Method and system for predicting fracturing wellhead pressure in real time

Abstract

The invention relates to the technical field of fracturing wellhead pressure prediction, and discloses a fracturing wellhead pressure real-time prediction method and system, and the method comprises the following steps: collection processing: collecting multi-field data in a fracturing wellhead fracturing process, and carrying out noise elimination and time-space alignment to obtain a standardized time series data set; parameter identification: based on the standardized time series data set, calculating fracture fractal dimensions, fractional order parameters, temperature-sensitive viscosity and random disturbance intensity in the fracturing process by analyzing fracture fractal features and a multi-field coupling relationship to obtain multi-field parameters; and model construction: constructing a physical model fusing fractional order characteristics and random disturbance based on the multi-field parameters. The method comprises the following steps: acquiring and processing multi-field data to obtain a standardized time series data set, extracting multi-field parameters, constructing a physical model fusing fractional order characteristics and random disturbance based on the multi-field parameters, solving by combining fracture expansion constraint conditions, and carrying out weighted fusion on pressure and residual errors of the physical model.

Description

Technical Field

[0001] This invention relates to the field of fracturing wellhead pressure prediction technology, specifically to a method and system for real-time prediction of fracturing wellhead pressure. Background Technology

[0002] In the field of oil and gas resource development, fracturing technology is a core means to improve the recovery rate of low-permeability oil and gas reservoirs. The safety and efficiency of its construction process directly affect the benefits of resource development. Fracturing wellhead pressure, as a key indicator reflecting the fracture propagation state, formation characteristics, and the matching of construction parameters, requires real-time and accurate pressure prediction. This provides crucial information for dynamic adjustment of construction parameters and early warning of potential risks, and is the core technological support for achieving intelligent fracturing.

[0003] Traditional real-time pressure prediction methods for fracturing wellheads mostly rely on mathematical models constructed based on theories such as seepage mechanics and fracture mechanics. However, in actual fracturing processes, formation heterogeneity is prominent, fractures exhibit fractal propagation characteristics, and multi-physics coupling effects are significant. Traditional models often make homogenization and linearization assumptions about formation conditions and fracture morphology, making it difficult to characterize the pressure evolution law under complex working conditions. This leads to the continuous accumulation of prediction errors as the construction progresses, affecting the accuracy of the prediction.

[0004] In view of this, the present invention is hereby proposed. Summary of the Invention

[0005] To address the aforementioned issues, this invention proposes a method and system for real-time prediction of pressure at the fracturing wellhead. This system solves the problem that traditional real-time prediction methods for fracturing wellhead pressure are unable to depict the pressure evolution under complex operating conditions, leading to the continuous accumulation of prediction errors as the construction progresses, thus affecting the accuracy of the prediction.

[0006] Specifically, the following technical solution was adopted: A method for real-time prediction of pressure at the fracturing wellhead includes: Data acquisition and processing steps: Collect multi-field data during the fracturing process at the fracturing wellhead, and perform noise removal and spatiotemporal alignment to obtain a standardized time-series dataset; Parameter identification steps: Based on the standardized time series dataset, by analyzing the fracture fractal characteristics and multi-field coupling relationships, the fracture fractal dimension, fractional-order parameters, temperature-sensitive viscosity, and random disturbance intensity during the fracturing process are calculated to obtain multi-field parameters; Model construction steps: Based on the multi-field parameters, construct a physical model that integrates fractional-order characteristics and random perturbations, and solve it in combination with crack propagation constraints to obtain the physical model pressure; Data compensation step: Based on the standardized time series dataset, construct a data-driven model with physical constraints, and train it using the standardized time series dataset to obtain residuals used to correct the errors of the physical model; Fusion optimization steps: The physical model pressure and the residual are weighted and fused to obtain the preliminary predicted pressure value at the fracture wellhead. Based on the error between the preliminary predicted pressure value and the measured pressure, the parameters of the physical model and the data-driven model are dynamically optimized, and the final predicted pressure value at the fracture wellhead is output.

[0007] As an optional embodiment of the present invention, the standardized time-series dataset includes microseismic signals, wellbore temperature distribution, and real-time wellhead pressure; The parameter identification step includes: Calculate the fractal dimension of the crack: Perform Fourier transform on the microseismic signals in the standardized time series dataset, extract the slope of their power spectral density, and calculate the fractal dimension of the crack based on fractal theory; Determine the fractional order parameters: Based on the fracture fractal dimension, the temporal fractional order parameters and spatial fractional order parameters are calculated through a preset correlation between the fracture and the fractional order parameters. Calculation of temperature-sensitive viscosity: Based on the wellbore temperature distribution in the standardized time-series dataset, combined with the fracturing fluid activation energy and shear rate, the temperature-sensitive viscosity is calculated through fractional constitutive relations; Calibrate the intensity of random disturbances: Calculate the kurtosis coefficient based on the real-time wellhead pressure in the standardized time-series dataset, and determine the intensity of random disturbances based on the kurtosis coefficient and the pressure standard deviation; Parameter summary: Using a data integration algorithm, the fractal dimension of the crack, fractional-order parameters, temperature-sensitive viscosity, and random disturbance intensity are integrated to obtain multi-field data.

[0008] As an optional embodiment of the present invention, the formula for calculating the fractal dimension of the crack is as follows: ,in, Let be the fractal dimension of the crack, characterizing the complexity of the crack network. The slope of the power spectral density is calculated from the frequency domain characteristics of the microseismic signal; The time fractional order parameter in the determination of fractional order parameters and spatial fractional parameters The calculation formula is: , Among them, the time fractional-order parameter This reflects the degree to which the fracturing fluid flow process depends on historical conditions, and its value ranges from 0 to 1; spatial fractional-order parameter. , which reflects the spatial correlation characteristics of the pressure field in heterogeneous fractures, and its value ranges from 1 to 2; The fractal dimension of the crack is obtained in the step of calculating the fractal dimension of the crack.

[0009] And / or, the formula for calculating temperature-sensitive viscosity is: ,in, For temperature-sensitive fracturing fluid viscosity, Viscosity at reference temperature The activation energy of the fracturing fluid characterizes the sensitivity of viscosity to temperature. The gas constant is The absolute temperature in the wellbore temperature distribution. For time fractional derivative operators, The viscosity memory index, with a value ranging from 0 to 1. The shear rate of the fracturing fluid was obtained by actual measurement using a rheometer. The formula for calculating the kurtosis coefficient in the calibration random perturbation intensity is as follows: ,in, The kurtosis coefficient characterizes the non-Gaussianity of pressure fluctuations. For mathematical expectation operators; Real-time pressure at the wellhead; This represents the average real-time pressure at the wellhead; when K > 3, it is determined by the formula... The random disturbance intensity σ is calculated, where std(P) is the standard deviation of the real-time pressure at the wellhead.

[0010] As an optional embodiment of the present invention, the model construction step includes: Equation establishment: Based on the aforementioned multi-field parameters, a physical model integrating fractional-order characteristics and random perturbations is constructed, wherein the physical model is a fractional-order stochastic partial differential equation; Solving the equations: The spatial fractional derivatives of the fractional-order stochastic partial differential equations are discretized using the spectral method, and the time fractional derivatives are discretized using the Grünwald-Letnikov formula. The fractional-order stochastic partial differential equations are then solved to obtain the preliminary solution of the pressure field. Constraints are introduced: variational inequalities are used as constraints for crack propagation to correct the initial solution of the pressure field and output the pressure of the physical model.

