Method and system for measuring particle size of downhole in-situ broken rock debris of PDC (Polycrystalline Diamond Compact) bit

Abstract

The invention discloses a PDC drill bit shaft bottom in-situ rock breaking debris particle size measurement method and system, and relates to the technical field of shaft bottom in-situ rock breaking debris particle size measurement, and the method comprises the steps: constructing a shaft bottom in-situ finite-discrete-infinite element rock model; the in-situ stratum rock at the well bottom is regarded as an infinite boundary, and PDC tooth cutting rock breaking parameter calibration and PDC tooth rock breaking model modeling are carried out; and under the non-bilinear damage criterion, through the interaction of the in-situ finite-discrete-infinite element rock model and the PDC tooth crushing rock model, the in-situ initial rock debris particle size of the well bottom is measured, and the performance of the drilling fluid is adjusted. According to the method, the well bottom in-situ rock debris particle size is measured based on the non-bilinear damage criterion of the typical rock stress-strain curve and the well bottom in-situ finite-discrete-infinite element rock model in a coupling mode, and the reliability and accuracy of well bottom in-situ rock breaking rock debris particle size measurement are improved; and the problem of high calculation cost or sound wave effect of a finite-discrete element model is avoided.

Description

A method and system for measuring the particle size of rock cuttings in situ at the bottom of a PDC drill bit. Technical Field

[0001] This invention relates to the field of in-situ rock breaking particle size measurement technology at the bottom of wells, and more specifically to a method and system for in-situ rock breaking particle size measurement using a PDC drill bit. Background Technology

[0002] my country possesses abundant ultra-deep (>9000 meters) oil and gas resources, representing a crucial area for future oil and gas discovery and scientific exploration of its boundaries. However, ultra-deep drilling has long faced the challenge of low cuttings carrying efficiency in wells with diameters of Φ444.5 mm and above. Predicting the bottom-hole cuttings size and adjusting drilling fluid properties accordingly is a highly efficient approach to improving cuttings carrying efficiency. This reduces the time cost associated with repeated trial-and-error adjustments based on the cuttings size returned from the surface, and helps lower drilling day costs, thus achieving cost reduction and efficiency improvement.

[0003] A literature review revealed a lack of systematic research reports focusing on predicting cuttings size at the bottom of the well, adjusting drilling fluid properties, and improving cuttings carrying efficiency. Therefore, to address the low cuttings carrying efficiency in large-diameter wells, a finite-discrete-infinite element bottom-hole rock model simulating the infinite boundary of the bottom-hole rock was established in Abaqus. A non-bilinear damage mathematical model was derived based on the stress-strain theory of typical rock fracture. Combining the finite-discrete-infinite element bottom-hole rock model with the non-bilinear damage mathematical model resulted in a method for predicting cuttings size at the bottom of the well.

[0004] Therefore, how to propose a method and system for measuring the particle size of rock cuttings in situ at the bottom of the well using PDC drill bits, and overcome the shortcomings of existing technologies, is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] In view of this, the present invention provides a method and system for measuring the particle size of in-situ rock breaking cuttings at the bottom of a PDC drill bit. Based on the finite-discrete element method (FEM) coupled with the infinite element method (IEM) to establish an in-situ finite-discrete-infinite element rock model at the bottom of the well, and derives a non-bilinear damage criterion based on the stress-strain curve of typical rocks to study the initial particle size of in-situ rock breaking cuttings at the bottom of the well. To achieve the above objectives, the present invention adopts the following technical solution: A method for measuring the particle size of in-situ rock breaking cuttings at the bottom of a PDC drill bit, comprising: constructing an in-situ finite-discrete-infinite element rock model at the bottom of the well by coupling the finite-discrete element method with the IEM; treating the formation rock at the bottom of the well as an infinite boundary, calibrating the rock breaking parameters of the PDC tooth cutting tool and modeling the rock breaking model of the PDC tooth cutting tool; constructing a non-bilinear damage criterion, and measuring the initial particle size of in-situ rock breaking cuttings at the bottom of the well through the interaction between the in-situ finite-discrete-infinite element rock model and the rock breaking model of the PDC tooth cutting tool under the non-bilinear damage criterion; and adjusting the drilling fluid performance according to the measured initial particle size of in-situ rock breaking cuttings at the bottom of the well.

[0006] Optionally, the rock may be sandstone or the like.

[0007] Optionally, the in-situ finite-discrete-infinite element rock model at the bottom of the well includes a finite-discrete-infinite element mesh model and a node model.

[0008] Optionally, the construction of the non-bilinear damage criterion includes: using cohesive elements to discretize and connect finite elements to simulate rock fracture, wherein the stress state at any point in the cohesive element is represented by a normal stress and shear stresses in two directions; determining the stress-strain curves under normal and shear stress conditions, and simplifying the stress-strain curves into two stages: the first stage is the linear elastic stage segment OA, and the second stage is the post-failure stage segment AB, wherein the stress corresponding to point A is the peak stress, and the rock deforms and fails beyond point A.

