Abstract
Sand plugging during hydraulic fracturing is one of the primary causes of operational failure. Existing methods for identifying sand plugging during fracturing suffer from issues such as time-consuming, low accuracy, and inability to provide real-time warning. Addressing these challenges, this study leverages offshore hydraulic fracturing operational data and reports to propose a novel method for intelligent identification and real-time warning of sand plugging. Initially, we employ an Attention Mechanism based Long-Short Term Memory Network (Att-LSTM) to establish a real-time pressure prediction model during fracturing, capable of forecasting pressure within 40 s with an accuracy exceeding 92%. Subsequently, we enhance the structure of an Attention Mechanism based Convolutional Long-Short Term Memory Network (Att-CNN-LSTM) to develop a model for identifying sand plugging during fracturing, achieving identification with an error margin of less than 1 min. Finally, through the integration of Att-LSTM and Att-CNN-LSTM networks coupled with transfer learning techniques, we introduce a continuously learning approach for sand plugging warning during fracturing operations, significantly improving accuracy and efficiency in sand plugging identification and advancing the intelligent decision-making process for hydraulic fracturing. These methodologies not only contribute theoretical innovations but also demonstrate substantial practical effectiveness, providing critical technical support and guidance to enhance safety and efficiency in hydraulic fracturing operations.
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Introduction
With continuous advancements in exploration and development technologies for oil and gas reservoirs, hydraulic fracturing has emerged as a pivotal technique for optimizing the recovery of unconventional reservoirs and enhancing production from low-productivity wells1,2,3,4,5,6,7. However, the complexity of geological formations introduces various risks during fracturing operations, with sand plugging being the most prevalent, leading to economic losses, environmental contamination, and impairments to reservoir permeability, necessitating efficient and accurate sand plugging risk early warning systems during hydraulic fracturing operations8,9,10.
Current methods for detecting sand plugging during hydraulic fracturing include micro-seismic monitoring11,12, manual judgment, the dual logarithm method13,14, and the inverse slope method10. Micro-seismic monitoring comprehensively monitors fracturing operations by analyzing micro-seismic events to assess fracture conditions and detect anomalies such as sand plugging. Despite its effectiveness, this method requires sophisticated equipment and incurs high technical service costs, limiting its domestic adoption. Manual identification involves real-time data acquisition to plot fracturing curves, allowing on-site personnel to assess sand plugging based on pressure trends. While cost-effective and suitable for on-site use, it relies heavily on individual experience, limiting early warning accuracy. The dual logarithm method calculates bottom-hole net pressure from wellhead pressure, creating a logarithmic-time dual curve to identify sand plugging based on slope magnitudes. Widely used, it offers convenience in data acquisition and signal analysis but assumes constant perforation friction, impacting net pressure accuracy. During sand addition, wellhead pressure curves typically decrease and then increase. The inverse slope method assesses sand plugging by analyzing pressure slopes, where the upward slope ideally matches the downward slope. However, field data noise often compromises slope analysis accuracy, affecting early warning precision. Overall, these methods struggle to balance efficiency and accuracy, highlighting the necessity for intelligent early warning systems with continuous learning capabilities to improve sand plugging incident detection.
The extensive integration of artificial intelligence in big data analysis has opened up new avenues for developing nonlinear models15,16,17,18. The petroleum industry is progressively embracing smart technologies19,20,21,22,23,24, utilizing wellfield sensors to establish an Internet of Things framework for data collection. Through the application of data mining techniques, crucial insights can be derived and risks predicted. Incorporating these techniques into hydraulic fracturing operations is essential for effectively preventing sand plugging incidents. Presently, while AI methods can identify sand plugging by analyzing sample data characteristics, current technologies predominantly rely on calculating pressure change slopes and lack comprehensive intelligent warning capabilities and continuous learning functionalities25,26,27. Zhang, et al.28 improved the BP neural network and proposed an intelligent prediction method for sand plugging risk, achieving an identification accuracy of 89.35%. However, this method can only qualitatively determine whether there is a sand plugging risk during construction and cannot provide the specific time when the sand plugging risk may occur, lacking the quantitative prediction ability in the time dimension. To achieve early warning of sand plugging, Soroush, et al.29 predicted the bottom hole pressure in the next 30 s based on the LSTM model and combined it with the random forest classification. This approach can issue a warning 30 s before the occurrence of sand plugging. In summary, intelligent real-time warning systems for sand plugging incidents are still nascent and necessitate the development of efficient, accurate systems that support continuous learning.
This paper improves data analysis and deep learning algorithms, based on on-site data and reports from offshore fracturing wells, to establish an intelligent identification and real-time warning method for sand plugging during hydraulic fracturing. This method framework is illustrated in Fig. 1, combining two different models’ side by side. First, an Attention Mechanism based Long-Short Term Memory Network (Att-LSTM) is employed to construct a real-time pressure prediction model during the fracturing process, capable of predicting pressure trends 40 s in advance. Subsequently, an Attention Mechanism based Convolutional Long-Short Term Memory Network (Att-CNN-LSTM) is developed to establish an intelligent model for identifying sand plugging during the fracturing process. Finally, by coupling Att-LSTM and Att-CNN-LSTM neural networks, a real-time warning model for sand plugging during fracturing processes is constructed, using pressure prediction data obtained from the pressure implementation prediction model as input for the intelligent sand plugging identification model to achieve intelligent identification and real-time warning of sand plugging during hydraulic fracturing processes.
Framework for intelligent identification and real-time warning of fracturing sand plugging.
