A method, system, medium, and product for testing the pressure-bearing capacity of deep well casing.

Abstract

A method, system, medium, and product for detecting the pressure-bearing performance of deep well casing are disclosed. In this method, a sensing fiber and a temperature sensor are fixed to the outer wall of the casing. Under variable temperature and pressure loading conditions, Brillouin frequency shift distribution data and temperature data are acquired. Based on the temperature data, the real-time temperature of the fiber core is calculated to eliminate the influence of thermal effects and obtain the apparent mechanical strain. Simultaneously, using a pre-established database of adhesive layer rheological properties, combined with the real-time temperature, the shear modulus of the adhesive layer is determined, a strain transfer model is constructed to calculate the transfer coefficient, and finally, the apparent mechanical strain is corrected to obtain the true mechanical strain value of the casing outer wall. This application aims to improve the accuracy of detecting the true pressure-bearing deformation of casing under variable temperature fracturing simulation conditions.

Description

Technical Field

[0001] This application belongs to the field of intelligent testing, and in particular relates to a method, system, medium and product for testing the pressure-bearing performance of deep well casing. Background Technology

[0002] As the core pressure-bearing component throughout the entire life cycle of oil and gas wells, deep well casing not only needs to withstand the static compression of formation rocks during the development of deep shale gas, but also must cope with the alternating loads and drastic temperature changes brought about by high-pressure fluid injection during large-scale volumetric fracturing operations. Therefore, accurately detecting the mechanical behavior and deformation characteristics of casing under complex working conditions through full-scale physical simulation tests in a laboratory environment is a key means to optimize casing string design and prevent downhole casing deformation failure.

[0003] Among related technologies, a distributed fiber optic sensing and detection system based on Brillouin optical time-domain reflectometry (BOTDR) or Rayleigh scattering technology can be used. This technology involves laying specially packaged sensing fibers along the entire length of the sleeve, either axially or helically, and using epoxy resin or a special adhesive to tightly bond and fix the fibers to the outer wall of the sleeve. When the sleeve is deformed under simulated ground pressure and internal pressure loads in the testing machine, the fiber undergoes corresponding deformation. By demodulating the frequency drift of the backscattered light signal inside the fiber, strain data from thousands of continuous measurement points along the fiber path can be obtained. This method enables panoramic monitoring of the mechanical behavior along the entire length of the sleeve, capturing stress concentration areas and early local deformation characteristics, thus improving the data richness and evaluation accuracy of the sleeve's pressure-bearing performance testing.

[0004] However, in simulating fracturing conditions, to recreate the process of rapidly injecting large amounts of cryogenic fracturing fluid into a high-temperature wellbore, the test system controls the casing temperature to drop drastically within a short period. According to the principle of fiber optic sensing, the frequency shift of the optical signal is a function of strain and temperature. To obtain accurate mechanical strain, the frequency shift component caused by temperature changes must be eliminated. Related technologies typically assume that the optical fiber closely attached to the casing and the casing substrate are in thermal equilibrium, directly using the temperature data of the casing surface for compensation. However, in the aforementioned scenario of rapid temperature changes, due to the presence of the sensing fiber core, protective coating, adhesive layer, and casing... Significant differences exist in the thermal conductivity and specific heat capacity among the four components of the casing steel matrix, and the adhesive layer itself has a certain thermal resistance effect. This causes the temperature change response speed of the optical fiber core to lag behind the temperature change of the casing steel matrix on the time axis. As a result, during the dynamic process of thermal shock, a nonlinear deviation occurs between the actual temperature felt by the optical fiber and the compensation temperature used by the demodulation system. Consequently, false strain signals that are difficult to remove by conventional static compensation algorithms are mixed into the demodulated strain data, reducing the accuracy of detecting the actual pressure deformation of the casing under variable temperature fracturing simulation conditions. Summary of the Invention

[0005] This application provides a method, system, medium, and product for testing the pressure-bearing performance of deep well casing, which is used to improve the accuracy of testing the actual pressure-bearing deformation of casing under simulated temperature fracturing conditions.

[0006] In the first aspect, this application provides a method for testing the pressure-bearing performance of deep well casing and establishes a database of rheological properties of the shear modulus of the bonding layer as a function of temperature.

[0007] The control simulation test device performs variable temperature and pressure loading tests on the bushing;

[0008] A distributed optical fiber demodulator was used to collect Brillouin frequency shift distribution data of the sensing optical fiber, and a temperature sensor was used to synchronously collect wall temperature data of the bushing.

[0009] Based on the wall temperature data, calculate the real-time internal temperature data of the core of the sensing fiber.

[0010] By using real-time internal temperature data, the fiber thermo-optic effect frequency shift component and the sleeve substrate thermo-expansion frequency shift component are removed from the Brillouin frequency shift distribution data to obtain the apparent mechanical strain data.

[0011] Real-time internal temperature data is mapped to a rheological database to retrieve and determine the real-time shear modulus value of the adhesive layer at the current moment.

[0012] A strain transfer model is constructed based on the real-time shear modulus value, the geometric parameters of the sensing fiber, and the thickness parameters of the adhesive layer.

[0013] The strain transfer coefficient at the current moment is calculated based on the strain transfer model.

[0014] The apparent mechanical strain data are corrected by using the strain transfer coefficient to obtain the true mechanical strain value of the outer wall of the casing.

[0015] By employing the above technical solution, a database of the rheological properties of the adhesive layer's shear modulus as a function of temperature is established. Combined with real-time temperature data collected by temperature sensors, the shear modulus values ​​of the adhesive layer at different temperatures are accurately obtained. Based on this, a strain transfer model is constructed to calculate the strain transfer coefficient. After obtaining fiber optic Brillouin frequency shift data, this method eliminates the effects of thermo-optical effects and thermostriction, obtaining apparent mechanical strain data. This data is then corrected using the strain transfer coefficient to finally obtain the true mechanical strain value of the casing's outer wall. This measurement method, which considers the influence of temperature on the adhesive layer's shear modulus, improves the accuracy of deep well casing pressure-bearing performance testing results and reduces systematic errors caused by neglecting the influence of temperature on the mechanical properties of the adhesive layer in traditional measurement methods. Simultaneously, by acquiring temperature data in real-time and performing dynamic correction, this method improves the reliability of testing results under varying temperature environments, making the measurement results closer to the actual pressure-bearing state of the casing. This improves the accuracy of detecting the true pressure-bearing deformation of the casing under simulated temperature fracturing conditions.

[0016] In conjunction with some implementations of the first aspect, in some implementations, the real-time internal temperature data of the core of the sensing optical fiber is calculated based on the wall temperature data, specifically including:

[0017] The thermal conductivity, specific heat capacity, and density parameters of the sensing fiber and the bonding layer are obtained. Combined with the cross-sectional radius of the sensing fiber, thermal inertial characteristic parameters that characterize the time delay effect of heat transfer in the radial process are constructed.

[0018] Based on thermal inertia characteristic parameters, a discretized heat conduction differential model is established to describe the dynamic response relationship between the sleeve wall temperature and the fiber core temperature. The discretized heat conduction differential model defines the numerical constraint relationship between the current core temperature and the current wall temperature and the previous core temperature.

[0019] The wall temperature data of the bushing is used as a time-varying input sequence and substituted into the discretized heat conduction differential model. The model is recursively calculated according to the time step and outputs the real-time internal temperature data of the core of the sensing fiber corresponding to the wall temperature data on the time axis.

[0020] By adopting the above technical solution and considering the thermal parameters of the sensing fiber and adhesive layer, thermal inertial characteristic parameters characterizing the time delay effect of radial heat transfer were constructed, and a discretized thermal conduction differential model describing the dynamic response relationship between the sleeve wall temperature and the fiber core temperature was established. By substituting the sleeve wall temperature data as a time-varying input sequence into the model for recursive calculation, real-time internal temperature data of the fiber core was obtained. This calculation method, which considers the time delay effect during heat conduction, improves the accuracy of the fiber core temperature calculation results and reduces the measurement error caused by directly using surface temperature as the fiber temperature in traditional methods. This method, by establishing a thermal conduction differential model, improves the accuracy of temperature field analysis and makes the fiber strain measurement results closer to actual conditions.

[0021] In conjunction with some implementations of the first aspect, in some implementations, a strain transfer model is constructed based on the real-time shear modulus value, the geometric parameters of the sensing fiber, and the thickness parameters of the adhesive layer, specifically including:

[0022] The interfacial shear stiffness of the adhesive layer on the optical fiber at the current moment is calculated using the real-time shear modulus value, the thickness parameter of the adhesive layer, and the outer diameter of the coating layer of the sensing optical fiber.

[0023] The shear hysteresis characteristic value at the current moment is calculated using the interfacial shear stiffness, the core elastic modulus of the sensing fiber, and the core radius.

