Method for predicting marine carbon dioxide blowout plume parameters based on attention mechanism and support vector regression

Abstract

This invention relates to a method for predicting parameters of marine carbon dioxide blowout plumes based on attention mechanisms and support vector regression, belonging to the field of carbon dioxide capture, utilization, and storage (CVS) technology. The method includes: Step 1: Constructing a simulation database based on a multiphysics coupling mechanism; Step 2: Extracting features from the blowout plume data using an improved Transformer encoder; the improved Transformer encoder includes two identical stacked layers, each stacked layer including two sequentially connected global interactive feature capture submodules and a gated residual module; Step 3: Predicting blowout plume parameters using Bayesian-optimized support vector regression; Step 4: Constructing and training a Transformer-BO-SVR model based on a machine learning model; Step 5: Predicting blowout plume parameters based on the database generated in Step 1. This invention not only fills the gap in end-to-end coupled prediction but also has significant engineering value for improving the safety assurance level of marine carbon sequestration projects.

Description

Technical Field

[0001] This invention belongs to the field of carbon dioxide capture, utilization and storage (CCUS) technology, specifically involving a method for predicting parameters of marine carbon dioxide blowout plumes based on attention mechanisms and support vector regression. Background Technology

[0002] To achieve carbon emission reduction, CCUS is considered an indispensable key technology. However, ensuring the long-term safe and stable sequestration of CO2 in geological reservoirs is a core prerequisite for the application of this technology. As the only channel connecting the surface and deep reservoirs, the structural integrity of the injection well is the weakest link in the system's safety. Once it fails, it may trigger serious leakage events, among which well blowouts are the most violent and dangerous leakage events.

[0003] To address the complex multiphysics coupling problem of CO2 well blowouts, existing methods have begun to incorporate artificial intelligence algorithms, leveraging their ability to handle nonlinear relationships to aid prediction. However, current simulations and research are mostly limited to single, isolated aspects of the leakage process, such as simulating multiphase flows within the wellbore or predicting ocean plume diffusion based on assumed fixed leakage source terms. In reality, a real well blowout event is a tightly coupled and dynamically interacting holistic process involving three subsystems: reservoir, wellbore, and plume. The reservoir's permeability determines the inflow rate at the bottom of the well, the thermodynamic state within the wellbore determines the ejection parameters (source terms) at the wellhead, and these source term parameters are the initial conditions that determine the diffusion range of the ocean plume. Unfortunately, existing methods lack a holistic approach that can overcome the barriers between these various stages, particularly a comprehensive prediction model that directly predicts blowout source term parameters using reservoir and wellbore information and dynamically correlates this with formation information; this remains a technological gap. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method for predicting ocean carbon dioxide blowout plume parameters based on attention mechanisms and support vector regression. This invention proposes a predictive model—the Transformer-BO-SVR model—that can integrate multi-dimensional information from the reservoir and wellbore to quickly and accurately predict key parameters of well blowouts (e.g., Figure 1 (As shown). This model not only fills the gap in end-to-end coupling prediction, but also has significant engineering value for improving the safety assurance level of marine carbon sequestration projects.

[0005] The technical solution of this invention is as follows: A method for predicting ocean carbon dioxide blowout plume parameters based on attention mechanism and support vector regression includes: Step 1: Construct a simulation database based on multiphysics coupling mechanisms; including: Generate multiphase flow dynamics data for the wellbore, including leakage point temperature, leakage pressure, and mass flow rate; Generate data on ocean plume diffusion behavior; The scope and division of the simulation data dataset; Step 2: Feature extraction from the blowout plume data using an improved Transformer encoder; the improved Transformer encoder comprises two identical stacked layers, each stacked layer including two sequentially connected global interactive feature capture submodules and a gated residual module; including: Feature embedding and position encoding processing of input parameters; Capture global interaction features based on a multi-head attention mechanism; Feature refinement and output based on gated residual modules; Step 3: Use Bayesian-optimized support vector regression to predict blowout plume parameters; Step 4: Build and train the Transformer-BO-SVR model based on the machine learning models in Steps 2 and 3; Step 5: Predict the parameters of the blowout plume based on the database generated in Step 1.

[0006] According to a preferred embodiment of the present invention, generating wellbore multiphase flow dynamics data includes: First, the basic parameters such as well depth, well depth structure parameters, formation temperature distribution, formation pressure distribution, gas production index, injection flow rate, injection temperature, injection pressure, initial gas content, gas-liquid interfacial tension, and leakage duration are used as the initial and boundary conditions for generating wellbore multiphase flow dynamics data. Next, a one-dimensional computational mesh is generated along the shaft axis, and a uniform mesh is generated in the radial direction; Based on the equations of mass conservation, momentum conservation, and energy conservation, a set of main governing equations for CO2 flow and heat transfer within the wellbore is established. The mass conservation equation is as follows: ; Where A is the cross-sectional area. Where is the CO2 density, v is the flow velocity, t is the time, and s is the flow distance; The momentum conservation equation is: ; Where f is the coefficient of friction. Equivalent diameter The well inclination angle; The energy conservation equation, with enthalpy H as the main variable, is in the form of: ; in, Here, T is the specific heat capacity, T is the fluid temperature, and H is the specific enthalpy per unit mass of CO2. The rate of heat exchange between the fluid and its surrounding environment; Introducing a flow work term to characterize the Joule-Thomson cooling effect, the specific enthalpy expression is modified as follows: ; in, The reference enthalpy under the injection state, For the injection temperature, To inject pressure, The coefficient of thermal expansion; The physical properties of CO2 were calculated in real time using the Span-Wagner equation of state and the Vesovic transport model. For possible gas-liquid two-phase flow scenarios, the drift flux model is used. Describe the phase slip effect, where, This represents the average velocity of gaseous CO2 along the wellbore axis. The apparent velocity of the gas-liquid mixture represents the overall flow intensity of the gas and liquid phases through the same wellbore cross section. is the distribution coefficient, used to characterize the non-uniform distribution of the gas phase on the pipe cross-section; Drift velocity, used to characterize the slip velocity of the gas phase relative to the flow of the mixture; Introducing the non-equilibrium phase transition relaxation time parameter The mass transfer rate is controlled by the gas-liquid mass transfer rate, expressed as follows: Where r is the gas-liquid phase mass transfer rate per unit volume, used to represent the rate of change of CO2 mass from liquid phase to gas phase or from gas phase to liquid phase per unit time. This refers to the density of CO2 in the gas phase. The equilibrium gas phase mass fraction determined by the phase equilibrium relationship under current pressure and temperature conditions; This represents the current actual gas phase mass fraction; Transient heat transfer between the wellbore and the formation occurs through the formation's thermal conductivity. Description, in which ,in For dimensionless time, The thermal diffusivity is the coefficient of formation thermal diffusion, used to characterize the ability of formation temperature disturbances to diffuse outwards; This refers to the duration of the leak or the current calculation time. Where is the wellbore radius; The governing equations, including the mass conservation equation, momentum conservation equation, and energy conservation equation, as well as the closure relations and physical property models, are mapped to a discrete mesh and solved using an implicit difference scheme through coupled iterative methods. The closure relations include the friction coefficient. Calculation relationship, heat exchange rate The calculation relationship, drift flux model, phase transition relaxation time parameters The corresponding mass transfer rate relationship, and the transient heat transfer function between the wellbore and the formation. The physical property model includes the Span-Wagner equation of state and the Vesovic transport model. It includes the following steps: First, within each time step, the temperature and pressure fields from the previous time step are read. These fields refer to the temperature and pressure distributions at each axial grid node and radial heat transfer grid node in the wellbore, including the fluid temperature T, fluid pressure p, and formation temperature distribution at each grid node. Then, based on the temperature T and pressure p at each grid node from the previous time step, the CO2 physical property parameters and closure parameters are calculated. Next, the updated physical property parameters and closure parameters are substituted into the mass conservation equation, momentum conservation equation, and energy conservation equation. The momentum equation is solved first to obtain the values ​​for each grid node. The pressure p and velocity v at each grid node are used to solve the energy equation and update the temperature T at each grid node. Based on the updated temperature T and pressure p, the CO2 physical properties and closure parameters are recalculated. This iterative process is repeated until the changes in pressure, temperature, and velocity obtained from two consecutive iterations are all less than the preset convergence threshold. When the entire field calculation converges, the axial grid node where the submarine leak is located is taken as the leak point node. The fluid temperature T at this leak point node is read as the leak point temperature. The hydrostatic pressure p at this leak point node is read as the leak point pressure. Based on the CO2 density ρ, velocity v, and leak outlet cross-sectional area A at this leak point node, the CO2 physical properties and closure parameters are recalculated. To calculate mass flow rate.

