Downhole pressure pulse signal processing system for high temperature and high pressure environment

Abstract

The present invention discloses a downhole pressure pulse signal processing system for high temperature and high pressure environment, and relates to the field of signal processing technology. It includes: a signal acquisition and compensation part, a feature processing part and a signal reconstruction part; the signal acquisition and compensation part is used to collect downhole fluid pressure pulse signals and downhole temperature signals in real time, and dynamically compensate the downhole fluid pressure pulse signals to obtain compensation signals; the feature processing part is used to extract features of the compensation signals based on the Helmholtz wave equation to obtain intermediate results, and then extract features from the intermediate results to obtain feature extraction results; the signal reconstruction part is used to perform multi-scale pulse detection to obtain detection results; the detection results are signal reconstructed to obtain the reconstructed downhole fluid pressure pulse signals. The present invention can effectively compensate for the distortion effect of the downhole environment on the signal, accurately extract multi-dimensional features, and improve the accuracy and robustness of signal processing.

Description

Technical Field

[0001] The present disclosure relates to the field of signal processing technology, and in particular to a downhole pressure pulse signal processing system for high temperature and high pressure environments. Background Art

[0002] The processing technology of downhole fluid pressure pulse signals is of great significance in the field of oil and gas development. The downhole environment is usually characterized by high temperature and high pressure, and the dynamic behavior of the fluid is complex and changeable, which makes the acquisition and processing of downhole signals face many challenges. In recent years, research based on fluid mechanics and signal processing technology has made certain progress, but in practical applications, the existing technology still has many problems and limitations.

[0003] In the prior art, pressure sensors are often used to collect downhole pressure signals, and pressure fluctuations are recorded by high-precision instruments. However, the complexity of the downhole environment causes the collected signals to usually have large noise and distortion, which mainly comes from the nonlinear dynamic behavior of multiphase fluids, density changes of fluids under high temperature and high pressure environments, and external environmental interference. In order to improve the accuracy of the signal, some technologies attempt to combine physical models (such as the Navier-Stokes equations and the heat conduction equation) to dynamically compensate the signal. These methods can achieve good results in laboratory environments, but in actual downhole applications, due to the complex and changeable dynamic characteristics of the fluid, the accuracy and applicability of the compensation model are still insufficient. Feature extraction of pressure signals is an important part of signal processing. The prior art usually uses methods based on frequency domain and time-frequency analysis, such as Fourier transform, wavelet transform or short-time Fourier transform. These methods can extract the spectral characteristics and local time-frequency distribution of the signal. However, downhole pressure signals have significant nonlinearity and randomness, and it is difficult to fully characterize the dynamic characteristics of the signal only through linear feature extraction methods. In recent years, some studies have attempted to introduce chaotic dynamics and entropy theory to extract the nonlinear characteristics of signals, such as analysis methods based on Lyapunov exponents or information entropy. However, these methods have limited effects in practical applications with large noise, and the accuracy and robustness of feature extraction are difficult to guarantee. The purpose of signal reconstruction is to restore the original characteristics of pressure signals in complex environments. In the existing technology, reconstruction is mainly performed through time series analysis methods or dynamic modeling. For example, the phase space reconstruction technology based on the Takens embedding theorem can expand a one-dimensional time series into a high-dimensional vector, thereby mining the intrinsic dynamic characteristics of the signal. However, this method is very sensitive to the selection of embedding parameters (such as time delay and embedding dimension), and the reconstruction accuracy will be significantly reduced under conditions of large noise. In addition, the existing technology usually ignores the multi-scale characteristics of the signal when reconstructing the signal, resulting in insufficient physical consistency and dynamic characteristics of the reconstructed signal. High temperature and high pressure environment places strict requirements on signal processing technology. Although some physical models (such as heat conduction equations and fluid mechanics equations) are introduced in the existing technology to model environmental parameters, these models are difficult to accurately describe the fluid characteristics under complex downhole conditions in practical applications. For example, the interaction between gas, liquid and solid in multiphase fluids, the viscoelastic effect of fluids, and the dynamic influence of high temperature on fluid viscosity and density are phenomena that have not been fully considered in existing models, limiting the scope of application of signal processing technology. Summary of the invention

[0004] The present invention provides a downhole pressure pulse signal processing system for high temperature and high pressure environments, which can effectively compensate for the distortion effect of the downhole environment on the signal, accurately extract multi-dimensional features, improve the accuracy and robustness of signal processing, and enhance the adaptability to complex fluid systems, thereby providing reliable technical support for high-precision analysis and real-time monitoring of downhole signals.

[0005] The technical solution of the present invention is achieved in this way:

[0006] A downhole pressure pulse signal processing system for high temperature and high pressure environment includes: a signal acquisition and compensation part, a feature processing part and a signal reconstruction part; the signal acquisition and compensation part is used to collect downhole fluid pressure pulse signals and downhole temperature signals in real time, and dynamically compensate the downhole fluid pressure pulse signals in combination with the coupling relationship between the Navier-Stokes equation and the heat conduction equation to obtain a compensation signal; the feature processing part is used to extract features of the compensation signal based on the Helmholtz wave equation to obtain an intermediate result, and then perform entropy dynamics based on the Boltzmann-Gibbs entropy on the intermediate result. The method comprises the following steps: extracting features to obtain feature extraction results; the signal reconstruction part is used to calculate the fluid dynamics information entropy of the feature extraction results; reconstructing the fluid dynamics information entropy in phase space based on the Takens embedding theorem to obtain the phase space vector; calculating the fluctuation characteristics according to the phase space vector based on the Langevin equation and the thermodynamic fluctuation theory; performing multi-scale pulse detection based on the Kolmogorov entropy and Lyapunov index in combination with the fluctuation characteristics, the phase space vector, the fluid dynamics information entropy and the compensation characteristics to obtain the detection results; and performing signal reconstruction on the detection results to obtain the reconstructed downhole fluid pressure pulse signal.

[0007] Furthermore, the downhole fluid includes: downhole oil and gas mixture and drilling fluid; the downhole fluid has multiphase characteristics, and the forms include: gas, liquid and solid particles; the temperature range of the downhole fluid is: 150-200°C; the pressure range of the downhole fluid is 30-100MPa.

[0008] Furthermore, the signal acquisition and compensation part dynamically compensates the downhole fluid pressure pulse signal by combining the coupling relationship between the Navier-Stokes equation and the heat conduction equation through the following formula to obtain a compensation signal:

[0009] ;

[0010] in, For time Downhole fluid pressure pulse signal at the time; The temperature of the downhole fluid The density under is the fluid velocity vector of the downhole fluid; is the enthalpy change of the downhole fluid; is the gas constant; is the specific heat capacity at constant pressure, which indicates the heat required to raise the temperature of the downhole fluid per unit mass by 1K under constant pressure conditions; is the specific heat capacity at constant volume, which indicates the heat required to raise the temperature of the downhole fluid per unit mass by 1K under constant volume conditions; is the compensation signal.

[0011] Furthermore, the feature processing part extracts the features of the compensation signal based on the Helmholtz wave equation through the following formula to obtain an intermediate result:

[0012] ;

[0013] in, is the intermediate result; is the Laplace operator; is the speed of sound, which is equal to the ratio of the bulk elastic modulus of the downhole fluid to the density of the downhole fluid; is the temperature attenuation coefficient, is the set value; is the intensity attenuation coefficient, which describes the intensity attenuation of the signal caused by the viscoelastic properties of the medium during propagation and is a set value; is the propagation distance.