[0011] As an optional embodiment of the present invention, the physical model that integrates fractional-order characteristics and random perturbations is constructed in the equation, and the expression is: ,in, For time fractional derivative operators, For time fractional order parameters, For spatial fractional derivative operators, For spatial fractional-order parameters, for Time and space location Pressure at the location, The diffusion coefficient is the ratio of formation permeability to the temperature-sensitive viscosity obtained from the viscosity calculation step. To calibrate the random perturbation intensity obtained in the intensity step, Both Gaussian white noise and other noise components characterize the randomness of crack propagation. To standardize the injection displacement in the time-series dataset, it is used as a source term to reflect the construction injection intensity; The solution equations include: for the discretization of the spatial fractional derivative, the spectral method is used with Chebyshev polynomials as basis functions to expand the pressure field in continuous space into a linear combination of finite-order polynomials, and spatial discretization is achieved through projection operations; for the discretization of the time fractional derivative, the Grünwald-Letnikov formula is used, and its expression is: ,in, For time step, The Grünwald weights are calculated using the combination formula; For the first Each time point; for The pressure value at time; by discretizing the spatial fractional derivative and the temporal fractional derivative, the fractional stochastic partial differential equation is transformed into a system of algebraic equations, and the preliminary solution of the pressure field is obtained by solving the system of equations; The introduced constraints employ variational inequalities as constraints for crack propagation, and their expression is: ,in The spatial region where the crack is located; The stress tensor generated by the coupling of pressure and temperature is calculated from the preliminary solution of the pressure field and the wellbore temperature distribution in the standardized time series dataset. The strain is related to the crack length; For variational operators; The boundary at the tip of the crack; For the fracture toughness of the strata, The length of the crack; It is a boundary infinitesimal element.

[0012] As an optional embodiment of the present invention, the data compensation step includes: Design structure: Based on a standardized time-series dataset, a physical information neural network architecture is adopted to construct a data-driven model with physical constraints, which is a neural network model; Determining the function: By embedding the constraints of the physical model into the loss function of the neural network model, a loss function containing data error terms and physical constraint terms is constructed; Training output: The neural network model is trained using a standardized time series dataset. By minimizing the loss function, the residuals used to correct the errors in the physical model are obtained.

[0013] As an optional embodiment of the present invention, the fusion optimization step includes: Weighted fusion: The physical model pressure and residual are weighted according to preset weights using a weighted summation method to obtain the preliminary predicted pressure value at the fracture wellhead; Dynamic optimization: Based on the error between the initial pressure prediction and the measured pressure in the standardized time series dataset, the fractional-order parameters, random disturbance intensity, and network parameters of the data-driven model are updated using an unscented Kalman filter algorithm to obtain the optimized model parameters; Output results: The orthogonal decomposition method is used to reduce the order of the model corresponding to the optimized model parameters and accelerate the process, outputting the predicted value of the fracturing wellhead pressure.

[0014] As an optional embodiment of the present invention, the expression for the weighted fusion is: ,in, This is a preliminary forecast of the pressure. The physical model of pressure reflects the pressure distribution based on the mechanism. The residuals represent the data-driven correction of model errors. and As preset weights, and Greater than To ensure the dominance of the mechanistic model, the sum of the two is 1; In the dynamic optimization process, the parameters to be optimized are integrated into a state vector. It includes the time fractional-order parameters, spatial fractional-order parameters, random perturbation intensity, and network weights of the data-driven model, i.e. ,in, The connection weights of the neural network are used; the state update formula for the unscented Kalman filter is: ,in, for The optimized state vector at time step; for The state vector at any given time; The Kalman gain is calculated from the prediction error covariance and the measurement noise covariance, and is used to adjust the parameter update amplitude. To standardize the real-time wellhead pressure in the time-series dataset; This is a preliminary forecast of the pressure. The output results employ orthogonal decomposition to compress the dimensionality of the dynamically optimized model, expressed as follows: ,in, These are orthogonal basis functions, representing the dominant modes, obtained from historical pressure field data through singular value decomposition, and characterizing the typical spatial features of pressure distribution. is the modal coefficient, reflecting the change of each dominant mode over time; n is the number of modes retained, selecting the first n modes with an energy percentage ≥ 99% to balance accuracy and efficiency.

[0015] As an optional embodiment of the present invention, the data acquisition and processing steps include: Sensor acquisition: Collect multi-field data during the fracturing process at the wellhead using sensing devices; Data preprocessing: Kalman filtering is used to remove noise from the multi-field data, and then the multi-field data are aligned by timestamps to form a standardized time series dataset; The sensing devices include distributed fiber optic sensors, fiber optic grating sensors, and high-frequency pressure sensors. The multi-field data includes microseismic signals, wellbore temperature distribution, real-time wellhead pressure, and injection parameters.

[0016] This invention also provides a system for real-time prediction of pressure at the wellhead of a fracturing well, comprising: Acquisition and processing module: Acquires multi-field data during the fracturing process at the fracturing wellhead, performs noise removal and spatiotemporal alignment to obtain a standardized time-series dataset; Parameter identification module: Based on the standardized time series dataset, by analyzing the fractal characteristics of the fracture and the multi-field coupling relationship, the fractal dimension of the fracture, fractional-order parameters, temperature-sensitive viscosity and random disturbance intensity during the fracturing process are calculated to obtain multi-field parameters; Model building module: Based on the multi-field parameters, a physical model integrating fractional-order characteristics and random perturbations is constructed, and the model is solved in combination with crack propagation constraints to obtain the physical model pressure; Data compensation module: Based on the standardized time series dataset, a data-driven model with physical constraints is constructed and trained using the standardized time series dataset to obtain residuals used to correct the errors of the physical model; Fusion optimization module: The physical model pressure and the residual are weighted and fused to obtain the preliminary predicted pressure value at the fracture wellhead. Based on the error between the preliminary predicted pressure value and the measured pressure, the parameters of the physical model and the data-driven model are dynamically optimized, and the final predicted pressure value at the fracture wellhead is output.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention collects and processes data from multiple fields to obtain a standardized time-series dataset, extracts parameters from multiple fields, and constructs a physical model that integrates fractional-order characteristics and random disturbances based on these parameters. This model is then combined with fracture propagation constraints to solve for the physical model, creating a data-driven model with physical constraints. By weighted fusion of pressure and residuals in the physical model and dynamically optimizing the parameters of both the physical and data-driven models based on errors, the invention achieves complementary advantages between physical mechanisms and data-driven approaches, as well as adaptive updates to model parameters. This reduces the cumulative effect of prediction errors as construction progresses, improving the accuracy and real-time performance of wellhead pressure prediction.

[0018] 2. This invention employs spectral methods and the Grünwald-Letnikov formula to discretize and solve fractional-order stochastic partial differential equations, combined with orthogonal decomposition to reduce the order of the model and accelerate computation. Simultaneously, it uses an unscented Kalman filter algorithm to dynamically optimize the parameters of the physical model and the data-driven model, ensuring rapid response even when construction parameters change abruptly or formation conditions change. This keeps the pressure prediction delay within the range required for real-time control, meeting the stringent real-time requirements of intelligent fracturing.

[0019] 3. This invention links pressure prediction with objectives such as risk warning and environmental optimization during the construction process. By adjusting construction parameters and environmental protection strategies in conjunction with the pressure prediction results, it not only provides accurate pressure basis for early risk warning, but also optimizes CO2 injection and fracturing fluid dosage based on pressure characteristics. This improves environmental benefits while ensuring construction safety and efficiency, and promotes the development of fracturing construction towards intelligence and greenness.