Sand plugging
During the hydraulic fracturing process in oil and gas extraction, sand plugging caused by solid particles carried by high-pressure fluids can lead to serious disruptions to operations8,9,30,31. This sand plugging mainly affects hydraulic fracturing operations in the following aspects:
Firstly, sand plugging may cause fractures or wellbores to close or impede permeability, thereby significantly reducing oil and gas production and potentially affecting the extraction efficiency of the entire oilfield. Secondly, the sand grains carried in the fracturing fluid can cause friction and wear inside the equipment, thereby increasing maintenance costs and equipment downtime. In addition, sand plugging may clog fractures that are supposed to remain unobstructed, damage the formation, and potentially trigger unexpected formation deformation and disturbances, which in turn will affect fluid permeability and recovery rates. Finally, if sand plugging causes fracturing fluid to leak to the surface or enter the groundwater system, it will lead to environmental pollution and related impacts.
Effectively preventing and promptly identifying sand plugging is crucial for carrying out hydraulic fracturing operations safely and efficiently. Sand plugging usually manifests as abnormal pressure, changes in fluid displacement, abnormal data from sensors of downhole equipment, abnormal pressure fluctuations during proppant injection, abnormal patterns in acoustic or micro seismic monitoring data, and reduced efficiency of the sand removal process. These signs usually need to be identified and confirmed for the existence of sand plugging with the help of real-time monitoring data and relevant experience so that prompt measures can be taken to mitigate the adverse effects on production and equipment operation.
Sand plugging can cause significant damage to production, forcing the operation company to delay subsequent fracturing operations, adding extra costs, and requiring the company to conduct long-term diagnostics and management of the risks caused by sand plugging. During the fracturing process, sand plugging events typically result in specific responses in operation pressure, such as a sudden increase. This paper utilizes big data analysis and machine learning methods to study intelligent early warning of sand plugging risks using data from 36 offshore fracturing wells, including 10 wells with sand plugging. The goal is to achieve early warning of sand plugging risks during the fracturing process and improve fracturing decision-making efficiency. The data from the 36 fracturing wells include 59 fracturing operation data, with the fracturing operation data from 3 sand plugging wells and 3 normal wells used as test data.
Extended parameters
The occurrence of sand plugging is closely related to sand concentration and fluid displacement rate, reflected in the changes of pressure curves on operation charts. Real-time surface operation data from operation sites are obtained through data acquisition systems in this study, focusing on parameters such as “pressure”, “displacement rate”, and “sand concentration”. Discrete data typically exhibit strong nonlinear characteristics, with important feature information often hidden across different time points, which conventional mathematical modeling cannot intuitively reveal or discover. This study enhances the hidden feature information of various data by calculating the rate of change, mean, deviation, and absolute deviation at different time points as supplementary input parameters for neural network models.
Using formulas (1)-(3), the neural network model’s input parameters are constructed using a sliding window approach, which better reflects the nonlinear relationships be-tween discrete data at different time points. This enables the neural network model to quickly capture hidden feature information between data points.
where, \(\frac{\Delta f}{{\Delta t}}\) represents average rate of change of parameters over a certain time period; \(\overline{{f(t_{i} )}}\) represents average value of parameters at the previous i time points; \(d(t_{i} )\) represents deviation, which is the difference between the parameter data at time ti and the average of the parameters at the previous i time points; f(t1) represents parameter data at the initial time; f(ti) represents parameter data at time ti ; i represents timestamp index; j represents calculation step size; t1 represents initial time of hydraulic fracturing; ti represents the i-th timestamp during hydraulic fracturing.
Real-time pressure prediction model
Pressure change is a critical parameter for determining sand plugging during hydraulic fracturing operations. Studies indicate that pressure anomalies are closely linked to operation conditions, geological factors, and the state of fracturing equipment. Furthermore, pressure changes often coincide with fluctuations in parameters such as fluid discharge volume and sand concentration. Therefore, to achieve real-time warning of sand plugging risks during hydraulic fracturing, it is essential to accurately predict and monitor pressure change trends.
Network structure
Long Short-Term Memory network (LSTM)
The Long Short-Term Memory network (LSTM) is a specialized type of Recurrent Neural Network (RNN) designed to address the vanishing gradient and exploding gradient problems inherent in traditional RNNs. This enables LSTM to effectively handle long-term dependencies in sequential data. The LSTM cell leverages three gating mechanisms—namely, the input gate, forget gate, and output gate—to regulate the flow of information into, out of, and within the memory cell. The input gate determines how current input information should be integrated into the memory cell. It achieves this by computing the current input and the hidden state and cell state from the previous time step using specific weight matrices and bias vectors. The Sigmoid activation function is employed to determine which information can be written into the cell state.
The forget gate governs the retention of information from the cell state at the previous time step. Similarly, it utilizes weight matrices, bias vectors, and the Sigmoid activation function to decide whether to discard certain past information, thus avoiding the accumulation of irrelevant data. The cell state, as the core memory unit of the LSTM, is responsible for preserving critical dependency information over time. It is updated by combining the results from the input gate and the forget gate, ensuring the continuous retention of significant information.
The output gate controls the output of the current hidden state based on the current input, the previous hidden state, and the updated cell state. Using weight matrices, bias vectors, and the operations of the Sigmoid and Tanh activation functions, it provides the appropriate information for subsequent processing.
At each time step t, the LSTM performs calculations according to Eqs. (4)–(9).
