Well drilling vibration measurement and real-time calibration system based on vibration sensor

Abstract

The invention discloses a well drilling vibration measurement and real-time calibration system based on a vibration sensor, and relates to the technical field of data processing. The system comprises a signal measurement part, a signal correction compensation part, a signal analysis part and a signal calibration part, the signal measuring part is used for installing a vibration sensor and an accelerometer near a drill bit or a drill column and generating a fundamental frequency vibration signal; the signal correction compensation part is used for performing stick-slip effect compensation on the fundamental frequency vibration signal to obtain a first compensation signal; calculating the resonant frequency of the drilling system; calculating the bending stress of the drill string; calculating well track deviation; the signal analysis part is used for calculating the dynamic load of the drilling system to obtain the vibration energy dissipation of the drilling system; calculating the system response of the drilling system; and the signal calibration part is used for calculating a calibration coefficient. According to the invention, the precision and calibration capability of vibration signal measurement are significantly improved.

Description

Technical Field

[0001] The present disclosure relates to the technical field of data processing, and in particular to a drilling vibration measurement and real-time calibration system based on a vibration sensor. Background Art

[0002] As the core link of oil and gas resource exploitation, the technical level of drilling engineering directly determines the efficiency and safety of resource exploration and development. During the drilling process, vibration is an important factor affecting the performance of the drilling system. Vibration problems include longitudinal vibration, lateral vibration, torsional vibration and coupling phenomena of various vibration forms. These vibrations not only cause mechanical loss to the drill bit, drill string and related equipment, but also affect the stability of the wellbore trajectory and the safety of drilling operations. Therefore, the research and application of drilling vibration measurement and real-time calibration technology has become a key area in modern drilling engineering.

[0003] At present, a variety of technical solutions have been proposed and applied in engineering practice for the measurement and analysis of drilling vibration. Common vibration monitoring technologies mainly rely on vibration sensors and accelerometers installed near the drill bit or drill string. These devices can collect three-axis acceleration signals generated during the drilling process in real time. These signals are used to extract the main frequency components and vibration amplitudes through signal processing technology, thereby providing data support for the monitoring of drilling status. For example, fast Fourier transform (FFT) is widely used in the spectrum analysis of drilling vibration signals, which can accurately extract the main vibration frequencies of the drilling system. In addition, some drilling companies have also adopted multi-sensor fusion technology to improve the spatial resolution and measurement accuracy of vibration monitoring by comprehensively processing the data of multiple vibration sensors.

[0004] However, the existing technology still has many problems and shortcomings in practical applications. First, most traditional vibration monitoring methods focus on the signal acquisition and preliminary processing stages, and lack effective countermeasures for the nonlinear interference problem in the vibration signal. For example, in the drilling process, the stick-slip effect is one of the main factors causing vibration signal distortion. This effect is caused by the complex friction behavior between the drill string and the well wall, resulting in intermittent jumps and nonlinear fluctuations in the vibration signal. The existing technology usually removes high-frequency noise in the signal through empirical filters or simple low-pass filtering methods, but these methods are difficult to effectively compensate for the nonlinear characteristics of the stick-slip effect, resulting in signal processing results deviating from the actual situation. Secondly, the existing technology lacks in-depth analysis and real-time adjustment capabilities for the resonance phenomenon of the drilling system. The resonance phenomenon is a common and dangerous vibration mode in the drilling process. When the resonant frequency of the system approaches or exceeds its natural frequency, the vibration amplitude will be significantly amplified, which may cause fatigue or even fracture of the drill string. Although the existing technology can identify the resonant frequency through spectrum analysis, since spectrum analysis is an offline process, it is impossible to track frequency changes in real time, and it is difficult to adjust drilling parameters in time to avoid resonance. Summary of the invention

[0005] The present invention provides a drilling vibration measurement and real-time calibration system based on a vibration sensor, which solves the deficiencies of the prior art in nonlinear interference processing, resonance frequency monitoring, trajectory deviation prediction and signal calibration. Its systematic and comprehensive nature significantly improves the accuracy and efficiency of drilling vibration management, and provides an efficient and reliable technical solution for modern drilling engineering.

[0006] The technical solution of the present invention is achieved in this way: The drilling vibration measurement and real-time calibration system based on a vibration sensor comprises: a signal measurement part, a signal correction and compensation part, a signal analysis part and a signal calibration part; the signal measurement part is used to install a vibration sensor and an accelerometer near a drill bit or a drill string, respectively record three-axis acceleration signals, and generate a fundamental frequency vibration signal according to the three-axis acceleration signals; the signal correction and compensation part is used to compensate the stick-slip effect of the fundamental frequency vibration signal to obtain a first compensation signal; the resonance frequency of the drilling system is calculated according to the first compensation signal; the bending stress of the drill string is calculated according to the resonance frequency of the drilling system; the wellbore trajectory deviation is calculated according to the bending stress of the drill string; the signal analysis part is used to calculate the dynamic load of the drilling system based on the output results of the signal measurement part and the signal correction and compensation part, so as to evaluate the vibration energy dissipation of the drilling system and obtain the vibration energy dissipation of the drilling system; the system response of the drilling system is calculated according to the vibration energy dissipation; the signal calibration part is used to calculate a calibration coefficient according to the system response, the resonance frequency of the drilling system, the vibration energy dissipation and the trajectory deviation, and multiply the fundamental frequency vibration signal by the calibration coefficient to obtain a calibrated vibration signal.

[0007] Furthermore, the signal measurement part generates a fundamental frequency vibration signal according to the three-axis acceleration signal, and the process specifically includes: sampling the three-axis acceleration signal to obtain a sampling signal; the sampling frequency is at least twice the vibration frequency of the drill bit; the synthetic acceleration amplitude is calculated according to the sampled three-axis acceleration signal as the amplitude of the fundamental frequency signal; the frequency of the fundamental frequency signal is calculated using the real-time rotation speed of the drill bit; the fundamental frequency signal is modulated using the drilling fluid pulsation frequency to form an actual vibration characteristic; and the drilling pressure and the moment of inertia of the drill bit are introduced to perform an exponential attenuation correction on the fundamental frequency signal to obtain the final fundamental frequency vibration signal.

[0008] Furthermore, the fundamental frequency vibration signal is expressed using the following formula: ; in, is the rotation frequency of the drill bit; is the triaxial acceleration component of the drill bit in the X-axis direction; is the triaxial acceleration component of the drill bit in the Y-axis direction; is the three-axis acceleration component of the drill bit in the Z-axis direction; is drilling pressure; For time; is the moment of inertia of the drill bit; is the drilling fluid pulsation frequency; is the fundamental frequency vibration signal.

[0009] Furthermore, the signal correction and compensation part uses the following formula to perform stick-slip effect compensation on the fundamental frequency vibration signal to obtain a first compensation signal: ; in, is the first compensation signal; is the dynamic friction coefficient, which represents the characteristic parameter of the friction force between the drill bit and the formation during relative sliding; is the static friction coefficient, which indicates the friction characteristics between the drill bit and the formation in a static state, which is greater than the dynamic friction coefficient; is the instantaneous speed of the drill bit; is the characteristic speed, is the set value; It is the maximum torsional moment of the drill bit under the action of drilling pressure and friction; is the torsional stiffness of the drill string; is the angular displacement difference between the two ends of the drill string, and is the torsion angle difference between the upper and lower ends of the drill string, which is used to characterize the degree of torsional deformation of the drill string; is the equivalent circulating density, is the set value, the greater the equivalent circulating density, the higher the stability of the drill string; is the formation pressure.

[0010] Furthermore, the signal correction and compensation part calculates the resonant frequency of the drilling system according to the first compensation signal using the following formula: ; in, is the resonant frequency of the drilling system; is the equivalent stiffness of the drilling system; is the equivalent mass of the drilling system; is the damping coefficient, which represents the dissipation effect of the drill string material and drilling fluid on the vibration energy; is the drill string length.