[0020] 4. This invention captures key characteristics such as fracture fractal features and temperature-sensitive viscosity through multi-field parameter identification, enabling the physical model to characterize complex laws such as nonlocality and randomness. The data-driven model strengthens its error correction capability under physical constraints, thereby enhancing the model's adaptability in new construction areas or complex strata. Attached Figure Description Figure 1 A flowchart of a method for real-time prediction of pressure at the wellhead in a fracturing well according to an embodiment of the present invention; Figure 2 A flowchart illustrating the data acquisition and processing process of a method for real-time prediction of pressure at the fracturing wellhead, according to an embodiment of the present invention; Figure 3 A flowchart illustrating parameter identification for a method of real-time prediction of pressure at the fracturing wellhead according to an embodiment of the present invention; Figure 4 This is a flowchart illustrating the model construction process of a method for real-time prediction of pressure at the fracturing wellhead, according to an embodiment of the present invention. Figure 5 This is a data compensation flowchart of a method for real-time prediction of pressure at the fracturing wellhead according to an embodiment of the present invention; Figure 6 This is a flowchart illustrating the fusion optimization of a method for real-time prediction of pressure at the fracturing wellhead according to an embodiment of the present invention. Figure 7 This is an architecture diagram of a system for real-time prediction of pressure at the wellhead of a fracturing well, according to an embodiment of the present invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0022] Therefore, the following detailed description of embodiments of the present invention is not intended to limit the scope of the claimed invention, but merely illustrates some embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0023] It should be noted that, unless otherwise specified, the embodiments and features and technical solutions in the present invention can be combined with each other.

[0024] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0025] In the description of this invention, it should be noted that the terms "upper," "lower," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of this invention is in use, or the orientation or positional relationship commonly understood by those skilled in the art. These terms are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention. In addition, the terms "first," "second," etc., are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0026] See Figure 1 As shown in the figure, this invention provides a method for real-time prediction of pressure at the fracturing wellhead, comprising the following steps: Data acquisition and processing steps: Collect multi-field data during the fracturing process at the fracturing wellhead, and perform noise removal and spatiotemporal alignment to obtain a standardized time-series dataset; Parameter identification steps: Based on the standardized time series dataset, by analyzing the fracture fractal characteristics and multi-field coupling relationships, the fracture fractal dimension, fractional-order parameters, temperature-sensitive viscosity, and random disturbance intensity during the fracturing process are calculated to obtain multi-field parameters; Model construction steps: Based on the multi-field parameters, construct a physical model that integrates fractional-order characteristics and random perturbations, and solve it in combination with crack propagation constraints to obtain the physical model pressure; Data compensation step: Based on the standardized time series dataset, construct a data-driven model with physical constraints, and train it using the standardized time series dataset to obtain residuals used to correct the errors of the physical model; Fusion optimization steps: The physical model pressure and the residual are weighted and fused to obtain the preliminary predicted pressure value at the fracture wellhead. Based on the error between the preliminary predicted pressure value and the measured pressure, the parameters of the physical model and the data-driven model are dynamically optimized, and the final predicted pressure value at the fracture wellhead is output.

[0027] This invention provides a method for real-time prediction of pressure at the fracturing wellhead. By employing the aforementioned technical solution, a standardized time-series dataset is obtained by collecting multi-field data and performing noise reduction and spatiotemporal alignment. Multi-field parameters, such as fracture fractal dimension, fractional-order parameters, temperature-sensitive viscosity, and random disturbance intensity, are extracted to characterize formation heterogeneity, fracture fractal propagation features, and multi-physics coupling effects. A physical model integrating fractional-order characteristics and random disturbances is constructed based on these multi-field parameters and solved using fracture propagation constraints, more closely reflecting the dynamic evolution of pressure during actual fracturing. By constructing a data-driven model with physical constraints, the error of the physical model is corrected using data fitting capabilities. To ensure that the correction process follows basic physical laws such as seepage and fracture propagation, the physical model pressure and residuals are weighted and fused, and the parameters of the physical model and the data-driven model are dynamically optimized based on the error. This achieves the complementary advantages of physical mechanisms and data-driven approaches, as well as the adaptive updating of model parameters. As a result, it can capture the pressure change characteristics under complex working conditions such as heterogeneous fracture propagation and multi-field coupling, effectively reducing the cumulative effect of prediction errors as construction progresses, and improving the accuracy and real-time performance of wellhead pressure prediction. This solves the problem that traditional real-time wellhead pressure prediction methods are unable to characterize the pressure evolution under complex working conditions, leading to the continuous accumulation of prediction errors as construction progresses, which affects the accuracy of prediction.

[0028] See Figure 2 As shown in the figure, the data acquisition and processing steps in the method for real-time prediction of pressure at the fracturing wellhead provided by this embodiment of the invention specifically include: Sensor acquisition: Collect multi-field data during the fracturing process at the wellhead using sensing devices; Data preprocessing: Kalman filtering is used to remove noise from the multi-field data, and then the multi-field data are aligned by timestamps to form a standardized time series dataset.

[0029] The data acquisition and processing steps in this embodiment involve collecting and processing data from multiple fields to obtain a standardized time-series dataset, extracting parameters from multiple fields, and constructing a physical model that integrates fractional-order characteristics and random disturbances based on these parameters. This model is then combined with fracture propagation constraints to solve for the physical constraints, thus constructing a data-driven model with physical constraints. By weighted fusion of pressure and residuals in the physical model and dynamic optimization of the parameters of the physical model and the data-driven model based on errors, the advantages of physical mechanisms and data-driven approaches are complemented, and the model parameters are updated adaptively. This reduces the cumulative effect of prediction errors as construction progresses, thereby improving the accuracy and real-time performance of wellhead pressure prediction.

[0030] Furthermore, the sensing devices include distributed fiber optic sensors, fiber optic grating sensors, and high-frequency pressure sensors, and the multi-field data includes microseismic signals, wellbore temperature distribution, real-time wellhead pressure, and injection parameters.

[0031] Specifically, the data acquisition and processing steps involve acquiring and preprocessing multi-source sensor data to construct a standardized time-series dataset, providing a foundation for subsequent analysis, as detailed below: In the sensing and acquisition process, the sensing equipment generally needs to cover the key physical fields of the fracturing process. Specifically, distributed fiber optic sensors are deployed along the wellbore to collect microseismic signals from 0 to 50 meters around the well using the backscattering effect of light, reflecting the dynamics of fracture propagation; fiber optic grating sensors are installed on the outer wall of the tubing, and based on the temperature-dependent characteristics of the grating wavelength, they collect the wellbore temperature distribution to characterize the heat exchange state; high-frequency pressure sensors are deployed at the wellhead to collect real-time wellhead pressure at a sampling frequency of 100Hz, capturing instantaneous fluctuations; and injection parameters, such as displacement and sand ratio, are recorded simultaneously to reflect the construction parameters.

[0032] In the data preprocessing step, as an option, Kalman filtering is used to eliminate noise, and its formula includes: Equations of state: ,in, for The state vector at any given time contains the actual values ​​of signals such as pressure and temperature. The state transition matrix is ​​set based on the signal time correlation. For process noise; observation equation: ,in, These are sensor observations, such as the measured real-time pressure at the wellhead. For the observation matrix, To filter out observation noise, noise is achieved by recursively calculating the Kalman gain, updating the state estimate and covariance matrix.

[0033] Furthermore, due to the different sampling frequencies of the sensors, such as 10Hz for microseismic signals and 1Hz for temperature data, the multi-source data is aligned using linear interpolation with the timestamp of the high-frequency pressure sensor as the reference, ultimately forming a standardized time-series dataset containing time labels and corresponding physical field parameters, providing a unified input for subsequent steps.