Here, \({x}_{t}\) represents the current input; \({h}_{t-1}\) denotes the hidden state from the previous time step; \({C}_{t-1}\) is the cell state from the previous time step; \(\widetilde{{C}_{t}}\) is the new candidate cell state; \({C}_{t}\) represents the current cell state; and \({h}_{t}\) represents the current hidden state. \({W}_{f}, {W}_{i}, {W}_{C}, {W}_{o}\) are the weight matrices for the forget, input, candidate, and output gates, respectively; \({b}_{f}, {b}_{i}, {b}_{C}, {b}_{o}\) are their corresponding bias vectors. \(\sigma\) represents the Sigmoid activation function, while tanh denotes the hyperbolic tangent activation function. The outputs of the forget gate, input gate, and output gate are denoted by \({f}_{t}\),\({i}_{t}\),\({o}_{t}\) respectively. \(\odot\) indicates the Hadamard product (element-wise multiplication).
Through these gating mechanisms, LSTM selectively retains and updates long-term information, effectively capturing the dynamic variation patterns in time-series data. In the real-time pressure prediction model developed in this study, LSTM leverages these capabilities to process time-varying data such as pressure, flow rate, and sand concentration during the fracturing process. By learning the long-term dependencies within the data, it provides strong support for accurate pressure prediction.
Attention mechanism
The attention mechanism is inspired by human visual attention, with its core idea being to enable the model to automatically focus on the most relevant parts of the input data for a given task, rather than treating all information equally. In this study, the attention mechanism assigns weights to each input data point by computing the correlation between different parts of the input data and the pressure data. Specifically, when processing input data x, it is first mapped to a high-dimensional space through a linear transformation and then converted into weight values \(\alpha\) using the Sigmoid function. The calculation formula is \(\alpha =\sigma ({W}_{1}\bullet x+b)\), where \({W}_{1}\) and b are learnable parameters. These weight values represent the importance of each part of the input data for pressure prediction. The model then performs a weighted summation of the input data, expressed as \(\widetilde{x}=\sum_{i=1}^{n}{\alpha }_{i}{x}_{i}\), highlighting key information and suppressing irrelevant information.
In this way, within the complex fracturing data, the attention mechanism enables the model to more accurately capture critical time-series features related to pressure prediction, thereby improving the accuracy and reliability of pressure predictions under complex conditions.
Attention-based long short-term memory (Att-LSTM)
The data in the hydraulic fracturing process has an obvious time-series nature, as parameters such as pressure, displacement rate, and sand concentration change over time. Therefore, the real-time pressure prediction model needs to have the ability to process time-series data. The Long Short-Term Memory (LSTM) model has unique advantages in dealing with time-series data. The LSTM structure can effectively remember long-term dependencies and selectively forget or update information through the gating mechanism, thus capturing the dynamic change patterns of data in the time series.
During the hydraulic fracturing process, although pressure change is a key parameter for judging sand plugging, the data situation in actual operations is complex and variable. On the one hand, pressure data is affected by a combination of multiple factors, including different geological conditions, diverse construction operations, and equipment status. These factors make the pressure data present complex change patterns in the time series, which not only contains valid information related to sand plugging but also a large amount of noise and interference signals. On the other hand, when analyzing pressure data, we need to pay attention to the correlation degree of pressure data at different moments. Although the traditional LSTM model can handle time-series data, it is difficult for it to automatically focus on those pressure change features that are most critical for pressure prediction when faced with such complex data where the key information is unevenly distributed.
Therefore, we introduced the attention mechanism. The attention mechanism can provide the model with the ability to adaptively focus on different parts of the input data. When processing the input data, it can dynamically allocate weights to the input data at different moments according to the correlation between the input data and the pressure data. In this way, the attention mechanism enhances the model’s ability to extract key time-series features from the input data and improves the accuracy and reliability of the real-time pressure prediction model in predicting pressure under the complex hydraulic fracturing environment.
In this study, an Att-LSTM neural network is employed to establish a real-time pressure prediction model for hydraulic fracturing processes. The model uses data from the preceding 60 s to forecast pressure data for the subsequent 40 s, anticipating pressure changes in advance. The embedded LSTM network within the Att-LSTM structure consists of three hidden layers, each containing 64 neurons (Fig. 2).
Structure of the Att-LSTM neural network.
The Att-LSTM network structure takes time, pressure, displacement rate, and sand concentration data as input sources and conducts data preprocessing first. Subsequently, the data flows into the attention mechanism part, where the linear layer, Sigmoid function, and other components work together to calculate the attention weights, enabling the network to focus on key information. Then, the output of this part serves as the input of the LSTM network. With its unique gate structure and cell state, the LSTM effectively handles the long-term dependencies of long sequence data through element-wise operations and gating processing. The output of the LSTM then passes through the pressure prediction module that contains a Dropout layer and a linear layer, and finally, the pressure prediction results are obtained. The overall structure aims to accurately predict pressure and handle the complexity of time-series data.
Input data
The model established in this paper will be used in series with the data acquisition system in the fracturing operation process. The data from the data acquisition system will be synchronized in real time to our established model. Since the data acquisition system mainly collects operation pressure, displacement rate, and sand concentration, other parameters are calculated based on these three parameters. For example, the stage displacement is the accumulation of the displacement rate, and the stage sand concentration is the stage sand volume divided by the stage displacement. Moreover, as pressure change is an important indicator of sand plugging occurrence, sand plugging will cause the fluid flow in fractures to be blocked, resulting in an abnormal increase in pressure. Displacement affects the conveying capacity of the sand-carrying fluid, and an unreasonable displacement may lead to the deposition of sand grains in fractures and then trigger sand plugging. Sand concentration is directly related to the distribution of sand grains in the fluid, and an excessively high sand concentration increases the risk of sand plugging. The change patterns of these parameters before, during, and after sand plugging occurrence provide crucial bases for us to predict and identify sand plugging through data analysis. Therefore, we choose these three basic factors, namely operation pressure, displacement rate, and sand concentration, as the main factors.