[0009] Optionally, it also includes determining the stress-strain constitutive relationship, strain-displacement relationship, and elastic matrix-stiffness relationship of segment OA; establishing a connection between the force and displacement of the discrete element based on the strain-displacement relationship and the elastic matrix-stiffness relationship; transforming the linear elastic constitutive relationship into a force-displacement relationship; when the rock reaches the peak stress intensity point A, the second nominal stress criterion is used as the judgment standard for damage initiation; damage state variables are introduced to represent the stiffness reduction of the cohesive element; damage calculation is performed in the initial state as if the rock is undamaged; after the rock is damaged, the stress is reduced; after the damage initiation, the form of damage evolution is determined by the damage state variables.

[0010] Optionally, the discrete element undergoes displacement under the combined action of normal and tangential deformation, with the effective displacement being... for: ;in, Indicates the normal stress component, , These represent the displacements under the two tangential stress components.

[0011] Optionally, the displacement of the discrete element under the combined action of normal and tangential deformation further includes the stress-displacement relationship of the discrete element under normal stress and shear stress conditions being divided into three stages: the linear elastic evolution stage of segment OA, the damage initiation stage at point A, and the exponential damage evolution stage of segment AB; wherein, This represents the peak intensity of the normal stress, and the opening displacement corresponding to the peak intensity is... This represents the peak shear strength under two shear stresses, and the opening displacement corresponding to the peak shear strength is... ; This represents the stiffness during the linear elastic evolution stage under normal stress. , Both represent the stiffness during the linear elastic evolution stage under shear stress; This represents the displacement at which complete failure occurs under normal stress. Both represent the displacement at which complete failure occurs under shear stress.

[0012] Optionally, it also includes: comparing and analyzing the constitutive relation of discrete elements under tensile and compressive stress conditions, the conceptual damage model of discrete elements, the theoretical fracture process zone model, and the fracture process of discrete elements; in the linear elastic stage, the discrete element generates micro-cracks after being subjected to force, and the displacement gradually increases as the load continues to increase; when the stress of the discrete element reaches When the cracking reaches the threshold, the discrete element begins irreversible failure; when the discrete element reaches its maximum failure displacement... At this point, the rock is no longer under stress, the failed discrete elements will be deleted, and the finite element will be separated; as the number of failed discrete elements increases, the finite elements that have not been destroyed by stress will form rock debris.

[0013] Optionally, the calibration of PDC tooth cutting rock breaking parameters and the modeling of PDC tooth rock breaking model include: during the PDC tooth rock breaking process, parameter calibration is performed using uniaxial compression simulation and Brazilian splitting; a finite-discrete element model of the rock is established by assigning material properties to the rock model; the mechanical parameters of the rock are adjusted, and the failure and damage of the rock are performed using a non-bilinear damage criterion to establish a PDC tooth rock breaking model.

[0014] Optionally, a PDC drill bit in-situ rock breaking cuttings particle size measurement system includes: a finite-discrete-infinite element rock model construction module: used to construct an in-situ finite-discrete-infinite element rock model at the bottom of the well by coupling the finite-discrete element method with the infinite element method; a parameter calibration and modeling module: used to calibrate the PDC tooth cutting rock breaking parameters and model the PDC tooth rock breaking model by treating the in-situ formation rock at the bottom of the well as an infinite boundary; a non-bilinear damage criterion construction module: used to construct a non-bilinear damage criterion; a measurement module: used to measure the initial rock cuttings particle size at the bottom of the well in-situ by the interaction between the in-situ finite-discrete-infinite element rock model and the PDC tooth rock breaking model under the non-bilinear damage criterion; and a drilling fluid performance adjustment module: used to adjust the drilling fluid performance according to the measured initial rock cuttings particle size at the bottom of the well.