[0014] Furthermore, the feature processing part performs entropy dynamic feature extraction based on Boltzmann-Gibbs entropy on the intermediate result through the following formula to obtain the feature extraction result:

[0015] ;

[0016] in, is the feature extraction result; is the Boltzmann constant; is the reference feature value, used to normalize the feature, and is the set value; is the volume integral differential element; is the volume of downhole fluid; is the viscosity of the downhole fluid; is the reference pressure value, used to normalize the pressure, and is the set value; is the gradient of the fluid velocity vector of the downhole fluid in the X-axis direction; is the gradient of the fluid velocity vector of the downhole fluid in the Y-axis direction; is the gradient of the fluid velocity vector of the downhole fluid in the Z-axis direction.

[0017] Furthermore, the signal reconstruction part calculates the fluid dynamics information entropy of the feature extraction result by the following formula:

[0018] ;

[0019] in, is the fluid dynamics information entropy; is the absolute value operator; is the specific enthalpy of the downhole fluid; the phase space vector is obtained by reconstructing the fluid dynamics information entropy based on the Takens embedding theorem through the following formula:

[0020] ;

[0021] in, is the phase space vector; is the time delay, is the set value; is the set embedding dimension.

[0022] Furthermore, the signal reconstruction part calculates the fluctuation characteristics according to the phase space vector through the following formula based on the Langevin equation and the theory of thermodynamic fluctuations:

[0023] ;

[0024] in, is the damping coefficient of the downhole fluid; is the potential energy function of the downhole fluid; potential energy function Calculated using the following formula:

[0025] ;

[0026] in, is the average height of the downhole fluid; is the acceleration due to gravity.

[0027] Furthermore, the signal reconstruction part performs multi-scale pulse detection based on Kolmogorov entropy and Lyapunov index, combined with fluctuation characteristics, phase space vector, fluid dynamics information entropy and compensation characteristics, and obtains the detection result through the following formula:

[0028] ;

[0029] in, For test results; is the L2 norm; is the maximum Lyapunov exponent; is the Kolmogorov entropy.

[0030] Furthermore, the detection result is reconstructed by the following formula to obtain the reconstructed downhole fluid pressure pulse signal:

[0031] ;

[0032] in, is the maximum fluid dynamics information entropy; is the reconstructed downhole fluid pressure pulse signal.

[0033] The downhole pressure pulse signal processing system for high temperature and high pressure environment of the present invention has the following beneficial effects:

[0034] In the signal acquisition and compensation part, the present invention performs real-time dynamic compensation for the downhole fluid pressure pulse signal by combining the coupling model of the Navier-Stokes equations and the heat conduction equation. This compensation method effectively captures the nonlinear dynamic characteristics of downhole multiphase fluids in high temperature and high pressure environments, and makes up for the shortcomings of static or single physical models in the prior art. Through the density dynamic adjustment term, velocity field gradient correction, and thermodynamic correction term of the formula, the present invention can accurately compensate for signal distortion caused by fluid density changes, velocity distribution fluctuations, and temperature effects, and ultimately obtain a compensated signal with high physical consistency. This dynamic compensation mechanism significantly improves the initial processing quality of the signal and provides a reliable input for subsequent feature extraction and reconstruction.

[0035] In the feature extraction part, the present invention innovatively combines the fluid dynamic characteristics with the thermodynamic state changes by combining the multidimensional method of the Helmholtz wave equation and the Boltzmann-Gibbs entropy, thereby realizing the comprehensive extraction of the complex characteristics of the downhole pressure signal. The Helmholtz wave equation is used to analyze the wave characteristics of the signal, and by capturing the local frequency and amplitude changes of the pressure signal, the intermediate characteristics reflecting the law of signal propagation are extracted. The Boltzmann-Gibbs entropy deeply explores the nonlinear dynamic characteristics in the signal by quantifying the randomness and chaotic characteristics of the signal. This multidimensional feature extraction method not only improves the robustness of feature extraction, but also can accurately characterize the dynamic evolution characteristics of the downhole signal, providing complete multi-scale feature information for subsequent signal analysis.

[0036] The present invention introduces phase space reconstruction, Langevin equation and thermodynamic fluctuation theory in the process of signal reconstruction. Through in-depth analysis of the dynamic behavior of the signal, the propagation law of the pressure signal in the complex downhole environment is revealed. Through the Takens embedding theorem, the signal is mapped into a high-dimensional phase space, and the dynamic state of the downhole fluid system is truly restored. Based on the fluctuation feature analysis of the Langevin equation, the random fluctuation of the signal and its relationship with external disturbances are further quantified. The dynamic calculation of information entropy provides a global description of the signal complexity. Combined with these dynamic and thermodynamic characteristics, the present invention can comprehensively characterize the dynamic characteristics of the signal from both the global and local levels, laying the foundation for the reliable reconstruction of the signal. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 A schematic diagram of the system structure of a downhole pressure pulse signal processing system for a high temperature and high pressure environment provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0038] 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.

[0039] Example 1, reference Figure 1 :A downhole pressure pulse signal processing system for high temperature and high pressure environment includes: a signal acquisition and compensation part, a feature processing part and a signal reconstruction part; the signal acquisition and compensation part is used to collect downhole fluid pressure pulse signals and downhole temperature signals in real time, and dynamically compensate the downhole fluid pressure pulse signals in combination with the coupling relationship between the Navier-Stokes equation and the heat conduction equation to obtain a compensation signal; the feature processing part is used to extract the features of the compensation signal based on the Helmholtz wave equation to obtain an intermediate result, and then perform entropy dynamics based on the Boltzmann-Gibbs entropy on the intermediate result The method comprises the following steps: extracting features to obtain feature extraction results; the signal reconstruction part is used to calculate the fluid dynamics information entropy of the feature extraction results; reconstructing the fluid dynamics information entropy in phase space based on the Takens embedding theorem to obtain the phase space vector; calculating the fluctuation characteristics according to the phase space vector based on the Langevin equation and the thermodynamic fluctuation theory; performing multi-scale pulse detection based on the Kolmogorov entropy and Lyapunov index in combination with the fluctuation characteristics, the phase space vector, the fluid dynamics information entropy and the compensation characteristics to obtain the detection results; and performing signal reconstruction on the detection results to obtain the reconstructed downhole fluid pressure pulse signal.