To better capture the change characteristics of these parameters in the time series, we calculate their change rates, means, variances, and absolute variances at different time points as supplementary input parameters. These derived parameters can reflect the dynamic change trends and fluctuations of the data. For example, the change rate can intuitively show the increase or decrease of a parameter within a unit time, helping the model more sensitively capture the abnormal change trends of parameters before sand plugging occurs. The mean and variance can describe the average level and dispersion degree of the data within a period of time, which are of great significance for understanding the overall change characteristics and stability of the parameters. Through these supplementary parameters, we can depict the complex data patterns in the hydraulic fracturing process more comprehensively, thereby improving the model’s ability to identify sand plugging phenomena.
Window size selection
Through theoretical research on the formation mechanism of sand plugging in the hydraulic fracturing process, we found that the formation of sand plugging is not completed instantaneously but is a dynamic process involving the interaction of multiple factors. In this process, changes in parameters such as pressure, displacement, and sand concentration will gradually appear and influence each other within a certain time range. Therefore, selecting an appropriate time window to calculate the change rate is crucial for accurately capturing the relationship between these parameters and sand plugging.
We conducted a series of comparative simulations and data analyses to determine the size of the time window. Firstly, we used historical hydraulic fracturing data for preliminary analysis, tried different time window sizes (such as 10 s, 20 s, 30 s, etc.) to calculate the parameter change rates, and observed the correlations between these change rates and sand plugging events. Through comparison, it was found that a smaller time window (such as 10 s) could reflect parameter changes timelier, but it was easily affected by short-term fluctuations and noise, resulting in poor data stability. While a larger time window (such as 30 s or more) would smooth out some key short-term change information, reducing the model’s early warning ability for sand plugging. After multiple comparisons and data analyses, we found that the time windows of 20 s and 30 s performed better in balancing data stability and sensitivity to sand plugging changes. Within this time range, the calculated change rates can effectively capture the abnormal change trends of parameters before sand plugging occurs, while also reducing noise interference and providing more reliable input features for the model.
Furthermore, to address the issue of significant fluctuations in collected data, a moving average filter with a stride of 5 is applied to reduce noise. Additional parameters are derived based on 20- and 30-time steps, including rate of change, mean, deviation, and absolute deviation for pressure and sand concentration. The rate of change for current displacement rate is calculated based on real-time readings. The sum of sand concentration at the current time step is computed to enhance data features. Given the substantial numerical differences in late-stage accumulated sand concentration compared to pressure and discharge volume, dividing cumulative sand concentration by 10,000 effectively reflects the intrinsic relationships among pressure, sand plugging, and sand concentration.
By integrating original hydraulic fracturing data with these extended parameters, the input data for the real-time pressure prediction model comprises 19 parameters (Table 1). Thus, the input for the pressure prediction model includes these 19 parameters corresponding to the preceding 60 s at the current time step.
Model performance verification
Based on the input data for the real-time pressure prediction model during hydraulic fracturing operations, sampling is conducted using a sliding window approach with a size of 60. To verify the effectiveness of the attention mechanism in the Att-LSTM model we constructed, we designed a testing and comparison scheme with the traditional LSTM structure. During the comparison process, we used all the data to build the dataset. The number of iterations for model training was set to 400 to ensure that the models could fully learn the inherent laws and feature information in the data. Meanwhile, the Mean Squared Error (MSE) was selected as the loss function to quantify the degree of deviation between the predicted values and the actual values of the models. By monitoring the dynamic change curve of MSE during the training process, we could intuitively present the substantial role that the attention mechanism played in improving the model performance, thereby providing theoretical basis and practical verification for the application of the Att-LSTM model in relevant fields. The test results are shown in Fig. 3. It can be seen that the loss of the LSTM with the attention mechanism decreased more rapidly and had more potential than the traditional LSTM. Moreover, both of them still had the potential to decline, indicating that neither of the models had reached the optimal convergence state.
Comparison of MSE results during the training process of Att-LSTM and LSTM.
Considering that hydraulic fracturing data is collected at a granularity of seconds and the overall dataset is large, this study embeds a transfer learning module in the neural network model training process. The model is trained using a two-step training method, aiming to increase the duration of hydraulic fracturing operations. This approach effectively accelerates network training efficiency and allows for seamless integration of new well hydraulic fracturing data without requiring training from scratch (Fig. 4).
Process for building real-time pressure prediction model during fracturing.
Pre-training: A subset of data is randomly selected to pre-train the real-time pressure prediction model, obtaining optimal model weights based on this subset. This forms the foundation model. Formal training: The hydraulic fracturing real-time pressure prediction model is trained using all available data. The transfer learning module initializes the Att-LSTM network model with the pre-trained model weights. This approach ensures efficient and effective model training, facilitating the integration of new well hydraulic fracturing data into the prediction framework.
The input data dimension of the Att-LSTM neural network is 60 × 19. Pre-training is conducted using data from 20 wells with 2000 iterations, while formal training consists of 300 iterations. The batch size is 2950, and the Adam optimizer is being used with the Mean Squared Error (MSE) loss function. The maximum learning rate is set to 0.0001, the minimum learning rate to 0.000001, and the learning rate changes according to the cosine annealing schedule.
As shown in Fig. 5, after pre-training, the Att-LSTM neural network achieves a minimum MSE loss function error of 0.24 with fewer utilized data points, indicating relatively low overall MSE loss. These weights obtained during pre-training are then used as the initial weights for formal training. After 300 formal iterations, the training set achieves a final MSE loss function error of less than 0.2, with a test set error below 0.24. This demonstrates that the neural network weights obtained from pre-training effectively serve as initial weights for formal training, achieving desirable results with only a few hundred iterations and effectively reducing training time.