[0015] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a method and system for measuring the particle size of in-situ rock breaking cuttings at the bottom of a PDC drill bit, which has the following beneficial effects: The present invention proposes a method for measuring the particle size of in-situ rock breaking cuttings at the bottom of a PDC drill bit, including: constructing a finite-discrete-infinite element rock model at the bottom of the well by coupling the finite-discrete element method with the infinite element method; treating the formation rock at the bottom of the well as an infinite boundary, calibrating the rock breaking parameters of the PDC tooth cutting and modeling the rock breaking model of the PDC tooth cutting; constructing a non-bilinear damage criterion, and measuring the initial particle size of the rock breaking cuttings at the bottom of the well by the interaction between the finite-discrete-infinite element rock model at the bottom of the well and the rock breaking model of the PDC tooth cutting under the non-bilinear damage criterion; adjusting the drilling fluid performance according to the measured initial particle size of the rock breaking cuttings at the bottom of the well. The present invention first establishes a finite-discrete-infinite element rock model at the bottom of the well based on the finite-discrete element theory and coupled with the infinite element theory, and derives a non-bilinear damage criterion based on the stress-strain curve of typical rocks. Secondly, the rock-breaking process of PDC cutting teeth cutting natural outcrops was carried out using finite-discrete element (FDE) rock models, finite-discrete-infinite element (FDI) rock models, and laboratory experiments. This verified the differences in rock-breaking simulation between the FDE and FDI models, and also validated the reliability and accuracy of the non-bilinear damage criterion and the FDI model in measuring the in-situ cuttings size at the bottom of the well, avoiding the high computational cost or acoustic effects of the FDE model. Finally, using drilling parameters and PDC bit characteristics during drilling in the HX well of a shale gas block in the Sichuan Basin as simulation parameters, the initial in-situ cuttings size of the formation was measured using the FDE model combined with the non-bilinear damage criterion. The measurement results guided the wellbore cleaning work, effectively mitigating the downhole risk of sand accumulation and stuck drill bit in one operation, demonstrating significant field application value. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0017] Figure 1 is a schematic diagram of the geometric model of the infinite boundary of the formation rock and the rock at the bottom of the well during in-situ drilling provided by the present invention.

[0018] Figure 2 is a schematic diagram of a PDC cutting tooth cutting a damaged rock model provided by the present invention.

[0019] Figure 3 is a schematic diagram of the mathematical model of rock damage provided by the present invention.

[0020] Figure 4 is a schematic diagram of the non-bilinear stress-displacement damage model provided by the present invention.

[0021] Figure 5 is a schematic diagram of the discrete element deformation failure model provided by the present invention.

[0022] Figure 6 is a schematic diagram of the uniaxial compression and Brazilian splitting stress-displacement curves provided by the present invention.

[0023] Figure 7 is a schematic diagram of the uniaxial compression and Brazilian splitting crack characteristics provided by the present invention.

[0024] Figure 8 is a schematic diagram of the position of the PDC cutting tooth at point A of the drill bit provided by the present invention and the rock breaking parameters of the PDC tooth.

[0025] Figure 9 is a schematic diagram comparing the predicted rock cuttings with the rock cuttings at the bottom of the well, provided by the present invention.

[0026] Figure 10 is a schematic diagram comparing the field application results provided by the present invention. Detailed Implementation

[0027] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0028] This invention proposes a method for measuring the particle size of rock cuttings from PDC drill bits in situ at the bottom of the well. First, a rock geometry model capable of reproducing the rock breaking action of PDC drill bits at the bottom of the well is designed using Abaqus. Then, a damage mathematical model suitable for PDC drill bit rock breaking is derived based on typical stress-strain curves of rock breaking. Finally, the rock geometry model and damage mathematical model of PDC drill bit rock breaking are combined to form a numerical simulation and prediction method for the particle size of rock cuttings at the bottom of the well. Through effective parameter calibration of this method, numerical simulation of PDC drill bit rock breaking at the bottom of the well can be achieved. After the simulation, the distribution of rock cuttings particle size at the bottom of the well is statistically analyzed.

[0029] In a specific implementation, the geometric model design for PDC-based rock breaking at the bottom of the well includes: in the Abaqus geometric model, rock is typically represented by a continuum finite element method; discrete elements are pre-set in the continuum mesh, and damage criteria are used to describe the rock failure process. To restore the boundary of the formation rock during in-situ drilling at an infinite distance to the bottom of the well, infinite elements are set around the perimeter and bottom surface of the rock geometric model. This setting can transmit the outgoing stress waves out of the mesh, effectively restoring the far-field boundary conditions of the rock at the bottom of the well. When the drill bit breaks rock at the bottom of the well, except for the fracture surface in contact with the drill bit, the other five surfaces are considered as far-field boundaries, as shown in Figure 1a. Therefore, arranging infinite elements around the perimeter and bottom surface of the finite-discrete element coupled model (the rock region in front of the drill bit) can effectively embed the finite computational domain into an unbounded medium, avoiding the contamination of the stress field of the cutting zone by boundary reflections, and reconstructing the geometry and boundary environment of the rock at the bottom of the well, as shown in Figure 1b. A partial schematic diagram of the finite-discrete element mesh is shown in Figure 1c.

[0030] As shown in Figure 2, rock breaking at the bottom of the well is mainly accomplished by PDC teeth. PDC teeth are added to the bottom-hole rock geometry model (length l, height h, width w), and the cutting speed (v), cutting depth (d), cutting angle (α), and cutting tooth diameter (d) are set according to the field conditions. PDC ), and the formation pressure (P) on the rocks. p ) and drilling fluid column pressure (P w This allows for the design of the geometric model for bottom rock breaking using PDC teeth. Given that, under the condition of a single tooth and the same equivalent linear velocity and cutting depth, straight-line cutting can approximate the local relative motion of rotary cutting, the rotary cutting of PDC teeth is equivalent to straight-line cutting in the simulation.