[0011] Furthermore, the signal correction and compensation part uses the following formula to calculate the drill string bending stress according to the resonant frequency of the drilling system: ; in, is the elastic modulus of the drill string material; The outer diameter of the drill string determines the bending stiffness of its cross section. The larger the outer diameter, the stronger the bending resistance. It is the lateral displacement of the drill string in the Z-axis direction, describing the lateral deviation of the drill string due to external forces, vibrations and wellbore bending; is the coordinate variable in the Z-axis direction; is the critical frequency, which is the first natural frequency of the drill string and reflects its lowest vibration mode. When the resonance frequency approaches or exceeds the critical frequency, the bending stress will increase. is the material density of the drill string; is the cross-sectional area of ​​the drill string; is the section moment of inertia of the drill string; is the drilling string bending stress; the wellbore trajectory deviation is calculated according to the drilling string bending stress by the following formula: : ; in, is the length of the bottom portion of the drill string; The well inclination angle indicates the inclination angle of the wellbore and reflects the degree to which the wellbore trajectory deviates from the vertical direction; is the maximum well inclination change rate; is the uniaxial compressive strength of the formation; is the reference formation strength, is the set value; is the drilling fluid pressure; is the drill bit area.

[0012] Furthermore, the signal analysis part calculates the dynamic load of the drilling system based on the output results of the signal measurement part and the signal correction and compensation part through the following formula: : ; in, is the axial tension on the top of the drill string; the vibration energy dissipation of the drilling system is evaluated by the following formula, and the vibration energy dissipation of the drilling system is obtained : ; in, is the damping coefficient of drilling fluid.

[0013] Furthermore, the signal analysis part calculates the system response of the drilling system according to the vibration energy dissipation through the following formula: : ; in, is the damping ratio of the drilling system; is the natural angular frequency of the drilling system, which means the angular frequency of free vibration under undamped conditions.

[0014] Furthermore, the signal calibration part calculates the calibration coefficient according to the system response, the resonant frequency of the drilling system, the vibration energy dissipation and the trajectory deviation through the following formula: : ; in, Represents the magnitude of the system response.

[0015] The drilling vibration measurement and real-time calibration system based on the vibration sensor of the present invention has the following beneficial effects: The signal measurement part of the present invention collects the three-axis acceleration signal through the vibration sensor and accelerometer installed near the drill bit or drill string, and ensures the signal integrity through high-frequency sampling. Compared with the traditional low sampling rate method, the present invention ensures the capture of high-frequency vibration characteristics and avoids signal distortion. At the same time, by calculating the composite amplitude of the three-axis acceleration signal, the signal representation is simplified, the directional redundancy problem is eliminated, and more physically meaningful basic data is provided for subsequent signal processing.

[0016] In addition, the signal is modulated and corrected in combination with the drill bit rotation frequency and the drilling fluid pulsation frequency, so that the measurement results can reflect the actual vibration behavior of the drilling system, laying a data foundation for the efficient operation of the entire system. The present invention introduces a nonlinear compensation model of the stick-slip effect in the signal correction and compensation part, which effectively solves the problem of insufficient stick-slip vibration processing capabilities in traditional methods. Through the coupling model of static friction coefficient, dynamic friction coefficient and drill bit speed, the dynamic influence of the stick-slip effect on the vibration signal is accurately captured, and the nonlinear distortion in the original vibration signal is corrected by the compensation signal. This compensation method fully considers the combined effects of the drill string torsional stiffness, angular displacement difference and formation pressure, so that the corrected signal is closer to the actual working condition, significantly improving the accuracy and reliability of signal processing.

[0017] The present invention realizes dynamic correction of vibration signals through the calibration coefficient formula of multi-parameter coupling in the signal calibration part. Taking into account various factors such as system response, resonant frequency, energy dissipation and trajectory deviation, the calibration parameters can be adaptively adjusted to ensure that the signal always matches the actual working conditions. Compared with the traditional static calibration method, the dynamic calibration capability of the present invention significantly enhances the adaptability of the system under complex drilling conditions. For example, when the resonant frequency approaches the critical frequency or the trajectory deviation increases, the calibration coefficient can reduce the signal amplitude in real time, avoid signal distortion or overload, and improve the accuracy of signal output. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 A schematic diagram of the system structure of a vibration sensor-based drilling vibration measurement and real-time calibration system provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0019] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present disclosure clearer and more understandable, the present disclosure is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present disclosure and are not used to limit the present disclosure.

[0020] Example 1, reference Figure 1 :A drilling vibration measurement and real-time calibration system based on a vibration sensor comprises: a signal measurement part, a signal correction and compensation part, a signal analysis part and a signal calibration part; the signal measurement part is used to install a vibration sensor and an accelerometer near a drill bit or a drill string, respectively record three-axis acceleration signals, and generate a fundamental frequency vibration signal according to the three-axis acceleration signals; the signal correction and compensation part is used to compensate the stick-slip effect of the fundamental frequency vibration signal to obtain a first compensation signal; the resonance frequency of the drilling system is calculated according to the first compensation signal; the bending stress of the drill string is calculated according to the resonance frequency of the drilling system; the wellbore trajectory deviation is calculated according to the bending stress of the drill string; the signal analysis part is used to calculate the dynamic load of the drilling system based on the output results of the signal measurement part and the signal correction and compensation part, so as to evaluate the vibration energy dissipation of the drilling system and obtain the vibration energy dissipation of the drilling system; the system response of the drilling system is calculated according to the vibration energy dissipation; the signal calibration part is used to calculate the calibration coefficient according to the system response, the resonance frequency, vibration energy dissipation and trajectory deviation of the drilling system, and the calibration coefficient is multiplied by the fundamental frequency vibration signal to obtain a calibrated vibration signal.

[0021] Specifically, during the drilling process, due to the complex formation structure, high-speed rotation of the drilling tool and the nonlinear mechanical characteristics of the drill string, the system will produce significant vibration phenomena. There are various forms of vibration, including longitudinal vibration, lateral vibration, torsional vibration and the coupling phenomenon of these vibration forms. Therefore, the signal measurement part adopts a three-axis measurement scheme through the vibration sensors and accelerometers arranged near the drill bit or drill string, that is, the components of the vibration signal in the three orthogonal directions of x, y and z are measured simultaneously to ensure the capture of the global information of the vibration. The three-axis acceleration signal not only contains the information of the vibration amplitude, but also carries the characteristic data of the vibration direction and frequency. This information is of great significance for analyzing the vibration characteristics of the drilling system. In order to extract the core characteristics of the vibration, the signal measurement part needs to separate the fundamental frequency vibration signal from the original three-axis acceleration signal through signal processing technology. The fundamental frequency vibration signal is the dominant frequency component of the system vibration and reflects the main dynamic characteristics of the system under the current working conditions. In the signal extraction process, the spectrum analysis method based on fast Fourier transform (FFT) is usually used to convert the acceleration signal in the time domain to the frequency domain space, so as to identify the dominant frequency components in the vibration signal. Specifically, by analyzing the energy distribution of frequency domain signals, the baseband signal can be accurately extracted and unnecessary high-frequency noise and background interference can be filtered out.

[0022] The uniqueness of the signal measurement part is that it needs to ensure the accuracy and reliability of the measurement results in a high-noise, high-interference drilling environment. Strong mechanical vibrations and complex environmental factors during drilling, such as temperature changes, tool friction, and fluid dynamic effects, will affect the performance of vibration sensors. Therefore, the signal measurement part not only relies on the high sensitivity and anti-interference ability of the hardware sensor, but also needs to pre-process the signal through real-time software algorithms. The preprocessing steps include zero drift calibration, signal denoising, and sensor array data fusion to eliminate the negative impact of environmental interference on vibration measurement. In addition, the signal measurement part is also carefully designed in terms of hardware layout. Vibration sensors and accelerometers are usually installed close to the vibration source, such as the drill bit or the key nodes of the drill string, so that the vibration signal can be captured to the maximum extent, while ensuring the stability of the sensor through high-precision installation technology. Considering the rotation of the drill string and the non-uniformity of the tool during drilling, the signal measurement part may also need motion compensation to eliminate measurement errors caused by drill string rotation and nonlinear displacement.

[0023] The stick-slip effect is one of the main sources of interference in drilling vibration signals. It is a nonlinear phenomenon caused by the complex friction and dynamic interaction between the drill string and the wellbore wall. This effect often manifests itself as intermittent changes or irregular jumps in the vibration signal, which not only affects the stability of the vibration signal, but also significantly changes the frequency component of the vibration, resulting in signal distortion. The first step in the signal correction and compensation part is to compensate for the stick-slip effect. This is usually achieved by introducing a stick-slip model, which is based on experimental data and drilling dynamics theory and can accurately describe the impact of the stick-slip effect on the signal. By real-time monitoring of the waveform characteristics of the vibration signal, such as changes in amplitude, frequency, and phase, the correction and compensation module can identify the main characteristics of the stick-slip effect and compensate it using model parameters. The compensated signal restores more of the original vibration characteristics, laying the foundation for further analysis.