MSE loss during iterative training of the real-time pressure prediction model.
The impact of transfer learning on training time
We designed a comparative experiment. Taking the previous training results as the control group, we selected all the fracturing operation data (59 fracturing operation data from 36 wells) to train the model, which served as the test group. In the test group, transfer learning was not applied, and the model was trained from scratch.
The comparison results (Fig. 6) showed that when transfer learning was not used, when the model was trained on the target data to reach the same number of iterations, the model had not yet achieved similar performance and required a longer training time. However, after using transfer learning (Fig. 5), similar performance could be achieved with only about 300 iterations, and the training time was significantly shortened. This was mainly because transfer learning took advantage of the general features and model weights learned from a small amount of data, enabling the target model to have a better performance starting point in the initial stage, thus accelerating the convergence speed on the target data. In actual offshore fracturing operations, data is constantly generated, and quickly training the model is of crucial significance for providing timely sand plugging warnings that meet the changes in block properties. Transfer learning effectively meets this requirement.
MSE loss during the iterative training of the real-time pressure prediction model for the test group.
To prevent the overfitting phenomenon caused by transfer learning, during the training process, we introduced Dropout and monitored the performance indicators of the model on the training set and the validation set. Dropout is an effective regularization technique, and its basic principle is to randomly “drop out” a part of neurons during the training process, making the network structure different in each iteration. This randomness forces the model not to overly rely on certain specific neurons, thus prompting the model to learn more generalized features. In the model established in this paper, the Dropout technique was introduced with a probability of 0.05. This means that in each training iteration, each neuron has a 5% probability of being temporarily ignored and not participating in the forward propagation and reverse propagation processes. Previous studies have shown32,33,34 that Dropout can effectively suppress the model’s overfitting to the training data and improve the model’s generalization ability.
Moreover, although using deep learning methods for data prediction and identification is quite popular, it also has certain limitations. It relies heavily on a large amount of on-site data. The acquisition and collation of data are cumbersome and time-consuming, and it is difficult to ensure the quality and integrity of the data. The research method in this study is constructed based on the data of offshore fracturing wells. When applied to onshore fracturing wells, there are significant differences in geological structures and operation conditions, which lead to changes in data fluctuations and sand plugging mechanisms and, in turn, have an adverse impact on the prediction effect of the model. During the model training process, a transfer learning module is introduced. When new data is introduced, this module can accelerate the training process and help obtain a model with stronger generalization ability, thereby reducing the training cost in new environments. However, it cannot be ignored that there are relatively large differences between offshore and onshore data, which may trigger the negative transfer phenomenon and, to some extent, limit the improvement of the model’s generalization ability. Nevertheless, we will continue to optimize data processing, improve transfer learning strategies, and accumulate more data to overcome these limitations, improve the performance and adaptability of the model, and provide support for more extensive applications.
In subsequent scenarios with new hydraulic fracturing well data, these pre-trained Att-LSTM weights can be directly used as new initial weights for continued training, re-quiring far fewer iterations compared to the initial pre-training phase.
Utilizing the trained real-time pressure prediction model, as depicted in Fig. 7, the predicted pressure closely fits the actual pressure data with a high degree of accuracy. The prediction accuracy exceeds 93%.
Examples of pressure prediction during fracturing for different wells.
We used the data of four new fracturing wells from four new platforms to test the performance of the model. It should be emphasized that the data of these four new wells are completely independent of the data originally used to construct the training set and the test set. They did not participate in the early training process of the model, so they can test the generalization ability and accuracy of the model when facing brand-new data in a more objective and effective manner. This is of great significance for evaluating the reliability and stability of the model in practical applications. It can reflect the performance of the model under different working conditions and geological conditions more truly, avoid the problem of performance overestimation caused by data overlap or correlation, and provide a solid basis for the further optimization and practical deployment of the model.
Well 3 and Well 4 are non-sand-plugging fracturing wells, while Well 4 and Well 5 are sand-plugging fracturing wells. Since the pressure prediction model aims to predict the data in the next 40 s, we saved the results of the first prediction for each piece of data and compared them with the actual data obtained after the completion of the fracturing. Considering the characteristics of real-time pressure data prediction, each data point will actually be predicted 40 times during the whole prediction process. However, in order to present the performance of the pressure prediction model clearly and intuitively, we only retained the data obtained from the first prediction of each data point. After the fracturing operation was completed and the real-time data reading stopped, we compared the saved predicted data with the actual data (Fig. 8). It can be clearly seen from the figure that the fitting degree between the actual data and the predicted data is over 90%, which fully proves that the pressure prediction model we constructed has good performance.
Comparison between the predicted pressure data and the true pressure data after the fracturing is completed.
Sand plugging automatic recognition model
Hydraulic fracturing operation data are recorded in real time by the data acquisition system at the rate of seconds. Traditional methods for identifying fracturing accidents rely heavily on manual judgment by on-site personnel, requiring extensive fracturing experience. This method poses dual challenges of efficiency and accuracy in sand plugging accident detection. To achieve efficient and accurate identification of sand plugging incidents during hydraulic fracturing, this study constructs an Att-CNN-LSTM neural network architecture. By utilizing data acquired from the data acquisition system, the model automatically identifies sand plugging, thereby enhancing detection efficiency and reducing the requirement for specialized knowledge among operation personnel.