[0031] In a specific implementation, the derivation of the non-bilinear damage mathematical model includes: In the PDC toothed rock breaking numerical simulation in Abaqus, rock failure is usually described by the traction-separation law and damage model; currently, a bilinear mathematical model is commonly used to calculate the softening process of rock failure, as shown in segment AB in Figure 3a. However, this model is insufficient in characterizing the softening process after peak strength under drilling loads, as shown in segment AB in Figure 3b. As shown in Figure 3c, the rock breaking process can be summarized into three stages: the first stage is the elastic stage (segment OA), in which the rock undergoes elastic deformation under external force and can recover its initial state after unloading; the second stage is the damage initiation point (point A), at which point the stress reaches the peak strength of the rock; the third stage is the post-failure stage (segment AB), in which a macroscopic fracture surface forms inside the rock and produces rock debris, resulting in irreversible failure. Based on the target curve in Figure 3c, the corresponding non-bilinear damage mathematical model is derived and implemented in the PDC toothed rock breaking numerical simulation in Abaqus. This mathematical model is derived from three sets of formulas, describing the three stages of rock fracturing: pre-fracturing (elastic), damage initiation, and damage evolution. Specifically, it converts stress-strain into stress-displacement (linear elastic stage OA) within the Abaqus traction-separation framework, where the nominal stress before fracturing is... and nominal strain Before crack initiation, a linear elastic relationship must be followed, which aligns with the initial stage of PDC toothed rock breaking. This process can be represented as: (1); where, For nominal stress, the normal stress component ( ) and two tangential stress components ( and Composition, MPa; For nominal strain, by normal strain component ( ) and two tangential strain components ( and Composed of dimensions, dimensionless; Let be the elasticity matrix, MPa.

[0032] To facilitate numerical simulation using displacement and to ensure the accuracy of rock cuttings generation calculations in the PDC rock breaking simulation, nominal strain is defined as relative displacement removal based on the initial thickness of the discrete element. The ratio: (2); (3); (4); In formulas (2) to (4) The initial thickness of the discrete element is represented in mm; Relative displacement downwards, in mm; and This represents the relative displacement between two tangential directions, in mm.

[0033] To simulate the rock-breaking process of PDC teeth within the traction-separation framework of Abaqus, the stress-strain stiffness needs to be converted into a stress-displacement stiffness. In numerical simulations, the normal stress and the two tangential stresses are usually considered to be uncoupled, and the following formula is used for the conversion: (5); (6); (7); In formulas (5) to (6) Indicates normal stiffness, MPa / mm; and This represents the shear stiffness in two tangential directions, expressed in MPa / mm.

[0034] Substituting formulas (2) to (7) into formula (1), we get (8); The derived formula (8) gives the linear elastic relationship of discrete elements during PDC rock breaking. This relationship can be directly used in the traction-separation elastic definition of Abaqus, so that the stress-displacement relationship of discrete elements can be expressed in an explicit form, which is consistent with the calculation framework of Abaqus and lays the foundation for subsequent damage and rock cutting formation calculations.

[0035] Specifically, the crack initiation point A (criterion for damage entry): secondary nominal stress criterion.

[0036] The rock damage caused by PDC tooth cutting is due to the combined action of normal stress and two tangential stresses. Therefore, the secondary nominal stress (traction) criterion is adopted as the damage initiation criterion. (9); indicates the critical moment and position at which the PDC tooth cuts rock from the elastic stage to the damage stage, as shown at point A in c of Figure 3. In formula (9) Represents the positive value of the normal stress, in MPa; and Represents two shear stresses, in MPa; Represents the peak intensity of the normal stress, in MPa; and It represents the peak shear strength under two tangential stresses, in MPa.

[0037] Specifically, the damage evolution in the nonlinear phase (segment AB)

[0038] To accurately represent the damage evolution process of segment AB after reaching peak strength under drilling load, as shown in segment AB in Figure 3b, and to derive the non-bilinear damage criterion, the calculation equations need to simultaneously control the curve shape and fracture energy of segment AB until the corresponding discrete element failure is deleted to form cuttings. First, the damage state variables are defined. , The process is monotonically increasing and irreversible, consistent with the actual conditions after rock fracturing. A value greater than 0 and less than 1 indicates that 0 represents no damage and 1 represents complete damage. When the value is 1, the discrete element is deleted as a failure element (i.e., the corresponding rock element is completely destroyed). To better represent segment AB, the stress value is first calculated according to the linear elastic relationship. Then, the actual stress is obtained by subtracting from the residual stiffness. The details are as follows: (10); where, Current actual stress, MPa; The damage state variable is dimensionless. The undamaged stress is calculated according to the linear elastic relationship, in MPa.