[0024] After the stick-slip effect compensation is completed, the signal correction and compensation part also needs to analyze and calculate the resonant frequency of the drilling system. The resonant frequency is a key parameter that reflects the dynamic characteristics of the system. It is determined by the stiffness and mass distribution of the drilling system. In the spectrum of the vibration signal, the resonant frequency often shows a significant concentration of energy. However, in a complex drilling environment, the resonant frequency may be affected by changes in the drill string structure, load conditions, and environmental interference. Therefore, its accurate calculation requires a combination of actual working conditions and dynamic models. The signal correction and compensation part dynamically adjusts the estimated results of the resonant frequency by inputting the compensated signal into the resonant frequency calculation module and using the inherent characteristics of the drilling system and real-time signal characteristics. This process can not only improve the calculation accuracy of the resonant frequency, but also dynamically track the frequency drift caused by changes in the drill string length or environmental disturbances during the drilling process. The determination of the resonant frequency provides the necessary conditions for further calculating the bending stress of the drill string. The bending stress in drilling vibration is determined by the bending moment caused by vibration and the geometric characteristics of the drill string. It is an important indicator reflecting the health of the drill string structure. The signal correction and compensation part uses the compensated vibration signal and resonant frequency to calculate the distribution of bending stress through a dynamic analysis model. The calculation of bending stress usually requires combining the amplitude and frequency characteristics of the vibration signal with the material and geometric parameters of the drill string. The calculation results can be used to evaluate the bearing capacity of the drill string under dynamic loads and predict its possible fatigue damage or structural deformation.

[0025] On the basis of bending stress calculation, the signal correction and compensation part also needs to analyze the impact of vibration on the wellbore trajectory. Wellbore trajectory deviation is a key issue in drilling engineering, which is directly related to the realization of drilling goals and the safety of the wellbore. Since drill string vibration may cause nonlinear movement of the drill bit, resulting in deviation of the wellbore trajectory, the signal correction and compensation part estimates the deviation range of the wellbore trajectory through comprehensive analysis of vibration signals and bending stress. This process is usually carried out in combination with the motion model of the drill bit and the geometric constraints of the wellbore, and the output results can provide data support for real-time trajectory adjustment. The output of the signal correction and compensation part is not a single compensation signal, but a multi-dimensional data set, including compensated vibration signals, resonant frequencies, bending stresses, and wellbore trajectory deviations. These data not only provide a variety of inputs for subsequent signal analysis and calibration, but also lay the foundation for the dynamic optimization of the entire system through a comprehensive description of drilling vibration characteristics and system responses. The drilling process is a dynamically changing process, and the characteristics of the vibration signal and environmental parameters may change significantly in a short period of time. Therefore, the signal correction and compensation part needs to have efficient computing power and fast response capabilities to adapt to complex and changing drilling conditions. In addition, through the organic combination of stick-slip effect compensation, resonance frequency calculation, bending stress analysis and trajectory deviation estimation, the signal correction and compensation part not only realizes the comprehensive correction of the vibration signal, but also provides a solid data foundation for the dynamic optimization and safe operation of the entire system.

[0026] During the drilling process, vibration will impose periodic and non-periodic dynamic loads on the drill string, drill bit and related equipment, which directly affect the stability of the drilling system and the service life of the tool. The signal analysis part accurately calculates the dynamic loads acting on each component of the system through the compensated three-axis acceleration signal combined with the mass parameters of the drill string and drill bit. This process is not just a direct application of physical formulas, but a complex multivariable calculation problem, because in the actual drilling environment, the distribution of dynamic loads is often affected by multiple factors such as the system resonant frequency, vibration mode and drilling conditions. By comprehensively considering these factors, the signal analysis part can restore the amplitude, direction and distribution characteristics of the dynamic load with high accuracy, thereby providing data support for judging the stress state of the system. Based on the calculation of dynamic loads, the signal analysis part further evaluates the vibration energy dissipation of the drilling system. Vibration energy dissipation is an important indicator to measure the energy conversion efficiency and vibration stability of the system. It reflects the process in which vibration energy in the drilling system is consumed in various forms (such as friction, impact and material internal friction). In actual calculations, the signal analysis part will first estimate the total energy of the system vibration by analyzing the time series of the vibration signal; then, combined with the mechanical characteristics and material properties of the drilling tool, the specific distribution of energy dissipation is calculated. Energy dissipation analysis can not only reveal the potential impact of vibration on system efficiency, but also identify the main vibration modes that may cause energy loss, such as high-frequency resonance or nonlinear stick-slip vibration. In addition, the energy dissipation results can also be used to evaluate the fatigue of the drill string and drill bit, thereby providing a basis for the maintenance and replacement of drilling tools.

[0027] With the in-depth analysis of dynamic loads and energy dissipation, another key task of the signal analysis part is to calculate the dynamic response of the drilling system. The dynamic response is a comprehensive description of the overall behavior of the system under vibration, including the stability, response speed and frequency characteristics of the system. In this process, the signal analysis part combines the aforementioned dynamic load and energy dissipation results, and simulates and predicts the response characteristics of the system through the dynamic model of the drilling system. For example, by analyzing the amplitude response of the system under vibration of different frequencies, the resonance state of the system can be determined and whether it is in a dangerous condition; by calculating the transient response characteristics of the system under a specific load, the deformation trend of the drill string and the motion trajectory of the drill bit can be predicted. These analysis results have direct guiding significance for the safety of system operation and drilling efficiency. Another important function of the signal analysis part is to integrate the results of dynamic loads, energy dissipation and dynamic response to form a global evaluation of the operating status of the drilling system. This evaluation not only provides a detailed description of the current working conditions, but also provides a reliable basis for real-time optimization and dynamic adjustment of the system. For example, if the analysis results show that a certain frequency of vibration causes significant energy dissipation and abnormal dynamic response, the system can adjust the drill bit speed or drilling parameters in real time to reduce the vibration intensity and improve system performance. In addition, through the long-term trend analysis of dynamic loads, the signal analysis part can also predict the structural risks that the system may face, such as fatigue fracture of the drill string or premature wear of the drill bit, thereby providing support for taking preventive measures in advance. The implementation of the signal analysis part requires the help of advanced algorithms and efficient computing power. In practical applications, this module usually relies on the combination of signal processing technology and numerical simulation methods. For example, in order to extract the key characteristics of the vibration signal, the signal analysis part will apply advanced signal processing methods such as wavelet transform or short-time Fourier transform, which can effectively identify the time-frequency characteristics of the signal and reveal the implicit dynamic characteristics. In addition, in order to ensure the real-time nature of the analysis results, the signal analysis part also needs to accelerate the processing process through parallel computing and efficient algorithm optimization to ensure that it can maintain sufficient response speed in the rapid dynamic changes of the drilling system.

[0028] The working principle of the signal calibration part is based on a closed-loop feedback control system. This system uses the system's dynamic response, resonant frequency, vibration energy dissipation, and trajectory deviation as input parameters, and calculates a calibration coefficient suitable for the current working condition through weight distribution and model optimization. The core function of the calibration coefficient is to eliminate the measurement errors caused by sensor characteristics, environmental interference, and nonlinear vibration effects, so that the corrected vibration signal is closer to the actual vibration state of the drilling system. In a complex drilling environment, this real-time calibration is particularly important because the motion characteristics of the drill string, the interaction between the drill bit and the formation, and the dynamic behavior of the system may change significantly over time, and these changes will directly affect the accuracy of the vibration signal. The signal calibration part first uses the system response data to perform a baseline adjustment on the overall amplitude and frequency characteristics of the vibration signal. The system response reflects the dynamic characteristics of the drilling system under the current working conditions. By comparing with historical data and model prediction results, the global errors that may exist in the vibration signal can be identified. This stage of calibration mainly relies on data fitting and pattern recognition algorithms, which can complete preliminary adjustments in a very short time and provide a basis for subsequent more refined calibration. During this process, the signal calibration part will also refer to the analysis results of the resonance frequency and vibration energy dissipation to ensure that the calibrated signal can accurately reflect the current main vibration mode and energy distribution characteristics.