Network structure
Hydraulic fracturing operation data contains various types of information such as time, pressure, displacement rate, and sand concentration, and these data possess different modal characteristics. The Att-CNN-LSTM model (Fig. 9) combines the advantages of the Convolutional Neural Network (CNN) and the LSTM, enabling it to effectively fuse multi-modal data. CNN can automatically extract spatial features in the data. For example, it can identify specific patterns or change trends in the pressure and sand concentration curves. LSTM, on the other hand, is responsible for handling the time-series information of the data. This structure allows the model to comprehensively understand and analyze the complex data relationships in the hydraulic fracturing process and improve the accuracy of sand plugging identification. Traditional methods often can only analyze a certain parameter separately or simply combine several parameters and are unable to fully exploit the multi-modal information in the data.
Structure of the Att-CNN-LSTM neural network.
The input layer of the sand plugging identification network structure receives the raw data containing time, pressure, displacement rate, and sand concentration and first conducts necessary data preprocessing operations. Subsequently, the data enters the CNN. It first passes through the 1 × 1 convolutional layer to preliminarily extract features and then continuously goes through two 3 × 3 convolutional layer to further explore more complex features. After each layer, the Tanh activation function is utilized to enhance the nonlinear expression ability and output the corresponding feature maps. After that, the feature maps are sent to the attention mechanism, which will assign different weights to each feature, screen out the key information for focused attention, and improve the efficiency of subsequent processing. The data output from the attention mechanism will serve as the input of the LSTM. LSTM processes the time-series features by relying on its memory units and gating structures and captures the long-term correlations among the data. Finally, the output of LSTM is transmitted to the sand plugging identification module, and through relevant operations, the result of sand plugging identification is obtained, helping to accurately judge the sand plugging phenomenon.
Traditional LSTM is mainly for time-series data prediction rather than classification tasks, while CNN performs better in classification. The combination of CNN-LSTM has notable advantages like synergistic feature extraction and sequence learning, and spatio-temporal feature integration with good adaptability and generalization ability35,36.
In this paper’s research on hydraulic fracturing sand plugging identification, the Att-CNN-LSTM model uses CNN to extract spatial features from operational data, like identifying sand plugging-related patterns in pressure and sand concentration. LSTM then models the extracted feature sequences over time to capture the long-term dependencies caused by sand plugging events.
Compared to using CNN or LSTM alone, CNN struggles with time-series info and may miss the temporal trend of sand plugging, while LSTM has limited ability in extracting spatial features from complex data.
In hydraulic fracturing data, it can be seen as having “time—parameter space” characteristics. CNN extracts feature in the “parameter space” and LSTM analyzes them in the time dimension, improving the model’s ability to identify sand plugging.
The embedded attention mechanism makes the model focus on key data. When handling complex data, it assigns different weights to key features, enhancing the focus on important ones and improving the accuracy of identifying sand plugging risks. Unlike traditional methods, the Att-CNN-LSTM model learns relevant feature representations automatically without complex manual feature engineering.
Input data
The training dataset for the automatic identification of sand plugging incidents during hydraulic fracturing is also based on "time, pressure, displacement rate, and sand concentration" data obtained from the data acquisition system. During the establishment of the sand plugging incident identification dataset, the timestamp data of each well’s fracturing operation is manually labeled. Timestamp data corresponding to non-occurrence of sand plugging incidents are labeled as 0, while timestamps indicating occurrences of sand plugging incidents are labeled as 1. Thus, the automatic sand plugging incident identification model analyzes fracturing operation data and automatically classifies timestamp data as 0 or 1 to determine the presence of sand plugging incidents, as illustrated in Fig. 10.
Illustration of classification and labeling of fracturing operation timestamps data.
Based on the data acquisition system, four types of data are obtained: time, operation pressure, displacement rate, and sand concentration. To address the issue of significant data fluctuations in the collected data, a moving average filter with a step size of 5 is applied to reduce noise. Additional parameters such as current time-step pressure change rate, mean, deviation, and absolute deviation are computed based on 20- and 30-time steps. Real-time sand concentration data is used to calculate the cumulative sand concentration at the current moment divided by 10,000.
The operation pressure real-time prediction model integrates the original fracturing data with these extended parameters, resulting in a total of 12 input parameters (Table 2). Using these 12 input parameters, data sampling is conducted in the direction of increasing fracturing time using a sliding window of size 60. This involves utilizing real-time data from the data acquisition system for the past 60 s to determine whether the data at the last moment indicates sand plugging.
As shown in Fig. 11, the sliding window moves along the direction of increasing fracturing time with a step size of 1 s. The data within the window is treated as the sample matrix xi, while the category yi corresponding to the last row of the sample matrix yi indicates whether sand plugging is present at the current moment. This setup forms a sample point (xi, yi), where yi is the input to the sand plugging incident automatic recognition model, yi represents the true category of the sample matrix xi, and k denotes the total number of sample points in a fracturing stage of length N, where k = N − j + 1.
Illustration of classification and labeling of fracturing operation timestamps data.
Model performance verification
To verify the crucial significance of the CNN in the process of model construction, we designed a set of comparative experiments. In these experiments, the pre-training step was abandoned to ensure that the performance of different models in the environment of raw data could be purely evaluated. We employed a variety of representative machine learning methods, covering the traditional Support Vector Machine (SVM), Random Forest (RF), and different architecture models integrated with CNN, namely CNN itself, CNN-LSTM, and Att-CNN-LSTM, to conduct in-depth analysis on all the raw data.
The entire experiment was set with an iterative training process of 200 times, aiming to examine the convergence characteristics of each model and the stability of the changes in the loss function, which were taken as the key indicators for measuring the performance of the models. The experimental results were presented in an intuitive graphical form (Fig. 12), providing us with evidence support.
Different effects of different models in the testing process.