[0007] According to a preferred embodiment of the present invention, generating ocean plume diffusion behavior data includes: The blowout source term data generated using blowout multiphase flow simulation includes the leak point temperature, leak point pressure, and mass flow rate. Combining jet dynamics methods, the penetration length scale of the jet, the ambient fluid velocity, and the Weber number are calculated and obtained; including: First, the momentum flux is calculated using the following formula. and buoyancy flux : ; ; in It is the density of the gas. It is the orifice area of ​​the gas leak. It is the mass flow rate of the leaked gas. The ambient seawater density is used as the basis for normalizing the kinetic momentum flux and buoyancy flux using the ambient seawater density, resulting in the kinetic momentum term M and the buoyancy term B: ; The penetration length of the jet was determined. : ; Assuming the ambient fluid velocity is [missing information] under single-phase gas release conditions. for: ; Weber number It is the ratio of kinetic momentum to surface tension, and since jetting occurs in the region of the jet entering the buoyancy plume, we get: ; Here, it is assumed to be a single-phase gas blowout. Right now , It is the surface tension of the gas; Calculate and generate the initial bubble size distribution characteristics of the leaking fluid under high-pressure conditions on the seabed; including: The average bubble diameter was calculated using an empirical formula fitted from the experimental data. : ; The bubble size distribution follows the Rosin-Rammler cumulative volume distribution function: ; Among them, the Rosin-Rammler cumulative volume distribution function is used to... The preset bubble size range is discretized by dividing it into several size intervals. The boundaries of each interval are substituted into the Rosin-Rammler cumulative volume distribution function, and the difference in cumulative volume fraction at adjacent boundaries is used as the volume distribution weight of the corresponding size interval, thereby obtaining the initial bubble size distribution characteristics in discrete form. The pre-set seawater parameters and leak size, along with the obtained initial bubble size distribution, are input into the improved TAMOC seawater plume integral model. The TAMOC seawater plume integral model includes an environmental module, a blowout module, a discrete bubble model, and a core plume module. The environmental module processes ocean background field parameters; the source term parameters are input through the blowout module to clarify the initial macroscopic characteristics of CO2 blowout leakage; the discrete bubble model, based on the source term information output by the blowout module, characterizes the formation mechanism, size distribution characteristics, and initial physicochemical properties of CO2 bubbles or droplets; the information output by the environmental module, blowout module, and discrete bubble model is jointly input into the core plume module, which uses an integral method combined with an Eulerian-Lagrange hybrid framework to simultaneously simulate the seawater entrainment effect, plume buoyancy motion, and plume intrusion behavior under ocean density stratification conditions, while simultaneously coupling the DBM module to analyze the dissolution process, phase transformation law, and final environmental fate of CO2 in the seawater environment; Among these measures, CO2 solubility characteristics were optimized by employing a previously established analytical model for CO2 solubility in brine. This model covers temperatures ranging from 0-250°C and 0-200 MPa, as well as multiple ion components. CO2 solubility in pure water was calculated using piecewise explicit functions, and the salting-out effect was described by a Pitzer-type exponential correction term. The formula is as follows: ; ; in This indicates the solubility of CO2 in salt water. , , , This indicates the degree of influence of different ions on CO2 solubility compared to Na ions. Parameters representing the interactions between Cl⁻, cations, and CO₂. A parameter representing the interaction between salt and CO2. Indicates temperature; Among them, the bubble migration velocity is characterized by: using the previously derived bubble migration velocity model in seawater, which is based on the drift flux relationship. ,in, Indicates gas phase velocity, Represents the distribution coefficient. Indicates drift speed; The initial bubble size is calculated according to... And the Rosin-Rammler cumulative volume distribution function is used to generate bubbles in hydrate shells. The mass transfer coefficient k is: ; in, Kinematic viscosity, Let R be the diffusion coefficient of CO2 in seawater, and R be the bubble radius. The thickness of the hydrate shell is given; the gas dissolution rate is obtained using the mass transfer coefficient k. for: ; in, This refers to the gas concentration at the gas-water interface or hydrate-water interface. The concentration of gas in seawater is denoted as ; the input bubble size distribution and gas dissolution rate are substituted into the discrete bubble model.

[0008] According to a preferred embodiment of the present invention, the improved Transformer encoder includes two identical stacked layers, each stacked layer including two sequentially connected global interactive feature capture submodules and gated residual modules; The global interaction feature capture submodule includes a multi-head attention mechanism, residual connections, and layer normalization; The gated residual module consists of a feedforward neural network, a gated generation unit, residual connections, and layer normalization.

[0009] According to a preferred embodiment of the present invention, the feature embedding and position encoding processing of the input parameters includes: An independent linear projection strategy is adopted, configuring an independent linear projection layer for each input parameter scalar; specifically, this includes: for the... scalar of input parameters , No. scalar of input parameters It is the first The single scalar value obtained after numerical preprocessing of each input parameter; Will Enter to The corresponding linear projection layer is transformed by matrix multiplication. Mapped to 3D eigenvectors This refers to the dimension of the input parameters; Subsequently, a learnable sequence of location embedding vectors of equal dimension is initialized. The location embedding vectors are then added element-wise to their corresponding feature vectors to obtain an initial feature sequence that includes identity and location information. The formula is shown below: ; in, and The first The weight matrix and bias vector corresponding to each feature For learnable position embedding vectors; Finally, the processed initial feature sequence The physical parameters are stacked in the input order to obtain the input matrix of the subsequent encoder. m refers to the number of input parameters; According to a preferred embodiment of the present invention, capturing global interaction features based on a multi-head attention mechanism includes: Input matrix After entering the encoder layer, processing is performed through the global interactive feature capture submodule. This submodule includes a multi-head self-attention mechanism, a residual connection layer, and a layer normalization layer, used to capture the coupling relationships between different physical parameters. Specifically, it includes: First, the input matrix is ​​subjected to layer normalization. The normalized data are mapped to a query matrix Q, a key matrix K, and a value matrix V, respectively. The attention weight matrix is ​​obtained by calculating the dot product of the query matrix and the transpose of the key matrix, and then normalizing it using the Softmax function. This attention weight matrix is ​​then used to perform a weighted summation of the value matrix to obtain the output of the input matrix across different attention heads. As shown in the formula below: ; Among them, the denominator This is the scaling factor; It is the attention mechanism function; Then, the outputs of different attention heads are concatenated to obtain the final output matrix of the multi-head self-attention mechanism; Finally, the residual connection layer and the layer normalization layer add the output matrix of the multi-head self-attention mechanism to the input matrix Z before layer normalization, and then normalize the result to obtain the intermediate interaction feature matrix. That is, global interaction features.

[0010] According to a preferred embodiment of the present invention, feature refinement and output based on a gated residual module includes: Intermediate Interaction Feature Matrix It then proceeds to the gated residual module for processing; The gated residual module sequentially comprises a feedforward neural network layer, a gated generation layer, an element-wise multiplier, an adder, and a layer normalization layer. The feedforward neural network layer is used to extract transformation features; the gated generation layer is used to calculate gate coefficients based on the transformation features; the element-wise multiplier is used to weight the transformation features and the gate coefficients; and the adder is used to combine the weighted result with the module input, i.e., the intermediate interaction feature matrix. Perform residual summation; layer normalization layer is used to output refined features; including: First, the intermediate interaction feature matrix The input to the feedforward neural network layer is transformed into transformed features after nonlinear mapping and dimensionality transformation. As shown in the formula below: ; in , and , These are the learnable weight parameters and biases, respectively; Next, the transformation features will be... The input is a gated generation layer, which calculates a gating coefficient vector with values ​​ranging from [0,1] using a linear transformation and a sigmoid activation function. As shown in the formula below: ; in, It's the sigmoid activation function. and These are learnable gating weights and biases; Subsequently, a gating operation is performed, and the gating coefficient vector is calculated. Transformation characteristics The element-wise product of the elements yields the weighted filtered features. Finally, residual fusion is performed, combining the weighted filtered features with the intermediate interactive feature matrix. The results are added together, and then the sum is normalized as shown in the following formula: ; in, This represents element-wise multiplication; For layer normalization; The final output features of the improved Transformer encoder are flattened through a flattening layer.

