A method for determining various interactions between a PDC bit and a rock

Abstract

The present invention belongs to the field of testing the physical and mechanical properties of rocks, and proposes a method for measuring various interactions between a PDC bit and a rock, including conducting drilling experiments under different drilling settings to obtain drilling data; establishing a bit-rock interaction mechanical model based on the cutting, friction, and indentation processes between the bit and the rock; processing the drilling data based on the bit-rock interaction mechanical model to obtain the cutting depth of the bit under different drilling settings d , the normal force per unit length of the bit w and the tangential force per unit length of the bit t , plot d - w graphs, d - t graphs and t - w graphs and perform linear fitting; interpret the intercept and slope of each fitting curve based on the bit-rock interaction mechanical model to obtain parameters of various interactions between the PDC bit and the rock. The present invention takes into account the characteristic of the indentation force, making it closer to the actual process of the bit drilling into the rock.

Description

Technical Field

[0001] The present invention belongs to the field of testing the physical and mechanical properties of rocks, and specifically discloses a method for determining various interactions between a PDC bit and a rock. Background Art

[0002] The interaction between a bit and a rock includes aspects such as the ease with which the rock resists the penetration of the bit, the ease with which the bit breaks the rock, and the friction between the bit and the rock. These interactions can be quantitatively evaluated using parameters such as drillability, specific energy, and friction coefficient, respectively. These parameters play a key role in optimizing drilling performance and estimating rock properties. Currently, the prior art has disclosed evaluation methods for specific interactions. Some techniques have disclosed evaluation methods for rock drillability, and some techniques have disclosed evaluation methods for the friction coefficient between a bit and a rock. However, there is rarely a method that can obtain multiple interaction parameters through a single experiment. In addition, it should be noted that the interaction parameters are not only related to the properties of the rock but also related to the performance of the bit. For example, the friction coefficients between the same rock and different bits are different, and the abilities of the same rock to resist the penetration of different bits are also different. However, some methods only focus on the properties of the rock itself and ignore the co-action between the bit and the rock. Therefore, the interaction parameters obtained from real drilling experiments using a specific bit are more valuable for guiding field engineering, but this depends on a reliable method to interpret the drilling data and obtain specific information about the interaction between the bit and the rock.

[0003] The bit-rock interface law, also known as the drilling response model, describes the relationship between the dynamic parameters of the bit and is the theoretical basis for interpreting drilling data. Many studies have focused on developing drilling response models specifically for PDC bits because PDC bits are widely used in petroleum engineering and geological exploration and can achieve large diameters and deep boreholes in almost all formations. The interaction between a PDC bit and a rock is usually regarded as the sum of the interactions between all single cutters and the rock. Therefore, the drilling process is usually simplified to a single cutter cutting experiment for research. The process of the single cutter cutting experiment is as follows: The cutter head is set at a specific cutting depth and moved parallel to the rock surface while measuring the force acting on the cutter head and the characteristics of the cuttings. Based on the understanding of the phenomena and results of the single cutter cutting experiment, many scholars have proposed various bit-rock interaction interface laws. Among them, the phenomenological model proposed by Detournay and Defourny for PDC bits is the most representative. This model has been verified, applied, and developed by a large number of single cutter cutting experiments. However, these models usually assume that there are two processes in the interaction between the bit and the rock: cutting and frictional contact, ignoring the process of the bit penetrating the rock. This makes these models face difficulties in interpreting full-scale drilling data in actual engineering.

[0004] In summary, there is an urgent need for a model suitable for interpreting the drilling data of full-size PDC bits to obtain information on the interaction between the bit and the rock in multiple aspects from a single drilling experiment. Therefore, in view of these problems, it is very necessary to study and design a new method for measuring various interactions between a PDC bit and the rock to solve the problems existing in the existing evaluation of the interaction between the bit and the rock. Summary of the Invention

[0005] In order to solve the problems existing in the existing evaluation of the interaction between the bit and the rock, that is, the existing method only focuses on the properties of the rock itself while ignoring the co-action between the bit and the rock, a single experiment cannot obtain multiple interaction parameters, and the process of the bit pressing into the rock is ignored, resulting in inaccurate data, the present invention proposes a method for measuring various interactions between a PDC bit and the rock.

[0006] The present invention provides a method for measuring various interactions between a PDC bit and the rock, including the following steps:

[0007] S1. Conduct drilling experiments under different drilling settings to obtain drilling data under different drilling settings;

[0008] S2. Based on the cutting, friction, and indentation processes between the bit and the rock, establish a bit-rock interaction mechanical model;

[0009] S3. Process the drilling data obtained in step S1 based on the bit-rock interaction mechanical model obtained in step S2 to obtain the cutting depth d of the bit, the normal force w per unit length of the bit, and the tangential force t per unit length of the bit under different drilling settings, and plot the cutting depth d of the bit, the normal force w per unit length of the bit, and the tangential force t per unit length of the bit in the d-w diagram, d-t diagram, and t-w diagram. After the plotting is completed, linearly fit the data in the d-w diagram, d-t diagram, and t-w diagram respectively, and obtain the intercept and slope of each fitting curve;

[0010] S4. Interpret the intercept and slope of each fitting curve obtained in step S3 based on the bit-rock interaction mechanical model obtained in step S2 to obtain the parameters of various interactions between the PDC bit and the rock.