[0039] This calculation method can characterize the damage evolution after the peak intensity under drilling load, thus realizing the non-bilinear damage evolution process.

[0040] Specifically, regarding the normal direction ( ) and two tangential components ( and The following formulas (11) to (13) can be used to calculate: (11); (12); (13); In formulas (11) to (13) Represents the current actual normal stress component, in MPa; and This represents the two actual tangential stress components, expressed in MPa. The normal stress component, measured in MPa, is calculated based on the linear elastic constitutive relation. and These represent the two tangential stress components, calculated based on the linear elastic constitutive relation, in MPa. The specific representation is shown in Figure 4.

[0041] When considering fracture energy in the calculation, the damage state variable is... This can be expressed as a mathematical formula: (14); among them, The effective opening displacement corresponding to the damage initiation point, in mm; The effective opening displacement corresponding to complete damage, in mm; The effective traction force at the onset of the injury, in MPa; For effective traction force, MPa; The fracture energy of the discrete element under stress is expressed in N / m. The elastic energy at the onset of damage is expressed in N / m.

[0042] To describe the relative separation displacement under the combined action of normal and tangential directions, an effective displacement is introduced. Its expression is: (15); among them, Indicates effective displacement, in mm; Indicates the positive value of the normal displacement, in mm.

[0043] After deriving the mathematical relationships in the above three stages, the typical stress-strain relationship is transformed into a stress-displacement expression, and a non-bilinear damage evolution is established. By embedding the above mathematical relationships into Abaqus, the PDC toothed rock fracture can be simulated based on this non-bilinear evolution model. The overall form is shown in Figure 4. The stress-displacement relationship under normal stress and shear stress conditions can be divided into three stages: segment OA is the linear elastic stage, point A is the damage initiation point, and segment AB is the "non-bilinear" damage evolution stage. The corresponding opening displacement is ; The corresponding opening displacement is ; and ( ) represent the stiffness of the linear elastic evolution stages under normal stress and two tangential stresses, respectively; The displacement corresponds to complete failure, at which point the rock is completely destroyed under the action of the PDC tooth.

[0044] To facilitate understanding of the process of PDC toothed rock breaking and rock cutting formation in Abaqus using a stress-displacement model, Figure 5 compares the non-bilinear stress-displacement damage model (Figure 5a), the rock damage evolution process (Figure 5b), the theoretical fracture process (Figure 5c), and the cohesive unit damage diagram (Figure 5d).

[0045] The linear elastic stage (OA segment in Figure 5a). Under the action of the PDC teeth, the rock undergoes elastic deformation, and internal microcracks begin to initiate (damage initiation area in Figure 5b). The width of the crack increases with the increase of the applied force (the first blue dashed line interval in Figure 5c), which is reflected in the numerical model as a gradual increase in relative displacement (crack initiation discrete element in Figure 5d). If the stress is unloaded at this time, the stress and displacement in Figure 5a can return to an approximate initial state (crack closure, separation amount approaches 0).

[0046] The crack initiation threshold (point A) is reached. When the stress exerted on the rock by the PDC tooth (point A in Figure 5a, the stress is...) When the secondary nominal stress damage initiation criterion is reached, the rock interior begins to transition from damage initiation to damage evolution (as shown by the middle blue dashed line in Figure 5b), the crack width reaches the reversible extreme value (as shown by the middle blue dashed line in Figure 5c), and the discrete element begins to transition from crack initiation to crack propagation (as shown by the middle blue dashed line in Figure 5d).

[0047] The damage evolution and failure stage after point A (segment AB in Figure 5a). After the rock model is continuously loaded with stress and reaches its peak, the damage evolution is as follows: the stress gradually decreases, and irreversible damage evolution occurs (damage evolution region in Figure 5b). The width of the rock cracks continues to increase (second blue dashed line interval in Figure 5c). The relative displacement of the discrete elements in the rock geometric model increases monotonically (crack propagation discrete element in Figure 5d). When the damage evolution meets the failure condition, the discrete elements are deleted, adjacent finite elements are completely separated, and the set of unfailed elements forms rock debris.

[0048] In the specific implementation, the rock geometry model and PDC tooth parameter calibration are carried out in the following steps: (1) Rock geometry model parameter calibration The field test of this study was carried out in rock strata. Therefore, the parameters of the outcrop rock in Xingcun Town, Haiyang City, Shandong Province were used as the benchmark to calibrate the rock geometry model. Since the rock breaking of PDC teeth is mainly tensile shear failure, the key mechanical parameters were obtained by uniaxial compression and Brazilian splitting experiments and calibrated by numerical simulation.