[0040] Specifically, in this system, the signal acquisition part uses a high-precision sensor, which can monitor the pressure pulse signal and ambient temperature signal of the downhole fluid in real time. The pressure pulse signal is a physical phenomenon caused by the movement of the downhole fluid, and its fluctuation characteristics directly reflect the dynamic behavior of the downhole fluid. However, since the high temperature environment will significantly affect the density and viscosity of the fluid, thereby changing the fluctuation characteristics of the pressure signal, the original signal obtained by direct acquisition alone often cannot accurately reflect the true dynamic state of the fluid. Therefore, the present invention further introduces a set of signal compensation methods based on physical models, using the Navier-Stokes equation as the basic model to describe the movement of the fluid, and combining the heat conduction equation to model and analyze the thermal effect of the fluid. The Navier-Stokes equation is the core equation to describe fluid dynamics, which can characterize the dynamic behavior of the change of the pressure signal over time and space. The heat conduction equation describes the spatiotemporal evolution of the temperature distribution in a high temperature environment. The coupling of these two models is one of the innovative points of the present invention. By introducing the temperature signal into the parameters of the Navier-Stokes equation, the influence of temperature on the density and viscosity of the fluid is dynamically reflected. The compensation mechanism uses this coupling relationship to correct the deviation of the pressure signal in real time, thereby eliminating the dynamic interference caused by temperature changes. Specifically, the temperature signal is used to correct the viscosity and density parameters of the fluid. These corrected parameters are used to recalculate the pressure gradient and flow velocity distribution of the fluid, so that the corrected signal more accurately reflects the actual dynamic state of the well. In this compensation process, a variety of numerical methods are combined at the algorithm level to ensure the efficiency and stability of the calculation. First, the acquisition and transmission of temperature signals usually have delays and noise. In order to solve this problem, the present invention introduces a signal preprocessing method based on filtering and interpolation to ensure the smoothness and timing consistency of the input data. Secondly, the numerical solution process of the Navier-Stokes equation adopts a stable discretization method to cope with the computational complexity caused by the rapid change of signals under high pressure environments. In addition, the solution of the heat conduction equation is quickly approximated by the finite difference method, thereby realizing the accurate modeling of the high temperature field. Through this series of physical modeling and numerical calculations, the signal compensation part of the present invention can dynamically and real-time correct the error of the pressure signal in a complex downhole environment.

[0041] In the first stage, the present invention extracts the characteristics of the wave characteristics of the compensated pressure signal through the Helmholtz wave equation. The essence of the downhole pressure pulse signal is the propagation behavior of the pressure wave generated in the fluid movement, which contains dynamic information closely related to the flow velocity, fluid density, fluid viscosity, etc. The Helmholtz wave equation is a mathematical tool to describe the wave propagation behavior. By deconstructing the pressure signal in space and time, the key parameters of the signal such as frequency, amplitude, phase, etc. can be extracted. These parameters directly reflect the dynamic characteristics of the downhole fluid, such as the propagation speed of the pressure wave and the evolution law of the waveform. More importantly, the Helmholtz equation has high flexibility in dealing with complex boundary conditions and propagation paths, which enables it to adapt to the influence of multiple reflections, refractions and scattering of the signal by the complex geological structure of the downhole. At this stage, by finely analyzing the wave characteristics of the compensated signal, high-frequency noise and environmental interference can be effectively eliminated, and the wave characteristics with physical significance in the pressure pulse signal can be retained. In the second stage, the present invention further explores the entropy characteristics of the signal based on the Boltzmann-Gibbs entropy. The core goal of this stage is to characterize the randomness and non-equilibrium characteristics of the pressure signal. In a high-temperature and high-pressure downhole environment, the dynamic behavior of fluids usually exhibits significant chaos and fluctuations, and traditional linear analysis methods are difficult to fully reflect these complex phenomena. Boltzmann-Gibbs entropy is an indicator that characterizes the degree of chaos and state distribution characteristics of a system. It can quantify the degree of disorder of information in a signal by analyzing the probability distribution of the signal. Specifically, by mapping the pressure signal to a multidimensional probability distribution space, the dynamic change trend of the signal in time and space scales can be captured. The extraction of this entropy characteristic can not only reflect the local fluctuation behavior of the signal, but also reveal the overall dynamic stability and complexity level of the signal. The innovation of the feature processing part lies in that it combines the fluctuation feature and the entropy feature to form a dual-level, multi-dimensional feature extraction framework. In traditional downhole signal processing methods, feature extraction is usually limited to a single analysis in the frequency domain or time domain, such as extracting the spectral characteristics of the signal through Fourier transform, or capturing the time-frequency distribution of the signal through wavelet transform. However, these methods are difficult to effectively deal with the nonlinear and random problems that are widely present in downhole pressure pulse signals. The present invention ensures that the dynamic characteristics of the signal are accurately characterized by extracting the fluctuation characteristics in the first stage; and in the second stage, the entropy-based analysis supplements the non-equilibrium information of the signal, thereby achieving a comprehensive characterization of the pressure signal. Another advantage of this two-layer feature extraction framework is its adaptability to high temperature and high pressure environments. The uncertainty of the signal propagation path and the strong randomness of the noise in the downhole environment make single-dimensional feature analysis difficult to deal with, and the multi-dimensional feature extraction method of the present invention can effectively separate and counteract these interferences.For example, when high-frequency noise in the environment affects the fluctuation characteristics of the signal, the extraction of entropy features can provide complementary information to help accurately identify the key characteristics of the signal. Conversely, when the entropy value of the signal becomes blurred due to excessive random disturbances, the fluctuation characteristic analysis can provide a stable dynamic reference. Therefore, through this complementary analysis, the feature processing part of the present invention can maintain the ability to efficiently extract pressure signals in complex environments.

[0042] The first step of signal reconstruction is to map the feature extraction results into a high-dimensional phase space based on the Takkens embedding theorem. The downhole pressure pulse signal is essentially a manifestation of a complex nonlinear dynamic system, and its timing characteristics are affected by many factors, such as fluid dynamics behavior, heat conduction effects, and environmental noise. The Takkens embedding theorem provides a theoretical basis for analyzing this complex dynamic system. It expands the one-dimensional time series into a high-dimensional phase space vector through time delay and the selection of embedding dimensions, so that the intrinsic dynamic structure of the system can be fully displayed. In the present invention, the compensated pressure signal and the feature extraction results are used as inputs, and the nonlinear dynamic laws hidden in the signal are captured through the reconstruction of the high-dimensional phase space. This process not only separates the various influencing factors in the complex downhole environment from the time domain, but also reflects the overall dynamic characteristics of the system through the geometric structure of the phase space, laying the foundation for subsequent multi-scale detection and reconstruction. After the phase space vector is generated, the present invention further uses the Langevin equation combined with the thermodynamic fluctuation theory to model and analyze the fluctuation characteristics of the signal. As a classical equation describing the random motion of a microscopic system, the Langevin equation can effectively capture the random fluctuations caused by environmental noise in the downhole pressure signal. These fluctuation characteristics are particularly significant in high-temperature and high-pressure environments. Traditional linear methods usually have difficulty distinguishing the true dynamic characteristics of noise and signals. The present invention constructs a sensitive fluctuation detection mechanism through the Langevin equation. Specifically, the system quantifies the amplitude and time scale of the impact of environmental noise on the signal by analyzing the microscopic perturbation characteristics of the pressure signal, thereby achieving effective suppression of noise in signal reconstruction. This process combines the theory of thermodynamic fluctuations and reveals the equilibrium trend of the signal in dynamic fluctuations by correlating the free energy change and entropy increase characteristics of the system, so that the reconstructed signal not only maintains physical consistency, but also can accurately capture the non-equilibrium behavior of the downhole dynamic system.