[0011] According to a preferred embodiment of the present invention, step 3 involves using Bayesian-optimized support vector regression to predict blowout plume parameters; including: For the three target variables involved in the blowout plume prediction task—mass flow rate, bottom hole pressure, and the proportion of fluid ejected to the sea surface—a multi-output support vector regression prediction model is constructed. The multi-output support vector regression prediction model uses the radial basis function (RBF) as the kernel function. The generalization ability and prediction accuracy of the multi-output support vector regression prediction model are highly dependent on the values ​​of three key hyperparameters: the penalty coefficient C, which balances the complexity of the multi-output support vector regression prediction model with the training error; the kernel function parameter γ, which controls the influence range of a single training sample; and the insensitivity loss coefficient ϵ, which determines the model's tolerance to noisy data. A Bayesian optimization algorithm based on the tree-structured Parzen estimator TPE is introduced for automated optimization. Based on the physical scale differences and distribution patterns of blowout data, a priori search space for each hyperparameter is constructed, and each parameter is assumed to follow a logarithmic uniform distribution. The process involves executing a Bayesian optimization algorithm based on the tree-structured Parzen estimator (TPE), specifically the iterative optimization and multi-output support vector regression (MSV) prediction model generation process. N-fold cross-validation is performed, using the negative mean squared error on the training set as the objective function. The TPE algorithm maintains an observation history set, fits the posterior probability distribution of the objective function using a Gaussian mixture model, and intelligently selects the next most promising hyperparameter combination for evaluation based on the maximization of expected gain criterion. After a preset number of iterative evaluations and observation history updates, the globally optimal hyperparameter combination with the best objective function score is automatically locked. Finally, the MSV prediction model is retrained on the complete training dataset using this globally optimal hyperparameter combination, resulting in the final blowout plume parameter prediction model, i.e., the MSV prediction model.

[0012] According to a preferred embodiment of the present invention, in step 4, a Transformer-BO-SVR model is constructed and trained based on the machine learning models in steps 2 and 3; including: The Transformer-BO-SVR model includes an improved Transformer encoder and a multi-output support vector regression prediction model. First, multidimensional raw data including well depth, water depth, geothermal gradient, wellbore size, formation gas production index, wellhead temperature, formation pressure, wellhead throttling size, and ocean current velocity are input into the improved Transformer encoder to mine the nonlinear coupling relationship between parameters and generate high-dimensional feature vectors. Subsequently, the high-dimensional feature vector is flattened and then passed as input to the multi-output support vector regression prediction model. Finally, the constructed Transformer-BO-SVR model was used to predict three key blowout plume parameters: wellhead mass flow rate, bottom hole pressure, and the proportion of fluid ejected to the sea surface.

[0013] According to a preferred embodiment of the present invention, the prediction of marine carbon dioxide blowout plume parameters is based on the simulation database generated in step 1; including: First, the blowout plume dataset, i.e., the simulation database, is standardized. Next, the jet plume dataset will be... The model is divided into training, validation, and test sets. The blowout plume data, i.e., the test set, is input into the trained Transformer-BO-SVR model to predict three key parameters: mass flow rate, bottom hole pressure, and the proportion of fluid that reaches the sea surface.

[0014] The beneficial effects of this invention are as follows: To predict CO2 well blowout plume parameters, this invention constructs a simulation database with multiple physical conditions and builds a Transformer-BO-SVR model. This model can effectively capture the implicit global interaction features between reservoir pressure, wellbore flow, and the marine environment, successfully solving the technical problem of insufficient feature extraction capability and precipitous drop in prediction accuracy of traditional models when dealing with such strongly coupled cross-physics problems. Attached Figure Description

[0015] Figure 1 This is an architecture diagram of the Transformer-BO-SVR model of the present invention; Figure 2 The main execution operation flowchart generated for the data; Figure 3 A scatter plot comparing the actual and predicted values ​​of mass flow rate on the test and training sets; Figure 4 A scatter plot comparing the actual and predicted values ​​of bottom hole pressure on the test and training sets; Figure 5 A scatter plot comparing the actual and predicted values ​​of the proportion of fluid ejected from the sea surface on the test and training sets; Figure 6 Line graphs showing the comparison of actual and predicted mass flow rates on the test and training sets; Figure 7 A line graph comparing the actual and predicted values ​​of wellbore pressure at the sea surface on the test and training sets. Figure 8 A line graph comparing the actual and predicted values ​​of the proportion of fluid ejected from the sea surface on the test and training sets; Figure 9 The graph shows the comparison results of R² for the five models. Detailed Implementation

[0016] The present invention will be further defined below with reference to the accompanying drawings and embodiments, but is not limited thereto.

[0017] Terminology Explanation: 1. Leak point temperature: refers to the temperature of the leaking fluid (CO2) at the point where a leak occurs in a CO2 storage well or pipeline on the seabed, just as it leaves the leak point.

[0018] 2. Leakage pressure: refers to the absolute static pressure of the leaking fluid at the leak outlet cross-section at the location where the leak occurs.

[0019] 3. Mass flow rate: refers to the total mass of CO2 passing through the cross-section of the leak outlet per unit time, that is, the sum of the mass flow rates of the CO2 gas and liquid phases at the leak outlet.

[0020] 4. Span-Wagner equation of state: This is a high-precision equation of state used to describe the thermodynamic properties of carbon dioxide.

[0021] 5. Vesovic transport model: This is an empirical-theoretical correlation model used to calculate the transport properties of CO2. It is mainly used to predict transport parameters such as viscosity and thermal conductivity of CO2 under different temperature and pressure conditions.

[0022] 6. TAMOC seawater plume integral model: This is a numerical model used to simulate the diffusion, rise, entrainment, dissolution and transport processes of a plume after a fluid leak in the marine environment.

[0023] 7. CO2 solubility analytical model: This refers to a mathematical model used to calculate the solubility of CO2 in water or salt water.

[0024] 8. Bubble migration velocity model in seawater: This refers to a calculation model used to describe the speed at which bubbles rise or migrate in seawater.

[0025] Example 1 A method for predicting ocean carbon dioxide blowout plume parameters based on attention mechanism and support vector regression includes: Step 1: Construct a simulation database based on multiphysics coupling mechanisms; including: Generate multiphase flow dynamics data for the wellbore, including leakage point temperature, leakage pressure, and mass flow rate; Generate data on ocean plume diffusion behavior; The scope and division of the simulation data dataset; Step 2: Feature extraction from the blowout plume data using an improved Transformer encoder; the improved Transformer encoder comprises two identical stacked layers, each stacked layer including two sequentially connected global interactive feature capture submodules and a gated residual module; including: Feature embedding and position encoding processing of input parameters; Capture global interaction features based on a multi-head attention mechanism; Feature refinement and output based on gated residual modules; Step 3: Use Bayesian-optimized support vector regression to predict blowout plume parameters; Step 4: Build and train the Transformer-BO-SVR model based on the machine learning models in Steps 2 and 3; Step 5: Predict the parameters of the blowout plume based on the database generated in Step 1.

[0026] Given the scarcity of marine CO2 geological storage blowout accidents and the extreme difficulty in obtaining field measurement data, this invention employs a high-fidelity numerical simulation method to construct a synthetic dataset. The main execution flow of this method is as follows: Figure 2 As shown, the calculation is mainly divided into two core stages: wellbore multiphase flow simulation and ocean plume diffusion simulation.

[0027] Example 2 The difference between the method for predicting ocean carbon dioxide blowout plume parameters based on attention mechanism and support vector regression described in Example 1 and the method described in Example 1 is as follows: Generate wellbore multiphase flow dynamics data; including: First, the following basic parameters are used as the initial and boundary conditions for generating wellbore multiphase flow dynamics data: well depth, well depth structural parameters (casing inner diameter, casing outer diameter, tubing inner diameter, tubing outer diameter, cement sheath outer diameter, pipe wall roughness), formation temperature distribution (such as surface temperature, geothermal gradient), formation pressure distribution (such as formation pore pressure, formation porosity, formation rock density, formation specific heat capacity, formation thermal conductivity), gas production index, injection flow rate, injection temperature, injection pressure, initial gas content, gas-liquid interfacial tension, and leakage duration. Next, a one-dimensional computational grid was created along the wellbore axis with a step size of 0.5 meters. A uniformly scaled grid was used in the radial direction with a scale factor of 1.5. The first five nodes corresponded sequentially to the inner diameter of the tubing, the outer diameter of the tubing, the inner diameter of the casing, the outer diameter of the casing, and the outer diameter of the cement sheath. For critical physical nodes with drastic pressure and temperature gradient changes (including the bottomhole fluid inflow section and the choke / leakage point at the subsea wellhead), a local mesh refinement strategy was implemented. Specifically, a finer grid was applied in the direction perpendicular to the heat exchange boundary layer of the wellbore wall, with a step size of 0.001 meters. This meshing method improved the numerical resolution for regions with abrupt pressure and temperature changes while maintaining computational efficiency.

[0028] Based on the equations of mass conservation, momentum conservation, and energy conservation, a set of main governing equations for CO2 flow and heat transfer within the wellbore is established. The mass conservation equation is as follows: ; Where A is the cross-sectional area. Where is the CO2 density, v is the flow velocity, t is the time, and s is the flow distance; The momentum conservation equation is: ; Where f is the coefficient of friction. Equivalent diameter The well inclination angle; The energy conservation equation, with enthalpy H as the main variable, is in the form of: ; in, Here, T is the specific heat capacity, T is the fluid temperature, and H is the specific enthalpy per unit mass of CO2. The heat exchange rate between the fluid and the surrounding environment is represented by ∂ / ∂t. The above equations retain time partial derivatives (∂ / ∂t). By updating the physical quantities of the entire field within each time step, the transient changes of parameters such as pressure, temperature, density, and flow rate during the blowout leakage process can be accurately captured.