[0024] Using the shear hysteresis eigenvalue and the effective bonding length of the sensing fiber as independent variables, a hyperbolic strain transfer distribution function is constructed.

[0025] The strain transfer distribution function is used as the strain transfer model.

[0026] By employing the aforementioned technical solution, a hyperbolic strain transfer distribution function was constructed by calculating the interfacial shear stiffness and shear hysteresis characteristic value of the adhesive layer on the optical fiber. This modeling method based on shear hysteresis theory considers the combined influence of the real-time shear modulus and thickness parameters of the adhesive layer, as well as the geometric dimensions of the optical fiber, on the strain transfer process, thus improving the accuracy of the strain transfer model. By using the strain transfer distribution function as the strain transfer model, this method improves the accuracy of strain transfer coefficient calculation, reduces the errors generated by traditional simplified models in calculating strain transfer characteristics, and makes the final sleeve strain value closer to the actual value.

[0027] In conjunction with some embodiments of the first aspect, in some embodiments, after calculating the gain correction of the apparent mechanical strain data using the strain transfer coefficient to obtain the true mechanical strain value of the outer wall of the casing, the method further includes:

[0028] Based on the fiber optic cable routing path, the first derivative of the actual mechanical strain value with respect to the position coordinates is calculated to obtain the strain gradient sequence.

[0029] High gradient segments in the strain gradient sequence whose absolute values ​​are greater than a preset gradient threshold are selected;

[0030] The pre-stored gradient-transfer efficiency correlation table is called, and the corresponding transfer efficiency attenuation coefficient is matched according to the strain gradient value of each point in the high gradient section; among them, the transfer efficiency attenuation coefficient is negatively correlated with the absolute value of the strain gradient value.

[0031] The mechanical strain value in the high gradient section is compensated by division using the transmission efficiency attenuation coefficient to obtain the gradient-corrected mechanical strain value.

[0032] By employing the above technical solution, a strain gradient sequence is obtained by calculating the first derivative of the actual mechanical strain value with respect to the position coordinates. High-gradient sections are then selected, and the strain values ​​within these sections are compensated and corrected using a pre-stored gradient-transfer efficiency correlation table. This correction method, which considers the influence of strain gradient on transfer efficiency, improves the accuracy of strain measurement in non-uniform deformation regions and reduces the measurement error of traditional methods in regions with large strain gradients. By establishing a correlation between strain gradient values ​​and the transfer efficiency attenuation coefficient, this method improves the measurement accuracy in high strain gradient regions, making the strain detection results more consistent with the actual strain distribution characteristics of the casing.

[0033] In conjunction with some implementations of the first aspect, in some implementations, the steps for constructing the gradient-transfer efficiency correlation table include:

[0034] Obtain the shear modulus and geometric parameters of the optical fiber coating and the adhesive layer used to bond the optical fiber;

[0035] Based on the shear hysteresis theory, a strain transmission differential equation including strain gradient variables is established.

[0036] The strain gradient values ​​are substituted into the strain transfer differential equation for numerical solution. The ratio of the fiber sensing strain to the actual strain of the substrate corresponding to each strain gradient value is calculated and used as the transfer efficiency attenuation coefficient.

[0037] Establish a one-to-one mapping relationship between strain gradient values ​​and transfer efficiency attenuation coefficients, and generate a gradient-transfer efficiency correlation table.

[0038] By employing the aforementioned technical solution, the shear modulus and geometric parameters of the fiber coating and adhesive layer are obtained. A strain transfer differential equation incorporating strain gradient variables is established, and the strain gradient value is substituted into the solution to obtain the transfer efficiency attenuation coefficient. This generates a gradient-transfer efficiency correlation table, enabling the system to accurately quantify the strain transfer efficiency under different strain gradient conditions. Since there is a nonlinear relationship between strain transfer efficiency and strain gradient, this theoretically modeled correlation table construction method avoids the accuracy loss that may result from traditional empirical formulas. By using the ratio of the actual strain to the fiber-sensed strain as the transfer efficiency attenuation coefficient, the system establishes a precise correspondence between strain gradient values ​​and transfer efficiency, improving the strain measurement accuracy in high strain gradient regions. Compared to simple linear correction methods, this theoretically model-driven method better reflects the nonlinear characteristics of the strain transfer process, improving the reliability of strain measurement results.

[0039] In some embodiments, in conjunction with the first aspect, after obtaining the gradient-corrected mechanical strain value, the method further includes:

[0040] Obtain the spatial impulse response function of the demodulation device used to acquire optical signals;

[0041] The gradient-corrected mechanical strain values ​​were used as the observation sequence.

[0042] A mathematical model is established in which the convolution of the local peak strain sequence to be determined with the spatial impulse response function equals the observed sequence.

[0043] The mathematical model is solved using a deconvolution algorithm, and the local peak strain sequence is output.

[0044] By employing the above technical solution, and by obtaining the spatial impulse response function of the demodulation device, using the gradient-corrected mechanical strain values ​​as the observation sequence, a mathematical model based on convolution operations is established and solved using a deconvolution algorithm. This effectively eliminates the ambiguity effect of the spatial impulse response function on the strain measurement results. Since the spatial resolution of the distributed fiber optic sensing system is limited by the pulse width, the measured strain distribution is actually the convolution result of the true strain distribution and the spatial impulse response function. Reconstructing the local peak strain sequence through deconvolution operations reduces the measurement deviation of strain peaks caused by the spatial impulse response characteristics and improves the spatial resolution of strain measurements. This mathematical reconstruction method can more accurately reflect the spatial distribution characteristics of local strain in the sleeve, enhancing the system's sensitivity to detecting local strain anomalies.

[0045] In conjunction with some embodiments of the first aspect, in some embodiments, after calculating the gain correction of the apparent mechanical strain data using the strain transfer coefficient to obtain the true mechanical strain value of the outer wall of the casing, the method further includes:

[0046] Calculate the radial expansion of the casing at the current moment based on the actual mechanical strain value;

[0047] The change in the radius of curvature of the sensing fiber is calculated based on the radial expansion and the initial helical winding angle of the sensing fiber.

[0048] The additional bending strain caused by the change in the geometric shape of the optical fiber is calculated based on the change in the radius of curvature.

[0049] Subtracting the additional bending strain value from the actual mechanical strain value yields the geometrically corrected mechanical strain value.

[0050] By employing the above technical solution, the radial expansion of the sleeve is calculated, and the change in radius of curvature is calculated in conjunction with the initial helical winding angle of the sensing fiber. This allows for the determination of the additional bending strain caused by the change in the fiber's geometry. Finally, this effect is subtracted from the actual mechanical strain value, resulting in a more accurate mechanical strain measurement. Because the fiber is helically wound on the sleeve surface, the radial expansion of the sleeve under pressure causes a change in the fiber's helical curvature, generating additional bending strain. By establishing a geometric correction model to quantitatively assess the impact of this bending effect, the strain measurement error caused by the fiber's deployment method is reduced, improving the system's strain measurement accuracy under sleeve radial deformation conditions. This compensation method, which considers geometric nonlinearity, improves the accuracy of strain measurement.

[0051] In a second aspect, embodiments of this application provide a pressure-bearing performance testing system for deep well casing. The pressure-bearing performance testing system for deep well casing includes: one or more processors and a memory; the memory is coupled to one or more processors, and the memory is used to store computer program code, the computer program code including computer instructions, and one or more processors call the computer instructions to cause the system to perform the method described in the first aspect and any possible implementation thereof.

[0052] Thirdly, embodiments of this application provide a computer-readable storage medium including instructions that, when executed on a system, cause the system to perform the method described in the first aspect and any possible implementation thereof.

[0053] Fourthly, embodiments of this application provide a computer program product that, when run on a system, causes the system to execute the method described in any possible implementation of the first aspect.

[0054] One or more technical solutions provided in the embodiments of this application have at least the following technical effects or advantages:

[0055] 1. This application provides a method for testing the pressure-bearing performance of deep well casing. By establishing a database of the rheological properties of the bonding layer's shear modulus as a function of temperature, and combining this with real-time temperature data collected by temperature sensors, the method accurately obtains the shear modulus values ​​of the bonding layer at different temperatures. Based on this, a strain transfer model is constructed to calculate the strain transfer coefficient. After obtaining fiber optic Brillouin frequency shift data, this method eliminates the effects of thermo-optical effects and thermostriction to obtain apparent mechanical strain data. This data is then corrected using the strain transfer coefficient to finally obtain the true mechanical strain value of the casing's outer wall. This measurement method, which considers the influence of temperature on the bonding layer's shear modulus, improves the accuracy of the pressure-bearing performance testing results for deep well casing and reduces systematic errors caused by neglecting the influence of temperature on the mechanical properties of the bonding layer in traditional measurement methods. Simultaneously, by acquiring temperature data in real time and performing dynamic correction, this method improves the reliability of the testing results under varying temperature environments, making the measurement results closer to the actual pressure-bearing state of the casing. This improves the accuracy of detecting the true pressure-bearing deformation of the casing under simulated temperature fracturing conditions.