[0043] At the same time, the signal reconstruction part also introduces Kolmogorov entropy and Lyapunov index in chaos theory to further analyze the complexity and stability characteristics of the system in the phase space. Due to multiple interferences, the downhole pressure pulse signal usually behaves as a nonlinear chaotic system, and its dynamic behavior has a highly sensitive initial value dependence. Kolmogorov entropy, as a quantitative indicator of the degree of chaos in the system, can characterize the disorder of the signal and the speed of information transmission, while the Lyapunov index is used to quantify the rate of trajectory separation of the signal in the phase space. By calculating these chaotic indicators, the present invention clarifies the evolution law of the pressure signal in the high-dimensional phase space, and then optimizes the dynamic modeling in the reconstruction process, so that the final reconstructed signal can truly reflect the complex chaotic characteristics and stability in the downhole environment. After completing the analysis of the fluctuation characteristics and chaotic characteristics, the signal reconstruction part further integrates multi-dimensional information such as phase space vectors, entropy characteristics and compensation signals through multi-scale detection and fusion strategies to ensure the comprehensiveness and accuracy of the reconstructed signal. The present invention innovatively adopts a multi-scale detection method to extract and reconstruct signal characteristics on different time scales layer by layer. This multi-scale method fully considers the characteristic variation of downhole pressure pulse signals at different time scales, such as the rapid change of pressure fluctuations on a short time scale and the trend evolution of signals on a long time scale. By integrating multi-scale detection results, the present invention can effectively eliminate the feature loss and deviation that may be caused by single-scale analysis, and ensure the consistency of the reconstructed signal in global and local characteristics.

[0044] Embodiment 2: The downhole fluid comprises: a downhole oil-gas mixture and a drilling fluid; the downhole fluid has a multiphase characteristic, and the forms include: gas, liquid and solid particles; the temperature range of the downhole fluid is: 150-200°C; the pressure range of the downhole fluid is: 30-100MPa.

[0045] Specifically, in the dynamic environment of downhole fluids, the interaction between the gas and liquid phases and at the liquid-solid interface plays an important role in the propagation characteristics of the pressure signal. The density difference between the gas phase and the liquid phase causes the pressure wave to be reflected and refracted during propagation, while the solid particles cause turbulence and energy dissipation. These phenomena are manifested in the pressure signal as irregular changes in the fluctuation characteristics and the enhancement of high-frequency noise. At the same time, the reduction of fluid viscosity under high temperature conditions and the introduction of thermal expansion effects also significantly change the propagation speed and waveform characteristics of the signal. The high-pressure environment further aggravates the compressibility of the fluid, making the fluctuation amplitude of the pressure signal particularly sensitive to small disturbances. Therefore, it is difficult for traditional static signal analysis methods to obtain accurate signals in such extreme environments and restore the true dynamic state of downhole fluids. The temperature range of downhole fluids is 150–200°C and the pressure range is 30–100MPa. This extreme condition places strict requirements on the signal processing system: high temperature will significantly reduce the viscosity of the fluid, thereby changing the propagation characteristics of the pressure wave. Temperature has a direct impact on the compressibility of the gas and the bulk modulus of the liquid, causing changes in the waveform and spectral structure of the signal. High temperatures may also trigger chemical reactions that change the physical properties of the fluid, thereby increasing signal uncertainty. In the high pressure range of 30–100 MPa, the density of the fluid changes significantly with pressure, affecting the propagation speed of the pressure pulse signal. High pressure may cause phase changes in the fluid, such as liquefied natural gas or gas phase precipitation, which will appear as sudden jumps or mutations in the signal. Solid particles may break or settle under high pressure, causing additional interference to the signal.

[0046] Embodiment 3: The signal acquisition and compensation part dynamically compensates the downhole fluid pressure pulse signal by combining the coupling relationship between the Navier-Stokes equation and the heat conduction equation through the following formula to obtain a compensation signal:

[0047] ;

[0048] in, For time Downhole fluid pressure pulse signal at the time; The temperature of the downhole fluid The density under is the fluid velocity vector of the downhole fluid; is the enthalpy change of the downhole fluid; is the gas constant; is the specific heat capacity at constant pressure, which indicates the heat required to raise the temperature of the downhole fluid per unit mass by 1K under constant pressure conditions; is the specific heat capacity at constant volume, which indicates the heat required to raise the temperature of the downhole fluid per unit mass by 1K under constant volume conditions; is the compensation signal.

[0049] Specifically, the core of the formula is based on fluid dynamics. The Navier-Stokes equations describe the motion of fluids, and the time and space variation terms they contain reflect the dynamic changes of pressure, velocity, and density in the complex environment of the well. and Represent the local acceleration term and the inertia term respectively. The former captures the trend of fluid velocity and density changing with time, while the latter describes the spatial coupling between density distribution and velocity field. Through these dynamic parameters, the formula can track the nonlinear behavior of fluid in pressure wave propagation in real time, thereby effectively compensating for the deviation of the signal caused by the dynamic changes of fluid density and velocity. The effect of temperature is through the density function and thermodynamic compensation Under high temperature conditions, the density of the fluid will change significantly with temperature, thus affecting the propagation speed and amplitude of the pressure wave. The heat conduction equation is used to describe the dynamic changes of the temperature field and the regulatory effect of temperature on density and pressure. The density function in the formula reflects this coupling relationship and incorporates the effect of temperature on the fluid dynamics into the compensation process. The thermodynamic compensation term further describes the temperature and enthalpy changes. The enthalpy quantifies the state change of the fluid during the energy conversion process, such as the energy release or absorption caused by phase change or chemical reaction. The exponential correction term shows that the nonlinear effect of temperature on the pressure signal has a significant amplification effect, especially in the high temperature range. This part is used in the formula to correct the distortion of the amplitude and frequency of the pressure pulse signal caused by temperature. In addition, the heat capacity ratio correction term It is an important parameter in the compensation process, which reflects the thermodynamic response characteristics of the fluid during compression and expansion. and specific heat at constant volume They respectively describe the amount of heat required to increase the temperature per unit mass of the fluid under constant pressure and constant volume conditions. This ratio is closely related to the expansibility and compressibility of the fluid, especially under the multiphase conditions of gas-liquid mixtures and solid particles downhole, and its dynamic changes directly affect the propagation characteristics of the pressure wave. Through this correction term, the formula can accurately adjust the physical characteristics of the signal during the compensation process to make it consistent with the actual fluid behavior downhole. Overall, the formula is based on time and space changes, and dynamically compensates the downhole pressure pulse signal through the combined effects of physical parameters such as density, velocity, temperature, and heat capacity ratio. This compensation mechanism not only focuses on the nonlinear behavior of the fluid in a dynamic environment, but also fully considers how the thermodynamic characteristics under high temperature and high pressure conditions are coupled with the propagation characteristics of the pressure signal. The final compensation signal is the original signal The corrected version of the formula effectively eliminates the distortion and interference caused by environmental changes, while retaining the key features of fluid dynamics and thermodynamics. The formula embodies the ability to accurately describe and correct the dynamic changes of signals in complex downhole fluid environments. Its physical principle comes from the close combination of fluid mechanics and thermodynamics, and can truly reproduce the propagation law of downhole pressure pulse signals.

[0050] Embodiment 4: The feature processing part performs feature extraction based on the Helmholtz wave equation on the compensation signal through the following formula to obtain an intermediate result:

[0051] ;

[0052] in, is the intermediate result; is the Laplace operator; is the speed of sound, which is equal to the ratio of the bulk elastic modulus of the downhole fluid to the density of the downhole fluid; is the temperature attenuation coefficient, is the set value; is the intensity attenuation coefficient, which describes the intensity attenuation of the signal caused by the viscoelastic properties of the medium during propagation and is a set value; is the propagation distance.