[0029] To accurately describe the real physical behavior of CO2 under high pressure and low temperature conditions, the traditional specific enthalpy model was improved by introducing a flow work term to characterize the Joule-Thomson cooling effect. The specific enthalpy expression was then revised as follows: ; in, The reference enthalpy under the injection state, For the injection temperature, To inject pressure, The coefficient of thermal expansion; The physical properties of CO2 (density, specific heat capacity, viscosity, thermal conductivity, coefficient of thermal expansion, specific enthalpy) are calculated in real time using the existing Span-Wagner equation of state and Vesovic transport model. For possible gas-liquid two-phase flow scenarios, the drift flux model is used. Describe the phase slip effect, where, This represents the average velocity of gaseous CO2 along the wellbore axis. The apparent velocity of the gas-liquid mixture represents the overall flow intensity of the gas and liquid phases through the same wellbore cross section. is the distribution coefficient, used to characterize the non-uniform distribution of the gas phase on the pipe cross-section; denoted as drift velocity, it is used to characterize the slip velocity of the gas phase relative to the mixture flow; through the above drift flux model, the interphase slip effect between gas phase CO2 and liquid phase CO2 in the wellbore caused by density difference, buoyancy and interphase interaction can be quantitatively described.

[0030] In addition, to accurately track the dramatic phase transition caused by a sudden drop in pressure, a non-equilibrium phase transition relaxation time parameter is introduced. The mass transfer rate is controlled by the gas-liquid mass transfer rate, expressed as follows: Where r is the gas-liquid phase mass transfer rate per unit volume, used to represent the rate of change of CO2 mass from liquid phase to gas phase or from gas phase to liquid phase per unit time. This refers to the density of CO2 in the gas phase. The equilibrium gas phase mass fraction determined by the phase equilibrium relationship under current pressure and temperature conditions; This represents the current actual gas phase mass fraction; Transient heat transfer between the wellbore and the formation occurs through the formation's thermal conductivity. Description, in which ,in For dimensionless time, The thermal diffusivity is the coefficient of formation thermal diffusion, used to characterize the ability of formation temperature disturbances to diffuse outwards; This refers to the duration of the leak or the current calculation time. Where is the wellbore radius; as As the diameter increases, the area of ​​thermal disturbance to the formation around the wellbore gradually expands. This changes accordingly, thus reflecting the characteristics of the evolution of transient heat transfer intensity between the wellbore and the formation over time; The governing equations, including the mass conservation equation, momentum conservation equation, and energy conservation equation, closure relations, and physical property models, are mapped to a discrete mesh and solved using an implicit difference scheme through coupled iterative methods. Closure relations refer to auxiliary relationships introduced to ensure the governing equations are closed and have definite solutions, including the friction coefficient. Calculation relationship, heat exchange rate The calculation relationship, drift flux model, phase transition relaxation time parameters The corresponding mass transfer rate relationship, and the transient heat transfer function between the wellbore and the formation. The physical property model includes the Span-Wagner equation of state and the Vesovic transport model. It includes the following steps: First, within each time step, the temperature and pressure fields from the previous time step are read. These fields refer to the temperature and pressure distributions at each axial grid node and radial heat transfer grid node in the wellbore, including the fluid temperature T, fluid pressure p, and formation temperature distribution at each grid node. Then, based on the temperature T and pressure p at each grid node from the previous time step, the CO2 physical property parameters and closure parameters are calculated. Next, the updated physical property parameters and closure parameters are substituted into the mass conservation equation, momentum conservation equation, and energy conservation equation. The momentum equation is solved first to obtain the values ​​for each grid node. The pressure p and velocity v at each grid node are used to solve the energy equation and update the temperature T at each grid node. Based on the updated temperature T and pressure p, the CO2 physical properties and closure parameters are recalculated. This iterative process is repeated until the changes in pressure, temperature, and velocity obtained from two consecutive iterations are all less than the preset convergence threshold. When the entire field calculation converges, the axial grid node where the submarine leak is located is taken as the leak point node. The fluid temperature T at this leak point node is read as the leak point temperature. The hydrostatic pressure p at this leak point node is read as the leak point pressure. Based on the CO2 density ρ, velocity v, and leak outlet cross-sectional area A at this leak point node, the CO2 physical properties and closure parameters are recalculated. These parameters are used to calculate mass flow rate. They serve as the core source terms for ocean plume simulation, providing fundamental input for subsequent plume evolution simulations.

[0031] Generate ocean plume dispersion behavior data; including: After a CO2 leak occurs on the seabed, it first enters a turbulent jet stage. The initial bubble size distribution in this stage is a key prerequisite for determining the subsequent evolution of the plume. Blowout source term data generated using blowout multiphase flow simulation includes the leak point temperature, leak point pressure, and mass flow rate.

[0032] Combining jet dynamics methods, the penetration length scale of the jet, the ambient fluid velocity, and the Weber number are calculated and obtained; including: First, the momentum flux is calculated using the following formula. and buoyancy flux : ; ; in It is the density of the gas. It is the orifice area of ​​the gas leak. It is the mass flow rate of the leaked gas. The ambient seawater density is used as the basis for normalizing the kinetic momentum flux and buoyancy flux using the ambient seawater density, resulting in the kinetic momentum term M and the buoyancy term B: ; The penetration length of the jet was determined. : ; Assuming the ambient fluid velocity is [missing information] under single-phase gas release conditions. for: ; Weber number It is the ratio of kinetic momentum to surface tension, and since jetting occurs in the region of the jet entering the buoyancy plume, we get: ; Here, it is assumed to be a single-phase gas blowout. Right now , It is the surface tension of the gas; Calculate and generate the initial bubble size distribution characteristics of the leaking fluid under high-pressure conditions on the seabed; including: Based on the previously calculated jet penetration length and Weber number, the average bubble diameter was calculated using an empirical formula fitted from the experimental data. : ; The bubble size distribution follows the Rosin-Rammler cumulative volume distribution function: ; in, =0.693, =5.2; using the Rosin-Rammler cumulative volume distribution function, for... The preset bubble size range is discretized by dividing it into several size intervals. The boundaries of each interval are substituted into the Rosin-Rammler cumulative volume distribution function, and the difference in cumulative volume fraction at adjacent boundaries is used as the volume distribution weight of the corresponding size interval, thereby obtaining the initial bubble size distribution characteristics in discrete form. The pre-set seawater parameters (including water depth, ocean crossflow velocity, seawater temperature and salinity profile) and the leak size are combined with the obtained initial bubble size distribution and input into the improved TAMOC seawater plume integral model. The TAMOC seawater plume integral model includes an environmental module, a blowout module, a discrete bubble model, and a core plume module. The core simulation process of the TAMOC seawater plume integral model relies on its modular coupled design. The environmental module is the foundational support, accurately handling ocean background field parameters such as water depth, current velocity, seawater temperature, and salinity, providing realistic ocean environmental boundary conditions for plume simulation. The blowout module inputs source term parameters such as mass flow rate, leakage pressure, and leakage diameter to clarify the initial macroscopic characteristics of CO2 blowout leakage. The discrete bubble model (DBM), as a key supporting module, accurately characterizes the formation mechanism, size distribution characteristics, and initial physicochemical properties of CO2 bubbles or droplets based on the source term information output from the blowout module. Information from the environmental module, blowout module, and discrete bubble model is jointly input into the core plume module. The core plume module uses an integral method combined with an Eulerian-Lagrange hybrid framework to simultaneously simulate seawater entrainment effects, plume buoyancy, and plume intrusion behavior under ocean density stratification conditions. Simultaneously, it couples with the DBM module to analyze the dissolution process, phase transformation laws, and final environmental fate of CO2 in the seawater environment. However, TAMOC is primarily designed for oil and gas leaks. Its default CO2 solubility calculation method is based on an iterative algorithm and does not fully consider the multi-ion salting-out effect. The bubble transport velocity model does not correct for the potential formation of hydrate shells on the CO2 bubble surface, and the initial bubble size distribution under high-momentum jets uses simplified assumptions, making it difficult to accurately adapt to the specific scenarios of offshore CO2 well blowout leaks. To address these shortcomings, this study makes three key improvements to TAMOC:

[0033] Among these measures, the CO2 solubility characteristics were optimized by employing a previously established analytical model for CO2 solubility in brine. This model covers temperatures from 0-250°C and 0-200 MPa, and includes multiple ion components such as Na⁺, K⁺, Ca²⁺, Mg²⁺, Cl⁻, and SO₄²⁻. The solubility of CO2 in pure water was calculated using piecewise explicit functions, and the salting-out effect was described by a Pitzer-type exponential correction term. The formula is as follows: ; ; in This indicates the solubility of CO2 in salt water. , , , This indicates the degree of influence of different ions on CO2 solubility compared to Na ions. Parameters representing the interactions between Cl⁻, cations, and CO₂. A parameter representing the interaction between salt and CO2. The model represents temperature; it is explicit, requires no iteration, and has continuous derivatives. After replacing the original iterative solver of TAMOC, the computational accuracy and efficiency are greatly improved. , , This refers to the temperature correlation (referring to the one mentioned above). The three constants in this formula (namely, constant A, constant B, and constant C); This refers to the solubility of CO2 in pure water; , , , , , This refers to the molar concentration of the corresponding ions in the salt water. , , , , , , , The solubility parameters are shown in Table 1.

