on the shear rock, and the expressions for the normal stress and shear stress in the shear zone are:

[0056] (11)

[0057] Normal stress N The expression for the plane acting at an angle of inclination of π / (2-α) is:

[0058] (12)

[0059] By increasing pore stress Due to the influence of the stress state in the shear zone, the expression for the stress state is as follows:

[0060] (13)

[0061] According to the formulas of mechanics of materials, we have:

[0062] (14)

[0063] Substituting the results from equations (9), (10), (11), and (12) into equation (13), and then substituting the result from equation (13) into equation (14), we get:

[0064] (15)

[0065] As shear stress on rock τ When the rock reaches its shear strength, the rock structure will undergo plastic failure, which conforms to the maximum shear stress strength theory.

[0066] (16)

[0067] Step 3: According to the maximum shear stress criterion, the shape of the failure surface is related to the maximum shear stress in the shear zone determined in Step 2. This is relevant for predicting the extent of damage.

[0068] Normal stress applied to the cutting surface during rock drilling N This leads to the amplification of shear failure, such as Figure 3 As shown, under the maximum shear stress criterion, the shape of the failure surface and the maximum shear stress are derived from equation (15). The shear failure surface is related to the distribution of shear stress; therefore, it can be obtained from the coordinates of the points corresponding to the maximum shear stress at different depths.

[0069] Taking the granite in Figure 4 as an example, the forward tilt angle is 5°. N The pressure is 45.2 MPa, and the cutting depth is... d The shear stress at different cutting depths is 1.5 mm. S They all maintain a trend of first increasing and then decreasing, and the peak point The surface corresponding to the damaged surface.

[0070] Step 4: Based on the maximum shear stress criterion, the force acting on the cutting surface is solved using an iterative method. The basic drilling parameters are input to determine the function of the failure surface, and the morphology of the failure surface is quantitatively presented.

[0071] First, input the basic drilling parameters. d v, w , α, in-situ stress hydrostatic stress In the model, as an initial condition, the functional expression of the failure surface is:

[0072] (17)

[0073] Compare (x) and τ Determine the x-axis coordinates of the failure surface;

[0074] Then, substitute the x-axis coordinate value into equation (17) to calculate the corresponding y-axis value, and introduce the concept of radius of curvature R in differential geometry to quantitatively determine the morphology of the failure surface.

[0075] Experimental verification

[0076] The model was validated through experiments. The reliability of the model was confirmed by comparing the predicted shape of the failure surface with the curves converted from the cutting marks obtained in the laboratory.

[0077] In the experiment, three homogeneous rock materials were used for drilling tests. The physical and mechanical properties of the laboratory rocks are shown in Table 1. Taking granite with a cutting depth of 0.3 mm as an example, the experimental logging data of cutting force and drilling speed are shown in the curves in Figure 5. Figure 5a The average value of the peak cutting force points obtained in the test is taken as the measured failure cutting force. Figure 5b medium wear angle β The maximum value is used to describe the degree of tool wear. Then, the experimentally obtained typical cutting force and wear angle are compared with the calculated cutting force and wear angle to verify the correctness of the model. This experiment introduces a statistical index s (standard deviation) to evaluate the difference between the measured and calculated results. For different types of rock, the cutting depth... d The effects on cutting force and wear angle are as follows: Figure 6a and Figure 6b As shown, the corresponding standard deviation s is illustrated in Table 3, which shows the evaluation of cutting force and wear angle. The cutting force data measured and predicted in the Akbari sandstone well are shown in Table 2, corresponding to the cutting forces for each pressure difference. Based on this model, the cutting forces of the Torrey Buff sandstone measured in Akbari under different confining pressures and pore stresses were predicted. A comparison of the cutting force prediction with the model developed by Cheng is shown below. Figure 7 As shown in the figure, a typical cutting mark (rock failure surface) shape was observed in a granite borehole with a cutting depth of 0.3 mm. The 3D scanned image was transformed into a Cartesian coordinate system using the maketform and interpolation functions integrated into MATLAB software. The predicted failure surface shape was compared with the transformed cutting mark shape, as shown in the figure. Figure 8 As shown. Based on the stress calculation results of each rock element, the failure surface can be represented as the connection distribution of the maximum shear stress points. The shear failure sections of different rock viscosities at different cutting depths are shown below. Figure 9a As shown, the variation of the radius of curvature R with cutting depth was studied. An inflection point was observed in the evolution of R, which is related to the cohesive strength of the rock. The failure surface function was fitted to a new coordinate system, as shown... Figure 9b , Figure 9c , Figure 9d As shown in Table 4, the fitting functions for the correlation between cutting force and wear angle for different rock types are presented. The maximum value of R appears on the rock surface, reflecting the shape characteristics of the failure surface, confirming that the distribution of the failure surface is related to the cutting depth. Table 5 lists the fitting parameters and parabolic functions under different cohesion strengths. As can be seen, the fitting parameters of the parabolic function increase with the increase of cutting depth.

[0078] The above comparison results show that the failure surfaces of the models used in the method of the present invention are basically consistent, indicating the reliability of the models used in the method of the present invention.