[0011] According to a method for measuring various interactions between a PDC bit and the rock according to some embodiments of the present application, step S1 includes:

[0012] S101. Equipment and sample preparation: Check whether the drilling rig, pressure control system, and data recorder are working properly, prepare rock samples, and ensure that the size and shape of the rock samples meet the experimental requirements;

[0013] S102. Initial setup: Install the PDC bit on the drill rig and ensure it is firmly fixed. Place the PDC bit on the rock surface, start the pressure control system, set the feed pressure to the initial value, and ensure the feed pressure is stable;

[0014] S103. Start drilling: When the PDC bit stabilizes at the initial feed pressure value, start the drilling process. The PDC bit drills the rock sample at a constant rotational speed; during the drilling process, the data recorder records the drilling data;

[0015] S104. Pressure increase and drilling: After drilling for a period of time, increase the feed pressure value and continue drilling at the new stable feed pressure value. The data recorder records the drilling data;

[0016] S105. Repeat the experiment: Repeat step S104 until the experiment ends when the maximum feed pressure value designed in the experiment or the predetermined test time is reached. The data recorder records the drilling data at each stage;

[0017] S106. Equipment shutdown and cleaning: Shut down the drill rig, pressure control system, and data recorder, clean the experimental site, and remove the PDC bit and rock sample.

[0018] According to a method for measuring various interactions between a PDC bit and a rock according to some embodiments of the present application, in step S1, the drilling data includes the thrust of the bit, the radius of the bit, the torque of the bit, the drilling speed of the bit, and the rotational speed of the bit.

[0019] According to a method for measuring various interactions between a PDC bit and a rock according to some embodiments of the present application, in step S2, the cutting, friction, and indentation processes between the bit and the rock include stage I and stage II;

[0020] In stage I, the normal force w per unit length of the bit is less than the critical contact force, and the bit rubs against the rock surface without generating an obvious cutting depth d of the bit;

[0021] In stage I, the relationship between the normal force w per unit length of the bit and the tangential force t per unit length of the bit is shown in formula (1):

[0022] (1)

[0023] Where, represents the friction angle between the bottom of the bit and the rock, represents the friction coefficient between the bottom of the bit and the rock;

[0024] The second stage is the effective drilling process. In the second stage, the normal force w per unit length of the drill bit is greater than the critical contact force, radial cracks in the rock begin to form, fissures propagating along a linear path are generated between the cuttings and the intact rock, the frictional force between the drill bit and the rock surface reaches the maximum value, the contact force between the drill bit and the rock surface is equal to the sum of the penetration force and the critical contact force, and the increase in the penetration force causes the drill bit to penetrate further into the rock, increasing the cutting depth d of the drill bit without increasing the frictional force between the drill bit and the rock surface;

[0025] In the second stage, the relationship between the normal force w per unit length of the drill bit and the cutting depth d of the drill bit is shown in Equation (2):

[0026] (2)

[0027] where, represents the contact force required to increase the unit cutting depth and is used to characterize the drillability of the rock, represents the ratio of the normal cutting force to the tangential cutting force on the cutting surface, represents the specific energy of the rock and is used to characterize the difficulty of cutting and breaking the rock, represents the critical contact force and is used to characterize the ease of the drill bit penetrating the rock surface;

[0028] In the second stage, the relationship between the tangential force t per unit length of the drill bit and the cutting depth d of the drill bit is shown in Equation (3):

[0029] (3)

[0030] In the second stage, the relationship between the normal force w per unit length of the drill bit and the tangential force t per unit length of the drill bit is shown in Equation (4):

[0031] (4)

[0032] where, represents the resistance coefficient of the effective drilling process, as shown in Equation (5):

[0033] (5)

[0034] The normal force w per unit length of the drill bit is as shown in Equation (6):

[0035] (6)

[0036] where, represents the thrust of the drill bit, represents the radius of the drill bit;

[0037] The tangential force t per unit length of the drill bit is as shown in formula (7):

[0038] (7)

[0039] Wherein, represents the torque of the drill bit;

[0040] The cutting depth d of the drill bit is as shown in formula (8):

[0041] (8)

[0042] Wherein, represents the drilling speed of the drill bit, represents the rotational speed of the drill bit.

[0043] According to a method for measuring various interactions between a PDC drill bit and a rock according to some embodiments of the present application, in step S3, the thrust, radius, torque, drilling speed, and rotational speed of the drill bit in the drilling data are input into the drill bit-rock interaction mechanical model obtained in step S2, and the cutting depth d, the normal force w per unit length of the drill bit, and the tangential force t per unit length of the drill bit are obtained through formulas (6)-(8).