[0034] Table 1. Solubility parameters of CO2 in salt water; Among them, the bubble migration velocity is characterized by: using the previously derived bubble migration velocity model in seawater, which is based on the drift flux relationship. ,in, Indicates gas phase velocity, Represents the distribution coefficient. Indicates drift velocity; distribution coefficient and drift speed The flow pattern-independent correlation proposed by Bhagwat & Ghajar is used for calculations, which is applicable to horizontal, inclined, and vertical seawater columns. The model comprehensively considers bubble size, gas content, Reynolds number, gas-liquid density ratio, and surface tension, and can select different drag coefficient sub-models based on whether the bubble surface is covered by a hydrate film, thereby accurately characterizing the slip-transport law of CO2 bubbles in seawater.

[0035] Among these factors, after high-momentum CO2 is injected into still or weakly flowing seawater, the initial bubble size and gas dissolution rate are the most important factors affecting the subsequent dissolution dissipation rate and slip transport velocity. The initial bubble size is calculated according to... The Rosin-Rammler cumulative volume distribution function is used to generate the gas-liquid mass transfer rate, which is based on a previously improved correlation. For bubbles containing hydrate shells, the mass transfer coefficient k is:

[0036] ; in, Kinematic viscosity, Let R be the diffusion coefficient of CO2 in seawater, and R be the bubble radius. The thickness of the hydrate shell (if it does not form) The gas dissolution rate is obtained using the mass transfer coefficient k. for: ; in, This refers to the gas concentration at the gas-water interface or hydrate-water interface. This represents the gas concentration in seawater; by substituting the input bubble size distribution and gas dissolution rate into the discrete bubble model, the overall accuracy of the plume evolution simulation can be improved.

[0037] This achieves full-process coupling of wellbore flow and seawater plume simulation, providing complete dataset support for subsequent intelligent prediction models.

[0038] The range and distribution of the data generated by the cascaded simulation algorithm in this invention are shown in Table 2. Simultaneously, the data is standardized, and the dataset is randomly sampled and divided into training, validation, and test sets according to a 7:1:2 ratio.

[0039] Table 2. Range and statistical distribution characteristics of the simulated data; Marine CO2 well blowouts are complex physical processes involving wellbore fluid dynamics, thermodynamics, and phase changes. Strong nonlinear coupling exists between input parameters such as well depth, throttling size, and formation pressure. To effectively capture the complex dependencies between different physical variables, this invention constructs a feature extractor based on a Transformer encoder. Through parallel attention computation, it ultimately outputs an enhanced feature vector containing global contextual information. Specifically, it consists of the following three steps:

[0040] The improved Transformer encoder consists of two identical stacked layers, each of which includes two sequentially connected global interactive feature capture submodules and a gated residual module; The global interaction feature capture submodule includes a multi-head attention mechanism, residual connections, and layer normalization; The gated residual module consists of a feedforward neural network, a gated generation unit, residual connections, and layer normalization.

[0041] Input parameter feature embedding and positional encoding processing; including: To address the characteristic of blowout plume data as continuous numerical scalars, this paper abandons the traditional lookup-based word embedding method in natural language processing and adopts an independent linear projection strategy, configuring an independent linear projection layer for each input parameter scalar; specifically, for the... scalar of input parameters , No. scalar of input parameters It is the first The single scalar value obtained after numerical preprocessing (such as normalization) of an input parameter; for example, the well depth above, one value is 3000 meters, which becomes 0.6 after preprocessing. This 0.6 is the scalar value.

[0042] Will Enter to The corresponding linear projection layer is transformed by matrix multiplication. Mapped to 3D eigenvectors This refers to the dimension of the input parameters; the specific mapping process is as follows: for the first... scalar of input parameters Configure an independent, learnable weight matrix of dimension (d, 1). Through matrix multiplication Will Mapped to a d-dimensional continuous eigenvector .

[0043] Subsequently, a learnable sequence of location embedding vectors of equal dimension is initialized. The location embedding vectors are then added element-wise to their corresponding feature vectors to obtain an initial feature sequence that includes identity and location information. The formula is shown below: ; in, and The first The weight matrix and bias vector corresponding to each feature For learnable position embedding vectors; Finally, the processed initial feature sequence The physical parameters are stacked in the input order to obtain the input matrix of the subsequent encoder. m refers to the number of input parameters; its value is 9.

[0044] Capture global interaction features based on a multi-head attention mechanism; including: Input matrix After entering the encoder layer, processing is performed through the global interactive feature capture submodule. This submodule includes a multi-head self-attention mechanism (MSA), a residual connection layer, and a layer normalization layer, used to capture the coupling relationships between different physical parameters. Specifically, it includes: First, the input matrix is ​​subjected to layer normalization. The normalized data is mapped to a query matrix Q, a key matrix K, and a value matrix V, respectively. This mapping is achieved through three independent linear layers: a query projection layer, a key projection layer, and a value projection layer. For an input matrix of... Execute the following formulas respectively:

[0045] ; in, , , These are the learnable weight matrices.

[0046] The attention weight matrix is ​​obtained by calculating the dot product of the query matrix and the transpose of the key matrix, and then normalizing it using the Softmax function. This attention weight matrix is ​​then used to perform a weighted summation of the value matrix to obtain the output of the input matrix across different attention heads. As shown in the formula below: ; Among them, the denominator This is a scaling factor used to balance the magnitude of the vector inner product, preventing the gradient from being too large or too small.

[0047] It refers to the attention mechanism function; that is... This whole.

[0048] Q-query matrix, K-key matrix, V-value matrix; Then, the outputs of different attention heads are concatenated to obtain the final output matrix of the multi-head self-attention mechanism; Finally, the residual connection layer and the layer normalization layer add the output matrix of the multi-head self-attention mechanism to the input matrix Z before layer normalization, and then normalize the result to obtain the intermediate interaction feature matrix. That is, global interaction features; intermediate interaction feature matrix. It is a feature representation that captures the global parameter coupling relationship through a multi-head self-attention mechanism. It retains the interaction information of each physical parameter in the input sequence with all other positions, providing basic features for the subsequent gating refining module.

[0049] Feature refinement and output based on gated residual modules; including: Intermediate Interaction Feature Matrix It then proceeds to the gated residual module for processing; The gated residual module sequentially comprises a feedforward neural network layer, a gated generation layer, an element-wise multiplier, an adder, and a layer normalization layer. The feedforward neural network layer is used to extract transformation features; the gated generation layer is used to calculate gate coefficients based on the transformation features; the element-wise multiplier is used to weight the transformation features and the gate coefficients; and the adder is used to combine the weighted result with the module input, i.e., the intermediate interaction feature matrix. Perform residual summation; the layer normalization layer is used to output refined features; This module replaces the traditional feedforward neural network structure of direct summation, aiming to adaptively select effective features and suppress noise. Specifically, it includes:

[0050] First, the intermediate interaction feature matrix The input to the feedforward neural network (FFN) layer is transformed into features after nonlinear mapping and dimensionality transformation. As shown in the formula below: ; in , and , These are the learnable weight parameters and biases, respectively; Next, the transformation features will be... The input is a gated generation layer, which calculates a gating coefficient vector with values ​​ranging from [0,1] using a linear transformation and a sigmoid activation function. As shown in the formula below: ; in, It's the sigmoid activation function. and These are learnable gating weights and biases; Subsequently, a gating operation is performed, and the gating coefficient vector is calculated. Transformation characteristics The element-wise product of the elements yields the weighted filtered features. Finally, residual fusion is performed, combining the weighted filtered features with the intermediate interactive feature matrix. The results are added together, and then the sum is normalized as shown in the following formula: ; in, This represents element-wise multiplication; For layer normalization; The final output features of the improved Transformer encoder are flattened through a flattening layer.