[0056] 2. This application provides a method for testing the pressure-bearing capacity of deep well casing. The method obtains a strain gradient sequence by calculating the first derivative of the actual mechanical strain value with respect to the position coordinates, identifies high-gradient sections, and compensates for the strain values ​​within these sections using a pre-stored gradient-transmission efficiency correlation table. This correction method, which considers the influence of strain gradient on transmission efficiency, improves the accuracy of strain measurement in non-uniform deformation regions and reduces measurement errors in regions with large strain gradients, as is common in traditional methods. By establishing a correlation between strain gradient values ​​and the transmission efficiency attenuation coefficient, this method improves the measurement accuracy in high strain gradient regions, making the strain detection results more consistent with the actual strain distribution characteristics of the casing. Attached Figure Description

[0057] Figure 1 This is a flowchart illustrating a method for testing the pressure-bearing performance of a deep well casing according to an embodiment of this application.

[0058] Figure 2 This is another schematic flowchart of a method for testing the pressure-bearing performance of a deep well casing in an embodiment of this application.

[0059] Figure 3 This is a schematic diagram of the physical device structure of a pressure-bearing performance testing system for deep well casing provided in an embodiment of this application. Detailed Implementation

[0060] The terminology used in the following embodiments of this application is for the purpose of describing particular embodiments only and is not intended to be limiting of this application. As used in the specification and appended claims of this application, the singular expressions “a,” “an,” “the,” “the,” “the,” and “this” are intended to include the plural expressions as well, unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used in this application refers to any or all possible combinations including one or more of the listed items.

[0061] Hereinafter, the terms "first" and "second" are used for descriptive purposes only and should not be construed as implying or suggesting relative importance or implicitly indicating the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature, and in the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more.

[0062] The following example is used in conjunction with Figure 1 The following describes a method for testing the pressure-bearing performance of a deep well casing in an embodiment of this application:

[0063] Please see Figure 1 This is a flowchart illustrating a method for testing the pressure-bearing performance of a deep well casing in an embodiment of this application.

[0064] S101. Establish a database of rheological properties of the adhesive layer as a function of temperature;

[0065] The adhesive layer refers to the polymer material layer located between the outer wall of the deep well casing and the sensing optical fiber, used to fix the optical fiber and transmit strain. Its material can include, but is not limited to, epoxy resin, silicone, or polyimide. Shear modulus is a physical quantity describing a material's resistance to deformation under shear force, characterizing the material's rigidity. The rheological property database refers to a structured data set storing the changes in the mechanical property parameters of the adhesive layer material over time or temperature under different temperature conditions. In this step, rheological properties refer to the viscoelastic properties exhibited by the adhesive layer material, meaning its mechanical response combines the characteristics of both elastic solids and viscous fluids. The system first identifies the type of adhesive used in the casing under test and obtains the material's basic physical properties. Subsequently, the system conducts standardized material mechanics tests on the adhesive layer sample within a preset temperature range (e.g., from room temperature to the highest temperature of the deep well simulation conditions, such as above 200 degrees Celsius) at predetermined temperature intervals (e.g., every 5 or 10 degrees Celsius). The system records the ratio of shear stress to shear strain at each temperature point, i.e., the shear modulus. For scenarios involving multiple thresholds, such as temperature thresholds, the system sets low-temperature, medium-temperature, and high-temperature thresholds to distinguish between the glassy, ​​elastic, and viscous flow states of a material, ensuring that the database covers the entire phase transition process. The system organizes, verifies, and structures these discrete experimental data points, creating a mapping table or fitted curve that allows for quick lookup of the corresponding shear modulus using a temperature index, thus establishing a complete rheological property database.

[0066] To establish this database, the system can employ Dynamic Thermomechanical Analysis (DMA) technology. In this technology, the system controls a DMA analyzer to apply sinusoidal alternating mechanical stress to the adhesive layer sample while simultaneously heating the sample at a set heating rate (e.g., 2°C / min). The system monitors the material's response to the alternating force in real time, separating the storage modulus (elastic component) and loss modulus (viscous component). The shear modulus is obtained through complex modulus calculation, and the modulus curve continuously changing with temperature is automatically recorded. Another approach is to use a rotational rheometer for steady-state shear testing. The system places the adhesive sample between the parallel plate or conical plate clamps of the rheometer and controls the heating unit to stabilize the ambient temperature at a specific target temperature. After temperature equilibrium is reached, the system applies a constant shear rate or shear stress, measures the resulting torque, and then calculates the shear modulus at that constant temperature. The system sequentially changes the temperature setpoint, repeating the above process to obtain a series of shear modulus values ​​at discrete temperatures, and then constructs a continuous temperature-modulus relationship model using an interpolation algorithm.

[0067] S102. Control the simulation test device to perform variable temperature and pressure loading tests on the bushing;

[0068] A simulation testing device refers to a large-scale physical experimental platform capable of simulating complex working conditions in deep wells. This device has the ability to apply axial loads, confining pressures, internal pressures, and regulate ambient temperature to full-size or scaled-down casing specimens. Variable temperature and pressure loading tests refer to the system dynamically changing the temperature and pressure fields applied to the casing according to a preset working condition curve during the test to reproduce the real stress environment during fracturing, steam injection, or extraction. The execution of the loading test involves the coordinated operation of multiple control loops. The system first initializes the testing device, checking the status of the hydraulic system, heating system, and data acquisition system. Next, the system reads the preset loading scheme, which defines the target values ​​for temperature and pressure, the rate of increase and decrease, and the holding time. For temperature control, the system controls the flow rate and temperature of the heating jacket or circulating hot fluid to make the casing wall temperature rise or fall at a predetermined slope. For pressure control, the system adjusts the output pressure of the hydraulic pump to apply internal pressure to the casing to simulate fluid pressure, or external pressure to simulate formation pressure. The system monitors various safety indicators in real time during the loading process to ensure that the test is conducted within the safe range allowed by the equipment. The system uses precise timing control to ensure that temperature loading and pressure loading are synchronized or carried out according to a specific phase difference, thereby simulating the sleeve response under thermo-mechanical coupling.

[0069] To achieve precise temperature and pressure control, the system can employ multi-loop feedback control technology based on the PID (Proportional-Integral-Derivative) algorithm. The system compares real-time feedback signals from temperature and pressure sensors with the set target values ​​to calculate the error signal. The PID controller dynamically adjusts the heater's power output and the hydraulic servo valve's opening based on the magnitude, integral, and derivative values ​​of the error to eliminate steady-state errors and suppress overshoot, ensuring the actual loading curve closely follows the preset trajectory. Another approach is to use an advanced control strategy based on Model Predictive Control (MPC). The system establishes a thermodynamic and fluid dynamic mathematical model of the simulated experimental device, using this model to predict the system response over a finite time domain. The system calculates the optimal control input sequence (such as heating power and pump pressure commands) at the current moment by solving an optimization problem online, addressing large hysteresis and nonlinear characteristics. This method can more effectively handle coupling disturbances between temperature and pressure; for example, when rapid heating causes fluid expansion and pressure fluctuations, the system can anticipate and compensate for these fluctuations in advance.

[0070] S103. Use a distributed optical fiber demodulator to collect Brillouin frequency shift distribution data of the sensing optical fiber, and use a temperature sensor to synchronously collect the wall temperature data of the sleeve.

[0071] A distributed fiber optic demodulator is a precision instrument based on the principles of optical time-domain reflectometry (OTDR) or optical frequency-domain reflectometry (OFDR), utilizing nonlinear scattering effects in optical fibers (such as Brillouin scattering) to measure the distribution of physical quantities along the fiber's length. Brillouin frequency shift distribution data refers to the distribution of the frequency shift of the center frequency of the Brillouin scattered light relative to the incident light frequency along the fiber's position. This frequency shift is linearly related to the temperature and strain state of the fiber. Temperature sensors, such as thermocouples, resistance temperature detectors (RTDs), or fiber Bragg grating sensors, are used to measure the surface temperature at specific locations on the sheath. Synchronous acquisition refers to the system controlling the fiber optic demodulator and temperature acquisition module to start data recording under the same time reference, ensuring strict alignment of the two data sets on the time axis. The system injects pulsed light into the sensing fiber, which is laid within the adhesive layer on the outer wall of the sheath, through an optical switch or modulator, and receives the backscattered light. The system performs spectral analysis on the received optical signal, extracting the Brillouin frequency shift values ​​at various points along the fiber, forming a spatially continuous data stream. Simultaneously, the system reads the values ​​from discrete temperature sensors closely attached to the sheath wall at a high sampling rate. The system adds a unified timestamp to the collected Brillouin frequency shift data and wall temperature data, and performs preliminary formatting processing for subsequent steps.