[0029] After the initial calibration is completed, the signal calibration part will further refine the calibration by combining the calculation results of trajectory deviation and bending stress. Trajectory deviation directly reflects the actual impact of vibration in the drilling system, such as changes in the borehole trajectory caused by drill string bending or drill bit deviation. In the signal calibration part, these deviation data are used to correct the directionality and phase characteristics of the vibration signal, so as to ensure that the calibrated signal is not only accurate in amplitude, but also can truly reproduce the spatial distribution of vibration. At the same time, the calculation results of bending stress are used to calibrate the local characteristics of the signal, such as abnormally high amplitude or low-frequency drift that may appear in certain frequency bands. These characteristics are often closely related to the structural characteristics and load conditions of the drill string. Another important function of the signal calibration part is to ensure that the entire system can maintain high-precision operation under dynamic conditions by calculating and applying calibration coefficients in real time. This real-time performance depends on highly optimized algorithms and fast computing capabilities. The signal calibration part needs to complete the comprehensive analysis of multiple parameters and the generation of calibration coefficients in a very short time, and immediately feed back the corrected signal to the system output. Through this closed-loop control mechanism, the signal calibration part can continuously maintain efficient correction of vibration signals in the rapid changes of the drilling environment, avoiding analysis deviations and decision-making errors caused by signal distortion. The generation of calibration coefficients is a highly complex process that requires comprehensive consideration of the drilling system's dynamic model, vibration characteristics, environmental conditions, and multiple input parameters of the measurement and analysis modules. The signal calibration part usually uses machine learning or optimization algorithms to model and weight these parameters to ensure that the generation of calibration coefficients can adapt to diverse drilling conditions. For example, through the learning of historical data and the feedback of real-time data, the system can gradually optimize the calculation model of the calibration coefficients, thereby achieving higher calibration accuracy in subsequent operations. In addition, the adaptive nature of the calibration coefficients also enables the signal calibration part to cope with signal anomalies under extreme environmental conditions, such as sensor failure or severe vibration interference.

[0030] Embodiment 2: The process of generating a fundamental frequency vibration signal according to a three-axis acceleration signal by a signal measurement part specifically includes: sampling the three-axis acceleration signal to obtain a sampling signal; the sampling frequency is at least twice the vibration frequency of the drill bit; the synthetic acceleration amplitude is calculated according to the sampled three-axis acceleration signal as the amplitude of the fundamental frequency signal; the frequency of the fundamental frequency signal is calculated using the real-time rotation speed of the drill bit; the fundamental frequency signal is modulated using the drilling fluid pulsation frequency to form an actual vibration characteristic; and the drilling pressure and the moment of inertia of the drill bit are introduced to perform an exponential attenuation correction on the fundamental frequency signal to obtain a final fundamental frequency vibration signal.

[0031] Specifically, the vibration sensor on the drill bit or drill string will capture the three-axis acceleration signals in real time, which record the vibration characteristics of the drill bit in three orthogonal directions. In order to ensure the integrity of signal acquisition and avoid aliasing effects, the sampling frequency is set to at least twice the vibration frequency of the drill bit, which conforms to the Nyquist sampling theorem. Through this high-frequency sampling, it is possible to ensure that the high-frequency components in the signal are not lost, thereby capturing the detailed characteristics of the vibration. Next, the synthetic acceleration amplitude is calculated based on the sampled three-axis acceleration signal. This process synthesizes the vibration components in the three directions into a scalar signal to represent the overall intensity of the vibration. Specifically, the synthetic acceleration amplitude is obtained by vector modulus of the acceleration signal, which can reflect the change of the vibration amplitude of the drill bit over time. This amplitude calculation method not only simplifies the complexity of signal processing, but also eliminates redundant information in the vibration direction, making the signal more physically meaningful.

[0032] After obtaining the amplitude of the baseband signal, the frequency of the baseband signal is calculated using the real-time rotation speed of the drill bit. The vibration frequency of the drill bit is closely related to its rotation speed, because the drill bit is subjected to periodic forces during rotation, thereby forming the main frequency of the baseband vibration signal. The signal measurement part can dynamically adjust the frequency parameters of the baseband signal by measuring the real-time rotation speed obtained by the sensor or estimating the algorithm, so that the generated signal is closer to the actual working condition. In order to further reflect the real vibration characteristics during the drilling process, this embodiment introduces the drilling fluid pulsation frequency to modulate the baseband signal. When the drilling fluid circulates in the drill string, regular pressure pulsations will be generated, and these pulsations will be superimposed on the vibration of the drill bit to form a more complex vibration mode. By using the drilling fluid pulsation frequency as a modulation signal to modulate the amplitude and frequency of the baseband vibration signal, the vibration behavior of the drill bit in the actual drilling environment can be more accurately reproduced. In addition, in order to further improve the physical significance and engineering applicability of the baseband signal, this embodiment also considers the influence of drilling pressure and drill bit moment of inertia on the vibration signal. The drilling pressure is the axial force applied to the drill bit during the drilling process, while the moment of inertia of the drill bit determines the dynamic response characteristics of the drill bit when it rotates. Since these two parameters have a significant impact on the amplitude and frequency attenuation characteristics of the drill bit vibration, the signal measurement part introduces an exponential decay model to correct the baseband signal. This exponential decay correction can well simulate the natural attenuation process of the vibration energy of the drill bit in a complex mechanical environment, thereby generating a vibration signal that is closer to the real physical phenomenon.

[0033] Embodiment 3: The fundamental frequency vibration signal is expressed using the following formula: ; in, is the rotation frequency of the drill bit; is the triaxial acceleration component of the drill bit in the X-axis direction; is the triaxial acceleration component of the drill bit in the Y-axis direction; is the three-axis acceleration component of the drill bit in the Z-axis direction; is drilling pressure; For time; is the moment of inertia of the drill bit; is the drilling fluid pulsation frequency; is the fundamental frequency vibration signal.

[0034] Specifically, the core idea reflected in the formula is that the main frequency characteristics of the drill bit vibration signal are determined by its rotational motion, which is determined by the rotation frequency of the drill bit. It directly connects the dominant characteristics of drilling dynamics behavior and signals. The rotation frequency of the drill bit is the basic parameter driven by the drilling rig, and its frequency directly reflects the number of rotations of the drill bit per second. Convert to frequency per second The formula not only captures the periodic characteristics of the vibration signal, but also provides an important basis for the subsequent signal frequency and amplitude calculation. During the drilling process, the rotation of the drill bit not only produces rotational motion, but also induces periodic mechanical disturbances, such as periodic changes in friction and contact forces. These disturbances are recorded by sensors and form the basis of the vibration signal. Combined with the drill bit rotation frequency is the composite amplitude of the triaxial acceleration signal , which is used as the amplitude factor of the signal in the formula. The three-axis acceleration signals represent the vibration components of the drill bit in the three orthogonal directions of X, Y, and Z, respectively, and the composite amplitude is the overall vibration intensity calculated by the vector modulus of the three-axis acceleration. The physical significance of this processing step is that the composite amplitude of the three-axis acceleration signal can remove directional redundant information, uniformly express the global amplitude characteristics of the drill bit vibration, and retain the energy characteristics of the signal. In the actual drilling environment, due to the dynamic changes in the vibration direction and intensity, a single-direction signal may be difficult to fully describe the vibration behavior. By calculating the composite amplitude, the amplitude characteristics directly related to the vibration energy can be extracted, making the signal more physically meaningful.

[0035] In addition, the exponential decay term introduced in the formula Describes the natural attenuation process of vibration signals. The physical principle of this part comes from the dissipation mechanism of vibration energy in the system. During the drilling process, the vibration energy of the drill bit gradually decays mainly through contact with the bottom formation, internal damping of the drill string, and the dynamic effect of the drilling fluid. The rate of this energy decay is related to the drilling pressure. and the drill bit's moment of inertia The drilling pressure is the axial force applied to the drill bit, and its magnitude directly affects the contact strength between the drill bit and the bottom of the well, thereby accelerating the dissipation of vibration energy. On the other hand, the moment of inertia determines the inertial characteristics of the drill bit to rotational changes. The larger the inertia, the slower the energy dissipation rate. In the formula, this exponential decay model is expressed through the time variable The exponential decrease of the vibration signal over time vividly reproduces the dynamic attenuation law of drill bit vibration. Then through the sinusoidal modulation term It reflects the influence of the external environment on the fundamental frequency vibration signal. The drilling fluid will produce periodic pressure fluctuations during the circulation process. This fluctuation is transmitted to the drill bit through the drilling system, forming an additional vibration component. By introducing the modulation term in the formula, this complex dynamic characteristic can be effectively superimposed on the fundamental frequency vibration signal, making the signal generation closer to the actual working conditions. For example, when the drilling fluid flow rate changes, its pulsation frequency will also change, thereby introducing additional dynamic characteristics into the signal. This modulation effect not only enriches the spectral characteristics of the signal, but also enhances the sensitivity of the signal to environmental changes, making the generated vibration signal more realistic and physically consistent.