[0051] Through the above mechanism, when the value of the gating coefficient G approaches 1, the important features extracted by the feedforward neural network will be preserved. Conversely, when G approaches 0, it means that the feature is redundant information or noise and will be suppressed. The normalized result is the final output feature of the current encoder layer, which is flattened by the flattening layer and then used as the input for subsequent prediction steps.

[0052] Step 3 involves using Bayesian-optimized support vector regression to predict blowout plume parameters; this includes: To predict the three target variables involved in well blowout plume forecasting—mass flow rate, bottom hole pressure, and the proportion of fluid reaching the sea surface—a multi-output support vector regression (SVR) prediction model is constructed. Due to the highly nonlinear and strongly coupled multi-parameter characteristics of well blowout physics, the SVR prediction model employs a radial basis function (RBF) as its kernel function. This aims to map the input global feature vector to a high-dimensional feature space, thereby finding the optimal regression hyperplane that minimizes the prediction error. In this process, the generalization ability and prediction accuracy of the SVR prediction model are highly dependent on the values ​​of three key hyperparameters: the penalty coefficient C, which balances the complexity of the SVR prediction model with training error; the kernel parameter γ, which controls the influence range of a single training sample; and the insensitivity loss coefficient ϵ, which determines the model's tolerance to noisy data.

[0053] Traditional manual trial and error and grid search methods suffer from inefficiency, high computational cost, and difficulty in converging to the global optimum when determining the above hyperparameters. Therefore, a Bayesian optimization algorithm based on the tree structure Parzen estimator TPE is introduced for automated optimization. Based on the physical scale differences and distribution patterns of blowout data, a priori search space for each hyperparameter is constructed, and each parameter is assumed to follow a logarithmic uniform distribution; as shown in Table 3.

[0054] Table 3. Search range and optimal value of SVR hyperparameters; Building upon this foundation, the iterative optimization process of the Bayesian optimization algorithm based on the tree-structured Parzen estimator (TPE) and the generation of the multi-output support vector regression prediction model are executed. N-fold cross-validation is performed, using the negative mean squared error on the training set as the objective function. The TPE algorithm maintains an observation history set, fits the posterior probability distribution of the objective function using a Gaussian mixture model, and intelligently selects the next most promising hyperparameter combination for evaluation based on the maximization of expected gain criterion. After a preset number of iterative evaluations and observation history updates, the globally optimal hyperparameter combination with the best objective function score is automatically locked. Finally, the multi-output support vector regression prediction model is retrained on the complete training dataset using this globally optimal hyperparameter combination, resulting in the final blowout plume parameter prediction model, i.e., the multi-output support vector regression prediction model. Five-fold cross-validation is used to calculate the generalization performance of the current hyperparameter combination. The training data is randomly divided into 5 subsets. One subset is used as the validation set, and the remaining 4 subsets are used as the training set in turn. A multi-output SVR model is trained, and the mean squared error (MSE) on the validation set is calculated. The average of the 5 MSEs is taken as the cross-validation error of that set of hyperparameters. The optimization objective is to minimize this error. The TPE algorithm maintains an observation history set, recording each set of evaluated hyperparameters and its cross-validation MSE. The algorithm considers the top 25% of hyperparameter combinations with the best MSE in the history as the "good" group, and the rest as the "poor" group. This process is repeated until a preset 20 iterations are reached. After the iterations, the set of hyperparameters with the smallest cross-validation MSE is selected from the observation history as the globally optimal combination. The multi-output SVR model is then retrained on the complete training dataset to obtain the final blowout plume parameter prediction model.

[0055] In step 4, the Transformer-BO-SVR model is built and trained based on the machine learning models from steps 2 and 3; this includes: like Figure 1 As shown, the Transformer-BO-SVR model includes an improved Transformer encoder and a multi-output support vector regression (SVR) prediction model. First, multidimensional raw data including well depth, water depth, geothermal gradient, wellbore size, formation gas production index, wellhead temperature, formation pressure, wellhead throttling size, and ocean current velocity are input into the improved Transformer encoder. The aim is to mine the nonlinear coupling relationship between parameters through its depth feature extraction capability and generate high-dimensional feature vectors. Subsequently, the high-dimensional feature vector is flattened and then passed as input to the multi-output support vector regression (SVR) prediction model. This achieves cascaded integration of the two. Finally, the constructed Transformer-BO-SVR model is used to predict three key blowout plume parameters: wellhead mass flow rate, bottom hole pressure, and the proportion of fluid ejected to the sea surface; see steps 2 and 3 above for details.

[0056] When using the improved Transformer encoder for feature extraction, the optimal encoder parameters were determined experimentally. The optimal values ​​for embedding dimension, number of encoder layers, number of multi-head attention heads, and batch size were found to be 32, 3, 2, and 32, respectively. During training, the MSE loss function and Adam optimizer were used, with 150 training epochs. To prevent overfitting, conserve computational resources, and improve the model's generalization ability, early stopping was implemented during training. The waiting period was set to 25 epochs, meaning training was terminated early if the validation loss did not show a lower value for 25 consecutive iterations.

[0057] After feature extraction, the obtained features are input into the SVR model, and Bayesian optimization is used to adjust the hyperparameters of the SVR model. During optimization, the number of iterations is set to 30, and five-fold cross-validation is used in each iteration to evaluate model performance, with negative mean squared error as the optimization objective. Finally, a completely independent test set is used to evaluate the model's performance; this test set has never been used during the entire training phase to ensure the objectivity of the evaluation results.

[0058] Prediction of marine carbon dioxide blowout plume parameters based on the simulation database generated in step 1; including: First, the blowout plume dataset, i.e., the simulation database, is standardized. Next, the blowout plume dataset was divided into training, validation, and test sets in a 7:1:2 ratio. The blowout plume data, i.e. the test set, was then input into the trained Transformer-BO-SVR model to predict three key parameters: mass flow rate, bottom hole pressure, and the proportion of fluid that reached the sea surface.

[0059] The model performance was evaluated using the coefficient of determination (R²), mean absolute error (MAE), and root mean square error (RMSE). Table 4 shows the R², MAE, and RMSE of these three features on the training and test sets.

[0060] Table 4. Comparison of Model Evaluation Indicators; Figures 3-8 The performance of the model was presented intuitively from different perspectives. Figure 3 , Figure 4 , Figure 5 The graph shows the scatter distribution of predicted and actual values. The closer the data points are to the y=x reference line, the higher the prediction accuracy. Figure 6 , Figure 7 , Figure 8 By comparing the degree of overlap between the predicted curve and the actual curve using a line graph, the model's ability to capture dynamic changes can be reflected.

[0061] Quantitative evaluation of the model's prediction results shows that the Transformer-BO-SVR model constructed in this invention exhibits excellent fitting performance and generalization ability on both the training and test sets. Specifically, for the three prediction targets—mass flow rate, bottom hole pressure, and the proportion of fluid ejected to the sea surface—the model's coefficients of determination (R²) on the test set reached 0.9810, 0.9566, and 0.9836, respectively, all remaining at a high level above 0.95, indicating that the model can explain more than 95% of the data variation. Simultaneously, all error indicators remained at extremely low levels; for example, the MAE for the proportion of fluid ejected to the sea surface on the test set was only 0.0089, and the test set indicators were highly similar to the training set indicators (e.g., the R² for mass flow rate decreased by only 0.01), confirming that the model did not exhibit significant overfitting. These results demonstrate that the model can effectively capture the nonlinear characteristics of the complex physical processes of well blowouts, meeting the practical engineering needs for high-precision prediction of well blowout accident parameters.

[0062] To further verify the superior performance of the proposed Transformer-BO-SVR model, this invention conducted comparative experiments on the same dataset with four commonly used machine learning models: K-Nearest Neighbors (KNN), Random Forest (RF), XGBoost, and Backpropagation Neural Network (BPANN). All models used the same input features, and their prediction performance on three key output parameters—mass flow rate, bottom hole pressure, and the proportion of fluid ejected to the sea surface—was evaluated on the test set. The comparison results are as follows: Figure 9As shown in the figure. The results show that KNN suffers from low overall accuracy due to the failure of distance metric; while RF and BPANN perform reasonably well in "mass flow rate", they fail severely in predicting the most complex physical mechanism, "proportion of fluid sprayed onto the sea surface", with R² dropping to 0.4054 and 0.2198 respectively, failing to meet engineering requirements. The XGBoost model performs relatively evenly, but is still slightly inferior to the model of this invention in various metrics. In contrast, the Transformer-BO-SVR model of this invention, with its deep feature extraction and adaptive optimization mechanism, achieves comprehensive superiority in all three objectives, with test set R² reaching 0.981, 0.9566, and 0.9836 respectively. Especially in the prediction of "proportion of fluid sprayed onto the sea surface", where other models generally fail, this model still maintains extremely high accuracy, fully demonstrating its robustness and superiority in handling strongly coupled nonlinear problems.