[0034] See Figure 3 As shown in the figure, the parameter identification step in the method for real-time prediction of pressure at the fracturing wellhead provided by this embodiment of the invention specifically includes: Dimensional calculation: Perform Fourier transform on the microseismic signals in the standardized time series dataset, extract the power spectral density slope, and calculate the fractal dimension of the crack based on fractal theory; Determine the parameters: Based on the fractal dimension of the crack, calculate the temporal and spatial fractional parameters through the correlation between the fractional-order parameters and the fractal dimension, and obtain the fractional-order parameters. Viscosity calculation: Based on the wellbore temperature distribution in the standardized time series dataset, combined with the fracturing fluid activation energy and shear rate, temperature-sensitive viscosity is calculated through fractional constitutive relations; Calibration intensity: Based on the real-time wellhead pressure in the standardized time series dataset, the intensity of random disturbance is determined by calculating the pressure kurtosis coefficient and then by using the kurtosis coefficient and the pressure standard deviation. Parameter summary: Using a data integration algorithm, the fractal dimension of the crack, fractional-order parameters, temperature-sensitive viscosity, and random disturbance intensity are integrated to obtain multi-field data.

[0035] Specifically, the parameter identification step is based on a standardized time-series dataset. Through multi-dimensional parameter calculation and integration, multi-field parameters reflecting the physical characteristics of the fracturing process are constructed, providing core input parameters for the physical model, as follows: In the dimension calculation step, it is generally necessary to extract the fractal features of the fracture network from the microseismic signal. Specifically, a Fourier transform is performed on the microseismic signals in the standardized time-series dataset to convert the time-domain signal into a frequency-domain signal, and the power spectral density is obtained by calculating the signal energy distribution at different frequencies. The slope of the power spectral density is quantitatively correlated with the fracture fractal dimension. Based on fractal theory, the formula for calculating the fracture fractal dimension is: ,in, Let be the fractal dimension of the crack, characterizing the complexity of the crack network. The slope of the power spectral density is calculated from the frequency domain characteristics of the microseismic signal. This formula can be used to transform signal characteristics into geometric parameters of the crack.

[0036] In the parameter determination step, as an option, the correlation between fractional-order parameters and fracture fractal dimension is obtained through fitting experimental data to quantify the memory and nonlocality of fractal fluid flow. In one possible implementation, the time fractional-order parameter... and spatial fractional parameters The calculation formula is: , ,in, This is a time fractional parameter that reflects the degree to which the fracturing fluid flow process depends on historical conditions, and its value ranges from 0 to 1. This is a spatial fractional-order parameter that reflects the spatial correlation characteristics of the pressure field in heterogeneous fractures, and its value ranges from 1 to 2. This refers to the fractal dimension of the crack obtained in the dimension calculation step. Through this correlation, the fractional-order parameters can be directly determined from the geometric characteristics of the crack, avoiding the errors of the traditional trial-and-error method.

[0037] In the viscosity calculation step, specifically, the calculation of temperature-sensitive viscosity needs to reflect the multi-field coupling relationship between the temperature field and fluid properties. Based on the wellbore temperature distribution in the standardized time-series dataset, combined with the rheological properties of the fracturing fluid, the viscosity is calculated using a fractional-order constitutive relation, with the following formula: ,in, For temperature-sensitive fracturing fluid viscosity, Viscosity at reference temperature The activation energy of the fracturing fluid characterizes the sensitivity of viscosity to temperature. The gas constant is The absolute temperature in the wellbore temperature distribution. For time fractional derivative operators, The viscosity memory index, with a value ranging from 0 to 1. The shear rate of the fracturing fluid is obtained from actual measurements using a rheometer. This formula uses fractional derivatives to reflect the memory property of viscosity, achieving a coupled characterization of temperature and fluid properties.

[0038] In the calibration intensity step, as an option, the determination of the random disturbance intensity needs to be based on the statistical characteristics of the pressure signal. In one possible implementation, the kurtosis coefficient of the real-time wellhead pressure in the normalized time-series dataset is first calculated, and its formula is... ,in, is the kurtosis coefficient, which characterizes the non-Gaussianity of pressure fluctuations; the kurtosis coefficient for the normal distribution is 3. For mathematical expectation operators; Real-time pressure at the wellhead; This represents the average real-time pressure at the wellhead. When the kurtosis coefficient is greater than 3, it is obtained by... Calculate the intensity of the random disturbance, where For the intensity of random disturbance, The standard deviation of the real-time pressure at the wellhead is used to quantify the randomness of fracture propagation, making the physical model more consistent with the uncertainties in actual construction.

[0039] In the parameter aggregation step, the parameters obtained from each sub-step are generally integrated into a unified multi-field parameter. Specifically, a data integration algorithm is used to correlate and store the fracture fractal dimension obtained from the dimension calculation step, the fractional-order parameters obtained from the parameter determination step, the temperature-sensitive viscosity obtained from the viscosity calculation step, and the random perturbation intensity obtained from the intensity calibration step, forming a multi-field parameter. This multi-field parameter contains multi-dimensional information such as fracture geometry, flow characteristics, fluid properties, and random perturbations, providing comprehensive parameter input for the physical model in the model building step, ensuring that the model can accurately characterize the multi-physics coupling characteristics of the fracturing process.

[0040] In some embodiments, the parameter aggregation process also needs to verify the rationality of each parameter. For example, when the fractal dimension of the crack exceeds the reasonable range, a data re-acquisition mechanism is triggered to ensure the reliability of multiple field parameters.

[0041] See Figure 4 As shown in the figure, the model construction steps in the method for real-time prediction of pressure at the fracturing wellhead provided by this embodiment of the invention specifically include: Equation establishment: Based on multiple field parameters, a physical model integrating fractional-order characteristics and random perturbation is constructed by coupling fractional derivatives with random perturbation terms. The physical model is a fractional-order stochastic partial differential equation. Solving the equations: The spatial fractional derivatives of the fractional-order stochastic partial differential equations are discretized using the spectral method, and the time fractional derivatives are discretized using the Grünwald-Letnikov formula. Then, the fractional-order stochastic partial differential equations are solved to obtain the preliminary solution of the pressure field. Constraints are introduced: variational inequalities are used as constraints for crack propagation to correct the initial solution of the pressure field and output the pressure of the physical model.

[0042] Specifically, the model construction steps are based on the multi-field parameters obtained from parameter identification. By establishing and solving a physical model that integrates fractional-order characteristics and random perturbations, and combining it with fracture propagation constraints, a physical model pressure reflecting the true pressure state of the fracturing process is obtained, as follows: In the equation-building process, the physical model generally needs to comprehensively reflect the memory, nonlocality, and stochasticity of fracturing fluid flow and fracture propagation. Specifically, based on the fractional-order parameters of temperature-sensitive viscosity and random perturbation intensity among the multi-field parameters, a fractional-order stochastic partial differential equation is constructed as the physical model by coupling fractional derivatives with random perturbation terms. Its expression is as follows: ,in, For time fractional derivative operators, The time fractional-order parameters obtained in the parameter determination step reflect the memory effect of fracturing fluid flow on historical states; For spatial fractional derivative operators, To determine the spatial fractional-order parameters obtained in the parameter determination step, the nonlocal spatial correlation of the pressure field is characterized; for Time and space location Pressure at the location; The diffusion coefficient is equal to the ratio of formation permeability to the temperature-sensitive viscosity obtained from the viscosity calculation step. To calibrate the random perturbation intensity obtained in the intensity step, Gaussian white noise, together with the other two, characterizes the randomness of crack propagation; To standardize the injection displacement in the time-series dataset, this equation serves as the source term reflecting the injection intensity during fracturing. Through the coupling of multiple field parameters, it provides a mathematical description of the multi-physics interactions during the fracturing process.