[0053] Specifically, the first part of the formula contains , that is, the Laplace operator acts on the spatial distribution term of the compensation signal. The Laplace operator is used to describe the gradient change of the compensation signal in space, reflecting the diffusion characteristics of the pressure wave on the propagation path. In the high temperature and high pressure environment underground, the pressure signal will be affected by the complex geological structure and multiphase fluid, which will cause the spatial distribution of the signal to be uneven. By calculating the second-order derivative of the spatial gradient, the formula can accurately capture the diffusion effect generated by the signal during the propagation process. This is an important step in analyzing the local propagation characteristics of the signal, because the diffusion characteristics are directly related to the density of the fluid and the elastic modulus of the medium. The second part of the formula, , describes the propagation behavior of the compensation signal in the time dimension, where Represents the speed of sound, which is the ratio of the bulk elastic modulus of the downhole fluid to its density. The speed of sound plays the role of a core parameter in the formula, and its value directly determines the speed at which the pressure wave propagates in the fluid. By introducing the second-order time derivative term, the formula can quantify the acceleration change of the pressure signal over time, thereby revealing the dynamic characteristics of the signal propagation process. This part and the spatial diffusion term together constitute the basic framework of the classical Helmholtz wave equation, which is used to describe the law of wave propagation. The third part of the formula, , further refines the propagation characteristics of the signal, especially introducing the influence of temperature and medium attenuation. The spatial gradient of the first-order rate of change of the pressure signal over time is calculated, reflecting the velocity change caused by medium resistance and heterogeneity during signal propagation. It describes the intensity attenuation of the signal during propagation. This term introduces the attenuation coefficient and propagation distance , simulating the loss of signal energy due to the viscoelastic properties of the downhole medium. The viscoelastic effect in downhole fluids is usually related to the friction between particles of the medium, the viscosity of the fluid, and the multiphase characteristics, which will cause the amplitude of the signal to decay exponentially with the propagation distance. In addition, the temperature attenuation coefficient It is used to describe the further effect of high temperature environment on the rate of change of the signal, because the increase in temperature will reduce the rigidity of the medium and the efficiency of sound wave propagation. Overall, this formula combines the space, time and medium characteristics of the wave equation to provide a compensation signal. The feature extraction of the formula provides a multi-dimensional analysis framework. By comprehensively describing the dynamic changes in time and space dimensions and introducing correction factors for temperature and intensity attenuation, the intermediate results generated by the formula It contains the core characteristics of the pressure signal propagation process. These characteristics include the propagation speed of the signal, the degree of spatial diffusion, and the influence of the medium and environment on the signal strength, which can provide rich information for subsequent feature analysis and signal reconstruction. The physical principle of this feature extraction process is based on the basic framework of the Helmholtz wave equation, and at the same time expands its scope of application so that it can adapt to the signal characteristics of complex downhole environments. The formula extracts dynamic characteristics from the compensation signal through a combination of spatial diffusion, time propagation and medium attenuation, revealing the hidden dynamic laws in the signal propagation process. This feature extraction method based on physical models ensures the accurate analysis of pressure signal characteristics, and provides a solid physical and mathematical foundation for further signal analysis and reconstruction.

[0054] Embodiment 5: The feature processing part performs entropy dynamic feature extraction based on Boltzmann-Gibbs entropy on the intermediate result through the following formula to obtain the feature extraction result:

[0055] ;

[0056] in, is the feature extraction result; is the Boltzmann constant; is the reference feature value, used to normalize the feature, and is the set value; is the volume integral differential element; is the volume of downhole fluid; is the viscosity of the downhole fluid; is the reference pressure value, used to normalize the pressure, and is the set value; is the gradient of the fluid velocity vector of the downhole fluid in the X-axis direction; is the gradient of the fluid velocity vector of the downhole fluid in the Y-axis direction; is the gradient of the fluid velocity vector of the downhole fluid in the Z-axis direction.

[0057] Specifically, the first part of the formula, , directly introduces the core idea of ​​Boltzmann-Gibbs entropy, and describes the relative characteristics between the compensation signal and the intermediate result in the form of statistical entropy. It is the scaling factor for entropy calculation, ensuring that the physical dimensions of the feature extraction results are consistent with the thermodynamic system. Represents the volume of fluid in the entire well The global statistics of signal characteristics can capture the distribution and change trend of the signal in the entire space. is the weighting factor of the signal characteristics, which depends on the downhole temperature , which reflects the non-uniformity of fluid distribution and the effect of density on signal propagation. Since fluid density changes significantly with temperature in a high-temperature and high-pressure environment, the introduction of density weights enhances the formula's ability to analyze the true dynamic characteristics of the wellbore. Logarithmic term It is the core expression of feature extraction, which reveals the complexity of the signal in a non-equilibrium state by calculating the relative change between the normalized intermediate result and the compensation signal. and compensation signal They come from the previous processing steps, their normalization (by reference eigenvalue and reference pressure The formula provides a universal and consistent feature extraction result for signals of different dimensions. By performing a logarithmic mapping of relative changes, the formula can amplify small differences in the signal, especially the nonlinear behavior caused by complex fluid systems in high temperature and high pressure environments. This amplification mechanism gives the formula a significant advantage in capturing changes in signal details, and can effectively characterize the transition process of the fluid system from an ordered state to a disordered state.

[0058] The second part of the formula, , which supplements the dynamic influence of fluid viscous dissipation on feature extraction results. It is an important parameter to measure the internal friction of the fluid, and its value directly determines the energy dissipation rate of the fluid. Downhole fluids usually exhibit significant viscoelastic properties, which will cause energy attenuation and distortion in signal propagation. Velocity gradient term They describe the rate of change of the velocity field in each direction, and their square values ​​represent the local energy dissipation caused by the velocity gradient. Through this term, the formula can reveal the dynamic characteristics of the fluid during signal propagation, especially how viscous dissipation changes the frequency distribution and amplitude change of the signal. It is worth noting that the results of this part are also consistent with the compensation signal. , which further reflects the dynamic changes of the compensated signal under the action of viscous dissipation. This combination mechanism ensures that the formula can accurately reflect the comprehensive influence of fluid viscosity on the signal, especially under high temperature and high pressure conditions, when the fluid density is large and the velocity changes drastically, viscous dissipation will significantly affect the propagation characteristics of the signal. The overall formula combines the statistical characteristics of entropy with the dynamic effects of viscous dissipation, and performs in-depth feature extraction of the signal from both the global and local levels. The entropy part captures the overall complexity of the signal in space through global integration and quantifies the non-equilibrium characteristics of the fluid system; while the viscous dissipation part focuses on local detail changes, revealing the dynamic characteristics of the fluid and its impact on signal propagation. This dual feature extraction method provides a comprehensive analytical framework that can effectively handle the multi-dimensional characteristics of signals in complex downhole environments. From a physical point of view, the feature extraction results It is a dynamic representation of the pressure signal of the fluid system under high temperature and high pressure environment. The change of entropy directly reflects the state transition process of the system from order to disorder. This transition is closely related to the thermodynamic properties of the fluid and is jointly affected by factors such as temperature, pressure and density distribution. The change of viscous dissipation reveals the dynamic behavior of the fluid, especially the energy loss caused by the resistance of the viscoelastic medium during the propagation of the signal. In the complex fluid system downhole, this feature extraction method lays a solid foundation for subsequent signal analysis and reconstruction. Whether it is global characteristics or local characteristics, the formula can analyze the key features of the signal in a highly accurate way and reveal the physical laws contained in the pressure signal. Each term in the formula is closely combined with the basic principles of fluid dynamics and thermodynamics, ensuring the physical consistency and theoretical completeness of the feature extraction results. By performing dual feature extraction on the global and local details of the signal, this method can capture the dynamic changes of the signal in the complex environment downhole, providing an effective means and physical basis for signal processing in complex fluid environments.