[0036] Embodiment 4: The signal correction and compensation part uses the following formula to perform stick-slip effect compensation on the fundamental frequency vibration signal to obtain a first compensation signal: ; in, is the first compensation signal; is the dynamic friction coefficient, which represents the characteristic parameter of the friction force between the drill bit and the formation during relative sliding; is the static friction coefficient, which indicates the friction characteristics between the drill bit and the formation in a static state, which is greater than the dynamic friction coefficient; is the instantaneous speed of the drill bit; is the characteristic speed, is the set value; It is the maximum torsional moment of the drill bit under the action of drilling pressure and friction; is the torsional stiffness of the drill string; is the angular displacement difference between the two ends of the drill string, and is the torsion angle difference between the upper and lower ends of the drill string, which is used to characterize the degree of torsional deformation of the drill string; is the equivalent circulating density, is the set value, the greater the equivalent circulating density, the higher the stability of the drill string; is the formation pressure.

[0037] Specifically, the stick-slip effect is a nonlinear vibration phenomenon that is common in the drilling process. Its essence is due to the change in friction between the drill bit and the formation. The friction compensation term in the formula is the core part of the stick-slip effect modeling. It is calculated by the static friction coefficient. , dynamic friction coefficient , and instantaneous speed of the drill bit and characteristic velocity The dynamic description of the conversion relationship between static and dynamic friction is a combination of the two. When the drill bit is at rest relative to the formation, the friction is mainly composed of When the drill bit enters the sliding state, the friction force transitions to The dynamic friction range of the control. The exponential decay term in the formula This accurately describes the transition process, and its physical meaning is: as the drill speed As the friction force increases, it gradually changes from static friction characteristics to dynamic friction characteristics, thus inducing nonlinear dynamic changes in stick-slip vibration. This speed-dependent friction behavior constitutes the fundamental dynamic characteristic of the stick-slip effect. At the same time, the torsional deformation effect of the drill string is also included in the compensation model through the denominator in the formula. The torsional stiffness of the drill string and the angular displacement difference between the two ends Together they describe the deformation behavior of the drill string under torsional loading, where It reflects the angular displacement difference between the upper and lower ends of the drill string and is an important parameter for measuring the torsional deformation of the drill string. When the elastic deformation of the drill string directly affects the transmission efficiency of the friction force, and modulates the amplitude and frequency characteristics of the vibration signal. Through the torsional mechanics model in the denominator, the formula closely combines the elastic and torsional dynamic behavior of the drill string with the friction characteristics of the drill bit, and can more accurately capture the dynamic characteristics of the stick-slip effect under different working conditions.

[0038] In addition, the formula also takes into account the influence of formation fluid dynamics, through the parameter and The regulation of drilling fluid and formation pressure on vibration signals is described. It is a comprehensive indicator of the drilling fluid flowing in the wellbore, reflecting the density, flow rate and flow characteristics of the drilling fluid. When the pressure increases, the damping effect of the drilling fluid on the drill string and drill bit is enhanced, which can significantly improve the overall stability of the drill string and inhibit the stick-slip effect to a certain extent. is a reaction force parameter that directly reflects the contact condition between the drill bit and the formation. Higher formation pressure will increase the contact friction of the drill bit, thereby changing the amplitude and frequency characteristics of the stick-slip effect. Through this combination of terms, the formula further enriches the physical meaning of the compensation signal, enabling it to reflect the dynamic regulation of the stick-slip effect by external environmental factors. Overall, the structure of the compensation formula shows the multi-level physical mechanism of stick-slip effect compensation. Fundamental frequency vibration signal After being processed by this compensation model, the signal amplitude and frequency characteristics are dynamically modified so that the first compensation signal It can not only reflect the actual vibration behavior of the drill bit more realistically, but also effectively eliminate the nonlinear interference caused by the stick-slip effect. The compensated signal provides high-quality data input for the subsequent signal analysis module, thereby improving the overall accuracy of the system in vibration energy analysis, dynamic load calculation and trajectory optimization. Compared with the traditional vibration signal compensation method, this formula not only focuses on the friction behavior between the drill bit and the formation, but also incorporates the elastic deformation of the drill string and the damping effect of the drilling fluid into the compensation model, so that the generated compensation signal can more comprehensively reflect the complex dynamic characteristics of the drilling system. This high-precision compensation method greatly improves the reliability and applicability of signal correction, especially in complex drilling conditions with significant stick-slip effects. Its performance advantages are particularly prominent. In addition, the formula is also highly real-time and engineering applicability. By collecting sensor data in real time and inputting it into the compensation formula, the system can dynamically generate compensation signals during the drilling process to adapt to the rapid changes in parameters such as drilling pressure, torsional stiffness, drill bit speed and formation pressure. This real-time compensation capability not only improves the accuracy of the signal, but also provides important data support for fault prediction and performance optimization of the drilling system. For example, when the compensation signal shows that the stick-slip effect is significantly enhanced, the further development of nonlinear vibration can be suppressed by adjusting the drill bit speed or drilling pressure, thereby ensuring the safety and stability of the drilling process.

[0039] Embodiment 5: The signal correction compensation part uses the following formula to calculate the resonant frequency of the drilling system according to the first compensation signal: ; in, is the resonant frequency of the drilling system; is the equivalent stiffness of the drilling system; is the equivalent mass of the drilling system; is the damping coefficient, which represents the dissipation effect of the drill string material and drilling fluid on the vibration energy; is the drill string length.

[0040] Specifically, in the formula, the basic part of the resonant frequency adopts the classical vibration theory ,here is the equivalent stiffness of the system, is the equivalent mass of the system. These two parameters together determine the vibration characteristics of the system under ideal conditions. Characterizes the elastic recovery ability of the drill string and drill bit under external forces, which depends on material properties and geometric parameters. Higher stiffness means that the system can recover to the equilibrium position more quickly, so the resonant frequency will be higher. describes the inertial characteristics of the drill string and its accessories, including the combined mass of the drill bit, drill string, and surrounding fluid. When the mass increases, the inertia of the system causes the vibration response to become slower, thereby reducing the resonant frequency. This basic formula provides a vibration frequency estimation model dominated by elastic restoring force and inertia, which is the physical basis of the entire formula. However, the actual working conditions of the drilling system are far more complicated than ideal conditions. The formula introduces a stick-slip effect compensation signal And fundamental frequency vibration signal Ratio , to describe the effect of stick-slip on the resonant frequency. This ratio is embedded in the correction factor The stick-slip effect is a nonlinear vibration phenomenon caused by the change in friction between the drill bit and the formation. By correcting the stick-slip vibration, the influence of the stick-slip effect on the vibration intensity and signal amplitude is reflected. The correction factor in the formula indicates that when the stick-slip compensation signal intensity increases, it indicates that the system is more significantly affected by the stick-slip effect, thereby reducing the effective stiffness and frequency. This dynamic adjustment enables the calculation of the resonant frequency to adapt to the nonlinear changes under actual working conditions, reflecting the complex regulatory effect of the stick-slip effect on the dynamic characteristics of the system.