[0043] In solving the equations, as an option, numerical methods should be used to discretize the fractional-order stochastic partial differential equations. Specifically, for the discretization of the spatial fractional derivative, the spectral method is used with Chebyshev polynomials as basis functions to expand the pressure field in continuous space into a linear combination of finite-order polynomials. Spatial discretization is achieved through projection operations. The core of this method is to transform the spatial fractional derivative into matrix operations to reduce the solution complexity. For the discretization of the time fractional derivative, the Grünwald-Letnikov formula is used, and its expression is: ,in, For time step, The Grünwald weights are calculated using the combination formula; For the first Each time point; for The pressure value at time t. Through the above spatial and temporal discretization, the fractional-order stochastic partial differential equation is transformed into a system of algebraic equations. Solving this system of equations yields a preliminary solution to the pressure field, which reflects the pressure distribution without considering crack propagation constraints.

[0044] In the constraint introduction step, the initial solution of the pressure field generally needs to be corrected using physical constraints on crack propagation to ensure the physical rationality of the solution. Specifically, a variational inequality is used as the constraint condition for crack propagation, and its expression is: ,in The spatial region where the crack is located; The stress tensor generated by the coupling of pressure and temperature is calculated from the preliminary solution of the pressure field and the wellbore temperature distribution in the standardized time series dataset. The strain is related to the crack length; For variational operators; The boundary at the tip of the crack; For the fracture toughness of the strata, The length of the crack; Let be a boundary infinitesimal element. When the calculated stress tensor satisfies this inequality for the driving force of crack propagation, it indicates that the crack may propagate. In this case, the initial solution of the pressure field needs to be corrected according to the change in crack length, and the final output is the pressure of the physical model after constraint correction.

[0045] In some embodiments, during the equation solving step, the discretized algebraic equation system can be accelerated by using the preprocessing conjugate gradient method to improve computational efficiency and ensure real-time output of the physical model pressure.

[0046] Specifically, the correction process after introducing constraints needs to be carried out iteratively. Each iteration calculates the stress intensity factor at the crack tip based on the current physical model pressure. When the stress intensity factor exceeds the fracture toughness, the crack length is adjusted and the fractional-order stochastic partial differential equation is solved again until the preliminary solution of the pressure field satisfies the variational inequality constraint, thereby ensuring that the output physical model pressure conforms to the flow law and reflects the actual constraint of crack propagation.

[0047] See Figure 5 As shown in the figure, the data compensation step in the method for real-time prediction of pressure at the fracturing wellhead provided by this embodiment of the invention specifically includes: Design structure: Based on standardized time-series datasets, a physical information neural network architecture is adopted to construct a data-driven model with physical constraints. The data-driven model is a neural network model. Determining the function: By embedding the constraints of the physical model into the loss function of the neural network model, a loss function containing data error terms and physical constraint terms is constructed; Training output: The neural network model is trained using a standardized time series dataset. By minimizing the loss function, the residuals used to correct the errors in the physical model are obtained.

[0048] Specifically, the data compensation step constructs a data-driven model with physical constraints based on a standardized time-series dataset. Residuals are obtained through training to correct errors in the physical model. By fusing the nonlinear fitting capability of neural networks with the constraint characteristics of the physical model, synergistic optimization of data-driven and mechanistic models is achieved, as detailed below: In the design and structural steps, the architecture of a data-driven model generally needs to consider the correlation between input features and output targets. Specifically, based on the feature dimensions of a standardized time-series dataset, a physical information neural network architecture is used to construct a neural network model. The input layer of this network includes the temperature-sand ratio and injection rate from the standardized time-series dataset, corresponding to the key temperature values, proppant sand ratio parameters, and injection intensity in the wellbore temperature distribution, respectively. The hidden layer consists of three layers, with the number of neurons in each layer determined according to the feature complexity to enhance the network's nonlinear mapping capability. The output layer is a single neuron, used to correct residual errors in the physical model. The hidden layer uses the Swish function as the activation function, whose expression is: ,in, For the input of neurons, The Sigmoid function is used as the activation function. This function enhances the network's ability to fit complex nonlinear relationships by introducing a nonlinear transformation. This architectural design enables the neural network to learn nonlinear error patterns that are not captured by the physical model from multi-source input features.

[0049] In the function determination step, as an option, the construction of the loss function must simultaneously satisfy data fitting and physical constraints. Specifically, by embedding the constraints of the physical model in the model construction step into the loss function of the neural network, a composite loss function containing data error terms and physical constraint terms is formed, the expression of which is: in, This is the data error term, which is equal to the square of the deviation between the real-time wellhead pressure in the standardized time series dataset and the sum of the physical model pressure and the residuals. It reflects the effect of the residuals on the correction of the physical model error. The physical constraint term is achieved by verifying whether the combination of residual and physical model pressure satisfies the fractional-order stochastic partial differential equation, that is, to ensure that the corrected pressure field conforms to physical laws. The weighting coefficients are used to balance the importance of data fitting and physical constraints, and are generally set according to the model's bias characteristics. This loss function avoids the black-box nature of pure data models through physical constraints, ensuring that residual correction always conforms to the physical mechanism of the fracturing process.

[0050] In the training output step, the neural network model is typically trained using a standardized time-series dataset. An optimization algorithm minimizes the loss function to obtain a stable residual. Specifically, the standardized time-series dataset is proportionally divided into a training set and a validation set. The training set is used for parameter learning, and the validation set is used to monitor overfitting. The training process employs an adaptive momentum optimization algorithm, iteratively updating the network weights to gradually converge the loss function. During iteration, the values ​​of the data error term and the physical constraint term are calculated in each round, and the connection weights between the hidden and output layers are adjusted using a backpropagation algorithm until the loss function reaches a stable value. In some embodiments, a learning rate decay mechanism may be introduced into the training process. When the validation set loss does not decrease significantly for several consecutive rounds, the learning rate is reduced to improve convergence accuracy. Through this training process, the residual output by the neural network can accurately capture the error characteristics of the physical model in scenarios such as complex crack propagation in heterogeneous strata, providing targeted correction for the physical model's stress.

[0051] Specifically, the residuals after training are complementary to the physical model pressure obtained in the model building steps. The magnitude of the residuals is dynamically adjusted according to the changes in the physical model error. When the physical model deviates due to sudden changes in formation parameters, the residuals amplify the correction amplitude through nonlinear mapping, and conversely, the correction effect is weakened, ultimately achieving a high-precision characterization of wellhead pressure.

[0052] See Figure 6 As shown in the figure, the fusion optimization step in the method for real-time prediction of pressure at the fracturing wellhead provided by this embodiment of the invention specifically includes: Weighted fusion: The physical model pressure and residuals are weighted according to preset weights using a weighted summation method to obtain the preliminary predicted pressure value at the fracture wellhead; Dynamic optimization: Based on the error between the initial pressure prediction and the measured pressure in the standardized time series dataset, the fractional-order parameters of the physical model, the intensity of random disturbances, and the network parameters of the data-driven model are updated using the unscented Kalman filter algorithm to obtain the optimized model parameters; Output results: The orthogonal decomposition method is used to reduce the order of the model corresponding to the optimized model parameters and accelerate the process, outputting the predicted value of the fracturing wellhead pressure.