[0079] Table 1. Physical and mechanical properties of laboratory rocks

[0080]

[0081] Table 2. Measured and predicted cutting forces in Akbari sandstone wells (2014)

[0082]

[0083] Table 3. Evaluation of cutting force and wear angle

[0084]

[0085] Table 4. Fitting functions of the correlation between cutting force and wear angle for different rock types

[0086]

[0087] Table 5. Fitting functions for the failure surface of the tested rock at different cutting depths

[0088]

[0089] In summary, the method of this invention modifies the drilling model, considering tool wear and ground stress to predict the failure surface. Based on the frictional and cutting contact between the rock and the cutting machine, the fracture zone and shear zone are considered in the modeling. In conclusion:

[0090] 1) Drilling test results for three rock types confirmed the reliability of the model predictions. The prediction errors for cutting force and tool wear at different cutting depths were all below 15%. The binarized images of the failure surface shape were basically consistent with the prediction results.

[0091] 2) A differential geometry-based index, radius of curvature R, is introduced to characterize the shape of the damaged surface. Depending on the maximum cutting depth, the evolution of R during the cutting cycle can be categorized into two types. When the cutting depth is less than 0.9 mm, the curvature of the damaged surface shows an increasing trend. When the cutting depth reaches 0.9 mm, R increases with the increase of the inflection point between 0.3 and 0.6 d.

[0092] 3) Several factors influencing cutting force and their effects were studied. The influence of cutting depth on cutting force showed an increasing trend, which is related to the cohesive strength of the rock. Furthermore, in-situ stress... and hydrostatic stress It has the opposite effect on the cutting force. The cutting force varies with... It decreases as it increases, and decreases with... It increases with the increase of curvature. and The effect is the opposite of the effect of cutting force.

Claims

1. A method of determining a rock failure surface in a drilling process, characterized by, Follow these steps: Step 1: Simulate and determine the drilling force model, and determine the relationships between the components in the model. The specific process is as follows: Let the thrust be Torque is During drilling, the tangential and normal components of the frictional force on the wear surface are respectively expressed as: The parameters of the cutting tool include the cutting depth. d ,inclination α wear angle β The stress distribution expression for the wedge with tool width l is: (1) (2) in, γ The apex angle of the rock wedge, Indicates the internal friction angle of the rock. The external stress of the wedge's x-axis in contact with the rock of the drill bit. P The angle between them The symbol is positive, and the symbol is in a clockwise direction. It is positive; A The rock-drill bit contact area is calculated using the following formula: A= ldcos α ; The area of ​​the wear zone is calculated using the following formula: =ldcos α sin β ;inclination α Fixed as wear angle β Friction is related to mechanical forces that cause wear; during drilling, friction is considered the primary cause of tool wear. β The range is 0~15°. Considered as a function of the drill bit's motion variables, the relationship is: (3) Where v and w represent the axial velocity and tangential velocity of the drill bit, respectively; Step 2: Calculate the maximum shear stress at which the rock structure undergoes plastic failure. The expression for the maximum shear stress is: (15) Among them, the in-situ stress is Hydrostatic stress is Normal stress is N Shear stress is S Inclination angle is α ; x, y These are the values ​​of the coordinates of the destruction point in rectangular coordinates; Step 3, according to the maximum shear stress criterion, the failure surface shape is determined by the maximum shear stress of the shear zone determined in Step 2 With this, the failure surface is predicted; Step 4: Based on the maximum shear stress criterion, the force acting on the cutting surface is solved using an iterative method. The basic drilling parameters are input to determine the function of the failure surface, and the morphology of the failure surface is quantitatively presented. The functional expression for the failure surface is: (17) wherein the basic drilling parameters include a depth of cut d , a wear angle β .

2. The method of claim 1, wherein: The specific process of step 2 is as follows: Assuming that the crushing zone is in a state of compressive stress, the state of the shear zone satisfies the stress condition of and Through the following stress analysis, the normal stress of the crushing zone has the following relationship with the shear stress of the shear zone: (4) (5) (6) wherein, is the friction angle of the crush zone, then the internal friction angle of the rock is the friction angle of the crush zone, The expression for the internal friction angle of the rock is (7) When a shear stress is applied to a rock S The expression for the stress state is: (8) In equation (8), the stress state of the shear zone is established in polar coordinates. The expression for equation (8) in rectangular coordinates is: (9) Similarly, normal stress N The stress state expression in the shear zone is: (10) In-situ stress and hydrostatic stress acting on the sheared rock at an angle of inclination α The normal stress and shear stress of the shear zone are expressed as (11) Normal stress N The expression for the plane with an inclination of π / (2 - a) is: (12) Increasing pore stress The stress state expression for the shear zone is given by (13) According to the formulas of mechanics of materials, we have: (14) Substituting the results from equations (9), (10), (11), and (12) into equation (13), and then substituting the result from equation (13) into equation (14), we obtain the following equation: ; as shear stress applied to rock τ When the rock reaches its shear strength, the rock structure will undergo plastic failure, which conforms to the maximum shear stress strength theory.

3. The method of claim 1, wherein: The specific process of step 3 is as follows: Normal stress applied to the cutting surface during rock drilling N This leads to the expansion of shear failure. Under the maximum shear stress criterion, the shape of the failure surface and the maximum shear stress are derived from equation (15). The distribution is related to the shear failure surface, therefore, the shear failure surface can be obtained from the coordinates of the points corresponding to the maximum shear stress at different depths.

4. The method of claim 1, wherein: The specific process of step 4 is as follows: First, input the basic drilling parameters. d v, w , α , In the model, this is used as an initial condition to obtain the functional expression of the failure surface, namely equation (17). Comparison (x) and τ Determine the x-axis coordinates of the failure surface; Then, substitute the x-axis coordinate value into equation (17) to calculate the corresponding y-axis value, and introduce the concept of radius of curvature R in differential geometry to quantitatively determine the morphology of the failure surface.

Images