[0072] One specific technique for acquiring Brillouin frequency shift is Brillouin Optical Time-Domain Analysis (BOTDA). The system injects pump pulses and continuous probes at both ends of the optical fiber. When the frequency difference between the two beams falls within the Brillouin gain spectrum, stimulated Brillouin scattering occurs. The system scans the frequency difference between the two beams, measures the Brillouin gain spectrum at various points in the fiber, and uses the Lorentz fitting algorithm to determine the frequency difference corresponding to the peak of the gain spectrum, which is the Brillouin frequency shift. This method features high signal-to-noise ratio and high measurement accuracy. Another technique is Brillouin Optical Time-Domain Reflectometry (BOTDR). The system injects an optical pulse from only one end of the optical fiber and uses heterodyne detection or direct detection techniques to receive the weak spontaneous Brillouin backscattered light. The system uses Fast Fourier Transform (FFT) or other spectral analysis methods to analyze the spectral information of the scattered light and extract the frequency shift distribution. The advantage of BOTDR technology is that it only requires single-end access and is suitable for scenarios where the fiber is broken or the loop cannot be closed. For wall temperature acquisition, the system can use multiple K-type thermocouple patches to convert analog voltage signals into digital temperature signals via a data acquisition card (DAQ); or it can use a series of fiber optic grating (FBG) sensor arrays to obtain multi-point temperatures by reading the drift of specific wavelengths through a wavelength demodulator.

[0073] S104. Calculate the real-time internal temperature data of the core of the sensing optical fiber based on the wall temperature data.

[0074] The system calculates the real-time internal temperature data of the fiber core of the sensing fiber based on the wall temperature data. Specifically, this includes: acquiring the thermal conductivity, specific heat capacity, and density parameters of the sensing fiber and its bonding layer, and constructing thermal inertia characteristic parameters that characterize the time delay effect of heat transfer in the radial direction, combined with the cross-sectional radius of the sensing fiber; establishing a discretized heat conduction differential model based on the thermal inertia characteristic parameters to describe the dynamic response relationship between the sleeve wall temperature and the fiber core temperature, defining the numerical constraint relationship between the current core temperature, the current wall temperature, and the previous core temperature; substituting the sleeve wall temperature data as a time-varying input sequence into the discretized heat conduction differential model, recursively calculating according to the time step, and outputting the real-time internal temperature data of the sensing fiber core corresponding to the wall temperature data on the time axis.

[0075] The fiber core of the sensing fiber is the core region for optical signal transmission, and its temperature directly determines the frequency shift caused by the thermo-optical effect. Real-time internal temperature data refers to the actual temperature value of the fiber core at any given time. Thermal inertia characteristic parameters are physical quantities that characterize the time lag and amplitude attenuation characteristics caused by the presence of material thermal capacity and thermal resistance during the transfer of heat from the cladding wall through the adhesive layer to the fiber core. The discretized thermal conduction differential model is a numerical calculation model obtained by discretizing the partial differential equation of thermal conduction in time and space. The system first reads the stored thermal properties parameters of the sensing fiber (including the core, cladding, and coating) and adhesive layer, including thermal conductivity (characterizing thermal conductivity), specific heat capacity (characterizing heat storage capacity), and density. The system combines the geometric dimensions of the fiber (cross-sectional radius) to calculate the comprehensive thermal diffusivity or thermal time constant, and constructs the thermal inertia characteristic parameters. Subsequently, based on the law of conservation of energy and Fourier's law of thermal conduction, the system establishes a difference equation describing the radial heat conduction process. This equation transforms a continuous physical process into numerical computation within discrete time steps, defining the current core temperature as determined by the core temperature of the previous time step, the current wall temperature, and the temperature difference between them. The system inputs the collected wall temperature time series as boundary conditions into the model, and through iterative calculation, it derives the core temperature response curve for each time step, thereby correcting the temperature measurement error caused by thermal conduction hysteresis.

[0076] To implement the discretized heat conduction differential model in this step, the system can employ the explicit finite difference method. The system divides the cross-section of the fiber and bonding layer into several concentric circular nodes, assuming a uniform temperature within each node. The system approximates the time derivative using a forward difference scheme and the spatial derivative using a central difference scheme, constructing a recursive formula. Within each time step, the system directly calculates the current temperature value using the temperature values ​​of each node from the previous time step. This method is computationally fast and simple to implement, but it requires stability conditions (the time step must be sufficiently small). Another implementation method is the Crank-Nicolson implicit difference scheme. The system approximates the spatial derivative by averaging the current and next time steps in the time direction, constructing a system of linear equations. Within each time step, the system obtains the current core temperature by solving a tridiagonal matrix of equations. This method is numerically unconditionally stable, allows for larger time steps, offers higher computational accuracy, and can more accurately capture the thermal hysteresis effect during rapid temperature changes.

[0077] S105. Using real-time internal temperature data, remove the fiber thermo-optic effect frequency shift component and the sleeve substrate thermo-expansion frequency shift component from the Brillouin frequency shift distribution data to obtain apparent mechanical strain data.

[0078] The fiber thermo-optic effect frequency shift component refers to the component that shifts the Brillouin frequency due to the change in the refractive index of the fiber caused by temperature changes. This frequency shift is only related to temperature and does not represent the mechanical stretching or compression of the fiber. The sleeve matrix thermo-scaling frequency shift component refers to the frequency shift component caused by the thermal expansion or contraction of the sleeve metal matrix due to temperature changes, which causes deformation of the fiber through the adhesive layer. Although this is deformation, it is thermally induced deformation, not mechanical strain caused by external force. Apparent mechanical strain data refers to the frequency shift or directly converted strain value corresponding to the strain caused only by external mechanical loads (such as pressure or tension) after deducting the two thermally related effects mentioned above from the total frequency shift. Based on Brillouin scattering theory, the total frequency shift is a function of temperature and strain. The system uses the real-time internal temperature data of the fiber core obtained in step S104, combined with the fiber's temperature sensitivity coefficient (usually obtained through calibration), to calculate the frequency shift caused by the thermo-optic effect. At the same time, the system uses this temperature data and the thermal expansion coefficient of the sleeve material to calculate the frequency shift caused by the thermal expansion of the matrix. Following the principle of linear superposition (under the assumption of small deformation), the system subtracts the two calculated thermally correlated frequency shift components point by point from the Brillouin frequency shift distribution data obtained in step S103. After this decoupling process, the system separates the signal component purely generated by mechanical load, i.e., the apparent mechanical strain data, providing a net value input for subsequent strain transfer correction.

[0079] S106. Map the real-time internal temperature data to the rheological property database, retrieve and determine the real-time shear modulus value of the adhesive layer at the current moment.

[0080] Mapping refers to establishing a correspondence between temperature values ​​and database indexes. Real-time shear modulus refers to the stiffness index of the adhesive layer material against shear deformation at a specific time and temperature. In this step, the system acts as the data processing center, receiving real-time internal temperature data of the sensing fiber core (or average temperature data of the adhesive layer, depending on the model accuracy requirements) from step S104. The system uses this temperature data as a query key to access the adhesive layer rheological property database established in step S101. Since the database stores modulus values ​​at discrete temperature points, the system needs to perform retrieval and numerical calculation operations. If the queried temperature matches a discrete point in the database, the system directly reads the corresponding shear modulus value; if the queried temperature is between two discrete points, the system performs interpolation calculations based on the values ​​of adjacent points to determine the shear modulus at the current precise temperature. This process is performed synchronously at each sampling point on the time axis, ensuring that the obtained shear modulus value strictly matches the current temperature state, thus reflecting the evolution of the mechanical properties of the adhesive layer during temperature changes.

[0081] Specifically, the system can employ linear interpolation to implement the retrieval and determination method for this step. The system finds the maximum temperature point T_1 below the current temperature and the minimum temperature point T_2 above the current temperature in the database, along with their corresponding shear moduli G_1 and G_2. The system then calculates the shear modulus G at the current temperature T using the formula G = G_1 + (T - T_1) * (G_2 - G_1) / (T_2 - T_1). This method has low algorithm complexity, fast response speed, and is suitable for databases with dense data points. Another implementation method is the function fitting and calling method. During the database establishment phase, the system has already parametrically fitted the curve of shear modulus versus temperature using the Arrhenius equation or the WLF (Williams-Landel-Ferry) equation, obtaining the analytical expression G(T). In step S106, the system directly substitutes the real-time temperature T into this analytical expression for function calculation and directly outputs the shear modulus value. This method provides a smooth and continuous modulus change curve, avoiding the piecewise linear errors that interpolation may introduce, and is particularly accurate in regions where the modulus changes exponentially with temperature.