[0053] Specifically, the fusion optimization step outputs high-precision predicted pressure values ​​at the fracturing wellhead through weighted fusion of physical model pressure and residuals, dynamic optimization of model parameters, and model order reduction, as follows: In the weighted fusion step, it is generally necessary to integrate the reliability of the physical model's mechanism with the error correction capability of the data-driven model. Specifically, a weighted summation method is used to couple the physical model pressure obtained in the model building step with the residuals obtained in the data compensation step according to preset weights to obtain a preliminary pressure prediction value, the expression of which is: ,in, This is a preliminary forecast of the pressure. The physical model of pressure reflects the pressure distribution based on the mechanism. The residuals represent the data-driven correction of model errors. and As preset weights, and Greater than To ensure the dominance of the mechanistic model, the sum of the two is 1. This weighting method ensures that the initial pressure prediction retains the mechanistic constraints of the physical model while incorporating the advantages of the nonlinear correction of the data model.

[0054] In the dynamic optimization step, as an option, an unscented Kalman filter algorithm is used to adjust the model parameters in real time based on the deviation between the initial pressure prediction and the measured pressure. Specifically, the parameters to be optimized are integrated into a state vector. It includes the temporal fractional-order parameters, spatial fractional-order parameters, random perturbation strength of the physical model, and the network weights of the data-driven model, i.e. ,in, Here are the connection weights of the neural network. The state update formula for the unscented Kalman filter is: ,in, for The optimized state vector at time step; for The state vector at any given time; The Kalman gain is calculated from the prediction error covariance and the measurement noise covariance, and is used to adjust the parameter update amplitude. To standardize the real-time wellhead pressure in the time-series dataset; This represents the initial predicted pressure value. This update mechanism allows the model parameters to adaptively adjust with the dynamic changes during the fracturing process, improving the model's ability to adapt to formation heterogeneity.

[0055] In the output results step, model reduction is generally required to ensure real-time prediction. Specifically, orthogonal decomposition is used to compress the dimensionality of the dynamically optimized model, which extracts the dominant mode from the pressure field data. The expression is: ,in, These are orthogonal basis functions, representing the dominant modes, obtained from historical pressure field data through singular value decomposition, and characterizing the typical spatial features of pressure distribution. represents the modal coefficients, reflecting the changes of each dominant mode over time; n represents the number of modes retained, selecting the top n modes with an energy percentage ≥ 99% to balance accuracy and efficiency. This order reduction process transforms the high-dimensional model into a system of low-order ordinary differential equations, reducing computational complexity.

[0056] In some embodiments, the dynamic optimization step may also introduce a forgetting factor, which assigns decreasing weights to historical errors, making parameter updates more focused on recent measurement data and enhancing the model's response speed to sudden stratigraphic changes.

[0057] Specifically, the output result step calculates the predicted pressure value at the fracturing wellhead using the model after order reduction. The value is equal to the result of the initial pressure prediction after parameter optimization. This maintains consistency with the physical model mechanism and eliminates systematic errors through data-driven correction and parameter optimization. The final output pressure prediction value can be directly used for real-time control and risk warning of fracturing operations.

[0058] See Figure 6 As shown in the figure, the fusion optimization step in the method for real-time prediction of pressure at the fracturing wellhead provided in this embodiment of the invention specifically includes: Risk warning: The sand blockage risk index is calculated based on the preliminary pressure forecast value. When the sand blockage risk index exceeds the preset threshold, a sand blockage warning is triggered. At the same time, the pressure channeling probability is calculated by combining the temperature distribution of adjacent wells in the standardized time series dataset. When the pressure channeling probability exceeds the preset threshold, a pressure channeling warning is triggered. Environmental optimization: A dynamic adjustment algorithm is adopted to adjust CO2 injection parameters based on pressure prediction values, and the fracturing fluid dosage is optimized according to the pressure fluctuation variance.

[0059] Furthermore, triggering sand blockage warning involves adjusting the residual weights of the data-driven model, strengthening residual correction by increasing the correction force of residuals on physical model pressure, and simultaneously outputting an adjustment command to reduce injection displacement. Triggering pressure channeling warning involves dynamically correcting the fracture toughness threshold in the fracture propagation constraint based on the pressure prediction value, and calculating the pressure fluctuation variance based on the real-time wellhead pressure in the standardized time series dataset.

[0060] Specifically, the fusion optimization step, based on weighted fusion, dynamic optimization, and output results, further integrates risk early warning and environmental protection optimization sub-steps to achieve coordinated control of pressure prediction and construction safety and environmental protection. This is based on multi-parameter coupling analysis and a dynamic response mechanism, as detailed below: In the risk warning process, construction risks are generally assessed based on a comprehensive evaluation of preliminary pressure forecasts and multi-source monitoring data. Specifically, when calculating the sand blockage risk index, the time change rate of the preliminary pressure forecast and the time change rate of the sand ratio in the standardized time-series dataset are considered. The assessment logic is that the sand blockage risk index increases with the rate of increase in both pressure and sand ratio. When the sand blockage risk index exceeds a first preset threshold, a potential sand blockage risk is identified, triggering a sand blockage warning. Simultaneously, the probability of pressure channeling is calculated by combining the temperature distribution of adjacent wells in the standardized time-series dataset. The probability of pressure channeling is calculated by considering the temperature deviation of adjacent wells and the ratio of fracture length to well spacing obtained in the model construction step. When the fracture length is close to the well spacing and the temperature of adjacent wells is abnormal, the probability of pressure channeling increases. When the probability of pressure channeling exceeds a second preset threshold, a pressure channeling warning is triggered. Through this multi-dimensional risk assessment, typical construction risks such as sand blockage and pressure channeling can be identified in advance.

[0061] As an option in the environmental optimization process, environmental parameters are dynamically adjusted based on predicted pressure values ​​and pressure fluctuation characteristics. Specifically, when adjusting CO2 injection parameters, the predicted pressure value is used as the basis. When the predicted pressure value reaches a preset pressure threshold, the CO2 injection volume is increased to enhance the formation's CO2 retention capacity. The injection volume increases in a stepwise manner as the predicted pressure value increases, ensuring that the CO2 retention rate matches the formation's bearing capacity. Simultaneously, the fracturing fluid usage is optimized based on the pressure fluctuation variance. The pressure fluctuation variance is calculated based on the real-time wellhead pressure in a standardized time-series dataset, reflecting the stability of the pressure field. When the pressure fluctuation variance is below a preset variance threshold, it indicates that the interaction between the formation and the fracturing fluid is stable, and water consumption can be reduced by decreasing the amount of clean water used, thereby improving the recycling rate. This optimization process dynamically adapts environmental protection measures to the fracturing operation status, balancing construction efficiency and environmental benefits.

[0062] When a sand blockage warning is triggered, the residual weights of the data-driven model are adjusted. By increasing the proportion of residuals in pressure correction, the residual correction effect is enhanced, making pressure prediction more sensitive to sand blockage precursors. Simultaneously, an adjustment command to reduce injection displacement is output to mitigate the sand blockage trend from the perspective of construction parameters. When a pressure channeling warning is triggered, the fracture toughness threshold of the fracture propagation constraint condition in the model construction step is dynamically corrected based on the pressure prediction value. By increasing the fracture toughness threshold, the formation's fracture resistance is enhanced, limiting excessive fracture extension and reducing the risk of pressure channeling from a physical constraint perspective.

[0063] In some embodiments, the risk warning step may also introduce a risk level classification mechanism, which classifies the risk into three levels: low, medium and high, based on the specific values ​​of the sand blockage risk index and the probability of pressure channeling. Different levels correspond to different levels of response measures. For example, when the risk is high, construction should be suspended immediately and an investigation should be initiated. When the risk is medium, the parameter optimization cycle should be shortened to improve the timeliness of control.