[0041] The formula further considers the effect of damping on the resonant frequency through the exponential decay term Describes the damping coefficient and drill string length The damping coefficient characterizes the ability of the drill string material and drilling fluid to dissipate vibration energy, and is an important factor in regulating the vibration behavior of the system. Higher damping will significantly reduce the resonance response intensity of the system by increasing the dissipation rate of vibration energy, thereby suppressing the vibration amplitude and reducing the resonance frequency. At the same time, the drill string length, as a geometric parameter, directly affects the inertia and flexibility characteristics of the system. As the drill string length increases, the inertia of the system increases, while the flexibility leads to a decrease in the equivalent stiffness, both of which will reduce the resonance frequency. In addition, the length of the drill string will also affect the distribution range of the damping effect, making the vibration response of the long drill string more complicated. By combining damping and drill string length, the formula can describe the dynamic adjustment process of the damping effect on the vibration frequency under different drilling conditions. The various parts of the formula are physically coupled, showing the dynamic mechanism behind the resonance characteristics of the drilling system. The ratio of stiffness to mass provides the basic framework of the resonance frequency, while the correction factor of the stick-slip effect and the exponential term of the damping effect dynamically adjust this framework, so that the calculated results of the resonance frequency can reflect the nonlinear changes under actual working conditions. This coupling relationship shows that the resonant frequency depends not only on the inherent properties of the system (stiffness and mass), but is also significantly affected by the dynamic characteristics (stick-slip effect, damping and drill string length). In practical applications, the physical basis of the formula makes it widely applicable to vibration optimization and working condition analysis during drilling. Real-time calculation of the resonant frequency can help drilling operators identify whether the system is close to the resonant state, so as to adjust the drill bit speed, drilling pressure or drilling fluid parameters to avoid excessive amplification of the vibration amplitude and damage to the equipment and wellbore. In addition, by introducing stick-slip effect correction and damping effect adjustment, the formula can accurately predict the resonant behavior of the system under complex working conditions, providing data support for optimizing drill string design and drilling parameter selection. For example, when the calculation shows that the resonant frequency is low and the system is close to the resonant state, the damping coefficient can be changed by adjusting the drill string length or optimizing the drilling fluid viscosity to reduce the risk of resonance.

[0042] Embodiment 6: The signal correction and compensation part uses the following formula to calculate the drill string bending stress according to the resonant frequency of the drilling system: ; Specifically, the core idea of ​​the formula is that the bending stress of the drill string is determined by its material properties, geometric parameters and vibration characteristics. and drill string outer diameter The elastic modulus reflects the ability of the material to return to its original state under stress, while the outer diameter directly determines the cross-sectional moment of inertia of the drill string. A larger elastic modulus and outer diameter will significantly increase the bending stiffness of the drill string, thereby reducing the bending stress. Through these parameters, the formula captures the basic mechanical behavior of the drill string under vibration and external forces, and provides a solid foundation for subsequent dynamic corrections. Lateral displacement of the drill string The second derivative of is an important parameter to describe the bending curvature. The lateral displacement reflects the degree of deviation of the drill string in the wellbore, while the second-order derivative is directly proportional to the bending stress. The formula quantifies the local bending effect of the drill string by combining the curvature with the material parameters. In addition, in order to more realistically reflect the complex dynamic behavior in the drilling environment, the formula introduces the resonant frequency and critical frequency The ratio of the squares of The bending stress is corrected. When the resonance frequency approaches or exceeds the critical frequency, the vibration energy of the system is significantly enhanced, resulting in a sharp increase in the bending stress. This correction mechanism reflects the nonlinear characteristics of the vibration system, making the formula adaptable to the vibration coupling effect under complex working conditions. In addition, the formula contains an exponential decay term related to the dynamic dissipation of the drill string , which is used to describe the effects of material density, cross-sectional area, and moment of inertia on bending stress. Material density and cross-sectional area Characterizes the inertial characteristics of the drill string. High density and large cross-sectional area can enhance the drill string's anti-inertial force, thereby reducing the impact of high-frequency vibration. reflects the structural resistance of the drill string, and its increase can significantly reduce the bending stress per unit length. The introduction of the exponential decay term not only reflects the geometric characteristics of the drill string, but also further quantifies the propagation and dissipation process of dynamic vibration energy inside the drill string. By coupling the above factors, the formula realizes a comprehensive modeling of the bending stress of the drill string. It starts from the static material properties and geometric parameters, combines the dynamic vibration characteristics and damping effect, and provides an accurate description of the force behavior of the drill string. Especially when the drilling system is close to the resonance state, the formula can capture the sharp change of bending stress caused by the vibration amplification effect. This ability is crucial for drill string design and safety management of the drilling process. In practical applications, the physical meaning of the formula is reflected in its high-precision prediction ability of the drill string bending stress. When the drilling system is close to the resonance state, the concentration of vibration energy may cause excessive local bending stress in the drill string, causing the risk of structural fatigue or even fracture. By calculating the bending stress in real time, the drilling parameters (such as drill bit speed, drilling pressure, etc.) can be dynamically adjusted, thereby effectively avoiding damage to the drill string caused by excessive vibration. At the same time, the formula can also provide a theoretical basis for drill string design and wellbore trajectory optimization. For example, by adjusting the outer diameter and material density of the drill string, the bending stiffness can be significantly improved and the bending stress can be reduced, thereby extending the service life of the drill string.

[0043] in, is the elastic modulus of the drill string material; The outer diameter of the drill string determines the bending stiffness of its cross section. The larger the outer diameter, the stronger the bending resistance. It is the lateral displacement of the drill string in the Z-axis direction, describing the lateral deviation of the drill string due to external forces, vibrations and wellbore bending; is the coordinate variable in the Z-axis direction; is the critical frequency, which is the first natural frequency of the drill string and reflects its lowest vibration mode. When the resonance frequency approaches or exceeds the critical frequency, the bending stress will increase. is the material density of the drill string; is the cross-sectional area of ​​the drill string; is the section moment of inertia of the drill string; is the drilling string bending stress; the wellbore trajectory deviation is calculated according to the drilling string bending stress by the following formula: : ; The core idea of ​​the formula is to convert the drill string bending stress Length of drill string bottom assembly and the moment of inertia of the area Combined with the cubic relationship, the influence of bending stress on the wellbore trajectory is described. Bending stress is the main driving force for the bending deformation of the drill string under lateral force, and its magnitude is determined by the material properties, vibration characteristics and external loads of the drill string. When the bending stress increases, the deformation amplitude of the drill string increases, and the length of the bottom component The increase in the section moment of inertia will further amplify this deformation effect. The role of is to limit the degree of deformation. The larger the moment of inertia, the stronger the resistance of the drill string to bending, thereby effectively reducing the wellbore trajectory deviation. This part of the modeling focuses on the influence of the material and geometric characteristics of the drill string on the trajectory stability. It is an important parameter that describes the degree to which the wellbore trajectory deviates from the vertical direction. Its function is reflected by the combination of cosine function and sine function. Describes the constraint effect of the well inclination angle on the wellbore trajectory. When the well inclination angle is small, the drill string has a stronger control over the wellbore trajectory, thereby reducing the trajectory deviation; as the well inclination angle increases, the support capacity of the drill string weakens, resulting in an increase in trajectory deviation. Sine function This characterizes the effect of the well inclination angle on the lateral force of the drill bit, which directly acts on the drill bit and further amplifies the trajectory deviation. Through the combined effect of these two angle-related functions, the formula can carefully characterize the dynamic regulation effect of the well inclination angle on the trajectory deviation.

[0044] The formula also introduces factors related to formation characteristics, such as the maximum well deviation change rate and uniaxial compressive strength of the formation The maximum wellbore inclination change rate reflects the severity of the wellbore curvature. When the curvature changes greatly, the bending deformation of the drill string increases, thereby significantly expanding the wellbore trajectory deviation. Formation uniaxial compressive strength describes the reaction force of the formation on the drill bit. Higher formation strength can provide stronger constraints on the drill bit and drill string, reducing trajectory deviation; while lower formation strength will lead to further increase in trajectory deviation. The formula is referenced by the formation strength Normalization is performed to make the trajectory deviation calculation under different formation conditions consistent and universal. In addition, drilling fluid pressure and drill area The effect on the wellbore trajectory is expressed by an exponential decay term The drilling fluid pressure provides an important fluid damping effect on the drill bit and drill string. When the pressure is high, the drill string is subjected to greater fluid damping when it bends and deforms, thereby reducing the trajectory deviation. The increase in the drill bit area increases the contact area between the drill bit and the formation, reducing the influence of the lateral force on the trajectory deviation. Through this item, the formula describes in detail the regulatory effect of fluid dynamics on the wellbore trajectory, making the calculation results closer to the actual working conditions. The structural design of this formula shows the progressive relationship from bending stress to trajectory deviation. By incorporating the material and geometric properties of the drill string, the lateral and axial distribution of external forces, and the combined influence of formation and fluid dynamics into the calculation framework, the formula can accurately predict the wellbore trajectory deviation under complex drilling conditions. This is of great significance for trajectory control and engineering optimization during drilling. In practical applications, the real-time calculated wellbore trajectory deviation can help drilling operators dynamically adjust the drilling pressure, drill bit speed and drilling fluid parameters, so as to control the deviation within an acceptable range and ensure the smooth progress of the drilling process. In addition, the formula can also provide a theoretical basis for drill string design, such as optimizing the length of the bottom component or adjusting material parameters to reduce the risk of wellbore trajectory deviation.