[0049] First, a finite-discrete element model of the rock was established and material properties were assigned. Then, using the compressive strength, tensile strength, and elastic modulus determined by uniaxial compression and Brazilian splitting experiments as benchmarks, the model parameters were adjusted through iterative calibration. When the stress-displacement curves and crack characteristics of the numerical simulation matched the experimental results, the parameters at that point were taken as the calibration results. The dimensions of the experimental specimen and the model are as follows: uniaxial compression specimen is cylindrical. 25×50 mm (consistent with experimental and simulation results); Brazilian split disk 36 × 18 mm (consistent with experimental and simulation results). The friction coefficient was 0.25 for all numerical simulations. A non-bilinear damage mathematical model was used for rock failure.

[0050] Figure 6 shows the experimental and numerical simulation results of uniaxial compression and Brazilian splitting. The stress-displacement curves of the simulation and experiment agree well. As shown in Figure 7, the numerical simulation crack characteristics of uniaxial compression and Brazilian splitting are highly consistent with the experimental crack characteristics. This indicates that the calibrated rock model parameters are effective. The mechanical parameters are shown in Table 1.

[0051] Table 1 Mechanical parameters

[0052] (2) Parameter calibration of PDC teeth

[0053] Since the hardness of PDC teeth can reach 50-80 GPa, while the compressive strength of hard rock formations is typically only 100-300 MPa, PDC teeth can be considered as rigid bodies and wear can be ignored within a single tooth and finite cutting stroke (this approximation is also used in the literature). The density of PDC is given as 3.51 g / cm³. 3 .

[0054] In a specific implementation, the numerical simulation prediction method for bottom-hole cuttings particle size was verified as follows: Well HX is a development well deployed in a shale gas block in the Sichuan Basin. The numerical simulation prediction method for bottom-hole cuttings particle size was verified in the 2955~3000 m rock layer. A finite-discrete-infinite element bottom-hole rock model and PDC tooth model were established using Abaqus, and the mechanical parameters of the rock and PDC teeth were calibrated respectively. Based on this, the cutting speed (v) and mechanical rotation speed (r) were set according to the field drilling parameters. pm ), depth of cut (d), cutting angle (α), formation pressure (P) p ), cutting tooth diameter (d) PDC Drilling fluid column pressure (P) w Parameters such as (see Table 2). Referring to the approach of Huang et al., the cutting speed is taken as the linear velocity of the center point of the corresponding cutting tooth of the PDC drill bit at point A in Figure 8.

[0055] After setting the rock-breaking parameters, a non-bilinear damage mathematical model was introduced into Abaqus for numerical simulation. After the simulation, the rock cuttings obtained from the numerical simulation were statistically analyzed according to different particle size ranges. To verify the accuracy of the numerical simulation prediction method for bottom-hole rock cuttings particle size, a reverse circulation retrieval basket was used to retrieve bottom-hole rock cuttings from the 2955–3000 m rock layer, while simultaneously collecting the rock cuttings returned to the vibrating screen from this section. The two types of rock cuttings were washed, dried, and their content in each particle size range was determined using a sieving method. Subsequently, classification statistics and corresponding cumulative distribution curves of simulated rock cuttings, bottom-hole rock cuttings, and vibrating screen rock cuttings were plotted sequentially. Error diagrams between simulated rock cuttings and bottom-hole rock cuttings in each particle size range were also plotted, as shown in Figure 9. a and ad represent: bottom-hole rock cuttings classification statistics and corresponding cumulative distribution curves; predicted rock cuttings classification statistics and corresponding cumulative distribution curves; surface rock cuttings classification statistics and corresponding cumulative distribution curves; and error statistics between predicted and bottom-hole rock cuttings, respectively.

[0056] The results in Figure 9 show that the distribution trends of simulated cuttings and bottom-hole cuttings are highly consistent across different particle size ranges; the maximum relative error between the two in each range does not exceed 5%, indicating that the numerical simulation prediction method for bottom-hole cuttings particle size has high accuracy (above 95%) and reliability. Further analysis reveals that the maximum cuttings particle size on the vibrating screen is less than 4 mm, while the maximum cuttings particle size at the bottom of the well is approximately 7–8.5 mm (about twice the former). This shows that the predicted simulated bottom-hole cuttings particle size is generally larger than the surface cuttings particle size. This phenomenon is consistent with actual drilling field conditions, because the bottom-hole cuttings undergo repeated crushing due to tubing compression and wellbore collisions during their return to the vibrating screen, resulting in a smaller particle size at the surface compared to the cuttings at the bottom of the well. This further verifies the rationality of the numerical simulation results.

[0057] Table 2. On-site engineering parameters used in the simulation

[0058] In the specific implementation, the designed well depth of HX well is 4828.89 m. Analysis of construction difficulties in the drilling engineering design indicated that drilling in the Silurian Hanjiadian Formation rock section using conventional drilling fluid carries a risk of sand accumulation and stuck pipe, requiring key prevention measures. When the well reached 3005 m, increased resistance was observed during lifting and lowering, with the drill string torque rising from 20 kN·m to 30 kN·m, exhibiting drastic torque fluctuations and signs of sand accumulation and stuck pipe. To facilitate the drilling operation, a numerical simulation prediction method for the bottom-hole cuttings particle size was used to predict the cuttings particle size at the bottom of the rock section (3005~3015 m). The predicted bottom-hole cuttings particle size distribution and cumulative distribution curves are shown in Figure 10a. The bottom-hole cuttings particle size distribution and cumulative distribution curves for this formation are shown in Figure 10b; the error statistics between the predicted cuttings and the bottom-hole cuttings are shown in Figure 10c; and the numerical simulation results are shown in Figure 10d.