[0044] According to a method for measuring various interactions between a PDC drill bit and a rock according to some embodiments of the present application, in step S3, the linear fitting of the data in the d-w diagram, d-t diagram, and t-w diagram respectively includes fitting the data in the first stage of the t-w diagram and the data in the second stage of the d-w diagram, d-t diagram, and t-w diagram respectively, to obtain the fitting curve of the first stage of the t-w diagram, the fitting curve of the second stage of the d-w diagram, the fitting curve of the second stage of the d-t diagram, and the fitting curve of the second stage of the t-w diagram.

[0045] According to a method for measuring various interactions between a PDC drill bit and a rock according to some embodiments of the present application, in step S3, obtaining the intercept and slope of each fitting curve respectively includes obtaining the slope of the fitting curve of the first stage of the t-w diagram, the intercept of the fitting curve of the second stage of the d-w diagram, the slope of the fitting curve of the second stage of the d-w diagram, the intercept of the fitting curve of the second stage of the d-t diagram, the slope of the fitting curve of the second stage of the d-t diagram, the intercept of the fitting curve of the second stage of the t-w diagram, and the slope of the fitting curve of the second stage of the t-w diagram.

[0046] A method for measuring various interactions between a PDC bit and a rock according to some embodiments of the present application. In step S4, the parameters of various interactions between the PDC bit and the rock include the difficulty of the bit penetrating the rock surface, the friction coefficient between the bottom of the bit and the rock, the drillability of the rock, the specific energy of the rock, and the resistance coefficient of the effective drilling process.

[0047] A method for measuring various interactions between a PDC bit and a rock according to some embodiments of the present application. In step S4, the friction coefficient between the bottom of the bit and the rock is determined by the reciprocal of the slope of the fitting curve in the first stage of the t-w diagram or by dividing the intercept of the fitting curve in the second stage of the d-t diagram by the intercept of the fitting curve in the second stage of the d-w diagram. The difficulty of the bit penetrating the rock surface is determined by the intercept of the fitting curve in the second stage of the d-w diagram. The specific energy of the rock is determined by the slope of the fitting curve in the second stage of the d-t diagram. The resistance coefficient of the effective drilling process is determined by the reciprocal of the slope of the fitting curve in the second stage of the t-w diagram. The drillability of the rock is determined by subtracting the ratio of the normal cutting force to the tangential cutting force on the cutting surface and the specific energy of the rock from the slope of the fitting curve in the second stage of the d-w diagram.

[0048] A method for measuring various interactions between a PDC bit and a rock proposed by the present invention divides the interaction process between the bit and the rock into cutting, friction, and indentation processes. Considering the characteristic of the indentation force, the contact force between the bit and the rock is divided into the critical contact force and the indentation force, making the mathematical model of the present invention describing the law of the bit-rock interface closer to the actual process of the bit drilling into the rock, and the obtained data more accurate. In addition, this method can effectively interpret the full-size PDC drilling data and obtain various information parameters of the interaction between the bit and the rock comprehensively from a single drilling experiment. These parameters are of great significance for evaluating the bit performance and the mechanical properties of the rock. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 is a schematic flow chart of a method for measuring various interactions between a PDC bit and a rock according to the present invention;

[0050] Figure 2 is a schematic diagram of the feed pressure setting for the drilling experiment of the embodiment of the present invention;

[0051] Figure 3 is a schematic diagram of the mechanical model of the interaction between the bit and the rock in the embodiment of the present invention, (a) schematic diagram of the mechanical model in the first stage, (b) schematic diagram of the mechanical model in the second stage;

[0052] Figure 4They are the d-w diagram, d-t diagram and t-w diagram of the white granite in the embodiments of the present invention. (a) is the d-w diagram of the white granite, (b) is the d-t diagram of the white granite, and (c) is the t-w diagram of the white granite;

[0053] Figure 5 They are the d-w diagram, d-t diagram and t-w diagram of the yellow granite in the embodiments of the present invention. (a) is the d-w diagram of the yellow granite, (b) is the d-t diagram of the yellow granite, and (c) is the t-w diagram of the yellow granite;

[0054] Figure 6 They are the d-w diagram, d-t diagram and t-w diagram of white sandstone, black sandstone, green sandstone, red granite, basalt, red sandstone and grey granite in the embodiments of the present invention. (a) is the d-w diagram of white sandstone, black sandstone, green sandstone, red granite, basalt, red sandstone and grey granite, (b) is the d-t diagram of white sandstone, black sandstone, green sandstone, red granite, basalt, red sandstone and grey granite, and (c) is the t-w diagram of white sandstone, black sandstone, green sandstone, red granite, basalt, red sandstone and grey granite. Detailed implementation manners

[0055] The following further describes in detail the implementation manners of the present invention with reference to the accompanying drawings and embodiments. The following embodiments are used to illustrate the present invention, but cannot be used to limit the scope of the present invention.