Claims

1. A method for predicting parameters of a marine CO2 blowout plume based on an attention mechanism and support vector regression, characterized in that, include: Step 1: Construct a simulation database based on multiphysics coupling mechanisms; including: Generate multiphase flow dynamics data for the wellbore, including leakage point temperature, leakage pressure, and mass flow rate; Generate data on ocean plume diffusion behavior; The scope and division of the simulation data dataset; Step 2: Feature extraction from the blowout plume data using an improved Transformer encoder; the improved Transformer encoder comprises two identical stacked layers, each stacked layer including two sequentially connected global interactive feature capture submodules and a gated residual module; including: Feature embedding and position encoding processing of input parameters; Capture global interaction features based on a multi-head attention mechanism; Feature refinement and output based on gated residual modules; Step 3: Use Bayesian-optimized support vector regression to predict blowout plume parameters; Step 4: Build and train the Transformer-BO-SVR model based on the machine learning models in Steps 2 and 3; Step 5: Predict the parameters of the blowout plume based on the database generated in Step 1.

2. The method of claim 1, wherein, Generate wellbore multiphase flow dynamics data; including: First, the basic parameters such as well depth, well depth structure parameters, formation temperature distribution, formation pressure distribution, gas production index, injection flow rate, injection temperature, injection pressure, initial gas content, gas-liquid interfacial tension, and leakage duration are used as the initial and boundary conditions for generating wellbore multiphase flow dynamics data. Next, a one-dimensional computational mesh is generated along the shaft axis, and a uniform mesh is generated in the radial direction; Based on the equations of mass conservation, momentum conservation, and energy conservation, a set of main governing equations for CO2 flow and heat transfer within the wellbore is established. The mass conservation equation is as follows: ； where A is the cross-sectional area, where p is the density of CO2, v is the flow rate, t is the time, and s is the flow distance. The momentum conservation equation is: ； wherein f is the coefficient of friction, D is the equivalent diameter, is the deviation angle; The energy conservation equation, with enthalpy H as the main variable, is in the form of: ； wherein, Cp is the specific heat capacity, T is the fluid temperature, H is the specific enthalpy of CO2 per unit mass, is the heat exchange rate of the fluid with the surrounding environment; Introducing a flow work term to characterize the Joule-Thomson cooling effect, the specific enthalpy expression is modified as follows: ； in, The reference enthalpy under the injection state, For the injection temperature, To inject pressure, The coefficient of thermal expansion; The physical properties of CO2 were calculated in real time using the Span-Wagner equation of state and the Vesovic transport model. For the gas-liquid two-phase flow scenario, the drift flux model is used. Describe the phase slip effect, where, This represents the average velocity of gaseous CO2 along the wellbore axis. The apparent velocity of the gas-liquid mixture represents the overall flow intensity of the gas and liquid phases through the same wellbore cross section. is the distribution coefficient, used to characterize the non-uniform distribution of the gas phase on the pipe cross-section; Drift velocity, used to characterize the slip velocity of the gas phase relative to the flow of the mixture; Introducing the non-equilibrium phase transition relaxation time parameter The mass transfer rate is controlled by the gas-liquid mass transfer rate, expressed as follows: Where r is the gas-liquid phase mass transfer rate per unit volume, used to represent the rate of change of CO2 mass from liquid phase to gas phase or from gas phase to liquid phase per unit time. This refers to the density of CO2 in the gas phase. The equilibrium gas phase mass fraction determined by the phase equilibrium relationship under current pressure and temperature conditions; This represents the current actual gas phase mass fraction; Transient heat transfer between the wellbore and the formation occurs through the formation's thermal conductivity. Description, in which ,in For dimensionless time, The thermal diffusivity is the coefficient of formation thermal diffusion, used to characterize the ability of formation temperature disturbances to diffuse outwards; This refers to the duration of the leak or the current calculation time. Where is the wellbore radius; The governing equations, including the mass conservation equation, momentum conservation equation, and energy conservation equation, as well as the closure relations and physical property models, are mapped to a discrete mesh and solved using an implicit difference scheme through coupled iterative methods. The closure relations include the friction coefficient. Calculation relationship, heat exchange rate The calculation relationship, drift flux model, phase transition relaxation time parameters The corresponding mass transfer rate relationship, and the transient heat transfer function between the wellbore and the formation. The physical property model includes the Span-Wagner equation of state and the Vesovic transport model. It includes the following steps: First, within each time step, the temperature and pressure fields from the previous time step are read. These fields refer to the temperature and pressure distributions at each axial grid node and radial heat transfer grid node in the wellbore, including the fluid temperature T, fluid pressure p, and formation temperature distribution at each grid node. Then, based on the temperature T and pressure p at each grid node from the previous time step, the CO2 physical property parameters and closure parameters are calculated. Next, the updated physical property parameters and closure parameters are substituted into the mass conservation equation, momentum conservation equation, and energy conservation equation. The momentum equation is solved first to obtain the values ​​for each grid node. The pressure p and velocity v at each grid node are used to solve the energy equation and update the temperature T at each grid node. Based on the updated temperature T and pressure p, the CO2 physical properties and closure parameters are recalculated. This iterative process is repeated until the changes in pressure, temperature, and velocity obtained from two consecutive iterations are all less than the preset convergence threshold. When the entire field calculation converges, the axial grid node where the submarine leak is located is taken as the leak point node. The fluid temperature T at this leak point node is read as the leak point temperature. The hydrostatic pressure p at this leak point node is read as the leak point pressure. Based on the CO2 density ρ, velocity v, and leak outlet cross-sectional area A at this leak point node, the CO2 physical properties and closure parameters are recalculated. To calculate mass flow rate.

3. The method for predicting ocean carbon dioxide blowout plume parameters based on attention mechanism and support vector regression according to claim 1, characterized in that, Generate ocean plume dispersion behavior data; including: The blowout source term data generated using blowout multiphase flow simulation includes the leak point temperature, leak point pressure, and mass flow rate. Combining jet dynamics methods, the penetration length scale of the jet, the ambient fluid velocity, and the Weber number are calculated and obtained; including: First, the momentum flux is calculated using the following formula. and buoyancy flux : ； ； in It is the density of the gas. It is the orifice area of ​​the gas leak. It is the mass flow rate of the leaked gas. The ambient seawater density is used as the basis for normalizing the kinetic momentum flux and buoyancy flux using the ambient seawater density, resulting in the kinetic momentum term M and the buoyancy term B: ； The penetration length of the jet was determined. : ； Assuming the ambient fluid velocity is [missing information] under single-phase gas release conditions. for: ； Weber number It is the ratio of kinetic momentum to surface tension, and since jetting occurs in the region of the jet entering the buoyancy plume, we get: ； Here, it is assumed to be a single-phase gas blowout. Right now , It is the surface tension of the gas; Calculate and generate the initial bubble size distribution characteristics of the leaking fluid under high-pressure conditions on the seabed; including: The average bubble diameter was calculated using an empirical formula fitted from the experimental data. : ； The bubble size distribution follows the Rosin-Rammler cumulative volume distribution function: ； Among them, the Rosin-Rammler cumulative volume distribution function is used to... The preset bubble size range is discretized by dividing it into several size intervals. The boundaries of each interval are substituted into the Rosin-Rammler cumulative volume distribution function, and the difference in cumulative volume fraction at adjacent boundaries is used as the volume distribution weight of the corresponding size interval, thereby obtaining the initial bubble size distribution characteristics in discrete form. The pre-set seawater parameters and leak size, along with the obtained initial bubble size distribution, are input into the improved TAMOC seawater plume integral model. The TAMOC seawater plume integral model includes an environmental module, a blowout module, a discrete bubble model, and a core plume module. The environmental module processes ocean background field parameters; the source term parameters are input through the blowout module to clarify the initial macroscopic characteristics of CO2 blowout leakage; the discrete bubble model, based on the source term information output by the blowout module, characterizes the formation mechanism, size distribution characteristics, and initial physicochemical properties of CO2 bubbles or droplets; the information output by the environmental module, blowout module, and discrete bubble model is jointly input into the core plume module, which uses an integral method combined with an Eulerian-Lagrange hybrid framework to simultaneously simulate the seawater entrainment effect, plume buoyancy motion, and plume intrusion behavior under ocean density stratification conditions, while simultaneously coupling the DBM module to analyze the dissolution process, phase transformation law, and final environmental fate of CO2 in the seawater environment; Among these measures, CO2 solubility characteristics were optimized by employing a previously established analytical model for CO2 solubility in brine. This model covers temperatures ranging from 0-250°C and 0-200 MPa, as well as multiple ion components. CO2 solubility in pure water was calculated using piecewise explicit functions, and the salting-out effect was described by a Pitzer-type exponential correction term. The formula is as follows: ； ； in This indicates the solubility of CO2 in salt water. , , , This indicates the degree of influence of different ions on CO2 solubility compared to Na ions. Parameters representing the interactions between Cl⁻, cations, and CO₂. A parameter representing the interaction between salt and CO2. Temperature is represented; among which, bubble migration velocity is characterized by: using the previously derived bubble migration velocity model in seawater, which is based on the drift flux relationship. ,in, Indicates gas phase velocity, Represents the distribution coefficient. Indicates drift speed; The initial bubble size is calculated according to... And the Rosin-Rammler cumulative volume distribution function is used to generate bubbles in hydrate shells. The mass transfer coefficient k is: ； in, Kinematic viscosity, Let R be the diffusion coefficient of CO2 in seawater, and R be the bubble radius. The thickness of the hydrate shell is given; the gas dissolution rate is obtained using the mass transfer coefficient k. for: ； in, This refers to the gas concentration at the gas-water interface or hydrate-water interface. The concentration of gas in seawater is denoted as ; the input bubble size distribution and gas dissolution rate are substituted into the discrete bubble model.