[0082] S107. Based on the real-time shear modulus value, the geometric dimensions of the sensing fiber, and the thickness parameters of the adhesive layer, a strain transfer model is constructed.

[0083] Based on the real-time shear modulus, the geometric parameters of the sensing fiber, and the thickness parameters of the adhesive layer, a strain transfer model is constructed. Specifically, this includes: calculating the interfacial shear stiffness of the adhesive layer on the fiber at the current moment using the real-time shear modulus, the thickness parameters of the adhesive layer, and the outer diameter of the coating layer of the sensing fiber; calculating the shear hysteresis characteristic value at the current moment using the interfacial shear stiffness, the core elastic modulus of the sensing fiber, and the core radius; constructing a hyperbolic strain transfer distribution function with the shear hysteresis characteristic value and the effective adhesive length of the sensing fiber as independent variables; and using the strain transfer distribution function as the strain transfer model.

[0084] The strain transfer model is a mathematical model describing how the mechanical deformation of the external substrate (sleeve) is transferred to the internal sensing fiber through the intermediate adhesive layer. Due to shear deformation in the adhesive layer, the strain sensed by the fiber is usually less than the actual strain of the substrate; this phenomenon is called shear hysteresis. Interfacial shear stiffness is a physical quantity characterizing the shear force generated by the adhesive layer under a unit shear displacement; it integrates the effects of material properties and geometric dimensions. The shear hysteresis characteristic value is a dimensionless or dimensionally specific parameter used to quantify the efficiency of strain transfer; the larger the value, the more efficient the strain transfer. The strain transfer distribution function is a hyperbolic function describing the strain transmissibility at various points along the fiber optic axis. The system first reads the geometric parameters of the sensing fiber (such as the core radius and coating outer diameter) and the thickness parameters of the adhesive layer (determined by the construction process or obtained through measurement). Combining the real-time shear modulus value obtained in step S106, the system calculates the interfacial shear stiffness of the adhesive layer on the fiber. Next, the system introduces the elastic modulus (Young's modulus) of the fiber core and derives the shear hysteresis characteristic value using the mechanical equilibrium equations. Finally, the system constructs a hyperbolic cosine or hyperbolic tangent function using this characteristic value and the effective bonding length of the optical fiber as parameters. This function defines the strain transfer ratio distribution from the end of the optical fiber to the central region, thus forming a complete strain transfer model.

[0085] Specifically, the system employs the classic Cox shear hysteresis model theory to construct the strain transfer model. The system assumes that both the optical fiber and the substrate are elastic bodies, and that the adhesive layer only bears shear force with a constant radial shear stress distribution. The system then uses formulas to calculate the shear hysteresis parameters. The formula includes terms such as the shear modulus G of the adhesive layer, the elastic modulus E_f of the optical fiber, the radius r_f of the optical fiber, and the outer radius r_m of the adhesive layer. Based on The system is constructed in the following form: The distribution function, where The length is the half-bonded length. This method has clear physical meaning and is computationally simple. Another implementation method is to use a three-layer cylindrical model. The system considers the multi-layer interactions between the core, coating layer, adhesive layer, and substrate. The system establishes a set of elasticity equations in cylindrical coordinates, considering the continuity conditions of radial and axial displacements between layers. By solving this set of equations, the system obtains a more refined shear hysteresis characteristic value, which considers not only the shear of the adhesive layer but also the shear contribution of the coating layer. This method is suitable for cases with thicker coating layers or softer materials, and can provide a more rigorous mechanical description.

[0086] S108. Calculate the strain transfer coefficient at the current moment based on the strain transfer model;

[0087] The strain transfer coefficient (STC) is a dimensionless value between 0 and 1, defined as the ratio of the strain value sensed by the optical fiber to the actual strain value of the sleeve substrate. It reflects the degree of strain loss from the measured object to the sensor. The closer the coefficient is to 1, the better the transfer effect and the closer the measurement result is to the true value; the smaller the coefficient, the more severe the shear hysteresis effect. After constructing the strain transfer model containing real-time parameters in step S107, the system substitutes the relevant variables at the current moment into the model for calculation. For the effective measurement area in the middle of the optical fiber, the system usually calculates the average transfer coefficient or the center point transfer coefficient of this area. The system obtains the specific coefficient value under the current temperature and material state by analytically calculating the value of the hyperbolic function. This coefficient is dynamically changing; as the temperature changes, the shear modulus of the adhesive layer changes, and the strain transfer coefficient fluctuates accordingly. The system recalculates this coefficient in each data acquisition cycle to ensure the real-time performance and accuracy of the correction factor.

[0088] Specifically, the system can employ an analytical function evaluation method to calculate the strain transfer coefficient, based on the hyperbolic function model determined in S107. (Assuming the origin is at the center of the fiber), the system determines the effective integration interval corresponding to the spatial resolution of fiber Brillouin scattering measurement. The system integrates the distribution function within this interval and calculates the average value to obtain the average strain transfer coefficient within this spatial resolution unit. This method directly utilizes mathematical analytical expressions, and the calculation accuracy depends on the accuracy of the model. Another implementation method is to use a numerical lookup table. The system pre-builds a detailed 3D fiber-adhesive layer-sleeve model using finite element analysis software (such as ANSYS or ABAQUS), performs simulation calculations under different combinations of shear modulus and geometric dimensions, obtains a series of strain transfer coefficients, and stores them in a multidimensional lookup table. In step S108, based on the real-time shear modulus obtained in S106 and the known geometric parameters, the system performs multilinear interpolation in the lookup table to directly obtain the corresponding strain transfer coefficient. This method avoids complex real-time analytical derivations and can include complex boundary effects considered in the finite element model.

[0089] S109. The apparent mechanical strain data is corrected by using the strain transfer coefficient to obtain the true mechanical strain value of the outer wall of the casing.

[0090] Gain correction calculation refers to the mathematical operation process of compensating for measured values ​​using the calculated transfer coefficient, aiming to restore signal loss during transmission. The true mechanical strain value refers to the actual geometric deformation rate of the outer wall of the bushing under external load, and is the final key indicator for evaluating the bushing's pressure-bearing performance and structural integrity. In this step, the system uses the apparent mechanical strain data obtained in step S105 as the divisor and the strain transfer coefficient obtained in step S108 at the current moment as the divisor. The system performs a division operation (or multiplies by the reciprocal of the coefficient) to restore the folded strain "seen" by the optical fiber to the "actual" strain of the bushing. For example, if the apparent strain is 500 microstrain and the calculated transfer coefficient is 0.8, the system calculates the true strain to be 625 microstrain. The system performs this correction operation on all data points distributed along the optical fiber, ultimately generating a strain distribution curve reflecting the true stress state of the bushing's outer wall. This result eliminates the error caused by the influence of temperature on material properties, providing engineers with a reliable basis for judging whether the bushing has yielded or ruptured.

[0091] Specifically, the system can employ point-by-point scalar division to implement gain correction calculations. The system performs element-wise division between the spatially aligned apparent strain array and the strain transfer coefficient array (if the coefficients vary along the axial direction). ,in This represents the sampling point index on the optical fiber. This method is logically simple, has extremely fast computation speed, and is suitable for real-time display. Another implementation method is to use a weighted moving average correction method. Considering the random noise in the experimental data, simple point-to-point correction may amplify the noise. Before or after the division correction, the system uses a Gaussian weighted average or rectangular window function to process the moving average of neighboring data points. The system sets the window size according to the spatial resolution, smoothing the data curve while correcting the amplitude, thus obtaining an accurate and smooth true mechanical strain distribution map.

[0092] In the above embodiments, by establishing a database of the rheological properties of the adhesive layer's shear modulus as a function of temperature, and combining it with real-time temperature data collected by temperature sensors, the shear modulus values ​​of the adhesive layer at different temperatures are accurately obtained. Based on this, a strain transfer model is constructed to calculate the strain transfer coefficient. After obtaining fiber optic Brillouin frequency shift data, this method eliminates the effects of thermo-optical effects and thermostriction to obtain apparent mechanical strain data. This data is then corrected using the strain transfer coefficient to finally obtain the true mechanical strain value of the casing's outer wall. This measurement method, which considers the influence of temperature on the shear modulus of the adhesive layer, improves the accuracy of the deep well casing's pressure-bearing performance testing results and reduces the systematic errors caused by neglecting the influence of temperature on the mechanical properties of the adhesive layer in traditional measurement methods. Simultaneously, by acquiring temperature data in real time and performing dynamic correction, this method improves the reliability of the testing results under varying temperature environments, making the measurement results closer to the actual pressure-bearing state of the casing. This improves the accuracy of detecting the true pressure-bearing deformation of the casing under simulated temperature fracturing conditions.