[0056] Embodiment 1. This embodiment provides a method for measuring various interactions between a PDC bit and a rock, as Figure 1 shown, including the following steps:

[0057] S1. Conduct drilling experiments under different drilling settings to obtain drilling data under different drilling settings;

[0058] S2. Based on the cutting, friction and indentation processes between the bit and the rock, establish a bit-rock interaction mechanical model;

[0059] S3. Process the drilling data obtained in step S1 based on the bit-rock interaction mechanical model obtained in step S2 to obtain the cutting depth d of the bit, the normal force w per unit length of the bit, and the tangential force t per unit length of the bit under different drilling settings, and plot the cutting depth d of the bit, the normal force w per unit length of the bit, and the tangential force t per unit length of the bit in the d-w diagram, d-t diagram and t-w diagram. After the plotting is completed, linearly fit the data in the d-w diagram, d-t diagram and t-w diagram respectively, and obtain the intercept and slope of each fitting curve;

[0060] S4. Interpret the intercept and slope of each fitting curve obtained in step S3 based on the bit-rock interaction mechanical model obtained in step S2 to obtain the parameters of various interactions between the PDC bit and the rock.

[0061] Example 2. This example provides a method for measuring various interactions between a PDC bit and a rock, including the following steps:

[0062] S1. Conduct drilling experiments under different drilling settings to obtain drilling data under different drilling settings;

[0063] Specifically, step S1 includes:

[0064] S101. Equipment and sample preparation: Check whether the drilling rig, pressure control system, and data recorder are working properly, prepare rock samples, and ensure that the size and shape of the rock samples meet the experimental requirements;

[0065] S102. Initial setting: Install the PDC bit on the drilling rig and ensure that the PDC bit is firmly fixed. Place the PDC bit on the rock surface, start the pressure control system, set the feed pressure to the initial value, and ensure that the feed pressure is stable;

[0066] S103. Start drilling: When the PDC bit is stable at the initial feed pressure value, start the drilling process. The PDC bit drills the rock sample at a constant rotational speed; during the drilling process, the data recorder records the drilling data;

[0067] S104. Pressure increase and drilling: After drilling for a period of time, increase the feed pressure value and continue drilling at the new stable feed pressure value. The data recorder records the drilling data;

[0068] S105. Repeat the experiment: Repeat step S104 until the maximum feed pressure value designed in the experiment or the predetermined test time is reached to end the experiment. The data recorder records the drilling data at each stage;

[0069] S106. Equipment shutdown and cleaning: Shut down the drilling rig, pressure control system, and data recorder, clean the experimental site, and remove the PDC bit and rock samples;

[0070] Among them, the drilling data includes the thrust of the bit, the radius of the bit, the torque of the bit, the drilling speed of the bit, and the rotational speed of the bit. More preferably, for each stable drilling stage, calculate the average value of the drilling data at this stage as a set of drilling data, so that a series of drilling response data under different drilling settings can be obtained from one drilling experiment;

[0071] Preferably, in this embodiment, a two-wing PDC bit with a diameter of 50 mm and a back rake angle of 15° was used in the experiment. Drilling experiments were carried out on nine rock samples, including white granite, yellow granite, white sandstone, black sandstone, green sandstone, red granite, basalt, red sandstone and grey granite. In this embodiment, different drilling settings were set with different feed pressures. The change of the feed pressure during the experiment is as Figure 2 shown. For Figure 2 each stage s i in it, the average value of the drilling data in this stage was calculated as a set of drilling data, so that a series of drilling data at different feed pressure levels could be obtained from one drilling experiment. In this embodiment, the PDC bits in all experiments were carried out at a constant rotational speed of 130 revolutions per minute.

[0072] S2. Based on the cutting, friction and indentation processes between the bit and the rock, establish a mechanical model of the bit-rock interaction;

[0073] In this embodiment, the concept of an equivalent cutter head is introduced to simplify the description of the interaction between the bit and the rock. The concept of an equivalent cutter head is that the force acting on the equivalent cutter head is considered equivalent to the force acting on the bit. Under this theoretical framework, the drilling response can be characterized by three basic quantities: the normal force w per unit length of the bit, the tangential force t per unit length of the bit, and the cutting depth d of the bit. The normal force w per unit length of the bit is as shown in formula (1):

[0074] (1)

[0075] where represents the thrust of the bit, represents the radius of the bit;

[0076] The tangential force t per unit length of the bit is as shown in formula (2):

[0077] (2)

[0078] where represents the torque of the bit;

[0079] The cutting depth d of the bit is as shown in formula (3):

[0080] (3)

[0081] where represents the penetration rate of the bit, represents the rotational speed of the bit.