[0064] Specifically, the adjustments to CO2 injection volume and fracturing fluid usage in environmental optimization are both based on model parameters obtained from the dynamic optimization process, ensuring that the adjustment range of environmental protection measures matches the actual formation conditions. For example, when the dynamically optimized pressure prediction value shows that the formation has strong pressure-bearing capacity, the incremental CO2 injection can be appropriately increased; when the pressure fluctuation variance calculation results show that the formation stability is good, the reduction ratio of clean water usage can be further increased to maximize environmental benefits.

[0065] The process involves acquiring multi-field data during the fracturing process at the wellhead through a data acquisition and processing step. After noise reduction and spatiotemporal alignment, a standardized time-series dataset is obtained, providing high-quality foundational data for subsequent analysis. Based on this standardized time-series dataset, a parameter identification step analyzes fracture fractal characteristics and multi-field coupling relationships, calculating parameters such as fracture fractal dimension, fractional-order parameters, temperature-sensitive viscosity, and random perturbation intensity to characterize formation heterogeneity, fracture fractal propagation characteristics, and multi-physics coupling effects. A model building step constructs a physical model integrating fractional-order characteristics and random perturbations based on these multi-field parameters, solving the model with fracture propagation constraints to better reflect the dynamic evolution of pressure during actual fracturing. Finally, a data compensation step constructs a data-driven model with physical constraints, trained using the standardized time-series dataset to obtain residual data. This method corrects errors in the physical model while ensuring that the correction process follows fundamental physical laws such as seepage and fracture propagation. Through a fusion optimization step, the pressure and residuals of the physical model are weighted and fused. Based on the error between the initial pressure prediction and the measured pressure, the model parameters are dynamically optimized, achieving complementary advantages between physical mechanisms and data-driven approaches, and adaptive updating of model parameters. This allows the method to capture pressure change characteristics under complex conditions such as heterogeneous fracture propagation and multi-field coupling, reducing the cumulative effect of prediction errors as construction progresses. This makes the pressure prediction results at the fracturing wellhead more closely match the actual evolution law, achieving accurate real-time prediction of fracturing wellhead pressure. This solves the problem that traditional real-time pressure prediction methods for fracturing wellheads struggle to characterize pressure evolution under complex conditions, leading to the continuous accumulation of prediction errors as construction progresses, thus affecting prediction accuracy.

[0066] See Figure 7 As shown, this embodiment also provides a system for real-time prediction of pressure at the fracturing wellhead, applicable to the aforementioned method for real-time prediction of pressure at the fracturing wellhead, including: Acquisition and processing module: used to acquire multi-field data during the fracturing process at the wellhead, and to perform noise reduction and spatiotemporal alignment to obtain a standardized time-series dataset; Parameter identification module: Based on a standardized time-series dataset, this module analyzes the fractal characteristics of fractures and the coupling relationships between multiple fields to calculate the fractal dimension, fractional-order parameters, temperature-sensitive viscosity, and intensity of random disturbances during the fracturing process, thereby obtaining multiple field parameters. Model building module: used to build a physical model that integrates fractional-order characteristics and random perturbations based on multiple field parameters, and solves the physical model pressure by combining crack propagation constraints; Data compensation module: Used to build a data-driven model with physical constraints based on a standardized time-series dataset, and to train the model using the standardized time-series dataset to obtain residuals for correcting errors in the physical model; The fusion optimization module is used to perform weighted fusion of the physical model pressure and residuals to obtain the preliminary predicted pressure value at the fracture wellhead. Based on the error between the preliminary predicted pressure value and the measured pressure, the parameters of the physical model and the data-driven model are dynamically optimized, and the predicted pressure value at the fracture wellhead is output.

[0067] The above embodiments are only used to illustrate the present invention and are not intended to limit the technical solutions described herein. Although the present invention has been described in detail with reference to the above embodiments, the present invention is not limited to the specific embodiments described above. Therefore, any modifications or equivalent substitutions to the present invention, as well as all technical solutions and improvements that do not depart from the spirit and scope of the invention, are covered within the scope of the claims of the present invention.

Claims

1. A method for real-time prediction of pressure at the wellhead in fracturing operations, characterized in that, include: Data acquisition and processing steps: Collect multi-field data during the fracturing process at the fracturing wellhead, and perform noise removal and spatiotemporal alignment to obtain a standardized time-series dataset; Parameter identification steps: Based on the standardized time series dataset, by analyzing the fracture fractal characteristics and multi-field coupling relationships, the fracture fractal dimension, fractional-order parameters, temperature-sensitive viscosity, and random disturbance intensity during the fracturing process are calculated to obtain multi-field parameters; Model construction steps: Based on the multi-field parameters, construct a physical model that integrates fractional-order characteristics and random perturbations, and solve it in combination with crack propagation constraints to obtain the physical model pressure; Data compensation step: Based on the standardized time series dataset, construct a data-driven model with physical constraints, and train it using the standardized time series dataset to obtain residuals used to correct the errors of the physical model; Fusion optimization steps: The physical model pressure and the residual are weighted and fused to obtain the preliminary predicted pressure value at the fracture wellhead. Based on the error between the preliminary predicted pressure value and the measured pressure, the parameters of the physical model and the data-driven model are dynamically optimized, and the final predicted pressure value at the fracture wellhead is output.

2. The method for real-time prediction of pressure at the wellhead of a fracturing well according to claim 1, characterized in that, The standardized time-series dataset includes microseismic signals, wellbore temperature distribution, and real-time wellhead pressure. The parameter identification step includes: Calculate the fractal dimension of the crack: Perform Fourier transform on the microseismic signals in the standardized time series dataset, extract the slope of their power spectral density, and calculate the fractal dimension of the crack based on fractal theory; Determine the fractional order parameters: Based on the fracture fractal dimension, the temporal fractional order parameters and spatial fractional order parameters are calculated through a preset correlation between the fracture and the fractional order parameters. Calculation of temperature-sensitive viscosity: Based on the wellbore temperature distribution in the standardized time-series dataset, combined with the fracturing fluid activation energy and shear rate, the temperature-sensitive viscosity is calculated through fractional constitutive relations; Calibrate the intensity of random disturbances: Calculate the kurtosis coefficient based on the real-time wellhead pressure in the standardized time-series dataset, and determine the intensity of random disturbances based on the kurtosis coefficient and the pressure standard deviation; Parameter summary: Using a data integration algorithm, the fractal dimension of the crack, fractional-order parameters, temperature-sensitive viscosity, and random disturbance intensity are integrated to obtain multi-field data.

3. The method for real-time prediction of pressure at the wellhead of a fracturing well according to claim 2, characterized in that, The formula for calculating the fractal dimension of the crack is as follows: ,in, Let be the fractal dimension of the crack, characterizing the complexity of the crack network. The slope of the power spectral density is calculated from the frequency domain characteristics of the microseismic signal; The time fractional order parameter in the determination of fractional order parameters and spatial fractional parameters The calculation formula is: , Among them, the time fractional-order parameter This reflects the degree to which the fracturing fluid flow process depends on historical conditions, and its value ranges from 0 to 1; spatial fractional-order parameter. , which reflects the spatial correlation characteristics of the pressure field in heterogeneous fractures, and its value ranges from 1 to 2; The crack fractal dimension obtained in the step of calculating the crack fractal dimension; And / or, the formula for calculating temperature-sensitive viscosity is: ,in, For temperature-sensitive fracturing fluid viscosity, Viscosity at reference temperature The activation energy of the fracturing fluid characterizes the sensitivity of viscosity to temperature. The gas constant is... The absolute temperature in the wellbore temperature distribution. For time fractional derivative operators, The viscosity memory index, with a value ranging from 0 to 1. The shear rate of the fracturing fluid was obtained by actual measurement using a rheometer. The formula for calculating the kurtosis coefficient in the calibration random perturbation intensity is as follows: ,in, is the kurtosis coefficient, characterizing the non-Gaussianity of pressure fluctuations, and is the mathematical expectation operator; Real-time pressure at the wellhead; This represents the average real-time pressure at the wellhead; when K > 3, it is determined by the formula... The random disturbance intensity σ is calculated, where std(P) is the standard deviation of the real-time pressure at the wellhead.