[0059] As shown in Figure 10, the cuttings particle size at the bottom of the well is mainly distributed between 5.5 and 7 mm, with the largest cuttings particle size between 8.5 and 10 mm. The maximum error between the predicted and actual bottom-hole cuttings particle size is 3.31%. Field drilling fluid engineers determined through laboratory experiments that when the drilling fluid density is 1.4–1.6 g / cm³, the dynamic-plastic ratio is >0.17 (plastic viscosity 30–10 mPa·s, dynamic shear force 10–13 Pa), and the flow rate is 26–28 L / s, it has a good cuttings-carrying capacity for the numerical simulation-predicted cuttings particle size. Subsequently, the drilling fluid properties in the mud pit were adjusted accordingly. The comparison of field parameters before and after the adjustment is shown in Table 3.

[0060] Drilling fluid performance continued, and the torque displayed on the drill rig returned to normal, stabilizing at 20-22 kN·m. Lifting and lowering were smooth, and the risk of stuck pipe due to sand buildup was eliminated. This demonstrates that the numerical simulation prediction method based on bottom-hole cuttings particle size can guide the optimization of drilling fluid parameters, effectively avoiding the occurrence of complex situations in the 3005-3015 m section of the well, while reducing reliance on traditional trial-and-error methods and associated costs.

[0061] Table 3 Drilling fluid parameters before and after adjustment based on numerical simulation prediction results of bottom hole cuttings size.

[0062] In summary, (1) based on the idea of ​​improving the rock-carrying capacity according to the rock cuttings particle size at the bottom of the well, a non-bilinear damage mathematical model applicable to PDC tooth-crushed rock was derived, and a bottom rock geometric model that can reconstruct PDC tooth-crushed rock at the bottom of the well was constructed. The parameters of the geometric model were calibrated, and then the non-bilinear damage mathematical model and the geometric model were combined to propose a numerical simulation prediction method for the rock cuttings particle size at the bottom of the well.

[0063] (2) On-site, the numerical simulation prediction method for the particle size of bottom-hole cuttings was verified using actual drilled bottom-hole cuttings. The results showed that the distribution trends of the predicted bottom-hole cuttings and the actual drilled bottom-hole cuttings in each particle size range were highly consistent, and the maximum relative error between the two in each range did not exceed 5%, indicating that the numerical simulation prediction method for the particle size of bottom-hole cuttings has good reliability and accuracy (higher than 95%).

[0064] (3) In well HX, the numerical simulation prediction method for bottom-hole cuttings particle size was used to eliminate the risk of stuck pipe due to sand accumulation. Drilling was stopped when signs of stuck pipe appeared at 3005 m. The numerical simulation prediction method for bottom-hole cuttings particle size was used to predict the particle size. Based on the prediction results, the field engineer adjusted the drilling fluid parameters, eliminating the risk of stuck pipe due to sand accumulation in this section in one go, improving the bottom-hole cuttings carrying capacity, and reducing the reliance on traditional experience and trial and error and the associated costs. The numerical simulation prediction method for bottom-hole cuttings particle size is expected to help ultra-deep and extra-deep wells with large-diameter wells to optimize drilling fluid in a timely manner based on the bottom-hole cuttings particle size, thereby reducing the risk of complex downhole accidents and improving the cuttings carrying capacity.

[0065] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0066] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for measuring the particle size of rock cuttings in situ at the bottom of a PDC drill bit, characterized in that, include: A finite-discrete-infinite element rock model at the bottom of the well is constructed by coupling the finite-discrete element method with the infinite element method. The formation rock at the bottom of the well is regarded as an infinite boundary, and the PDC tooth cutting rock breaking parameters are calibrated and the PDC tooth rock breaking model is modeled. A non-bilinear damage criterion is constructed, and the initial rock cutting particle size at the bottom of the well is measured by the interaction between the finite-discrete-infinite element rock model and the PDC tooth rock breaking model under the non-bilinear damage criterion. The drilling fluid performance is adjusted according to the measured initial rock cutting particle size at the bottom of the well.

2. The method for measuring the particle size of rock cuttings in situ at the bottom of a PDC drill bit according to claim 1, characterized in that, The in-situ finite-discrete-infinite element rock model at the bottom of the well includes a finite-discrete-infinite element mesh model and a node model.