[0059] Embodiment 6: The signal reconstruction part calculates the fluid dynamics information entropy of the feature extraction result by the following formula:

[0060] ;

[0061] in, is the fluid dynamics information entropy; is the absolute value operator; is the specific enthalpy of the downhole fluid; the phase space vector is obtained by reconstructing the fluid dynamics information entropy based on the Takens embedding theorem through the following formula:

[0062] ;

[0063] in, is the phase space vector; is the time delay, is the set value; is the set embedding dimension.

[0064] Specifically, the calculation formula of fluid dynamics information entropy is from the characteristic signal and intermediate results Starting from the ratio relationship of , the relationship between the two and their time-varying characteristics are characterized by the introduction of logarithmic functions. The absolute value operator and logarithmic function in the formula quantify the dynamic changes of the characteristic signal. This quantification is not just a simple numerical calculation, but a mathematical expression of the signal propagation characteristics in the downhole fluid. Describes the relative strength of characteristic signals, and its value reflects the relative change amplitude of the signal under different states. By comparing the rate of change of the signal, the dynamic relationship between the two characteristic signals is further explored. Since the logarithmic function has the characteristic of amplifying small changes, this term is particularly sensitive to weak but important changes in the signal, thus being able to capture the subtle characteristics of the pressure wave propagation process in the downhole fluid. The formula further introduces the fluid density and specific enthalpy Time rate of change , which describes the state evolution of the downhole fluid from a thermodynamic perspective. It is a physical property of fluid under different temperature conditions, and its value directly affects the propagation speed and energy distribution of pressure waves. Describes the thermal energy state of the fluid, which is the thermal energy per unit mass of fluid under specific pressure and temperature conditions. The product of the two represents the thermodynamic energy density of the fluid, while its time rate of change reflects the dynamic adjustment of the thermodynamic state over time. By introducing this term, the formula can directly relate the change of the signal to the change of the thermodynamic state of the fluid, thereby revealing the coupling effect of downhole fluid dynamics and thermodynamics.

[0065] At the same time, the square root ratio term in the formula The relationship between the signals is corrected nonlinearly. This correction emphasizes the dynamic balance of the signal in the amplitude and frequency dimensions through the square root ratio of the characteristic signal. The introduction of the square root ensures the stability of the calculation results and avoids numerical deviations caused by large differences in signal amplitudes. In the high-temperature and high-pressure environment underground, the intensity and frequency of the signal are often affected by changes in fluid density, temperature, and pressure. This item makes the results of the fluid dynamics information entropy more physically meaningful by amplifying important features while suppressing the influence of interference factors. Based on the calculated fluid dynamics information entropy , the formula further uses Takkens embedding theorem to reconstruct its phase space. Embedding formula In, time delay and embedding dimension It is a key parameter for constructing high-dimensional phase space. Takkens embedding theorem provides a mathematical framework for reconstructing high-dimensional dynamical systems from time series. Its principle is to map the dynamic behavior of one-dimensional time series to high-dimensional space through delayed embedding method, so that the dynamic characteristics of the original system can be clearly displayed in high-dimensional phase space. The choice of ensures the dynamic independence of each dimension, while the embedding dimension This determines the geometric complexity of the phase space. The result of phase space reconstruction is a high-dimensional vector Its physical meaning lies in that it reflects the time evolution law of the signal through multi-dimensional description. Each dimension of the vector corresponds to the entropy value of the signal at a specific time point, and the relationship between the multi-dimensional vectors reflects the dynamic evolution trajectory of the signal. By analyzing the phase space trajectory, we can find possible periodic behaviors, asymptotic states or dynamic patterns in the signal. This analysis method provides a new perspective on the dynamic characteristics of signals in downhole fluid systems. It can not only be used to analyze the past state of the signal, but also predict its future behavior. The exponential weight term in the formula The phase space vector is weighted. Reference eigenvalue and reference pressure value The introduction of is used to normalize the signal, thereby eliminating the dimensional differences between signals of different amplitudes. This normalization process ensures that the reconstructed phase space vector can accurately reflect the true characteristics of the signal without being affected by the amplitude of the original signal. The exponential weight term enhances the sensitivity of the reconstruction result to dynamic changes by amplifying the contrast between characteristic signals.

[0066] Embodiment 7: The signal reconstruction part calculates the fluctuation characteristics according to the phase space vector through the following formula based on the Langevin equation and the theory of thermodynamic fluctuations:

[0067] ;

[0068] in, is the damping coefficient of the downhole fluid; is the potential energy function of the downhole fluid; potential energy function Calculated using the following formula:

[0069] ;

[0070] in, is the average height of the downhole fluid; is the acceleration due to gravity.

[0071] Specifically, the first part of the formula describes the time variation of the phase space vector and its force characteristics based on the Langevin equation. The Langevin equation is a classic stochastic dynamics model, which is usually used to describe the motion state of a system under the action of random external forces. Represents the phase space vector The time derivative of reflects the dynamic evolution of the signal in time. The physical meaning of this term is to capture the instantaneous rate of change of the signal trajectory and reveal how the dynamic behavior of the signal is affected by time changes. The damping coefficient describes the damping effect of the fluid system. Characterizes the influence of the internal friction characteristics of downhole fluid in high pressure and high temperature environment and the viscoelasticity of the medium on signal propagation. The introduction of the damping term reflects the energy dissipation mechanism of the signal during propagation. When the signal amplitude is large, it will be significantly attenuated, showing a strong dissipation characteristic; When it is smaller, the fluctuation amplitude of the signal is easier to maintain, which is manifested as higher dynamic stability. Based on the potential energy function The rate of change of reflects the regulation of the force of the fluid system in the potential energy field on the signal. The calculation is done by the integral formula Completed, taking into account the kinetic energy, gravitational potential energy and thermodynamic state of the fluid. It represents the kinetic energy per unit volume of fluid, where density and flow rate It is the core parameter describing fluid dynamics. Gravitational potential energy It describes the potential energy change of the fluid caused by the height difference, where is the average height of the fluid, reflecting the distribution characteristics caused by gravity effect in the downhole environment. represents the specific heat correction of the fluid under thermodynamic conditions, where is the constant pressure specific heat capacity of the fluid, which is used to describe the relationship between heat and temperature in thermodynamic processes. Combined with the gradient term of the potential energy function , the formula can describe how the dynamic changes of the signal are regulated by the fluid dynamics potential field. This term is particularly critical in the calculation of fluctuation characteristics because it reveals the direct connection between the evolution trajectory of the phase space vector and the change of the downhole fluid state. The last part of the formula is a feature correction term used to quantify information entropy , Feature extraction results and intermediate results The design of this correction term further amplifies the relationship between these signal features through the absolute value of the ratio and the square root operation, enhancing the sensitivity of the fluctuation feature to the dynamic changes of the signal. Specifically, the calculation of the ratio term reflects the relative changes of the signal in different feature dimensions, while the introduction of the square root ensures that the result remains numerically stable while improving the ability of the eigenvalue to resolve small changes. Fluctuation Features The physical meaning of is to describe the random fluctuation behavior of the fluid system in a non-equilibrium state. This feature is one of the key results of signal reconstruction because it directly quantifies the randomness and fluctuation in the downhole fluid system. The random fluctuation of the fluid comes from the interaction between external disturbances (such as temperature gradients, pressure changes, etc.) and the complex dynamics inside the system. Through the combination of the Langevin equation and the potential energy gradient, the formula can fully characterize the impact of these fluctuations on the signal and provide physically meaningful characteristic quantities for subsequent signal processing and analysis.