4. The method for real-time prediction of pressure at the wellhead of a fracturing well according to claim 3, characterized in that, The model construction steps include: Equation establishment: Based on the aforementioned multi-field parameters, a physical model integrating fractional-order characteristics and random perturbations is constructed, wherein the physical model is a fractional-order stochastic partial differential equation; Solving the equations: The spatial fractional derivatives of the fractional-order stochastic partial differential equations are discretized using the spectral method, and the time fractional derivatives are discretized using the Grünwald-Letnikov formula. The fractional-order stochastic partial differential equations are then solved to obtain the preliminary solution of the pressure field. Constraints are introduced: variational inequalities are used as constraints for crack propagation to correct the initial solution of the pressure field and output the pressure of the physical model.

5. The method for real-time prediction of pressure at the wellhead of a fracturing well according to claim 4, characterized in that, The established equations construct a physical model that integrates fractional-order characteristics and random perturbations, expressed as follows: ,in, For time fractional derivative operators, For time fractional order parameters, For spatial fractional derivative operators, For spatial fractional-order parameters, for Time and space location Pressure at the location, The diffusion coefficient is the ratio of formation permeability to the temperature-sensitive viscosity obtained from the viscosity calculation step. To calibrate the random perturbation intensity obtained in the intensity step, Both Gaussian white noise and other noise components characterize the randomness of crack propagation. To standardize the injection displacement in the time-series dataset, it is used as a source term to reflect the construction injection intensity; The solution equations include: for the discretization of the spatial fractional derivative, the spectral method is used with Chebyshev polynomials as basis functions to expand the pressure field in continuous space into a linear combination of finite-order polynomials, and spatial discretization is achieved through projection operations; for the discretization of the time fractional derivative, the Grünwald-Letnikov formula is used, and its expression is: ,in, For time step, The Grünwald weights are calculated using the combination formula; For the first Each time point; for The pressure value at time; by discretizing the spatial fractional derivative and the temporal fractional derivative, the fractional stochastic partial differential equation is transformed into a system of algebraic equations, and the preliminary solution of the pressure field is obtained by solving the system of equations; The introduced constraints employ variational inequalities as constraints for crack propagation, and their expression is: ,in The spatial region where the crack is located; The stress tensor generated by the coupling of pressure and temperature is calculated from the preliminary solution of the pressure field and the wellbore temperature distribution in the standardized time series dataset. The strain is related to the crack length; For variational operators; The boundary at the tip of the crack; For the fracture toughness of the strata, The length of the crack; It is a boundary infinitesimal element.

6. The method for real-time prediction of pressure at the wellhead of a fracturing well according to claim 4, characterized in that, The data compensation steps include: Design structure: Based on a standardized time-series dataset, a physical information neural network architecture is adopted to construct a data-driven model with physical constraints, which is a neural network model; Determining the function: By embedding the constraints of the physical model into the loss function of the neural network model, a loss function containing data error terms and physical constraint terms is constructed; Training output: The neural network model is trained using a standardized time series dataset. By minimizing the loss function, the residuals used to correct the errors in the physical model are obtained.

7. The method for real-time prediction of pressure at the wellhead of a fracturing well according to claim 6, characterized in that, The fusion optimization steps include: Weighted fusion: The physical model pressure and residual are weighted according to preset weights using a weighted summation method to obtain the preliminary predicted pressure value at the fracture wellhead; Dynamic optimization: Based on the error between the initial pressure prediction and the measured pressure in the standardized time series dataset, the fractional-order parameters, random disturbance intensity, and network parameters of the data-driven model are updated using an unscented Kalman filter algorithm to obtain the optimized model parameters; Output results: The orthogonal decomposition method is used to reduce the order of the model corresponding to the optimized model parameters and accelerate the process, outputting the predicted value of the fracturing wellhead pressure.

8. The method for real-time prediction of pressure at the wellhead of a fracturing well according to claim 7, characterized in that, The expression for the weighted fusion is: ,in, This is a preliminary forecast of the pressure. The physical model of pressure reflects the pressure distribution based on the mechanism. The residuals represent the data-driven correction of model errors; and For preset weights, and Greater than To ensure the dominance of the mechanistic model, the sum of the two is 1; In the dynamic optimization process, the parameters to be optimized are integrated into a state vector. It includes the time fractional-order parameters, spatial fractional-order parameters, random perturbation intensity, and network weights of the data-driven model, i.e. ,in, The connection weights of the neural network are used; the state update formula for the unscented Kalman filter is: ,in, for The optimized state vector at time step; for The state vector at any given time; The Kalman gain is calculated from the prediction error covariance and the measurement noise covariance, and is used to adjust the parameter update amplitude. The standard time-series dataset contains the real-time wellhead pressure; is the preliminary pressure prediction. The output results employ orthogonal decomposition to compress the dimensionality of the dynamically optimized model, expressed as follows: ,in, These are orthogonal basis functions, representing the dominant modes, obtained from historical pressure field data through singular value decomposition, and characterizing the typical spatial features of pressure distribution. These are modal coefficients, reflecting the changes of each dominant mode over time; To determine the number of modes to retain, the top modes with an energy percentage ≥ 99% are selected. The first mode is used to balance accuracy and efficiency.

9. The method for real-time prediction of pressure at the wellhead of a fracturing well according to claim 1, characterized in that, The data acquisition and processing steps include: Sensor acquisition: Collect multi-field data during the fracturing process at the wellhead using sensing devices; Data preprocessing: Kalman filtering is used to remove noise from the multi-field data, and then the multi-field data are aligned by timestamps to form a standardized time series dataset; The sensing devices include distributed fiber optic sensors, fiber optic grating sensors, and high-frequency pressure sensors. The multi-field data includes microseismic signals, wellbore temperature distribution, real-time wellhead pressure, and injection parameters.

10. A system for real-time prediction of pressure at the wellhead in fracturing operations, characterized in that, include: Acquisition and processing module: Acquires multi-field data during the fracturing process at the fracturing wellhead, performs noise removal and spatiotemporal alignment to obtain a standardized time-series dataset; Parameter identification module: Based on the standardized time series dataset, by analyzing the fractal characteristics of the fracture and the multi-field coupling relationship, the fractal dimension of the fracture, fractional-order parameters, temperature-sensitive viscosity and random disturbance intensity during the fracturing process are calculated to obtain multi-field parameters; Model building module: Based on the multi-field parameters, a physical model integrating fractional-order characteristics and random perturbations is constructed, and the model is solved in combination with crack propagation constraints to obtain the physical model pressure; Data compensation module: Based on the standardized time series dataset, a data-driven model with physical constraints is constructed and trained using the standardized time series dataset to obtain residuals used to correct the errors of the physical model; Fusion optimization module: The physical model pressure and the residual are weighted and fused to obtain the preliminary predicted pressure value at the fracture wellhead. Based on the error between the preliminary predicted pressure value and the measured pressure, the parameters of the physical model and the data-driven model are dynamically optimized, and the final predicted pressure value at the fracture wellhead is output.

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