3. The method for measuring the particle size of rock cuttings in situ at the bottom of a PDC drill bit according to claim 1, characterized in that, The construction of the non-bilinear damage criterion includes: using cohesive elements to discretize and connect finite elements to simulate rock fracture, where the stress state at any point in the cohesive element is represented by a normal stress and shear stresses in two directions; determining the stress-strain curves under normal and shear stress conditions, and simplifying the stress-strain curves into two stages: the first stage is the linear elastic stage OA segment, and the second stage is the post-failure stage AB segment, where the stress corresponding to point A is the peak stress, and the rock deforms and fails beyond point A.

4. The method for measuring the particle size of rock cuttings in situ at the bottom of a PDC drill bit according to claim 3, characterized in that, It also includes determining the stress-strain constitutive relationship, strain-displacement relationship, and elastic matrix-stiffness relationship of segment OA; establishing a connection between the force and displacement of discrete elements based on the strain-displacement relationship and the elastic matrix-stiffness relationship; transforming the linear elastic constitutive relationship into a force-displacement relationship; when the rock reaches the peak stress intensity point A, the second nominal stress criterion is used as the judgment standard for damage initiation; damage state variables are introduced to represent the stiffness reduction of cohesive elements; damage calculation is performed initially as if the rock is undamaged; after the rock is damaged, the stress is reduced; after the damage initiation, the form of damage evolution is determined by the damage state variables.

5. The method for measuring the particle size of rock cuttings in situ at the bottom of a PDC drill bit according to claim 4, characterized in that, The discrete element undergoes displacement under the combined action of normal and tangential deformation, with an effective displacement. for: ;in, Indicates the normal stress component, 、 These represent the displacements under the two tangential stress components.

6. The method for measuring the particle size of rock cuttings in situ at the bottom of a PDC drill bit according to claim 5, characterized in that, The displacement of the discrete element under the combined action of normal and tangential deformation also includes, The stress-displacement relationship of the discrete element under both normal and shear stress conditions is divided into three stages: the linear elastic evolution stage of segment OA, the damage initiation stage at point A, and the exponential damage evolution stage of segment AB; among them, This represents the peak intensity of the normal stress, and the opening displacement corresponding to the peak intensity is... This represents the peak shear strength under two shear stresses, and the opening displacement corresponding to the peak shear strength is... ； This represents the stiffness during the linear elastic evolution stage under normal stress. 、 Both represent the stiffness during the linear elastic evolution stage under shear stress; This represents the displacement at which complete failure occurs under normal stress. Both represent the displacement at which complete failure occurs under shear stress.

7. The method for measuring the particle size of rock cuttings in situ at the bottom of a PDC drill bit according to claim 6, characterized in that, Also includes: The constitutive relation of discrete elements under tensile and compressive stress conditions, the damage concept model of discrete elements, the theoretical fracture process zone model, and the fracture process of discrete elements are compared, plotted, and analyzed. In the linear elastic stage, the discrete element develops tiny cracks after being subjected to force, and the displacement gradually increases as the load continues to increase; when the stress of the discrete element reaches... When the cracking reaches the threshold, the discrete element begins irreversible failure; when the discrete element reaches its maximum failure displacement... At this point, the rock is no longer under stress, the failed discrete elements will be deleted, and the finite element will be separated. As the number of failed discrete elements increases, the finite elements that are not destroyed by stress form rock fragments.

8. The method for measuring the particle size of rock cuttings in situ at the bottom of a PDC drill bit according to claim 1, characterized in that, The calibration of PDC tooth cutting rock breaking parameters and the modeling of PDC tooth rock breaking model include: during the PDC tooth rock breaking process, parameter calibration is performed using uniaxial compression simulation and Brazilian splitting; by assigning material properties to the rock model, a finite-discrete element model of the rock is established; the mechanical parameters of the rock are adjusted, and the failure and damage of the rock are performed using a non-bilinear damage criterion to establish a PDC tooth rock breaking model.

9. A PDC drill bit bottom-hole in-situ rock cuttings particle size measurement system, characterized in that, include: The module includes: Finite-Discrete-Infinite Element Rock Model Construction Module: Used to construct an in-situ finite-discrete-infinite element rock model at the bottom of the well by coupling the finite-discrete element method with the infinite element method; Parameter Calibration and Modeling Module: Used to calibrate PDC tooth cutting rock breaking parameters and model the PDC tooth rock breaking model, treating the in-situ formation rock at the bottom of the well as an infinite boundary; Non-Bilinear Damage Criterion Construction Module: Used to construct a non-bilinear damage criterion; Measurement Module: Used to measure the initial cuttings particle size in-situ at the bottom of the well under the non-bilinear damage criterion through the interaction between the in-situ finite-discrete-infinite element rock model and the PDC tooth rock breaking model; Drilling Fluid Performance Adjustment Module: Used to adjust the drilling fluid performance based on the measured initial cuttings particle size in-situ at the bottom of the well.

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