[0082] This equivalent cutterhead concept is based on the following assumptions: the force is evenly distributed across the entire drill bit, and the interface law between the drill bit and the rock is independent of the rate. Then, the dynamic variables of the drill bit can be represented by the normal force w per unit length of the drill bit and the tangential force t per unit length of the drill bit, and the motion variable of the drill bit can be represented by a single variable, the cutting depth d of the drill bit;

[0083] The proposed mechanical model of drill bit - rock interaction assumes that there are two different drilling response stages as the normal force w per unit length of the drill bit increases, including Stage I and Stage II. The critical contact force controls the transition between these two stages. Figure 3 The physical processes of these two stages and the forces acting on the drill bit are shown below and are described in detail as follows:

[0084] In Stage I, as shown in Figure 3 (a), the normal force w per unit length of the drill bit is less than the critical contact force, and the drill bit rubs against the rock surface, and no obvious cutting depth d of the drill bit is generated. The frictional force t f increases with the increase of the contact force because the actual contact area between the drill bit and the rock also increases with the increase of the contact force . The relationship between the contact force and the frictional force t f depends on the friction angle between the bottom of the drill bit and the rock. It should be noted that due to the elastic deformation and damage accumulation caused by the repeated frictional contact between the drill bit and the rock, a small cutting depth d of the drill bit may be generated in this stage. In this stage, the interaction between the drill bit and the rock only involves the frictional contact process;

[0085] The relationship between the normal force w per unit length of the drill bit and the tangential force t per unit length of the drill bit in Stage I is shown in Equation (4):

[0086] (4)

[0087] where represents the friction angle between the bottom of the drill bit and the rock, and represents the friction coefficient between the bottom of the drill bit and the rock;

[0088] Stage II is the effective drilling process. In Stage II, as shown in Figure 3 (b), the normal force w per unit length of the drill bit is greater than the critical contact force, and radial cracks in the rock begin to form, and fissures propagating along a linear path are generated between the cuttings and the intact rock. At the bottom of the drill bit, since the actual contact area between the drill bit and the rock has reached the maximum value, the component of used for frictional action reaches the limit value, the critical contact force , the frictional force between the drill bit and the rock surface reaches its maximum value , and the frictional force between the drill bit and the rock surface does not increase with . Subsequently, the remaining contact force, that is, the difference between the contact force and the critical contact force , is expressed as the penetration force . The contact force between the drill bit and the rock surface is equal to the sum of the penetration force and the critical contact force . The increase in the penetration force causes the drill bit to penetrate deeper into the rock, thereby increasing the cutting depth d of the drill bit without increasing the frictional force between the drill bit and the rock surface. On the cutting surface of the drill bit and the rock, there are a tangential cutting force and a normal cutting force . The relationship between the tangential cutting force and the normal cutting force is related to the back rake angle θ of the drill bit and the friction angle between the cutting surface of the drill bit and the rock. Among them, the friction angle between the cutting surface of the drill bit and the rock is a function of the back rake angle θ of the drill bit and a constant.

[0089] The second stage is the effective drilling process, which involves three independent processes: cutting, penetration, and frictional contact. The tangential force t per unit length of the drill bit can be divided into the tangential cutting force acting on the cutting surface and the maximum frictional force between the drill bit and the rock surface acting on the contact surface, as shown in Equation (5):

[0090] (5)

[0091] The normal force w per unit length of the drill bit can be divided into the normal cutting force acting on the cutting surface, the critical contact force acting on the contact surface, and the penetration force , as shown in Equation (6):

[0092] (6)

[0093] On the cutting surface of the drill bit and the rock, the tangential cutting force and the normal cutting force increase linearly with the cutting depth d of the drill bit. The increase rate is related to the properties of the rock, as shown in Equations (7) and (8):

[0094] (7)

[0095] (8)

[0096] Among them, represents the specific energy of the rock, which represents the energy required to break a unit volume of rock under given drill and bit conditions, represents the normal cutting force on the cutting surface and the tangential cutting force The ratio of is shown in formula (9):

[0097] (9)

[0098] Due to the friction angle between the drill bit cutting surface and the rock only depends on the back rake angle θ of the drill bit and has nothing to do with the rock. Therefore, ζ can be regarded as a constant, and the parameter ζ can be determined according to the back rake angle of the drill bit and rock cutting experiments, or according to the data in relevant papers;

[0099] On the contact surface between the drill bit and the rock, the critical contact force and the maximum value of the frictional force between the drill bit and the rock surface acting on the contact surface The relationship between them follows the friction law, as shown in formula (10):

[0100] (10)

[0101] On the contact surface between the drill bit and the rock, the indentation force increases linearly with the cutting depth d of the drill bit, as shown in formula (11):

[0102] (11)

[0103] Among them, represents the contact force required to increase the unit cutting depth, which is used to characterize the drillability of the rock, reflects the resistance of the rock to the indentation of the drill bit and is related to the rock properties;

[0104] According to formulas (6), (8), (9), and (11), the relationship between the normal force w per unit length of the drill bit and the cutting depth d of the drill bit in the second stage can be obtained as shown in formula (12):

[0105] (12)