[0093] Building upon the strain measurements considering temperature effects described above, and considering the possibility of uneven strain distribution due to localized deformation of the casing during pressure bearing, this application proposes another method for testing the pressure bearing performance of deep well casing to further improve the accuracy of strain measurements. This method analyzes the spatial characteristics of strain distribution and performs targeted compensation for high-gradient regions, thereby obtaining more accurate measurement results. The following section will combine... Figure 2 Another method for testing the pressure-bearing performance of deep well casing in this application embodiment is described below:

[0094] Please see Figure 2 This is another flowchart illustrating a method for testing the pressure-bearing performance of a deep well casing in this application.

[0095] S201. Based on the fiber optic cable routing path, calculate the first derivative of the actual mechanical strain value with respect to the position coordinates to obtain the strain gradient sequence.

[0096] The fiber optic deployment path refers to the geometric trajectory of the sensing fiber on the outer wall of the deep well casing, typically a spiral or straight laying. This path defines the spatial correspondence between the sensing points on the fiber and the physical location of the casing. The true mechanical strain value refers to the strain data obtained after temperature compensation and preliminary strain transfer correction in the preceding steps, removing the influence of thermal effects. The position coordinates are distance scalars along the fiber length, used to identify the absolute spatial position of each sampling point. The first derivative mathematically represents the rate of change of a function value with respect to the independent variable; in this context, it physically represents the rate of change of strain along the fiber axis. The strain gradient sequence is an ordered set of strain rate values ​​calculated at all sampling points. The system first reads the spatial sampling interval set by the fiber demodulator (i.e., the distance difference between two adjacent data points), and then extracts the true mechanical strain values ​​of adjacent or nearby sampling points sequentially according to the fiber deployment order. The system uses a numerical differential algorithm to calculate the ratio of strain increment to position increment, thereby obtaining the strain gradient value corresponding to each spatial location point. This step aims to quantify the non-uniformity of the casing deformation and identify areas of stress concentration or severe deformation, where traditional uniform strain transfer models will produce large errors.

[0097] To specifically implement the calculation of strain gradient sequences, the system can employ the Central Difference Method. For any data point in the middle of the sequence, the system selects the preceding and following data points, calculates the strain difference between these two points, and divides it by the distance between them (i.e., twice the sampling interval). This method has a second-order truncation error, offering higher computational accuracy than simple forward or backward differencing, and more accurately reflects the local variation trend of the current point. Another implementation method is to use a Savitzky-Golay smoothing differential filter. The system selects a certain number of data points within the current point and its left and right neighborhoods (e.g., a window size of 5 or 7 points), and uses the least squares method to fit these points into a low-order polynomial (such as a second- or third-order polynomial). The system directly differentiates the fitted polynomial and calculates the derivative value at the center point. This method effectively suppresses drastic fluctuations in the gradient calculation value caused by measurement noise while calculating the gradient, making it particularly suitable for distributed fiber optic sensing data with low signal-to-noise ratios.

[0098] S202. Select high gradient segments in the strain gradient sequence whose absolute values ​​are greater than the preset gradient threshold;

[0099] A high-gradient section refers to a localized area on a deep well casing where the strain distribution changes drastically, typically corresponding to buckling, necking, or crack propagation locations. Absolute value refers to the magnitude of the strain change, regardless of whether it increases or decreases. A preset gradient threshold is a boundary value used to distinguish between "uniform deformation regions" and "non-uniform deformation regions." This threshold can be set as a single fixed value or as a multi-level threshold system including low, medium, and high thresholds; however, in this step's filtering logic, the primary focus is on whether the minimum threshold for triggering correction is exceeded. The system iterates through the strain gradient sequence generated in step S201, calculating the absolute value of the gradient at each point and comparing it with the preset gradient threshold. When the absolute gradient values ​​of multiple consecutive sampling points exceed the threshold, the system records the start and end positions of these points on the optical fiber, marking them as a high-gradient section. This filtering process essentially performs a binarization classification of the entire data length, aiming to locate key areas requiring special algorithm compensation, thereby improving the measurement accuracy of key areas while ensuring computational efficiency.

[0100] Specifically, to screen high-gradient segments, the system can employ an energy detection method based on a sliding window. The system sets a fixed-length sliding window (e.g., covering 10 sampling points) and slides it across the strain gradient sequence. The system calculates the root mean square (RMS) or mean absolute magnitude of all gradient values ​​within the window. If this statistical value exceeds a preset energy threshold, the system determines that the area covered by the current window belongs to a high-gradient segment. This method is more robust than the single-point comparison method and effectively avoids misjudgments caused by individual noise points. Another implementation method is to use hysteresis thresholding. The system sets two thresholds: a high threshold and a low threshold. During the scanning process, the starting point of a high-gradient segment is only marked when the gradient value exceeds the high threshold; once in the marking state, as long as the gradient value remains above the low threshold, the segment continues to extend until the gradient value falls below the low threshold, at which point the ending point is marked. This method can...

[0101] S203. Call the pre-stored gradient-transfer efficiency correlation table and match the corresponding transfer efficiency attenuation coefficient according to the strain gradient value of each point in the high gradient section.

[0102] The system calls a pre-stored gradient-transfer efficiency correlation table and matches the corresponding transfer efficiency attenuation coefficient based on the strain gradient values ​​at each point within the high-gradient region; the transfer efficiency attenuation coefficient is negatively correlated with the absolute value of the strain gradient value. The steps for constructing the gradient-transfer efficiency correlation table include:

[0103] The shear modulus and geometric parameters of the optical fiber coating and the adhesive layer used to bond the optical fiber are obtained. Based on the shear hysteresis theory, a strain transfer differential equation including strain gradient variables is established. The strain gradient values ​​are substituted into the strain transfer differential equation for numerical solution, and the ratio of the optical fiber sensed strain to the actual strain of the substrate corresponding to each strain gradient value is calculated. The ratio is used as the transfer efficiency attenuation coefficient. A one-to-one mapping relationship between strain gradient values ​​and transfer efficiency attenuation coefficient is established, and a gradient-transfer efficiency correlation table is generated.

[0104] The gradient-transfer efficiency correlation table is a pre-built digital look-up table (LUT) that stores the quantitative mapping relationship between the magnitude of the strain gradient and the strain transfer efficiency attenuation coefficient. The transfer efficiency attenuation coefficient is a dimensionless value less than or equal to 1, representing the ratio of the strain sensed by the optical fiber to the actual strain of the matrix under a specific strain gradient. This coefficient is negatively correlated with the absolute value of the strain gradient; that is, the larger the gradient, the more significant the shear hysteresis effect, the lower the transfer efficiency, and the smaller the attenuation coefficient. After identifying high-gradient sections, the system reads the strain gradient value for each sampling point within the section. The system uses this gradient value as an index key to search the correlation table. If the gradient value falls between two discrete nodes in the table, the system calculates the exact corresponding attenuation coefficient using an interpolation algorithm. The core of this step lies in using the results of complex offline calculations to guide real-time online corrections, avoiding the high computational cost of online solution of differential equations.

[0105] The specific technical solution for constructing the gradient-transfer efficiency correlation table includes the following sub-steps: First, the system obtains the material mechanical parameters (such as shear modulus) and geometric dimensional parameters (such as radius and thickness) of the fiber coating layer and the adhesive layer used to bond the fiber. Second, based on shear hysteresis theory, the system establishes a strain transfer differential equation that includes strain gradient variables. In this equation, the matrix strain is no longer considered a constant but is described as a function of position. Then, the system uses numerical solution methods (such as the fourth-order Runge-Kutta method or the finite difference method) to solve the differential equation, obtaining the sensed strain distribution along the fiber axis. The system calculates the ratio of the sensed strain of the fiber to the actual strain of the matrix at a specific location (usually the center point), and defines this ratio as the transfer efficiency attenuation coefficient. Finally, the system changes the input strain gradient value and repeats the above solution process to obtain a series of paired data of gradient values ​​and attenuation coefficients, establishes a one-to-one mapping relationship, and generates a correlation table. Another implementation method is to use finite element simulation software (such as ANSYS). The system establishes a three-dimensional solid model of optical fiber-adhesive layer-substrate, applies displacement loads of different gradients to the substrate, extracts the average strain of the optical fiber core, calculates the transfer coefficient and tabulates it.

[0106] S204. The mechanical strain value in the high gradient section is compensated by division using the transmission efficiency attenuation coefficient to obtain the gradient-corrected mechanical strain value.