[0072] Embodiment 8: The signal reconstruction part performs multi-scale pulse detection based on Kolmogorov entropy and Lyapunov index, combined with fluctuation characteristics, phase space vector, fluid dynamics information entropy and compensation characteristics, and obtains the detection result through the following formula:

[0073] ;

[0074] in, For test results; is the L2 norm; is the maximum Lyapunov exponent; is the Kolmogorov entropy.

[0075] Specifically, the first part of the formula is the maximum Lyapunov exponent The Lyapunov exponent is a measure of the sensitivity of a dynamic system, which is used to describe how small changes in initial conditions are magnified over time. The maximum Lyapunov exponent is used in the formula , focusing on the phase space vector The trajectory separation rate in the highest dimension directly reflects the chaotic characteristics of the system. In the complex downhole environment, the pressure pulse signal is affected by the interaction of multiphase fluids, thermodynamic disturbances of high temperature and high pressure, and the viscoelastic properties of the medium, showing significant nonlinear behavior. , the formula can quantify the dynamic change trend of the signal in the time dimension and reveal the stability and nonlinear characteristics of the signal. The relevant part is , that is, the fluctuation characteristics Phase space vector The L2 norm of the time derivative of . The L2 norm is the Euclidean length of a vector, which represents the overall intensity of the fluctuation characteristics on the change of the phase space vector. The physical significance of this part is to quantify the distribution of the fluctuation characteristics in the phase space and its impact on the overall behavior of the signal. The fluctuation characteristics come from the Langevin equation and the theory of thermodynamic fluctuations. Its essence is the wave characteristics of the fluid system in a non-equilibrium state. By combining it with the phase space vector, the formula captures the complex dynamic changes in the signal caused by the fluctuations.

[0076] The middle part of the formula is based on the Kolmogorov entropy The Kolmogorov entropy reflects the rate of information loss in a system within a finite time and is a key indicator for describing the chaotic characteristics of the system. The exponential form of the information entropy of fluid dynamics The ratio reflects the relationship between information generation and thermodynamic state. Information entropy It is a measure of the complexity of the system state and describes the global characteristics of the downhole pressure pulse signal. and temperature The introduction of further couples the kinetic properties with the thermodynamic properties. Through this part, the formula can reveal how the temporal complexity of the signal is regulated by the thermodynamic state, providing a broader kinetic perspective for the detection results. Another key part of the formula is the entropy calculation formula for the combination of ratio and logarithmic terms This item analyzes the feature extraction results through ratio and logarithmic operations. and intermediate results Dynamic change relationship of. reflects the relative strength of the characteristic signals, while the difference term It describes the difference of the signal in the characteristic dimension. The introduction of the logarithmic function amplifies the small changes, so that it can capture the detailed characteristics of the signal during the detection process. This part not only quantifies the local change characteristics of the signal, but also provides key mathematical support for the overall complexity of the signal. It describes the state change of the fluid system from the perspective of thermodynamics. It is the basic physical property of the fluid, describing the distribution of the fluid downhole, while specific enthalpy The time rate of change of the two directly reflects the dynamic adjustment of the signal due to temperature and pressure changes during the propagation process. Through this term, the formula can closely combine the dynamic change of the signal with the physical properties of the fluid, providing support for the physical meaning of the detection results. It combines the Kolmogorov entropy, information entropy and signal ratio. The design of this weight term emphasizes the comprehensive characteristics of the signal at multiple scales through exponential functions and weighting methods. The combination of ratios and weights further enhances the sensitivity of the formula to dynamic changes, while avoiding the deviation caused by the dominance of a single feature. The introduction of weight terms ensures the balance of detection results between different time scales and signal characteristics, providing a powerful mathematical tool for the comprehensive analysis of complex underground signals. Finally, the detection results It is a comprehensive reflection of all parts of the formula, and its physical meaning lies in describing the multi-scale dynamic characteristics of the downhole pressure pulse signal. Through the Lyapunov exponent and Kolmogorov entropy, the formula reveals the nonlinear characteristics and time complexity of the signal; through the fluctuation characteristics, phase space vector and information entropy, the formula analyzes the dynamic characteristics of the signal from both global and local perspectives. The combination of exponential weights and logarithmic terms enables the detection results to fully reflect the changing laws of the signal and capture the dynamic characteristics in a multi-scale environment.

[0077] Embodiment 9: The detection result is reconstructed by the following formula to obtain a reconstructed downhole fluid pressure pulse signal:

[0078] ;

[0079] in, is the maximum fluid dynamics information entropy; is the reconstructed downhole fluid pressure pulse signal.

[0080] Specifically, the first part of the formula This part is the basis of reconstruction. Combined with the correction term based on thermodynamic fluctuation theory, it reflects the core dynamic characteristics of the signal and its relationship with the thermodynamic state of the system. It is the core feature quantity obtained through multi-scale analysis and nonlinear dynamic feature extraction, which contains the main dynamic information of the signal. Through the fluctuation characteristics The Boltzmann constant describes the dynamic adjustments in the signal due to non-equilibrium fluctuations. and temperature The introduction of couples the fluctuation characteristics of the signal with the thermodynamic state of the fluid, and the decay characteristics of the exponential term reflect the regulation of the thermodynamic fluctuation on the signal intensity. When it is high, this term will significantly attenuate the signal and avoid signal distortion due to thermodynamic noise. On the contrary, when the fluctuation is small, the main dynamic characteristics of the signal are preserved. This part ensures the physical consistency of the signal from a thermodynamic point of view and makes an effective physical correction to the dynamic characteristics of the signal. The second part of the formula Describes the gradient change characteristics of the signal in the spatial dimension. Pressure gradient It is the spatial change rate of the downhole pressure distribution, which directly reflects the propagation characteristics of the signal and its evolution in complex media. The normalization formula can eliminate the deviation caused by the absolute amplitude difference and emphasize the local variation characteristics of the signal along the propagation path. The physical meaning of this part is to capture the spatial variation pattern of the signal and normalize it to the standard framework to ensure that the reconstructed signal can accurately reflect the true distribution state of the downhole fluid. Especially in multiphase fluids and complex downhole geological conditions, the change in pressure gradient directly affects the propagation speed and amplitude fluctuation of the signal. The normalized gradient ratio enhances the spatial resolution of signal reconstruction by emphasizing these local characteristics.