[0106] Among them, represents the contact force required to increase the unit cutting depth, which is used to characterize the drillability of the rock, represents the ratio of the normal cutting force to the tangential cutting force on the cutting surface, represents the specific energy of the rock, which is used to characterize the difficulty of cutting and breaking the rock, represents the critical contact force, which is used to characterize the ease of the drill bit penetrating the rock surface;

[0107] According to formulas (5), (7), and (10), the relationship between the tangential force t per unit length of the drill bit and the cutting depth d of the drill bit in the second stage is shown in formula (13):

[0108] (13)

[0109] According to formulas (12) and (13), the relationship between the normal force w per unit length of the drill bit and the tangential force t per unit length of the drill bit in the second stage is shown in formula (14):

[0110] (14)

[0111] Wherein, represents the resistance coefficient of the effective drilling process, which characterizes the ratio of the tangential force to the normal force during the effective drilling process of the rock without considering the friction effect, as shown in formula (15):

[0112] (15)

[0113] Obviously, formulas (4), (12)-(14) describe a series of linear relationships among the normal force w per unit length of the drill bit, the tangential force t per unit length of the drill bit, and the cutting depth d of the drill bit. The intercepts and slopes of these relationships quantitatively reflect the interaction characteristics between the drill bit and the rock.

[0114] S3. Process the drilling data obtained in step S1 based on the drill-bit-rock interaction mechanical model obtained in step S2 to obtain the cutting depth d of the drill bit, the normal force w per unit length of the drill bit, and the tangential force t per unit length of the drill bit under different drilling settings, and plot the cutting depth d of the drill bit, the normal force w per unit length of the drill bit, and the tangential force t per unit length of the drill bit in the d-w diagram, d-t diagram, and t-w diagram. After the plotting is completed, perform linear fitting on the data in the d-w diagram, d-t diagram, and t-w diagram respectively, and obtain the intercept and slope of each fitting curve respectively;

[0115] Specifically, in step S3, the thrust of the drill bit, the radius of the drill bit, the torque of the drill bit, the drilling speed of the drill bit, and the rotational speed of the drill bit in the drilling data are input into the drill-bit-rock interaction mechanical model obtained in step S2, and the cutting depth d of the drill bit, the normal force w per unit length of the drill bit, and the tangential force t per unit length of the drill bit are obtained through formulas (1)-(3).

[0116] Calculate the average value of the drilling data for each stable stage as a set of drilling response data, and plot each set of response data into the d-w diagram, d-t diagram, and t-w diagram. The linear fitting of the data in the d-w diagram, d-t diagram, and t-w diagram includes respectively fitting the data in the I-th stage of the t-w diagram and the data in the II-th stage of the d-w diagram, d-t diagram, and t-w diagram, to obtain the fitting curve of the I-th stage of the t-w diagram, the fitting curve of the II-th stage of the d-w diagram, the fitting curve of the II-th stage of the d-t diagram, and the fitting curve of the II-th stage of the t-w diagram. In this embodiment, the d-w diagram of white granite is as shown in Figure 4 Figure (a), the d-t diagram is as shown in Figure 4 Figure (b), and the t-w diagram is as shown in Figure 4 Figure (c). The d-w diagram of yellow granite is as shown in Figure 5 Figure (a), the d-t diagram is as shown in Figure 5 Figure (b), and the t-w diagram is as shown in Figure 5 Figure (c). The d-w diagrams of white sandstone, black sandstone, green sandstone, red granite, basalt, red sandstone, and gray granite are as shown in Figure 6 Figure (a), the d-t diagrams are as shown in Figure 6 Figure (b), and the t-w diagrams are as shown in Figure 6 Figure (c). The characteristics of the data in the II-th stage are that the cutting depth d of the drill bit increases linearly with the normal force w per unit length of the drill bit and the tangential force t per unit length of the drill bit. The characteristics of the data in the I-th stage are that the cutting depth d of the drill bit does not change with the normal force w per unit length of the drill bit and the tangential force t per unit length of the drill bit.

[0117] In step S3, obtaining the intercept and slope of each fitting curve respectively includes obtaining the slope of the fitting curve of the I-th stage of the t-w diagram, the intercept of the fitting curve of the II-th stage of the d-w diagram, the slope of the fitting curve of the II-th stage of the d-w diagram, the intercept of the fitting curve of the II-th stage of the d-t diagram, the slope of the fitting curve of the II-th stage of the d-t diagram, the intercept of the fitting curve of the II-th stage of the t-w diagram, and the slope of the fitting curve of the II-th stage of the t-w diagram.