[0107] The system compensates for the actual mechanical strain value in the high gradient section by performing a division operation using the transmission efficiency attenuation coefficient to obtain the gradient-corrected mechanical strain value. After executing step S204, the system also obtains the spatial impulse response function of the demodulation device used to acquire the optical signal. The gradient-corrected mechanical strain value is used as the observation sequence. A mathematical model is established in which the convolution of the local peak strain sequence to be determined with the spatial impulse response function equals the observation sequence. The mathematical model is solved using the deconvolution algorithm to output the local peak strain sequence.

[0108] Division compensation refers to using mathematical inverse operations to recover the signal amplitude attenuated by the system. The gradient-corrected mechanical strain value is the final physical quantity after spatial gradient effect correction, which more realistically restores the peak strain characteristics of the sleeve in the stress concentration region. In step S203, the system has matched a specific transmission efficiency attenuation coefficient (e.g., 0.85) for each point in the high gradient section. In this step, the system reads the actual mechanical strain value of that point (e.g., 1000 microstrain) and divides it by the corresponding attenuation coefficient. Since the attenuation coefficient is less than 1, the result after calculation will be greater than the original measurement value, which means that the system "amplifies" the measurement signal to compensate for the signal loss caused by shear hysteresis. The system performs this operation on all data points in the high gradient section one by one, while for non-high gradient sections, the system can keep the original value unchanged or apply a unit coefficient (i.e., coefficient of 1). Through this process, the strain peak value that was originally "flattened" due to transmission loss is pulled up again, thereby improving the accuracy of the assessment of strain concentration.

[0109] Specifically, the system can implement this compensation calculation using a point-to-point matrix operation algorithm. The system constructs a coefficient vector of the same length as the full-length strain sequence. For indices within high-gradient sections, the attenuation coefficient matched by S203 is entered; for other regions, 1.0 is entered. The system uses vector division instructions to complete the correction calculation for the entire data in one go. This method utilizes the SIMD (Single Instruction Multiple Data) characteristics of modern processors, resulting in extremely high computational efficiency. Another implementation method is a weighted fusion correction method. Considering that direct division may cause numerical jumps at the edges of sections, the system introduces a weighting function (such as a trapezoidal window or cosine window) during correction. In the central region of the section, the calculated attenuation coefficient is fully applied for division; at the edges of the section, the attenuation coefficient gradually transitions to 1. The system calculates the weighted sum of the corrected value and the original value as the final output. This method ensures a smooth transition of the corrected strain curve at the connection points, avoiding artificially introduced data abrupt changes.

[0110] In the above embodiments, a strain gradient sequence is obtained by calculating the first derivative of the actual mechanical strain value with respect to the position coordinates. High-gradient sections are then selected, and the strain values ​​within these high-gradient sections are compensated and corrected using a pre-stored gradient-transfer efficiency correlation table. This correction method, which considers the influence of strain gradient on transfer efficiency, improves the accuracy of strain measurement in non-uniform deformation regions and reduces the measurement error of traditional methods in regions with large strain gradients. By establishing a correlation between strain gradient values ​​and the transfer efficiency attenuation coefficient, this method improves the measurement accuracy in high strain gradient regions, making the strain detection results more consistent with the actual strain distribution characteristics of the sleeve.

[0111] Furthermore, in another embodiment, after using the strain transfer coefficient to perform gain correction calculation on the apparent mechanical strain data to obtain the true mechanical strain value of the outer wall of the casing, the system also calculates the radial expansion of the casing at the current moment based on the true mechanical strain value.

[0112] The change in the radius of curvature of the sensing fiber is calculated based on the radial expansion and the initial helical winding angle of the sensing fiber.

[0113] The additional bending strain caused by the change in the geometric shape of the optical fiber is calculated based on the change in the radius of curvature.

[0114] Subtracting the additional bending strain value from the actual mechanical strain value yields the geometrically corrected mechanical strain value.

[0115] Radial expansion refers to the incremental change in the cross-sectional radius of a deep well casing relative to its initial state under internal fluid pressure or formation compression. It is a physical quantity characterizing the degree of circumferential deformation of the casing. The initial helical winding angle refers to the angle between the fiber tangent direction and the casing axis (or cross-sectional direction, depending on the definition system, usually referring to the angle with the axis) when the sensing fiber is laid on the outer wall of the casing in an unstressed state. This angle determines the winding density and geometric trajectory of the fiber per unit length of casing. The change in radius of curvature refers to the difference in the local bending radius of the fiber along the helical path before and after casing deformation. Since the fiber is tightly attached to the casing surface in a helical form, when the casing radius changes, the geometric parameters of the helix inevitably change, leading to a change in the degree of fiber bending. The additional bending strain value refers to the strain component generated inside the fiber core solely by the bending change of the fiber's geometry. This strain does not represent the stretching or compression of the casing matrix, but rather a "pseudo" strain generated by the fiber itself to adapt to the new geometric path. The geometrically corrected mechanical strain value refers to the net strain value reflecting the tensile or compressive deformation of the sleeve substrate surface after removing the additional bending effect from the true mechanical strain, which includes geometric coupling effects. The system first uses the measured true mechanical strain value (which includes the combined projection of axial tension and circumferential expansion) to infer the radial displacement of the sleeve using the mechanical constitutive relation of the sleeve. Then, the system combines the helical geometry equation of the optical fiber to analyze the curvature evolution of the optical fiber space curve caused by the radial displacement, quantifies the resulting bending strain, and subtracts it from the total measurement value. This step aims to decouple the "deformation" and "bending" effects in optical fiber sensing and eliminate geometric nonlinear errors introduced by the deployment method.

[0116] Specifically, the system can calculate and correct for additional bending strain using an analytical geometric method based on the small deformation assumption. First, based on the measured actual mechanical strain value, combined with the Poisson's ratio of the sleeve material and the initial spiral winding angle of the optical fiber, the system uses a strain conversion formula to separate the circumferential strain component of the sleeve. The system multiplies the circumferential strain component by the initial outer diameter of the sleeve to calculate the radial expansion. Next, the system calls the curvature calculation formula for the helix, which describes the functional relationship between curvature and the helix radius and winding angle. The system substitutes the initial radius and the deformed radius (initial radius plus radial expansion) into the formula to calculate the initial curvature and the current curvature. The system calculates the difference between the two to obtain the curvature change, and multiplies this change by the distance from the fiber core to the neutral axis (usually the fiber radius) to obtain the additional bending strain value. Finally, the system performs a subtraction operation to complete the correction. Another implementation method is an iterative approximation method based on dynamic updates of geometric parameters. Considering the slight change in fiber winding angle during sheath expansion, the system establishes a set of geometric constraint equations including both radius and angle variables. The system first calculates the initial radius change assuming a constant angle, then updates the winding angle based on geometric constraints of fiber length conservation or pitch variation. The system recalculates the instantaneous radius of curvature of the fiber using the updated radius and angle. Through multiple iterations until the radius and angle numerically converge, the system obtains the precise amount of curvature change and then calculates the additional bending strain. This method can more accurately capture geometric nonlinear characteristics when the sheath undergoes significant deformation.

[0117] In the above embodiments, the radial expansion of the sleeve is calculated, and the change in radius of curvature is calculated in conjunction with the initial helical winding angle of the sensing fiber. This allows for the determination of the additional bending strain caused by the change in the fiber's geometry. Finally, this effect is subtracted from the actual mechanical strain value to obtain a more accurate mechanical strain measurement result. Because the fiber is helically wound on the sleeve surface, the radial expansion of the sleeve under pressure causes a change in the fiber's helical curvature, resulting in additional bending strain. By establishing a geometric correction model to quantitatively assess the impact of this bending effect, the strain measurement error caused by the fiber's deployment method is reduced, improving the system's strain measurement accuracy under sleeve radial deformation conditions. This compensation method, which considers geometric nonlinearity, improves the accuracy of strain measurement.

[0118] The system in the embodiments of this invention is described below from the perspective of hardware processing. Please refer to [link / reference needed]. Figure 3 This is a schematic diagram of the physical device structure of a pressure-bearing performance testing system for deep well casing provided in an embodiment of this application.

[0119] It should be noted that, Figure 3 The structure of the system shown is merely an example and should not impose any limitations on the functionality and scope of use of the embodiments of the present invention.

[0120] like Figure 3 As shown, the system includes a Central Processing Unit (CPU) 301, which can perform various appropriate actions and processes based on a program stored in Read-Only Memory (ROM) 302 or a program loaded from storage portion 308 into Random Access Memory (RAM) 303, such as executing the methods described in the above embodiments. The RAM 303 also stores various programs and data required for system operation. The CPU 301, ROM 302, and RAM 303 are interconnected via a bus 304. An Input / Output (I / O) interface 305 is also connected to the bus 304.