[0045] in, is the length of the bottom portion of the drill string; The well inclination angle indicates the inclination angle of the wellbore and reflects the degree to which the wellbore trajectory deviates from the vertical direction; is the maximum well inclination change rate; is the uniaxial compressive strength of the formation; is the reference formation strength, is the set value; is the drilling fluid pressure; is the drill bit area.

[0046] Embodiment 7: The signal analysis part calculates the dynamic load of the drilling system based on the output results of the signal measurement part and the signal correction and compensation part through the following formula: : ; in, is the axial tension on the top of the drill string; the vibration energy dissipation of the drilling system is evaluated by the following formula, and the vibration energy dissipation of the drilling system is obtained : ; in, is the damping coefficient of drilling fluid.

[0047] Specifically, the dynamic load formula describes the drilling string in space and time The mechanical distribution on the drill string is derived based on the elastic bending theory and dynamic response of the drill string. describes the mechanical effects caused by the bending stiffness of the drill string, where and are the elastic modulus and section inertia moment of the drill string material, respectively, reflecting the drill string's ability to resist bending. This is partly achieved through the spatial variation of curvature. And its space The derivative of describes the load distribution caused by bending at different positions of the drill string. When the drill string is bent under force, the change in curvature at different positions directly leads to the difference in load. The formula accurately captures this mechanical relationship. Describes the inertial force of the drill string, which is related to the material density and cross-sectional area This part is related to the mass distribution characteristics of the drill string. The effect of vibration on the dynamic response of the drill string is captured. When the drill string is accelerated by vibration, the inertial force changes accordingly and plays an important role in the dynamic load. In addition, this part is also reflected by the exponential decay term Describes the regulating effect of wellbore trajectory deviation on inertial force. When increases, the lateral deformation of the drill string increases, and the effective range of the inertial force decreases accordingly. This item reflects the dynamic influence of trajectory deviation on dynamic characteristics.

[0048] The last term of the formula The axial tension at the top of the drill string is introduced to regulate the dynamic load. and drilling pressure It is the main axial load applied to the drill string during drilling. In the formula, this part is calculated by the drilling pressure with depth. The distribution of axial force describes how the axial force gradually changes along the length of the drill string. The influence of axial tension on dynamic load is reflected in a nonlinear form, combined with the cross-sectional compressive stiffness , which can effectively adjust the axial constraint of drill string vibration. This design not only reflects the coupling of axial force and vibration behavior, but also shows the profound impact of drilling pressure distribution on the dynamic characteristics of drill string. Based on the dynamic load, the formula further analyzes the vibration energy dissipation of the drilling system. Vibration Energy Dissipation The calculation of quantifies the transfer and dissipation of vibration energy in the system in an integral form. Captures the dynamic load effect on vibration displacement velocity This section describes how the load transfers mechanical energy into the drill string through vibration and reveals where the energy is concentrated during the vibration process. Describes the dissipation effect of drilling fluid damping on vibration energy. The damping coefficient It reflects the viscosity and flow characteristics of the drilling fluid. As increases, the energy dissipated by damping increases significantly. This part of the formula reflects the control effect of fluid damping on vibration energy dissipation. Finally, the formula is Describes the effect of system frequency on energy dissipation. Resonant frequency and critical frequency The ratio of is used to adjust the intensity of dissipated energy. When the resonant frequency is close to the critical frequency, the vibration energy in the system increases and the dissipation effect is enhanced. The exponential decay term accurately captures the regulatory effect of frequency coupling on energy dissipation, so that the formula can reflect the dynamic behavior of energy dissipation caused by changes in vibration frequency during drilling.

[0049] Embodiment 8: The signal analysis part calculates the system response of the drilling system according to the vibration energy dissipation through the following formula: : ; in, is the damping ratio of the drilling system; is the natural angular frequency of the drilling system, which means the angular frequency of free vibration under undamped conditions.

[0050] Specifically, the core structure of the formula is based on the classical second-order differential equation of the vibration system, in which the response of the system is divided into acceleration term, velocity term and displacement term, which respectively reflect the dynamic inertia, damping characteristics and stiffness characteristics of the system. In this formula, the response of the system is defined as the ratio of vibration energy dissipation to dynamic load. This ratio describes how the input dynamic load of the drilling system is transmitted and dissipated within the system through vibration energy dissipation during the vibration process. By analyzing the dynamic changes of this ratio, the overall dynamic behavior of the system under vibration can be revealed. The first term of the formula is the second-order derivative term that describes the acceleration component of the system response. This term reflects the rapid dynamic changes of the system caused by inertial forces during vibration, especially when the system is subjected to high-frequency vibration or transient loads. The acceleration term captures the inertial effect in the drilling system response and is the system's immediate response to changes in dynamic loads and energy dissipation. The second term of the formula is a first-order derivative term, reflecting the damping characteristics of the system. Damping ratio It is a key parameter that describes the energy dissipation capacity of the system. It combines the viscous damping of the drilling fluid and the internal dissipation characteristics of the drill string material. The third term of the formula is: is a displacement term that describes the stiffness characteristics of the system. This term is proportional to the square of the natural frequency of the system and reflects the rigid response capability of the system in a state of vibration equilibrium. The natural angular frequency of the drilling system It is related to the stiffness and mass of the system, so this term actually reflects the contribution of the inherent dynamic characteristics of the drilling system to the response. When the stiffness of the system is high or the mass is small, the natural frequency increases and the rigid response of the system is enhanced; conversely, when the stiffness of the system is low or the mass is large, the response amplitude will be significantly reduced. The entire formula constructs a complete description of the system response by superimposing the three terms of acceleration, velocity and displacement. Each term has a clear physical meaning and works together to calculate the system response: the acceleration term dominates the transient dynamic behavior of the system, the velocity term regulates the energy dissipation process of the system, and the displacement term reflects the rigid characteristics of the system. In this formula, the ratio of vibration energy dissipation to dynamic load is the core variable, which not only runs through the modeling of the entire system response, but also captures the multi-level response of the drilling system in a complex vibration environment through its time derivative and dynamic changes.

[0051] Embodiment 9: The signal calibration part calculates the calibration coefficient according to the system response, the resonant frequency of the drilling system, the vibration energy dissipation and the trajectory deviation through the following formula: : ; in, Represents the magnitude of the system response.