[0118] S4. Based on the mechanical model of the drill bit-rock interaction obtained in step S2, interpret the intercept and slope of each fitting curve obtained in step S3 to obtain the parameters of various interactions between the PDC drill bit and the rock;

[0119] Specifically, the parameters of various interactions between the PDC drill bit and the rock in step S4 include the ease of the drill bit penetrating the rock surface, the friction coefficient between the bottom of the drill bit and the rock, the drillability of the rock, the specific energy of the rock, and the resistance coefficient of the effective drilling process. These parameters quantitatively characterize the interaction between the drill bit and the rock;

[0120] In step S4, the friction coefficient between the bit bottom and the rock is determined by the reciprocal of the slope of the fitting curve in the first stage of the t-w diagram or the friction coefficient between the bit bottom and the rock is determined by dividing the intercept of the fitting curve in the second stage of the d-t diagram by the intercept of the fitting curve in the second stage of the d-w diagram , the ease of penetration of the bit through the rock surface, i.e., the critical contact force, is determined by the intercept of the fitting curve in the second stage of the d-w diagram , the specific energy of the rock is determined by the slope of the fitting curve in the second stage of the d-t diagram , the resistance coefficient of the effective drilling process is determined by the reciprocal of the slope of the fitting curve in the second stage of the t-w diagram , the drillability of the rock, i.e., the contact force required to increase the unit cutting depth, is determined by subtracting the ratio of the normal cutting force to the tangential cutting force on the cutting surface from the slope of the fitting curve in the second stage of the d-w diagram and the specific energy of the rock These parameters are of great significance for evaluating the bit performance and the mechanical properties of the rock. In this embodiment, the back rake angle of the bit used in the experiment is 15°, and the ratio of the normal cutting force to the tangential cutting force on the corresponding cutting surface is 0.60. The data identified in the model in this embodiment are shown in Table 1:

[0121] Table 1

[0122]

[0123] Among the experimental data of this embodiment, the experimental results of white granite and yellow granite exhibit the characteristics of the first stage and the second stage. Through the slope of their t-w curves in the first stage, the friction coefficient between the bit bottom and the rock can be identified , denoted as . According to the intercepts of the d-w and d-t curves in the second stage, the friction coefficient between the bit bottom and the rock can also be identified , denoted as . The identification results show that both and of white granite are 1.01, and both and of yellow granite are 1.19. This indicates that the identified parameters are consistent whether based on the data of the first stage or the second stage. For other types of rocks, since the feed pressure set in the experiment is always higher than the intercept of these rocks in the first stage, only the data of the second stage are obtained, but this does not affect the parameter identification. This method can comprehensively evaluate various interactions between the bit and the rock through a single drilling experiment.

[0124] The embodiments of the present invention are given for purposes of illustration and description, and are not exhaustive or limit the invention to the disclosed forms. Many modifications and variations are obvious to those of ordinary skill in the art. The embodiments are chosen and described in order to best explain the principles of the invention and its practical application, and to enable those of ordinary skill in the art to understand the invention and design various embodiments with various modifications suitable for a particular purpose.

Claims

1. A method for determining multiple interactions between a PDC drill bit and a rock, characterized in that: The steps include: S1. Performing drilling experiments under different drilling settings to obtain drilling data under different drilling settings; S2. Based on the cutting, friction and indentation process between the drill bit and the rock, a mechanical model of drill bit-rock interaction is established; S3. Based on the drill bit-rock interaction mechanical model obtained in step S2, the drilling data obtained in step S1 are processed to obtain the cutting depth d, the normal force w per unit length of the drill bit, and the tangential force t per unit length of the drill bit under different drilling settings, and the cutting depth d, the normal force w per unit length of the drill bit, and the tangential force t per unit length of the drill bit are plotted in a dw diagram, a dt diagram, and a tw diagram. After the plotting is completed, linear fitting is performed on the data in the dw diagram, the dt diagram, and the tw diagram, respectively, to obtain the intercept and slope of each fitting curve; S4. Based on the drill bit-rock interaction mechanical model obtained in step S2, the intercept and slope of each fitting curve obtained in step S3 are interpreted to obtain parameters of various interactions between the PDC drill bit and the rock; In step S1, the drilling data includes the thrust of the drill bit, the radius of the drill bit, the torque of the drill bit, the drilling speed of the drill bit and the rotation speed of the drill bit; In step S2, the cutting, friction and pressing process between the drill bit and the rock includes stage I and stage II; In the first stage, the normal force w per unit length of the drill bit is less than the critical contact force. The relationship between the normal force w per unit length of the drill bit and the tangential force t per unit length of the drill bit in the first stage is shown in formula (1): （1） in, Indicates the friction angle between the bottom of the drill bit and the rock, Indicates the coefficient of friction between the bottom of the drill bit and the rock; The second stage is an effective drilling process. In the second stage, the normal force w per unit length of the drill bit is greater than the critical contact force, radial cracks in the rock begin to form, cracks propagating along a linear path are generated between the rock cuttings and the intact rock, the friction between the drill bit and the rock surface reaches the maximum value, and the contact force between the drill bit and the rock surface is equal to the sum of the pressing force and the critical contact force. The relationship between the normal force w per unit length of the drill bit and the cutting depth d of the drill bit in the second stage is shown in formula (2): （2） in, It indicates the contact force required to increase the unit cutting depth and is used to characterize the drillability of rock. It represents the ratio of normal cutting force to tangential cutting force on the cutting surface. Represents the specific energy of rock, used to characterize the difficulty of cutting and crushing rock. represents the critical contact force, which is used to characterize the difficulty of the drill bit penetrating the rock surface. The relationship between the tangential force t per unit length of the drill bit and the cutting depth d of the drill bit in the second stage is shown in formula (3): （3） The relationship between the normal force w per unit length of the drill bit and the tangential force t per unit length of the drill bit in the second stage is shown in formula (4): （4） in, The resistance coefficient of the effective drilling process is shown in formula (5): （5） The normal force w per unit length of the drill bit is as shown in formula (6): （6） in, Indicates the thrust of the drill bit, The radius of the drill bit, The tangential force t per unit length of the drill bit is as shown in formula (7): （7） in, Indicates the torque of the drill bit, The cutting depth d of the drill bit is as shown in formula (8): （8） in, Indicates the drilling speed of the drill bit. Indicates the speed of the drill bit.