The comparison results show that during the training of models such as SVM and RF that do not adopt the CNN structure, the loss values fluctuated violently. This implies that the models had difficulties in learning data features and optimizing parameters and were hard to converge to the ideal state. Conversely, when CNN was used alone for training, the loss curve tended to be stable, indicating that CNN had strong stability when processing raw data and could effectively capture key features, making the model training approach the optimal solution more stably.
It can be analyzed that after introducing LSTM to combine with CNN, the feature sequences extracted by CNN were integrated and analyzed under the time-series modeling ability of LSTM. This not only reduced the loss value but also significantly improved the stability of the loss changes. This represents that the model performed excellently in grasping the time-series dependency relationships of the data and achieved more efficient training and optimization.
Finally, after introducing the attention mechanism on the basis of CNN-LSTM, the loss decreased significantly faster and remained highly stable throughout the process. This strongly proves that the attention mechanism enabled the model to focus on key information, enhanced the learning and feature extraction efficiency, and made it converge to a better performance state more quickly. Through this series of comparison, verification, and analysis, the crucial position of CNN in model construction and the synergistic effect generated by its combination with other structures have been confirmed.
Model training and evaluation
The model training process also adopts a two-stage training approach and incorporates a transfer learning module (Fig. 13) to expedite network training efficiency, allowing for seamless integration of new well fracturing data without the need for starting training from scratch. The Att-CNN-LSTM neural network has an input data dimension of 60 × 12. Pre-training involves 500 iterations, while formal training consists of 200 iterations. Each training iteration captures 50 data samples. The optimizer used is the Adam optimizer, with a maximum learning rate of 0.0001, a minimum learning rate of 0.000001, and learning rate variation follows the cosine annealing schedule.
Process for building automatic identification model for sand plugging.
The sand plugging automatic recognition model categorizes each second of fracturing operation data into “0” and “1” to assess the occurrence of sand plugging incidents. Following formal training, the model achieves an accuracy of 0.95 and an MSE loss error of less than 0.01 (Fig. 14). The performance of the sand plugging event identification model on the test set is presented in Fig. 15a. Among them, the black area reflects the actual pressure fluctuation during the occurrence of sand plugging, while the green area clearly shows the determination of sand plugging events by the sand plugging automatic identification model. According to statistics, the identification error of sand plugging events is controlled within 1 min, showing a high degree of accuracy.
Iterative training loss of sand plugging automatic recognition model (Left), testing set iterative training accuracy (Right).
Example of automatic identification of sand plugging in fracturing sand plugging well.
To explore the applicability and reliability of the sand plugging event identification model for fracturing data on new platforms and new wells more comprehensively and deeply, we also utilized two newly acquired fracturing wells (namely Well 5 and Well 6) with sand plugging events and used their data to conduct further testing and verification work on the sand plugging event identification model, hoping to provide a more convincing basis for the performance evaluation of the model. The identification results are shown in Fig. 15b.
We used recall, precision, and F1 score to evaluate the performance of the established sand plugging event identification model. The F1 score is based on the confusion matrix (Table 3) and combines precision and recall to evaluate the network model. Precision is the proportion of true positive samples in the total number of predicted positive samples (Eq. 10), recall is the proportion of true positive samples in the total number of actual positive samples (Eq. 11), and the F1 score is the harmonic mean of the two (Eq. 12), with a value ranging from 0 to 1. The closer it is to 1, the stronger the model performance.
In sand plugging event identification, relying solely on precision or recall will lead to a one-sided evaluation of the model’s performance. For example, a high precision and low recall mean that although the model makes few misclassifications, it is prone to missed detections; a high recall and low precision will result in a large number of misclassifications. The F1 score can comprehensively consider both situations, preventing the model from sacrificing one aspect too much while pursuing the other, and is more suitable for the comprehensive and accurate evaluation requirements of the model’s performance in practical applications.
In this paper, the data at the moment of sand plugging is set to 1, and the normal fracturing time-series data is set to 0. In the identification results of the sand plugging risk identification network model, the sand plugging area is regarded as a positive sample, and the rest is regarded as a negative sample. TP represents the number of true positive samples in the sand plugging identification results, FP represents the samples misclassified as non-sand plugging, FN represents the samples that are actually sand plugging but classified as normal fracturing time-series data, and TN represents the samples that are correctly classified as non-sand plugging data.
The confusion matrix can clearly show the accuracy of the model under different classification results. The TP and TN values on the diagonal reflect the correctly identified situations, while the FP and FN values off the diagonal reveal the false positive and false negative situations. A low FP value indicates that the model makes fewer false positives, and a low FN value means that the model can better detect the actual sand plugging events.
During the training process, the change of the F1 score is shown in Fig. 16. It can be seen that the F1 score kept rising and the maximum score was 0.97. On the test set, the confusion matrix is shown in Table 4, with the precision being 0.96 and the recall being 0.92. The calculated F1 score is 0.94. As for the confusion matrices of Well 1 and Well 2, which are shown in Table 5, the precision of Well 1 is 1, the recall is 0.90, and the F1 score is 0.95. The precision of Well 2 is 0.96, the recall is 0.84, and the F1 score is 0.90. The precision of Well 5 is 1, the recall is 0.85, and the F1 score is 0.92. The precision of Well 6 is 0.95, the recall is 0.97, and the F1 score is 0.96. This indicates that the model has a relatively good performance in identifying sand plugging.
Trend of F1 score changes in the training set.
Sand plugging risk real-time warning model
Coupling the real-time pressure prediction model for fracturing operations with the sand plugging automatic recognition model, we establish a real-time warning model for sand plugging risk during hydraulic fracturing. The pressure prediction model forecasts current pressures, relying on the preceding 40 s' data of displacement rate and sand concentration as corresponding parameter data for pressure prediction, as illustrated in Fig. 17.