4. The method for predicting ocean carbon dioxide blowout plume parameters based on attention mechanism and support vector regression according to claim 1, characterized in that, The improved Transformer encoder consists of two identical stacked layers, each of which includes two sequentially connected global interactive feature capture submodules and a gated residual module; The global interaction feature capture submodule includes a multi-head attention mechanism, residual connections, and layer normalization; The gated residual module consists of a feedforward neural network, a gated generation unit, residual connections, and layer normalization.

5. The method for predicting ocean carbon dioxide blowout plume parameters based on attention mechanism and support vector regression according to claim 1, characterized in that, Input parameter feature embedding and positional encoding processing; including: An independent linear projection strategy is adopted, configuring an independent linear projection layer for each input parameter scalar; specifically, this includes: for the... scalar of input parameters , No. scalar of input parameters It is the first The single scalar value obtained after numerical preprocessing of each input parameter; Will Enter to The corresponding linear projection layer is transformed by matrix multiplication. Mapped to 3D eigenvectors This refers to the dimension of the input parameters; Subsequently, a learnable sequence of location embedding vectors of equal dimension is initialized. The location embedding vectors are then added element-wise to their corresponding feature vectors to obtain an initial feature sequence that includes identity and location information. The formula is shown below: ； in, and The first The weight matrix and bias vector corresponding to each feature For learnable position embedding vectors; Finally, the processed initial feature sequence The physical parameters are stacked in the input order to obtain the input matrix of the subsequent encoder. m refers to the number of input parameters.

6. The method for predicting ocean carbon dioxide blowout plume parameters based on attention mechanism and support vector regression according to claim 1, characterized in that, Capture global interaction features based on a multi-head attention mechanism; including: Input matrix After entering the encoder layer, processing is performed through the global interactive feature capture submodule. This submodule includes a multi-head self-attention mechanism, a residual connection layer, and a layer normalization layer, used to capture the coupling relationships between different physical parameters. Specifically, it includes: First, the input matrix is ​​subjected to layer normalization. The normalized data are mapped to a query matrix Q, a key matrix K, and a value matrix V, respectively. The attention weight matrix is ​​obtained by calculating the dot product of the query matrix and the transpose of the key matrix, and then normalizing it using the Softmax function. This attention weight matrix is ​​then used to perform a weighted summation of the value matrix to obtain the output of the input matrix across different attention heads. As shown in the formula below: ； Among them, the denominator Scaling factor It is the attention mechanism function; Then, the outputs of different attention heads are concatenated to obtain the final output matrix of the multi-head self-attention mechanism; Finally, the residual connection layer and the layer normalization layer add the output matrix of the multi-head self-attention mechanism to the input matrix Z before layer normalization, and then normalize the result to obtain the intermediate interaction feature matrix. That is, global interaction features.

7. The method for predicting ocean carbon dioxide blowout plume parameters based on attention mechanism and support vector regression according to claim 1, characterized in that, Feature refinement and output based on gated residual modules; including: Intermediate Interaction Feature Matrix It then proceeds to the gated residual module for processing; The gated residual module sequentially comprises a feedforward neural network layer, a gated generation layer, an element-wise multiplier, an adder, and a layer normalization layer. The feedforward neural network layer is used to extract transformation features; the gated generation layer is used to calculate gate coefficients based on the transformation features; the element-wise multiplier is used to weight the transformation features and the gate coefficients; and the adder is used to combine the weighted result with the module input, i.e., the intermediate interaction feature matrix. Perform residual summation; layer normalization layer is used to output refined features; including: First, the intermediate interaction feature matrix The input to the feedforward neural network layer is transformed into transformed features after nonlinear mapping and dimensionality transformation. As shown in the formula below: ； in , and , These are the learnable weight parameters and biases, respectively; Next, the transformation features will be... The input is a gated generation layer, which calculates a gating coefficient vector with values ​​ranging from [0,1] using a linear transformation and a sigmoid activation function. As shown in the formula below: ； in, It's the sigmoid activation function. and These are learnable gating weights and biases; Subsequently, a gating operation is performed, and the gating coefficient vector is calculated. Transformation characteristics The element-wise product of the elements yields the weighted filtered features. Finally, residual fusion is performed, combining the weighted filtered features with the intermediate interactive feature matrix. The results are added together, and then the sum is normalized as shown in the following formula: ； in, This represents element-wise multiplication; For layer normalization; The final output features of the improved Transformer encoder are flattened through a flattening layer.

8. The method for predicting ocean carbon dioxide blowout plume parameters based on attention mechanism and support vector regression according to claim 1, characterized in that, Step 3 involves using Bayesian-optimized support vector regression to predict blowout plume parameters; this includes: For the three target variables involved in the blowout plume prediction task—mass flow rate, bottom hole pressure, and the proportion of fluid ejected to the sea surface—a multi-output support vector regression prediction model is constructed. The multi-output support vector regression prediction model uses the radial basis function (RBF) as the kernel function. The generalization ability and prediction accuracy of the multi-output support vector regression prediction model are highly dependent on the values ​​of three key hyperparameters: the penalty coefficient C, which balances the complexity of the multi-output support vector regression prediction model with the training error; the kernel function parameter γ, which controls the influence range of a single training sample; and the insensitivity loss coefficient ϵ, which determines the model's tolerance to noisy data. A Bayesian optimization algorithm based on the tree-structured Parzen estimator TPE is introduced for automated optimization. Based on the physical scale differences and distribution patterns of blowout data, a priori search space for each hyperparameter is constructed, and each parameter is assumed to follow a logarithmic uniform distribution. The process involves executing a Bayesian optimization algorithm based on the tree-structured Parzen estimator (TPE), specifically the iterative optimization and multi-output support vector regression (MSV) prediction model generation process. N-fold cross-validation is performed, using the negative mean squared error on the training set as the objective function. The TPE algorithm maintains an observation history set, fits the posterior probability distribution of the objective function using a Gaussian mixture model, and intelligently selects the next most promising hyperparameter combination for evaluation based on the maximization of expected gain criterion. After a preset number of iterative evaluations and observation history updates, the globally optimal hyperparameter combination with the best objective function score is automatically locked. Finally, the MSV prediction model is retrained on the complete training dataset using this globally optimal hyperparameter combination, resulting in the final blowout plume parameter prediction model, i.e., the MSV prediction model.

9. The method for predicting ocean carbon dioxide blowout plume parameters based on attention mechanism and support vector regression according to claim 1, characterized in that, In step 4, the Transformer-BO-SVR model is built and trained based on the machine learning models from steps 2 and 3; this includes: The Transformer-BO-SVR model includes an improved Transformer encoder and a multi-output support vector regression prediction model. First, multidimensional raw data including well depth, water depth, geothermal gradient, wellbore size, formation gas production index, wellhead temperature, formation pressure, wellhead throttling size, and ocean current velocity are input into the improved Transformer encoder to mine the nonlinear coupling relationship between parameters and generate high-dimensional feature vectors. Subsequently, the high-dimensional feature vector is flattened and then passed as input to the multi-output support vector regression prediction model. Finally, the constructed Transformer-BO-SVR model was used to predict three key blowout plume parameters: wellhead mass flow rate, bottom hole pressure, and the proportion of fluid ejected to the sea surface.

10. The method for predicting ocean carbon dioxide blowout plume parameters based on attention mechanism and support vector regression according to claim 9, characterized in that, Prediction of marine carbon dioxide blowout plume parameters based on the simulation database generated in step 1; including: First, the blowout plume dataset, i.e., the simulation database, is standardized. Next, the blowout plume dataset was divided into a training set, a validation set, and a test set. The blowout plume data, i.e. the test set, was then input into the trained Transformer-BO-SVR model to predict three key parameters: mass flow rate, bottom hole pressure, and the proportion of fluid that reached the sea surface.

Images