2. A method for determining multiple interactions between a PDC drill bit and a rock according to claim 1, characterized in that: The step S1 comprises: S101. Equipment and sample preparation: Check that the drilling rig, pressure control system and data logger are functioning properly, prepare rock samples, and ensure that the size and shape of the rock samples are suitable for the experimental requirements; S102. Initial setting: install the PDC drill bit on the drilling rig and ensure that the PDC drill bit is firmly fixed, place the PDC drill bit on the rock surface, start the pressure control system, set the feed pressure to the initial value, and ensure that the feed pressure is stable; S103. Start drilling: When the PDC drill bit stabilizes at the initial feed pressure value, the drilling process begins, and the PDC drill bit drills the rock sample at a constant speed; during the drilling process, the data recorder records the drilling data; S104. Pressure increase and drilling: After drilling for a period of time, the feed pressure value is increased and the drilling continues at a new stable feed pressure value, and the data recorder records the drilling data; S105 repeat the experiment: repeat step S104 until the maximum feed pressure value of the experimental design or the predetermined test time is reached to end the experiment, the data recorder records the drilling data at each stage; S106. Equipment shutdown and cleaning: shut down the drilling rig, pressure control system and data recorder, clean up the experimental site, and remove the PDC drill bit and rock samples.

3. The method for determining multiple interactions between a PDC drill bit and a rock according to claim 1, characterized in that: In step S3, the drill bit thrust, drill bit radius, drill bit torque, drill bit drilling speed and drill bit rotation speed of the drilling data are input into the drill bit-rock interaction mechanical model obtained in step S2, and the cutting depth d of the drill bit, the normal force w per unit length of the drill bit and the tangential force t per unit length of the drill bit are obtained by formula (6) to formula (8).

4. A method for determining multiple interactions between a PDC drill bit and a rock according to claim 1, characterized in that: The linear fitting of the data in the dw graph, dt graph and tw graph respectively in step S3 includes fitting the data in stage I in the tw graph and the data in stage II in the dw graph, dt graph and tw graph respectively, to obtain the fitting curve of stage I in the tw graph, the fitting curve of stage II in the dw graph, the fitting curve of stage II in the dt graph and the fitting curve of stage II in the tw graph.

5. A method for determining multiple interactions between a PDC drill bit and a rock according to claim 4, characterized in that: The step S3 of obtaining the intercept and slope of each fitting curve includes respectively obtaining the slope of the fitting curve of the tw graph stage I, the intercept of the fitting curve of the dw graph stage II, the slope of the fitting curve of the dw graph stage II, the intercept of the fitting curve of the dt graph stage II, the slope of the fitting curve of the dt graph stage II, the intercept of the fitting curve of the tw graph stage II and the slope of the fitting curve of the tw graph stage II.

6. A method for determining multiple interactions between a PDC drill bit and a rock according to claim 5, characterized in that: The various interaction parameters between the PDC drill bit and the rock in step S4 include the difficulty of the drill bit penetrating the rock surface, the friction coefficient between the bottom of the drill bit and the rock, the drillability of the rock, the specific energy of the rock and the resistance coefficient of the effective drilling process.

7. A method for determining multiple interactions between a PDC drill bit and a rock according to claim 6, characterized in that: In step S4, the friction coefficient between the bottom of the drill bit and the rock is determined by the inverse of the slope of the fitting curve of the stage I of the tw diagram or by dividing the intercept of the fitting curve of the stage II of the dt diagram by the intercept of the fitting curve of the stage II of the dw diagram, the difficulty of the drill bit penetrating the rock surface is determined by the intercept of the fitting curve of the stage II of the dw diagram, the specific energy of the rock is determined by the slope of the fitting curve of the stage II of the dt diagram, the resistance coefficient of the effective drilling process is determined by the inverse of the slope of the fitting curve of the stage II of the tw diagram, and the drillability of the rock is determined by subtracting the ratio of the normal cutting force to the tangential cutting force on the cutting surface and the specific energy of the rock from the slope of the fitting curve of the stage II of the dw diagram.

Images