[0052] Specifically, the core idea of ​​the formula is to combine the dynamic behavior of the drilling system with the environmental characteristics to establish a dynamic adjustment factor Part 1 The dependence of the calibration coefficient on the system response amplitude and the initial value of the fundamental frequency vibration signal is described. It is a dynamic reflection of the system in its current vibration state, indicating how the vibration energy is propagated and concentrated in the system. The initial value of provides a reference for the signal, reflecting the original characteristics of the system in an uncompensated state. By combining these two variables, the formula can dynamically correct the signal amplitude to ensure that the signal is consistent with the actual system state. The second part of the formula It reflects the coupling relationship between the resonant frequency and the critical frequency. is the main vibration frequency of the system under the current dynamic conditions, and the critical frequency is the natural first mode frequency of the system, reflecting the static characteristics of the system. When the resonant frequency is close to the critical frequency, the dynamic behavior of the system will change significantly, which may cause vibration amplitude amplification and nonlinear response. By introducing this frequency ratio, the formula can adapt to the calibration requirements of the system under resonant state and avoid signal distortion caused by frequency deviation. Part III This reflects the effect of vibration energy dissipation on the calibration coefficient. It is the vibration energy consumed by the system through mechanisms such as damping and friction, which describes the dynamic characteristics of the system stability. This provides the time scale for the system to operate and normalizes the energy dissipation to the performance under real-time conditions. This exponential term ensures that the calibration coefficient can dynamically reflect the state of energy conversion and dissipation of the system. When the energy dissipation is large, the calibration coefficient is reduced accordingly to suppress high-frequency noise and unstable factors in the signal. The last part of the formula The effect of borehole trajectory deviation on signal calibration is considered. is a quantitative indicator of the wellbore geometry deviation, and the drill string length It provides a geometric reference for the system. When the trajectory deviation increases, the dynamic response of the drill string may be affected, resulting in signal distortion. By introducing this correction factor, the formula can dynamically adjust the calibration coefficient to compensate for the signal anomaly caused by trajectory deviation. Overall, the calibration coefficient The formula is a multi-level dynamic adjustment model. It achieves accurate calibration of the signal by comprehensively considering key factors such as the amplitude, frequency characteristics, energy dissipation and trajectory deviation of the system response. This calibration method can not only dynamically adapt to complex drilling conditions, but also reflect the dynamic changes of the system in real time, improving the accuracy and reliability of the signal. In practical applications, the calibration coefficient The calculation of is of great significance for the real-time monitoring and control of the drilling process. By continuously adjusting the signal amplitude and frequency characteristics, the calibration coefficient can ensure that the signal output is always close to the actual working conditions, thereby providing reliable data support for subsequent signal analysis, fault prediction and working condition optimization. For example, during the drilling process, when the resonant frequency approaches the critical frequency and the trajectory deviation increases, the calibration coefficient will automatically reduce the signal amplitude to avoid signal overload and analysis errors. In addition, the calibration coefficient can also dynamically adjust the time resolution and frequency characteristics of the signal according to the real-time changes in energy dissipation, further improving the stability and response speed of the system.

[0053] The preferred embodiments of the present disclosure are described above with reference to the accompanying drawings, but the scope of the present disclosure is not limited thereby. Any modification, equivalent substitution and improvement made by those skilled in the art without departing from the scope and essence of the present disclosure shall be within the scope of the present disclosure.

Claims

1. A drilling vibration measurement and real-time calibration system based on a vibration sensor, characterized in that: include: A signal measuring part, a signal correction and compensation part, a signal analyzing part and a signal calibration part; the signal measuring part is used to install a vibration sensor and an accelerometer near the drill bit or the drill string, respectively record the three-axis acceleration signals, and generate a fundamental frequency vibration signal according to the three-axis acceleration signals; the signal correction and compensation part is used to compensate the stick-slip effect of the fundamental frequency vibration signal to obtain a first compensation signal; the resonant frequency of the drilling system is calculated according to the first compensation signal; the bending stress of the drill string is calculated according to the resonant frequency of the drilling system; the wellbore trajectory deviation is calculated according to the bending stress of the drill string; the signal analyzing part is used to calculate the dynamic load of the drilling system based on the output results of the signal measuring part and the signal correction and compensation part, so as to evaluate the vibration energy dissipation of the drilling system and obtain the vibration energy dissipation of the drilling system; The system response of the drilling system is calculated according to the vibration energy dissipation; the signal calibration part is used to calculate the calibration coefficient according to the system response, the resonant frequency of the drilling system, the vibration energy dissipation and the trajectory deviation, and use the calibration coefficient to multiply the fundamental frequency vibration signal to obtain a calibrated vibration signal.

2. The drilling vibration measurement and real-time calibration system based on vibration sensor according to claim 1, characterized in that: The signal measurement part generates a fundamental frequency vibration signal according to the three-axis acceleration signal, and the process specifically includes: sampling the three-axis acceleration signal to obtain a sampling signal; the sampling frequency is at least twice the vibration frequency of the drill bit; the synthetic acceleration amplitude is calculated according to the sampled three-axis acceleration signal as the amplitude of the fundamental frequency signal; the frequency of the fundamental frequency signal is calculated using the real-time rotation speed of the drill bit; the fundamental frequency signal is modulated using the drilling fluid pulsation frequency to form an actual vibration characteristic; the drilling pressure and the moment of inertia of the drill bit are introduced to perform an exponential attenuation correction on the fundamental frequency signal to obtain the final fundamental frequency vibration signal.

3. The drilling vibration measurement and real-time calibration system based on vibration sensor according to claim 2, characterized in that: The fundamental frequency vibration signal is expressed using the following formula: ； in, is the rotation frequency of the drill bit; is the triaxial acceleration component of the drill bit in the X-axis direction; is the triaxial acceleration component of the drill bit in the Y-axis direction; is the three-axis acceleration component of the drill bit in the Z-axis direction; is drilling pressure; For time; is the moment of inertia of the drill bit; is the drilling fluid pulsation frequency; is the fundamental frequency vibration signal.

4. The drilling vibration measurement and real-time calibration system based on vibration sensor according to claim 3, characterized in that: The signal correction and compensation part uses the following formula to compensate for the stick-slip effect of the fundamental frequency vibration signal to obtain a first compensation signal: ； in, is the first compensation signal; is the dynamic friction coefficient, which represents the characteristic parameter of the friction force between the drill bit and the formation during relative sliding; is the static friction coefficient, which indicates the friction characteristics between the drill bit and the formation in a static state, which is greater than the dynamic friction coefficient; is the instantaneous speed of the drill bit; is the characteristic speed, is the set value; It is the maximum torsional moment of the drill bit under the action of drilling pressure and friction; is the torsional stiffness of the drill string; is the angular displacement difference between the two ends of the drill string, and is the torsion angle difference between the upper and lower ends of the drill string, which is used to characterize the degree of torsional deformation of the drill string; is the equivalent circulating density, is the set value, the greater the equivalent circulating density, the higher the stability of the drill string; is the formation pressure.

5. The drilling vibration measurement and real-time calibration system based on vibration sensor according to claim 4, characterized in that: The signal correction and compensation part calculates the resonant frequency of the drilling system according to the first compensation signal using the following formula: ； in, is the resonant frequency of the drilling system; is the equivalent stiffness of the drilling system; is the equivalent mass of the drilling system; is the damping coefficient, which represents the dissipation effect of the drill string material and drilling fluid on the vibration energy; is the drill string length.

6. The drilling vibration measurement and real-time calibration system based on vibration sensor according to claim 5, characterized in that: The signal correction and compensation part uses the following formula to calculate the drill string bending stress based on the resonant frequency of the drilling system: ； in, is the elastic modulus of the drill string material; The outer diameter of the drill string determines the bending stiffness of its cross section. The larger the outer diameter, the stronger the bending resistance. It is the lateral displacement of the drill string in the Z-axis direction, describing the lateral deviation of the drill string due to external forces, vibrations and wellbore bending; is the coordinate variable in the Z-axis direction; is the critical frequency, which is the first natural frequency of the drill string and reflects its lowest vibration mode. When the resonance frequency approaches or exceeds the critical frequency, the bending stress will increase. is the material density of the drill string; is the cross-sectional area of ​​the drill string; is the section moment of inertia of the drill string; is the drilling string bending stress; the wellbore trajectory deviation is calculated according to the drilling string bending stress by the following formula: : ； in, is the length of the bottom portion of the drill string; The well inclination angle indicates the inclination angle of the wellbore and reflects the degree to which the wellbore trajectory deviates from the vertical direction; is the maximum well inclination change rate; is the uniaxial compressive strength of the formation; is the reference formation strength, is the set value; is the drilling fluid pressure; is the drill bit area.

7. The vibration sensor-based drilling vibration measurement and real-time calibration system according to claim 6, characterized in that: The signal analysis part calculates the dynamic load of the drilling system based on the output results of the signal measurement part and the signal correction and compensation part through the following formula: : ； in, is the axial tension on the top of the drill string; the vibration energy dissipation of the drilling system is evaluated by the following formula, and the vibration energy dissipation of the drilling system is obtained : ； in, is the damping coefficient of drilling fluid.

8. The vibration sensor-based drilling vibration measurement and real-time calibration system according to claim 7, characterized in that: The signal analysis part calculates the system response of the drilling system according to the vibration energy dissipation through the following formula: : ； in, is the damping ratio of the drilling system; is the natural angular frequency of the drilling system, which means the angular frequency of free vibration under undamped conditions.

9. The drilling vibration measurement and real-time calibration system based on vibration sensor according to claim 8, characterized in that: The signal calibration part calculates the calibration coefficient according to the system response, the resonant frequency of the drilling system, the vibration energy dissipation and the trajectory deviation through the following formula: : ； in, Represents the magnitude of the system response.

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