[0121] The following components are connected to I / O interface 305: input section 306 including a camera, infrared sensor, etc.; output section 307 including a liquid crystal display (LCD) and speakers, etc.; storage section 308 including a hard disk, etc.; and communication section 309 including a network interface card such as a LAN (Local Area Network) card and a modem, etc. Communication section 309 performs communication processing via a network such as the Internet. Drive 310 is also connected to I / O interface 305 as needed. Removable media 311, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., are installed on drive 310 as needed so that computer programs read from them can be installed into storage section 308 as needed.

[0122] In particular, according to embodiments of the present invention, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of the present invention include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing computer programs for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via communication section 309, and / or installed from removable medium 311. When the computer program is executed by central processing unit (CPU) 301, it performs the various functions defined in the present invention.

[0123] It should be noted that the computer-readable medium shown in the embodiments of the present invention can be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. A computer-readable storage medium can be, for example,—but not limited to—an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of a computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM), flash memory, optical fiber, portable compact disc read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In the present invention, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. In the present invention, a computer-readable signal medium can include a data signal propagated in baseband or as part of a carrier wave, wherein a computer-readable computer program is carried. The transmitted data signal can take many forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof.

[0124] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. Each block in a flowchart or block diagram may represent a module, segment, or portion of code, which contains one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram or flowchart, and combinations of blocks in a block diagram or flowchart, may be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0125] In another aspect, the present invention also provides a computer-readable storage medium, which may be included in the system described in the above embodiments; or it may exist independently and not assembled into the system. The storage medium carries one or more computer programs that, when executed by a processor of a system, cause the system to implement the methods provided in the above embodiments.

[0126] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit it. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

[0127] As used in the above embodiments, depending on the context, the term "when..." can be interpreted as "if...", "after...", "in response to determining...", or "in response to detecting...". Similarly, depending on the context, the phrase "when determining..." or "if (the stated condition or event) is interpreted as "if determining...", "in response to determining...", "when (the stated condition or event) is detected", or "in response to detecting (the stated condition or event)".

[0128] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state drive), etc.

[0129] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. This program can be stored in a computer-readable storage medium, and when executed, it can include the processes described in the above method embodiments. The aforementioned storage medium includes various media capable of storing program code, such as ROM or random access memory (RAM), magnetic disks, or optical disks.

Claims

1. A method for testing the pressure-bearing capacity of deep well casing, characterized in that, The system, which includes a simulation testing device, a distributed fiber optic demodulator, a sensing fiber, and a temperature sensor, is applied to a system comprising a simulation testing device, a distributed fiber optic demodulator, a sensing fiber, and a temperature sensor. The sensing fiber is fixed along its entire length to the outer wall of a sleeve via an adhesive layer. The temperature sensor is located beside the laying path of the sensing fiber. The method includes: Establish a database of the rheological properties of the adhesive layer as a function of temperature; The simulation test device is controlled to perform a variable temperature and variable pressure loading test on the bushing; The distributed optical fiber demodulator is used to collect the Brillouin frequency shift distribution data of the sensing optical fiber, and the temperature sensor is used to synchronously collect the wall temperature data of the sleeve. Based on the wall temperature data, calculate the real-time internal temperature data of the core of the sensing optical fiber; Using the real-time internal temperature data, the fiber thermo-optic effect frequency shift component and the sleeve substrate thermo-expansion frequency shift component are removed from the Brillouin frequency shift distribution data to obtain the apparent mechanical strain data. The real-time internal temperature data is mapped to the rheological property database, and the real-time shear modulus value of the adhesive layer at the current moment is retrieved and determined. Based on the real-time shear modulus value, the geometric parameters of the sensing fiber, and the thickness parameters of the adhesive layer, a strain transfer model is constructed. The strain transfer coefficient at the current moment is calculated based on the strain transfer model. The apparent mechanical strain data are calculated by performing gain correction using the strain transfer coefficient to obtain the true mechanical strain value of the outer wall of the casing.

2. The method according to claim 1, characterized in that, The calculation of the real-time internal temperature data of the core of the sensing optical fiber based on the wall temperature data specifically includes: The thermal conductivity, specific heat capacity, and density parameters of the sensing optical fiber and the adhesive layer are obtained, and combined with the cross-sectional radius of the sensing optical fiber, thermal inertia characteristic parameters characterizing the time delay effect of heat transfer in the radial process are constructed. Based on the aforementioned thermal inertia characteristic parameters, a discretized thermal conduction differential model is established to describe the dynamic response relationship between the sleeve wall temperature and the fiber core temperature. The discretized thermal conduction differential model defines the numerical constraint relationship between the current core temperature and the current wall temperature and the previous core temperature. The wall temperature data of the sleeve is used as a time-varying input sequence and substituted into the discretized heat conduction differential model. The model is recursively calculated according to the time step and outputs the real-time internal temperature data of the core of the sensing optical fiber corresponding to the wall temperature data on the time axis.

3. The method according to claim 1, characterized in that, The strain transfer model is constructed based on the real-time shear modulus value, the geometric parameters of the sensing optical fiber, and the thickness parameters of the adhesive layer, specifically including: Using the real-time shear modulus value, the thickness parameter of the adhesive layer, and the outer diameter of the coating layer of the sensing fiber, the interfacial shear stiffness of the adhesive layer on the fiber at the current moment is calculated. The shear hysteresis characteristic value at the current moment is calculated using the interface shear stiffness, the core elastic modulus of the sensing fiber, and the core radius. Using the shear hysteresis characteristic value and the effective bonding length of the sensing fiber as independent variables, a strain transfer distribution function in hyperbolic form is constructed. The strain transfer distribution function is used as the strain transfer model.

4. The method according to claim 1, characterized in that, After calculating the gain correction of the apparent mechanical strain data using the strain transfer coefficient to obtain the true mechanical strain value of the outer wall of the casing, the method further includes: Based on the fiber optic cable's routing path, the first derivative of the actual mechanical strain value with respect to the position coordinates is calculated to obtain the strain gradient sequence. High gradient segments in the strain gradient sequence whose absolute values ​​are greater than a preset gradient threshold are selected; The pre-stored gradient-transfer efficiency correlation table is invoked, and the corresponding transfer efficiency attenuation coefficient is matched according to the strain gradient value of each point in the high gradient section; wherein, the transfer efficiency attenuation coefficient is negatively correlated with the absolute value of the strain gradient value; The actual mechanical strain value in the high gradient section is compensated by division using the transmission efficiency attenuation coefficient to obtain the gradient-corrected mechanical strain value.

5. The method according to claim 4, characterized in that, The steps for constructing the gradient-transfer efficiency association table include: Obtain the shear modulus and geometric parameters of the optical fiber coating layer and the adhesive layer used to bond the optical fiber; Based on the shear hysteresis theory, a strain transmission differential equation including strain gradient variables is established. The strain gradient values ​​are substituted into the strain transfer differential equation for numerical solution to calculate the ratio of the fiber sensing strain to the actual strain of the substrate corresponding to each strain gradient value, and the ratio is used as the transfer efficiency attenuation coefficient. Establish a one-to-one mapping relationship between the strain gradient value and the transmission efficiency attenuation coefficient, and generate a gradient-transmission efficiency correlation table.

6. The method according to claim 4, characterized in that, After obtaining the gradient-corrected mechanical strain value, the method further includes: Obtain the spatial impulse response function of the demodulation device used to acquire optical signals; The gradient-corrected mechanical strain values ​​are used as the observation sequence; A mathematical model is established in which the convolution of the local peak strain sequence to be determined with the spatial impulse response function equals the observed sequence. The mathematical model is solved using a deconvolution algorithm, and the local peak strain sequence is output.

7. The method according to claim 1, characterized in that, After calculating the gain correction of the apparent mechanical strain data using the strain transfer coefficient to obtain the true mechanical strain value of the outer wall of the casing, the method further includes: Calculate the radial expansion of the sleeve at the current moment based on the actual mechanical strain value; Based on the radial expansion and the initial helical winding angle of the sensing fiber, the change in the radius of curvature of the sensing fiber is calculated. Based on the change in radius of curvature, calculate the additional bending strain value of the optical fiber caused by the change in its geometric shape; Subtracting the additional bending strain value from the actual mechanical strain value yields the geometrically corrected mechanical strain value.

8. A pressure-bearing performance testing system for deep well casing, characterized in that, The system includes: One or more processors and a memory; the memory is coupled to the one or more processors, the memory being used to store computer program code, the computer program code including computer instructions, the one or more processors invoking the computer instructions to cause the system to perform the method as described in any one of claims 1-7.

9. A computer-readable storage medium comprising instructions, characterized in that, When the instructions are executed on the system, the system performs the method as described in any one of claims 1-7.

10. A computer program product, characterized in that, When the computer program product is run on the system, the system performs the method as described in any one of claims 1-7.

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