Schematic diagram of data input and output for different models.
Applying these models and methods to offshore fracturing wells for sand plugging risk warning, the model outputs the probability of sand plugging risk concurrently with the warning. This includes the current moment’s sand plugging risk probability and the risk probability within the next 40 s. To forecast the sand plugging risk probability for the next 40 s, this study calculates the average of the highest five sand plugging probability values.
The alerting effect is depicted in Fig. 18, where the yellow region represents the predicted pressure changes over 40 s. The blue arrow indicates the current fracturing moment, while the green arrow signifies the sand plugging warning. Green lines outside the yellow region indicate previous sand plugging identifications during past fracturing times, and the black arrow indicates the actual sand plugging occurrence. The real-time sand plugging warning model detects sand plugging within the predicted pressure region at the current fracturing moment, thus achieving early warning of sand plugging incidents.
Real time warning effect of sand plugging risk in two sand plugging wells.
Figure 18 demonstrates the effectiveness of the warning model, showing that it can promptly identify sand plugging incidents and provide insights into the probability of their occurrence. This underscores the model’s effective role in preemptively alerting operators to potential sand plugging incidents.
Regarding the fracturing data used in Fig. 18, the data of (a) and (b) are from the fracturing operation data of two wells in the test set, and the data of (c) and (d) are taken from the fracturing data of two new sand-plugged wells. We use the established sand plugging risk early-warning model to carry out sand plugging risk early-warning work for the new wells, so as to examine the performance and effectiveness of the model in actual scenarios and thus enhance its practical application value.
It can be found from Fig. 18 that the model has a good early-warning effect on sand plugging events for the two wells in the test set, and it can also issue early warnings for sand plugging events of the two new wells. The sand plugging early-warning model can effectively predict fracturing data and identify sand plugging events based on existing data and predicted data, thus achieving the early warning of sand plugging risks. Specifically, the model can detect sand plugging risks in advance and provide decision-making support for on-site operations.
In offshore fracturing operations, operators need to take quick actions based on real-time warning information to mitigate the risk of sand plugging. By evaluating the operation procedures and response times, we found that the 40-s real-time warning time is sufficient for operators to adjust the flow rate, change the proppant concentration, and monitor pressure changes. In actual cases, the real-time warnings issued by the model enabled operators to promptly adjust parameters, successfully avoiding the risk of sand plugging and ensuring the smooth progress of operations. Through theoretical analysis and case validation, we believe that the 40-s warning time is of practical significance in the current offshore fracturing environment, providing operators with adequate time to respond to risks. We will continue to optimize the model and the real-time warning system to further enhance operational efficiency and effectiveness.
Conclusion
This research focuses on the early warning of fracturing sand plugging risks. Through offshore hydraulic fracturing data and reports, an intelligent real-time early warning system has been constructed. In terms of model construction, the real-time pressure prediction model built with the Att-LSTM neural network structure has played a crucial role, with a prediction accuracy of over 92% for the pressure data in the next 40 s, laying the foundation for subsequent sand plugging identification. The sand plugging event identification model established by the Att-CNN-LSTM neural network structure controls the identification time error within 1 min. The real-time early warning model for hydraulic fracturing sand plugging risks, which is formed by coupling the two, has the ability to continuously learn with the advantage of transfer learning technology.
Compared with existing studies, in terms of parameter consideration and data processing, this paper not only focuses on pressure changes but also incorporates parameters such as displacement rate, sand concentration, and stage sand volume. Additionally, data cleaning and feature enhancement are performed on these parameters to more comprehensively extract data information and provide richer inputs for the model.
In terms of model construction, when predicting pressure in real-time, the traditional LSTM is improved by adding an attention mechanism. This leads to improvements in both prediction duration and accuracy compared to other models. The established sand plugging automatic recognition model can identify sand plugging automatically without the need for manual judgment, enhancing the recognition efficiency and accuracy. The coupling of the two models forms a real-time warning model, enabling unattended sand plugging warning.
Regarding application scenarios, a transfer learning module is introduced. In view of the differences among cross-regional and cross-platform wells, especially the complex impacts of different geological conditions and construction operations on sand plugging and pressure, the model can be retrained based on the weights of existing neural networks and fine-tuned to quickly adapt to new environments and continuously update to enhance generalization ability. This aspect has not been fully explored in previous studies.
In summary, through improvements and innovations in multiple aspects, this paper effectively makes up for the deficiencies of existing studies, provides a more efficient, accurate, and adaptable method for sand plugging warning in offshore fracturing wells, and promotes the progress of technology in this field and the improvement of practical application levels.
Data availability
The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.
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Funding
This research was funded by Intelligent Early Warning System for Hydraulic Fracturing Sand Plugging Research Project (G2415B-1120C032). Wei Zhang wishes to acknowledge the funding from the Shandong Postdoctoral Science Foundation (SDBX2023017).
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Conceptualization, Y.X. and B.G.; methodology, B.Y. and W.Z.; validation, W.Z. and J.S.; data cu-ration, Y.X., B.G., W.Z. and J.S; writing—original draft preparation, M.Z., A.J., H.X. and J.S.; writing—review and editing, M.Z., Y.X., B.G. B.Y. and W.Z.; visualization, A.J. and H.X.; super-vision, Y.X. and B.G.; funding acquisition, Y.X., B.G., W.Z. and J.S.; All authors have read and agreed to the published version of the manuscript.
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Xu, Y., Guo, B., Zhang, W. et al. Real-time warning method for sand plugging in offshore fracturing wells. Sci Rep 15, 6062 (2025). https://doi.org/10.1038/s41598-025-90768-9
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DOI: https://doi.org/10.1038/s41598-025-90768-9
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