[0081] Normalized term for information entropy Is another important component of the formula. Information entropy It is a quantitative indicator of the complexity of the system state, and its value directly reflects the nonlinear characteristics of the signal and the trend of time evolution. Through standardization, the formula ensures that the signal matches the overall complexity of the system in dynamic changes. The introduction of information entropy not only captures the global characteristics of the signal, but also enhances the dynamic adaptability of the signal through standardization. In the high-temperature and high-pressure environment underground, the complexity of the signal is usually affected by the combined effects of fluid dynamics, thermodynamics and external environmental interference. The standardization of information entropy ensures that the overall characteristics of the signal are retained during the reconstruction process, while avoiding the excessive influence of local characteristics on global characteristics. The last part It is the weight adjustment term between the feature signal and the compensation signal, which exponentially amplifies the dynamic difference between the two. Feature extraction results and compensation signal They represent the characteristics of the signal at different stages. This part highlights the dynamic changes of the signal in the multidimensional feature space by weighting the absolute value of the difference between the two. This weight adjustment can amplify the impact of key features on the reconstructed signal, while weakening the interference of secondary features, making the reconstruction result more consistent with the true characteristics of the signal. The exponential weight term converts the difference in signal characteristics into a dynamic adjustment factor of the reconstructed signal through a nonlinear amplification mechanism, thereby enhancing the physical expression of the signal. Overall, the reconstruction formula It is a multi-dimensional, multi-scale signal reconstruction model that combines multiple theories of dynamics, thermodynamics, and information theory. Each part of the formula corrects or amplifies specific signal characteristics, and together constructs a complete reconstruction framework. The first part ensures the authenticity and consistency of the signal through thermodynamic fluctuation correction; the second part captures the spatial characteristics of the signal through gradient normalization; the information entropy normalization term enhances the global dynamic characteristics of the signal, and the feature difference weight term further highlights the dynamic changes of the signal. The final reconstructed signal It is a true restoration of the downhole pressure pulse signal. It not only retains the main dynamic characteristics of the signal, but also ensures the physical integrity and reliability of the signal by eliminating environmental interference and thermodynamic fluctuations. This formula provides powerful mathematical tools and theoretical support for the processing and reconstruction of complex downhole signals through rigorous physical modeling and multi-dimensional feature analysis. Its design is not only applicable to downhole pressure signals, but can also be extended to signal processing scenarios in other complex environments, providing a new solution to signal reconstruction problems in multiple fields. At the same time, the formula's comprehensive analysis of dynamic characteristics, thermodynamic states and multi-dimensional characteristics also provides valuable reference value for theoretical research in the field of signal processing. This multi-scale, multi-dimensional reconstruction method significantly improves the accuracy and robustness of signal reconstruction, and provides technical support for signal analysis and monitoring in complex downhole environments.

[0082] 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 downhole pressure pulse signal processing system for high temperature and high pressure environments, characterized in that: include: A signal acquisition and compensation part, a feature processing part and a signal reconstruction part; the signal acquisition and compensation part is used to acquire downhole fluid pressure pulse signals and downhole temperature signals in real time, and dynamically compensate the downhole fluid pressure pulse signals in combination with the coupling relationship between the Navier-Stokes equation and the heat conduction equation to obtain a compensation signal; the feature processing part is used to extract features of the compensation signal based on the Helmholtz wave equation to obtain an intermediate result, and then extract entropy dynamic features of the intermediate result based on the Boltzmann-Gibbs entropy to obtain a feature extraction result; The signal reconstruction part is used to calculate the fluid dynamics information entropy of the feature extraction result; The phase space vector is obtained by reconstructing the fluid dynamics information entropy based on Takens embedding theorem. Based on the Langevin equation and the theory of thermodynamic fluctuations, the fluctuation characteristics are calculated according to the phase space vector; based on the Kolmogorov entropy and Lyapunov index, multi-scale pulse detection is performed in combination with the fluctuation characteristics, phase space vector, fluid dynamics information entropy and compensation characteristics to obtain the detection results; the detection results are reconstructed to obtain the reconstructed downhole fluid pressure pulse signal; The feature processing part extracts the features of the compensation signal based on the Helmholtz wave equation through the following formula to obtain an intermediate result: ； in, is the intermediate result; is the Laplace operator; is the speed of sound, which is equal to the ratio of the bulk elastic modulus of the downhole fluid to the density of the downhole fluid; is the temperature attenuation coefficient, is the set value; is the intensity attenuation coefficient, which describes the intensity attenuation of the signal caused by the viscoelastic properties of the medium during propagation and is a set value; is the propagation distance; is the compensation signal; For time; The feature processing part performs entropy dynamic feature extraction based on Boltzmann-Gibbs entropy on the intermediate result through the following formula to obtain the feature extraction result: ； in, is the feature extraction result; is the Boltzmann constant; is the reference feature value, used to normalize the feature, and is the set value; is the volume integral differential element; is the volume of downhole fluid; is the viscosity of the downhole fluid; is the reference pressure value, used to normalize the pressure, and is the set value; is the gradient of the fluid velocity vector of the downhole fluid in the X-axis direction; is the gradient of the fluid velocity vector of the downhole fluid in the Y-axis direction; is the gradient of the fluid velocity vector of the downhole fluid in the Z-axis direction; The temperature of the downhole fluid The density below.

2. The downhole pressure pulse signal processing system for high temperature and high pressure environment according to claim 1, characterized in that: The downhole fluid includes: downhole oil and gas mixture and drilling fluid; the downhole fluid has multiphase characteristics, and the form includes: gas, liquid and solid particles; the temperature range of the downhole fluid is: 150-200°C; the pressure range of the downhole fluid is 30-100MPa.

3. The downhole pressure pulse signal processing system for high temperature and high pressure environment according to claim 2, characterized in that: The signal acquisition and compensation part dynamically compensates the downhole fluid pressure pulse signal by combining the coupling relationship between the Navier-Stokes equation and the heat conduction equation through the following formula to obtain a compensation signal: ； in, For time Downhole fluid pressure pulse signal at the time; is the fluid velocity vector of the downhole fluid; is the enthalpy change of the downhole fluid; is the gas constant; is the specific heat capacity at constant pressure, which indicates the heat required to raise the temperature of the downhole fluid per unit mass by 1K under constant pressure conditions; It is the specific heat capacity at constant volume, which means the heat required to raise the temperature of downhole fluid per unit mass by 1K under constant volume conditions.

4. The downhole pressure pulse signal processing system for high temperature and high pressure environment according to claim 3, characterized in that: The signal reconstruction part calculates the fluid dynamics information entropy of the feature extraction result by the following formula: ； in, is the fluid dynamics information entropy; is the absolute value operator; is the specific enthalpy of the downhole fluid; the phase space vector is obtained by reconstructing the fluid dynamics information entropy based on the Takens embedding theorem through the following formula: ； in, is the phase space vector; is the time delay, is the set value; is the set embedding dimension.

5. The downhole pressure pulse signal processing system for high temperature and high pressure environment according to claim 4, characterized in that: The signal reconstruction part calculates the fluctuation characteristics according to the phase space vector through the following formula based on the Langevin equation and the theory of thermodynamic fluctuations: ； in, is the damping coefficient of the downhole fluid; is the potential energy function of the downhole fluid; potential energy function Calculated using the following formula: ； in, is the average height of the downhole fluid; is the acceleration due to gravity.

6. The downhole pressure pulse signal processing system for high temperature and high pressure environment according to claim 5, characterized in that: The signal reconstruction part performs multi-scale pulse detection based on Kolmogorov entropy and Lyapunov index, combined with fluctuation characteristics, phase space vector, fluid dynamics information entropy and compensation characteristics, and obtains the detection result through the following formula: ； in, For test results; is the L2 norm; is the maximum Lyapunov exponent; is the Kolmogorov entropy.

7. The downhole pressure pulse signal processing system for high temperature and high pressure environment according to claim 6, characterized in that: The detection result is reconstructed by the following formula to obtain the reconstructed downhole fluid pressure pulse signal: ； in, is the maximum fluid dynamics information entropy; is the reconstructed downhole fluid pressure pulse signal.

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